Ms. Salazar’s car averages 25 miles per gallon of gasoline. She filled the 10-gallon tank with gasoline before traveling 200 miles on a trip. Which graph BEST represents this situation?

Answers

Answer 1

Answer:

Step-by-step explanation:

2524 ÷ 23 = 24a6u= 7

bengek hyung

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One side of a triangular garden is x feet long. The other two sides of the garden are both 5 feet less than twice the length of the first side of the garden.Part A: Write a simpiflied expression for perimeter, in feet, of the garden.
A fence is placed along the entire perimeter of the triangular garden. The roll of fencing is 40 ft long.
Part B: Write a simplified expression to show the amount of fencing, in feet, which is left from the roll of fencing.

Answers

A: If the 1st side of the garden is x feet long then the other sides are 2x - 5. The perimeter is simply the measure of the distance around the triangle, so the length of all three sides added up. So the equation to find the perimeter (p) would be...

p = x + (2x+5) + (2x+5)
or
p = x + 2(2x+5)

This is actually an equation so the expression to represent perimeter would simply be...

x + 2(2x+5)

B: Since we know the equation for the perimeter and we know that we have 40 feet of fencing, then the equation to find the left over fencing would just be the length of fencing minus the perimeter...

40 - x + 2(2x+5) = the leftover amount of fencing

so the expression is...

40 - x + 2(2x+5)

derive the equation of the parabola with a focus at (4,-7) and a directrix of y=-15. put the equatiom in standard form

Answers

Answer:

The equation of the parabola with a focus at (4,-7) and a directrix of y=-15 is $y=(x^(2))/(16)-(x)/(2)-10$

Step-by-step explanation:

we need to drive the equation of the parabola with a focus at ( 4, -7) and a directrix of y= -15

From the given focus ( 4, -7) and equation of directrix y = - 15 calculate p

$p=(1)/(2)(y_0-y)$

where $y_0$ is is ordinate of focus and y is equation of directrix.

$p=(1)/(2)(-7-(-15))$

$p=(1)/(2)(-7+15)$

$p=(1)/(2)(8)$

$p=4$

Calculate the vertex (h,k)

$h=4\; \text{and}\; k=(-7+(-15))/(2)=-11$

vertex (h,k) =(4,-11)

Since, vertex form is :

$(x-h)^(2)=4p(y-k)$ (positive 4p shows it open upward)

$(x-4)^(2)=4(4)(y-(-11))$

$(x-4)^(2)=16(y+11)$

$x^(2)+16-8x=16y+176$

subtract both the sides by 176,

$x^(2)-8x-160=16y$

Divide both the sides in above by 16,

$(x^(2))/(16)-(8x)/(16)-(160)/(16)=y$

$(x^(2))/(16)-(x)/(2)-10=y$

Hence, the equation of the parabola with a focus at (4,-7) and a directrix of y=-15 is $y=(x^(2))/(16)-(x)/(2)-10$

$\sqrt{(x_(0) - 4)^(2) + (y_(0) - (-7))^(2)} = |y_(0) - (-15)|$
$(\sqrt{(x_(0) - 4)^(2) + (y_(0) + 7)^(2))^(2)} = (y_(0) + 15)^(2)$
$(x_(0) - 4)^(2) + (y_(0) + 7)^(2) = (y_(0) + 15)^(2)$
$(x_(0)^(2) - 8x_(0) + 16) + (y_(0)^(2) + 14y_(0) + 49) = y_(0)^(2) + 30y_(0) + 225$
$x_(0)^(2) + y_(0)^(2) - 8x_(0) + 14y_(0) + 16 + 49 = y_(0)^(2) + 30y_(0) + 225$
$x_(0)^(2) + y_(0)^(2) - 8x_(0) + 14y_(0) + 65 = y_(0)^(2) + 30y_(0) + 225$
$x_(0)^(2) - 8x_(0) - 16y_(0) - 160 = 0$
$16y_(0) = x_(0)^(2) - 8x_(0) - 160$
$(16y_(0))/(16) = (x_(0)^(2) - 8x_(0) - 160)/(16)$
$y_(0) = (1)/(16)x_(0)^(2) - (1)/(2)x_(0) - 10$
$y = (1)/(16)x^(2) - (1)/(2)x - 10$

P is a point on the terminal side of θ in standard position. Find the exact value of the six trigonometric functions for θ.18. P(-3, 2)
19. P(4, -2)
20. P(0, -6)
21. P(-3, -4)

Answers

Answer:

see below

Step-by-step explanation:

When you're doing a bunch of these, it is helpful to make a table with reminders as to how they're calculated. That table is shown below.

In the attached, we have used ...

r² = x² +y²

√20 = 2√5

√36 = 6

√25 = 5

and 1/(2√5) = √5/10. (The division is outside the radical.)

On Friday, a local restaurant served 150 customers. Of these, 114people ordered soup. What percent of the customers ordered soup?

A: 13%

B: 66%

C: 34%

D: 76%

Answers

The answer is D, because we will divide 114 by 150 and the total converted to percentage is 76

Convert the following decimal to a common fraction. Reduce to lowest terms 0.2 = 2/1 0/2 1/2 1/5

Answers

0.2 = $(2)/(10) = (1)/(5)$
So, $(1)/(5)$

In a small company of 10 people the salaries are as follows: 5 people earn $25,000, 3 earn $27,000, 1 earns $34,000, and the owner earns $60,000 What is the mean and standard deviation (to the nearest dollar) of their salaries?Mean salary: $________a0

Standard Deviation: $_________a1