Given: SQ and TQ trident angle PQR
measure of angle PQT = 7x+6
measure of angle TQS = -2x +8y-13
measure of angle RQS = 5x +2y
find measure of angle PQR
Answers
Answer:
[tex]10x+10y-7[/tex]
Step-by-step explanation:
We just need to add up all of the angles, PQT, TQS, and RQS to find the measure of angle PQR.
[tex]PQT=7x+6\\TQS=-2x+8y-13\\RQS=5x+2y\\PQT+TQS+RQS=PQR\\7x+6+TQS+RQS=PQR\\7x+6+(-2x+8y-13)+RQS=PQR\\7x+6+(-2x+8y-13)+5x+2y=PQR\\7x+6-2x+8y-13+5x+2y=PQR\\7x-2x+5x+8y+2y+6-13=PQR\\5x+5x+8y+2y+6-13=PQR\\10x+8y+2y+6-13=PQR\\10x+10y+6-13=PQR\\10x+10y-7=PQR[/tex]
9514 1404 393
Answer:
123°
Step-by-step explanation:
Each of the parts of the trisected angle is equal to the others.
∠PQT = ∠TQS
7x +6 = -2x +8y -13
9x -8y +19 = 0 . . . . . . subtract the right-side expression
∠TQS = ∠RQS
-2x +8y -13 = 5x +2y
7x -6y +13 = 0 . . . . . . subtract the left-side expression
__
These equations can be solved by any of your favorite methods to give ...
(x, y) = (5, 8)
Then the angle measures are ...
∠PQT = 7x +6 = 7(5) +6 = 41
∠TQS = -2x +8y -13 = -2(5) +8(8) -13 = 64 -23 = 41
∠RQS = 5x +2y = 5(5) +2(8) = 41
The measure of angle PQR is 3·41° = 123°.
_____
Additional comment
Using Cramer's rule, the solution is ...
x = (-8(13) -(-6)(19))/(9(-6) -7(-8)) = 10/2 = 5
y = (19(7) -13(9))/2 = 16/2 = 8
I prefer a method like this, or the graphical solution, when the numbers don't lend themselves to substitution or elimination.
__
Obviously, once we have found angle PQT, we can simply multiply it by 3 to find angle PQR. We chose to compute the values of the other angles as a check on our math.
Related Questions
Multiply
(s - 5)(2s + 7)
(s - 5)(25+7)=(Simplify your answer.)
(SOMEONE PLEASE ANSWER)
Answers
(s - 5)(2s + 7) =
= 2s² + 7s - 10s - 35 =
= 2s² - 3s - 35
Answer:
2s² - 3s - 35 {final answer}
Step-by-step explanation:
Let's find simplest form of equation,
→ (s - 5)(2s + 7)
→ 2s² + 7s - 10s - 35
→ 2s²- 3s - 35
Thus, the answer is 2s²- 3s - 35.
Under her cell phone plan, Gianna pays a flat cost of $57 per month and $3 per
gigabyte. She wants to keep her bill under $90 per month. Which inequality can be
used to determine x, the maximum number of gigabytes Gianna can use while
staying within her budget?
Answers
Answer:
3x + 57 ≤ 90
Step-by-step explanation:
Answer:
3x+57<90
Step-by-step explanation:
Have a good day :)
select the correct answer
1.caul will be the measure of one of the legs of a right triangle, if its hypotenuse is 10 cm and leg b is 6 cm, what will be the measure of leg a?
a) 8 cm
b) 5 cm
c) 4 cm
d) 12 cm
please
Answers
Answer:
answer us a) 8cm
Step-by-step explanation:
a^2 + 6^2 = 10^ 2
a^2 + 36 = 100
subtract 36 from 100
a^2 = 64
square root of 64 is 8
What is the distance from the origin to point A graphed on the complex plane below
Answers
Answer:
B) [tex]\sqrt{13}[/tex]
Step-by-step explanation:
1. [tex]d = \sqrt{(-3-0)^2+(-2-0)^2}[/tex]
2. [tex]d=\sqrt{(-3)^2+(-2)^2}[/tex]
3. [tex]d=\sqrt{9+4}[/tex]
4. [tex]d=\sqrt{13}[/tex]
[tex]\sqrt{13} = 3.60555..[/tex]
Evaluate x + 2.7 for x= -1.5.
The value of the expression is
Answers
[tex]\text{x}=-1,5\\\\\text{x}+2,7=-1,5+2,7=2,7-1,5=\boxed{1,2}[/tex]
5. The graph shows the relationship between the number of cups of flour and the propos
number of cups of sugar in Lin's favorite brownie recipe.
3
cups of flour
1
.
1 2 3 4 5
cups of sugar
The table shows the amounts of flour and sugar needed for Noah's favorite brownie
recipe.
Answers
Answer:
what are you confused on??
