Answer:
the given set of solutions {−7,4} is y=x2+3x−28 y = x 2 + 3 x - 28 .
On a coordinate plane, a parabola opens up. Solid circles appear on the parabola at (negative 4, 14), (negative 3, 9.5), (negative 2, 6), (0, 2), (1, 1.5), (2, 2), (4, 6), (5, 9.5), (6, 14).
Which is the rate of change for the interval between 2 and 6 on the x-axis?
Answer:
Step-by-step explanation:
The rate of change for the interval between x = 2 and x = 6 is simply asking you for the slope of the line that connects these 2 coordinates. If you were in calculus, you could find the instantaneous slope at any point on this parabola, but you're not quite that lucky yet, so we will go about it the only way we can:
by finding the slope. Remember, that slope is the same thing as rate of change.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] and filling in:
[tex]m=\frac{14-2}{6-2}=\frac{12}{4}=3[/tex]
A chef cooked 7kg of mashed potatoes for a banquet. If guests only ate 3/4 of the amount he cooked, how much of the potatoes were eaten?
Answer:
5.25 kg of the mashed potatoes were eaten.
Step-by-step explanation:
(3/4) * 7 = 5.25
I hope this is helpful :)
Times for an ambulance to respond to a medical emergency in a certain town are normally distributed with a
mean of 450 seconds and a standard deviation of 50 seconds.
Suppose there are 97 emergencies in that town.
In about how many emergencies are the response times expected between 400 seconds and 500 seconds?
31
33
47
66
Answer:
66
Step-by-step explanation:
The Empirical Rule states that 68% of data is between 1 standard deviation in a dataset of normal distribution, 95% falls between 2 standard deviations, and 99.7% between 3.
The mean is 450, and one standard deviation is between 450 ± 50 = 400 and 500. Therefore, we can say that 68% of the data falls between 400 and 500 seconds.
The data includes 97 emergencies, so we just need to find 68% of that, which is 0.68*97 = 65.96 (rounding up to 66)
There are 66 emergencies are the response times expected between 400 seconds and 500 seconds.
What is Addition?The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.
Given that;
mean = 450 sec
standard deviation = 50 sec
Hence, We get;
450-50 =400
450+50=500
Now, In Between 400 sec and 500 sec means one deviation above and one deviation below the mean, and it is 68%.
68% = 0.68
Thus,
0.68 x 97 = 65.96 ≈ 66
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Ai đó giúp mình với. Bài này mình không nghĩ ra cách giải
Answer:
-3 -2. 1 0 2 3 -2 3Step-by-step explanation:
please make it a brainliest answer.
Samia created the following tables of values for a linear system. She concluded that there is no
solution to the system
Since the two linear relations are parallel to each other, no solution to the system exists. Hence, Samia's conclusion is correct.
How many solutions do a system of linear lines have?A system of equations, involving two linear lines has solutions as follows:
Unique Solution: When the lines intersect, the point of intersection is the solution.No Solution: When the lines are parallel, no solution exists.Infinite Solution: When the lines coincide, then all points on the line become solutions, giving an infinite number of solutions.How to solve the question?In the question, we are informed that Samia created the given tables for a linear system, and concluded that no solution exists for the system.
We are asked to comment on her conclusion.
To check for her conclusion, we calculate the slopes of both the lines to check whether the relations are parallel or not, as, for parallel relations, the slopes are equal.
Slope can be calculated using the formula, m = (y₂ - y₁)/(x₂ - x₁), when (x₁, y₁), and (x₂, y₂) are the points on the line.
Thus, the slope for:-
Relation 1, is m₁ = (22 - 8)/(4 - (-3)) = 14/7 = 2.
Relation 2, is m₂ = (12 - (-2))/(4 - (-3)) = 14/7 = 2.
Since the slope of the two relations is equal, that is, m₁ = m₂, and they are not coinciding with each other, we can say that the two relations are parallel to each other.
Since the two linear relations are parallel to each other, no solution to the system exists. Hence, Samia's conclusion is correct.
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Find the value of x-8 when x=16.
Answer:
8
Step-by-step explanation:
x=16
x(16)-8=8
I am a 4 digit number all my digits are different they add up to 20 the hundred's digit is double than the one's digit
Answer:
- 2864
Step-by-step explanation:
Given that,
The number is of 4 digits
All are different
The sum of the 4 digits = 20
Hundred's digit is twice than one's digit
A.T.Q.
