Answer:
A)
c = 0.20m + 144
Where c is total cost and m is miles driven.
B)
c = (200 + 0.20m) + 144
C)
174 = 0.20m + 36x4
174 = 0.20m + 144
30 = 0.20m
30/0.20 = m
m = 150+200
m = 350miles
Hope that helps
in the equation 8x - 1 = 3x + 4 the variable x represents the same value. Which value of x is the solution of the equation; x = 0, 1, 2, or 3? Explain.
Given the following expression:
a.) 8x - 1 = 3x + 4
Let's determine the value of x,
8x - 1 = 3x + 4
8x - 1 + 1 - 3x = 3x + 4 + 1 - 3x
8x - 3x = 4 + 1
5x = 5
5x/5 = 5/5
x = 1
Therefore, x = 1.
2. The polygon on the grid represents the floor plan of a factory. The manager labeled each side to describe it. For example, N1 means North 1. у 84 5 N1 W1 E1 S2 --10-8-8-7-6-5-4-3-2-11 B 1 2 3 W2 2 -3 si -6 (a) The polygon has six sides. Find the length of each side of the polygon. (b) Each unit on the grid represents 25 feet. Find the perimeter of the factory. Show your work. Denne
Solution:
Given:
A polygon on a grid.
Question 2a:
The length of each side of the polygon on the grid is given by;
[tex]\begin{gathered} N1=13\text{units} \\ E1=7\text{units} \\ S1=5\text{units} \\ W2=4\text{units} \\ S2=8\text{units} \\ W1=3\text{units} \end{gathered}[/tex]Question 2b:
Perimeter is the sum of the outer sides enclosing a shape.
Hence, the perimeter of the factory is;
[tex]P=N1+E1+S1+W2+S2+W1[/tex]Thus,
[tex]\begin{gathered} P=N1+E1+S1+W2+S2+W1 \\ P=13+7+5+4+8+3 \\ P=40\text{units on the grid} \\ \\ \text{But each unit on the grid represents 25 f}eet. \\ \text{Hence, } \\ P=40\times25 \\ P=1000\text{feet} \end{gathered}[/tex]Therefore, the perimeter of the factory is 1000 feet.
Gavin rides motocross in competition. A competition-level bicycle costs $1,800. He can borrow themoney from the bank at 3.596 interest for two years. By the end of the loan, how much money willGavin end up paying the bank?
The simple interest formula is:
[tex]I=Prt\text{ }[/tex]where P is the principal, r is the interest rate and t is the time.
In this case the principal is $1800, the interest rate is 0.035 (in decimal form) and t is 2. then the interest he pays is:
[tex]I=(1800)(0.035)(2)=126[/tex]Therefore in total he will pay $1926
Using synthetic division what is the first row for the dividend (divided) and the divisor value using synthetic division process:
2x3−10x+2/x−4
Using synthetic division, the solution to the polynomial fraction expression is; 2x² - 10 + 12/(x - 4)
How to use Synthetic Division?We are given the polynomial fraction as;
(2x³ - 10x + 2)/(x- 4)
This means that we want to divide the polynomial (2x³ - 10x + 2) by (x - 4) using synthetic division.
For the divisor, we have x - 4, and that means x - 4 = 0, x = 4
So, we'll be using 4 for the synthetic division and we have;
-1 | 2 0 -10 2
× 0 0 10
-------------------------
2 0 -10 12
Now we will form the expression in the form of fraction again;
2x² - 10 + (12/(x - 4))
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Andrew is writing a coordinate proof to show that the triangle formed by connecting the midpoints of the sides of an isosceles triangle is itself an isosceles triangle. He starts by assigning coordinates as given.
Enter the answers in the boxes to complete the coordinate proof.
P is the midpoint of DE. Therefore, the coordinates of P are ( answer, b ).
Q is the midpoint of DF. Therefore, the coordinates of Q are (3a, answer).
