Answer:
a) Side lengths
= GH = 5 units
HI = 6 units
GI = 7.81 units
b) Angle measures
Angle G = 39.81°
Angle H = 90°
Angle I = 50.2°
Step-by-step explanation:
The coordinates of the vertices of △GHI are G(−7,2), H(−2,2), and I(−2,8). Find the side lengths to the nearest hundredth and the angle measures to the nearest degree.
Step 1
We find the side lengths using the coordinates formula
= √(x2 - x1)² + (y2 - y1)²
When we are given vertices (x1, y1) and (x2 , y2)
Coordinates of the vertices of △GHI are G(−7,2), H(−2,2), and I(−2,8).
For side length
GH = G(−7,2), H(−2,2)
= √(-2 - (-7))² + (2 - 2)²
= √(-2 + 7)² + (0)²
= √5²
= √25
= 5 units
For side length HI
HI = H(−2,2), and I(−2,8)
= √(-2 -(-2))² + (8 - 2)²
= √(0)² + (6)²
= √36
= 6 units
For side length GI
G(−7,2), I(−2,8)
= √(-2 -(-7))² + (8 - 2)²
= √(5)² + (6)²
= √25 + 36
= √61
= 7.81 units
Step 2
Angle measures
We find this using Cosine rules
Angle a = arc cos (b² + c² - a²/2bc)
Hence:
Finding
Angle G = arc cos (6² + 7.81² - 5² / 2 × 6 × 7.81)
= 39.81°
Angle H = arc cos (5² + 6² - 7.81² / 2 × 5 × 6)
= 90°
Angle I = arc cos (5² + 7.81² - 5² / 2 × 5 × 7.81)
= 50.2°
Answer:
GH = 5, HI = 6, GI ≈ 7.81
m∠H = 90°, m∠G ≈ 50°, m∠I ≈ 40°
Step-by-step explanation:
Question 2
Tahlia solved the equation 5 - 56 -0 by factoring.
Part A: Select the factors of ?-56
(x-7)
(+7)
(x-4)
(+14)
(X-8)
(x+8)
(x+4)
(x-14)
Answer:
The factors are: (x - 8) and (x + 7)
Step-by-step explanation:
Given
[tex]x^2 - x - 56 = 0[/tex] -- the right equation
Required
Select the factors of the equation
[tex]x^2 - x - 56 = 0[/tex]
Expand the equation
[tex]x^2 + 7x - 8x - 56 = 0[/tex]
Factorize:
[tex]x(x+7)-8(x+7) =0[/tex]
Factor out x + 7
[tex](x-8)(x+7) =0[/tex]
Hence, the factors are: (x - 8) and (x + 7)
Anya’s team won 4 games out of every 9 games this season. If the team played 45 games, how many games did they win?
Answer:20
Step-by-step explanation:4:9
9x5=45
4x5=20
20:45
NEED HELP ASAP PLEASE HELP PROVIDE EVIDENCE HOW IT IS CORRECT
Answer:
1204 in²
Step-by-step explanation:
To find the area of a trapezoid, use the following formula: [tex]\frac{b_{1} + b_{2} }{2} h[/tex]. First add the two bases together: 46 + 40 = 86. Now divide that by 2: 86/2 = 43. Now multiply this by the height (28): 43 x 28 = 1204. This is your area: 1204 in².
Hope it helps!
Answer:
1204
Step-by-step explanation:
1rst add the top numbers then divide it by 2. Then with the answer you have, multiply it by the height. Hope it helps! =D
What is the answer to a + b =
Answer:
a + b
Step-by-step explanation:
Answer:
a+b=ab
Step-by-step explanation:
you have to combine the two variables and multiply them by phi then divide by gamma
Plz help!!
What is the value of x when f(x)=20? What does this mean in context?
Answer:
It means that x = 20
Step-by-step explanation:
To buy a laptop computer, Jane borrowed $5,000 for 3 years at an annual rate of 6%.
How much interest will she pay if she pays the entire loan off at the end of the third
year?
Answer:
5955.08
Step-by-step explanation:
First year: 5000×(6÷100)=300
Second year : 5300×(6÷100)=318
Third year : 5618×(6/100)=337.08
And = 5955.08
2. Gerald was given the following problem to solve for the length of the "?". He has made a mistake in his work. Identify and describe how he made his mistake. Then, solve the problem correctly.
