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3 years ago

14

Type the correct answer in each box. Use numerals instead of words.

1 answer:

DedPeter [7]3 years ago

8 0

Answer:

c = 7

d = 5

Step-by-step explanation:

combining coefficient a with the nth root of b: a√ⁿb = √ⁿ((a)ⁿb). This is the reverse of simplifying a radical.

8x³√²7x = √²((8x³)²)√²(7x) = √²(64x⁶)√²(7x) = √²((64x⁶)(7x)) = √²((64 × 7)(x⁶ × x)) = √²((448)(x⁷)) = √²448x⁷ →

√²448x⁷ = √²448xᶜ.

7 → c, √²448x⁷ = √²448x⁷, c = 7.

4x√³9x² = √³((4x)³)√³(9x²) = √³(64x³)√³(9x²) =

√³((64x³)(9x²)) = √³((64 × 9)(x³ × x²)) = √³((576)(x⁵)) = √³576x⁵ →

√³576x⁵ = √³576xᵈ.

5 → d, √³576x⁵ = √³576x⁵, d = 5.

You might be interested in

Log(x)²=(logx)², find the value of x

Gnesinka [82]

Answer:

x = 7.39

Step-by-step explanation:

log(x)²=(logx)², find the value of x

log x² = log x * log x

2log x = log x * log x

2 = log x

Take the exponent pf both sides

e² = e^logx

e² = x

x = e²

x = 7.39

6 0

3 years ago

Cidnee is weighing combinations of geometric solids. She found that 4 cylinders and 5 prisms weigh 32 ounces and that 1 cylinder

vitfil [10]

Answer:

The weights of each cylinder and prism are 3 and 4 ounces, respectively.

Step-by-step explanation:

Let be $x$ and $y$ the masses of a cylinder and a prism, measured in ounces, respectively. After a careful reading of the statement we get the following linear equations by interpretation:

i) <em>She found that 4 cylinders and 5 prisms weigh 32 ounces:</em>

$4\cdot x +5\cdot y = 32\,oz$ (Eq. 1)

ii) <em>And that 1 cylinder and 8 prisms weigh 35 ounces:</em>

$x + 8\cdot y = 35\,oz$ (Eq. 2)

Now we solve the system of linear equations algebraically:

From (Eq. 2):

$x = 35 - 8\cdot y$

(Eq. 2) is (Eq. 1):

$4\cdot (35-8\cdot y) + 5\cdot y = 32$

$140-32\cdot y +5\cdot y = 32$

$32\cdot y - 5\cdot y = 140-32$

$27\cdot y = 108$

$y = 4\,oz$

From (Eq. 2):

$x = 35 - 8\cdot (4)$

$x = 35 - 32$

$x = 3\,oz$

The weights of each cylinder and prism are 3 and 4 ounces, respectively.

4 0

3 years ago

A computer can sort x objects in t seconds, as modeled by the function

r-ruslan [8.4K]

Answer:

36 objects

Step-by-step explanation:

You want the value of x when t=9, so you're solving ...

9 = 0.007x^2 +0.003x

9 = 0.007(x^2 + 3/7x)

From here, we observe that an approximation is probably sufficient.

9/0.007 = x(x +3/7) . . . . . the expression on the right is nearly x^2

x ≈ 3/√.007 ≈ 35.9 ≈ 36

We can check:

.007(36)(36 3/7) = 9.18

.007(35)(35 3/7) = 8.68

To keep the computer busy for 9 seconds, it needs to sort 36 objects.

6 0

3 years ago

Two mechanics worked on a car. The first mechanic charged $65 per hour, and the second mechanic charged $90 per hour. The mechan

Katena32 [7]

Answer:

First mechanic worked 20 hours and second mechanic worked 5 hours

Step-by-step explanation:

Let the number of hours the first mechanic worked = $a$

Let the number of hours the second mechanic worked = $b$

Therefore, we can write 2 equations and then solve them simultaneously:

$a+b=25$

$65a+90b=1750$

Rearranging the first equation: $a=25-b$

and substituting into the second equation to find $b$ :

$65(25-b)+90b=1750$

$1625-65b+90b=1750\\
25b=125\\
b=5$

Now sub $b=5$ into the first equation to find $a$

$a+5=25\\
a=20$

Therefore, first mechanic (a) worked 20 hours and second mechanic (b) worked 5 hours

4 0

2 years ago

The first side of a triangle is 3 inches shorter than the second side, and 2 inches longer than the third side. How long is each

ziro4ka [17]

Answer:

the length of the first side of the triangle is $\frac{28}{3}\ in$

the length of the second side of the triangle is $\frac{37}{3}\ in$

the length of the third side of the triangle is $\frac{19}{3}\ in$

Step-by-step explanation:

Let

x-----> the length of the first side of a triangle

y----> the length of the second side of a triangle

z---> the length of the third side of a triangle

we know that

$x=y-3$

$y=x+3$ -----> equation A

$x=z+3$

$z=x-3$ -----> equation B

The perimeter of the triangle is equal to

$P=x+y+z$

$P=28\ in$

so

$28=x+y+z$ -----> equation C

substitute equation A and equation B in equation C

$28=x+(x+3)+(x-3)$

solve for x

$28=3x$

$x=\frac{28}{3}\ in$

Find the value of each side

the first side of a triangle is x

$x=\frac{28}{3}\ in$

the second side of a triangle is y

$y=\frac{28}{3}+3=\frac{37}{3}\ in$

the third side of a triangle is z

$z=\frac{28}{3}-3=\frac{19}{3}\ in$

7 0

4 years ago