In the diagram shown below, ∠K=18º and ∠H=18º.
Prove KJ=13.75. Justify your steps in a paragraph proof.
Answers
Since all 3 angles of each triangle are equal, the triangles are similar.
Since the triangles are similar, all 3 sides must be in the same proportion.
8 / 5 = 22 / KJ
(5 * 22) / 8 = KJ
KJ = 13.75
In triangle KIJ, ∠ K=18° (GIVEN), ∠J=112° , then ∠ I = 180-(112+18) = 50°
Since Δ FGH & Δ KJI have all their respective angles EQUAL, then these
2 triangles are SIMILAR and all their respective sides are proportional.
If so we can write the following proportions:
GF/JI = GH/JK
8/5 = 22/JK. Cross multiplication → 8.JK = (5).(22) → 8.JK = 110
And JK = 110/8 → JK = 13.75 (JK or KJ are the same)
Related Questions
Name 3 decimals between 16.4 and 16.5 draw a number line estmating the placement of all five decimals
Answers
Which statement best explains whether △PQR is congruent to △XYZ?
△PQR is congruent to △XYZ because △PQR can be mapped to △XYZ by a rotation of 180° about the origin.
△PQR is congruent to △XYZ because △PQR can be mapped to △XYZ by a translation 5 units down followed by a reflection across the y-axis.
△PQR is not congruent to △XYZ because there is no sequence of rigid motions that maps △PQR to △XYZ.
△PQR is congruent to △XYZ because △PQR can be mapped to △XYZ by a reflection across the y-axis followed by a reflection across the x-axis.
Answers
The 440 yard dash in track has been replaced by the 400 meter dash. which is the longer distance and by how many meters? hint: 1 yard = 3 feet
Answers
Final answer:
The 400 meter dash is the longer distance by 2.336 meters.
Explanation:
In order to determine which is the longer distance, we need to convert both the 440 yards and the 400 meters into the same unit of measurement. Since 1 yard is equal to 0.9144 meters, we can convert the 440 yards into meters by multiplying it by 0.9144:
440 yards * 0.9144 meters/yard = 402.336 meters
Therefore, the 400 meter dash is the longer distance by 2.336 meters.
TEXASCHIC! :)
1. Sam is observing the velocity of a car at different times. After three hours, the velocity of the car is 51 km/h. After five hours, the velocity of the car is 59 km/h.
Part A: Write an equation in two variables in the standard form that can be used to describe the velocity of the car at different times. Show your work and define the variables used. (5 points)
Part B: How can you graph the equation obtained in Part A for the first six hours? (5 points)
My answer:
Part A:
y - 51 = 59 - 51 / 5 - 3 (x-3)
y - 51 = 4 (x-3)
y = 4x -12 + 51
y= 4x + 39
where x is the time and y is the velocity of car at any time x.
Part B:
y =4 * 6 + 39 = 24 + 39 = 63 ~km/h
Answers
slope = (59 - 51) / (5 - 3) = 8/2 = 4
y = mx + b
slope(m) = 4
(3,51)...x = 3 and y = 51
sub and find b, the y int
51 = 4(3) + b
51 = 12 + b
51 - 12 = b
39 = b
so ur equation is : y = 4x + 39...but u need it in standard form
y = 4x + 39
-4x + y = 39
4x - y = -39 <==== this is ur equation...x = number of hrs and y = total velocity
====================
ur x axis is the number of hrs
ur y axis is total velocity in km
y = 4x + 39......slope = 4.....y int = (0,39)....x int is (- 9.75,0) or -9 3/4 for graphing purposes)....so start at (-9.75,0)...and since the slope is 4, go up 4 and to the right 1....plot that...then up 4 and to the right 1...plot that...u will cross the y axis at (0,39)....and just connect ur plotted points and u have ur line......or what u can do since it is asking for the first 6 hrs....sub in 1 for x and solve for y....then sub in 2 for x and solve for y...keep doing this up till 6 and u will have ur line up till 6 hrs
The velocity of the car is represented by the equation y = 4x + 39, where 'x' is time and 'y' is the velocity. You can graph this for the first six hours by substituting x=6 to find: y=63 km/h. Thus, the car's velocity after six hours would be 63 km/h.
