Jim drove 153 miles in 3 hours. If he can keep the same pace, how long will it take him to drive 1377 miles?

A plumber charges $25 for a service call, plus $50 per hour of service. (Linear Equation)

DochEvi [55]

Answer:

y=50x+25

y-interept=(0,25)

slope: 50

8 0

2 years ago

Petra made the following observation:

AleksandrR [38]

Answer:A ratio compares two numbers or two quantities that are measured with the same unit. The ratio of a to b is written a to b,ab,ora:b. ... When a ratio is written in fraction form, the fraction should be simplified. If it is an improper fraction, we do not change it to a mixed number.

Step-by-step explanation:

A ratio compares two numbers or two quantities that are measured with the same unit. The ratio of a to b is written a to b,ab,ora:b. ... When a ratio is written in fraction form, the fraction should be simplified. If it is an improper fraction, we do not change it to a mixed number.

3 0

3 years ago

Suppose a and b are both non zero real numbers. Find real numbers c and d such that 1/a+ib= c+id

Thepotemich [5.8K]

$\begin{gathered} c=\frac{a}{a^2+b^2} \\ d=\frac{-b}{a^2+b^2} \end{gathered}$

Explanation

$\frac{1}{a+bi}=c+di$

Step 1

multiplicate by the conjugate

$\begin{gathered} \frac{1}{a+bi}\cdot\frac{a-bi}{a+bi}=\frac{a-bi}{(a+bi)(a-bi)}=\frac{a-bi}{a^2-(bi)^2} \\ \frac{1}{a+bi}\cdot\frac{a-bi}{a+bi}=\frac{a-bi}{(a+bi)(a-bi)}=\frac{a-bi}{a^2-(-b^2)}=\frac{a-bi}{a^2+b^2} \end{gathered}$

notice that

$\begin{gathered} \frac{1}{a+bi}=\frac{a-bi}{a^2+b^2}=\frac{a}{a^2+b^2}-\frac{b}{a^2+b^2}i \\ \frac{a}{a^2+b^2}-\frac{b}{a^2+b^2}i=c+di \\ so \\ \end{gathered}$ $\begin{gathered} c=\frac{a}{a^2+b^2} \\ d=\frac{-b}{a^2+b^2} \end{gathered}$

I hope this helsp you

6 0

1 year ago

Can anyone factor this?? I'm a little lost tysm!!!! 5x^2+12x+4 5x 2 +12x+4

Sergio039 [100]

For a polynomial of the form ax^2+bx+c rewrite the middle term as a sum of two terms whose product is a⋅c=5⋅4=20 and whose sum is b=12.

Factor 12 out of 12x.

5x^2+12(x)+4

Rewrite 12 as 2 plus 10

5x^2+(2+10)x+4

Apply the distributive property.

5x^2+2x+10x+4

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(5x^2+2x)+10x+4

Factor out the greatest common factor (GCF) from each group.

x(5x+2)+2(5x+2)

Factor the polynomial by factoring out the greatest common factor, 5x+25x+2.

(5x+2)(x+2)

6 0

2 years ago

A recipe calls for 3 cups of milk to make 30 biscuits. How many cups of milk will you need to make 45 biscuits?

anastassius [24]

The answer is: 4.5 cups.

The explanation is shown below:

1. You need 3 cups of milk to make 30 biscuits.

2. Therefore, to solve the exercise you only need to multiply 45 biscuits by 3 cups and divide this by 30 biscuits.

3. Let's call the cups you will need to make 45 biscuits $x$ . Then, you have:

$x=\frac{(45)(3)}{30}\\x=4.5$

4. Therefore, you will need 4.5 cups to make 45 biscuits.

4 0

3 years ago