There are 33 times as many boys as girls in a room. If 4 boys and 4 girls leave the room, then there will be 5 times as many boys as girls in the room. In total, how many boys and girls were in the room originally

Answer:

Step-by-step explanation:

Apply the slope formula to be sure. The slope formula is

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

Filling in with our coordinates gives us:

[tex]m=\frac{-2-10}{-2-4}=\frac{-12}{-6}=2[/tex]

The slope is 2. If you don't want to use the slope formula you could just look at the line and pick 2 points the line goes through and use a slope triangle, but that's a bit more difficult to explain without the benefit of being there to point out the idiosyncrasies of it.

Answer:

is there any more details?

Step-by-step explanation:

Answer:

any more details please?

Answer:

x = 1

y = 6

Step-by-step explanation:

y = 6x   --------------(I)

7x - 8y = -41   ------------(II)

Substitute y =6x in equation (II)

7x - 8*(6x) = -41

7x - 48x    = -41   {Combine like terms}

     -41x = -41

          x = -41/-41

x = 1

Plug in x = 1 in equation (I)

y = 6*1

y = 6

Answer:

consecutive interior angles equal 180 not equal to each other

Step-by-step explanation:

Answer:

6x− 1 0 = 4 + 4 0

6x-10=4x+40

6x−10=4x+40

Solve

1

Add  

1 0

10

10

to both sides of the equation

6 − 1 0 = 4 + 4 0

6x-10=4x+40

6x−10=4x+40

6 − 1 0 + 1 0 = 4 + 4 0 + 1 0

6x-10+{\color{#c92786}{10}}=4x+40+{\color{#c92786}{10}}

6x−10+10=4x+40+10

2

Simplify

Add the numbers

Add the numbers

6 = 4 + 5 0

6x=4x+50

6x=4x+50

3

Subtract  

4 4x 4x

from both sides of the equation

6 = 4 + 5 0

6x=4x+50

6x=4x+50

6 − 4 = 4 + 5 0 − 4

6x{\color{#c92786}{-4x}}=4x+50{\color{#c92786}{-4x}}

6x−4x=4x+50−4x

4

Simplify

Combine like terms

Combine like terms

2x=50

5

Divide both sides of the equation by the same term

2x=50

2 /2 = 5 0 /2

\frac{2x}{{\color{#c92786}{2}}}=\frac{50}{{\color{#c92786}{2}}}

22x​=250​

6

Simplify

Cancel terms that are in both the numerator and denominator

Divide the numbers

= 2 5

Solution

= 2 5

Step-by-step explanation:

I'm sorry my stuff is coming off weird

Answer: 2 minutes

Step-by-step explanation:

1/8 multiplied by 4 twice

Answer:

3

Step-by-step explanation:

If you multiply 3/4 and 4 days together you will get 3 so the answer is 3

Answer:

The coordinates are (-5,5)

Step-by-step explanation:

We use the internal division formula here

(x,y) = (nx1 + mx2)/m+ n , (ny1 + my2)/(m + n)

where m = 1

n = 4

(x1,y1) = (-8,8)

(x2,y2) = (7,-7)

Substituting these values, we have

(x,y) = (4(-8) + 1(7))/5 , (4(8)+ 1(-7)/5

(x,y) = (-25/5, 25/5)

(x,y) = (-5,5)

Answer:

6

Step-by-step explanation:

Answer:

y = -6x - 39

Step-by-step explanation:

A parallel line will have the same slope so m= -6, but it will have different points.

So we have y= -6x + b and the points are (8,9)

Substitute that in

9 = -6*-8 + b

9 = 48 + b

subtract 48 on both sides

9-48 = 48 - 48 + b

-39 = b

so equation is

y = -6x -39

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Answer:

y=-6x+9

0=-6x+9

6x=9

x=9/3

x=3/2

Answer:

Fraction: 23/100

Decimal: 0.23

Percent: 23%

Step-by-step explanation:

Hope this helps!

Answer:

y=-1x+5.

Step-by-step explanation:

Replace m with -1, which is the slope you gave, and

replace b with 5, the y-intercept you gave,

in the equation y=mx+b.

y=-1x+5

Answer:

equation is then y= -5x + 9

Step-by-step explanation:

First the equation of a line is y=mx+b

if parallel the slope is the same

so m= -5

y= -5x +b

plug in point (1,4) into equation to find by

4= -5(1) + b

b=9

equation is then y= -5x + 9

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Answer:

There are 18 dimes in the jar

Step-by-step explanation:

Let

x = number of dimes in the jar

y = number of quarters in the jar

Total = $3.80

There are ten less quarters than dimes

y = x - 10

0.1x + 0.25y = 3.80

0.1x + 0.25(x - 10) = 3.80

0.1x + 0.25x - 2.5 = 3.80

0.35x = 3.80 + 2.5

0.35x = 6.30

x = 6.30/0.35

x = 18

Answer:

1) £2 = €2.32

£5 = €5.80

£50 = €58

2) The graph will be a straight line

3) (0, 0)

4) Label the independent variable, £ on the x-axis and dependent variable € on the y-axis

Step-by-step explanation:

1) The given conversion factors is £1 = €1.16

Therefore;

