A taxi service charges a base fee of

$4. 00 and then charges $2. 00 per

mile driven


1. What is the y-intercept in this

scenario and what does it

represent?


2. What will the cost of a taxi

ride be that is exactly 7 miles?


3. What is the rate of

change/slope in this scenario

(please include labels with

your ratio)?

The GCF of these numbers. 2^5 · 5· 11 and 2^3· 5^2 · 7 is D. 2³.5

The greatest common factor is the largest number that can divide evenly into two or more other numbers (GCF). The highest common factor is another name for this (HCF). A factor is a smaller number that could divide into a larger one evenly.

Before determining the greatest common factor, enumerate the prime factors of each integer. The greatest common factor of two or more integers is the biggest integer that is a factor of each.

In this case, 2 appears three times as the most frequent factor and 5 only once as the most frequent factor among the numbers.

Hence 2³.5 is the GCF of the given number.

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Answer:

Step-by-step explanation:

1. 60 ft = 7.3 yd (60 ft * 0.3333 = 19.98 ft)

2. 100 meters = 10,000 cm (100 m * 100 = 10,000 cm)

3. 5 hr = 300 min (5 hr * 60 = 300 min)

4. 12 meters = 39.37 ft (12 m * 3.281 = 39.37 ft)

5. 16 in = 40.64 cm (16 in * 2.54 = 40.64 cm)

6. 5 liters = 1.32 qt (5 L * 0.2642 = 1.321 qt)

7. 2076 cm = 2.29 yd (2076 cm * 0.0109 = 22.7 yd)

8. 15 pounds = 6,803.86 grams (15 lb * 453.59 = 6,803.86 g)

well, the charge for a year is just 5.5% of the amount so 5.5% of 125000

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{5.5\% of 125000}}{\left( \cfrac{5.5}{100} \right)125000}\implies \text{\LARGE 6875}[/tex]

Answer:

$ 9.625

Step-by-step explanation:

75% = 0.75

5.50 x 0.75 = $4.125

5.50 + 4.125 = $ 9.625

For a right triangle, use the Pythagorean Theorem.

The length of a triangle’s third side must always be between (but not equal to) the sum and difference of its other two sides. Take, for example, the numbers 2, 6, and 7. As a result, the length of the third side must be larger than 4 but less than 8.

Use the Pythagorean Theorem to get the area of a right triangle. Use the area formula for an isosceles triangle to calculate the area of an isosceles triangle. Use the law of cosines or the law of sines if you know some of the angles and other side lengths.

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Answer:

40 paintings and 60 bracelets

Step-by-step explanation:

40 x 10$ = 400

60 x 4$ = 240

400 + 240 = 640

The only option that satisfies both constraints is Option 4: 40 paintings and 60 bracelets, which generates a total revenue of $640.

Two or more expressions with an Equal sign is called as Equation.

Let's calculate the total revenue for each option and see which one satisfies the given constraints.

Option 1: 20 paintings and 60 bracelets

Total revenue = (20 x $10) + (60 x $4) = $200 + $240 = $440

Option 2: 25 paintings and 80 bracelets

Total revenue = (25 x $10) + (80 x $4) = $250 + $320 = $570

Option 3: 30 paintings and 70 bracelets

Total revenue = (30 x $10) + (70 x $4) = $300 + $280 = $580

Option 4: 40 paintings and 60 bracelets

Total revenue = (40 x $10) + (60 x $4) = $400 + $240 = $640

Therefore, the only option that satisfies both constraints is Option 4: 40 paintings and 60 bracelets, which generates a total revenue of $640.

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The solution of the given quadratic equation [tex]x^{2} +5x+6[/tex] = 0 is x = -2 and -3

Now, According to the question:

What is quadratic equation?

A quadratic equation is a second-order polynomial equation in a single variable x ax2+bx+c=0. with a ≠ 0 . Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

The given quadratic equation is:

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

To solve the equation:

Comparing the above equation with the standard form of quadratic equation:

[tex]ax^{2} +bx+c=0[/tex]

a =1 , b = 5 , c = 6

The roots of quadratic equation are given as follows:

x = (-b ± √ (b^2 - 4ac) )/2a.

x = (-5 ±√([tex]5^2[/tex]- 4(1)(6)) / 2 ×1

x = -5 ± 1/2

x = -2 , -3

Hence, The solution of the given quadratic equation [tex]x^{2} +5x+6[/tex] = 0 is x = -2 and -3

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The solution to -4.5 x (-2) is 9.

