what is standard form of quadratic equation
Answer:
y = ax
[tex]y = {ax}^{2} + bx + c[/tex]
AI's Auto Shop charges $149 for parts and $53 per hour of labor for a repair job. Edna's Engine Repair charges a flat fee of $280 for the same job.
a. Write a system of equations to represent the situation.
b. Graph the system of equations.
c. Which shop is cheaper if the job takes 2 hours? 3 hours?
Answer:
AI's Auto Shop: y = 149 + 53x
Edna's Engine Repair: y = 280
Explanation:
The system of equations represent the costs of the two different repair shops. The first equation, y = 149 + 53x, represents the total cost of AI's Auto Shop. The variable x represents the number of hours of labor required, and the variable y represents the total cost. The second equation, y = 280, represents the flat fee charged by Edna's Engine Repair.
The graph of the system of equations would show two lines, one for each equation. The line for AI's Auto Shop would have a slope of 53 and a y-intercept of 149, representing the cost of parts and hourly labor. The line for Edna's Engine Repair would be a horizontal line at y = 280, representing the flat fee charged.
When the job takes 2 hours, AI's Auto Shop would charge $149 + $53*2 = $255 and Edna's Engine Repair would charge $280. So, AI's Auto Shop would be cheaper.
For a job that takes 3 hours, AI's Auto Shop would charge $149 + $53*3 = $308 and Edna's Engine Repair would charge $280. So, AI's Auto Shop would be more expensive.
Question 7 of 25
f(x)=√x-4. Find the inverse of f(x) and its domain.
O A. f¹(x) = x² + 4; x≥0
OB. f¹(x) = (x+4)²; x≥-4
O c. f¹(x) = x² + 4; x ≥-4
O D. f¹(x) = (x+4)²; x≥0
The inverse of the function f(x) and its domain include the following: D. f⁻¹(x) = (x + 4)²; x ≥ 0.
What is an inverse function?In Mathematics, an inverse function simply refers to any type of function that is typically generated by reversing the mathematical operation in a given function (f(x)).
In order to determine the inverse of any function, you should swap both the input value (x-value) and output value (y-value) as follows;
f(x) = √x - 4
y = √x - 4
x = √y - 4
√y = x + 4
Taking the square of both sides of this inverse function, we have:
f⁻¹(x) = (x + 4)²
For the domain of this function, we have:
f(x) = √x - 4
When x= 0, we have:
f(0) = √0 - 4
f(0) = 0.
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What is the volume of a box shape of a right rectangular prism with height 10 inches, length 7 inches, and width 4 inches?
The volume of a box shape of a right rectangular prism with height 10 inches, length 7 inches, and width 4 inches would be 280 cubic inches.
What is Volume?
Volume can be defined as the amount of space occupied by any three-dimensional solid. These solids can be anything from a cube to a cuboid, a cone, a cylinder or a sphere.
It is also the measure of the capacity that an object holds.
Volume = h x l x w
where
h = 10 inches
l = 7 inches
w = 4 inches
Volume = 10 x 7 x 4
Volume = 280 cubic meters
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Term 4
1/7
Gustavo is driving a bus along a motorway with a
speed limit of 70 miles per hour. In 30 minutes, he
travels 36 miles. Is his average speed during this
period exceeding the speed limit? And what is his average speed
Yes, his average speed during this time exceeded the posted speed limit; it was 35 miles per hour.
what is equation ?Take a look at the formula 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the word "equal." The standard form, the point-slope form, and the slope-intercept form are the three primary kinds of linear equations. Algebra is used in many equations. When it comes to arithmetic, algebra is used when it's difficult to compute an exact amount.
given
His average speed throughout this time was 35 miles per 30 minutes (average speed = 70 / 2 = 35 miles per 30 minutes),
which is over the speed limit because he traveled 36 miles during that time.
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Let’s begin with a 30°-60°-90° triangle. A 30°-60°-90° triangle with a hypotenuse of 2 units is shown.
If another right triangle contains a 30° or a 60° angle but is a different size, what can you say about the side lengths of that triangle in terms of the given triangle? Explain your answer.
The side lengths of the new right triangle can be determined by the ratio of the given triangle.
