The smallest possible value of the entire expression is 7.5, which occurs when A = 5, B = 2, and C = 4.
We are given the three different numbers 4, and C represent three different numbers from 2 through 5 and we have to find out the smallest possible value of the entire expression 10 - A B/C.
To find the smallest possible value, we need to take the greatest value of A, the smallest value of B, and the smallest value of C.
The given number 4 is in between 2 and 5, so it cannot be the greatest value.
Therefore, A must be 5. Now, the other two numbers must be chosen from the remaining three numbers 2, 3, and 4.
We need to choose the smallest possible value of B and C to make the entire expression the smallest. The smallest value of B is 2.
Now, we need to choose the smallest possible value of C. If C is 4, then the entire expression becomes:10 - 5(2/4) = 10 - 2.5 = 7.5If C is 5, then the entire expression becomes:10 - 5(2/5) = 10 - 2 = 8
Thus, the smallest possible value of the entire expression is 7.5.
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find the exact value of sin(2arccos(-3/5)) .
ASAP
Answer:
[tex]\sin(2\arccos(-\frac{3}{5}))=-\frac{24}{25}[/tex]
Step-by-step explanation:
Let [tex]\sin(2\arccos(-\frac{3}{5}))=\sin(2\theta)=2\sin\theta\cos\theta[/tex] and [tex]\theta=\arccos(-\frac{3}{5})[/tex] so that [tex]\cos\theta=-\frac{3}{5}[/tex]. Now we'll need to find [tex]\sin\theta[/tex] having known [tex]\cos\theta[/tex]:
[tex]\displaystyle \cos\theta=\frac{\text{Adjacent}}{\text{Hypotenuse}}=\frac{-3}{5}\\\\\sin\theta=\frac{\text{Opposite}}{\text{Hypotenuse}}=\frac{\sqrt{5^2-(-3)^2}}{5}=\frac{\sqrt{25-9}}{5}=\frac{\sqrt{16}}{5}=\frac{4}{5}[/tex]
Therefore, [tex]2\sin\theta\cos\theta=2(\frac{4}{5})(-\frac{3}{5})=2(\frac{-12}{25})=-\frac{24}{25}[/tex], which makes [tex]\sin(2\arccos(-\frac{3}{5}))=-\frac{24}{25}[/tex]
In what percentage of years is the snowfall between 31 and 41 inches?
Where the above mean and standard deviation is given, the approximately 47.72% of the years have a snowfall between 31 and 41 inches in this town. Thus the nearest answer is (Option B)
How is this so?Standardizing the values of 31 and 41 inches, we must use the following formula
Z = (X - μ) / σ
Where -
Z is the standard score (Z-score)X is the given valueμ is the mean of the distributionσ is the standard deviation of the distributionFor 31 inches -
Z1 = (31 - 41) / 5 = -2
For 41 inches -
Z2 = (41 - 41) / 5 = 0
The probability of the snowfall being less than or equal to 31 inches is the same as the probability ofthe Z-score being less than or equal to -2, which is approximately 0.0228.
P (31 ≤ X ≤41) = P(X ≤ 41) - P (X ≤ 31)
= 0.5 -0.0228
= 0.4772
Finally, we convert this probability to a percentage by multiplying by 100 -
Percentage = 0.4772 * 100
= 47.72%
Hence , approximately 47.72% of the years have a snowfall between 31 and 41 inches in this town.
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A group of cyclists recorded the distance they have traveled.
Draw a line plot and answer the questions below.
Name
Gina
Rey
Faye
Mark
John
James
Albert
William
Nathan
Kate
Mary
Risa
Paul
Abi
Joan
Distance in
miles
40 1/2
50
35 3/4
60
45
55 1/4
60
45
40 1/2
50
45
40 1/2
60
40 1/2
35 3/4
Title:
1. How many cyclists were there?
2. What was the longest distance traveled?
3. How many cyclists traveled less than 50 miles?
4. What was the most common distance traveled by
the cyclists?
5. How many more cyclists traveled 45 miles than
55 1/4 miles?
6. How many cyclists traveled more than 45 miles
A total of 7 Cyclists traveled more than 45 miles. 4 cyclists traveled 50 miles or more, and 3 cyclists traveled more than 54 1/4 miles.
A line plot is drawn with the cyclists' names plotted on the x-axis and their corresponding distances covered plotted on the y-axis.
