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A triangle has vertices at S(1, 1), T(2, −3), and U(4, 0). The triangle is translated up 3 units. What are the coordinates of the vertices of the image?

A. S'(4, 1), T'(5, −3), and U'(7, 0)
B. S'(1, 4), T'(2, 0), and U'(4, 3)

C. S'(1, 4), T'(2, −3), and U'(4, 0)
D. S'(1, −2), T'(2, −6), and U'(4, −3)

Answer:

204q+228

Step-by-step explanation:

ANSWER

[tex]12(17q + 19) = 204q + 228[/tex]

EXPLANATION

The given expression is:

[tex]12(17q + 19)[/tex]

Recall the distributive property,

If a, b, and c are real numbers, then

a(b+c)=ab+ac

We apply this property to expand the parenthesis and obtain:

[tex]12(17q + 19) = 12 \times 17q + 12 \times 19[/tex]

[tex]12(17q + 19) = 204q + 228[/tex]

Answer:

[tex]\log_{13}(169)=2[/tex]

Step-by-step explanation:

The given exponential form is:

[tex]169=13^2[/tex]

The base of the given expression on the right is 13 and the exponent is 2.

The number is 169.

In terms of logarithms, the base still remains the base and the exponent becomes the result of the logarithm of the number 169 to the given base 13.

[tex]\log_{13}(169)=2[/tex]

Answer:

A

Step-by-step explanation:

The only one you can eliminate on sight is C. You are going to get an x^3 somewhere along the line.

You can eliminate D on sight as well. The x^3 term is 12x^3 not 7x^3

Doesn't leave much does it?

(3x + 2)(4x^2 - 2x - 7)

3x: 12x^3 - 6x^2 - 21x

2 :              8x^2 - 4x   - 14

=======================     Add

     12x^3 + 2x^2 - 25x - 14

Answer: A

[tex](3x + 2)(4x^{2} - 2x - 7) \\ \: a. = 12 {x}^{3}+ 2x^{2} - 25x - 14[/tex]

OK so first you find the square root of 363 which is 19.05255888325765 then you find the square root of 27 which is 5.196252422706632 then times that by 3 you get 15.5884572681199 so then you have 19.05255888325765 subtract 15.5884572681199 which equals 3.46410161513775

Hope this helped!

Answer:

D) 6 in

Step-by-step explanation:

The length is 24 feet. The blueprint scales 1 ft : ¹/₄ in.

So, we can set up a proportion: 1 ft / ¹/₄ in = 24 ft / x in

Cross-multiply: 24 * ¹/₄ = x

Multiply: x = 6 in

Answer:

[tex]a_n=3(3)^{n-1}[/tex]

Step-by-step explanation:

We have the following sequence

3,9,27,81,243

Note that if you divide each term of the sequence between the previous term you get:

[tex]\frac{9}{3} = 3\\\\\frac{27}{9} = 3\\\\\frac{81}{27} = 3[/tex]

then the radius of convergence of the series is r.

therefore this is a geometrical series.

The formula to find the general term [tex]a_n[/tex] of the geometric sequence is:

[tex]a_n=a_1(r)^{n-1}[/tex]

Where

[tex]a_1[/tex] is the first term of the sequence

Then the general term for this sequence is:

[tex]a_n=3(3)^{n-1}[/tex]

a) The graph of the function is illustrated below.

b) The rocket's maximum height is 64 feet, it takes 2 seconds to reach this height.

c) The total time it was in the air is 4 seconds.

(A) Quadratic Function: To model the height of the rocket as it moves upward, we use a quadratic function in the form h(t) = at² + bt + c, where h(t) represents the height of the rocket at time t seconds. Since the rocket is moving vertically, we consider the acceleration due to gravity, which is -32 feet per second squared. The initial velocity of the rocket is 64 feet per second, so the coefficient of the linear term, b, is 64.

