If the coordinates of A and B are (-3, a) and (1, a+4) respectively and the mid point of AB is (-1, 1),
then find the value of 'a'.​

Given:

The sum of three numbers is 212 .

The ratio of the first to the second is 13:16 and that of the second to the third is 2:3.

To find:

The unknown numbers.

Solution:

We have,

First : Second = 13:16

Second: Third = 2:3

We need to combine these ratios, to get a single ratio for all three numbers.

Second: Third = 2×8:3×8 = 16:24

Now,

First: Second: Third = 13:16:24

Let the first, second and third numbers are 13x, 16x and 24x respectively.

[tex]13x+16x+24x=212[/tex]

[tex]53x=212[/tex]

[tex]x=\dfrac{212}{53}[/tex]

[tex]x=4[/tex]

So, the numbers are,

[tex]First=13x[/tex]

[tex]First=13(4)[/tex]

[tex]First=52[/tex]

Similarly,

[tex]Second=16x[/tex]

[tex]Second=16(4)[/tex]

[tex]Second=64[/tex]

And,

[tex]Third=24x[/tex]

[tex]Third=24(4)[/tex]

[tex]Third=96[/tex]

Therefore, the three unknown numbers are 52, 64, 96.

Answer:

j = 25+3

im pretty sure :)

Step-by-step explanation:

Answer:

j=25+3 which means j=28

Answer:

120 in^2

Step-by-step explanation:

Answer:

y=x+6

Step-by-step explanation:

y intercept = 6

gradient = rise/run = 1/1

y = x +6

Answer:

Find x,If x + 15 = 30.

Step-by-step explanation:

Answer:

59.5 feet

Step-by-step explanation:

Set up a proportion

Tree 1

17 feet tall

10 feet shadow

Tree 2

35 feet tall

x feet shadow

17/10= 35/x

(17)(35)= (10)(x)

595= 10x

/10    /10

59.5= x

The cast shadow of the second tree is 59.5 feet

Answer:

c. sin 8x + sin 2x

Step-by-step explanation:

1. Convert the product into sum or differences: 2 sin 5x cos 3x

Solution:

2 sin 5x cos 3x = sin (5x + 3x) + sin (5x -3x), [Since 2 sin A cos B = sin (A + B) + sin (A - B)]

= sin 8x + sin 2x

Answer:

Total possible outcomes = 12

{A1 ; A2 ; A3 ; B1; B2;B3;C1;C2;C3;D1;D2;D3}

Step-by-step explanation:

Bag 1 = { 1, 2, 3}

Bag 2 = {A, B, C, D}

Sample space :

Size of bag A * size of bag B

3 * 4

= 12

Answer:

40, 42 and 44

Step-by-step explanation:

Mark these even consecutive integers as (2n-2), 2n and (2n+2)

Note that since they are integers, n > 0 and 2n is always even

Writing the equation

(2n-2) * 2n = 38 * (2n+2) + 8

// divide both sides by 2

(2n-2) * n = 19 * (2n+2) + 4

[tex]2n^{2}[/tex] - 2n = 38n + 38 + 4

[tex]2n^{2}[/tex] - 2n - 38n - 38 - 4 = 0

[tex]2n^{2}[/tex] - 40n - 42 = 0

// divide both sides by 2

[tex]n^{2}[/tex] - 20n - 21 = 0

// rewrite the equation

[tex]n^{2}[/tex] + n - 21n - 21 = 0

n * (n+1) - 21n - 21 = 0

n * (n+1) - 21 * (n+1) = 0

(n+1) * (n-21) = 0

// separate the two possible cases

n + 1 = 0 and n - 21 = 0

n = -1              n = 21

Note that here n has to be an integer, so case n = -1 can't be a solution. Therefore we use n = 21

Calculating the consecutive even integers

2n - 2 = 2 * 21 - 2 = 40

2n = 2 * 21 = 42

2n + 2 = 2 * 21 + 2 = 44

The slope of the table is 2

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line. The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

here, we have,

to determine the slope:

From the table, we have the following points:

(x,y) = (0, 4) and (1,7)

The slope is then calculated as:

m = (y2 - y1)/(x2 - x1)

Substitute known values

m = (7 - 4)/(1 - 0)

Evaluate the differences

m = 3/1

Divide

m = 2

Hence, the slope of the table is 2

Read more about slopes at:

brainly.com/question/3493733

#SPJ7

Answer:

Step-by-step explanation:

Vertices of the given quadrilateral are A(-4, 3), B(2, -1), C(2, -5) and D(-4, -1)

