The amount of the coupon is $30 which gives a discount of 60%.
Regular price of item = p
Final price paid by the buyer = 0.7p - 15
Discount = Regular price - Price paid by the buyer
Discount = p - (0.7p - 15)
Discount = p - 0.7p - 15.
p - 0.7p = 15
0.3p = 15.
Price = 15/0.3
Price = $50
Therefore, the amount paid by the person will be:
= 0.7p - 15
= 0.7(50) - 15
= 35 - 15
= 20
Therefore, the discount will be:
= 50 - 20 = 30
Discount percentage = 30/50 × 100 = 60%
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In Triangle ABC with vertices A(-5,-4), B(3,-2), and C(-1,6), M is the midpoint of AB and N is the midpoint of BC. Show that MN = 1/2 AC. Provide your complete solutions and proofs in your paper homework and enter the numeric answers online
The midpoint of a line divides the line into equal segments.
See below for the proof of [tex]\mathbf{MN = \frac{1}{2}AC}[/tex]
The given parameters are:
[tex]\mathbf{A = (-5,-4)}[/tex]
[tex]\mathbf{B = (3,-2)}[/tex]
[tex]\mathbf{C = (-1,6)}[/tex]
The coordinates of M (midpoint of AB) are calculated as follows:
[tex]\mathbf{M = \frac{1}{2}(x_1 + x_2, y_1+y_2)}[/tex]
So, we have:
[tex]\mathbf{M = \frac{1}{2}(-5 + 3, -4-2)}[/tex]
[tex]\mathbf{M = \frac{1}{2}(-2, -6)}[/tex]
[tex]\mathbf{M = (-1, -3)}[/tex]
The coordinates of N (midpoint of BC) are calculated as follows:
[tex]\mathbf{N = \frac{1}{2}(x_1 + x_2, y_1+y_2)}[/tex]
So, we have:
[tex]\mathbf{N = \frac{1}{2}(3 - 1, -2 +6)}[/tex]
[tex]\mathbf{N = \frac{1}{2}(2, 4)}[/tex]
[tex]\mathbf{N = (1, 2)}[/tex]
Distance MN is:
[tex]\mathbf{MN = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}}[/tex]
So, we have:
[tex]\mathbf{MN = \sqrt{(-1 - 1)^2 + (-3 - 2)^2}}[/tex]
[tex]\mathbf{MN = \sqrt{29}}[/tex]
Distance AC is calculated as follows:
[tex]\mathbf{AC= \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}}[/tex]
So, we have:
[tex]\mathbf{AC= \sqrt{(-5 - -1)^2 + (-4 - 6)^2}}[/tex]
[tex]\mathbf{AC= \sqrt{116}}[/tex]
Split
[tex]\mathbf{AC= \sqrt{4 \times 29}}[/tex]
Take positive square root of 4
[tex]\mathbf{AC= 2\sqrt{29}}[/tex]
To prove that:
[tex]\mathbf{MN = \frac{1}{2}AC}[/tex]
We have:
[tex]\mathbf{\sqrt{29} = \frac{1}{2} \times 2\sqrt{29}}[/tex]
[tex]\mathbf{\sqrt{29} = \sqrt{29}}[/tex]
The above equation is true.
Hence. [tex]\mathbf{MN = \frac{1}{2}AC}[/tex]
Read more about midpoints and distance at:
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Take some time but answer correctly
Answer:
c) 2⁻⁹
Step-by-step explanation:
1) use negative power rule: [tex]x^{-a} =\frac{1}{x^{a} }[/tex]
1/2⁹
2) simplify ₂⁹ to 512
1/512 ( same as (8) ⁻3
Answer:
c
Step-by-step explanation:
Using the rule of exponents
[tex](a^m)^{n}[/tex] = [tex]a^{mn}[/tex]
note that 8 = 2³ , then
[tex](8)^{-3}[/tex]
= [tex](2^3)^{-3}[/tex]
= [tex]2^{3(-3)}[/tex]
= [tex]2^{-9}[/tex] → c
One eight of a pizza pie is sold for 65 cent. How much will be received
Answer:
I don't know haha
Step-by-step explanation:
Salamat nalang sa points
Answer:
the whole pizza would cost $5.20
Step-by-step explanation:
1/8 = $0.65
8/8 = 1 = $5.20
0.65 × 8 = 5.2
is this what you mean??