The equation for the height of the rocket is: h(t) = -16t² + 64t

(B) Graphing on the Coordinate Plane: To graph the quadratic function, we plot points on a coordinate plane. The vertex of the parabola represents the maximum height of the rocket, and the t-intercepts correspond to the times when the rocket hits the ground. The vertex of a quadratic function in the form h(t) = at² + bt + c is given by the coordinates (t_v, h(t_v)), where

t_v = -b / 2a.

In this case,

t_v = -64 / 2(-16) = 2 seconds.

(C) Finding Rocket's Maximum Height and Time in the Air: The vertex point we found earlier is (2, 64). This means that the rocket reaches its maximum height of 64 feet after 2 seconds of flight. To find the maximum height, we plug the value of t_v back into the equation:

h(t_v) = -16(2)² + 64(2) = -16(4) + 128 = 64 feet.

The rocket's maximum height is 64 feet, and it takes 2 seconds to reach this height. To find the total time the rocket is in the air, we look at the t-intercepts on the graph, which correspond to the times when the rocket hits the ground. From the equation h(t) = -16t² + 64t, we set h(t) to 0 and solve for t:

0 = -16t² + 64t t(0) = 0 (corresponding to the initial time of launch) t(4) = 4 seconds.

The rocket is in the air for 4 seconds.

To know more about function here

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The answers are:

Second step:

First box, 4

Second box,

The width is:

[tex]x+4[/tex]

Fourth step:

Box, 16

The length cant be -16in,  the length is 12in, and the width is 16in.

To solve the problem, we are using the formula to calculate the area of a rectangle, however, since the dimensions of the rectangle are not constant numbers, we will work with the variable "x", also, we know that the area of the cookie sheet is equal to 192 square inches.

So, solving we have:

First step:

We have the expression:

[tex]x^{2} +x[/tex]

Which is equal to: [tex]192in^{2}[/tex]

So,

[tex]x^{2} +4x=492[/tex]

Second step:

We have that the common factor of the left side of the equation is "x", so, we can simplify the expression in the following way:

[tex]x(x+4)=492[/tex]

Now, using the formula to calculate the area of a rectangle, we have:

[tex]length*width=Area\\\\length*width=92in^{2}\\\\x(x+4)=192in^{2}[/tex]

Where,

The length of the rectangle is "x"

The width of the rectangle is "x+4"

Third step:

Rewriting the expression, we have:

[tex]x^{2} +4x-192=0[/tex]

We need to find the roots (zeroes) of the quadratic function, in order to find the width of the rectangle without using the variable "x".

So, finding the values of "x" (roots or zeroes of the expression), we have:

[tex]x^{2} +4x-192=0[/tex]

Fourth step:

We need to find two numbers which it product gives as result the number -192 (including its sign) and their algebraic sum gives as result "4", those numbers are, -12 and 16,

[tex]-12*(16)=-192\\-12+16=4[/tex]

Then, rewriting the equation, we have:

[tex](x+16)(x-12)=0[/tex]

So, we that the expression is equal to 0 for two values of "x", these values are:

[tex]x_1=-16\\x_2=12[/tex]

Now, since the length can't be -16in, its equal to 12in.

[tex]length=x=12in[/tex]

[tex]length=12[/tex]

Then, from the second equation, we have that:

[tex]width=x+4[/tex]

Substituting "x" we can find the value of the width, so:

[tex]width=x+4=\\\\width=12+4=16in[/tex]

Hence, we have:

[tex]length=12in\\width=16in[/tex]

Have a nice day!

Answer:

 The measure of G = 9.2°

Step-by-step explanation:

From the figure we can write,

The measure of <G is half the  the measure of arc AD

To find the value of x

We have  AD = (6x - 80)° and 2G = (x + 2)°

6x - 80 = (x + 2)

6x - 80 = x + 2

6x - x = 82

5x = 82

x = 82/5 = 16.4

To find the measure of <gG

m<G = (x + 2 )/2

 = (16.4 + 2)/2 = 18.4 = 9.2

Therefore the measure of <G =  9.2°

Answer:

Step-by-step explanation:

Use the Pythagorean theorem:

[tex]leg^2+leg^2=hypotenuse^2[/tex]

