Answer:
x=9
if
a^b = a^c
then b=c
so in this case x=9
What is the multiplicative rate of change of the function? two-thirds three-fourths four-thirds three-halves
The multiplicative rate of change is 2/3
How to determine the multiplicative rate of change?The complete question is in the image
The multiplicative rate of change is then calculated as:
r = y2/y1
This gives
r = 4/6
Simplify
r = 2/3
Hence, the multiplicative rate of change is 2/3
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Answer:
b.
Step-by-step explanation:
Hey y’all I need this answer quickly!!!
3/4 - 1/5
Answer:
[tex]\sf \dfrac{11}{20} \quad or \quad 0.55[/tex]
Explanation:
[tex]\rightarrow \sf \dfrac{3}{4} - \dfrac{1}{5}[/tex]
make the denominators same by lcm
[tex]\rightarrow \sf \dfrac{5(3)}{20} - \dfrac{4(1)}{20}[/tex]
expand the following
[tex]\rightarrow \sf \dfrac{15}{20} - \dfrac{4}{20}[/tex]
Join the fractions together
[tex]\rightarrow \sf \dfrac{15-4}{20}[/tex]
Subtract the integers
[tex]\rightarrow \sf \dfrac{11}{20} \quad or \quad 0.55[/tex]
Answer:
11/20 or 0 whole 11/20 or 0.55
Step-by-step explanation:
[tex]3/4 - 1/5[/tex]Find the least common multiple (LCM) of 4 and 5 at first:
We can't do the LCM of 5 and 4,so just multiply them, 5*4 = 20
Now,
For 3/4 : divide 20 by 4,then multiply the result by 3.For 1/5 : divide 20 by 4, then multiply the result by 1. Simple!
[tex] \cfrac{15 - 4}{20} [/tex]Subtracting the numerators,
[tex] \boxed{\cfrac{11}{20} }[/tex]As a whole number:
[tex]\boxed{0 \cfrac{11}{20} }[/tex]As a decimal:
[tex]\boxed{0.55 }[/tex]What is the range of the function graphed below?
O (-∞0,4]
O [-4.0) [2,00)
O [-4,00)
O (-4,0] (2,00)
Answer: B. [–4, 0) ∪ [2, ∞)
To find the range, find out what y-values are possible for the function in the graph.
SymbolsWe need to pay attention to what symbols to use.
Reading the diagramSolid circle
The function touches the point.Empty circle
The function gets close, but does not touch the point.Arrow
The function keeps going to infinity.Writing range in set notationSquare brackets: [ and ]
These show that the function touches the point.Curved brackets: ( and )
These show that the function gets close but does not touch the point.Infinity always uses a curved bracket.Union of sets: ∪
This symbol shows that sets of values are talking about the same thing. It's almost like the word 'and'.Finding the range of the graphed functionLower blue lineLet's start by looking for the lowest possible y-value at the bottom of the diagram. On the graph, the point (4, –4) marked with a solid circle.
The function touches the point and stops. Since the y-value is –4, the lowest possible y-value is: [tex]-4[/tex]
If we follow the blue line upwards, we find an empty circle at (0, 0). The y-value in (0, 0) is 0. This means that the function gets close, but does not include: [tex]0[/tex]
So, the first part of our range is:
[–4, 0)Upper blue lineThe blue line on the top starts where y = 2 at a solid circle. So, the function includes the y-value: [tex]2[/tex]
If we follow this blue line upwards, it ends with an arrow. This means it will keep going to infinity, which is the symbol: [tex]\infty[/tex]
So, the second part of our range is:
[2, ∞)Putting it togetherPut the lower and upper blue lines together with the union of sets symbol. The range is expressed as: [–4, 0) ∪ [2, ∞)
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20.
(05.07 MC)
A scatter plot is made to model the amount of money left to pay on a mortgage. The data used for the scatter plot are shown in the table:
Number of Months 3 5 1 2 0 4
Money Owed $114,000 $100,000 $118,000 $116,000 $120,000 $112,000
What does the y-intercept of the model represent? (1 point)
The amount of the mortgage that has been paid that month
The monthly payments
The original amount of the mortgage
The number of months it takes to pay off the mortgage
Option third "The original amount of the mortgage" is correct because every month that passes, the amount left to pay decreases.
