Twice last month, Judy Carter rented a car from a car rental company and traveled around the Southwest on business. The company rents its car for a daily fee, plus an additional
charge per mile driven. Judy recalls that her first trip lasted 4 days, she drove 450 miles, and the rental cost her $222.00. On her second business trip she drove 200 miles in 3 days, and
paid $139.00 for the rental. Find the daily fee, and find the mileage charge.
Daily fee is $, and the mileage charge is $.

=========================================================

Work Shown:

The green triangle in the back has height 2.6 and an unknown base x. Half of this is x/2, which I'll call y. So y = x/2.

The green triangle in the back is split along the vertical dotted line to get two right triangles. The base of each right triangle is y = x/2.

Use the Pythagorean theorem to find y. Use that to find x

a^2+b^2 = c^2

y^2+(2.6)^2 = (3.2)^2

y^2 + 6.76 = 10.24

y^2 = 10.24 - 6.76

y^2 = 3.48

y = sqrt(3.48) .... apply square root

y = 1.8654758 approximately

x/2 = 1.8654758

x = 2*1.8654758

x = 3.7309516 also approximate

The base of the triangle is roughly 3.7309516 meters

We can now find the area of one green triangle

area of triangle = base*height/2 = 3.7309516*2.6/2 = 4.85023708

two triangles have approximate area 2*(4.85023708) = 9.70047416

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So far we've only considered the triangular faces. There are 3 more faces which are the rectangular sides. These are known as the lateral sides.

One way to get the lateral surface area is to multiply the perimeter of the triangle by the depth of the prism

perimeter of triangle = (side1)+(side2)+(side3)

perimeter = 3.7309516 + 3.2 + 3.2

perimeter = 10.1309516

lateral surface area = (depth)*(perimeter)

lateral surface area = (8.26)*(10.1309516)

lateral surface area = 83.681660216

----------------------------------

The last step is to add this lateral surface area onto the area of the two triangles to get the full surface area

surface area = (triangular area) + (lateral surface area)

surface area = (9.70047416) + (83.681660216)

surface area = 93.382134376

surface area = 93.382 square cm

4 ounces ate 328 calories : 1312 calories.

This technique allows us to calculate both the value of multiple units from the value of a single unit and the value of single unit from the value of multiple units.

A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary technique.

We typically utilize this technique for math calculations.

This approach will be helpful to you while tackling problems involving ratio and proportion, algebra, geometry, etc.

According to our question-

The given 4 ounces ate 328 calories

and 1 pound = 16 ounces

16/4= 4

4 * 328 = 1312

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Answer:

d) y= -2/3x+3 1/2

Step-by-step explanation:

Points on the graph: ( -4, 6) and ( -7, 8)

Slope:

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

m=(8-6)/(-7+4)

m= 2/(-3)

m= -2/3

Slope-intercept:

y - y1 = m(x - x1)

y - 6 = -2/3(x + 4)

y - 6 = -2/3x - 8/3

y = -2/3x + 3 1/2

Answer:

Step-by-step explanation:

Y la pregunta?

Answer:

it is he answer is 7.

Step-by-step explanation:

Answer:

$4

Step-by-step explanation:

12÷4=3

7÷7=1

3+1=4

therefore she spent 4 dollars

Answer:

Step-by-step explanation:

D is correct

Answer: D

Step-by-step explanation:

The quadrilateral you're describing is a Kite. A kite is a quadrilateral with two pairs of consecutive congruent sides, and its diagonals meet at a right angle.

a = amount that paid 11% profits

b = amount that lost 5% profits

we know that whatever those values are, a + b = 28000.

how much is 11% of "a"? well, (11/100) * a = 0.11a.

how much is 5% of "b"? well (5/100) * b = 0.05b.

