Answers
Answer:
4x+3y=12
Step-by-step explanation:
y=mx+b
m=-4/3,b=4
y=mx+b
y=-4/3x+4
3(y=-4/3x+4)
3y=-4x+12
4x+3y=12
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Related Questions
Verify that the function satisfies the three hypotheses of Rolle’s Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle’s theorem. (Enter your answers as a comma-separated list.) f(x) = x^3 - 4x^2 - 16x + 8, [-4,4] Find c =
Answers
There are no values within the interval that satisfies the condition stated by Rolle's theorem.
What numbers does satisfy Rolle's theorem?In accordance to Rolle's theorem, a function existing within an closed interval [a, b] has at a least a value c within that interval such that the first derivative f'(c) is equal to the slope of the secant line that passes through the two interval limits. That is to say, Rolle's theorem is defined by the following formula:
f'(c) = [f(b) - f(a)] / (b - a), where a < c < b
Where:
f(a), f(b) - Values of the function evaluated at each interval limit.f'(c) - First derivative of the function evaluated at x = c.First, evaluate the function f(x) at x = - 4:
x = - 4
f(- 4) = (- 4)³ - 4 · (- 4)² - 16 · (- 4) + 8
f(- 4) = - 64 - 64 + 64 + 8
f(- 4) = - 56
Second, evaluate the function f(x) at x = 4:
x = 4
f(4) = 4³ - 4 · 4² - 16 · 4 + 8
f(4) = 64 - 64 - 64 + 8
f(4) = - 56
Third, determine the first derivative of the function f(x) and evaluate it at x = c:
f(x) = x³ - 4 · x² - 16 · x + 8
f'(x) = 3 · x² - 8 · x - 16
x = c:
f'(c) = 3 · c² - 8 · c + 16
Fourth, find the roots of the quadratic function found in the previous step.
3 · c² - 8 · c + 16 = 0
In accordance with the quadratic formula, the roots of the expression are 4 / 3 + i 4√2 / 3 and 4 / 3 - i 4√2 / 3, which are not real numbers.
Fifth, determine whether Rolle's theorem are applicable on the roots found in the previous step.
Since the roots of the polynomial 3 · c² - 8 · c + 16 are not real numbers, there are no number within the interval that satisfies Rolle's theorem.
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y= 3x + a / 2x -5
express x in terms of a and y
Answers
The equation y = 3x +a / 2x - 5 can be expressed in terms of a and y as x = (a - 5y) / (2y-3)
Given equation y = 3x + a / 2x - 5
= y(2x - 5) = 3x + a
= 2xy - 5y = 3x + a
= 2xy - 3x = a - 5y
= x(2y-3) = a - 5y
Hence, x = (a - 5y) / (2y - 3)
First, we will move the denominator 2x-5 and multiply it by y giving us 2xy-5y. Next, we will move all the terms which contain only a and y to one side and the rest remaining to another side, giving us 2xy - 3x = a - 5y. Since we need to express the equation in terms of x we take it as common from left-hand side of the equation and the remaining part we move to the right-hand side as the denominator. Hence we get our equation in terms of a and y as x = (a - 5y) / (2y - 3).
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Britney can do a job in 12 hours. if she works with jimmy, together they can get the job done in eight hours. how long would it take jimmy to do the job alone?
Answers
Jimmy will take 24 hours to do the given job alone.
What is the teamwork equation for problem solving?
Problems with teamwork are resolved using this technique. If the first person completes a task in 'A' units of time and a second person completes a task in 'B' units of time, they can complete a task in 'T' units of time together (total).
The teamwork equation can be applied, that is: (1/A) + (1/B) = (1/T)
Given, time taken by Britney to do the job individually = B = 12 hours
Also, time taken by Britney and Jimmy to do the job together = A = 8 hours
Let the time taken by Jimmy to do the job individually = A hours
Thus, using the equation established in the literature above and substituting the given values, we have:
(1/A) + (1/B) = (1/T) ⇒ (1/A) + (1/12) = 1/8 ⇒ 1/A = (1/8) - (1/12)
⇒ 1/A = (3/24) - (2/24) ⇒ 1/A = 1/24 ⇒ A = 24
Thus, Jimmy will take 24 hours to do the given job alone.
