Answer:
diagonal is 20.68 ft; shorter base is 17.21 ft
Step-by-step explanation:
If base angles add up to 140, then each is 70 since this is an isosceles trapezoid. We can use the Law of Cosines now to find the length of the diagonal which I will call d:
[tex]d^2=7^2+22^2-2(7)(22)cos(70)[/tex] and
[tex]d^2=533-308cos(70)[/tex] and
[tex]d^2=533-105.3422041[/tex],
[tex]d^2=427.6577959[/tex]
so the length of the diagonal is
d = 20.68 ft
The length of the shorter base is a little more tedious. First drop an altitude from each of the upper vertices to the base measuring 22 ft. We have 2 smaller right triangles now, each with unknown height (we need to find this), each with unknown base measures (we need to find this, too!), each with a base angle of 70 degrees, and each with a hypotenuse of 7. We need only work with one of these since they are both the same.
We will first find h, the height of each of these right triangles. Using the sin ratio:
[tex]sin(70)=\frac{h}{7}[/tex] and
[tex]7 sin(70)=h[/tex] so
h = 6.577848
Now we can use that along with the hypotenuse measure to find the base measure, b:
[tex]7^2-6.577848^2=b^2[/tex],
[tex]b^2=5.731911137[/tex] so
b = 2.394141002
Because we have 2 identical small right triangles with base measures of 2.394141002 each, we can subtract 2(2.394141002) from 22 to get the measure of the shorter base, which I will call x:
22 - 2(2.394141002) = x so
x = 17.21 ft
A man steps out of a plane at a height of 4,000m above the ground falls 2,000m very quickly and then opens his parachute and slowly falls the remaining 2000m to the ground what height above the ground would be the best Choice for a reference point
Answer:
Step-by-step explanation:
A man steps out of a plane at 4,000m of height above the ground.The point at which he jumps out of the plane would make a good reference point. However, if his acceleration is going to change as a result of him opening his parachute 2000m above the ground, a good reference point would be there. Keep in mind though, that his velocity at that instant would need to be known for it to be useful- otherwise the airplane reference point would be just as good with appropriate modeling....
Answer:4000m easy !!
Geometry:
The vertices of triangle ABC are A(0,9), B(-9,-9), C(9,-9) Find the scale factor if the image of ABC has vertices A'(3,10),B'(-1,2),C'(7,2)
Answer:
4/9
Step-by-step explanation:
The easiest segment to work with is BC, since the y-values are the same for coordinates B and C and for B' and C'.
The length of BC = 9 -(-9) = 18.
The length of B'C' = 7 -(-1) = 8.
The scale factor is B'C'/BC = 8/18 = 4/9.
Six pairs of data yield r = 0.444 and the regression equation y = 5x + 2. also, y = 18.3. what is the best predicted value of y for x = 5?
The best predicted value of y for x = 5 is 27.
Explanation:A regression equation is a mathematical model that represents the relationship between a dependent variable and one or more independent variables. It expresses the linear or nonlinear association between these variables and is derived from statistical methods like linear regression analysis.
To predict the value of y for x = 5 using the regression equation, you can substitute x = 5 into the equation y = 5x + 2:
y = 5(5) + 2 = 27
Therefore, the predicted value of y for x = 5 is 27.
The best predicted value of [tex]\( y \) for \( x = 5 \) is \( y = 27 \).[/tex]
To find the best predicted value of [tex]\( y \) for \( x = 5 \),[/tex]we substitute [tex]\( x = 5 \)[/tex] into the regression equation:
[tex]\[ y = 5x + 2 \] \[ y = 5(5) + 2 \] \[ y = 25 + 2 \] \[ y = 27 \][/tex]
To reconcile this discrepancy, if we assume that the provided value of [tex]\( y = 18.3 \)[/tex] corresponds to [tex]\( x = 5 \),[/tex] then we would set the regression equation equal to 18.3 and solve for \( x \):
[tex]\[ 18.3 = 5x + 2 \] \[ 16.3 = 5x \] \[ x = \frac{16.3}{5} \] \[ x = 3.26 \][/tex]
Anthony is saving for a Xbox one he currently has the $165 saved and earned $40 per week doing chores around the house if an Xbox cost 500+10% sales tax how long will it take for him to save that amount
Answer:
10 weeks
Step-by-step explanation:
Let w represent the number of weeks Anthony will be saving. Then he wants ...
