Answer:
[tex]y = -8x - 39[/tex]
Step-by-step explanation:
First, find the rate of change [slope]:
-y₁ + y₂\-x₁ + x₂ = m
[tex] \frac{7 + 9}{4 - 6} = -\frac{16}{2} = -8[/tex]
Then use the Point-Slope Formula since we are given points. Now, according to this formula, all negative symbols give the OPPOSITE terms of what they really are, so be EXTREMELY careful inserting the coordinates into the formula with their CORRECT signs. It does not matter which one you choose:
y - y₁ = m(x - x₁)
y - 9 = -8(x + 6)
y - 9 = -8x - 48
+ 9 + 9
______________
y = -8x - 39
__________________________________________________________
y + 7 = -8(x + 4)
y + 7 = -8x - 32
- 7 - 7
______________
y = -8x - 39
** You see? I told you it did not matter which ordered pair you choose because you will always get the exact same result.
I am joyous to assist you anytime.
what is the value of x in the equation 2(x-3)+9=3(x+1)+x?
Answer:
X=0
Step-by-step explanation:
Since x is on the right side of the equation, switch the sides so it is on the left side of the equation.
3(x+1)+x=2(x−3)+93(x+1)+x=2(x-3)+9
Simplify the left side.
4x+3=2(x−3)+94x+3=2(x-3)+9
Simplify 2(x−3)+92(x-3)+9.
4x+3=2x+34x+3=2x+3
Move all terms containing xx to the left side of the equation.
2x+3=32x+3=3
Move all terms not containing xx to the right side of the equation.
2x=02x=0
Divide each term by 22 and simplify.
x=0
If f(x) = 2x2 +5/(x-2), complete the following statement:
f(3) = ___
Answer: The answer is 19
Step-by-step explanation:
If [tex]f(x) = 2x^{2} + \frac{5}{x-2}[/tex], Then
[tex]f(x) = 2*3^{2} + \frac{5}{3-2}[/tex]
[tex]f(x) = 2*9 + \frac{5}{1}[/tex]
[tex]f(x) = 18 + 1 =19[/tex]
A chessboard has an area of 324 square inches. There is a 1 - inch border around 64 squares on the board. What is the length of one side of the region containing a small squares?
The length of one side of the region containing the small squares is 64 inches.
Let x be the length of one side of the region containing the small squares.
The area of the small squares is 64 * 1 = 64 square inches.
The area of the border is (x + 2)^2 - x^2 = 4x + 4 square inches.
Since the area of the small squares and the border is equal to the area of the chessboard, we have:
64 + 4x + 4 = 324
68 + 4x = 324
4x = 256
x = 64
Therefore, the length of one side of the region containing the small squares is 64 inches.
Charlie jogs 3 miles south and then 4 miles west. If Charlie were to jog straight home, without changing direction, how far would he have to jog?
Answer:
He would to jog 5 miles to go direct to his home
Step-by-step explanation:
* Lets explain how to solve the problem
- Charlie jogs 3 miles south and then 4 miles west
- We need to know if Charlie were to jog straight home, without
changing direction how far he have to jog
- Remember: the East-west line is perpendicular to the north-south line
∵ He jogs 3 miles south
∵ He jogs 4 miles west
∵ South ⊥ west
- We can consider that the west and east distance with the straight
distance to home formed a right triangle its legs are the south and
west distance and the straight distance is its hypotenuse
∴ By using Pythagoras Theorem we can find the straight distance
- Remember: In Pythagoras Theorem [tex]c=\sqrt{a^{2}+b^{2}}[/tex]
where c is the hypotenuse , a and b are the legs of the right Δ
∴ The straight distance = [tex]\sqrt{(3)^{2}+(4)^{2}}\sqrt{9+16}=\sqrt{25}=5[/tex]
∴ He would to jog 5 miles to go direct to his home
What is the volume of this rectangular prism?
Answer:
It would be A.
Step-by-step explanation:
It is a because you multiply 2 and 2 to get 4 then multiply 4 and 7 to get 28cm cubed
Answer:
Answer: A 28 cm^3
Step-by-step explanation:
Multiply your three values together to get your volume
Hope this is helpful! :)
A line is drawn so that it passes through the points (3, 4) and (4,1).
