write (2 4) and (6 16) in the form y=mx+b

Answer:

y=5

Step-by-step explanation:

1/3(y+7)=(y-1)

I will multiply by 3 on each side to get rid of the fractions

3*1/3(y+7)=(y-1)*3

y+7 = 3*(y-1)

Distribute the 3

y+7 = 3y -3

Subtract y from each side

y-y+7 = 3y-y-3

7 = 2y-3

Add 3 to each side

7+3 = 2y-3+3

10=2y

Divide each side by 2

10/2 = 2y/2

5 =y

Answer:

5

Step-by-step explanation:

It is 5 because no matter how many stamps he sells, he has $5.

Answer:

The y-intercept of Ben's graph is [tex]y = 5[/tex].

Step-by-step explanation:

The function for Ben's amount of money y, depending on the number of stamps sold x, is as follows:

[tex]y = ax + b[/tex]

In which a is the price of each stamp and b is his initial money.

Building the function:

Ben has $5. This means that if he sells no stamps, he is still going to have $5. So [tex]b = 5[/tex].

For each stamp sold, he gains $3. So if sells 1 stamp, he will have $8, if he sells 2, he will have $11. So [tex]a = 3[/tex].

The function is:

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

Which will be the y-intercept of Ben's graph?

This is the value of y when x = 0.

So

[tex]y = 3*0 + 5 = 5[/tex]

The y-intercept of Ben's graph is [tex]y = 5[/tex].

Answer:

333°

Step-by-step explanation:

Minor arc ST is the difference between minor arc RT and minor arc RS:

... 153° -126° = 27°

Major arc SPT is the remainder of the circle:

... 360° -27° = 333°

Answer:

D) 91 °F

Step-by-step explanation:

        C = 5/9(F - 32)

      33 = 5/9 (F – 32)     Multiply each side by 9

  9×33 = 5(F- 32)           Divide each side by 5

9×33/5 = F – 32             Add 32 to each side

        F = 9×33/5 + 32

        F = 59.4 + 32

        F = 91 °F

Answer:

Its D

Step-by-step explanation:

USA TP

Answer:

8 cm

Step-by-step explanation:

... BO/OD = AO/OC = 3/1

Written another way, this is ...

... OD : BO = 1 : 3

Now, BD = OD + BO, so we have

... BD : BO = (OD +BO) : BO = (1 +3) : 3 = 4 : 3

That is, BD = 4/3 × BO

... BD = 4/3 × 6 cm = 8 cm

To find the length of diagonal BD in trapezoid ABCD, we set up an equation using the fact that the diagonals bisect each other. We solve for x and then substitute it into the equation for BD.

To find the length of diagonal BD in trapezoid ABCD, we can use the fact that the diagonals of a trapezoid bisect each other. Let AO = 3x and OC = x. Since the diagonals intersect at point O, we can set up the equation (3x + 6) / x = 3 / 1. Solving for x, we find that x = 1.5. Therefore, BD = 2 * x + 6 = 2 * 1.5 + 6 = 9 cm.

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Answer:

63

Step-by-step explanation:

Answer:

25 degrees.

Step-by-step If one of the angles is 38 degrees then in order for the sum to be 63, the answer is 25

Answer:

7.9

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you of the relationship of the hypotenuse and the side opposite an angle:

... Sin = Opposite/Hypotenuse

For your geometry, this is ...

... sin(21°) = x/22

Multiplying by 22 gives ...

... x = 22·sin(21°) ≈ 7.9

Answer:

[tex]1.13x[/tex]

Step-by-step explanation:

We have been given that Camacho is buying a monster truck. The price of the truck is x dollars, and he also has to pay a 13% monster truck tax. We are asked to find the total amount paid by Camacho for the monster truck.

The total cost of monster truck would be x plus 13% of x.

[tex]\text{The total cost of monster truck}=x+\frac{13}{100}x[/tex]

[tex]\text{The total cost of monster truck}=x+0.13x[/tex]

[tex]\text{The total cost of monster truck}=1.13x[/tex]

Therefore, Camacho paid [tex]1.13x[/tex] dollars in total for the truck.

Final answer:

To find the total cost of the monster truck, convert the 13\% tax to decimal form (0.13), multiply it by the price of the truck (xx dollars), then add the result to the original price to get the total cost, which is 1.13xx.

Explanation:

To determine the total amount Camacho will pay for the monster truck, we need to calculate the sales tax and add it to the original price of the truck. The sales tax is 13\%, which can be converted to a decimal for calculation purposes. First, convert 13\% to a decimal by dividing by 100, which gives us 0.13. Then multiply 0.13 by the price of the truck (xx dollars) to find the amount of tax Camacho will have to pay.

