Unit 4 Homework 2 Gina Wilson all things algebra,
Pls help!
Answer:
1. m∠1 = 45°
2. m∠1 = 129°
3. m∠1 = 37°
4. m∠1 = 88°
m∠2 = 42°
m∠3 = 113°
5. m∠1 = 62°
m∠2 = 45°
m∠3 = 24°
6. m∠1 = 128°
m∠2 = 52°
m∠3 = 47°
m∠4 = 133°
7. m∠1 = 41°
m∠2 = 85°
m∠3 = 95°
m∠4 = 85°
m∠5 = 36°
m∠6 = 50°
m∠7 = 107°
8. x = 9°
10. x = 5°
11. x = 7°
Step-by-step explanation:
1. m∠1 = 180° - (76° + 59°) = 45°
m∠1 = 45°
2. m∠1 = 62° + 67° = 129°
m∠1 = 129°
3. m∠1 = 152° - 115° = 37°
m∠1 = 37°
4. m∠2 = 42° (Alternate angles)
m∠1 = 180° - (50° + m∠2) = 180° - (50° + 42°) = 88°
m∠1 = 88°
m∠3 = 180° - (25° + 42°) = 113°
m∠3 = 113°
5. m∠3 = 73° - 49° = 24°
m∠3 = 24°
m∠2 = 118° - 73° = 45°
m∠2 = 45°
m∠1 = 180° - (73° + 45°) = 62°
m∠1 = 62°
6. m∠2 = 52° (Alternate interior angles)
m∠1 = 180° - 52° = 128° (The sum of angles on a straight line)
m∠1 = 128°
m∠3 = 47° (Alternate interior angles)
m∠4 = 180° - 47° = 133° (The sum of angles on a straight line)
m∠4 = 133°
7. m∠3 = 95° (Vertically opposite angles)
m∠2 = m∠4 (Vertically opposite angles)
m∠3 + 95° + m∠2 + m∠4 = 360° (The sum of angles at a point)
2 × 95° + 2 × m∠2 = 360°
m∠2 = (360° - 2 × 95°)/2 = 85°
m∠2 = 85° = m∠4
m∠2 = 85°
m∠4 = 85°
m∠1 = 360° - (85° + 140° + 90°) = 41°
m∠1 = 41°
m∠5 = 180° - 144° = 36°
m∠5 = 36°
m∠6 = 180° - (m∠5 + m∠3) = 180° - (36 + 95°) = 50°
m∠6 = 50°
m∠7 = 360° - (m∠4 - 38° - (180° - m∠6)) = 360° - (85° - 38° - (180° - 50°)) = 107°
m∠7 = 107° (Sum of angles in a quadrilateral)
8. (10·x - 11)° + (3·x - 2)° + (3·x + 1)° = 180°
Using an online application, we have;
(6·x - 12)° = 180°
x = (180 + 12)°/6 = 32°
x = 32°
9. (3·x - 5)° + (7·x + 5)° + 90° = 180°
Using an online application, we have;
10·x = 180° - 90° = 90°
x = 90°/10 = 9°
x = 9°
10. 151° = (11·x - 1)° + (20·x - 3)°
151° = 31·x - 4°
31·x = 151° + 4° = 155°
x = 155°/31 = 5°
x = 5°
11. (14·x - 13)° = (4·x + 13)° + (6·x + 2)°
(14·x - 13)° = (10·x + 15)°
(14·x - 10·x)° = (13 + 15)° = 28°
4·x = 28°
x = 28°/4 = 7°
x = 7°
1. 45°
2. 51°
3. 37°
4. 88°, 42°, 113°
5. 62°, 45°, 24°
6. 128 degrees, 52°,, 47°, 43° 83°
7. I have no clue
8. 12
9. 9
10. 5
11. 7
Mental Math Situation: You exercised 24 hours each month for a year. How many hours did you exercise by the end of the year? You may be able to do the math mentally thanks to expanded notation and the Distributive Property.
Answer:
So 24 hours each month times 12 would be 288 hours of working out of one year.
Hope this helps!