What is the slope of the line
Answer:
-2
Step-by-step explanation:
the formula to find slope with two points is y2-y1/x2-x1.
for this problem it would be solved as follows:
1-3/4-3
-2/1 = -2
The slope of a line is the change in the y values over the corresponding x values.
The slope of the line that passes through (3, 4) and (4,1) is -3
Given that:
[tex](x_1,y_1) = (3,4)[/tex]
[tex](x_2,y_2) = (4,1)[/tex]
The slope (m) is calculated using:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
So, we have:
[tex]m = \frac{1-4}{4-3}[/tex]
[tex]m = \frac{-3}{1}[/tex]
[tex]m = -3[/tex]
Hence, the slope is -3.
Read more about slopes at:
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What is 1,000,000,000x 3,000,000,000
Answer:
Step-by-step explanation: the answer is
3,000,000,000,000,000
Answer:
3e+18
Step-by-step explanation:
write 6X10X10X10X10 with an exponent.
Answer:
6 × 10 × 10 ×10 × 10 = [tex]6 \times 10^{4}[/tex]
Step-by-step explanation:
The exponent of any number shows that how many times that number can be used in multiplication. It is the power raised to any number which show the number of times that number is raised by.
6 × 10 × 10 ×10 × 10
Here 10 is multiplied 4 times, therefore the exponent of 10 is 4.
∴ 6 × 10 × 10 ×10 × 10 = [tex]6 \times 10^{4}[/tex]
Final answer:
The expression 6X10X10X10X10 written with an exponent is 6x10⁴, indicating that 10 is multiplied by itself four times and then multiplied by 6.
Explanation:
To write 6X10X10X10X10 with an exponent, we identify the repeated multiplication of 10s. Since there are four 10s multiplied together, we use the exponent 4 to represent this, and the expression becomes 6x10⁴. This is because when you have repeated multiplication of the same number, you can express that number raised to the power of how many times it is multiplied by itself.
The product of 2.5 and a number minus 4.7 is 10.3
Answer:
2.5(x-4.7)=10.3
Step-by-step explanation:
What does this maths sign mean?
Answer:
Step-by-step explanation:
in discrete math, a single vertical line usually means "such that" as it relates to data sets. In this case it looks like a typo.
What is the measure of ∠ A C D ? Upper A is labeled as 33 degree and the angle formed at the vertex Upper B is labeled as 117. The angle formed at the vertex Upper A is labeled as 33 degree and the angle formed at the vertex Upper B is labeled as 117 A. 30 ° B. 63 ° C. 147 ° D. 150
To find the measure of angle ACD, subtract the measures of angles ABC and BCD from 180 degrees.
Explanation:To find the measure of angle ACD, we need to subtract the measures of angles ABC and BCD from 180 degrees since the sum of the angles in a triangle is always 180 degrees.
Given that angle ABC measures 117 degrees and angle BCD measures 33 degrees, we have:
∠ACD = 180 degrees - 117 degrees - 33 degrees
= 147 degrees.
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Nick bought a music player. The price was $172, and the sales tax rate was 7 percent. How much sales tax did Nick pay when he bought the
music player?
A.
$7.20
B. $12.04
C.
$12.45
Answer:
B
Step-by-step explanation:
7% of 172 is 12.04
A line passes through the point (6,3) and has a slope of 3/2. Write an equation point-slope for this line.
Step-by-step explanation:
Given :- The line passes through the point ( 6 , 3 ) and has a slope of 3/2
• Also , to form an equation when a point through which line passes and slope of line is given we use the formula ;
( y - y1 ) = m ( x - x1 )
Where , y and x are variables and
( x1 , y1 ) are the points through which line passes also, m = slope of the required line
Here , x1 = 6 and y1 = 3
also, m = 3/2
[ Refer to the attached file for further process ]
Hey!
-------------------------
Formula:
y - y1 = m(x - x1)
-------------------------
We Know:
x = 6
y = 3
m = 3/2
-------------------------
Answer:
y - 3 = 3/2(x - 6)
-------------------------
Hope This Helped! Good Luck!
If A = (0,0) and B = (8, 2), what is the length of AB?
Answer:
2√17
Step-by-step explanation:
√((8 - 0)² + (2 - 0)²)
√(64 + 4)
√68
2√17
The length of segment AB, where A = (0,0) and B = (8, 2), is calculated using the distance formula, resulting in a length of AB is √68.
