In the image below ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯∥⎯⎯⎯⎯⎯⎯⎯⎯⎯LM¯∥OP¯. Given the lines are parallel, ∠≅∠∠LMN≅∠PON because and that ∠≅∠∠LNM≅∠ONP by the , you can conclude the triangles are similar by the AA Similarity Theorem. If NP = 20, MN = x+ 6, NO = 15, and LN = 2x - 3 then x = .
Answers
Given:
Required:
We need to answer the questions
Explanation:
Angle LMN and angle PON are the congruent because both are alternate angles
Now angle LNM and angle ONP are also congruent because those two triamgles are similar and both are internal angles
Now to find the value of x
[tex]\begin{gathered} \frac{NP}{MN}=\frac{NO}{LN} \\ \\ \frac{20}{x+6}=\frac{15}{2x-3} \\ \\ 40x-60=15x+90 \\ 25x=150 \\ x=6 \end{gathered}[/tex]Final answer:
x=6
Related Questions
5. A ball is thrown from a platform. The equation h = -4.9t2 + 18t + 14 gives the ball's height, h, in meters in terms of time, t, in seconds. Part A: What was the initial velocity of the ball? Part B: From what height was the ball thrown? Part C: If we measure the height in feet, how would the function change? What would be the gravity coefficient?
Answers
We have the following:
[tex]h=-4.9t^2+18t+14[/tex]now,
This equation is divided as follows:
The quadratic part (-4.9t ^ 2) that represents the acceleration (gravity coefficient), the linear part (18t) that represents the velocity and the constant part (14) that is the initial height, therefore
Part A:
The initial velocity is 18 meters per seconds, the number that accompanies the linear term
Part B:
The initial height corresponds to 14 meters
Part C:
the equivalence between meters and feet is as follows
1 meter = 3.28 feet
Therefore the change of the function would be
[tex]\begin{gathered} h=3.28\cdot(-4.9t^2+18t+14) \\ h=-16.072t^2+59.04+45.92 \end{gathered}[/tex]The gravity coefficiente is -16.072 feet per square seconds
Find the value of x, if m<3 is 13x-13 and m<4 is 8x+67.2 points43Your answer
Answers
Answer
x = 6
Explanation:
m<3 and m<4 are supplementary angles
supplementarrh angles is 180 degrees
m<3 + m<4 = 180
13x - 13 + 8x + 67 = 180
collect the like terms
13x + 8x - 13 + 67 = 180
21x + 54= 180
Isolate 21x
21x = 180 - 54
21x = 126
divide both sides by 21
21x/21 = 126/21
x = 6.
Therefore, x = 6
i need the x and y intercept
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so, the x intercept is when the line touches the x-axis, we can see from the graph, the line touches x-axis on 3, so the point is
[tex](3,0)[/tex]the y intercept is when the lone touches the y-axis, we can see from the graph, the line touches y-axis on -9, so the point is
[tex](0,-9)[/tex]Find two numbers whose sum is 256, but whose product is a maximum?
Answers
ANSWER
The two numbers are 128 and 128
EXPLANATION
Let the two numbers be x and y.
We have that:
[tex]\begin{gathered} x+y=256 \\ x\cdot y=A \end{gathered}[/tex]where A is a maximum.
From the first equation:
[tex]x=256-y[/tex]Substitute that into the second equation:
[tex]\begin{gathered} (256-y)\cdot y=A \\ \Rightarrow256y-y^2=A \\ \Rightarrow y^2-256y+A=0 \end{gathered}[/tex]The equation above is a quadratic equation in the general form:
[tex]ax^2+bx+c=0[/tex]The parabola is downward facing and so, its vertex will be the maximum.
We can find the vertex (x, y) of the parabola by using:
[tex]x=\frac{-b}{2a}[/tex]In the case given, the vertex can be found by using:
[tex]\begin{gathered} y=\frac{-(-256)}{2(1)}=\frac{256}{2} \\ y=128 \end{gathered}[/tex]Recall that:
[tex]x=256-y[/tex]Therefore, we have that:
[tex]\begin{gathered} x=256-128 \\ x=128 \end{gathered}[/tex]Hence, the two numbers are 128 and 128.
Two ships were 700 miles apart at midnight and were headed directly towards each other if they collided at 10 a:m find the speeds of both ships if one was traveling 30 miles faster than the other
Answers
Given:
Two ships were 700 miles apart at midnight .
Let x be the speed of first ship and (x+30) be speed of second ship (faster ship).