R is the midpoint of EF. Therefore, the coordinates or R are ( answer, answer)
The length of PR is √ a^2+b^2. The length of QR is √ a^2 +b^2.
Comparing the expressions for the lengths of PR and QR shows that the lengths are equal. therefore, △PQR is isosceles
The area of triangle DEF = 4 ( area of triangle QRP) which is determined that by comparing the expression for the lengths of PR and QR.
What are congruent triangles?Two triangles are said to be congruent if their corresponding sides and angles are equal.
According to the data provided,
Triangle ΔDEF is an isosceles triangle having DE, EF, and FD sides.
Since DE = EF and P,R, and Q are the midpoints of the sides DF, EF, and DE,
We know from isosceles triangle theorems that the area of a triangle formed by uniting the midpoints of two isosceles triangles is one-fourth the area of the isosceles triangle.
As evidence, consider the following:
Because point Q is the halfway of DE, its coordinates are (a, b). (Because the midpoint of a line segment always has coordinates that are half the total of the coordinates of the end points.)
Because point R is the midpoint of FE, its coordinates are (3a,b).
The length of the base, DF, in triangle DEF is 4a and the height is 2b. As a result, its area is 4ab. (Because the area of a triangle equals 1/2 its base × height.)
The length of the base, QR, of the triangle QRP is 2a, while the height is b.
As a result, its area is ab.
Therefore, the area of triangle DEF is four times that of triangle QRP.
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A rectangular driveway is 9 feet wide, and it has an area of 135 square feet. How lo g is the driveway
Area of a Rectangle
Given a rectangle of length L and width W, the area is calculated as follows:
A = L.W
We are given the area of A=135 square feet and the width is W= 9 ft. Solving for L:
[tex]L=\frac{A}{W}=\frac{135ft^2}{9ft}=15ft[/tex]The driveway is 15 feet long
Pls answer very desperate ty
The science club members are using transformations on coordinate grids to track the movement of constellations in the sky. Choose the left side of the constellation depicted by the line passing through (1,7) and (2.5,1), and find the linear functions that correspond to the series of motions of the side given below.
1) Shift the side down 5 units.
2) Vertically stretch the result of the shift by 3.
3) Shift the result of the stretch 2 units to the left.
The linear function passing through points (1,7) and (2.5, 1) is given by:
y = -4x + 11.
What is a linear equation?
It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
y = mx + b
In which the coefficients are described as follows:
The coefficient m is the slope of the function, representing the rate of change of the function.The coefficient b is the y-intercept of the function, representing the value of y when the function crosses the y-axis(x = 0).For this problem, the two points that form the function are given as follows:
(1,7) and (2.5, 1).
The slope is given by change in y divided by change in x, hence it is given by:
m = (1 - 7)/(2.5 - 1) = -4.
Then:
y = -4x + b.
When x = 1, y = 7, hence we can find the intercept b of the function as follows:
7 = -4(1) + b
b = 7 + 4
b = 11.
Hence the equation is:
y = -4x + 11.
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I’m trying to do my homework help
The average rate of change f(x) on the interval -6 ≤ x ≥ 2 is; 5
What is the Average Rate of Change of the function?
Average rate of change is a measure of how much the function changed per unit, on average, over that interval. This is derived from the slope of the straight line connecting the interval's endpoints on the function's graph.
Now, the formula for the average rate of change over the interval (a, b) is;
f'(x) = [f(b) - f(a)]/(b - a)
Now, we are given the interval as -6 ≤ x ≥ 2.
From the given polynomial graph, we see that;
f(2) = 0 and f(-6) = 40
Thus;
f'(x) = [f(-6) - f(0)]/(2 - (-6))
f'(x) = (40 - 0)/8
f'(x) = 5
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Find the length, width, area, and aspect ratio of a SAMSUNG Flat 75-Inch 4K 8 Series UHD Smart TV with HDR and Alexa Compatibility.