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A health food store makes trail mix using dried fruit and nuts.the cost of the dried fruit is $2.50 per pound,and the cost of the nuts is $2.00 per pound .the total cost to make the trail mix is $225.if the total cost can be represented by the equation 2.5x +2y=225,what does the term 2.5x represent?
I need help:’)
Answers
The equation 2.5x + 2y = 225 represents the total cost and 2.5x represents the cost of dried fruit when its quantity is x.
A health food business prepares trail mixes out of dried fruit and nuts. The dried fruit costs $2.50 per pound, while the nuts cost $2.00 per pound. The overall cost of making the trail mix is $225.
Let the quantity of the dried fruit is x,
And the quantity of nuts is y,
As per the given question, the equation would be as:
2.5x + 2y = 225
The above equation represents the total cost and 2.5x represents the cost of dried fruit when its quantity is x.
Thus, 2.5x represents the cost of dried fruit when its quantity is x.
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A swimming pool is to be constructed in a 1,176-ft2 backyard. there is to be a fence that will surround a 14-by-28-foot pool. the pool builder wants to build a concrete paver deck of a uniform width, x, surrounding the pool and filling the entire area of the backyard. what is the width of the pool deck? 7 ft 14 ft 28 ft 56 ft
Answers
The width of pool deck is 7 ft and new dimensions of pool and deck are 21 ft and 35 ft .
In the given question we have,
Area of whole background ( pool + deck) = 1176 ft²------(1)
Area is a two dimensions quantity . so, we work here in 2-D.
length of pool = 28 ft , width of pool= 14 ft
let the width of deck be x ft . Now, the new dimensions are following
length of pool and deck = 28 + x + x = (28+2x ) ft
width of pool and deck = 14 + x + x = (14+ 2x) ft
here, 2x include in lenth and width for surronding deck.
total area of pool and deck ( backyard ) = lenth × width = 1176 ft² ( from (1) )
(28+2x) ( 14+2x) = 1176 ----(2)
Now, we shall solve above equation (2) and find out value of x
28×14 + 56x + 28x + 4x^2 = 1176
=> 4x²+ 84x + 392 - 1176 = 0
=> 4x² + 84x - 784=0 => x² + 21x - 196 = 0
=> x²+ 28x - 7x - 196 = 0 => x(x+ 28) - 7(x+28)=0
=> (x+28) (x-7) = 0
either x + 28= 0 or x - 7 = 0 =>either x= -28 or x= 7
but width can't be negative value so, discard
x= -28.
Hence, the width of pool deck is 7 ft.
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what sample size is necessary for a 90% confidence interval about the mean height of a shrub if we want a margin of error of 0.5 inches and the population standard deviation is known as 1.3 inches.
Answers
The sample size necessary for a 90% confidence interval about the mean height of a shrub with a margin of error of 0.5 inches and a population standard deviation of 1.3 inches is 18.
Margin of error is defined as the degree of the sampling errors in statistics. It can be calculated using the formula below.
MOE = z x (SD / √n)
where MOE = margin of error = 0.5 inches
z = found by using a z-score table
SD = sample standard deviation = 1.3 inches
n = sample size
At 90% confidence interval, the area in each tail of the standard normal curve is 5, and the cumulative area up to the second tail is 95.
(100 - 90) / 2 = 5
100 - 5 = 95
Find 0.95 in the z-table to get the value of z.
At p = 0.95, z = 1.647
Plug in the values to the formula and solve for the sample size, n.
MOE = z x (SD / √n)
0.5 = 1.647 x (1.3 / √n)
√n = 1.647(1.3) / 0.5
n = 18.34
n = 18
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Identify three segments parallel to AE using the figure shown. Assume lines and planes that appear to be parallel or perpendicular are parallel or perpendicular, respectively
Answers
From the figure, the lines parallel to AE are DH, CG, and EF.
