Solve each system of equations by substitution.
2x + 2y = 3 x - 4y = -1

Final answer:

The base area of a cylinder with a volume of 150 cubic cm and a height of 10 cm is 15 square centimeters, obtained by dividing the volume by the height.

Explanation:

To find the base area of a cylinder with a known volume and height, we can use the formula for the volume of a cylinder: V = πr²h, where V is the volume, r is the radius of the base, and h is the height. Since the volume (V) is 150 cubic cm and the height (h) is 10 cm, we can rearrange the formula to solve for the base area (A): A = V/h.

By substituting the given values into our rearranged formula, we get: A = 150 cm³ / 10 cm = 15 cm². Thus, the base area of the cylinder is 15 square centimeters.

Answer:

14x-19

Step-by-step explanation: Now can someone answer my question look at my page

Answer:

(3x+7)(x+3)

Step-by-step explanation:

Factors 3x^2+16x+21

3x^2+16x+21

=(3x+7)(x+3)

Answer:

[tex]3 {x}^{2} + 16x + 21 \\ 3 {x}^{2} + 9x + 7x + 21 \\ 3x(x + 3) + 7(x + 3) \\ = (3x + 7)(x + 3)[/tex]

Answer:

15-4 11 -4x

Step-by-step explanation:

Answer:

90 degree CW

Step-by-step explanation:

Since the point is at (24, -15) and was rotated to (-15, -24):

x, y  -->   y, -x

This is a 90 degree rotation clockwise

Answer:

5.8 and 7.4

Step-by-step explanation:

Answer:

For both graph I would choose the following points: 0°, 90°, 180°, 270° and 360°. I would connect the points (in both cases) with an smooth arc.

Step-by-step explanation:

x          sin(x)     cos(x)

0°        0            1

90°      1             0

180°     0           -1

270°    -1            0

360°    0            1

Answer:

816.4

Step-by-step explanation:

i multiplied 65,4 and 3.14 to get 816.4

Answer:

Picture #1: x=16 ; y=10

Picture #2: x=21 ; y=15

Picture #3: x=18

Step-by-step explanation:

Picture #1:

(8x-14)* and (5x+34)* are Alternate Exterior Angle so they are congruent. And (8x-14)* and (5y+16)* are supplementary so they equal 180*.

Picture #2:

(6x+7)* and (3x-16)* are supplementary so they equal 180*. And (6x+7)* and (11y-32)* are Vertical Angles so they are congruent.

Picture #3:

(7x-6)* and (4x-7)* are supplementary so they equal 180*.

From the given set of fractions, 13/16 is the largest fraction.

The given set of fractions are 13/16, 3/4, 7/10, and 5/8.

We need to check which of the given fractions is the largest.

To order fractions from least to greatest, start by finding the lowest common denominator for all of the fractions. Next, convert each of the fractions by dividing the lowest common denominator by the denominator and then multiplying the top and bottom of the fraction by your answer.

Now, the LCM of denominators of the fractions is as follows:

16, 4, 10 an 8 LCM= 2×2×2×2×5=80

Make the denominators equal to LCM.

That is, 65/80, 60/80, 56/80, and 50/80

Here, 65/80 is the largest, since the numerator is the greatest number.

Therefore, from the given set of fractions 13/16 is the largest fraction.

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Answer:

101

Step-by-step explanation:

Answer:

The correct answer is 71.

Answer:

15

Step-by-step explanation:

Square root of 5=√5

Square of the square root=(√5)^2

=5

Square root of 3=√3

Square of the square root=(√3)^2

=3

So (square root of 5)^2×(square root of 3)^2

5×3

15

Therefore the final answer is 15

Answer:

25 and 15

You can easily make a system of equations:

x + y = 40

x - y = 10

Solving for x on equation 2 gets x = 10 + y.

Plugging in this into the first equation, you get 10 + y + y = 40

Thus, 10 + 2y = 40

y = 15.

Plugging this back into either equation gets x = 25.

Answer:

(x+12)

Step-by-step explanation:

The middle number is 8 and the last number is -48.

Factoring means we want something like

(x+_)(x+_)

Which numbers go in the blanks?

We need two numbers that...

Add together to get 8

Multiply together to get -48

Can you think of the two numbers?

Try -4 and 12:

-4+12 = 8

-4*12 = -48

Fill in the blanks in

(x+_)(x+_)

with -4 and 12 to get...

(x-4)(x+12)

But, since (x-4) isn't an option, the answer would be (x+12)

Answer:

(x + 12)

Step-by-step explanation:  It's D on edg

Answer:

[tex]9\pi[/tex] sq. units.

Step-by-step explanation:

It is given that a circle has a sector with area [tex]\frac{1}{2}\pi[/tex] and central angle of [tex]\frac{1}{9}\pi[/tex] radians.  

We know that, the area of sector is

[tex]A=\dfrac{1}{2}r^2\theta[/tex]

where, r is radius and [tex]\theta[/tex] is central angle in radian.

Substitute the values of A and [tex]\theta[/tex].

[tex]\dfrac{1}{2}\pi=\dfrac{1}{2}r^2(\dfrac{1}{9}\pi)[/tex]

[tex]1=r^2(\dfrac{1}{9})[/tex]

[tex]9=r^2[/tex]

[tex]3=r[/tex]

The radius of the circle is 3 units.

So, the area of circle is

[tex]A=\pi r^2[/tex]

[tex]A=\pi (3)^2[/tex]

[tex]A=9\pi[/tex]

Therefore, the area of circle is [tex]9\pi[/tex] sq. units.

Answer:

-0.4x - 0.30  or   [tex]-\frac{2x}{5} - \frac{3}{10}[/tex]

Step-by-step explanation:

Change all the fractions to decimals.

-2/5 = -0.4  Distribute that over x and 0.8   1/50 =  0.02

you get -0.4x -0.32 + 0.02

Change all the decimals to fractions.

0.8 is 8/10  so  -2/5 times 8/10  is -16/50

-2x/5  - 16/50 + 1/50   add or subtract the fractions to get -15/50 Then reduce (÷5)

-2x/5 - 3/10

Answer:

114°

Step-by-step explanation:

By property of intersecting chords inside a circle.

[tex] \because \angle \: 1 = \frac{1}{2} (x + y) \\ \\ \therefore \: \angle \: 1 = \frac{1}{2} (96 + 132) \\ \\ \therefore \: \angle \: 1 = \frac{1}{2} \times 228\\ \\ \huge \red { \boxed{\therefore \: \angle \: 1 = 114 \degree}}[/tex]

Answer:

y=6

Step-by-step explanation:

y² - 10y + 24

factor: y - 4

24 / -4 = -6

y - 6 is the other factor.

(y-4)(y-6) ⇒ y(y-6) -4(y-6) = y² - 6y -4y + 24 ⇒ y² - 10y + 24

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The other factor of the expression y² - 10y + 24, other than y - 4, is y - 6. The expression can be factored as (y - 4)(y - 6).

The given expression is y² - 10y + 24. You have given that one factor is (y - 4). To find the other factor of the equation, we can divide the whole equation by (y - 4). By doing this, we find out that the other factor is (y - 6).

So, the expression y² - 10y + 24 can be factored as (y - 4)(y - 6).

This concludes that other than (y - 4), the other factor of the expression y² - 10y + 24 is (y - 6).

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Answer:

16x -20

Step-by-step explanation:

12(x - 4) + 4(x + 7)

12x - 48 + 4x +28

16x - 20

Answer:

16x - 20

Step-by-step explanation:

Given

12(x - 4) + 4(x + 7) ← distribute both parenthesis

= 12x - 48 + 4x + 28 ← collect like terms

= 16x - 20

Answer:

(a)Initial Number of Bacteria=600

(b)[tex]\text{Number of bacteria after 5 days}=19200[/tex]

Step-by-step explanation:

Given an initial number  [tex]b_0[/tex] of bacteria in a petri dish, and each bacteria splits into 2 bacteria after one day.

The function [tex]b(d) = 600 \cdot 2^d[/tex] models  the number of bacteria, b after d days.

Part A

Given  [tex]b(d) = 600 \cdot 2^d[/tex]

When d=0,

The initial number of bacteria in the petri dish,

[tex]b_0=b(0) = 600 \cdot 2^0=600[/tex]

Part B

After 5 days, when d=5

[tex]b(5) = 600 \cdot 2^5=600 \cdot 32\\\text{Number of bacteria after 5 days}=19200[/tex]

Answer:

If your solving for y...

The answer would be: y = -9/8x + 17/8 I believe.

For the second one... it would be : y = -1/7x + 8/7

Step-by-step explanation:

Answer:

$8.35 per hour

Step-by-step explanation:

Take the dollars and divide by the hours to determine the dollars per hour

25.05/3

$8.35 per hour

Answer:

Base

Step-by-step explanation:

To give an example, in the expression [tex]10^6[/tex], 10 is our base and 6 is our exponent or power.

Answer:

19 weeks

Step-by-step explanation:

Make an equation

120+20x=500

Subtract 120 on both sides

20x=380

Divide by 20 on both sides

x=19

Hope this helps!

Answer:

she will use 900 ounces for 9 people

Step-by-step explanation:

Answer:

900 ounces

Step-by-step explanation:

you would take 300 and divide it by 3 because thats how many people were listed, then you would get 100 per person as a unit rate. Multiply 100 by 9 and you have your answer!

Answer:

1) B. on, 2) D. 19.2, 3) C. 0

Step-by-step explanation:

1) The value of y according to the regression line is:

[tex]y = 3.2\cdot (8) - 6.4[/tex]

[tex]y = 19.2[/tex]

Hence, the point (8,19.2) is on the least-squares regression line.

2) The value of y according to the regression line is 19.2.

3) The residual is the difference between the value from the regression line and the real value. In this case, the residual value is 0.

Final answer:

The data point (8,19.2) lies on the least-squares regression line. The value of the least-squares regression line at x=8 is 19.2. Hence, the residual of the data point (8,19.2) is 0.

Explanation:

The data point (8,19.2) is on the least-squares regression line since when we substitute x=8 into the equation y=3.2x−6.4, we get y=3.2(8)−6.4 which simplifies to y=25.6−6.4, yielding y=19.2, which is exactly the y-value of the given data point.

The value of the least-squares regression line at x=8 is therefore 19.2 which corresponds to option D.

Since the observed y-value is exactly predicted by the regression line at this x-value, the residual for the data point (8,19.2) is 0, which represents the difference between the observed y-value and the value predicted by the regression formula. Therefore, option C is correct for the residual.

Answer:

0.33

Step-by-step explanation:

because 0.45 plus 0.22 is 0.67 which means the other probability is 0.33.

The probability of dying from some other cause will be 0.33. Probability always lies between 0 and 1.

The chances of an event occurring are defined by probability. Probability has several uses in games, in business to create probability-based forecasts,

The given data in the problem is;

P(A) is the probability of dying from cardiovascular disease = 0.45

P(B) is the  probability of dying from cancer = 22

P is the probability of dying from some other cause =?

The probability of dying from some other cause will be found as;

[tex]\rm P =1- P(A)+P(B) \\\\ \rm P =1- 0.45+0.22 \\\\ \rm P =0.33[/tex]

Hence the probability of dying from some other cause will be 0.33.

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