The dimensions that we must use in this problem, are the dimensions of the screen of a TV of 75 inches:
• W = width = 65.4" ,
,• H = heigh = 36.8".
• The form of the TV is a rectangle, we compute the area A of the rectangle by the following formula:
[tex]A=W\cdot H=65.4in\cdot36.8in=2406.72in^2.[/tex]• The aspect ratio r is given by the quotient of the width (W) by the height (H):
[tex]r=\frac{W}{H}=\frac{65.4in}{36.8in}=1.777.[/tex]• The length of the TV diagonal L can be computed using Pitagoras Theorem:
[tex]L=\sqrt[]{W^2+H^2}=\sqrt[]{(65.4in)^2+(36.8in)^2}\cong75.04in.[/tex]Answer
• width = 65.4",
,• heigh = 36.8",
,• area = 2406.72in²,
,• aspect ratio = 1.777
,• length of the diagonal = 75.04in.
This math is new to me please help so I can take notes
We have here two sets of numbers, and we have to find the value for one of the operations of sets, that is, the intersection operation.
The result of this operation is the values that are common to both sets.
If we saw set A and set B, we will have:
[tex]A=\mleft\lbrace1,4,8,13,15\mright\rbrace[/tex][tex]B=\mleft\lbrace2,3,5,12,17\mright\rbrace[/tex]Both sets have five elements. However, they have no common elements (or nothing in common). Therefore, the result will be the empty set:
[tex]A\cap B=\varnothing[/tex]That means both sets have no common elements ---> empty set.
In summary, we have that:
[tex]A\cap B=\varnothing[/tex]What is the volume of a prism that is 10 mi tall with a right triangle for a base with side lengths 6 mi, 8 mi, and 10 mi ?
The expression for the volume of the Prism is 1/3(Base area x Height)
In the given prism
Height = 10 mi
Base is in the shape of right angle triangle
Area of right angle triangle = 1/2 x Base x Height
Area of right angle triangle = 1/2 x 8 x 6
ARea of right angle triangle = 24
Area of base of the prism = 24mi².
Volume of the prism = 1/3 (Base area x Height)
Volume of the prism = 1/3 (24 x 10)
Volume of the prism = 1/3(240)
Volume of the prism = 80mi³.
The volume of prism is 80 mi³.
Which expression can be used to determine the number of downloads on the meh day after the game was available
we have the sequence
1,790 2,555 3,320 4,085 4,850
so
a1=1,790 ----> first term
a2=2,555
a3=3,320
a4=4,085
a5=4,850
Find out the difference between consecutive terms
a2-a1=2,555-1,790=765
a3-a2=3,320-2,555=765
a4-a3=4,085-3,320=765
a5-a4=4,850-4,085=765
This is an arithmetic sequence
The common difference is d=765
so
[tex]a_n=a_1+d\left(n-1\right)[/tex]we have
d=765
a1=1,790
substitute
[tex]\begin{gathered} a_n=1,790+765(n-1) \\ a_n=1,790+765n-765 \\ a_n=1,025+765n \end{gathered}[/tex]The answer is option BSelect all the figures that have sides that to be perpendicular
A
B
C
D
E
HELP
The figures that have sides that to be perpendicular are figures A and E.
What is defined as the perpendicular?Perpendicular lines are two distinct lines that intersect at 90°, or a right angle.The symbol " represents perpendicular lines. If m and n are two lines that intersect at 90°, they are perpendicular to one another and are symbolized as m ⊥ n. The intersection of two perpendicular lines is known as the foot of a perpendicular.Perpendicular Line PropertiesThese lines are always at right angles when they intersect.If two lines have become perpendicular to each other, they are parallel and will not intersect.Adjacent square and rectangle sides always are perpendicular to the other.For the given question;
As we can see that the only in figures A and E, there are two lines making an angle of 90 degrees.
Thus, only figures A and E have the sides perpendicular to each other.
