45 less than twice Jose’s savings. Use the variable J to represent Jose’s savings

Jessica drew a circle divided into 8 equal parts she shaded six of the parts what fraction is equivalent to the part of the circ

Anni [7]

Answer:

3/4

Step-by-step explanation:

Jessica shaded 6/8 of the circle. That fraction can be reduced by removing a factor of 2 from numerator and denominator. The reduced fraction is 3/4.

$\dfrac{6}{8}=\dfrac{2\cdot 3}{2\cdot 4}=\dfrac{2}{2}\cdot\dfrac{3}{4}=1\cdot\dfrac{3}{4}\\\\=\dfrac{3}{4}$

3 0

3 years ago

Find the least common multiple (LCM) of 8y^6+ 144y^5+ 640y^4 and 2y^4 + 40y^3 + 200y^2.

Mice21 [21]

Answer:

LCM = $8y^{4}(y+ 10)^{2}(y + 8)$

Step-by-step explanation:

Making factors of $8y^{6}+ 144y^{5}+ 640y^{4}$

Taking $8y^{4}$ common:

$\Rightarrow 8y^{4} (y^{2}+ 18y+ 80)$

Using factorization method:

$\Rightarrow 8y^{4} (y^{2}+ 10y + 8y + 80)\\\Rightarrow 8y^{4} (y (y+ 10) + 8(y + 10))\\\Rightarrow 8y^{4} (y+ 10)(y + 8))\\\Rightarrow \underline{2y^{2}} \times 4y^{2} \underline{(y+ 10)}(y + 8)) ..... (1)$

Now, Making factors of $2y^{4} + 40y^{3} + 200y^{2}$

Taking $2y^{2}$ common:

$\Rightarrow 2y^{2} (y^{2}+ 20y+ 100)$

Using factorization method:

$\Rightarrow 2y^{2} (y^{2}+ 10y+ 10y+ 100)\\\Rightarrow 2y^{2} (y (y+ 10) + 10(y + 10))\\\Rightarrow \underline {2y^{2} (y+ 10)}(y + 10) ............ (2)$

The underlined parts show the Highest Common Factor(HCF).

i.e. HCF is $2y^{2} (y+ 10)$ .

We know the relation between LCM, HCF of the two numbers 'p' , 'q' and the numbers themselves as:

$HCF \times LCM = p \times q$

Using equations (1) and (2): $\Rightarrow 2y^{2} (y+ 10) \times LCM = 2y^{2} \times 4y^{2}(y+ 10)(y + 8) \times 2y^{2} (y+ 10)(y + 10)\\\Rightarrow LCM = 2y^{2} \times 4y^{2}(y+ 10)(y + 8) \times (y + 10)\\\Rightarrow LCM = 8y^{4}(y+ 10)^{2}(y + 8)$

Hence, LCM = $8y^{4}(y+ 10)^{2}(y + 8)$

5 0

2 years ago

Which of the following are factors of x^2+5x+4

soldier1979 [14.2K]

Answer:

(x + 4) and (x + 1)

Step-by-step explanation:

x² + 5x + 4

Consider the factors of the constant term (+ 4) which sum to give the coefficient of the x- term (+ 5)

The factors are 4 and 1 , since

4 × 1 = 4 and 4 + 1 = 5 , then

x² + 5x + 4 = (x + 4)(x + 1) ← in factored form

3 0

2 years ago

a parking garage charges $2.50 base free plus an hourly rate of $4.00. If you hve most $12.50 how many parking you can

snow_lady [41]

Answer: 2.5 hours or 2 hr and 30 min

Step-by-step explanation:

We can set up an equation to find how many hours you can park.

2.5+4x=12.5

The 2.5 comes from the base fee. The 4x is the hourly rate, where x is hours. The 12.5 is the total amount of money you have.

Since we have our equation, we can solve for x.

4x=10

x=2.5

You can park for 2.5 hours, or 2 hours and 30 min.

7 0

3 years ago

A student earned grades of C, A, B, and A. Those courses had these corresponding numbers of credit hours: 44, 66, 11, and

asambeis [7]

Answer:

The grade point average of the student is 49.92.

Step-by-step explanation:

A student earned grades : C, A, B, and A

Corresponding numbers of credit hours : 44, 66, 11, and 66

Assigns quality points to letter grades :

A = 4 , B = 3 , C = 2 , D = 1 , F = 0

The grade point average (GPA):

$\frac{\sum (\text{grade point}\times \text{credit hours})}{\sum (\text{grade point})}$

$=\frac{2\times 44+4\times 66+3\times 11+4\times 66}{2+4+3+4}$

$=\frac{649}{13}=49.9230\approx 49.92$

The grade point average of the student is 49.92.

4 0

3 years ago