The dots are then joined to form a line, revealing the relationship between the cyclist's names and their corresponding distance traveled. The cyclist names and their corresponding distances are given in the table below.
Name Distance (in miles) Gina 40 1/2 Rey 50 Faye 35 3/4 Mark 60 John 45 1/2 James 40 1/2 Albert 40 1/4 William 54 1/4 Nathan 40 Kate 40 1/4 Mary 60 Risa 40 Abi 35 3/4 Joan 50 1/2 1. The number of cyclists is 14. 2. The longest distance covered by a cyclist is 60 miles.
Mary and Mark both covered this distance.3. A total of 7 cyclists traveled less than 50 miles. 4. The most common distance traveled by cyclists is 40 1/2 miles. Gina, James, and Albert covered this distance. 5. 2 more cyclists traveled 45 miles than 55 1/4 miles. Only William traveled 55 1/4 miles, while John and James both traveled 45 1/2 miles.6.
A total of 7 cyclists traveled more than 45 miles. 4 cyclists traveled 50 miles or more, and 3 cyclists traveled more than 54 1/4 miles.
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In this module, you will consider the floor plan in which this emergency trauma center will be housed. The current trauma location is 1,500 square feet. You may configure this square footage however you prefer. Below is a list of equipment items and their dimensions.
To configure the emergency trauma center within the given 1,500 square feet, consider the dimensions of equipment items such as patient beds, medical carts, examination tables, imaging equipment, surgical equipment, workstations, and storage areas.
To configure the emergency trauma center within the given 1,500 square feet, we need to consider the dimensions of the equipment items and plan an efficient layout. Here is a list of equipment items and their dimensions:
Patient beds: These typically have dimensions of around 3 feet by 6 feet. Depending on the number of beds required, we can allocate sufficient space for them, keeping in mind the need for walkways around each bed.
Medical carts: These can vary in size, but a common dimension is around 2 feet by 3 feet. Allocate a designated area or storage space for the medical carts, ensuring easy access and mobility.
Examination tables: These usually have dimensions of approximately 2.5 feet by 5 feet. Plan a separate area for examination rooms where the tables can be placed along with other necessary equipment.
Imaging equipment: Such as X-ray machines or CT scanners, which may require a designated room or area with specific shielding and safety considerations. Ensure enough space for patient accessibility and the equipment's operation.
Surgical equipment: Depending on the specific surgical procedures performed, allocate adequate space for surgical tables, anesthesia carts, surgical instruments, and any required sterilization equipment.
Workstations: Create workstations for medical staff, including computers, desks, and storage areas for paperwork and supplies. Consider the need for privacy and comfortable working conditions.
Storage areas: Allocate space for storing medical supplies, medications, and other equipment that may not be immediately needed but should be easily accessible.
When planning the layout, consider factors such as patient flow, accessibility, and safety regulations. It's essential to create a functional and efficient floor plan that allows for smooth operations and optimal patient care within the given square footage.
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I'll give you brainliest!!
Answer: b
Step-by-step explanation:
∠B=angle, B, equals
^\circ
∘
degrees
Round your answer to the nearest hundredth.
The value of the angle B from the trigonometric ratios is 53.13 degrees
What is the Pythagorean theorem?The Pythagorean theorem is a powerful tool for solving various problems involving right triangles. It allows us to find the length of a missing side in a right triangle when the lengths of the other two sides are known. It is also used to identify whether a triangle is a right triangle or not.
We have that;
TanB = 4/3
B= Tan-1(4/3)
B = 53.13 degrees
Hence we are going to have by the use of tan that the angle is 53.1 degrees
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A family has two cars. During one particular week, the first car consumed 20 gallons of gas and the second consumed 40 gallons of gas. The two cars drove a combined total of l400 miles, and the sum of their fuel efficiencies was 55 miles per gallon. What were the fuel efficiencies of each of the cars that week?
Answer:
Car 1: 40 mpg; Car 2: 15 mpg
Step-by-step explanation:
Car 1:
fuel: 20 gal
distance: x
efficiency: a
Car 2:
fuel: 40 gal
distance: y
efficiency: b
x + y = 1400
a + b = 55
efficiency equation:
efficiency in mpg = distance (in miles) / fuel used (in gallons)
Car 1:
a = x/20
Car 2:
b = y/40
We have 4 equations in 4 variables:
a = x/20
b = y/40
x + y = 1400
a + b = 55
20a = x
40b = y
20a + 40b = 1400
a + b = 55
20a + 40b = 1400
20b + 20b = 1100
20b = 300
b = 15
a + b = 55
a + 15 = 55
a = 40
Answer: Car 1: 40 mpg; Car 2: 15 mpg
A school has 415 third graders, and 338 second graders. How many more third graders there than second graders.
