One of two or more Expressions that are multiplied together to get a product

Answer:

The possible distance in miles that Amelia can drive without exceeding her budget is 270 miles

Step-by-step explanation:

Given:

Amelia's budget for renting a car for a day trip = $ 89

Rental cost  = $35

cost per mile  = $0.20

To Find:

The possible distance in miles that Amelia can drive without exceeding her budget = ?

Solution:

Let M be the number of miles

The equation representing the situation can be

Total budget  less than or equal to rental + (number of mile x cost per mile)

That is

[tex]89 \leq 35 +(0.20 \times M)[/tex]

Solving for M, we get

[tex]89-35 \leq 0.20 M\\[/tex]

[tex]54 \leq 0.20M\\[/tex]

[tex]M \leq \frac{54}{0.20}[/tex]

[tex]M \leq 270[/tex]

Amelia's budget: $89. Rental: $35/day + $0.20/mile. Inequality: [tex]\( M \leq 270 \)[/tex] . Amelia can drive ≤270 miles.

let's break it down step by step.

1. Setting up the total cost equation:

  We're given that the rental cost is $35 per day plus $0.20 per mile. So, the total cost [tex]\( C \)[/tex] can be represented as:

 [tex]\[ C = 35 + 0.20M \][/tex]

  Where [tex]\( M \)[/tex] is the number of miles driven.

2. Setting up the inequality:

  We're told that Amelia can spend no more than $89. Therefore, we set up the inequality:

 [tex]\[ 35 + 0.20M \leq 89 \][/tex]

  This inequality represents that the total cost (rental cost plus mileage cost) should be less than or equal to $89.

3. Solving the inequality:

  To solve for [tex]\( M \),[/tex] we first subtract $35 from both sides to isolate the term involving [tex]\( M \):[/tex]

 [tex]\[ 0.20M \leq 89 - 35 \] \[ 0.20M \leq 54 \][/tex]

4. Dividing both sides by 0.20 to isolate [tex]\( M \):[/tex]

  [tex]\[ M \leq \frac{54}{0.20} \] \[ M \leq 270 \][/tex]

5. Interpreting the result:

  The inequality [tex]\( M \leq 270 \)[/tex] tells us that Amelia can drive at most 270 miles without exceeding her budget of $89.

So, in detail, Amelia can drive a maximum of 270 miles to stay within her budget. Any distance beyond that would exceed her budget of $89 for the day trip.

Answer: 75

Step-by-step explanation:

Answer:

75

Step-by-step explanation:

multiple of 15

7+5=12

Answer:

The statement that is true about deep currents is :

They move cold water along the bottom of the ocean from the Atlantic Ocean to the Pacific Ocean.

The correct option for this is the second option, Option B.

Step-by-step explanation:

The statement that is true about deep currents is :

They move cold water along the bottom of the ocean from the Atlantic Ocean to the Pacific Ocean.

Answer:

Therefore,

The Length is longer than Width by 2 units.

[tex]Length=Width+2[/tex]

Step-by-step explanation:

Given:

Let the vertices of a Rectangle be  

A ( -7 , 6)

B ( 3 , 6)

C ( 3 , -6)

D ( -7 ,-6)

To Find:

Relation between Length and Width = ?

Solution:

First we will find the Length and Width of Rectangle by Distance Formula ,

[tex]l(AB) = \sqrt{((x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} )}[/tex]

Substituting the values we get

[tex]l(AB) = \sqrt{((3-(-7))^{2}+(6-6)^{2} )}[/tex]

[tex]l(AB) = \sqrt{((10)^{2}+(0)^{2} )}\\l(AB)=\sqrt{100}=10\ unit[/tex]

Similarly for BC we will have,

[tex]l(BC) = \sqrt{((3-3)^{2}+(-6-6)^{2} )}\\l(BC)=\sqrt{144}=12\ unit[/tex]

Now

Length = 12 units.

Width = 10 units.

Therefore,

Let Length be denoted by "L" and Width by "W" then

[tex]Length=Width+2=10+2=12\\\\\therefore L=W+2[/tex]

Therefore,

The Length is longer than Width by 2 units.

[tex]Length=Width+2[/tex]

Answer:

rational number

Step-by-step explanation:

Answer:

It's a rational. You can convert this to a simplified fraction

An irrational number is a number which cannot be expressed in a ratio of two integers. In rational numbers, both numerator and denominator are whole numbers, where the denominator is not equal to zero. While an irrational number cannot be written in a fraction.

