Gas mileage actually varies slightly with the driving speed of a car​ (as well as with highway vs. city​ driving). Suppose your car averages 26


miles per gallon on the highway if your average speed is 45


miles per​ hour, and it averages 18


miles per gallon on the highway if your average speed is 65


miles per hour. Answer parts​ (a) and​ (b) below.

a. What is the driving time for a 2500

​-mile

trip if you drive at an average speed of 45


miles per​ hour? What is the driving time at 65


miles per​ hour?

Answer:

[tex]18 \:ft^2[/tex]

Step-by-step explanation:

The area of a trapezoid.

[tex](a+b)h\frac{1}{2}[/tex]

[tex](8+4)3 \times \frac{1}{2}[/tex]

[tex](12)3 \times \frac{1}{2}[/tex]

[tex]36 \times \frac{1}{2}[/tex]

[tex]=18[/tex]

Answer:

0.15p+3=9

Lyda ordered 40 photos or p=40

Step-by-step explanation:

The formula for this is:

0.15p+3

Where p is the amount of pictures ordered.

0.15p+3=9

Subtract 3 from both sides

0.15p=6

Divide both sides by 0.15

p=40

Lyda ordered 40 photos

Answer:

B.

Step-by-step explanation:

= [tex]\sqrt[4]{9} ^{x/2}[/tex]

= Since [tex]\sqrt[4]{} = 1/4[/tex]

= So,  [tex]9^{1/4*x/2}[/tex]

= [tex]9^{\frac{x}{8}[/tex]

Answer:

option B

Step-by-step explanation:

[tex](\sqrt[4]{9})^{\frac{1}{2}x} =(9^{\frac{1}{4}})^{\frac{1}{2}x}\\\\=9^{\frac{1}{4}*\frac{1}{2}x}\\\\=9^{\frac{1}{8}x}[/tex]

Answer: the correct answers is $14.50

Step-by-step explanation:

The amount that the cafe pays per hour will be $14.50 per hour.

A straight line on the coordinate plane is represented by a linear function.

A linear function always has the same and constant slope.

In another word, a linear function is a function that varies linearly with respect to the changing variable.

As per the given,

The rate of the library = $13 per hour.

For 12.5 hours.

Earning from library = 13 x 12.5 = $162.5

Cafe pay per hour = x

For 20.5 hours.

Earning from cafe = 20.5x

Total earning = 162.5 + 20.5x

20.5x = 459.75 - 162.5

x = 14.5

Hence "The amount that the cafe pays per hour will be $14.50 per hour".

For more about the linear function,

brainly.com/question/21107621

#SPJ2

Answer:

Step-by-step explanation:

[tex](\sqrt{2}+3)^2=(\sqrt{2})^2 + 6\sqrt{2}+9 = 6\sqrt{2} +9+2=6\sqrt{2}+11[/tex]

hope this helps

Answer:

C ) B = [tex]\left[\begin{array}{ccc}1\\3\\-5\end{array}\right][/tex]

Step-by-step explanation:

Answer:

y=-4x+9

Step-by-step explanation:

y=-4x+9

m=y2-y1/x2-x1

m= 5-(-7)/1-4

m=12/-3=-4

y=-7   m=-4   x=4 find b

y=mx+b

-7=4*4 +b

b=-7+16 = 9

Answer:

There are 6 ways to run 10 m between two cones of the four cones giving a maximum available distance to run as 60 meters

Step-by-step explanation:

The parameters given are

Distance between two cones = 10 m

Number of cones = 4

Therefore, number of ways to choose two 10 m distances (distance between two cones) from the four cones = [tex]\binom{4}{2}[/tex] = 6

Hence there are only six 10 m distances to run between two cones which gives a maximum distance available to run as 60 m.

Answer:

Angle 2 measures 58°

Step-by-step explanation:

Sum of all three angles formed = 180

Because the sum of angles on a straight line is always 180

Angle 1 =3x-4

Angle 2 = 4x+10

Angle 3= 90° (given)

So,

90+3x-4+4x+10=180

(4x+3x)+(90+10-4)= 180

7x+96=180

Bring 96 to the other side, making it negative,

7x = 180-96 = 84

x = 12

Therefore angle 2

= 4x+10

= (4)(12)+10

=48+10

=58°

Answer:

QST = 2x= 2*20 = 40°

Step-by-step explanation:

RSQ+QST= RST

we know that RST is 124

So,

84+2x= 124

Bringing 84 to the other side it becomes negative

2x= 124-84

= 40

Therefore,

x= 40/2

= 20 °

Here's your answer :)

Answer:

C. The answer is correct

Step-by-step Explanation:

One of the rules that applies when simplifying radical expressions, is that, only like radicals can be added together or subtracted from each other. In other words, the radicand, which is the number inside the "√" must be the same for two or more radicals to be added together or subtracted from each other.