The equation is,
[tex]\begin{gathered} Dis\tan ce=rate\times time \\ 10x+10(x+30)=700 \\ 10x+10x+300=700 \\ 20x=700-300 \\ 20x=400 \\ x=\frac{400}{20} \\ x=20 \end{gathered}[/tex]Answer: the speed of first ship ( slower) is 20 miles and the speed of second ship ( faster) is 20+30=50 miles.
If trapezoid ABCD was dilated by a scale factor of 2\3 to form trapezoid A'B'C'D,what is the area of trapezoid ABCD?The area of trapezoid A'B'C'D is 12 units^2
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As a general rule, we know that the area of a dilated figure is the area of the original figure multiplied by the square of the scale factor. We can see this in the following formula:
[tex]A=A^{\prime}\cdot k^2[/tex]where A is the area of the original figure, A' is the area of the dilated figure and k is the scale factor.
In this case, we have that the area of the dilated figure (trapezoid A'B'C') is 12 square units, and the scale factor is k = 2/3. Then, using the equation we get the following:
[tex]\begin{gathered} A^{\prime}=12 \\ k=\frac{2}{3} \\ \Rightarrow A=12\cdot(\frac{2}{3})^2=12\cdot(\frac{4}{9})=\frac{12\cdot4}{9}=\frac{48}{9}=5\frac{1}{3} \\ A=5\frac{1}{3}u^2 \end{gathered}[/tex]therefore, the area of trapezoid ABCD is 5 1/3 square units
evaluate each using the values given y+y-(y-x); use x = 1, and y = 4Options12154
Answers
The given expression is
y + y - (y - x)
We would substitute x = 1 and y = 4 into the expression. it becomes
4 + 4 - (4 - 1)
8 - 3
= 5
the correct answer is 5
Find the intersection if possibleExpress your answer in interval notation
Answers
Solution:
The first set given as;
[tex][-9,-1)[/tex]Then in list form, the set is;
[tex]\lbrace-9,-8,-7,-6,-5,-4,-3,-2\rbrace[/tex][tex]\lbrace-9,-8,-7,-6,-5,-4,-3,-2\rbrace[/tex]Also, the second set given as;
[tex](-3,4)[/tex]Then, in list form, the set is;
[tex]\lbrace-2,-1,0,1,2,3\rbrace[/tex]The intersection of the two sets is;
[tex]\begin{gathered} \lbrace-9,-8,-7,-6,-5,-4,-3,-2\rbrace\cap\lbrace-2,-1,0,1,2,3\rbrace=\lbrace-2\rbrace \\ \\ \text{ Note that there are some real numbers on the number line} \end{gathered}[/tex]Thus, the solution in interval notation is;
[tex](-3,-1)[/tex]ANSWER: (-3,-1)
For the function f(x) = x2 + 2x - 15 solve the following.f(x) = 0
Answers
Given:
[tex]f\mleft(x\mright)=x^2+2x-15[/tex]To find: The value of x when
[tex]f(x)=0[/tex]Explanation:
Since,
[tex]f(x)=0[/tex]We can write it as,
[tex]\begin{gathered} x^2+2x-15=0 \\ x^2+5x-3x-15=0 \\ x(x^{}+5)-3(x-5)=0 \\ (x+5)(x-3)=0 \\ x=-5,3 \end{gathered}[/tex]Hence, the solution is x = -5, and 3.
Final answer: The solution is,
[tex]\mleft\lbrace-5,3\mright\rbrace[/tex]Suppose you are measuring a moving box to see if it has enough room in it. The moving box is a cube, and the length of one side is 2 ft. long. What is the volume of the box?
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Solution:
Suppose you are measuring a moving box to see if it has enough room in it.
The moving box is a cube.
Given that the length of one side is 2 ft. long, i.e.
[tex]l=2\text{ ft}[/tex]To find the volume of a cube, the formula is
[tex]V=l^3[/tex]Substitute for l into the formula above
[tex]\begin{gathered} V=l^3=2^3=8\text{ ft}^3 \\ V=8\text{ ft}^3 \end{gathered}[/tex]Hence, the volume of the box is 8 ft³
Arithmetic and Geometric Sequences (Context)
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The formula for compound interest
A = P( 1 + r/n) ^ (nt)
A is the amount in the account at the end
P is the principal balance or the amount initially invested
r is the annual interest rate in decimal form
n is the number of times it is coupounded per year
t is the number of years
A = 1800 ( 1+ .0375/1) ^ (1*6)
A = 1800 ( 1.0375)^6
A = 2244.92138
Rounding to the nearest cent
A = 2244.92
Just need help with number 3. Please. Thankyou! Been stuck on this one for a while now.
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A cosine function is given in the form:
[tex]y=A\cos(x-h)+k[/tex]where |A| is the amplitude, h is the horizontal shift (also called a phase shift) and k is the vertical shift.