What is the line of best fit?A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.
[tex]\rm m = \dfrac{n\sum xy-\sum x \sum y}{n\sum x^2 - (\sum x)^2}[/tex]
[tex]\rm c = \dfrac{\sum y -m \sum x}{n}[/tex]
As we know the line of best is represented by:
y = mx + c
Here m is the slope and c is the y-intercept.
A scatter plot is made to model the amount of money left to pay on a mortgage.
Every month that passes, the amount left to pay decreases.
Plug x = 0 to get the y-intercept
y = c
The y-intercept representing the original amount of the mortgage.
Thus, option third "The original amount of the mortgage" is correct because every month that passes, the amount left to pay decreases.
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PLEASE ANSWER ASAP!!!!!!!!!!
The graph of a cosine function has an amplitude of 3, a vertical shift of 1, and a period of 4. These are the only transformations of the parent function.
Use the Sine tool to graph the function.
The first point must be on the midline, and the second point must be a maximum or minimum value on the graph closest to the first point.
(please include a graph when you answer)
The equation of the sin function is y = 3sin(πx/2) + 1, and the graph of the function is shown in the picture.
What is sin function?It is defined as a function that is sinusoidal in nature, and it has a domain of all real numbers and lies between the [a, a]where is the amplitude of the function.
As we know the sin function is represented by:
y = Asin(Bx) + C
Here,
A = The amplitude = 3
C = The vertical shift = 1
B - The period in terms of π
B = 2π/amplitude
B = 2π/4
B = π/2
The becomes:
[tex]\rm y = 3sin(\dfrac{\pi }{2}x)+1[/tex]
Thus, the equation of the sin function is y = 3sin(πx/2) + 1, and the graph of the function is shown in the picture.
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Suppose s and t are directly proportional. If s=14 when t=12, what is s when t=7 ?
which wifi standards use the 2.4ghz frequency
The standards that use 2.4 GHz are:
IEEE 802.11bIEEE 802.11gIEEE 802.11n (it uses both 2.4 GHz and 5 GHz)IEEE 802.11ax (it uses both 2.4 GHz and 5 GHz)What is a wifi standard?
A wifi standard defines two characteristics of the wi-fi network, which are speed and frequency.
Such that there are two common frequencies, 2.4 GHz (usually with larger speed) and 5 GHz (usually with lower speed)
The standards that use 2.4 GHz are:
IEEE 802.11bIEEE 802.11gIEEE 802.11n (it uses both 2.4 GHz and 5 GHz)IEEE 802.11ax (it uses both 2.4 GHz and 5 GHz)If you want to learn more about wifi:
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Event A: Spinning violet or yellow on the spinner.
Event B: Rolling an even number on a number cube.
What is P(A and B)?
Answer:
[tex]\sf P(A \cap B)=\dfrac{1}{4}[/tex]
Step-by-step explanation:
[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]
Event A - spinning violet or yellow
Assuming that the spinner has 4 different colors (red, orange, violet and yellow) - see attachment.
[tex]\implies \sf P(A) = \dfrac{2}{4}=\dfrac{1}{2}[/tex]
Event B - rolling an even number
Assuming the number cube has 6 sides numbered 1, 2, 3, 4, 5 and 6. Therefore, the even numbers are 2, 4 and 6.
[tex]\implies \sf P(B)=\dfrac{3}{6}=\dfrac{1}{2}[/tex]
Events A and B are independent events as the outcome of one event does not affect the outcome of the other event.
For independent events A and B:
[tex]\implies \sf P(A \cap B)=P(A)P(B)[/tex]
To find P(A and B), substitute the found values of P(A) and P(B):
[tex]\implies \sf P(A \cap B)=\dfrac{1}{2} \times \dfrac{1}{2}=\dfrac{1}{4}[/tex]
P(A)
2/41/20.5P(B)
3 even nos are 2,4,6
3/61/20.5P(A[tex]\cap[/tex])
0.5²0.25 or 1/4What two numbers differ by 46. (29,17,38,71,35,63,24)
Answer: 63 and 17 differ by 46.
Step-by-step explanation:
63-17=46
Subtraction is what you do when trying to find the difference of something.
what is 11x2 – 4x = 1?