In the expression given in the question, step 1 and step 2 are correct, as well as the final answer.

The final answer is correct because only like radicals can be added as 3√19 and 8√38 are unlike radicals. Their radicands, √19 and √38, are not the same, hence, the radicals do not need to be added.

The answer "3√19 + 8√38" is correct.

Answer:

Step-by-step explanation:

Firstly, I believe that the equation should be represented as [tex]8x^{3} -6x^{2} y^{2} +4x^{2}y[/tex] and [tex]2x^{2} .[/tex] Please correct me if I am wrong and I will fix the equation accordingly.

To find the greatest common factor of this equation, we firstly need to factor the polynomial [tex]8x^{3} -6x^{2} yx^{2} +4x^{2} y[/tex]. To do this:

1. Find a GCF for all of the coefficients of the equation. To do this, you can make factor trees, or you can simply just use the prime factorization method.

The prime factorization method is simply a technique used to list the prime numbers used to find the total value. For example, what two prime numbers do you multiply to get four? 2 and 2. 2 is a prime number.

The prime factorization for each of the coefficients is as follows.

8: 2³

6: 2 · 3

4: 2²

We have 2s as values in every prime factorization, but we only one of each. We must take the greatest common value, and 2 is this value. So, our GCF coefficient is 2.

Now, we look at our x variables and y variables.

For x, we have x³ and x². So, our GCF is x².

Our GCF is now 2x². Now, let's look at our y-variables.

We don't have y variables for our entire polynomial, so it can't be a common factor. Therefore, our GCF is 2x².

Answer:

(1,1)

This is the answer

Answer:

b

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

This is an arithmetic sequence. The explicit formula for an arithmetic sequence is aₙ = a₁ + (n - 1)d where a₁ is the first term and d is the common difference. In this case a₁ = 9 and d = 6 so we have:

aₙ = 9 + (n - 1) * 6

aₙ = 9 + 6n - 6

aₙ 6n + 3

Answer:

1.54 million

Step-by-step explanation:

If 45% of the population are males, then 55% are females. 55%=55/100=0.55. Multiplying this by the total population of the city, you can find that it has 0.55*2,800,00=1.54 million females. Hope this helps!

Answer:

the answer for this question is 1.54×10^6

Step-by-step explanation:

45%- Male

100%-45%=55%

55/100×(2.8×10^6)=1540000

=1.54×10^6

Answer:

y = 1/4 x -3

Step-by-step explanation:

The y intercept ( or where it crosses the y axis ) is -3

Pick 2 points to find the slope

(0,-3) and (4,-2)

The slope is

m = (y2-y1)/(x2-x1)

   = (-2 --3)/ (4-0)

   = (-2+3)/4

   1/4

The slope intercept form of the equation is

y = mx+b where m is the slope and b is the y intercept

y = 1/4 x -3

Answer:

Step-by-step explanation:

We will use the general area formula for finding the area of triangle when you are given information for SAS, which we have been.

[tex]A=\frac{1}{2}absinC[/tex] , where a and b are the given side lengths and C is the included angle. You can ONLY use this when you have the info for SAS in a triangle. For us,

a = 17, b = 15 and C = 35 degrees.  Filling in:

[tex]A=\frac{1}{2}(17)(15)sin35[/tex]

Do that on your calculator in degree mode and you'll find the area to be

73.1 meters squared

Answer:

26miles

Step-by-step explanation:

Let Nina's husband's (Ed) mileage = x miles

Nina = (x + 6) miles

Combined mileage = 46

Nina's miles + Ed's miles = 46

x + (x+6) = 46

x+x+6 = 46

2x +6 = 46

2x = 46-6

2x = 40

x = 40/2 = 20miles

Nina's husband covered 20miles

Nina covered = x+6 = 20+6 = 26miles

Nina walked 26miles

Answer:

The second answer

Step-by-step explanation:

Answer:

