Step-by-step explanation:
Say that x = 1, since x can be any real number.
From part a -> x +2 = 3
and -> 10-x =9
then multiply the two results to get y -> 3x9 = 27
Now look at y=20+8x-x and plug in the same value for x where x = 1
you get -> y = 20 + 8(1) -(1) which simplifies out to 27. Therefore the equation is proven since they equal the same value.
Volume of cylinders, spheres, and cones word problems
A graduated cylinder is filled with 367 cm3 of liquid. The liquid is poured into a different cylinder that has a
radius of 3 cm.
What will the height of the liquid be in the new cylinder?
cm
What is the value of b:
-8-b=-6
1) b=-2
2) b=2
Answer:
b = -2
Step-by-step explanation:
Add 8 to both sides: -8 - b + 8 = -6 + 8
-b = 2
Divide both sides by -1: -b/-1 = 2/-1
b = -2
I NEED HELP!!!!!!!!!!!!!!!!
Step-by-step explanation:
just think back to the standard circle of radius = 1.
there the trigonometric functions are all represented as sides of right-angled triangles, where the radius is the baseline.
just like the triangle we are seeing here.
the only difference : the baseline (radius) is 17 and not 1.
and that is fine. everything is as in the standard circle, but multiplied by the radius (which is also true for the standard circle, but multiplying by 1 does not change anything, right ?).
a)
angle A is or focus. so, just imagine the triangle turned counterclockwise by 90° (so that AC is horizontal and CB is vertical).
do you see it now ?
sin is the vertical leg, cos the horizontal leg. and the leg lengths here are the standard functions multiplied by the radius.
so,
17 × sin A = 8
sin A = 8/17 = 0.470588235... ≈ 0.47
b)
17 × cos A = 15
cos A = 15/17 = 0.882352941... ≈ 0.88
c)
now B is our focus. imagine the triangle being mirrored at point B, so that B is left, and AC is right. your see it now ?
tan B = sin B / cos B
sin B = 15/17 = 0.882352941... ≈ 0.88
cos B = 8/17 = 0.470588235... ≈ 0.47
tan B = 15/17 / 8/17 = 15/8 = 1.875 ≈ 1.88
d)
cos B = 8/17 = 0.470588235... ≈ 0.47
What is the area of a square that had side length of x-6?
area square= side²
= (x-6)²
= x²-12x+36
Answer:
36
Formula:
Side² = Area
Step-by-Step Explanation
-6 x -6 = 36
WORTH 80 sorry its zoomed out but is there cluster or outliers where and explain why
Answer:
15.42, 25.49, 46.19
Step-by-step explanation:
although 32.28, 40.40 could also be considered
How many vertices, edges, and faces are in the polyhedron below? List them.
Based on observation, in this polyhedron, there are a total of six vertices, nine edges, and five faces.
What are vertices?In geometry, this refers to the point where two line meet. In this case, the vertices are A, B, C, D, E, F for a total of six vertices.
What are the edges?This term refers to line segments, for example the line between B and C is an edge. Based on this, there are nine edges in this shape.
What are faces?This refers to flat surfaces; in this, case the total of flat surfaces are five.
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1. Josie lives at the coordinates (8,-4). Ruby lives at (-4, 2). When
Josie rides her bike to Ruby's house, she stops by the ice cream shopthat is 2/3 of the way from her house to Ruby's. What is the location of the shop?
There are 8 hamburger buns in a package. which number of hamburger buns would fill a whole number of packages: 18, 32, 44, 56?
Answer:
32 and 56?
Step-by-step explanation:
32 and 56 are related to 8.
32=8x4
56=8x7
The number that would fill a whole number of packages of hamburger buns is 32 ad 56.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
18, 32, 44, 56
We need to find which number can be evenly divided by 8 because there are 8 hamburger buns in a package.
Now,
18 is not divisible by 8, because 8 x 2 = 16, and 18 is greater than 16.
32 is divisible by 8 because 8 x 4 = 32.
44 is not divisible by 8, because 8 x 5 = 40, and 44 is greater than 40.
56 is divisible by 8 because 8 x 7 = 56.
