Rita's family is moving to Grand Junction to Dallas. The moving van averages 60 miles each hour. About how many hours does the van take to reach Dallas? Explain your work

Answer:

x = [tex]\frac{4}{35}[/tex]

Step-by-step explanation:

Given

32x + 1 = - 3x + 5 ( add 3x to both sides )

35x + 1 = 5 ( subtract 1 from both sides )

35x = 4 ( divide both sides by 35 )

x = [tex]\frac{4}{35}[/tex]

Answer:

[tex]x = \frac{ - 6}{29} [/tex]

Step-by-step explanation:

[tex]32x + 1 - 3x + 5[/tex]

Collect like terms

[tex]32x - 3x + 1 + 5[/tex]

[tex] 29x + 6[/tex]

For simplifying, equate the expression to zero. Thus,

[tex]29x + 6 = 0[/tex]

Add -6 to both sides of the equation

[tex]29x + 6 - 6 = 0 - 6[/tex]

[tex]29x = - 6[/tex]

Divide through by 29

[tex] \frac{29x}{29} = \frac{ - 6}{29} [/tex]

[tex]x = \frac{ - 6}{29} [/tex]

Answer:

answer b

Step-by-step explanation:

The coordinates of p are (3, -2). Option D is correct.

A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.

From the graph, the coordinates of A = (9,-8) and the coordinates of B =(-6, 7) p divides the line segmentin 2/3 thus,

We can use the section formula to find the coordinates of the point P that divides the line segment AB into the ratio 2:3.

The section formula states that if a line segment AB is divided by a point P into two line segments, with lengths in the ratio m:n, then the coordinates of P are:

[tex][Px = (nA_x + mB_x)/(m+n), \\Py = (nA_y + mB_y)/(m+n)][/tex]

In this case, we want to divide the line segment AB into the ratio 2:3, so we have m:n = 2:3. This means that m = 2 and n = 3.

Substituting the given values, we get:

[tex]P_x = (3*9 + 2(-6))/(2+3) = 3\\Py = (3*(-8) + 2*7)/(2+3) = -2[/tex]

Therefore, the coordinates of P are (3, -2).

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Answer:

the first blank is 10

and the second blank is 5

Step-by-step explanation:

Answer:

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

Step-by-step explanation:

We will find the probability of rolling a 5 and then probability of rolling a 3 and then multiply the numbers to get the probability that he will roll a 5 and then a 3 in two rolls.

There are 6 total possibilities (1 through 6).

There are one 5s, so the probability of rolling a 5 would be:

P(roll 5) = 1/6

Also, there is one 3, so rolling a 3 would have the same probability.

P(roll 3) = 1/6

Hence,

Probability of rolling a 5 and then a 3 is:

P(5,3) = 1/6 * 1/6 = 1/36

Answer:

Table C represents an exponential function.

Answer: is c 3/2

Step-by-step explanation:

The answer is option C) 3/2.

To find out how many 1/4 cup servings are in 3/8 cups of pudding, we can use the formula:

First, let's convert 3 8/10 cups to an improper fraction.

To do this, we multiply the whole number (3) by the denominator (10) and add the numerator (8) to get the numerator of the improper fraction. The denominator remains the same.

(3/8) ÷ (1/4) = (3/8) × (4/1) = 12/8 = 3/2

Therefore, there are 3/2 or 1 1/2 servings of 1/4 cup in 3/8 cups of pudding.

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Answer:

[tex]\frac{a}{p}\times (q-r)+\frac{b}{q}\times (r-p)+\frac{c}{r}\times (p-q)\neq 0[/tex]  is proved for the sum of pth, qth and rth terms of an arithmetic progression are a, b,and c respectively.

Step-by-step explanation:

Given that the sum of pth, qth and rth terms of an arithmetic progression are a, b and c respectively.

