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3 years ago

Solve each equation. Leave the answer as an improper fraction. 16x^2 = 49

Mathematics

2 answers:

vitfil [10]3 years ago

7 0

Answer:

The Answer would be 7/4 as an Improper fraction

Step-by-step explanation:

zmey [24]3 years ago

5 0

Answer:

7/4

Step-by-step explanation:

You might be interested in

Understanding Mathematics, Resource 2, Chapter Nine.

VikaD [51]

Answer:

6. 6 is the number I thought of

8. -15 is the number I thought of

Step-by-step explanation:

6. Let x represent the number you thought of.

x/2 . . . halve it

x/2 -5 . . . take away 5 (from the previous result)

x/2 -5 +3x . . . then add on 3 times the number I thought of

= . . . I end up with ...

4 + . . . four more than ...

4 + 2x . . . ... twice the number I first thought of.

So, the equation is ...

x/2 -5 +3x = 4 +2x

Subtracting 2x we have

x/2 -5 +3x -2x = 4

Adding 5 and collecting terms, we get

(3/2)x = 9

Multiplying by the inverse of the coefficient of x, we get ...

x = (2/3)(9)

x = 6

The number I first thought of was 6.

Check

After I halve it, take away 5 and add back 3 times 6, I have ...

3 -5 +18 = 16

After I add 4 to twice the number, I have ...

4 +2·6 = 16

So, the first set of manipulations gives the same result as the second. 6 is the answer.

_____

8. Let x represent the number I thought of.

x +4 . . . add 4

5(x +4) . . . multiply the answer by 5

= . . . . I could get the same final answer by ...

4x . . . multiplying my number by 4

4x +5 . . . then adding 5

So, the equation is ...

5(x +4) = 4x +5

5x +20 = 4x +5 . . . . eliminate parentheses

x + 20 = 5 . . . . . . . . subtract 4x

x = -15 . . . . . . . . . . . subtract 20

The number I thought of was -15.

Check

Add 4 and multiply the result by 5: 5(-15+4) = 5(-11) = -55.

Multiply the result by 4 and add 5: 4(-15)+5 = -60+5 = -55, the same final answer.

The answer of -15 checks with the problem statement.

6 0

4 years ago

Find the values of x, y, and z. The diagram is not to scale.

Kruka [31]

we know that

The sum of the internal angles in the triangle must be $180$ degrees

see the attached figure with letters to better understand the problem

Step $1$

Find the measure of the angle x

In the triangle ABC

$63\°+36\°+x\°=180\°$

solve for x

$99\°+x\°=180\°$

$x\°=180\°-99\°$

$x=81\°$

therefore

the answer Part a) is

the measure of angle x is $81\°$

Step $2$

Find the measure of the angle z

we know that

$x+z=180\°$ --------> by supplementary angles

substitute the value of x

$81\°+z=180\°$

$z=180\°-81\°$

$z=99\°$

therefore

the answer Part b) is

the measure of angle z is $99\°$

Step $3$

Find the measure of the angle y

In the triangle ACD

$13\°+z\°+y\°=180\°$

solve for y

$13\°+99\°+y\°=180\°$

$112\°+y\°=180\°$

$y\°=180\°-112\°$

$y\°=68\°$

therefore

the answer Part c) is

the measure of angle y is $68\°$

5 0

3 years ago

Read 2 more answers

What is the justification for step 4 in the solution process?

iogann1982 [59]

Answer:

Multiplication property of equality

Step-by-step explanation:

Given

Step 4: b = -27/8

Required

Which property justifies it?

First, it should be noted that step 4 is a result of step 3

When step 3 is multiplied by 3/8 on both sides, we have step 4;

i.e.

$\frac{8}{3b} = -9$

$\frac{8}{3b} * \frac{3}{8} = -9 * \frac{3}{8}$

$b = -9 * \frac{3}{8}$

$b = \frac{-9 * 3}{8}$

$b = \frac{-27}{8}$

The property that allows 3/8 be multiplied on both sides is referred to as the multiplication property of equality

3 0

3 years ago

Amelia ,Hayden and Sophie did a test the total for the test was 75 marks Amelia got 56% of 75 marks Hayden got 8/15 0f the 75 ma

boyakko [2]

Step-by-step explanation:

Amelia got 56% of 75 so

(56/100)*75=(56*75)/100=4200/100=42

Hayden got 8/15 of 75 so

(8/15)*75=(8*75)/15=600/15=40

and Sophie that got 43 out of 75

so we see that Sophie got the highest points.

6 0

3 years ago

Read 2 more answers

−4x+35>2 Whats the innequality

geniusboy [140]

-4x + 35 > 2

Subtract 35 from both sides:

-4x> -33

Divide both sides by -4:

X > -33 s -4

Because you are dividing the inequality. Y a negative value, reverse the inequality sign.

X < 33/4

7 0

4 years ago

Solve each equation. Leave the answer as an improper fraction. 16x^2 = 49​

Solve each equation. Leave the answer as an improper fraction. 16x^2 = 49