Tony can cycle a distance of 9 5/6 in 3/5 hours. What is his unit rate?
Answer:
19.66
Step-by-step explanation:
9.83 / 0.5
19.66
Sorry if it is not correct but I think that this is the corrcet answer.
What is the answer for this question:12+2c+6d-8c+d
Answer:
12+10c+7d
Step-by-step explanation:
There is no possible way to really describe the value of the variables, so I simplified it.
HELP PLEASE I NEED HOW TO DO IT AND THE ANSWER FAST PLEASE
Answer:
4
Step-by-step explanation:
factor the numerator and denominator and cancel the common factors
Your mom opens an account to save money for a family vacation. The account earns an animal interest rate of 4%. She earns $37 in simple interest after 6 months. How much money did she put in the account when she opened it? Use the formula: I=prt
Answer:
I = $ 0.74
Step-by-step explanation:
First, converting R percent to r a decimal
r = R/100 = 4%/100 = 0.04 per year,
putting time into years for simplicity,
6 months ÷ 12 months/year = 0.5 years,
then, solving our equation
I = 37 × 0.04 × 0.5 = 0.74
I = $ 0.74
The simple interest accumulated
on a principal of $ 37.00
at a rate of 4% per year
for 0.5 years (6 months) is $ 0.74.
BRAINLIEST PLEASE
Write the equation of the line in fully simplified slope-intercept form.
Answer:
y= [tex]\frac{5}{6} x[/tex] + 4
Step-by-step explanation:
Pick two points: (-6,-10) and (0,4)
Then solve for m (slope): I picked (0,4)
[tex]m= \frac{4-(-1)}{0-(-6)} =\frac{5}{6}[/tex]
Then put in slope intercept form:
4= [tex]\frac{5}{6} (0)[/tex] + b
4=b
Then put in final form:
y= [tex]\frac{5}{6} x[/tex] + 4
Hope this helps!
Answer:
y=5/6x+4
Step-by-step explanation:
can someone answer this
Answer:
b.d-6 that's the correct answer
Answer:
it is a
Step-by-step explanation:
Help me Plz :))
What are the dimensions of AB?
Answer:
c 2*3
Step-by-step explanation:
I think its correct
Ms.Jensen surveyed her class and found that 2/3 of her class has a dog.Of those students who have a dog,1/4 also have a cat.What fraction of the students have both?
Sorry im confused:
Answer:
1/6
Step-by-step explanation:
2/3 of the class has a dog, and 1/4 of the class has a cat. This means that some people will have both a cat and a dog.
You have to find the fraction of students who have both, so you have to multiply 2/3 and 1/4, 2*1 = 2, and 3*4 = 12, so the fraction is 2/12.
2/12 can be simplified to 1/6.
So, the amount of students in the class that have both a cat and a dog are 1/6.
Answer:
The answer is 1/6.
Which equation represents the line with slope 1/4 that passes through (-4, 8)?
A
y = 1x + 7
B
y = -4x + 24
С
y = -4x – 8
D
y = 1x + 9
Answer
B DID THE TEST
Step-by-step explanation:
YOU WILL DO YOU GOOD LUCK
For brainily please help
write an inequality whose solutions are represented by the shaded part of the graph
Answer:
x > 3
Step-by-step explanation:
A city has 1,242 law enforcement officers in the police department. If the officers are divided equally into 18 groups, how many officers will be in each group?
