Find the values of x and y if (-x + 5, 1) = (-y, 2x - 5y).

Given:

The preimage and image of a triangle in the given figure.

To find:

The dilation scale factor.

Solution:

From the given figure it is clear that the vertices of the triangle ABC are A(-2,-2), B(-1,2) and C(2,1).

The vertices of the triangle A'B'C' are A'(-4,-4), B'(-2,4) and C'(4,2).

If a figure is dilated by factor K with (0,0) as the center of dilation, then

[tex](x,y)\to (kx,ky)[/tex]

Let the scale factor be K, then the image of point A is:

[tex]A(-2,-2)\to A'(k(-2),k(-2))[/tex]

[tex]A(-2,-2)\to A'(-2k,-2k)[/tex]

From the given figure it is clear that the image of point A is A'(-4,-4).

[tex]A'(-2k,-2k)=A'(-4,-4)[/tex]

On comparing both sides, we get

[tex]-2k=-4[/tex]

[tex]k=\dfrac{-4}{-2}[/tex]

[tex]k=2[/tex]

Therefore, the dilation scale factor is 2.

Answer:

Yes it can

Step-by-step explanation:

To check wether it's a right angle triangle we need to apply the Pythagoras theorem

h^2= a^2 +b^2

Hypotenuse is always the longest side so

5^2 = 3^2 + 4^2

This is correct, so the triangle is a right angle triangle

Answer from Gauthmath

Answer:

HT = 17 cm

<T = 58°

<H = 32°

Step-by-step explanation:

✔️Find HT:

Since it's a right triangle, we would apply the Pythagorean Theorem given as c² = a² + b²

Where,

a = HW = 15 cm

b = WT = 8 cm

c = HT

Plug in the values:

HT² = 15² + 8²

HT² = 289

HT = √289

HT = 17 cm

✔️Find <T by applying trigonometric ratio formula:

Recall: SOH CAH TOA

Reference angle (θ) = <T

HW = 15 cm = Opposite side length

WT = 8 cm = Adjacent side length

Apply CAH:

Cos θ = Adj/Hyp

Substitute

Cos T = 8/15

T = [tex] cos^{-1}(0.5333) [/tex]

T ≈ 58°

✔️Find <H:

Sun of interior angles of a triangle = 180°

Therefore,

m<H + m<T + m<W = 180°

Substitute

m<H + 58° + 90° = 180°

m<H + 148° = 180°

m<H = 180° - 148°

m<H = 32°

Answer:

It is the second option down

Step-by-step explanation:

Answer:

Step-by-step explanation:

Patrick thinks that when 'a' is a negative integer and 'b' is a positive,

Let "a = -2" and "b = 3"

a). a - b is positive.

a - b = -2 - 3

            = -5 {negative]

Therefore, statement is False.

(a - b) is negative.

b). b - a is positive.

b - a = 3 - (-2)

       = 3 + 2

       = 5 [Positive]

Statement is True.

c). a - (-b) is negative.

a - (-b) = a + b

          = -2 + 3

          = 1 [Positive]

False.

But it's true when a = -5 and b = 3

a - (-b) = -5 - 3

           = -8 [Negative]

Answer:

D. having students write a definition for each term in their own words in their native language

Step-by-step explanation:

In Mr Fischer's mathematics class, we are presented with two categories of learners. Those that are native speakers of English and those who are learners of English.

Both categories of students would show their understanding best in this lesson if they were to write in their own native language.

The native english-speakers would have no issues writing in English, but those who are English learners would have problems communicating their understanding of the lesson in English. So it is best they give their definitions in their native language.

Answer:

the answer is c

Step-by-step explanation:

when solving for theta, we are given the side length adjacent to it (5) and the length of the hypotenuse ( 14).

the trigonometric function that deals with adjacent and hypotenuse values is cosine.

you can use SOH CAH TOA

stands for :

sin = opposite/hypotenuse

cos = adjacent/ hypotenuse

tan = opposite/adjacent

we dont know theta so :

cos(theta) = 5/14

cos = about 69

check :

cos(69) = 5/14

                   cos(69) = 0.35836794954

                   5/14 = 0.35714285714

Answer:

See explanation

Step-by-step explanation:

The question is incomplete, as the total orders is not given.

To solve this question, I will assume a value for the total number of order.

