Find the inverse, picture below!
Answer:
[tex]f^{-1}(x) = (x+7)^2[/tex]
Step-by-step explanation:
[tex]y=f(x) = \sqrt x - 7 \\\\\text{Replace x with y and then solve for y:}\\\\~~~~~~~~x= \sqrt y -7\\\\\implies \sqrt y = x+7\\\\\implies y = (x+7)^2\\\\\implies f^{-1}(x) = (x+7)^2[/tex]
You plan to build a house that is 1 ½ times as long as it is wide. You want the land around the house to be 20 feet wider than the width of the house, and twice as long as the length of the house, as shown at the right.
The total area with land based on the information given is 3x² + 60x.
How to find the area?Let the width = x
Let the length = (1.5 × x) = 1.5x
Area = 1.5x × x = 1.5x²
The area along with land:
Width = x + 20
Length = 3 × x = 3x
The total area with land:
= Length × Width
= 3x(x + 20)
= 3x² + 60x.
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A convenience store was charging $3.83 for a
bag of chips but raised the price 13%. The new price after the increase is $4.33.
Enter an expression to show how the new price
was calculated.
Answer:
See below
Step-by-step explanation:
4.33 = 3.83 * (1.13) .13 is decimal for 13%
A line intersects the points (-5, 1) and (-2,7). What is the slope of the line in simplest form? m=[?}
Step-by-step explanation:
To find slope : y2- y1 / x2 - x1
we have ( -5 , 1 ) which is ( x1 , y1 )
and ( -2 , 7 ) is ( x2 , y2 )
so; 7 - 1 / -2 - (-5)
6/3
= 2
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
i need help on my diagnostic
pleases
Answer:
4th one is correct
Step-by-step explanation:
it perfectly matches all the given condition
Question 4 of 5
Drag each label to the correct location on the triangle. Not all labels will be used.
Find the unknown measurements. Round all values to the nearest tenth.
cm
8.9 cm
65°
Answer:
long side: 19.1 cmmissing angle: 25°hypotenuse: 21.1 cmStep-by-step explanation:
You can use this information to "guess" at the answers without doing any "work."
The sum of angles in a triangle is 180°.The shortest side is opposite the smallest angle.__
qualitative solutionThe missing angle is the complement of the marked acute angle in the right triangle, so is ...
C = 90° -65° = 25°
This angle is opposite the side of length 8.9 cm. The next-smallest angle is 65°, which is more than double the smallest angle. Hence the side opposite 65° will not be either of 3.8 or 9.8.
Of the two remaining measures, the longer one, 21.1, will be the hypotenuse, BC. The shorter of those, 19.1, will be the long side, AC.
Our solution is ...
AC = 19.1 cmC = 25°BC = 21.1 cm__
quantitative solutionThe mnemonic SOH CAH TOA reminds you of the relations between trig functions and right triangle sides. Here, we're given an angle and the length of its adjacent side. We are asked for the opposite side and for the hypotenuse. This suggests useful relations might be ...
Cos = Adjacent/Hypotenuse
Tan = Opposite/Adjacent
Solving the first of these for the hypotenuse gives ...
hypotenuse = adjacent/cos(65°)
BC = 8.9 cm/cos(65°) ≈ 21.059 cm ≈ 21.1 cm
Solving the second relation above for the opposite side gives ...
opposite = adjacent×tan(65°)
AC = 8.9 cm×tan(65°) ≈ 19.086 cm ≈ 19.1 cm
As above, the missing angle is the complement of the given one:
C = 90° -65° = 25°
Then the quantitative solution is ...
AC = 19.1 cmC = 25°BC = 21.1 cm_____
Additional comment
If AC were 9.8 cm, the angle at B would be about 48°. That is, the two acute angles in the triangle would be very nearly equal.