Alix is 6 inches shorter thelan Ben. Alix is p inches tall. Write an expression to show how tall Ben is
Answers
Answer:
p+6
Step-by-step explanation:
What is the coefficients and Constants for 5x-10
Answers
Answer:
coefficient
5
constant
-10
Step-by-step explanation:
5x-10
The coefficient is the number in front of the variable
5
The constant is the number alone
-10
Make up a data set (n = 10) that has the same minimum value, same median, and same maximum value, but a larger IQR than the boxplot shown.
a. Give your 10 numbers.
b. Give the 5-number summary for your data.
c. Describe your strategy for figuring this out.
Answers
The 10 hypothetical numbers which meets the conditions given on the question may include :
1, 2, 3, 5, 6, 6, 7, 10, 10, 12
The five number summary include the maximum, minimum, lower quartile, Median and upper quartile of a distribution.
The five number summary of the hypothetical data are:
Median: 6
Minimum: 1
Maximum: 12
Lower quartile: 2.75
Upper quartile: 10
Comparing the 5 - number summary of the hypothetical data with that of the given boxplot.
From the given boxplot shown :
Minimum value = 1
Maximum value = 12
Median = 6
LOWER QUARTILE, Q1 = 4
UPPER QUARTILE, Q3 = 8
IQR = (Q3 - Q1) = 8 - 4 = 4
THE 10 made up numbers :
1, 2, 3, 5, 6, 6, 7, 10, 10, 12
The five number summary for the made up data :
Median = 1/2(n+1)th term = 5.5th term = (6+6)/2 = 6
Minimum: 1
Maximum: 12
First quartile = 1/4(n+1)th = 2.75th term = (2+3)/2 = 2.5
Third quartile: 3/4(n+1)th term = 8.25 = (10+10)/2 = 10
Interquartile Range: (10 - 2.5) = 7.5
The original data values and hypothetical data have the same minimum and maximum and median values. The hypothetical data has an higher IQR value than the original data.Learn more : https://brainly.com/question/12992903?referrer=searchResults
What is |—14|?
A. —14
B. —7
C. 7
D. 14
E. 1 1/4
Answers
Answer:
14
Step-by-step explanation:
If the negative was outside of the lines, then the answer would be -14, but that is not the value. It is 14.
Answer:
D
Step-by-step explanation:
-14 is in Absolute Value signs. This means that if a number is in the absolute value signs, It's always positive. So that leaves us with C, D, or E. Absolute value signs also mean they are the same number as if it was negative, so that tells us that the answer is D!
Solve (q - 3/4) ( q + 1/4) using the FOIL method. QUICK PLEASE !
Answers
Answer: q^2 - 1/2q - 3/16
Step-by-step explanation:
(q - 3/4) ( q + 1/4)
First: (q)(q) = q^2Outer: (q)(1/4) = 1/4qInner: (-3/4)(q) = -3/4qLast: (-3/4)(1/4) = -3/16(q - 3/4) ( q + 1/4)
= q^2 + 1/4q - 3/4q - 3/16
= q^2 - 1/2q - 3/16
if BC=2x-3 and AC=2x+10, find the length of AB
Answers
Answer:
ac
Step-by-step explanation:
xcsddddssss
Which is equivalent to (2 x
5)^4
Answers
Answer:
10000
Step-by-step explanation:
2*5=10
10^4=10*10*10*10=10000
Can someone help (Geometry)
Answers
Answer:
∠DAC is 35°
Step-by-step explanation:
Given:
Measure of ∠DAB = 64°
Measure of ∠CAB = 29°
Solution:
∠DAB shows the value of the overall angle.
∠CAB shows the value for almost half of the angle.
∠DAB - ∠CAB = ∠DAC
64° - 29° = ?
∴ 64° - 29° = 35°
Hence, the value of ∠DAC is 35°
given g(x) = x2−4
find g(-3)
Answers
Answer:
Step-by-step explanation:
First we have to match these two terms
g(x)= g(-3)
Now we just replace the -3 with the x
-3^2 - 4
9-4
5 ----> the final answer
(btw the negative turned positive because it is squared)
Convert 6% to a fraction in a simplest form
Answers
Answer:
[tex]\frac{3}{50}[/tex]
Step-by-step explanation:
6% = [tex]\frac{6}{100}[/tex]
= 0.06
= [tex]\frac{0.06}{1}[/tex] × [tex]\frac{100}{100}[/tex]
= [tex]\frac{6}{100}[/tex]
= [tex]\frac{3}{50}[/tex]
Find the distance between the pair of points. E(9,-4) F(-3,5)
Answers
Answer:
5
Step-by-step explanation:
√
(
−
3
−
9
)
2
+
(
5
−
−
4
)
2
=
√
(
−
12
)
2
+
9
2
=
√
144
+
81
=
√
225
= 15
Distance between points (9, -4) and (-3, 5) is 15
If f(x)=3x-2 and g(x)=2x+1, find (f-g)(x)
A. 5x-3
B. 5x-1
C. X-3
D. 3-x
I need step by step explanation please
Answers
Answer:
B
Step-by-step explanation:
3x - 2 + 2x + 1
5x - 1
Solve the equation for y.