Answer:
x=5 1/4 or 5.25
Step-by-step explanation:
11x2-4x=1
22-4x=1
22-1-4x=
21-4x=
21=4x
x=5 1/4 or 5.25
Answer:
Using the formula of quadratic equation, we find x = 0.534 and x = -0.17.
Step-by-step explanation:
It is a quadratic equation.
11x² - 4x - 1 = 0
Find the determinant of the quadratic equation.
D = b² - 4ac
D = 16 + 44
D = 60
One of the values of x will be
x = (-b+√D)/2a
x = (4+2√15)/22
x = 0.534
The second value will be
x = (-b-√D)/2a
x = (4-2√15)/22
x = -0.17
The two values of x, from the quadratic formula are 0.534 and -0.17.
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Use the drawing tool(s) to form the correct answer on the number line.
Graph the solution to this inequality on the number line.
-4x+7>x-13
Answer:
Let's solve your inequality step-by-step.
−4x+7>x−13
Step 1: Subtract x from both sides.
−4x+7−x>x−13−x
−5x+7>−13
Step 2: Subtract 7 from both sides.
−5x+7−7>−13−7
−5x>−20
Step 3: Divide both sides by -5.
−5x/−5>−20/−5
x<4
Answer:
x<4
IMAGINE AN ARROW ABOVE THE NUMBERS
⇔
−7−6−5−4−3−2−1 0 1 2 3 4 5 6 7
4 is where the line is circled and the arrow is facing left
←Ф
like that
Answer:
x<4
Step-by-step explanation:
So you will put an open circle on positive 4 and a ray going to the left of the graph.
The graph of which function has a minimum located at (4, –3)?
f(x) = one-halfx2 + 4x – 11
f(x) = –2x2 + 16x – 35
f(x) = one-halfx2 – 4x + 5
f(x) = 2x2 – 16x + 35
The parabola with the minimum at (4, -3) is the third option:
[tex]y = 0.5*x^2 - 4x + 5[/tex]
Which of the given parabolas has a minimum at (4, -3)?
Remember that for a parabola of the form:
[tex]y = a*x^2 + b*x + c[/tex]
If a > 0, the minimum is at the x-value of the vertex:
[tex]x = \frac{-b}{2a}[/tex]
If a < 0, there is no minimum (so we discard option 2).
Taking the third option:
[tex]y = 0.5*x^2 - 4x + 5[/tex]
The x-value of the vertex is:
[tex]x = \frac{-(-4)}{2*0.5} = 4[/tex]
As expected.
To get the y-value of the vertex (and minimum) we just evaluate the parabola equation in x = 4.
[tex]y = 0.5*(4)^2 - 4*4 + 5 = -3[/tex]
So the minimum is at (4, -3), as expected, so that is the correct option.
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1
2 3
4
5
6
7
8
9 10
Which set of angle measures could be the measures of the interior angles of a triangle?
O 90°, 42°, and 58°
O 60°, 60°, and 60°
O 100°, 48°, and 42°
O 31°, 75°, and 70°
TIME REMAI
42:34
Answer:
1) -
2) +
3) -
4) +
Step-by-step explanation:
сумма внутренних углов треугольника не должна превышать 180 градусов
21, Given: AC=FC, CB = CD
Prove:
Answer:
in triangle ACD and BCE
AC = EC
angle ACD = angle ECB ( COMMON ANGLE).
CB = CD
BY side and side criteria
triangle ACD is congruent to triangle BCE
so angle a is congruent to angle E
hence, proved
URGENT PLEASE DUE TONIGHT ;(( functions
The value of (f/g)(-1) is 0, value of (g . f) (2) is -3√3, the value of (g - f)(-1) is √15, and the value of (g + f) (2) is √3 - 3
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have two functions:
f(x) = 1 - x²
g(x) = √(11 - 4x)
f(-1) = 0
g(-1) = √15
f(2) = -3
g(2) = √3
(f/g)(-1) = f(-1)/g(-1) = 0/√15 = 0
(g . f) (2) = g(2)f(2) = (√3)(-3) = -3√3
(g - f)(-1) = g(-1) - f(-1) = √15 - 0 = √15
(g + f) (2) = g(2) + f(2) = √3 + (-3) = √3 - 3
Thus, the value of (f/g)(-1) is 0, value of (g . f) (2) is -3√3, the value of (g - f)(-1) is √15, and the value of (g + f) (2) is √3 - 3
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I keep getting this question wrong
I have to get this done bc its the last day of school fm. So please help me :)))
Answer: it is the median
Step-by-step explanation:
Answer:
it is the Mode,Median,and Mean.