Let

[tex]x \to 12-cup[/tex]

[tex]n_x = 18[/tex] ---- number of 12-cup

[tex]y \to 36-cup[/tex]

[tex]n_y = ??[/tex] ---- number of 36-cup

[tex]n \to[/tex] Total order

Required

Calculate [tex]n_y[/tex]

To do this, we make use of the following equation:

[tex]n_x * x + n_y * y = n[/tex]

Substitute known values

[tex]18 * 12 + n_y * 36 = n[/tex]

[tex]216 + 36n_y= n[/tex]

Collect like terms

[tex]36n_y= n - 216[/tex]

Divide both sides by 36

[tex]n_y= \frac{n - 216}{36}[/tex]

Assume the number of orders is: 540 cups

The equation becomes

[tex]n_y= \frac{540 - 216}{36}[/tex]

[tex]n_y= \frac{324}{36}[/tex]

[tex]n_y= 9[/tex]

Answer:

(8x + 3)²

Step-by-step explanation:

Since our polynomial is 64x² + 48x + 9, we multiply 64x² by 9 to get 64x² × 9 = 576x² since we cannot simplify the expression any further.

Next, we need to find the factors of 576x² that add up to give 48x, these are 24x and 24x.

So the expression is re-written as

64x² + 48x + 9 = 64x² + 24x + 24x + 9

Writing out all the common factors, we have,

64x² + 48x + 9 = 8x × 8x + 3 × 8x + 3 × 8x + 3 × 3

Factorizing we have

64x² + 48x + 9 = 8x(8x + 3) + 3(8x + 3)

64x² + 48x + 9 = (8x + 3)(8x + 3)

64x² + 48x + 9 = (8x + 3)²

Answer:

Value of given expression x is -4

Step-by-step explanation:

Given equation in question;

4 + 2|3x + 4| = -4

Find:

Value of given expression

Computation:

4 + 2|3x + 4| = -4

Using BODMAS rule;

⇒ 4 + 2|3x + 4| = -4

⇒ 2|3x + 4| = - 4 - 4

⇒ 2|3x + 4| = - 8

⇒ |3x + 4| = - 8 / 2

⇒ |3x + 4| = - 4

⇒ 3x + 4 = - 8

⇒ 3x = -8 - 4

⇒ 3x = -12

⇒ x = -12 / 3

⇒ x = -4

Value of given expression x is -4

The function is negative for all real values of x where x < -3 or x > -1 and the domain of the function is -∝ < x < ∝

The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.

The range is the set of outputs of a relation or function. In other words, it's the set of possible y values. Recall that ordered pairs are of the form (x,y) so the y coordinate is listed after the x. The output is listed after the input.

Given data ,

Let the function be represented as f ( x )

Now , the value of f ( x ) is

f ( x ) = - ( x + 3 ) ( x - 1 )   be equation (1)

Now , the values of x which makes the function negative are

when x < -3

f ( x ) = - ( -ve ) ( -ve ) = -ve

when x > 1

f ( x ) = - ( +ve ) ( +ve ) = -ve

So , the domain of the function is all real numbers and -∝ < x < ∝

Hence , the function is solved

To learn more about domain and range click :

https://brainly.com/question/28135761

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Answer:

Using a calculator;

A is approximately 51.34°

G is approximately 28.36°

Step-by-step explanation:

Part 1

The given trigonometric ratio is presented as follows;

tan A = 5/4

Therefore, the angle, A = arctan(5/4)

Using a calculator,  the value of A is found as follows;

1. Ensure the angle mode of the calculator is set to the correct value (the selected mode here is degrees)

2. Entering 5/4 into the calculator, using the keypad

3 . Selecting the arctan button to give, A ≈ 51.34°

Part 2

The given trigonometric ratio is cos G = 0.88

Therefore, G = arccos(0.88)

1. Ensure the angle mode of the calculator is set to the correct value (the selected mode here is degrees)

2. Enter 0.88 into the calculator by typing

3. Select arccos from the function menu, to give

arcos(0.88) = G ≈ 28.36°.

