Answers
Let's find this length first
6√2 is the hypotenuse, then
[tex]\begin{gathered} (6\sqrt{2})^2=6^2+y^2 \\ \\ y^2=(6\sqrt{2})^2-6^2 \\ \\ y^2=36\cdot2-36 \\ \\ y^2=36 \\ \\ y=\sqrt{36}=6 \end{gathered}[/tex]Then we can find x because
[tex]\begin{gathered} x^2=y^2+12^2 \\ \\ x^2=6^2+12^2 \\ \\ x^2=36+144 \\ \\ x^2=180 \\ \\ x=\sqrt{180} \\ \\ x=6\sqrt{5} \end{gathered}[/tex]The length of x is
[tex]x=6\sqrt{5}[/tex]
Related Questions
A 43-inch piece of steel is cut into three pieces so that the second piece is twice as long as the first
piece, and the third piece is three inches more than five times the length of the first piece. Find the
lengths of the pieces.
What is the length of the first piece?
Answers
The length of the first piece is 5 inches when a 43-inch piece of steel is cut into three pieces.
According to the question,
We have the following information:
A 43-inch piece of steel is cut into three pieces so that the second piece is twice as long as the first piece, and the third piece is three inches more than five times the length of the first piece.
Now, let's take the length of the first piece to be x inches (as shown in the figure).
Length of second piece = 2x inches
Length of third piece = (3+5x) inches
Now, we have the following expression for addition:
x + 2x + 3 + 5x = 43
8x+3 = 43
8x = 43-3
8x = 40
x = 40/8
x = 5 inches
Hence, the length of the first piece is 5 inches.
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the output is 9 less than 5 times the input"
Answers
Let the output is y and the input is x, then
output is means y =
9 less than 5 times input means 9 less than 5x
Then
y = 5x - 9
how to calculate 1+2?
Answers
1. What would you do with each problem in order to get it in its simplest properform? Use words to explain the specific details to why you used thatprocess/rule.Number 2 a and b
Answers
Given
[tex]-6y^0\text{ and \lparen-6y\rparen}^0[/tex]The solutions can be seen below.
Explanation
[tex]\begin{gathered} a)\text{ }-6y^0=-6\times y^0=-6\times1=-6 \\ b)\text{ }(-6y)^0=1 \end{gathered}[/tex]In "a," only the y-value is raised to the power of 1 hence, the reason why y^0 became 1 which then multiplies -6 to get -6. However, in "b", the entire expression is raised to the power of zero, which will then give 1 as the answer.
There are 17 girls at a party with 30 guests. What fraction
of the party guests are girls?
Answers
Answer:
17/30
Step-by-step explanation:
There are 17 girls at a party with 30 guests. What fraction of the party guests are girls?
17/30
Alani want to buy a 3366 buycie She reconsidering e payment options. The image shows Option A, which consists of making an initial down payment then smallet. equesized weekly payments. Option consists of making 6 equal payments over a week WE Weekly Bike Payments A-What factors should Alanl take into consideration before deciding between Option A and Option B? B- Communicate Precisely Suppose Alani could modify Option A and still pay off the bike in 5 weeks. Describe the relationship between the down payment and the weekly payments.
Answers
RATIOS/UNIT RATESRead and answer the question.Jessica sold 4 out of 32 boxes of the cookies her Girl Scout troop sold onSaturday. Select ALL the choices that display an equivalent ratio to thenumber of boxes Jessica sold to the total boxes sold.8 to 641:80 11O 21602:15
Answers
HighByte Entertainment sells four types of products: video games, DVDs, CDs, and radios. The numbers sold for 2020 and 2021 are shown in the double bargraph below. Use this graph to answer the questions.
Answers
Solution
Use this graph to answer the questions below:
The numbers sold for 2020 and 2021 are shown in the double bar above
1. The number of radio sold in 2021 = 440
2. Which products sold more in 2021 than in 2020 :
The only products that sold more in 2021 than in 2020 is video games
3. Which products sold the least over the two years
The products that sold the least = DVDS
Divide polynomial and monomial 49c^2 d^2 - 70c^3 d^3 - 35c^2d^4 /7cd^2
Answers
start separating the fraction into smaller fractions
[tex]\frac{49c^2d^2}{7cd^2}-\frac{70c^3d^3}{7cd^2}-\frac{35c^2d^4}{7cd^2}[/tex]then, divide each of the fractions
[tex]7c-10c^2d-5cd^2[/tex]find the area of figure using 3.14 for pi. round your answer to nearest tenth if necessary.