What is the arithmetic calculation?

Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.

The reason for this is that when two negative numbers are multiplied together, the result is positive.

This is because the negative sign on a number is similar to a "minus" sign, indicating that the number is less than zero.

When you have two "minus" signs together (in this case, one on -4.5 and one on -2),

they cancel each other out, leaving the positive product of 4.5 and 2, which is 9.

-4.5 is a negative decimal number, and -2 is also a negative integer number. When multiplied, it results in a positive number, which is 9.

Hence, the solution to -4.5 x (-2) is 9.

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Answer:

Step-by-step explanation:

We can begin to solve this problem using mathematics. Let's name the total sales for the month "S".

We know that the salesman receives a 10% commission on sales over $300,000 and a 12% commission on sales above 500,000. As a result, we may construct the following equation:

Commission = 0.10 (S - 300,000) + 0.12 (S - 500,000) = 0.10 (S - 30,000) + 0.12 (S - 60,000) = 0.22 (S - 90,000).

We also know that the salesman receives a total commission of $13,900. So we can plug that number into the equation:

13,900 = 0.22S - 90,000

To obtain the value of S, multiply both sides of the equation by 90,000:

13,900 + 90,000 = 0.22S

103,900 = 0.22S

Finally, we can obtain the value of S by dividing both sides of the equation by 0.22: S = 472,273.63

As a result, the total sales for the month were Sh 472,273.63.

Answer:

x<-3

Step-by-step explanation:

The unknown number we can write as x.

2(x-10) > -26

2x - 20 > - 26

2x > -6

x< -3 Divide by negative so reverse the sign

The numbers on the left, or y-axis, represents the number of students studying for each time spent. 12 students spent 2 or more hours studying while ? students spent fewer than 2 hours a night studying.

A bar graph is a chart that uses bars to represent different values or quantities. The bars can be arranged horizontally or vertically, and they can be of different heights or lengths to indicate the size of the value or quantity they represent. Bar graphs are often used to compare data and to show trends over time. They are also called bar charts or column charts.

The bar graph shows the number of hours spent studying on the x-axis while the number of students on the y-axis.

Analyzing the bar graph, there are 12 students who spent 2 or more hours studying.

2-2:59 ⇒ 7

3-3:59 ⇒ 4

4-4:59 ⇒ 1

7 + 4 + 1 = 12

On the other hand, there are 8 students who spent fewer than 2 hours a night studying.

0-0:59 ⇒ 3

1-1:59 ⇒ 5

3 + 5 = 8

Hence, 12 students spent 2 or more hours studying while 8 students spent less than 2 hours.

The problem seems incomplete, it must be...

"A bar graph titled Time Students Spent Studying with hours on the x-axis and students on the y-axis. 3 students spent 0 to 59 minutes, 5 students spent 1 to 1 hour and 59 minutes, 7 students spent 2 to 2 hours and 59 minutes, 4 students spent 3 to 3 hours and 59 minutes, and 1 student spent 4 to 4 hours and 59 minutes.

Use the drop-down menus to answer the questions.

What do the numbers on the left, or y-axis, represent?

How many students spent 2 or more hours studying?

How many students spent fewer than 2 hours a night studying?"

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Answer:

Number of students

12

8

Step-by-step explanation:

Answer: is, 4.  All of the above are equivalent statements.

The x-intercept is where the graph crosses the x-axis.

here, we have,

The x-intercept is the point at which a line crosses the x-axis.

now,

The roots of a function are the x-values of the x-intercepts.

Therefore, if (-3, 0) is an x-intercept, then -3 is a root.

The zeros of the function are the x-values when y = 0.

(-3, 0) means x = -3 when y = 0.

Therefore, -3 is a zero.

According to the factor theorem, if f(x) is a polynomial, and f(a) = 0, then (x – a)  is a factor of f(x).

Given (-3, 0), then f(-3) = 0.  Therefore, (x - (-3)) = (x + 3) is a factor.

Therefore, all given statements are equivalent statements.

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Edith has a better ratio of the basket to shots.

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

Given, Edith and Rashida are shooting free throws.