After calculating the tax, you can find the total cost by adding the tax to the original price of the truck.

Step 1: Convert 13\% to a decimal = 0.13
Step 2: Multiply the price of the truck (xx dollars) by 0.13 to find the tax = 0.13 * xx
Step 3: Add the tax to the original price to find the total cost: xx + (0.13 * xx).

Total cost = xx + 0.13xx = 1.13xx

Answer:

slope = .4

She ran .4 laps per min.

She ran 12 laps in 30 minutes

Step-by-step explanation:

The slope is the rate of change.  It can be found by using the formula

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

 The given points are (11, 4.4)  (5.5 ,2.2)

slope = (2.2-4.4(/ (5.5-11)

           = -2.2/-5.5

          .4

The slope represents .4 laps per min  since y is in laps and x is in minutes.

If she  ran 30 minutes, we multiply the time by the slope to calculate the laps.

30 * .4 = 12

She ran 12 laps.

A) The slope is the change in Y over the change in X.

Using the 2 points given on the graph (11,4.4) and (5.5, 2.2)

The first number in the parenthesis are the X value and the 2nd numbers are the Y values.

Slope = (4.4 - 2.2) / (11-5.5)

= 2.2 / 5.5

= 0.4

B) From the slope, she ran 0.4 laps per minute.

C) To find the total laps, multiple laps per minute by total minutes:

30 minutes x 0.4 laps per minute = 12 laps.

Answer:

10 Valentines

Step-by-step explanation:

1/2 = 4/8

3/4 = 6/8

Julie has a total of 4/8 + 6/8 = 10/8 yards of ribbon. If color doesn't matter, she can make 10 Valentines.

_____

10/8 = 10 × 1/8

Answer:

B. h=2A/(b1+b2) . . . . parentheses are needed

Step-by-step explanation:

Multiply the equation by the inverse of the coefficient of h. That coefficient is (b1 +b2)/2, so its inverse is 2/(b1 +b2). Parentheses are needed.

... 2A/(b1 +b2) = h

_____

Comment on the answer choices

As written, none of them are correct. The denominator can only be written without parentheses if the division bar is horizontal, and so serves also as a grouping symbol.

Answer:

7.9 ft

Step-by-step explanation:

The hypotenuse is the side opposite of the right angle, hence the hypotenuse for this triangle is 11 ft.

Side [tex]x[/tex] is adjacent to the angle given. So we need adjacent and we have hypotenuse. Which trigonometric ratio relates adjacent and hypotenuse? It is COSINE.

Thus, we can write:

[tex]cos(A)=\frac{adjacent}{hypotenuse}\\cos(44)=\frac{x}{11}[/tex]

Cross multiplying, we can solve for [tex]x[/tex]:

[tex]cos(44)=\frac{x}{11}\\x=cos(44)*11\\x=7.91[/tex]

Rounding to nearest tenth, we have [tex]x=7.9[/tex] ft.

Answer:

1/27

Step-by-step explanation:

The probabaility of rolling a number less than 3 is 2/6 = 1/3, since only two of the six numbers are less than 3.

Assuming the die rolls are independent, the probability of doing this 3 times is the product of the probabilities of doing it each time:

... (1/3)^3 = 1/27

The slope of AB is ...

... slope = (change in y)/(change in x) = (-6-(-3))/(8-2) = -3/6 = -1/2

The slope of AD is ...

... slope = (change in y)/(change in x) = (0 -(-3))/(8 -2) = 3/6 = 1/2

We note that the differences have the same magnitudes in both cases (y changes by 6; x changes by 3). This tells us the line segments are the same length. (Each side of the figure is equivalent to the hypotenuse of a right triangle with legs 3 and 6.)

The opposite reciprocal of a number is found by dividing -1 by that number. Thus the opposite reciprocal of the slope of AB is ...

... -1/(-1/2) = (-1/1)·(-2/1) = 2

This value is not the same as the slope of AD, so the slopes are NOT opposite reciprocals.

_____

Plotting the points, we see that we have a rhombus, not a rectangle (or square).

Answer:

a. x = 1, y = -2

Step-by-step explanation:

The given equations are 2x + 3y = -4 -------------(1)

x - 2y = 5 -----------------(2)

From the second equation, we get x = 2y + 5

Now plug in x = 2y + 5 in the first equation, we get

2(2y + 5) + 3y = - 4

4y + 10 + 3y = -4

7y + 10 = -4

7y = -14

y = -2

Now plug in y = -2 in x = 2y + 5 to find the x value.

x = 2(-2) + 5

x = -4 + 5

x = 1

Therefore, x = 1, y = -2

Thank you.