Answer:

[tex] MN= \boxed{15}[/tex]

Step-by-step explanation:

refer the attachment

therefore Let,

according to the question

[tex] \displaystyle (x - 3 ) (x + 13) =( x + 3 {)}^{2} [/tex]

simplify square and Multiplication:

[tex] \displaystyle {x}^{2} + 10x - 39 = {x}^{2} + 6x + 9[/tex]

cancel x² from both sides:

[tex] \displaystyle 10x - 39 = 6x + 9[/tex]

cancel 6x from both sides:

[tex] \displaystyle 4x - 39 = 9[/tex]

add 39 to both sides:

[tex] \displaystyle 4x = 48[/tex]

divide both sides by 4:

[tex] \displaystyle \boxed{x = 12}[/tex]

given that,

[tex] MN= x + 3[/tex]

substitute the got value of x:

[tex] MN= 12 + 3[/tex]

simplify addition hence,

[tex] MN= \boxed{15}[/tex]

Answer:

50.7

Step-by-step explanation:

38+1.3+90 from the right angle=129.3

180-129.3=50.7

Step-by-step explanation:

1. The length is one more thrice it's width. The height is 4 more than it width. We can represent the

[tex](3x + 1)(x + 4)[/tex]

[tex](3 {x}^{2} + 13x + 4)x = 720[/tex]

Multiply it by x.

[tex]3 {x}^{3} + 13 {x}^{2} + 4x = 720[/tex]

[tex] 3{x}^{3} + 13 {x}^{2} + 4 x - 720[/tex]

The possible roots

The possible roots are plus or minus is1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 120, 144, 180, 240, 360, and 720. By a long list of substitution, 5 is a root. So this means that x=5. So the width has to be

[tex]x = 5[/tex]

2. First. we apply the Rational Root Theorem so the possible roots are plus or minus 1,2,3,6.

Let check via synethic division to see which are roots.

Let try 1 and -1 first. If we plug 1 into the equation, we get

[tex]1 - 2 - 5 + 6 = 0[/tex]

So 1 or (x-1) is a solution. Since it's a solution we can divide this into our original polynomial to get us a new polynomial that is more simplified. If we apply synthetic division, we get a new polynomial in

[tex] {x}^{2} - x - 6[/tex]

We can then factor this into

[tex](x - 3)(x + 2)[/tex]

So our roots or factors is

[tex](x - 1)(x - 3)(x + 2)[/tex]

Answer:

m∠1 = 103

m∠2 = 103

Step-by-step explanation:

by definition, the opposite angles of a kite are congruent.

we know that a quadrilateral's angles add up to 360.

117 º+ 37º + 2xº = 360º

2xº = 206º

xº=103º

In case of Nina:

slope of graph = speed = 48-32/6-4 = 16/2 =8

y-32 =8(x-4)

y-32=8x-32

y=8x

d=8t

at x= 0 i.e at t= 0

d= 0m

In case of Ryan:

slope =speed = 47.5-35=6-4 = 12.5/2 =6.25

y-35=6.25(x-4)

y-35=6.25x-25

y=6.25x+10

d=6.25t+10

at t = 0, d= 10m

RYAN had a head start of 10 m

Answer:

B. False

Step-by-step explanation:

There is not enough information to make that conclusion. The two statements are completely unrelated, so the transitive property cannot be used. None of the given statements say that ABC is congruent to MNO or PQR. That means that nothing can be assumed about DEF. To use the transitive property you would need proof that ABC=MNO or ABC=PQR. But neither of those statements are there so the answer is false.

Answer:

true

Step-by-step explanation:

a pe c

Answer:

32 years

Step-by-step explanation:

8x12 because there are 12 inches in a foot

8x12=96

96/3

96/3=32

Answer:

32 years

Step-by-step explanation:

y = years

1 foot  = 12 inches

12 × 8 = 96

Now, plug in random numbers into the expression below to find how long it takes for the tree to grow 8 feet.

3y

3 × 10 = 30

3 × 20 = 60

3 × 30 = 90

3 × 31 = 93

3 × 32 = 96

It will take the pine tree 32 years to grow 8 feet, or 96 inches.

Answer: 1⅓ batch of cookies

Step-by-step explanation:

From the question, we are given the information that a cook has 4 cups of raisins to make oatmeal cookies and that the recipe requires 3 cup of raisins for each batch of cookies.