We have

[tex]leg=x,\ leg=15.6cm:2=7.8cm,\ hypotenuse=8.8cm[/tex]

Substitute:

[tex]x^2+7.8^2=8.8^2[/tex]

[tex]x^2+60.84=77.44[/tex]          subtract 60.84 from both sides

[tex]x^2=16.6\to x=\sqrt{16.6}\\\\x\approx4.1\ cm[/tex]

Answer:

-2

Step-by-step explanation:

I believe its -2 :) :3

[tex]\bf (\stackrel{x_1}{-3}~,~\stackrel{y_1}{4})~\hspace{10em} slope = m\implies \cfrac{5}{6} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-4=\cfrac{5}{6}[x-(-3)]\implies y-4=\cfrac{5}{6}(x+3) \\\\\\ y-4=\cfrac{5}{6}x+\cfrac{5}{2}\implies y=\cfrac{5}{6}x+\cfrac{5}{2}+4\implies y=\cfrac{5}{6}x+\stackrel{\textit{LCD of 2}}{\cfrac{(1)5+(2)4}{2}}[/tex]

[tex]\bf y=\cfrac{5}{6}x+\cfrac{13}{2}\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

Answer:

77.79 yard

Step-by-step explanation:

Given in the question that,

falcon flying at a height of 200 yards

sparrow flying at a height of 150 yards

Suppose, distance between Falcon and Sparrow = x yards

Step 1

Difference between the height of falcon and sparrow = 200-150 = 50 yards

Step 2

We will use Trigonometry Identity to find the distance between Falcon and Sparrow

SinФ = opposite / hypotenuse

Sin(40) = 50 / x

x = 50 / Sin(40)

x = 77.79 yard

Answer:

78

Step-by-step explanation:

Answer:

3 lawns per hour

Step-by-step explanation:

Divide the lawns by the time: 6/2=3

6/2 = 3

So, Mia mowed 3 lawns in an hour.

Answer: 6 divided by 2 equals 3

Answer:

6

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

Answer:

Slope = 0

Step-by-step explanation:

(y2 - y1) ÷ (x2 - x1) = (-3 - [-3]) ÷ (1 - [-9]) = 0 ÷ 10 = 0

Answer:

The 2.50a is the constant. He's getting paid 2.50 dollars weekly

Step-by-step explanation:

When theres a variable next to a number, that means that's the constant.

Answer:

no. Hes getting paid 290, guaranteed.

Step-by-step explanation:

...

Answer:

9/100

Step-by-step explanation:

There are 10 marbles in the bag

There are 3 pink marbles.

P (1st marble pink) = pink marbles/ total marbles

                              = 3/10

We put the marble back.

There are 10 marbles in the bag

There are 3 pink marbles.

P (2nd marble pink) = pink marbles/ total marbles

                                      = 3/10

Multiply the probabilities together

P (pink, then pink) = 3/10 * 3/10 = 9/100

Answer:

yes

Step-by-step explanation:

The formula to finding the hypotenuse of a right triangle is a^2+b^2=c^2. So since the longest side is the hypotenuse, the 82 in. is the hypotenuse. 18^2+80^2= 6724, then we square root it, square root of 6725 is 82.

Answer:

This is a right triangle

Step-by-step explanation:

We can check this using the Pythagorean theorem

a^2 +b^2 = c^2

where a and b are the legs and c is the hypotenuse

18^2  + 80^2 = 82^2

324+6400=6724

6724 = 6724

True, so this is a right triangle

The answer is:

The first and second options:

f(x) and g(x) intersect at exactly two points.

The x-intercepts of f(x) are common to g(x)

To find the correct option (or options) , we need to remember the following:

- When a function intercepts the y-axis, it means that the "x" coordinate will be equal to 0.

- When a function intercepts the x-axis, it means that the "y" coordinate will be equal to 0.

Now, to find the correct option, we also need to compare the graphed function (f(x))  to the given table (g(x)).

So, discarding each of the given options to find the correct option, we have:

- First option, f(x) and g(x)  intersect at exactly two points: True.

