Answers
Answer:
x=28
Step-by-step explanation:
We can use similar triangles and proportions to solve this problem. Put the side of the small triangle over the same side of the larger triangle.
x 42
---------- = ----------
x+10 42+15
Simplify
x 42
---------- = ----------
x+10 57
Using cross products
57x = 42 (x+10)
Distribute
57x = 42x+420
Subtract 42x from each side
57x-42x = 42x-42x +420
15x = 420
Divide each side by 15
15x/15 = 420/15
x=28
Answer: The value of x is 28 units.
Step-by-step explanation:
Since we have given that
DC ║ PA
So, By Basic Proportionate theorem, if a line drawn parallel to the third side and intersect the other two sides, then the other two sides are divided into same ratio.
So, it becomes,
[tex]\frac{RC}{CA}=\frac{RD}{DP}\\\\\frac{x}{10}=\frac{42}{15}\\\\15\times x=10\times 42\\\\x=\frac{420}{15}=28\\\\x=28[/tex]
Hence, the value of x is 28 units.
Related Questions
Which equivalent expression will be generated by applying the Distributive Property and combining like terms in the expression 11 + 4(x + 2y + 4)?
Answers
= 11 + 4x + 8y + 16 ..........distributive property
= 4x + 8y + 27 .................combine like terms
PLZ HELP!! 20 points!
Is (3,-2) the solution to this system of equations? show how you determined your answer.
-2x-4y=2
3x+4y=8
Answers
Let's plug it into the first equation first:
-2(3) - 4(-2) might = 2
-6 + 8 = 2
The first equation is true.
Now, we need to check the second equation:
3(3) + 4(-2) might =8
9 - 8 does not = 8
Therefore, even if the point satisfies one equation, it does not satisfy the other. We can conclude that this is not a solution.
Hope this helps!
Find the solution of the differential equation that satisfies the given initial condition. du/dt = (2t+sec^2t)/2u, u(0) = -3
Answers
Two cones have a radius of 2 cm. The height of one cone is 8 cm. The other cone is 14 that height. Which of these statements is NOT true?
Answers
Two cones have a radius of 2 cm. The height of one cone is 8 cm. The other cone is 1/4 that height. Which of these statements is NOT true?
the statements in the attached figure
we know that
r=2 cm
h1=8 cm
h2=(1/4)*8=2 cm
[Volume of cone 1]=(π*r²*h)/3--------> (π*2²*8)/3= 33.49 cm³
[Volume of cone 2]=(π*r²*h)/3--------> (π*2²*2)/3---------> 8π/3= 8.37 cm³
Statements A)
The volume of the smaller cone is (1/4)(1/3π • 2 • 2 • 8) cm3---------> is true
Statements B)
The volume of the smaller cone is (1/3)(4π • 2) cm3.-----------> is true
Statements C)
The volume of the smaller cone is (8/3)π cm3. -----------> is true
Statements D)
The volume of the smaller cone cannot be determined because its height is unknown-----------> is not true
the answer is the Statements D)
The volume of the smaller cone cannot be determined because its height is unknown-----------> is not true
A carpenter builds a rectangular bookcase that is 37 inches long and 60 inches tall. the carpenter uses two braces along the diagonals to support the bookcase. what is the length of the one of the braces, to the nearest tenth of a inch?
Answers
The diagonal of the rectangle can be calculated by using the Pythagorean Theorem , because the diagonal and the two sides , length and width, of the rectangle , makes a right triangle .
Now we have the measure of length and width and we have to find the measure of diagonal
So according to the Pythagorean theorem
[tex] d^2 = a^2 +b^2 [/tex]
where , d is the diagonal , a is the length and b is the width
lets plug the values
[tex] d^2 = 37^2 +60^2 [/tex]
[tex] d^2 = 1369+3600 [/tex]
[tex] d^2 = 4969 [/tex]
Taking square root on both sides
d=70.49 Inches
d=70.5 inches
hence the length of one of the braces is 70.5 inches
A hiker maintains an average speed of 3 3 /4 km/h. How many kilometers will the hiker walk in 3/5 h
Answers
Answer:
2 1/4
Step-by-step explanation:
3 3/4 times 3/5= 15/4 times 3/5=45/20=9/4=2 1/4
I did this because speed times time equals distance and we are finding distance
HOPE THIS HELPS!!!!! :)
The distance walked in 3/5 hours is 2(1/4) km.
What is speed?Speed is the ratio of distance and time.
It shows how fast an object is moving at a given time.
