One side of triangle is half the longest side. the third side is 7 feet less than the longest side. the perimeter is 43. find all three sides.
Answers
2y = x
If z is 7 less than x then that equation would look like
X = z +7
The perimeter is the sum of all the sides
P = x + y + z = 43
Now by using all three equations, we can find the value of each variable by plugging into the equations.
First, let's start by changing the first two equations to compare the values of z and y to x.
Y = x/2
Z = x - 7
Now we can use these new equations to plug into the perimeter equation and find the value of x.
43 = x + y + z Plug in your variables
43 = x + x/2 + x-7 Add 7 to both sides
50 = x + x/2 + x Multiply both sides by 2 to get rid of the fraction
100 = 2x + x + 2x Add all your x's together
100 = 5x Divide both sides by 5
X = 20
No we can use the value of x to find the values of y and z by plugging into the two equations before.
2y = 20
Y = 10
Z = 20 - 7
Z = 13
Therefore, the lengths of the sides are 20, 10, and 13
Related Questions
Jessica attains a height of 4.7 feet above the launch and landing ramps after 1 second. Her initial velocity is 25 feet per second. Find the angle of her launch. a. Which equation can you use with the given information to solve for ?
Answers
Height = 4.7 ft x (1 m/ 3.28 ft) = 1.43 m
Velocity = 25 ft / s x (1 m / 3.28 ft) = 7.62 m/s
The maximum height that can be attained by an object following a projectile path is calculated through the equation,
H = (v₀²)(sin²θ) / 2g
where v₀ is the initial velocity, H is the maximum height and g is the acceleration due to gravity.
Transforming the equation to calculate for θ,
sinθ = sqrt ((H)(2g) /(v₀²))
sinθ = sqrt ((1.43)(2)(9.8)) / (7.62²))
sinθ = 0.76
We calculate for the angle by getting the arcsin.
sin⁻¹ (0.76) = 49.46°
ANSWER: 49.46°
You and six friends play a game where each person writes down his or her name on a scrap of paper, and the names are randomly distributed back to each person. Find the probability that everyone gets back his or her own name.
Answers
Answer with explanation:
Total number of different candidates who are playing the game=7
Suppose, Seven candidates are represented by ={A,B,C,D,E,F,G}
Total Possible Outcome =7
→Probability that , "A" gets his scrap of paper , means the paper on which he or she has written his or her name
[tex]=\frac{\text{total favorable outcome}}{\text{total favorable outcome}}\\\\=\frac{1}{7}[/tex]
→Now, 6 candidates are left.
Probability that , "B" gets his scrap of paper , means the paper on which he or she has written his or her name
[tex]=\frac{\text{total favorable outcome}}{\text{total favorable outcome}}\\\\=\frac{1}{6}[/tex]
→Now, 5, candidates are left.
Probability that , "C" gets his scrap of paper , means the paper on which he or she has written his or her name
[tex]=\frac{\text{total favorable outcome}}{\text{total favorable outcome}}\\\\=\frac{1}{5}[/tex]
→Now, 4 candidates are left.
Probability that , "D" gets his scrap of paper , means the paper on which he or she has written his or her name
[tex]=\frac{\text{total favorable outcome}}{\text{total favorable outcome}}\\\\=\frac{1}{4}[/tex]
→Now, 3 candidates are left.
Probability that , "E" gets his scrap of paper , means the paper on which he or she has written his or her name
[tex]=\frac{\text{total favorable outcome}}{\text{total favorable outcome}}\\\\=\frac{1}{3}[/tex]
→Now, 2 candidates are left.
Probability that , "F" gets his scrap of paper , means the paper on which he or she has written his or her name
[tex]=\frac{\text{total favorable outcome}}{\text{total favorable outcome}}\\\\=\frac{1}{2}[/tex]
→Now, a single candidates is left.
