Finding slope from an equation
Answer:
[tex]\frac 15[/tex]
Step-by-step explanation:
Hello!
We can convert it into slope intercept form: [tex]y = mx + b[/tex]
m = slopeb = y-interceptConvert:[tex]-15 - x = -5y[/tex][tex](-15 - x)\div(-5) = y[/tex][tex]3 + \frac15x = y[/tex][tex]y = \frac15x + 3[/tex]The slope is [tex]\frac15[/tex].
Finding the slope of a line from its equation depends on the equation's form. If it's already in slope-intercept form (y = mx + b), the coefficient of x (m) is the slope. If not, rewrite it to that form by isolating y. Alternatively, use the point-slope form (y - y1 = m(x - x1)) with a known point on the line and solve for m. Remember, the slope tells you how much the line rises/falls per unit move to the right. For the equation in the image, the slope is 1/5.
• Using the slope-intercept form: This is the most straightforward way to find the slope if the equation is already in slope-intercept form, which is y = mx + b. In this form, the slope (m) is the coefficient of the x term. For example, if the equation is y = 2x + 3, the slope is 2.
• Using the standard form: If the equation is not in slope-intercept form, you can first rewrite it in slope-intercept form. To do this, you need to isolate the y term. For example, if the equation is 3x + 2y = 6, you would first subtract 3x from both sides to get 2y = -3x + 6. Then, you would divide both sides by 2 to get y = -3/2x + 3. Once the equation is in slope-intercept form, you can find the slope as described in the first method.
• Using the point-slope form: The point-slope form of the equation of a line is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. To find the slope using this form, you need to plug in the coordinates of a point on the line. For example, if the equation is y - 2 = 3(x - 1), and you know that the point (3, 7) is on the line, you can plug in x = 3 and y = 7 to get 5 = 3(2). Solving for m, you get m = 5/3.
The slope of a line tells you rise over run, or how much the line goes up or down for every unit it goes to the right. A positive slope means the line goes up as you move to the right, a negative slope means the line goes down as you move to the right, and a zero slope means the line is horizontal.
In the image, the equation is -15 - x = -5y. To find the slope using the slope-intercept form, we need to rewrite the equation so that y is isolated on one side. We can do this by adding x and dividing both sides by -5:
y = (1/5)x + 3
Therefore, the slope of the line is 1/5.
find the product of: (4x-4y)(2x+y)
Answer:
Step-by-step explanation:
(4x - 4y)(2x + y) =
4x(2x + y) - 4y(2x + y) =
8x²+4xy-8xy-4y²=
8x²-4y²-4xy
Factorise term
4(2x²-y²-xy)
PLEASE MARK BRAINLIEST.
Alice had 4 1/4 pounds of walnuts at the beginning of the week. At the end of the week, she had 2 3/4 pounds. How much has she used? A. 1 3/4 B. 1 1/2 C. 2 1/2 D. 1 1/4
Answer: The correct option is (B) [tex]1\dfrac{1}{2}.[/tex]
Step-by-step explanation: Given that Alice had [tex]4\dfrac{1}{4}[/tex] pounds of walnuts at the beginning of the week. At the end of the week, she had [tex]2\dfrac{3}{4}[/tex] pounds.
We are to find the quantity of walnuts that she had used.
We have
The quantity of walnuts that Alice has is
[tex]q_1=4\dfrac{1}{4}=\dfrac{17}{4}~\textup{pounds}[/tex]
and the quantity of walnut that she had at the end of the week is
[tex]q_2=2\dfrac{3}{4}=\dfrac{11}{4}~\textup{pounds}.[/tex]
Therefore, the quantity of walnut that she has used is given by
[tex]Q=q_1-q_2=\dfrac{17}{4}-\dfrac{11}{4}=\dfrac{6}{4}=\dfrac{3}{2}=1\dfrac{1}{2}.[/tex]
Thus, the required quantity of walnut that she has used is [tex]1\dfrac{1}{2}~\textup{pounds}.[/tex]
Option (B) is CORRECT.