We have,
Average speed = 3(3/4) km per hour
This can be written as,
3(3/4) km = 1 hour
15/4 km = 1 hour
15/4 km = 1 hour
Multiply 3/5 on both sides.
3/5 x 15/4 km = 3/5 hours
9/4 km = 3/5 hours
2(1/4) km = 3/5 hours
Thus,
2(1/4) km is walk in 3/5 hours.
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Find the number of positive integers not exceeding 1000 that are either the square or the cube of an integer
Answers
There are 31 perfect squares between 1 and 1000 (squares from 1-31)
Out of these, 3 perfect squares are also perfect cubes,
{1^2=1^3, 8^2=4^3, 27^2=9^3}.
By the law of inclusion/exclusion, the number of positive integers not exceeding 1000 that are either the square or the cube of an integer
=10+31-3
=38
We want to find the number of positive integers not exceeding 1000 that are either the square or the cube of an integer.
We will get that there are 38 of these.
First, the squares:
To get the number of square numbers not exceeding 1000, we need to find the largest integer that when squared is equal or smaller than 1000.
This is given by:
√1000 = 31.6
Then the largest square number smaller than 1000 is given by:
31^2 = 961
From this, we can conclude that there are 31 integers not exceeding 100 that are the square of an integer.
For the cubes we do the same thing:
∛1000 = 10
The largest cube number that meets the condition is:
10^3 = 1000
Then there are 10 cube numbers that meet the condition.
Now we need to find the common numbers in bot groups (this is, numbers that are a cube and a square of two integers and that are smaller than 1000).
The numbers that meet this condition are:
1)
1^2 = 1
1^3 = 1
64)
4^3 = 64
8^2 = 64
81)
9^3 = 279
27^2 = 729
These 3 numbers are in both groups, so we are counting them twice, thus we need to subtract 3 to the final result, in order to avoid counting the same number two times.
Then the total number of positive integers not exceeding 1000 that are either the square or the cube of an integer is:
31 + 10 - 3 = 38
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Solve using the arrow way
430-230?
Answers
430 --( -200 )---> 230 --( -30 )---> 200
Therefore, the solution of the mathematical operation 430-230, using the arrow way, is: 200
What is the approximate volume of the cylinder with a height of 5 and a diameter of 4? round to the nearest tenths place
Answers
V=πr²h
Here height, h= 5 units
Diameter, d= 4 units
So, radius, r= d/2 = 4/2 =2 units
Put values in formula.
V= (3.14)(2)²(5)
V=62.8 Cubic units
Answer: 62.8 cubic units
What is the circumference of circle p? Express your answer in terms of pi , ab = 14
Answers
Answer:
14 pi in.
Step-by-step explanation:
hop this helps!
Martha is standing on a street corner in a big city, facing south. She walks 5 blocks to the south. Then, she turns right and walks 3 blocks. Then, she turns right as walks 2 blocks. Then, she turns right again and walks 1 block. Finally, she turns left and walks 5 blocks. What direction is she facing when she is done?
Answers
In the north direction, Martha facing if the Martha is standing on a street corner in a big city, facing south.
What is direction?The four cardinal directions, sometimes known as cardinal points, are the four principal compass directions: north, east, south, and west, which are frequently abbreviated as N, E, S, and W.
We have:
Martha is standing on a street corner in a big city, facing south. She walks 5 blocks to the south.
Then, she turns right and walks 3 blocks. Then, she turns right as walks 2 blocks. Then, she turns right again and walks 1 block.
If we draw a line diagram, we will see:
She will be facing at North.
Thus, in the north direction Martha facing if the Martha is standing on a street corner in a big city, facing south.
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HELP SUPER FAST PLS A rectangular cardboard has dimensions as shown. The length of the cardboard can be found by dividing its area by its width. What is the length of the cardboard in inches?
Rectangle with width labeled on the right, width equals 4 and 1 over 2 inches. Below the rectangle, it says, length equals question mark. Inside the rectangle, it says area equals 36 and 3 over 4 square inches
Answers
then they gave you mixed fractions
they want you to practice converting mixed fractions into improper fractions and dividing them
rmember, improper fractions are a/b where a>b sometimes
and also remember that [tex]\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{ad}{bc}[/tex]
okie dokie
width
4 and 1/2=width
4+1/2=width
8/2+1/2=width
9/2=width
area=36 and 3/4
area=36+3/4
area=144/4+3/4
area=147/4
so area/width=length
[tex]\frac{\frac{147}{4}}{\frac{9}{2}}=length[/tex]
[tex]\frac{(147)(2)}{(4)(9)}=length[/tex]
[tex]\frac{294}{36}=length[/tex]
[tex]\frac{49}{6}=length[/tex]
[tex]\frac{48}{6}+\frac{1}{6}=length[/tex]
[tex]8+\frac{1}{6}=length[/tex]
so the length is [tex] 8 \space\ and \space\ \frac{1}{6} \space\ in[/tex]
Answer:
8 1/6
Step-by-step explanation:
hope it helps
What does the random variable for a binomial experiment of n trials measure?the random variable measures the number of successes out of n trials.the random variable measures the number of failures out of n trials. the random variable measures the standard deviation of n trials.the random variable measures the mean of n trials?