For Edith

B     1     2     3      4       5

S     3     6     9     12     15

ratio = 3/1

the ratio of Edith's shots = 3

For Rashida

B     2      4      6      8      10

S     5     10     15     20     25

Ratio = 5/2

The ratio of Rashida's shots = 2.5

Therefore, Edith has the better ratio of the basket to shots

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Complete question:

Answer: -11.74

Step-by-step explanation: The reason for this is if you minus 14.6 from 2.86 you get -11.74.

Answer: D. (3, 2).

Step-by-step explanation: The solution of the system is in the intersections of both of the inequalities, and (3, 2) is in the area of intersection.

Answer:

I have no clue but you should get the free trial so a expert can tutor you and you get all your questions right

The solution to the complex number (-5 - i)/(-6 - 9i) is (1 - i)/3

An equation shows the relationship between numbers and variables in an expression.

Complex numbers are in the form a + bi, where both a and b are real numbers and i = √(-1)

Given that:

[tex]\frac{-5-i}{-6-9i} \\\\To\ solve\ multiply\ numerator\ and\ denominator\ by\ conjugate:\\\\=\frac{-5-i}{-6-9i} *\frac{-6+9i}{-6+9i}\\ \\=\frac{30-45i+6i+9}{36+81}\\ \\=\frac{39-39i}{117} \\\\=\frac{1-i}{3}[/tex]

The solution is (1 - i)/3

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Total cost in single service crew is greater than double service crew. So, double service crew is cheaper.

We have, a crew of mechanics at the highway department garage repair vehicles. In case of poisson distribution,

λ = 3 vehicles every 12 minutes

= 3×60/12 = 3× 5

λ = 15 vehicles per hour

When time distribution is approximates an exponential distribution,

The mechanic crew can service an average, μ = 3 vehicles every 10 minutes

μ = 3×60/10 = 18 vehicles per hour

Cost for one service crew =$150 per hour

Cost associated with lost productivity from the breakdown or wait cost

=$50 per hour

For single crew, number of vehicles out of cost, Lₛ = 15/(18 - 15) = 15/3 = 5

Single service crew cost = $150 per hour

wait cost = $5×50 = $250 per hour

Total cost = $400 per hour

For double service crew, Number of vehicles out of service cost = 15/(36 - 15)

= 15/21 = 0.7143

Double service crew cost = 2× $150

= $300

Wait cost = $0.7143×50 = $35.715

Total cost = $335.715 per hour

As we see, the double service crew is cheaper.

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The value of k for the given expression is, 2.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The expression is,

⇒ 8 (k + 10) = 48k

Now, We can solve the expression for k as;

⇒ 8 (k + 10) = 48k

Divide by 8,

⇒ k + 10 = 48k/8

⇒ k + 10 = 6k

Subtract k,

⇒ 10 = 6k - k

⇒ 10 = 5k

⇒ 5k = 10

Divide by 5;

⇒ k = 10/5

⇒ k = 2

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The value of a+b+c will be 16 if  [tex]\frac{5}{2-\sqrt{3}}[/tex] rationalize as  [tex]\displaystyle{\frac{a + b\sqrt{3}}{c}}[/tex].

Given,

y = [tex]\frac{5}{2-\sqrt{3}}[/tex]

To solve the given expression we multiply the numerator and denominator by the conjugate of the denominator

[tex]= \frac{5}{2-\sqrt{3}} \frac{2+\sqrt{3} }{2+\sqrt{3}}[/tex]

[tex]= \frac{10+5\sqrt{3} }{2^2 - \sqrt{3}^2 }[/tex]

[tex]= \frac{10+5\sqrt{3} }{4-3 }[/tex]

[tex]= \frac{10+5\sqrt{3} }{1 }[/tex] = [tex]\displaystyle{\frac{a + b\sqrt{3}}{c}}[/tex]

Now, by comparing the result we get

a = 10, b = 5, c = 1

hence, a+b+c = 10+5+1 = 16

Therefore, the value of a+b+c will be 16.

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The equation of line that passes through the point (-3, 8) and has a slope of 4 is y = 4x + 20.

In the given question, we have to find the equation of the line that passes through the point (-3, 8) and has a slope of 4.

From the given question, m = 4 and point (x(1), y(1)) = (-3, 8).

