A car rental company's standard charge includes an initial fee plus an additional fee for each mile driven. (READ PICTURE FOR RESTc=

Answer: 5.3

Step-by-step explanation:

[tex]-16t^2 +126t=217\\ \\ 16t^2 -126t+217=0\\\\t=\frac{-(-126) \pm \sqrt{(-126)^2 -4(16)(217)}}{2(16)}\\\\t \approx 5.3 \text{ } (t > 0)[/tex]

If f(x) has a remainder of -2 when divided by x-7, f(7) is -2.

The leftover is -2 when the function f(x) is divided by x-7, according to the question.

hence the result will be -2 if we use the value x = 7 in the function.

This has the same meaning as "f(7)" because "f(7)" also means to enter "x = 7" in the function and "-2" as the response.

Therefore, if f(x) is divided by x-7 with a remainder of 2, f(7) is equal to -2.

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Answer: [tex]x= \frac{3}{4}[/tex]

Step-by-step explanation:

Solve for x by simplifying both sides of the equation, then isolating the variable.

The amount spent on brother is $16, on sister is $26 and that on wife is $58.

According to the question,

We have the following information:

Mark is buying Christmas presents for members of his family. He wants to spend $10 less on his brother than he spends on his sister, and six dollars more than twice the amount he spends on his sister on his wife. And Mark

has $100 to spend.

Let's take the amount spent on sister to $s.

Amount spent on brother = $(s-10)

Amount spent on wife = $(6+2s)

So, we have the following expression:

s+s-10+6+2s = 100

4s-4 = 100

4s = 104

s = 104/4

s = $26

Amount spent on brother = 26-10 = 16

Amount spent on wife = 6+2*26

Amount spent on wife = 6+52

Amount spent on wife = $58

Hence, the amount spent on brother is $16, on sister is $26 and that on wife is $58.

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the interior angles of the triangle must sum 180°

if we have two angles that measure 100° the sum of interior angles of a triangle will be more than 180°, and that can't be true.

so the answer is FALSE

SOLUTION

3(a)

The diagram below would be helpful

From the diagram above, a segment has been made from C to O indicating the radius of the circle, so CO is a radius.

Also any line drawn from the center of a circle to touch the circumference is a radius, So, OB is a radius too.

Since CO and OB are radii of the circle, then their sides are equal,

Hence triangle COB is an isosceles triangle.

Also the line OA represents the radius of the circle just like CO. Since OA and CO are radii,

Hence triangle COA is an isosceles triangle.

(b) Statement: AOB is a straight line and at the center of a circle

Reason: Given

Statement: AOB is also an angle, which is 180 degrees

Reason: Angle on a straight line is 180 degrees

Statement: Angle AOB is an angle at the center of the circle, and angle C is at the circumference

Reason: same arc AB

Statement: Angle AOB = 2C

Reason: Angle at the center of a circle is twice angle at the circumference.

Hence

Therefore C is a right-angle (90 degrees)

SOLUTION

Let's look at the graphical solution of the pair of simultaneous equations

From the graph, we can see that the equations have at least one solution, which are 2.556, and -0.333. Hence, it is said to be consistent.

Now, since the solutions intersect only at one place, it means that it has exactly one solution. If a consistent equation has exactly one solution, it is said to be independent.

Therefore, the systems of equations are consistent and independent

Answer:

[tex]7.3 \times 10^7[/tex]

Step-by-step explanation:

[tex]\frac{2.92 \times 10^6}{4 \times 10^{-2}} \\ \\ =\frac{2.92 \times 10^8}{4} \\ \\ =0.73 \times 10^8 \\ \\ =7.3 \times 10^7[/tex]

Answer:

I believe the top is 50 because 50 is the b value while the bottom would be 25 because that is the ac value of the expression

Step-by-step explanation:

above

The greatest number of eggs laid by the chicken any day is 7

A frequency table is a table that lists items and shows the number of times the items occur.Frequency refers to the number of times an event or a value occurs.

A frequency table lists a set of values and how often each one appears.

The frequency table above shows the number of eggs laid for 3weeks.

From the table, the least number of egg laid in anyday is 3 and the greatest number of egg laid in a day is 7.

Therefore the greatest number of egg that can be laid by the chickens in anyday is 7

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Answer:

The distribution is spread from 3 eggs to 7 eggs.

The mass of the petrol is 8.88 kg.

Given, Petrol has a density of 740 kg/m³.

A container holds 12 litres of petrol.

One litre is equal to 0.001 m³.

As, Density = Mass/Volume

1 litre = 0.001 m³

12 litres = 0.012 m³

Now, using the formula, we get

740 = mass/0.012

mass = 740×0.012

mass = 8.88 kg

Hence, the mass of the petrol is 8.88 kg.

