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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Answers
Answer:
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
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Step-by-step explanation:
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Answer:
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Answer:
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Step-by-step explanation:
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Step-by-step explanation:
Answer:
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Answer:
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Answer:
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Step-by-step explanation:
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Answers
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
Answer:
D
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Answers
Answer:
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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
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Mass of zinc = [tex]\frac{7}{18}[/tex] x 3.6 = 1.4kg
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Answer:
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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:
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So your total is up to: $66.25
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Answer:
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Step-by-step explanation:
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Tip:
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Answer:
66.25+11.25= 77.50
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Answers
Solution :
From the figure,
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Answer:
Step-by-step explanation:
Find the value of c that completes the square
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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]
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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
Create a polynomial with the following attributes:
* degree is 3
* zeros are -2, 4, and 7
Answers
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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...
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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