Question 13 (5 points)
m_1 = (4x + 9)º and m_2 = (x - 14)° in the given figure. Find x.
Answers
Answer:
x=19°
Step-by-step explanation:
Line n and l form a right angle. We know that because line m and l are parallel to each other and line n crosses through them as a vertical line.
Right angles always add up to 90°.
So, Angle 1 add Angle 2 equals 90°.
4x+9+x-14=90°
Collect the like terms:
Like terms are terms with the same variables and powers.
4x+x=5x
9-14= -5
Form an equation:
5x-5=90°
Do inverse operations to isolate x.
90+5=95°
95÷5=19° (We divide by 5 because, in algebra, when a number is next to a letter, it means times, so we have to do the opposite and divide).
So, x=19°
Hope this helps :)
Related Questions
The number of booker borrowed from a library each week follows a normal distribution. When sample is taken for several weeks, the mean is found to be 190 and the standard deviation is 30
Answers
Answer:
2.5%
Step-by-step explanation:
Given :
Mean, μ = 190
Standard deviation, σ = 30
Probability that more than 250 books are borrowed ;
x = 250
P(Z > z)
Z = (x - μ) / σ
P[Z > (x - μ) / σ] = P[Z > (250 - 190) / 30]
P(Z > z) = P(Z > 2)
P(Z > 2) = 1 - P(Z < 2) = 1 - 0.97725
P(Z > 2) = 1 - P(Z < 2) = 0.02275
(0.02275 * 100)% = 2.275%
2.5% is closest to 2.275%
What is the equation of a straight line which passes through (-1,4) and parallel to the line 3x+27-7-0?*
Answers
Step-by-step explanation:
3x+27-7-0=3x+20
gradient=3
y=mx+c
4=3(-1)+c
4+3=7
c=7
y=3x+7
When a coin and die are tossed together find the probability of getting:
a)coin with head and die with prime number
b)coin with head and die with composite number
c)coin with tail and die with even prime number
Answers
Answer:
a) 1/4
b) 1/6
c) 1/12
Step-by-step explanation:
Let S be the sample space.
S={H1,H2,H3,H4,H5,H6,T1,T2,T3,T4,T5,T6}
n(s) =12
Events
A: coin with head and die with prime number .
B:coin with head and die with composite number.
C:coin with tail and die with even prime number.
a) A={H2,H3,H5}
n(A) = 3
P(A) =n(A)/n(S)
=3/12
= 1/4
b) B={H4,H6}
n(B)= 2
P(B) = n(B)/n(S)
= 2/12
= 1/6
c) C ={T2}
n(C) = 1
P(C) = n(C)/n(S)
= 1/12
The heights of 200 adults were recorded and divided into two categories
Which two-way frequency table correctly shows the marginal frequencies
Answers
Answer:
C
Step-by-step explanation:
male total= 98
female total =102
total total=200
in 1990 sausage cost an average of $2.42 per pound. In 1994 it cost 51.35 per pound. What was the percent of depreciation (percent of decrease)?
*(show your work)*
Answers
Answer:
Cumulative price change 105.96%
Average inflation rate 2.36%
Converted amount ($100 base) $205.96
Price difference ($100 base) $105.96
CPI in 1990 130.700
Step-by-step explanation:
The robotics team purchased 3 androids for the purpose of programming. Each of the robots was $398, which included tax. If the tax rate is 8%, what is the TOTAL TAX to be paid?
Answers
Answer:
$95.52
Step-by-step explanation:
Number of robots = 3
Cost of each robots = $398
Tax rate = 8%
Amount of tax of each robots = 8% of $398
= 8/100 × $398
= 0.08 × $398
= $31.84
TOTAL TAX to be paid = Amount of tax of each robots × Number of robots
= $31.84 × 3
= $95.52
TOTAL TAX to be paid = $95.52
I need to know the transformation of the shape
Answers
Answer:
is there anything underneath it? it says which of the following
Step-by-step explanation:
Find the slope.
Directions: For problems 1 through 3, graph the line by using the given X values and find its slope.
Answers
Answer:
Answer is in the picture.
Someone plz help me on this one
Answers
Answer:
76
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan ? = opp side/ adj side
tan ? = 40 / 10
tan ? = 4
Taking the inverse of each side
tan ^ -1 (tan ?) = tan ^-1(4)
? =75.96375653
To the nearest degree
? = 76
What is Index Law 2?
please give definition
Answers
LAW 2: The second law of indices tells us that when dividing a number with an exponent by the same number with an exponent, we have to subtract the powers. In algebraic form, this rule is as follows . The a represents the number that is divided by itself and m and n represent the powers.
Answer:
The second law of indices tells us that when dividing a number with an exponent by the same number with an exponent, we have to subtract the powers. The a represents the number that is divided by itself and m and n represent the powers. Here is an example for this rule.
On a world , the distance between city A and city B is 5,625 inches. The two cities are actually 1688 miles apart. On the same , what would be the distance between city C and city D, two cities that are actually 1296 miles apart? Use a proportion to solve this problem.