Answers
Given a figure to find the area of the figure.
The given figure is the combination of two triangles and a semi-circle.
Here the radius and the base of the triangle is 10 yd and the height of the triangle is 21 yd. So, the area of the figure is;
[tex]\begin{gathered} A=2\times\frac{1}{2}\times\text{base}\times\text{height}+\frac{\pi r^2}{2} \\ =10\times21+\frac{3.14\times10^2}{2} \\ =210+\frac{314}{2} \\ =210+157 \\ =367 \end{gathered}[/tex]Thus, the area of the figure is 367 yd^2.
the area of a triangular wedge is 90 square inches the height is 18in what is the base
Answers
it is given that,
the height of the wedge is h = 18 in
the area of the wedge is A = 90 square in.
we know that the area of a triangle is
A = 1/2 x base x height
put values,
90 = 1/2 x base x 18
90/18 = 1/2 x base
5 = 1/2 x base
base = 5 x 2
base = 10 inches,
thus, the base of the wedge is 10 inches,
6x + 14y what is the letter y in this problem?
Answers
The value of letter y in this problem is y = 6x / -14
How to solve the equationThe equation says that 6x + 14y
To solve the equation that we have here, we would have to equate to 0
such that we would have the equation as 6x + 14y = 0
6x + 14y = 0
then we would have
6x = - 14y
remember that when positives crosses over we would have it turn as negative.
Next we would have to divide through by - 14 in order to get the value of y
hence we would have
-14y / -14 = 6x / -14
then we would have y as
y = 6x / -14
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What is 150% of 38.
Answers
We are asked to find 150% of 38
Step 1:
Convert the 150% to decimal by removing the % sign which means dividing by 100.
150/100 = 1.5
Step 2:
Now simply multiply the decimal percentage with the number 38
1.5×38 = 57
Therefore, 150% of 38 is found to be 57
tristan asked his coworkers about how much time they spent commuting each morning Find the median
Answers
SOLUTION
In a box and whisker plot, the firt dot on the box is Q1
The second dot on the box is Q2
The third dot on the box is Q3
Q2 is the median
From what we see,
[tex]Q2=25[/tex]Hence the answer is 25, option D
SKIPPYTHEWALRUS U CAN'T ANSWER THIS QUESTIONI NEED CORRECT ANSWER 100 POINTS ONLY ANSWER CORRECTLY
A line passes through the points (7,9) and (10,1). What is its equation in point-slope form?
Use one of the specified points in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
Answers
Answer:
y - 1 = -8/3(x - 10)
also valid:
y - 9 = -8/3(x - 7)
Step-by-step explanation:
Point-slope equation is a fill-in-the-blank formula that is sort of a shortcut for writing the equation of a line. Point-slope is named that bc you fill in a point and the slope.
Point-slope Eq:
y - Y = m(x - X)
fill in the slope for the m and fill in any point on the line for the X,Y.
First slope:
Slope is y-y over x-x
9-1 / 7-10
= 8/ -3
= -8/3
So slope is -8/3 fill that in for the m.
y -Y = -8/3(x-X)
Pick one of the points (either one it totally doesn't matter)
Let's use (10,1)
fill in 10 for X and 1 in place of Y.
the y in the very front stays a y and the first x in the parentheses stays an x, so there will be two variables in your completed answer.
y - 1 = -8/3(x - 10)
make sure the parentheses on the right is beside the -8/3 fraction and is NOT written on the bottom, beside the 3 only.
Taylor has $430 in her savings account. The annual simple interest at the bank is 2%. How much intreast will she earn on her savings in 9 months?
Answers
we have the following equation
[tex]m(t)=430+430\cdot0.02\cdot t[/tex]where t is the time in years, as we have 9 months, we have to change to years
[tex]t=\frac{9}{12}=\frac{3}{4}=0.75[/tex]so after 9 months we get
[tex]430+430\cdot0.02\cdot0.75=430+6.45[/tex]So she will earn $6.45 in 9 month
1. Input, X 9753 1 Output, y 1 2 2 3 4 Function - Yes or no
Answers
before we can dtermone whether it is a function, there must be a relationship between X and y i.e they must have a constannt of proportionality as shown:
From the table:
when x = 9, y = 1
when x = 7, y = 2
when x = 5, y = 2
when x = 3, y = 3
when x = 1, y = 4
let us determine the constant of proportionality from the given values as shown:
k = y2-y1/x2-x1
when x = 9, y = 1
when x = 7, y = 2
k = 2-1/7-9
k = 1/-2
k = -1/2
Also
when x = 5, y = 2
when x = 3, y = 3
k = 3-2/3-5
k = 1/-2
k = -1/2
Also;
when x = 5, y = 2
when x = 3, y = 3
k = 3-2/3-5
k = 1/-2
k = -1/2
Since all the constant of proportionality are the same;
Hence y = kx
y = -1/2 x
This shows that the tabke is a function and X is directly proportional to y. hence the answer is YES, it is function
Reason
For every x value there is a unique y value, so the x value “input” cannot be repeated. If there are two like x values, there will be two points on your graph that will not pass the vertical line test. The vertical line test is used to determine if a set is a function or not.
