Answers
Solution:
Note that:
4x - 27 = 3x + 4 (Vertically opposite angles)Using the equation (4x - 27 = 3x + 4), solve for x.
4x - 27 = 3x + 4=> -3x + 4x - 27 = 3x + 4 - 3x=> x - 27 = 4=> x - 27 + 27 = 4 + 27=> x = 31The measure of x is 31.
Solve for X ~
[tex] \bf4x - 27 = 3x + 4[/tex]
[tex] \bf \: 4x - 3x = 4 + 27[/tex]
[tex] \boxed{ \bf \: x = 31}[/tex]
Now, Finding each angle⤵️[tex] \tt \: ∠1 = 2x + 21 \\ \tt \: = 2 \times 31 + 21 \\ \tt \: ∠1= 83 \degree[/tex]
[tex] \tt \: ∠2 = 4x + 27\\ \tt \: = 4\times 31 - 27 \\ \tt \: ∠2= 97 \degree[/tex]
[tex] \tt \: ∠3 = 3x + 4 \\ \tt \: = 3\times 31 + 4 \\ \tt \: ∠3= 97 \degree[/tex]
Related Questions
Consider in the figure below.
The perpendicular bisectors of its sides are , , and . They meet at a single point .
(In other words, is the circumcenter of .)
Suppose , , and .
Find , , and .
Note that the figure is not drawn to scale.
Answers
Here BD is perpendicular bisector
So
UB=BV=74[tex]\\ \tt\hookrightarrow UV=74+74=148[/tex]
Apply Pythagorean theorem
[tex]\\ \tt\hookrightarrow BD^2=UD^2-UB^2=UD^2-VD^2[/tex]
UD=VD=78=TD[tex]\\ \tt\hookrightarrow TC^2=TD^2-CD^2[/tex]
[tex]\\ \tt\hookrightarrow TC^2=78^2-30^2[/tex]
[tex]\\ \tt\hookrightarrow TC^2=6084-900=5184[/tex]
[tex]\\ \tt\hookrightarrow TC=72[/tex]
Answer:
UV = 148
VD = 78
TC = 72
Step-by-step explanation:
BD is the perpendicular bisector of side UV.
Therefore, ΔUDV is an isosceles triangle.
This implies that UD = VD and BV = UB so UV = 2 x BV
Given that UD = 78, and UD = VD, then VD = 78Given that BV = 74, and BV = UB, then UV = 2 x 74 = 148ΔUDC is a right triangle.
Given CD = 30 and UD = 78,
and using Pythagoras' Theorem, we can calculate UC:
UC = √(UD² - CD²)
⇒ UC = √(78² - 30²)
⇒ UC = 72
CD is the perpendicular bisector of side UT.
Therefore, ΔUDT is an isosceles triangle, so UC = TC
Since UC = 72, then TC = 72
What is the area of the drawing of the trophy shown?
Answers
Answer:
The area of the drawing is 12 Squares
MULTIPLE CHOICE QUESTION
SOLVING SYSTEMS OF EQUATIONS BY ELIMINATION
(5x-y=74
x + 4y = 14
2x=y=5
7x+2y=-10
Which of the following will be the new
equation when the top equation
is multiplied by 4?
5x-4y=7
20x-4y=7
20x-4y=28
5x-y=28
Answers
Answer:
It will be: ( 5x - y =7 )4
20x - 4y = 28
Option (C)
Find slope: PLEASE HELP !
Answers
Take 2 points
(-7,4)(2,6)Slope:-
[tex]\\ \rm\hookrightarrow m=\dfrac{6-4}{2+7}[/tex]
[tex]\\ \rm\hookrightarrow m=\dfrac{2}{9}[/tex]
[tex]\\ \rm\hookrightarrow m=0.2[/tex]
calculate each of the following
9/25÷3/50
Answers
Answer:
6
Step-by-step explanation:
First divide 9 by 25 to get 0.36 and then divide 3 by 50 to get 0.36 . Finally divide the first result which os 0.36 by the second result which is 0.06 to get 6
find the value of x.