165 + 40w = 500 +0.10×500
40w = 385 . . . . . subtract 165 and simplify
w = 9.625 . . . . . . divide by 40
It will take Anthony 9.625 ≈ 10 weeks to save that amount.
Danny is installing a fence around his rectangular yard. His yard is 20 feet long by 45 feet wide. If the fencing he picked out costs 25$ per foot, how much money will Danny spend on the fence?
Find the perimeter of the yard ( the distance around the yard).
A rectangle has two sides of each dimension.
The perimeter is 20 + 20 + 45 + 45 = 130 feet.
Now multiply the total feet by the cost per foot:
130 feet x 25 per foot = $3,250 total.
Danny needs to spend on his yard $3250 to fencing.
What is a rectangle?The rectangle is a geometrical figure in which opposite sides are equal.
The angle between any two consecutive sides will be 90 degrees.
Area of rectangle = length × width.
Perimeter of rectangle = 2( length + width).
Length of fence = Perimeter of his yard(rectangle)
Perimeter of rectangle = 2( length + width).
Perimeter of fence =2 ( 20 + 45 )
The perimeter of fence =130 foot.
Now
Cost = $25 per foot
So,
Cost of 130 feet at the rate of $25 per foot
⇒ 130 × 25 = $3250
Hence, Danny needs to spend on his yard $3250 to fencing.
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Wei has $150.00 to make a garland using 60-cent balloons. He wants to purchase 100 blue balloons and some number of white balloons. He learns that the white balloons are on sale for half price. He writes and solves an equation to find the number of white balloons he can purchase. Which models can be used to solve the problem? ; ; ; ;
Answer:
0.60b + 0.30w = 150; 60 + 0.30w = 150
Step-by-step explanation:
Answer:
C. 0.60b + 0.30w = 150; 60 + 0.30w = 150
Step-by-step explanation:
If a cone-shaped water cup holds 23 cubic inches and has a radius of 1 inch, what is the height of the cup? Use 3.14 to for pi. Round your answer to the nearest hundredth. 6.76 inches 18.56 inches 21.97 inches 23.00 inches
Answer:
21.97 in
Step-by-step explanation:
Use the formula for the volume of a cone, fill in the given information, and solve for the height.
V = (1/3)πr²h
23 in³ = (1/3)(3.14)(1 in)²h . . . . . . . . with given numbers
3·23 in³/(3.14 in²) = h ≈ 21.97 in . . . . . divide by the coefficient of h
Answer:
21.97 inches
Step-by-step explanation:
If a cone-shaped water cup holds 23 cubic inches and has a radius of 1 inch, the height of the cup is 21.97 inches.
Round your answer to the nearest hundredth.
What would be the steps for finding the equation for the function f(x) based on the graph (the blue line) and what would the equation be? Please include steps that are universal to finding the equation of any possible graphed function, as I really don't even know where to begin and would like to be able to solve problems like this on my own one day. Thanks! :)
Answer:
f(x) = -2|x-2| +4
Step-by-step explanation:
Step 1: recognize this as an inverted, scaled, and translated absolute value function.
Step 2: identify the scale factor as 2, because each section has a "rise" of 2 for each "run" of 1. The scale factor is -2 because the function is inverted (reflected across the x-axis).
Step 3: identify the vertex* as (2, 4).
Step 4: Use the scale factor and translation information to make the transformation ... (let abs(x) represent the absolute value function)
f(x) = (scale factor)×abs(x -horizontal shift) + (vertical shift)
f(x) = -2|x -2| +4
_____
* The vertex is an identifiable point on the graph of this function. Knowing how the vertex is translated tells you how the whole function is translated. In general, you want to use an identifiable point (a turning point, point of symmetry, extreme point, whatever) when you're trying to determine the translation. For some functions, like a line, there is no specific identifiable point, so determining any specific translation is difficult or impossible.
