Given triangle PRS is congruent to triangle CFH, find the values of x, y, and z.
Answers
Answer:
x = 23
y = 7
z = 11
Step-by-step explanation:
Since ∆PRS ≅ ∆CFH, therefore,
m<R = m<F
13y - 1 = 90° (substitution)
Add 1 to both sides
13y - 1 + 1 = 90 + 1
13y = 91
Divide both sides by 13
13y/13 = 91/13
y = 7
Since ∆PRS ≅ ∆CFH, therefore,
PS = CH
2x - 7 = 39 (substitution)
Add 7 to both sides
2x - 7 + 7 = 39 + 7
2x = 46
Divide both sides by 2
2x/2 = 46/2
x = 23
Since ∆PRS ≅ ∆CFH, therefore,
m<S = m<H
Find m<S
m<S = 180 - (m<P + m<R) (sum of ∆)
m<S = 180 - (28 + (13y - 1)) (substitution)
Plug in the value of y
m<S = 180 - (28 + (13)(7) - 1))
m<S = 180 - (28 + 91 - 1)
m<S = 180 - 118
m<S = 62°
Therefore, since m<S = m<H,
62° = 6z - 4 (substitution)
Add 4 to both sides
62 + 4 = 6z - 4 + 4
66 = 6z
Divide both sides by 6
66/6 = 6z/6
11 = z
The values of x, y, and z are;
x = 23
x = 23y = 7
x = 23y = 7z = 11
We are told that triangle PRS is congruent to triangle CFH.
Since both triangles are congruent, by inspection we can see that;
m<R = m<F
m<F is a right angle = 90°. Thus;
13y - 1 = 90
13y = 90 + 1
13y = 91
y = 91/13
y = 7
Also by inspection;
PS = CH
2x - 7 = 39
2x = 39 + 7
2x = 46
x = 46/2
x = 23
Since m<R is 90°, then;
m<S = 180 - (90 + 28)
m<S = 62°
By inspection;
m<S = m<H
Thus;
6z - 4 = 62
6z = 66
z = 66/6
z = 11
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Related Questions
Find the value of "x".
Answers
Answer:
x = 4.52984
Step-by-step explanation:
Since the triangle has a right angle you need to use the the trigonometric function cos (theta which is the angle given that isn't 90°) = adjacent / hypotenuse (adjacent is the side close to the angle you're using which is 22° and the hypotenuse is the longest side of the triangle that is in the away from the right angle)
From there you plug in the numbers which now become cos (22°) = 4.2 / x
Then you isolate the x by multiplying it to both sides so it's on the left and divide both sides by cos (22°) which will end you up x = 4.2 / cos (22°)
Then you just divide and you 4.52984
Find the slope of the line that passes through the pair of points.
(-2,3), (-5,2)
Answers
Answer:
A. 1/3
Step-by-step explanation:
2-3/-5--2=
2-3/-5+2=
-1/-3=
1/3
Question: (help please?!?!)Bridget has $2,835 in her savings account. Each pay period, $945 is deposited into
her savings account. If her paycheck deposits are the only transactions, which of the
following equations could be used to find y, the amount in her savings account based
on x, the number of times she is paid?
A y = 2,835 - 945x
B 2,835y = 945x
C y = 945x + 2,835
D y = 2,835x + 945
Answers
Answer:
C. y = 945x + 2,835
Step-by-step explanation:
Each pay period 945 dollars is deposited so that's the slope, which x stands for each pay period. She already started with 2,835 in her savings account so that is the y-intercept.
Slope: 945x
Y- intercept: 2,835
Therefore,
equation: y = 945x + 2,835
What is the value of x? Please provide an explanation, thanks!
Answers
Step-by-step explanation:
x + 1 + 2x + 2 + 12x - 18 = 180 (sum angles in triangle)
15x - 15 = 180
15x = 195
x = 13deg
Topic: Angles
If you like to venture further, do check out my insta (learntionary) where I constantly post math tips! Thanks!