See attachment for example.
Solve 2/3 (6w+12) this equation
Answers
Answer:
4w+8
Step-by-step explanation:
identify the constant of proportionality in the following questions. 1) y= 2x + 32) y= -3x - 4
Answers
Answer:
0. k=2
,1. k=-3
Explanation:
The constant of proportionality is the number that is beside the variable x in both equations.
(1)For the equation:
[tex]y=2x+3[/tex]The constant of proportionality is 2.
(2)For the equation:
[tex]y=-3x-4[/tex]The constant of proportionality is -3.
a man pushes a car with a force of 127.5n along a straight horizontal road.he manages to increase the speed of the car from 1 m/s to 2.8 m/s in 12 seconds. find the mass of the car. figure out acceleration first.
Answers
In order to determine the mass of the car, you first calculate the acceleration of the car, by using the following formula:
[tex]a=\frac{v_2-v_1}{\Delta t}[/tex]where:
v2: final speed of the car = 2.8 m/s
v1: initial speed of the car = 1 m/s
Δt: time interval = 12 s
You replace the previoues values into th formula for the acceleration:
[tex]a=\frac{2.8m/s-1.0m/s}{12s}=0.15\frac{m}{s^2}[/tex]Next, you the Newton's second law to find the mass of the car. You proceed as follow;
[tex]F=ma[/tex]where:
m: mass of the car = ?
a: acceleration of the car = 0.15m/s²
F: force exerted on the car by the man = 127.5N
You solve for m in the formula for F, and you replace the values of the other parameters to obtain m, just as follow:
[tex]m=\frac{F}{a}=\frac{127.5N}{0.15m/s^2}=850\operatorname{kg}[/tex]Hence, the mass of the car is 850kg
the circumference of a circle is 18pi ft. what is the area in square feet.
Answers
We have first the formula of the circumference of a circle
[tex]C=2\pi r[/tex]In order to know the area we need to know the radius of the circle, it can be obtained using the formula above and the next information.
C=18pi
r is the radius
[tex]18\pi=2\pi r[/tex]then we isolate the r
[tex]\begin{gathered} r=\frac{18\pi}{2\pi} \\ r=9 \end{gathered}[/tex]the radius is 9 ft
then we can calculate the area using the next formula
[tex]A=\pi r^2[/tex]we substitute the value of the radius
[tex]\begin{gathered} A=\pi(9)^2 \\ A=81\pi ft^2 \\ A=254.47ft^2 \end{gathered}[/tex]mathematics assignment
Answers
Examining the function the graph that is correct is the graph in option C
What is graph ?A graph is a representation of data using accepted means of presentation.
The graph used in the question is in cartesian coordinate and it a parabolic graph
How to find the correct graphThe given data is h(x) = -x² - 4
Examining the given function
The term -x² is a negative term hence the graph opens downwards
The value of h(x) when x = 0 is -4. Therefore the graph will have an intercept at -4
The graph of option C is the one that meets the required criteria hence the nest option
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write the equation of the line in slope-intercept form given the follow[tex]slope = - \frac{5}{4} \: y - intercept \: (0 \: - 8)[/tex]
Answers
Let's begin by identifying key information given to us:
[tex]\begin{gathered} slope=-\frac{5}{4}\: \\ y-intercept\: (0\: -8) \end{gathered}[/tex]The point-slope equation is given by:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-intercept\: (0\: -8)\Rightarrow(x_1,y_1)=(0,-8) \\ (x_1,y_1)=(0,-8) \\ m=-\frac{5}{4} \\ y-\mleft(-8\mright)=-\frac{5}{4}(x-0) \\ y+8=-\frac{5}{4}x-0 \\ y=-\frac{5}{4}x-8 \\ \\ \therefore\text{The slope-intercept form is }y=-\frac{5}{4}x-8 \end{gathered}[/tex]Find the product of -0.6 and -2/5
Express your answer as a fraction or
mixed number in simplest form.