What are parallel and perpendicular lines?Geometry is heavily reliant on parallel and perpendicular lines, and they can be easily distinguished thanks to a few unique qualities. If two lines never cross each other, are in the same plane, and are at the same distance from one another, then they are said to be parallel. Perpendicular lines are those that cross at an angle of 90 degrees.
If two straight lines are in the same plane and never intersect, they are said to be parallel lines.
So from the figure, we can see that the lines parallel to AE are DH, CG, and EF, as the lines are in the same plane.
As equidistant lines, they are always the same distance apart.
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The hypotenuse of a right triangle measures 8 cm and one of its legs measures 4 cm.
Find the measure of the other leg. If necessary, round to the nearest tenth.
Answers
Answer:
4√3 (about 6.9) cm.
Step-by-step explanation:
In a 30°-60°-90° triangle, the length of the hypotenuse is twice the length of the shorter leg, and the length of the longer leg is √3 times the length of the shorter leg.
Here, the length of the longer leg is 4√3, or about 6.9, cm.
Given p=q=0
, what is the equation of the line that passes through the points (–p, –q) and (p, q)?
y = –x
y = q
y = 2x + (2p – q)
Answers
Equation of the line which passes through the given points (-p ,-q) and
(p, q) where p ≠ q ≠ 0 is given by y = (q/p)x.
As given in the question,
Given condition is :
p ≠ q ≠ 0
Equation of the line which passes through the given points (-p ,-q) and
(p, q) is given by:
(x₁ , y₁) = (-p ,-q)
(x₂ , y₂) = (p, q)
(y -y₁)/ (x -x₁) = (y₂ -y₁)/ (x₂ -x₁)
⇒(y +q)/(x+ p) = (q +q)/(p +p)
⇒(y +q)/ (x +p) = 2q /2p
⇒p(y+ q) =q( x +p)
⇒yp + pq = qx +pq
⇒yp = xq
⇒y = (q /p)x
Therefore, equation of the line which passes through the given points (-p ,-q) and (p, q) where p ≠ q ≠ 0 is given by y = (q/p)x.
The complete question is :
Given p ≠ q ≠ 0, what is the equation of the line that passes through the points (–p, –q) and (p, q)?
A. y = –x
B. y = q/px
C. y = q
D. y = 2x + (2p – q)
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Answer:
b
Step-by-step explanation:
just did it
PLEASE HELPPP ILL BRAINLIST/5 STAR.
The total surface area of a cube with a side length of 8cm is:
A) 513 cm square
B) 384 cm square
C) 96 cm square
D) 64 cm Square
The letter representing the gradient in the formula y = mx + c is:
A) y
B) m
C) x
D) c
The gradient and y - intercept of the line y = -3x + 4 is:
A) -3x and 4
B) 3 and 4
C) -3 and 4
D) 4 and -3
The gradient of the line passing through the points (3, -2) and (2,-3) is:
A) 1
B) -1
C) 3b (b+4) - 4 (b-5)
Answers
Answer:
1. 384 cm square
2. m
3. -3 and 4
4. 1
Answer:
1) B
2) B
3) C
4) A
Step-by-step explanation:
Area of cube:[tex]\sf \boxed{\text{Area of cube = $6a^2$}}[/tex]
Here, a is the side of the cube.
Area of cube = 6 * 8 * 8
= 384 square cm
Option B
2) y = mx + c.
Here, m is the slope or gradient and c is the y-intercept.
Option B
3) y = -3x + 4
Compare with y =mx + c,
where m is the gradient and c is the y-intercept.
m = -3 and = 4
Option C
4)
[tex]\sf Slope = \dfrac{y_2-y_1}{x_2-x_1}\\\\[/tex]
[tex]\sf =\dfrac{-3-[-2]}{2-3}\\\\=\dfrac{-3+2}{-1}\\\\=\dfrac{-1}{-1}\\\\=1[/tex]
Option A
HELP PLS GIVING BRAINLIEST TO PERSON WHO ANSWERS FIRST
A rental car company charges $26.03 per day to rent a car and $0.13 for every mile driven. Malik wants to rent a car, knowing that:
He plans to drive 250 miles.