From the graph we can see that f(x) intercepts the x-axis at two points (-1,0) and (1,0), also, from the table we can see that g(x) intercepts the x-axis at the same two points (-1,0) and (1,0), it means that the functions intersect at exactly two points.

Hence,  we have that f(x) and g(x)  intersect at exactly two points.

- Second option, the x-intercepts of f(x) are common to g(x): True.

From the graph we can see that f(x) intercepts the x-axis at two points (-1,0) and (1,0), also, from the table we can see that g(x) intercepts the x-axis at the same two points (-1,0) and (1,0), so, both functions intercepts the x-axis at common points.

Hence,we have that the x-intercepts of f(x) are common to g(x)

- Third option, he minimum value of f(x) is less than the minimum value of g(x): False.

From the graph, we can see that the minimum value of f(x) is located at the point (0,-1), also, from the given table for g(x) we can see that there are values below the point (2,-3), meaning that the minimum value of f(x) is NOT less than the minimum value of g(x).

Hence, we have that the minimum value of f(x) is NOT less than the minimum value of g(x).

- Fourth option, f(x) and g(x) have the same y-intercept: False.

We can see that for the function f(x) the y-intercept is located at (0,-1) while from the given table, we can see the y-intercept for the function g(x) is located at (0,1)

Hence,  we have that f(x) and g(x) have differents y-intercepts.

Therefore, the correct answers are:

The first and second options:

f(x) and g(x) intersect at exactly two points.

The x-intercepts of f(x) are common to g(x)

Have a nice day!

Note: I have attached an image for better understanding.

The graph of f(x) overlaps with the graph of g(x). Then the correct option is A.

A statement, principle, or policy that creates the link between two variables is known as a function.

The table of values represents the function g(x) and the graph shows the function f(x).

The graph of f(x) overlaps with the graph of g(x).

Then the correct option is A.

More about the function link is given below.

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Answer:

Step-by-step explanation:The solution is x > 3

Answer:

[tex]\large\boxed{\bold{No\ solution}}[/tex]

Step-by-step explanation:

[tex]C:\ y=6x+9\\\\D:\ y=6x+2\\\\\left\{\begin{array}{ccc}y=6x+9&(1)\\y=6x+2&(2)\end{array}\right\\\\\text{substitute (1) to (2):}\\\\6x+9=6x+2\qquad\text{subtract 6x from both sides}\\\\9=2\qquad\bold{FALSE}\\\\\text{Therefore the answer is:}\ \bold{no\ solution}[/tex]

Answer:

c. x = -9.

Step-by-step explanation:

The excluded value is the value of x which gives a value of 0 to the denominator, so that value would be x =  -9.

Note: (x - 7) / 0 is undefined.

Answer:

See below

Step-by-step explanation:

Givens

Jenny's Stats

t = m - 2

d = 60 miles

r = r1 + 10

Maureen's stats

d = 50 miles

t = m

r = r1

=======

60 = (r1 + 10) * (m - 2)

50 = r1 * m

m = 50/r1

60 = (r1 + 10)* (50/r1 - 2)  

60 = 50 + 500/r1 - 2r1 - 20

60 = 30 + 500/r1 - 2r1

60r1 = 30r1 + 500 - 2*r1^2

30r1 = 500 - 2r1^2

2r1^2 + 30r1 - 500

This quadratic factors into

2 (r1 - 10)(r1 + 25)

r1 = 10 mph             The 25 has no meaning.

m = 50/r1

m = 50/10

m = 5 hours

m - 2 = 3 hours.

First you must combine like terms (x and x)

2y + 2 + (x + x)

2y + 2 + 2x

^^^All have the number two in common so we can take a two out like so...

2 (y + 1 + x)

or

2(x + y + 1)

There fore the answer is A!

Hope this helped!

~Just a girl in love with Shawn Mendes

The answers are:

B. Before practice, there are 648 ounces of sports drink in the cooler.

C. Each plater drinks approximately 24 ounces of sports drink at practice.

E. For each additional player that takes a drink, there will be approximately  24 fewer ounces of sporks drink remaining after the practice.