Answer:

[tex]m\angle RST=41^o[/tex]

Step-by-step explanation:

The picture of the question in the attached figure

we know that

The measure of the external angle is the semi-difference of the arcs it covers.

so

[tex]m\angle RST=\frac{1}{2}[arc\ RT-arc\ UV][/tex]

substitute the given values

[tex]m\angle RST=\frac{1}{2}[107^o-25^o][/tex]

[tex]m\angle RST=\frac{1}{2}[82^o][/tex]

[tex]m\angle RST=41^o[/tex]

Answer:

Step-by-step explanation:

f(x) = -4x^2 - 6x - 1  ........ g(x) = -x^2 - 5x + 3

find (f + g)(x)

-4x^2 - 6x - 1 + (-x^2 - 5x + 3) =

-4x^2 - 6x - 1 - x^2 - 5x + 3 =

-5x^2 - 11x + 2 <====

Answer: B

Step-by-step explanation:

Answer:

Statement (reason):

∆ABC is an isosceles triangle with vertex angle B (Given).

Angle A is congruent to angle E (Given).

Angle BCA is congruent to angle DCE (Given).

BC is congruent to DC (Given).

∆ABC is congruent to ∆EDC (AAS).

AC is congruent to CE (CPCTC).

C is the midpoint of AE (Definition of midpoint).

Answer:

e

Step-by-step explanation:

because the lines are less scattered and they all are going straight up. they are also higher then all of the other ones.

After calculating the cost per hawk for each company, Company C offers the best buy at $2.71 per hawk.

The goal is to find out which company offers the best buy for the plush toy hawks. To do so, we'll calculate the cost per hawk from each company and compare them.

Company C offers the lowest cost per hawk at $2.71, thus they have the best buy.

James has pennies, nickles and dimes in his bank. he has more than $1.60 and less than $2.00 in the bank. there are 5 times as many pennies as dimes. there is an equal number of nickels and dimes. what is the exact amount of money in his bank?

Answer:

The exact amount of money in his bank is $ 1.8

Solution:

Let "p" be the number of pennies

Let "d" be the number of dimes

Let "n" be the number of nickels

Given that,

There are 5 times as many pennies as dimes

Number of pennies = 5 times the number of dimes

p = 5d ----------- eqn 1

There is an equal number of nickels and dimes

n = d -------- eqn 2

We know that,

value of 1 dime = 0.10 dollar

value of 1 nickel = 0.05 dollar

value of 1 penny = 0.01 dollar

The total value of coins is:

total value = d(0.10) + n(0.05) + p(0.01)

Substitute eqn 1 and eqn 2

total value = d(0.10) + d(0.05) + 5d(0.01)

total value = 0.2d

Given that he has more than $1.60 and less than $2.00 in the bank

Therefore, 0.2d must be greater than 1.60 and less than 2.00

Try for d = 8

total value = 0.2 x 8 = 1.6

But value must be greater than 1.6

Try for d = 9

total value = 0.2 x 9 = 1.8

Thus 1.8 is greater than 1.60 and less than 2.00

Therefore, the exact amount of money in his bank is $ 1.8

The  absolute value of the melting point of neon greater than the absolute value of the melting point of hydrogen.

Step-by-step explanation:

In positive numbers, when the number gets larger then it is considered to be the greatest number.

for example: 20 > 5.

Meanwhile, For negative numbers, when the number gets larger then it is considered to be the smallest.

For example: -21 > - 40.

From the given table, we are given with the values of Melting point:

Hydrogen= -259.

Neon = -248.

Oxygen = -218.

We have to compare the melting points of hydrogen and neon,

⇒ - 248 > - 259.

Thus the melting point of the neon is greater than the melting point of the hydrogen.

Answer:

800

Step-by-step explanation:

1400 (the whole) / 7 (the whole) =200 (the partial) 200*4=800

Answer:

800

Step-by-step explanation:

4 out of 7 equals x out of 1400?

4/7 = x/1400

Cross multiply.

7x = 4 * 1400

Divide both sides by 7.

x = 4 * 1400/7

x = 4 * 200

x = 800

Answer: 800 dentists

Answer:

6. a=22, b= 11

7. a =4, b=

[tex]2 \sqrt{2} [/tex]

Step-by-step explanation:

6.