He has at most $350 to spend.
Which inequality can be used to determine d, the maximum number of days Malik can afford to rent for while staying within his budget?
Answers
The inequality that can be used to determine d, the maximum number of days Malik can afford to rent for while staying within his budget is 26.03d + 0.13m ≤ 350.
What is an inequality?Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.
In this case, the rental car company charges $26.03 per day to rent a car and $0.13 for every mile driven
Let the number of days be d.
Let the number of miles be m.
The appropriate inequality to illustrate this is 26.03d + 0.13m ≤ 350.
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7(x+4)-2[x-3(5+x)]=2/3(x-6)
With detailed workings
Answers
Ur Welcome hope this helps you and I hope it’s also right have a good day
0.38 in expanded form
Answers
Answer:
0 + 0.30 + 0.08
Step-by-step explanation:
hope it helps :)
A polygon has vertices A (5, -1), B (21, 11), C (26, -1), and D (2, -8).
Part A. What is the perimeter of ABCD to the nearest tenth of a unit?
Part B. What is the area of ABCD to the nearest tenth of a square unit?
Enter the correct answers in the boxes.
A. Perimeter: units
B. Area: square units
Answers
The graph of the coordinate points of the vertices of ABCD indicates;
Part A The perimeter of ABCD ia approximately 61.2 units
Part B. The area of ABCD is 199.5 square units
What is the perimeter of a figure in geometry?The perimeter of a figure is length of the line that goes round the figure.
A. The perimeter of the polygon is the sum of the length of the sides of the polygon, which is found as follows;
AB = √((21-11)²+(11-(-1))²) ≈ 15.6
BC = √((21-26)²+(11-(-1))²) = 13
CD = √((26-2)²+(-1-(-8))²) = 25
AD = √((2-5)²+(-8-(-1))²) ≈ 7.6
The perimeter of the polygon = 15.6 + 13 + 25 + 7.6 = 61.2
The polygon has a perimeter of approximately 61.2 unitsB. Plotting the figure indicates that the figure consists of two triangles, ΔABC and ΔACD
The base length of triangle ΔABC = 26 - 5 = 21
The height of triangle ΔABC = 11 - (-1) = 12
The area of triangle ΔABC = 0.5 × 21 × 12 = 126
Base length of triangle ΔADC = 21
Height of triangle ΔADC = -1 - (-8) = 7
Area of triangle ΔADC = 0.5 × 21 × 7 = 73.5
Area of the composite figure is therefore;
A = 126 + 73.5 = 199.5
The area of the figure is therefore; 199.5 square units
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Find the missing side lengths. Leave your answers as radicals in simplest form
Answers
Answer:
Step-by-step explanation:
Hi Mia, are you aware that the last name Hamilton is a famous math person? :) anyway,
The triangle in the picture is an isosceles triangle, we know that b/c the angle of the one is 45° meaning the other side must also be a 45° angle. So we know the two sides are the same length.
side n = 7 [tex]\sqrt{2}[/tex] / 2
then use Pythagoras to find m
[tex]c^{2}[/tex] = ( 7 [tex]\sqrt{2}[/tex] / 2)^2 + ( 7 [tex]\sqrt{2}[/tex] / 2)^2
[tex]c^{2}[/tex] = 49*2/4 + 49*2/4
[tex]c^{2}[/tex] = 49/2 + 49/2
[tex]c^{2}[/tex] = 98/2
[tex]c^{2}[/tex] = 49
c = 7
side m = 7 :) nice, huh ?
a) Sin X = O/H
Sin 45 = [tex]7\sqrt{2}[/tex]/2/H
H= [tex]7\sqrt{2}[/tex]/2/ Sin 45
m= 7
b) cos X = A/H
cos 45= A/7
A= cos45*7
n= 4.95
answer please will give 20 points
Answers
Answer:plot the point (2,5)
Step-by-step explanation:
-5/8 + 1/4. Add.