\(a+b=28000\implies b=28000 - a \\\\[-0.35em] ~\dotfill\\\\ \stackrel{paid~11\%}{0.11a}~~ \stackrel{\stackrel{loss}{\downarrow }}{-} ~~\stackrel{lost~5\%}{0.05b}~~ = ~~\stackrel{overall~paid}{2920} \\\\\\ \stackrel{\textit{substituting on the 2nd equation}}{0.11a~~ - ~~0.05(28000-a)}=2920\implies 0.11a+0.05a-1400=2920 \\\\\\ 0.16a-1400=2920\implies 0.16a=4320\implies a=\cfrac{4320}{0.16} \\\\\\ \boxed{a=27000}~\hspace{10em}\boxed{\stackrel{28000-a}{b=1000}}\)

Answer:

*facepalm* 7 lol thats an oldie > u <

Step-by-step explanation:

7 - s = even

Answer: seven

Step-by-step explanation:the number 7 is odd but then you take away the s and it becomes even.

The image vertices of the polygon  K′L′M′N′ are K′(0, 0), L′(−2, 5), M′(5, 5), N′(3, 0).

option A is the correct answer.

We have,

To rotate a point 90° clockwise, we can use the following formula:

(x', y') = (y, -x)

where (x, y) are the coordinates of the original point and (x', y') are the coordinates of the rotated point.

Using this formula, we can find the image vertices of K′L′M′N′ as follows:

K′(0, 0) remains the same as it is the origin of the coordinate system.

L′(−2, 5):

To find the coordinates of L′, we can use the formula as follows:

(x', y') = (y, -x) = (2, -5) ⇒ (-5, -2)

Then,

We can subtract 5 from the x-coordinate and add 2 to the y-coordinate to get L′(−2, 5).

M′(5, 5): To find the coordinates of M′, we can use the formula as follows:

(x', y') = (y, -x) = (-5, -5) ⇒ (5, 5)

Then, we can swap the x and y-coordinates to get M′(5, 5).

N′(3, 0):

To find the coordinates of N′, we can use the formula as follows:

(x', y') = (y, -x) = (-3, 0) ⇒ (0, 3)

Then, we can swap the x and y-coordinates to get N′(3, 0).

Therefore,

The image vertices of the polygon  K′L′M′N′ are K′(0, 0), L′(−2, 5), M′(5, 5), N′(3, 0).

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Answer:

its b  i took the test

Step-by-step explanation:

the other persons wrong the "formula" for that it

(x, y) to (y,-x)

Answer:

p = -2550

Step-by-step explanation:

340 - p=2890​

Subtract 340 from each side

340-340 - p=2890-340​

-p = 2550

Multiply each side by -1

p = -2550

Answer:

3230 you need to add 340+ 2890 since you subtracted 340 from p

Step-by-step explanation:

Part a: Carl earning per hour is $18.

Part b: More Money is earned by Carl.

Part c: The  graph that represents Carl's earnings is drawn.

For the given question,

The amount of the money Louis have is defined by the equation.

Carl's Earnings

Time (h)  Hours      3     5     8    10

Money earned($)  54 90 144 180

Part a: Carl earning per hour.

For 3 hours Carl earns $54.

For one hour-$54/3 = $ 18.

Part b: More Money is earned by-

For 1 hours Carl earns $8.

For 1 hour Louis earning is y = 14×1 = $14.

Thus, Carl earns more.

Part c: The  graph that represents Carl's earnings over time in hours is drawn.

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If the radius of the circle is 5 m and angle subtended by arc LKM is 70° then the length of the arc LNM is 25.29 m.

Given that the radius of the circle is 5 m and angle subtended by arc LKM is 70°.

From the figure given we can estimate that the length of arc LNM can be circumference of circle subtracted by length of arc LKM.

Circulference of the circle is basically the length of whole arc of the circle. It is also know as perimeter of the circle. The formula of calculating circumference of a circle is 2πr in which r is the radius.

So,

length of arc LNM=Circumference of circle-length of arc LKM.

We know that length of an arc =Θr

in which Θ is the angle in radian.

length of arc=70*π\(/180*5\)

=70π\(/36\)

Circumference of circle=2π*5

=10π

Length of arc LNM=10π-70π\(/36\)

=(360π-70π)\(/36\)

=290π\(/36\)

Put π=3.14

=290*3.14\(/36\)

=910.6\(/36\)

=25.29m

Hence the length of arc LNM is 25.29 m.

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The value of t for which the rockets height is 25 meters is 40.7 seconds

From the information, the ball is thrown with an initial height of 4 feet with an initial velocity of 36 ft/s. h= 4 + 36t - 16t².