Let the unit digit be 4. So, the hundred's digit would be 4 * 2 = 8
Now, we have
_8_4
We know that the sum of four digits is 20. Thus,
_ + 8 + _ + 4 = 20
∵ _ + _ = 20 - 12 = 8
The possible numbers must make a sum of 8. Thus, one possibility can be 2 and 6.
Therefore, the number can be
2864
( 2 + 8 + 6 + 4 = 20)
What is 4,327 rounded to the nearest thousand?
Answer: 4,000
Step-by-step explanation: To round 4,327 to the nearest thousand, we first find the digit in the rounding place, which in this case is the 4 in the thousands place. Next, we look at the digit to the right of the 4, which is 3.
According to the rules of rounding, since the digit to
the right of the rounding place is less than 5, we round down.
So the 4 in the rounding place stays the same
and all digits to the right of the 4 become 0.
So 4,327 rounded to the nearest thousand is 4,000.
What are the roots of this equation x^2-4x+9=0?
Answer:
Roots is a fancy word for zero, which is also another fancy word for the x intercept.
You can factor a quad or use the quadratic equation to get zeros.
In this case, its non-factorable. So you gotta use the quadratic.
Using the quadratic equation you get : x = -2 ± √-1 (√5),
which can be rewritten as x = -2 ± i(√5)
Function was : x^2 + 4x + 9
For quad, I identified the following:
A = 1
B = 4
C = 9
I also added a picture of the formula in the attached.
If x = 2y + 3 and 4x – 5y = 9, what is the value of y?
A. 2
B. 1
C. -1
D. -2
Answer:
Steps shown in picture provided
HELP PLEASE IM GONNA FAIL
21. Identify as a function or not a Function
Answer:
First one: function
Second one: not a function
Step-by-step explanation:
A function is a relationship where each input has it's own unique output. If an input has more than one output then the relationship is not a function
For the first one no x value repeats meaning each input has it's own output therefore it is a function
For the second one the x value 8 has more than 1 output therefore the second one is not a function
Let $G$ be the center of equilateral triangle $XYZ.$ A dilation centered at $G$ with scale factor $-\frac{4}{3}$ is applied to triangle $XYZ,$ to obtain triangle $X'Y'Z'.$ Let $A$ be the area of the region that is contained in both triangles $XYZ$ and $X'Y'Z'.$ Find $\frac{A}{[XYZ]}.$
The area divided by XYZ is 16/9
i.e. [tex]\frac{A}{[XYZ]} = \frac{16}{9}[/tex]
The given parameters can be represented as:
[tex]r = -\frac{4}{3}[/tex] --- the ratio of dilation
The area of the second triangle is as follows:
[tex]A =r^2 * \triangle XYZ[/tex]
Make [tex]r^2[/tex] as subject
[tex]r^2 = \frac{A}{\triangle XYZ}[/tex]
Substitute value for [tex]r^2[/tex]
[tex](\frac{4}{3})^2 = \frac{A}{\triangle XYZ}[/tex]
[tex]\frac{16}{9} = \frac{A}{\triangle XYZ}[/tex]
Rewrite as:
[tex]\frac{A}{\triangle XYZ} = \frac{16}{9}[/tex]
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Answer:
Step-by-step explanation:
Let each side of triangle XYZ have length s. We therefore have:
s = YZ = YQ + QR + RZ = x + 2y
Since each side of triangle X1 Y2 Z2 is 3/4 the length of the corresponding side of triangle XYZ, we have:
3/4s = X1 Z1 = X1 Q + QP + P Z1 = 2x +y.
The system of equations:
x + 2y = s
2x + y = 3/4s
Multiply the second equation by 2, then subtract the first equation.
3x = 1/2s, so x = 1/6s.
Now we have y = 3/4s-2x = 5/12s.
A/[XYZ] = [XYZ] - 3[YPQ]/[XYZ]
= {[XYZ] - 3[(25)/144] * [XYZ]} / [XYZ]
={23/48* [XYZ]} / [XYZ]
= 23/48
what do you mean by trigonometry
Answer:
Trigonometry is a branch of mathematics that studies relationships between the sides and angles of triangle
need help refer to picture
Answer:
203 ft.
Step-by-step explanation:
Since we are given the measurements of two sides, we can use trig to find the angle (or our reference angle, we'll call it x) the sides form.
