question 5 only. determine the missing side length QP. the triangles are not drawn to scale.
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This is a simple question.
First, we can see both triangles are proportional, it means it has the same relation between its sides even if one is in a large scale and the other on a a small scale.
Now we can identify which side corresponds to which side. Once side AC is the longest one for triangle ABC it means its equivalent for triangle PQR is the side RP, so the equivalent for side AB is side QP. Once we know that we can write the following relation and calculate:
Related Questions
the line that passes through point (-1,4) and point (6,y) has a slope of 5/7. find y.
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Question: the line that passes through the point (-1,4) and point (6,y) has a slope of 5/7. find y.
Solution:
By definition, the slope of a line is given by the formula:
[tex]m\text{ = }\frac{Y2-Y1}{X2-X1}[/tex]where m is the slope of the line and (X1,Y1), (X2,Y2) are any two points on the line. In this case, we have that:
(X1,Y1) = (-1,4)
(X2,Y2) = (6,y)
m = 5/7
thus, replacing the above data into the slope equation, we get:
[tex]\frac{5}{7}\text{= }\frac{y-4}{6+1}\text{ }[/tex]
this is equivalent to:
[tex]\frac{5}{7}\text{= }\frac{y-4}{7}\text{ }[/tex]By cross-multiplication, this is equivalent to:
[tex]\text{5 = y-4}[/tex]solving for y, we get:
[tex]y\text{ = 5+ 4 = 9}[/tex]then, we can conclude that the correct answer is:
[tex]y\text{ =9}[/tex]Laura needs summer blouses. She bought 1 blouseand 2 sweaters. How much did she spend? Did shebuy clothes that matched her summer needs?
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Given:-
Cost of blouse is $27.50
Cost of sweater is $34.99
To find the cost if laura bought :-
So since laura bought one blouse and two sweaters, we get
[tex]27.50+2(34.99)=97.48[/tex]So the cost is $97.48 and she bought the cloths of her summer needs.
A system of equations is shown below:Equation A: 3c = d − 8Equation B: c = 4d + 8Which of the following steps should be performed to eliminate variable d first?Multiply equation A by −4.Multiply equation B by 3.Multiply equation A by 3.Multiply equation B by 4.
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We have the following: system of equations:
A: 3c=d-8
B: c=4d+8
To eliminate variable d first, if we want to use elimination method, we need to have variable d in both equations with the same coefficient but with different signs.
As in equation B, the coefficient of d is 4, then we need to have in equation A a coefficient of -4 for variable d.
Then the answer is we need to multiply equation A by -4.
ranslateSave & Exit CertifyLesson: 10.2 Parabolas11/15Question 9 of 9, Step 1 of 1CorrectFind the equationof the parabola with the following properties. Express your answer in standard form.
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Given
[tex]undefined[/tex]Solution
Standard from of a parabola
[tex](x-H-h)^2=4p(y-k)[/tex]Identify the inverse g(x) of the given relation f(x). f(x)={(8,3),(0,-1),(-4,-3)}
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The function is given as.
f(x)={(8,3),(4,1),(0,-1),(-4,-3) }
The inverse function is determined as a function, which can reverse into another function.
Therefore the inverse function g(x) is obtained as
[tex]g(x)=\lbrace(3,8),(1,4),(-1,0),(-3,-4)\rbrace[/tex]Hence the correct option is D.
Suppose that $6000 is placed in an account that pays 19% interest compounded each year. Assume that no withdrawals are made from the account.