Explanation:In order to solve this problem, we first find the equation representing the change in the car's velocity. The point (3, 51) represents the condition that after three hours, the car is moving at 51 km/h. Similarly, the point (5, 59) stands for the velocity being 59 km/h after five hours. We derive the slope of the line connecting these two points by subtracting the y-coordinates and dividing by the difference of the x-coordinates, (59-51)/(5-3) = 4.
This slope represents an increase of 4 km/h for every hour that passes. Our equation then becomes y - 51 = 4(x - 3) which simplifies to y = 4x + 39. In this equation, 'x' represents time in hours and 'y' is the car's velocity at any given time 'x'.
For Part B, we graph the equation over the first six hours by inputting x=6 into the equation, giving us y = 4*6 + 39 = 63 km/h. Therefore, after six hours, the car would be moving at a velocity of 63 km/h.
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If TOWN A has a yearly population of 3,225 and is growing by 100 people each year and TOWN B has a yearly population of 3,300 and is growing by 75 people per year, after how many years will the two populations be equal?
Answers
so Town A arithmetic progressive expression =
tn=3225+(n-1)100
tn= 3225+100n-100 = 3125+100n
for Town B you have
tn= 3300+(n-1)75 = 3300+75n-75 = 3225+75n
equating both A and B
3125+100n=3225+75n
100n-75n=3225-3125
25n= 100
n=100÷25=4
n=4years
they'll be equal after 4years
What is the answer for 35=-7z
Answers
Find the coordinates of the other endpoint of the segment with the given endpoint (6,2) and midpoint (2,0)
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Need help doing this problem!!
Answers
6x + 4x + 10 = 90 (the 90 is from the right angle)
You then combine like terms.
10x + 10 = 90
To isolate the variable you need to subtract 10 to both sides leaving you with...
10x = 80
Then you divide 10 from both sides and your final answer is x=8.
Lets check our work shall we???
6(8) +4(8) + 10 = 90
48 + 32 + 10 = 90
48 + 42 = 90
90 = 90
It is a solution! Yayyyyy!!!! So 8 is your answer. I hope this helps love! :)
License plates in a particular state display 22 letters followed by 33 numbers. how many different license plates can be manufactured for this state?
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Since there are 10 numbers, you would be 10*33= 330
Afterwards, to find all combinations, it would be 330*572= 188,760
The answer is 188,760 different license plates
The total number of different license plates that can be manufactured in this state is 676,000. This is calculated by multiplying the 676 combinations of letters by the 1,000 combinations of numbers.
To find out how many different license plates can be manufactured in this state,
2 letters followed by 3 numbers. Each letter can be any of the 26 letters in the alphabet, and each number can be any digit from 0 to 9.Therefore, the total number of combinations for the letters is:
26 (choices for the first letter) * 26 (choices for the second letter) = 676The total number of combinations for the numbers is:
10 (choices for the first number) * 10 (choices for the second number) * 10 (choices for the third number) = 1000By multiplying these together, we get the total number of license plates:
676 * 1000 = 676,000Therefore, there can be 676,000 different license plates manufactured in this state.
Sarah has a collection of nickels, dimes, and quarters worth $13.80. she has 10 more dimes than nickels and twice as many quarters as dimes. how many coins of each kind does she have?
Answers
22 dimes = $2.20
44 quarters = $11.00
11.00
2.20
+ .60
———
13.80
The clean up hitter on a baseball tean batted 1/3 of the runs the team scored. The hitter batted in 3 runs. Select the equation that represents the number of n of runs the team scored. Then solve the equation:
a.1/3n=3B.n/3=1/3C.3n=1/3D.3n=9
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a. 1/3 (n)=3
n=9
How to do this ?? How
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The two bars | | is used to indicate the function absolute value.
