Bruce bought two books.One book costs $4.00 more than three times the other.Together, the two books cost him $72.
Write the statement using symbolic language

Answer:

  9

Step-by-step explanation:

The first simplification we can make is to replace 6^0 with 1.

The first rules of exponents we can apply are ...

  (a·b)^c = a^c·b^c . . . . . . similar to the distributive property

  (a^b)^c = a^(b·c)

This reduces your expression to ...

  [tex](2^8\cdot 3^{-5})^{-2}\cdot\left(\dfrac{3^{-2}}{2^3}\right)^4\cdot 2^{28}=2^{8(-2)}\cdot 3^{-5(-2)}\cdot\dfrac{3^{-2(4)}}{2^{3(4)}}\cdot 2^{28}\\\\=2^{-16}\cdot 3^{10}\cdot\dfrac{3^{-8}}{2^{12}}\cdot 2^{28}[/tex]

Now we can apply another two rules of exponents:

  (a^b)(a^c) = a^(b+c)

  1/a^b = a^-b

Using these, we have ...

  [tex]=2^{-16-12+28}\cdot 3^{10-8}\\\\=2^0\cdot 3^2\\\\=1\cdot 9=9[/tex]

The value of the expression is 9.

Answer:

The area of the larger square is 20 [tex]cm^2[/tex]

Step-by-step explanation:

Given:

The area of the smaller square   =  [tex]10 cm^2[/tex]

To Find:

The are of the larger square = ?

Solution:

The diagonal of the smaller square = diameter of the circle = sides of the larger square

The diagonal of the smaller square is

=>[tex]\sqrt{2(10)}[/tex]

=>[tex]\sqrt{20}[/tex]

=>[tex]\sqrt{2\times 2 \times 5}[/tex]

=>[tex]2\sqrt{5}[/tex]

Now this diagonal is equal to the side of the larger square

so the are of the larger square is

=>[tex](2\sqrt{5})^2[/tex]

=>[tex](2\sqrt{5}) \times (2\sqrt{5}) [/tex]

=> 20 [tex]cm^2[/tex]

It will take Eli 2.4 minutes to complete 6 laps

Step-by-step explanation:

Given

Speed = s = 1000 meters per minute

Length of one lap = 400 meters

We have to compute time for 6 laps,, so we have to find the length of 6 laps combined

[tex]Length\ of\ laps = Length\ of\ one\ lap * 6\\= 400 * 6\\= 2400\ meters[/tex]

So our total distance will be: 2400 meters

using the formula for speed

[tex]s = \frac{d}{t}\\1000 = \frac{2400}{t}\\t = \frac{2400}{1000}\\t = 2.4[/tex]

So

It will take Eli 2.4 minutes to complete 6 laps

Keywords: Speed, distance

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Answer: The graph is a parabola facing up ,

Step-by-step explanation:

Since the coefficient of [tex]x^{2}[/tex] is positive , then the graph is a parabola facing up.

The minimum point is at x = -2 ( using the formula for calculate vertex , x = [tex]\frac{-b}{2a}[/tex] )

And the y - intercept = 4

Answer:

w=3 9\17

Step-by-step explanation:

Multiply the miles per gallon by the total gallons:

32.4 x 12.7 = 411.48 total miles.

Answer:

411.48

Step-by-step explanation:

411.48

Answer:

slope is undefined

Step-by-step explanation:

Using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

If x₂ - x₁ = 0

Since division by zero is undefined then the slope of the line is undefined

This applies to a vertical line parallel to the y- axis

Answer:

4,2,0,-1

Step-by-step explanation:

Let

x ----> the independent variable or input value

y ----> the dependent variable or output value

we have the ordered pairs

(-1,2),(-3,-1),(6,0),(-1,4)

The input values are -1,-3,6,-1

The output values are 2,-1,0,4

Orders the output values from greatest to least

4>2>0>-1

therefore

4,2,0,-1

Answer:

4,2,0,-1

hope this helps

m = 90 - 6d is the equation to determine m, the number of measures Harita still needs to  memorize, as a function of d, the number of days of practice since she began learning the piece

Solution:

Given that Harita must memorize 90 measures of music for her cello solo at a concert

To find: equation to determine m, the number of measures Harita still needs to  memorize, as a function of d, the number of days of practice since she began learning the piece