SOH-CAH-TOA
We'll use cosine since the adjacent and hypotenuse were given for our reference angle.
Cos(x) = (adj/hyp)
Cos(x) = (396/445)
[Cos(x)]cos^-1 = (396/445)(cos^-1)
x ≈ 27.1409 (Nearest ten-thousandth)
And now we find the missing side using our now known angle.
SOH-CAH-TOA
Tan(x) = (opp/adj)
Tan(27.1409) = (opp/396)
0.5126 ≈ (opp/396)
(0.5126)(396) ≈ (opp/396)(396)
Opp = 203
Missing Side = 203 ft
97. An elevator in a tall building goes up 7 floors, then
down 9 floors, down 4 floors, up 8 floors, and
down 2 floors. Now it is on floor 14. On what
floor did the elevator start?
so, start floor = x
x + 7 - 9 - 4 + 8 - 2 = 14
x = 14
the elevator started on the 14th floor.
to verify: 14 + 7 = 21 - 9 = 12 - 4 = 8 + 8 = 16 - 2 = 14
Determine the measure of the interior angle at vertex E.
Answer:
135
Step-by-step explanation:
(n−2) × 180° = sum of the interior angles where n is the number of sides
There are 6 sides
(6 -2) * 180
4*180
The sum is 720
2x+2x+3x+3x+3x+3x = 720
16x = 720
Divide by 16
16x/16 = 720/16
x = 45
Angle E = 3x= 3(45) = 135
how do you solve this
Answer:
√2
Step-by-step explanation:
tan(x) = -1
x = arctan(-1)
x = -π/4
Now since x is between 3π/2 and 2π use use the general form
nπ-π/4
taking n = 2
2×π-π/4
= 7π/4
now tan (7π/4) = -1
so sec (7π/4) = √2
Answered by GAUTHMATH
Zoe walks at a speed of 10 miles/h and jogs at a speed of 20 miles/h.
She goes to the park to walk 2 miles on a Monday. How long will she take to jog 2 miles?
Answer:
6 minutes
Step-by-step explanation:
20 miles jogs at 1 hour, so for 2 miles,
2/20
= 1/10 hours
= 1/10×60
= 6 minutes
Answered by GAUTHMATH
assume abc=def. if ab=5, ac=9 and ef=7, what is the length of bc?
Answer:
bc= 7
Step-by-step explanation:
i have 17 coins. N of them are nickels and the rest are dimes. write an expression in two different ways for the amount of money that i have. (Hint: one is the other simplified)
Answer:
Step-by-step explanation:
Total amount in cents (unsimplified): 5N +17(10-N)
Simplified: 170-5N
Last year there were 45 memebers of the tennis club at Marks Middle school. This year although the number of boys increeased by 20%, the number of girls decresed by 20%, the total numbers decresed by 1. Find how many boys anf girls are in the tennis club this year.
Answer:
24 boys & 20 girls
Step-by-step explanation:
Last year:
Number of boys = x
Total number = 45
Number of girls = 45 - x
An increase of 20% is the same as multiplying by 1.2
A decrease of 10% is the same as multiplying by 0.8
This year:
New number of boys: 1.2x
New number of girls: 0.8(45 - x)
New total number = 45 - 1 = 44
1.2x + 0.8(45 - x) = 44
1.2x + 36 - 0.8x = 44
0.4x + 36 = 44
0.4x = 8
x = 20
Last year there were 20 boys and 25 girls.
This year there are 20 * 1.2 = 24 boys
and 44 - 24 = 20 girls
Answer: 24 boys & 20 girls
i need help with this one please
Answer:
A
Step-by-step explanation:
a geometric sequence is where we multiply a factor from element to element.
a1 = $900
a2 = 981 = a1 × f = 900 ×
a3 = 1069.29 = a2 × f = a1 × f × f = s1 × f²
[tex]an = 900 \times {f}^{n - 1} [/tex]
so, now let's try and get f.
remember, 981 = 900 × f
f = 981/900 = 109/100 = 1.09
just to control, we check for s3 :
900 × (1.09)² = 900 × 1.1881 = 1069.29
correct.
so,
a13 = 900 × (1.09)¹² = 2,531.398304
s13 is then the sum of all a1, ..., a13
there is a nice formula for sums of finite sequences
s13 = 900 × (1-f¹³) / (1-f) = 900×(1-(1.09)¹³) / (1-1.09) =
= 900×(1-3.065804612) / (-0.09) =
= 900×(-2.065804612) / (-0.09) = 20,658.04612
.
