[tex]\bf \qquad \qquad \textit{joint compound proportional variation} \\\\ \begin{array}{llll} \textit{\underline{y} varies directly with \underline{x}}\\ \textit{and inversely with \underline{z}} \end{array}\implies y=\cfrac{kx}{z}\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \stackrel{\textit{W varies jointly as its width, squared heght and inversely with length}}{W=\cfrac{wh^2}{L}}[/tex]
[tex]\bf \textit{now we also know that }~~ \begin{cases} w=\frac{1}{4}\\ h=\frac{1}{3}\\ L=12\\ W=30 \end{cases}\implies 30=\cfrac{~~k\frac{1}{4}\left( \frac{1}{3} \right)^2~~}{12} \\\\\\ 360=\cfrac{k}{36}\implies 12960=k~\hfill \boxed{W=\cfrac{12960wh^2}{L}}[/tex]
[tex]\bf \textit{when } \begin{cases} w=\frac{1}{4}\\ h=\frac{1}{2}\\ L=12 \end{cases}\textit{ what is \underline{W}?}\qquad W=\cfrac{12960\left( \frac{1}{4} \right)\left(\frac{1}{2} \right)^2}{12} \\\\\\ W=1080\left( \cfrac{1}{4} \right)\left( \cfrac{1}{4} \right)\implies W=1080\cdot \cfrac{1}{16}\implies W=\cfrac{135}{2}\implies W=67\frac{1}{2}[/tex]
Using the joint variation, A similar beam can support [tex]67 \frac{1}{2}[/tex] feet if the beam is one-fourth foot wide and half a foot high, and 12 feet long.
What is Proportion
A proportion is an equation stating that two rational expressions are equal. Simple proportions can be solved by applying the cross products rule.
If [tex]\frac{a}{b} = \frac{c}{d}[/tex] then ab = bc.
What is Direct variation?
The phrase “ y varies directly as x” or “ y is directly proportional to x” means that as x gets bigger, so does y, and as x gets smaller, so does y. That concept can be translated in two ways.
[tex]\frac{y}{x} = k[/tex] for some constant k.
The k is called the constant of proportionality. This translation is used when the constant is the desired result.
What is Inverse Proportion?
According to the expressions "y varies inversely as x" and "y is inversely proportionate to x," y decreases as x increases or vice versa. There are two translations for this idea. For any constant k, referred to as the constant of proportionality, yx = k. If the constant is wanted, use this translation.
What is Joint Variation?
Joint variation is the term used to describe when one variable changes as the sum of other variables. There are two translations for the phrase "y fluctuates concurrently as x and z."
So, In the given question:
Weight that a rectangular beam can support varies jointly as its width and the square of its height and inversely as its length;
It is in joint proportion;
[tex]\begin{aligned}&\mathbf{W}=\frac{\mathbf{w h}^2}{\mathbf{L}} \\&\left\{\begin{array}{l}w=\frac{1}{4} \\h=\frac{1}{3} \\L=12 \\W=30\end{array} \quad \Longrightarrow 30=\frac{\mathbf{k} \frac{1}{4}\left(\frac{1}{3}\right)^2}{12}\right.\end{aligned}[/tex]
[tex]360=\frac{\mathrm{k}}{36} \Longrightarrow 12960=\mathrm{k}[/tex]
Now,
[tex]\text { when }\left\{\begin{array}{l}w=\frac{1}{4} \\h=\frac{1}{2} \\L=12\end{array}\right.[/tex]
[tex]W=\frac{12960\left(\frac{1}{4}\right)\left(\frac{1}{2}\right)^2}{12}[/tex]
[tex]W=1080\left(\frac{1}{4}\right)\left(\frac{1}{4}\right) \\\Longrightarrow W=1080 \cdot \frac{1}{16}[/tex]
[tex]\\\Longrightarrow\mathrm{W}=\frac{135}{2} \\\Longrightarrow \mathrm{W}=67 \frac{1}{2}[/tex]
Hence, A similar beam can support [tex]67 \frac{1}{2}[/tex] feet if the beam is one-fourth foot wide and a half a foot high, and 12 feet long.
