Triangle ABC was translated to form triangle A'B'C'. Which describes the transformation? Check all that apply.
A.
It is non rigid
B.
The size is preserved
C.
It is rigid
D.
The angles are not preserved
E.
It is isometric

Answer:

do it yourself what do you do while teacher is teaching

Answer:

A withdrawal of 72 dollars & E) a depth of 72 feet

Step-by-step explanation:

It is negative, which means subtract. So we will take away 72 dollars.

A depth of 72 feet is also negative since we are going down.

If we restrict the domain of the function to the portion of the graph with a positive slope, the domain of the inverse function will be the range of the original function for values of x greater than 4, and its range will be all real numbers greater than or equal to 4.

The given function f(x) = |x – 4| + 6 is a piecewise function that contains an absolute value. The absolute value function has a V-shaped graph, and the slope of the graph changes at the point where the absolute value function changes sign. In this case, that point is x=4.

If we restrict the domain of f(x) to the portion of the graph with a positive slope, we are essentially considering the piece of the graph to the right of x=4. This means that x is greater than 4, or x>4.

The domain of the inverse function, f⁻¹(x), will be the range of the original function f(x) for values of x greater than 4. This is because the inverse function reflects the original function over the line y=x. So, if we restrict the domain of f(x) to values greater than 4, the reflected section of the graph will be the range of f⁻¹(x).

The range of f(x) is all real numbers greater than or equal to 6 because the absolute value function always produces a positive or zero value and when x is greater than or equal to 4, we add 6 to that value. The range of f⁻¹(x) will be all real numbers greater than or equal to 4, as this is the domain of the reflected section of the graph.

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Answer:

165 minutes

Step-by-step explanation:

To solve for the number of minutes that Joaquin played for, we can use this expression:

(let 'a' represent how much time passed from the time Joaquin started playing basketball until the time he arrived at home)

Subtracting 1:10 from each side:

1:10 - 1:10 cancels out to 0, while 3:35 - 1:10 is equal to 2:25.

So, the expression is now:

So, 2 hours and 25 minutes passed.

If we know that 1 hour is equivalent to 60 minutes, we can use this expression to solve for however many minutes are in 2 hours:

Now we need to add on the number of minutes and the time it took him to get home:

Therefore, 165 minutes passed from the time Joaquin started playing basketball until the time he arrived at home.

Answer:

Options D, E, F

Step-by-step explanation:

Given the following system of linear inequalities in two variables:

\(\displaystyle\sf\ System\:of\:Linear\:Inequalities = \begin{cases}\displaystyle\sf\ 2x < y} \\\displaystyle\sf\ y > 7}\end{cases}\)

We can substitute the given ordered pairs to see whether they satisfy both linear inequalities.

\(\displaystyle\sf\ System\:of\:Linear\:Inequalities = \begin{cases}\displaystyle\sf\ 2x < y} \\\displaystyle\sf\ y > 7}\end{cases}\)

2x < y

 ⇒  2(8) < 2

 ⇒  16 < 2  (False statement).  

y > 7

 ⇒  2 > 7 (False statement).  

 ⇒  (8, 2) is not a solution to the system.  

\(\displaystyle\sf\ System\:of\:Linear\:Inequalities = \begin{cases}\displaystyle\sf\ 2x < y} \\\displaystyle\sf\ y > 7}\end{cases}\)

2x < y

 ⇒  2(0) < 2

 ⇒  0 < 2  (True statement).  

y > 7

 ⇒  0 > 7 (False statement).  

 ⇒  (0, 0) is not a solution to the system.  

\(\displaystyle\sf\ System\:of\:Linear\:Inequalities = \begin{cases}\displaystyle\sf\ 2x < y} \\\displaystyle\sf\ y > 7}\end{cases}\)

2x < y

 ⇒  2(5) < 5

 ⇒  10 < 2  (False statement).  

y > 7

 ⇒  5 > 7 (False statement).  

 ⇒  (5, 5) is not a solution to the system.  

\(\displaystyle\sf\ System\:of\:Linear\:Inequalities = \begin{cases}\displaystyle\sf\ 2x < y} \\\displaystyle\sf\ y > 7}\end{cases}\)

2x < y

 ⇒  2(1) < 9

 ⇒  2 < 9  (True statement).  

y > 7

 ⇒  9 > 7 (True statement).  

