20 POINTS! WRONG ANSWERS WILL BE REPORTED!
Isaiah sketches a model of a skateboard ramp. The model has two surfaces on which to skate, represented by sides AB and AD in the diagram.
The steepest side of the model, AB, measures 4 inches. What is the length of the other skating surface, AD?
A) 2 square root 2
B) 2 square root 3
C) 4 square root 2
D) 4 square root 3
Answers
AB = 4 so AC = 2 square root 2
triangle ACD 30-60-97
AC = 2 square root 2
AD = 2(AC)
AD = 4 square root 2
answer is
C) 4 square root 2
Answer:
(C)
Step-by-step explanation:
It is given that The steepest side of the model, AB, measures 4 inches, thus
From ΔABC, using the trigonometry, we have
[tex]\frac{AC}{AB}=sin45^{\circ}[/tex]
Substituting the given value, we have
⇒[tex]\frac{AC}{4}=sin45^{\circ}[/tex]
⇒[tex]AC=4{\times}\frac{1}{\sqrt{2}}[/tex]
⇒[tex]AC=2\sqrt{2}[/tex]
Now, from ΔACD, we have
[tex]\frac{AC}{AD}=sin30^{\circ}[/tex]
⇒[tex]\frac{2\sqrt{2}}{AD}=\frac{1}{2}[/tex]
⇒[tex]AD=4\sqrt{2}[/tex]
Therefore, the length of AD will be [tex]4\sqrt{2}[/tex]
thus, option C is correct.
Related Questions
Simplify six to the -3rd power over six to the fifth power
Answers
if a polynomial has one root in the form a+√b , it has a second root in the form of a_√b
Answers
That is,
The conjugate of (a + √b) is (a - √b) and vice versa.
To show that the given conjugates come from a polynomial, we should create the polynomial from the given factors.
The first factor is x - (a + √b).
The second factor is x - (a - √b).
The polynomial is
f(x) = [x - (a + √b)]*[x - (a - √b)]
= x² - x(a - √b) - x(a + √b) + (a + √b)(a - √b)
= x² - 2ax + x√b - x√b + a² - b
= x² - 2ax + a² - b
This is a quadratic polynomial, as expected.
If you solve the quadratic equation x² - 2ax + a² - b = 0 with the quadratic formula, it should yield the pair of conjugate radical roots.
x = (1/2) [ 2a +/- √(4a² - 4(a² - b)]
= a +/- (1/2)*√(4b)
= a +/- √b
x = a + √b, or x = a - √b, as expected.
Answer:
a - √b
Step-by-step explanation:
If you solve the quadratic equation x² - 2ax + a² - b = 0 with the quadratic formula, it should yield the pair of conjugate radical roots.x = (1/2) [ 2a +/- √(4a² - 4(a² - b)] = a +/- (1/2)*√(4b) = a +/- √bx = a + √b, or x = a - √b, as expected.
If matrix A has dimensions 3 x 2 and matrix B has dimensions 3 x 2, can matrix A and matrix B be multiplied?
Answers
Matrix B has 3 rows, 2 columns
The number of columns in matrix A (which is 2) does not match up with the number of rows in matrix B (which is 3).
So the matrix multiplication A*B is undefined. We cannot multiply the matrices.
Answer:
we can not multiply matrix A and B.
Step-by-step explanation:
We have been given that
dimension of matrix A = 3 x 2
dimension of matrix B = 3 x 2
Rule of multiplying two matrices:
Two matrix can be multiplied if the column of first matrix is equal to the row of second matrix.
column of first matrix = row of second matrix
Here, we have
Column of first matrix A = 2
Row of second matrix b = 3
Since,, column of matrix A ≠ Row of matrix B
Hence, we can not multiply matrix A and B.
how do you reduce the fraction of 28/49
Answers
reduce by 7
28/7 4
---- = ----
49/7 7
your answer will be: 4/7
hope this helps :D
28/7 4
---- = ----
49/7 7
your answer will be: 4/7
A bicycle wheel makes 5 revolutions. Determine how far the bicycle travels in feet. The diameter of the wheel is 32in.