Answers
A binomial random variable is defined as the number of successes x in n repeated trials of a binomial experiment. It is more feasible to measure the number of successes than the number of failures because the more successes you have, the nearer you are to your desired goal in a binomial experiment.
Answer:
The random variable measures the number of successes out of n trials.
James Callahan has available a 10% alcohol solution and a 60% alcohol solution. Find how many liters of each solution he should mix to make 50 liters of a 40% alcohol solution?
Answers
x-------------> liters of 10% alcohol solution
y-------------> liters of 60% alcohol solution
we know that
x+y=50----------------------> x=50-y-----------------> equation 1
0.10x+0.60y=0.40*50----------> 0.10x+0.60y=20---------> equation 2
substitute 1 in 2
0.10*(50-y)+0.60y=20---------> 5-0.10y+0.60y=20
5+0.50y=20------------> 0.50y=15-----------------> y=30
x+y=50----------> x=50-30---------> x=20
the answer is
20 liters of 10% alcohol solution
30 liters of 60% alcohol solution
Hayden is a manager at a landscaping company. He has two workers to landscape an entire park, Cody and Kaitlyn. Cody can complete the project in 8 hours. Kaitlyn can complete the project in 6 hours. Hayden wants to know how long it will take them to complete the project together.
Write an equation and solve for the time it takes Cody and Kaitlyn to complete the project together. Explain each step.
Answers
Explanation:
1) The basis to solve this kind of problems is that the speed of working together is equal to the sum of the individual speeds.
This is: speed of doing the project together = speed of Cody working alone + speed of Kaitlyin working alone.
2) Speed of Cody
Cody can complete the project in 8 hours => 1 project / 8 h
3) Speed of Kaitlyn
Kaitlyn can complete the project in 6 houres => 1 project / 6 h
4) Speed working together:
1 / 8 + 1 / 6 = [6 + 8] / (6*8 = 14 / 48 = 7 / 24
7/24 is the velocity or working together meaning that they can complete 7 projects in 24 hours.
Then, the time to complete the entire project is the inverse: 24 hours / 7 projects ≈ 3.4 hours / project.Meaning 3.4 hours to complete the project.
Denote all work that should be done as 1. Then if Cody can complete the project in 8 hours, he can do [tex] \frac{1}{8} [/tex] per hour and if Kaitlyn can complete the project in 6 hours, then she can do [tex] \frac{1}{6} [/tex] per hour. Together they complete [tex] \frac{1}{8}+\frac{1}{6} [/tex] per hour.
Simplify this expression:
[tex] \dfrac{1}{8} +\dfrac{1}{6} =\dfrac{3}{24} +\dfrac{4}{24}=\dfrac{7}{24} [/tex].
Then it will take them to complete the project together [tex] \dfrac{1}{\frac{7}{24}} =\dfrac{24}{7} =3\dfrac{3}{7} [/tex] hours
Answer: It will take them to complete the project together [tex] 3\dfrac{3}{7} [/tex] hours.
Let x be a random variable that takes integer values and is symmetric, that is, p(x = k) = p(x = âk) for all integers k. what is the expected value of y = cos(xÏ) and y = sin(xÏ)?
Answers
[tex]\cos(-kx)=\cos kx[/tex]
[tex]\sin(-kx)=-\sin kx[/tex]
If [tex]Y=\cos(\pi X)[/tex], then
[tex]\mathbb E[Y]=\displaystyle\sum_{k\in\mathbb Z}\cos(k\pi)\,\mathbb P(X=k)[/tex]
By the symmetry of [tex]X[/tex],
[tex]\mathbb E[Y]=\mathbb P(X=0)+2\displaystyle\sum_{k\ge1}\cos(k\pi)\,\mathbb P(X=k)[/tex]
Splitting on the even and odd [tex]k[/tex], and using the fact that [tex]\cos(k\pi)=(-1)^k[/tex] for [tex]k\in\mathbb Z[/tex], we can write this as
[tex]\mathbb E[Y]=\mathbb P(X=0)+2\displaystyle\sum_{\ell\ge1}\bigg(\mathbb P(X=2\ell)-\mathbb P(X=2\ell-1)\bigg)[/tex]
but without knowing how [tex]X[/tex] is distributed, we can't go any further as far as I'm aware.
