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FinnZ [79.3K]
3 years ago
7

Evaluate: 2a + 4b when a = 10 & b = 6

Mathematics
1 answer:
Tcecarenko [31]3 years ago
7 0

Answer: Option C: 44

Step-by-step explanation:

so, here we have the equation:

H(a,b) = 2a + 4b

"evaluate" means change the values of the variables for specific values, here we must replace the "a" for 10, and the "b" for a 6.

So we have:

H(10, 6) = 2*10 + 4*6 = 20 + 24 = 44

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in parallelogram abcd diagonals ac and bd intersect at point l . If Al= x-2 and ac =3x-16 , then which of the following represen
TiliK225 [7]

Answer:

The length of CI is 10 units.

Step-by-step explanation:

It is given that ABCD is a parallelogram and diagonals AC and BD intersect at point I.

The diagonals of a parallelogram bisect each other.

AI=CI

AC=AI+CI

AC=AI+AI                 [\because AI=CI]

AC=2AI

3x-16=2(x-2)

3x-16=2x-4

3x-2x=16-4

x=12

The value of x is 12.

CI=AI=x-2=12-2=10

Therefore the  length of CI is 10 units.

4 0
3 years ago
This week, we are covering relationships that can be approximated by linear equations. For instance, y = 453x + 3768 represents
lana [24]

Answer:

See explanation below.

Step-by-step explanation:

We assume that the data is given by :

x: 30, 30, 30, 50, 50, 50, 70,70, 70,90,90,90

y: 38, 43, 29, 32, 26, 33, 19, 27, 23, 14, 19, 21.

Where X represent the cost for scholarships in thousands of dollars and y represent the cost of life for an academic semester (The data comes from the web)

We can find the least-squares line appropriate for this data.  

For this case we need to calculate the slope with the following formula:

m=\frac{S_{xy}}{S_{xx}}

Where:

S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}

S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}

So we can find the sums like this:

\sum_{i=1}^n x_i = 30+30+30+50+50+50+70+70+70+90+90+90=720

\sum_{i=1}^n y_i =38+43+29+32+26+33+19+27+23+14+19+21=324

\sum_{i=1}^n x^2_i =30^2+30^2+30^2+50^2+50^2+50^2+70^2+70^2+70^2+90^2+90^2+90^2=49200

\sum_{i=1}^n y^2_i =38^2+43^2+29^2+32^2+26^2+33^2+19^2+27^2+23^2+14^2+19^2+21^2=9540

\sum_{i=1}^n x_i y_i =30*38+30*43+30*29+50*32+50*26+50*33+70*19+70*27+70*23+90*14+90*19+90*21=17540

With these we can find the sums:

S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=49200-\frac{720^2}{12}=6000

S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}=17540-\frac{720*324}{12}{12}=-1900

And the slope would be:

m=-\frac{1900}{6000}=-0.317

Nowe we can find the means for x and y like this:

\bar x= \frac{\sum x_i}{n}=\frac{720}{12}=60

\bar y= \frac{\sum y_i}{n}=\frac{324}{12}=27

And we can find the intercept using this:

b=\bar y -m \bar x=27-(-0.317*60)=46.02

So the line would be given by:

y=-0.317 x +46.02

We have an inverse linear relationship since the slope is negative between the variables of interest.

8 0
3 years ago
A car is 180 inches long. A truck is 75% longer than the car. How long is the truck?
nasty-shy [4]

Answer:

The answer is 315 inches

Step-by-step explanation:

180+75%

4 0
2 years ago
Let f(x)=3x-7 and g(x)=2x². Perform the function operation and then find the domain of the result.
olya-2409 [2.1K]

Answer: A

Step-by-step explanation:

f(x)=3x-7\\g(x)=2x^2

(f-g)(x)=3x-7-(2x^2)\\(f-g)(x)=3x-7-2x^2\\(f-g)(x)=-2x^2+3x-7

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A box with a volume of 40 cubic inches holds 10 balls. A box with a volume of 60 cubic inches holds 15 of the same kinds of ball
lesya692 [45]
Pretend these are coordinates that you can use to find the slope of the line.
(10, 40) and (15, 60). Fit these into the slope formula to find the slope of the line you are looking for:
m= \frac{60-40}{15-10} and the slope is 4. Now use one of the points and the slope of 4 to solve for b, the y-intercept:
40 = 4(10) + b so b = 0.  The equation of the line then is y = 4x + 0 or just
y = 4x
6 0
3 years ago
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