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cos(70° )cos(20° )+sin(70° )sin(20° )=cos(___°)?
Answer:
Step-by-step explanation:
Sum and Difference Formula
cos( U +/- V ) = cosU*cosV -/+ sinU*sinV
cos( U - V ) = cos(70)cos(20) + sin(70)sin(20)
cos( U - V ) = cos (70 - 20)
cos( 50 ) = .642788
He uses the slope of 2
Answer:
y = 2x + 3
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = 2
The line passes through the y- axis at (0, 3) ⇒ c = 3
y = 2x + 3 ← equation of line
On a coordinate grid, the coordinates of vertices P and Q for Polygon PQRS are P(1, 2) and Q(−1, 2). What is the length of Side PQ of the polygon?
Answer:
3 units
Step-by-step explanation:
Answer:
I know I am a little late but the answer is 3
Step-by-step explanation:
I took the test part 1
Annika sells 6 inch pies for $5.00 and 8 inch pies for $9.00 each. Last week she sold twice as many 6 inch pies as she did 8 inch pies. She made $133.00 from her sales. Annika defined x as the number of 6 inch pies she sold and y as the number of 8 inch pies she sold. She wrote the system below.
6x+8y=133
2x=y
Jade can buy a maximum of 6 magazines or 2 pies with her $24 weekly budget. The slope of her budget constraint is -2, representing the trade-off between pies and magazines. The opportunity cost of purchasing a pie is 3 magazines.
Jade has a weekly budget of $24, which she allocates between magazines and pies. Let's address the questions one by one:
Magazines: If the price of a magazine is $4 each, Jade can buy 6 magazines in a week since $24 divided by $4 equals 6.Pies: If the price of a pie is $12, Jade can purchase 2 pies in a week, as $24 divided by $12 equals 2.Budget constraint: On a graph with pies on the horizontal axis and magazines on the vertical axis, Jade's budget constraint would be a straight line starting at 6 magazines (if she buys 0 pies) and ending at 2 pies (if she buys 0 magazines). The slope of this budget constraint is -2 (the price of a pie divided by the price of a magazine).Opportunity cost: The opportunity cost of purchasing one pie is the number of magazines she has to give up, which is 3 magazines ($12/$4).help quick pls---
(I'm terrible at math-)
Answer:
n= -0.7
Step-by-step explanation:
so first subtract 1.8 from 3.2 and then divide by -2
-2n = 1.4
n = -0.7
hope this helps!!
The first term of a geometric sequence is 5 and the common ratio is 2 what is the fourth term of the sequence?
A: 40 B: 80 C:250 D:1250
Answer:
the answer is a
Step-by-step explanation:
5*2 is 10
10*2 is 20
20*2 is 40
5,10,20,40
Which measure of central tendency is least appropriate for describing the given data set?
6, 6, 6, 7, 8, 8, 29
mode
median
mean
Answer: Third option is correct.
Step-by-step explanation:
Since we have given that
6, 6, 6, 7, 8, 8, 29
We will calculate the measures of central tendency:
1) Mode - the most occurring element in the data set.
So, Mode = 6
2) Median - the middle value of organised data set
So, Median = 7
3) Mean - the average of all data set
So, Mean = [tex]\dfrac{6+6+6+7+8+8+29}{7}=\dfrac{70}{7}=10[/tex]
So, we can see that Mode and Median are giving the closest value to each other, whereas Mean is giving the farthest value as compared to rest.
Hence, Mean is the least appropriate for describing the given data set.
Thus, Third option is correct.
PLZ HELP 10 POINTS!!!!!!!!!!!
Answer: The answer is D) 126in3
Step-by-step explanation:
When you multiply 42 and 9 you get 378, so from there you divide your answer by 3 which gets you
126in
Explain how direct variation equations and inverse variation equations are different.