Whats 5(-2/3) and 3(1/4)?
Which pair of quantities is LEAST likely to be directly proportional? CLEAR CHECK Area and side length of a rhombus , Distance and time when speed is constant, Total cost and the number of movie tickets purchased ,and Hours worked and money earned please answer this question quickly ...
Answer:
Area and Side length of a rhombus.
Step-by-step explanation:
1. Area and side length of a rhombus - This is least proportional as they are inversely proportional.
2. Distance and time when speed is constant is proportional.
Distance = speed x time
When speed is constant, the distance increases with respect to speed.
3. Total cost and the number of movie tickets purchased.
As the number of tickets purchased increases, the cost also increases.
4. Hours worked and money earned
When the number of hours increases, the money earned also increases.
In the inverse variation function, what happens to the output when the function's inputvalue is multiplied by 4?
Stein Co. issued 13-year bonds two years ago at a coupon rate of 10.3 percent. The bonds make semiannual payments. If these bonds currently sell for 95 percent of par value, what is the YTM?
Nper = 11*2 = 22 (indicates the period over which interest payments are made)
PMT = 1000*10.3%*1/2 = 51.5 (indicates sem-annual interest payments)
PV = 1000*95% = 950 (indicates the current selling price of the bonds)
FV = 1000 (indicates the face value of bonds)
Rate = ? (Indicates YTM)
YTM = Rate(Nper,PMT,PV,FV)*2 = Rate(22,51.5,-950,1000)*2 = 11.098% or 11.10%
Answer is 11.098% or 11.10%.
Carlotta is constructing an equilateral triangle. She has already constructed the line segment and arc shown. What should Carlotta do for her next step?
Use the straightedge to draw a line that passes through point Q and intersects the arc.
Place the point of the compass on point Q and draw an arc that intersects the first arc, using the same width for the opening of the compass as the first arc.
Use the straightedge to draw a line that passes through point P and intersects the arc.
Place the point of the compass on point Q and draw an arc that intersects the first arc, using a width for the opening of the compass that is less than 1/2 PQ.
Juanita receives her paycheck and knows that her gross pay and federal tax are correct. Using the fact that Social Security tax is 6.2% of gross pay, Medicare tax is 1.45% of gross pay and state tax is 19% of federal tax, determine if Juanita's net pay is correct.
Earnings
Deductions
Week Ended
Regular
FED. SOC. MED STATE
WITH. WITH. CARE. WITH.
NET PAY
11/17
$1,020.00
$107.00 $63.24 $14.79 $20.33
$814.64
Choose the true statement below.
a.
The net pay is correct.
b.
The Social Security tax is not correct.
c.
The Medicare tax is not correct.
d.
The state tax is not correct.
The answer is A. The net pay is correct.
Mr. Ernesto spent $72 for 3 bags of grass seed. How much did he spend for EACH bag?
URGENT!!!
someone help asap !! is this the right answer?
The cost of producing x soccer balls in thousands of dollars is represented by h(x) = 5x + 6. The revenue is represented by k(x) = 9x – 2. Which expression represents the profit, (k – h)(x), of producing soccer balls?
Answer:
(K-h) (x) = 4(x-2)
Step-by-step explanation:
The cost of producing x soccer balls in thousands of dollars is represented by h (x) = 5x + 6
Revenue generated is represented by K(x) = (9x-2)
Them ( K-h) (x) will represent
( K-h )x = cost of revenue - production
= profit
( K-h )x = K(x) - h(x)
= (9x-2) - (5x + 6)
= (9x - 5x) - (2+6)
= 4x - 8
Profit = (K-h) (x) = 4(x-2)
The top and bottom margins of a poster are 4 cm and the side margins are each 8 cm. if the area of printed material on the poster is fixed at 388 square centimeters, find the dimensions of the poster with the smallest area.