Since, slope of a line passing through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by,

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

Slope of AB = [tex]\frac{3+1}{-4-2}[/tex]

                    = [tex]-\frac{2}{3}[/tex]

Slope of AD = [tex]\frac{3+1}{-4+4}[/tex]

                    = Not defined (Parallel to y-axis)

Slope of DC = [tex]\frac{-5+1}{2+4}[/tex]

                     = [tex]-\frac{2}{3}[/tex]

Slope of BC = [tex]\frac{-1+5}{2-2}[/tex]

                   = Not defined (Parallel to y-axis)

Slope of AB = slope of DC = [tex]-\frac{2}{3}[/tex]

Slope of BC = slope of AD = Not defined (parallel to y-axis)

As per property of a parallelogram,

"Opposite sides of a parallelogram are parallel and equal in measure"                  

Therefore, ABCD is a parallelogram.

Answer:

y

=

x

−

1

4

x

+

7

y

=

5

y

=

2

x

−

5

Step-by-step explanation:

sorry if u cant read my thing is being weird

Answer:

(8, -4)

Step-by-step explanation:

When you cancel the terms out by subtracting the second equation by the first, you get 4y = -16, which means y = -4. Then you can plug it back in to any eauation. For example, we can do the second one, 4x + 6(-4) = 8. This sumplifies to 4x + -24 = 8. Add 24 to both sides which gets us 4x = 32, and then you get x which is 8. The ordered pair is (8, -4). Hope this helps! (this is my first answer)

Answer:

the answer is b

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Lets go one step at a time

That would already knock out option A because, in 10 minutes it says Keith only traveled 3 miles.

option C would be incorrect because, he was stationary and that doesn't mean that Keith should be wiggling on the graph.

So it is between B and D. They both have the time aspect however, B travels farther and D travels backwards.

Therefore, your only possible answer choice would be B.

Answer:

The answer is D im pretty sure

Answer:

A. The point represents the turning point of the graph

B. The cost of making 4,000 bicycles is $265,000

The slope of the cost function, F(x) = 1.25 + 0.35·x, is less than the average slope of the graph of the total profit for sales

C. The company should plan on making fewer than 4,000 bicycles, to maximize profit

Step-by-step explanation:

A. The point represents the turning point after which increase in the x-coordinate values leads to a decrease in the y-coordinate values

B. The cost function is presented as follows;

F(x) = 1.25 + 0.35·x

Where;

F(x) = The cost in hundreds of thousands of dollars of making 'x' (in thousands) bicycles

x = The number of bicycles made in thousands

The cost of making 4,000 bicycles is given by plugging in x = 4(thousand) in  F(x) = 1.25 + 0.35·x, as follows;

F(x) = 1.25 + 0.35·x

∴ F(4) = 1.25 + 0.35 × 4 = 2.65

Therefore, the cost of making 4,000 bicycles = 2.65 × $100,000 = $265,000

The slope of the cost function, F(x) = 1.25 + 0.35·x, is given by the coefficient of 'x' which is 0.35

The average slope of the graph of the profit function is ((3.5 - 0)/(4 - 0)) = 0.875

The slope of the cost function is less than the average slope of the graph of the profit function taken from the origin to the maximum point of the graph

C. When the company produces 5,500 bicycles, x = 5.5, we have;

F(5.5) = 1.25 + 0.35 × 5.5 = 3.175

The cost is 3.75 × $100,000 = $375,000 and the profit from te graph is $300,000

Therefore, the cost of making the 5,500 bicycles is more than the profit made in sales

The company should plan on making fewer than 4,000 bicycles, to reduce cost of producing more bicycles and to increase profit per unit of bicycle sold

Let x be number of $10 dollar bills

Let y be number of $5 dollar bills

Let z be number of $1 dollar bills

From the question, we can come up with three equations (so we can find the values of x, y & z) :

The first equation comes from finding the total money Elizabeth has, which is $101.

The second equation comes from value of y (number of $5 bills) is more than value of x (number of $10 bills) by 5 dollars.

The third equation comes from the value of z (number of $1 bills) being 4 times more than the value of x (number of $10 bills).

Now, we will begin to find the value of x, y & z.

From the first equation,

10x + 5y + z = 101

Substitute the third equation (z = 4x) into z:

10x + 5y + 4x = 101

Simplify this and you get,

14x + 5y = 101

Now, we use the second equation. The second equation is y - x = 5. If we try to make y as the subject, it becomes y = 5 + x.