 ⇒  (1, 9) is a solution to the system.  

\(\displaystyle\sf\ System\:of\:Linear\:Inequalities = \begin{cases}\displaystyle\sf\ 2x < y} \\\displaystyle\sf\ y > 7}\end{cases}\)

2x < y

 ⇒  2(17) < 50

 ⇒  34 < 50  (True statement).  

y > 7

 ⇒  50 > 7 (True statement).  

 ⇒  (17, 50) is also a solution to the system.  

\(\displaystyle\sf\ System\:of\:Linear\:Inequalities = \begin{cases}\displaystyle\sf\ 2x < y} \\\displaystyle\sf\ y > 7}\end{cases}\)

2x < y

 ⇒  2(-1) < 10

 ⇒ -2 < 10  (True statement).  

y > 7

 ⇒  10 > 7 (True statement).  

 ⇒  (-1, 10) is also a solution to the system.  

Therefore, Options D, E, and F are the solutions to the given system of linear inequalities.  

Linear Inequalities in two variables

System of linear inequalities  

________________________________

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The volume of the given cone.

\(\large\boxed{Formula:V= \frac{1}{3}\pi{r}^{2}h}\)

\(\large\boxed{\red \pi \red = \red 3 \red . \red 1 \red 4}\)

Let's solve!

Substitute the values according to the formula.

\(V= \frac{1}{3}×3.14×{3}^{2}×8\)

\(\large\boxed{V= 75.36 \: {yd}^{3}}\)

Therefore, the volume of the given cone is 75.36 cubic yards.

we get that the length of the rectangular field is 15.6 m, width is 56.5 m and the perimeter is 44.2 m.

The diagonal of a rectangular field = 16.9 m

d = 16.9 m

Ratio of length to the width is 12 : 5

Let length be 12 x

Width = 5 x

We get that:

16.9² = (12 x)² + (5 x)²

285.61 = 144 x² + 25 x²

169 x² = 285.61

x² = 285.61 / 169

x² = 1.69

x = √1.69

x = 1.3 m

Length = 12 (1.3 m) = 15.6 m

Width = 5 (1.3 m ) =6.5 m

Perimeter = 2 ( l + w)

P = 2( 15.6 + 6.5)

P = 2(22.1) m

P = 44.2 m

Therefore, we get that the length of the rectangular field is 15.6 m, width is 56.5 m and the perimeter is 44.2 m.

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Answer: 64%

Step-by-step explanation:

Given: Size of photo = 7-by-5-inch

Area of photo = 7 x 5 = 35 sq. inches   [ Area = Length x width]

Required size = 4.2 inches by 3 inches

Area of required size = 4.2 x 3 =12.6 sq. inches

Area reduced =Area of photo  - Area of required size = 35-12.6 =22.4 sq. inches

Percentage of the photo need to be reduced to in order for it to fit in the allotted space

\(=\dfrac{22.4}{35}\times100=64\%\)

Percentage of the photo need to be reduced to in order for it to fit in the allotted space = 64%

H

\(\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{"y" varies inversely with "x"}}{y = \cfrac{k}{x}}\hspace{5em}\textit{we also know that} \begin{cases} x=4\\ y=16 \end{cases} \\\\\\ 16=\cfrac{k}{4}\implies 64 = k\hspace{9em}\boxed{y=\cfrac{64}{x}} \\\\\\ \textit{when x = 32, what's "y"?}\qquad y=\cfrac{64}{32}\implies y=2\)

Answer: A

Step-by-step explanation:

Volume= LxWxH so we get 20x28x24 as given.

Volume= 13,440 which is the volume of the box given. ANd so if the box is 10,500cubic inches, we subtract to find the difference.

13,440-10,500= 2,940 Cubic Inches

Option A

Answer:

Part A:  13440 cubic inches.

Part B: A - 2940 cubic inches.

Step-by-step explanation:

The volume of the box = 24x20x28 = 13440 cubic inches.

The problem tells us that his gift is 10,500 cubic inches. So subtract that from the volume of the box.

13440-10500 = 2940 cubic inches. The answer is A.

The hypotenuse will always be the longest side of the triangle. Option C is correct: AB > DC.

AB is the hypotenuse of triangle ABC. Therefore, it is greater than leg AC. AC is the hypotenuse of triangle ACD. If AC is less than AB, then DC must also be less than AB because DC is less than AC.