Answer: It would be 80
Step-by-step explanation:
cos a(2sec a+tan a)(sec a-2tan a)=2cos a-3tan a
The trigonometric identity cos a(2sec a + tan a)(sec a - 2tan a) = 2cos a - 3tan a
What are trigonometric identities?Trigonometric identities are equations that contain trigonometric ratios.
Given the trigonometric identity cos a(2sec a + tan a)(sec a - 2tan a) = 2cos a - 3tan a, we need to show that Left hand side (L.H.S) equals Right hand side (R.H.S). We proceed as follows
L.H.S = cos a(2sec a + tan a)(sec a - 2tan a)
Expanding the brackets, we have that
cos a(2sec a + tan a)(sec a - 2tan a) = cos a(2sec² a - 4tan asec a + tan a sec a - 2tan² a)
= cos a(2sec² a - 3tan a sec a - 2tan² a)
Now using the trigonometric identity 1 + tan² a = sec² a, we have that
cos a(2sec² a - 3tan a sec a - 2tan² a) = cos a(2(1 + tan² a) - 3tan a sec a - 2tan² a)
= cos a(2 + 2tan² a - 3tan a sec a - 2tan² a)
Collecting like terms in the equation, we have that
= cos a(2 + 2tan² a - 2tan² a - 3tan a sec a)
= cos a(2 + 0 - 3tan a sec a)
= cos a(2 - 3tan a sec a)
Expanding the bracket, we have that
= 2cos a - cos a × 3tan a sec a
= 2cos a - cos a × 3tan a/cos a (since sec a = 1/cos a)
= 2cos a - 1 × 3tan a
= 2cos a - 3tan a
= R.H.S
So, since L.H.S = R.H.S,
cos a(2sec a + tan a)(sec a - 2tan a) = 2cos a - 3tan a
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why isnt it 21 whats being multiplied here 7*3
Answer:
(f ○ g)(- 1) = 11
Step-by-step explanation:
to evaluate ( f ○ g)(- 1) find g(- 1) then substitute the value obtained into f(x)
g(- 1) means what is the value of g(x) when x = - 1
from the table when x = - 1 , g(x) = - 3
now evaluate f(- 3) , which means what is the value of f(x) when x = - 3
from the table when x = - 3 , f(x) = 11
13
Select the correct answer from each drop-down menu.
A composite figure is shown.
6 ft
6 ft
6 ft
20 ft
What is the surface area for each part of the figure? What is the total surface area of the figure?
The surface area of the pyramid is
The surface area of the square prism is
The surface area of the cube is
The total surface area is
square feet.
square feet.
✓square feet.
✓square feet.
4 ft
The surface area of the figures are
Pyramid = 96 ft²
Square base prism = 552 ft²
Cube = 216 ft²
Total surface area = 756 ft²
How to find the surface areasTo find the surface area of different shapes, you can use specific formulas depending on the shape.
Here are the formulas used for each shape:
Pyramid:
Surface Area = Base Area + (1/2 × Perimeter × Slant Height)
Base Area = 6² = 36 ft²
Perimeter = 4(6) = 24 ft
Slant Height = √3² + 4² = √9 + 16 = √25 = 5 ft
Surface Area = 36 + (1 / 2 × 24 × 5) = 96 ft²
Square base prism:
Surface Area = 2(Base Area) + (Perimeter of Base × Height)
Base Area = 36
Perimeter of Base = 4(6)= 24
Height = 20
Surface Area = 2(36) + (4 * 6) * 20 = 552 ft²
Cube
The surface area of the cube = 6 x length² = 6 × 6² = 6 × 36 = 216 ft²
Total surface area
Total surface area = 96 ft² + 552 ft² + 216 ft²= 864 ft²
corrected total surface area = 864 ft² - 36 ft² - 36 ft² - 36 ft² = 756 ft²
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Question 6 of 20
What is the effect on the graph of f(s) = |s when the function is changed to
s(s) = (s - 1)|?