Step-by-step explanation:
Answer: 288h
Step-by-step explanation:
There are 12 months in a year if you exercise 24h per month you have to multiply 12 x 24 = 288h
9. During training, a hurdler wants to raise the height of the hurdles from the high school standard of 39 inches to the
NCAA standard of 42 inches. His best race from last season included a clear over a 39-inch hurdle that was modeled by
h(t) = (-0.0251)(1-25), where t is time (in tenths of a second) after his lead leg left the track and h is the height (in feet).
If he runs as well as his best race last year, will this hurdler clear the new height? Why or why not
Answer:
Something doesn't make sense. The time when his height is 0 is time t=0 and t=25.
The vertex would be halfway in between at time t=(0+25)/2 = 12.5 seconds.
But plugging that in, we get a height of:
3.90625 inches
I think you must have a typo... let's try this equation instead:
h(t) = (-0.25t)(t - 25)
In that case, the maximum at h(12.5) is 39.0625 inches.
Answer:
No, the function for his height has him just barely clearing 39 inches. He can't clear 42 inches.
10
No, according to the function for his height, he only just clears 39 inches. He is unable to jump 42 inches.
The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Something doesn't make sense. The time when his height is 0 is time t=0 and t=25.
The vertex would be halfway in between at time t=(0+25)/2 = 12.5 seconds.
But plugging that in, we get a height of:
3.90625 inches
h(t) = (-0.25t)(t - 25)
In that case, the maximum at h(12.5) is 39.0625 inches.
Therefore, the according to the function for his height, he only just clears 39 inches. He is unable to jump 42 inches.
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Merry is making an abstract triangular collage for the wall. She has 14 feet of edging to go around the collage. If the longest side is twice the smallest and the other side is four less than three times the smallest, find the length of each side of the triangular collage
Answer:
The length of each side of the triangular collage:
a = smallest side = 3 feet
b = other side(second side) = 5 feet
c = Longest side = 6 feet
Step-by-step explanation:
She has 14 feet of edging to go around the collage.
14 feet = Perimeter of the triangle
The Perimeter of a Triangle = a + b + c where
a = smallest side
b = other side(second side)
c = Longest side
From the question, we are told that:
If the longest side is twice the smallest
c = 2a
The other side is four less than three times the smallest,
The other side = b
b = 3 × a - 4
b = 3a - 4
Hence,
P = a + b + c
14 = a + 3a - 4 + 2a
14 = a + 3a + 2a -4
14 = 6a - 4
Collect like terms
14 + 4 = 6a
18 = 6a
a = 18/6
a = 3ft
Therefore the smallest side = 3
The Longest side(c) = 2a
c = 2 × 3
c = 6ft
The other side(b) = 3a - 4
= 3(3) - 4
= 9 - 4
= 5 feet.
Therefore, the length of each side of the triangular collage:
a = smallest side = 3 feet
b = other side(second side) = 5 feet
c = Longest side = 6 feet
Is the relationship proportional? Explain.
Answer:
What relationship??
Step-by-step explanation:
Convert 40 g to mg
Plz help me
Answer:
40000 milligrams
Hope it helps :)
Jeremy is $124.60 in debt to his grandparents. He determines that he can pay them back in five months. What effect will his repayment have on his monthly bank account? Will give brainliest!
Answer:
https://brainly.com/question/11536615
Step-by-step explanation:
Using the known angle, what side is known? What side is unknown? Use opposite, adjacent, or hypotenuse in your answer.
Answer: know side: 3
Unknown side: 5
Step-by-step explanation:
Adrian eats 8 fries for every chicken finger on his plate. If there are 3 chicken fingers on his plate, how many fries will he eat?
Answer: he will eat 24 fries
Step-by-step explanation: just cuz
0.7 bigger than 7/9 ?
Answer: no it’s the opposite
Step-by-step explanation: 7/9is greater than 0.7
Clare is paid $90 for 5 hours of work. At this rate, how long will it take her to save $360?
Answer:
20 hours
Step-by-step explanation:
We can use a ratio to solve
90dollars 360 dollars
--------------- = -----------
5 hours x hours
Using cross products
90x = 5* 360
Divide each side by 90
90x/90 = 5 * 360/90
x = 20
20 hours
the sum of two fractions is 9 1^4 their difference is 3 1^8, what are the two fractions?