For [tex]Y=\sin(\pi X)[/tex], we would have
[tex]\mathbb E[Y]=\mathbb E[\sin(\pi X)]=\displaystyle\sum_{k\in\mathbb Z}\sin(k\pi)\,\mathbb P(X=k)[/tex]
but [tex]\sin(k\pi)=0[/tex] for all integers [tex]k[/tex]. Thus [tex]\mathbb E[\sin(X\pi)]=0[/tex].
The expected value of y = cos(xÏ) is 0 and the expected value of y = sin(xÏ) is also 0, due to the symmetry of the random variable x.
Explanation:The expected value (mean) of y = cos(x Ï) is 0.
The expected value (mean) of y = sin(x Ï) is also 0.
Since the random variable x is symmetric, the probability of both positive and negative values cancel out, resulting in an expected value of 0 for both cosine and sine functions.
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A city council consists of six democrats and five republicans. If a committee of seven people is selected, find the probability of selecting four Democrats and three republicans.
Answers
d=number of Democrats selected
D=total number of Democrats = 6
r=number of Republicans
R=total number of Republicans =5
Then
[tex]P(d,r)=\frac{C(D,d)C(R,r)}{C(D+R,d+r)}[/tex]
where
[tex]C(n,r)=\frac{n!}{(n!(n-r)!)}[/tex] = combination of r items selected from n,
D+R=total number of members = 6+5 =11
d+r=number of members selected = 7
[tex]P(d,r)=\frac{C(D,d)C(R,r)}{C(D+R,d+r)}[/tex]
[tex]P(4,3)=\frac{C(6,4)C(5,3)}{C(6+5,4+3)}[/tex]
[tex]=\frac{C(6,4)C(5,3)}{C(11,7)}[/tex]
[tex]=\frac{15*10}{330}[/tex]
[tex]=\frac{5}{11}[/tex]
Answer: the probability of selecting 4 Democrats and 3 Republicans is 5/11
kenny wants to buy gifts for all 18 of his co workers. He can buy t shirts for $10 and hats for $12. He plans on spending $200 for all 18 gifts. If Kenny wants to spend all of his money, how many of each type of gift can he buy?
Answers
10X12=120 8X10=80 12+80=200
If one of the 99 test subjects is randomly selected, what is the probability of getting a subject who is pregnant?
Answers
To calculate the probability of selecting a pregnant subject from the 99 test subjects, the exact number of pregnant subjects in the group is needed. Without this data, the probability cannot be determined.
Explanation:To ascertain the probability of randomly selecting a pregnant subject from a group of 99 test subjects, additional information is required regarding how many subjects are actually pregnant within the group. Without this information, we cannot compute an exact probability.
However, if we had data—let's say 15 out of the 99 subjects are pregnant—the probability would then be calculated using the formula for probability, which is the number of favorable outcomes divided by the total number of possible outcomes. In this scenario, the probability would then be 15/99.
Final answer:
Without specific information on the number of pregnant subjects among the 99 test subjects, it's impossible to compute the exact probability of randomly selecting a pregnant subject.
Explanation:
To answer the question about the probability of randomly selecting a pregnant subject from the 99 test subjects, we would need to know the number of pregnant subjects within the group. Without that information, we cannot calculate the exact probability. However, if we had that information, the probability (P) of selecting a pregnant subject would be calculated as P = (Number of Pregnant Subjects) / (Total Number of Subjects), which in this case is 99.
This is an example of a probability question that falls under the broader subject of mathematics, specifically within the topic of probability and statistics commonly covered at the high school level.
Emily measures 3 pieces of string. The first piece measures 642 cm. The second piece measures 124 cm, and the third piece is 134 cm. How many meters of string does she have altogether? (hint: 1 meter equals 100 centimeters)
Answers
Jose and Sue are playing a board game. If they land on a red or blue square, they lose 1 point. The inequality statement compares the magnitude of their scores at the end of the game. |−2|<|−5| What does the inequality statement show?
Answers
The inequality statement |−2|<|−5| shows that 2 is less than 5.
Explanation:In mathematics, an inequality compares two expressions or values, indicating their relative size. Symbols such as < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to) represent inequalities.
The inequality statement |−2|<|−5| compares the magnitude of two numbers, -2 and -5. To find the absolute value of a number, we remove the negative sign. So, |−2| is equal to 2 and |−5| is equal to 5. Therefore, the inequality statement |−2|<|−5| means that 2 is less than 5.