Hope this helps!

Answer:

495

Step-by-step explanation:

using the definition

n\(C_{r}\) = \(\frac{n!}{r!(n-r)!}\)

where n! = n(n - 1)(n - 2) ... × 3 × 2 × 1

then

12\(C_{4}\)

= \(\frac{12!}{4!(12-4)!}\)

= \(\frac{12!}{4!(8!)}\)

cancel 8! on numerator/ denominator

= \(\frac{12(11)(10)(9)}{4!}\)

= \(\frac{11880}{4(3)(2)(1)}\)

= \(\frac{11880}{24}\)

= 495

Rounding to two decimal places, the Z-score corresponding to the youngest senator of age 39 is -1.40.

To find the Z-score corresponding to a particular value in a normal distribution, we use the formula:

Z = (x - μ) / σ

where x is the value of interest, μ is the mean, and σ is the standard deviation.

Part 1 of 2: For the oldest senator of age 85:

Z = (x - μ) / σ = (85 - 56.5) / 12.5 ≈ 2.28

Rounding to two decimal places, the Z-score corresponding to the oldest senator of age 85 is 2.28.

Part 2 of 2: For the youngest senator of age 39:

Z = (x - μ) / σ = (39 - 56.5) / 12.5 ≈ -1.4

Rounding to two decimal places, the Z-score corresponding to the youngest senator of age 39 is -1.40.

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Answer:

5

Step-by-step explanation:

Answer:

the answer to your question how many outcomes is really gonn adepend on you you slove you problem but my amswer is gonna be 7.

Answer:

C) When two fractions have equal denominators, the fraction with the greater numerator is the greater fraction.

Step-by-step explanation:

When comparing fractions, you do not use the denominator to compare. You use the numerator. Whichever fraction has the largest numerator, when the denominators are equal, is the greater fraction. When the fractions have unequal denominators, you find the least common denominator between them and then compare the numerators. Whichever one has the bigger numerator is the greater fraction.

Thus, the best answer is C.

hope this helps!

Answer:

The answer is C.

Step-by-step explanation:

The limit of Un as n approaches infinity is equal to 1/2(1+√5), confirming the given statement.

To prove that the limit of Un as n approaches infinity is equal to 1/2(1+√5), we can use the concept of limits and apply algebraic manipulation.

First, let's assume that the limit of Un as n approaches infinity is L. Mathematically, we can write:

lim (n→∞) Un = L

Since the given recurrence relation states that Un+1 = √(Un + 1)₁, we can substitute n+1 for n in the recurrence relation:

lim (n→∞) Un+1 = √(lim (n→∞) Un + 1)₁

Since the limit of Un as n approaches infinity is L, we can rewrite the equation as:

L = √(L + 1)₁

To solve for L, we can square both sides:

L^2 = L + 1

Rearranging the equation, we have:

L^2 - L - 1 = 0

This is a quadratic equation. By solving it using the quadratic formula, we find two possible values for L:

L = [1 ± √(1 + 4)] / 2

Simplifying the expression, we get:

L = [1 ± √5] / 2

The positive value, L = (1 + √5) / 2, corresponds to the golden ratio, which is approximately 1.618. The negative value can be ignored as the limit of Un cannot be negative.

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Answer:

x=2, y=5. (2, 5).

Step-by-step explanation:

x=7-y

x=-2y+12

----------------

7-y=-2y+12

7-y-(-2y)=12

7-y+2y=12

7+y=12

y=12-7

y=5

x=7-5=2

Mikey Johnson shipped out 34 2/7 pounds of electrical supplies. The supplies are placed in individual packets that weigh 2 1/7 pounds each. Therefore, Mikey shipped out 16 packets of electrical supplies.

To solve the problem, we can use the following steps.Step 1: Find the weight of each packet.

We are given that the weight of each packet is 2 1/7 pounds.

To convert this mixed number into an improper fraction, we can multiply the whole number by the denominator and add the numerator.

This gives us: 2 1/7 = (2 × 7 + 1) / 7= 15 / 7 pounds.

Therefore, the weight of each packet is 15/7 pounds.

Now, divide the total weight by the weight of each packet.

We are given that the total weight of the supplies shipped out is 34 2/7 pounds.

To convert this mixed number into an improper fraction, we can multiply the whole number by the denominator and add the numerator.

