use the substitution method to solve the system of equations

3x+2y=13

y=x-1

Answer:

4x² + 3x + 5

Step-by-step explanation:

Given:

- 4x² + 2x - 5(1 + x)

Open parenthesis

= - 4x² + 2x - 5 - 5x

= - 4x² + 2x - 5x - 5

= - 4x² - 3x - 5

Multiply through by -1

= - 1( - 4x² - 3x - 5)

= 4x² + 3x + 5

Write

4 in the first box

3 in the second box

5 in the third box

Answer:

Enlargement

k =[tex]\frac{18}{4}[/tex] =  [tex]\frac{9}{2}[/tex]

Step-by-step explanation:

k = [tex]\frac{new}{old}[/tex]

If k > 1 then its an enlargement.

If k < 1 then its a reduction

Answer:

y=2x

Step-by-step explanation:

Hi there!

Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when x is 0).

1) Determine the slope (m)

The slope is the rate of change, or the number of units the line moves up divided by the number of units the line moves to the right.

Looking at the graph, we can see that for every 1 space the line travels to the right, the line travels 2 spaces up. This makes the slope of the line 2. Plug this into [tex]y=mx+b[/tex]:

[tex]y=2x+b[/tex]

2) Determine the y-intercept (b)

When x=0 on the graph, y=0. Therefore, the y-intercept is 0. Plug this into [tex]y=2x+b[/tex]:

[tex]y=2x+0\\y=2x[/tex]

I hope this helps!

Answer:

[tex]2c+2b+17[/tex]

Step-by-step explanation:

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

Given:

[tex]2c-3b+6+7b-2b+11[/tex]

---------->>>>

Collect like terms.

[tex]2c+(-3b+7b-2b)+(6+11)[/tex]

---------->>>>

Simplify

[tex]2c+2b+17[/tex]

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

Hope this is helpful.

Answer:

2c-2b+17 if using algebra

Step-by-step explanation:

firstly group like terms 2c+(-3b)+7b-2b+6+11

2c-2b+17

9514 1404 393

Answer:

  p = 30

  angles 30°, 45°; exterior: 75°

Step-by-step explanation:

The exterior angle is equal to the sum of the remote interior angle:

  3p -15 = p + (p +15)

  p = 30 . . . . . . . . . . . . . add 15-2p

The interior angles are 30°, 45°; the exterior angle is 75°.

Answer:

Step-by-step explanation:

This is a 30°-60°-90° right triangle.

AC is hypotenuse, AB is opposite side to 30° angle.

We know that in such a triangle the side opposite to 30° angle is half the hypotenuse.

So we have:

Answer:

260 square centimeters

Step-by-step explanation:

The formula for the area of a parallelogram is:

b x h

Where the base (b) is multiplied by the height (h) perpendicular to it.

The base here is 20 cm

The height perpendicular to the base is 13 cm

20 x 13 = 260

Or you can decompose and rearrange it into a rectangle. You will get 20 cm as the length and 13 cm as the width. The answer will be just the same!

Hope this helps!

Answer: 260 cm²

Step-by-step explanation: A parallelogram is a

quadrilateral with two pairs of parallel sides.

The formula for the area of a parallelogram is A = bh.

Since the base of the parallelogram is 20 cm and the height

of the parallelogram is 13 cm, we can plug this information into the formula

to get (20 cm)(13 cm) which gives us 260 cm².

So the area of the parallelogram shown is 260 cm².

Answer:

They should walk on a bearing of 59.4 degrees

Step-by-step explanation:

Given

[tex]South = 4.2km[/tex]

[tex]West = 7.1km[/tex]

Required

The bearing back to the base

The given question is illustrated with the attached image.

To do this, we simply calculate the measure of angle a using:

[tex]\tan(a) = \frac{Opposite}{Adjacent}[/tex]

[tex]\tan(a) = \frac{7.1}{4,2}[/tex]

[tex]\tan(a) = 1.6905[/tex]

Take arctan of both sides

[tex]a = \tan^{-1}(1.6905)[/tex]

[tex]a = 59.4^o[/tex]

The bearing that the scout should work is N59.4W for the shortest distance

Trigonometric ratio is used to show the relationship between the sides and angles of a right angled triangle.

Let  A represent the angle that the scouts walk

tan∠A = 4.2/7.1

A = 30.6°

The bearing that the scout should work is N59.4W (90 - 30.6) for the shortest distance

Find out more on Trigonometric ratio at: https://brainly.com/question/4326804

Answer:

length divided by breadth divided by  height

pls add me as brainliest

Solution:

20 - 1 1 = 9 cm

We can divide figure in 2 parts

rectangle = 14 cmx 11 cm

square = 9 cm x 9  cm

Area of rectangle = 14 * 11 = 154 cm²

Area of square = 9 * 9 = 81 cm²

Total area = 154 + 81

= 235 cm²

Answer:

The single equation is [tex]y = 0[/tex]

Step-by-step explanation:

We are given the following system of equations:

[tex]x + y = 0[/tex]

[tex]x + 2y = 0[/tex]