Answer:
[tex]6\frac{3}{16}~,~3\frac{1}{16}[/tex]
Step-by-step explanation:
let the fractions be x and y,then
[tex]x+y=9\frac{1}{4}=\frac{37}{4}=\frac{74}{8}\\x-y=3\frac{1}{8}=\frac{25}{8}\\adding\\2x=\frac{74}{8}+\frac{25}{8}=\frac{99}{8}\\x=\frac{99}{16}=6\frac{3}{16}\\again ~subtracting\\2y=\frac{74}{8}-\frac{25}{8}=\frac{49}{8}\\y=\frac{49}{16}=3\frac{1}{16}\\[/tex]
Write an explicit formula for an, the nth term of the sequence 112, -28, 7, ....
Answer:
[tex]a_n=112\left(-\frac{1}{4}\right)^{n-1}[/tex]
Step-by-step explanation:
Geometric Sequences
There are two basic types of sequences: arithmetic and geometric. The arithmetic sequences can be recognized because each term is found as the previous term plus a fixed number called the common difference.
In the geometric sequences, each term is found by multiplying (or dividing) the previous term by a fixed number, called the common ratio.
We are given the sequence:
112, -28, 7, ...
It's easy to find out this is a geometric sequence because the signs of the terms are alternating. If it was an arithmetic sequence, the third term should be negative like the second term.
Let's find the common ratio by dividing each term by the previous term:
[tex]\displaystyle r=\frac{-28}{112}=-\frac{1}{4}[/tex]
Testing with the third term:
[tex]\displaystyle -28*-\frac{1}{4}=7[/tex]
Now we're sure it's a geometric sequence with r=-1/4, we use the general equation for the nth term:
[tex]a_n=a_1*r^{n-1}[/tex]
[tex]a_n=112\left(-\frac{1}{4}\right)^{n-1}[/tex]
what is the rule for the reflection ?
a. rx-axis(x, y) - (-x, y)
b. ry-axis(x, y) - (-x, y)
c. rx-axis(x, y) - (x,-y)
d. ry-axis(x, y) - (x,-y)
Answer: Choice C
We have an x axis reflection
[tex](x,y) \to (x,-y)[/tex]
The x coordinate stays the same while the y coordinate flips from positive to negative, or vice versa.
For example, point L is located at (-4,2) and it moves to L ' (-4, -2). The other points follow this same pattern.
Please help ASAP I’m stuck!!!
Answer:
q <= 1 or q >= 20
Step-by-step explanation:
3q + 2 / 4 <= 5
multiply by 4 to both sides
3q + 2 <= 5
substract 2 to both sides
3q <= 3
divide by 3 to both sides
q <= 1
q - 7 >= 13
add 7 to both sides
q >= 20
Segment AB has endpoints on the coordinate grid where A is (-18,5) and B is (-4,5). Point Z is located exactly 1/8 of the distance from A to B. Determine the value of the x-coordinate of point Z.
Answer:
The coordinates of point Z is (-16.25, 5)
Step-by-step explanation:
The given information are;
The coordinates of the endpoint A on segment AB = (-18, 5)
The coordinates of the endpoint B on segment AB = (-4, 5)
Therefore, given that the endpoints A and B have the same y-coordinate value, (5), then segment AB is horizontal, and the length of segment AB = -4 - (-18) = -4 + 18 = 14
The point Z located at exactly 1/8 from A to B is given as follows;
[tex]Z = \left (-18 + (-4 - (-18)) \times \dfrac{1}{8} , \ 5 + (5 - 5)\times \dfrac{1}{8} \right ) = (-16.25, \ 5)[/tex]
The coordinates of point Z = (-16.25, 5).