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Answer:

54 mph

Step-by-step explanation:

18 miles / 20 minutes = 18 miles / 1/3 hour

18 ÷ 1/3 = 18 × 3 = 54 mph

The constant speed with given distance and time is 54 miles per hour.

The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.

Given that, you drove  18  miles in  20  minutes at a constant speed.

Here, 20 minutes =20/60 =1/3 hours

Now, Speed = Distance÷Time

Speed= 18÷1/3

Speed=54 miles per hour

Therefore, the constant speed is 54 miles per hour.

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The ratio shows how many times one value is contained in another value.

1 part = $28

2 parts = $56

3 parts = $84

The amount 84 in the ratio 2:1 is 56:28.

The ratio shows how many times one value is contained in another value.

Example:

There are 3 apples and 2 oranges in a basket.

The ratio of apples to oranges is 3:2 or 3/2.

We have,

Amount = $84.

We will divide the amount into 2:1

This means,

There are 3 parts.

2 + 1 = 3

The amount for each part.

= 84/3

= 28

Now,

1 parts = $28

2 parts = 2 x $28

2 parts = $56

The ratio 2:1 of 84 is 56:28

Thus,

The amount 84 in the ratio 2:1 is 56:28.

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The interest rate that would be required in order for Sarah to end up with $121,000 is R=6.1%

Compound interest, often known as interest on principal and interest, is the adding of interest to the loan or deposit principal. It occurs when interest is reinvested, added to the lent capital instead of being paid out, or the borrower is required to pay it, resulting in the next period's interest being generated on the principal amount plus any accumulated interest. Finance and economics both use compound interest frequently.

compound interest allows for the accumulation of interest from prior periods.

Given that Sarah is going to invest $79,000 and leave it in an account for 7 years.

We have to assume that the interest is compounded quarterly then,

A=P[tex](1+(R/400))^{4n}[/tex]

121000=79000[tex](1+(R/400))^{28}[/tex]

(121000/79000)=[tex](1+(R/400))^{28}[/tex]

[tex](1.53)^{1/28}[/tex]= [tex](1+(R/400))[/tex]

1.0153=[tex](1+(R/400))[/tex]

0.0153=R/400

R=6.1372

R=6.1%

Therefore, the interest rate is R=6.1%

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Step 1: For solving this exercise, we need to know the speed of sound. We will calculate it this way:

Speed = Distance/Time

Replacing with the values Josh has.

Speed = 5 miles/12 seconds

Speed = 0.417 miles per second

Step 2: Now, let's calculate the distance after 7 seconds:

Using the same formula, we can find the distance, as follows:

Distance = Speed * Time

Distance = 0.417 * 7

Distance = 2.919

Distance = 3 miles (Rounding to the nearest whole number)

Step 3: Interpretation of the answer, as follows:

The lightning was 3 miles away when Josh counted 7 seconds between the next flash of lightning and thunder.

Let cheryl score "c", Adam score "a", Laura score "l" and Tom score "t", points.

Now, let's write equations for statements given.

Adam scores 8 more than Cheryl, so:

a = c + 8

or

c = a - 8

Laura scored twice as Adam, so:

l = 2a

Tom scores 10 less than Laura:

t = l - 10

or

t = 2a - 10

Altogether, they scored 66, so:

c + a + l + t = 66

Putting the 3 bold equations in the last one, we can solve for "a" first. Shown below:

So,

c = a - 8

c = 14 - 8

c = 6

l = 2a

l = 2(14)

l = 28

t = 2a - 10

t = 2(14) - 10

t = 28 - 10

t = 18

So,

Adam = 14 points

Cheryl = 6 points

Laura = 28 points

Tom = 18 points

Answer:

3ggjurfyeyryeyryryryr

Answer:

see the answer

Step-by-step explanation:

4x-3y=1xy

Answer:

≈ 466 cm

Step-by-step explanation:

the total length of wire required is

outside sides of square + 4 straight pieces + circumference of circle

= (4 × 70) + (4 × 15) + (π d ← d is the diameter )

= 280 + 60 + 40π

= 340 + 125.66

= 465.66

≈ 466 cm ( to the nearest cm )

We need to find out the total length of wire needed to make this design. We can do this by finding out the perimeter of square and Circle and finally adding the lengths of the four 15cm wire used .

Given data:-

Perimeter of the square:-

[tex]\longrightarrow p_s = 4(side) \\ [/tex]

[tex]\longrightarrow p_s = 4(70cm) \\ [/tex]

[tex]\longrightarrow p_s = 280cm \\ [/tex]

Perimeter/circumference of the circle:-

[tex]\longrightarrow p_c = 2\pi r \\ [/tex]

[tex]\longrightarrow p_c = 2(3.14)(20cm) \\ [/tex]

[tex]\longrightarrow p_c = 125.71 cm \\ [/tex]

Additionally length of four wires would be 15cm*4 = 60cm .