We are given the equation:

[tex]y=f(x)=648-24x[/tex]

Let's discard each of the given options in order to find the three correct options.

A. The cooler is meant to be used only by 24 players: False.

If we want to calculate how many players can use the cooler, we need to isolate "x" (rate of change) from the given equation, so, isolating we have:

[tex]f(x)=648-24x[/tex]

[tex]0=648-24x[/tex]

[tex]648=24x\\\\24x=648\\\\x=\frac{648}{24}=27[/tex]

We have that the cooler can be used by 27 players, so, the first option that states that "The cooler is meant to be used only by 24 players" is false.

B. Before practice, there are 648 ounces of sports drink in the cooler: True.

We have that before the practice when the cooler is not being used by any player (or there is no any player) has 648 ounces (full), we can calculate it making the variable "x" equal to 0, so, calculating we have:

[tex]f(x)=648-24x[/tex]

[tex]f(0)=648-24*(0)=648[/tex]

Therefore, we have that the statement "Before practice, there are 648 ounces of sports drink in the cooler." is true.

C. Each plater drinks approximately 24 ounces of sports drink at practice: True.

From the statement, we know that the rate of change is equal to (-24), and it's equal to the number of ounces that each player drinks.

Hence, we have that the statement  "Each plater drinks approximately 24 ounces of sports drink at practice." is true.

D. If  24 players get drinks from the cooler, they will drink a total of 648 ounces of sports drink: False.

If we want to calculate the number of ounces that 24 players will drink, we need to use the slope value. If we know that each player drinks 24 ounces, so, to calculate how many ounces of sports drink will 24 players drink, we need to use the following equation:

[tex]DrankOunces=24oz*Players\\\\DrankOunces=24oz*24=576oz[/tex]

We have that 24 players will drink a total of 576 ounces, so, the statement "If  24 players get drinks from the cooler, they will drink a total of 648 ounces of sports drink." is false.

E. For each additional player that takes a drink, there will be approximately 24 fewer ounces of sporks drink remaining after the practice: True.

From the statement and the equation, we know that the slope (rate of change) is negative, meaning that for each player (x) it will be 24 fewer ounces of sports drink after practice, for example, calculating for 1 and 2 players, we have:

[tex]f(1)=648-24*1=624[/tex]

[tex]f(x)=648-24*2=600[/tex]

We can see that for each player, it will be 24 fewer ounces of sports drink after practice.

Hence, we have that the statement "For each additional player that takes a drink, there will be approximately  24 fewer ounces of sporks drink remaining after the practice." is true.

Therefore, the correct options are:

B. Before practice, there are 648 ounces of sports drink in the cooler.

C. Each plater drinks approximately 24 ounces of sports drink at practice.

E. For each additional player that takes a drink, there will be approximately  24 fewer ounces of sporks drink remaining after the practice.

Have a nice day!

Answer: $8.35

Step-by-step explanation:

Given: The amount as gross pay= $576.00

The rate of Medicare tax =1.45%  = 0.0145

Now, to calculate the medicare tax we need to multiply the rate of Medicare tax with the gross pay , we get

[tex]\text{Medicare tax=0.0145*Gross Pay}\\\\\Rightarrow\ \text{Medicare tax}=0.0145\times576.00\\\\\Rightarrow\ \text{Medicare tax}=\$8.352\approx\$8.35[/tex]

Answer:scott

Step-by-step explanation:

I’m pretty sure Scott. Hope this helps!!!

Answer: [tex]x(11-x)=0[/tex]

Step-by-step explanation:

Given the quadratic equation [tex]11x-x^2=0[/tex], you need to factor it.

In order to find the form asked of the given equation, you need to factor out the common factor of the terms.

You can observe that the common factor of the terms of the equation is: [tex]x[/tex]

Now, knowing this, you must factor out [tex]x[/tex]. Then you get the following form:

[tex]x(11-x)=0[/tex]

Therefore, the factored fom of the equation  [tex]11x-x^2=0[/tex] is:

 [tex]x(11-x)=0[/tex]