Answer:
x = 18.7
Step-by-step explanation:
Gerald's answer is almost correct.
He just needs to switch the 14 and the x.
it should be
24/x = 18/14
solve for x by cross multiplication
18x = (24)(14)
18x = 336
x = 18.7
Roosevelt High School is known for their marching band's attention to detail. Each band member makes sure that every step is exactly 2 feet so that the whole group stays in sync as they march across the football field. For the first part of their performance, every band member starts on the 50-yard line and marches to the 40-yard line. How many steps does each band member take for this part of the performance
Answer:
15 steps
Step-by-step explanation:
Find the value of "n" in the following equation
( n^2 x n = 216 )
plz answer asap
Answer:
Yoy add them to be 2n squared then divide by 2 on both sides then take the square root
What does -(-5) equal/mean?
Answer:
it means positive 5. because negative + negative = positive or you can think like -1 times -5 which is 5.
Step-by-step explanation:
Alberto buys a 600 balloons. Some of the balloons are pink.and the rest is green. He wants a estimate of the number of pink balloons in the bag. He ask 4 of his friends to each select a random sample of 10 balloons. Each friend returns the sample before the next friend selects a sample.
What is the estimate number of the pink balloons in the bag
Answer: there are 120 baloons in the bag
Step-by-step explanation:
10/ 600 = 4/x
10x = 1200
10/1200
x= 120
a=2x3^4x5 b=2^3x3^2x5^5 write down the night common factor of A and B PLEASE HELP ASAP PLEASEE!
Answer:
The HCF of [tex]a=2^1 \cdot 3^4 \cdot 5^1[/tex] and [tex]b = 2^3 \cdot 3^2 \cdot 5^2[/tex] is [tex]90[/tex].
Step-by-step explanation:
To calculate the HCF of two numbers given their prime factorization, we take the lowest exponent of every prime when comparing the two numbers.
So the HCF of [tex]a=2^1 \cdot 3^4 \cdot 5^1[/tex] and [tex]b = 2^3 \cdot 3^2 \cdot 5^2[/tex] is [tex]2^1 \cdot 3^2 \cdot 5^1 = 90[/tex].
Write an inequality that represents the graph. Please help me.
Answer:
y > 1/2x + 2
Step-by-step explanation:
Emir flew home from vacation with a heavy bag. With the first airline he flew, Emir had to pay $20 to check his bag, plus $10 for every pound that his bag was over the weight limit. The next flight was with another airline that had the same weight limit. Emir had to pay $5 per pound that his bag was over the weight limit, in addition to the checked bag fee of $30. By coincidence, the fees ended up being the same with both airlines. How large was each airline's fee?
Answer:
$27.5
Step-by-step explanation:
Let
x = pound over weight limit
Airline 1 = 20 + 10x
Airline 2 = 5 + 30x
Equate the fees
20 + 10x = 5 + 30x
20 - 5 = 30x - 10x
15 = 20x
x = 15/20
x = 0.75 pounds
How large was each airline's fee?
Airline 1 = 20 + 10x
= 20 + 10(0.75)
= 20 + 7.5
= $27.5
Airline 2 = 5 + 30x
= 5 + 30(0.75)
= 5 + 22.5
= $27.5
a farmer has enough food to feed 50 animals in his cattle for 15 days . how long will the food last if there are 25 more animals in his cattle?
Answer:
The food will last for 10 days
Step-by-step explanation:
Proportions
The amount of food the farmer needs to feed his animals is proportional to the number of animals and to the number of days they are fed.
This can be written as:
Food=k*N*D
Where k is a constant, N is the number of animals and D is the number of days.
We know that the farmer has enough food to feed N=50 animals for D=15 days, thus:
Food=k*50*15=750k
If the same amount of food is used for 50+25=75 animals, then:
750k=k*75*D
Simplifying:
750=75*D
Dividing by 75:
D=10
The food will last for 10 days
A fitness center opens to provide exercise opportunities for a community. The fitness
center charges customers a $35.95 monthly fee plus a one-time $125 administration fee.
What is the total cost of a 12-month membership at the fitness center?
The ratio of dogs to cats in the Bark and Meow Pet Center is 4:7. If there are 35 cats staying at the Bark and Meow Pet Center, how many dogs are staying at the pet center?
Answer:
20.