[tex] \tan(30) = \frac{b}{11 \sqrt{3} } \\ or \: \: ( \frac{1}{ \sqrt{3} } ) = \frac{b}{11 \sqrt{3} } \\ or \: \: \: b = 11 \\ and \: \sin(30) = \frac{11}{a} \\ or \: \ \: \frac{1}{2} = \frac{11}{a} \\ \: \: \: \: a = 22[/tex]

Hope u understand....

[tex]48 {in}^{2} [/tex]

Answer: B . 48 in²

Step-by-step explanation:

First o all complete the block and find the area

       The area of the completed block which looks like a rectangle

                                                                          =  L x B

                                                                          = 9 x 6

                                                                          = 54 in²

Step 2 : Find the area of the removed right angled triangle using the formula

                                                                         = ¹/₂b x h

where the base is 3 in and the height is 4 in

                                                                        = ¹/₂ x 3 x 4

                                                                        = 6 in².

Therefore, to find the area of the remaining  figure :

Area of the complete block less the area of the right  angled triangle

                                                                        = ( 54 - 6 ) in²

                                                                        = 48 in²

The option therefore is  B

[tex]1\frac{2}{3}[/tex] can be rewritten as 5/3 which is improper fraction.

A fraction represents a part of a whole.

Fractions are three types, Proper, improper and mixed fractions.

In proper fractions, denominator is less than numerator.

Improper fractions are fractions whose denominator is greater than numerator.

Mixed fractions can be converted to improper fractions.

The given fraction is improper fraction.

[tex]1\frac{2}{3}[/tex] is a mixed fraction.

((3×1)+2))/3=5/3

Hence, [tex]1\frac{2}{3}[/tex] can be rewritten as 5/3 which is improper fraction.

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Answer:

5/26

Step-by-step explanation:

red / all = 10 / (15+5+10+12 +10)

=10 / 52

=5/26

Probability of choosing a red candy is 5 / 26

Given that:

Number of brown candy = 15

Number of blue candy = 10

Number of red candy = 10

Number of green candy = 5

Number of yellow candy = 12

Find:

Probability of choosing a red candy

Computation:

Total number of candies = 15+5+10+12+10

Total number of candies = 52

Probability of choosing a red candy = Number of red candy / Total number of candies

Probability of choosing a red candy = 10 / 52

Probability of choosing a red candy = 5 / 26

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Answer: x² + y² + 22x + 16y + 169 = 0

Step-by-step explanation:

Equation of a circle with center (a,b) , and radius r i.e center is  not the origin

The equation becomes

( x - a )² + ( y - b )² = r² ------------------------------ 1

a = -11, b = -8

[( x - (-11 )]²  +  [( y - (-8)]² = 4²

      ( x + 11 )² + ( y + 8 )² = 4²

Carry out expansion

x² + 22x + 121 +  y² + 16y + 64 = 16

Rearrange the expression,

x² + y² + 22x + 16y + 121 + 64 - 16 = 0

x² + y² + 22x + 16y + 169 = 0

The equation of the circle is

x² + y² + 22x + 16y + 169 = 0

Answer:

Calvin's first step is to simplify the expression is to apply the quotient of powers to get (r Superscript negative 13 Baseline s Superscript negative 1 Baseline) Superscript negative 4 is the correct step

That is [tex](\frac{r^{-5}s^{-3}}{r^8s^{-2}})^{-4}=(r^{-13}s^{-1})^{-4}[/tex] Calvin's step is the correct step.Because this is the correct way to do simplify the rational expression. And also because Nadine made a blender mistake in her operations in step

Step-by-step explanation:

Given that Nadine and Calvin are simplifying the expression (StartFraction r Superscript negative 5 Baseline s Superscript negative 3 Baseline Over r Superscript 8 Baseline s Superscript negative 2 Baseline EndFraction) Superscript negative 4

Their expression can be written as below

[tex](\frac{r^{-5}s^{-3}}{r^8s^{-2}})^{-4}[/tex]

Nadine's first step is to simplify the expression is to raise the numerator and denominator to the power of 4 to get StartFraction r Superscript negative 20 Baseline s Superscript negative 12 Baseline Over r Superscript 32 Baseline s Superscript 8 Baseline EndFraction

