a) The slope of the new road is given by m = -4
b) The equation of line is y = -4x + 32
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the first point be represented as P ( 4 , 7 )
Let the second point be represented as Q ( 2 , 15 )
Now , the slope is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 15 - 7 ) / ( 2 - 4 )
Slope m = 8 / -2
Slope m = -4
Now , the equation of line is y - y₁ = m ( x - x₁ )
Substituting the values in the equation , we get
y - 4 = ( -4 ) ( x - 7 )
On simplifying the equation , we get
y - 4 = -4x + 28
Adding 4 on both sides of the equation , we get
y = -4x + 32
Hence , the equation of line is y = -4x + 32
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Alecia had save 60% of the cost of a new cell phone. If she has saved $105, what is the full price of the cell phone?
Please hurry; Which function increases the fastest? A. y 5 14x B. y 5 23 · 17x C. y 5 120x D. y 5 2275x^x
a y = 14^x
b y = -3 (17)^x
c y = 120x
d y = -275x
Answer: y = 14^x
Step-by-step explanation:
Here the options are:
a y = 14^x
b y = -3*(17)^x
c y = 120x
d y = -275x
to see which function increases the fastest (or which function is steeper) we need to look at the first derivations of each one of these, and see which one is larger for every value of x:
the derivations are:
a y = x*14^(x - 1)
b y = -x*3*(17)^(x - 1)
c y = 120
d y = -275
So we can already discard options c and d, because have constant rate of change.
Then we keep options a and b.
Always when we have an exponential function, like a^x and b^x
The one with the larger base will be steeper.
So if a > b, then:
a^x is steeper than b^x
In this case, the function:
y = -3*(17)^x
has a larger base, but, this function is negative.
This means that as x increases, our function will decrease, then this function will not "increase the fastest" (because it does not increase)
Then the left option (a: y = 14^x)
Will be the correct one.
(this will happen after some value of x, because two of the options have constant derivatives, these may be steeper for smaller values of x, and as x increases, we will see that y = 14^x is the one that increases the fastest)
Help me please quick!
Answer:
28
Step-by-step explanation:
All angles together in the triangle are 180.
62+90+x=180
x=180-(90+62)
x=180-152
x=28
Using the equation 2 + 3/41 = 5, what does the value of I equal?
Answer:
i did't see the value I in the equation
Step-by-step explanation:
Find o% of 176:
Find 100% of 176:
Find 50% of 176:
Find 25% of 176:
Find 75% of 176:
Use the slope formula to determine the slope of the line containing the two points.
(-1, -7) and (-6, -3)
A. 10/7
B. -4/5
C. -1/2
D. -5/4
the value of the 5 in the number 40.52 is _____ the value of the 5 in 115.78?
The value of each digit in a number is known as the place value. The value of the 5 in the number 40.52 is 10 times the value of the 5 in 115.78.
What is the place value of a digit in a number?The value of each digit in a number is known as the place value. The 5 in 350, for example, represents 5 tens, or 50, whereas the 5 in 5,006 represents 5 thousand, or 5,000. It is critical that children that while a digit can be the same, its value is determined by its position in the number.
Identification of the place value of a digit in a number:
The place values on the left of the decimal point start as ones, tens, hundreds, and so on.The place value on the right of the decimal point starts from the point and goes to the right as tenths, hundredths, and so onThe tens mean multiply by 10The tenth means the tenth part of that digit which is that digit divided by 10The value of 5 in the given numbers can be written as,
The value of the 5 in the number 40.52 is 0.5.The value of the 5 in the number 115.78 is 5.Now, we can write the value of the two numbers as,
5 = 0.5 × x
x = 5/0.5
x = 10
Hence, the value of the 5 in the number 40.52 is 10 times the value of the 5 in 115.78.
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calcule el cociente de los siguientes ejercicios
(-8)/(+2)
Answer:
-4
Step-by-step explanation:
Reuben invested his savings in two investment funds. The $18,000 that he invested in Fund A returned a 5% profit. The amount that he invested in Fund B returned a 1% profit. How much did he invest in Fund B, if both funds together returned a 4% profit?
Answer:
He invested $13500 in fund A, and $4500 in Fund B
Step-by-step explanation:
maths
Calculate the slope look at pic. Help plz!