A mouse traveled a total distance of StartFraction 3 Over 24 EndFraction of a mile in a maze over the past 3 hours. The mouse traveled the same distance each hour. To determine the distance that the mouse traveled each hour, Matt performed the calculations below. StartFraction 3 Over 24 EndFraction divided by 3 = StartFraction 3 Over (24 divided by 3) EndFraction = StartFraction 3 Over 8 EndFraction He concluded that the mouse traveled StartFraction 3 Over 8 EndFraction of a mile each hour. What is Matt's error?
Answer: the correct answer is C.
I took the quiz and got it right.
Answer:
im not sure but i think is c
Step-by-step explanation:
Complete the equation describing how x and y are related. Please Help!!
Answer:
muddin
Step-by-step explanation:
ya put it in the but and pull out wit some fecal matter on it
PLZ RESPOND ASAP
1:The total earnings from mowing a lawn for 3 hours is $19.50. What equation can be used to model the total earnings for mowing a lawn x hours?
2:The ratio of students to adults at a school is 14 : 2. Suppose there are a total of 490 students. How many adults are at the school?
Answer:6.5x=y
Step-by-step explanation:1- divide 19.50
2- get 6.5
3- add variable
4- get 6.5x=y
Answer:
1.) 3x = 19.50 (they got 6.5 and hour)
2.) 70 adults
Step-by-step explanation:
Work for #2
[tex]\frac{14}{2}[/tex] [tex]\frac{490}{x}[/tex] then cross multiply. 14*x = 14x 490*2 = 980
So 980 = 14x (divide by 14)
x = 70
So 70 adults
Hope this helps!!!
HELP PLZZ ASAP WILL GIVE 50 POINTS
Adrienne said that a vertical stretch by a factor of 4, a horizontal shift to the left 1 unit, and a vertical shift down 3 units of the graph of the parent function f(x)=ex produce the graph of the function g(x)=4ex−1+3. Explain whether Adrienne is correct and, if not, determine the transformations that produce the graph of the function g(x)=4ex−1+3 from f(x)=ex.
Answer:
known facts:
The graph of y=f(x−a), a>0
y=fx-a, a>0
can be obtained by shifting graph y=f(x)
y=fx, a units right side of x-axis. The graph of y=f(x)+a, a>0 y= fx+ a,a>0
can be obtained by shifting graph y=f(x)
y=fx, a units upwards along y-axis.
Adrienne said:
a vertical stretch by a factor of 4, a horizontal shift to the left 1 unit and a vertical shift down 3 units of the graph of the parent function f(x)=ex
f(x)=e^x
produce the graph of the function g(x)=4ex−1+3
g(x)=4e^x-1+3.
by the above known facts, it can be concluded that
Adrienne is not correct
Step-by-step explanation:
i hope this helps you, i'm still doing it but i have to go for a min, one sec! <3
the correct transformations for the function g(x) = 4eˣ - 1 + 3 from the parent function f(x) = eˣ are:
- Vertical Stretch by a factor of 4.
- Horizontal Shift to the Right 1 unit.
- Vertical Shift Down 3 units.
Adrienne's statement about the transformations applied to the parent function f(x) = eˣ is not entirely correct. Let's analyze the given function g(x) = 4eˣ - 1 + 3 and determine the correct transformations.
1. Vertical Stretch by a factor of 4: This transformation is correct. Multiplying the function by 4 causes a vertical stretch, which magnifies the y-values by a factor of 4.
2. Horizontal Shift to the Left 1 unit: Adrienne incorrectly mentioned a horizontal shift to the left. In the given function, g(x), there is no explicit horizontal shift. The -1 in g(x) = 4eˣ - 1 + 3 is actually a reflection of the graph across the y-axis, causing a horizontal shift to the right by 1 unit. So, there is a horizontal shift to the right by 1 unit, not to the left.
3. Vertical Shift Down 3 units: This transformation is correct. Adding 3 to the function shifts the graph vertically downward by 3 units.
Therefore, the correct transformations for the function g(x) = 4eˣ - 1 + 3 from the parent function f(x) = eˣ are:
- Vertical Stretch by a factor of 4.
- Horizontal Shift to the Right 1 unit.
- Vertical Shift Down 3 units.