Probability that , "G" gets his scrap of paper , means the paper on which he or she has written his or her name
[tex]=\frac{\text{total favorable outcome}}{\text{total favorable outcome}}\\\\=\frac{1}{1}=1[/tex]
Required Probability
[tex]=\frac{1}{7} \times\frac{1}{6} \times\frac{1}{5} \times\frac{1}{4} \times\frac{1}{3} \times\frac{1}{2} \times 1\\\\=\frac{1}{5040}[/tex]
Larry travels 60 miles per hour going to a friend’s house and 50 miles per hour coming back, using the same road. he drove a total of 5 hours. what is the distance from larry’s house to his friend’s house, rounded to the nearest mile?
Answers
V2=50
T=t1+t2=5. 5-t2=t1
60×(5-t2)=50×t2
300-60×t2=50×t2
300=50×t2+60×t2
300=t2×(50+60)
300=t2×110
300/110=t2
S=50×300/110
Final answer:
To find the distance from Larry's house to his friend's house, we use the relationship between distance, speed, and time for his trip to and from his friend's house, taking into account the different speeds and total travel time of 5 hours.
Explanation:
The student's question asks to find the distance from Larry's house to his friend's house given his speed and total travel time in both directions. To solve this problem, we use the formula distance = speed × time. Let's call the distance one way d, the time to travel to the friend's house t1, and the time to travel back t2. Larry's speed going to the friend's house is 60 miles per hour and coming back is 50 miles per hour. The total travel time is 5 hours.
So for the trip to the friend's house we have:
d = 60 × t1
And for the trip back:
d = 50 × t2
Since the total travel time is 5 hours:
t1 + t2 = 5
Substituting the expressions for d from the first two equations into the third, we get:
60t1 + 50t2 = 60(5)
Using the fact that t1 + t2 = 5, we solve for either variable, say t1, which gives us t2 as well. After finding t1 and t2, we plug either of those back into the original distance equations to find d, which will be the distance from Larry's house to his friend's house. The answer should be rounded to the nearest mile.
The three sides of a triangle are consecutive odd integers. If the perimeter of the triangle is 39 inches find the lengths of the sides of the triangle
Answers
To answer that question
Answers
please help me idk how to do this at all I've been stuck on it for awhile.
Answers
(x,y)
we are given x=2
find what y is when x=2
subsitute 2 for x
y=2x+5
y=2(2)+5
y=4+5
y=9
so the blank is 9
when numbers are in parenthesis the first number is x the second is y
(x,y)
sine they give you (2, blank)
2 = x so replace x in the equation with 2
so y=2x+5 becomes y=2(2)+5
so y = 2*2+5 = 9
y=9
so it should be (2,9)
slope of -8 and Y intercept of (0, 12) in slope intercept form.
Answers
Hey there! I would like some help please :) Thanks!
Answers
Congruent triangles have exactly the same three angles, so ∠D = ∠B.
An ice cream store sells 2 2 drinks, in 3 3 sizes, and 8 8 flavors. in how many ways can a customer order a drink?
Answers
If an ice cream store sells 2 drinks, in 3 sizes, and 8 flavors, the number of ways can a customer order a drink will be 48.
What are permutation and combination?A permutation is the number of different ways a set can be organized; order matters in permutations, but not in combinations.
It given that, An ice cream store sells 2 drinks, in 3 sizes, and 8 flavors.
We have to find the number of ways can a customer order a drink,
It is obtained by multiplying all the possible cases for that event, Multiplication is one type of arithmetic operation. There are basically four types of arithmetic operations.
=2×3×8
=48
Thus, if an ice cream store sells 2 drinks, in 3 sizes, and 8 flavors, the number of ways can a customer order a drink will be 48.
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Use the table to determine the appropriate model of the function, x 1 2 3 4 5 f(x) 15 12 9 6 3 linear quadratic cubic exponential
Answers
The actual line is just f(x)= -3x+18
The appropriate model of the function is:
Linear model
Step-by-step explanation:We are given a table of values as:
x f(x)
1 15
2 12
3 9
4 6
5 3
Clearly we could observe that with each increasing value of x the value of function decreases by 3.
This means that the range of change is constant.
Hence, the relation is linear ( as the rate of change is constant )
Also, the equation that models this data set is given by:
[tex]y=f(x)=18-3x[/tex]
Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 13 in. by 8 in.