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We are going to use the formula for the compound interest, which is
[tex]A=P\cdot(1+\frac{r}{n})^{nt}[/tex]A = the future value of the investment
P = the principal investment amount (the initial deposit or loan amount)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per unit t
t = the time the money is invested or borrowed for
Replacing the values in the first question we have:
[tex]\begin{gathered} A=P\cdot(1+\frac{r}{n})^{nt} \\ A=6000,r=0.19,n=1,t=1 \\ A=6000\cdot(1+\frac{0.19}{1})^1=7140 \end{gathered}[/tex]Answer for the first question is : $7140
Then, replacing the values in the second question we have:
[tex]\begin{gathered} A=P\cdot(1+\frac{r}{n})^{nt} \\ A=6000,r=0.19,n=1,t=2 \\ A=6000\cdot(1+\frac{0.19}{1})^2=8497 \end{gathered}[/tex]Answer for the second question is : $8497
13(10+2) could be used to simplify which of the following problems?A 013/20)B O13(12)C 0130(26)
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Explanation:
The expression is given below as
Algebra 1B CP find the zeros of the function by factoringexercise 2 please
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2) y = 8x² +2x -15
(4x -5)(2x +3)
S={-3/2, 5/4}
3) y= 4x² +20x +24
(4x +8)(x +3)
S={-2,3}
1) Factoring these quadratic functions we have:
2) y = 8x² +2x -15
Let's call u, and v two factors.
Multiplying 8 by -15 = we have u*v = -120 Adding u + v= 2, so u = 12 and v =-10
12 x -10 = -120
12 +(-10) = 2
So, now we can rewrite it following this formula:
(ax² + ux) +(vx +c)
(8x² +12x) +(-10x-15) Rewriting each binomial in a factored form
4x(2x +3) -5(2x+3)
(4x -5)(2x +3)
Equating each factor to zero to find out the roots:
(4x -5) =0
4x =5
x=5/4
(2x +3) = 0
2x = -3
x= -3/2
Hence, the solution set is S={-3/2, 5/4}
3) y= 4x² +20x +24
Proceeding similarly we have:
u * v = 96
u + v = 20
So u = 12, and v =8 12x 8 = 96 12 +8= 20
Rewriting into (ax²+ux)+(vx +c)
(4x²+12x) +(8x+24) Factoring out each binomial
4x(x+3) +8(x+3) As we have a repetition we can write:
(4x +8)(x +3)
3.2) Now to find out the roots equate each factor to zero, and solve it for x:
4x +8 = 0
4x = -8
x =-2
x+3 =0
x=-3
4) Hence, the answers are:
2) y = 8x² +2x -15
(4x -5)(2x +3)
S={-3/2, 5/4}
3) y= 4x² +20x +24
(4x +8)(x +3)
S={-2,3}
3)A space shuttle achieves orbit at 9:23am. At 9:31am it has traveled an additional 2309.6 miles in orbit. Find the rate of change in miles per minutes.
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Answer: 288.7 miles per minute.
Step-by-step explanation:
Considering:
Distance = Rate / Time
We are given the distance as 2309.6 miles in orbit.
We can calculate the time required to travel 2309.6 miles by doing:
End time - Start time.
In this case it would be 9:31 - 9:23 = 8 minutes.
Therefore it takes 8 minutes to travel 2309.6 miles.
Now we need to find the Rate of Change in miles per minutes.
In other words we need how many miles the shuttle traveled every minute.
Right now we have the shuttle traveled 2309.6 miles in 8 minutes. To find how many traveled in 1 minute, we need to divide.
2309.6 / 8 = 288.7 miles per minute.
find the rate of the discount of a $12 99 novel on sale for $5.50
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In order to find the rate of discount, calculate what is the associated percentage of 5.50 related to 12.99, just as follow:
(5.50/12.99)(100) = 42.34
5.50 is the 42.34% of 12.99.
Hence, the discount was 100% - 42.34% = 57.65%
Find the midpoint M of the line segment joining the points R = (-5. -9) and S = (1. -1).
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Answer:
(-2,-5)
Step-by-step explanation:
(-5+1÷2, -9+(-1)÷2)
=(-4÷2, -10÷2)
=(-2,-5)
What is the average rate of change of the function f(x) = 2x^2 + 4 over the interval (-4,-1] ?
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The average rate of change is:
[tex]\frac{f(-1)-f(-4)}{-1+4}=\frac{f(-1)-f(-4)}{3}[/tex][tex]f(-1)=2(-1^2)+4=6[/tex][tex]f(-4)=2(-4^2)+4=2(16)+4=36[/tex]then computing the first formula, the average rate of change of f(x) is
[tex]\frac{6-36}{3}=-10[/tex]helpppppppppppppppppppppppppppppp
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skill issue hahahahahhaahahhahaha
What are the unknown angles?
