Answers
Answer:
x = 20
Step-by-step explanation:
(see attached for reference)
From the diagram, we can see that angle A and angle C are base angles of an isoceles triangle. Hence they are equal. i.e
m∠A = m∠C
(3x+10) = (2x+30)
3x+10 = 2x+30 (subtract 2x from both sides)
3x + 10 - 2x = 30
x + 10 = 30 (subtract 10 from both sides)
x = 30 - 10
x = 20
Related Questions
Given: GH || KL, J is the midpoint of HK
Prove: AGHJ ALKJ
STATEMENT
REASON
1. GH | KL
Given
2. J is the midpoint of HK
Given
3
4
5
6.GHJ=LKJ
Answers
Answer:
Step-by-step explanation:
From the picture attached,
Given:
GH║KL and J is the midpoint of HK.
To Prove:
ΔGHJ ≅ ΔLKJ
Statements Reasons
1. GH║KL 1. Given
2. J is the midpoint of HK 2. Given
3. JH ≅ JK 3. Definition of the midpoint of a segment
4. ∠JKL ≅ ∠JHG 4. Alternate interior angles
5. ∠GJH ≅ ∠KJL 5. Vertically opposite angles
6. ΔGHJ ≅ ΔLKJ 6. By ASA theorem of congruence
Statements Reasons
1. GH║KL 1. Given
2. J is the midpoint of HK 2. Given
3. JH ≅ JK 3. Definition of the midpoint of a segment
4. ∠JKL ≅ ∠JHG 4. Alternate interior angles
5. ∠GJH ≅ ∠KJL 5. Vertically opposite angles
6. ΔGHJ ≅ ΔLKJ 6. By ASA theorem of congruence
We have to prove the statement, ∠GHJ = ∠LKJ
Given; GH || KL, J is the midpoint of HK.
To prove; ∠GHJ = ∠LKJ
Given; J is the midpoint of HK,
By definition midpoint of a segment,
The midpoint is the middle part of the line segment J, it is equidistant from both endpoints it is the centroid of the segment of the endpoints.
JH ≅ HK
Then, by the property of alternate interior angles,
∠JKL≅ ∠JKH
Therefore, by the property of vertically opposite angles,
When two lines intersect they form four angles. Vertical angles are the angles that are opposite to each other. Any two intersecting lines form two pairs of vertical angles that are opposite to each other.
∠GJH ≅ KJL
By ASA congruence theorem,
When two triangles are congruent to each other - If two angles and the involved side of one triangle is equivalent to the two angles and the included side of the other triangle.
ΔGHJ ≅ ΔLKJ
Hence Proved.
For more details refer to the link.
https://brainly.com/question/1751208
What is the solution: –3(3x –2) = –30
Answers
Answer:
x=4
Step-by-step explanation:
–3(3x –2) = –30
Divide each side by -3
–3(3x –2)/-3 = –30/-3
3x –2 = 10
Add 2 to each side
3x –2+2 = 10+2
3x = 12
Divide each side by 3
3x/3 = 12/3
x = 4
Answer:
X = 4
Step-by-step explanation:
1: Distribute
-3 (3x - 2) = -30 (Multiply 3x and -2 by -3)
-9x + 6 = -30
2: Combine Like Terms
-9x + 6 = -30 (Subtract 6 from -30)
-9x = -36
3: Divide
-9x = -36 (Divide -36 by -9 to get x by itself)
x = -36 / -9
4: Solve
x = -36 / -9
X = 4
What is the area of a rectangle with a length of 5 inches and a with of 2 inches
Answers
Answer:
10 inches
Step-by-step explanation:
f(x) = 2x+3 and g(x) = x - 7. Find f(-2)+g(4)
Answers
f(-2) = 2(-2)+3
f(-2) = -4+3
f(-2) = -1
g(4) = (4) - 7
g(4) = -3
f(-2) + g(4) is -1 + (-3) which is -4
A car travels at a rate of 45 miles per hour for 5 hours. Let y be the source, in miles, the car travels for a given amount of time, x, in
hours. This situation can be modeled by a function
What is the domain of the function?
Answers
Answer:
8
Step-by-step explanation:
Answer:
0 ≤ x ≤ 5
Step-by-step explanation:
I used the Desmos calculator
Please help (: Solve the equation.
n – 29 – 33 = –49
13
–111
–53
–13
Answers
Answer:
13
Step-by-step explanation:
Put the following equation of a line into slope-intercept form, simplifying all fractions.
4x+6y= -30
Answers
Answer: y=-2/3x-5
Step-by-step explanation:
I need the answer to this please help.
