Mrs. Magdalino kept records on how much she spent on gasoline and the maintenance of her car. She found that it cost $485 to drive 500 mi in a month Find the cost per mileWrite an equation that relates the cost for gasoline and maintenance of a car to the number of miles m the car is driven. Use the equation to find the cost for driving 1200 miles. About how many miles are driven for a cost of $820?​

Answer:

  y = x² +8x -9

Step-by-step explanation:

You want the least-degree polynomial with roots 1 and -9, written in standard form.

Each root p means there is a factor (x-p). The two roots make the factored form of the polynomial be ...

  y = (x -1)(x +9)

Expanding this to standard form, we get ...

  y = x² +8x -9

__

Additional comment

A quadratic that has two roots, p and q, will have the standard form ...

  y = (x -p)(x -q) = x² -(p+q)x +pq

That is, the linear term coefficient is the opposite of the sum of the roots, and the constant is their product. This means you can write down the equation directly from the roots:

  y = x² -(1-9)x +(1)(-9) = x² +8x -9

Answer:

hello\\

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Distribute 1st

-3 x 8 +232 /8

Multiply -3 and 8

-24 +232 /8

Divide 232 and 8

-24+29

Add -24 and 29

5

The value of game is 0.0769 .

Formula for Expected Value of Game :

Expected Value of Game = ( Probability of Winning * Profit ) + ( Probability of Losing * Loss )

According to question ,

P ( getting a face card ) = 12 / 52

                                   = 3 / 13

P ( not getting a face card ) = 1 - ( 3 / 13 )

                                             = 10 / 13

Expected value for this game = [ 7 * ( 3 / 13 ) ] + [ ( - 2 ) * ( 10 / 13 ) ]

                                                   = 0.0769

Hence , the value of game is 0.0769 .

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Call the number of hours of labor x.

A flat rate of $500 -> just $500.
$50 for each hour of labor -> 50x (for x hours)

Therefore, we can represent the amount needed for x hours of labor as the function : 500 + 50x.

We substitute :
20 hours of labor = 500 + 50 x 20 = $1500
50 hours of labor = 500 + 50 x 50 = $3000

RIGHT function should be used to extract the last four digits from a column containing phone numbers.

The Excel TEXT functions section includes the RIGHT Function[1]. A predetermined number of characters from the end of a provided text string will be returned by the function.

The RIGHT function can be helpful in the financial analysis if we want to extract characters from a text string's right side. It is typically used in conjunction with functions like VALUE, SUM, COUNT, DATE, DAY, etc.

Formula is=RIGHT(text,[num chars])

The following arguments are used by the RIGHT function:

Text is the original text string (mandatory argument).

The number of characters to be returned from the end of the provided text is specified by the optional argument Num chars. It specifies how many characters will be taken, beginning on the right side of the text. If the argument is omitted, the value of 1 by default is used.

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Step-by-step explanation:

so, we have 2 cost functions. each consisting of 1 large centerpiece, and x smaller arrangements.

cost1(x) = 19x + 50

cost2(x) = 23x + 42

to get the value for x we know that the cost is the same either way.

that means

cost1(x) = cost2(x) = 19x + 50 = 23x + 42

19x + 50 = 23x + 42

50 = 4x + 42

8 = 4x

x = 2

so, she orders 2 small arrangements.

the total cost is

19×2 + 50 = 38 + 50 = $88

cross check with the other function :

23×2 + 42 = 46 + 42 = $88

correct

I think you would just add 8 + 5, because if NO is the same length as MN, then the length from MN is 5 and NP makes up the rest of the line.

Answer: MP = 13

The sides of ΔTUV in order from longest to shortest is as follows -

TV > TU > VU

A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically -

∠x + ∠y + ∠z = 180°

The sum of two sides of a triangle is greater then the third side. Mathematically -

a + b > c

There are different types of triangles such as -

equilateral triangle , scalene triangle , isosceles triangle etc.

Given is ΔTUV, m∠T = 58° and m∠U = 97°.