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A= 53°
B= 53°
C=127°
Explanation:
To find angle a, it is the same as the 53° angle given because they are corresponding angles. (Same place but on different lines)
To find angle b, we know that it is across from angle a. These types of angles are called alternate interior angles and they are always equal just like corresponding angles. So, therefore, angle b must equal angle a which is 53°.
To find angle c we know that a straight line equals 180°. Subtract the known 53 from 180 to figure out the degree of angle c.
180-53=127
Angle c=127°
You can always check your answer by making sure the line adds up to 180°
b is 53
c is 127
5. Monty compared the minimum of the function f(x) = 2x2 - x + 6 to theminimum of the quadratic function that fits the values in the table below.X-3-2-101g(x)0-5-6-34What is the horizontal distance between the minimums of the twofunctions?A 0.25B. 1C. 1.5D. 12
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The function f is given by:
[tex]\begin{gathered} f(x)=2x^2-x+6 \\ \text{ Rewrite the quadratic function in vertex form} \\ f(x)=2(x^2-\frac{1}{2}x)+6 \\ =2((x-\frac{1}{4})^2-(-\frac{1}{4})^2)+6 \\ =2(x-\frac{1}{4})^2-2(\frac{1}{16})+6 \\ =2(x-\frac{1}{4})^2+\frac{47}{8} \end{gathered}[/tex]If a quadratic function is written in the form:
[tex]\begin{gathered} a(x-h)^2+k \\ where: \\ a>0 \end{gathered}[/tex]Then the function has a minimum point at (h,k)
And the minimum is k
In this case,
[tex]\begin{gathered} a=2\gt0 \\ h=\frac{1}{4}=0.25 \\ k=\frac{47}{8}=5.875 \end{gathered}[/tex]Therefore, the minimum of the function f is at (0.25, 5.875)
The minimum of the function given by the table is at (-1, -6).
Therefore, the required horizontal distance is given by:
[tex]0.25-(-1)=1.25[/tex]Therefore, the horizontal distance is 1.25
A bug is moving along a straight path with velocity v(t)= t^2-6t+8 for t ≥0. Find the total distance traveled by the bug over interval [0,6].
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Answer
Explanation
Given:
A bug is moving along a straight path with velocity
[tex]V(t)=t^2-6t+8\text{ }for\text{ }t>0[/tex]What to find:
The total distance traveled by the bug over interval [0, 6].
Solution:
To find the total distance traveled by the bug over interval [0, 6], you first integrate v(t)= t² - 6t + 8
[tex]\begin{gathered} \int_0^6t^2-6t+8 \\ \\ [\frac{t^3}{3}-\frac{6t^2}{2}+8t]^6_0 \\ \\ (\frac{t^3}{3}-3t^2+8t)^6-(\frac{t^{3}}{3}-3t^2+8t)^0 \\ \\ (\frac{6^3}{3}-3(6)^2+8(6))-(\frac{0^3}{3}-3(0)^2+8(0)) \\ \\ (\frac{216}{3}-3(36)+48)-(0-0+0) \\ \\ 72-108+48-0 \\ \\ =12\text{ }units \end{gathered}[/tex]I really need help with this can somebody help me ?
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Answer
a. Vertical shrink by a factor of 1/3
Step-by-step explanation
Function transformation
• a,f(x) vertically compresses f(x) when 0 < a < 1
Given the function:
[tex]f(x)=x^2[/tex]Multiplying f(x) by a = 1/3, we get:
[tex]\frac{1}{3}f(x)=\frac{1}{3}x^2=h(x)[/tex]Then, f(x) is vertically shrunk by a factor of 1/3
Find the limit. (If an answer does not exist, enter DNE.)
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Given:
[tex]\lim _{\Delta x\to0}\frac{6(x+\Delta x)-6x_{}}{\Delta x}[/tex]Solve as:
[tex]\begin{gathered} \lim _{\Delta x\to0}\frac{6x+6\Delta x-6x}{\Delta x}=\lim _{\Delta x\to0}\frac{6\Delta x}{\Delta x} \\ =6 \end{gathered}[/tex]Hence, the required answer is 6.
help meeeeeeeeee pleaseee !!!!!