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name a number that is not a whole number
Whole numbers are the numbers 0, 1, 2, 3, 4, etc. (the natural numbers and zero). Negative numbers are not considered whole numbers. All natural numbers are whole numbers, but not all whole numbers are natural numbers since zero is a whole number but not a natural number.
For example.
- 2, - 10
8.20y + 4) = 6.7s +5.2
distribute the parentheses
[tex]\begin{gathered} 8.2y+32.8=6.7s+5.2 \\ \end{gathered}[/tex]substract 32.8 on both sides
[tex]undefined[/tex]Simplify the following expression. -7x²-2+5x+13x² - 15x
Answer: 2(3x^2-5x-1) or 6x^2-10x-2
Step-by-step explanation: combine like terms, and then factor by grouping :)
Four year after a maple tree was planted its height was 9 feet. By 8 years is grew to 12 feet. What is the growth rate and how tall was it when it was planted!
The Growth rate is 3/4 ft/year
What is Growth rate ?
Growth rates are computed by dividing the difference between the ending and starting values for the period being analyzed and dividing that by the starting value. Formula is, Growth rate = Absolute change / Previous value.
growth rate = (12-9)/(8-4)
= 3/4 ft/year
Therefore, The Growth rate is 3/4 ft/year
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fastest answer gets brainlyest
Answer:
see my photo bro. hope it can help.
Answer:
[tex]\textsf{(a)} \quad \overline{v}=-8t-4h-2[/tex]
[tex]\textsf{(b)} \quad v(t)=-8t-2[/tex]
[tex]\textsf{(c)} \quad L(t)=-26t+41[/tex]
(d) See attachment.
Step-by-step explanation:
Given equation for displacement:
[tex]s(t)=-4t^2-2t+5[/tex]
Part (a)Average velocity formula:
[tex]\boxed{\overline{v}=\dfrac{s(t_2)-s(t_1)}{t_2-t_1}}[/tex]
where:
[tex]\overline{v}[/tex] = average velocitys(t₁) = position function at t₁s(t₂) = position function at t₂t₁ = initial timet₂ = final timeTo find the average velocity of s(t) between the inputs t and t+h:
[tex]\textsf{Let}\;t_1 = t[/tex][tex]\textsf{Let}\; t_2 = t+h[/tex]Find expressions for s(t) at t₁ and t₂:
[tex]\implies s(t_1)=s(t)=-4t^2-2t+5[/tex]
[tex]\begin{aligned}\implies s(t_2)=s(t+h)&=-4(t+h)^2-2(t+h)+5\\&=-4(t^2+2th+h^2)-2t-2h+5\\&=-4t^2-8th-4h^2-2t-2h+5\end{aligned}[/tex]
Substitute the found values into the average velocity formula:
[tex]\begin{aligned}\implies \overline{v} =\dfrac{s(t_2)-s(t_1)}{t_2-t_1}}&=\dfrac{(-4t^2-8th-4h^2-2t-2h+5)-(-4t^2-2t+5)}{(t+h)-t}}\\\\&=\dfrac{-4t^2-8th-4h^2-2t-2h+5+4t^2+2t-5}{t+h-t}\\\\&=\dfrac{-8th-4h^2-2h}{h}\\\\ &=-8t-4h-2\\\\ \end{aligned}[/tex]
Therefore, the average velocity between the inputs t and t+h is:
[tex]\boxed{\overline{v}=-8t-4h-2}[/tex]
Part (b)To find the equation for instantaneous velocity v(t), differentiate the equation for displacement:
[tex]\begin{aligned}\implies v(t)&=s'(t)\\&=2 \cdot -4t^{(2-1)}-1 \cdot 2t^{(1-1)}+0\\&=-8t-2\end{aligned}[/tex]
Part (c)Find the value of s when t = 3:
[tex]\begin{aligned}\implies s(3)&=-4(3)^2-2(3)+5\\&=-4(9)-6+5\\&=-36-6+5\\&=-42+5\\&=-37\end{aligned}[/tex]
To find the gradient of s(t) at t = 3, substitute t = 3 into the differentiated function:
[tex]\begin{aligned}\implies s'(3)=v(3)&=-8(3)-2\\&=-24-2\\&=-26\end{aligned}[/tex]
Substitute the found gradient and found point (3, -37) into the point-slope form of a linear equation to find the equation of the tangent line L(t):
[tex]\begin{aligned}\implies s-s_1&=m(t-t_1)\\s-(-37)&=-26(t-3)\\s+37&=-26t+78\\s&=-26t+41\\\implies L(t)&=-26t+41\end{aligned}[/tex]
Part (d)See attachment.