Answers
2) Call x the length of the sides of the squares cut off.
3) The base of the box will have dimensions: (13 - 2x) and (8 - 2x)
4) The height of the box will be x
5) The volume of the box will be the area of the base times the height:
Volume = (13 - 2x)(8 -2x)x = (4x^2 - 42x + 104)x = 4x^3 - 42x^2 + 104x
6) The maximum volume is calculated by finding the point where the derivative of the volume is zero =>
d (volume) / dx = 12x^2 - 84x + 104 = 0
7) Solve the quadratic equation 12x^2 - 84x + 104 = 0
=> 4(3x^2 - 21x + 26) = 0
=> 3x^2 - 21x + 26 = 0
=> 3 (x^2 - 7x) + 26 = 0
=> 3 [(x - 7/2)^2 - (7/2)^2] + 26 = 0
=> 3 (x - 7/2)^2 - 3* 49/4 + 26 = 0
=> 3 (x - 7/2)^2 = 3*49/4 - 26
=> (x -7/2)^2 = (49/4 - 26/3)
=> x = 7/2 +/- √(49/4 - 26/3)
x = 7/2 + √3.583 and x = 7/2 - √3.583
x = 5.393 and x = 1.607
=> Volume =
1) 4(5.393)^3 - 42(5.393)^2 + 104(5.393) = -33.26 ---> it does not have physical meaning
2) 4(1.607)^3 - 42(1.607)^2 + 104(1.607) = 75.27 ---> this is the answer
Answer: 75.27 in^3
find the point on the terminal side of θ = negative three pi divided by four that has an x coordinate of negative 1
Answers
[tex]\bf tan(\theta)=\cfrac{opposite}{adjacent}\qquad tan\left( -\frac{3\pi }{4} \right)=\cfrac{y}{x}\implies tan\left( -\frac{3\pi }{4} \right)=\cfrac{y}{-1} \\\\\\ -1\cdot tan\left( -\frac{3\pi }{4} \right)=y\implies -1\cdot \cfrac{sin\left( -\frac{3\pi }{4} \right)}{cos\left( -\frac{3\pi }{4} \right)}=y \\\\\\ -1\cdot \cfrac{-1}{-1}=y\implies -1[/tex]
The point on the terminal side is (1,-1) and this can be determined by using the trigonometric functions.
Given :
The point on the terminal side of θ = negative three [tex]\pi[/tex] divided by four that has an x coordinate of negative 1.
The following steps can be used in order to determine the point on the terminal side:
Step 1 - Write the given expression.
[tex]\theta = -\dfrac{3\pi}{4}[/tex]
Step 2 - The value of the trigonometric function is given by:
[tex]\rm tan \dfrac{3\pi}{4} =-1[/tex]
Step 3 - The trigonometric function can also be written as:
[tex]\rm tan \theta=\dfrac{y}{x}=-1[/tex]
Step 4 - Substitute the value of 'x' in the above expression.
y = -1
So, the point on the terminal side is (1,-1).
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A sports recreation company plans to manufacture a beach ball with a surface area of 7238 in.2 find the radius of the beach ball. use the formula , where a is the surface area and r is the radius of the sphere. 576 in. 48 in. 75 in. 24 in.
Answers
The given problem supplies as with the surface area of the beach ball and we are to look for the required radius. Assuming that the beach ball is perfectly shaped in the form of a sphere, then the formula for calculating the surface area of a sphere is given as:
SA = 4 π r^2
where r is the radius of the sphere and SA is the surface area which is given to be 7238 in^2
Rewriting the formula in terms of r:
r^2 = SA / 4 π
r = sqrt (SA / 4 π)
Solving for r:
r = sqrt (7238 in^2 / 4 π)
r = 24 in
Answer:
24 inches
help me plox 20 points
Answers
if they were rounded to the tens place
18 would round to 20
16 would round to 20
17 would round to 20
14 would round to 10
so April would be different.
Probability theory predicts that there is a 44% chance of a water polo team winning any particular match. If the water polo team playing 2 matches is simulated 10,000 times, in about how many of the simulations would you expect them to win exactly one match?