Answers
need help, thank you!
2x+3y=5x−y
y=0
x=?
Answers
2x -5x = -y - 3y
-3x =-4y
X=4\3 y
Answer:
X=4\3
Step-by-step explanation:
Please help!! I attached an image, will give most brainliest
Answers
The stem is the value in the left and the leaf is the values listed on the right side of the table. In this case, it represents the tens and ones place.
The smallest of those values are 2 which is answer choice F.
-cz+6z=tz+83 solve for z
Answers
6z - cz - tz = 83
z (6 - c - t) = 83
z = 83 / (6 - c - t)
hope that helps
Answer:
The value of the equation for z is [tex]z=\frac{83}{6-c-t}[/tex].
Step-by-step explanation:
Consider the provided equation.
[tex]-cz+6z=tz+83[/tex]
Subtract tz from both the sides.
[tex]-cz+6z-tz=tz-tz+83[/tex]
[tex]-cz+6z-tz=83[/tex]
Take z common.
[tex]z(-c+6-t)=83[/tex]
[tex]z(6-c-t)=83[/tex]
Divide 6-c-t from both the sides.
[tex]\frac{z(6-c-t)}{6-c-t}=\frac{83}{6-c-t}[/tex]
[tex]z=\frac{83}{6-c-t}[/tex]
Thus, the value of the equation for z is [tex]z=\frac{83}{6-c-t}[/tex].
517.21 km what is the nearest 10km?
Answers
Final answer: 520 km
What is the value of x/3y , when x = 18 and y = 3?
3/18
2
3
6
Answers
x = 18
y = 3
x/3y becomes 18/3(3) = 18/9 = 2
Daniel and Sofia both solve this system of equations: y = -1.5x + 5.7 y = 0.5x + 0.3 Daniel's solution is (1.1, 2.4). Sofia's solution is (2.7, 1.65). They graph the equations to check their work. Based on the graph, whose solution is more likely to be correct?Daniel is more likely to be correct. The x-coordinate of the intersection is between 1 and 2 and the y-coordinate of the intersection is between 2 and 3. Sofia is more likely to be correct. The x-coordinate of the intersection is between 2 and 3 and the y-coordinate of the intersection is between 1 and 2. or niether
Answers
y = 0.5x + 0.3
-1.5x + 5.7 = 0.5x + 0.3
-1.5x - 0.5x = 0.3 - 5.7
-2x = - 5.4
x = -5.4/-2
x = 2.7
y = 0.5x + 0.3
y = 0.5(2.7) + 0.3
y = 1.35 + 0.3
y = 1.65
solution is (2.7, 1.65)
Sophia is more likely to be correct because the x coordinate is between 2 and 3 and the y coordinate is in between 1 and 2
Answer:
Sofia is more likely to be correct
=)
Step-by-step explanation:
A quadrilateral has vertices A(3, 5), B(2, 0), C(7, 0), and D(8, 5). Which statement about the quadrilateral is true?
Answers
A sphere has a radius of 3 and a hemisphere has a radius of 6. Compare the ratio of the volume of the sphere to the volume of the hemisphere.
Answers
S/H=2rs^3/rh^3
S/H=(2*3^3)/6^3
S/H=54/216
S/H=1/4
So the volume of the hemisphere is 4 time the volume of the sphere.
V=4/3 π r³
V=4/3 π 3³ = 113.097335529
Volume of a Hemisphere:
V=½(4/3 π r³)
V=½(4/3 π 6³) = 452.389342117
113.097335529 to 452.389342117
Pretty much 1/4 right on the nuts (0.24999999999944737866981989309472)
Find the area of the composite figure.Use 3.14 for pi.