We know that the side ratios in a 30°-60°-90° right triangle are 1 : √3 : 2. This triangle has a larger angle greater than 60°, so its longer side will be more than √3 times the short side. That means a length of 9.8 cm is way too short.
solve log base 6 (x-6) - log base 6 (x + 4) = 2
Answer:
no solutions
Step-by-step explanation:
Since the two terms have the same base, we are able to use the rule for subtracting logarithms:
[tex]log_{b}(x) - log_{b}(y) = log_{b}(\frac{x}{y} )[/tex]
Therefore, the equation can be written as:
[tex]log_{6}(\frac{x-6}{x+4} )=2[/tex]
By using the definition of a logarithm we can say that:
[tex]\frac{x-6}{x+4} = 6^{2}\\\frac{x-6}{x+4} = 36\\x -6 = 36x+144\\35x = -150\\x =-\frac{30}{7}[/tex]
When plugging this solution in, you find that the term [tex]log_{6}(x-6)[/tex] has x-6 evaluate to a number less than 0. This is not included in the domain of log functions, so [tex]-\frac{30}{7}[/tex] is not a valid solution. This means that there are no solutions.
Determine the composition of
transformations that would map figure ABCD to figure A'B'C'D"
1. The transformation that would map vertex B to B' is
It's translation B to B’, is the composition of transformations that would map figure ABCD to figure A'B'C'D".
What is transformation of quadrilateral?Transformations are changes done in the shapes on a coordinate plane by rotation, reflection or translation.
here, we have,
from the given figure we get,
there is a transformation of ABCD to A'B'C'D".
now,
Reason: choices are translation, reflection, rotation, or dilation, this is translation.
Hence, It's translation B to B’, is the composition of transformations that would map figure ABCD to figure A'B'C'D".
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Statistics
Assume there are 20 advanced English level students, 8 intermediate English
level students and 15 beginner English level students at statistics class. What
is the probability of selecting 10 advanced English level students and 10
non_ advanced English level students?
Answer:
no thank you sorry 4h he'll be a great day of school and I have been a while ago but it's a good time 44
Answer:
o
Step-by-step explanation:
What is the value of the expression 30+(-6)?
A -180
B -5
C 5
D 24
Answer:
24
Step-by-step explanation:
from the question above,
30+(-6) =
when plus is multiplying minus it's minus
+ × - = -
30-6 = 24
Solve for X.
21
14
X
42
x = [?]
Enter the number that belongs in the green box.
Answer:
x = 28
Step-by-step explanation:
By Triangle Proportionality Theorem,
14/x = 21/42
14 * 42/21 = x
x = 28
Write the equation of the circle whose center is (-5, -8) with diameter 12
Answer:
(x + 5)^2 + (y + 8)^2 = 6^2
Step-by-step explanation:
A circle formula: (x - h)^2 + (y - k)^2 = r^2
We are given diameter. To find the radius divide diameter by 2.
d = 12
12/2 = r = 6
H and K are given to be (-5 , -8)
(x - (-5))^2 + (y - (-8))^2 = 6^2
(x + 5)^2 + (y + 8)^2 = 6^2
I have plot this equation to confirm my answer is correct where the origin is (-5 , -8) and has a radius of 6.
simplify 2 2/3-1.25+5/6
Answer:
2.25or21/4
Step-by-step explanation:
hope it helps
Answer:
2 1/4 or 2.25Step-by-step explanation:
GivenExpression:
2 2/3 - 1.25 + 5/6SolutionSimplify it in below steps:
2 2/3 - 1.25 + 5/6 = 2 + 2/3 - 1 - 0.25 + 5/6 = 1 + 4/6 + 5/6 - 1/4 =1 + 9/6 - 1/4 =1 + 1 + 3/6 - 1/4 = 2 + 2/4 - 1/4 = 2 + 1/4 = 2 1/4 or 2.25The difference between two numbers is 31. Four times the smaller is equal to eight more than the larger. What are the numbers?
Answer:
13 and 44
Step-by-step explanation:
let x and y be the 2 numbers with y < x , then
x - y = 31 ( add y to both sides )
x = y + 31 ( subtract 31 from both sides )
x - 31 = y → (1)
4y = x + 8 → (2)
substitute y = x - 31 into (2)
4(x - 31) = x + 8
4x - 124 = x + 8 ( subtract x from both sides )
3x - 124 = 8 ( add 124 to both sides )
3x = 132 ( divide both sides by 3 )
x = 44
substitute x = 44 into (1)
44 - 31 = y , then
y = 13
the 2 numbers are 13 and 44
If events A and B are independent, what must be true?
