After finding the ratio for each person, Ben will get $72
What is a Ratio?
A ratio shows the relative sizes of two or more values. Ratios can be shown in different ways:
using the ":" to separate example valuesusing the "/" to separate one value from the totalas a decimal, after dividing one value by the totalas a percentage, after dividing one value by the totalIt was given that Alice, Ben and Charlie are to share $213.
Ratio of Alice's share to Ben = 4 : 3
Ratio of Ben's share to Charlie = 8 : 5
Combining these ratios, their shared item (Ben's share) must be the same in each ratio.
Taking Alice's share to Ben, 4 : 3 and multiplying both parts by 8 to get an equivalent ratio, we have:
Alice : Ben = 4(8) : 3(8) = 32 : 24
Likewise, taking Ben's share to Charlie, 8 : 5 and multiplying both parts by 3, we have:
Ben : Charlie = 8(3) : 5(3) = 24 : 15
Combining these ratios, we have:
Alice : Ben : Charlie = 32 : 24 : 15
Adding the ratios together, we have: 32 + 24 + 15 = 71
If the money to be shared is $213, Ben's share will be:
[tex]\frac{24}{71}[/tex] × [tex]$213[/tex] = 72
Therefore, Ben will get $72 from the total amount of $213
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i really need help. Strawberries cost $2.13 per pound and Annie purchased 1.2 pounds. How much did she pay for strawberries if her answer is rounded to the nearest cent?
Annie paid a total of $2.6 for 1.2 pounds of strawberries
How to determine the amount paid?In this question, we have the following parameters:
Unit cost per pound = $2.13 per pound
Number of pounds = 1.2 pounds
The amount paid for the number of pounds is represented by the equation
Amount paid = Unit cost per pound x Number of pounds
Substitute the known values in the above equation So, we have the following equation
Amount paid = 2.13 * 1.2
Evaluate the products
Amount paid = 2.556
Approximate
Amount paid = 2.6
Hence, the amount is $2.6
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Answer:
2.56
Step-by-step explanation:
Wyatt says that both red lines are lines of symmetry. Is he correct? Why or why not?
Answer:
Step-by-step explanation:
There is only one line of symmetry:
because the one that is vertical is not representing symmetry.
If a gallon of paint costs $18 and covers 180 ft²,
how much does it cost to paint a 900 ft² wall
Answer:
$90
Step-by-step explanation:
180x5 equal 00
$18x5 equals $90
Does the function y=x have an inverse? If so does it pass the horizontal line test?
Yes, y=x has an inverse.
Yes, y=x passes the horizontal line test.
If it didn't pass the horizontal line test, it would not have an inverse.
The 10 number from one to 10 are plit into two group. The um of the number in one group i N, and the product of the number in the other group i N. What i the larget poible value of N?
The largest possible value of N is 42, which is equal to the sum of numbers of one group and product of numbers of other group.
We have provided the following informations,
total number = 10 and possible numbers are,
S = {1, 2,3,4,5,6,7,8,9,10}
Now, we have to split the 10 numbers into two groups. The conditions for group making are
Sum of number in one group is Nproduct of the number of other group is Nmaximum possible sum of numbers from S is 55.
because given numbers are in A.P and sum of A 10 terms is 55 in A.P.
but according to question, t the maximum possible value of N which follow the conditions is 42.
we can splits the set S elements in two groups such that one is P={6,7} and other one Q={ 1,2,3,4,5,8,9,10}
sum of numbers of Q is 42 and product of second group (P) = 42
No other value of N greater than 42 is possible for N .
Hence, 42 is largest possible value of N.
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You have $18 and earn $0.25 for each cup of orange juice you sell. Write an equation that represents the total amount A (in dollars) you have after selling j cups of orange juice.
Answer:
A = 0.25*j + 1
Step-by-step explanation:
Answer:
[tex]A = 18 + \frac{j}{4}[/tex]
Step-by-step explanation:
A = 18 + j/4
A = Amount in $
Starting amount is 18 and a 1/4 dollar is earned for every cup of juice sold.
A cubic polynomial function f has a leading coefficient of 2 and a constant term of -5. When f(1) is zero and f(2) is three what is f(-5). Explain?