Answers
Answer:
x = 145
Step-by-step explanation:
The sum of the angles of a quadrilateral is 360
35+x+35+x = 360
2x+70 = 360
Subtract 70 from each side
2x+70-70 = 360-70
2x = 290
Divide by 2
2x/2 =290/2
x = 145
Answer:
x=145
(145+145+35+35=360)
Step-by-step explanation:
This question is very simple to answer if you remember that all parallelograms have two pairs of equal and opposite angles, and that the four angles in any quadrilateral must add up to 360 degrees.
Help me please please please
Answers
Answer:
GPA ≈ 2.67
Step-by-step explanation:
Grade points are weighted by credit hours:
GPA = ∑(grade points×credit hours) / ∑(credit hours)
GPA = (3×2 +2×4 +4×3 +2×3)/(2 +4 +3 +3)
= (6 +8 +12 +6)/12 = 32/12 = 2 2/3
GPA ≈ 2.67
Seven times the product of negative six and a number
Answers
Hi!
I can help you with joy! :)
7 times the product of -6 and a number. Let the number be
a. Now, "the product of" means we multiply.
Multiply -6 times a: -6a
If you notice, we write the number before the variable.
Now, multiply 7 times -6a:
7(-6a)
Simplify:
-42a
I hope this helps!
Have a Great Day!
-Content Girl
[tex]\bf{Mysterious^a^n^d\:M^a^gi^ca^l[/tex]
35% of what number is 105?
Answers
Answer:
35 percent of 105 is 36.75 .
Billy has a credit card with a current balance of $3,500 and a 16% APR. With his current monthly payment, he will be able to pay off this debt in 15 months. But Billy just learned that he is getting a raise at work. If he puts all of the extra income from his raise into his monthly credit card payment, how much additional monthly income would he require from his raise to pay off the credit card in 12 months?
Answers
Answer:
It's A :)
Step-by-step explanation:
ur welcome
Answer:
✅ A. $58.57i took the test⬇️
10. There are 100 patients willing to join a study trying out a new drug for high
blood pressure. Of these participants, 42 are male and 58 are female. If two
people are chosen at random, what the probability that both are female?
Answers
Answer:
551/1650
Step-by-step explanation:
(58/100)(57/99)=551/1650
If (-3, y) lies on the graph of y = (1/2)^x, then y =
-8
8
1/8
Answers
the answer is 8
How do you do this? Please help.
Answers
Find the Value of y when y=3x+45 and x=7
102
15
35
66
Answers
Answer:
y = 66
Step-by-step explanation:
y=3x+45
putting the value of x in equation which is 7 .
=> y = 3(7)+45
=> y = 21+45
=> y = 66
Almost all medical schools in the United States require students to take the Medical College Admission Test (MCAT). The total score of the four sections on the test ranges from 472 to 528. In spring of 2019, the mean score was 500.9, with a standard deviation of 10.6.
Find the median of the MCAT scores.
Give your answer to three decimal places.
Answers
Using the normal distribution, it is found that the median of the MCAT scores was of 500.9.
Normal Probability Distribution
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.The median is also the 50th percentile, hence, in the normal distribution, it is equals to the mean.In this problem, the mean score was 500.9, hence the median score was also of 500.9.
You can learn more about the normal distribution at https://brainly.com/question/24663213
For a 15 year mortgage of $200000 at 5.125%, how much money was paid back to the lender at the end of the 15 years?
Answers
Answer:
Step-by-step
Monthly payments on a $200,000 mortgage
At a 4% fixed interest rate, your monthly mortgage payment on a 30-year mortgage might total $954.83 a month, while a 15-year might cost $1,479.38 a month.explanation:
hope this helped
Monthly payments on a $200,000 mortgage
At a 4% fixed interest rate, your monthly mortgage payment on a 30-year mortgage might total $954.83 a month, while a 15-year might cost $1,479.38 a month.
The amount of money which is paid back to the lender at the end of the 15 years is $353,750.
What is Interest?Interest in simple terms is the extra amount that you have to pay if you borrow money or the extra money you get if you lend the money.
Given that,
Principal amount of the mortgage = $200,000
Rate of interest, r = 5.125% = 0.05125
Number of years, t = 15 years
Simple interest = Prt
= 200,000 × 0.05125 × 15
= 153,750
Total money paid back to lender = Principal amount + Interest amount
= $200,000 + $153,750
= $353,750
Hence the money paid back is $353,750.