To find the smallest poster area with a fixed printed area of 388 square centimeters, calculate optimized values for the width and height of the printed area, considering the margins, and derive the poster's dimensions by adding the margins to these values.
Explanation:To find the dimensions of the poster with the smallest area given a fixed printed area, we should first determine the dimensions of the printed area. We know that the printed area is 388 square centimeters and that the margins do not change. Let's denote the width of the printed area as w and the height as h.
The area of the printed material is given by Area = w × h = 388 cm². The total width of the poster would be w + 2×(8 cm) (since there are two side margins), and the total height would be h + 2×(4 cm) (since there are top and bottom margins).
To minimize the area of the poster, we need to minimize the function for the total area of the poster A(w,h) = (w + 16)(h + 8). As the printed area is fixed, we can express h in terms of w using h = 388/w and substitute this into the function to get A(w) = (w + 16)((388/w) + 8).
Taking the derivative dA/dw and setting it to zero, we find the optimal value for w, and consequently, we calculate h. The dimensions of the poster that minimize the total area can then be determined by adding the margins to these optimized values of w and h.
The rule (x,y)→(2x,2y) maps △DEF to △D′E′F′. Which statement correctly describes the relationship between △DEF and △D′E′F′ ?
A. The triangles are congruent because △D′E′F′ is a rotation of △DEF , and a rotation is a rigid motion.
B. The triangles are not congruent because △D′E′F′ is a dilation of △DEF , and a dilation is not a rigid motion.
C. The triangles are not congruent because △D′E′F′ is a translation of △DEF , and a translation is not a rigid motion.
D. The triangles are congruent because △D′E′F′ is a reflection of △DEF , and a reflection is a rigid motion.
Answer: B. The triangles are not congruent because △D′E′F′ is a dilation of △DEF , and a dilation is not a rigid motion.
Step-by-step explanation:
Given : The rule (x,y)→(2x,2y) maps △DEF to △D′E′F′.
We can see that a scale factor (2) is used in the above rule.
Rigid motions do not use any scale factor.
The transformation that uses scale factor to transforms figure is dilation.
And Dilation is not rigid motion because it does not produce congruent images.
Hence, The triangles are not congruent because △D′E′F′ is a dilation of △DEF , and a dilation is not a rigid motion.
Can someone please help me with this? Preferably ASAP
What percent of 320 is 208?
208 is 65 percent of 320.
What is percent?A percentage is a number that tells us how much out of 100 and can also be written as a decimal or a fraction.
A percentage is a number that tells us how much out of 100 and can also be written as a decimal or a fraction, To change the percentage to a fraction, just put the percentage number in the numerator and 100 in the denominator.
We can write a percentage in the form of fraction as well.
For example :- 10%, 78%, 56%, 98%
Given that, what is percent of 320 is 208,
Using the concept of percentage,
Divide 208 by 320 and multiply it by 100
= 208 / 320 x 100
= 0.65 x 100
= 65%
Hence, 208 is 65 percent of 320.
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Andy ran 436.8 meters in 62.08 seconds. Use place value, multiplication with powers of 10, or equivalent fractions to explain what is happening mathematically to the decimal points in the divisor and dividend before dividing!!
IM GIVING AWAY ALL MY POINTS FOR THIS!!
Answer:
If you round, he runs 7 meters in a second.
436.8 m 62.08 s
x m 1 s
(436.8 X 1) / 62.08 = 7.03 m/s
7.03 m 1 s
y m 1/10 s
(7.03 X 0,1 ) /1 = 0,703 m
Step-by-step explanation:
To find Andy's running speed, divide distance by time, adjusting for decimals by multiplying both the divisor and dividend by powers of 10, shifting the decimal point to simplify division.