What is triangle?A triangle is a three-sided polygon with three straight sides that are connected at three corners. It is one of the most basic shapes in geometry and is found in many areas of mathematics. Triangles can be classified according to their angles, sides, and size. They can be equilateral, isosceles, or scalene, depending on the size of their angles and sides. Triangles are used in a variety of fields, including architecture, engineering, construction, art, and design.
The side opposite the 30° angle will always be half the length of the hypotenuse, while the side opposite the 60° angle will always be equal to the square root of three times the length of the side opposite the 30° angle. This means that if the hypotenuse of the given triangle is 2, then the side opposite the 30° angle will be 1 and the side opposite the 60° angle will be √3.
Therefore, for any other right triangle containing a 30° or a 60° angle, the side length can be found by multiplying the side length of the given triangle by the same ratio. For example, if the hypotenuse of the new triangle is 6, then the side opposite the 30° angle will be 3 and the side opposite the 60° angle will be 3√3.
In conclusion, for any right triangle containing a 30° or a 60° angle, the side lengths can be determined by multiplying the side lengths of the given triangle by the same ratio.
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PLEASE HELP 100 POINTS
A line has a slope of 5/3 and passes through the point (4,6). Write its equation in slope-intercept form.
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer:
y = [tex]\frac{5}{3}[/tex] x - [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given m = [tex]\frac{5}{3}[/tex] , then
y = [tex]\frac{5}{3}[/tex] x + c ← is the partial equation
to find c substitute (4, 6 ) into the partial equation
6 = [tex]\frac{5}{3}[/tex] (4 ) + c = [tex]\frac{20}{3}[/tex] + c ( subtract [tex]\frac{20}{3}[/tex] from both sides )
[tex]\frac{18}{3}[/tex] - [tex]\frac{20}{3}[/tex] = c , so
c = - [tex]\frac{2}{3}[/tex]
y = [tex]\frac{5}{3}[/tex] x - [tex]\frac{2}{3}[/tex] ← equation of line
given segment CE and point D that lies on CE, find CD =27, CD=76-7x, and ED=39-4x
Answer:
use c and d
Step-by-step explanation:
which function below has a great rate of change
None of the functions listed have a great rate of change.
What is rate of change?Rate of change is a major of house quickly one quantity change in relation to another it is parisu of the changing 122 the changing another quantity over specified time period it is commonly used mathematics physics economic and other discipline to make operate of vijay process is a caring rate of changing also known as velocity, derivative or slope.
Function (a) is a linear equation, and its rate of change is constant. Function (b) is a linear equation, and its rate of change is also constant. Function (c) is a set of coordinates, so it does not have a rate of change.
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Which graph shows a linear equation?
The correct option is A.
The linear equation y = 2x + 1 is shown in Graph A.
The equation of a straight line's shape with slope and y-intercept is as follows:
y = mx + b
where
y is equal to a point's y-coordinate on a line.
m is the line's slope.
The point on the line whose y-coordinate is y has the x-coordinate of x.
B is the line's y-intercept, or b.
As opposed to y = mx + b, y = 2x + 1
As we can see, the
m = 2 slope
b = 1 as the y-intercept
The graph that crosses the y-axis at the point where y = 1 is only option A, as shown by the intercept value.
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Note the correct question would be as bellow,
Which graph shows the linear equation y = 2x + 1
A pet aardvark that regularly sells for $125.70 is on sale for 30% off. Find the sale price of the aardvark someone please tell me i only got 10 mins for this
Answer: $87.99
Step-by-step explanation: ($125.70) x (1 - 0.30)
= $87.99
Answer: $87.99
Step-by-step explanation:
Use Is/Of=%/100
Step 1: Plug in Points
Aardvark=$125.70 is on sale for 30% off
is/125.70=30/100 ---> 125.70(30)/100=$37.71
Step 2: Subtract Discount to Original Price
125.70-37.71=$87.99
Which of the following tables represent a proportional relationship?
Answer: The answers are A and B because when you divide all the numbers you get 6. It is not C and D because when you get different quotients.