Answers
Answer:
The distance between C and D is 4.2768 inches.
Step-by-step explanation:
As from A to B the distance is 5.625 inches and actual is 1688 miles
so,
1 mile = 5.625/1688 = 0.0033 inches
So, the distance between C and D is 1296 miles
= 1296 x 0.0033 inches = 4.2768 inches
If a point is chosen inside the square, what is the probability that it will also be inside the circle?
Answers
Answer:
[tex]79\%[/tex]
Step-by-step explanation:
The probability that the point is chosen in the circle is equal to the area of the circle divided by the area of the square.
Formulas used:
Area of a square with side length [tex]s[/tex] is given by [tex]A=s^2[/tex] Area of a circle with radius [tex]r[/tex] is given by [tex]A=r^2\pi[/tex]The segment marked as 1 represents not only the radius of the circle, but also half the side length of the square. Therefore, the side length of the square is 2, and we have:
Area of square: [tex]A=2^2=4[/tex]
Area of circle:
[tex]A=1^2\pi=\pi[/tex]
Therefore, the probability that the point will be inside the circle is:
[tex]\frac{\pi}{4}=0.78539816339\approx \boxed{79\%}[/tex]
simplify.
[tex] {y }^{ - 3} [/tex]
Options:
3/y
-1/y^3
-3y
1/y^3
Answers
Answer:
Rewrite the expression using the negative exponent rule [text]{b}^{-n } = 1/bn
Step-by-step explanation:
1/y^3
If 12 is the greatest common factor of y and 36, how many possible values for y are in between 20 and 80 ?
Answers
Answer: 3
Step-by-step explanation: I don’t have an explanation but I got the same question on a quiz and 3 was the correct answer.
the possible values for y are in between 20 and 80 will be 3.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
If 12 is the greatest common factor of y and 36.
The value of y will be a multiple of 12 and greater than 36.
Then the numbers will be
12 x 4 = 48
12 x 5 = 60
12 x 6 = 72
Then the possible values for y are in between 20 and 80 will be 3.
More about the Algebra link is given below.
https://brainly.com/question/953809
#SPJ2
The graph of a relation is shown.
Which of these values could be the slope of the line?
Select two options.
-2
-8/5
0
7/4
3
Answers
Answer:
4th option, 7/4 and
5th option, 3
Step-by-step explanation:
The line seems like it will have a positive slope and will not be 0 since it's not passing through the origin
so, possible values are 7/4 and 3
Answered by GAUTHMATH
Answer: The answer would be 7/4, 3
Step-by-step explanation:
Please i need the correct answer, no funny business.
Answers
Answer:
Age of the spear head = 6349 years.
Step-by-step explanation:
Expression to be used to calculate the age of the spear head,
[tex]N_t=N_0e^{-kt}[/tex]
Here, [tex]N_t[/tex] = Final amount of C-14
[tex]N_0[/tex] = Initial amount
[tex]k[/tex] = 0.0001
[tex]t[/tex] = Time in years
If [tex]N_t[/tex] = 53% of [tex]N_0[/tex] = [tex]N_0\times (0.53)[/tex]
[tex]0.53N_0=N_0e^{-0.0001\times t}[/tex]
[tex]0.53=e^{-0.0001t}[/tex]
[tex]\text{ln}(0.53)=\text{ln}(e^{-0.0001t})[/tex]
[tex]-0.634878=(-0.0001)t[/tex]
[tex]t=6348.78[/tex] years
[tex]t[/tex] ≈ [tex]6349[/tex] years
Therefore, age of the spear head = 6349 years.
Write as an equation: a triangle has two equal sides and a third side that is 15cm long. How long is each of the equal sides if the perimeter is 50?
Answers
Answer:
Step-by-step explanation:
X+x+15=50
please help!! 15 points! I need 5 and 9 answered
Answers
Answer:
B: Subtraction property of equality
match the absolute value functions with their vertices
Answers
Vertex: (5, 2/3) - > f(x) = 3/5 |x - 5| + 2/3
Vertex: (-1, -3/7) - > f(x) = 1/2 |x + 1| - 3/7
Vertex: (0, -4/5) - > f(x) = 1/2 |x| - 4/5
Vertex: (2/5, 5/3) - > f(x) = 3/2 |x - 2/5| + 5/3
Step-by-step explanation:
Please help!!!!!!!!!!!!!!
Answers
Answer:
choice A is the answer
Step-by-step explanation:
[tex]5 + 2.75s \leqslant 21 \\ 2.75s \leqslant 21 - 5 \\ s \leqslant 16 \div 2.75 \\ s \leqslant 5.82[/tex]
but since we only can have a whole number in the number of stops, she can only travel 5 stops with the money she has.
How far apart are -14 1/2 and 2 on the number line
Answers
Need helppppp I’m stuckkkk
Answers
Answer:
b) 94
Step-by-step explanation:
The Total Degree of a Triangle is 180 degrees. Knowing this, set up an equation.