170$

Step-by-step explanation:

Answer:

x= AP, y= GP

Step-by-step explanation:

x = 1, 2, 3, 4, 5 - difference in terms = 1, this is AP

y = 5, 25, 125, 625, 3125 - the ratio of increase= 5, this is GP

Answer:

x= AP, y= GP

Step-by-step explanation:

Answer:

b = 7

Step-by-step explanation:

4b + 11 = 39

Subtract 11 to both sides

4b = 39-11

4b = 28

Dividing both sides by 4

b = 7

Answer: [tex](x^2+9)^2[/tex]

Step-by-step explanation:

Rewrite it in the form [tex]a^2+2ab+b^2[/tex] , where [tex]a=x^2 and b=9.[/tex]

[tex](x^2)^2+2(x^2)(9)+9^2[/tex]

Use Square of Sum: [tex](a+b)^2= a^2+2ab+b^2[/tex]

[tex](x^2+9)^2[/tex]

Answer:

False

Step-by-step explanation:

This statement is false.

The set of whole numbers include the set of Natural numbers "N" = {1, 2, 3, 4, 5, 6, ...}, the set of the negatives of the natural numbers: {-1, -2, -3, -4,...}, and the zero: {0}

We see then that the set of Natural numbers is a subset of the set of whole numbers Z = {... -4,-3,-2,-1, 0,1, 2, 3, 4, 5, ...}

Answer:

false

brainliest to me!

Step-by-step explanation:

0 is a whole number but not a natural number so its false!

Answer:

C.  2 1/2

Step-by-step explanation:

Since there is a distance of 6 1/2 units, you have to add and subtract 6 1/2 from the number.

-4 - 6 1/2 = -10 1/2

-4 + 6 1/2 = 2 1/2

Looking at the answer choices, 2 1/2 can represent point Q.

Answer:

87 packages

Step-by-step explanation:

First we need to find the volume of the cone-shaped vase.

The volume of a cone is given by:

V_cone = (1/3) * pi * radius^2 * height

With a radius of 9 cm and a height of 28 cm, we have:

V_cone = (1/3) * pi * 9^2 * 28 = 2375.044 cm3

Each package of sand is a cube with side length of 3 cm, so its volume is:

V_cube = 3^3 = 27 cm3

Now, to know how many packages the artist can use without making the vase overflow, we just need to divide the volume of the cone by the volume of the cube:

V_cone / V_cube = 2375.044 / 27 = 87.9646 packages

So we can use 87 packages (if we use 88 cubes, the vase would overflow)

Answer:

Step-by-step explanation:

 This problem bothers on the mensuration of solid shapes, a cone

the expression for the volume of a cone is

[tex]v=\frac{1}{3} \pi r^2h[/tex]

Given data

height h= 28cM

radius r= 9cm

substituting the data the data into the expression for the volume we can solve for the volume

[tex]v=\frac{1}{3} *3.142*9^2*28\\\v= \frac{7126.056}{3}\ \\v= 2375.35cm^3\\\\[/tex]

we know that a pack contains a cube, we then need to calculate the volume of a cube in a pack, given that the length of a cube is 3cm

the volume is = [tex]l^3= 3^3= 27cm^3\\[/tex]

now the volume of a pack is [tex]27cm^3[/tex], hence the amount of packs needed to fill the cone is calculated as,

[tex]=\frac{2375.35}{27}\\ = 87.97 packs[/tex]

Answer:

SA: 456

V: 408

Step-by-step explanation:

To find the volume of this prism, you first need to find the area of the triangular base. The base has dimensions 6 by 8, and since it's a triangle, the area of the base is 6*8/2=24. Multiplying this by the length of the prism, you get a volume of 24*17=408. For the surface area, you need to find and add together the areas of all of the surfaces. We have already determined that the area of the two triangular bases are 24. The rectangle formed by the leg with length 6 has area 6*17=102, the one with length 8 has area 136, and the hypotenuse has area 170. Adding all of this together, you get a surface area of 24+24+102+136+170=456 square centimeters. Hope this helps!

Formula of surface area: T.S.A = ph + 2b

p: represents the perimeter of the base, h

h: the height of the prism and B

B: the area of the base.

6 + 8 + 10 = 24

24 x 17 = 408cm^2

Formula of Volume:

V: of a prism is the area of the base

B: times the height h

h: height

V=Bh

8 x 7 = 56cm^3