which equation represents a line that is parallel to y= -4x+3 and passes through the point (-3,2)

Answer:

3xy+6x+3y+6

Step-by-step explanation:

You just need to combine like terms.

5x and x are like terms so you can add them to 6x.

2 and 4 are like terms so you can add them to 6

Answer:

[tex]y=\frac{4}{3}x+\frac{38}{3}[/tex]

Step-by-step explanation:

So we want to find an equation of a line passing through (-8,2) with a slope of 4/3.

To do so, we can use the point-slope form. This is:

[tex]y-y_1=m(x-x_1)[/tex]

So, substitute (-8,2) for x₁ and y₁, and let m be 4/3:

[tex]y-2=\frac{4}{3}(x+8)[/tex]

Distribute the right:

[tex]y-2=\frac{4}{3}x+\frac{32}{3}[/tex]

Add 2 to both sides. Note that 2 can be written as 6/3. Thus:

[tex]y=\frac{4}{3}x+\frac{32}{3}+\frac{6}{3}[/tex]

Simplify:

[tex]y=\frac{4}{3}x+\frac{38}{3}[/tex]

And this is our equation :)

Answer:

x = 0

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

2*x+8/6-(1/3*(x+4))=0

Simplify 1/3

Equation at the end of step  1 :

(2x +  8/6) -  (1/3 * (x + 4))  = 0  

STEP  2 :

Equation at the end of step 2

 (2x + 8/6) -  (x+4)/3  = 0  

STEP  3 :  

Simplify 4/3

Equation at the end of step  3 :

(2x + 4/3) -  (x+4)/3  = 0  

STEP  4 :

Rewriting the whole as an Equivalent Fraction

Adding a fraction to a whole

Rewrite the whole as a fraction using  3  as the denominator :

2x =  2x/1  =  2x*3/3

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

2x * 3 + 4/3  =  6x+4/3

Equation at the end of step  4 :

(6x+4)/3 -  (x+4)/3  = 0  

STEP  5 :  Pulling out like terms

Pull out like factors :

6x + 4  =   2*(3x + 2)  

Adding fractions which have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

2*(3x+2)-((x+4))/3  =  5x/3

Equation at the end of step  5 :

5x/3 = 0  

STEP  6:  When a fraction equals zero

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now, to get rid of the denominator, multiply both sides of the equation by the denominator.

Here's how:

5x/3*3 = 0*3

Now, on the left hand side, the 3 cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

5x  = 0

Solving a Single Variable Equation:

Solve  :    5x = 0  

Divide both sides of the equation by 5:

x = 0

Answer:

1. 1.23

2. 15400

3. 0.0025

4. 0.567

5. 100000000

6. 0.00000001

Step-by-step explanation:

you just move the decimal point left for negative and right for positive

Answer:

Step-by-step explanation:

1  2/3  + 3 3/4 = 1  8/12 + 3  9/12 = 4 17/12 = 5 5/12

4 1/2 + 2 5/7 = 4 7/14 + 2 10/14 = 6 17/14 = 7 3/14

3/4 + 2/3 + 1/5 = 45/60 + 40/60 + 12/60 = 97/60 = 1 37/60

Answer:

Step-by-step explanation:

boom  = 1 37/60

Answer:

0.193877

Step-by-step explanation:

The data given to us is

Pre-Employment Drug Screening Results

                    Positive test result                 Negative test result

                    Drug Use Is Indicated            Drug Use Is Not Indicated

Subject Uses Drugs:            38                                         12

Subject Is Not a drug user: 19                                         29

Now the total of this is = 38+19+12+29= 98

Now the probability of false positive is = 19/98= 0.193877

The Subject Is Not a drug user  would suffer from a false positive. He is not a user and has a positive result.

Answer:

x>0

Step-by-step explanation:

We want to solve for x in the inequality:

4^x > 1

ln(4^x)=xln(4) > ln(1)=0

x > 0/ln(4) =0

x>0

So for any value of x greater than 0, you will have 4^x be greater than 1.

Answer:

22 square feet

Step-by-step explanation:

Area of shaded region = Area of square - Area of circle. The diameter of the circle is also the length of the side of the square as the circumference of the circle is on the circumference of the square.

Area of circle = 3.14 × r × r

r = 10 ÷ 2

= 5

Area of circle = 3.14 × 5 × 5

= 78.5

Area of square = length × length

Area of square = 10 × 10

= 100

Area of shaded region = Square - Circle

= 100 - 78.5

= 21.5

= 22 (to the nearest square foot)

I hope this helps :)

Answer:

c

Step-by-step explanation:

Given

sinN = [tex]\frac{a}{b}[/tex] ( multiply both sides by b ) , then

a = bsinN → (a)

And

sinM = [tex]\frac{a}{y}[/tex] ( multiply both sides by y ), then

a = ysinM → (b)

Thus a is both (a) and (b)

Answer:

2/6 or 1/3

Step-by-step explanation:

Answer:

A and B.

