Answer:
the correct answer is B
Step-by-step explanation:
A function g is the inverse for the function f if for y-f(x), x-g(y)
y=7x-6
Replace x with y
x=7y-6
Solve for y in x=7y-6
Switch sides
7y-6=x
Add 6 to both sides
7y-6+6=x+6
Simplify
7y=x+6
Divide both sides by the coefficient of y, which is 7. We have:
7y/7 = x/7+6/7
7y & 7 are cancelled out and we're left with: x/7 & 6/7
Now we find the LCM of the denominators which is 7.
7 divide the denominators equal 1, we use the to multiply the numerators, x & 6
our final answer= x+6/7
I hope this helps.
Which function is represented by the graph?
Answer:
D. f(x) = -|x+4| +3
The graph is flipped over the x-axis (facing down) so there's a negative sign in front of the function. It's shifted to the left 4 units so it'll be |x+4|. Finally, it's shifted up 3 units so it'll be +3 outside of the absolute bracket.
NOTE: if there's a change to the x value then it's inside the bracket or parenthesis, if there's a change to the y value then it's outside of the bracket or parenthesis
Please show how you solved
Answer:
x = 7 degrees
Step-by-step explanation:
The unlabelled angle at M PLUS 12x + 24 = 180
then the unlabelled interior angle is 180 - (12x+24)
The sum of the interior angles then = 180
80 + 4x + 180-(12x+24) = 180
236 -8x = 180
x = 7
You have a glass paperweight that is shaped like a cone. The diameter of the paperweight is 7 centimeters. The slant height is 4 centimeters. Find the surface area of the cone. Use 3.14 to approximate pi.
Step-by-step explanation:
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A researcher develops a cage for a living cell in the shape of a square-based pyramid. A scale model of the cage is shown. What is the volume of the model?
A square pyramid-shaped cage with base edge labeled “20 micrometers” and height labeled “20 micrometers”.
The total volume of this squared-base pyramid based on the information provided is 2666 micrometers.
How to calculate the volume of the pyramid?The general formula to calculate the volume of a squared-based pyramid is:
base = area x height/ 3What is the volume of the model?Base area: 20 x 20 = 400
400 micrometers x 20/ 3 = 2666 micrometers.
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Phyllis invested 800 dollars into two different accounts, a portion earning a yearly interest rate of
4
percent per year compounded monthly and the rest earning a rate of
6
percent per year compounded quarterly
After 12 years the investments were worth $1579.05. How much money did she invest at each rate
The amount of money that Phyllis invested at each given rate of 4 and 6 percent is = $394.57 and $591.86 respectively.
Calculation of the total capital investedThe time the investment lasted= 12 years.
Simple interest = 1579.05 - 800= $779.05
The principal capital= $800
Rate of the both capital invested;
= SI × 100/P ×T
= 779.05 × 100/800 × 12
= 77,905/9600
= 8.11%
To find the amount of money that Phyllis invested at each given rate,
Rate 1 = 4/8.11× 800
= 3200/8.11
= $394.57
Rate 2 = 6/8.11× 800
= 4800/8.11
= $591.86
The amount of money that Phyllis invested at each given rate of 4 and 6 percent is = $394.57 and $591.86 respectively.
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The ratio of the one leg of
the right triangle to the other
leg of the right triangle must
be 8:7. Determine the
greatest length of one leg of
the right triangle given the
other leg of the right triangle
is 10.5 feet.
The legs of the triangle are 6.91 feet, 7.9 feet, and 10.5 feet.
What is a Pythagoras theorem?The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.
The Pythagoras theorem formula is given as
H² = P² + B²
The ratio of the one leg of the right triangle to the other leg of the right triangle must be 8:7.
Let x be one leg and y be another leg. Then we have
x/y = 8/7
y = 7x/8
Then the greatest length of one leg of the right triangle given the other leg of the right triangle is 10.5 feet will be
10.5² = x² + (7x/8)²
110.25 = x² + 49x²/64
110.25 = 113x²/64
x² = 62.44
x = 7.902
x ≅ 7.9 feet
Then the other leg will be
y = 7.9 x 7 / 8
y = 6.91
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In a year, a hospital admitted 4500 patients. If of the patients had heart or lung diseases,
how many patients had heart or lung diseases?