Answers
Answer:
see below
Step-by-step explanation:
sin x = cos x
opp/ hyp = adj /hyp
Multiply each side by the hypotenuse
opp = adj
The opposite side must equal the adjacent
Since this is a right triangle
opp ^2 + adj ^2 = hypotenuse^2
opp ^2 + opp ^2 = hypotenuse^2
2 opp ^2 = hypotenuse^2
Take the square root of each side
sqrt(2 opp ^2) =sqrt( hypotenuse^2)
sqrt(2) opp = hyp
We know sin X = opp / hyp
sin x = opp / (sqrt(2) / hyp)
sin x = 1 / sqrt(2)
sin x = sqrt(2) /2
Taking the inverse sin of each side
x = sin ^-1 ( sqrt(2) /2)
Please help again!!!!!!
y−3/14 = 3/7
Answers
Answer:
PLEASE HELP WILL MARK BRAINLIEST
Answers
Answer:
1000 grams of fish= 1500 calories
1334 grams of fish= 2001 calories
1 gram of fish= 1.5 calories
A marketing professional sells advertising slots at a baseball stadium with pricing based on the predicted number of spectators. The stadium holds 41,915 spectators. When the gates open, there are 1,000 spectators already inside, and 1.25 hours after opening, there are 38,500 spectators. Choose the values for the model that the marketing professional can use.
Answers
Answer:
A= 41,915
B= 40.915
C= 4.9072
Step-by-step explanation:
help me pls il give me branilest
Answers
Answer:
point b
Step-by-step explanation:
[tex] \frac{3}{2} = 1.5[/tex]
Answer:
B
Step-by-step explanation:
It is actually pretty simple if you know what to do.
First you simplify 3/2. That will get you 1 1/2
If you look closley you can see that B is in the 1 1/2 place.
Thats it!
Hope this helped! :)
Mr. Gatti is looking to buy some apples to bake a fresh & tasty apple pie. He goes to the store and sees two deals that are going on for apples: Deal A - 3/4 of a pound for $2.50 Deal B - LaTeX: 2\frac{2}{10}2 2 10 pounds for $5.25 1. Which is the better deal, and why? Explain your answer. Put your answer in $ per pound format
Answers
Answer:
Deal A is best
Step-by-step explanation:
Given
Deal A:
3/4 lb for $2.50
Deal B:
2/10 lb for $5.25
Required
Which deal is the better
To do this, we simply calculate the lb/dollar ratio
i.e.
[tex]Ratio = \frac{Amount}{Size}[/tex]
For Deal A:
[tex]Ratio = \$2.50/\frac{3}{4}lb[/tex]
[tex]Ratio = \$2.50 * \frac{4}{3}lb[/tex]
[tex]Ratio = \frac{\$10}{3}lb[/tex]
[tex]Ratio = \$3.33/lb[/tex]
For Deal B:
[tex]Ratio = \$5.25/\frac{2}{10}lb[/tex]
[tex]Ratio = \$5.25 * \frac{10}{2}lb[/tex]
[tex]Ratio = \frac{52.5}{2}lb[/tex]
[tex]Ratio = \$26.25/lb[/tex]
The better deal is the least expensive:
Hence: Deal A is better
Davos has $150,000 to invest. His intent is to earn 7.5% interest on his investment. Davos will invest part of the money at 5.6% interest and part at 9.7% interest. How much does Paul need to invest in each option to earn a 7.5% return on the $150,000? Round to the nearest dollar.
Answers
Answer:
The amount invested on 5.6% interest = $80488
The amount invested on 9.7% interest = $69512
Step-by-step explanation:
Given that total amount of investment = $150,000
Let the amount invested on 5.6% interest = $[tex]x[/tex]
Now, amount invested on 9.7% interest = $(150000-[tex]x[/tex])
Total interest to be earned = 7.5%
Formula to be used:
[tex]Simple\ Interest = \dfrac{P\times r\times t}{100}[/tex]
Where, [tex]P[/tex] is the amount invested
[tex]r[/tex] is the rate of interest
[tex]t[/tex] is the time for which amount is invested.
As per question statement:
[tex]\dfrac{x\times 5.6}{100}+\dfrac{(150000-x)\times 9.7}{100}=\dfrac{150000\times 7.5}{100}\\\Rightarrow 5.6x-9.7x=150000(7.5-9.7)\\\Rightarrow 4.1x=150000\times 2.2\\\Rightarrow x = \dfrac{330000}{4.1}\\\Rightarrow x \approx \bold{\$80488}[/tex]
The amount invested on 5.6% interest = $80488
The amount invested on 9.7% interest = $150000 - $80488 = $69512
The graph of a linear function is shown on the coordinate grid below.
What are the slope and y-intercept of the linear function shown in the grid?
A) Slope = –0.4, y-intercept = –5
B) Slope = 2.5, y-intercept = –5
C) Slope = –2.5, y-intercept = 2
D) Slope = 0.4, y-intercept = 2
Answers
Answer:
B) Slope = 2.5, y-intercept = –5
Step-by-step explanation:
Given the following points on the grid, (-1.5, -8.75) and (3.5, 3.75), the slope can be calculated as follows using the formula, [tex] m = \frac{y_2 - y_1}{x_2 - x_1} [/tex]
Let,
[tex] (-1.5, -8.75) = (x_1, y_1) [/tex]
[tex] (3.5, 3.75) = (x_2, y_2) [/tex]
[tex] m = \frac{3.75 -(-8.75)}{3.5 -(-1.5)} [/tex]
[tex] m = \frac{3.75 + 8.75}{3.5 + 1.5} [/tex]
[tex] m = \frac{12.5}{5} [/tex]
[tex] m = 2.5 [/tex]
Slope = 2.5.
The y-intercept is the point at which the line intercepts the y-axis. On the graph, the line intercepts the y-axis at y = -5. Therefore, the y-intercept = -5.
A department store is offering the same percentage discount on all of their shoes Suppose one pair of shoes is marked down from $70 to $49. Based on that percentage discount, what would the new price be for a pair ol
shoes that originally cost $110
Answers
Answer:
$77Step-by-step explanation:
Discount is:
$70 - $49 = $21Discount % is:
21/70*100% = 30%Applying same discount to pair of shoes for $110:
$110 - 30% = $110*(100 - 30)/100 = $110*0.7 = $77
Which interval for the graphed function contains the
local maximum?
Of3, -2]
0 (-2, 0]
O [0, 2]
O [2, 4]
Answers
Answer:
[ 0, 2 ] is the interval for the graphed function that contains the local maximum. Hence, the answer is [ 0, 2 ] is the answer.
Step-by-step explanation:
Write the point slope form and the slope intercept form and Standard Form of the equation of the line that goes through the points (-10, 1) and (5, 11).
Answers
Answer:
m=2/3
Step-by-step explanation:
You buy 80 stamps for 17 dollars some stamps were 15 cents each and the others were 25 cents each. how many of each kind did you buy
Answers
Answer:
30 of the 15 cent stamps and 50 of the 25 cent stamps
Step-by-step explanation:
Create a system of equations, where x is the number of 15 cent stamps and y is the number of 25 cent stamps:
x + y = 80
0.15x + 0.25y = 17
Solve by substitution by rearranging the first equation:
x + y = 80
x = 80 - y
Substitute 80 - y as x into the second equation:
0.15x + 0.25y = 17
0.15(80 - y) + 0.25y = 17
12 - 0.15y + 0.25y = 17
12 + 0.1y = 17
Solve for y:
0.1y = 5
y = 50
Plug in 50 as y into the first equation, and solve for x:
x + y = 80
x + 50 = 80
x = 30
So, you bought 30 of the 15 cent stamps and 50 of the 25 cent stamps
answer: ten 15¢ stamps and forty 20¢ stamps.
Step-by-step explanation:
because i just took the quiz
Jackrabbits are capable of reaching speeds up to 40 miles per hour. How fast is this in feet per second? Round to the nearest whole number
Answers
Answer:
59 feet per second
Step-by-step explanation:
[tex]40 mph = \frac{40*5280feet}{1hour} \\40mph = 211200 feet/per/hour[/tex]
to convert 211200 feet per hour to feet per second, we need to know how many seconds are in one hour
60seconds * 60 minutes = 3600 seconds
[tex]211200/3600 = 58.66666666666.... =59[/tex]
(5) • (–9) • (–2) bruhhh ik i keep asking math questions but I struggle with math so lol
Answers
Answer:
90
Step-by-step explanation:
5*-9=-45
-45*-2=90
Answer:
90
Step-by-step explanation:
Let's solve this step by step:
(5) · (-9) · (-2)
First, there are two negatives in this equation. They will cancel each other out, to simply make 9 · 2:
5 · 9 · 2 =
Now, we do the multiplication:
5 · 9 · 2 = 45 · 2 = 90
90 is the answer!
3 x 9+2 x 20+5 x 3.50
simpilfied
Answers
2 x 20 = 40
5 x 3.50 = 17.5
27 + 40 + 17.5 = 84.5
Translate please... Six less than the product of nine and a number is equal to seven
Answers
Triangle JKL is shown below.
K
84
67
L
M
What is the measure of KLM?
Answers
Answer:
29
Step-by-step explanation:
sum of angles in a triangle=180°
180-(67+84)=29°
Identify the slope of the line that passes through the two points (3, 4) and (9, 12).
Answers
Answer:
4/3
sorry if its wrong. i tried
Help ASAP!!!! *Screenshot of the problem included*
Answers
Answer:
x=2 y= negative6
Step-by-step explanation:
pls help me solve this i will give lots of pointsssss
Answers
Answer:
10.7 cm
Step-by-step explanation:
A= bh
[tex]\sqrt{115}[/tex] = 10.7 cm
Line A passes through the points (1, 2) and (3, 6). What is the slope of a line parallel to
line A?
Answers
Answer:
1/4 x
Step-by-step explanation:
from 1 to 3 is 2, and from 2 to 6 is 4
2/4 simplifies to 1/2
can i get brainliest please?
Rex deposited $1,000 into an account that earns 5% compound interest annually. How much interest will Rex earn after 10 years?
Answers
Answer:
1,628.89
Step-by-step explanation:
Determine if the two triangles below are similar.
Answers
Answer:
they are similar because they both are equilateral triangles
Step-by-step explanation:
they are both equilateral triangles because there sides added together equal 60 degrees, but they are not congruent because to be congruent they need to be the same shape AND size
hope this helps :)
- may i get brainliest