Answer:
For direct variation, use the equation y = kx, where k is the constant of proportionality. For inverse variation, use the equation y = k/x, again, with k as the constant of proportionality. These problems might use the word 'proportion' instead of 'variation,' but it means the same thing.
Step-by-step explanation:
Final answer:
Direct and inverse variation equations have distinct relationships between variables: direct variation involves both variables increasing at a constant rate, while inverse variation involves one variable decreasing as the other increases.
Explanation:
Direct variation equations and inverse variation equations are different in their structures and relationships between variables. In direct variation equations, as one variable increases, the other also increases at a constant rate, while in inverse variation equations, as one variable increases, the other decreases at a constant rate.
For example, in a direct variation equation like y = kx, as x increases, y increases at a constant rate determined by k. In contrast, in an inverse variation equation like y = k/x, as x increases, y decreases at a constant rate determined by k.
Simplify the expression using the rules for exponents
[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\bf \cfrac{(a^{-3}b^{-1}c^{-5})^{-2}}{(a^5b^4c^2)^5}\implies \stackrel{\textit{distributing the exponent}}{\cfrac{(a^6b^2c^{10})}{(a^{25}b^{20}c^{10})}}\implies \cfrac{c^{10}c^{-10}}{a^{25}a^{-6}b^{20}b^{-2}} \\\\\\ \cfrac{c^{10-10}}{a^{25-6}b^{20-2}}\implies \cfrac{c^0}{a^{19}b^{18}}\implies \cfrac{1}{a^{19}b^{18}}[/tex]
easy chose a,b,c,d wich ones please help easy
Answer:
A; The integer is 16
B; The integer has an absolute value of 16
D; The integer has an absolute value of 16
Answer:
b and d
Step-by-step explanation:
For a field trip 8 students rode in cars and the rest filled ten buses. How many students were in each bus if 538 students were on the trip?
Answer:
538-8=530
530/10=53
your answer is 53 students
Step-by-step explanation:
The graph of a linear equation contains the points (4,1) and (-2,-11). Which point also lies on the graph?
Answer:
Step-by-step explanation:
Answer: Option B is correct.(1, -5) lies on the graph
Answer:
(1,-5)
Step-by-step explanation:
find the slope (4,1 2/3) (-2,2/3)
formula for slope y2-y1 over x2-x1 so the answer should be -1.1 over -6.3
Based on data set shown which of the following is a true statement? -1, -1, 0, 1, 1, 1, 1, 2, 2, 2, 3. Mean = mode, mean less than median , mode less than median
Answer:
"Mean = Mode"
Step-by-step explanation:
Let's find the mean, median, and mode of the number set.
-1, -1, 0, 1, 1, 1, 1, 2, 2, 2, 3
Mean:
this is the average. We add up all of the numbers and divide by the number of numbers (11).
Mean = [tex]\frac{-1+-1+0+1+1+1+1+2+2+2+3}{11}\\=\frac{11}{11}\\=1[/tex]
the mean is 1
Median:
this is the "middle" number when arranged from least to greatest. From 11 numbers, the 6th number is the middle one. We can see from the arrangement below, that "1" is the middle number.
the median is 1
Mode:
this is the number that occurs the "most". Looking at the numbers, "1" occurs 4 times, which is the most. So
mode is 1
From the 3 choices, the first choice is right "mean = mode".
Working alone, Pablo can put up a tent in 12 minutes. His mom can put it up by herself in 4 minutes. How many minutes would they take to put up the tent working together?
Pablo amd his mom would take Eight minutes
Final answer:
Pablo and his mom would take 3 minutes to put up the tent working together, as they combine their work rates to determine their joint effectiveness.
Explanation:
To determine how many minutes Pablo and his mom would take to put up the tent working together, we can use the concept of combined work rates. Pablo can put up a tent in 12 minutes and his mom can do it in 4 minutes. We calculate their combined work rate by adding the reciprocal of each person's time because working together means their rates add up.