Remember this definition:
| x | = - x if x < 0 and x if x > 0
So, | x | > c =>
x > c or x > - c
Therefore:
|ax - b| > c => ax - b > c or ax - b > - c
That is the third option of the answer list.
how do you find the derivative of 4
Answers
by rule the derivative of a constant is 0
so the answer for this is 0
How does the volume of a cone compare to the volume of a cylinder with the same radius and height?
Answers
cone volume: π * r^2 * h/3
cylinder volume: π * r^2 * h
Now if you compare both of them with information that the radius and height is same, then the cone:cylinder volume ratio would be:
Cone volume/cylinder volume=
π * r^2 * h/3 / π * r^2 * h= 1/3
Cone volume is 1/3 of cylinder volume
what are the zeros of the quadratic function f(x)=8x2-16x-15
Answers
Answer: The zeroes of the given polynomial f(x) are
[tex]x=1-\sqrt{\dfrac{23}{8}},~~~x=1+\sqrt{\dfrac{23}{8}}.[/tex]
Step-by-step explanation: We are given to find the zeroes of the quadratic function below:
[tex]f(x)=8x^2-16x-15.[/tex]
To find the zeroes, we must find the roots of the following equation
[tex]f(x)=0\\\\\Rightarrow 8x^2-16x-15=0~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex].
We know that the roots of the quadratic equation of the form [tex]ax^2+bx+c=0,~a\neq 0[/tex] is given by
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}.[/tex]
In the given quadratic equation , a = 8, b = -16 and c = - 15.
Therefore, the roots of the equation are
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\\\\Rightarrow x=\dfrac{-(-16)\pm\sqrt{(-16)^2-4\times 8\times (-15)}}{2\times 8}\\\\\\\Rightarrow x=\dfrac{16\pm\sqrt{256+480}}{16}\\\\\\\Rightarrow x=\dfrac{16\pm\sqrt{786}}{16}\\\\\\\Rightarrow x=\dfrac{16\pm4\sqrt{46}}{16}\\\\\\\Rightarrow x=\dfrac{4\pm\sqrt{46}}{4}\\\\\\\Rightarrow x=1\pm\sqrt{\dfrac{46}{16}}\\\\\\\Rightarrow x=1\pm\sqrt{\dfrac{23}{8}}\\\\\\\Rightarrow x=1-\sqrt{\dfrac{23}{8}},~~~x=1+\sqrt{\dfrac{23}{8}}.[/tex]
Thus, the zeroes of the given polynomial f(x) are
[tex]x=1-\sqrt{\dfrac{23}{8}},~~~x=1+\sqrt{\dfrac{23}{8}}.[/tex]
Option (C) is correct.
The zeroes of the given polynomial f(x) = 8x^2-16x-15 are x = 1 + [tex]\sqrt{23}[/tex] / 8 and x = 1 -[tex]\sqrt{23}[/tex] / 8 Thus, Option C is correct.
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
We are given to find the zeroes of the quadratic function f(x) = 8x^2 - 16x-15
f(x) = [tex]8x^2-16x-15[/tex] = 0
We know that the roots of the quadratic equation ax² + bx + c = 0 is
x = -b ± [tex]\sqrt{b^2 - 4ac}[/tex] / 2a
In the given quadratic equation , a = 8, b = -16 and c = - 15.
So,
x = -b ± [tex]\sqrt{b^2 - 4ac}[/tex] / 2a
x = -(-16) ± [tex]\sqrt{(-16)^2 - 4(8)(-15)}[/tex] / 2(8)
x = 16 ± [tex]\sqrt{256+ 480}[/tex] / 16
x = 16 ± [tex]\sqrt{786}[/tex] / 16
x = 4 ± [tex]\sqrt{46}[/tex] / 4
x = 1 ± [tex]\sqrt{23}[/tex] / 8
Thus, the zeroes of the given polynomial f(x) are
x = 1 + [tex]\sqrt{23}[/tex] / 8 and x = 1 -[tex]\sqrt{23}[/tex] / 8. Option C is correct.