Therefore, the values of t for which the rockets height is 25 meters will be:

h= 4 + 36t - 16t².

where h = 25

25 = 4 + 36t - 16t².

Collect like terms

25 - 4 - 36t + 16t² = 0

16t² - 36t -21 = 0

Using almighty formula

t = 40.7 seconds.

Therefore, the value of t for which the rockets height is 25 meters is 40.7 seconds

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Answer:

1/8

Step-by-step explanation:

The following is deduced from the equation f(x)=(x - 1)^3 + 5

Horizontal shift: 1 left

Vertical shift: 5 down

Vertical stretch factor: 1

Vertical compression factor: 1

Axis of reflection: -x + 6

Domain: all real numbers

Range: all real numbers

Inflection Point: (1, 5)

The vertical stretch factor is a term used in mathematics to describe the transformation that changes the height of a graph while leaving the horizontal axis unchanged. In other words, it's a factor by which the y-values of a function are multiplied to produce a new, stretched or compressed version of the original graph.

The stretch factor is usually represented by the symbol "k". For example, if the equation of a function is y = f(x), then the equation of its vertically stretched image would be y = k * f(x). A positive value of k stretches the graph upward, while a negative value of k compresses the graph downward. If k > 1, the graph is stretched vertically; if 0 < k < 1, the graph is compressed vertically; if k = 1, the graph remains unchanged.

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Answer:

x = 10/243

Step-by-step explanation:

3^5x = 10

243x = 10

Divide 243 on both sides

10/243

Answer:

Step-by-step explanation:

Diagonals of a parallelogram bisect each other.

Intersection point is the midpoint of either diagonal.

Let's take QS and calculate midpoint using midpoint formula:

Point (-0.5, 2) is the answer

Answer:

The answer is 16pi or 50.3cm² to 1 d.p

Step-by-step explanation:

The non shaded=area of shaded

d=8

r=d/2=4

A=pir³

A=p1×4²

A=pi×16

A=16picm² or 50.3cm² to 1d.p

Answer:

3.45 cm (3 s.f.)

Step-by-step explanation:

We have been given a 5-sided regular polygon inside a circumcircle. A circumcircle is a circle that passes through all the vertices of a given polygon. Therefore, the radius of the circumcircle is also the radius of the polygon.

To find the radius of a regular polygon given its side length, we can use this formula:

\(\boxed{\begin{minipage}{6 cm}\underline{Radius of a regular polygon}\\\\$r=\dfrac{s}{2\sin\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $r$ is the radius.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}\)

Substitute the given side length, s = 8 cm, and the number of sides of the polygon, n = 5, into the radius formula to find an expression for the radius of the polygon (and circumcircle):

\(\begin{aligned}\implies r&=\dfrac{8}{2\sin\left(\dfrac{180^{\circ}}{5}\right)}\\\\ &=\dfrac{4}{\sin\left(36^{\circ}\right)}\\\\ \end{aligned}\)

The formulas for the area of a regular polygon and the area of a circle given their radii are:

\(\boxed{\begin{minipage}{6 cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{nr^2\sin\left(\dfrac{360^{\circ}}{n}\right)}{2}$\\\\\\where:\\\phantom{ww}$\bullet$ $A$ is the area.\\\phantom{ww}$\bullet$ $r$ is the radius.\\ \phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}\)

\(\boxed{\begin{minipage}{6 cm}\underline{Area of a circle}\\\\$A=\pi r^2$\\\\where:\\\phantom{ww}$\bullet$ $A$ is the area.\\\phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}\)

Therefore, the area of the regular pentagon is:

\(\begin{aligned}\textsf{Area of polygon}&=\dfrac{5 \cdot \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\sin\left(\dfrac{360^{\circ}}{5}\right)}{2}\\\\&=\dfrac{5 \cdot \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\sin\left(72^{\circ}\right)}{2}\\\\&=\dfrac{\dfrac{80\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}}{2}\\\\&=\dfrac{40\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}\\\\&=110.110553...\; \sf cm^2\end{aligned}\)

The area of the circumcircle is:

\(\begin{aligned}\textsf{Area of circumcircle}&=\pi \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\\\\&=\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\&=145.489779...\; \sf cm^2\end{aligned}\)

The area of the shaded area is the area of the circumcircle less the area of the regular pentagon plus the area of the small central circle.