The function is given to be:
[tex]\begin{gathered} y=8\cos(\frac{1}{4}x) \\ A=8 \end{gathered}[/tex]Therefore, the amplitude is 8.
4.A pet store sells cats for $50 and dogs for $100. If one day it sells a total of 4pets and makes $300, find out how many cats and dogs it sold by writing asystem of equations and graphing to solve it.Representations:Equations:
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Answer:
2 cats and 2 dogs
Explanation:
Representations:
x = number of cats sold
y = number of dogs sold
Equations:
We know that it sells a total of 4 pets, so the sum of the number of cats and dogs is 4. So:
x + y = 4
On the other hand, they make $300, and they make $50 for each cat and $100 for each dog, so:
$50x + $100y = $300
So, the system of equation is:
x + y = 4
50x + 100y = 300
Graph:
Now, we need to graph the equations, so we need to identify two points for each equation:
For x + y = 4
If x = 0, then:
0 + y = 4
y = 4
If x = 4, then:
4 + y = 4
4 + y - 4 = 4 - 4
y = 0
For 50x + 100y = 300
If x = 0, then:
50(0) + 100y = 300
100y = 300
100y/100 = 300/100
y = 3
If x = 4, then:
50(4) + 100y = 300
200 + 100y = 300
200 + 100y - 200 = 300 - 200
100y = 100
100y/100 = 100/100
y = 1
Therefore, we have the points (0, 4) and (4, 0) to graph the line of the first equation and the points (0, 3) and (4, 1) to graph the line of the second equation.
So, the graph of the system is:
Therefore, the solution is the intersection point (2, 2), so they sold 2 cats and 2 dogs that day.
solve the equation 3.75x+3.7=1.7+1.75xA 10 B -1 C 1D .1
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The question is given to be:
[tex]3.75x+3.7=1.7+1.75x[/tex]Step 1
Multiply every number by 100:
[tex]\begin{gathered} 3.75x\cdot100+3.7\cdot100=1.7\cdot100+1.75x\cdot100 \\ 375x+370=170+175x \end{gathered}[/tex]Step 2
Subtract 370 from both sides:
[tex]\begin{gathered} 375x+370-370=170+175x-370 \\ 375x=175x-200 \end{gathered}[/tex]Step 3
Subtract 175x from both sides:
[tex]\begin{gathered} 375x-175x=175x-200-175x \\ 200x=-200 \end{gathered}[/tex]Step 4
Divide both sides by 200:
[tex]\begin{gathered} \frac{200x}{200}=-\frac{200}{200} \\ x=-1 \end{gathered}[/tex]ANSWER
The correct option is OPTION B, the SECOND OPTION.
unit 4: solving quadratic equations
Homework 9: quadratic equations applications
Help please !
Answers
Answer:
what is the Question
Step-by-step explanation:
math is ezy :3
I need help on this problem, it’s from my act prep guide
Answers
Answer:
Recall that:
[tex]\begin{gathered} \log _bx+\log _by=\log _b(xy), \\ \log _bx-\log _by=\log _b(\frac{x}{y})\text{.} \end{gathered}[/tex]Therefore, Arjun used the properties incorrectly, he should´ve written:
[tex]\log _7x+\log _7y-\log _7z=\log _7(xy)-\log _7z=\log _y(\frac{xy}{z})\text{.}[/tex]We want to factor the following expression: x^3 - 25 which pattern can we use to factor the expression? U and V are either constant integers or single variable expression.
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The pattern that is used to factor the expression x³ - 25 is given as follows:
B. (U - V)(U + V).
What is the subtraction of perfect squares?The subtraction of perfect squares is a notable product that gives the simplification of an expression containing the subtraction of perfect squares, as the multiplication of the square roots of the two terms subtracted by the square of the two terms subtracted, as follows.
a² - b² = (a - b)(a + b).
In the context of this problem, the expression is presented as follows:
x³ - 25.
The square root of x³ is obtained as follows:
sqrt(x³) = (x³)^(0.5) = x^(3 x 0.5) = x^1.5 = [tex]\sqrt{x^3}[/tex]
The square root of 25 is obtained as follows:
5.
Because 5² = 25.
Then, applying the subtraction of perfect squares notable product, the factored expression is given as follows:
[tex]x^3 - 25 = (\sqrt{x^3} - 5)(\sqrt{x^3} + 5)[/tex]
Which is the pattern given by option B.
Missing InformationThe complete problem is given by the image shown at the end of the answer.
A similar problem, also featuring subtraction of perfect squares, is presented at https://brainly.com/question/28792378
#SPJ1
Can someone please help me find the valu of X?
