A sign for truck drivers states that the road ahead has a constant slope of 2 in 11. This means that for every 11m horizontally its rises 2m.
a. Over what horizontal distance will the road rise 300m?
b. What is the length of the road [AB]?
​

Answer:If (x + 1) is a factor of the polynomial p(x), then p(x) can be written as:

p(x) = (x + 1) q(x)

for some polynomial q(x). By substituting x = -1 into this expression, we can find the value of c:

p(-1) = (-1 + 1) q(-1) = 0 q(-1) = 0

So,

0 = 5(-1)^4 + 7(-1)^3 - 2(-1)^2 - 3(-1) + c

= -5 + 7 - 2 + 3 + c

= c = 3

So, the value of c that makes (x + 1) a factor of the polynomial p(x) = 5x^4 + 7x^3 - 2x^2 - 3x + c is c = 3.

The value of the variable is x = -6/9

A fraction is defined as the part of a whole number.

The different types of fractions are;

We are given the equation:

4/x = -18/3

To make 'x' the subject, cross multiply

-18x = 12

Now, divide both sides by the coefficient of x, we get;

x = 12/-18

x = -6/9

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The amount of money that Amelia is expected to raise is given as follows:

£78.13.

The outcomes of a person winning, and their probabilities, as given as follows:

Hence the probabilities of winning and losing are given as follows:

Then the distribution of earnings for each person is given as follows:

Hence, considering 250 people, the expected amount raised is given as follows:

E(X) = 250/16 x (2.5 x 6 - 1 x 10)

E(X) = £78.13.

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The requried two sides are equal, this triangle is an isosceles triangle, which means that two of the angles are equal to 45 degrees or less, and the triangle is acute.

A triangle with two sides and two congruent angles is called an isosceles triangle.

To determine the value of x and the third side of the triangle, we need to first ensure that the triangle is a valid triangle, meaning that the sum of the lengths of the two shorter sides must be greater than the length of the longest side.

In this case, the two shorter sides are 2 and 3x, and the longest side is 9. We have,

2 + 3x > 9

Solving for x, we get:

3x > 7

x > 7/3

Since x must be a whole number, the smallest possible value for x that would make the triangle valid is 3. With x = 3, the third side of the triangle would be 3 × 3 = 9, which is equal to the longest side.

Therefore, the triangle has sides 2, 9, and 9.

Since two sides are equal, this triangle is an isosceles triangle, which means that two of the angles are equal to 45 degrees or less, and the triangle is acute.

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To determine the total energy consumption of refrigerator A in a day, we need to first convert the power usage from watts to kilowatts.

500 watts/hour * 1 kilowatt/1000 watts = 0.5 kilowatts/hour

Next, we can calculate the energy consumption in kilowatt-hours (kWh) per day:

0.5 kilowatts/hour * 12 hours/day = 6 kilowatt-hours/day

To find the daily cost of running the refrigerator, we can multiply the energy consumption by the cost per kWh:

6 kWh/day * $0.12/kWh = $0.72/day

To calculate the yearly cost of running the refrigerator, we can multiply the daily cost by 365 days:

$0.72/day * 365 days = $262.80/year

To calculate the total cost of running the refrigerator for 20 years, we can multiply the yearly cost by 20:

$262.80/year * 20 years = $5,256.00

In addition to the cost of running the refrigerator, there is also the cost of purchasing the unit itself. In this case, the cost is $1,000.

Therefore, the total cost of owning and operating Refrigerator A for 20 years is:

$5,256.00 (operating cost) + $1,000.00 (purchase cost) = $6,256.00

It's worth noting that this calculation assumes that the cost of electricity remains constant over the 20-year lifespan of the refrigerator. In reality, the cost of electricity may increase over time, which would increase the overall cost of running the refrigerator.

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There are 29% of the Planes are Green.

The percentage is defined as a ratio expressed as a fraction of 100.

Total number of green planes = 250

The total number of green vehicles = 870

The percent of green planes = (number of green planes/number of total green vehicles) x 100

The percent of green planes = (250/870) x 100

The percent of green planes = 0.2873 x 100

The percent of green planes = 28.73

Round to the nearest percent, and we get

The percent of green planes = 29%

Thus, 29% of Planes are Green.

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Answer: To solve for the length of all sides, we need to set the perimeter equal to the sum of the lengths of the three sides:

30 cm = 3x + 2 + x + 4x - 6

30 cm = 8x + 2

Now we can solve for x:

30 cm = 8x + 2

28 cm = 8x

x = 28/8

x = 3.5

So each of the sides is 3.5 cm long, and the lengths of the three sides are:

3x + 2 = 3 * 3.5 + 2 = 11.5 cm

x = 3.5 cm

4x - 6 = 4 * 3.5 - 6 = 11.5 cm

Therefore, the lengths of the sides are 11.5 cm, 3.5 cm, and 11.5 cm.

Step-by-step explanation:

Answer:

(3x+2+4x-6)2=30

7x-4=30

7x=34

x=34/7

To find the side lengths of the rectangle;

3x+2=116/7. and. 4x-6=94/7

The range of ages that are within one standard deviation of the mean age are given as follows:

M - 14.8 ≤ M ≤ M + 14.8.