Answer:
4500
Step-by-step explanation:
all of them were admitted.
which choices are in the solution set of the equation below check all that apply 4x=30
The choice in the solution set of the equation 4x = 30 is x = 7.5
How to determine the solution set?The equation is given as:
4x = 30
Divide both sides of the equation by 4
4x/4 = 30/4
Evaluate the quotients
x = 7.5
Hence, the choice in the solution set of the equation 4x = 30 is x = 7.5
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A community organization wants to determine area support for the construction of a new skate park in the center of town. The organization decides to survey 500 people to see whether they are willing to have their taxes increased for one year to fund the construction of the skate park.
What is the best way to randomly choose these 500 people?
The method that can be used to randomly choose these 500 people is the use of systematic random sampling.
What is random sampling?Random sampling is defined as the method of sampling in which the whole sampling frame is being considered.
In order the survey a community of people to see whether they are willing to have their taxes increased for one year to fund the construction of the skate park, both the male and female should be considered.
The systematic random sampling will give the both male and female equal opportunity to the chosen.
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Which of the following correctly replaces the question mark in Aisha's proof?
OHL
O SSS
O SAS
O AAS
The option that correctly replaces the question mark in Aisha's proof is SAS (Option C). See it explained below.
Mathematical proofs are statements that are used to demonstrate that a mathematical expression or logic of true.
Since the portion of the question that shows the question mark is missing, we can rewrite the proof as follows:
Step 1
AB Dissects BC
AE ║ BD
Reason - It is given
Step 2
BC ≅ BE
Reason - Definition of Segment Bisector
Step 3
∠ABE ≅ ∠CBD
Step 4
∠BCD ≅ ∠BEA
Reason
Alternative Interior Angles
Step 5
ΔBCD ≅ ΔBEA
Reason
SAS Postulate
Step 6
QED
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Which data set could be represented by the box plot shown below?
Answer:
B
Step-by-step explanation:
A box and whisker plot is a graphical representation of the 5-number summary of a data set. It shows the minimum, maximum, median, and the values of the 1st and 3rd quartiles. Here, you're asked to identify the data set having the same 5-number summary as that shown in the plot.
__
extremesThe minimum of the data set is shown by the end of the left "whisker." The plot shows a minimum value of 41. Choice C has a minimum of 40, so is not the data set we're looking for.
The maximum of the data set is shown by the end of the right whisker. The plot shows a maximum of 50, matching all of the answer choices shown.
medianThe median of the data set is shown by the vertical line in the middle of the box. Here, the median of the data set is indicated as 44. This will be the middle value, or the average of the two middle values of the set of data.
These sets of data have 10 values, an even number, so the median is the average of the middle two.
Choices A and B have a middle pair of 43 and 45, which means their median is (43+45)/2 = 44. Choice D has a middle pair of 43 and 47, so a median of (43+47)/2 = 45. Choice D is not the data set we're looking for.
quartilesThe 1st and 3rd quartiles of the data set are shown by the left and right ends of the box, respectively. They are indicated as being 43 and 48.
The median divides the data set into two parts. It is not considered to be a member of either part. The 1st quartile is the median of the lower (left) part. The 3rd quartile is the median of the upper (right) part.
Here, each part has 5 data values, so the quartile values are 3rd from the ends of the data set. In choice A, they are 43 and 49, not a match to the given plot. In choice B, they are 43 and 48, matching the values in the given box plot.
The data set in choice B could be represented by the box plot shown.
A train leaves Little Rock, Arkansas, and travels north at 85 kilometers per hour. Another train leaves at the same time and travels south at 85 kilometers per hour.
How long will it take before they are 680 kilometers apart?
Answer:
4hours
Step-by-step explanation:
1hour =85+85
=170km/h
time= distance÷
speed=170km/h
680÷170=time
=4h
Consider this function.
please help!
the zeros of the function f(x) = x² + 5x - 6 are show your work
Answer:
x = - 6 , x = 1
Step-by-step explanation:
to find the zeros let f(x) = 0 , that is
x² + 5x - 6 = 0
consider the factors of the constant term (- 6) which sum to give the coefficient of the x- term ( + 5)
the factors are + 6 and - 1 , since
6 × - 1 = - 6 and 6 - 1 = + 5 , then
(x + 6)(x - 1) = 0 ← in factored form
equate each factor to zero and solve for x
x + 6 = 0 ⇒ x = - 6
x - 1 = 0 ⇒ x = 1
A triangular prism is shown. A cylinder is cut out of the center of the prism. The triangular base has side lengths of 14 and 10 units. The heights of both the cylinder and prism are 8 units. The cylinder has a diameter of 5 units.
Which expression represents the volume, in cubic units, of the shaded region of the composite figure?