Step-by-step explanation:

So we want to select the fractions that equal -1/7.

Let's go through each of the answer choices.

A)

A is -1/7, the exact same.

A is correct.

B)

B is 1/-7.

We can move the negative to the top.

So, 1/-7 is equivalent to -1/7.

B is also correct.

C)

C is 1/7

There are no negatives whatsoever.

C is not correct.

D)

We have -1/-7.

Again, move the negative to the top. We will have:

-(-1)/7

The two negatives cancel:

=1/7.

So, D is not correct.

Our answers are A and B.

Complete Question:

In ABC, the measure of sides c is 3.9 cm If DEF is a dilation ABC with a scale factor of 2.5 what is the measure of side f

Answer:

f = 9.75

Step-by-step Explanation:

From the information given, a sketch of ∆ABC and ∆DEF with their corresponding sides and angles have been attached below.

∆DEF is a dilation of ∆ABC, which is said to be on a scale factor of 2.5.

The scale factor is a whole number, this implies that ∆DEF is an enlargement of ∆ABC.

Since side c = 3.9 cm, in ∆ABC corresponds to side f, in ∆DEF, therefore, the measure of f would be:

f = measure of c × scale factor

f = 3.9 cm × 2.5

f = 9.75

Answer:

BC=11

Step-by-step explanation:

we need to find BC

and we  know that

AB= x+2

AC=13

BC=2x+11

A, B and C are collinear

that means that

AB+BC=AC

x+2+2x+11=13

3x+13=13

3x=0

x=0

so BC=2(0)+11

BC=11

Answer:

c

Step-by-step explanation:

Please see attached picture for full solution.

Answer:

Step-by-step explanation:

[tex]6x-10=-8+3x\\\\\mathrm{Add\:}10\mathrm{\:to\:both\:sides}\\6x-10+10=-8+3x+10\\\\\mathrm{Simplify}\\6x=3x+2\\\\\mathrm{Subtract\:}3x\mathrm{\:from\:both\:sides}\\6x-3x=3x+2-3x\\\\Simplify\\3x=2\\\\\mathrm{Divide\:both\:sides\:by\:}3\\\frac{3x}{3}=\frac{2}{3}\\\\Simplify\\x=\frac{2}{3}[/tex]

Answer:

x = 2/3

Step-by-step explanation:

This equation can be solved by using conventional algebraic techniques.

We firstly want to make sure to get our constants on one side of the equation and then get our variables on the other.

6x - 10 = -8 + 3x Subtract 3x from both sides of the equation.

3x - 10 = -8 Add 10 to both sides of the equation.

3x = 2 Divide by 3 on both sides of the equation.

x = 2/3

Then, you can voluntarily check your answer.

6(2/3) - 10 = -8 + 3(2/3)

4 - 10 = -8 + 2

-6 = -6

Answer:

A.  r = ∛ 15V / 2π

Step-by-step explanation:

Volume of a sphere = 4/3 π r³    

And to be divided into 10 equal wedges parts.

Volume of each wedge = V = 2/15 π r³

find r

V = 2 π r³ / 15

15 V = 2 π r³

15V / 2π = r³

r = ∛ 15V / 2π

The correct option will be option A i.e., r = [tex]\sqrt[3]{\frac{15}{2\pi } }[/tex]

It is given that a solid sphere is cut into 10 equal wedges , with each wedge having volume V = [tex]\frac{2}{15} \pi r^{3}[/tex]

We have to solve it to get the value of radius r.

What is the formula for volume of sphere ?

The volume of sphere is given by V = [tex]\frac{4}{3} \pi r^{3}[/tex] where , r is the radius of the sphere.

As per the question ;

Volume of sphere =  [tex]\frac{4}{3} \pi r^{3}[/tex]

To be divided into 10 equal wedges ;

Volume of each wedge of sphere will be ;

V = [tex]\frac{2}{15} \pi r^{3}[/tex]

15 V = 2[tex]\pi r^{3}[/tex]

or

r³ = [tex]\frac{15V}{2\pi }[/tex]

or

r = [tex]\sqrt[3]{\frac{15}{2\pi } }[/tex]

Thus , the correct option will be option A i.e., r = [tex]\sqrt[3]{\frac{15}{2\pi } }[/tex]

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Answer: 250 words in 5 minutes

Step-by-step explanation:

Answer:

7.00

Step-by-step explanation:

so you have to round to the narest 0.01 the easy way to do it is round to the hundreth place. And you will get your answer which is 7.00

Answer:

  5/6 cups/lemon

Step-by-step explanation:

(15 cups)/(18 lemons) = (15/18) cups/lemon = 5/6 cups/lemon

Answer:

150 feet

Step-by-step explanation:

A rectangle has 2 pairs of equal sides.