Refer to the image attached.

TV > VU

TU + VU > TV

TV > TU + VU

So we can arrange the sides as follows -

TV > TU > VU

Therefore, the sides of ΔTUV in order from longest to shortest is as follows -

TV > TU > VU

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The model which properly represent the information in given axioms is Cross geometry (+).

In the given question we have following information,

by using the above axioms we draw a geometry of Cross sign Geometry as seen above .

We can draw a line which contains three points and these points are only from given five points another line also follow this . this geometry follows all given axioms . The two lines intersect each other at a point . The point of intersection is one of point from five points . both of lines are linear and consists three points .

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Answer:

a) 6 km

b) 66 km

Step-by-step explanation:

a) According to the graph:

To find how much further, subtract the distance cycled those two days:

22 - 16 = 6 km

b) The three days he cycled the most are the three days with the highest lines on the graph, so that would be:

Add them all up to find the total distance cycled:

24 + 22 + 20 = 66 km

The highest common factor (HCF) for the expression 4x³yz"; 30x²y²z² and 36x³y²z³ is 2x²yz.

The H.C.F. defines the highest common factor present in between given two or more numbers or mathematical expression.

We shall derive the HCF of the three expressions by expressing them as multiples of their factors as follows;

4x³yz = 2 × 2 × x × x × x × y × z

30x²y²z² = 2 × 3 × 5 × x × x × y × z × z

36x³y²z³ = 2 × 2 × 3 × 3 × x × x × x × y × y × z × z × z

HCF = 2 × x × x × y × z

HCF = 2x²yz

Therefore, the highest common factor for the expressions 4x³yz"; 30x²y²z² and 36x³y²z³ with the understanding of HCF is 2x²yz.

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Answer for Part I: x² - 3x - 10

Step-by-step explanation:

    The FOIL method means to multiply the "First, Outside, Inside, and Last" in order of the terms. See attached for a visual and the work behind the answer.

    Using this method, we end up with;

                           x² - 3x - 10

Answer:

see image

Step-by-step explanation:

Use new exponent rules like:

A power raised to a power is the product of the powers. (power to a power, times the exponents)

and,

Square root is a half power. (Converting radicals to fractional exponents)

Also, you can multiply in any order, like since you learned multiplying (example: 2×6 is the same as 6×2)

see image.

Here's the plan:

Change the radical to a 1/2 exponent. Now 3 and 1/2 are both exponents. Rearrange the order. Rewrite in radical form again.

see image.

The proof of the equation  (√5)³ = √(5³) is given below.

Exponentiation is one of the mathematics operation.

Let mᵃ, where m and a are the real numbers.

And m is multiplied by a times to itself.

So, a is the exponent of m.

Given:

A radical equation,

(√5)³ = √(5³).

LHS =  (√5)³

Simplifying,

(√5)³ = {(5[tex])^{1/2}[/tex]}³

        = [tex]5^{3/2}[/tex]

        = √(5³)

        = RHS.

Therefore,  (√5)³ = √(5³).

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The complete question:

Simplify and prove the equation (√5)³ = √(5³) by using exponent rules.

Answer:

21/18 or 1 and 3/18

Step-by-step explanation:

6/9 = 12/18

3/6 = 9/18

12/18 + 9/18 = 21/18 or 1 3/18

Answer:

The probability of Sid takes at random counters from the bag is 24/55

The total number of counters = 11

Total number of green counters = 8

Total number of blue counters = 3

Probability = Number of favorable outcomes / Total number of outcomes

Total number of outcome = 55

Number of outcome that Sid will get both green = 28

Number of outcome that Sid will get both blue = 3

Number of favorable outcome = 55 - 28 - 3

= 24

Probability = Number of favorable outcomes / Total number of outcomes

= 24/55

Hence, the probability of Sid takes at random counters from the bag is 24/55

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The probability that there is a continuous stripe encircling the cube is 3/16.