Answer:
69
Step-by-step explanation:
1,242 ÷ 18 = 69
Since the problem says divided equally, you will need to divide the total number of officers into 18 groups.
-kiniwih426
Members per group:-
[tex]\\ \sf\longmapsto \dfrac{1242}{18}[/tex]
[tex]\\ \sf\longmapsto 69[/tex]
If ALTU ASBP
then TU = [?]
Enter the letters that belong in the
green box.
Enter
Answer:
BP
Step-by-step explanation:
the letters are congruent in order, so the last 2 letters of both sides are congruent
3(x+1)=2(x-3) whats the answer
The answer is -9
I dont know the step-by-step used a calculator
How to solve this question ????
Help me please
if i fill the 42 L tank in my car and take a 360km trip. If my car consumes gasoline at a rate of 8 L per 100km how muck farther can i go before i run out of gasoline.
Using the principle of proportional relationship, the 42 L of gas can go for a further 165 km
Consumption rate = 8L for 100 km
Km per Litre :
8L = 100km
1 L = m
8m = 100
m = (100 ÷ 8)
= 12.5 kilometer per Litre
Number of kilometers for 42 L
12.5 km = 1 L
m = 42 L
Cross multiply
m = 12.5 × 42
m = 525 km
The difference in the distance = 525 - 360 = 165 km
Therefore, the gas can go for a further 165 km
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State if the triangle are similar amd if they are, give the reasons AA SSS SAS
which triangles?
i see no triangles
try again bro
Solve for y in terms of v, w, x, and z.
wy=–zvx
Answer:
y = (-zvx)/w
........
Find the value of x. Then find the measure of each labeled angle.
Answer:
x = 114°
Step-by-step explanation:
x + (x - 48) = 180
2x = 228
x = 114
114 - 48 = 66
add 8 to m, multiply the result by 4, then add 3 to what you have
(8 + m)4 + 3
This is ur answer have a good day
PLEASE HELP complete the construction a perpendicular line to segment AB through point P.
Answer:
.
Step-by-step explanation:
sorry i can't help
10, 8) and (-5, 8) What is the formula and slope for the points above?
Answer:
formula: (y_2-y_1)/(x_2-x_1)
slope: 0
Step-by-step explanation:
1. The formula to find the slope given two points is [tex]\frac{y_2-y_1}{x_2-x_1}[/tex].
2. (Solving)
[tex]\frac{8-8}{-5-10}[/tex] [tex]\frac{0}{-15}[/tex] [tex]0[/tex]Therefore, the slope is 0.
Is g correct? I need help in this
are two of the same looking triangle but different sizes mean they are congruent?
Answer:
No
Step-by-step explanation:
They are similar
Answer:
Congruent triangles Two or more triangles that have the same size and shape are called congruent triangles. The four triangles are congruent with each other regardless whether they are rotated or flipped. The congruence of two objects is often represented using the symbol
Step-by-step explanation:
LOL LAST 1 IM SORRY AHHHH !!!!
Answer:
102
Step-by-step explanation:
Answer:
Fairly easy just 180-102-30= 48 degrees So since you know the third angle within that triangle just take 180 - 48 which gives you 132 degrees. 132 is the angle FGH.
Step-by-step explanation:
180- 102 - 30= 48 degrees
180 - 48 = 132 degrees
complete the following statements of congruence zyx
Answer:
cba
Step-by-step explanation:
yes correct answer x yimes h yomes z
(√5+1)²
guys pls help me
[tex]( \sqrt{5} + 1 {)}^{2} \\ calculate \\ \\ 5 + 2 \sqrt{5} + 1 \ \\ \\ = 6 + 2 \sqrt{5} \\ \\ in \: \: alternate \: \: form \: \\ \\ 10.47214 \\ \\ hope \: it \: \: helps \\ \\ [/tex]
Step-by-step explanation:
Here is your answer . The logic I have shared above to solve this equation