One of the sides is 100 feet, meaning another side is 100 feet.

If we subtract 200 feet we are left with 300, which are the last two sides.

Divide 300 by 2 to get each side length.

150 feet

Answer:

[tex]\lim_{x \to 5^{-}} f(x)= 54[/tex]

[tex]\lim_{x \to 5^{+}} f(x) = -17[/tex]

Step-by-step explanation:

+ means we are approaching from the right

- means we are approaching from the left

We are given that if x < 5, it is x² + 5x + 4

So to find [tex]\lim_{x \to 5^{-}} f(x)[/tex] we would plug in 5 into that piecewise function part:

5² + 5(5) + 4 = 54

We would be approaching y = 54 if we approach from the left.

We are given that x > 5, it is -4x + 3

So to find [tex]\lim_{x \to 5^{+}} f(x)[/tex] we would plug in 5 into that piecewise function part:

-4(5) + 3 = -17

We would approach y = -17 if we approached from the right.

Answer:

[tex]\lim_{x \to 5^-}f(x)=54\\\lim_{x \to 5^+}f(x)=-17[/tex]

Step-by-step explanation:

So, we have the function:

[tex]f(x)=x^2+5x+4,x<5\\f(x)=8,x=5\\f(x)=-4x+3,\text{ otherwise}[/tex]

And we want to show that this has a jump discontinuity.

As directed, calculate the limit at x=5 from the left and from the right. Thus:

[tex]\lim_{x \to 5^-}f(x)[/tex]

To calculate this, since we're coming from the left, x is less than 5. So, use the first equation:

[tex]\lim_{x \to 5^-}f(x)\\= \lim_{x \to 5^-}(x^2+5x+4)\\[/tex]

Use direct substitution:

[tex]=(5)^2+5(5)+4\\=25+25+4\\=54[/tex]

Thus, as the limit approaches f(5) from the left, the function approaches 54.

Now, calculate the limit at x=5 from the right. Since we're coming from the right, use the third equation:

[tex]\lim_{x \to 5^+}f(x)\\= \lim_{x \to 5^+}(-4x+3)[/tex]

Direct substitution:

[tex](-4(5)+3)\\=-20+3\\=-17[/tex]

Thus, as the limit approaches f(5) from the right, the function approaches -17.

As you can picture, there's a huge gap between y=54 and y=-17. The limits are not equal and both of the limits do exist. Thus, we have jump discontinuity.

Answer:

EZ

Step-by-step explanation:

EZ

Answer:

Sum of the sequence (Sn) = 33,859

Step-by-step explanation:

Given:

Sequence = 685+678+671+664+...+6

Find:

Sum of the sequence (Sn)

Computation:

a = 685

d = 678 - 985 = -7

an = 6

an = a+(n-1)d

6 = 685+(n-1)(-7)

-679 = (n-1)(-7)

97 = n-1

n = 98

So,

Sum of the sequence (Sn) = (n/2)[a+an]

Sum of the sequence (Sn) = (98/2)[685+6]

Sum of the sequence (Sn) = (49)(691)

Sum of the sequence (Sn) = 33,859

Answer:

2,640 miles in 12 hours.

Step-by-step explanation:

440/2=220mph

220*12 hours=2,640

rate of speed=220pmh

Answer:o

Step-by-step explanation:

Answer:

49

Step-by-step explanation:

area if a square: side length x side length (s^2)

7 x 7 = 49

Area of Square is 49 square feet

Given that;

Side length of square = 7 feet

Find:

Area of Square

Computation:

Area of Square = Side²

Area of Square = 7²

Area of Square = 49 square feet

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Step 1) Set up a proportion

180 girls / x boys = 4 girls / 3 boys

540 = 4x

x = 135 boys

Step 2) Add the number of boys and girls together

180 + 135 = 315

Answer: 315 total students

Answer:

Step-by-step explanation:

[tex]\left(\dfrac{143}{4}-\dfrac38\right)+\left(\dfrac{207}{8}-\dfrac38\right)=\dfrac{286}{8}-\dfrac38+\dfrac{204}{8}=\dfrac{283}{8}+\dfrac{204}{8}=\dfrac{487}{8}[/tex]