7. Law of cosines

a² = b² + c² - 2bc cos A

where a is the side opposite to ∠A and b and c are adjacent sides to ∠A.

Here, a=BC= 3.8

b=CA =4.8

c = AB = 3.2

Substituting the values in the formula,

3.8² = 4.8² + 3.2² - 2(4.8)(3.2) cos A

30.72 cos A =23.04 + 10.24 -14.44=18.84

cos A = 18.84/30.72 = 0.6133

∴ cos A =0.6133

8. It is a right angled triangle.

Pythagoras theorem

hypotenuse² = Perpendicular² + base²

Here, hypotenuse = 6.7, base = 5.4

Perpendicular² = 6.7² -5.4²=44.89 - 29.16 =15.73

Perpendicular = √15.73 = 3.966 = 3.97

∴ The length of the missing side is 3.97.

9. Given:   Side of new cube = 5 * Side of original cube

Let the side of the original cube measure 1 unit.

So, volume of original cube = side³ = 1

The side of new cube = 5 * 1 =5 units

So, volume of new cube = side³ = 5³ =125

The volume of the bigger cube is 125 times larger than the original cube.

10. Given : Height of the cone = 7 in

Radius of the base of the cone = 2 in

Volume of cone = (1/3) πr²h

                           =(1/3)π(2²)(7)

                           =29.32 cubic inches

∴ Volume of the cone is 29.32 cubic inches.

11. The given equation is:

x² -18x +10 =0

(x² -18x + 9²) +10 -9² =0

(x-9)²-71 =0

(x-9)² =71

x-9 =√71

x = 9 + √71

∴ x = 9+√71

Answer:

(x, y) = (-0.3, -1.6)

Step-by-step explanation:

The graph below shows these equations graphed. Their point of intersection is (-0.3, -1.6).

_____

Analytical solution

You can equate the expressions for y to get ...

... 12x +2 = 2x -1

... 10x = -3  . . . . subtract (2x+2)

... x = -0.3 . . . . . divide by 10

... y = 2(-.3)-1 = -1.6 . . . . use the 2nd equation to find y.

Answer:

A)55

B)110

Step-by-step explanation:500 /11%=55

55*2=110

The interest is $110 and the amount paid to the bank is $610.

Simple interest is calculated just on the loan's principal amount, whereas compound interest is calculated on both the principal and the cumulative interest.

It is given that you decide to borrow $500 to go on a trip to whatever land. You go to the bank and borrow the money at 11% for 2 years.

A. The simple interest is,

SI = ( Principle x rate x time ) / 100

SI = ( 500 x 11 x 2 ) / 100

SI = $110

B. The amount paid to the bank after 2 years is,

Amount = P + SI

Amount = $500 + $110 = $610

Therefore, the interest is $110 and the amount paid to the bank is $610.

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Answer:

$1.25

Step-by-step explanation:

Step-by-step explanation:

sqrt of 81 is 9 so rational

Sqrt of 89 is irrational

Sqrt of 121 is 11 so rational

Sqrt of 131 is irrational.

We can let x represent the width of the barn in feet. Then the length of the barn is 2x. The portion of width not used for stalls is (x-10). The height of that is (x-6).

So, the product of length, width not used for stalls, and height must be 1920 ft³. The equation for that is ...

... 2x(x -10)(x -6) = 1920 . . . . the equation

Solution

I generally find it convenient to use a graphing calculator to find the solutions to higher-order equations. Rearranging this so we're looking for a zero, it becomes ...

... 2x(x -10)(x -6) -1920 = 0

The graph shows one real root, at x = 16.

The dimensions of the lower floor should be 16 feet wide, 32 feet long, and a ceiling height of 10 feet.

_____

Alternate solution

Dividing by 2, we have

... x(x-6)(x-10) = 960

If we look at the factors of 960, we find that it is the product of 16, 10, and 6, which would let us assign x=16.

___

There are 28 divisors of 960. According to the Rational Root theorem, any of them might be a solution. There are arguments that can be made regarding reasonable dimensions that suggest x will be more than 12 (6 ft ceiling, 2 ft aisle). So, the number of trial-and-error possibilities is reduced somewhat.

The dimensions of the lower barn floor should be a width of 8 feet, a length of 16 feet, and a height of 2 feet, determined by setting up and solving a polynomial equation based on the given parameters.