Answers
area for the triangle section is 1/2 x b x h: 1/2 x 16 x 10 = 80 square m
area for half circle = 1/2 x 3.14 x 8^2 = 100.48 square m
100.48 + 80 = 180.48 square meters
Write 2 expressions that represent the areas of 4 triangles
Answers
Solve 2a 2 - 3a - 2 = 0
{-1/2, 2}
{1/2, -2}
{}
Answers
a^2-3a-4
(a-4)(a+1)
(a-2)(2a+1)
Find zeros
a-2=0
a=2
2a+1=0
2a=-1
a=-1/2
Final answer: {-1/2, 2}
Suppose you roll two standard number cubes once. Find the probability. P(7 or even)
Answers
To roll a seven you could have (1,6) (6,1) (2,5) (5,2) (3,4) (4,3)
6 different ways so 6/36 reduces to 1/6 way of getting a 7
For getting an even number as sum, we can have (1,1) or (1.3) or (1,5) or (2,2) or (2,4) or (2,6) or (3,1) or (3,3) or (3,5) or (4,2) or (4,4) or (4,6) or (5,1) or (5,3) or (5,5) or (6,2) or (6,4) or (6,6) 18 ways, probability is 18/36 reduces to ½
So for either one you now have 1/6 + 1/2 = 6+2/12 = 8/12 reduced to 2/3
Stuart is buying a pair of jeans that regularly cost $40. They are on sale for 20% off. If the tax rate is 8%,what is the sale price of the jeans including tax?
Answers
In a casino, the chance of winning a certain game is 14.5%. If you play the game 20 times, what’s your best estimate for the number of times you would win? Round off your answer to the nearest whole number.
Answers
w=20(14.5/100)
w=20(0.145)
w=2.9
w≈3
So you would expect to win 3 times out of 20 attempts (rounded to the nearest whole number of wins)
Use the law of cosines to find the missing third side
Answers
a^2=7.4^2+15.8^2-2(7.4)(15.8)cos54°
a^2=304.4-233.84cos54°
a=√(304.4-233.84cos54°) units
a≈12.92 units (to the nearest hundredth of a unit)
The missing third side BC is approximately 16.93 units. To use the Law of Cosines to find the missing third side (BC), we'll use the formula:
[tex]c^2 = a^2 + b^2 - 2ab * cos(C)[/tex]
where:
c is the side opposite angle C (BC in this case)
a and b are the known sides (AC and AB, respectively)
C is the angle opposite side c (angle BAC in this case)
Given values:
Angle BAC (C) = 54 degrees
AC (a) = 7.4
AB (b) = 15.8
Now, we can plug the values into the formula and solve for BC (c):
[tex]BC^2 = 7.4^2 + 15.8^2 - 2 * 7.4 * 15.8 * cos(54)[/tex]
To find cos(54), we can use a calculator:
[tex]cos(54 degrees) \approx 0.5878[/tex]
Now, we can continue the calculation:
[tex]BC^2 = 54.76 + 249.64 - 2 * 7.4 * 15.8 * 0.5878\\BC^2 = 54.76 + 249.64 - 17.44\\BC^2 = 286.96[/tex]
Now, find the square root of both sides to get the value of BC:
[tex]BC = \sqrt{286.96} \\BC \approx 16.93[/tex]
So, the missing third side BC is approximately 16.93 units.
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If f(x)=6x and g(x) = 4x+1, find ( f o g)(x)
Answers
(f○g)(x)=6(4x+1)
(f○g)(x)=24x+6
Evaluate the expression : (0.4)^3=
Answers
The expression when evaluated, can be found to be 0. 064.
How to evaluate the expression ?( 0 . 4 ) ³ means raising the number 0. 4 to the power of 3 , which is the same as multiplying 0. 4 by itself three times. This is how the expression is evaluated.
Start with:
0 . 4 * 0 . 4 * 0 . 4
Calculate each multiplication step:
1st multiplication: 0 . 4 * 0 . 4 = 0 . 16
2nd multiplication: 0 . 16 * 0 . 4 = 0 . 064
So, when you multiply 0. 4 by itself three times ( 0 . 4 * 0 . 4 * 0 . 4), you get the result of 0 . 064.