The value of f(-5) = -130
A cubic equation is an equation with degree three. All cubic equations have either one real root and two imaginary roots or three real roots. When polynomials have degree three, they are referred to as cubic polynomials.
A Cubic polynomial function is a polynomial function with the highest degree of exponents as 3. A cubic polynomial function has the following standard form:
Ax3 + bx2 + cx +d = 0
For the given question the cubic equation will be:
2x3 + bx2 + cx - 5 = 0
Given
Leading coefficient (a) = 2
Constant (T) = -5
f(1) = 0
f(2) = 9
Therefore the equation formed will be:
2x3 + bx2 + cx - 5 = 0
Now f(1) = 0
2(1)3 + b(1)2 + c(1) - 5 = 0
2 + b + c -5 = 0
b + c = 3
b = 3-c -----(1)
On solving f(2) = 3
2(2)3 + b(2)2 + c(2) - 5 =3
16 + 4b + 2c – 5 =3
4b +2c = 3 – 11
4b + 2c = -8 ----(2)
Now substitute the b value in equation (2)
4(3-c) + 2c = -8
12 – 4c +2c = -8
-2c = -20
C =10
Now substitute the c value in equation (1)
b= 3 – c
b = 3 -10
b = -7
Now substitute the b and c values in the cubic equation
2x3 - 7x2 + 10x - 5 = 0
Now calculate f(-5)
2(-5)3 - 7(-5)2 + 10(-5) - 5
= -250 + 175 – 50 -5
= -130
Therefore the value of f(-5) = -130
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Callie has a rope that is 14.7 inches long. She cuts the rope into 3 pieces. If each piece is the same length, how long is each piece of rope?
Answer:
Each piece will be 4.9 inches long
Step-by-step explanation:
All you have to do is divide 14.7 by three as the rope itself is cut into 3 equal parts
therefore: 14.7/ 3= 4.9
what is the vertex of -2x^2 +12x -10
The vertex of the function f(x) = x^2 + 12x is (-6, -36).
How can the vertex be expressed?The concept that will be used here is the concept of Standard equation of a curve in vertex form.
The standard equation can be written as
f (x) = ax^2 + bx + c
Then the Vertex is the (h,k)
Then the X-coordinate of the vertex can be written as (h = -b/2a) where k = f(h)
If we compare the given equation with the standard form, then we have
a = 1, b = 12 and c = -10
Then we can input the values into the (h = -b/2a)
h =[ -12/2(1)] = - 6
Then we can substitute the value of h in f (x) which is f(x) = x2 + 12x
k = f(h)= f (-6) =[ (-6)2 + 12 (-6)]
= [36 - 72] = -36
In conclusion the vertex is (-6, -36).
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HWLP ASPP PLEASE SHOW UR WORK
Answer: 1. 3
5. -3
Step-by-step explanation:
Which of the following represents the series?
–12 + (–5) + 2 + 9 + 16
sum from k equals 0 to 4 of negative 19 plus 7 times k
sum from k equals 1 to 5 of negative 19 minus 7 times k
sum from k equals 0 to 4 of negative 12 plus 7 times k
sum from k equals 1 to 5 of negative 12 minus 7 times k
(image includes proper visuals for each option)
The expression that represents the sum of the arithmetic series that has a first term of -12, a common difference of +7 and a number of terms of 5 is the option with the following;
[tex]\sum\limits_{k = 0}^4-12+7\cdot k[/tex]What is an arithmetic series?An arithmetic series one that consists of the sum of an arithmetic sequence, such that each term of the series is obtained from the previous term by the addition or subtraction of a constant.