Step-by-step explanation:
A. 6/1=6
12/2=6
18/3=6
24/6=6
36/6=6
———————————————————————————————————————
B.14/-4=-3.5
7/-2=-3.5
-14/4=-3.5
-21/6=-3.5
What is the value of x? round to the nearest tenth, if necessary. Responses x = 4 x, = 4 x = 5 x, = 5 x = 6. 2 x, = 6. 2 x = 9. 4.
The value of x is 6.2 units.
Now by using the Pythagorean theorem
Hypotenuse² = Perpendicular² + Base²
Now in the Δ ABD
As given DB² = DA² + AB²
As given
DB = 13 units
AB = 9 units
Putting values in the above
13² = 9²+ DA²
169 - 81 = DA²
88 = DA²
DA=√88
In ΔABC
AB² = AC² + CB²
(As given AB = 9 units , CB = x)
9² = AC² + x²
AC ² = 81 - x²
Now in ΔADC.
AD² = AC² + DC ²
As AC ² = 81 - x²
DC = 13 - x
AD=√88
(√88)²=81-x²+(13-x)²
(By using the formula (a + b)² = a² + b² + 2ab )
88=81-x²+13²-2*13*x+x²
88=81-x²+13²-26x+x²
88-81 - 169 = -26x
88-250 =-26x
-162 = - 26x
x=162/26
x = 6.2 (Approx)
Therefore the value of x is 6.2 units.
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I Bet you can't answer
"5(2x+4)-3(-6-x)"
answer this with full formula
also expand simplify them
Answer:
13x+38
Step-by-step explanation:
someone help
f(-3x)
-3f(x)
f(3x)
3f(x)
Answer:
Step-by-step explanation:
f(-3x) = -3f(x)
f(3x) = 3f(x)
This is assuming that f is an existing function and it follows this rule for any input. If not, it will not necessarily be true for all inputs.
Is 0 and 3 a function?
Answer:
Yes it is!
Step-by-step explanation:
Hope it helps!
Answer: If I'm correct it's 3
Step-by-step explanation:
0 + 3 = 3
What is the third quartile of this data set?
14, 18, 20, 21, 25, 32, 40, 44, 48
Answer: 42
Step-by-step explanation:
Math
Yoo can someone help me please and show the work
A triangle is a polygon with three sides and three vertices. The triangle's interior angle, which is 180 degrees, is formed.
What is a triangle definition?Three sides and three vertices make up a triangle, which is a polygon. There is a 180 degree angle created inside the triangle. In other words, a triangle's internal angles add up to 180 degrees.
A closed triangle has 3 sides, 3 angles, and 3 vertices. It is a 2-dimensional shape. Polygons include triangles as well. ABC is a triangle that is depicted in the previous illustration.
An "opposite" side in a right triangle is the one that is across from a specific angle, while a "adjacent" side is the one that is next to a specific angle. The hypotenuse is the longest side in a right triangle.
Therefore, the answer is:
Side LN = 4.33013 = 5√3/2
Side MN = 5
Side c = 2.5
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3. A skydiver started his jump from the airplane. He fell 4.9 m in the 1st second, 14.7 m
in the 2nd second, 24,5 m in the 3rd second. How far did he fall between the 7th and the
10th seconds?
Arithmetic or geometric
The distance between the 7th seconds and the 10th seconds is 29.4 m.
It is arithmetic.
How to determine how far did he fall between the 7th and the 10th seconds?An arithmetic progression (AP) is a sequence of numbers in which the difference between any two consecutive terms is always the same, called the common difference.
Since the height in the 1st second, 2nd second and 3rd second are 4.9m, 14.7 and 24.5 respectively.
They have a common difference (d) of 9.8. That is:
d = 14.7 - 4.9 = 9.8
Thus, it is arithmetic
The formula for determining nth of an AP is given by:
nth = a + (n-1)d
where a is the first term, d is the common difference and n is the number of terms
7th seconds:
nth = a + (n-1)d
nth = 4.9 + (7-1)9.8 = 63.7 m
10th seconds:
nth = a + (n-1)d
nth = 4.9 + (10-1)9.8 = 93.1 m
distance between the 7th and the 10th seconds:
10th seconds - 7th seconds = 93.1 - 63.7 = 29.4 m
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5x^3 + 8x^2 +2x^1 + 7 if x = 10
Answer:
5,827
Step-by-step explanation:
substitute x = 10 into the expression
5(10)³ + 8(10)² + 2(10) + 7
= 5(1000) + 8(100) + 20 + 7
= 5000 + 800 + 27
= 5,827
Solve the following...