In which M is the mean age.

The standard deviation of a data-set is given by the square root of the sum of the difference squared between each observation and the mean, divided by the number of observations.

The values that are within one standard deviation of the mean M have the bounds given as follows:

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Answer:

aiaiiwakkaoajdjsjzjhsjaj

The solution is, the value of  (f• Hºg)(x) = 4x+2.

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

here, we have,

given that,

f(x) = x-4

g(x) = x+ 2,

and h(x) = 4x+1

now, (f• Hºg)(x)

= (f•(4(x+2)+1)(x)

=((4x+6)-4)

=4x+2

Hence, The solution is, the value of  (f• Hºg)(x) = 4x+2.

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Answer:

Step-by-step explanation:

y=16. There are sixteen 1/2 in 8

PREMISES

y=8/.5

CALCULATIONS

y=8/.5

y=8(2)

y=

16

PROOF

If y=16, then the dependent value D(y) 8/.5 returns

y(.5)=8

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

The coordinates of points where the two lines intersect, is the solution of the equations/lines, that is (6, 64)

Answer:

Step-by-step explanation:

75 x 0.40= £30

The two pieces relate to the number of minutes used, since there's the 400-minute limit.

Piece #1: When you use less than or equal to 400 minutes:

Cost calculation: $47.35 + $13.94 = $61.29

Piece #2: When you use more than 400 minutes:

Cost calculation: $47.35 + $13.94 + $0.60(x-400)

The x-400 piece is because you're only charged the $0.60/minute beyond the 400 minutes, so 401 minutes needs just 1 minute of extra charge

Cost calculation cleaned up: 61.29 + 0.60x - 240 = 0.6x - 178.71

Now it looks weird to have that -178.71, but keep in mind that this is only used if x > 400.

[tex]C(x) = \left \{ {{61.29 ~~~~~~~~~~~~~~ \text{ if } ~0 \leq x\leq 400} \atop {0.6x - 178.71~~~~ \text{ if } x > 400} \right.[/tex]

Your system might not require the "0≤x", but it technically should be there.

Answer:

$90.12

Step-by-step explanation:

The principal amount of the loan is ...

 (sale price)(1 + sales tax rate) - (down payment)

 = $19,725×1.0475 -2175 = $18,486.94

For a secured loan, the APR charged for an average credit rating appears to be 5.85%, so the interest for the first month is

 i = Prt = ($18,486.94)(0.0585)(1/12)

 i = $90.12

Answer:do homework

Step-by-step explanation:

Answer:

20√5x7

Step-by-step explanation:

Answer:

Step-by-step explanation:

The length of the line segment between two points in a plane can be calculated using the distance formula. Given two points (x1, y1) and (x2, y2), the distance between them is given by the following formula:

d = √((x2 - x1)^2 + (y2 - y1)^2)

In this case, the two points are (3, 5) and (7, 3). Plugging these values into the formula, we get:

d = √((7 - 3)^2 + (3 - 5)^2)

d = √((4^2) + (2^2))

d = √(16 + 4)

d = √20

So, the length of the line segment between the two points (3, 5) and (7, 3) is √20.

Answer:

2. 56°

4. 56°

For number 6, it is not shown on the photo, sorry!

Step-by-step explanation:

2. The square at the corner means that it is 90°, so 90 - 34 = 56

4. The line is straight, so it means that it is 180°, so 180 - 124 = 56

Answer:

Step-by-step explanation:

12

144 divided by 12 is 12

The equivalent trigonometric expression to sin(2x)cos(x) is given as follows:

sin(2x)cos(x) = 2sin(x)cos²(x).

The expression for this problem is defined as follows:

sin(2x)cos(x).

The trigonometric identity used to simplify sin(2x) is given as follows:

sin(2x) = 2sin(x)cos(x).

Hence the expression can be written as follows:

sin(2x)cos(x) = 2sin(x)cos(x)cos(x)

sin(2x)cos(x) = 2sin(x)cos²(x).

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For given ratio of orange juice and pineapple juice i.e. 5/6, proportion used to find the amount of orange juice, j, that is needed to add to 21 L of pineapple juice will be 5 over 6 equals j over 21 i.e. 5/6=j/21.

What exactly is a ratio?

Fractions are commonly used to describe ratios and proportions. A ratio is demonstrated when a fraction is expressed as a:b, whereas a percentage indicates that two ratios are equal. a and b can be any two numbers in this situation. The ratio and proportion are two fundamental ideas that lay the groundwork for comprehending other concepts in mathematics and science.

We use the concept of ratio and proportion in our daily lives, such as in business when dealing with money or in cooking.

As a result, when b is larger than zero, the ratio, such as a:b, defines the relationship between two variables. For example, the 2:4 ratio is expressed as 2:4 = 1:2.