L C R
U (4, 14) (9, 6) (5, 3)
M (8, 2) (6, 12) (1, 7)
D (11, 5) (16, 3) (9, 8)
I am thinking the answer is 8, because it's bisecting, and I was told when a bisection is taking place in an angle, the sides are congruent, and by just the look of the eye, they look the same length. If I'm wrong, could I get a explanation on how to find the length?
BISECTRIZ: Divide the interior or exterior angle of each vertex into two congruent angles. Then we have that the angle that ES starts and that shares the 2 right triangles is the same:
As we can see, both triangles share the angle and the hypotenuse, that is, their height is also the same, so the height of PC is equal to 8
Hi! I am struggling on 41-44. Can you help me with 44?
Let:
The coordinates for the new figure will be given by:
[tex]Do,k(x,y)=(k(x-a)+a,k(y-b)+b)[/tex]Where:
O = Center of dilation at (a,b) = (3,2)
k = Scale factor = 0.1
So:
[tex](1,1)->(0.1(1-3)+3,0.1(1-2)+2)=(2.8,1.9)[/tex][tex]\begin{gathered} (1,2)->(0.1(1-3)+3,0.1(2-2)+2)=(2.8,2) \\ (2,1)->(0.1(2-3)+3,0.1(1-2)+2)=(2.9,1.9) \\ (2,2)->(0.1(2-3)+3,0.1(2-2)+2)=(2.9,2) \end{gathered}[/tex]Since:
(2.8,2), (2.8,1.9), (2.9, 1.9) and (2.9,2) are much closer to the center of dilation we can conclude that the dilated figure is closer to the center of dilation.
While studying abroad, Alan wants to make 6 batches of his mothers enchilada recipe to feed his classmates. The recipe calls for 20oz of cheese for each batch. The local market sells cheese by the gram. How many grams of cheese alan should by. USE 1 oz = 28 g AND DON'T ROUND ANY COMPUTATIONS.
The total cheese used by Alan to make 6 batches of recipe is 3360 g
What is an equation?An equation is an expression that is used to show the relationship between two or more numbers and variables.
1 oz = 28 g
The recipe calls for 20 oz. of cheese for each batch. Hence:
Total cheese in gram for each recipe = 20 oz. * 28 g per oz. = 560 g
There are 8 batches, hence:
Total cheese = 560 g * 6 batches = 3360 g
The total cheese is 3360 g
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I need help with homework I got the picture with the questions
We have the following:
[tex]\begin{gathered} \text{CAE}=135-45=90\degree \\ \text{EAF}=45-15=30\degree \\ \text{CAF}=\text{CAE}+\text{EAF}=90+30=120\degree \end{gathered}[/tex]8. Jen receives 8 dollars each week for allowance. She also had 35 dollars saved from birthday gifts. If she currently has 195 dollars, write an equation to represent how many weeks Jen has been saving money. a. 8w + 195 +35 b. 8 + 35 = 195w c. 8w + 35 = 195 d. 8w-35 = 195
the equation for the saved money is
195 = 8w + 35
here w = no. of weeks.