A single, thin stripe is painted from the center of one edge to the center of the other edge on each face of a cube. Each face's edge pairing is selected independently and at random.

For each of the cube's six faces, there are two possible stripe orientations, resulting in a total of 2 x 6 = 64 possible stripe permutations. Since there are three sets of parallel faces, the stripe orientation for the remaining faces is determined uniquely by the pair of faces that does not contribute to the encircling stripe. Additionally, there are two possible orientations for the stripe on each face that is non-contributing.

A continuous stripe surrounds the cube as a consequence of a total of

3 * 2 * 2 = 12 stripe variations.

The necessary probability is 12/64, which equals 3/16.

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The volume of the composite solid is 340.4 cubic inches

The composite solid is made up of two parts one has

The volume for the uniform height  

= base area * height

base area = 0.5 base * height = 0.5 * 8 * 6.9 = 27.6

= 27.6 * 10

= 276 cubic inches

The volume for the varying height

= 1/3 base area * height

base area = 27.6 (both share same base)

= 1/3 * 27.6 * 7

= 64.4 cubic inches

The total volume

= 276 + 64.4

= 340.4 cubic inches

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The required equation will be y = -1/3x + 21/4 in slope-intercept form.

The general equation of a line is y = mx + c

where m is the slope of the line and c is the intercept.

First, we need to determine the slope of the given line.

y = 4/9x - 6

Here the slope of the given line is 4/9.

The required line is perpendicular to a given line

So the  required line's slope will be m₂ = -1 / (4/9) = -9/4

The line passes through the point (5, -6) which is given in the question,

Now we can use the point-slope form of a line to create the equation of the new line:

(y + 6) = (-9/4) (x - 5)

y = (-9/4)x + 45/4  - 6

y = -1/3x + 21/4

Hence, the required equation will be y = -1/3x + 21/4 in slope-intercept form.

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Norman will measure the light pole to be 12 feet tall

Information from the question

Norman uses his sextant to measure the angle of elevation to be 36

5 feet from the ground. if he is 10 feet away from the light pole

how tall is the light pole = ?

The height of the light pole is calculated using SOH CAH TOA

The direction of movements describes a right angle triangle of

opposite = height of the light pole

adjacent = 10 feet away from the light pole

The height is is calculated using tan, TOA let the angle be x = 36

tan x = Opposite / Adjacent

tan 36 = opposite  / 10

opposite = tans 35 * 10

opposite = 7 feet

this is height 5 feet from the ground, so total height is calculated to be

5 + 7 = 12 feet

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The speed at which raina can swim if there is no current is 3 km/hor 3 kilometers per hour.

Given that,

In the same length of time it took raina to swim kilometers with the river, she was able to swim 8 kilometers against it. The current flowed at a kilometer per hour rate.

Distance 1 * (Raina's velocity - current velocity) = Distance2 * (Raina's velocity + current velocity)

16 * (Raina's velocity - 1) = 8 * (Ivan's velocity + 1)

(16 * Raina's velocity) - 16 = (8 * Ivan's velocity) +8

8 * Raina's velocity = 24

Raina's velocity = 3 kilometers per hour

As a result, Raina can swim at a speed of 3 km/hr in the absence of a current.

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Answer

you do 420x0.7= 29.40

Answer:

The sales tax is 29.4

Step-by-step explanation:

Just divide in half until you reach 5 and then calculate the other 2 percent of it and add the 2 percent back onto it.

The length of the line segment defined by two endpoints; negative 3 comma 10 to 4 comma negative 1 as required in the task content is; 13.04.

It follows from the task content that the length of the line segment whose endpoints are as given in the task content is to be determined.

Recall; The length of a line segment whose endpoints are defined by; (x1, y1) and (x2, y2) is given as;

Length = √{ (y2 - y1)² + (x2 - x1)² }

Therefore, since the given endpoints are; (-3, 10) and (4, -1), it follows that the length of the line segment in discuss is;

Length = √{ (-1 - 10)² + (4 - (-3))² }

Length = √(121 + 49)

Length = √170

Length = 13.04.