To calculate the length of segment AB where A = (0,0) and B = (8, 2), we can use the distance formula derived from the Pythagorean theorem. The distance formula for two points A(x1, y1) and B(x2, y2) in a coordinate plane is the square root of the sum of the squares of differences between corresponding coordinates:
Distance AB = √[(x2 - x1)² + (y2 - y1)²]
Plugging in the coordinates of points A and B, we get:
Distance AB = √[(8 - 0)² + (2 - 0)²] = √[64 + 4] = √68
Therefore, the length of AB is √68, which is the exact length of the segment AB between points A and B.
Community Gym charges a $70 membership fee and a $60 monthly fee. Workout Gym charges a $210 membership fee and a $50 monthly fee. After how many months will the total amount of money paid to both gyms be the same? What will the amount be?
After months the amount paid to both gyms will be $.
Final answer:
After 14 months, the total amount paid to both Community Gym and Workout Gym will be the same, at $910 each.
Explanation:
To determine after how many months the total amount paid to both Community Gym and Workout Gym will be the same, we set up two equations representing the total cost for each gym over time. Let's let x represent the number of months. For Community Gym, the total cost is given by $70 + $60x, and for Workout Gym, it's $210 + $50x.
We set these two expressions equal to find the point where the costs are the same: $70 + $60x = $210 + $50x. Solving for x, we subtract $50x from both sides, getting $70 + $10x = $210. Then, we subtract $70 from both sides to get $10x = $140. Finally, we divide by $10 to find that x equals 14. So, after 14 months, the total cost for both gyms will be the same.
To find out what this total amount will be, we substitute x = 14 back into either gym's total cost equation. Using Community Gym's equation: $70 + $60(14) = $70 + $840 = $910. Therefore, after 14 months, the amount paid to both gyms will be $910.
What percent of 200 is 0.5?
Nine increased by the product of a number and 2 is less than or equal to 27.
Use the variable w for the unknown number.
Answer:
x≤9
Step-by-step explanation:
9+2x≤27
1) Subtract both sides by 9:
2x≤18
2) Divide both sides by 2:
x≤9
Final answer:
Translate the verbal statement into an inequality, 9 + 2w ≤ 27, then solve for w by subtracting 9 and dividing by 2 to find w ≤ 9.
Explanation:
The statement 'Nine increased by the product of a number and 2 is less than or equal to 27' can be translated into the following inequality: 9 + 2w ≤ 27, where w represents the unknown number. To solve for w, we will follow these steps:
Subtract 9 from both sides: 2w ≤ 18.
Divide both sides by 2: w ≤ 9.
Therefore, the solution to the inequality is w being any number less than or equal to 9.
Quick help guys thanks :)
Answer:
[tex]\large\boxed{t^{-58}u^{-88}v^{-71}w^{-1}}[/tex]
Step-by-step explanation:
[tex]\dfrac{tuv^4w^0}{t^{59}u^{89}v^{75}w}\qquad\text{use}\ \dfrac{a^n}{a^m}=a^{n-m}\\\\=t^{1-59}u^{1-89}v^{4-75}w^{0-1}=t^{-58}u^{-88}v^{-71}w^{-1}[/tex]
The sales tax on a coat that is priced at $45 is 8%.find the total cost of the coat
Answer:
48.6
Step-by-step explanation:
45 * 1.08 = 48.6
Determine if the statement is always, sometimes or never true.
An exterior angle of a triangle is 180 degrees.
always
sometimes
never
Answer: It is always.
Step-by-step explanation: In an obtuse angle in a triangle, it will range from 90 degrees to 180, but that angle has to connect to the other two angles (and the other two angles plus the obtuse angle will always be 180 degrees).
Answer:
always
Step-by-step explanation:
Which pair of fractions are proportional? A)36/54 and 6/9 B)6/7and 16/21 C) 21/36and 21/42 D) 14/35 and 21/42
Option A
Answer:
[tex]\frac{36}{54} \text { and } \frac{6}{9}[/tex] are proportional.
Solution:
If two fractions are equal, than it is said to be in proportion.
Case 1:
Consider option A
Given fractions are [tex]\frac{36}{54} \text { and } \frac{6}{9}[/tex]
[tex]\frac{36}{54}=\frac{9 \times 2 \times 2}{9 \times 2 \times 3}=\frac{2}{3} \text { and } \frac{6}{9}=\frac{2 \times 3}{3 \times 3}=\frac{2}{3}[/tex]
Hence both the fractions are equal. So they are propotional.
Case 2:
Consider option 2
Given fractions [tex]\frac{6}{7} \text { and } \frac{16}{21}[/tex] cannot be simplified further. Also both the fractions are not equal. So they are not propotional.
Case 3:
Consider option 3
Given fractions are [tex]\frac{21}{36} \text { and } \frac{21}{42}[/tex]
[tex]\frac{21}{36}=\frac{7 \times 3}{6 \times 6}=\frac{7}{12} \text { and } \frac{21}{42}=\frac{7 \times 3}{6 \times 7}=\frac{1}{2}[/tex]
Hence [tex]\frac{7}{12} \text { and } \frac{1}{2}[/tex] are not equal. Hence they are not propotional.
Case 4:
Consider option 4
Given fractions are [tex]\frac{14}{35} \text { and } \frac{21}{42}[/tex]
[tex]\frac{14}{35}=\frac{7 \times 2}{7 \times 5}=\frac{2}{5} \text { and } \frac{21}{42}=\frac{7 \times 3}{7 \times 6}=\frac{1}{2}[/tex]
Hence [tex]\frac{2}{5} \text { and } \frac{1}{2}[/tex] are not equal. Hence they are not propotional.
The answer for the given question is option A
Simplify the following expression. 12a^3b^6c^5/3a^2b^4c^5
A. 4ab^2
B. 9ab^2c
C. 9ab^2
D. 4ab^2c
Answer:
A. 4ab^2.
Step-by-Step Explanation.
12 a^3 b^6 c^5 / 3 a^2 b^4 c^5
Dividing each pairs of terms:
12 / 3 = 4.
a^3 / a^2 = a.
b^6 / b^4 = b^2.
c^5 / c^4 = 1.
So it is 4ab^2.
Consumer price index is an
Answer:
The Consumer Price Index (CPI) is a measure that examines the weighted average of prices of a basket of consumer goods and services, such as transportation, food, and medical care. It is calculated by taking price changes for each item in the predetermined basket of goods and averaging them
to solve the equation 3x-7=x-2, Alex says the first step is to subtract x from both sides. Danny says the first step is to add 7 to both sides.
a.Solve the equation using Alex's method of first subtracting x from both sides.
b.Solve the equation using Danny's method of first adding 7 to both sides.
c.Who is correct, Alex or Danny? Justify your answer.
d. Is there another correct first step for solving this equation? If so, identify it and use it to solve the equation. If not,explain why not.
Answer:
[tex]x=\frac{5}{2}[/tex]
Step-by-step explanation:
Given : Equation [tex]3x-7=x-2[/tex]
To find : Solve the equation ?
Solution :
a) Solve the equation using Alex's method of first subtracting x from both sides.
Equation [tex]3x-7=x-2[/tex]
Subtract x from both side,
[tex]3x-7-x=x-2-x[/tex]
[tex]2x-7=-2[/tex]
[tex]2x=-2+7[/tex]
[tex]2x=5[/tex]
[tex]x=\frac{5}{2}[/tex]
b) Solve the equation using Danny's method of first adding 7 to both sides.
Equation [tex]3x-7=x-2[/tex]
Adding 7 from both side,
[tex]3x-7+7=x-2+7[/tex]
[tex]3x=x+5[/tex]
[tex]2x=5[/tex]
[tex]x=\frac{5}{2}[/tex]
c) Both are correct in their ways.
d) Is there another correct first step for solving this equation? If so, identify it and use it to solve the equation. If not,explain why not.
Equation [tex]3x-7=x-2[/tex]
We can isolate the terms as like terms place together,
[tex]3x-x=-2+7[/tex]
[tex]2x=5[/tex]
[tex]x=\frac{5}{2}[/tex]
What is the slope of the line that passes through the points (−4,4) and
(−6,6)? Write your answer in simplest form.
Answer:-1
Step-by-step explanation:
The slope of the line passing through the points (-4,4) and (-6,6) can be calculated using the formula for slope (m = (y2 - y1)/(x2 - x1)). Substituting the provided points into the formula gives m = 2/-2 = -1. Thus, the slope is -1.
Explanation:To determine the slope of a line passing through the two points (-4,4) and (-6,6), we use the following formula for calculating slope, often associated with the letter 'm':
m = (y2 - y1)/(x2 - x1)
Where x1, y1, x2, and y2 are the coordinates of the points the line passes through. In this case, (x1, y1) is (-4,4) and (x2, y2) is (-6,6).
Substitute
these values into the formula:
m = (6 - 4) / (-6 - -4)
this gives us:
m = 2/-2 = -1
So, the slope of the line passing through the points (-4,4) and (-6,6) is -1.
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3t − 2t + 2 = 9
t =
Answer:
t = 7
Step-by-step explanation:
Combine like terms
3t - 2t + 2 = 9
t + 2 = 9
Move the variable
t + 2 = 9
- 2 -2
t = 7
Answer:t=7
Step-by-step explanation:
Combine like terms
3t-2t+2=9
t+2=9
Subtract both sides with 2
t+2-2=9-2
t=7
Solve the system of equations below. x − y = 6 3x − 2y = 22
The solution for system of equations x-y=6 ,3 x-2 y=22 is x = 10 and y = 4
Solution:
Using substitution method of algebraic equations,
x - y = 6 --------equation 1
3x - 2y = 22 --------equation 2
Multiplying equation 1 by 2, equation 1 becomes
2 x - 2 y = 12
Multiplying equation 2 by -1, equation 2 becomes,
-3 x + 2 y = -22
Solving,
2 x - 2 y = 12
-3 x + 2 y = -22
-x = -10
x = 10
Substitute x = 10 in equation 1, 10 - y = 6
y = 10 -6
y = 4
Answer:
10,4
Step-by-step explanation:
^^
A coffee mixture has beans that sell for $0.20 a pound and beans that sell for $0.68. If 120 pounds of beans create a mixture worth $0.54 a pound, how much of each bean is used? Model the scenario then solve it. Then, in two or more sentences explain whether your solution is or is not reasonable.
Plz give me a step by step answer i need to figure this out.
Answer:
Step-by-step explanation:
$ 0.68 type →85lb
$ 0.20 type →35lb
Hey!
-----------------------------------------------
Let $0.68 per pound beans be (b)
Let $0.20 per pound beans be (p)
-----------------------------------------------
~Total amount of pounds:
b + p = 120
~Total cost
b + p = 120 × 0.54
b + p = 64.8
~Expression
0.68b + 0.20p = 64.8
~Multiply 10 to both sides
0.68b * 10 + 0.20p * 10 = 64.8 * 10
~Simplify
6.8b + 2p = 648
~Divide 2 to both sides
6.8b/2 + 2p/2 = 648/2
~Simplify
3.4b + p = 324
~Subtract
3.4b + p = 324
- b + p = 120
~Simplify
2.4b = 204
~Divide 2.4 to both sides
2.4b/2.4 = 204/2.4
~Value of b
b = 85
~New expression
85 + p = 120
~Subtract 85 to both sides
85 + p - 85 = 120 - 85
~Value of p
p = 35
-----------------------------------------------
[tex]\large\boxed{Of~the~0.68~dollars~per~pound~there~are~85~pounds!}\\\large\boxed{Of~the~0.20~dollars~per~pound~there~are~35~pounds!}[/tex]
-----------------------------------------------
My answer is reasonable because 85 + 35 equals 120 pounds.
~If we check
85 * 0.68 = 57.8
35 * 0.2 = 7
57.8 + 7 = 64.8
We get 64.8 which we can say it is correct because if we go back into our work we can see that we used the expression b + p = 64.8 which in this case by checking our work our answer is reasonable.
-----------------------------------------------
Hope This Helped! Good Luck!
(+30)÷(-10)+(-20)÷(-1)
6x + 5y = 147
8x + 4y = 156
Answer:
[12, 15]
Step-by-step explanation:
{6x + 5y = 147
{8x + 4y = 156
-¾[8x + 4y = 156]
{6x + 5y = 147
{-6x - 3y = -117 ← New Equation
________________
2y = 30
___ ___
2 2
y = 15 [Plug this back into both equations to get the x-coordinate of 12]; 12 = x
So, using the Elimination Method, what I did here was took the bottom equation and multiplied it by -¾, turning 8x to -6x, canceling out all x-terms. It does not matter which variable you choose to eliminate, as long as you know what you are doing.
I am joyous to assist you anytime.