Write the coordinates of the vertices after a reflection across the line x=-1
Answer:
U is (0,-8)
V is (0,-10)
T is (5,-8)
S is (5,(-10)
What is the value of the expression below when n=5
Answer:
-6 (i can explain if its needed)
Step-by-step explanation:
[tex]2 - {n}^{2} + 3 \times 14 - {n}^{2} = \\ 2 - {n}^{2} + 42 - {n}^{2} = \\ 2 - 25 + 42 - 25 = - 6[/tex]
All even numbers
greater than two, can be written
as the sum of two prime numbers
Peter
Give three examples that show that Peter is correct.
Answer:
Step-by-step explanation:
3 + 5 = 8
7 + 11 = 18
11 + 19 = 30
“Half of a number (n) is at least 22."
translate and solve
Answer:
n >_44
Step-by-step explanation:
1/2n>_22
(times 2 on both sides)
n >_44
*** >_ is greater than or equal to sign
4/5 divided by 3/4 =
Answer:
16/15 or 1 1/15
Step-by-step explanation:
4/5 divided by 3/4
Flip 3/4 so it is 4/3
Multiply 4/5 by 4/3
16/15
i just started taking a math class today and i'm really rusty. my question is
simplify 28-(6+4)=(4-2)
what are scale drawings
Answer:
A drawing that shows a real object with accurate sizes reduced or enlarged by a certain amount (called the scale). The scale is shown as the length in the drawing, then a colon (":"), then the matching length on the real thing.
Step-by-step explanation:
Answer:
Answer down below!
Step-by-step explanation:
A scale drawing is a drawing that is downsized. They are usually used to see how small to make a particular thing.
A cable TV company charges $28 for the basic service plus $8 for each movie channel. Let y be the total cost
in dollars of subscribing to cable TV, using x movie channels. Find the slope-intercept form of the equation.
Look at pic
Answer:
y= 28x+8
Step-by-step explanation:
Help with this work please.
Answer: x= 10, y= 13. i dont know for sure so i'd wait for someone else to answer
Answer:
x = 12
y = 13
Step-by-step explanation:
by pythagoras theorem
x²=20²-16²
x²=400-256
x²=144
x=12
y²=x²+5²
y²=12²+5²
y²=144+25
y²=169
y=13
What is the sale price of a hardcover book with a markdown of 46% and original price of 29.00 what is the discount amount
Answer:
15.66
Step-by-step explanation:
First you find what is 46% of 29.00 which is 13.34
Next do 29-13.34 and that is 15.66
that is your answer hope I helped. :)
How Many Times Done 16 go Into 78!??!!!!?!!?!??!?!?! HELP ME!!!
Answer:
4.87500
Step-by-step explanation:
hope this helps
Answer:
4.875
Step-by-step explanation:
78 divided by 16 = 4.875
(20,-6)(6,5) find the slope
Which ordered pair best represents the coordinates of
a point that could be the third vertex of the right
triangle?
A (5,-5)
B (-4,6)
© (-3,-6)
D (3,4)
PLS HURRY I HAVE A TEST
Use distributive property to solve the problem
3 (9 - 10a) - 3a
Answer:
27- 1 = 26
Step-by-step explanation:
A coat at a store is originally priced at $85. The store marks the price down to $68. To the nearest percent, what is the percent markdown of the coat ?
Answer:
20%
Step-by-step explanation:
This is because the amount decreased is 17 and 17 is what percent of 85? The answer is 20%.
11 b = 5, what is a
B. 25
C, 75
D. 125
Answer:
2.2
Step-by-step explanation:
use the bar diagram to help you solve the equation 4x-12=16.
Answer:
x = 7
Step-by-step explanation:
4x−12=16
Step 1: Add 12 to both sides.
4x−12+12=16+12
4x=28
Step 2: Divide both sides by 4.
4x/4 = 28/4 = 7
x=7
The daily temperature in the month of March in a certain city varies from a low of 24 degrees F to a high of 40 degrees F. Find a sinusoidal function to model daily temperature and sketch the graph. Let t=0 correspond to noon, when the highest temperature of the day occurs.
Please help I'm in the test.