From the first equation:

[tex]x = -y[/tex]

Replacing in the second equation:

[tex]-y + 2y = 0[/tex]

[tex]y = 0[/tex]

The single equation is [tex]y = 0[/tex]

Answer:

=x^2 +4x+11

Step-by-step explanation:

f(x) = x^2 + 7,

Replace x with x+2

f(x+2) = (x+2)^2 + 7

         = (x+2)(x+2) +7

     FOIL

     = x^2 +2x+2x+4 +7

Combine like terms

    =x^2 +4x+11

Answer:

[tex]f(x+2)=x^2+4x+11[/tex]

Step-by-step explanation:

In [tex]f(x)=x^2+7[/tex], for all values of [tex]x[/tex], we substitute [tex]x[/tex] (what is in the parentheses) into [tex]x^2+7[/tex] to output a [tex]y[/tex] value.

In [tex]f(x+2)[/tex], the term [tex](x+2)[/tex] is in the parentheses. Therefore, substitute [tex](x+2)[/tex] for [tex]x[/tex] in [tex]x^2+7[/tex] to find [tex]f(x+2)[/tex]:

[tex]f(x+2)=(x+2)^2+7[/tex]

Expand using [tex](a+b)^2=a^2+2ab+b^2[/tex],

[tex]f(x+2)=x^2+4x+4+7[/tex]

Combine like terms:

[tex]\boxed{f(x+2)=x^2+4x+11}[/tex]

Answer:  A) -0.5

Explanation:

Each tickmark is an increment of 30. Start at 270 and move 1 tickmark over to get to 270+30 = 300. Then another tickmark to the right gets us to 330.

Then from here, head straight down until you get to the curve. You should arrive at the point (330, -0.5)

So q = 330 pairs up with y = -0.5

Answer: The answer is 3.60 dollars.

Step-by-step explanation:

1 bottle = 10 cents

12 bottles = 120 cents

100 cents = 1 dollar

1 cent = 1/100

120 = 1/100 * 120 = 1.2 dollars

now

1 aluminium can = 5 cents

48 cans = 5*48 = 240 cents

240 cents = 1/100 * 240 = 2.4 dollars

so total = (1.2+2.4) dollars

= 3.6 dollars

Answer:

so what we have to do first is multiply 9*10

which is 90 now we divide by two to get 45

now we multiply 45 by 20 to get

900

Hope This Helps!!!

Hi there!  

»»————-　★　————-««

I believe your answer is:  

[tex]\huge x=-6[/tex]

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\boxed{\text{Solving for 'x'...}}\\\\-8x-4(x-4)=88\\-------------\\\rightarrow -8x-4x+16=88\\\\\rightarrow -12x + 16 = 88\\\\\rightarrow -12x + 16 - 16 = 88 - 16\\\\\rightarrow -12x = 72\\\\\rightarrow \frac{-12x=72}{12}\\\\\rightarrow \boxed{x=-6}[/tex]

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer: x = -6

Step-by-step explanation: Start by changing the - 4 to plus a negative 4 so that you know you're distributing a -4 through the parentheses.

So we have -8x - 4x + 16 = 88.

Simplifying the left side further gives us -12x + 16 = 88.

Now subtract 16 from both sides to get -12x = 72.

From here it should be easy to find the x = -6.

Answer:

991

Step-by-step explanation:

We are looking for a number that is one more than a multiple of 9(denoted by the 9k) and is a three digit number. We can start by looking for 3-digit number divisible by 9 which are close to 1,000, since that is the next number larger than the largest three-digit number. We can tell that 999 is divisible by 9 because when divided it does not leave a remainder(you can also figure this out with divisibility tricks). We add one to get 1,000. This is not a three-digit number,  so we need to look for a smaller multiple of 9. Subtracting 9 from 999, we get the next largest multiple of 9. We can add 1, and this time, the number, 991, is a three digit number, and the largest that can be in the form 9k + 1.

Answer:

Step-by-step explanation:

Vertices of ΔABC are,

A(-3, 6), B(2, 1) and C(9, 5)

Use the formula to get the distance between two points [tex](x_1,y_1)[/tex] and[tex](x_2,y_2)[/tex],

Distance = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

By using the formula,

AB = [tex]\sqrt{(1-6)^2+(2+3)^2}[/tex]

     = [tex]\sqrt{50}[/tex] units

BC = [tex]\sqrt{(5-1)^2+(9-2)^2}[/tex]

     = [tex]\sqrt{65}[/tex] units

AC = [tex]\sqrt{(6-5)^2+(-3-9)^2}[/tex]

     = [tex]\sqrt{145}[/tex]

Use cosine rule to find the measure of ∠ABC.