First term of given arithmetic progression is A

and common difference is D

ie., [tex]a_{1}=A[/tex] and common difference=D

The nth term can be written as

[tex]a_{n}=A+(n-1)D[/tex]

pth term of given arithmetic progression is a

[tex]a_{p}=A+(p-1)D=a[/tex]

qth term of given arithmetic progression is b

[tex]a_{q}=A+(q-1)D=b[/tex] and

rth term of given arithmetic progression is c

[tex]a_{r}=A+(r-1)D=c[/tex]

We have to prove that

[tex]\frac{a}{p}\times (q-r)+\frac{b}{q}\times (r-p)+\frac{c}{r}\times (p-q)=0[/tex]

Now to prove LHS=RHS

Now take LHS

[tex]\frac{a}{p}\times (q-r)+\frac{b}{q}\times (r-p)+\frac{c}{r}\times (p-q)[/tex]

[tex]=\frac{A+(p-1)D}{p}\times (q-r)+\frac{A+(q-1)D}{q}\times (r-p)+\frac{A+(r-1)D}{r}\times (p-q)[/tex]

[tex]=\frac{A+pD-D}{p}\times (q-r)+\frac{A+qD-D}{q}\times (r-p)+\frac{A+rD-D}{r}\times (p-q)[/tex]

[tex]=\frac{Aq+pqD-Dq-Ar-prD+rD}{p}+\frac{Ar+rqD-Dr-Ap-pqD+pD}{q}+\frac{Ap+prD-Dp-Aq-qrD+qD}{r}[/tex]

[tex]=\frac{[Aq+pqD-Dq-Ar-prD+rD]\times qr+[Ar+rqD-Dr-Ap-pqD+pD]\times pr+[Ap+prD-Dp-Aq-qrD+qD]\times pq}{pqr}[/tex]

[tex]=\frac{Arq^{2}+pq^{2} rD-Dq^{2} r-Aqr^{2}-pqr^{2} D+qr^{2} D+Apr^{2}+pr^{2} qD-pDr^{2} -Ap^{2}r-p^{2} rqD+p^{2} rD+Ap^{2} q+p^{2} qrD-Dp^{2} q-Aq^{2} p-q^{2} prD+q^{2}pD}{pqr}[/tex]

[tex]=\frac{Arq^{2}-Dq^{2}r-Aqr^{2}+qr^{2}D+Apr^{2}-pDr^{2}-Ap^{2}r+p^{2}rD+Ap^{2}q-Dp^{2}q-Aq^{2}p+q^{2}pD}{pqr}[/tex]

[tex]=\frac{Arq^{2}-Dq^{2}r-Aqr^{2}+qr^{2}D+Apr^{2} -pDr^{2}-Ap^{2}r+p^{2}rD+Ap^{2}q-Dp^{2}q-Aq^{2}p+q^{2}pD}{pqr}[/tex]

[tex]\neq 0[/tex]

ie., [tex]RHS\neq 0[/tex]

Therefore [tex]LHS\neq RHS[/tex]

ie.,[tex]\frac{a}{p}\times (q-r)+\frac{b}{q}\times (r-p)+\frac{c}{r}\times (p-q)\neq 0[/tex]  

Hence proved

The equation solved for s is s = 4p - 48h

Solution:

Given that equation a company uses to  calculate pay checks is p = 12h +0.25s

Therefore the given equation is:

p = 12h + 0.25s

Where "h" is the number of hours worked

"s" is the total sales

To find: equation for "s"

Let us solve the given equation for "s"

p = 12h + 0.25s

Now move 12h from R.H.S to L.H.S

p - 12h = 0.25s

Now move from 0.25 from R.H.S to L.H.S

[tex]s = \frac{p-12h}{0.25}\\\\s = \frac{p}{0.25} -\frac{12h}{0.25}[/tex]

We know that, [tex]0.25 = \frac{1}{4}[/tex]

[tex]s = \frac{p}{\frac{1}{4}} -\frac{12h}{\frac{1}{4}}\\\\s = p \times \frac{4}{1} - 12h \times \frac{4}{1}\\\\s = 4p - 48h[/tex]

Thus the equation for s is s = 4p - 48h

Answer:

The recursive formula of the arithmetic sequence

[tex]a_{1}=First term of the arithmetic sequence[/tex]

[tex]a_{n}= a_{n-1}+common difference(d)[/tex].

Step-by-step explanation:

A recursive formula is used to find any term of an arithmetic sequence using a function of the preceding term. Each term is the sum of the previous term and the common difference.