O
A. The graph is stretched vertically and shifted up 1 unit.
B. The graph is compressed horizontally and shifted down 1 unit.
C. The graph is compressed vertically and shifted 1 unit to the left.
D. The graph is stretched horizontally and shifted 1 unit to the right.
Answer:D. The graph is stretched horizontally and shifted 1 unit to the right.
Step-by-step explanation: The absolute value function |s| reflects the part of the graph below the x-axis to above the x-axis, resulting in a V-shape. The modification (s - 1)|s| shifts this V-shape 1 unit to the right and stretches it horizontally by a factor of 1. Therefore, option D is the correct answer.
please find the p-value
The statistical analysis of the data using a two-sample t-test indicates;
(a) B. Yes, the Meters On data appears to have higher speeds
A. No, there does not appear to be any outlier
(b) H₀; [tex]\mu_{on}[/tex] = [tex]\mu_{off}[/tex]
H₁; [tex]\mu_{on}[/tex] > [tex]\mu_{off}[/tex]
The P-value for the test is about 0.037
What is a two-sample t-test?A two-sample t-test is used to determine if there is a difference between the means of two independent groups of data.
(a) The average of the data values are;
Ramp meters on;
[tex]\mu_{on}[/tex] = (29+47+55+38+32+25+42+47+51+36+55+41+43+25+47)/15 ≈ 40.87
[tex]\mu_{off}[/tex] = (25+25+43+35+36+31+48+37+19+29+22+40+36+50+40)/15 ≈ 34.4
The higher average value for the speed with the Ramp meters on indicates;
B. Yes, the Meters On data appears to have higher speeds
The five number summary are;
Ramp Meters On
Min = 25, Max = 55, Q₁ = 32, Q₂ = 42, Q₃ = 47
IQR = 47 - 32 = 15
Outlier = 47 + 1.5 × 15 = 69.5
32 - 1.5 × 15 = 9.5
Therefore, there are no outliers for the Ramp Meters On
Ramp Meters Off
Min = 19, Max = 50, Q₁ = 25, Q₂ = 36, Q₃ = 40
IQR = 40 - 25 = 15
Outlier = 40 + 1.5 × 15 = 62.5
25 - 1.5 × 15 = 2.5
Therefore, there are no outliers for the Ramp Meters Off data
(b) The null hypothesis is; H₀; [tex]\mu_{on}[/tex] = [tex]\mu_{off}[/tex]
The alternative hypothesis is; H₁; [tex]\mu_{on}[/tex] > [tex]\mu_{off}[/tex]
(c) The two sample t-test, can be obtained using the formula;
[tex]t_{cal} = \frac{(\bar{x}_1 - \bar{x}_2)}{\sqrt{(\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2} ) } }[/tex]
Where; [tex]\bar{x}_1[/tex] = 40.87
[tex]\bar{x}_2[/tex] = 34.40
s₁ = 9.91
s₂ = 9.20
n₁ = n₂ = 15
Therefore; [tex]t_{cal}[/tex] = 1.8516. The degrees of 15 + 15 - 2 = 28, and the one-tailed hypothesis, indicates, using an online tool;
The p-value = 0.037328The p-value is less than 0.05, therefore, the result is significant.
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Select the correct answer
Consider functions f. g. and h below
f(x)=x²+2x+3
X
-1
0
1
2
3
h(x) -7 4 -1 2 5
Order the above functions, from least to greatest, by the rate of change of functions over the interval 10. 21.
A g.h.f
B. th.g
C g.f.h
D Lg.h
The order of the functions from least to greatest rates is (a) g(x), h(x), f(x)
How to order the functions, from least to greatestFrom the question, we have the following parameters that can be used in our computation:
f(x) = x² + 2x + 3
x -1 0 1 2 3
h(x) -7 4 -1 2 5
The interval is given as [0, 2]
For the functions, we have
f(0) = 0² + 2(0) + 3 = 3
f(2) = 2² + 2(2) + 3 = 11
h(0) = 4
h(2) = 2
So, we have the average rates of change at this interval to be
f(x) = (11 - 3)/(2 - 0) = 4
h(x) = (2 - 4)/(2 - 0) = -1
When ordered, we have
h(x), f(x)
Hence, the order is (a) g(x), h(x), f(x)
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In a test out of 40, the marks of 15 students were 31, 18, 6, 26, 36, 24, 23, 14, 29, 28, 32, 9, 11, 22, 21. a Calculate the mean mark for the test. b Express the mean mark as a percentage. 10) Ten Atlan h find be t Ex Fin
Answer:
The mean is 22. So, as a percentage its 22%.