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The solution of the composition functions are represented as follows;
(fog)(x) = [tex]\sqrt{-2x+3}[/tex](g o f)(x) = -2√x + 3How to solve composite functions?Composite functions are when the output of one function is used as the input of another.
In other words, a composite function is generally a function that is written inside another function.
Therefore, the composite function can be solved as follows:
f(x) = √x
g(x) = - 2x + 3
Hence,
(fog)(x) = f(g(x)) = [tex]\sqrt{-2x+3}[/tex]
(g o f)(x) = g(f(x)) = - 2√x + 3 = -2√x + 3
Therefore, the composite function expression is as follows:
(fog)(x) = [tex]\sqrt{-2x+3}[/tex](g o f)(x) = -2√x + 3learn more on composite function here: https://brainly.com/question/24464747
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Find the slope and y intercept of the line 5x - 3y =12
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Answer:
slope = 5/3
y-intercept = -4
Step-by-step explanation:
First, move the x to the other side of the equation:
-3y=-5x+12
Then, divide BOTH sides by -3, so that there is no coefficient next to y:
y=5/3x-4
Then, just look at the constant and coefficient next to x (m). The slope is 5/3 and the y-intercept is -4.
Hope this helps!
Answer:
[tex]y = \frac{5}{3}x - 4[/tex]
Step-by-step explanation:
move the 5x to a -5x
-3y= -5x+12
-3/-3= -5x÷ -3 12÷ -3
You are taking 2 shirts(white and red) and 3 pairs of pants (black, blue, and gray) on a trip. How many different choices of outfits do you have?
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csc 0 (sin2 0 + cos2 0 tan 0)=sin 0 + cos 0= 1
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Okay, here we have this:
Considering the provided expression, we are going to prove the identity, so we obtain the following:
[tex]\frac{csc\theta(sin^2\theta+cos^2\theta tan\theta)}{sin\theta+cos\theta}=1[/tex][tex]\frac{\frac{1}{sin\vartheta}(sin^2\theta+cos^2\theta\frac{sin\theta}{cos\theta})}{sin\theta+cos\theta}=1[/tex][tex]\frac{\frac{1}{sin\vartheta}(sin^2\theta+cos\text{ }\theta sin\theta)}{sin\theta+cos\theta}=1[/tex][tex]\frac{(\frac{sin^2\theta}{sin\theta}+\frac{cos\text{ }\theta sin\theta}{sin\theta})}{sin\theta+cos\theta}=1[/tex][tex]\frac{(sin\text{ }\theta+cos\text{ }\theta)}{sin\theta+cos\theta}=1[/tex][tex]\frac{1}{1}=1[/tex][tex]1=1[/tex]what is the slope of a line perpendicular to this linewhat is the slope of a line parallel to this line
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Answer:
• Slope perpendicular to the line: 8/5
,• Slope parallel to the line: –5/8
Explanation
Given
[tex]5x+8y=7[/tex]To know the result, it is better if we work with the slope-intercept form:
[tex]y=mx+b[/tex]Then, to get this kind of form we have to isolate y from the given equation:
[tex]8y=7-5x[/tex][tex]y=\frac{7-5x}{8}[/tex][tex]y=-\frac{5}{8}x+\frac{7}{8}[/tex]Thus, in this case, m = –5/8 and b = 7/8.
Perpendicular lines have negative reciprocal lines:
[tex]m_2=-\frac{1}{m_1}[/tex]where m₁ is the slope of line 1 and m₂ is the line perpendicular to line 1.
Then, replacing the values:
[tex]m_2=-\frac{1}{-\frac{5}{8}}[/tex][tex]m_2=\frac{8}{5}[/tex]Finally, the slopes of parallel lines are the same, meaning:
[tex]m_2=m_1[/tex]where m₁ is the slope of line 1 and m₂ is the line parallel to line 1.
(C3) In how many distinct ways can theletters of the word LILLYPILLY bearranged?A. 3.628.800B. 480C. 7.560D. 120.960.