To find the recursive formula of the arithmetic sequence

[tex]a_{1}=First term of the arithmetic sequence[/tex]

[tex]a_{n}= a_{n-1}+common difference(d)[/tex]

Answer:

The value of r is $0.95 and b is $6.5 , The graph of given equation plotted as shown

Step-by-step explanation:

Given as :

The two line equation are

2 r + b = $8.40              .........A    and

3 r + b = $9.35               .........B

Now, Solving equations A and B

i.e (3 r + b) - (2 r + b) = $9.35 - $8.40

Or, (3 r - 2 r) + (b - b) = 0.95

or, r + 0 = 0.95

∴ r = $0.95

Now, put the value og r into eq A

∵ 2 r + b = $8.40  

So, 2× $0.95 + b = $8.40  

Or, $1.9 + b = $8.40  

Or, b = $8.40 - $1.9

∴ b = $6.5

So, The value of r = $0.95 and b = $6.5

Now, for plotting the equation on graph

let put r on x axis

and put b on y-axis

Hence, The value of r is $0.95 and b is $6.5 , The graph of given equation plotted as shown . Answer

Answer:

OA there is not enough information

Step-by-step explanation:

only the angles are congruent in both squares

Answer:

OA there is not enough information to determine whether the squares are congruent.

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

18x9/0-12.6 x 14 x 13.2 = 18

f(x)=x2+7

f(4)=4*2+7

4*2=8

8+7=15

Answer:

x=-1 and x=5

Step-by-step explanation:

we have

[tex]x^{2} -4x=5[/tex]

Solve it by completing the square method

We take the coefficient of x that is -4, divide it by 2 and then square it

so

[tex]-\frac{4}{2}=-2[/tex]

square it

[tex](-2)^2 = 4[/tex]

Adds 4 both sides

[tex]x^{2} -4x+4=5+4[/tex]

Combine like terms right side

[tex]x^{2} -4x+4=9[/tex]

Rewrite as perfect squares

[tex](x-2)^{2}=9[/tex]

take square root both sides

[tex]x-2=\pm3[/tex]

[tex]x=2\pm3[/tex]

therefore

[tex]x=2+3=5[/tex]

[tex]x=2-3=-1[/tex]

Answer:

C. 64 pie m^3

Answer: 64[tex]\pi[/tex][tex]m^{3}[/tex]

Step-by-step explanation:

The volume of cylinder is given as

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

r = 4m

h = 4m

Substituting into the formula , we have

V = [tex]\pi[/tex]  x [tex]4^{2}[/tex] x 4

V = [tex]\pi[/tex] x 16 x 4

V = [tex]\pi[/tex] x 64

Therefore : V = 64[tex]\pi[/tex][tex]m^{3}[/tex]

Answer:

The greatest number of pairs of skis and snowboards the group can rent are 21 pairs of skis and 9 pairs of snowboards.

Step-by-step explanation:

Given:

A group can rent pairs of skis and snowboards by the week. They get a reduced rate if they rent 7 pairs of skis for every 3 snowboards rented. The reduced ski rate is $45.50 per pair of skis per week, and the reduced snowboard rate is $110 per snowboard per week.

The sales tax on each rental is 16%.

The group has $2,500 available to spend on ski and snowboard rentals.

If the ratio of pairs of skis to snowboards is 7:3.

Now, to find the greatest number of pairs of skis and snowboards rentals.

So, the rent of 7 pairs of skis = [tex]7\times 45.50=\$318.50.[/tex]

And the rent of 3 pairs of snowboards = [tex]3\times 110=\$330.[/tex]

So, total rental amount of 7 pairs of skis and 3 pairs of snowboards:

[tex]318.50 + 330 = 648.50.[/tex]

Now, to get the rental amount after sales tax:

648.50 + 16% of $648.50.

[tex]=648.50 +\frac{16}{100}\times 648.50.[/tex]

[tex]=648.50+103.76[/tex]

[tex]=\$752.26.[/tex]

The total rental amount after sales tax = $752.26.

As the group has available $2,500.

So, the sets according to the given ratio:

[tex]2500\div 752.26 = 3.32.[/tex]

[tex]=3\ sets.[/tex]

Thus, there are 3 sets of the ratio 7:3.

So, the rental price according to sets are:

The rent of Skis:

[tex]7\times 3 = 21[/tex] 

[tex]21\times 45.50= 955.50[/tex]

The rent of snowboards:

[tex]3\times 3 = 9[/tex]

[tex]9\times 110 = 990[/tex]

So. the total rental amount of skis and snowboards according to sets are:

[tex]955.50 + 990 = 1,945.50[/tex]

Now, the amount of rent after sales tax:

$1945.50 + 16% of $1945.50.