Let "m" be the number of measures Harita still needs to  memorize

Let "d" be the number of days of practice since she began learning the piece

Given that She plans on memorizing 18 new measures for  every 3 days of practice

Rate per day is given as:

[tex]\frac{18}{3} = 6[/tex]

Therefore she memorises 6 per day

Therefore, the equation that relates 'm' to 'd' is:

m = total measures of music she must memorise - (number of measures she memorises per day x d)

m = 90 - 6(d)

m = 90 - 6d

Thus the required equation is found

Answer:

m = 90 - 6d is the equation to determine m, the number of measures Harita still needs to  memorize, as a function of d, the number of days of practice since she began learning the piece

Step-by-step explanation:

Answer: Jamie is incorrect

Step-by-step explanation:

The same number 10 is subtracted from both numbers 19 and 20. There result will only be the same if both numbers are equal.

We compare both numbers;

19 and 20

On the number line 19 comes before 20, which means 20 is greater than 19. Hence the result of subtracting the same number 10 from both of them cannot be the same.

So Jamie is incorrect.

Answer:

she is wrong 19-10 equals to 9

Step-by-step explanation:

you subtract 19 from 10 and get 9:)

For this case we have the following quadratic equation:

[tex]-2x ^ 2 -6x + 5 = 0[/tex]

Where:

[tex]a = -2\\b = -6\\c = 5[/tex]

The roots will be given by the following formula:

[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}[/tex]

Substituting the values we have:

[tex]x = \frac {- (- 6) \pm \sqrt {(- 6) ^ 2-4 (-2) (5)}} {2 (-2)}\\x = \frac {6 \pm \sqrt {36 + 40}} {- 4}\\x = \frac {6 \pm \sqrt {76}} {- 4}\\x = \frac {6 \pm \sqrt {2 ^ 2 * 19}} {- 4}\\x = \frac {6 \pm2 \sqrt {19}} {- 4}\\x = \frac {3 \pm \sqrt {19}} {- 2}[/tex]

We have two roots:

[tex]x_ {1} = \frac {-3- \sqrt {19}} {-2}\\x_ {2} = \frac {-3+ \sqrt {19}} {2}[/tex]

Answer:

[tex]x_ {1} = \frac {-3- \sqrt {19}} {2}\\x_ {2} = \frac {-3+ \sqrt {19}} {2}[/tex]

Answer:1Vertical angles theoram

Step-by-step explanation:2 coverse of alternate interior angles theoram

Answer:

1. Reason options for 3rd statement:

Alternate Interior Angles Theorem

2.Reason options for 9th statement:

Converse of Alternate Interior Angles Theorem

Step-by-step explanation:

In this question, we're trying to find out how much Jamal spent on apples.

We know that he bought 2 pounds of red apples and 3.2 pounds of green apples.

We also know that each pound of apples, no matter what kind it is, are $1.65 a pound.

In order to find the total cost of these apples, we would need to multiply the amount of pounds he has to the cost per pound.

Solve:

2 · 1.65 = 3.3‬0

3.2 · 1.65 = 5.28‬

Add those numbers together:

5.28‬ + 3.30 =  8.58‬

This means that Jamal spent $8.58‬ on apples.

Answer:

$8.58‬

Answer:

$8.58‬

Step-by-step explanation: this ok?

Answer:

$986

I attempted to do the simple math. I feel brain dead right now.  

Answer:

32=2(10+x)

32=20+2x

2x=12

x=6

therefore breadth is 6 cm

area=l×b

10×6=60

Step-by-step explanation:

Ribbon B is [tex]\frac{11}{15}[/tex] meters long

Solution:

Given that,

Ribbon A is 1/3 meter long. It is 2/5 meter shorter than ribbon B

To find: length of Ribbon B

From given information in question,

Length of Ribbon A = [tex]\frac{1}{3} \text{ meter }[/tex]

Length of Ribbon A is 2/5 meter shorter than ribbon B

Therefore we can say,

Length of Ribbon A = length of ribbon B - [tex]\frac{2}{5}[/tex]

[tex]\frac{1}{3} = \text{ length of ribbon B } -\frac{2}{5}\\\\\text{length of ribbon B } = \frac{1}{3} + \frac{2}{5}\\\\\text{length of ribbon B } = \frac{ 5 + 6}{15} = \frac{11}{15}[/tex]