Step-by-step explanation:
(x+1)°+(2x+2)°+(12x-18)°=180°
15x+3°-18°=180°
15x+15°=180°
15x=180°-15°
x=165°/15°
x=11° Answer..
rewrite the equation by completing the square 3+x=x^2+3x
Answers
Answer:
[tex](x+1)^2=4[/tex]
Step-by-step explanation:
[tex]3+x=x^2+3x[/tex] is our equation first, get all the x terms on one side so the equation equals a constant number[tex]3+x-(x)=x^2+3x-x\\3=x^2+2x\\x^2+2x=3[/tex] Then add to both sides the square of half of the coefficient of x : the coefficient of x here is 2 sothe square of half of 2 is [tex](1)^2[/tex] then[tex]x^2+2x+(1)^2=3+(1)^2\\x^2+2x+1=4\\[/tex] If you factor the left side you get [tex]x^2+2x+1=4\\(x+1)^2=4[/tex]Answer:
(x+1)^2 =4
x=-1±2
Step-by-step explanation:
I got it right on khan
Please help! Only if you know though :))$
Answers
Answer:
180
Step-by-step explanation:
Solve For X:
25 + 8x = 1
Answers
Answer:
x=-3
Step-by-step explanation:
Answer:
x=-3
Step-by-step explanation:
25+8x=1
8x=-24
x=-3
There were 43 children at the playground. Now there are 27 children at the playground. How many children left the playground? Ben says that 13 children left the playground. He thinks that 43 – 30 is easier to subtract than 43 – 27. He subtracts 43 – 30 and gets 13. Why is Ben's reasoning not correct?
Answers
Ben is incorrect because Ben did not answer the question according to the available information. The fact that subtracting 43 from 30 is easier for Ben does not mean it is the correct answer.
Find the value of c that completes the square
x^2+7x+c
Please help me with how to do this, and show me. Thank you.
Answers
Answer:
c = [tex]\frac{49}{4}[/tex]
Step-by-step explanation:
Given
x² + 7x + c
To complete the square
add ( half the coefficient of the x- term )² to x² + 7x
x² + 2([tex]\frac{7}{2}[/tex] )x + [tex]\frac{49}{4}[/tex] , thus
= (x + [tex]\frac{7}{2}[/tex] )² ← a perfect square
with c = [tex]\frac{49}{4}[/tex]
Create a polynomial with the following attributes:
* degree is 3
* zeros are -2, 4, and 7
Answers
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
Zeros :
[tex]x = - 2[/tex]
[tex]x = 4[/tex]
[tex]x = 7[/tex]
Thus ;
[tex]x + 2 = 0[/tex]
[tex]x - 4 = 0[/tex]
[tex]x - 7 = 0[/tex]
Multiply above equations :
[tex](x + 2)(x - 4)(x - 7) = 0[/tex]
Expand
[tex]( {x}^{2} - 2x - 8)(x - 7) = 0[/tex]
[tex] {x}^{3} - 7 {x}^{2} - 2 {x}^{2} + 14x - 8x + 56 = 0 \\ [/tex]
[tex] {x}^{3} - 9 {x}^{2} + 6x + 56 = 0[/tex]
[tex]y = f(x) = {x}^{3} - 9 {x}^{2} + 6x + 56 \\ [/tex]
Done...
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
what is 3c² + d³ when c = 1 and d=2 = please
Answers
Answer:
11
Step-by-step explanation:
3(1)^2 = 3
2^3 = 8
3+8=11
Solve the inequality 4y + 3 > 2y + 14
Answers
9514 1404 393
Answer:
y > 11/2
Step-by-step explanation:
Subtract 2y+3 to get the variable term alone on one side.
2y > 11
y > 11/2 . . . . . . divide by the coefficient of y
Quadrilateral ABCD undergoes a reflection across the x-axis to form quadrilateral a b c d the coordinates of a r the reflected quadrilateral a b c d is then translated three units to the right and third and two units up to form quadrilateral a quotation b quotation quotation see quotation
Answers
Solution :
From the figure,
The coordinates of --
A = (-5,-3)
B = (-6,-1)
C = (-3,-1)
D = (-2,-3)
When it undergoes reflection about x-axis, we have the coordinates of the quadrilateral as
A' = (-5,+3)
B' = (-6,+1)
C' = (-3,+1)
D' = (-2,+3)
Now A'B'C'D' is translated 3 units to right, so the coordinates will be --
A" = (-2,3)
B" = (-3,1)
C" = (0,1)
D" = (1,3)
When the quadrilateral moves third and two units up, we get
A"' = (3,3)
B"' = (2,1)
C"' = (5,1)
D"' = (6,3)
Answer:
Step-by-step explanation:
Find the fraction, decimal, or percent that is NOT equivalent to 2.3?
23/10
230%
2.3%
Answers
Answer:
23/10
Step-by-step explanation:
Write the following numbers in scientific notation 56,089
Answers
Answer:5.6089*10^4
Step-by-step explanation:
Is 56/8 an interger
Please help....
Answers
An alloy consists of nickel, zinc, and copper in the ratio 2:7:9.
a
How much of each metal is needed to make 3.6 kg of this alloy?