Learn more about Interest here :
https://brainly.com/question/13803142
#SPJ3
Will give 50points Pleasee help urgent!
Answers
Answer:
a = 10; a = 2
Step-by-step explanation:
Step 1: Use the Pythagorean theorem to solve this equation
1. Orignal eqaution: (a + 2)² + (a - 5)² = (a + 3)²
2. Expand (a + 2)² + (a - 5)² which will give us 2a² - 6a + 29
3. Expand (a + 3)² giving us a² + 6a + 9
4. Simplified equation: 2a² - 6a + 29 = a² + 6a + 9
Step 2: Subtract 9 from both sides
1. 2a² - 6a + 29 - 9 = a² + 6a + 9 - 9
2. Simplify: 2a² - 6a + 20 = a² + 6a
Step 3: Subtract 6a from both sides
1. 2a² - 6a + 20 - 6a = a² + 6a - 6a
2. Simplify: 2a² -12a + 20 = a²
Step 4: Subtract a2 from both sides
1. 2a² - 12a + 20 - a² = a² - a²
2. Simplify: a² - 12a + 20 = 0
Step 5: Use the quadratic formula to solve for a
1. Quadratic formula: a = -b += √b² - 4ac/2a
2. Plug in the correct values: a = -(-12) += √(-12)² + 4(1)(20)/2(1)
3. Simplify the numerator and denominator: 12 += 8/2
4. Final equation: a = 12 - 8/2 or a = 12 + 8/2
5. Hence, the answer is 10 or 2
Use the fact that the quantity of a radioactive substance after t years is given by
q = q0(2−t/k),
where q0 is the original amount of radioactive material and k is its half-life (the number of years it takes for half the radioactive substance to decay).
The half-life of strontium-90 is 25 years. Find the amount of strontium-90 remaining after 20 years if
q0 = 87 kg.
(Round your answer to the nearest kg.)
Answers
Answer:
50 kg
Step-by-step explanation:
Put the given numbers into the given formula and do the arithmetic.
q = q0(2^(-t/k))
q = (87 kg)(2^(-20/25)) = (87 kg)(0.574349)
q ≈ 50 kg
The amount remaining after 20 years is about 50 kg.
A daycare charges a base fee of $25 per week plus $3/hour for a child.
Write an equation that relates the weekly charge C (in dollars) to the number, x, hours, that a child is in daycare
Answers
According to the question ,
The base price is $25 per week . And per hour charge is $3/hour .So as per the question if we assume that the babysitter looked after the child for x hours in a week then , the total charge will be ,
→ Charge = $3/hr * x hr= $3x
So the total cost for a week , will be ,
→ Total cost = Base price + Charge
→ Total cost = $25 + $3x
And in the question we are told to assume total cost to be $C . Therefore ,
→ $C = $ (25 +3x)
→ C = 25 + 3x
Hence the required equation is C = 25 + 3x.
I hope this helps.
HELP Solve the system of equations using the substitution method.
-7x - 4y = -11
y = x
Answers
Answer:
y = - 7/4 x + 1 1 / 4
Step-by-step explanation:
Need help on these two please
Answers
Answer:
Given below.Step-by-step explanation:
Q.1.
[tex]ln\left(4\right)+\:ln\left(x\right)=ln\left(24\right)[/tex]
apply ln rules:
[tex]ln( 4 * x) = ln (24)[/tex]
cancel ln from both sides:
[tex]4x = 24[/tex]
divide both sides by 4:
[tex]x = 6[/tex]
Q.2.
[tex]2ln\left(x\right)=ln\left(4\right)+ln\left(9\right)[/tex]
apply ln rules:
[tex]ln\left(x^2\right)=ln\left(4*9\right)[/tex]
cancel ln from both sides:
[tex]x^2 = 36[/tex]
[tex]x = \pm6[/tex]
as ln cannot be negative:
[tex]x = 6[/tex]
Which values are greater than -2?
-5 -4 -3 -2 -1 0 1 2 3 4 5
WILL MARK BRAINLIEST
Answers
Answer:
-1, 0, 1, 2, 3, 4, 5 are the values greater than -2
Step-by-step explanation:
Let's imagine a number line.
Numbers that are bigger are on the right side of the number line.