Answers
water polo team wins none, wins 1 or wins both games.
chance that they win both matches are:
0.44*0.44 = 0.1936 in relative value
Chance that they lose both matches are:
(1-0.44)*(1-0.44) = 0.3136 in relative value
If we multiply these relative values by number of matches and subtract that from number played double games (10000) we will get number of times they won only once.
10000 - 10000* (0.3136+ 0.1936) = 4928
Find the selling price of an item listed at $400 subject to a discounted series of $25%, 10%, and 5%
A. $256.50
B. $270.00
C. $225.00
D. $300.00
Answers
$300 - ($300 x 0.10) = $270
$270 - ($270 x 0.05) = $256.50
answer
A. $256.50
Answer:
Selling price of an item is $256.50 (A).
Step-by-step explanation:
Given : WE have given an item listed at $400 subject to a discounted series of $25%, 10%, and 5% .
To find : Find the selling price of an item.
Formula used : Selling price = marked price - discount.
Solution : We have an item listed at = $400.
Discount percentage = $25% , $10% , $5.
Discount 1 = $400 ×[tex]\frac{25}{100}[/tex] = $100.
Selling price = $400-100 = $300.
Discount 2 = $300 ×[tex]\frac{10}{100}[/tex] = $30.
Selling price = $300-30 = $270.
Discount 3 = $270 ×[tex]\frac{5}{100}[/tex] = $13.50.
Final selling price = $270-13.50 = $256.50.
Therefore, Selling price of an item is $256.50 (A).
You are 9 miles away from home. You start biking home at a speed of 6 miles per hour.
a. write an equation. in standard form that represents your distance from home y after x hours.
b. find the y-intercept of the graph. what does this represent?
c. find the x-intercept of the graph. what does this represent?
Answers
6x+y=9
b) from the first, we had it in slope intercept form, mx+b where b is the y-intercept. y=-6x+9
So the y-intercept is the point (0,9) which represents the starting distance before you start biking. You start being 9 miles from your house.
c) The x intercept occurs when y=0 so:
y=9-6x, so if y=0
0=9-6x
6x=9
x=9/6
x=1.5
This represent the time when you will arrive home and the total time that has elapsed to get there.
The distance and speed are illustrations of linear equations
The standard form is [tex]\mathbf{6x + y = 9}[/tex]The y-intercept is 9The x-intercept is 1.5The given parameters are:
[tex]\mathbf{Rate = 6}[/tex]
[tex]\mathbf{Initial = 9}[/tex]
(a) The standard equation
Because the distance reduces with time, the equation is:
[tex]\mathbf{y = Initial-Rate \times x}[/tex]
This gives
[tex]\mathbf{y = 9 - 6\times x}[/tex]
[tex]\mathbf{y = 9 - 6x}[/tex]
Add 6x to both sides
[tex]\mathbf{6x + y = 9}[/tex]
(b) The y-intercept
This is the initial distance away from home.
So, the y-intercept is 9
(c) The x-intercept
Set y to 0, to calculate the x-intercept
[tex]\mathbf{6x + y = 9}[/tex]
[tex]\mathbf{6x + 0 = 9}[/tex]
[tex]\mathbf{6x = 9}[/tex]
Divide both sides by 6
[tex]\mathbf{x = 1.5}[/tex]
This is the initial time away from home.
So, the x-intercept is 1.5
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Kenji buys 3 yards of fabric for 7.47$. Then he realizes that he needs 2 more yards. How much will the extra fabric cost?
Answers
7.47 / 3 = 2.49
Now that we know that each yard costs $2.49, we can multiply it by the number of yards you need to buy (two).
2 • 2.49 = 4.98
Your total for two yards of fabric is $4.98
Probability theory predicts that there is a 22.4% chance of a particular soccer player making four penalty shots in a row. If the soccer player taking four penalty shots is simulated 2500 times, in about how many of the simulations would you expect at least one missed shot?
Answers
100 -22.4 = 77.6%
So the number of simulations that he/she will miss at least one shot in 2500 simulations would be...