Step-by-step explanation:
5x7=35
5x4=20
Step-by-step explanation:
answer:20
good work :))
how to do expected frequency for chi^2 goodness fit test
Step-by-step explanation:
So basically you're going to start with your (expected value - observed value) squared
(O-E)²
You're then gonna divide that by your expected value that you just used
(O-E)²/E
The product of c and 8 is greater than or equal to - 16.
HELPPPPP
What comes next!T,F,S,S,M
Answer:
E,D
Step-by-step explanation:
100 POINTS PLEASE HELP I BEG YOU ONLY ANSWER IF YOU ANSWER ALL THE QUESTIONS
a) Maximum: 10
b) Minimum: - 2
To determine the amplitude we first recognize the midline, so I will answer part d first,
d) We have our maximum as 10, and our minimum as - 2. The midline, by it's name, is a line that divides the graph in half. What we do is determine the average of 10 and - 2 => 10 - 2/2 = 8/2 = 4
Midline: y = 4
Now I will go back to part c,
c) The amplitude would be 6. We take the difference between the maximum and the midline, or the minimum and the midline.
e) Period => The difference between two respective points on the graph
=> 3π/2 - π/2 = π, Period = π
f) We know that the period = π...
2π/b = π, b = 2π/π = 2
Vertical Shift => up 4
Equation: f(x) = 6cos(2x) + 4
Which expression is equal to the expression below?
(7•2)^7
NEED ASAP 7TH GRADE MATH
A scale drawing of a billboard uses the scale 4 cm :11 ft. The length of the billboard in the drawing is 15 cm. How long is the actual billboard?
Answer:
24.75 ft
Step-by-step explanation:
7(2а - 3) - 5a = -3
please show the work
Answer:
a = 2
Step-by-step explanation:
14a - 21 - 5a = -3
9a - 21 = -3
9a = -3 + 21
9a = 18
a = 2
Parallelogram R S T U is shown. Diagonals are drawn from point R to point T and from point U to point S and intersect at point V. The length of line segment U V is (x + 3) meters and the length of line segment V S is (2 x minus 7) meters. In parallelogram RSTU, what is SU? 10 m 13 m 23 m 26 m
Answer:
26m
Step-by-step explanation:
The diagonals of a parallelogram bisects each other. Hence the length of UV is equal to the length of VS
UV = VS
x+3 = 2x-7
x-2x = -7-3
-x = -10
x = 10
Get SU
SU = UV+VS
SU = x+3+2x-7
SU = 3x-4
Substitute x=10 into the expression
SU = 3(10)-4
SU = 30-4
SU = 26m
Length of SU is 26m
Answer:
26m i just did it on edg
Step-by-step explanation:
Simplify and write the trigonometric expression in terms of sine and cosine:
tan u + cot u = 1/f(u)
Answer:
we have the expression as;
1/sin u cos u
Step-by-step explanation:
tan u = sin u/cos u
cot u = cos u/sin u
Thus;
sin u/cos u + cos u/sin u
The lcm is sin u cos u
Thus, we have that;
(sin^2 u + cos^2 u)/sin u cos u
But ; sin^2 u + cos^2 u = 1
so we have ;
1/sin u cos u
The requested trigonometric expression in terms of sine and cosine is;
[tex]f(u) = \frac{1}{ \frac{sinu}{cosu} + \frac{cosu}{sinu} } [/tex]
Trigonometric expressions:We must remember,
tan u = sin(u)/cos(u)and cot u = cos(u)/sin(u).Therefore we have;
sin(u)/cos(u) + cos(u)/sin(u) = 1/f(u)
By Cross-product; we have;
[tex]f(u) = \frac{1}{ \frac{sinu}{cosu} + \frac{cosu}{sinu} } [/tex]
Therefore, the required function, f(u) in terms of sin u and cos u is as represented above.
Read more on trigonometry;
https://brainly.com/question/20519838
3rd times the charm. Someone please help me.
What is the product of 45.23 and 7.4?
simplify -z + 17x ??
Answer:
Step-by-step explanation:
This expression has two terms. They have nothing in common, so we cannot factor. We could write it at 17x - z.
Was there more to this problem?
write an equation of the line that passes through the two given points: (-5, -5) and (1,-3)
Answer:
slope-intercept formula -----> Y2-Y1/X2-X1
Step-by-step explanation:
X1= -5 X2= 1
Y1= -5 Y2= -3
-3+5/1+5=1/3