Now, substitute this into the value of y of the last working we did:

14x + 5(5+x) = 101

Simplify that and it becomes:

x = 4

Then, substitute this value of x into the second and third equations to find y and z.

y - x = 5

y - 4 = 5

y = 9

z = 4x

z = 4(4)

z = 16

Finally, let's check these answers by substituting them into the first equation to try and see if the total value is really $101.

10x + 5y + z = 10(4) + 5(9) + 16

10x + 5y + z = 40 + 45 + 16

10x + 5y + z = 101

Thus, our answers are correct. Elizabeth has FOUR $10 bills, NINE $5 bills and SIXTEEN $1 bills.

Answer:

Thus, our answers are correct. Elizabeth has FOUR $10 bills, NINE $5 bills and SIXTEEN $1 bills.

Step-by-step explanation:

;)

Step-by-step explanation:

[tex] \tt{(4 {x}^{3} + 2x + 6) + (2 {x}^{3} - {x}^{2} + 2) }[/tex]

Remove the unnecessary parentheses.

⟶ [tex] \tt{4 {x}^{3} + 2x + 6 + 2 {x}^{3} - {x}^{2} + 2}[/tex]

Combine like terms. Like terms are those which have the same base. Note that only coefficients of like terms can be added or subtracted.

⟶ [tex] \tt{4 {x}^{3} + 2 {x}^{3} + 2x + 6 + 2 - {x}^{2} }[/tex]

⟶ [tex] \tt{6 {x}^{3} + 2 x + 8 - {x}}^{2} [/tex]

As we are asked to write the answer in standard form , we have to rewrite the expression 6x³ +2x + 8 - x² in such a way that the power of the variables goes from highest to lowest.

[tex] \red{ \boxed{ \boxed{ \tt{Our \: final \: answer : \boxed{ \tt{6 {x}^{3} - {x}^{2} + 2x + 8}}}}}}[/tex]

Hope I helped ! ♡

Have a wonderful day / night ! ツ

▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁

Answer:

Step-by-step explanation:

I think x=39°

Answer:

i dunno

Step-by-step explanation:

Answer:

mark brainlist please

Step-by-step explanation

-2x+7y=16 x=-8,0 y=0,16/7

8x-6y=24 y=(3,0) x=(0,-4)

Answer:

185

Step-by-step explanation:

14.8 / 0.08 = 185

Best of Luck!

Answer:

185

Step-by-step explanation:

next time you get a question like that use symbolab

Answer:

$15

Step-by-step explanation:

First you move the decimal in the percent 2 times to the left and get .25. And then you multiply that by 60 and get 15.

Answer:

Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.

15

Step-by-step explanation:

Hope it is helpful....

Answer:

The Square root of 225 is 15

Answer:

Caleb bought groceries and paid \$1.60$1.60dollar sign, 1, point, 60 in sales tax. The sales tax rate is 2.5\%2.5%2, point, 5, percent. What was the price of Caleb's groceries, before tax

Step-by-step explanation:

This is all I know~

Hope it helps!

Good luck with your work!!~

Answer:

(1,-3)

Step-by-step explanation:

Step-by-step explanation:

1(

m<1= 62°

2)

m<1=90°

3)

180-70-65=45

m<1= 45°

4)

180-90-30=60

m<1= 60°

Step-by-step explanation:

The location of A is 3.2

The location of A' is 6.4

A represent pre image A' represent the new image.

The scale factor of A to A' is 2 since 3.2 x 2 =6.4

Since you didnt provide B coordinates, just multiply 2 by the B coordinate to find the B prime coordinate.

Answer: A.)The scale factor is 0.8 and the coordinates of point B prime are (–3.2, –4.8).

Step-by-step explanation: i hope this helps im sorry if this didnt help

Answer:

the answer is 5 hope this could help

The answer is -13 and -15.

Answer:

8

Step-by-step explanation:

x is 8

[tex]8x + 3y = 70[/tex]

with given condition where y = 2.

Therefore, substitute the value of y in the equation.

[tex]8x + 3(2) = 70 \\ 8x + 6 = 70[/tex]

[tex]8x = 70 - 6 \\ 8x = 64 \\ x = \frac{64}{8} \longrightarrow \frac{8}{1} \\ x = 8[/tex]

[tex]8x + 3y = 70 \\ 8(8) + 3(2) = 70 \\ 64 + 6 = 70 \\ 70 = 70[/tex]

Hence, the equation is true for x = 8 and y = 2.

[tex] \large{x = 8}[/tex]