P(A|B) = P(B)
P(A|B) = P(A)
P(A) = P(B)
P(A|B) = P(B|A)
Answer: P(A|B) = P(A)
Step-by-step explanation:
If they are independent, one event being given doesn't impact the probability of the other event.
Answer:b
Step-by-step explanation:
b
Explain a time in your life you underwent metamorphosis
Answer: Maybe when you Grew from a Baby to a toddler because that would be you growing over time
Step-by-step explanation:
I Hope This Helps!
Solve the system of equations algebraically.
4x-3y = 8
5x-4y = 5
a. (16,21)
b. many solutions
c. No solution
d.(17,20)
An equation is formed of two equal expressions. The value of x and y is 17 and 20, respectively. Thus, the correct option is D.
What is an equation?
An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Solving the first equation for y,
4x - 3y = 8
-3y = 8 - 4x
y = (8-4x)/(-3)
Solving the second equation for y,
5x - 4y = 5
-4y = 5 - 5x
y = (5 - 5x)/(-4)
Equate the value of y,
y = y
(8-4x)/(-3) = (5 - 5x)/(-4)
-32 + 16x = -15 + 15x
16x - 15x = -15 + 32
x = 17
Substitute the value of x in any one of the equation,
4x - 3y = 8
4(17) - 3y = 8
68 - 3y = 8
-3y = -60
y = 20
Hence, the value of x and y is 17 and 20, respectively. Thus, the correct option is D.
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# 18 I can solve problems involving e and In.
0.0.15t
3. The expression 1 e models the balance, in thousands of dollars, where t represents
time in years after the account was opened.
a. What does the 0.015 represent in this context?
b. Write an expression and for the number of years after which there will be $8,000 in the
account and simplify.
4. Explain why In 16 is greater than 2 but less than 3.
The expression is assumed here as it's unclear looking
If it's P=(P_o)ln0.015t then the below solution of Part B is correct else they may vary.
#a
0.015 represents rate of change with respect to t.#b
As per our assumed equation
It's.
8000=(P_o)ln0.015^tSimplify
tln0.015=8000/P_oInitial amount of account is not given so you have to solve the above equation after putting known P_o
#3
ln16ln4²2ln42(1.38)2.76(Approx)Hence it's less than 3 and greater than 2
There are ten cards numbered from 1 to 10. Take out three cards from them.
i) the probability that the product of the numbers of the three cards is an odd number is
ii) the probability that the sum of the numbers of the three cards is an even number is
Answer:
Step-by-step explanation:
Part A
There are 5 odd numbers from 1 to 10. All three of them must be odd when drawn. I have to assume that there is no replacements.
Probability (odd) = (5 * 4 * 3) / (10 * 9 * 8) = 60 / 720
Probability (odd) = 0.083333
Part B
This is a little harder because 1 even number will turn everything even. So the way to handle this is to assume that there is (1 - probability(odd)) *720 that you have even
So the chances of an even result is 1 - odd/ total or
(1 - 1/12) * 720 = 660/720 = 0.917
Answer
Odd: 0.0833
Even: 0.917
The distribution of head circumference for full term newborn female infants is approximately normal with a mean of 33.8 cm and a standard deviation of 1.2 cm.
Determine the approximate percentage of full term newborn female infants with a head circumference between 31 cm and 36 cm. Enter your answer using two decimal places.
Using the normal distribution, it is found that 95.65% of full term newborn female infants with a head circumference between 31 cm and 36 cm.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given, respectively, by:
[tex]\mu = 33.8, \sigma = 1.2[/tex]
The proportion of full term newborn female infants with a head circumference between 31 cm and 36 cm is the p-value of Z when X = 36 subtracted by the p-value of Z when X = 31, hence:
X = 36:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{36 - 33.8}{1.2}[/tex]
Z = 1.83
Z = 1.83 has a p-value of 0.9664.
X = 31:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{31 - 33.8}{1.2}[/tex]
Z = -2.33
Z = -2.33 has a p-value of 0.0099.
0.9664 - 0.0099 = 0.9565.
0.9565 = 95.65% of full term newborn female infants with a head circumference between 31 cm and 36 cm.
