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ss7ja [257]
3 years ago
15

Evaluate -3.25 - 2.75z for z = -4.

Mathematics
1 answer:
Usimov [2.4K]3 years ago
4 0
The answer is $7.75 -3.25-2.75x-4=$7.75
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Boris invested his savings in two investment funds. The $12,000 that he invested in fund a returned a 6% profit the amount that
Sedbober [7]

Answer:

$4000

Step-by-step explanation:

Let B represent amount invested in account 'b'.  

We have been given that an amount of $12,000 that Boris invested in fund a returned a 6% profit.

So the profit earned from fund 'a' would be 12,000\times\frac{6}{100}=12,000(0.06).

We are also told that the amount that he invested in fund b returned at 2% profit. So the profit earned from fund 'b' would be B\times\frac{2}{100}=B(0.02)=0.02B.

Further, both funds together returned a 5%. We can represent this information as:

(12,000+B)\times\frac{5}{100}=0.05(12,000+B)

Now, we will equate profit earned from account 'a' and 'b' with profit earned from both accounts as:

12,000(0.06)+0.02B=0.05(12,000+B)

720+0.02B=600+0.05B

600+0.05B=720+0.02B

600-600+0.05B=720-600+0.02B

0.05B=120+0.02B

0.05B-0.02B=120+0.02B-0.02B

0.03B=120

\frac{0.03B}{0.03}=\frac{120}{0.03}

B=4000

Therefore, Jason invested $4000 in fund 'b'.

4 0
3 years ago
24 - 7/8 I’m taking a test so I don’t have much time.
HACTEHA [7]

Answer:

23.125

Step-by-step explanation:

7/8= 0.875

24-0.875=23.125

3 0
3 years ago
Find equations of the spheres with center(3, −4, 5) that touch the following planes.a. xy-plane b. yz- plane c. xz-plane
postnew [5]

Answer:

(a) (x - 3)² + (y + 4)² + (z - 5)² = 25

(b) (x - 3)² + (y + 4)² + (z - 5)² = 9

(c) (x - 3)² + (y + 4)² + (z - 5)² = 16

Step-by-step explanation:

The equation of a sphere is given by:

(x - x₀)² + (y - y₀)² + (z - z₀)² = r²            ---------------(i)

Where;

(x₀, y₀, z₀) is the center of the sphere

r is the radius of the sphere

Given:

Sphere centered at (3, -4, 5)

=> (x₀, y₀, z₀) = (3, -4, 5)

(a) To get the equation of the sphere when it touches the xy-plane, we do the following:

i.  Since the sphere touches the xy-plane, it means the z-component of its centre is 0.

Therefore, we have the sphere now centered at (3, -4, 0).

Using the distance formula, we can get the distance d, between the initial points (3, -4, 5) and the new points (3, -4, 0) as follows;

d = \sqrt{(3-3)^2+ (-4 - (-4))^2 + (0-5)^2}

d = \sqrt{(3-3)^2+ (-4 + 4)^2 + (0-5)^2}

d = \sqrt{(0)^2+ (0)^2 + (-5)^2}

d = \sqrt{(25)}

d = 5

This distance is the radius of the sphere at that point. i.e r = 5

Now substitute this value r = 5 into the general equation of a sphere given in equation (i) above as follows;

(x - 3)² + (y - (-4))² + (z - 5)² = 5²  

(x - 3)² + (y + 4)² + (z - 5)² = 25  

Therefore, the equation of the sphere when it touches the xy plane is:

(x - 3)² + (y + 4)² + (z - 5)² = 25  

(b) To get the equation of the sphere when it touches the yz-plane, we do the following:

i.  Since the sphere touches the yz-plane, it means the x-component of its centre is 0.

Therefore, we have the sphere now centered at (0, -4, 5).

Using the distance formula, we can get the distance d, between the initial points (3, -4, 5) and the new points (0, -4, 5) as follows;

d = \sqrt{(0-3)^2+ (-4 - (-4))^2 + (5-5)^2}

d = \sqrt{(-3)^2+ (-4 + 4)^2 + (5-5)^2}

d = \sqrt{(-3)^2 + (0)^2+ (0)^2}

d = \sqrt{(9)}

d = 3

This distance is the radius of the sphere at that point. i.e r = 3

Now substitute this value r = 3 into the general equation of a sphere given in equation (i) above as follows;

(x - 3)² + (y - (-4))² + (z - 5)² = 3²  

(x - 3)² + (y + 4)² + (z - 5)² = 9  

Therefore, the equation of the sphere when it touches the yz plane is:

(x - 3)² + (y + 4)² + (z - 5)² = 9  

(b) To get the equation of the sphere when it touches the xz-plane, we do the following:

i.  Since the sphere touches the xz-plane, it means the y-component of its centre is 0.

Therefore, we have the sphere now centered at (3, 0, 5).

Using the distance formula, we can get the distance d, between the initial points (3, -4, 5) and the new points (3, 0, 5) as follows;

d = \sqrt{(3-3)^2+ (0 - (-4))^2 + (5-5)^2}

d = \sqrt{(3-3)^2+ (0+4)^2 + (5-5)^2}

d = \sqrt{(0)^2 + (4)^2+ (0)^2}

d = \sqrt{(16)}

d = 4

This distance is the radius of the sphere at that point. i.e r = 4

Now substitute this value r = 4 into the general equation of a sphere given in equation (i) above as follows;

(x - 3)² + (y - (-4))² + (z - 5)² = 4²  

(x - 3)² + (y + 4)² + (z - 5)² = 16  

Therefore, the equation of the sphere when it touches the xz plane is:

(x - 3)² + (y + 4)² + (z - 5)² = 16

 

3 0
3 years ago
Which point is a solution to the inequality shown in this graph?
Rina8888 [55]

Answer:

D

Step-by-step explanation:

It is on the line so it is a solution, hope this helps

6 0
2 years ago
Read 2 more answers
Please help me if you can thank you. For question A the answer is 5000 brochures. My question is how did they get that answer?
Sophie [7]

Answer:

Step-by-step explanation:

Company A's equation is 900+0.50x5,000

Company B's equation is 1,500+0.38x5,000

Both equal 3,400 and have to be multiplied by 5,000

8 0
2 years ago
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