_____
Comment on writing functions from graphs
One of the reasons for studying different functions is so you can learn to recognize their shape, and associate a formula and certain properties with that shape.
_____
The attached graph shows the parent absolute value function in blue and the transformed function f(x) in red.
A curve passes through the point ????0, 5???? and has the property that the slope of the curve at every point P is twice the y-coordinate of P. What is the equation of the curve?
Answer:[tex]y=2x^2[/tex]
Step-by-step explanation:
Given Curve passes through [tex]\left ( 0,5\right )[/tex]
Also the slope of the curve at every point p is twice the Y-coordinate of p
Let the coordinate of p be[tex] \left ( x,y\right )[/tex]
Therefore
[tex]\frac{\mathrm{d} y}{\mathrm{d} x}=2y[/tex]
[tex]\frac{dy}{y}=2dx[/tex]
Integrating both sides
[tex]\int \frac{dy}{y}=\int 2dx[/tex]
[tex]\ln y=2x+c[/tex]
Substituting values
[tex]\ln 5=c[/tex]
[tex]\ln \frac{y}{5}=2x[/tex]
[tex]y=2x^2[/tex]
Ten of 16 students in Nyack's class are girls. His teacher selected two helpers by randomly drawing names. He drew a boys name first and then a girls names. Nyack thinks that the probability of this happening is 15/64. Is he correct? If not, Explain his error.
[tex]|\Omega|=16\cdot15=240\\|A|=6\cdot10=60\\\\P(A)=\dfrac{60}{240}=\dfrac{1}{4}[/tex]
He's wrong.
How to find the surface area of a regular pyramid?
Step-by-step explanation:
[tex]l \times w + l \sqrt{( \frac{w}{2}) ^{2} + {h}^{2} } + w \times \sqrt{( \frac{l}{2} )^{2} + {h}^{2} } [/tex]
L = length base
w = width base
h = height
Answer:
[tex]S=\dfrac{ns^2}{4}\left(\cot{\left(\dfrac{180^{\circ}}{n}\right)}+\sqrt{3}\right)[/tex]
Step-by-step explanation:
A "regular pyramid" is a pyramid whose base is a regular polygon and whose edges are all the same length. Thus each face is an equilateral triangle.
A hexagonal regular pyramid will look like a hexagonal pancake, as the vertical height of it will be zero. A regular pyramid with 7 or more faces cannot exist, because the apexes of the triangular faces cannot meet at a point.
__
For an edge length of "s", the area of each triangular face is (√3)/4×s². There are n of those faces, so the lateral area (LA) will be ...
LA = ns²(√3)/4
The area of the regular polygon base will be the product of half its perimeter and the length of its apothem (a). The apothem is ...
a = (s/2)cot(180°/n)
So, the area of the base (BA) is ...
BA = (1/2)(ns)(s/2)cot(180°/n) = ns²cot(180°/n)/4
The total surface area of the regular pyramid is then ...
S = BA + LA
S = (ns²/4)(cot(180°/n) +√3) . . . . for edge length s and n faces (3≤n≤5)
Please help show that the following are TRUE.
Answer:
see below
Step-by-step explanation:
The formula for the sum of an infinite geometric series with first term a1 and common ratio r (where |r| < 1) is ...
sum = a1/(1 -r)
Applying this to the given series, we get ...
a. sum = 5/(1 -3/4) = 5/(1/4) = 20
b. sum = d/(1 -1/t) = d/((t-1)/t) = dt/(t-1)
_____
The derivation of the above formula is in most texts on sequences and series. In general, you write an expression for the difference of the sum (S) and the product r·S. You find all terms of the series cancel except the first and last, and the last goes to zero in the limit, because r^∞ → 0 for |r| < 1. Hence you get ...
S -rS = a1
S = a1/(1 -r)
Julio uses 3/4 cups of honey to make a batch of granola bars. Julio used 7 1/2 cusp of honey when he made some granola bars yesterday.
Write an equation that models this situation, using x to represent the number of batches of granola bars julio made.
How many batches of gronola bars did julio make?
