Answer:
d. y= 5x+18
Step-by-step explanation:
y=mx+b is slope intercept form
Now we plug in the information given to us which is slope(m) is 5 and a point (x,y) which is (2,28).
So by substituting we get 28=5(2)+b
simplify to 28=10+b and when we subtract 10 from both sides to isolate 'b', we get that b = 18.
So now we use the values of slope(m) and the y-intercept(b) to write the equation:
y=5x+18
Hey there! I'm happy to help!
Slope-intercept form is a way to write the equation of a line, and it is very useful. It is y=mx+b. This equation shows how y is related to x on a line. The m represents the slope, which is the incline of the line. The b represents the y-intercept, or where the line hits the y-axis.
If you find any value for x and plug it into the equation, you will figure out what y-value it matches on the line. If you had the equation you could draw the line by plugging in x-values and plotting points and connecting the dots!
Anyways, we have a slope of 5. This means that so far our equation looks like y=5x+b. It does not tell us what the y-intercept is, so we need to figure it out!
If we have the values for m, x, and b, we can solve for y. Well, we don't have b, but we do have values for y, x, and m, so we should be able to solve for b!
We will plug in our point (2,28) and solve for b!
28=5(2)+b
28=10+b
b=18
Our y-intercept is 18.
So, we can write this equation in slope-intercept form for the line that follows the condition of slope 5 and passing through (2,28) below.
y=5x+18
Therefore, our answer is d. 5x+18.
Now you can find the equation of a line given the slope and a point! Have a wonderful day! :D
A company is building a new park in the shape of a circle with a 25 ft diameter. Portions of the new park will be covered with grass. A diagram of the park is given below, with the shaded region representing the areas that will be covered in grass. Use 3.14 for. Note: image is not drawn to scale. The area of the regions covered by grass is approximately sq ft.
Answer: The area of the regions covered by grass is approximately 313.375 sq ft.
Step-by-step explanation:
Given: A company is building a new park in the shape of a circle with a 25 ft diameter.
Then radius = [tex]\dfrac{25}{2}=12.5\ ft[/tex]
Required area = Area of circle - Area of rectangle + Area of triangle
Formula: Area of circle = [tex]\pi r^2[/tex]
Area of rectangle = length x width
Area of triangle = 0.5 x base x height
Area of circle = [tex](3.14)(12.5)^2=490.625\ \text{ft}^2[/tex]
Area of rectangle = 20 ft x 10ft = 200 ft²
Area of triangle = 0.5 x 7 x 6.5 = 22.75 ft²
Required area = 490.625 -200+22.75 = 313.375 ft²
Hence, The area of the regions covered by grass is approximately 313.375 sq ft.
What is the measure of ACE in the diagram below?
A. 46
B. 104
C. 29
D. 58
Answer:
C
Step-by-step explanation:
The secant- secant angle ACE is half the difference of the measures of the intercepted arcs, that is
∠ ACE = [tex]\frac{1}{2}[/tex] (AE - BD ) = [tex]\frac{1}{2}[/tex] (104 - 46)° = [tex]\frac{1}{2}[/tex] × 58° = 29° → C
Akira receives a prize at a science fair for having the most informative project. Her trophy is in the shape of a
square pyramid and is covered in shiny gold foil.
3 in
How much gold foil did it take to cover the trophy, including the bottom?
inches
Answer:
45 square inches
Step-by-step explanation:
Akira receives the prize at the science fair for having the most informative project her trophy is in the shape of a square pyramid and is covered in shiny gold foil how much gold foil did it take to cover the trophy including the bottom
Total surface = surface area of the base square + area of 4 triangles
Calculate the surface area of the base square
surface area of the square = s^2
where s= side length
s=3 in
The surface area of the base =s^2
=3^2
= 9 square inches
The surface area of the side triangles
The area of the triangle = (1/2)* side length* slant height
Side length=3 in
Slant height=6 in
substituting the values,
The area of the triangle =1/2*3*6
= 18/2
= 9 square inches
There are 4 triangles
The area of 4 triangles = 4 x 9
= 36 square inches
Therefore,
Total surface = surface area of the base square + area of 4 triangles
= 9 + 36
= 45 square inches
Answer:
IT'S 216 TRUST ME!
