what is the equation in standard form of the line that passes through the point (1,24) and has a slope of (-3/5)
y = -3/5x - 123/5 is slope-intercept form .
What is an explanation of the slope-intercept form?
A line's equation can be written in the slope-intercept form so that the slope (steepness) and y-intercept (where the line crosses the vertical y-axis) are immediately visible. This form is frequently known as the y = mx + b form.Point = ( 1,24 )
slope = -3/5
the equation in standard form of the line that passes through the point
y - y₁ = m ( x - x₁)
y - 24 = -3/5 ( x - 1)
5 (y - 24) = -3( x - 1 )
5y - 120 = -3x + 3
5y = -3x + 3 + 120
5y = -3x + 123
y = -3/5x - 123/5
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The ratio of the number of red cubes to the total number of small plastic cubes in a classroom is 3:14. How many red cubes are there if there are 560 cubes altogether?
Answer:
red cubes = 99, plastic cubes = 462
Step-by-step explanation:
total number of cubes/total ratio
= 560/17
= 33 (approximately)
red cubes
= 33 × 3
= 99
plastic cubes
= 33 × 14
= 462
Though 462 + 99 equals 561 rather than 560, I had to approximate the values because if not, the result will be 461 which is a prime number.
express the vector with initial point (1,-1) and terminal point (4,2) as a linear combination of the standard unit vectors.
a. 3i + 3j
b. 5i + j
c. 3i - 3j
d. -3i + 3j
e. 3i + 4j
f. none of these
The vector as a linear combination of the standard unit vectors is written as 3i+3j , the correct option is (a) .
In the question ,
it is given that ,
the initial point of the vector = (1 , -1)
the terminal point of the vector = (4,2)
we know that the vector with initial point (x₁ , y₁) and (x₂ , y₂) is calculated using the formula
V = (x₂ - x₁)i + (y₂ - y₁)j
Substituting the values from the point ,
we get the vector as
V = (4 - 1)i + (2 -(-1))j
V = 3i + (2 + 1)j
V = 3i + 3j
Therefore , The vector as a linear combination of the standard unit vectors is written as 3i+3j , the correct option is (a) .
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Chris earned $17,000 last year. If the first $25,000 is taxed at 8% and income above that is taxed at 16%, how much does Chris owe in tax?
well, we know the first $25,000 is taxed at 8%, wait a second!!!!! Chris didn't make 25,000 bucks, he only made $17,000, so he'd be in the range of $0 - $25,000 because $17,000 is in that range, that means he owes 8% of 17,000
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{8\% of 17000}}{\left( \cfrac{8}{100} \right)17000}\implies 1360[/tex]
The amount Chris owes in tax is $1360.
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
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
The first $25,000 is taxed at 8%.
This means,
Amount from 0 to $25000 is taxed at 8%.
Now,
Chris earned = $17,000
Tax amount.
= 8% of 17,000
= 8/100 x 17,000
= 8 x 170
= $1360
Thus,
The tax amount is $1360.
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50 POINTS TO WHOEVER SOLVES THIS QUESTION!!!! PLEASE HELP
The total segment AE is 46.
What is SAS(Side -Angle-Side) triangle?
"SAS" is when we know two sides and the angle between them.
To solve an SAS triangle we use "The Law of Cosines" to calculate the unknown side.
The Law of Cosines = a² = b² + c² − 2bc cosA
where
'b' and 'c' are two given sides
'A' is the angle between side 'b' and 'c' and
a' is the unknown side which we have to find.
In ΔABC , b=21, c=20, a= AC
By the Cosine law
a² = 21²+20² - 2*21*20 cos90°
a² =441 + 400 - 0 (∵cos 90° =0)
a² = 841
a=√841
a=29= AC.
Now, in ΔCDE, b=8, c=15 and a = CE
By the Cosine law
a² = 8² + 15²- 2*8*15cos90°
a² = 64 + 225 - 0 (∵cos 90° =0)
a²= 289
a = 17 = CE.
AE = AC + CE
AE = 29+17= 46.
Therefore, the total segment AE is 46.