Simplest form.
Answers
Answer: -3/8 or -0.375
Step-by-step explanation:
you have to get similar denominators to simplify
so times 1/4 by 2 to get 2/8
and then just do 2/8 - 5/8 and you get the answer
−8×{108÷12−(−3×11−15)÷12}
Answers
Answer:
[tex] - 8(9 - ( - 33 - 15) \div 12[/tex]
[tex] - 8(9 - ( - 48) \div 12[/tex]
[tex] - 8(9 + 4)[/tex]
[tex] - 8(13)[/tex]
[tex] - 104[/tex]
Answer:
-104
Step-by-step explanation:
Divide 108 by 12
Calculate -3 × 11 - 15 which is 48
Remove the parentheses
Divide 48 by 12 which is 4
9 + 4 is 13
-8 × 13 = -104
If f(x) = -3x - 5 and g(x) = 4x - 2, find (f+ g)(x).
Answers
Answer:
(f+g)(x) = x - 7
Step-by-step explanation:
(f+g)(x) tells you to add the functions together. It means
f(x) + g(x)
= -3x - 5 + 4x - 2
combine like terms.
= 4x-3x - 5 - 2
= x - 5 - 2
simplify.
= x - 7
(f+g)(x) means
f(x) + g(x)
= x - 7
a student was asked to find the equation of the tangent plane to the surface at the point . the student's answer was (a) at a glance, how do you know this is wrong. what mistakes did the student make? select all that apply. a. the answer is not a linear function. b. the (x - 5) and (y - 4) should be x and y. c. the partial derivatives were not evaluated a the point. d. the -131 should not be in the answer. e. all of the above (b) find the correct equation for the tangent plane.
Answers
The answer is not a linear function, and the evaluation of the partial derivatives was done to a point. Thus, options (a) and (c) are correct. The correct equation for the tangent plane is z = 3x - 108y - z + 241 = 0.
In a given point (x₀, y, z₀) the equation of the tangent plane to a surface given by the function S = f(x, y)can be obtained by
z-z₀ = f ₓ (x₀, y₀, z₀) (x - x₀) + fᵧ (x₀, y₀, z₀) (y - y₀) ... (i)
where f ₓ (x₀, y₀, z₀) and fᵧ (x₀, y₀, z₀) (y - y₀) are the partial derivatives of f(x, y) with respect to x and y respectively. These two derivatives are evaluated at the point (x₀, y₀, z₀) .
Thus, we need to find two missing inputs, the z₀ coordinate and the two partial derivatives, in our problem in order to use equation (i).
In the case of z₀, evaluation of the given function gives us z = -80.
The partial derivatives are thus-
δf(x,y) / δx = fₓ (x, y) = 3x²
fₓ (x₀, y₀) = fₓ (1, 3) = 3
δf(x,y)/δxy= fᵧ (x, y) = -4y³
fᵧ (x₀, y₀) = fᵧ (1, 3) = -108
Now, arranging these values in equation (i) we obtain:
z-z₀ = f ₓ (x₀, y₀, z₀) (x - x₀) + fᵧ (x₀, y₀, z₀) (y - y₀)
z +80 = 3x² (x -1) - 4y³ (y - 3)
z = -80 +3x² (x -1) - 4y³ (y - 3)
Now, we will substitute the values of the partial derivatives at the given point:
z = -80 + 3x² (x -1) - 4y³ (y - 3)
z = 3x² (x -1) - 108 (y - 3)
z = 241 + 3x -108y
i.e., 3x - 108y - z + 241
Thus, the correct equation is 3x - 108y - z + 241.
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The complete question is-
A student was asked to find the equation of the tangent plane to the surface z = x³−y⁴ at the point (x, y) = (1, 3). The student's answer was z = −80 + 3x²(x−1)−(4y³)(y−3).