Step-by-step explanation:
There are ALWAYS three measures of the “center"
Kiki works in a furniture store. Her base salary is $150 per day, plus 8 percent commission on her sales. She sells several high-priced items.
A 3-column table with 3 rows. Column 1 is labeled Day with entries 1, 2, 3. Column 2 is labeled Item with entries sofa chair, loveseat, couch. Column 3 is labeled Price with entries 350 dollars, 500 dollars, 1,200 dollars.
What is the total amount she earned over these three days?
The amount of money earned by Kiki earned $614 in three days.
What is the salary?The amount paid by any company or industry to the employees after deductions of the several taxes is the salary.
Given that:
Per day salary of Kiki = $150
Commission = 8% of sales
Worth of sold items = $350+$500+$1200 = $2050
Amount of commission = 0.08 x 2050 = $164
Total amount earned in three days = Base salary per day * Number of days + Commission
Total amount earned = 150*3 + 164
Total amount earned = 450 + 164 = $614
Hence, Kiki earned $614 in three days.
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9. The results of a random survey is displayed in the histogram as shown.
Number
of
Walkers
25
50
25
20
15
10
75
5
0
1-4
Walking Record
5-8
How many people are in the sample survey?
O 100
9-12
13-15
16-19
Miles per Weeks
The number of people in the sample survey is 75.
Survey sampling, as used in statistics, is the process of choosing a sample of constituents from a target population to perform a survey. The word "survey" can be used to describe a wide range of observational methods or procedures. Most frequently, a questionnaire meant to assess people's traits and/or opinions is employed in survey sampling. The topic of survey data collecting involves various methods of contacting sample participants after they have been chosen. Sampling is done to cut down on the expense and/or labor required to survey the complete target population. A census is a survey that includes all members of the target population. A sample is a subset or segment of a population from which data will be drawn.
The sample survey has
5 people in 1-4 miles per week
10 people in 5-8 miles per week
15 people in 9-12 miles per week
20 people in 13-15 miles per week
25 people in 16-19 miles per week
The number of people in the sample survey is
5 + 10 + 15 + 20 + 25
=5(1 + 2 + 3 + 4 + 5)
=5(15)
=75
Hence, the number of people in the sample survey is 75.
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help please
what is the answer?
Answer:
y = 25°
Step-by-step explanation:
115° and x are a linear pair and sum to 180° , so
x + 115° = 180° ( subtract 115° from both sides )
x = 65°
the sum of the 3 angles in the triangle = 180° , then
x + x + 2y = 180°
65° + 65° + 2y = 180°
130° + 2y = 180° ( subtract 150° from both sides )
2y = 50° ( divide both sides by 2 )
y = 25°
Its math please help
Answer:
g
Step-by-step explanation:
for this function, we put in the value of "g" (because it is the cause of the function--it is the independent variable [it changes; and it doesn't rely on something else to change] )
so, because the part independently changing is the gas used, that is our input of this graph.
(you can imagine this to be a graph, which typically has the independent variable that we are directly changing--x--along the x-axis, which is where we would place g.)
hope this helps!!
Which length is equivalent to 12 yards?
Answer:
36 feet
Step-by-step explanation:
1 yard 3 feet
Please help! Multiply the following two numbers in scientific notation.
Answer:
d) 5.88×10^9
Step-by-step explanation:
Answer:
d) 5.88 × 10⁻⁹
Explanation:
[tex]\rightarrow \sf \left(1.2\cdot 10^7\right)\left(4.9\cdot 10^2\right)[/tex]
[tex]\sf apply \ exponent \ rule : a^b + a^c = a^{b + c}[/tex]
[tex]\rightarrow \sf 1.2\cdot \:4.9\cdot \:10^{7}\cdot \:10^{2}[/tex]
[tex]\rightarrow \sf 1.2\cdot \:4.9\cdot \:10^{7+2}[/tex]
[tex]\rightarrow \sf 1.2\cdot \:4.9\cdot \:10^9[/tex]
[tex]\rightarrow \sf 5.88 \cdot \:10^9[/tex]
You have a coupon for $5 off an oil change. When you arrive at the auto repair
shop, you learn that the store is holding a customer appreciation sale, and all
customers will receive 10% off the cost of the repair. Write a function p (x) that
represents how much you would pay if you use the coupon first, followed by
applying the discount from the repair shop.