so the answer is 8w + 35 = 195
solve for x5x - 7 = 2x + 11
Answer:
Explanation:
Given the below equation;
[tex]5x-7=2x+11[/tex]To solve for x, the 1st step is to subtract 2x from both sides of the equation;
[tex]\begin{gathered} 5x-2x-7=2x-2x+11 \\ 5x-2x-7=11 \\ 3x-7=11 \end{gathered}[/tex]The 2nd step is to add 7 to both sides of the equation;
[tex]\begin{gathered} 3x-7+7=11+7 \\ 3x=18 \end{gathered}[/tex]The final step is to divide both sides of the equation by 3;
[tex]\begin{gathered} \frac{3x}{3}=\frac{18}{3} \\ x=6 \end{gathered}[/tex]Evaluate the following expressionsYour answer must be an exact angle in radians and in the interval Example: Enter pi/6 for lceil- pi 2 , pi 2 ] pi R
What subset of real numbers does 1/2 belongs to?
Answer:
It belongs to the sets of natural numbers, {1, 2, 3, 4, 5, …}.
It is a whole number because the set of whole numbers includes the natural numbers plus zero. It is an integer since it is both a natural and whole number.
Answer: rational numbers if thats an answer
Step-by-step explanation:
Becky a sales women is offered two salary plans. Plan 1 is 400 per week salary plus 2% commission sales. Plan 2 is a 300 per week salary plus a 18% commission of sales. How much would Becky need to make in sales for the salary to be the same from both plans?
Let the commission sales = X
Salary Plan 1
salary per week = $400
commission sales = 2%
[tex]\text{Commision sales = 2\%}\times X=\text{ \$0.02X}[/tex]Salary Plan 2
salary per week = $300
commission sales = 18%
[tex]\text{ Commission sales = 18\%}\times X=\text{ \$0.18X}[/tex]Becky's salary for both plans (inclusive of commission sales) would be:
Plan 1:
[tex]\text{ \$400+0.02X}[/tex]Plan 2:
[tex]\text{ \$300+0.18X}[/tex]In order to find how much Becky needs to make in sales for salary to be the same from both plans would be:
[tex]\begin{gathered} \text{ \$400+0.02X= \$300+0.18X} \\ \text{collect like terms} \\ 0.18X-0.02X=400-300 \\ 0.16X=100 \\ X=\frac{100}{0.16}=625 \end{gathered}[/tex]Therefore, the commission sales should be $625
The students in Cassie's class got to choose between pizza and burgers for the celebration on the last day of school. 8 students picked the pizza. If there are 10 students in all in Cassie's class, what percentage of the students picked the pizza? Write your answer using a percent sign (%).
Describe a series of transformations Matt can perform to device if the two windows are congruent
Combining the three different transformations—rotations, reflections, and translations—will result in congruent shapes. Actually, any pair of congruent shapes can be matched to one another using a combination of one or more of these three transformations.
Define transformations.There are four possible transformations of a point, line, or geometric figure, each of which changes the object's shape and/or location. Pre-Image denotes the shape of the object before transformation, while Image denotes the final position and shape of the object.
Given Data
We now know that during rigid transformations, the size and shape of the figures are maintained (reflections, translations, and rotations). The pre-image and the image are always in agreement.
Matt has the following transformational abilities:
Reflection (Flip)
A reflection keeps its original shape because the comparable points from the pre-image to the image stay at the same distance from the line of reflection.
Rotations as a Congruence Transformation
A figure twists when it rotates. The figurine looks to have fallen over, although being the same size and shape. A great illustration of a rotation in the actual world is a clock. The connecting arms of a clock rotate around its axis every hour or every day. A rotation is defined by its degree; common rotations include 90 degrees, 180 degrees, and 270 degrees. The figure completes a full 360-degree rotation before returning to its starting point. The direction of a rotation, whether it be in a clockwise or counterclockwise counterclockwise. This information can be used to calculate the degree, quantity, and direction of a revolution.
Translational congruence transformation
We refer to a movement as a translation when an object or shape is moved from one place to another without changing its size, shape, or orientation. Every point on an item or shape is moved by the same amount and in the same direction during a translation, sometimes referred to as a slide.
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