Therefore,
32 and 56 would fill a whole number of packages of hamburger buns.
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Leo buys pasta for 12 people,
(a)
Each person eats 100 grams of pasta.
One packet has 500 grams of pasta.
How many packets must Leo buy?
Answer:
3
Step-by-step explanation:
If each packet has 500 grams, and each person eats 100 grams, then one packet will feed five people (500/100=5). Since he will be buying pasta for 12 people, he will need to buy three packets, because 3*500=1500 grams. While there is some extra, buying only two packets would result in not enough pasta.
A gift box in the shape of a
rectangular prism has a base area
of 56 square inches and a height of
4 inches. What is the volume of the
box in cubic inches?
F) 224
G) 448
H) 896
J) 12,544
Pls help pls pls ple
Answer:
10.5 ft
Step-by-step explanation:
This problem is using scaling.
Basically:
2.5(RV) = WZ
Meaning our scale factor is 2.5.
Multiply 4.2 * 2.5
Your answer is 10.5 ft.
Given that you have a pentagon. What would be the measure of the sum of the exterior angles?
Answer:
360°
Step-by-step explanation:
the sum of the exterior angles of any polygon = 360°
Repost bc I forgot something.
You throw a football and it leaves your hand of 5 feet. Its initial velocity is 20 feet per second. What is the maximum height the ball will reach? Also, how long will it take the ball to hit the ground? (Equation used: h(t)= -16t^2 + v0t + h0.)
Please show work
Answer:
The max height is 11.25 feet and the ball will take 1.464 seconds to hit the ground
Step-by-step explanation:
The quickest way to solve this equation is by using the equation that you gave, which is h(t)= -16t^2 + v0t + h0. This equation models the trajectory of the football, which means that at the equation's vertex, we can model what the height of the ball is. Along with that, by finding the positive root of where h(t) = 0, we can find how long it will take for the ball to hit the ground.
First, lets find h0 and v(0)
h0 is the initial height of the ball. So we know that the ball leaves your hand of 5 feet, so h0 = 5. Similarly, the initial velocity is 20 ft/sec, so v0 = 20.
Plugging 5 in for h0 and 20 for v0, we get h(t) = -16t^2 + 20t + 5.
Second, find max height.
To find the vertex of a parabola, use -b/2a to find the time, and plug that into h(t) to get the height.
b=20
a=-16
t = -b/2a = -20/2(-16) = .625 seconds
h(.625) = 11.25 feet
The max height is 11.25 feet
Third, find how long.
To find this, we need to find the t-intercepts of the equation.
set h(t) = 0
-16t^2 + 20t + 5 = 0
Use quadratic formula to find t
t = (- 20 ± [tex]\sqrt{20^{2} - 4(-16)(5)}[/tex])/2(-16)
t = {1.464}, -.214
The ball will take 1.464 seconds to hit the ground.
Find the value of x. If necessary, round your answer to the nearest tenth. The figures are not drawn to scale.
AB = 12, BC = 9, and CD = 8
Step-by-step explanation:
By the secant-secant theorem, (AC)(BC)=(DC)(x+DC)
Substituting in the given values, (21)(9)=(8)(8+x)
So, 189=64+8x, meaning x = 15.625, or about 15.63.
15. A plane took off and rose at an angle of 8º with the horizontal ground. As the plane flies over a water tower, it has covered a distance from the take off point of 2000 feet. How far apart are the take off point and the water tower?
The required distance between the take-off point and the water tower is 1980.1 feet.
Given that,
A plane took off and rose at an angle of 8º with the horizontal ground. As the plane flies over a water tower, it has covered a distance from the take-off point of 2000 feet.
To determine how far apart are the take-off point and the water tower.
These are the equation that contains trigonometric operators such as sin, cos.. etc.. In algebraic operation.
Here,
Now,
The distance flying over inclination is 2000 feet at an angle of 8° with horizontal.
Now,
Required horizontal distance = 2000 * cos 8°
= 1980.1 feet.
Thus, the required distance between the take-off point and the water tower is 1980.1 feet.