So , total length of the wire required,

[tex]\longrightarrow l =( 125.71 + 280+60)cm \approx \boxed{466\ cm}\\ [/tex]

and we are done!

Solution

Step1

The AA criterion for triangle similarity states that if two triangles have two pairs of congruent angles, then the triangles are similar.

Step2

Two pairs angles are equal, hence they are similar

Answer

Are similar by AA

Answer:

KM = √53

Step-by-step explanation:

K is at (-4, 8), and M is at (-2, 1).

KM

[tex] \sqrt{ {( - 4 - ( - 2))}^{2} + {(8 - 1)}^{2} } [/tex]

[tex] \sqrt{ {( - 2)}^{2} + {7}^{2} } = \sqrt{4 + 49} = \sqrt{53} [/tex]

Using exponential function to calculate the exponential decrease, the population in 2025 is 22278

An exponential function is a mathematical function, which is used in many real-world situations. It is mainly used to find the exponential decay or exponential growth or to compute investments, model populations and so on. Exponential function, as its name suggests, involves exponents. But note that, an exponential function has a constant as its base and a variable as its exponent but not the other way round (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function).

We can write the function as

A = N(1 + r)⁻ˣ

Let's plug in our values and solve

A = 24597(1 + 0.02)⁻⁵

A = 22,278

The population in 2025 is 22278

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Answer:

15/120 simplified is 1/8

The y intercept of the graph of the linear equation 2y = x - 4 is -2 obtained through the following graph.

Linear equation:

Linear equation means an equation in which the highest power of the variable is always 1 also known as a one-degree equation.

The standard form of a linear equation is ax + b = c

Given,

Here we have the linear equation 2y = x - 4.

Now, we have to find the y - intercept from this equation's graph.

In order to plot the graph for this equation we have to rewrite the given equation then we get,

=> 2y = x - 4

=> y = (x-4)/2

Now we have to take sample value for x, in order to get the table for the equation.

For that we have to take the sample value of x as -2, -1, 0, 1, and 2, then we get the table like the following.

By using the table we have to plot the graph, then the resulting graph is attached below.

Through the graph we have identified that the y - intercept is -2.

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The greatest possible sum of c and d? is 5.

From the information, the product is -6. The numbers that can given this value include:

(-1) × (6) = -6

(-2) × (3) = -6

(-6) × 1 = -6

(-3) × (2) = -6

Therefore from the information, the number that will give the greatest sum will be:

-1 + 6

= 5

Therefore, the greatest sum is 5.

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rock with 35% and country with 25% are the highest percentages, therefore the answer is: B

By simplifiying the linear equation we will see that it is false, then the correct option is C, there are no solutions.

Here we have the following linear equation:

2x - 5x - 9 = -3x + 2 - 9

We want to solve this linear equation for the variable x, to do so, we need to isolate the variable x in one of the sides of the equation, so let's do that.

First we move all te terms with x to the left side and the terms without x to the right side, so we get:

2x - 5x + 3x = 2 - 9 + 9

(2 - 5 + 3)*x = 2

0*x = 2

0 = 2

So we have a false equation, this means that there is no value of x such that the equation is true, then the equation has no solutions, and the correct option is C.

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Pythagoras theorem is used to find the length of sides in geometry. The number of strips of Balsa wood having length of 13cm is  8 approximately.

Pythagoras theorem states that the square of the hypotenuse in a right angled triangle is equal to the sum of the squares of the remaining two sides.

Given that,

The length of each pole = 100cm.

The distance between the pole = 12cm.

The length of each strip of Balsa wood = 13cm.

The diagram for the given question is as follows,

Apply Pythagoras theorem, h² = p² + b² in the given triangle to find the hypotenuse as,

h² = 100² + 12²

=> h² = 10144

=> h = 100.71

Now, the number of strips of balsa wood is equal to hypotenuse divided by 13 which is given as,

100.71 ÷ 13 = 7.74.

Hence, the number of small strips of Balsa wood is 8 approximately.

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Since the amount of yarn available is what defines the size of the blanket, the amount of yarn is the independent variable, and it is the input for the table or equation.

The size of the blanket depends on the amount of yarn, so the size of the blanket is the dependent variable, and it is the output of the table or equation.

Therefore the option that shows the true statement is C.

Given: A triangle ABC with sides, AB= 4cm

BC=6cm and

AC=8cm

Required: To find out the triangle's highest corner.

Explanation: Let us first draw a triangle with given sides,

We use the followig property of triangles:

• One side cannot be equal or greater than the sum of the other two sides

The sides of this triangle are: 11, 9 and 17.

The sum of the first two sides is: 11+9=20

The sum of the two sides is greater than the other remaining side (17).

Thus, 11, 9 and 17 do not make a triangle.