The function that represents how much you would pay is:
p(x) = (x - $5)*0.9
How to find the function?
Let's say that the cost of the repair is x.
First, we apply the coupon, so we discount $5 for the cost.
x - $5.
Then we apply another discount of the 10%, this is written as:
(x - $5)*(1 - 10%/100%)
(x - $5)*(1 - 0.1)
(x - $5)*0.9
Then the function that represents how much you would pay is:
p(x) = (x - $5)*0.9
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Pls explain this to me, I don't understand why the answer is a^3 +b^3 and not a^3-b^3
Answer:
[tex](a+b)(a^2-ab+b^2)=a^3+b^3[/tex]
Step-by-step explanation:
Given expression:
[tex](a+b)(a^2-ab+b^2)[/tex]
Using the Distributive Property Law, expand the brackets:
[tex]\implies a(a^2-ab+b^2)+b(a^2-ab+b^2)[/tex]
[tex]\implies a^3-a^2b+ab^2+a^2b-ab^2+b^3[/tex]
Group like terms:
[tex]\implies a^3+b^3-a^2b+a^2b+ab^2-ab^2[/tex]
As -a²b+a²b=0 and ab²-ab²=0 then:
[tex]\implies a^3+b^3[/tex]
Sarah made a deposit of $100 into a savings account with 3
percent interest compounded annually. How much money will
the account yield in five years?
(The options are)
A:$97
B:$103
C:$115
D:$116
Answer: D, $116
Step-by-step explanation:
A = 100(1 + 0.03)^5
A = 100(1.03)^5
A = 100(1.1593)
A = 115.92
Hope this helped!
which statements about square roots are true ?check all that apply
please help and answer it in a sentence :)
Answer:
x = $1 & y = $2.
Each doughnut cost $1 and hot chocolate cost $2.
Solve the proportion for x. When applicable, simplify all radicals and show all of your
3/X = x/4
The simplified radical for the given equation is 2√3.
The given equation is [tex]\frac{3}{x} =\frac{x}{4}[/tex].
What are radicals?Radical of any number is the same as the root of the number. The root can be a square root, cube root, or in general, it is nth root. Thus, any expression or number that uses a root is known as a radical.
To compute for the values of x given the proportion, we can cross-multiply both sides of the equation as follows:
[tex]\frac{3}{x} =\frac{x}{4}[/tex]
⇒x×x=3×4
⇒x²=12
⇒x=±√12
From this, we can see that the solutions for the equation are the positive and negative roots of 12.
By simplifying the radical, we get √12 = √(2² x 3) = 2√3
Therefore, the simplified radical for the given equation is 2√3.
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A boat is heading towards a lighthouse, where Mason is watching from a vertical
distance of 122 feet above the water. Mason measures an angle of depression to the
boat at point A to be 16°. At some later time, Mason takes another measurement and
finds the angle of depression to the boat (now at point B) to be 66°. Find the distance
from point A to point B. Round your answer to the nearest foot if necessary.
The distance between point A and point B is 371 ft if the Mason measures an angle of depression to the boat at point A to be 16°.
What is trigonometry?Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.
We have:
A boat is heading towards a lighthouse, where Mason is watching from a vertical distance of 122 feet above the water. Mason measures an angle of depression to the boat at point A to be 16°.
We can draw the above situation as a form of a right-angle triangle.
From the figure, the distance between AB is x ft
From the right angle triangle DBC:
tan66 = 122/CB
CB = 54.31 ft
From the right angle triangle DAC
tan16 = 122/AC
AC = 425.46 ft
x = AC - CB
x = 425.46 - 54.31
x = 371.15 ft ≈ 371 ft
Thus, the distance between point A and point B is 371 ft if the Mason measures an angle of depression to the boat at point A to be 16°.
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