I don know what you're trying say for: 10) Ten Atlan h find be t Ex Fin
Jim ate two slices of pizza, which is 25% of the pizza. How many slices were in the whole pizza?Sonya buys a baseball jersey for her brother on sale for 20% off. If the price she paid was $6 lower than the regular price, what was the original price of the jersey
There were 8 slices in the whole pizza.
How many slices were in the whole pizza if Jim ate two slices?An equation means the formula that expresses the equality of two expressions by connecting them with the equals sign =. Let us assume the number of slices in the whole pizza is "x".
Since Jim ate two slices which is 25% of the pizza, we will set up the equation:
2 = 0.25x
To solve for "x":
2 / 0.25 = x
x = 8.
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If you vertically stretch the cubic parent function, F(x) = y, what is the
equation of the new function?
Vertically stretch the cubic parent function, we multiply the function by the vertical stretch factor, a. The new equation of the function is y = a(x^3).
If you vertically stretch the cubic parent function, the equation of the new function is y = a(x^3) where a is the vertical stretch factor. A cubic parent function is a polynomial function with a degree of three and an equation of y = x^3.
A vertical stretch is a transformation that increases the distance between each point on a graph and the x-axis. This transformation does not change the shape of the graph, but it affects the height of the graph.
To vertically stretch the cubic parent function, we multiply the function by a vertical stretch factor, a. Therefore, the equation of the new function is y = a(x^3).
For example, let's say we want to vertically stretch the cubic parent function y = x^3 by a factor of 2. To do this, we multiply the function by 2, which gives us y = 2(x^3). This means that the new function is twice as tall as the original function.
On the other hand, if we want to vertically shrink the cubic parent function y = x^3 by a factor of 1/2, we divide the function by 1/2. This gives us y = (1/2)(x^3), which means that the new function is half as tall as the original function.
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Set up the appropriate equation to solve for the missing angle.
Answer:
x = 52.7°
Step-by-step explanation:
To find the value of x in the given right triangle, we can use the tangent trigonometric ratio.
[tex]\boxed{\begin{minipage}{7 cm}\underline{Tangent trigonometric ratio} \\\\$\sf \tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle.\\\end{minipage}}[/tex]
The unknown angle is x, so θ = x.
The side opposite the angle measures 21 units, so O = 21.
The side adjacent the angle measures 16 units, so A = 16.
Substitute the values into the ratio and solve for x:
[tex]\tan x=\dfrac{21}{16}[/tex]
[tex]x=\tan^{-1}\left(\dfrac{21}{16}\right)[/tex]
[tex]x=52.6960517...[/tex]
[tex]x=52.7^{\circ}\; \sf (nearest\;tenth)[/tex]
Therefore, the value of x is 52.7°.
The equation for the missing angle is
Tan x = 21 / 16
How to determine the equation for the missing angleThe problem will be solved using Trigonometry - SOH CAH TOA
SOH for Sin = Opposite / Hypotenuse
CAH for Cos = Adjacent / Hypotenuse
TOA for Tan = Opposite / Adjacent
The given part is
opposite = 21
Adjacent = 16
using TOA
Tan x = 21 / 16
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A rock thrown vertically upward from the surface of the moon at a velocity of 28 m/sec reaches a height of s=28t-0.8t^2 meters in t sec.
a. Find the rock's velocity and acceleration at time t.
b. How long does it take the rock to reach its highest point?
c. How high does the rock go?
d. How long does it take the rock to reach half its maximum height?
e. How long is the rock aloft?
Answer:
a. To find the velocity and acceleration of the rock at time t, we need to take the first and second derivatives of the height equation with respect to time:
s = 28t - 0.8t^2
v = ds/dt = 28 - 1.6t
a = dv/dt = -1.6
So the velocity of the rock at time t is v = 28 - 1.6t m/s, and its acceleration is a = -1.6 m/s^2.
b. To find how long it takes the rock to reach its highest point, we need to find the time at which the velocity is zero. We can set v = 28 - 1.6t = 0 and solve for t:
28 - 1.6t = 0
t = 17.5 seconds
So it takes 17.5 seconds for the rock to reach its highest point.