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Explain how you can use a part:part ratio to determine the part:whole ratio.
Let's say we have blue and red balls
Blue : Red
3 : 5
Now we can add another ratio for the whole.
Blue : Red : Total
Total is Blue + Red = 3 + 5 = 8
So
Blue : Red : Total
3 : 5 : 8
Then the part : whole ratio for Blue is...
Blue : Total
3 : 8
2 3/5 x 1 3/7 i need help
Answer:
26x/7
Step-by-step explanation:
Chloe has 4 sundaes for her friends. She has 8
4
9
ounces of sprinkles to put equally on the sundaes. How many ounces of sprinkles will be on each sundae?
There are 19/9 ounces in each sprinkle of sundae
How to determine the number of ounces of sprinkles on each sundaeFrom the question, we have the following parameters that can be used in our solution:
Number of sundaes = 4
Ounces of sprinkles = [tex]8\frac49[/tex] ounces
From the above parameter, we can calculate the amount of sprinkles using the constant of proportionality formula
This is represented as
Ounces per sprinkle = Ounces of sprinkles/Number of sprinkles
Substitute the known values in the above equation
So, we have the following equation
Ounces per sprinkle = [tex]8\frac49[/tex]/4
Evaluate the quotient
Ounces per sprinkle = 19/9
Hence, the ounces per sprinkle is 19/9 ounces
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A line intersects the points
(4, -2) and (3, 3).
m = -5
Write an equation in point-slope form
using the point (4, -2).
y - [?] =(x-[
Answer:
y-(-2)= -5(x-4)
= -5x-y+18
Step-by-step explanation:
y-(-2)= -5(x-4)
y+2= -5x +20
y= -5x+18
-5x-y+18= 0
So if I get paid every 12 days and I put 80$ back every 12 days how long would it take to get to 2000 dollars
It will take 300 days to get to 2000 dollars.
According to the question,
We have the following information:
One gets paid every 12 days and one puts back $80 every 12 days.
Now, the total amount of dollars is $2000.
Now, we have the following progression:
80, 160, 240, ...
This is an arithmetic progression.
an = a+(n-1)d where a is the first term and d is the common difference
2000 = 80+(n-1)80
2000 = 80+80n-80
2000 = 80n
n = 2000/80
n = 25
Now, the number of days one is paid is after 12 days.
So, the number of days to get 2000 dollars:
25*12
300 days
Hence, it will take 300 days to get to 2000 dollars.
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Can anyone explain to me how to do this if so u get 90 points or wtv
The transformations to function f(x) that results in function g(x) are described as follows:
5. Reflection over the x-axis, vertical stretch by a factor of 2.
6. Shift right of 6 units, shift up of 4 units.
7. The rule for g(x) after the transformation is given as follows:
[tex]g(x) = \sqrt[3]{-x + 7}[/tex]
What are the transformations to each function?For item 5, the functions are given as follows:
Parent function: [tex]f(x) = \sqrt{x}[/tex]Transformed function: [tex]g(x) = -2\sqrt{x}[/tex]The transformation is a multiplication by -2, which means that the function was:
Vertically stretched by a factor of 2, due to the multiplication by a number with absolute value of 2.Reflected over the x-axis, due to the multiplication by a negative number.For item 6, the functions are given as follows:
Parent function: [tex]f(x) = \sqrt[3]{x}[/tex]Transformed function: [tex]g(x) = \sqrt[3]{x - 6} + 4[/tex]Then the transformations are explained as follows:
Shift right of six units, due to the transformation x -> x - 6.Shift up of four units, due to the addition by 4.For item 7, the parent function is:
[tex]f(x) = \sqrt[3]{x}[/tex]
Then the transformations and their effects are given as follows:
Reflection over the y-axis: x -> -x.Translation 7 units right: -x -> -x + 7.Hence the function is:
[tex]g(x) = \sqrt[3]{-x + 7}[/tex]
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Rio went to Wal-mart and bought 1 pounds of Turkey for $5.50
What is the cost per pound of Turkey?
Round your answer to the nearest CENT, if necessary.