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Ice cream shop is open within the month of june,july and august The shop served 100 fewer customers than they did in july They served twice as many customers in august as they did in june In total they served 400 customers over these three months
The number of customers served in the ice cream shop in June, July and August are 125, 25 and 250 customers respectively
How to write and solve equation?let
June = xJuly = x - 100August = 2xTotal customers = 400Total = June + July + August
400 = x + (x- 100) + 2x
400 = x + x - 100 + 2x
400 = 4x - 100
400 + 100 = 4x
500 = 4x
x = 500/4
x = 125
So,
June = x
= 125 customers
July = x - 100
125 - 100
= 25 customers
August = 2x
= 2(125)
= 250 customers
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Use the Law of Detachment to draw a conclusion from the two given statements. If two angles are complementary, then the sum of their measures is 90°. E and F are complementary.
Using the law of detachment, the conclusion we can draw from the two given statements is: C. m∠E + m∠F = 90°.
What is the Law of Detachment?The law of detachment states that, if two statements are true, a third statement that is true can be derived also.
From the information given, we have:
First statement: If 2 angles are complementary, then their sum equals 90 degrees (If p, then q).
Second statement: Angles E and F are complementary (p).
The third true statement (q) would be:
m∠E + m∠F = 90°. (option C)
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this shape is a triangular Pyramid the 3 sides slant height is 14 the base width is 8 and the base height is 6.9
The surface area of a triangular prism with the 3 sides slant height as 14 the base width as 8 and the base height as 6.9 is 155. 705 in²
What is the surface area of a triangular prism?
The surface area of a triangular pyramid is the total area of all it's faces.
The properties of a triangular prism are;
It has a triangular base It is bounded y three lateral triangular faces meeting at one vertex. It has all its faces as trianglesHow to determine the surface area
Surface area = Base Area + 1÷2 (perimeter × base height)
But base area = 1÷2 (base side × height)
Base area = 1÷ 2 (8 × 14) = 0.5 × 112 = 56 in²
Perimeter = sum of all the sides = 14 + 8 + 6.9 = 28. 9 in
Base height = 6. 9in
Surface area = 56 + 1 ÷ 2 ( 28.9× 6. 9) = 56 + 0.5 × 199.41 = 56 + 99. 705 = 155. 705 in²
Surface area = 155. 705 in²
Therefore, the surface area of the triangular prism is 155. 705 in²
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Hurry HELP :The net of a solid figure is shown below: Four squares are shown side by side in a row. The second square has a square above it and a square below it. All the squares have side lengths equal to 5 inches Which calculation will give the total surface area of the solid figure? (1 point) a 5 ⋅ 6 ⋅ 6 square inches b 6 ⋅ 5 ⋅ 5 square inches c 6 ⋅ 5 ⋅ 5 ⋅ 5 square inches d 5 ⋅ 6 ⋅ 6 ⋅ 6 square inches
The calculation that will give us the total surface area of the solid figure that is made up of square faces is: B. 6 × 5 × 5
What is the Area of a Square?Area of a square = (side length)².
Therefore are six (6) square faces that make up the solid figure.
Area of the 6 square faces = total surface area of the solid figure = 6(5²)
Total surface area of the solid figure = 6 × 5 × 5
Total surface area of the solid figure is: B. 6 × 5 × 5
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A triangle has sides measuring 2 inches and 7 inches.If x represents the length in inches of the third side, which inequality gives the range of possible values for x?
Answer:
I would say A is the answer.
(a-4)(a-11) please answer this
Can someone help me with. This please
Answer:
wouldn't be 4.5 or something close too that maybe 5 or 5.5
Step-by-step explanation:
I got you I think
The distance between two cities is 13 kilometers. There are approximately 1.6 kilometers in 1 mile. What is the number of miles between the two cities?
The number of miles between the two cities is 8.13 miles.
What is the number of miles between the two cities?In order to determine the number of miles between the two cities, we would have to divide 13 kilometers by 1.6 miles. Division is when a number is grouped into equal numbers using another number.
Number of miles = 13 / 1.6 = 8.13 miles
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chuck is making a map of his neighborhood. each grid unit represents one city block. He uses the following coordinates, with north being the direction of the positive y axis