This gives us: 34 2/7 = (34 × 7 + 2) / 7= 240 / 7 pounds.

Therefore, the total weight of the supplies is 240/7 pounds.

To find the number of packets that Mikey shipped out, we can divide the total weight by the weight of each packet.

This gives us: 240/7 ÷ 15/7 = 240/7 × 7/15= 16.

Therefore, Mikey shipped out 16 packets of electrical supplies.

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Answer:

13 out of 16 (13/16)

Step-by-step explanation:

Add all of the items together.

5 stress balls + 3 notepads + 2 gift cards + 6 sticky notes = 16 items

So, now you have to find the probability out of 16.

Since there are 5 stress balls and 2 gift cards, there is a 5 out of 16 chance of passing out stress balls(5/16) and a 2 out 16 chance of handing out gift cards(2/16)

So, she has a 3 out 16 chance of handing out stress balls more than gift cards.

hope this helps and makes sense:)

We may predict that, when rοunded tο the clοsest whοle number, 185 persοns οught tο be present at Sοcial Prοblems οn Sunday.

Detailed numbers the set οf integers that cοntains zerο and the natural numbers. nοt a decimal and fractiοn. Integer 0 thrοugh 2, 3, 4, 5, 6, 7, 8, 9, 10, and sο οn. a cοunting number, a negative number, οr zerο.

The library saw a sum οf 416 + 448 + 341 = 1205 visitοrs οn Saturday. By dividing the entire number οf visitοrs by the number οf visitοrs whο visited Sοcial Prοblems, and then multiplying the result by 100% tο represent the results as a percentage, we can determine what percentage οf these visitοrs visited Sοcial Issues:

Percentage οf visitοrs whο went tο Sοcial Issues = (448 ÷ 1205) x 100%

Percentage οf visitοrs whο went tο Sοcial Issues ≈ 37.18%

We may assume that a similar percentage οf Saturday's visitοrs will return οn Sunday in οrder tο estimate the number οf persοns whο can be expected tο attend Sοcial Prοblems οn that day. Tο determine hοw many peοple will visit Sοcial Prοblems οn Sunday, we can utilize the prοpοrtiοn mentiοned abοve:

Estimated number οf visitοrs tο Sοcial Issues οn Sunday = (37.18% οf 500 visitοrs)

Estimated number οf visitοrs tο Sοcial Issues οn Sunday ≈ 185

We may calculate that, if we rοund tο the next whοle number, 185 persοns shοuld be anticipated tο attend Sοcial Prοblems οn Sunday.

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Kira has $19, Boris has $75, and Deshuan has $25.

We will denote as follows:

From information, we can set up equations:

B = 3D (Boris has 3 times what Deshuan has)

D = K + 6 (Deshuan has $6 more than Kira)

K + B + D = 119 (The total amount of money they have is $119)

Substituting equation 2 into equation 1, we have:

B = 3(K + 6)

Substituting equations 1 and 2 into equation 3:

K + 3(K + 6) + (K + 6) = 119

K + 3K + 18 + K + 6 = 119

5K + 24 = 119

5K = 119 - 24

5K = 95

K = 95 / 5

K = 19

Using equation 2, we can find D:

D = K + 6

D = 19 + 6

D = 25

Using equation 1, we can find B:

B = 3D

B = 3 * 25

B = 75.

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Answer:

1. d)

4.a)

2.a)

5.d)

Step-by-step explanation:

Answer:

X=6

Step-by-step explanation:

5x+(x+54)=90

6x+54=90

6x=36

X=6

The general solution of the partial differential equation is:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

The partial differential equation (PDE) is given as:

Uxx = (1/2)Ut with the boundary and initial conditions as 0< X <3 with U(0,t) = U(3, t)=0, U(0, t) = 5sin(4πx)

Assume that the solution can be written as a product of two functions:

U(x, t) = X(x)T(t)

Substituting this into the PDE, we have:

X''(x)T(t) = (1/2)X(x)T'(t)

Dividing both sides by X(x)T(t), we get:

(X''(x))/X(x) = (1/2)(T'(t))/T(t)

Since the left side only depends on x and the right side only depends on t, both sides must be equal to a constant, denoted as -λ²:

(X''(x))/X(x) = -λ²

(1/2)(T'(t))/T(t) = -λ²

Simplifying the second equation, we have:

T'(t)/T(t) = -2λ²

Solving the second equation, we find:

T(t) = Ce^(-2λ²t)

Applying the boundary condition U(0, t) = 0, we have:

U(0, t) = X(0)T(t) = 0

Since T(t) ≠ 0, we must have X(0) = 0.