$4.75
$4.40
$5.00
$0.23
Answer:
It says right there that he bought a pound of turkey for $5.50.
One pound of turkey is $5.50?
Step-by-step explanation:
This is extremely confusing
What effect do you think the sample size have on the mean of the sampling distribution of the mean?.
The effect of the sample size on the mean of the sampling distribution is that it effects the variations .
In the question ,
If the sample size is increased ,
that is if the number of sample is increased then the errors in the sampling distribution becomes less .
and if the sample size is decreased then it will lead to the increase in the errors of the distribution .
The formula for relationship between variation and sample size is given as ,
σx = σ / sqrt (n)
we can see that variation and sample size are inversely proportional .
that means increase in the sample size results in reduction of variation.
Therefore , The effect of the sample size on the mean of the sampling distribution is that it effects the variations .
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Write the correct function in the table below
Answer:
y = 2x + 3
Step-by-step explanation:
The slope
As the y changes by 2, the x changes by 1. 2/1 is 2
The y intercpet is 3. This what y is when x is 0.
refer to exercise 9. what proportion of 9-ounce bags of this brand of potato chips weigh more than 9.2 ounces?
Percentage of bags that weigh more than 9.25 ounces is 19.3%.
Given:
Mean μ = 9.12
standard deviation σ = 0.15
z = x - μ / σ
= 9.25 - 9.12 / 0.15
= 0.13/0.15
= 0.867
P(x>Z) = 0.193
= 0.193/100
= 19.3%
Therefore Percentage of bags that weigh more than 9.25 ounces is 19.3%.
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Maxine and her daughter are going grocery showing after she gets off work. Maxine sees that apples are $0.25, while bananas are $0.79. She has $2.50 to spend on apples, x, and bananas. y. Write the equation, in standard form that represents her situation.
HELP ME PLEASE
Her situation can be modeled by the linear equation (in standard form):
x*$0.25 + y*$0.79 = $2.50
How to write the equation that represents her situation?The variables that we will use here are:
x = number of apples that she can buy.
y = number of bananas that she can buy.
We know that she has $2.50 to spend, that each apple costs $0.25 and each banana costs $0.79, then the cost of the x apples and y bananas is:
x*$0.25 + y*$0.79
and that must be equal to the amount she has to spend, then we can write the linear equation:
x*$0.25 + y*$0.79 = $2.50
That is the linear equation in standard form that represents her situation.
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Flooring costs £10 per m². How much will it cost to buy enough flooring for this room?
Check the picture below.
[tex]18m^2~~ + ~~10m^2\implies 28m^2\hspace{5em}(\stackrel{m^2}{28})(\stackrel{\pounds}{10})\implies \text{\LARGE \pounds280}[/tex]
(REPOST) 13. Find the measure of
(5x +27)°
(2x + 10)°
(4x + 2)°
The measure of angles of ( 5x + 27 )° , ( 2x + 10 )° and ( 4x + 2 )° are 102° , 40° and 62° respectively
What is a Triangle?
A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
Given data ,
The angles of the triangle ABC are
∠A = ( 2x + 10 )°
∠B = ( 4x + 2 )°
Let angle ∠C be y
The sum of ∠A + ∠B + ∠C = 180°
So ,
( 2x + 10 )° + ( 4x + 2 )° + y = 180° be equation (1)
Now , we can see that AD is a straight line and C is a point on the line AD
The total angle of C on the line AD is 180°
So , ( 5x + 27 )° + y = 180°
y = 180° - ( 5x + 27 )° be equation (2)
Substituting the value of equation (2) in equation (1) , we get
( 2x + 10 )° + ( 4x + 2 )° + 180° - ( 5x + 27 )° = 180°
On Simplifying , we get
( 2x + 10 )° + ( 4x + 2 )° - ( 5x + 27 )° = 0
( 2x + 4x - 5x ) + ( 10 + 2 - 27 ) = 0
x - 15 = 0
Adding 15 on both sides , we get
x = 15°
Substituting the value of x in the ∠A , ∠B and ∠C equation , we get
∠A = ( 2x + 10 )°
= 40°
∠B = ( 4x + 2 )°
= 62°
∠C = 180° - ( ∠A + ∠B )
= 180° - 102°
= 78°
Therefore , the angles of the triangle ABC are 40° , 62° and 78°
The measure of ( 5x + 27 )° is
= ( 5 x 15 + 27 )°
= 102°
Hence , the measure of angles of ( 5x + 27 )° , ( 2x + 10 )° and ( 4x + 2 )° are 102° , 40° and 62° respectively
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Can anybody help me with this?