Please Show work
Answer:
[tex]8\frac{2}{8}[/tex]
Step-by-step explanation:
x = number of granola bars
[tex]\frac{3}{4} + 7\frac{1}{2} = \frac{6}{8} + 7\frac{4}{8} = 7\frac{10}{8} = 8\frac{2}{8}[/tex] = x[/tex]
Solve the equation
A piece of thread is 52,000 nanometers thick. How many meters thick is the
thread? Write your answer in standard form.
1 nanometer = 1.0 x 10 meters
Answer:
0.000052
1 nanometer = .000000001 meters
.000000001 x 52000 = 0.000052
To convert 52,000 nanometers to meters, divide by the conversion factor of 1,000,000,000 nanometers per meter, resulting in a thickness of 5.2 x 10-8 meters in standard form.
To convert the thickness of a piece of thread from nanometers to meters, we need to use the conversion factor that 1 meter equals 1,000,000,000 nanometers, or 1 m = 109 nm.
Using this conversion factor, we can set up the following calculation:
Thickness in meters = Thickness in nanometers \/ Conversion factor
Thickness in meters = 52,000 nm \/ (109 nm/m)
Thickness in meters = 52,000 nm \/ 1,000,000,000 nm/m
Thickness in meters = 0.000000052 m or 5.2 x 10-8 meters when expressed in standard form.
The terminal side of θ passes through the point (−5,−6). What is the exact value of cosθ in simplified form?
5√61/61
−5√61/61
−6√61/61
6√61/61
Answer:
proof my answer is correct
Step-by-step explanation:
The exact value of cosθ in simplified form is -5√61 / 61.
What is Trigonometry?One area of mathematics known as trigonometry examines the relationship between the sides and angles of a right triangle. The relationship between sides and angles is defined for 6 trigonometric functions.
We have,
The terminal side of θ passes through the point (−5,−6).
Now, Hypotenuse
= √(-5)² + (-6)²
= √25+36
=√61
Using Trigonometry
cos θ = Adjacent side/ Hypotenuse
cos θ = -5/ √61
Now, rationalizing
cos θ = -5/√61 x √61/√61
cos θ = -5√61 / 61
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For 20 Points.
============
Answer:
D) 33
Step-by-step explanation:
The sum of the lengths of the segments is equal to the overall length:
(3x -5) + 8 = 4x -7
10 = x . . . . . . . . . . . . add 7-3x to both sides
Then the overall length is ...
MO = 4·10 -7 = 33
Answer:
Step-by-step explanation:
(3x -5) + 8 = 4x -7
10 = x what you wnat to do is add 7-3x to both sides
= 4·10 -7 = 33
and that should be your answer 33
Match the vocabulary word to its correct definition.
Answer:
1 -> f
2 -> e
3 -> d
4 -> a
5 -> c
6 -> g
7 -> b
Step-by-step explanation:
Let consider the options as a,b,c,d,e,f,g
1. Bell curve -> f
2. Data set -> e
3. Histogram -> d
4. Mean -> a
5. Normal distribution -> c
6. Standard deviation -> g
7. Variance -> b
The task is to match vocabulary words to their definitions, a common task in an English class. It involves comparing words with definitions and identifying matches. This helps students understand new words.
Explanation:Given that the task at hand is to match vocabulary words to their correct definitions, this is a task typically found in an English class. This activity involves comparing a list of words with a list of definitions, then identifying which definition corresponds to each word. For example, the word 'gratify' can be matched with the definition 'give (someone) pleasure or satisfaction'. This process helps students better understand and remember the meanings of new words.
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Please help on these questions about Slopes on Graphs !!!!
Answer:
a) {C, D}, {B, E}, A . . . . four possible equivalent answers (explanation below)
b) Line C shows a "directly proportional" relationship
Step-by-step explanation:
Slope is the ratio of "rise" (vertical change) to "run" (horizontal change). Positive changes are "up" and "right".
Line A -- has no vertical change, so its slope is 0.
Line B -- changes 1 unit vertically for each 4 units horizontally, so its slope is 1/4.
Line C -- changes 1 unit vertically for each 2 units horizontally, so its slope is 1/2.
Line D -- changes 1 unit vertically for each 2 units horizontally, so its slope is 1/2. This is the same slope as line C, so neither is greater than the other.