-4x+ 3y = 12
Answers
Answer:
[tex] - 4x + 3y = 12 \\ 3y = 12 + 4x[/tex]
divide through out by 3:
[tex]y = 4 + \frac{4}{3} x \\ \\ { \boxed{ \boxed{y = \frac{4}{3}x + 4 }}}[/tex]
Answer:
y = 4/3x + 4
Step-by-step explanation:
-4x + 3y = 12
-4x + 3y + 4x = 12 + 4x
3y = 4x + 12
3y/3 = (4x + 12)/3
y = 4/3x + 4
Luis buys 0.56 pound of power pasta. Mariana buys 0.27 pound of power pasta. How much do they buy in all?
Answers
Add the two amounts together:
0.56 + 0.27 = 0.83 pounds total
Luis buys 0.56 pound of power pasta. Mariana buys 0.27 pound of power pasta. How much do they buy in all?
Solution:First, understand the problem.
Luis buys 0.56 pounds of power pasta.
Mariana buys 0.27 pound of power pasta.
Then, add the bus of Luis and Mariana.
Luis buys + Mariana buys = N0.56 + 0.27 = NN = 0.83Answer:Therefore, 0.83 buy in all.please show work 3d – 4 + d = 8d – (-12)
Answers
Answer:
d = -4
Step-by-step explanation:
3d – 4 + d = 8d – (-12)
3d - 4 + d = 8d + 12
4d - 4 = 8d + 12
(4d - 4d) - 4 = (8d - 4d) + 12
-4 = 4d + 12
-4 - 12 = 4d (+ 12 - 12)
-16 = 4d
-16/4 = 4d/4
d = -4
Answer:
d= -4
Step-by-step explanation:
3d- 4 +d = 8d + 12
4d - 4 = 8d + 12
4d = 8d + 16
-4d = 16
d= -4
Check
-12 - 4 - 4 = -32 + 12
-20 = -20
Choose the correct equivalent expression that includes a set of parentheses so that the value of the expression is 20.
(12 + 32) ÷ 4
12 + (32 ÷ 4)
pls give the right answer i will make you brainlist
Answers
Answer:
12 + (32 ÷ 4)
Step-by-step explanation:
Step 1:
12 + (32÷ 4)
Step 2:
12 + 8
Answer:
= 20
Hope it helps :)
Referring to the figure, does the triangle shown have
rotational symmetry?
a. yes
b. no
Answers
Referring to the figure, does the triangle shown have
rotational symmetry?
a. yes
b. no
What is the equation of the axis of symmetry?
Answers
Answer:
x = 0
Step-by-step explanation:
you could hold a mirror perpendicular to the page with an edge aligning on the y axis and the reflected curve would imitate the actual curve.
2) One bag has a 2 red tiles, 4 blue tiles, and a green tile. A second bag has
yellow tile and 2 brown tiles. Alex draws one tile from each bag. What are all
the possible outcomes? How large is the sample space?
Answers
Answer:I donno
Step-by-step explanation:
are All integers are real numbers.
Answers
Answer:
no
Step-by-step explanation:
all integers are not real numbers.integers are negative and positive numbers. but real numbers don't include negative numbers.
Which of the following shows the prime factorization of 72 using exponential notation?
Answers
Answer:
2^3 .3^2
Step-by-step explanation:
if 2×2×2 = 8
and 3×3=9 then 8×9=72
Answer:
2³ × 3²
Step-by-step explanation:
Repeatedly divide by 2 until finish, then divide by 3
72 ÷ 2 = 36
36 ÷ 2 = 18
18 ÷ 2 = 9 , then
9 ÷ 3 = 3
3 ÷ 3 = 1 ← finish when 1 is reached
Then
72 = 2 × 2 × 2 × 3 × 3 = 2³ × 3²
For the function f(x) = -x^3 + 2x^2 + x - 2
a. Show that (x - 1) is a factor of f(x).
b. Find other factors.
c. Sketch the graph of f(x) = -x^3 + 2x^2 x - 2
Answers
Answer:
Step-by-step explanation:
a)
[tex]f(1)=-1^3+2*1^2+1-2=-1+2+1-2=0\\\\[/tex]
b)
Rationnel roots are divisor of -2: -1,1,-2,2
[tex]f(-1)=-(-1)^3+2*(-1)^2+(-1)-2=1+2-1-2=0\\\\\begin{array}{c|cccc}&x^3&x^2&x&1\\---&---&---&---&---\\&-1&2&1&-2\\x=1&&-1&1&2\\&-1&1&2&0\\\\x=-1&&1&-2\\&-1&2&0\\---&---&---&---&---\\\end {array}\\\\\\f(x)=-x^3+2x^2+x-2=(x-1)(x+1)(-x+2)\\\\[/tex]
c) see picture
Trevor has 40 contacts in his phone. Six are coworkers, 8 are
family members, and 26 are friends. If Trevor accidentally
calls a random contact, what is the probability he will call a
friend?
Answers
Answer:
0.65
Step-by-step explanation:
There are 26 friends on his phone.
There's a total of 40 contacts.
P(Friend) = 26/40
P(Friend) = .65
Which of the below measures of central tendency is/are always unique ?
Answers
Answer:
A measure of central tendency is a single value that attempts to describe a set of data by identifying the central position within that set of data
