Given:
An architect designs two similar triangular patios.
The first patio has angle measures of (x + 10)°, (y + 15)°, and 70°.
The second patio has angle measures of (x + 20)°, 50°, and 60°.
To find:
The values of x and y.
Solution:
We know that, corresponding angles of similar triangles are equal. So, the value of (x + 20)° must be 70°.
[tex]x+20=70[/tex]
[tex]x=70-20[/tex]
[tex]x=50[/tex]
The value of x is 50.
Now,
[tex](x+10)^\circ=(50+10)^\circ[/tex]
[tex](x+10)^\circ=(60)^\circ[/tex]
So, remaining angles must be equal, i.e., (y + 15)° and 50° are equal.
[tex]y+15=50[/tex]
[tex]y=50-15[/tex]
[tex]y=35[/tex]
Therefore, the values of x and y are 50 and 35 respectively.
The values of x and y are 50 and 35 respectively.
The corresponding angles of similar triangles are equal. Therefore,
The first patio angles are:
x + 10
y + 15
70°
The second patio angles are ;
x + 20
50°
60°
Therefore,
x + 20 = 70
x = 70 - 20
x = 50
y + 15 = 50
y = 50 - 15
y = 35
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Jordan throws a ball from a cliff 12 feet above the ground with an initial velocity of 32 feet per second. In the following functions, h(t) represents the height of the ball above the ground, in feet, with respect to time, t, in seconds, after the ball was thrown. Which of the following functions models the amount of time the ball is in the air?
h(t)= -4(t-1)^2 +3
h(t)= -16(t-1)^2 -4
h(t)= -16(t-1)^2 +12
h(t)= -16(t-1)^2 +28
Answer:
Your answer will be the third function
Step-by-step explanation:
The base function you need to know is h(t)= 1/2at^2
Your acceleration in this problem is going to be gravity which they give to you, 32 feet per second squared. Since the ball is falling, it means it will have negative acceleration. Now you have the equation h(t)= -16t^2. The final step is to add the initial height from which the ball was dropped giving you: h(t)= -16t^2 +12
−10)−3 = A) 0.01 B) 1000 C) −0.001 D) −1000
Answer:
A
Step-by-step explanation:
I am kinda positive this is it but it might not be
-10^-3 = -0.001
the answer is C
which of the following equationa apply to line below
a- y=-4x-6
b -y-2=-4(x+2)
c-y+3=-4(x+6)
d-Y-6=-4(x+3)
Answer:
1+1=magelan
2plus2 lapulapu
Answer:
b and d
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
m is the slope and (a, b) a point on the line
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 3, 6) and (x₂, y₂ ) = (- 2, 2) ← 2 points on the line
m = [tex]\frac{2-6}{-2+3}[/tex] = - 4
Using (a, b ) = (- 3, 6 ), then
y - 6 = - 4(x - (- 3)), that is
y - 6 = - 4(x + 3) → d
Using (a, b ) = (- 2, 2 ), then
y - 2 = - 4(x - (- 2)) , that is
y - 2 = - 4(x + 2) →b
A shopper bought 6 shirts and 8 hats for $700. A week later, at the same prices, he bought 9 shirts and 6 hats for $660. What was the cost of one shirt?
Answer:
Cost of one shirt = $ 30
Step-by-step explanation:
Let cost of 1 shirt = s
Cost of 1 hat = h
A shopper bought 6 shirts and 8 hats for $700.
6s + 8h = 700 -------------------(I)
A shopper bought 9 shirts and 6 hats for $660
9s + 6h = 660 -----------------(II)
Multiply equation (I) with 9 and multiply equation (II) with (-6) and then add. SO, now 's' will be eliminated and we can find the value of 'h'
(I) * 9 54s + 72h = 6300
(II)*(-6) -54s - 36h = - 3960 {Now add}
36h = 2340
h = 2340/36
h = 65
Cost of one hat = $ 65
Substitute h = 65 in equation (I)
6s + 8 * 65 = 700
6s + 520 = 700
6s = 700 - 520
6s = 180
s = 180/6
s = 30
Cost of one shirt = $ 30
Answer: One shirt is $30
Step-by-step explanation: Have a great day
3y+11 + 7x-30 = 5x+14
Answer:
2x + 3y = 33
Step-by-step explanation:
Hold on let me double check
Caroline's family took a road trip to the Grand Canyon. Caroline fell asleep 58% of the way through the trip. If Caroline fell asleep after they had travelled 348 miles, what was the total length of the trip?
Answer:600 miles
Step-by-step explanation:
Hello!
