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3 years ago

Find the equation for the line passing through the point (−1,1) ( − 1 , 1 ) and parallel to the line whose equation is y=2x+12.

1 answer:

7 0

So, parallel lines have the same slope, therefore a parallel line to 2x+12, will have the same slope as that one, so which is it? $\bf y=\stackrel{slope}{2}x\stackrel{y-intercept}{+12}$

so, we're really looking for the equation of a line whose slope is 2, and runs through -1,1.

$\bf \begin{array}{lllll}
&x_1&y_1\\
% (a,b)
&({{ -1}}\quad ,&{{ 1}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies 2
\\\\\\
% point-slope intercept
\stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-1=2[x-(-1)]
\\\\\\
y-1=2(x+1)\implies y-1=2x+2\implies y=2x+3$

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ASAP please help!!!

Serggg [28]

Y+4<9
subtract 4
y<5
y is smaller than and equal to 5
so you shade from 5 to the negative end to infinity (to the left) and shade the 5 to show that it is included (attachment says A)

6 less than (-6) 2 times a number (2 time x) is greater than (>) 8 (8)

-6+2x>8
add 6
2x>14
divide 2
x>7
so
x is bigger than 7
shade from 7 to the positive end to infinity (to the right) and don't shade 7 but put a circle around it to show that it is not included (attachment says B )

I have included pictures of the number lines

4 0

3 years ago

Suppose you are asked to find the area of a rectangle that is 2.1-cm wide by 5.6-cm long. Your calculator answer would be 11.76

IRINA_888 [86]

Answer:

The area of the rectangle is 12 cm² (to two significant figures)

Step-by-step explanation:

To determine the area of a rectangle that is 2.1-cm wide by 5.6-cm long,

The area of a rectangle is given by

Area = l × w

where l is the length

and w is the width

From the question,

l = 5.6 cm

and w = 2.1 cm

Hence, Area of the given rectangle will be

Area = 5.6 cm × 2.1 cm

Area = 11.76 cm²

Now, we will convert the answer to two significant figures

Then,

Area = 12 cm²

Hence, the area of the rectangle is 12 cm² (to two significant figures)

3 0

3 years ago

Which of the following is the discriminant of the polynomial below x^2+4x+5

steposvetlana [31]

Answer:

$\huge\boxed{\sf Discriminant = -4}$

Step-by-step explanation:

Comparing it with quadratic equation $ax^2 + bx + c = 0$ , we get:

a = 1 . b = 4 and c = 5

So,

Discriminant = $b^2-4ac$

D = (4)²-4(1)(5)

D = 16 - 20

D = -4

Hence,

Discriminant = -4

$\rule[225]{225}{2}$

Hope this helped!

4 0

2 years ago

I’m Atlanta, the tax on a property assessed at $930,000 is $19,530. If tax rates are proportional in this city, how much would t

igomit [66]

Answer:

The tax on property assessed at $660,000 is $13860 .

Step-by-step explanation:

Given:

In Atlanta the tax on a property assessed at $930,000 is $19,530.

The tax rates are proportional to this city.

Now, to find the tax on a property assessed at $660,000.

So, we need to get the tax rate of Atlanta first.

Tax Rate = Tax / Property assessed × 100.

$Tax\ rate=\frac{19530}{930000} \times 100$

$Tax\ rate=0.021 \times 100$

$Tax\ rate=2.1\%$

According to question the tax rates are proportional.

So, for getting the tax in this city we use the same rate of Atlanta:

Tax = tax rate of property assessed.

$Tax = 2.1\% of\ \$660,000$

$Tax = \frac{2.1}{100}\times 660000.$

$Tax = 0.021\times 660000$

$Tax=\$13860$

Therefore, the tax on property assessed at $660,000 is $13860.

6 0

3 years ago

The formula for a trapezoid relates the area A, the two bases, a and b, and the height, h. Solve for a

den301095 [7]

Answer:

$a=\frac{2A}{h}-b$

Step-by-step explanation:

we know that

The formula to calculate the area for a trapezoid is equal to

$A=\frac{1}{2}(a+b)h$

where

a and b are the parallel bases

h is the height of trapezoid

A is the area

Solve for a

That means ----> isolate the variable a

Multiply by 2 both sides to remove the fraction in the right side

$2A=(a+b)h$

Divide by h both sides

$\frac{2A}{h}=a+b$

Subtract b both sides

$\frac{2A}{h}-b=a$

Rewrite

$a=\frac{2A}{h}-b$

8 0

3 years ago