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Help me please thanks
Answers
A personal trainer buys a weight bench for $500 and some weights (w) for $24 each. the trainer has a budget of $860.00. how many weights can the personal trainer purchase
Answers
Final answer:
To find out how many weights the personal trainer can purchase, subtract the cost of the weight bench from the budget and divide the remaining amount by the cost of each weight. The personal trainer can purchase 15 weights within the given budget.
Explanation:
To find out how many weights the personal trainer can purchase, we need to subtract the cost of the weight bench from the budget and divide the remaining amount by the cost of each weight.
Step 1: Subtract the cost of the weight bench ($500) from the budget ($860): $860 - $500 = $360.
Step 2: Divide the remaining amount ($360) by the cost of each weight ($24): $360 ÷ $24 = 15.
The personal trainer can purchase 15 weights within the given budget.
This budgeting approach demonstrates a systematic way for the personal trainer to allocate funds effectively, ensuring that both essential equipment and a sufficient quantity of weights can be acquired. By following these steps, the trainer maximizes the utility of the available budget, making informed decisions to support an efficient and well-equipped training environment.
Evaluate the determinant for the following matrix [144] [522] [155]
Answers
1 4 4
5 2 2
1 5 5
=> Determinant =
1 * (2*5 - 2*5) - 4 * (5*5 - 1*2) + 4 * ( 5*5 - 2*1)
= 1*(10 - 10) - 4*(25 - 2) + 4*(25 -2) = 1*0 + 4* 23 + 4*(25 - 2) = 0 - 4*23 + 4*23 = 0
Answer: 0
One leg of a right triangle is 6 in. longer than the other leg. the hypotenuse of the triangle is 25 in. what is the length of each leg to the nearest inch?
Answers
longer leg = x+6
hypotenuse = 25
Using the Pythagorean theorem x^2 + (x+6)^2 = 25^2
I use a graphing calculator and
x = 14.421 so the longest leg = 20.421
or 14 and 20 inches
The problem can be solved using the Pythagorean theorem. The lengths of the legs of the triangle are calculated as 15 inches for the shorter leg and 21 inches for the longer leg.
Explanation:In solving this mathematical problem, we can employ the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides- This theorem is normally written as a² + b² = c². We can let one leg of the right triangle be 'a', the other leg be 'a+6' (since one leg is 6 inches longer than the other), and the hypotenuse is 25 inches. From the equation, we substitute a and b with the values and get:
a² + (a + 6)² = 25²
This equation is solved to get the lengths of the legs. Solving results in 'a' being 15 inches (the shorter leg) and 'a+6' equals to 21 inches (the longer leg).
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I feel really stupid but how do you solve: v+9/3+8
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The answer is v +11.
The answer would be simply
V 11
what is the slope of the line given by the equation y=2.3x
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making the slope of this equation 2.3
I believe this is the correct answer. I hope it helps.
Solve quadratic equations using completing the square then write in vertex form
Answers
Assuming you have;
ax²+bx+c=y
a(x²+b/ax)+c=y
a(x²+b/ax+(b/2a)²-(b/2a)²)+c=y
a(x²+b/ax+(b/2a)²)+c-a(b/2a)²=y
a(x+b/2a)²+c-a(b/2a)²=y
Try to use this format to solve the problems.
Hope I helped :)
The volume of air inside a rubber ball with radius r can be found using the function v(r)=4/3 πr3 . What does v[5/7] represent?
a. the radius of the rubber ball when the volome equals 5/7 cubic feet
b. the volome of the rubber ball when the radius equals 5/7 feet
c. that the volume of the rubber ball is 5 cubic feet when the radius is 7 feet
d. that the volume of the rubber ball is 7 cubic feet when the radius is 5 feet
Answers
we know that
The volume of a sphere (rubber ball) is equal to
[tex]V=\frac{4}{3} \pi r^{3}[/tex]
where
r is the radius of the sphere (rubber ball)
The volume in function notation is equal to
[tex]V(r)=\frac{4}{3} \pi r^{3}[/tex]
in this problem we have
[tex]V(\frac{5}{7})[/tex]
that means
The radius of the rubber ball is [tex]\frac{5}{7}\ ft[/tex]
and
The volume of the rubber ball is [tex]V(\frac{5}{7})\ ft^{3}[/tex]
therefore
the answer is the option B
the volume of the rubber ball when the radius equals [tex]5/7[/tex] feet
Write the fraction 20/32 in simplest form.