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We have:
L = 5 L's
I = 2 I's
P = 1 P
Y = 2 Y's
so:
[tex]\frac{10!}{5!2!2!}=7560[/tex]The expression below is scientificnotation for what number? 4.58 • 10^-2
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We are given the number in scientific notation:
[tex]4.58\times10^{-2}[/tex]To convert it to decimal format, we need to move the decimal point two spaces to the left.
Since we don't have enough digits before the decimal point, we add two zeros before the 4:
[tex]004.58\times10^{-2}[/tex]Now we move the point as required:
[tex]004.58\times10^{-2}=0.0458[/tex]The required number is 0.0458
Can anybody help me out with this? I would really appreciate it! I don't need a huge explanation just the answer and a BRIEF explanation on how you got it.
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The range of the following function is
[tex]\mleft\lbrace y>1\mright\rbrace[/tex]We can also call the range of a function an image, the range or image of a function is a set, we can see this set looking at the graph and see which values of y the function have, remember that we can have the same y value for different x value, looking at our graph we can see that this function comes from high y values, have a vertex on (3,1), in other words, it stops at y = 1 and then start growing again, and go on repeated values of y, then we can say that the image (values of y that the function assumes) is all values bigger than 1, therefore {y > 1}.
10. Calculate the circumference of cylinder that is 34cm tall and has a volume of560cm#9
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The Solution.
By formula, the volume of the planet (sphere) is given as below:
[tex]V=\frac{4}{3}\pi r^3[/tex]In this case,
[tex]\begin{gathered} V=5.10^{18}km^3 \\ r=\text{?} \end{gathered}[/tex]Substitting these given values into the formula above, we can solve for r, the radius of the planet.
[tex]\frac{4}{3}\pi r^3=5(10^{18})[/tex]Dividing both sides by
[tex]\frac{4}{3}\pi[/tex]We get
[tex]r^3=\frac{5\times10^{18}}{\frac{4}{3}\pi}=\frac{5\times10^{18}}{4.188790205}[/tex]Taking the cube root of both sides, we have
[tex]\begin{gathered} r=\sqrt[3]{(}\frac{5\times10^{18}}{4.188790205})=(1.060784418\times10^6)km^{} \\ Or \\ r=1060784.418\text{ km} \end{gathered}[/tex]Thus, the correct answer is 1060784.418km.
f (x) = 4x^2+2x+6find the value of the discriminate of f and how many distinct real number zeros f has.
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The Solution:
Given:
Required:
To find the discriminant of f.
By formula, the discriminant (D) is:
[tex]D=b^2-4ac[/tex]Where:
[tex]\begin{gathered} a=4 \\ b=2 \\ c=6 \end{gathered}[/tex]Substitute:
[tex]\begin{gathered} D=2^2-4(4)(6)=4-96=-92 \\ No\text{ real root since D}<0 \end{gathered}[/tex]Therefore, the correct answers are:
Discriminant = -92
No distinct real root.
What is the value of y in the solution set of the system of linear equations shown below?y = -x + 124x - 2y = 36A.10B. 8C. 6D. 2
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y = 2 (option D)
Explanation:y = -x + 12
4x - 2y = 36
rewriting the equations:
y + x = 12 ....equation 1
-2y + 4x = 36 ....equation 2
Using elimination method:
we will be eliminating y. So we need to make the coefficient of y to be the same in both equation. We will be multiplying the first equation by 2.
2y + 2x = 24 ....equation 1
-2y + 4x = 36 ....equation 2
Add both equations:
2y + (-2y) + 2x + 4x = 24 + 36
2y-2y + 6x = 60
6x = 60
x = 60/6 = 10
Insert the value of x in any of the equation. Using equation 2:
4(10) - 2y = 36
40 -2y = 36
-2y = 36 - 40
-2y = -4
y = -4/-2
y = 2 (option D)
Find the volume of the solid. Round your answer to the nearest hundredth. I keep getting the wrong answer. Need help!
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Volume is area * height
area of pentagon is 1/4 * root(5(5 + 2root(5))) a^2
a being length of 1 side
if a =2, area is 6.88
6.88 * 4 = 27.52 yards^3