Answers
Answer:
x = 10
Explanation:
Because the transverse lines are parralell, the following must be true
[tex]\frac{x+8}{x+2}=\frac{3}{2}[/tex]cross multipication gives
[tex]\begin{gathered} 2(x+8)=3(x+2) \\ \end{gathered}[/tex]which simplifies to give
[tex]\begin{gathered} 2x+16=3x+6 \\ \end{gathered}[/tex]subtracting 2x from both sides gives
[tex]16=x+6[/tex]subtracting 6 from both sides gives
[tex]10=x[/tex]Hence the value of x is 10.
Jonathan finds some nickels and quarters in his change purse. How many coins does he have if he has 12 nickels and 4 quarters? How many coins does he have if he has xx nickels and yy quarters?Total coins, 12 nickels and 4 quarters: Total coins, xx nickels and yy quarters:
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Each nickel is worth 5 cents, and each quarter is worth 25 cents.
So, if we have 12 nickels, we can multiply this value by 5 to get its value in cents:
[tex]12\cdot5=60[/tex]Similarly, if we have 4 quarters, we can multiply this value by 25 to get its value in cents:
[tex]4\cdot25=100[/tex]So, in total, we have:
[tex]60+100=160[/tex]So, for 12 nickels and 4 quarter, we have the value of 160 cents.
We can do this generally by setting the values of nickel and quarter to x and y.
If we have x nickels and each one is worth 5 cents, we have the value:
[tex]5x[/tex]And if we have y quarters and each is worth 25 cents, we have the value:
[tex]25y[/tex]So, in total, we have:
[tex]5x+25y[/tex]So, for x nickels and y quarter, we have the value of 5x + 25y cents.
A board game uses a spinner like one below, where 0, 1, 2, and 3 are all equally likely.Each turn, a player spins twice and subtracts the results of the spins. The game only looks at non-negativedifferences. For example, if a player spins a 1 and a 3, the difference is 2.Let X represent the difference in given turn.Which tables represents the theoretical probability distribution of X?Choose 1 answer:
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The possible outcomes are:
0: 1-1, 2-2, 3-3, 4-4 => 4
1: |2-1|, |3-2|, |4-3|, |1-2|, |2-3|, |3-4| => 6
2: |3-1|, |4-2|, |1-3|, |2-4| => 4
3: |4-1|, |1-4| => 2
The total number of outcomes is 4+6+4+2 = 16. Then, the table that represents the theoretical distribution is:
Answer:
It should be B, the one that has 0,1,2,3 on the top.
Step-by-step explanation:
right on khan
Morgan wants to order at least $45 worth of merchandise, so she will get free shipping. If Morgan has picked out a key chain for $8 and a bag for $19, which inequality represents the amount of money, m, she needs to spend to get free shipping?
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Morgan wants to order at least $45 worth of merchandise.
She spent $8 and $19. m represents the amount of money she needs to spend to get free shipping. The inequality is:
8 + 19 + m ≥ 45
m ≥ 45 - 8 - 19
m ≥ 18
57 es 95% de que número
Answers
60
1) Considerando que 57 es 95% de algun numero, vamos escribir esta ecuacion
0.95x = 57 Escribindo 95% como 0.95, dividir los dos lados por 0.95
x =57/0.95
x=60
2) Asi 57 es 95% de 60.
I’m sorry to keep bothering you guys but you’re the third person that I’m trying the last two their answers went partway and then stopped I just need to see how this is worked out
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01
Data:
Graph:
Height of Golf Ball
Step 02:
functions:
We must analyze the graph to find the solution.
Function:
Non linear
intercepts:
x-intercepts: 0 and 120
y-intercept: 0
symmetry:
x = 50
positive:
domain: (0 , 120)
negative:
there are no negative values
increasing:
interval on x: (0 , 50)
decreasing:
interval on x: (50, 120)
That is the full solution.
6x - 5y = - 4Direct variationХ5?k=Not direct variation2y = 14xDirect variationk ==Not direct variation
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Direct Variation is of the form (directly proportional);
[tex]\begin{gathered} y\propto x \\ y=kx \end{gathered}[/tex]While indirect variation (inversely proportional) is of the form;
[tex]\begin{gathered} y\propto\frac{1}{x} \\ y=\frac{k}{x} \end{gathered}[/tex]So, for each of the given question we want to determine if they are direct or indirect variation;
1.
[tex]\begin{gathered} 6x-5y=-4 \\ -5y=-4-6x \\ -5y=-6x-4 \\ y=\frac{-6x-4}{-5} \\ y=\frac{6}{5}x+\frac{4}{5} \end{gathered}[/tex]Therefore, this is a Direct variation with proportionality constant;
[tex]k=\frac{6}{5}[/tex]2.
[tex]\begin{gathered} 2y=14x \\ y=\frac{14x}{2} \\ y=7x \end{gathered}[/tex]Therefore, this is a Direct variation with proportionality constant;
[tex]k=7[/tex]2.Solve the inequality for x. Show each step to the solution.12x > 3(5x – 2) – 15
Answers
we have the inequality
12x > 3(5x-2)-15
step 1
apply distributive property right side
12x > 15x-6-15
combine like terms right side
12x > 15x-21
step 2
Adds both sides 21
12x+21 > 15x-21+21
simplify
12x+21 > 15x
step 3
subtract 12x both sides
12x+21-12x > 15x-12x
21 > 3x
step 4
Divide by 3 both sides
21/3 > 3x/3
7 > x
Rewrite
x < 7What is the image of (8,−4) after a dilation by a scale factor of 1/4 centered at the origin?
Answers
Answer:
[tex](2, -1)[/tex]
Step-by-step explanation:
When dilating with a scale factor of [tex]k[/tex] about the origin, [tex](x,y) \longrightarrow (kx, ky)[/tex].
You might need: Calculator h(r) = 72 +11r - 26 1) What are the zeros of the function? Write the smaller r first, and the larger r second.
Answers
1) Notice that:
[tex]r^2+11r-26=r^2+13r-2r-2(13).[/tex]Grouping like terms we get:
[tex]\begin{gathered} r^2+13r-2r-2(13)=r(r+13)-2(r+13) \\ =(r-2)(r+13). \end{gathered}[/tex]Therefore:
[tex]h(r)=(r-2)(r+13).[/tex]Then the zeros of h(r) are:
[tex]r=2\text{ and }r=-13.[/tex]2) Notice that:
[tex]\begin{gathered} h(r)=r^2+11r-26=r^2+11r+(\frac{11}{2})^2-(\frac{11}{2})^2-26 \\ =(r+\frac{11}{2})^2-\frac{121}{4}-26=(r+\frac{11}{2})^2-\frac{225}{4}. \end{gathered}[/tex]Therefore the vertex of the given parabola is:
[tex](-\frac{11}{2},-\frac{225}{4}).[/tex]Answer:
1)
[tex]\begin{gathered} smaller\text{ r=-13,} \\ larger\text{ r=2.} \end{gathered}[/tex]2) Vertex:
[tex](-\frac{11}{2},-\frac{225}{4}).[/tex]
Find the value of x that makes A || B.AB5423142 3x10 and 23 = x + 30X=[? ]
Answers
∠2 and ∠3 are alternate interior angles. In order to A II B, the alternate interior angles must be equal.
Then,
[tex]\begin{gathered} \angle2=\operatorname{\angle}3 \\ 3x-10=x+30 \end{gathered}[/tex]To find x, subtract x from both sides of the equation:
[tex]\begin{gathered} 3x-10-x=x+30-x \\ 3x-x-10=x-x+30 \\ 2x-10=30 \end{gathered}[/tex]Now, add 10 to both sides of the equation:
[tex]\begin{gathered} 2x-10+10=30+10 \\ 2x=40 \end{gathered}[/tex]Finally, divide both sides by 2:
[tex]\begin{gathered} \frac{2x}{2}=\frac{40}{2} \\ x=20 \end{gathered}[/tex]Answer: x = 20.
The area of A triangle with base b and height h is given by A 1/2bh. Find the area when b=24 m and h=30
Answers
Given:
Base of a triangle 24m and height = 30m
Required:
Find the area of a triangle.
Explanation:
We have formula for area of triangle
[tex]A=\frac{1}{2}\times b(base)\times height(h)[/tex]Now,
[tex]\begin{gathered} A=\frac{1}{2}\times24\times30 \\ A=360m^2 \end{gathered}[/tex]Answer:
The area of triangle is 360 meter square.
in DEF, DE =29 feet, EF = 26 feet, and DF = 32 feet. Which correctly gives the order of the angle measure from largest to smallest?
Answers
Answer:
Choice A.
Explanation:
The sketch of the triangle is given below
The angle opposite the longest side is the widest.
The longest side is DF; therefore, the angle opposite to it (angle E) is the widest.
The second-longest side is DE; therefore, the angle opposite to it (angle F) is the second widest.
Lastly, the third-longest side is EF; therefore, the angle opposite to it (angle D) is the third widest (or the smallest angle).
Hence, the angle measures when ordered from greatest to smallest are
∠E, ∠F, ∠D
which is given by choice A.