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3 years ago

Fator by grouping ab+2a+5b+10

Mathematics

1 answer:

Alenkasestr [34]3 years ago

3 0

Ab + 2a + 5b + 10

= a(b + 2) + 5(b + 2)

= (b + 2) (a + 5)

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Sari wrote the equivalent ratios below to convert cups to fluid ounces. StartFraction 8 fluid ounces Over 1 cup EndFraction = St

Amiraneli [1.4K]

Answer:

(B)72 fluid ounces

Step-by-step explanation:

To convert cups to fluid ounces, Sari wrote the equivalent ratios.

$\dfrac{8 \text{ fluid ounces}}{1\text{ cup}} =\dfrac{\text{? fluid ounces}}{9\text{ cups}}$

Let the question mark be represented by x.

We then have:

$\dfrac{8 \text{ fluid ounces}}{1\text{ cup}} =\dfrac{\text{x fluid ounces}}{9\text{ cups}}\\$Cross multiply\\x \times 1 = 8 \times 9\\x=72$ fluid ounces$

We conclude that there are 72 fluid ounces in 9 cups.

7 0

2 years ago

Read 2 more answers

Wat is x in 1/3x - 11 = 5

kirza4 [7]

=48

Multiply by 1

Add 1 1 11 11

to both sides of the equation

6 0

3 years ago

Read 2 more answers

Solve y'' + 10y' + 25y = 0, y(0) = -2, y'(0) = 11 y(t) = Preview

svetlana [45]

Answer: The required solution is

$y=(-2+t)e^{-5t}.$

Step-by-step explanation: We are given to solve the following differential equation :

$y^{\prime\prime}+10y^\prime+25y=0,~~~~~~~y(0)=-2,~~y^\prime(0)=11~~~~~~~~~~~~~~~~~~~~~~~~(i)$

Let us consider that

$y=e^{mt}$ be an auxiliary solution of equation (i).

Then, we have

$y^prime=me^{mt},~~~~~y^{\prime\prime}=m^2e^{mt}.$

Substituting these values in equation (i), we get

$m^2e^{mt}+10me^{mt}+25e^{mt}=0\\\\\Rightarrow (m^2+10y+25)e^{mt}=0\\\\\Rightarrow m^2+10m+25=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{since }e^{mt}\neq0]\\\\\Rightarrow m^2+2\times m\times5+5^2=0\\\\\Rightarrow (m+5)^2=0\\\\\Rightarrow m=-5,-5.$

So, the general solution of the given equation is

$y(t)=(A+Bt)e^{-5t}.$

Differentiating with respect to t, we get

$y^\prime(t)=-5e^{-5t}(A+Bt)+Be^{-5t}.$

According to the given conditions, we have

$y(0)=-2\\\\\Rightarrow A=-2$

and

$y^\prime(0)=11\\\\\Rightarrow -5(A+B\times0)+B=11\\\\\Rightarrow -5A+B=11\\\\\Rightarrow (-5)\times(-2)+B=11\\\\\Rightarrow 10+B=11\\\\\Rightarrow B=11-10\\\\\Rightarrow B=1.$