[tex]\sf 2+x =-9[/tex]
Answer:
x is equal to -11Step-by-step explanation:
Since adding a negative to a positive is inverse subtracting, use this as an advantage and act as if you're subtracting to get the result, or output value, -9.
Hope this helps! :)
Answer:
[tex] \sf \: x = - 11[/tex]
Step-by-step explanation:
Now we have to,
→ find the required value of x.
The equation is,
→ 2 + x = -9
Then the value of x will be,
→ 2 + x = -9
→ x + 2 = -9
→ x = -9 - 2
→ [ x = -11 ]
Hence, the value of x is -11.
Briana estimates the length of a living room to be 24 feet. Ariane estimates it to be 9 yards. If the actual length is 26 feet, which is the better estimate explain
Answer:
9 yards is a better estimate.
Step-by-step explanation:
This is because it is closer to the actual answer. 9 yards is only 1 foot off while the other is 2.
What is midpoint formula Class 9?
In class 9, the midpoint formula is a mathematical formula used to find the midpoint of a line segment given the coordinates of its two endpoints. The midpoint formula is:
(x, y) = ( (x1 + x2) / 2, (y1 + y2) / 2)
Where (x1, y1) and (x2, y2) are the coordinates of the two endpoints of the line segment, and (x, y) are the coordinates of the midpoint.
For example, if the coordinates of the two endpoints of a line segment are (3, 4) and (7, 10), you can use the midpoint formula to find the coordinates of the midpoint:
(x, y) = ( (3 + 7) / 2, (4 + 10) / 2)
(x, y) = (5, 7)
So the midpoint of the line segment with endpoints (3, 4) and (7, 10) is (5, 7)
The midpoint formula is used in class 9 to find the midpoint of a line segment in coordinate geometry. It's a simple way to find the point which is exactly in the middle of two given points. It can be used to find the center of a circle if we know the coordinates of two points on the circumference.
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π
A sector with a central angle measure of
(in radians) has a radius of 12 cm.
6
||
π
6
What is the area of the sector?
r = 12 cm
Therefore , the solution to the given problem of surface area is the sector's area is 12 square centimeters.
What is surface area ?Surface is a unit used to describe how much overall space a object's surface occupies. A three-dimensional shape's surface area is equal to the sum of its surroundings. The overall surface region of a tri shape is referred to as surface area. The surface area of a cube with six square faces can be calculated by adding up each face's specific area. As an alternative, you can identify the box's measurements using the formula below: Surface (SA) is equal to two times two times two. The total amount of space that a three-dimensional shape takes up is used to determine its surface area.
Here,
The parameters in this case are:
Radius, r = 12 Angle, x = /6
The sector's geographic area is
A = (1/2) × r^2x
We thus have:
A = (1/2) × 12^2 * π/6
Evaluate
A = 12π
Therefore , the solution to the given problem of surface area is the sector's area is 12 square centimeters.
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Consequently, the sector's area is 12 square centimeters in which the parameters are Radius, r = 12 Angle, x =π /6 .
what is circle ?A circle is created when every place in the line that is a specific distance apart from another point does so (center). As a result, it is a curve made up of points that are spaced apart from one another in the plane. It is rotationally symmetric the about center at all angles. Every pair of endpoints in the plane that make up a circle are uniformly distributed out from the "center" and form a closed, two-dimensional object. A specular symmetries line is produced by a line that passes through the circle. It is rotationally equal about the center at all angles.
given
The parameters are as follows:
Radius, r = 12 Angle, x =π /6
The sector's geographic area is
A = (1/2) × r^2x
We thus have:
A = (1/2) × 12^2 * π/6
Evaluate
A = 12π
Consequently, the sector's area is 12 square centimeters in which the parameters are Radius, r = 12 Angle, x =π /6 .