£2 = 2 × €1.16 = €2.32

£2 = €2.32

£5 = 5 × €1.16 = €5.80

£5 = €5.80

£50 = 50 × €1.16 = €58

£50 = €58

2) The shape of the plot of the directly proportional currencies graph will be a straight line

3) Given that the £ is directly proportional to the € and that the value of the € can be found directly by multiplying the amount in £ by 1.16, without the addition of a constant, the graph crosses the axes at the origin (0, 0)

4) The y-axes which is the dependent variable should be labelled €, while the x-axis which is the independent variable should be labelled £

Answer:(x-1)^2 -96

Step-by-step explanation:

Not sure if this is correct but I included the workings out

Answer:

D

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

For a pentagon with n = 5 , then

sum = 180° × 3 = 540° , thus

x = 540° ÷ 5 = 108

For an octagon with n = 8, then

sum = 180° × 6 = 1080° , thus

y = 1080° ÷ 8 = 135

Thus

x + y = 108 + 135 = 243 → D

Answer:

The coordinates of the new vertices are:

K'(4,4), L'(0,- 2), and M'(-6,4).

Step-by-step explanation:

In order to dilate a shape by 2, you can simply multiply the coordinates of the orignal triangle each by 2 to find the new coordinates of the new vertices.

K(2,2), L(0,- 1), and M(-3,2)

K'(2*2,2*2), L'(0*2,- 1*2), and M'(-3*2,2*2).

Now become...

K'(4,4), L'(0,- 2), and M'(-6,4).

You can now graph ∆K'L'M' using these coordinates.

Answer:

6 10

Step-by-step explanation:

Answer:

6, 10

Step-by-step explanation:

The first point is on 6, and ending at 10.

Answer:

There is no values to make the equation true. Please check the equation.

Step-by-step explanation:

Answer:

19

Step-by-step explanation

Answer:

30%

Step-by-step explanation:

Answer:

Open

Step-by-step explanation:

The <, > signs will have an open circle and the greater than or equal to or less than or equal to will be a be a closed circle.

Hope this helps and I hope u have an Amazing day!!

Answer:

(A) Yes, x = 2 is a zero of the polynomial.

The quotient is x² + 26x + 160 and the remainder is 0

Step-by-step explanation:

Given;

p(x) = x³ + 24x² + 108x - 320

Using remainder theorem to test if x = 2 is a zero of the given function

p(2) = (2)³ + 24(2)² + 108(2) - 320

       = 8 + 96 + 216 - 320

        = 0

Thus, x = 2 is zero of the function

(ii) to get the quotient and the remainder of the given function, divide the function by 'x - 2'

                     x² + 26x + 160

     x - 2    √ x³ + 24x² + 108x - 320

                 -  (x³ -  2x²)                      

                     0   + 26x² + 108x - 320

                          - (26x²  - 52x)                  

                               0      + 160x - 320

                                        -  (160x - 320)        

                                              0     +   0  

The quotient is x² + 26x + 160

The remainder is 0                      

Thus, the correct option is A.

Yes, x = 2 is a zero of the polynomial.

The quotient is x² + 26x + 160 and the remainder is 0            

Answer:

It would be $1,590.75 more if it were compounded quarterly than monthly.

Step-by-step explanation:

In order to solve this problem, you need to understand the Compound Interest Formula.

[tex]A= P(1 + \frac{r}{n})^t[/tex]

Where A is the Amount, P is the principal or the initial amount received, r is the rate, n is the number of times (per year) it is compounded, and t is the time in years.

The question gives you all of the information to input into the formula. You have the principal, $5000, the rate, 6% (.06), it's being compounded monthly (12 & 4 per year), and we have the years, 25.

We need to compare the two formulas where the only thing that will change is n. n will be 12 (compounded monthly) and 4 (compounded quarterly).

Compounded monthly

[tex]A=5000(1+\frac{0.06}{12})^{25}\\A = 5663.98[/tex]

Compounded monthly, the account would have $5,663.98 or $5,664 (simplified).

Compounded quarterly

[tex]A=5000(1+\frac{0.06}{4})^{25}\\A =7254.73[/tex]

Compounded quarterly, the account would have $7,254.73 or $7,255 (simplified).

Now, we need to find the difference between monthly and quarterly.

7254.73 - 5663.98 = $1,590.75

It would be $1,590.75 more if it were compounded quarterly than monthly.

Answer:

square is the answer for this question

im too

good luck

im lucky cat

Answer: 1/2x + 1/3

Step-by-step explanation:

Given:

1/4(x) + 3/4(x) - 1/2(x) + 1 - 2/3

Step 1: Combine like terms

1/4(x) and 3/4(x) have a common denominator of 4.  This means that you can add them together.

1/4(x) + 3/4(x) = 4/4(x) = x

Step 2: Find the common denominator of x in step 1 and combine like terms  

x - 1/2(x) = 2/2(x) - 1/2(x)

Now that we have the common denominator of x, we can combine like terms.  Its the same as adding or subtracting fractions without a variable.  In this case, you must subtract 1/2(x) from 2/2(x).

2/2(x) - 1/2(x) = 1/2(x)

Step 3: Find the common denominator of the constants and combine like terms

1 - 2/3 = 3/3 - 2/3

Now combine like terms.  Simply subtract 2/3 from 3/3.

3/3 - 2/3 = 1/3

Step 4: Write the simplified equation

1/2(x) + 1/3

This is the answer