One-half(14)(10)(8) – π(2.52)(8)
One-half(14)(10)(8) + π(2.52)(8)
One-third (one-half)(10)(8)(14) – π(2.52)(8)
One-third (one-half)(10)(8)(14) + π(2.52)(8)
The expression that represents the volume, in cubic units, of the shaded region of the composite figure is option: A. One-half(14)(10)(8) – π(2.52)(8).
How to find the volume of a prism?If the prism is such that if we slice it horizontally at any height smaller or equal to its original height, the cross-section is same as its base,
then its volume is:
V = B x h
where h is the height of that prism and B is the area of the base of that prism.
Given:
Base side length =14 and 10 units
Height=8 units
Diameter=5 units
The volume of the shaded region is;
Expression = 1-( half 14)(10)(8) - π(2.52)(8)
Expression = 1-(7) (10)(8) - π(2.52)(8)
Expression = 1- (560)- 63.33
Expression = -559-63.33
Expression = -622.33
Hence, The expression that represents the volume, in cubic units, of the shaded region of the composite figure is option: A. One-half(14)(10)(8) – π(2.52)(8).
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answer: A
the first one
x – y = 2 2x = 3y in elimination method
Answer:
x=6, y=4
Step-by-step explanation:
x - y = 2
2x = 3y => 2x - 3y = 0
x - y = 2 | ×(-2) => -2x + 2y = -4
2x - 3y = 0
-2x + 2y = -4
2x - 3y = 0
___________
0 - y = - 4 | ×(-1)
y = 4
Substitution in x - y = 2:
x - 4 = 2 | +4
x = 2+4 = 6
n⃗ =〈−2,−1〉 and D=[−4 4 2 3].
What is D⋅n⃗ ?
Enter your answer as a vector by filling in the boxes.
The dot product of the two matrices D and n is determine as (4, - 7).
Dot product of the vector
The dot product of the two matrices is calculated as follows;
n = (-2, -1), and D = [-4 2]
[4 3]
D.n = (-2, -1). [-4 2] = (-2 x -4) + (-1 x 4) = 4
[4 3] = (-2 x 2) + (-1 x 3) = -7
D.n = (4, - 7)
Thus, the dot product of the two matrices D and n is determine as (4, - 7).
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Tera buys 10 pencils for $1.99.
About how much $ does each pencil
cost?
Answer:
19 cents or 0.199
Step-by-step explanation:
Hope it helped!
Answer:
19 cents
Step-by-step explanation:
divide total cost by amount of items
Kyle is going grocery shopping today. He has $35 to spend. He must buy a gift card for $10. If burgers cost $5.75 per pound, how many pounds of burgers can he buy?
Answer:
4
Step-by-step explanation:
35-10=25
25÷5.75= 4.3
Find the probability that a randomly
selected point within the circle falls
in the red shaded area.
r = 4 cm
[?]%
Round to the nearest tenth of a percent.
Enter
Answer:
[tex]31.8\%[/tex]
Step-by-step explanation:
The area of the circle is [tex]A=\pi r^2=\pi(4)^2=16\pi[/tex]
The area of the triangle is [tex]A=\frac{bh}{2}=\frac{8*4}{2}=\frac{32}{2}=16[/tex]
Hence, the probability of a randomly selected point within the circle falls in the red shaded area is [tex]\frac{16}{16\pi}=\frac{1}{\pi}\approx0.318\approx31.8\%[/tex]
what is linear relationship
Step-by-step explanation:
a linear relationship is simply a straight line relationship.
any equation that can be pot in the form of y = mx + b is a linear relationship.
linear = straight
hope this helps
What is true about AngleQRT? Select two options.
Measure of angleQRT = 90°
Measure of angleQRT = Measure of angleSRT
AngleQRT Is-congruent-to AngleSTQ
Measure of angleQRT = 2*Measure of angleRTQ
AngleQRT Is-congruent-to AngleRTQ
The complete question is
"Triangle QST is isosceles, and Line segment R T bisects AngleT. Triangle Q S T is cut by bisector R T. The lengths of sides S T and Q T are congruent. Line segments S R and R Q are congruent. Angles S T R and R T Q are congruent. What is true about AngleQRT?
Select two options. Measure of angleQRT = 90° Measure of angleQRT = Measure of angleSRT AngleQRT Is-congruent-to AngleSTQ Measure of angleQRT = 2*Measure of angleRTQ AngleQRT Is-congruent-to AngleRTQ"
The true about AngleQRT options are A abd B; ∠QRT = 90 and ∠QRT = ∠SRT
What is the congruent triangle?Two triangles are said to be congruent if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.