The slope of the line -1 and the y-intercept is 3.
From the question, we have
x+y = 3
y = -x+3
The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation.
m = -1
c = 3
Slope of a Line :
A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate.
Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively.
As a result, m = change in y/change in x = y/x is the formula for the change in y-coordinate with respect to the change in x-coordinate.
where "m" represents a line's slope. The slope, m, is a measure of how steep a line is. Sometimes, the gradient of a line is referred to as its slope. A line's y-intercept, ab, denotes the y-coordinate of the location where the line's graph crosses the y-axis.
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What is the square root of 144?
Answer:
12
Step-by-step explanation:
12*12=144
Answer: 12 is the correct answer
Step-by-step explanation:
144 = a × a = 122
Then a = √144 = √(12 × 12)
12 × 12 = 144 or -12 × -12 = 144
The square root of 144 is +12 or -12
This shows that 144 is a perfect square.
Can you write an equation to show how much the total cost, y, to travel in x miles?
Don’t forget: in slope-intercept form, y=mx+b, m is the slope and b is the y-intercept.
Answer:
y = 3x + 2
Step-by-step explanation:
The slope is the rate of change. The y intercept is the y value when x is 0.
In this triangle, angle W equals (3x-24) degrees, and angle C equals (4x-11) degrees, and angle T equals 2x degrees, what does angle W equal?
Traingle is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
The sum of the three angles is equal to 180 degrees.
The value of angle W is 47.67
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
In this triangle:
angle W = (3x-24) degrees.
angle C = (4x-11) degrees.
angle T = 2x degrees.
Now,
The sum of the three angles is equal to 180 degrees.
3x - 24 + 4x - 11 + 2x = 180
9x - 35 = 180
9x = 180 + 359x = 215
x = 215/9
Now,
The angle W.
= 3x - 24
= (3 x 215/9) - 24
= 215/3 - 24
= 71.67 - 24
= 47.67
Thus,
The value of angle W is 47.67
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✓ Completed
Part 1 of 3
In Progress
Given the following functions, find the indicated values.
f(x)=8-4x
(a) f(-7) (b) f(0) (c) f(4)
(a) f(-7)=
Answer:
(a) 36, (b) 8, (c) - 8======================
Given functionf(x) = 8 - 4xFind the indicated values(a) f(-7)
f(-7) = 8 - 4(-7) = 8 + 28 = 36(b) f(0)
f(0) = 8 - 4(0) = 8 - 0 = 8(c) f(4)
f(4) = 8 - 4(4) = 8 - 16 = - 8Answer:
a) f(-7) = 36 b) f(0) = 8 c) f(4) = -8Step-by-step explanation:
a) f(-7) = ?
→ f(x) = 8 - 4x
→ f(-7) = 8 - 4(-7)
→ f(-7) = 8 + 28
→ f(-7) = 36
Hence, f(-7) = 36.
b) f(0) = ?
→ f(x) = 8 - 4x
→ f(0) = 8 - 4(0)
→ f(0) = 8 - 0
→ f(0) = 8
Hence, f(0) = 8.
c) f(4) = ?
→ f(x) = 8 - 4x
→ f(4) = 8 - 4(4)
→ f(4) = 8 - 16
→ f(4) = -8
Hence, f(4) = -8.
A rain gutter is made from sheets of
aluminum that are 14 inches wide by
turning up the edges to form right
angles. Determine the depth of the
gutter that will maximize its cross-
sectional area and allow the greatest
amount of water to flow. What is the
maximum cross-sectional area?