2500 x 77.6% =
2500 x .776 = 1940
1940 ~~~~~~~~~~~~ APEX
Find the slopes of the asymptotes of the hyperbola with the following equation.
36 = 9x ^{2} - 4y^{2}
Answers
The given equation is a hyperbola, and by converting it to standard form we find a = 2 and b = 3. Therefore, the slopes of the asymptotes are ±3/2.
Explanation:The equation given is in the form of a hyperbola equation which could be written as [tex]x^2/a^2 - y^2/b^2 = 1.[/tex] This suggests that the transverse axis is horizontal meaning the hyperbola opens to the left and right. The slopes of the asymptotes for hyperbola is given by ±b/a.
First, we need to rewrite our equation in standard form. The equation given is [tex]36 = 9x^{2} - 4y^{2}.[/tex] To convert it into the standard form, we divide whole equation by 36 to isolate 1 on one side. This yields [tex](x^2/4) - (y^2/9) = 1.[/tex] Now, it is in the standard form of hyperbola.
By comparing it with the standard equation, we see that [tex]a^2 = 4 \ and\ b^2 = 9[/tex]which gives a = 2 and b = 3. Based on these, we can now find the slope of the asymptotes which is ±b/a = ±3/2.
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Line segment LM is dilated to create L'M' using point Q as the center of dilation and a scale factor of 2.
What is the length of segment QM'?
Answers
Answer: 6 units
Step-by-step explanation:
Given: Line segment LM is dilated to create L'M' using point Q as the center of dilation and a scale factor of 2.
Since in dilation , to calculate the distance of a point on image from center point we need to multiply scale factor to the distance of corresponding point on pre-image from center point .
Thus we have,
[tex]QM'=2\times QM\\\\\Rightarrow QM'=2\times3\\\\\Rightarrow QM'=6[/tex]
Hence, the length of segment QM' = 6 units.
Answer:
6 units
Step-by-step explanation:
Find the slope in line perpendicular x-y=16
Answers
X - y = 16
-y = -x + 16
So slope = - 1 / 1
Which graph represents the solution to the system of inequalities? x + y ≥ 4 2x + 3y < 12
Answers
x + y ≥ 4
2x + 3y < 12
For the first step, let's disregard the inequality symbols and take it like any conventional algebraic equation. This is to be able to graph the lines on a Cartesian planes first.
For the first equation, x+y=4. To find the x- and y-intercepts, let the other variable be 0. For example,
x-intercept:
x+0=4
x=4
y-intercept:
0+y=4
y=4
Therefore, you can graph the equation line by plotting the intercepts (4,0) and (0,4) and connecting them together. The same thing is done to the second equation:
x-intercept:
2x + 0 = 12
x=12/2=6
y-intercept:
0 + 3y =12
y= 12/3 = 4
Therefore, you can graph the equation line by plotting the intercepts (6,0) and (0,4) and connecting them together. The graph is shown in the left side of the picture.
The next step would be testing the inequalities. Let's choose a point that does not coincide with the lines. That point could be (-5,-1).
x + y ≥ 4
-5 + -1 ≥4
-6 ≥ 4 --> this is not true. Thus, the solution of the graph must not include the area of this point. It includes everything to the right of the line denoted by the blue-shaded region.
2x + 3y < 12
2(-5) + 3(-1) <12
-13 < 12 ---> this is true. Thus, the solution would include this point. That includes all points to the left of the orange line denoted by the orange-shaded the region.
The region where blue and orange overlap is the solution of the system of equations, denoted by the green-shaded region.
The length of a rectangle is 22 meters longer than the width. if the area is 2626 square meters, find the rectangle's dimensions. round to the nearest tenth of a meter.
Answers
l*w=2626
Substitute 22w for l, getting 22w^2=2626. Divide by 22 to get 119.36 (and more decimals!), and square root that to get 10.9 (rounded) for the width and 240.4 (rounded) for the length
Given the functions f(x) = 3x2, g(x) = x2 − 4x + 5, and h(x) = –2x2 + 4x + 1, rank them from least to greatest based on their axis of symmetry. f(x), g(x), h(x) f(x), h(x), g(x) g(x), h(x), f(x) g(x), f(x), h(x)
Answers
Answer:
f(x), h(x), g(x)
Can someone simplify 2y-3x^2+6x^2-3y ?
