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
maggie owes billy $14, her mother $45 and her sister $32. if Maggie has $100 in her purse and pays everyone back, how much money will maggie have left over
If maggie owes billy $14, her mother $45 and her sister $32. if Maggie has $100 in her purse and pays everyone back then 9 is the money maggie have left over
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
maggie owes billy $14
Maggies mother $45
Maggies sister $32
Maggies has $100 in her purse and pas everyone bills, we need to find how much money will maggie have left over
To do this we have to add all the bills and subtract from 100
Fourteen plus forty five plus thirty two
14+45+32
Ninety one
91
Now subtract 91 from 100.
100-91
9
Hence, $9 is the money will maggie have left over
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−8×{108÷12−(−3×11−15)÷12}
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
What is the slope of the line that
passes through these two points?
(-1,4)
(2,2)
Answer:
-2/3
Step-by-step explanation:
y2-y1/x2-x1
2-4/2-(-1)
-2/2+1
-2/3
Please mark as brainliest
Find the missing side lengths. Leave your answers as radicals in simplest form
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
Answer:plot the point (2,5)
Step-by-step explanation:
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 :
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.
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
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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a) What is the area of the shape below?
The area of the shape is 32 square yards
The given consist of one rectangle and a right triangle
The area of the figure = The area of the rectangle + The area of the right triangle
The area of the rectangle = The length × The width
The length of the rectangle = 6 yards
The width of the rectangle = 4 yards
The area of the rectangle = 6×4
= 24 square yards
The area of the triangle = (1/2)bh
The base of the triangle = 9 - 5 = 4 yards
The height = 4 yards
The area = (1/2)× 4 × 4
= 8 square yards
The area of the figure = 24 + 8
= 32 square yards
Hence, the area of the shape is 32 square yards
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What is the area of the shape below?
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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.
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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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 =
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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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:
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.
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.
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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-5/8 + 1/4. Add.
Simplest form.
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
Deshaun's gas tank is 1/10 full. After he buys 6 gallons of gas, it is 2/5 full. How many gallons can Deshuan's tank hold?
Answer:
20 gallons
Step-by-step explanation:
2/5 = 4/10
3/10 = 6 gallons
1/10 = 6 : 3= 2 gallons
10/10 = 2 * 10 = 20 gallons
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)
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
What are the x and y intercepts? What do they mean in terms of the graph?
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 ?
y= 3x + a / 2x -5
express x in terms of a and y
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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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.
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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Plot the x- and y-intercepts to graph the equation. y = 1/3x + 1
The graph that shows the x- and y-intercepts to graph the equation. y = 1/3x + 1 is added as an attachment
How to plot the equation on a graph?From the question, we have the following equation that can be used in our computation:
y = 1/3x + 1
We set x = 0 to determine the y-intercept
So, we have
y = 1/3 x 0 + 1
Evaluate
y = 1
So, we have
(x, y) = (0, 1)
We set y = 0 to determine the x-intercept
So, we have
0 = 1/3x + 1
Evaluate
1/3x = -1
This gives
x = -3
So, we have
(x, y) = (-3, 0)
So, the intercepts are (0, 1) and (-3, 0)
See attachment for the graph
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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.
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.
how many copies for every 10 minutes
What is the slope of a line perpendicular to the line whose equation is 2x-12y=-120? Fully simplify your answer.
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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A delivery truck has 4 stops to make in a neighborhood. How many different sequences of stops can the driver make?
The number of different sequences of stops that the driver can make is 24.
What is permutation?Permutation is simply used it illustrate the number of ways for a given information. The formula is illustrated as:
n! / (n – r)!
N is the number of things you are choosing from,
r is the number of items.
“!” is a factorial of a number
Since the delivery truck has 4 stops to make in a neighborhood, the sequences of stops will be:
= n! / (n – r)!
= 4!
= 4 × 3 × 2
= 24 stops.
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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?
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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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
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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Express each improper fraction as a mixed or whole number
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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0.38 in expanded form
Answer:
0 + 0.30 + 0.08
Step-by-step explanation:
hope it helps :)
PLSSS HELP IF YOU TURLY KNOW THISS
Step-by-step explanation:
we have 11k + 4k.
this is like saying "I have 11 apples and then get 4 more apples - how many apples do I have ?"
in other words, how many "k" do I have ?
11 + 4 = 15.
we have 15k.
and then there is -3 + 8 = 5
so, the answer is
15k + 5
Answer:
15k + 5
Step-by-step explanation:
Now we have to,
→ Simplify the given expression.
The expression is,
→ 11k - 3 + 4k + 8
Let's simplify the expression,
→ 11k - 3 + 4k + 8
→ 11k + 4k - 3 + 8
→ (11k + 4k) + (-3 + 8)
→ (15k) + (5)
→ 15k + 5
Hence, the answer is 15k + 5.
Fractions DIDES Change this improper fraction to a mixed number. Click OK when you are done. ME 10 6 Question 3 out of 10 TUTOR-EXERCISE | what is 10 over 6 as a improper fraction??
The improper fraction of [tex]\frac{10}{6}[/tex] is [tex]1\frac{2}{3}[/tex] .
Converting [tex]\frac{10}{6}[/tex] into improper fraction,
[tex]\frac{10}{6}\\\\=\frac{5}{3}[/tex]
Divide 5 by 3, we get 1 with remainder 2
Now, write 1 as whole number , 2 as new numerator and denominator remains same i.e. 3
Now, Improper fraction is [tex]1\frac{2}{3}[/tex] .
Thus, the improper fraction of [tex]\frac{10}{6}[/tex] is [tex]1\frac{2}{3}[/tex] .
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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:’)
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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