Therefore, the number of batches of cookies that the cook can make will be the number of cups of rasins that the cook has divided by the number of reasons needed for each cookie. This will then be:

= 4/3

= 1⅓ batch of cookies

Answer:

D

Step-by-step explanation:

We are given the two functions:

[tex]f(x) = 5x^2-x+1 \text{ and } g(x) = -3x[/tex]

And we want to find:

[tex](f \circ g)(1)[/tex]

Recall that this is equivalent to:

[tex]=f(g(1))[/tex]

Evaluate g(1):

[tex]g(1) = -3(1) = -3[/tex]

Substitute:

[tex]=f(-3)[/tex]

Evaluate f(-3):

[tex]f(-3)=5(-3)^2-(-3)+1=49[/tex]

Therefore:

[tex](f \circ g)(1) =49[/tex]

Our answer is D.

Answer:

49

Step-by-step explanation:

ƒ(x) = 5x2 – x + 1 and g(x) = –3x

(ƒ ∘ g)(1)

First find g(1) = -3(1) = -3

Then find f(g(1) = f(-3)

f(-3) = 5(-3)^2 - (-3) +1 = 5(9) +3+1 = 45+4 = 49

First, we'll set up two equations. One for the amount of each coin and another for the value of the coins.

N will represent nickels

D will represent dimes

N + D = 30

---The problem tells us that there are 30 total coins

0.05N + 0.10D = 2.95

---Nickels are worth 5 cents and dimes are worth 10 cents, and the total value of the coins is 2.95

Now that we have our equations, we need to solve for one of the variables in the first equation. I will solve for N.

N + D = 30

N = 30 - D

Then, we take that equation and substitute our new value for N into the second equation (value) and solve for D.

0.05(30 - D) + 0.10D = 2.95

1.5 - 0.05D + 0.10D = 2.95

1.5 + 0.05D = 2.95

0.05D = 1.45

D = 29

Now that we know how many dimes there are, we can plug that value into our equation for N and solve for N.

N = 30 - D

N = 30 - 29

N = 1

Therefore, there are 29 dimes and 1 nickel.

Hope this helps!

Answer:

V =48 cm^3

Step-by-step explanation:

The volume of a prism is given by

V = l*w*h

V = 3*4*4

V =48 cm^3

V =48 cm^3

Step-by-step explanation:

The volume of a prism is given by

V = l*w*h

V = 3*4*4

V =48 cm^3

Answer:

30 words per minute

Step-by-step explanation:

Take the number of words and divide by the number of minutes

150/5 = 30

300/10 =30

450/15 = 30

600/20 = 30

30 words per minute

Answer:

janae types 30 words each minutes.

Step-by-step explanation:

if 5minutes = 150 words

[tex]1 \: minute = \frac{150words}{5minutes} [/tex]

[tex] = \: 30words[/tex]

Answer:

32.61° is the answer

Step-by-step explanation:

Tanx=17.6/27.5

Answer:

The equation of the circle is given by:

(x-a)^2+(y-b)^2=r^2

where:

(a,b) is the center  of the circle

given that the center of our circle is (2,3) with the radius of 5, the equation will be:

(x+2)^2+(y+3)^2=5^2

expanding the above we get:

x^2+4x+4+y^2+6y+9=25

this can be simplified to be:

x^2+4x+y^2+6y=25-13

x^2+y^2+4x+6y=12

Answer:

[tex]\sf\longrightarrow \boxed{\sf x^2+y^2-4x-6y-12=0}[/tex]

Step-by-step explanation:

Here we are given the radius of circle as 5cm and the centre of the circle is (2,3) . We need to find the equation of the circle. Here we can yse the Standard equation of circle to find the equation .

Standard equation of circle :-

[tex]\sf\implies \green{ (x - h )^2+(y-k)^2 = r^2 }[/tex]

Substitute the respective values ,

[tex]\sf\longrightarrow ( x - 2 )^2 + ( y - 3)^2 = 5^2 [/tex]

Simplify the whole square ,

[tex]\sf\longrightarrow x^2 + 4 -4x + y^2+9-6y = 25[/tex]

Rearrange and add the constants ,

[tex]\sf\longrightarrow x^2 + y^2 -4x -6y +13 = 25 [/tex]

Subtract 25 on both sides ,

[tex]\sf\longrightarrow x^2 +y^2-4x-6y+13-25=0[/tex]

Simplify ,

[tex]\sf\longrightarrow \boxed{\blue{\sf x^2+y^2-4x-6y-12=0}}[/tex]