Applying the boundary condition U(3, t) = 0, we have:

U(3, t) = X(3)T(t) = 0

Again, since T(t) ≠ 0, we must have X(3) = 0.

Therefore, we can conclude that X(x) must satisfy the following boundary value problem:

X''(x)/X(x) = -λ²

X(0) = 0

X(3) = 0

The general solution to this ordinary differential equation is given by:

X(x) = Asin(λx) + Bcos(λx)

Applying the initial condition U(x, 0) = 5*sin(4πx), we have:

U(x, 0) = X(x)T(0) = X(x)C

Comparing this with the given initial condition, we can conclude that T(0) = C = 5.

Therefore, the complete solution for U(x, t) is given by:

U(x, t) = Σ [Aₙsin(λₙx) + Bₙcos(λₙx)]*e^(-2(λₙ)²t)

where:

Σ represents the summation over all values of n

λₙ are the eigenvalues obtained from solving the boundary value problem for X(x).

To find the eigenvalues λₙ, we substitute the boundary conditions into the general solution for X(x):

X(0) = 0: Aₙsin(0) + Bₙcos(0) = 0

X(3) = 0: Aₙsin(3λₙ) + Bₙcos(3λₙ) = 0

From the first equation, we have Bₙ = 0.

From the second equation, we have Aₙ*sin(3λₙ) = 0. Since Aₙ ≠ 0, we must have sin(3λₙ) = 0.

This implies that 3λₙ = nπ, where n is an integer.

Therefore, λₙ = (nπ)/3.

Substituting the eigenvalues into the general solution, we have:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

where Aₙ are the coefficients that can be determined from the initial condition.

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Answer:

Step-by-step explanation:

f(x)  = 2x² + 14x - 4

= 2(x² + 7x) - 4

= 2(x² +7x + 3.5²) - 2(3.5²) - 4

= 2(x+3.5)² - 28.5

vertex (3.5, -28.5) = (7/2, -57/2)

The vertical intercept is the y-intercept, i.e., f(0) = -4.

The x-intercepts are the values of x for which y=0.

2x² + 14x - 4  = 0

x = [-14±√(14²-4(2)(-4))]/[2(2)] = [-7±√57]/2 ≅ -7.27, 0.27

Answer:

hmm this is a tricky one but C

Step-by-step explanation:

Answer:

No solution

Step-by-step explanation:

−7x−10−15x=−22x+83

Subtract 15x from −7x.

−22x−10=−22x+83

Move all terms containing x to the left side of the equation.

−10=83-10=83

Since −10≠83, there are no solutions.

No solution

Hope this helps! :) Plz mark as brainliest

Answer:

There is no sufficient evidence to support the claim

Step-by-step explanation:

From the question we are told that

     The level of significance is  \(\alpha = 0.05\)

     The  sample proportion is  \(\r p = 0.08\)

     The  sample size is  \(n = 250\)

Generally for normal sampling distribution can  be used

     \(n * p > 5\)

So  

     \(n* p = 250 * 0.12 = 30\)

Since  

     \(n * p > 5\) then  normal sampling distribution can  be used

The null hypothesis is  \(H_o : p = 0.12\)

  The alternative hypothesis is  \(H_a : p > 0.12\)

The  test statistic is evaluated as

            \(t = \frac{\r p - p }{ \sqrt{ \frac{p(1- p)}{n} } }\)

substituting values

            \(t = \frac{0.08 - 0.12 }{ \sqrt{ \frac{0.12 (1- 0.12)}{250 } } }\)

            \(t = -1.946\)

The  p-value is obtained from the z  table and the value is

        \(p-value = P(t > -1.9462) =0.97512\)

Since the \(p-value > \alpha\)

    Then we fail to reject the null hypothesis

Hence it means there is no sufficient evidence to support the claim

Answer:

2/10

Step-by-step explanation:

The are 10 tiles

There are 2 that are green and odd ( 3 and 5)

P ( green and odd) = green and odd/total

                               =2/10

                                =1/5