Step-by-step explanation:
PLZ I WILL GIVE BRAINLIEST AND IT HAS 20 POINTS The volume of a cylinder is approximately 72 feet cubed. Which is the best approximation of the volume of a cone with the same base and height as the cylinder? 24 feet cubed 216 feet cubed 24 pi feet cubed 216 pi feet cubed
Answer:
24 feet cubed
Step-by-step explanation:
When comparing the volume formula for a cone and the volume formula for a cylinder, a cone is 1/3 of a cylinder. Therefore, divide 72 by 3 to get the volume of a cone with the same base and height. It would not be 24 pi feet cubed because 72 feet cubed is already multiplied by the pi.
Answer:
24 feet cubed
Step-by-step explanation:
Volume formula:
V cylinder = BhV cone = 1/3BhThe ratio:
V cylinder / V cone = Bh ÷ 1/3BhV cylinder / V cone = 3 ÷ 1Plugging in the value of cylinder to find the value of cone:
72 ÷ x = 3 ÷ 1x= 72 ÷ 3x= 24 ft³24 feet cubed is the best estimate
Compare 6 ⋅ 108 to 3 ⋅ 106.
Answer:
6*108>3*106
Step-by-step explanation:
If you multiply 6, and 108, you would get 648.
And if you were to multiply 3 and 106 you would get 318. And 648>318.
Therefore, 6*108>3*106
In its first year of operations, Roma Company reports the following. Earned revenues of $53,000 ($45,000 cash received from customers). Incurred expenses of $29,500 ($23,050 cash paid toward them). Prepaid $8,750 cash for costs that will not be expensed until next year.
Complete question :
In its first year of operations, Roma Company reports the following. Earned revenues of $53,000 ($45,000 cash received from customers). Incurred expenses of $29,500 ($23,050 cash paid toward them). Prepaid $8,750 cash for costs that will not be expensed until next year. calculate the first year's net income under both the cash basis and the accrual basis of accounting.
Answer:
Kindly check explanation
Step-by-step explanation:
Given the following :
Earned revenue = $53,000
Cash received from customers = $45000
Incurred expenses = $29,500
Cash paid towards incurred expenses = $23,050
Cash which will not be expensed till next year = $8,750
Cash Accounting:
Cash received $45,000
Expenses ($23,050 + $8750) = $31,800
Net Income $(45,000 - 31,800) = $13,200
Accrual Accounting :
Revenue earned $53,000
Expenses incurred $29,500
Net income $(53,000 - 29,500) = $23500
Leah wants to carpet a room that is 12 feet wide and 15 feet long. Carpeting is sold by the square yard. Find the length and width of the room in yards. Then find the number of square yards needed to carpet the room.
Answer:
length: 5 yd
width: 4 yd
area: 20 yd^2
Step-by-step explanation:
1 yd = 3 ft
15 ft * (1 yd)/(3 ft) = 5 yd
12 ft * (1 yd)/(3 ft) = 4 yd
A = LW
A = 5 yd * 4 yd = 20 yd^2
Answer:
20 yd²
Step-by-step explanation:
1 yd = 3 ft =>
=>w = 12ft×yd/3ft = 4 yd
=> l = 15ft×yd/3ft = 5 yd
A = l × w
= 5yd × 4yd
= 20 yd²
PLEASE HELP Draw the reflection of the figure over the line shown.
The answer is in the picture
*PLEASE ANSWER* If we decrease a dimension on a figure, how is the figure’s area affected? a.) The area decreases. b.) The area becomes 0. c.) The area increases. d.) The area remains the same.
Example: we have a 2 by 3 rectangle with area of 2*3 = 6. If we cut the first dimension in half, then we have a 1 by 3 rectangle that has area 1*3 = 3. The area has decreased. To keep the area the same, we would have to increase the other dimension some specific amount.