To calculate Andy's running speed, you would divide the distance he ran (436.8 meters) by the time it took (62.08 seconds). When you divide or multiply decimals by powers of 10, the decimal point is shifted. For instance, if we multiply or divide a number like 1.9436 by 10, 100, or 1000, our decimal point moves to the right or left accordingly. If dividing by 10, it moves one place to the left; by 100, two places; by 1000, three places, turning our number into 0.19436, 0.019436, and 0.0019436 respectively. The same principle applies to Andy's calculation, where the numbers would be easier to handle if we removed the decimal points by multiplying both the divisor and dividend by the same power of 10. Consequently, when dividing 436.8 by 62.08, we can multiply both by 100 to remove the decimal and divide 43680 by 6208, ultimately giving the same answer but with much simpler arithmetic.
If you rotate a right triangle, what feature of the triangle changes?
If a company issues 2,500,000 shares with voting rights how many shares must an investor by to be assured control of the company
You are sending your friend a coded message by rearranging the letters in the word “STRIKE.” That is, your code can be any arrangement of the letters in the word “STRIKE” except one, “S-T-R-I-K-E.”
How many different ways can you code your message?
A) 720
B) 719
C) 120
D) 119
Answer:
Option B) 719 ways
Step-by-step explanation:
Given that you are sending your friend a coded message by rearranging the letters in the word “STRIKE.” That is, your code can be any arrangement of the letters in the word “STRIKE” except one, “S-T-R-I-K-E.”
This means any code we can send using the given letters without strike.
There are 6 different letters and order matters for coding i.e. st is different from ts
Hence no of ways of arranging strike in different ways
[tex]= 6!= 6*5*4*3*2*1\\= 720[/tex]
We must subtract the arrangement strike from this as strike is not allowed.
Hence total number of different ways we code this message
=720-1 =719 ways
An airplane on autopilot took 9 hours to travel 6,561 kilometers. What is the unit rate for kilometers per hour
divide total km by time
6561 / 9 = 729 km per hour
Amanda exercised for 10 minutes every day in the first week, 20 minutes in the second week, 30 minutes in the third week, and 40 minutes in the fourth week.
Billy exercised for 5 minutes every day in the first week, 10 minutes in the second week, 20 minutes in the third week, and 40 minutes in the fourth week.
Which statement best describes the methods used by Amanda and Billy to increase the time they spent exercising? (1 point)
Amanda's method is linear because the number of minutes increased by an equal number every week.
Billy's method is linear because the number of minutes increased by an equal factor every week.
Both Billy's and Amanda's methods are exponential because the number of minutes increased by an equal factor every week.
Both Billy's and Amanda's methods are exponential because the number of minutes increased by an equal number every week.
Answer:
Amanda's method is linear because the number of minutes increased by an equal number every week.Step-by-step explanation:I took the test and got it right.
Amanda
Billy1st week 10 52nd week 20 10 3rd week 30 204th week 40 40A)
Amanda's method is linear because the number of minutes increased by an equal number every week.common difference is 10.1st week 0 + 10 = 102nd week 10 + 10 = 203rd week 20 + 10 = 304th week 30 + 10 = 40Billy's method is exponential:5(2)^x1st week 5(2⁰) = 5(1) = 52nd week 5(2¹) = 5(2) = 103rd week 5(2²) = 5(4) = 204th week 5(2³) = 5(8) = 40Mark
In the deli, meat and cheese are sold by the pound. There is usually a unit price in each variety in the refrigerator case. If honey ham costs $5.99 per lb, how much would 1.5 lbs cost? Enter your answer as a decimal rounded to the nearest cent.
The formula for the future value V (in dollars) of an investment earning simple interest is V=p+prt, where p (in dollars) is the principal, r is the annual interest rate (in decimal form) and t is the time (in years). a. Solve the formula for p
.
p=
b. An investment earns 6% simple interest. What amount of principal is needed to have $3000 after 5 years? Round your answer to the nearest cent.
Amount of principal: $
The answer is for the equation...
V/(1+rt)
It is written as a fraction... and the V goes on top and the (1+rt) goes on the bottom. Make sure that the V is a capital.
