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3 years ago

Theresa is 14 years younger than her brother. Together, their total age in years is 35.

1 answer:

4 0

Let :
T = Theresa age
H = her brother
We know :
T = H - 14
T + H = 35
Substitute T
H -14 + H = 35
2H - 14 = 35
2H = 49
H = 49/2 = 24.5
Since we know H = 24.5 we then can substitute it to either equation.
T = H - 14
T = 24.5 - 14
T = 10.5
Theresa is 10.5 years old
Her brother is 24.5 years old

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A pattern has 3 blue triangles to every 24

NARA [144]

Answer:

It is 3 : 27

Step-by-step explanation:

Ratio of blue to yellow = 3:24

${ \sf{total \: ratio = 24 + 3 = 27}}$

ratio of blue to all triangles:

$= 3 : 27$

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2 years ago

What is the solution to this system of equations?

Ede4ka [16]

Answer:

First choice.

Step-by-step explanation:

You could plug in the choices to see which would make all the 3 equations true.

Let's start with (x=2,y=-6,z=1):

2x+y-z=-3

2(2)+-6-1=-3

4-6-1=-3

-2-1=-3

-3=-3 is true so the first choice satisfies the first equation.

5x-2y+2z=24

5(2)-2(-6)+2(1)=24

10+12+2=24

24=24 is true so the first choice satisfies the second equation.

3x-z=5

3(2)-1=5

6-1=5

5=5 is true so the first choice satisfies the third equation.

We don't have to go any further since we found the solution.

---------Another way.

Multiply the first equation by 2 and add equation 1 and equation 2 together.

2(2x+y-z=-3)

4x+2y-2z=-6 is the first equation multiplied by 2.

5x-2y+2z=24

----------------------Add the equations together:

9x+0+0=18

9x=18

Divide both sides by 9:

x=18/9

x=2

Using the third equation along with x=2 we can find z.

3x-z=5 with x=2:

3(2)-z=5

6-z=5

Add z on both sides:

6=5+z

Subtract 5 on both sides:

1=z

Now using the first equation along with 2x+y-z=-3 with x=2 and z=1:

2(2)+y-1=-3

4+y-1=-3

3+y=-3

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So the solution is (x=2,y=-6,z=1).

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3 years ago

Sylvia ran 3km 290m in the morning then she ran some more in the evening if she ran a total of 10km how far did Sylvia run in th

MAXImum [283]

Answer:

She ran 6.71km in the evening

Step-by-step explanation:

3km 290m = 3.29km

10 - 3.29 = 6.71km

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3 years ago

Find the area of the figure. Round to the nearest hundredth when necessary.

Delvig [45]

Answer:

215.20 ft^2

Step-by-step explanation:

The figure has 2 semi-circles.

First we find the area of each circle using the formula $\pi r^{2}$ because that is the area formula for a circle.

The semi-circle to the left gives the diameter which is 22 feet. The radius would be half the diameter thus r=11 for semi-circle one.

Then we are to find the diameter of the second semi-circle. Given the entire length to be 30 feet, 30-22 leaves us with 8 feet as its diameter thus r=4.

Left: r=11

Right: r=4

Then, plugging both into the formula for area of a circle, we get

Left: 380.1327

Right: 50.26548

We must divide each by two because we are only looking for semi-circle which is exactly half the area of a full circle.

Then,

Left: 190.066

Right: 25.1327

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3 years ago

Which of the following is a non-real complex number?

Nat2105 [25]

A I think Sorry if it’s wrong

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2 years ago