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Write 9/10 as an equivalent fraction with a denominator of 100 then write the fraction as a decimal
Answer:
Since the denominator has to be 100 and 9/10, 0.90, and 90% are all equal the you would just need to make the 9 into a 90. Therefore, yout answer will be 90/100.
Sasha's family traveled 2/7 of the distance to her aunt’s house on Saturday. They traveled 4/5 of the remaining distance on Sunday. What fraction of the total distance to her aunt’s house was traveled on Sunday?
The fraction of the total distance Sasha traveled to her aunts house is 6/7
Step-by-step explanation:
Need Help! Please!
Tara found a pair of jeans that were regularly priced at $35. She has a coupon for 15% off. What is the price of the jeans after applying the coupon?
$20
$7
$29.75
$33.50
Answer:
The price is $29.75
Step-by-step explanation:
Because it is 15 percent off, that means that the jeans are priced at 100%-15%=85%. To convert a percent to a decimal, move the decimal two places to the left. This gives us .85. Multiply 35 by .85 and you will get 29.75. Hope this helps!
Cedar Point amusement park has some of the tallest roller coasters in the United States. The Mantis is 165 feet shorter than the Millennium Force.
Write and solve an equation that can be used to find the height x of the Mantis.
b. Tyler's playlist has 36 songs. Noah's playlist has one quarter as many songs as
Tyler's playlist. How many songs are on Noah's playlist?
w = 4 times 36
w = 36 divided by 4
4w = 36
w/4 = 36
Answer:
9 songs
Step-by-step explanation:
¼ of 36
¼ × 36 = 9
in a cyclic quadrilateral ABRS, if AR=BS, prove that AS=RB and AB is parallel to SR
HELP!
The function f(x) = ax^2 + bx +c has an axis of symmetry of x = -3. The graph opens downwards and passes through the point (0,5). Write a possible equation for f(x).
Joseph researched the ages of some of his favorite professional
football players. He recorded his results in the dot plot below.
Which of the following statements about the distribution are true?
I. There are two peaks at 27 and 28.
II. The distribution is skewed.
III. The distribution does not have an outlier.
IV. The distribution shows a spread of 5.
I only
I, II, and III only
I, III, and IV only
I, II, III, and IV
The statements that are true about the dot plot are: I, III, and IV only.
What is the Spread of a Data in a Dot Plot?The range, which is the difference between the maximum and minimum value, is a measure of the spread of a data distribution.
In the dot plot given, the spread of the data is: 30 - 25 = 5.
The peak points are at 27 and 28, and the data looks symmetrical in shape with no clear outlier.
Therefore, the statements that are true about the dot plot are: I, III, and IV only.
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Find the product of 5.21 and 3.4
Step-by-step explanation:
5.21× 3.4 = 17.714
thank u
What is the slope of a line that goes through the points (3, 7) and (8, 11)
Question 4 options:
117
54
−83
45
Answer:
[tex]\sf \dfrac{4}{5}[/tex]
Step-by-step explanation:
(3,7) ⇒ x₁ = 3 & y₁ = 7
(8 ,11) ⇒ x₂ = 8 & y₂= 11
Slope
[tex]\boxed{Slope = \dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}}[/tex]
[tex]\sf =\dfrac{11 -7}{8 -3}\\\\\\ = \dfrac{4}{5}[/tex]
Milan is drawing a triangle. One side has a length of 9 cm, and another side has a length of 6 units. What could be the length of the third side?
3 cm
7 cm
15 cm
18 cm
Answer: 7 cm
Step-by-step explanation:
C
250
4.9 cm
80°
A
3.8 cm
D
B
ABC is a triangle.
D is a point on AB.
Work out the area of triangle BCD.
Give your answer correct to 3 significant figures.