(a) At a glance, how do you know this is wrong? What mistakes did the student make? Select all that apply. A. The (x - 1) and (y - 3) should be x and y. B. The -80 should not be in the answer. C. The partial derivatives were not evaluated at this point. D. The correct answer is not a linear function. E. All of the above.
(b) What is the correct equation for the tangent plane? z=
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Express each improper fraction as a mixed or whole number
Answers
All the improper fractions in mixed or whole numbers are as follows:
(A) 8/8 = 8(B) 15/3 = 5(C) 16/5 = 3⅕(D) 9/2 = 4½(E) 25/6 = 4⅙(F) 43/4 = 10¾(G) 24/2 = 12(H) 28/5 = 5⅗What are whole numbers?A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder. n amalgam of a whole number and a legal fraction is a mixed fraction.So, the given improper fractions in the mixed or whole numbers are:
(A) 8/8 = 8(B) 15/3 = 5(C) 16/5 = 3⅕(D) 9/2 = 4½(E) 25/6 = 4⅙(F) 43/4 = 10¾(G) 24/2 = 12(H) 28/5 = 5⅗Therefore, all the improper fractions in mixed or whole numbers are as follows:
(A) 8/8 = 8(B) 15/3 = 5(C) 16/5 = 3⅕(D) 9/2 = 4½(E) 25/6 = 4⅙(F) 43/4 = 10¾(G) 24/2 = 12(H) 28/5 = 5⅗Know more about whole numbers here:
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A school needs to buy new notebook and desktop computers for its computer lab. The
notebook computers cost $200 each, and the desktop computers cost $400 each.
How many total computers would someone buy if they get 12 notebooks and 15
desktop computers? How many total computers would someone buy if they get n
notebooks and d desktop computers?
Total computers, 12 notebooks and 15 desktop computers:
Total computers, n notebooks and d desktop computers:
Answers
Answer: 27
Step-by-step explanation:
Well we already know that n is 12 and d is 15
So based on what I see we do n + d which would equal 27.
If the ratio of men to women in a movie theater is 3:2 and there are 45 men in the theater, how many total people are in the theater?
Answers
Answer:
113 people (112.5 if you don't round but you can't have half a person)
Step-by-step explanation:
45 men plus the number of women (x) is how many people there are
so you would do 3/x=2/45 since x is the number of women
do some basic algebra, and you get 67.5 women so round if you want to to 68 (i will round because you can't have half a person)
68+45=113 people
A toy company puts 25 toy cars in each box.
How many toy cars are in 1,000 boxes? Use the expression 25 × 1,000 to find the answer. Then, describe the value of 25 in the result.
A. 2,500
The place value of 25 increases by 1 place to the left.
B. 2,500
The place value of 25 increases by 2 places to the left.
C. 25,000
The place value of 25 increases by 3 places to the left.
D. 25,000
The place value of 25 increases by 4 places to the left.
Answers
The number of toy cars are in 1,000 boxes is 25000 and the place value of 25 increases by 4 places to the left.
How to calculate the value?It should be noted that place value is used to know the value of the numbers that are given in a data.
In this case, toy company puts 25 toy cars in each box, the number of toy cars that are in 1,000 boxes will be:
= 25 × 1000
= 25000
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What is the slope of a line perpendicular to the line whose equation is 2x-12y=-120? Fully simplify your answer.
Answers
The slope of the line perpendicular to the line 2x - 12y = 120 will be -6.
What is the general equation of a Straight line?The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.
The equation of a straight line can be also written as -
Ax + By + C = 0
By = - Ax - C
y = (- A/B)x - (C/A)
We have the following equation -
2x - 12y = - 120
Rearranging the equation, we get -
2x - 12y = 120
12y = 2x - 120
6y = x - 60
y = (1/6)x - 10
The slope of the line perpendicular to the line 2x - 12y = 120 will be -
m[2] = -1 / (1/6) = - 6
m[2] = - 6
Therefore, the slope of the line perpendicular to the line 2x - 12y = 120 will be -6.