So you know that 348 miles is equal to 58% so you want to figure out what 1% of the total trip is
348 / 58 = 6
You know that 1% of the trip is 6 miles so now to figure out what the total trip is you multiply 6 by 100
6 * 100 = 600
So you know that the total length of the trip is 600 miles long.
1 is 25% of what number
Answer: 4
Step-by-step explanation: 1/4 = 25% Hope This Helps
The temperature is changing every day by negative 7 over 18 degree Fahrenheit. What will be the change in the temperature after 3 days?
Answer:
whhhhhhhhhhattttatttttttt
Answer:
look it up
Step-by-step explanation:
?can someone help meh
Answer:
Step-by-step explanation:
C
How would you write 10 DIVIDED BY A NUMBER as an algebraic expression?
b / 10
10 / 10
10 / b
which one?
Answer: C
Step-by-step explanation: 10/b
10/b is the answer
say thanks in the chat
What would the exponential equation be ?
Answer:
The equation of the exponential function will be:
[tex]f\:\left(x\right)\:=\:ab^x[/tex]
[tex]=\:\frac{3}{2}\left(2\right)^x[/tex]
Step-by-step explanation:
Given the table
Day Bacteria
1 3
2 6
3 12
4 24
5 48
as
the x values have the same increment i.e. +1and
the y values have common ratio i.e. 6/3 = 2, 12/6=2, 24/12=2so it is indeed an exponential function
As we know that the exponential function is of the form
[tex]f\:\left(x\right)\:=\:ab^x[/tex]
As we know that the y-intercept of [tex]f\:\left(x\right)\:=\:ab^x[/tex] is (0, a).
so
[tex]\frac{3}{a}=2[/tex] ∵ common ratio = successor y-value ÷ previos y-value
[tex]a=\frac{3}{2}[/tex]
so the value of a will be: 3/2
We also know that the common factor i.e. multiplier is 2 in this table, we know the value for b is 2.
Therefore, the equation of the exponential function will be:
[tex]f\:\left(x\right)\:=\:ab^x[/tex]
[tex]=\:\frac{3}{2}\left(2\right)^x[/tex]
Is a repeating decimal a rational number
A. Yes because it can be written as a/b and a and b are integers and b =0
B. Yes because it can be written in the form a•b where a and b are integers
Answer:
Option A
Step-by-step explanation:
The answer to this question is option A or "Yes because it can be written as a/b and a and b are integers and b =0." Any number that can be written as a fraction is a rational number. In this case repeating decimals can be written as a fraction using different types of algebraic methods making it a rational number.
Hope this helps.
i need help please.
Which of the following expressions are equivalent to 7x + 14 − 3x + 12?
1. 21x + 8x
2. 7x − 3x + 14 + 12
3. 4x + 14 + 12
4. 4x − 2
5. 7x + 26 − 3x
Answer:
I just did this quetio with the tutor the answers are 2, 3, and 5.
Pls help its confuzing
Answer:
Step-by-step explanation:
x-int (2/7, 0)
y-int (0, -2)
x-int
7x - 0 = 2
7x = 2
x = 2/7
(2/7, 0)
7(0) - y = 2
-y = 2
y = -2
(0, -2)
Find "both answers.
The answer to the different" question is
The answer to the same three questions is
The slope of the line is 3
The difference between the consecutive term of the sequence is (1, 3)
To get the slope of the graph, we will use the coordinate points (2, 10) and (3, 13)
Slope = 13-10/3-2
Slope = 3/1
Slope = 3
Hence the slope of the line is 3
The difference in the term for the x-coordinate is given as:
x = 3 - 2 = 4 - 3 = 5 -4 = 1The difference in the term for the y-coordinate is given as:
x = 13 - 10 = 16 - 13 = 19 -16 = 3Hence the difference between the consecutive term of the sequence is (1, 3)
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A rectangular carpet measures 12 m by 5 m.
Part of the carpet is covered by a square rug of length 2 m.
What fraction of the carpet is covered by the rug? Give your answer in its simplest form.
I'm pretty sure the answer is 1/15 or 4/60 because the whole carpet measures 60m and the covered part's area is 4m and that would be 4/60 but simplified 1/15. Sorry if this is wrong!
To find the fraction of the carpet covered by the rug, we need to determine the area of the rug and divide it by the total area of the carpet.
The area of the square rug can be calculated by squaring its side length: 2m x 2m = 4m². The total area of the rectangular carpet can be found by multiplying its length and width: [tex]12m x 5m = 60m²[/tex]. To find the fraction, divide the area of the rug by the area of the carpet: 4m² / 60m².