The area of the figure decreases when the dimension is decreased
What is the Area of a Rectangle?The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle
Area of Rectangle = Length x Width
Given data ,
Let the figure be represented as ABCD
where ABCD is a rectangle
Now , the measures of the sides of the rectangle be
The length of the rectangle = L
The width of the rectangle = W
And , Area of Rectangle = Length x Width
On simplifying , we get
Area of rectangle = LW
when the dimension of one of the unit is decreased , we get
when L = L/2
Area of rectangle = ( LW) / 2
So , the area of the figure is decreased bu ( 1/2 )
Hence , the area of the figure decreases
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Given: F(x) = 2x - 4; GX) = 3x + 2; Hpx)=x2
Find FG H(2)
0 121
27
071
Answer:
FG H(2) = F*G*H(2) = 0
Step-by-step explanation:
Your F(x) = 2x - 4; GX) = 3x + 2; Hpx)=x2 requires a bit of guesswork for the reader to understand it. I believe you meant:
F(x) = 2x - 4; G(X) = 3x + 2; H(x)=x2 Find FG H(2)
First find F(2): f(2) = 2(2) - 4 = 0
Because this multiplicand is zero, further multiplication will result in zero also. Thus, the final answer is zero (0).
two fifths of a number equals 564. what is the number
Answer:
1410
Step by step explanation:
2/5x=564
5/2*2/5x=564*5/2
x=1410
Proof: 2/5*1410=564
Hope it helps <3
Answer:
1410
Step-by-step explanation:
The questions no l and p.
please help me as soon as possible!!!!!
Answer:
l = 2cosΘ p = see attachment
Step-by-step explanation:
√2+√2+2cos 4Θ
√2+√2(1 + cos 4Θ)
√2 + √2(2 cos² 2Θ)
√2 + √4 cos² 2Θ cos 2Θ = 2 cos²Θ - 1
√2 + 2cos 2Θ
√2(1 + cos 2Θ)
√4cos²Θ
2cosΘ
Answer:
Step-by-step explanation:
I'm only going to do the first one, because the tangent problem is going to give us both night mares.
Start with cos(4*theta), There are various places on the internet which solves this, so I won't bother. Basically it comes down to using cos(2*theta).
cos(4theta) = 8*cos^4(theta) - 8*cos^2 (theta) + 1
2*cos(4*theta) = 16*cos^4(theta) - 16cos^2(theta) + 2
2 + 2cos(4*theta) = 16cos^4(theta) - 16cos^2(theta) + 4
(2 + 2cos(4*theta) = (4 cos^2(theta) - 2 )^2
sqrt(2 + 2cos(4theta) = 4cos^2(theta) - 2
=====================================
sqrt(2 + 4cos^2(theta) -2 ) = sqrt( 4 cos^2(theta) = 2 cos(theta) = RHS
Image attached: some sort of triangle stuff
Answer:
C
Step-by-step explanation:
On edg 2020
Rewrite the formula to determine the number of tickets they need to sell
Answer:
n = [tex]\frac{p}{(d-c)}[/tex]
Step-by-step explanation:
The goal is to solve for n meaning n needs to be by itself. In the current formula, n is multiplied by (d-c). Get n by itself by dividing both sides by (d-c).
Based on the function F(x) = x^4 - 3x^3+ x^2 +2 and the graph of G(X) below,
which of the following statements is true?
Answer:
Option A
Step-by-step explanation:
According to the graph it never crosses the x axis meaning that it has 0 roots beecasue roots is another word for x-values.
what's four to the six power times four to the seventh power
Answer:
67,108,864 or 4^13
Step-by-step explanation:
4^6*4^7=4^13 you basically just add the exponents since the base is the same.
Since these two powers have the same base of 4, you can multiply
them together by simply adding their exponents to get 4¹³.
This idea is called the product rule.
A common mistake in this problem would be to multiply
the bases together and give an answer of 16¹³.
It's important to understand however that the 4's in this problem can't
be multiplied together because they're not coefficients, they're bases.
When applying your exponent rules, your base will never change.
Harrison ordered 6 cases of pickles for his restaurants. Each case contained p jars of pickles. Harrison delivered an equal number of jars to each of his 7 restaurants. Which expression represents the number of jars of pickles that each restaurant received? A. 6p-7 B. [tex]\frac{6p}{7}[/tex] C. 6p+7 D. 7(6+p) E. [tex]\frac{6}{7p}[/tex]
Answer:
B. 6p/7
Step-by-step explanation:
6p = the total amount of pickles
The problem says that he distributes them evenly to 7 restaurants, so that's dividing.
So your answer is 6p/7
Answer: b 6p/7
Step-by-step explanation: 6p = the total amount of pickles. The problem says that he distributes them evenly to 7 restaurants, so that's dividing. So your answer is 6p/7.