Therefore ribbon B is [tex]\frac{11}{15}[/tex] meters long

Answer:

Step-by-step explanation:

Let us suppose r be the total number of meals eaten in a restaurant

Let us suppose c be the total number of meals eaten in a car

Let us suppose h be the total number of meals eaten in a home

Substituting Equation [B] into [A],

[tex]r + c + h = 171.....[A][/tex]

[tex]r + r + 11 = 171[/tex]

[tex]2r + 11 = 171[/tex]

[tex]2r = 160[/tex]

[tex]r = 80[/tex]

Putting [tex]r = 80[/tex] in [tex]r = h + 20.....[C][/tex]

[tex]80 = h + 20[/tex]

[tex]h = 60[/tex]

Putting [tex]r = 80[/tex] and [tex]h = 60[/tex] in [tex]r + c + h = 171.....[A][/tex]

[tex]80 + c + 60 = 171[/tex]

[tex]c = 171 - 60 - 80[/tex]

[tex]c = 31[/tex]

Therefore,

Verification:

[tex]r + c + h = 171[/tex]

Putting [tex]r = 80[/tex], [tex]c = 31[/tex] and [tex]h = 60[/tex] in [tex]r + c + h = 171[/tex]

[tex]80 + 31 + 60 = 171[/tex]

[tex]171 = 171[/tex]

Keywords: number, equation

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Answer:

m+n = 337

Step-by-step explanation:

Lets start from the first triangle, It is given to be as 30-60-90.

The hypotenous of first rectangle be 2x, then other sides are by default x and

[tex]\sqrt{3}(x)[/tex] , using laws of trigonometry.

(sin(30) = 0.5  and cos(30) = [tex]\frac{\sqrt{3}}{2}[/tex])

The perimeter of first triangle is ,

= [tex]2x + x + \sqrt{3}(x) = x(3+\sqrt{3}) = \sqrt{3}x(1+\sqrt{3})[/tex]

Now, for second triangle, the longer leg is 2x, and similarly again,

other 2 sides are [tex]\frac{2x}{\sqrt{3}}  and \frac{4x}{\sqrt{3}}[/tex].

Again the perimeter of triangle comes out as,

= [tex]\sqrt{3}(x)(1+\sqrt{3})(\frac{2}{\sqrt{3}})[/tex]

Thus, the repeating pattern is identified. The consecutive perimeters differ by, multiplying by factor [tex]\frac{2}{\sqrt{3}}[/tex]

Thus, we can say that perimeter of 4th triangle is,

= [tex](\frac{2}{\sqrt{3}})^{3}(X)[/tex], where X is the repeating constant.

And of 12th triangle is,

= [tex](\frac{2}{\sqrt{3}})^{11}(X)[/tex],

Evaluating the above ratio, we get,

= [tex]\frac{81}{256}[/tex]

Thus, m =256 and n=81.

Thus, m+n = 256+81 = 337.

Answer:

-7

Step-by-step explanation:

Lets assume the number Peggy is thinking of be "x".

Now as given, when twice the number is added to three times one more than the number. We can write it as

∴ [tex]2x+3(x+1)[/tex]--- Equation 1

Again, it is given that Peggy gets the same result as when she multiplies four times one less than the number.

∴ [tex]4(x-1)[/tex]-- equation 2

Next, we can equate both the equation 1 and 2 as it is given that result is same.

[tex]2x+3(x+1)= 4(x-1)[/tex]

Let´s distribute 3 into [tex](x+1)[/tex] and 4 into [tex](x-1)[/tex]

⇒ [tex]2x+3x+3=4x-4[/tex]

⇒ [tex]5x+3=4x-4[/tex]

Subtract both side by 4x and 3

∴ [tex]x=-7[/tex]

∴ Peggy was thinking of -7

The correct answer is:

Jessica can wax approximately 34,533,185 square meters per hour at her constant rate of waxing the floor.

To find out how many square meters Jessica can wax per hour, we first need to convert the square miles to square meters, then divide by the time taken.