[tex]=1945.50+\frac{16}{100}\times 1945.50[/tex]

[tex]=1945.50+311.28=\$2256.78.[/tex]

Thus, the total cost = $2256.78.

Now, to get the greatest number of pairs of skis to snowboards that can be rent:

[tex]2,500 - 2,256.78 = 243.22[/tex]

The cost of 21 pair of skis and 9 pairs of snowboards is $2256.78 and the group has available only $2500 to spend.

Thus, they can rent only 21 pairs of skis and 9 pairs of snowboards.

Therefore, the greatest number of pairs of skis and snowboards the group can rent are 21 pairs of skis and 9 pairs of snowboards.

Answer:

yes it is!

Step-by-step explanation:

if you add 8+10=18

11+10+21

8+11=19

if the numbers do not repeat or add up to one of the numbers you've got as an option it is a right triangle.

Using ants on a stretching ruler to illustrate Hubble's Law shows how objects further away move faster relative to an observer, much like galaxies in the universe, while highlighting the organization and communication in ant colonies.

The scenario described involves ants on various points of a stretchable ruler, illustrating a concept similar to Hubble's Law in cosmology. One ant measures how the distance to the other ants increases as the ruler stretches, showing that ants further away appear to move faster relative to the observing ant. This phenomenon occurs not because the ants are moving of their own volition, but because the ruler itself is stretching, much like space-time expands in the universe.

Furthermore, ants in a colony communicate using pheromones, and their large groups, called colonies, are highly organized with different roles such as workers, soldiers, and a queen. The example of ants traveling on a ruler and cooperating in a colony also demonstrates principles of coordination, communication, and perception from a relative standpoint.

Answer:

Step-by-step explanation:

A horizontal line has the equation "y = " something, while a vertical line has the equation "x = " something.  If our line is horizontal through (3, 6), it will be horizontal through the y coordinate (and vertical through the x coordinate).  Our equation is y = 6

(The vertical equation through this point would be x = 3, just so you understand what I meant above.)

Two division equations were found for each given multiplication equation. The division equations are the inverse of the multiplication equations, essentially reversing the operation.

The goal is to find two division equations that correspond to each given multiplication equation. Basically, we are undoing or reversing the multiplication operation.

a. 15 x 2/5 = 6

b. 6 x 4/3 = 8

c. 16 x 7/8 = 14

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Answer:

Step-by-step explanation:

she works 20 hrs each week....so far, she has worked 5.25 hrs and 5.5 hrs

h = hours remaining

so we are basically taking the total hrs and subtracting the combined hrs she has worked

h = 20 - (5.5 + 5.25) <== ur equation

The sentence that could be used to find h, the number of hours remaining for Kendra to work this week is h = 20 - (5.5 + 5.25).

An expression is a sentence with a minimum of two numbers or variables and at least one math operation.

Kendra works 20 hours each week. So far this week, she has worked 5.5 hours on Tuesday and 5.25 hours on Thursday.

Let h be the number of hours remaining for Kendra to work this week.

The sentence that could be used to find h, the number of hours remaining for Kendra to work this week is;

A number of hours remaining for Kendra to work this week = Total number of hours - working on Tuesday - working on Thursday.

h = 20 - 5.5 - 5.25

h = 20 - (5.5 + 5.25)

Hence, the sentence that could be used to find h, the number of hours remaining for Kendra to work this week is h = 20 - (5.5 + 5.25).

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Answer:

The y-coordinate of the original point is negative and the y-coordiinate of the new point is positive.

The transformation is:

[tex](-7.5, 6)[/tex] →  [tex](-7.5, -6)[/tex]

Step-by-step explanation:

For this exercise it is important to remember the definition of "Reflection".

A Reflection is a transformation that consists in folding an figure over a line called "Line of reflection",

In tranformations, the original figure is called "Pre-image" and the figure obtained after the transdformation is called "Image".

Given a point [tex](x,y)[/tex], if this is reflected across the x-axis, the x-coordinate of the point does not change, but the sign of the y-coordinate is transformed into its opposite. Then:

 [tex](x,y)[/tex] →  [tex](x,-y)[/tex]

So, given the new point:

[tex](-7.5, 6)[/tex]

You can determine that the original point is:

[tex](-7.5, -6)[/tex]

Answer:

Yes, both expressions for the two method are equivalent.

