The required equation of the line is 5y=x.
We are given to find the equation of the line passing through the points (0, 0) and (15, 3).
We know that
What is the slope point form of the line?The equation of a line passing through two points (a, b) and (c, d) is given by
[tex]y-b=\frac{d-b}{c-a}(x-a)[/tex]
Therefore, the equation of the line passing through the points (0, 0) and (15, 3) is given by,
Thus, the required equation of the line is
[tex]y-0=\frac{3-0}{15-0}(x-0)\\y=\frac{3}{15}x\\ y=\frac{1}{5}x\\ 5y=x[/tex]
Thus the required equation of the line is 5y=x.
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Find the value of x in the diagram below. x =
Answer:
x=101
Step-by-step explanation:
Fun angles......................
Answer:
x = 79°
Step-by-step explanation:
The arrows on the line segments indicate that the lines are parallel.
As the parallel line segments are the same length, the other pair of opposite line segments are also parallel and the same length. Therefore, we can apply the Alternate Interior Angles Theorem.
Alternate Interior Angles Theorem
If a line intersects a set of parallel lines in the same plane at two distinct points, the alternate interior angles that are formed are congruent.
Therefore, the missing angle in the triangle including angle x is 28°.
Interior angles of a triangle sum to 180°
⇒ 73° + 28° + x = 180°
⇒ x = 180° - 73° - 28°
⇒ x = 79°
A city has 5 new houses for every 9 old houses. If there are 35 new houses in the city, how many old houses are there?
Answer:
20 I guess
Step-by-step explanation:
because maybe 1 is 9
Consider a triangle ABC like the one below. Suppose that a = 31, b = 23, and c = 20. (The figure is not drawn to scale.) Solve the triangle. Carry your intermediate computations to at least four decimal places, and round your answers to the nearest tenth. If there is more than one solution, use the button labeled "or".
The solution to the triangle is A = 92.0, B = 47.9 and C = 40.1
How to solve the triangle?The figure is not given;
However, the question can still be solved without it
The given parameters are:
a = 31, b = 23, and c = 20
Calculate angle A using the following law of cosine
a² = b² + c² - 2bc * cos(A)
So, we have:
31² = 23² + 20² - 2 * 23 * 20 * cos(A)
Evaluate
961 = 929 - 920 * cos(A)
Subtract 929 from both sides
32 =- 920 * cos(A)
Divide both sides by -920
cos(A) = -0.0348
Take the arc cos of both sides
A = 92.0
Calculate angle B using the following law of sine
a/sin(A) = b/sin(B)
So, we have:
31/sin(92) = 23/sin(B)
This gives
31.0189 = 23/sin(B)
Rewrite as:
sin(B) =23/31.0189
Evaluate
sin(B) =0.7415
Take arc sin of both sides
B = 47.9
Calculate angle C using:
C = 180 - 92.0 - 47.9
Evaluate
C = 40.1
Hence, the solution to the triangle is A = 92.0, B = 47.9 and C = 40.1
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Find the area of this triangle.
Answer:
120 ft²
Step-by-step explanation:
The formula to find the area of a triangle is :
Area = [tex]\frac{1}{2}[/tex] × base × height
Given that,
base ⇒ 30 ft
height ⇒ 8 ft
Let us solve it now.
Area = [tex]\frac{1}{2}[/tex] × base × height
Area = [tex]\frac{1}{2}[/tex] × 30 ft × 8 ft
Area = [tex]\frac{1}{2}[/tex] × 240 ft²
Area = 120 ft²
In this question we are provided with the base and height of a triangle. We are asked to calculate the area of the triangle.
Base = 30 feet
Height = 8 feet
We know,
[tex] \large \star \: \small\boxed{ \rm{ Area_{(triangle)} = \dfrac{1}{2} × b × h}}[/tex]
Where,
b stand for baseh stand for heightSubstituting the values we get
[tex] \small\sf{ Area_{(triangle)} = \dfrac{1}{ \cancel{2}} × 30 × \cancel{8} \: \: 4}[/tex]
[tex] \longmapsto \small\rm Area_{(triangle)} = 30 × 4[/tex]
[tex] \small \underline{ \boxed{\sf {Area_{(triangle)} =120 \: {feet}^{2} }}}[/tex]
Hence,the area of the triangle is 120 feet².
[tex]\underline{\rule{71mm}{3pt}}[/tex]
Which of the
following ordered
pairs make this
equation true?
Answer:
D. (2, 3)
Step-by-step explanation:
The equation will be true when the values of x and y are substituted and the result matches what you know about sums.
__
The values in each ordered pair are (x, y).
A.x = -2, y = -3
Substituted into the equation, we get ...
-3 = -2 +1 . . . . . . false
__
B.x = 5, y = 4
Substituted into the equation, we get ...
4 = 5 +1 . . . . . . false
__
C.x = 0, y = -1
Substituted into the equation, we get ...
-1 = 0 +1 . . . . . . false
__
D.x = 2, y = 3
Substituted into the equation, we get ...
3 = 2 +1 . . . . . . true
11.85 is 75% of what number
Answer:
20.14
Step-by-step explanation:
so to find it i added 75% to 11.85 so 11.85 + 75% = 20.14
Hope This Helped
Answer:
15.8
Step-by-step explanation:
11.85/75 = x/100
x = 15.8
11.85 is 75% of 15.8
Brainliest please!
hope this helps :)
Which expression is equivalent to the given expression
Answer:
i think the answer is A. 2x^3y^2
A composite figure is shown.
Diagram shows a composite shape formed by placing a cube before a square prism and a square pyramid next to it that share a common square base. Cube has sides labeled 6 feet. Length of the square prism is 20 feet and height of the pyramid is 4 feet.
What is the surface area for each part of the figure? What is the total surface area of the figure?
The surface area of the pyramid is
square feet.
The surface area of the square prism is
square feet.
The surface area of the cube is
square feet.
The total surface area is
square feet.
The surface area of the pyramid is 60 square feet
The surface area of the square prism is 480 square feet
The surface area of the cube is 180 square feet
The total surface area is 720 square feet
Area of Composite figuresFrom the question, we are to calculate the surface area of each part of the composite figure
For the cubeSurface area of a cube is given by
[tex]S = 6l^{2}[/tex]
Where [tex]l[/tex] is the length of a side
But only have 5 surfaces of the cube are part of the composite figure
∴ Surface area of the cubic part of the figure = [tex]5l^{2}[/tex]
From the given information,
[tex]l = 6 \ feet[/tex]
∴ Surface area of the cubic part of the figure = 5 × 6²
Surface area of the cubic part of the figure= 180 square feet
For the square prismThe surface area of a square prism is given by the formula,
[tex]S = 2l^{2} + 4lh[/tex]
Where [tex]l[/tex] is the length of the sides and
[tex]h[/tex] is the height
But the square surfaces are not part of the surface of the figure
∴ Surface area of the square prism in the figure = [tex]2l^{2} + 4lh - 2l^{2}[/tex]
Surface area of the square prism in the figure = [tex]4lh[/tex]
From the given information,
[tex]l = 6 \ feet[/tex]
[tex]h = 20 \ feet[/tex]
Thus,
Surface area of the square prism part of the figure = 4×6×20
Surface area of the square prism part of the figure = 480 square feet
For the pyramid
The pyramid is a square pyramid
The surface area of a square pyramid is given by
[tex]S = l^{2} + 2l\sqrt{\frac{l^{2} }{4}+h ^{2} }[/tex]
Where [tex]l[/tex] is the base length
and [tex]h[/tex] is the height of the prism
But the square base is not part of the surface of the figure
∴ Surface area of the pyramid part of the figure = [tex]l^{2} + 2l\sqrt{\frac{l^{2} }{4}+h^{2} }\ - ( l^{2})[/tex]
Surface area of the pyramid part of the figure = [tex]2l\sqrt{\frac{l^{2} }{4}+h^{2} }[/tex]
From the given information,
[tex]l = 6 \ feet[/tex]
[tex]h = 4 \ feet[/tex]
∴ Surface area of the pyramid part of the figure = [tex]2(6)\sqrt{\frac{6^{2} }{4}+4^{2} }[/tex]
= [tex]12\sqrt{\frac{36 }{4}+16}[/tex]
= [tex]12\sqrt{9+16 }[/tex]
= [tex]12\sqrt{25}[/tex]
= 12 × 5
= 60 square feet
Hence, the surface area of the pyramid is 60 square feet
Thus,
The total surface area = 180 square feet + 480 square feet + 60 square feet
The total surface area = 720 square feet
Hence, the total surface area is 720 square feet
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Answer:
1: 60
2: 480
3: 180
4: 720
Step-by-step explanation:
plato answer :)
7 of 10
Work out
(1.5 × 10¹⁰) ÷ (3 × 10-4)
Give your answer in standard form.
Answer:
5 × 10¹³
Step-by-step explanation:
(1.5 × 10¹⁰) ÷ (3 × 10⁻⁴) = 50,000,000,000,000
The lines below are parallel. If the slope of the green line is -3, what is the slope of the red line?
Answer:
The lines would be equal, meaning the slope of the red line is also -3.
Step-by-step explanation:
SIMPLE:
Parallel lines have the same slope.
Find the slope
Will mark brainlist
Answer:
2/3
Step-by-step explanation:
PLEASE PLEASE HELP
An archer makes two attempts to hit a target, and the probability that he hits the target on any one attempt is 1/7.
What is the probability that the archer will miss the target on both attempts?
A. 1/49
B. 48/49
C. 6/7
D. 36/49
Answer:
The answer would be D.
Step-by-step explanation:
If there is a 1/7 chance that the archer will hit it, there is a 6/7 chance he/she wont. 6/7 times 6/7 is equal to 36/49, getting you your answer of D. I hope this helps! :)
3p+6
Which phrase represents the algebraic expression 7p-9?
Answer:
The answer is the sum of three times a number and six, divided by the difference of seven times the number and nine
Step-by-step explanation:
3p = three x a number
7p = seven x a number
3p+6 = sum of three x a number plus six
7p-9 = difference of seven x the number minus nine
(3p+6)/(7p-9) = sum of three times x number plus six, divided by the difference of seven x the number - nine
A cube's edge lengths are each 5 inches. A rectangular prism's length and width are also 5 inches, but its height is 7
1
2
inches.
How many cubic inches larger is the rectangular prism than the cube?
The rectangular prism is 187.5 - 125 = 62.5 cu.inches greater than the volume of cube.
What is Volume?Volume is defined as the space occupied by a three dimensional figure.
It is given that
A cube's edge lengths are each 5 inches
A rectangular prism's length and width are also 5 inches, but its height is [tex]\rm 7\dfrac{1}{2}[/tex]
The volume of the cube is given by side * side * side
Volume of cube = 5 *5 * 5 = 125 cu. inches
The volume of cuboid = length * width * height
Volume of Cuboid = 5 * 5 * 15/2Volume of Cuboid = 187.5 cu.inches.
Therefore the rectangular prism is 187.5 - 125 = 62.5 cu.inches greater than the volume of cube.
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Must show work-Solve the conjunction and describe the solution set. −5 < 2x + 3 < 9
The solution set of the inequality −5 < 2x + 3 < 9 is (-4,3)
How to solve the inequality?The compound inequality is given as:
−5 < 2x + 3 < 9
Expand the inequality
−5 < 2x + 3 or 2x + 3 < 9
Rewrite as:
2x + 3 > -5 or 2x + 3 < 9
Subtract 3 from both sides
2x > -8 or 2x < 6
Divide both sides by 2
x > -4 or x < 3
Rewrite as:
(-4,3)
Hence, the solution set of the inequality is (-4,3)
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Help please ………………….
Answer:
Step-by-step explanation:
Write a rule to describe the transformation.
Step-by-step explanation:
The function translation / transformation rules: f (x) + b shifts the function b units upward. f (x) − b shifts the function b units downward. f (x + b) shifts the function b units to the left
Five identical machines cover a total of 32 1/2 ft.² of floor space how much floor space occupied by each machine
Using proportions, it is found that the floor space occupied by each machine is of 6.5 ft².
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In this problem, five identical machines cover a total of 32 1/2 ft² = 32.5 ft², hence the space occupied by each machine is given as follows, applying the proportion:
32.5 ft²/5 = 6.5 ft².
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What number would you add to both sides of x² + 7x = 4 to complete the square?
Answers:
A. 2²
B. 7²
C. 7²/2
D. [⁷/2]²
The number would you add to both sides of x² + 7x = 4 to complete the square option C 7²/2.
What is completing the squares method for solving the quadratic method?Suppose the considered quadratic equation is of the form
ax^2 + bx + c = 0
Then, completing the squares method tries to make a squared term in terms of x in the left side, so that x comes in linear form, instead of quadratic.
The given quadratic equation is
x² + 7x = 4
add 7²/2 to both sides of x² + 7x = 4 to complete the square
7²/2 = 49/4
x² + 7x + 49/4 = 4+ 49/4
(x + 7/2)² = 4+ 49/4
Thus, option C 7²/2 is correct.
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Suppose that you have a square pyramid like the one pictured. Which plane section will produce a triangle? Question 6 options: A) A cut parallel to the vertical axis, directly through the vertical axis B) A cut parallel to the vertical axis, but off the vertical axis C) A cross section cut parallel with the bottom D) Cutting off one of the bottom corners
The plane that would produce a triangle is A, a cut parallel to the vertical axis, directly through the vertical axis.
What is a squared pyramid?
A square pyramid is a geometric shape having four triangles, five faces and a square.
Properties of a squared pyramidIt has a five bases It has four or greater equilateral triangular faces meeting above the baseAll the edges, sides and angles are equalSince the sides are equal, cutting parallel to the vertical axis forms a triangle.
Therefore, a cut parallel to the vertical axis, directly through the vertical axis would produce a triangle.
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make c the subject v=c/4-5
Answer:
c = -v
Step-by-step explanation:
v = [tex]\frac{c}{4-5}[/tex]
v = [tex]\frac{c}{-1}[/tex]
v = -c (anything divided by -1 is the negative itself)
c= -v
Hope this helped and brainliest please
james got 19 questions right on a math test. These questions made up 76% of the test.How many questions were there on the test?
Answer:
25 Questions.
Explanation:
Original or full is always 100%
Mentioned:
76% ⇒ 19
=========
1% ⇒ (19 ÷ 76) = 0.25
Solve for Total:
100% ⇒ 0.25 × 100 = 25
The mapping diagram shows a function R(x)
Answer:
Answer is C
Step-by-step explanation:
It's the same as the mapping diagram but the values are flipped. It's going backward instead of forwards.
What is the surface area of the rectangular prism
represented by the net shown?
6 in.
1.5 in.
1.5.in.
Answer:
40.5 inch²
Step-by-step explanation:
(((6×1.5)×4)+((1.5×1.5)×2) = 40.5
Solve for x. Round to the nearest tenth, if necessary.
56
Z
43°
x
M
60.2 is the value of x in Trigonometric ratios
What are the trigonometric ratios?
Trigonometric ratios are used to describe the side ratios of a right triangle. The sine (sin), the cosine (cos), and the tangent are three popular trigonometric ratios (tan).
Greek is the language of measuring, "metric," and "trigon" is the language of triangles. It is possible to measure a right triangle specifically using its trigonometric ratios.
43 degree as reference angle
using tan rule
tan 43 = opposite / adjacent
0.93 = x / 56
x = 56/0.93
x = 60.21
x = 60.2
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Find the missing side length of side c, a and b are both 25
Answer: x=25, y=2
Step-by-step explanation:
use Pythagorean theorem to get that 1250= c^2. then sqaure root both sides. c= sqrt(1250). jailbreak to get c=(5 x 5 x 5 x 5 x 2), and take the fives out from under the square root to get 25 x sqrt2.
Is 35 cm greater than 3.5 m
Answer:
no
Step-by-step explanation:
3.5m=350cm
35cm<350cm
4. PLEASE HELP!!!!!!
You have a cup with 17 coins inside. The total inside the cup is $5.50. Determine how many half dollars and quarters are inside the cup. Use a system of equations. Be sure to define the variables and show all work.
The number of half dollars coins are 5 and the number of the quarters dollars coins are 12.
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
You have a cup with 17 coins inside.
The total inside the cup is $5.50.
Let x be the number of half dollars and y be the number of the quarters dollars.
Then the equations will be
x + y = 17 ............1
0.5x + 0.25y = 5.5 ...........2
By solving equations 1 and 2, we have
x = 5 and y = 12
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Karl wants to rent a bike for at most $55. He can rent a bike for $7 per hour plus a $9.50 flat fee. Any portion of an hour is charged as a full hour.
What is the maximum number of hours Karl can Rent the bike?
How many 5-digit numbers are there, that are "even"? Show all work/ calculations.
Answer: The correct answer is 13776.
Explanation: There are 3024 five-digit numbers that begin with the digit 4 with no repetition.