Ultimately, the length of the line segment as required is; 13.04.

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Answer: [tex]x=13, y=132[/tex]

Step-by-step explanation:

Using the same-side interior angles theorem, [tex]y=132[/tex].

Using the alternate interior angles theorem, [tex]5x-17=48 \implies x=13[/tex]

Answer: -22/5 or -4.4

Step-by-step explanation:

Simplify so 2(22/7*10)(10+h)=352

Distribute so (2*22/7*10)(10) + (2*22/7*10)(h) = 352

Which would equal 4400/7 +440/7h=352

Subtract 4400/7 to both sides

That equals 440/7h=-1396/7

Multiply both sides by 7/440

h=-22/5

Answer:

$1053

Step-by-step explanation:

If we have that £1 = $1.62, then we can multiply both sides by 650 in order to get £650 on the left side of the equality. We must multiply the right side also by 650, and so we get £650=$1.62 * 650.

To do this multiplication, we can break 1.62 down  simply into $1.00 +$0.6+$0.02

650*$1.00=$650, 650*$0.6=650*6/10=65*6=$390, and 650*$0.02=650*2/100=6.5*2=$13.

When we add these three products together, we get $650+$390+$13=$1053. And so, £650=$1053

The table of solutions for this quadratic equation (y = -2x²) include the following:

x                    y_

-2                  -8

-1                   -2

0                   -0

1                    -2

2                   -8

A graph of the solution of the given quadratic equation has been plotted in the image attached below.

In Mathematics, the graph of any quadratic equation or function always forms a parabola, which simply means a u-shaped curve. In order to determine the correct solutions to the given quadratic equation, we would have to substitute the x-values contained in the table into the quadratic equation.

At point x = -2, the y-value of this quadratic equation is given by:

y = -2x²

y = -2(-2)²

y = -2 × 4

y = -8

At point x = -1, the y-value for this quadratic equation is given by:

y = -2x²

y = -2(-1)²

y = -2 × 1

y = -2

At point x = 0, the y-value of this quadratic equation is given by:

y = -2x²

y = -2(0)²

y = -2 × 0

y = 0

At point x = 1, the y-value of this quadratic equation is given by:

y = -2x²

y = -2(1)²

y = -2 × 1

y = -2

At point x = 2, the y-value of this quadratic equation is given by:

y = -2x²

y = -2(2)²

y = -2 × 4

y = -8

In conclusion, we can logically deduce that the graph of this quadratic equation forms a downward parabola.

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The length and width of the rectangle are 50 feet and 25 feet respectively, the product of which gives the area of the rectangle which is 1250 feet.

Given, 100 feet of fence to make a rectangular play area that is side by side with the wall of your house.

The perimeter of the rectangle is = 2x+2y, since the wall bounds from one side as given in the question perimeter changes to = x+2y.

Perimeter = x+2y

100 = x+2y

100 = 50+2y

2y = 50

y = 25

Using this we found the length and width of the rectangle which is equal to 50 feet and 25 feet respectively. The area which is the final answer comes out to be 1250 feet.

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Answer:-2(3+(-4)+(-8)*7)=114

Step-by-step explanation: You wrote the equation wrong, but if you use PEMDAS that's the answer you'll get.

The value of x is 10.6 which is equivalent to 11.

In the given triangle

the triangle is divided into two triangles which are both right angled

However in the bigger triangle

we would use the Pythagoras Theorem

( y + 6 )² = x² + 100 ---------- equation 1

In the smaller triangle;

x² = y² + 64 --------------equation 2

Thus substituting the value of x in equation 1

Thus the equation becomes

( y + 6 )² = y² + 64 + 100

y² + 36 + 12x = y² + 164

Cancelling y² on both sides we will get

36 + 12x = 164

12x = 164 - 36

this implies 12 x = 128

x = [tex]\frac{128}{12}[/tex]

x = 10.6 ≈ 11

Thus the required value of x is 10.6 or 11

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