The series in the question is; -12 + (-5) + 2 + 9 + 16
Each term in the series is obtained from the previous term by the addition of a 7The series in therefore a series of an arithmetic sequence
The equation of the series when the first term is -12 can therefore be presented as follows;
-12 + 7·k
Where;
-12 is the first term, 7 is the common difference, n is the number of terms, and k = n - 1
When n = 1, k = 0, which gives;When k = 0, the expression, -12 + 7·k = -12 + 7 × 0 = -12When k = 1, -12 + 7·k = -12 + 7 × 1 = -5When k = 2, -12 + 7·k = -12 + 7 × 2 = 2When k = 3, -12 + 7·k = -12 + 7 × 3 = 9When k = 4, -12 + 7·k = -12 + 7 × 4 = 16The above values for the terms of the series is obtained by using values of k that range from k = 0 to k = 4
The expression that represents the series is therefore the option;
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the united nations stores data about the kilowatt-hours of wind power produced around the world. the following data set gives information of the united states for 25 years, from 1990 to 2014, in units of million kilowatt-hours. using a calculator or statistical software, find the linear equation of the first 11 years of data, from 1990 to 2000. round the slope to two decimal places and the y-intercept to the nearest whole number. provide your answer below:
The value that the linear equation predicts for the year 2001 is 4652.15
The discrepancy between the actual and anticipated value is 2173.85
Given data;
Here, we present the dataset from the United Nations, which contains information on the number of kilowatt-hours of wind energy generated globally. The data set provides statistics on the US for 25 years, from 1990 to 2014, in millions of kilowatt-hours.
The linear equation for the first 11 years of data, from 1990 to 2000, must be determined.
To determine how much the actual value and anticipated value for the year 2001 differ in Quantity, we must first forecast the value for the year 2001 using our fitted equation with y-intercept.
It will be written as y = m(x) + c.
where,
The dependent variable is y. (in our example is quantity)
The independent variable is x. (in our example is the year)
'm' is equal to the slope of the variable X.
'C' is a constant.
The fitted equation is provided as follows:
Quantity = 186.87 (year) - 369274.72
Now that the value for the year 2001 has been provided,
Quantity = -1868.87 -369274.72
Quantity = 4652.15
The value that the linear equation predicts for the year 2001 is 4652.15.
The precise figure for 2001 is 6806.
For the year 2001, the discrepancy between the actual and anticipated values is
6806 - 4652.15 = 2173.85
The distinction is 2173.85.
(2173.85/6806)*100 is the percentage difference.
As a result, the difference between the actual value and the forecasted value for the year 2001 is 31.94%.
Hence,
The value that the linear equation predicts for the year 2001 is 4652.15
The discrepancy between the actual and anticipated value is 2173.85
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the 6th term of an arithmetic progreion i 35 and the 13th term i 77. find the 20th term
The 20th term of the given arithmetic progression is 119.
What is arithmetic progression?An arithmetic progression is a set of integers with a fixed difference between any two succeeding numbers (A.P.).
3,6,9,12,15,18, and 21 are A.P. examples.
So, the formula for the nth term:
a+(n-1)d, where d is the common difference
Now, take out the equation:
6th term = 35
a+(6-1)d= 35
a+5d=35 ....(1)
13th term = 77
a+12d= 77 .....(2)
Then, subtract equation (1) from equation (2):
a+12d-(a+5d)= 77-35
a+12d-a-5d= 42
7d=42
d=6
Calculate from equation (1):
a= 35-5d= 35-5(6)= 35-30 = 5
20th term= a+19d= 5+19(6)= 119
Therefore, the 20th term of the given arithmetic progression is 119.
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Find the surface area and volume of each triangular prism (base is a right triangle).
triangle legs are 3 ft and 4 ft, hypotenuse is 5 ft, height of prism is 8 ft
The surface area of a triangular prism = 108cm2
The volume of the triangular prism = 48cm3
The space occupied by a two-dimensional flat surface is called the area. It is measured in square units. The area occupied by a three-dimensional object by its outer surface is called the surface area.
Given that
The Triangle legs are 3 and 4 feet long, the hypotenuse is 5 feet long, and the prism height is 8 feet tall.
We have to determine the surface area and volume of each triangular prism
here a = 3ft b = 4ft c = 5ft and height h = 8ft
Surface area of triangular prism = ab + h(a+b+c)
= 3x4 + 8(3+4+5)
= 12 + 8(12)
= 12 + 96
= 108cm2
Volume of triangular prism = ½(abh)
= ½ (3x4x8)
=1/2(96)
= 96/2
= 48cm3
Therefore
The surface area of a triangular prism = 108cm2
The volume of the triangular prism = 48cm3
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Part A: Without calculating the values, compare the expressions using <, >, or =.
Write the correct symbol. Draw a model if it helps you.
(5+15)x13
31×(15+5)
The difference between 15 fours and
6 fours.