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Kareem cannot decide which of two washing machines to buy. The selling price of each is 600$. The first is marked down by 50%. The second is marked down by 30% with an additional 20% off. Find the sale price of each washing machine. Use pencil and paper. Explain why should buy the first washing machine rather than the second if the machines are the same except for the selling price.
Answers
The selling price of the first washing machine is $300
The selling price of the second washing machine is $336
The first washing machine appear to have more savings in cost
How to determine the selling prices of the two machinesThe question is a percentage problem
The first is marked down by 50%
= 50 percent
= 50 / 100
= 0.5
marked down factor = 1 - 0.5 = 0.5
selling price of the first machine = 600 * 0.5 = 300
Similarly the second selling washing machine has mark down of 30%
30% = 0.3
marked down factor = 1 - 0.3 = 0.7
selling price of the second washing machine at first mark down
= 600 * 0.7 = 420
second mark down
20% = 0.2
marked down factor = 1 - 0.2 = 0.8
selling price of the second washing machine at second mark down
= 420 * 0.8 = 336
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Use Heron's Formula to find the area of AHKP if h' = 24 ft, k = 21 ft, and p = 13 ft. *
(1 Point)
192. 67 sq units
435. 90 sq units
113. 38 sq units
136. 23 sq units
Answers
The area of the triangle HKP found by the Heron's Formula is 136.23 sq. ft.
Define the term Heron's Formula?This formula is well-known for its straightforward computation that supports the length for three triangle sides. If the lengths of the 3 sides are a, b, and c, the semi-perimeter is; s = (a+b+c)/2.Area ; A = √s(s−a)(s−b)(s−c)The three sides of the triangle are-
h = 24 ft, k = 21 ft, and p = 13 ft.
s = ( 24 + 21 + 13 ) / 2
s = 29
s - a = 29 - 24 = 5
s - b = 29 - 21 = 8
s - c = 29 - 13 = 16
Put in the formula,
Area = √s(s−a)(s−b)(s−c)
A = √ 29 x 5 x 8 x 16
A = 136.23
Thus, the area of the triangle HKP found by the Heron's Formula is 136.23 sq. ft.
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while eating out, mike and joe each tipped their server 22 dollars. mike tipped 10\% of his bill and joe tipped 20\ % of his bill. what was the difference, in dollars between their bills?
Answers
Joe, for the most part, tipped 20% of his bill, compared to 10% for Mike, which is particularly noteworthy. The actually difference between their invoices in dollars was approximately 10.
Let be Mike's bill and be Joe's bill.
(10/100) *m = 2
M = 20
(20/200 )*j = 2
J = 10
So the desired difference is
m-j = 20 – 10
= 10
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What are the x and y intercepts? What do they mean in terms of the graph?
Answers
Step-by-step explanation:
these intercepts are the points where the graph intersects with the coordinate axes (x and y).
the x-intercept is a point on the x-axis, meaning when y = 0.
the y-intercept is a point on the y-axis, meaning when x = 0.
so, the x-intercept here is 14 at the point (14, 0).
the y- intercept is 7 at the point (0, 7).
that means the object started falling from a height of 7 meters and hit the ground after 14 seconds.
the falling speed was then
7 meters / 14 seconds = 0.5 meters / second
what are we talking about ? an asteroid with very little gravity ?
Zyndy is twice the age of Vyndel. The sum of their age is twenty-one. Determine their ages.
Pa sagot po pls pasahan na po namin bukas :
Answers
Answer:
Zyndy is 14, Vyndel is 7.
Step-by-step explanation:
Let Zyndy's age be represented by 'z', and Vyndel's age be represented by 'v'.
Zyndy is twice the age of Vyndel, so z=2v
The sum of their age is twenty-one, so z+v=21
Sub the first equation above into the second to get:
2v+v=21
3v=21
v=7
Knowing v=7, we can say z=2(v)=14.