Answers
Answer:
6/25Step-by-step explanation:
1) -0.6 = -6/10
= -3/5
2) -0.6*-2/5 = (-3/5)*(-2/5)
=(-3*-2)/(5*5)
=6/25Find a given that the line through M(-2, a) and N(0, -2) has gradient -4
Answers
a=6
1) Given that we have M (-2, a), N(0, -2), and the gradient -4. Let's start by applying the formula for the gradient.
G = (y_2 - y_1 ) / (x_2- x_1)
2) So "a", the second coordinate of point M is equal to 6, and as the gradient is a negative number indicates a "downhill" a decreasing direction of that line.
Solve for a side in right triangles. AC = ?. Round to the nearest hundredth
Answers
The length of segment AC is 2.96 units
How to determine the side length AC?From the question, the given parameters are
Line segment AB = 7 units
Angle A = 65 degrees
The line segment AC can be calculated using the following cosine ratio
cos(Angle) = Adjacent/Hypotenuse
Where
Adjacent = Side length AC
Hypotenuse = Side length AB
So, we have
cos(65) = AC/AB
This gives
cos(65) = AC/7
Make AC the subject
AC =7 * cos(65)
Evaluate
AC = 2.96
Hence, the side length AC has a value of 2.96 units
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The table gives a set of outcomes and their probabilities. Let A be the event "the outcome is less than 8". Find P(A). Outcome Probability 1 0.12 2 0.11 3 0.4 4 0.02 5 0.04 6 0.17 7 0.02 00 0.09 9 0.03
Answers
We want to calculate the probability of this event A: "the outcome is less than 8". To calculate this probability, we should first note that we have a total of 9 outcomes. So, we will first identify out of this outcomes cause the event A to happen.
Since the event A is saying that the outcome is less than 8, then the outcomes that would make the event A to happen would be the numbers from 1 to 7. However, to calculate this probabilty, we will use this property of probability.
Given an event A, we have the
State what additional information is required in order to know that the triangles are congruent for the
reason given.
SSS
C
D
Y
X
A) WX = ED or XY = DC
C) YW = CE
B) ZW
ZE
D) XY = DC
Answers
Answer:
C. YW≅CE
Step-by-step explanation:
SSS is used when three pairs of sides are congruent. Two pairs of congruent sides are given. YW≅CE would be the third pair and therefore prove the triangles are congruent by SSS.
Solve F(x) for the given domain. Include all of your work in your final answer. Submit your solution.
F(x) = x2 + 3x - 2
F(a) =
Answers
For a given function f(x) = x² + 3x - 2, f(a) is a² + 3a - 2 and f(x - 1) = x² + x - 4
Given,
The function f(x) = x² + 3x - 2
We have to find f(a) and domain f(x - 1)
Here,
f(x) = x² + 3x - 2
Then,
f(a) = a² + 3a - 2
Now,
f(x - 1) = (x - 1)² + 3(x - 1) - 2
f(x - 1) = x² - 2x + 1 + 3x - 3 - 2
f(x - 1) = x² + x - 4
That is,
For a given function f(x) = x² + 3x - 2, f(a) is a² + 3a - 2 and f(x - 1) = x² + x - 4
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A group of 23 students want to see the show at the planetarium. Tickets cost $11 for each student who is a member of the planetarium’s frequent visitor program and $13 for each student who is not a member. The total cost of the students’ tickets is $261.
Answers
Out of 23 students 19 students are the member of planetarium's frequent visitor program and 4 students are not the members.
Given,
The total number of students in a group = 23
Cost of ticket for member of planetarium's frequent visitor program = $11
Cost of ticket for the student who is not a member = $13
The total cost of the students ticket = $261
Lets take,
The number of students with membership = x
The number of students without membership = y
Total number of students, x + y = 23 -----------(1)
Now,
Total cost for the tickets, 11x + 13y = 261
Now, Multiply 13 with (1)
We get,
13x + 13y = 299
Solve for x
13x + 13y = 299 -
11x + 13y = 261
2x + 0 = 38
2x = 38
x = 38/2
x = 19
Now, put x in (1)
19 + y = 23
y = 23 - 19
y = 4
That is,
The number of students with membership is 19 and the number of students without membership is 4.
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