What equation is represented by the equation on the graph?
X
OA. y = x - 2
OB. y=-X-2
OC. y=-3x+2
OD. y=-X+2
Reset Meet
Answer:
y= -x +2
Step-by-step explanation:
This is a negative slope of one because the line is going down and has a ride over run of 1/1. Then the y intercept is +2 because this line intercepts the y axis at positive 2.
hope it helps!
Answer:
y = -x +2
Step-by-step explanation:
just trust me on this
Three-eighths of the teachers at Naran's school are math teachers, and 30 of the teachers are not math teachers.
How many teachers are there at Naran's school??
Answer:
48 teachers
Step-by-step explanation:
Here's two solutions:
Solution 1: Build an equation.
Let $T$ be the number of teachers. The number of math teachers is $\frac{3}{8}T$, and the number of non-math teachers is $30$. Since each teacher is either a math teacher or not a math teacher, we have
$$\frac{3}{8}T + 30 = T.$$Multiplying each side of this equation by $8$ gives us
$$3T + 240 = 8T.$$Subtracting $3T$ from each side gives us $240 = 5T$, and dividing both sides by $5$ gives us $48=T$. Therefore, there are $48$ teachers at Naran's school.
Solution 2: Think proportionally.
Since three-eighths of the teachers are math teachers, the other five-eighths are not math teachers. So, these $30$ non-math teachers are five-eighths of the total number of teachers. Therefore, $\dfrac{30}{5} = 6$ teachers are one-eighth of the total. So, there are $6\cdot 8 = \boxed{48}$ teachers in all.
What
is the value of In e^4
Answer:
[tex]\displaystyle lne^4 = 4[/tex]
General Formulas and Concepts:
Algebra II
Natural Logarithms ln and Euler's number e
Logarithmic Property [Exponential]: [tex]\displaystyle log(a^b) = b \cdot log(a)[/tex]Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle lne^4[/tex]
Step 2: Evaluate
Rewrite [Logarithmic Property - Exponential]: [tex]\displaystyle 4lne[/tex]Simplify: [tex]\displaystyle 4(1)[/tex]Solve for x: 9(3x+3)=10(3x+9)
Answer:
-21 =x
Step-by-step explanation:
9(3x+3)=10(3x+9)
Distribute
27x +27 = 30x +90
Subtract 27x from each side
27x+27 -27x = 30x-27x +90
27 = 3x+90
Subtract 90 from each side
27-90 = 3x +90-27
-63 = 3x
Divide by 3
-63/3 = 3x/3
-21 =x
Answer:
x = -21
Step-by-step explanation:
9(3x+3) = 10(3x+9)
27x + 27 = 30x + 90
-30x + 27x = 90 - 27
-3x = 63
x = -21
six boys each have the same number of sweets.the total number of sweet is 78. how many sweet did each boy have?
Determine the measure of the angle theta to the nearest degree
Answer: B. θ = 36°
Step-by-step explanation:
Concept:
Here, we need to know the idea of the Law of sines.
In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of a triangle (any shape) to the sines of its angles.
The Law of sines: a / sinA = b / sinB = c / sinC
If you are still confused, please refer to the attachment below for a graphical explanation.
Solve:
a = 10 m
c = 11.2 m
C = 41°
Given formula
a / sinA = c / sinC
Substitute the value into the formula
10 / sinA = 11.1 / sin (41)
Cross-multiply to simplify the equation
sinA × 11.1 = 10 · sin (41)
Divide 11.1 on both sides
sinA × 11.1 / 11.1 = 10 · sin (41) / 11.1
sinA = 10 · sin (41) / 11.1
Apply arcsine or the inverse of sine (basically representing the division of sine)
A = sin⁻¹ (10 · sin (41) / 11.1)
A = 36°
Hope this helps!! :)
Please let me know if you have any questions
A number line is divided into fifths. How many equal segments are there between the point at zero and the point 4/5?
Answer:
3?
Step-by-step explanation:
A little confused by the question but is it just
1/5 2/5 3/5 4/5
1 2 3 4
so theres 3 in between
Solve the equation √2 – 1 = 3.
Question 5 options:
A)
x = 4
B)
x = 16
C)
x = 8
D)
x = 2
Answer:
C x=8
Step-by-step explanation:
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