AC² = AB² + BC²- 2(AB)(BC)cos(B)

[tex](\sqrt{145})^2=(\sqrt{50})^2+(\sqrt{65})^2-2(\sqrt{50})(\sqrt{65})\text{cosB}[/tex]

145 = 50 + 65 - 2(√3250)cosB

cos(B) = [tex]-(\frac{145-115}{2\sqrt{3250}})[/tex]

          = -0.26312

B = [tex]\text{cos}^{-1}(-0.26312)[/tex]

B = 105.26°

Answer:

12/37

Step-by-step explanation:

We know ,

=> sin B = p/h

=> sin B = 12/ 37

Answer:

Step-by-step explanation:

[tex]Sin \ B = \frac{opposite \ side }{hypotenuse}\\\\Sin \ B = \frac{35}{37}\\\\[/tex]

Answer:

58

Step-by-step explanation:

Hello :)

We know that :

30g of cornflakes ⇒ 2.5g of fat

320g of cornflakes ⇒ xg of fat

x = 320 * 2.5 ÷ 30 ≈ 26.7 g of flat

Have a nice day!

Answer:

13.86

Step-by-step explanation:

In ∆ ABC ,

Answer: B) [tex]f\left(x\right)=\frac{1}{3}\left(-x-1\right)^{5}[/tex]

Step-by-step explanation:

When graphing x5 the parent function and plugging in the equation for B the only equation that fits the criteria of

*shifting left 1 unit

*vertically compressed by 1/3

*reflect over the y-axis

So the answer is B

The function after the transformation is f ( x ) = ( 1/3 ) ( -x + 1 )⁵

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Left shift by c units: y=f(x+c) (same output, but c units earlier)

Right shift by c units: y=f(x-c)(same output, but c units late)

Vertical shift:

Up by d units: y = f(x) + d

Down by d units: y = f(x) - d

Stretching:

Vertical stretch by a factor k: y = k × f(x)

Horizontal stretch by a factor k: y = f(x/k)

Given data ,

Let the function be represented as f ( x )

Now , the value of f ( x ) is

f ( x ) = x⁵

On reflecting over the y axis , we get

f ( x ) = ( -x )⁵

On vertically compressing by a factor of ( 1/3 ) , we get

f ( x ) = ( 1/3 ) ( -x )⁵

And , shifting 1 unit to the left , we get

f ( x ) = ( 1/3 ) ( -x + 1 )⁵

Hence , the transformed function is f ( x ) = ( 1/3 ) ( -x + 1 )⁵

To learn more about transformation of functions click :

https://brainly.com/question/26896273

#SPJ7

Answer:

[tex]A(0,3)(x_1,y_2)[/tex]

[tex]B(2,-5)(x_2,y_2)[/tex]

[tex]slope(m)=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\longrightarrow[/tex] [tex]\frac{-5-3}{2-0}[/tex]

[tex]\longrightarrow \frac{8}{2}[/tex]

[tex]\longrightarrow -4[/tex]

[tex]y-y_2=m(x-x_2)[/tex]

[tex]\longrightarrow y-(-5)=-4(x-2)[/tex]

[tex]\longrightarrow y+5=-4(x-2)[/tex]

[tex]ANSWER:B[/tex]

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

hope it helps...

have a great day!!

Answer:

the answer is 1

Step-by-step explanation:

(√4 / √6) + (√6 / √4)

(2 / 2√3) + (2√3 / 2)

√3 / √3

= 1

If a student receives a score of 80, how many questions did this student answer ... (5). Let x = the first number, and y = the second number ... If John only has 25 coins in his pocket, how many of the coins are quarters?

Answer:

8 and 10

Step-by-step explanation:

Given

[tex]\frac{1}{x}[/tex] + [tex]\frac{1}{x+2}[/tex] = [tex]\frac{9}{40}[/tex] ← combine the fractions on the left side

[tex]\frac{x+2+x}{x(x+2)}[/tex] = [tex]\frac{9}{40}[/tex]

[tex]\frac{2x+2}{x^2+2x}[/tex] = [tex]\frac{9}{40}[/tex] ( cross- multiply )

9(x² + 2x) = 40(2x + 2) ← distribute both sides

9x² + 18x = 80x + 80 ( subtract 80x + 80 from both sides )

9x² - 62x - 80 = 0

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 9 × - 80 = - 720 and sum = - 62

The factors are - 72 and + 10

Use these factors to split the x- term

9x² - 72x + 10x - 80 = 0 ( factor the first/second and third/fourth terms )

9x(x - 8) + 10(x - 8) = 0 ← factor out (x - 8) from each term

(x - 8)(9x + 10) = 0

Equate each factor to zero and solve for x

x - 8 = 0 ⇒ x = 8

9x + 10 = 0 ⇒ 9x = - 10 ⇒ x = - [tex]\frac{10}{9}[/tex]

x is an integer , then x = 8 and x + 2 = 8 + 2 = 10

The integers are 8 and 10

Answers: Integers are x=8, x=10.

Answer: D

Step-by-step explanation:

360° - 90° - 90° - 108° = 72°

(Sum of angles in a quadrilateral = 360°)

Answer:

5

Step-by-step explanation:

xy= 6

x= 2

x + y = ?

Plug in x=2 in the first equation:

2y=6

y=3

then plug x=2 and y=3 into the one you're solving for:

2+3=5

Hope that helps!