The problem can be solved using polynomial equations. First, let's denote the width of the lower barn floor as x. Given that the length of the barn is twice the width, the length is 2x. The height of the lower barn floor is 6 feet less than the width of the barn, so it's x - 6 feet.

The volume of a rectangular solid is given by length times width times height. So according to the information provided, we can set up the following polynomial equation: 2x * x * (x - 6) = 1920.

By simplifying the equation, we get 2x^3 - 12x^2 - 1920 = 0.

This equation can be solved using various methods such as the rational root theorem, synthetic division, or factoring. After solving, we find that the root x = 8 is the only physically meaningful solution (length width and height must be positive). Therefore, the width of the lower floor should be 8 feet, the length should be 2 * 8 = 16 feet, and the height should be 8 - 6 = 2 feet.

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Answer:

74°

Step-by-step explanation:

The triangle is isosceles and the congruent base angles are 53°. The sum of angles in a triangle is 180°, so the apex angle (∠EDF) will be ...

... 180° - 2×53° = 74°

Answer:

74* is the answer

Step-by-step explanation:

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Answer: Your answer would come out to be 3.5

Step-by-step explanation: it would be 3.5 due to the fact that you have to break these numbers down to the smallest one possible meaning simplify which would result in this equation 7 over 2  

7 over 2 = 3 1 over 2 this equals 3.5      

Answer:

132°

Step-by-step explanation:

Sum of the interior angles of a polygon is given by the formula:

[tex](n-2)*180[/tex]

Where [tex]n[/tex] is the number of sides of the polygon.

The figure shows a 5 sided polygon (aka Pentagon). So the sum of all the angles is:

Sum = [tex](5-2)*180\\=3*180\\=540[/tex]

If we add up all the expressions/angles given and equate to 540, we can figure out [tex]x[/tex]. So:

[tex]84+13x+6+9x-16+92+12x=540\\34x+166=540\\34x=540-166\\34x=374\\x=\frac{374}{34}=11[/tex]

But angle B measures [tex]12x[/tex], so plugging in [tex]x=11[/tex], we have:

Angle B = [tex]12x=12(11)=132[/tex]°

Second answer is right.

Answer:

-3c^2 +6

Step-by-step explanation:

The equation will be an identity (0=0) when M is equal to the contents of the parentheses. That polynomial can be used directly, or it can be simplified by combining the c^2 terms.

The contents of parentheses simplify as follows:

... (4c^2 -7c^2 +6) = (c^2(4 -7) +6) = (-3c^2 +6)

Answer:

4c^4-7c^2+6

Step-by-step explanation:

So let's break down this sentence (Let n = unknown number):

Now, let's solve our prior equation found in A. To solve for the unknown number, n, we need to isolate the variable onto 1 side of the equation. Firstly subtract both sides by 16 to cancel out the + 16 on the left side:

[tex]\frac{2n+1}{5}=2[/tex]

Next, multiply both sides by 5 to cancel out the division on the left side:

[tex]2n+1=10[/tex]

Next, subtract both sides by 1 to cancel out the + 1:

[tex]2n=9[/tex]

Lastly, divide both sides by 2 to cancel out the multiplication:

[tex]n=\frac{9}{2}\ \textsf{OR}\ 4.5[/tex]

In short, the number is 9/2 or 4.5.

None of the above. All the answers refer to price. The given equation refers to value. We imagine price may stay the same or actually increase year-to-year. The problem statement gives insufficient information to conclude anything about price.

Math is about attention to detail. The equation tells you ...

... The value of the boat decreases by 12% every year.

The value of the boat is multiplied by 0.88 each time X increases by 1. That means the value is 88% of what it was the year before, a decrease of 12%.

Answer:

213.7°

Step-by-step explanation:

The bearing of B from D is angle ADB, which is ...

... ∠ADB = arctan(30/45) ≈ 33.7°

The bearing of D from B is that angle plus 180°, so is ...

... 180° +33.7° = 213.7°

_____

We use angle ADB because the reference direction for bearings is North.

The tangent of an angle (ADB) is the ratio of its opposite side (AB) to its adjacent side (AD).

AAS Congruence Postulate proves that ∆MNQ ≅ ∆PNQ

Considering    ΔMNQ   and   ΔPNQ

                         ∠QMN   =      ∠QPN   (given)

                          ∠QNM   =       ∠ QNP  ( both are right angles)

                            Side NQ is common

∴        ΔMNQ   and   ΔPNQ are congruent by AAS congruency since two angles and a side are considered to prove the congruency.

The correct answer is option B.   AAS congruency postulates.

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