Pablo's rate is 1 tent per 12 minutes, or 1/12 tents per minute. His mom's rate is 1 tent per 4 minutes, or 1/4 tents per minute. Combined, their rate is (1/12) + (1/4) tents per minute.
First, find a common denominator for the fractions, which would be 12 in this case, so we get:
(1/12) + (3/12) = 4/12
Therefore, their combined rate is 4/12 or 1/3 tents per minute. To find out how long it would take them to set up one tent, we take the reciprocal of the combined rate. Thus, 1 tent would take them 1/(1/3) minutes, or simply 3 minutes.
Working together, Pablo and his mom can put up the tent in 3 minutes.
graph x = -2
Kfkdjfjdjdjf
Ifidjfjdjjfjfj
Answer:
This is a vertical line, that passes through x=-2
Step-by-step explanation:
This is a vertical line, x=-2 means that no matter what value has 'y' the variable 'x' will be -2.
Watch the attached picture
Convert the angle 0=133π/72 radians to degrees
The result is 332.5 degrees.
To convert an angle from radians to degrees, we use the conversion factor that 1 radian = 180/π degrees. In this case, the angle is 133π/72 radians.
So, to convert 133π/72 radians to degrees, we multiply by the conversion factor:
(133π/72) * (180/π) degrees.
Solving this gives us the angle in degrees:
133 * 180 / 72 = 332.5 degrees.
Gox2
can I have help on this question plz and if you help me I would be glad to help you too
if you mean 60 × 2 it will be 120
Answer:
12
Step-by-step explanation:
just use google or a calculater or a phone
if f(x)=-2x-4 then f^-1(x)=
Answer:
y = [tex]\frac{x+4}{-2}[/tex] or [tex]\frac{-x}{2}[/tex] -2
Step-by-step explanation:
This question is asking to find the inverse of the equation therefore you will have to interchange x and y
ie : x= -2y-4
THEN solve for y ( perform opposite operation )
x = -2y -4
(take -4 to the other side ) [it will be a +4 ]
x+ 4 = -2y
NOW take -2 to the other side [ you will divide everything on the left by -2]
[tex]\frac{x+4}{-2}[/tex] ( this could be your final answer )
OR
simplify
( NOT complusory)
[tex]\frac{-x}{2} - 2[/tex]
Final answer:
To find the inverse function of f(x) = -2x - 4, switch x and y and solve for the new y to get the inverse function f¹(x) = -0.5x - 2.
Explanation:
The question asks to find the inverse function of f(x) = -2x - 4. To find the inverse, we switch the roles of x and y in the equation and solve for the new y. Here are the steps:
Write the function as y = -2x - 4.
Swap x and y to get x = -2y - 4.
Solve for y to find the inverse function. Add 4 to both sides to get x + 4 = -2y, and then divide by -2 to find y = -0.5x - 2.
Therefore, the inverse function, f⁻¹(x), is y = -0.5x - 2.
What is the slope of the line that passes through
the points (12,-3) and (-36,25)?
The slope is found by the change in Y over the change in X.
Slope = (25 - -3) / (-36 - 12)
Slope = 28 / -48
Simplify:
Slope = -7/12
Solve for s. 2s = 7 + s
Hello, let's solve this step by step.
You're asking, 2s=7+s and to solve for S.
Now first, simplify both sides of the equation.
2s=s+7
Then, subtract s from both sides.
2s−s=s+7−s
Simplify to get 7.
Therefore, S = 7.