Line E -- changes 1 unit vertically for each 4 units horizontally, so its slope is 1/4. This is the same slope as line B, so neither is greater than the other.
If we use alphabetical order to rank equal slopes, then the slopes (greatest to least) are ...
C (1/2), D (1/2), B (1/4), E (1/4), A (0)
_____
A "directly proportional" relationship graphs as a straight line through the origin. The only line passing through the point where the x- and y-axes meet is line C.
Line C represents a proportional function.
Consider the system of linear equations. 5x+10y=15 10x+3y=13 To use the linear combination method and addition to eliminate the x-terms, by which number should the first equation be multiplied?
A- -2
B- -1/2
C- 1/2
D- 2
Answer:
A: -2
Step-by-step explanation:
You want some factor k such that k(5x) +(10x) = 0. That is, 5k+10 = 0. The solution to this is k=-2, corresponding to selection A.
k = -2 for sure
I normally multiply 5x+10y=15 by -2 to cancel out the x's.
This is because you can only solve the problem if one of your variables is canceled out and then you solve!
Write the point-slope form of the line satisfying the given conditions. Then use the point-slope form of the equation to write the slope-intercept form of the equation. Slopeequals6, passing through (negative 2,5)
[tex]\bf (\stackrel{x_1}{-2}~,~\stackrel{y_1}{5})~\hspace{10em} slope = m\implies 6 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-5=6[x-(-2)]\implies y-5=6(x+2) \\\\\\ y-5=6x+12\implies y=6x+17\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
NEED HELP QUICK!!!!Charmaine is riding her bike. The distance she travels varies directly with the number of revolutions (turns) her wheels make. See the graph below.
(a) How many revolutions does Charmaine make per foot of distance traveled?
(b) What is the slope of the graph?
Answer:
Step-by-step explanation:
Circumference of the wheel = (pi)d = 45*3.14 = 141.3 inches
----
Distance traveled in inches: 5*141.3 = 706.5 inches
---
Distance traveled in feet: 706.5/12 = 58.875 feet
Matilda sits on her back porch for one hour every morning for a week and record the types and numbers of birds that viste her bird feeder what kind of study is this ?
Observational study.
------APEX
Answer:
d.Step-by-step explanation:
The choices for this question are
a. Double-blind study
b. Experiment
c. Sample survey
d. Observational study
The right answer would be d. Observational study, because this type of study is defined as an empirical and non-experimental research where all information is obtained by observation. When we apply this study, we try to find a cause-effect relation by observing the phenomenon as it naturally happens, that is, without interfering with the course of events like experimental investigations do.
So, in this case, Matilda is just observing, without altering anything that could influence the birds. She just sits observe and recover information, that's an observational study.
Therefore, the right answer is d.
Suppose you just received a shipment of six televisions. Three of the televisions are defective. If two televisions are randomly selected, compute the probability that both televisions work. What is the probability at least one of the two televisions does not work?
Answer:
.6094
Step-by-step explanation:
Vineet solved a system of equations by substitution. In his work, he substituted an expression for one of the variables and solved for the value of the other. This resulted in the equation 7 = 9. What can Vineet conclude?
He can conclude that the system of equations has no solution since one equation in it always results with false equivalency.
Hope this helps.
r3t40
He can conclude that the system of equations is inconsistent, i.e. it has no solution.
Step-by-step explanation:We know that we get a no solution when we get a expression which is always false.
Here,
Vineet solved a system of equations by substitution.
In his work, he substituted an expression for one of the variables and solved for the value of the other.
This resulted in the equation 7 = 9.
which is a false identity.
since 7 can never be equal to 9.
Hence, the system of equations is inconsistent , it has no solution.
I’m confused. Please help?