Answers
Bring like terms together:-
6x^2 - 3x^2 + 2y - 3y
= 3x^2 - y <----- Answer
3x^2-y
Find an exact value. sin(17pi/12)
a. √6 - √2 / 4
b. -√6 - √2 / 4
c. √6 + √2 / 4
d. √2 - √6 / 4
Answers
feel free to ask if you have any doubts.
The required exact value of the given trigonometric function is sin(17π/12) = (√6 + √2)/4
What are Trigonometric functions?Trigonometric functions are defined as the functions which show the relationship between the angle and sides of a right-angled triangle.
The trigonometric function is given in the question, as follows:
sin(17π/12)
To find the value of sin(17π/12), we can use the following trigonometric identity:
sin(a + b) = sin(a)cos(b) + cos(a)sin(b)
In this case, we can write:
sin(17π/12) = sin(π/3 + π/4)
We know that sin(π/3) = √3/2 and cos(π/3) = 1/2, and sin(π/4) = cos(π/4) = √2/2.
Therefore, we can use the above identity to get:
sin(17π/12) = sin(π/3)cos(π/4) + cos(π/3)sin(π/4)
= (√3/2)(√2/2) + (1/2)(√2/2)
= (√6/4) + (√2/4)
= (√6 + √2)/4
So the answer is option (c): √6 + √2 / 4.
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Use basic identities to simplify the expression. sin^2θ + tan^2θ + cos^2θ
Answers
so it simplifies to 1 + tan^2 theta
and this = sec^2 theta
Write a segment addition problem using three points that asks the student to solve for x but has a solution x = 20
Answers
The segment addition problem was given below which gives the value of x as 20.
Segment addition problem:
Consider three points on a line: A, B, and C. Point B is located between points A and C.
The lengths of the line segments are as follows:
Length of segment AB: 12
Length of segment BC: x
Length of segment AC: 32
Find the value of x.
We have the equation for segment addition: AB + BC = AC
Substitute the given values:
12 + x = 32
Now, solve for x:
x = 32 - 12
x = 20
Therefore, the value of x is indeed 20, and the lengths of the segments satisfy the segment addition property.
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To construct a segment addition problem with a solution of x = 20, use three collinear points A, B, and C and set AB = x and BC = 20 - x, with the entire segment AC being 20 units. Solving the equation x + (20 - x) = 20 confirms that x = 20 is the solution.
Explanation:To write a segment addition problem that solves for x where the solution is x = 20, let’s use three collinear points A, B, and C with point B between A and C. We can then express the lengths of segments AB and BC in terms of x. For instance, if AB is x units long and BC is 20 - x units long, the total length of AC would be 20 units. We can write an equation based on this:
AB + BC = AC
x + (20 - x) = 20
By simplifying, x cancels out on the left-hand side, leaving 20 = 20, which is true for x = 20. Therefore, this is a valid segment addition problem where solving for x yields 20 as the solution.
Here is the step-by-step problem phrased as a question:
Let points A, B, and C be collinear with B between A and C.If AB = x and BC = 20 - x, and AC = 20, find the value of x.True or false an inscribed angle is formed by two radii that share an endpoint
Answers
True or false an inscribed angle is formed by two radii that share an endpoint
the correct answer is : FALSE
Answer:
The given statement : an inscribed angle is formed by two radii that share an endpoint is an FALSE statement.
Step-by-step explanation:
Inscribed angle is a angle which is formed inside the circle by joining of two intersecting chords inside a circle.
The inscribed angle is explained with the help of a diagram below :
In the diagram attached below, ∠ABC is an inscribed angle with an intercepted minor arc from A to C.
Thus, the inscribed angle is not formed with the help of radii that share a common end point.
Hence, The given statement : an inscribed angle is formed by two radii that share an endpoint is an FALSE statement.