Answers
The fraction given 20/32 can be written as 5/8 in its simplest form.
How to simplify fractions?The principle of simplifying fraction is to make both the numerator and the denominator smaller numbers but as proportional as the original fraction. This is convenient for mathematical operations and even for understanding proportions.
Now, to simplify fractions we need to divide the nominator and the denominator, the process is shown below:
20/32 divide both numbers by 420/ 4 = 532/ 4 = 8This means the new fraction is 5/8.
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Heather works as a waitress at her family`s restaurant. she works 2 hours every morning during the breakfast shift and returns to work work each evening for the dinner shift. In the last 4 days ,she worked 28 hours. If Heather works the same number of hours every evening, how many hours did she work during each dinner shift?
Answers
2 hours x 4 days = 8 hours
Subtract,
28 hours - 8 hours = 20 hours
Divide
20 hours ÷ 4 days = 5 hours each day.
Check you work by Multiplying and adding
5 hours x 4 days = 20
20 hours + 8 hours = 28 hours
Heather worked 5 hours each dinner shift
Factor this expression completely.
mn - 4m - 5n + 20
Answers
Factor by grouping.
[tex]mn-4m-5n+20[/tex]
[tex]m(n-4)-5(n-4)[/tex]
Find the GCF.
[tex](n-4)(m-5)[/tex]
Hope this helps.
-Benjamin
Soda is sold in aluminum cans that measure 6 inches in height and 2 inches in diameter. how many cubic inches of soda are contained in a full can?
Answers
v=πr²h (now put in the values to find volume)
v=π(1)²(6)
v=18.85 inches cubed
Therefore, 18.85 inches cubed can be fit into the full can.
Hope I helped :)
A cylinder is a three-dimensional figure that has a radius and a height.
The volume of a cylinder is given as:
Volume = π r²h
The amount of soda in a full can is 18.84 cubic inches.
What is a cylinder?A cylinder is a three-dimensional figure that has a radius and a height.
The volume of a cylinder is given as:
Volume = π r²h
Example:
The volume of a cup with a height of 5 cm and a radius of 2 cm is
Volume = 3.14 x 2 x 2 x 5 = 62.8 cubic cm
We have,
Aluminum cans:
Height = 6 inches
Diameter = 2 inches
Radius = diameter/2 = 2 / 2 = 1 inches
The aluminum can is in the shape of a cylinder.
The volume of the aluminum can:
= πr²h
= 22/7 x 1 x 1 x 6
= 18.84 cubic inches
The amount of soda in a full can is 18.84 cubic inches.
Thus,
The amount of soda in a full can is 18.84 cubic inches.
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What is the standard form of the following equation?
y=−2/5x+4 Use integers for A, B, and C. Enter your answer in the box.
Answers
so
[tex] \frac{-2}{5} x -y=-4 [/tex]
multiply by -1 to make the x coefficient positive
[tex] \frac{2}{5} x+y=4 [/tex]
so we multiply by 5 to make them integers
[tex]2x+5y=20[/tex]
A=2,B=5,C=20
I will give you 25 points for my other qusetion
Answers
MATH HELP 20 POINTS!!!
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A) Variable = x ( miles Tim walked )
B) Tim walked X miles, Molly walked 4+x miles ( 4 more than Tim)
Equation: x + x+4 = 10
C) x +x+4 = 10
2x+4 = 10
2x =6
x = 3
D)
Tim walked 3 miles, Molly walked 7 miles