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Nine times the sum of a number and 8 is equal to 4
The answer is 9x+8=4
What is the solution to a linear equation?The solution of a linear equation is defined as the points, in which the lines represent the intersection of two linear equations. In other words, the solution set of the system of linear equations is the set of all possible values to the variables that satisfies the given linear equation.
Given here: Nine times the sum of a number and 8 is equal to 4
let the number be x then we have as per question
9x+8=4
x=-4/9
Hence, The required equation is 9x+8=4
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I need the sender to 2x4 x x3
Answer: two times four times three ( or if you meant 3x) then three x
Step-by-step explanation:
Evaluate (-6)^8/(-6)^5.
Answer:
[tex] \sf \: {( - 6)}^{3} = - 216[/tex]
Step-by-step explanation:
Given problem,
→ (-6)⁸/(-6)⁵
Let's evaluate the problem,
→ (-6)⁸/(-6)⁵
→ 1679616/-7776
→ (1679616) ÷ (-7776)
→ -216
→ (-6)³
Hence, the answer is (-6)³.
You can complete 40 push-ups in 2 minutes. Your friend can complete 57 push-ups in 3 minutes. Do these rates form a proportion? Explain by finding the unit rates.
_____ (yes or no), the rates _____(are or are not) equivalent. I can complete _____ push-ups per minute and my friend can complete _____ push-ups per minute.
Response:
---------------------------------------------
----------------------------------------------
----------------------------------------------
----------------------------------------------
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
1.2=6
6=40
A 1. 50-kilogram ball is attached to the end of a 0. 520-meter string and swung in a circle. The velocity of the ball is 9. 78 m/s. What is the tension in the string? do not round your answer during any of your calculations until the end and then round to the nearest whole number. 3. 39 n 28. 2 n 276 n 74. 6 n.
The the tension in the string is 276 N. Thus, the correct answer is B.
The tension in the string provides the centripetal force needed to keep the ball moving in a circular motion. As the tension in the string increases, the centripetal force increases as well, and the ball will move in a smaller circle (the radius will decrease). Therefore, if the tension increases, the radius decreases and the velocity increases, and if the tension decreases, the radius increases and the velocity decreases.
To determine the tension in the string, we can use the equation:
Tension = m * v^2 / rWhere m is the mass of the ball, v is the velocity of the ball, and r is the radius of the circle.
In this problem:
m = 1.50 kgv = 9.78 m/sr = 0.520 mSo, tension:
= (1.50 kg) * (9.78 m/s)^2 / (0.520 m) = (1.50 kg) * 96.0864 m^2/s^2 / (0.520 m)= 276 NThe tension in the string is 276 N. Hence, the correct answer is B.
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What is 50% dilated?
Dilation is a process of changing the size of an object or shape by decreasing or increasing its dimensions by some scaling factors.
What is Dilation ?Dilation is a transformation, which is used to resize the object. Dilation is used to make the objects larger or smaller. This transformation produces an image that is the same as the original shape. But there is a difference in the size of the shape. A dilation should either stretch or shrink the original shape. This transformation is expressed by the term “scale factor.The basic formula to find the scale factor of a dilated figure is: Scale factor = Dimension of the new shape ÷ Dimension of the original shape.A dilation (similarity transformation) is a transformation that changes the size of a figure. It requires a center point and a scale factor , k . The value of k determines whether the dilation is an enlargement or a reduction. If |k|>1 , the dilation is an enlargement. If |k|<1 , the dilation is a reduction.To learn more about Dilation refers to:
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Dilation is the practice of altering an object's or shape's size by either enlarging or decreasing its dimensions by a certain amount.
Dilation: What is it?A transform called dilation is used to alter an object's size. Dilation is a technique for enlarging or contracting objects.
The result of this transformation is an image that has the same shape as the original. A stretched figure can be enlarged by using given formula:
Scale is equal to the difference between the original and new shapes' sizes.
Stretch transformations (similarity transformations) enlarge or shrink shapes. You require a scale factor of k and a central point. Depending on the value of k, the expansion either grows or shrinks. Elongation is elongation for |k| > 1. If 1 is stretched, for |k|.
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