The linear combination method gives a solution of (–4, 2) for which of these systems of linear equations?
Answer:
[tex]3x + 13y = 14[/tex]
[tex]6x + 11y = -2[/tex]
Step-by-step explanation:
See Attachment for complete question
To determine which of the options has (-4,2) as its solution; we have to test each linear combination until we arrive at an answer;
Given that
[tex](x,y) = (-4,2)[/tex]
Testing Option A
[tex]3x + 13y = 14[/tex]
[tex]6x + 11y = -2[/tex]
Substitute [tex]x = -4[/tex] and [tex]y = 2[/tex] in [tex]3x + 13y = 14[/tex]
[tex]3(-4) + 13(2) = 14[/tex]
Open Brackets
[tex]-12 + 26 = 14[/tex]
[tex]14 = 14[/tex]
Substitute [tex]x = -4[/tex] and [tex]y = 2[/tex] in [tex]6x + 11y = -2[/tex]
[tex]6(-4) + 11(2) = -2[/tex]
Open Brackets
[tex]-24 + 22 = 2[/tex]
[tex]2 = 2[/tex]
In both cases, the expression on the right hand side equates to that on the left hand side;
Hence, there's no need to check for other options.
What properties must a quadrilateral possess in order for the quadrilateral to be classified as a.. trapezoid isosceles trapezoid
Answer:
Step-by-step explanation:
The typical isosceles trapezoid will have a uniform width, measured vertically, but two ends that are not square (not perpendicular to the x-axis. The two sloping ends are congruent (their slopes have exactly the same slope.
The same could be said of an isosceles trapezoid that is vertical; the sloping ends have the same slope.
Answer:
2 parallel sides
2 non-parallel, congruent sides
Step-by-step explanation:
As any other quadrilateral, an isosceles trapezoid has 4 sides. 2 sides must be parallel. The other two sides cannot be parallel but must be congruent.
13. If 16 people are needed to run 7 machines, how many people are needed to run 35 machines?
Answer:
80
Step-by-step explanation:
16 people =7
7*5= 16*5
35=80 people
Answer:
80 people are required to run 35 machines
Step-by-step explanation:
Write and solve an equation of ratios:
p 35
------- = -----
16 7
where p is the number of people needed to run 35 machines.
Cross-multiplying yields 7p = 16(35), or p = 16(5), or p = 80
80 people are required to run 35 machines.
Jeremy is taking a photography class, but he doesn't own a camera. The class organizers will rent him a camera for $6 per day. Jeremy can spend up to $50 for the class, but he has to pay $15 to register for the class as well as rent the camera. The number of days, d, that Jeremy can rent the camera is represented by the inequality 6d + 15 < 50. Select the number of days Jeremy can rent the camera with the money he has. A. 5 B. 6 C. 8 D. 9 E. 10
Answer:
A. 5
Step-by-step explanation:
6d+15<50
subtract 15 from both sides
6d<50-15
6d<35
divide both sides by 6
d<35/6
d<5 5/6
So he can only rent it for 5 days. If he rented for 6, it would be $51, which is too much.
Solving the given inequality for d, we get...
6d + 15 < 50
6d + 15-15 < 50-15 <<-- subtract 15 from both sides
6d < 35
6d/6 < 35/6 <<--- divide both sides by 6
d < 5.83
Which means that d can be any of the values in this set: {0, 1, 2, 3, 4, 5}
The smallest d can be is 0. In this scenario, Jeremy pays the $15 registration but doesn't rent the camera at all
The largest d can be is 5. In this scenario, Jeremy rents the camera for 5 days
Any larger value of d is not allowed as it would make the total cost go over $50
Notice how I'm rounding down regardless how close 5.83 is to 6
Please help
simplify the expression
a²b⁴-b²a⁴/ab(a+b)
Answer:
ab² - a²b
Step-by-step explanation:
a²b⁴ - b²a⁴ can be factored as a²b²(b² - a²) which becomes a²b²(b + a)(b - a). Since the numerator and denominator both have (a + b) and ab the final answer is ab(b - a) = ab² - a²b.
What is the value of x to the nearest tenth? The figure is not drawn to scale.
5.4
6.3
11.2
x
Answers:
A. x=2.1
B. x=3.4
C. x=9.6
D. x=13.1
Answer:
we need picture
Step-by-step explanation:
probaby d tho
Find the angle between the given vectors to the nearest tenth of a
degree.