Now,

Given that In recipe ratio of  orange juice / pineapple juice =5/6

then to make a recipe with 21 L of pineapple juice, the orange juice (j)

needed will be

5/6=j/21

j=17.5 L

hence,

           proportion used to find the amount of orange juice, j will be 5 over 6 equals j over 21 i.e. 5/6=j/21.

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Answer: its D

Step-by-step explanation:

pls i belieive most of yall are npcs

Answer:

Simplifying

-27 = 19 + -2x

Solving

-27 = 19 + -2x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '2x' to each side of the equation.

-27 + 2x = 19 + -2x + 2x

Combine like terms: -2x + 2x = 0

-27 + 2x = 19 + 0

-27 + 2x = 19

Add '27' to each side of the equation.

-27 + 27 + 2x = 19 + 27

Combine like terms: -27 + 27 = 0

0 + 2x = 19 + 27

2x = 19 + 27

Combine like terms: 19 + 27 = 46

2x = 46

Divide each side by '2'.

x = 23

Simplifying

x = 23

Answer:

Step-by-step explanation:

ax+bx=c

x(a+b)=c

x(a+b)/(a+b)=c/(a+b)

x=c/(a+b)

Answer:

[tex]x=\dfrac{c}{a+b}[/tex]

Step-by-step explanation:

To make x the subject of the equation ax + bx = c, rearrange the equation using algebraic operations to isolate a single x-variable.

Given equation:

[tex]ax + bx = c[/tex]

Factor out x from the left side of the equation:

[tex]x(a+b)=c[/tex]

Divide both sides of the equation by (a + b):

[tex]\dfrac{x(a+b)}{(a+b)}=\dfrac{c}{(a+b)}[/tex]

Simplify:

[tex]x=\dfrac{c}{a+b}[/tex]

The values of the composite functions are (f + h)(5) = 7, (h - f)(2) = 0, (fh)(3) = 0 and (h/f)(0) = 3/5

From the question, we have the following parameters that can be used in our computation:

The graphs

Using the graphs as a guide, we have the following:

(f + h)(5) = f(5) + h(5)

(f + h)(5) = 3 + 4

(f + h)(5) = 7

(h - f)(2) = h(2) - f(2)

(h - f)(2) = 1 - 1

(h - f)(2) = 0

(fh)(3) = f(3) * h(3)

(fh)(3) = 4 * 0

(fh)(3) = 0

(h/f)(0) = h(0)/f(0)

(h/f)(0) = 3/5

Hence, the value of the function (h/f)(0) is 3/5

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Answer:

$29.68 to drive 350 miles

Step-by-step explanation:

To find the cost of driving 350 miles, we first need to calculate the amount of gasoline required for driving 350 miles. We can use the formula:

gasoline = distance ÷ miles per gallon

Plugging in the given values:

gasoline = 350 ÷ 33

gasoline = 10.606060606060606

So, we need 10.61 gallons of gasoline to drive 350 miles.

Next, we multiply the amount of gasoline needed by the cost per gallon to find the total cost:

total cost = gasoline × cost per gallon

total cost = 10.61 × 2.80

total cost = 29.6780

Therefore, it would cost approximately $29.68 to drive 350 miles when gasoline costs $2.80 per gallon and your car gets 33 miles per gallon.

Answer: 350 mi * 1 gal / 33 miles * $2.80 / 1 gal  = 29.69$

which means the cost is 2.8*(350/33)=29.69$

Step-by-step explanation:

Here, 2.80$/1 Gal.

Now we need to cancel out gallons, so we add a ratio with gallons.

2.80$/1 Gal. x 1 Gal/33 mi.

Now add the last data element to cancel out miles.

2.80$/1 Gal. x 1 Gal/33 mi. x 350 mi.

Cancelling out units and numbers gives,

(2.80$ x 350)/33. Continue reducing to an answer:

980$/33 = 29.69$

Answer:a=-2

b=5

Step-by-step explanation:

[tex]\frac{a}{b} =\frac{\frac{-1}{4} }{\frac{5}{8} } \\\frac{a}{b} =\frac{-1}{4}*\frac{8}{5}\\\frac{a}{b}=-2/5[/tex]

The values of the vacant spaces are $3.75, 4 oranges, 10 oranges, $15 and 20 percent of 160 is 32

The table can be completed using the following values

If 8 oranges cost $10,

Then 1 orange will cost 10/8 = $1.25

This means that  3 oranges will cost 1.25*3 = $3.75

$5 can buy 8/10*5 = 40/10 = 4 oranges

In the same way, $12.50 will buy 8/10 * 12.50 = 10 Oranges

In the same manner, 12 oranges will cost 1.25*12 = $15

20% of 160 can be calculated as follows

Recall that percentage is a proportion of 100

This implies that 20/100 * 160 = 3200/100 = 32

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The length of each piece is 10 in and 8 in.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

The total length of the string = 18 in

One piece = x + 2

Another piece = x

Now,

Solve for x.

x + 2 + x = 18

2x + 2 = 18

2x = 18 - 2

2x = 16

x = 8

Now,

One piece = 8 + 2 = 10 in

Another piece = 8 in

Thus,

The length of each piece is 10 in and 8 in.

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