Answers
Answer:
0.4kg, 1.4kg and 1.8kg
Step-by-step explanation:
Given parameters:
Mass of alloy = 3.6kg
Ratio of elements in the alloy = 2:7:9
Unknown:
Mass of each element in the alloy = ?
Solution:
To find the mass of each element in the alloy, first find the sum of the ratio;
2+7+9 = 18
Mass of nickel = [tex]\frac{2}{18}[/tex] x 3.6 = 0.4kg
Mass of zinc = [tex]\frac{7}{18}[/tex] x 3.6 = 1.4kg
Mass of copper = [tex]\frac{9}{18}[/tex] x 3.6 = 1.8kg
The mass of each metal is 0.4kg, 1.4kg and 1.8kg
Answer:
Nickle=0.4
Zinc=1.4
Copper=1.8
Step-by-step explanation:
after eating at a restaurant the bill for your table is $62.50. There is a 6% sales tax and you want to leave a tip for 18% based on the pre-tax amount. How much money do you need to cover your final bill?
Answers
Answer:
Step-by-step explanation:
Your bill is $62.50
$62.50 * .06 = $3.75 (this is your sales tax added)
So your total is up to: $66.25
Adding the tip the same way using $66.25 *.18 = $11.93
Tip would be $11.93
Total coming to: $78.17
hope this helps
Answer:
$77.50
Step-by-step explanation:
Tax:
62.50x0.06= 3.75
3.75+62.50= 66.25
Tip:
62.50x0.18= 11.25
Answer:
66.25+11.25= 77.50
Please help! Thank you!!
Answers
I thought i had the right answer, but it was wrong. So anyone want to to help me with this? Please dont steal points. 7 points each!
Answers
Answer:16 dollars per shirt
Step-by-step explanation:
Answer:
$16 profit per sweater
Step-by-step explanation:
$130-$50=$80
$80÷5=$16
HELP ION GET THIS :(
Answers
Answer:
-2
Step-by-step explanation: use rise over run, start from bottom point, you go up 4, to the left 2. 4/-2=-2
Answer:
m=-2
Step-by-step explanation:
m=(y2-y1)/(x2-x1)=(-3-1)/(2-0)=-4/2=-2
Hope this helps; please vote brainliest.
954÷70
and remainder
Answers
Answer:
13 with a remainder of 44
Step-by-step explanation:
.
please help me out with this question.
much appreciation. Thanks.
Answers
Answer:
there is nothing
Step-by-step explanation:
Please help me!!
Really fast PLEASE
Answers
Answer:
The answer to your question is $7
Answer:
Purchase Price:
$28
Discount:
(28 x 75)/100 = $21.00
Final Price:
28 - 21.00 = $7.00
cuanto es 100+100+0+0+0+0+0
Answers
Answer:
es 200
Step-by-step explanation:
100+100=200
0+0+0+0+0=0
PLEASEEEE HELP ASAPPPP
Answers
Answer:
I think its A
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
The y intercept is 2, visible on the graph.
The way I think about counting slope is (in this case)
"up one, over 5"
1/5
c=1/5m+2
D is your answer if there are 4 options (A, B, and C are incorrect; D isn't shown so I assume it's what I got)
HTH :)
Jake bought two shirts and one pair of pants for six dollars mike bought one shirt and one pair of pants for four dollars how much is each shirt and each pair of pants the system of equations used to solve this would be 2X plus Y equals six and X plus Y equals four
Answers
Using the elimination method, we can solve this system of equations. You must find a common multiple of both equation for either x or y. I chose to multiply equation 2 by (-2) so that the x would be eliminated, allowing us to solve for y.
Work:
Help ASAP if you want brainliest
Answers
Answer:
Its C
Step-by-step explanation:
Answer:
c.27/31 fluid ounce...
is y = -4 + 2x linear?
Answers
Answer: it is linear
Step-by-step explanation: Find the degree of the equation to determine if linear.
Answer:
Yes
Step-by-step explanation:
Look up Desmos, it is graphing calculator... it will really help. REAL EXPLANATION: You put one point on -4, then do rise over run (2/1x), thus go up to over one. So on and so forth; this will result in a linear line.
Which ones are equivalent?
Answers
Answer:
1st one, 3rd one, and 5th one.
Answer:
The first, third and the fifth.
Step-by-step explanation:
First one is equivalent
√(8^2*8^2)
= √64*64
= √64.
8^1/2 * 8^1/2
= 8^1
= √64.
√(16*4)
= √64.