Answer:
d(t)=8cos((pi/12)t)
Step-by-step explanation:
I think this is correct...
A=8 b/c 40-24=16, 16/2 = 8
B=2pi/per, 2pi/24, B = pi/12
1. Find the coordinates of the centroid of the triangle with the given vertices.
A(2,3), B(8, 1), C(5,7)
The centroid is ( , )
9514 1404 393
Answer:
(5, 3 2/3)
Step-by-step explanation:
The centroid is the average of the vertex coordinates:
(A +B +C)/3 = ((2, 3) +(8, 1) +(5, 7))/3 = (2+8+5, 3+1+7)/3 = (5, 3 2/3)
Answer:
46940064
Step-by-step explanation:
1)
The angle of inclination is the angle between the horizontal and the ramp.
Using the sine ratio in the right triangle formed by the ground and the ramp
let x be the angle of inclination, then
sinx = \frac{opposite}{hypotenuse}
hypotenuse
opposite
= \frac{0.7}{4.2}
4.2
0.7
, then
x = sin^{-1}sin
−1
(\frac{0.7}{4.2}
4.2
0.7
) ≈ 10° ( to the nearest degree )
(2)
Again there is a right triangle between the ground and the vertical height of the kite, with hypotenuse being length of string.
let y be the height of the kite and x the horizontal distance, then
sin27° = \frac{opposite}{hypotenuse}
hypotenuse
opposite
= \frac{y}{176}
176
y
( multiply both sides by 176 )
176 × sin27° = y , then
y ≈ 80m ( to the nearest metre ) ← height of kite
and
cos27° = \frac{adjacent}{hypotenuse}
hypotenuse
adjacent
= \frac{x}{176}
176
x
( multiply both sides by 176 )
176 × cos27° = x , then
x ≈ 157m ( to the nearest metre ) ← horizontal distance
A person who filed bankruptcy in the past is able to get a 30-year mortgage loan at a rate that is 6% higher than what they could have received if they had not filed. The interest rate this person pays on a $150,000 loan is 11%, compounded monthly. Assume the person could have received the lower interest rate on the loan and saved all of the difference in the payments for the first 10 years of the loan. If this person invested this total amount in an account paying simple interest at the rate of 2.5%, how much money would have accumulated in interest by the time the mortgage is paid off? a. $37,395.18 b. $74,790.37 c. $623.25 d. $3,739.52
Answer:
A. $37,395
Step-by-step explanation:
correct on edge! hope it helps :)
The savings from the difference between the 30–year loan at 11%, which
is 6% gives an interest when the mortgage is paid of approximately;
a. $37,395.18
How can the amount interest accumulated be calculated?
The amount paid is given as follows;
[tex]Monthly \ payment, \ M = \mathbf{\dfrac{P \cdot \left(\dfrac{r}{12} \right) \cdot }\left(1+\dfrac{r}{12} \right)^n }{\left(1+\dfrac{r}{12} \right)^n - 1}[/tex]
Which gives;
[tex]M = \dfrac{150000 \times \left(\dfrac{0.11}{12} \right) \cdot \left(1+\dfrac{0.11}{12} \right)^{30 \times 12} }{\left(1+\dfrac{0.11}{12} \right)^{30 \times 12} - 1} \approx \mathbf{1,428.49}[/tex]
Payment in 10 years = $1,428.49 × 120 ≈ $171,418.8
At the lower interest rate the person could have received (11 - 6 = 5)%, we have;
[tex]M = \mathbf{\dfrac{150000 \times \left(\dfrac{0.05}{12} \right) \cdot \left(1+\dfrac{0.05}{12} \right)^{30 \times 12} }{\left(1+\dfrac{0.05}{12} \right)^{30 \times 12} - 1}} \approx 805.23[/tex]
Payment in 10 years = $805.23 × 120 ≈ $92,227.6
Savings = $171,418.8 - $96,627.6 = $74,791.2
The time duration the savings is invested in the account = 30 years - 10 years = 20 years
Which gives;
Simple interest after 20 years = $74,791.2 × 0.025 × 20 ≈ $37,396.6
Therefore;
The option that best gives the amount of money that would have accumulated in interest is the option a.
a. $37,395.18
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