The area of the unshaded area is the area of the regular pentagon less the area of the small central circle.

Given the shaded area is equal to the unshaded area:

\(\begin{aligned}\textsf{Shaded area}&=\textsf{Unshaded area}\\\\\sf Area_{circumcircle}-Area_{polygon}+Area_{circle}&=\sf Area_{polygon}-Area_{circle}\\\\\sf 2\cdot Area_{circle}&=\sf 2\cdot Area_{polygon}-Area_{circumcircle}\\\\2\pi r^2&=2 \cdot \dfrac{40\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}-\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\2\pi r^2&=\dfrac{80\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}-\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\\end{aligned}\)

                                                 \(\begin{aligned}2\pi r^2&=\dfrac{80\sin\left(72^{\circ}\right)-16\pi}{\sin^2\left(36^{\circ}\right)}\\\\r^2&=\dfrac{40\sin\left(72^{\circ}\right)-8\pi}{\pi \sin^2\left(36^{\circ}\right)}\\\\r&=\sqrt{\dfrac{40\sin\left(72^{\circ}\right)-8\pi}{\pi \sin^2\left(36^{\circ}\right)}}\\\\r&=3.44874763...\sf cm\end{aligned}\)

Therefore, the radius of the small circle is 3.45 cm (3 s.f.).

5th term of the sequence is -4

To find the 5th term in the sequence, we need to substitute n =  5 into the expression given

 \(a_5\) =  26- 6( 5)  

\(a_5\) =  26- 30

\(a_5\) = -4  

The formula given, an =  26- 6n, represents an  computation sequence with a common difference of-6.

This means that each term in the sequence is  attained by obtain 6 from the  former term.  

It's important to note that the formula is written in general form, meaning that it can be used to find any term in the sequence by simply plugging in the  matching value of  n.

 In this case, we were asked to find the 5th term, so we substituted n =  5 into the formula to get a5 = -4.

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The equation of the line of best fit that Brianna drew is: c. y = 2x + 5

Recall:

Thus:

Slope of a line (m) = change in y/change in x

Change in y = 2 units

Change in x = 1 unit

Slope = 2/1 = 2

The y-intercept is the point where the line of best fit intercepts the y-axis which is at y = 5.

y-intercept (b) = 5

Substitute b = 5 and m = 2 into y = mx + b

y = 2x + 5

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Answer:

c    ..)

Step-by-step explanation:

Population of this survey is community service group.

Population in statistics is a set group of individuals from which a statistical sample is drawn for a survey or study.

Kitchen Guillermo randomly surveys 15 members of his community service group and gains ideas for the next community service project.

The population of his survey is community service group.

Out of his community he select just 15 members as a sample for his survey.

Hence, population of this survey is community service group.

Complete question:

Guillermo randomly surveys 15 members of his community service group to gain ideas for the next community service project. What is the population of this study?

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Answer:

the answer is 90%

Step-by-step explanation:

hope this helped

The fence in dead center is about 399 feet from the third base.

The Pythagorean Theorem states that in the case of a right triangle, the square of the length of the hypotenuse, which is the longest side,  is equals to the sum of the squares of the lengths of the other two sides.

Hence the equation for the theorem is given as follows:

c² = a² + b².

In which:

For the triangle in this problem, we have that:

Hence the distance is obtained as follows:

d² + 90² = 409²

\(d = \sqrt{409^2 - 90^2}\)

d = 399 ft.

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The line which is on the same plane can be parallel, two lines are never parallel when they are in different planes, so option C is correct.

An object having an endless length and no width, depth, or curvature is called a line. Since lines can exist in two, three, or higher-dimensional environments, they are one-dimensional things.

Given:

The given planes are A and B,

A new line, p, is drawn parallel to line l,

Line l in the diagram is located on plane A. Line p must be drawn on plane A in order to be parallel to line l. As a result, line p, which is located on plane B, will be perpendicular to line n and parallel to lines l and n.

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The image of the remaining question is attached below.

Answer:

the answer is A )An approximate solution of the equation p(x ) = q(x ) is (-3, 1).

Step-by-step explanation: