Solve the following system of equations by linear combination:


3d – e = 7

d + e = 5



The solution is (3, 2).

The solution is (2, –1).

There is no solution.

There are an infinite number of solutions.

The volume of rubber used to make the hollow ball is approximately 636.4 cm^3, which is calculated by subtracting the inner space volume from the total volume of the ball.

To find the volume of rubber used to make a hollow ball, we need to calculate the volume of the entire ball and then subtract the volume of the inner empty space. The ball's external radius is 6 centimeters, and the rubber thickness is 2 centimeters, which makes the inner radius 4 centimeters (6cm - 2cm).

The formula to calculate the volume of a sphere is V = (4/3)
y. Using
for pi and plugging in the numbers, we get:

To find the volume of the rubber used, we subtract the smaller volume from the larger volume:

904.32 cm - 268.08 cm = 636.24 cm

Therefore, option c. 636.4cm is the approximate volume of rubber used to make the ball.

Answer:

kerries because they are spending money not gaining and it will be B

Step-by-step explanation:

Final answer:

The equivalent ratios to 4:9 are 20:45, 12:27, and 8:18 because they all simplify proportionally to 4:9.

Explanation:

To determine which of the given ratios are equivalent to 4:9, we need to have ratios that can be simplified to 4:9 or for which 4:9 can be scaled up proportionally. We check each given ratio by either simplifying it or finding a common multiplier that would lead us back to 4:9.

Therefore, 20:45, 12:27, and 8:18 are equivalent ratios to 4:9.

Answer:

15/24 i think'

Step-by-step explanation:

They have less chlorine than the safety standards require.

Answer: With the help of Ratio we can compare Park Pool's chlorine to the safety standards.

Step-by-step explanation:

Since we have given that

Safety standards requires a pool to add 3 chlorine tablets to every 2,000 gallons of water.

Number of chlorine tablets = 3

Volume of water = 2000 gallons

So, Ratio will be

[tex]3:2000\\\\=1:\frac{2000}{3}\\\\=1:666.67[/tex]

Now, According to question, the lifeguards at Park Pool added 8 chlorine tablets to their pool's 10000 gallons of water.

So, Number of chlorine tablets = 8

Volume of water = 10000 gallons

So, Ratio will be

[tex]8:10000\\\\1:1250[/tex]

Hence, with the help of Ratio we can compare Park Pool's chlorine to the safety standards.

The height of the kite above the ground is approximately 134.82 feet.

To find the height of the kite above the ground, we can use trigonometry. The string of the kite forms a right triangle with the height of the kite as the vertical side and the length of the string as the hypotenuse. We can use the sine function to find the height. sine(64°) = height/150. Rearranging the equation, we get height = 150 * sine(64°).

Using a calculator, we find that sine(64°) ≈ 0.8988. Therefore, height ≈ 150 * 0.8988 ≈ 134.82 feet.

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This should get you a hundred on the 4.11 quiz. :)

The probability of picking a blue shirt from the drawer is 4/5 or 0.8

The probability of picking a blue shirt from a drawer with 8 blue shirts and 2 white shirts can be calculated as follows:

Probability of picking a blue shirt = Number of blue shirts / Total number of shirts

Probability of picking a blue shirt = 8 / (8 + 2)

Probability of picking a blue shirt = 8/10

Probability of picking a blue shirt = 4/5

Therefore, the probability of picking a blue shirt from the drawer is 4/5 or 0.8.

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7 pounds costs $16.4 I think

Answer:

the answer is -1

Step-by-step explanation:

Answer:

[tex]m<1=156\°[/tex]

[tex]m<2=24\°[/tex]

[tex]m<3=24\°[/tex]

[tex]m<5=156\°[/tex]

Step-by-step explanation:

Part 1) If line a is parallel to line b

then

[tex]m<1=m<4[/tex] -----> by alternate exterior angles

so

we have

[tex]m<4=156\°[/tex]

therefore

[tex]m<1=156\°[/tex]

Part 2) we know that

[tex]m<1+m<2=180\°[/tex] -----> by supplementary angles

we have

[tex]m<1=156\°[/tex]

substitute

[tex]156\°+m<2=180\°[/tex]

[tex]m<2=180\°-156\°=24\°[/tex]

Part 3) If line a is parallel to line b

then

[tex]m<3=m<2[/tex] -----> by alternate interior angles

so

we have

[tex]m<2=24\°[/tex]

therefore

[tex]m<3=24\°[/tex]

Part 4) If line b is parallel to line c

then

[tex]m<5=m<4[/tex] -----> by corresponding angles

so

we have

[tex]m<4=156\°[/tex]

therefore

[tex]m<5=156\°[/tex]

To find "What fraction of students prefer Mt Rushmore over Grand Canyon ?", we need to take away Grand Canyon [tex] (\frac{8}{28} ) [/tex] from Mt Rushmore [tex] (\frac{14}{28} ) [/tex]

[tex] \frac{14}{28} - \frac{8}{28}\\\\ When \; we \; have\; like\; fractions\; with\; same\; denominator,\; we \; should\; combine \; numerator \\ \\ \frac{14-8}{28} \\ \\ \frac{6}{28} [/tex]

[tex] Divide \; numerator\; and \; denominator\; by \; common\; factor\; 2\\ \\ \frac{6 \div2 }{28 \div 2} = \frac{3}{14} [/tex]

Conclusion:

6/28 fraction of students prefer Mt Rushmore over Grand Canyon.

3/14 is the simplest form of above fraction.

250% is scale factor will Caroline need to use to draw the original-size image.

A scale factor is a numerical value that can be used to alter the size of any geometric figure or object in relation to its original size.

To adjust the size of a figure without altering its shape, a scale factor is a number or conversion factor that is utilised. It is employed to change the size of an object.

Given:

Scale Factor= 40%

As, Jacob use the scale factor= 40%

So, the new image size

= 100 x 40/100

= 40

let Caroline use x% scale factor

then, 40x/100= 100

x= 100 x 100 /40

x= 250%

Hence,  250% is scale factor will Caroline need to use to draw the original-size image.

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9(x ∙ y), the distributive property is not used because (x ∙ y) = xy which means that only one term can be multiplied by the term outside the parenthesis. 

 (7 ∙ a)(b), the distributive property is not used because (7 ∙ a) = 7a which means that only one term can be multiplied by the term outside the parenthesis. 

Answer: The angles are 100 degrees, and 80 degrees.

Here's an explanation:

It says that the ratio of the angles are 4:5. In a rhombus, the opposite angles are equal to each other. So, the it would be (4*2)+(5*2) = 360 degrees, since the ratio symbolizes the angle measurements. So, if you calculate that, then 18 units is 360 degrees. 4 units is 80 degrees, and 5 units is 100 degrees.

A rhombus is a quadrilateral. The angles of the rhombus are 80°, 100°, 80°, and 100°.

A rhombus is a quadrilateral such that the pair of opposite sides of the quadrilateral are parallel, and all the sides of the quadrilateral are equal.

As we know that if the ratio of the angles formed by the diagonals and the sides is 4:5, then the ratio of the angles of the rhombus is also 4:5. Also, the pair of opposite angles of a rhombus are equal to each other. Therefore, the angles of the rhombus are 4x, 5x, 4x, and 5x.

Now, as the sum of adjacent angles of a rhombus is 180. Therefore, we can write the sum as,

[tex]4x+5x=180\\\\ 9x=180\\\\x=20[/tex]

Further, the measure of the angles can be written as,

[tex]4x = 4(20) =80^o\\\\5x = 5(20) =100^o\\\\4x = 4(20) =80^o\\\\5x = 5(20) =100^o\\[/tex]

Hence, the angles of the rhombus are 80°, 100°, 80°, and 100°.

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