That is [tex]\frac{r^{20}s^{12}}{r^{-32}s^8}[/tex]

Calvin's first step is to simplify the expression is to apply the quotient of powers to get (r Superscript negative 13 Baseline s Superscript negative 1 Baseline) Superscript negative 4

That is [tex]r^{-13}s^{-1}[/tex]

Now simplify the given expression to check whose step is correct:

[tex](\frac{r^{-5}s^{-3}}{r^8s^{-2}})^{-4}[/tex]

[tex]=(r^{-5}s^{-3}r^{-8}s^{2})^{-4}[/tex] ( using the property [tex]\frac{1}{a^m}=a^{-m}[/tex] )

[tex]=(r^{-5-8}s^{-3+2})^{-4}[/tex]

[tex]=(r^{-13}s^{-1})^{-4}[/tex]

Therefore [tex](\frac{r^{-5}s^{-3}}{r^8s^{-2}})^{-4}=(r^{-13}s^{-1})^{-4}[/tex]

Therefore Calvin's first step is to simplify the expression is to apply the quotient of powers to get (r Superscript negative 13 Baseline s Superscript negative 1 Baseline) Superscript negative 4 is the correct step.

That is [tex](\frac{r^{-5}s^{-3}}{r^8s^{-2}})^{-4}=(r^{-13}s^{-1})^{-4}[/tex] Calvin's step is the correct step .Because this is the correct way to do simplify the rational expression.And also because Nadine made a blender mistake in her operations in step

The solution to the system of linear equations 4x - 2y = 8 and y = (3/2)x - 2 is x = 4 and y = 4, found by substituting y in the first equation with the expression from the second equation and solving for x.

The student is asking to solve a system of linear equations. The equations provided are:

4x - 2y = 8

y = (3/2)x - 2

We will solve this system using substitution since the second equation is already solved for y. Here are the steps:

Substitute y in the first equation with the expression from the second equation: 4x - 2((3/2)x - 2) = 8.

Simplify the equation: 4x - 3x + 4 = 8.

Solve the simplified equation for x: x + 4 = 8, which leads to x = 4.

Substitute x back into the second equation to find y: y = (3/2)4 - 2.

Calculate the value of y: y = 6 - 2, which leads to y = 4.

The solution to the system of equations is x = 4 and y = 4.

Answer:

You multiply, the answer is 3,521.6084.

Step-by-step explanation:

Answer:

3521.6084

Step-by-step explanation:

Answer:

The correct answer is A. Jim is better positioned to invest in bonds because he makes less and has longer before his investment matures.

Step-by-step explanation:

Jim is better positioned to invest in bonds for two reasons:

1. He can invest and take advantage of long-term bonds, between 12 and 20 years of term of maturity, that are those that usually have the highest interest rate. His goal is to invest and save for his daughter's college education, that is a newborn.

2. The real interest rates are rising. It means the bonds interest rates are clearly above the inflation rate in the country where Jim and his family live, having a better return for his investment.

Answer:

29

Step-by-step explanation:

Look at image

60 percent of 78 is the same as 65 percent of 72.

Step-by-step explanation:

Let,

x be the unknown number.

According to given statement;

60% of 78 = 65% of x

[tex]\frac{60}{100}*78=\frac{65}{100}x\\0.60*78=0.65*x\\46.8=0.65x\\0.65x=46.8\\[/tex]

Dividing both sides by 0.65

[tex]\frac{0.65x}{0.65}=\frac{46.8}{0.65}\\x=72[/tex]

Therefore;

60 percent of 78 is the same as 65 percent of 72.

Keywords: percentage, division

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Answer:

72

Step-by-step explanation:

sheesh kinda bussing

btw shesh

Answer:

y = 3x +2

Step-by-step explanation:

The first answer

Answer:

5% less of 180, or 95% of 180

Step-by-step explanation:

FInd 10% of 180, 18, multiply 18 by 9.

18 x 9 = 162, find half of 18 which is 9.

Add to 162.

162 + 9 = 171.

Therefore,

5% less of 180 is 171.

Answer: The top one

Step-by-step explanation:

Because there can only be one input for one output. (X’s can’t repeat)

Answer:

x = 1

Step-by-step explanation:

If you graph this, you will see that you will get a line that is straight up and down (or perpendicular to the x axis).  No matter what y is, x will always be 1.