To simplify the fraction, we can find the greatest common divisor (GCD) of 4 and 60, which is 4. Dividing both the numerator and denominator by the GCD, we get: [tex]4m² ÷ 4 / 60m² ÷ 4 = 1m² / 15m²[/tex] . Therefore, the fraction of the carpet covered by the rug is 1/15, which means that 1/15th of the carpet is covered by the rug.
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The graph shows the printing rate of Printer A. Printer B can print at a rate of 25 pages per minute.
How does the rate for Printer B compare to the rate for Printer A? Use the drop-down menus to explain your answer.
Printer Rates
y
40
30
Printer A
Number of Pages
20
10
0
0
х
2 4 6
Time (min)
The rate for Printer Bis Choose..
the rate for Printer A because the rate of 25 pages per minute is choose...
the
rate of Choose
pages per minute for Printer A.
Answer:
printer A = 10 pages a min
Step-by-step explanation:
please help i will mark brainliest
Answer:
Reflections and rotations
Step-by-step explanation:
Reflections and rotations preserves the distance and angle measurements.
Solve for x and y
Need a answer plz
Answer:
Angle x = 12
Angle y = 49
Property = Isosceles triangles
what is 9 time 64 what does it equal to
Answer:
It's 576 if you mean 64 times 9!
Step-by-step explanation:
Whats the answer I will give brainliest, thanks, and five star
Answer:
B
Step-by-step explanation:
the one you have selected is correct
30 POINTS GUYS!!!
What is the value of x?
Enter your answer, as a decimal, in the box.
x=
Answer:
[tex]x=3.5[/tex]
Step-by-step explanation:
Notice that CD bisects Angle C.
Then by the Angle Bisector Theorem, we can write the following proportion:
[tex]\frac{6}{4.2}=\frac{5}{x}[/tex]
Now, we can solve for x. Cross multiply:
[tex]5(4.2)=6(x)[/tex]
Multiply:
[tex]21=6x[/tex]
Divide both sides by 6:
[tex]x=21/6=7/2=3.5[/tex]
Hence, the vale of x is 3.5.
Answer:
4.2
Step-by-step explanation:
Martin needs help being a better friend and remembering how old his friends are. He can't remember their ages but he knows how to find their ages. He knows that
Jennifer is three years less than twice his age. Sally is three years more than Martin. His friend, Gabby, is five years less than him.
Write an expression for Jennifer's, Sally's and Gabby's age, where x represents Martins age.
Jennifer:
Sally:
Gabby:
Answer:
well first of martin needs some help cus he cants remember anything
Step-by-step explanation:
he needs new friends and a new life.
60 8th grade students chose to watch a movie on the last day of school. this is 20% of the class. how many students are there in 8th grade?
Answer:
the answer is 300 8th grade students
Step-by-step explanation:
What is the equation of this graphed line?
Answer:
Step-by-step explanation:
(-7 + 3)/(6 + 6) = -4/12 = -1/3
y + 3 = -1/3(x + 6)
y + 3 = -1/3x - 2
y = -1/3x - 5
Which of the following is equivalent to (5x^2)(4x^3)
Answer:
20x^5
Step-by-step explanation:
You just multiply 5 by 4 and get 20 and when multiplying exponents you just add them together so you get 20x^5
Solve the equation 5x+9=1
Answer:
x = -1.6
Step-by-step explanation:
Original equation:
5x + 9 = 1
Subtract 9 from both sides
5x = -8
Divide both sides by 5
x = -1.6
Hope this helps :)
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HALP QUICKKKKK!!!
Giving 25 points for whoever answers soon
Answer:
b is the y-intercept
Step-by-step explanation:
Help(Worth 20 Points)
I start by multiplying -4 by 3. I then multiply the answer by 2. Then, I take the negation of the result. What number do I get at the end?
Answer:
24
Step-by-step explanation:
1.-12
2.-12×2=-24
3.24
Answer:
-24
Step-by-step explanation:
-4 times 3 is -12 then times that by 2 is -24
i need help with this slope problem
Answer:
It is the first one and the second one. If it is the same, then the slope will be constant.
Step-by-step explanation:
Answer:
I think it's the second one ( Any two points on the line will produce the same slope)
Step-by-step explanation:
Any two points on a line will ALWAYS have the same slope. There's no way that it won't be that way. That's why you are able to choose any two points on a graph to find a slope.
For the first one, i think it's wrong because although the slope is 1/2, Jennifer used the slope 2/4 while Marshall used 1/2. Even though it's the same, Jennifer didn't technically use 1/2...
And the third option is wrong. The slope isn't 2.
Hopefully this wasn't confusing... :)