Then the amount of principal is 2,307.69
Using the formula given, we find that:
a) The solution for p is [tex]p = \frac{V}{1 + rt}[/tex]b) The principal will be of $2,307.69.------------------
Item a:
The future value formula is given by:
[tex]V = p + prt[/tex]
Solving for p:
[tex]p + prt = V[/tex]
[tex]p(1 + rt) = V[/tex]
[tex]p = \frac{V}{1 + rt}[/tex]
------------------
Item b:
6% interest means that [tex]r = 0.06[/tex]Amount of $3000 means that [tex]V = 3000[/tex]5 years means that [tex]t = 5[/tex]The principal is:
[tex]p = \frac{V}{1 + rt} = \frac{3000}{1 + 5(0.06}} = 2307.69[/tex]
The principal will be of $2,307.69.
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What is 4 to the 2/3 power
Calculate the area of the regular pentagon below:
A.164.025 square inches
B.238.95 square inches
C.351.78 square inches
D.477.9 square inches
Answer:
B. 238.95 is correct
Step-by-step explanation:
the length of a rectangle is 5cm less than 3 times the width.if the perimeter of a rectangle is 54cm, find the length and the width
To solve for the length and width of the rectangle, equations were set up based on the given perimeter and the relation between length and width. The width was found to be 8 cm, and substituting this into the length formula gave a length of 19 cm.
The question concerns finding the length and width of a rectangle given that the length is 5 cm less than three times the width and the perimeter is 54 cm. To solve this, let's denote the width of the rectangle as 'w' and the length as 'l'. The relationship between the length and width can be expressed as 'l = 3w - 5 cm'. The perimeter (P) of a rectangle is given by P = 2l + 2w, and substituting our expressions in terms of 'w' into the formula gives us 2(3w - 5) + 2w = 54. Simplifying and solving for 'w' gives us the width. Subsequently, we can substitute this width into the equation for length to find 'l'.
So, let's start by setting up the equation:
2(3w - 5) + 2w = 54
6w - 10 + 2w = 54
8w - 10 = 54
8w = 64
w = 8 cm
Now we substitute w = 8 cm into the length formula:
l = 3(8) - 5
l = 24 - 5
l = 19 cm
Therefore, the width of the rectangle is 8 cm and the length is 19 cm.
A bag contains 144 ping-pong balls. more than half of the balls are painted orange and the rest are painted blue. two balls are drawn at random without replacement. the probability of drawing two balls of the same color is the same as the probability of drawing two balls of different colors. how many orange balls are in the bag?
There are approximately 72 orange balls in the bag.
We have,
Let's assume the number of orange balls in the bag is x.
Given that more than half of the balls are painted orange, we have the inequality:
x > 144/2
x > 72
Now, let's consider the probability of drawing two balls of the same color:
The probability of drawing two orange balls.
= (x/144) * ((x-1)/(144-1))
= (x(x-1))/(144*143)
The probability of drawing two blue balls.
= ((144-x)/144) * ((144-x-1)/(144-1))
= ((144-x)(143-x))/(144*143)
Given that the probability of drawing two balls of the same color is the same as the probability of drawing two balls of different colors, we can set up the equation:
(x(x-1))/(144143) = ((144-x)(143-x))/(144143)
Simplifying the equation:
x(x-1) = (144-x)(143-x)
x^2 - x = 144143 - 287x + x^2
288x = 144143
x = (144*143)/288
x ≈ 72
Therefore,
There are approximately 72 orange balls in the bag.
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At the city museum, child admission is $5.20 and adult admission is $9.10. on saturday, three times as many adult tickets as child tickets were sold, for a total sales of $975.00. how many child tickets were sold that day?
A store is having a sale on chocolate chips and walnuts. For
5
pounds of chocolate chips and
2
pounds of walnuts, the total cost is
$10
. For
3
pounds of chocolate chips and
8
pounds of walnuts, the total cost is
$23
. Find the cost for each pound of chocolate chips and each pound of walnuts.