To find the equation of line we put the values in the equation:

y - y(1) = m(x - x(1))

Now putting the value

y - 8 = 4(x - (-3))

Now simplifying the bracket first

y - 8 = 4(x + 3)

Now solving the expression using the distributive property

y - 8 = 4x + 12

Add 8 on both side, we get

y = 4x + 20

Hence, the equation of the line that passes through the point (-3, 8) and has a slope of 4 is y = 4x + 20.

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The complete question is:

What is the equation of the line that passes through the point (-3, 8) and has a slope of 4?

Answer: -9

Step-by-step explanation:

Equations may be solved and x-intercepts can be found very quickly when a quadratic expression is in factored form and equal to 0. Vertices, as well as the expression's maximum and minimum values, can also be identified.

A polynomial equation of degree 2 is a quadratic equation. A quadratic equation has the conventional form a[tex]x^2[/tex] + bx + c=0, where a, b, and c are all real values and a[tex]\neq[/tex]0.

The quadratic function y=a[tex]x^2[/tex] + bx + c, whose graph will be a parabola, is obtained if we substitute 0 with y.

The solutions to the equation a[tex]x^2[/tex]+bx+c=0 will be at the spots where the graph intersects the x-axis. In other words, if the polynomial a[tex]x^2[/tex]+bx+c can be factored to (x-p)(x-q), then (x-p)(x-q)=0 or (x-p)(x-q)=0 according to the zero product property. As a result, p and q are the x-intercepts of the quadratic equation and the solutions to the equation a[tex]x^2[/tex] + bx + c=0.

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The length (in cm) of an arc of a circle 5π

60°=π/3 radians

A unit circle's arc length is expressed in radians.

We may get the length of an arc using the following formula given an angle and a circle's diameter: ArcLength = (angle / 360) * (2 * pi * radius) Pi equals 22/7, diameter equals 2 * radius, and angle is in degrees.

If a unit circle's arc length is π/3,

(that is a circle with a radius of 1)

For a circle with a radius of 15, the arc length for the same angle would be

X15xπ/3

=5π

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Answer: x=86, y=81

Step-by-step explanation: opposite angles and are same on parallelograms and x+9=95

Option A. Angle A = 46.8 degrees, side A C = 1.9 meters, Side A B = 3.7 meters satisfies the conditions of the problem: angle C is 90 degrees, angle B is 43.2 degrees, and side B C is 3.2 meters.

A right triangle is a type of triangle in which one of the angles is a right angle (90 degrees). The side opposite the right angle is called the hypotenuse and is typically the longest side of the triangle.

The other two sides are called the legs and are typically shorter than the hypotenuse. The Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs, applies to all right triangles

Therefore, the remaining options (b, c, and d) do not satisfy the conditions of the problem and therefore are not correct.

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The equation of a line that passes through the point (2, 3) and (4, 7) is y = 2x - 1.

In the given question, we have to find the equation of a line that passes through the point (2, 3) and (4, 7).

The general equation of line that passes through point is:

y - y(1) = m(x - x(1))

To find the equation of line we have to first find the slope of line by using the formula:

m = [tex]\frac{y(2)-y(1)}{x(2)-x(1)}[/tex]

The given points:

(x(1), y(1)) = (2, 3), (x(2), y(2)) = (4, 7)

m = [tex]\frac{7-3}{4-2}[/tex]

m = [tex]\frac{4}{2}[/tex]

m = 2

Now finding the line of equation.

We can use any of the point of the given.

m = 2, (x(1), y(1)) = (2, 3)

y - 3 = 2(x - 2)

Solving the equation using distributive property

y - 3 = 2x - 4

Add 3 on both side, we get

y = 2x - 1

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The complete question is:

What is the equation of a line that passes through the point (2, 3) and (4, 7)?

The angle that is equal to 90° is ∠ABC.

What is an angle?

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. Dihedral angles are these.

Here, we have

Given the following diagram and we have to determine that in circle O, which angle is equal to 90°.

We concluded that

If one side of a triangle inscribed in a circle is the diameter of the circle, then the triangle is a right triangle and the angle opposite the diameter is the right angle.

Hence, the angle that is equal to 90° is ∠ABC.

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The ratio of C:D:F is 5:3:18.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

here, we have,

given that,

The ratio of C:D is 5:3,

the ratio of F:D is 6:1.

i.e. F:D= 18:3

now,

C:D:F= 5:3:18.

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Answer:

5 2/3

Step-by-step explanation:

17 / 3 = 5 and 2/3