Learn more about transformations here
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What is the value of 7/3 divided by 5/6
Answer:
14/5 or 2.8
Step-by-step explanation:
Answer:
2.8 or 2 4/5
Step-by-step explanation:
The price of a DVD is 24.00 plus 8%tax. What is the total Price on this DVD in dollars and cents?
Answer: $25.92
Step-by-step explanation: Using proportions, I found what 8% of 24 is. 8/100 = x/24, as shown in the photo. 8 x 24 = 192. Divide by 100 for 1.92 and that is the tax. Add 1.92 to the original of 24 to get $25.92
How many group's of 10 are there in 230?
Answer:
the answer is 23
Step-by-step explanation:
Answer:
23
Step-by-step explanation:
if you do 230 divided by 10 you get 23, or you can distribute 230 in 10 groups.
What is 2.4(x-10)=8+1.2x-5
Answer:
x = 22.5
Step-by-step explanation:
Step 1: Write equation
2.4(x - 10) = 8 + 1.2x - 5
Step 2: Solve for x
Distribute 2.4: 2.4x - 24 = 8 + 1.2x - 5Combine like terms: 2.4x - 24 = 1.2x + 3Subtract 1.2x on both sides: 1.2x - 24 = 3Add 24 to both sides: 1.2x = 27Divide both sides by 1.2: x = 22.5Step 3: Check
Plug in x to verify it's a solution.
2.4(22.5 - 10) = 8 + 1.2(22.5) - 5
2.4(12.5) = 8 + 27 - 5
30 = 8 + 22
30 = 30
Answer:
x=22.5
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
2.4(x−10)=8+1.2x−5
(2.4)(x)+(2.4)(−10)=8+1.2x+−5(Distribute)
2.4x+−24=8+1.2x+−5
2.4x−24=(1.2x)+(8+−5)(Combine Like Terms)
2.4x−24=1.2x+3
2.4x−24=1.2x+3
Step 2: Subtract 1.2x from both sides.
2.4x−24−1.2x=1.2x+3−1.2x
1.2x−24=3
Step 3: Add 24 to both sides.
1.2x−24+24=3+24
1.2x=27
Step 4: Divide both sides by 1.2.
1.2x
1.2
=
27
1.2
x=22.5
Answer:
x=22.5
Which of the following functions is graphed below?
Answer:
C
Step-by-step explanation:
A delivery person uses a service elevator to bring boxes of books up to an office. The delivery person weighs 170lb and each box of books weighs 60 lb. The maximum capacity of the elevator is 1240lb. How many boxes of books can the delivery person bring up at one time?
Answer:
17.83 boxes
Step-by-step explanation:
Lets represent the number of boxes of books that can be brought up per time = x
From the question: The delivery person weighs 170lb and each box of books weighs 60 lb. The maximum capacity of the elevator is 1240lb.
Hence we have the Algebraic Expressions
170lb + 60 × x = 1240lb
170lb + 60x = 1240lb
Collect like terms
60x = 1240lb - 170lb
60x = 1070lb
x = 1070lb/60
x = 17.833333333
x = 17.83 boxes
Therefore, the delivery person can bring up 17.83 boxes per time
Which is an equation of the line that is parallel to y = 2x - 2 and passes
through the point (7, 8)?
A) 2x + y = 6
B) 2x + y = 22
C) 2x - y = 2
D) 2x - y = 6
Answer:
Option D ( 2x-y = 6 )
Step-by-step explanation:
They have the same gradient and when x,y values are substituted in this equation, they are equal.
Express 8.3% as a ratio. OR Find 7% of 500.
Answer:
8.3 / 1
Step-by-step explanation:
Its simple... search it up
Answer:
7% of 500=7/100*500=35
Which scale factors produce an expansion under a dilation of the original image?
Select each correct answer.
−8
−0.7
0.8
7
Answer:
The correct answer is -8 and 7
Hope you have a wonderfull day :)
PLEASE HELP ME this is really hard please
Answer:
1100
2200
Step-by-step explanation:
Since speed is constant, the distance is proportional to the time. We notice that the number in the second column is 1650/3 = 550 times the number in the first column, so the two missing numbers are ...
2 × 550 = 1100
4 × 550 = 2200