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x y
0 -3
2 5
3 9
4 13
Which equation matches the table?
A) y = x - 3
B) y = x + 3
C) y = 4x - 3
D) y = 4x + 3
Answers
A) y=x-3
x=0→y=0-3→y=-3=-3 ok
x=2→y=2-3→y=-1 different to 5 No
B) y=x+3
x=0→y=0+3→y=3 different to -3 No
C) y=4x-3
x=0→y=4(0)-3=0-3→y=-3=-3 ok
x=2→y=4(2)-3=8-3→y=5=5 ok
x=3→y=4(3)-3=12-3→y=9=9 ok
x=4→y=4(4)-3=16-3→y=13=13 ok
D) y=4x+3
x=0→y=4(0)+3=0+3→y=3 different to -3 No
Answer: Option C) y=4x-3
One positive integer is 6 less than twice another. The sum of their squares is 468. Find the integer
Answers
The two integers are 12 and 18.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, one positive integer is 6 less than twice another.
Let positive integer be x and the other positive integer is 2x-6
x²+(2x-6)²=468
x²+4x²-24x+36=468
5x²-24x+36-468=0
5x²-60x+36x-432=0
5x(x-12)+36(x-12)=0
(x-12)(5x+36)=0
(x-12)=0
x=12
So, 2x-6=18
Therefore, the two integers are 12 and 18.
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Please help me with questions 8 and 9
Answers
Answer: Choice A
Coordinates have been multiplied by a scale factor of 0.5
For instance
A = (-3, 4)
Multiply the coordinates by 0.5 to get
-3*0.5 = -1.5
4*0.5 = 2
So the coordinates of A' are (-1.5, 2) which is what matches what we're given above. The same will happen with B and C as well.
-----------------------------------------------------------
Problem 9
Answer: choice C) x = 25; larger angle is 107 degrees
Work Shown:
(3x+32)+(x+48) = 180
4x+80 = 180
4x = 100
x = 25
If x = 25, then,
3x+32 = 3*25+32 = 107
x+48 = 25+48 = 73
So the larger angle is 107
108+621 is the same as 100+ what
Answers
Francisca purchased 425 shares of Kellogg Company stock at $14.15 apiece. She earns $374.00 in dividends every year. What is the yield on Francisca's Kellogg Company stock?
Answers
This is found by dividing the dividend per share by the cost per share. Since she earned $374 on 425 shares, her dividend per share is 374/425=$0.88. Divide this by the cost per share:
0.88/14.15= 0.06219 ≈ 6.22%.
Melinda has a map of her city the map uses a scale of 1 inch equals 8 miles when does house is 1 1/2 inches from the library on the map how far apart with her house in the library be on the map if the scale is 1 inch equals 6 miles
Answers
So, the house is 12 miles away from the library because 1 1/2*8 is 12. Now, Just divide 12 by the new rate, 6, to get 2. Your answer is 2 boxes away.
Hope this helped!
Quadrilateral ABCD is inscribed in this circle.
What is the measure of ∠A ?
Enter your answer in the box.
Answers
Given that angle C is 43 degrees
180 = 43 + A
subtract 43 from both sides
137 = A
Hope this helps!
Applying the inscribed quadrilateral conjecture, the measure of m∠A = 137°.
What is the Inscribed Quadrilateral Conjecture?The inscribed quadrilateral conjecture states that the opposite angles in any inscribed quadrilateral in a circle measures up to 180 degrees.
Thus:
43° + m∠A = 180°
m∠A = 180 - 43
m∠A = 137°
Thus, applying the inscribed quadrilateral conjecture, the measure of m∠A = 137°.
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if possible find the area of the triangle defined by the following: a=32, b=24, y=75°
Answers
To answer further, we use the sine function to do the calculation.
The area is given by
Area = absin(y)/2 = 32*24*sin(75)/2 = 370.92 to two decimal places.
Find the difference (7a-6b+7) - (8a-2)
Answers
Let's set up our expression:
(7a-6b+7)-(8a-2)
In order to simplify, we can use that subtraction sign and distribute it, using the distributive property. We have:
7a-6b+7-8a+2
Notice how it's plus two, because a negative times a negative two is a positive two. Now, it's a matter of finding the like terms and adding or subtracting them. These like terms can either have no variable, or have different coefficients but the same variable. That means our like terms are the 7a and -8a, and the 7 and 2. There's no like term for the 6b. That means we have:
(7a-8a) - 6b + (7+2) =
-a - 6b + 9
Hope this helps!