The numbers to the right of -2 are:
-1 one greater0 two greater1 three greater2 +43 +5 4 +65 +7And so on...
Numbers that would be less than -2 will be on the left side
-3 1 less-4 2 lessetc...
-Chetan K
Answer:
-1,0,1,2,3,4,5
ep-by-step explanation:
think of it on a number line
There is exactly
1 pair of parallel sides in the following shape.
What is the area of the shape?
Answers
The given properties of one pair of parallel sides in the four sided
quadrilateral, indicates that the shape is a trapezium.
Response:
The area of the shape is 35 square unit How can the area of the given quadrilateral be calculated?Given that the side with length 6 is parallel to the side with length 8, we
and that the figure is four sided, we have;
The given figure is a trapezium;
[tex]Area \ of \ a \ trapezium = \mathbf{ \dfrac{a + b }{2} \times h}[/tex]Where;
a and b = The lengths of the parallel sides
h = The height of the figure = 5
Which gives;
[tex]Area = \dfrac{6 + 8 }{2} \times 5 = \mathbf{35}[/tex]
The area of the shape = 35 square unitLearn more about trapeziums here:
https://brainly.com/question/96136
Answer:35 sq units
Step-by-step explanation:
For the functions f(x) = x+2 and g(x) = x^2 - 3 which expression has the greatest value?
A. f(g(1))
B. f(g(-2))
C. g(f(-4))
D. g(f(-2))
2. Find g(f(-4)) when f(x)= 4x+5 and g(x) = 4x^2 -5x - 3
A. 9
B.8
C.329
D.536
Answers
The expression which has the greatest value is; Choice B: f(g(-2))
The value of g(f(-4)) when f(x)= 4x+5 and g(x) = 4x^2 -5x - 3 is; 586
The value of functionsQuestion 1;
From the information given;
g(f(x)) = x²+4x +1f(g(x)) = x² -1.Hence, from the options given; upon substitution, it follows that the expression with the greatest value is;
f(g(-2)) = (-2)² -1 = 4-1 = 3.Question 2;
From the task content;
g(f(x)) = 64x² + 140x + 122Hence, upon substitution of -4 into the function;
g(f(-4)) = 64(-4)² + 140(-4) + 122g(f(-4)) = 586Read more on functions of functions;
https://brainly.com/question/4528336
Number 3
Number 2 is done but part of it
Answers
Answer:
I believe the answer is B.1
i really need help please
Answers
The answer is the third option
plsss help!!!!! Mhanifa
Answers
Answer:
See belowStep-by-step explanation:
Total number of ornaments:
24 + 12 + 8 + 19 = 63a)
P(gold) = gold / total = 12/63 = 4/21b)
P(silver) = silver/total = 24/63 = 8/21c)
P(gold or silver) = (12 + 24)/63 = 36/63 = 4/7Answer:
8)
total ornament: 24 + 12 + 8 + 19 = 63
a. probability its a gold ornament: [tex]\frac{12}{63}[/tex] → [tex]\frac{4}{21}[/tex]
b. probability its a silver ornament: [tex]\frac{24}{63}[/tex] → [tex]\frac{8}{21}[/tex]
c. probability she will get gold or silver ornament: [tex]\frac{24}{63}[/tex] + [tex]\frac{12}{63}[/tex] = [tex]\frac{4}{7}[/tex]
If (2^a)=(3^b), what is the ratio of a to b?
Please use logarithms in the solution and explain.
Answers
Answer:
Step-by-step explanation:
Taking the log of both sides, we get:
a log 2 = b log 3
b log 3
Dividing both sides by log 2 yields a = ------------------
log 2
Finally, dividing both sides by b yields the desired ratio, a/b:
a log 3
---- = --------------
b log 2
Find the area of the shaded region.
Answers
Answer:
56
Step-by-step explanation:
8 x 8 = 64
4 x 4 = 16
16/2 = 8
64-8 =56
Un aventurero realiza 2/5 de un viaje en todo terreno,1/3 a caballo y el resto andando. Si la caminata ha sido de 80 km, ¿cuál es la longitud total de su recorrido?
Answers
Answer:
Todo terreno+ caballo+caminado=distancia ; (2/5)d+(1/3)d+80=d
Step-by-step explanation: