Answer: x = 12, y = 15
Step-by-step explanation: 12/15 reduces to 4/5 because 12 divided by 3 is 4 and 15 divided by 3 is 5. 12 + 3 is 15 so if you add 3 to the numerator, you get 15/15, which is equal to 1.
The slope-intercept form of the equation of a line that passes through point (-3, 8) is y= -1/2x + 6. What is the point slope form of the equation for this line?
The point- slope of equation is y- 8 = -1/2 ( x+ 3).
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the
change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx
where, m is the slope
Given:
line that passes through point (-3, 8)
and, line is y= -1/2 x + 6
From above equation the slope of line is -1/2
Now, the point slope form of line
y- [tex]y_1[/tex] = m (x- [tex]x_1[/tex])
y- 8 = -1/2 ( x - (-3))
y- 8 = -1/2 ( x+ 3)
Hence, the point- slope of equation is y- 8 = -1/2 ( x+ 3).
Learn more about slope here:
https://brainly.com/question/3605446
#SPJ1
Mary leaves her house at noon , traveling in her car at 45mi / h . Later , Mary's brother Joe leaves their house and travels in the same direction at 60mi / h . If Joe leaves at 2:00 PM., at what time will he catch up with Mary ?
The time that it will take Joe to catch up with Mary is; 8 hours
How to solve Algebra Word Problems?We are told that;
Time Mary leaves the house = 12 pm
Time that Joe leaves the house = 2 pm
Speed of Mary = 45 mi/hr
Speed of Joe = 60 mi/hr
This means that Mary had a 2 hour time lead over Joe.
Thus;
Distance is calculated from the formula;
Distance = Speed * time
Thus;
Distance covered by Mary in the 2 hours lead is;
Distance = 45 * 2 = 90 miles
Thus, time that it will take Joe to catch up with mary is;
t = 2 + (90/(60 - 45))
t = 2 + 6
t = 8 hours
Read more about Algebra Word Problems at; https://brainly.com/question/13818690
#SPJ1
Jordan answered 69 questions on his test correctly. He answered 92% of the test questions correctly. How many questions were on the test?
92% = 69 questions
100% = 75 questions
The total number of questions on the test is 75 questions.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
We have,
Total number of answers answered correctly = 69
The percentage of the test questions answered correctly = 92%
This means,
92% = 69
The total number of questions in percentage = 100%
Now,
92% = 69
Multiplying 100/92 on both sides.
100% = 100/92 x 69
100% = 75
Thus,
The total number of questions on the test is 75 questions.
Learn more about percentages here:
https://brainly.com/question/11403063
#SPJ1
10-6x + 9x = x+2 solving variables
The required value of the variable x is - 4
What are variables ?A variable in mathematics is an alphabet or phrase that stands in for an unknowable amount, unknowable value, or unknowable number. Particularly in the case of algebraic expressions or algebra, the variables are utilised. As an illustration, the linear equation x+9=4 has the variables x and 9 as constants.
The given equation is :
10-6x + 9x = x+2
On solving this equation we get :
10 + 3x = x + 2
Subtract - 3x on both sides and we will get
10 = - 2 x + 2
Subtract 2 on both sides
we get
8 = -2x
On dividing both sides of the equation by 2 we get
x = - 4
Thus the required value of the variable x is - 4
To know more about variables or related problems you may visit the link which is mentioned below:
https://brainly.com/question/17436857
#SPJ1
What is the answer to this question
She bought 13 books in $58.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
Let b represent the number of books.
So, the equation will be
5b - 7 = 58
Now, add 7 to both sides of the equation
5b = 65.
b = 13.
Thus, she bought 13 books at 5 dollars a piece.
After she gets a 7 dollar discount off of 65 dollars, so she paid a total of 58 dollars after the discount.
Learn more about equation here:
https://brainly.com/question/10413253
#SPJ1
what are the solutions for IxI = 64
Answer: -64 and 64
Step-by-step explanation:
92+78x96838-52/2? please help quick!
the scatterplot above shows the number of registered voters, x, and the number of people who voted in the last election, y, for seven districts in a town. a line of best fit for the data is also shown. which of the following could be the equation of the line of best fit?
The line of best fit for the data presented in the scatterplot is y = 0.5x. (Option B)
A line of best fit represents a straight line that is the best approximation of the given set of data used to examine the nature of the relation between two variables. It is an educated guess about where a linear equation might fall in a set of data plotted on a scatter plot. The slope-intercept form of a linear equation is given by y = mx + b where m is the slope of the line and b is the y intercept of the graph. For any two points (x1, y1) and (x2, y2), the slope is given by:
m = (y2-y1)/(x2-x1)
Choosing two points from the line say (180, 90) and (220,110),
m = (110 – 90)/(220 – 180) = 20/40 = 0.5
Hence, y = 0.5x + b
Substituting a point from the graph into the equation say (240, 120)
120 = 0.5(240) + b
120 = 120 + b
b = 0
Hence, the equation is y = 0.5x
Note: The question is missing the scatterplot (which is attached) and options which are A. y = -0.5x, B. y = 0.5x, C. y = -2x, D. y = 2x.
Learn more about Line of best fit:
https://brainly.com/question/1441182
#SPJ4
please help me I will give you brainiest please
+ 9 = 13
3 = 12
+ 5 − 9 = 0
2 + 5 = 17
5 − 3 = 17
− 3 = 1
7x = 35
[tex]\frac{4x}{4} =4[/tex]
3 + 4 = 15
8 + − 5 = 7
Answer:
Step-by-step explanation:
1 ) + 9 = 13
+ 9 ≠ 13
False
2 ) 3 = 12
3 ≠ 12
False
3 ) + 5 − 9 = 0
-4 ≠ 0
False
4 ) 2 + 5 = 17
7 ≠ 17
False
5 ) 5 − 3 = 17
2 ≠ 17
False
6 ) − 3 = 1
− 3 ≠ 1
False
7 ) 7x = 35
a ) Divide both sides by 7...
[tex]\frac{7x}{7} = \frac{7}{35}[/tex]
[tex]x = 5[/tex]
8 ) [tex]\frac{4x}{4}=\ 4[/tex]
a ) Multiply both sides by 4...
[tex]\frac{4x}{4}=\ 4[/tex]
[tex]\frac{4x}{4}[/tex] × [tex](4)=(4)[/tex] × [tex](4)[/tex]
[tex]4x=16[/tex]
b ) Divide both sides by 4...
[tex]\frac{4x}{4}= \frac{16}{4}[/tex]
[tex]x=4[/tex]
9 ) 3 + 4 = 15
7 ≠ 15
False
10 ) 8 + − 5 = 7
3 ≠ 7
False
Hope this helps! :)
Order the following numbers from least to greatest.
Put the least value on the left.
Answer:
-5.2,-4.75,-9/2
Step-by-step explanation:
Answer:-5.2 -4.75 -9/2
Step-by-step explanation:
I am in need for answers please!
The y-intercept is y = 10, and that is the initial height of the flower in inches.
And the rate of change between n = 1 and n = 5 is:
R = 0.21
What is the y-intercept?For any function y = f(x), the y-intercept is the value that y takes when we evaluate in x = 0.
In this case, we have the exponential function:
g(n) = 10*(1.02)^n
Evaluating in n = 0 we get:
g(0) = 10*(1.02)^0 = 10*1 = 10
The y-intercept is y = 10, and it means that the initial height of the flower is 10 inches.
Now we want to get the average rate of change on the interval [1, 5].
Remember that for a function f(x) the average rate of change on an interval [a, b] is:
R= [ f(b) - f(a)]/(b - a)
In this case we will have:
R = [ g(5) - g(1)]/(5 - 1) = [g(5) - g(1)]/4
Where:
g(5) = 10*(1.02)^5 =11.041
g(1) = 10*(1.02) = 10.200
Replacing that:
R = [11.041 - 10.200]/4 = 0.21
This means that the plant increases about 0.21 inches per day on these 4 days.
Learn more about exponential functions:
https://brainly.com/question/11464095
#SPJ1
Of all the closed right circular cylindrical cans of volume 128πcm
3, find the dimensions of the can which has minimum surface area.
The can's minimum surface area should have a height of 8 cm and a radius of 4 cm.
Given:
The volume of closed right circular cylindrical cans = 128π cm³
As we know the volume of a cylinder = πr²h
By equating;
πr²h = 128π
h = 128/r²
To get the dimensions of a can with minimum surface area;
S = 2πrh + 2πr
Put h = 128/r²;
Therefore, S(r) = 256π/r + 2πr²
S'(r) = -256π/r² + 4πr
S''(r) = -(2*256π)/r³ + 4π
Now, for S(r) = 0;
r = 4cm
for S''(4) > 0 at r = 4 is minimum point.
Hence,
h = 128π/(π*4*4)
h = 8cm
Therefore, the minimum surface area of the can should have a radius of 4 cm and a height of 8 cm.
To learn more about right circular cylinder click here:
brainly.com/question/28448651
#SPJ4
Please solve both blanks and round to the nearest tenth please
The inequality is x ≤ 39.2. The actual number of items that can be bought is 39.
There is a set budget of $145 to buy some items. The price of each item is $3.70. We need to form an inequality for the given information and solve it.
Let the number of items be denoted by the variable "x". Then we can say that :
3.70*x ≤ 145
x ≤ 145/3.70
x ≤ 39.2
The actual number of items that can be bought must be a whole number. We will take the greatest integer less than or equal to the solution.
The actual number of items that can be bought is 39.
To learn more about inequalities, visit :
https://brainly.com/question/28823603
#SPJ1
HELP ASPPP SHOW YOUR WORK PLEASE DO 6 AND 7 IF YOU LIKE
Answer: 7. 0 cause there is not a number next to the 3
-2 is the slope you distribute the -2 by the parenthese
Step-by-step explanation:
Let h(x) = x² + 1 and g(x) = 2x.
FIND (h-g)(2).
A.)3
B.)10
C.)1
D.)9
Answer:
C
Step-by-step explanation:
(h - g)(2)
= h(2) - g(2)
= 2² + 1 - 2(2) = 4 + 1 - 4 = 1
Negative ten is no less than two times a number plus 14
The expression is -10 > 2x+ 14.
What is Expression?A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:
An absolute numerical number is referred to as a constant.Variable: A symbol without a set value is referred to as a variable.Term: A term can be made up of a single constant, a single variable, or a mix of variables and constants multiplied or divided.Coefficient: In an expression, a coefficient is a number that is multiplied by a variable.Given:
Negative ten is no less than two times a number plus 14
let the number x
so, two times a number plus 14
= 2x+ 14
and, Negative ten is no less than two times a number plus 14
-10 > 2x+ 14
hence, the expression is -10 > 2x+ 14.
Learn more about expression here:
https://brainly.com/question/14083225
#SPJ1
Keystone Question: A lube gun dispenses the same amount of oil each time
it is used. The equation below shows the relationship between the number
of times (x) that oil is dispensed and the number of gallons of oil (y)
remaining in the gun. y = (-0.03125)x + 6 How many gallons of oil are in
the gun when it is full?
The amount of gallons of oil that are in the gun when it is full is 6 gallons , the correct option is (c) .
In the question ,
it is given that
A lube gun dispenses the same amount of oil each time , and
the equation is y = (-0.03125)x + 6
where , x is the number of times the oil is dispensed and
y is the number of gallons of oil remaining in the gun ,
when the gun is full , the number of times oil dispensed will be zero .
that is x = 0 ,
Substituting x = 0 in the given equation ,
we get ,
y = (-0.03125)(0) + 6
y = 0 + 6
y = 6
Therefore , The amount of gallons of oil that are in the gun when it is full is 6 gallons .
Learn more about Equations here
https://brainly.com/question/2459604
#SPJ1
What is the location of the image of P(-8, 1) after a counterclockwise rotation of 90° about the origin?
O (1, -8)
O (-8,-1)
O (-1,8)
O (8, -1)
Answer:
(-1, -8)
Step-by-step explanation:
You want the image of P(-8, 1) after rotation 90° counterclockwise about the origin.
RotationThe transformation for 90° CCW is ...
(x, y) ⇒ (-y, x)
Then
P(-8, 1) ⇒ P'(-1, -8)
__
Additional comment
We observe that this answer is not among the choices listed in this problem statement. We suspect a typo somewhere. The transformations represented by the given choices are ...
A: reflection across the x-axis and rotation 90° CCW
B: reflection across the x-axis
C: reflection across the x-axis and rotation 90° CW
D: reflection across the origin
These are shown in the second attachment.
plsss solve these two questions I stuck hello meeeeeeee
Answer:
a) 0.566 b)8.62
Step-by-step explanation:
0.56565656...
4th number after decimal is 6, which is greater than 5. the value of 3rd number after dp goes up by 1
therefore 0.566
7×12%=0.84
7+0.84=7.84
7.84×10%=0.784
7.84+0.784=8.62
y=5x+2
4x−y=0
Is (2,12)(2,12)left parenthesis, 2, comma, 12, right parenthesis a solution of the system?
The solution to the given system of linear equations is x = -2 and y = -8. That is, (-2, -8).
Solving system of linear equationsFrom the question, we are to determine the solution to the given system of linear equations.
The given system of linear equations is
y = 5x + 2 ---------- (1)
4x - y = 0 ---------- (2)
Substitute equation (1) into equation (2)
4x - y = 0
4x - (5x + 2) = 0
4x - 5x -2 = 0
-x -2 = 0
-2 = x
x = -2
Substitute the value of x into equation (1)
y = 5x+ 2
y = 5(-2) + 2
y = -10 + 2
y = -8
Hence, the solution is x = -2 and y = -8
Learn more on Solving system of linear equations here: https://brainly.com/question/13729904
#SPJ1
for breakfast you eat a bowl of oatmeal and 1/4 cup of added raisins, for lunch, a turkey sandwich and a glass of fresh orange juice. how many servings of fruit and cereal have you had?
For breakfast, you have had 1/2 a serving of cereal and 1/4 cup of raisins, which count as one serving of fruit.
For breakfast, you have had one serving of cereal and one serving of fruit. In general, one serving of cereal is considered to be one cup, while one serving of fruit is considered to be one half cup. Therefore, in your bowl of oatmeal, you would have had two servings of cereal, and in your quarter cup of raisins, you would have had one serving of fruit. For lunch, you have had one serving of fruit in your glass of orange juice.
Learn more about fruit at : https://brainly.com/question/13048056
#SPJ4
If Chan throws 20 darts that hit the dart board, how many should land in an odd number?
F. 20
G. 5
H.10
J.12
J.12 is incorrect … PLEASE HELP
Answer: The Answer Would be H because in the 20 darts there are 10 odd numbers 1,3,5,7,9,11,13,15,17,19
Step-by-step explanation: :)
what is the slope of the line that passes through the pair of points (3,8) and (8,5)
Answer:
The slope is -3/5=-0.6
Step-by-step explanation:
Slope: (5-8)/(8-3)= -3/5=-0.6
Answer:
[tex]m=-\frac{3}{5}[/tex]
Step-by-step explanation:
Step 1: Slope
Slope = m[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]Step 2: Set up equation and solve for m
y₂ = 5y₁ = 8x₂ = 8x₁ = 3[tex]m=\frac{5-8}{8-3}=\frac{-3}{5}[/tex]1. Margo can jump 58 times in 1 minute. About how many times can Margo jump in
5 minutes? (Show your work. Write your final answer on the line.)
2. Write the decimal number that the shaded portion of the model represents on the line.
Answer: 290
Step-by-step explanation:
58 x 5 = 290
Margo jumps 290 times in five minutes
HELPPP so the man bought a tv worth $1,700, and then each week he continued to spend $700 weekly WHAT IS THE EXPRESSION???? HELP (variable is X)
HELP
Answer: 700x+1700
This represents the total amount spent over the x weeks that have gone by.
===========================================
Explanation:
x = number of weeks
700x = amount spent over those x weeks ($700 per week)
700x+1700 = total amount spent when adding on the $1700 tv.
------
An example:
Let's say x = 10 weeks have elapsed. He spends $700 a week, so 700x = 700*10 = 7000 dollars have been spent so far if we ignore the tv. Then add on the $1700 tv cost to get 7000+1700 = 8700 dollars total spent.
Then note how 700x+1700 = 700*10+1700 = 8700 matches what we got earlier.
I recommend trying out other values of x to get a better idea of what's going on.
True or false :If an integer is negative, its absolute value is also its additive inverse.
The statement 'If an integer is negative, its absolute value is also its additive inverse.' is True.
In this question, we have been given a statement 'If an integer is negative, its absolute value is also its additive inverse.'
We know that for any non zero real number 'm', the additive inverse is '-m'
as m + (-m) = 0
We know that the absolute value of any non-zero real number is always positive.
Consider a negative integer -p.
The absolute value of -p is |-p| = p
We can observe that -p + p = 0
-p + |-p| = 0
Therefore, the statement 'If an integer is negative, its absolute value is also its additive inverse.' is True.
Learn more about additive inverse here:
https://brainly.com/question/23579796
#SPJ1
(figure: capital and labor xii) which of the following statements is (are) true? a graph titled graph (a) plots labor (l) along the horizontal axis and capital (k) along the vertical axis. the horizontal axis values range from 0 to 28 with intervals of 4 units and the vertical axis values range from 0 to 20 with intervals of 4 units. two concave up decreasing curves q equals 20 and q equals 50 originate at (4, 12) (10, 19) and end at (17, 1) (25, 7). point (10, 4) is marked on curve q equals 20 and (20, 8) is marked on curve q equals 50. a dashed line from this point extends to the respective coordinate on the horizontal axis. all data are approximate. a graph titled graph (b) plots labor (l) along the horizontal axis and capital (k) along the vertical axis. the horizontal axis values range from 0 to 28 with intervals of 4 units and the vertical axis values range from 0 to 20 with intervals of 4 units. two concave up decreasing curves q equals 35 and q minus 70 originate at (4, 13) (13, 19) and end at (14, 3) (23, 9). point (8, 6) is marked on curve q equals 20 and (17, 12) is marked on curve q equals 50. a dashed line from this point extends to the respective coordinate on the vertical axis. i. panel a illustrates constant returns to scale. ii. panel b illustrates decreasing returns to scale. iii. panel a illustrates increasing returns to scale iv. panel b illustrates constant returns to scale. iii and iv i and iv i and iii ii and iii
Option (A) is the correct answer: Panel a illustrate Increasing Return to Scale and panel b illustrate Constant Return to Scale.
Return to Scale:
It is the Variation or change in productivity that is the outcome from a proportionate increase of all the input.
Increasing Return to Scale:
An increasing return to scale occurs when the output increase by a larger proportion than the increase in inputs during the production process. For Example: if input is increased by 3 times but output increases by 3.75 times, then the firm or economy has experienced an increasing return to scale. This increase is due to many reasons like division external economies of scale.
Constant Return of Scale:
Constant Return of Scale refers to the production situation in which output increases exactly in the same proportion in which factors of production are increased. In simple words, if factors of production are doubled output will also be doubled. In this case, internal and external economies are exactly equal to internal and external diseconomies. This situation arises when after reaching a certain level of production, economies of scale are balanced by diseconomies of scale. For Example: A car wash in which one car wash takes 30 minutes. If there is one wash space and two workers running two 8 hours shifts total product would be 32.
Learn more about Increasing rate of Scale:
https://brainly.com/question/23776775
#SPJ4
h(t)=( 1)/(3) t-10, find h(t) when t =27 and when t= -15
Work out
a) 5 - 21
b) 7/3/3 + 2/1/20
Order the sides of DEF in order from least to greatest
The sides of DEF in order from least to greatest will be x + 6, (5x - 8) and (9x + 2).
How to calculate the angle?The total angles that can be found in a triangle is 180°.
Therefore, the angles will be illustrated thus:
x + 6 + (5x - 8) + (9x + 2) = 180°
x + 6 + 5x - 8 + 9x + 2 = 180°
15x = 180°
Divide
x = 180° / 15.
x = 12°
Therefore,
x + 6 = 12 + 6 = 18°
(5x - 8) = 5(12) + 8
= 60 + 8
= 68°
(9x + 2) = 9(12) + 2
= 108 + 2
= 110°
Learn more about triangles on:
brainly.com/question/11886953
#SPJ1