Explanation:
Let x = depth of the gutter
then
14-2x = width of the gutter
:
Cross section area:
A = depth * width
A = x(14-2x)
A = 14x - 2x^2
:
Axis of symmetry will give x value for max area: x = -b/(2a)
x = -14/2 * -2
x = -14/-4
x = +3.5 inches is the depth for max area
:
:
Max area: 3.5 * 9 = 31.5 sq/in
531/4
Please give step by step explanation, must be long division.
Answer: 132.5
Step-by-step explanation:
Answer:
132.75
Step-by-step explanation:
*in picture below*
Which inequality is represented by the graph
Inequality represented by the given graph is equal to 5x -3y > 9.
As given in the question,
For the given graph,
Consider two points on the line represented on the graph ,
( x₁ , y₁) = (0,-3)
(x₂ , y₂) = ( 3,2)
Equation of the line given by two points on the graph,
( y - y₁)/ (x -x₁) = ( y₂ - y₁)/ (x₂ -x₁)
⇒(y +3)/(x-0) = ( 2 + 3)/(3 -0)
⇒(y + 3) / x = 5/3
⇒3(y+ 3) = 5x
⇒3y + 9 = 5x
⇒5x -3y = 9
As per shaded region inequality of the graph is given by,
5x -3y > 9
Therefore, inequality represented by the given graph is equal to 5x -3y> 9.
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A scientist measures the mass of a metal to be 682 grams. There are 1000 grams in a kilogram and a kilogram is equal to about 2.2 pounds.
What is the mass of the metal in pounds?
Answer: The answer to this question is: the mass of the metal in pounds is 1.5 grams.
Step-by-step explanation: Search a free gram to pounds calculator and input your given input or output into there for further help if needed.
Hope this helps
The mass of the metal in pounds is 1.5 pounds.
What is unit conversion?A unit conversion expresses the same property as a different unit of measurement.
Given that, a scientist measures the mass of a metal to be 682 grams
682 grams = 0.682 kg
0.682 kg = 0.682*2.2 = 1.5 pounds.
Hence, The mass of the metal in pounds is 1.5 pounds.
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Quadrlateral proofs (Reasons Only)
prove abcd is a rhombus
help pls i hate proofs....
Write an equation of the line passing through point
P(-8, 0) that is perpendicular to the line y=-3
The equation of line passing through the point P(-8,0) that is perpendicular to the line y=-3 is y=0 which can be found out from slope intercept formula.
It is given to us that -
The point is P(-8,0)
The line is represented as y=-3
The point P is perpendicular to the given line.
We have to find out the equation of the line passing through P which is perpendicular to the given line.
We know that the equation of a line is given by -
y = mx + c
where, (x, y) = coordinates of the point
m = slope of the line
c = a constant
Comparing this with the equation of the given line, we have
m=0 and c =-3
This implies that the slope of the perpendicular is also equal to 0.
The slope intercept formula for the perpendicular line can be represented as -
y = mx + c
Using the coordinates of P(-8,0), we have
0 = 0*(-8) +c
=> c = 0.
Thus, the equation of line passing through the point P(-8,0) that is perpendicular to the line y=-3 is y=0.
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Lucy i making the ame bracelet for eight of her Friend he ha 32 bead how many bead can you put on each bracelet?
Using the fraction concept, we can say that The number of beads each friend will get is 4.
What are fractions?
Fractions are referred to as the components of a whole in mathematics. A single object or a collection of objects might be entire. When we cut a piece of cake in real life from the entire cake, the part represents the percent of the cake. The word "fraction" is derived from Latin. "Fractus" means "broken" in Latin. The fraction was expressed verbally in earlier times. It was afterward presented in numerical form.
A piece or sector of any quantity is another name for the fraction. It is indicated by the sign "/," such as a/b. For instance, in the fraction 2/4, the lower part represents the denominator, and the top part the numerator.
In the given question, we have:
Number of bead = 32 bead;
Total number of friends = 8;
So,
we need to find how many beads will one friend get:
So,
The number of beads each friend will get : [tex]\frac{32}{8}[/tex]
The number of beads each friend will get is 4.
Hence,
using the fraction concept, we can say that The number of beads each friend will get is 4.
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