Answer:
[tex]10.4\: \sf cm^2\:(3\:sf)[/tex]
Step-by-step explanation:
[tex]\Large\boxed{\sf Formulae}[/tex]
Sine Rule
[tex]\dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}[/tex]
(where A, B and C are the angles and a, b and c are the sides opposite the angles)
Cosine rule
[tex]c^2=a^2+b^2-2ab\cos C[/tex]
Area of a triangle
[tex]\textsf{Area of a triangle}=\dfrac12ab\sin C[/tex]
where:
C is the anglec is the side opposite the anglea and b are the sides adjacent the angle[tex]\Large\boxed{\sf Calculation}[/tex]
To find the area of ΔBCD, find:
length of CDangle CDBlength of BDThen use the sine rule for area of a triangle
Calculate length CD using cosine rule:
[tex]\implies CD^2=4.9^2+3.8^2-2(4.9)(3.8)\cos 80^{\circ}[/tex]
[tex]\implies CD^2=31.98334186...[/tex]
[tex]\implies CD=5.655381673...\:\sf cm[/tex]
Calculate ∠ADC using sine rule:
[tex]\implies \dfrac{\sin 80}{CD}=\dfrac{\sin ADC}{4.9}[/tex]
[tex]\implies ADC=\sin^{-1}\left(\dfrac{4.9 \sin 80}{CD}\right)=58.568949^{\circ}[/tex]
Therefore, ∠CDB = 180° - 58.568949° = 121.431051°
Use sine rule to calculate DB:
[tex]\implies \dfrac{DB}{\sin 25}=\dfrac{CD}{\sin CBD}[/tex]
[tex]\implies DB=\dfrac{5.655381673\sin25}{\sin 33.568949}=4.322471258..\: \sf cm[/tex]
[tex]\Large\boxed{\sf Solution}[/tex]
Use the sine rule for area of a triangle to find area of ΔBCD:
[tex]\implies A=\dfrac12(CD)(DB)\sin CDB[/tex]
[tex]\implies A=\dfrac12(5.655381673)(4.322471258)\sin (121.431051)[/tex]
[tex]\implies A=10.4\: \sf cm^2\:(3\:sf)[/tex]
solve for the measure of angle JKL in the diagram below? Show your work and explain the steps you used to solve
Question: calculate the measure of angle JKL, i.e. mJKM+mMKL
Answer:
78°
Step-by-step explanation:
angle JKM is a tangent-chord intersection angle and equals half of the intercepted arc KM of 76°. Thus
mJKM = 76/2 = 38°
angle MKL is an inscribed angle and equals half of the intercepted arc ML of 80°, Thus
mMKL = 80/2 = 40°.
Therefore angle JKL = 38°+40° = 78°.
What is the approximate area of Laura’s yard?
To find the area of an irregular shape (in general)
⇒ is best to split it into different regular shapes
⇒ (in this case), let's split into a half-circle and a square
Area of the half-circle:
⇒ half the area of a circle ([tex]\pi r^2[/tex])
⇒ Area of half-circle = [tex]\frac{1}{2}\pi r^2[/tex]
r: length of radius ⇒ half of length of the diameter ⇒ 8.5m[tex]\pi[/tex] = 3.14Area of Half Circle = [tex]\frac{1}{2}\pi (8.5)^2 = 113.5m^2[/tex]
Area of square
⇒ length * width
⇒ Area of Square = 17 * 17 = 289[tex]m^2[/tex]
Total Area = 113.5 + 289 = 402.5 ≈ 402[tex]m^2[/tex]
Hope that helps!
Find the area of the trapezoid.
8 cm
6 cm
13 cm
A. 78 cm2
B. 48 cm2
C. 63 cm
D. 104
Answer:
c; 63 square cm
Step-by-step explanation:
the area of a trapezoid can be described by the equation a = (1/2)(h)(b1 + b2)
this means the height times base 1 and base 2 added together divided by 2
(1/2)(6)(8 + 13) is the equation
this can become 3(21)
which is ultimitaly 63
Answer:
it's gonna be 63cm^2
Step-by-step explanation:
First, were gonna find the area of the rectangular portion, which is 8x6, which is 48cm^2
Next, well do the triangle part. So, we have to subtract 13-8 to get the width of the triangle.
Next, we have to find the area for the triangle. The formula is length x width / 2.
So, we have to multiply 6x5 to get 30.
Then, well divide it by 2, which will give us 15cm^2
Finally, we add the areas of rectangle and the triangle together. 15 + 48 is 63.
Bada-bing, bada-boom, we got 63cm^2 as our answer :)