1. Convert square miles to square meters:

  Since 1 mile = 1609.34 meters, to convert square miles to square meters, we square this conversion factor:

[tex]\[ 1 \text{ mile}^2 = (1609.34)^2 \text{ meters}^2 \] \[ 1 \text{ mile}^2 = 2,589,988.36 \text{ meters}^2 \][/tex]

  So, 20 square miles would be:

[tex]\[ 20 \text{ miles}^2 \times 2,589,988.36 \text{ meters}^2/\text{mile}^2 = 51,799,767.2 \text{ meters}^2 \][/tex]

2. Calculate the rate per hour:

  Jessica waxes 20 square miles in [tex]\( \frac{3}{5} \)[/tex] of an hour.

  So, her rate per hour is:

 [tex]\[ \frac{20 \times 2,589,988.36}{\frac{3}{5}} \text{ meters}^2/\text{hour} \][/tex]

  To simplify the calculation, we'll first find the reciprocal of [tex]\( \frac{3}{5} \): \[ \frac{1}{\frac{3}{5}} = \frac{5}{3} \][/tex]

  Now, we multiply the reciprocal by 20 square miles:

 [tex]\[ 20 \times 2,589,988.36 \times \frac{5}{3} \text{ meters}^2/\text{hour} \] \[ \text{meters}^2/\text{hour} = 34,533,184.8 \][/tex]

So, Jessica can wax approximately [tex]\( 34,533,184.8 \)[/tex] square meters per hour at her constant rate.

Answer:

15.7 years

Step-by-step explanation:

Use the formula for compound interest. A = P(1 + i)ⁿ

A is the total amount of money. A = 7200

P is the principal, starting money. P = 3000

i is the interest per compounding period in decimal form. Since interest is compounded annually, i = 0.0575

n is the number of compounding periods. n = ?

Substitute the information into the formula and isolate n.

A = P(1 + i)ⁿ

7200 = 3000(1 + 0.0575)ⁿ    Solve inside the brackets

7200 = 3000(1.0575)ⁿ

7200/3000 = 1.0575ⁿ       Divide both sides by 3000

2.4 = 1.0575ⁿ

n = (㏒ ans) / (㏒ base)

n = (㏒ (2.4)) / (㏒ (1.0575))

n = 15.659.....     Exact answer

n ≈ 15.7       Rounded to the nearest tenth of a year

Therefore the person must leave the money in the bank for 15.7 years until it reaches 7200 dollars.

Step-by-step explanation:

4x + 10 = 32

4x = 32 - 10

4x = 22

x = 11/2

if we add 4 to both sides of the equation :

4x + 10 + 4 = 32 + 4 ➡ 4x + 14 = 36

4x = 36 - 14 ➡ 4x = 22 and x = 11/2

as you can see the value for x didn't change because when we add/subtract or multiple/divide same number from both sides of an equation the result won't change.

Answer:

Admission fee charged = $3

Cost of each ride = $10

Step-by-step explanation:

Let admission fee charged by amusement park in dollars be =[tex]x[/tex]

Let cost of each ride in dollars be =[tex]y[/tex]

Given:

Admission plus four rides cost $22

If each ride cost in dollars = [tex]y[/tex]

Cost of 4 rides in dollars will be  = [tex]4y[/tex]

So, the total cost in dollars will be given as =[tex]x+4y[/tex]

So, we have

[tex]x+4y=22[/tex]

Admission plus seven ride cost $31.

If each ride cost in dollars = [tex]y[/tex]

Cost of 7 rides in dollars will be  = [tex]7y[/tex]

So, the total cost in dollars will be given as =[tex]x+7y[/tex]

So, we have

[tex]x+7y=31[/tex]

So, we have the system of equation as:

A) [tex]x+4y=22[/tex]

B) [tex]x+7y=31[/tex]

Solving the system by elimination method.

Eliminating [tex]x[/tex] by subtracting equation A from B.

   [tex]x+7y=31[/tex]

- [tex]x+4y=22[/tex]

   -       -      -  [Sign of each term of subtract-ant gets reversed]

-----------------------------

      [tex]3y=9[/tex]

Dividing both sides by 3.

[tex]\frac{3y}{3}=\frac{9}{3}[/tex]

∴ [tex]y=3[/tex]

Plugging in [tex]y=3[/tex] in equation A.

[tex]x+4(3)=22[/tex]

[tex]x+12=22[/tex]

Subtracting both sides by 12.

[tex]x+12-12=22-12[/tex]

∴ [tex]x=10[/tex]

Thus, admission fee charged = $3

Cost of each ride = $10

Answer:

This is just a relation.