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What type of stock receives an equal part of the profits on each share to be distributed after all other obligations of a company have been satisfied?
Answers
Sarah received $55 for her birthday. She used some of that money to buy 3 shirts priced at m dollars each.
How much money does Sarah have left?
Write your answer as an expression.
Answers
You could figure out the equation if the 3 were M and M had a number but this is unsolvable. SORRY
m=11
each shirt is $11
Of the 240 shirts on a rack, 40 percent are size medium. How many shirts on the rack are size medium?
Answers
First, let’s check for the given:
Shirts on the rack = 240
Medium size shirts = 40% of 240
With the following given, we can now solve for the total
number of shirts on the rack that are size medium.
So, in order to solve for the problem, we multiply 40% to 240:
The decimal equivalent of 40% is 0.4.
240 shirts * .4 = 96 shirts
Therefore, out of 240 shirts on the rack, there are 96 shirts on the rack that are size medium.
To add, the number or ratio that represents a fraction of 100 is called a percentage.
Which is the general form of the equation of the circle shown? x2 + y2 + 4x – 2y – 4 = 0 x2 + y2 + 4x – 2y + 2 = 0 x2 + y² – 4x + 2y – 4 = 0 x2 + y² – 4x + 2y + 2 = 0
Answers
For the second picture, the center is (-2,1) and the radius is square root of 3.
For the third picture, the center is (2,-1) and the radius is 3.
For the last picture, the center is (2,-1) and the radius is square root of 3.
Answer:
THE ANSWER IS A
Step-by-step explanation:
Solve the system of equations.
11x+4y=-46
7x-4y=10
Answers
7x-4y=10
---------------add
18x = -36
x = -2
7x-4y=10
7(-2)-4y=10
-4x = 24
y = - 6
answer
(-2,-6)
The solution is x = -2 and y = -6.
What are linear equations?First-order equations are linear equations. The coordinate system defines the linear equations for lines. A linear equation in one variable is one in which there is only one variable and the equation has a homogeneous variable of degree 1. There can be more than one variable in a linear equation. When there are two variables in a linear equation, it is referred to as a "linear equation with two variables" and so on.
Given equations 11x + 4y = -46
and 7x - 4y = 10
add both equations
11x + 4y + 7x - 4y = -46 + 10
18x = -36
x = -36/18
x = -2
substitute the value of x in equation
11x + 4y = -46
11(-2) + 4y = -46
4y = -46 + 22
4y = -24
y = -6
Hence the solution for given equations is x = -2 and y = -6.
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The temperature at 9 a.m. is 2 degrees. The temperature rises 3 more degrees by noon. Which expression describes the temperature at noon?
2 + 3
2 + (–3)
–2 + (–3)
–2 + 3
Answers
it starts at 2 degrees which is not a negative number and temperature rises so it isn't a negative number either
so it would be 2+3
An expression is defined as a set of numbers, variables, and mathematical operations. The correct option is A, 2+3.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
Given that the temperature at 9 a.m. is 2 degrees. Further, the temperature rises 3 more degrees by noon.
As two whole numbers are added together, the total quantity or sum of those values is obtained. Therefore, the expression that describes the temperature at noon is 2 + 3.
This is because the temperature is positive and after the temperature rises, the temperature will be added.
Hence, the expression that describes the temperature at noon is 2 + 3.
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25/150 in simplest form
Answers
Divide bothe the numerator and denominator by 25 to get the simplest form.
25/25=1
150/25=6
Final answer: 1/6
PLease Answer!
The Mali Empire of West Africa was known far and wide for the great wealth of its rulers. The empire fell in the year 1610.
Let x represent any year. Write an inequality in terms of x and 1610 that is true only for values of x that represent years after the year the Mali Empire fell.
Answers
The year 1610 is not inclusive as this is the year when the Empire fell
the answer is x>1610