Step-by-step explanation:
[tex] f(x) = \log_a x [/tex]
[tex] \dfrac{f(x + h) - f(x)}{h} = [/tex]
[tex] = \dfrac{log_a(x + h) - \log_a x}{h} [/tex]
[tex] = \dfrac{log_a \dfrac{x + h}{x}}{h} [/tex]
[tex] = \dfrac{1}{h}log_a ( 1 + \dfrac{h}{x} ) [/tex]
[tex] = log_a ( 1 + \dfrac{h}{x} )^{\frac{1}{h}} [/tex]
Its in the picture below
a: 1% decay
b: 10% decay
c: 9% growth
d: 90% growth
Answer:
b: 10% decay
Step-by-step explanation:
Expressed as a percentage change, the growth is usually the value of the base of the exponential function after 1 has been subtracted. That result is expressed as a percent:
0.9 - 1 = -0.10 = -10% . . . . . 10% decay
_____
The "t/12" exponent means this is the decay that is experienced over 12 units of time. This might be the annual decay, where t is expressed in months, for example.
Wave Corporation began the current year with a retained earnings balance of $25,000. During the year, the company corrected an error made in the prior year, which was a failure to record depreciation expense of $5,000 on equipment. Also, during the current year, the company earned net income of $15,000 and declared cash dividends of $5,000. Compute the year-end retained earnings balance.
Answer:
$30,000.
Step-by-step explanation:
Wave Corporation began the current year with a retained earnings balance of $25,000.
Depreciation expense was of $5000
During the current year, the company earned net income of $15,000
Also gave cash dividends of $5,000.
So, year end retained earnings will be :
Year end retained balance = total net income minus net losses and dividends.
[tex]25000-5000+15000-5000=30000[/tex] dollars
The answer is $30,000.
The driver of a car traveling at 60 ft/sec suddenly applies the brakes. The position of the car is s(t) = 60t − 1.5t2, t seconds after the driver applies the brakes. How many seconds after the driver applies the brakes does the car come to a stop?
Answer:
20 seconds
Step-by-step explanation:
Given:
Position of car = s(t) = 60t-1.5t^2
The speed is the change in position.
So,
[tex]Speed\ of\ car=\frac{ds}{dt} = \frac{d}{dt} (60t) -\frac{d}{dt} (1.5t^2)\\=60-2t(1.5)\\=60-3t[/tex]
When the car will stop, the speed will be zero.
[tex]60-3t=0\\3t=60\\t = \frac{60}{3}\\ t=20[/tex]
Therefore, the car will stop after 20 seconds of applying the break ..
Kathy distributes jelly beans among her friends. Alia gets 4^2 fewer jelly beans than Kelly, who gets 3^3 jelly beans. How many jelly beans does Alia get? A. 4^2 ? 3^3 B. 3^3 + 4^2 C. 4 ? 3^3 D. 3^3 ? 4^2 E. 3^2 ? 4^3
"Alia gets 4^2 fewer than Kelly, who gets 3^3."
So it's about a subtraction.
[tex]\boxed{3^3-4^2}[/tex]
Hope this helps.
r3t40
Answer:
D. 3^3 - 4^2
Step-by-step explanation:
4^2 fewer than 3^3 is ...
3^3 - 4^2 . . . . . matches choice D
It's going to be Lindsay's birthday soon, and her friends Martin, Sylvia, Tad, and Yvonne have contributed equal amounts of money to buy her a present. They have $25.00 to spend between them. Determine how much each contributed.
Aaron reads 9 books from the library each month for p months in a row. Write an expression to show how many books Aaron read in all. Then, find the number of books Aaron read if he read for 6 months.
Answer: 1) Each friend had contributed $6.25.
2)The expression to show how many books Aaron read in p months :
[tex]y=9p[/tex]
He reads 54 books in 6 months.
Step-by-step explanation:
1) Given : The total number of friends who contributed equal amounts of money to buy a present. : 4
The total amount they have = $25
Since all the friends contributed the same amount.
Thus , the amount each had contributed :
[tex]=\dfrac{\text{Amount collected}}{\text{Number of friends}}\\\\=\dfrac{25}{4}=6.25[/tex]
Hence, each friend had contributed $6.25.
2) Given : The number of books Aron reads each month = 9 books
Let the number of months be 'p'.
Then the expression to show how many books Aaron read in p months .
[tex]y=9p[/tex]
Then , the number of books Aaron read if he read for 6 months.
[tex]y=9(6)=54[/tex]
Hence, he reads 54 books in 6 months.