Step-by-step explanation:

It is easy to see if a set of ordered pairs is a relation or a relation that is a function.

If all the points are distinct, then you just have to look at the [tex]x[/tex]-coordinates.

If all the [tex]x[/tex]-coordinates are different, then it is a function. Otherwise, it is a just a relation.

So this cannot be a function because there is at least two different points that have [tex]x=0[/tex].

Answer:

Step-by-step explanation:

(n/4)-1

Divide total slices by 4 friends then subtract 1 to get Harrison’s amount

Answer: [tex]x=105\°[/tex]

Step-by-step explanation:

You can identify from the given figure that the angle  that measures 70 degrees is formed by two intersecting Chords.

It is important to remembe that, by definition:

[tex]Angle\ Formed\ by\ Two\ Chords =\frac{1}{2}(Sum\ of\ Intercepted\ Arcs)[/tex]

Based on this, you know that:

[tex]70\°=\frac{35\°+x}{2}[/tex]

Having this equation, the final step is to solve for "x" in order to find its value. You get that this is:

[tex](70\°)(2)=35\°+x\\\\140\°=35\°+x\\\\140\°-35\°=x\\\\x=105\°[/tex]

Explanation:

The equation is already in standard form.

A is 1. The number 1 is often unwritten.

B is -3. The negative or positive sign is included with the equation.

C is -6. (If using this for the quadratic formula, c is actually 6 because the equation should equate to 0).

Answer: 1/9

Step-by-step explanation:

Total number of cards = 6

Probability = required outcome/ all possible outcome

number of kings=4

number of jack=1

Probability of drawing a king = 4/6

probability of drawing a jack = 1/6

Probability of drawing a king and then a jack is p(king and jack) = p(king) × p(jack) = 4/6 × 1/6 = 4/36

= 1/9

Answer:

1/9

thats all

Step-by-step explanation:

Answer:

Step-by-step explanation:

Two pairs of jeans cost $32 dollars so multiply 32 x 2 and get $64.

Three shirts cost $18, multiply 18 x 3 to get $54.

One jacket costs $54 so just do 1 x 54 and you will get $54.

54 + 54 + 64 = $172.

I hope this helped!

Amanda needs $172 to buy all the clothes she wants.

To calculate the total cost of the clothes Amanda wants to buy, we need to add up the cost of each item.

To find the total cost, we add up these amounts:

= $64 + $54 + $54

= $172.

Therefore, Amanda needs $172 to buy all the clothes she wants.

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Answer:

The area of the hexagon is 108 cm².

Step-by-step explanation:

Consider the below figure attached with this question.

From the below figure we get

Length of rectangle = 12 cm

width of rectangle = 5 cm

It is given both triangles are identical.

Base of each triangle = 12cm

Height of each triangle = (13-5)/2 = 4 cm

Area of rectangle is

[tex]Area=length\times width=12\times 5=60[/tex]

Area of rectangle is

[tex]Area=\frac{1}{2}\times base\times height[/tex]

[tex]Area=\frac{1}{2}\times 12\times 4=24[/tex]

Area of one triangle 24 cm². So, area of both triangle is

[tex]2\times 24=48[/tex]

Area of hexagon = Area of rectangle + Area of both triangles

                            = [tex]60+48[/tex]

                            = [tex]108[/tex]

Therefore, the area of the hexagon is 108 cm².

By finding the areas of the rectangle and the two triangles separately and adding them together, we determine that the area of the hexagon is 125 cm².

To find out the area of the hexagon, you would need to find the areas of the rectangle and the triangles separately, and then add them together. The rectangle's area can be calculated easily using the formula for the area of a rectangle: Length x Breadth.

Assuming the rectangular part length to be 13cm and breadth to be 5cm, area of rectangle = 13cm x 5cm = 65cm².

The two triangles appear to be right triangles. You can use the formula for the area of a right triangle: 0.5 x Base x Height.

Assuming the base and height of the triangles to be 12cm and 5 cm, therefore the area of one triangle is 0.5 x 12cm x 5cm = 30cm². Since there are two of these triangles, their combined area = 2 x 30cm² = 60cm².

Finally, combining the areas of the rectangle and triangles equals the area of the hexagon: 65cm² + 60 cm² = 125 cm².

The area of the hexagon is

125 cm²

.

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