U = 13i - 8j V = 2i + 9j
Answer: 109.1 degrees
Step-by-step explanation:
To find the angle between the given vectors, we will use the formula below:
Cos(θ) = (U.V)/ |U|.|V|
Where
U = 13i - 8j
V = 2i + 9j
U.V = (2x13) + (-8×9)
U.V = 26 - 72
U.V = - 46
|U| = sqrt ( 13^2 + 8^2)
= sqrt ( 233) = 15.264
|V| = sqrt( 2^2 + 9^2)
= sqrt ( 85 ) = 9.22
Substitute all the value of the parameters into the formula
Cos ø = -46 / (15.3 × 9.2)
Cos ø = - 46 / 140.72
Cos Ø = - 32687
Find the cos inverse of the value
Ø = cos^-1( -32687)
Ø = 109.079 degrees
Therefore, the angle between the given vectors to the nearest tenth of a degree is 109.1 degrees
If 20a-16=12(3-a), then a=?
a)5/8
b)13/8
c)21/16
d)5/2
ANSWER: B. 13/8
STEP BY STEP THING:
20a−16=12(3−a)
20a−16=−12a+36
32a−16=36
32a=52
32a/32 = 52/32
a = 13/8
Answer:
13/8 or 1.625
Step-by-step explanation:
1)combine like terms 2)isolate the variable(a) to one side of the equation 3) use multiplicative or division properties x=13/8 or 1.625
The volume of a soup can with height of 6 cm and diameter of 4.4 cm = ____________ cm3. Use 3.14 for pi.
Answer:
about 91.2 cm³
Step-by-step explanation:
Radius (r) = diameter / 2 = 4.4 / 2 = 2.2
Volume of cylinder = πr²h, we know π = 3.14, r = 2.2 and h = 6
V = 3.14 * 2.2² * 6 = 91.2
Answer:
91.2
Step-by-step explanation:
To find the volume you need to use the formula [tex]\pi r^2h[/tex]
When you substitute all of the numbers the answer will be 91.1856
State the domain of the glven relation.
Answer:
x ≤ -1
Step-by-step explanation:
The domain is the x-values. Since the graph shows all numbers up to -1, the domain would be all numbers less than or equal to -1:
x ≤ -1
HELP FIRST GET BRAINLLEST Measure the difference between the lower quartile of Data Set A and the lower quartile of Data Set B. Round to the nearest tenth when performing all operations.
Answer:
29
Step-by-step explanation:
To find the lower quartile you need to split it into 2 by finding the median
Set A: 73, 75, 79, 81, 84, 85
Set B: 47, 49, 51, 51, 55, 56
Now you have to find the median of each
A: 80
B: 51
Lastly, you subtract and get 29
What’s the slope for this graphed?
A.5
B.1/3
C.2
D.3
Graph the image of this triangle after a dilation with a scale factor of 2 centered at the origin.
==================================================
Explanation:
Let's label the corner points of the triangle A,B,C starting at the origin and moving clockwise
A = (0,0)
B = (2,-4)
C = (-4,-4)
Dilating with a scale factor 2 means we multiply each coordinate of each point by the value 2
A = (0,0) becomes A' = (0,0). No change happens. This point is fixed
B = (2,-4) becomes B' = (4,-8). This point does move
C = (-4,-4) becomes C' = (-8,-8). This moves as well
So all you need to do from here is draw triangle A'B'C'.
-----------------
Side note: the lengths of triangle A'B'C' are twice as long as their counterparts on triangle ABC. Consequently, this means the perimeter of A'B'C' is twice as long as the perimeter of ABC. Also, triangle A'B'C's area is four times larger than the area of triangle ABC.
Triangle with the three corner points at
A' = (0,0). B' = (4,-8). C' = (-8,-8). what is Dilation?Meaning of Dilation in Math. Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the objects. The result of this transformation is an image with the same shape as the original.
Given:
Let's label the corner points of the triangle A,B,C starting at the origin and moving clockwise
A = (0,0)
B = (2,-4)
C = (-4,-4)
Dilating with a scale factor 2
A = (0,0) --> A' = (0,0).
B = (2,-4) --> B' = (4,-8).
C = (-4,-4) --> C' = (-8,-8).
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