Step-by-step explanation:

Let the cost of the dress be p as given.

Marta want to evaluate the tax which is proportional to the cost.

8% sales tax will correspond to (8/100)*p=0.08p

Then she will add 0.08 p to p to obtain 0.08p+p= p(0.08+1)= 1.08p

On the other hand, Esther thinks that the cost of the dress, p, should be multiplied by 1.08 to obtain 1.08p at once!

Thus both expressions are equivalent. Only that Martha is wanting to pay much attention to the details , while Esther is a quick one :-)!

Answer:

[tex]A=125.66\ cm^2[/tex]

Step-by-step explanation:

The complete question is

The area of the shaded region is the area inside the larger circle and outside the smaller circle

so

To find out the area of the shaded region subtract the area of the smaller circle from the area of the larger circle

Remember that

The area of the circle is

[tex]A=\pi r^{2}[/tex]

therefore

The area of the shaded region is

[tex]A=\pi [r_1^2-r_2^2][/tex]

where

[tex]r_1=11\ cm[/tex] ---> radius of the larger circle

[tex]r_2=9\ cm[/tex] ---> radius of the smaller circle

assume

[tex]\pi =3.1416[/tex]

substitute

[tex]A=3.1416 [11^2-9^2][/tex]

[tex]A=3.1416 [40][/tex]

[tex]A=125.66\ cm^2[/tex]

Answer:

$162÷24=$6.75

$6.75-per each

five pairs of socks-$6.75x5=$33.75

Final answer:

To determine the cost of five pairs of socks when the coach spent $162 for 24 pairs, we find the cost per pair ($6.75) and multiply it by 5, resulting in $33.75 for five pairs.

Explanation:

The student's question is, "A soccer coach spent 162 dollars on 24 pairs of socks for his players. How much did five pairs of socks cost?" To solve this, we start by determining the cost per pair of socks. We divide the total cost by the number of pairs to get the price for each pair:

Cost per pair = Total cost / Number of pairs
= $162 / 24 pairs
= $6.75 per pair

Now, to find the cost for five pairs of socks, we multiply the cost per pair by the number of pairs desired:

Cost for five pairs = Cost per pair x 5
= $6.75 x 5
= $33.75

Therefore, five pairs of socks cost $33.75.

Answer:

3780 feet

Step-by-step explanation:

49/7*60*3(be careful that it is 3 minutes,not seconds)

=1260

Now,we have to convert yards into feet.

1260 yards = 3780 feet

Because feet is three times yard.

Hope this answer helps! ;)

Answer:

Distance ran by Sara in 3 minutes is 3780 feet.

Step-by-step explanation:

We know that,

1 yard = 3 feet

So, 49 yards = 49 × 3 feet = 147 feet

Now, it is given that Sara can run 49 yards in 7 seconds. So, we can say that, Sara can run 147 feet in 7 seconds

So, distance ran by Sara in 7 seconds = 49 yards = 147 feet

Now, distance ran by Sara in 1 second = (147 ÷ 7) feet = 21 feet

Now, 1 min = 60 sec, then 3 min = 3 × 60 sec = 180 sec

So, distance ran by Sara in 3 min or 180 sec = 21 × 180 = 3780 feet

∴ distance ran by Sara in 3 minutes is 3780 feet.

The coefficients in the expression W - 8x + 20y + 6z are -8 for x, 20 for y, and 6 for z. W is not considered a variable with a coefficient but would implicitly have a coefficient of 1.

The coefficients in the expression W - 8x + 20y + 6z are the numerical factors that are multiplied by the variables. In this case:

Coefficients are important as they determine the rate at which the value of the expression changes with respect to changes in the variable values.

Note that W in this expression is not preceded by a coefficient, and if it is supposed to have a coefficient, it is implicitly 1.

However, as the question does not consider W as a variable with a coefficient, we exclude it from the list of coefficients.

Answer:

5/6

Step-by-step explanation:

1/3+3/6=2/6+3/6=5/6

Answer:

25%

Step-by-step explanation:

180+60=240

60/240=0.25

0.25*100

25%

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Answer:

x^14

Step-by-step explanation:

(x^7)^2=x^7×2

=x^14