68+26+x=180.
x is the complementary angle of the "?" angle.
Solve the equation.
94+x=180
x=86
Then Subtract 86 from 180 to find "?"
180-86=94
I hope this helps!
Answer:
94;b
Step-by-step explanation:
68+26=94. 180-94=86. 180-86=94.
Find the volume of this solid.
Answers
Answer:
Step-by-step explanation:
area of side surface=50×20+20×35=1000+700=1700 m²
voume of solid=1700×12=204,00 m³
Amanda asked each student in her class: How many pets do you have? The data collected is below.
Amanda's Class: 0, 0, 2, 1, 1, 0, 5, 0, 3, 2, 1, 1, 0, 2, 4, 0, 2, 1, 1, 1, 2, 3, 1, 0, 2
Charley asked the same question to each student in his class (which is no
class as Amanda's). The data he collected is below.
Charley's Class: 1, 2, 1, 3, 1, 1, 0, 0, 1, 0, 0, 2, 3, 1, 2, 5, 2, 0, 0, 4, 1, 1, 2, 0, 0, 1, 1
Whose class had a larger percentage of students with no pets?
Answers
Answer:
Charley's class.
Step-by-step explanation:
There are 25 students in Amanda class and 27 in Charley's.
Number of students with no pets in Amanda's = 7 which is 100 * 7/25 = 28%.
In Charley's class this is 8 which is 100 * 8/27 = 29.6%.
Answer:
Charley's class
Step-by-step explanation:
Amanda's class has 7 students with zero pets out of 25 total students. Charley's class has 8 students with zero pets out of 27 total students.
7/25 = 28% with zero pets
8/27 = around 30% with zero pets
Charley's class has a larger percentage of students with no pets
2. Dentre as formas de representar um número decimal, a mais comum é a que utiliza vírgula. Valor como 0,25 está presente nos comércios, nos hospitais, nas lanchonetes e em muitos outros lugares. Esse valor também pode ser representado por A. ( ) 25/10 B. ( ) 1/4 C. ( )1/25 D. ( ) 1/25
Answers
Answer:
B: 0.25 = 1/4
Step-by-step explanation:
Queremos encontrar otra representación del número 0.25
Notar que hay dos decimales luego de la coma, por lo que podemos multiplicar este número y dividir por 100.
0.25 = 0.25*1 = 0.25*(100/100) = (0.25*100)/(100) = 25/100
Ahora tenemos el número escrito como una fracción, la cual debemos simplificar.
25/100
Podemos ver que tanto el numerador como el denominador son multiplos de 5, por lo que podemos dividir ambos por 5:
25/100 = (25/5)/(100/5) = 5/20
Nuevamente, ambos son multiplos de 5, por lo que podemos dividir ambos por 5.
5/20 = (5/5)/(20/5) = 1/4
así tenemos:
0.25 = 25/100 = 5/20 = 1/4
0.25 = 1/4
La opción correcta es B.
Can someone help me with this please
Answers
Answer:
.574
Step-by-step explanation:
This can be inputted in a calculator to achieve .57357643
To three decimal places that is .574
Instructions: Find the missing side. Round your answer to the nearest
tenth.
49
х
66°
X
Answers
[tex]\sin(66) = \frac{49}{x} \\ 0.913 = \frac{49}{x} \\ x = 53.6 \\ x = 54[/tex]
The missing side is 53.6 units for the given right triangle.
What is the right triangle?A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.
The right triangle is given in the question, as shown.
The ratio of the length of the side opposite the angle to the length of the hypotenuse of the triangle. The sine function is denoted by the symbol "sin" and is defined as follows:
sin(θ) = opposite / hypotenuse
Here, θ = 66°
Using the sine ratio in the given triangle, we get
sin 66° = perdenicular/hypertanuas
Substitute the known values in the above ratio,
sin 66° = 49/x
x = 49/sin 66°
x = 53.63717
Rounded to the nearest tenth,
x ≈ 53.6
Thus, the missing side is 53.6 units for the given right triangle.
Learn more about the right triangle here:
https://brainly.com/question/11899922
#SPJ7
use the information in the diagram, set up a proportion to solve for the height of the tree
Answers
Answer:
Step-by-step explanation:
There are a couple of ways you could solve this problem. B is one of them.
The correct answer is going to be Small hypotenuse / Large hypotenuse = tree / building height
Let the tree equal x
100/220 = x / 176 Multiply both sides by 176
100 * 176 / 220 = x
x = 80
Notice that 80 is almost 1/2 of 176 so the answer should be right since 100 is nearly 1/2 of 220
please help me solve the equations, I re-wrote the question under each of them so you can read it better. Ty
Answers
45. 13/36
46. 86/63
47. 19/42
48. 17/30
Answer:
45:13/36
46:86/63
47:19/42
48:9/10
49:1/12
factor x^2-3x-28 using the x method
Answers
Answer:
[tex] {x}^{2} - 7x + 4x - 28 \\ = x(x - 7) + 4(x - 7) \\ = (x - 7)(x + 4)[/tex]