c. To find the maximum height reached by the rock, we can substitute t = 17.5 seconds into the height equation:
s = 28t - 0.8t^2
s = 28(17.5) - 0.8(17.5)^2
s = 245 meters
So the rock reaches a height of 245 meters.
d. To find how long it takes the rock to reach half its maximum height, we can set s = 245/2 = 122.5 meters and solve for t:
s = 28t - 0.8t^2
0.8t^2 - 28t + 122.5 = 0
t = 7.5 seconds or t = 20 seconds
So it takes the rock 7.5 seconds to reach half its maximum height.
e. To find how long the rock is aloft, we need to find the time at which it returns to the surface. We can set s = 0 and solve for t:
s = 28t - 0.8t^2
0 = 28t - 0.8t^2
t = 35 seconds
So the rock is aloft for 35 seconds.
Find the measure of the indicated angle.
101°
62.5°
113°
50.5°
101.
S
T
V
P
125
U
Answer:
? = 113°
Step-by-step explanation:
the chord- chord angle TVU is half the sum of the measures of the arcs intercepted by the angle and its vertical angle, then
∠ TVU = [tex]\frac{1}{2}[/tex] (UT+PS) = [tex]\frac{1}{2}[/tex] (125 + 101)° = [tex]\frac{1}{2}[/tex] × 226° = 113°
Rewrite each expression in factored form.
a. x²-3x - 28
b. x² + 3x - 28
c. x² + 12x - 28
d. x² - 28x - 60
a. The factored form of the expression x² - 3x - 28 is (x - 7)(x + 4).
b. The factored form of the expression x² + 3x - 28 is (x - 4)(x + 7).
c. The factored form of the expression x² + 12x - 28 is (x + 14)(x - 2).
d. The factored form of the expression x² - 28x - 60 is (x - 30)(x + 2).
a. To factorize the expression x² - 3x - 28, we can use the factoring method. We look for two numbers that multiply to give the constant term (-28) and add up to the coefficient of the linear term (-3). In this case, the numbers are -7 and 4.
Split the middle term (-3x) using -7x and 4x:
x² - 7x + 4x - 28
Group the terms and factor by grouping:
(x² - 7x) + (4x - 28)
x(x - 7) + 4(x - 7)
Factor out the common binomial (x - 7):
(x - 7)(x + 4)
b. For the expression x² + 3x - 28, we follow a similar process:
Split the middle term (3x) using 4x and -x:
x² + 4x - x - 28
Group the terms and factor by grouping:
(x² + 4x) + (-x - 28)
x(x + 4) - 1(x + 28)
Factor out the common binomial (x + 4):
(x + 4)(x - 7)
c. Moving on to x² + 12x - 28:
Split the middle term (12x) using 14x and -2x:
x² + 14x - 2x - 28
Group the terms and factor by grouping:
(x² + 14x) + (-2x - 28)
x(x + 14) - 2(x + 14)
Factor out the common binomial (x + 14):
(x + 14)(x - 2)
d. Finally, let's factorize x² - 28x - 60:
Split the middle term (-28x) using -30x and 2x:
x² - 30x + 2x - 60
Group the terms and factor by grouping:
(x² - 30x) + (2x - 60)
x(x - 30) + 2(x - 30)
Factor out the common binomial (x - 30):
(x - 30)(x + 2)
By following these steps, we can factorize the given expressions into their respective factored forms.
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find the lettered angles in the diagram below and state the law
There is no solution for the given Angle measures and side length of the right-angled triangle.
In a right-angled triangle ABC, the given angle measures are:∠A = 40°, ∠C = 90° and AB = 7.5 cm.Law of sines:Sine rule, also known as the law of sines, is a theorem in trigonometry that defines the relationship between the angles and sides of a triangle. This law is generally used in trigonometry when we have a triangle with angle measures and a side length which are known or have been given.
Law of cosines:The law of cosines, also known as the cosine formula or the cosine rule, relates to the lengths of the sides of a triangle to the cosine of one of its angles. In geometry, it is a statement that explains the relationship between the sides and angles of a triangle.Let ∠B = x
We have the side adjacent to ∠A which is AB and the side opposite to ∠B which is BC.For the ∆ABC using sine rule:AB/sin ∠C = BC/sin ∠A=> AB/sin 90 = BC/sin 40=> AB = BC.sin 40⇒ AB = 7.5 sin 40 ≈ 4.83 cmNow we can use cosine rule:AC² = AB² + BC² - 2 AB BC cos ∠C=> AC² = 7.5² + BC² - 2 × 7.5 × BC × 0=> AC² = 7.5² + BC²⇒ AC² = 56.25 + BC²Also, we have the angle opposite to the hypotenuse of the right-angled triangle.
Using the cosine rule:cos ∠C = AB/ACcos 90 = AB/AC=> 0 = AB/AC⇒ AB = 0 (which is not possible)
Therefore, there is no solution for the given angle measures and side length of the right-angled triangle.
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The expression 3s + s + 3 represents how much Alex and his family will spend to go to the movies. Which statement explains how this expression can be simplified?
Answer:
Step-by-step explanation:
The expression 3s + s + 3 represents the total amount Alex and his family will spend to go to the movies. To simplify this expression, we can combine like terms.
The terms 3s and s are like terms because they both have the variable "s" raised to the power of 1. To combine them, we add their coefficients:
3s + s = (3 + 1)s = 4s
Therefore, the simplified expression is 4s + 3, which represents the total amount Alex and his family will spend to go to the movies.
Please Help!! - Find constants a and b so that (8, −7) is the solution of the system. Please answer in exact numbers.
Answer:
a=3, b=2
Step-by-step explanation:
Let's fill in the given solution:
8a - 7b = 10
8b - 7a = -5
To solve, let's eliminate b. To do that, we want equal terms in both equations.
This can be achieved by multiplying the first by 8, the second by 7:
64a - 56b = 80
56b - 49a = -35
If we add the equations, we get:
64a - 49a - 56b + 56b = 80 - 35 =>
15a = 45
a = 3
In the original equation, this gives:
8*3 - 7b = 10 =>
-7b = -14
b = 2
if h(x) = (f o g) (x) and h(x) = square root x+5 find g(x) if f(x)= square root x+2
The function g(x) = x + 3 is a component of the composite function.
How to determine one of the functions that form a composite function
In this question we find the case of a composite function, of which one of its components must be deducted. This can be done by means of algebra properties. First of all, the composition of functions is defined below:
f ° g (x) = f [g(x)]
First, write the entire function:
√(x + 5)
Second, derive the expression g(x):
√(x + 5)
√[(x + 3) + 2]
f(x) = √(x + 2), g(x) = x + 3
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18
X
24
18
These shapes
are similar.
Find X.
8
12
Answer:
the answer is 16 please give me brainlest
Find the missing measure for a right circular cone given the following information.
Find h if r = 5 and V = 100.
O 30
04
012
The missing measure, h (height), for a right circular cone with a radius of 5 and a volume of 100 is approximately 3.82.
What is the measure of the height of the cone?A cone is simply a 3-dimensional geometric shape with a flat base and a curved surface pointed towards the top.
The volume of a cone is expressed as;
V = (1/3) × π × r² × h
Where r is the radius of the base, h is the height of the cone and π is constant pi.
Given that:
Volume V = 100
Radius r = 5
Height h =?
Plug the given values into the above equation and solve for height h:
V = (1/3) × π × r² × h
100 = (1/3) × π × 5² × h
3 × 100 = 3 × (1/3) × π × 25 × h
300 = π × 25 × h
300 = 25π × h
h = 300 / 25π
h = 12/π
h = 3.82 units
Therefore, the height is approximately 3.82 units.
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expand [x-1] [x-2] [x-6]
[tex](x - 1)(x - 2)(x - 6) \\ ({x}^{2} - 2x - x + 2)(x - 6) \\ ( {x}^{2} - 3x + 2)(x - 6) \\ {x}^{3} - 6 {x}^{2} - 3 {x}^{2} + 18x + 2x - 12 \\ {x}^{3} - 9 {x}^{2} + 20x - 12 [/tex]
PLEASE GIVE ME BRAINLIEST
Need help solving this piecewise average value question! Thanks!
The value of the integral is [tex]\int\limits^{10}_4 {f(x)} \, dx = 6[/tex]
The average rate of change over the interval [4, 10] is 3/2
How to evaluate the integralFrom the question, we have the following parameters that can be used in our computation:
[tex]f(x) = \left\{ \begin{array}{lr} -4, & \text{if } 4 \le x < 7\\ 5, & \text{if } 7 \le x < 10 \end{array}[/tex]
The integral expression is given as
[tex]\int\limits^{10}_4 {f(x)} \, dx[/tex]
So, we have
[tex]\int\limits^{10}_4 {f(x)} \, dx = \int\limits^{10}_4 {[5 - 4]} \, dx[/tex]
Evaluate the difference
[tex]\int\limits^{10}_4 {f(x)} \, dx = \int\limits^{10}_4 {[1]} \, dx[/tex]
Integrate
[tex]\int\limits^{10}_4 {f(x)} \, dx = [x]\limits^{10}_4[/tex]
Expand
[tex]\int\limits^{10}_4 {f(x)} \, dx = 10 - 4[/tex]
Evaluate the difference
[tex]\int\limits^{10}_4 {f(x)} \, dx = 6[/tex]
How to evaluate the average rate of changeHere, we have
[tex]f(x) = \left\{ \begin{array}{lr} -4, & \text{if } 4 \le x < 7\\ 5, & \text{if } 7 \le x < 10 \end{array}[/tex]
The interval is [4, 10]
So, we have
Average rate = (5 + 4)/(10 - 4)
Evaluate
Average rate = 3/2
Hence, the average rate of change is 3/2
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Joe tried to prove that the sum of a triangle's interior angle measures is 180 ° 180°180, degree Triangle A B C with a dashed horizontal line labeled l passing through point C. Angle A is labeled one. Angle B is labeled two. Angle A C B is labeled three. The exterior angle formed by the dashed horizontal line, point C, and point A is labeled four. The exterior angle formed by the dashed horizontal line, point C, and point B is labeled five. Triangle A B C with a dashed horizontal line labeled l passing through point C. Angle A is labeled one. Angle B is labeled two. Angle A C B is labeled three. The exterior angle formed by the dashed horizontal line, point C, and point A is labeled four. The exterior angle formed by the dashed horizontal line, point C, and point B is labeled five. Statement Reason 1 Construct line ℓ ℓell through � CC parallel to � � ↔ AB A, B, with, \overleftrightarrow, on top. 2 � ∠ 4 = � ∠ 2 m∠4=m∠2m, angle, 4, equals, m, angle, 2 and � ∠ 1 = � ∠ 5 m∠1=m∠5m, angle, 1, equals, m, angle, 5 Alternate interior angles formed by parallel lines have equal measures. 3 � ∠ 5 + � ∠ 4 + � ∠ 3 = 180 ° m∠5+m∠4+m∠3=180°m, angle, 5, plus, m, angle, 4, plus, m, angle, 3, equals, 180, degree Angles that combine to form a straight angle have measures that sum to 180 ° 180°180, degree. 4 � ∠ 1 + � ∠ 2 + � ∠ 3 = 180 ° m∠1+m∠2+m∠3=180°m, angle, 1, plus, m, angle, 2, plus, m, angle, 3, equals, 180, degree Substitution (2,3) What was the first mistake in Joe's proof? Choose 1 answer: Choose 1 answer: (Choice A) Constructing a parallel line like this isn't necessarily possible. A Constructing a parallel line like this isn't necessarily possible. (Choice B) Angles ∠ 4 ∠4angle, 4 and ∠ 2 ∠2angle, 2 are not alternate interior angles, and neither are ∠ 1 ∠1angle, 1 and ∠ 5 ∠5angle, 5. B Angles ∠ 4 ∠4angle, 4 and ∠ 2 ∠2angle, 2 are not alternate interior angles, and neither are ∠ 1 ∠1angle, 1 and ∠ 5 ∠5angle, 5. (Choice C) Angles ∠ 3 ∠3angle, 3, ∠ 4 ∠4angle, 4, and ∠ 5 ∠5angle, 5 don't form a s
Joe made the first mistake in the proof by making the assumption that line l is parallel to AB without providing any evidence or justification for this claim. This suspicion subverts the ensuing thinking and conclusion of the proof.
How to prove that the sum of a triangle's interior angle measures is 180 ° degreeJoe's first error in his proof was assuming, without any evidence or justification, that line l is parallel to line AB. In order to construct a parallel line, specific information or conditions are required, such as the use of particular construction techniques or predetermined angles.
Joe's proof's subsequent reasoning and conclusions become questionable if the parallel relationship between the lines is not established. For the purpose of establishing that the sum of the interior angles of the triangle equals 180 degrees, the congruence or equality of angles must be demonstrated using the parallel line assumption.
Joe's proof cannot be considered accurate or valid because it lacks a solid logical foundation for the parallel line assumption.
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