Find the GCF of the three terms below
20xy^2+10xy^3+15x^3y^2
and rewrite the expression by factoring out the GCF
ANSWER
[tex]GCF=5x {y}^{2}
[/tex]
[tex]5x {y}^{2} (4+ 2y + 3{x}^2 )[/tex]
EXPLANATION
The given expression is
[tex]20x {y}^{2} + 10x {y}^{3} + 15 {x}^{3} {y}^{2} [/tex]
This can be rewritten as:
[tex] {2}^{2} \times 5x {y}^{2} + 2 \times 5x {y}^{3} + 3 \times 5{x}^{3} {y}^{2} [/tex]
The greatest common factor is the product of the least powers of the factors common to all the terms;
[tex]GCF=5x {y}^{2}
[/tex]
We factor to obtain;
[tex]5x {y}^{2} (4+ 2y + 3{x}^2 )[/tex]
What is the surface area of a cube with side lengths of 1/7
Please help
Answer: 0.122449
Step-by-step explanation:
If one side is 1/7, first convert that into a decimal, which is 0.14286. Than square that 0.14286 x 0.14286= 0.020408. That’s the area of one square. Now multiply that by 6 (the number of sides in a cube) and you get 0.122449.
Can you help me find the surface area?
Formula-
Area of base + Area of lateral faces.
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I will mark you
BRAINLIEST
❤️❤️❤️❤️❤️❤️❤️❤️❤️
Answer:
[tex]\large\boxed{SA=397.5\ in^2}[/tex]
Step-by-step explanation:
The formyla of an area of a triangle:
[tex]A=\dfrac{bh}{2}[/tex]
b - base
h - height
Area of a base:
[tex]B=\dfrac{(15)(13)}{2}=97.5\ in^2[/tex]
Area of one triangle of lateral area:
[tex]L=\dfrac{(15)(10)}{2}=75\ in^2[/tex]
The Surface Area:
[tex]SA=B+4L\to SA=97.5+4(75)=397.5\ in^2[/tex]
on the vent diagram, which region represent the intersection of set a and set b (AnB)
Answer:
Step-by-step explanation:
Section II would be correct
ANSWER
ii
EXPLANATION
The region that represents A intersection B is region ii.
This is the region that contains elements that belongs to A or B or both.
From the Venn Diagram,
[tex]A\cap B = ii[/tex]
The correct choice is A.
Find the area of a circle that has a diameter of 11 inches. Approximate as 3.14. Round your answer to the nearest hundredth
formula for area of circle is
[tex]\pi {r}^{2} [/tex]
the diameter is 2 times the radius.
so if diameter is 11 then radius is 5.5
so then the answer will be 94.985
Which is the vertex of x 2 + 10x = - 17?
Answer:
(-5,-8)
Step-by-step explanation:
Given in the question an equation,
x² + 10x = - 17
x² + 10x + 17 = 0
here a = 1
b = 10
c = 17
Step 1
Find the value of x using the formula
x = -b/2a
x = -10/2
x = -5
Step 2
Find the value of y by plugging x = -5 in the equation above
(-5)² + 10(-5) + 17 = y
25 - 50 + 17 = y
y = -8
vertex (h,k) = (-5,-8)
Plz help me with this
Answer: C) y ≥ 3x - 2; [tex]y\leq \dfrac{1}{2}x+3[/tex]
Step-by-step explanation:
Blue line:
y-intercept (b) = -2
slope (m) is 3 up, 1 right = 3
shading is above
⇒ y ≥ 3x - 2
Yellow line:
y-intercept (b) = 3
slope (m) is 1 up, 2 right = [tex]\dfrac{1}{2}[/tex]
shading is below
[tex]\implies \bold{y\leq \dfrac{1}{2}x+3}[/tex]
The measure of ECD is 35. What is the measure of EOD?
Answer is 70
Angle *2 = 35*2 = 70
The measure of angle EOD, formed by arc ED at the center O, is 70 degrees, given that angle ECD on the same arc is 35 degrees.
let's break down the step-by-step calculation for finding the measure of EOD, given that ECD is 35 degrees:
Recall that for any angle formed by an arc at the center of a circle (EOD in this case), it is twice the measure of the angle formed by the same arc at any point on the circumference (ECD).
Given that ECD is 35 degrees, we will use this information to find the measure of EOD.
Apply the rule that EOD = 2 × ECD.
Substitute the value of ECD into the formula: EOD = 2 × 35.
Calculate the result: EOD = 70 degrees.
Therefore, the measure of EOD, which is the angle made by the arc ED at the center O, is 70 degrees.
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