Given information;
The triangle QST is isosceles with QT ≅ ST.
The ∠STR and ∠RTQ are congruent.
Now, consider two triangles ∠QTR and ∠STR
In the following triangle
TR ≅ TR
QTR ≅ STR
QT ≅ ST
Now, according to SAS rule, two congruent triangles have congruent corresponding to their sides,
1. QR ≅ SR
2. QRT ≅ SRT
Since the above two angles are congruent so, they will have the same measure
That will be 90 degree.
Hence, The correct options are; ∠QRT = 90 and ∠QRT = ∠SRT
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Solve for x in the triangle. Round your answer to the nearest tenth.
X
9
64°
Answer:
x = 23.0
Step-by-step explanation:
To solve, you have to make the equation:
[tex]cos(64)=\frac{9}{x}[/tex]
Now multiply x to both sides:
[tex]cos(64)*x=9[/tex]
Next divide both sides by cos(64):
[tex]x=\frac{9}{cos(64)}[/tex]
x = 22.9675486404
Round to the tenth:
x = 23.0
Hope it helps and have a nice day!
Calculate the percent change if a city that used to produce 2050 kilowatt hours has reduced their consumption to 1125 kilowatt hours
The percent change if a city that used to produce 2050 kilowatt hours has reduced their consumption to 1125 kilowatt hours is 45.122% decrease.
What is percentage change?Percent increase and percent decrease are measures of percent change, which is the extent to which a variable gains or loses intensity, magnitude, extent, or value.
we know,
% change = (final- initial) / initial * 100
=(1125-2050)/1125 *100
=45.122%
Hence, percentage change be 45.122% decrease.
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what percentage of 5/2 hours is 15 minutes?
Answer:
10 %
Step-by-step explanation:
15 mn = 1/4 h
We have :
[tex]\frac{\frac{1}{4} }{\frac{5}{2} } =\frac{1}{4} \times \frac{2}{5} =\frac{2}{20} =\frac{1}{10}=0.1[/tex]
Then the percentage that 15 mn represents of 5/2 h is :
0.1 × 100 = 10 %
Wendy winholtz 8 year savings certificate pays an annual interest rate of 5.3% at the end of 5 years she cashed out the 6,000 CD and paid a penalty of 12 month simple interest. What penalty did she pay
Answer:
318
Step-by-step explanation:
The rate of 5.3% is an annual rate, and specifies the amount of interest earned in a 12-month period by the principal amount of the CD. The interest amount is found by multiplying the interest rate by the principal amount.
__
penaltyThe amount of the penalty is 5.3% of 6000:
0.053 × 6000 = 318
Wendy paid a penalty of 318 for her early withdrawal.
Which of the following is equidistant from a given directrix and focus?
The term used to describe the equidistance from a given directrix and focus is: C. a locus of points called a parabola.
What is a Parabola?A parabola can be defined as a curve on a plane where any given point is at equal distance from the focus (fixed point), and from a directrix (fixed straight line).
Thus, we can conclude that what is a locus of points called a parabola is equidistant from a given directrix and focus.
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Krista got paid $43.75 for working 3.5 hours. How much did she earn per hour?
Answer:
12.5
Step-by-step explanation:
divide 43.75 by 3.5 to get your answer
Paul and Krystal spent 1 1/2 hours at the pool
Answer:
Paul and Krystal spent 13 hours at the pool
Step-by-step explanation:
I Thank
A bag contained $24.20 worth of coins. There were 20-cent and 50-cent coins only. The number of 20-cent coins was 5 fewer than the number of 50-cent coins. How many coins were there in the bag
Answer:
Their will be 2 coins in allThere were 67 coins in the bag, 36 of which were 50-cent coins and 31 of which were 20-cent coins.
Let x be the number of 50-cent coins in the bag,
And y be the number of 20-cent coins.
From the problem,
we know that y = x - 5,
Since there were 5 fewer 20-cent coins than 50-cent coins.
We can also set up an equation for the total value of the coins in the bag,
⇒ 0.5x + 0.2y = 24.20
Now we can substitute y = x - 5 into the equation,
⇒ 0.5x + 0.2(x - 5) = 24.20
Simplifying, we get,
⇒ 0.7x - 1 = 24.20
⇒ 0.7x = 25.20
⇒ x = 36
So there were 36 50-cent coins in the bag.
Using y = x - 5,
We can find that there were 31 20-cent coins.
Therefore, there were a total of 67 coins in the bag (36 + 31 = 67).
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