The sum of 4 fours and 5
fours
Part B: Explain how you compared the expressions without calculating.
The amount of cookies baked was 28 cookies
Solution for how many cookies your mother bake altogetherlet the number of pumpkin cookies be x
half of them on a plate for your brother and you
= x - x/2 = x/2
Your dog Gobbles ate six
= x/2 - 6
Your brother ate half of what was left
= (x/2 - 6)) / 2
= x/4 - 3
you ate the last four means that what was left is equal to 4
x/4 - 3 = 4
x - 12 = 16
x = 16 + 12
x = 28
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In the diagram below of triangle
F
G
H
FGH,
I
I is the midpoint of
F
H
‾
FH
and
J
J is the midpoint of
G
H
‾
GH
. If m
∠
H
F
G
=
57
−
6
x
∠HFG=57−6x, and m
∠
H
I
J
=
−
4
x
+
49
∠HIJ=−4x+49, what is the measure of
∠
H
I
J
∠HIJ
Applying the corresponding angles theorem, the measure of ∠HIJ = 33°.
What is the Corresponding Angles Theorem?If two triangles are similar to each other, their corresponding angles would be equal. Also, based on the corresponding angles theorem, corresponding angles are equal to each other.
Triangles IHJ and FGH are similar to each other, therefore, angles HFG and HIJ are corresponding angles.
Therefore:
The measure of angle HFG = the measure of angle HIJ
m∠HFG = 57 − 6x
m∠HIJ = −4x + 49
Thus:
57 − 6x = -4x + 49
Combine like terms
4x - 6x = -57 + 49
-2x = -8
Divide both sides by -2
-2x/-2 = -8/-2
x = 4
m∠HIJ = −4x + 49 = -4(4) + 49
m∠HIJ = 33°
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Complete Question:
In the diagram below of triangle FGH, I is the midpoint of FH and J is the midpoint of GH. If m∠HFG = 57 − 6x, and m∠HIJ = −4x + 49, what is the measure of ∠HIJ?
A family buys a studio apartment for 150,000. They pay a down payment of $22,500. a.Their down payment is what percent of the purchase price?
b. What percent of the purchase price would a $60,000 down payment be?
please help!!!
polynomial function
Answer: (2x+1)(x−3) ( 2 x + 1 ) ( x - 3 )
Step-by-step explanation:
To write a polynomial in standard form, simplify and then arrange the terms in descending order. Expand (2x+1)(x−3) ( 2 x + 1 ) ( x - 3 ) using the FOIL Method.
Help please
I need this by tomorrow
Answer:
I hope this will help. Tip: reuse the formula!
Please help me solve it WITHOUT THE USE OF A GRAPHING CALCULATOR OR ANY ONLINE TOOL.
Answer:
a) See attached (sorry if its a bit unneat, use 5 points for more accuracy while drawing. 3 points is generally accepted though.)
b) 80 mins
c) 4000 meters, 40 minutes
Step-by-step explanation:
First, lets define the literal meaning of the questions.
A) Graph the function (I will explain how to do below)
B) What is the absolute value of the distance of the x-intercepts?
C) What is the y value of the vertex (maximum/ minimum value). What is the x value of the vertex?
Lets solve these problems. To graph a quadratic equation by hand, first you must find the vertex. Formula for the x-value of the vertex:
[tex]\frac{-b}{2a}[/tex]
Because a quadratic equation is in the form:
[tex]ax^2 + bx + c = 0[/tex]
We can find the values of a and b.
Values of a and b in this equation:
a: -2.5
b: 200
Plug into the vertex formula (shown above), -b/2a
[tex]\frac{(-)(200)}{(2)(-2.5)}[/tex]
Simplify.
[tex]\frac{-200}{-5}[/tex]
Simplify.
-200/-5 = 40
Now we have 40, the x value of the vertex. Plug 40 back into the x values of the problem (t in this word problem) to find the y value of the vertex.
The equation:
[tex]h=-2.5t^2+200t[/tex]
Plug in 40 to the t values.
[tex]h = -2.5(40)^2 + 200(40)[/tex]
Simplify.
[tex]h = -4000 + 8000[/tex]
Add.
h = 4000
Now, we have the values of the vertex.
Values of vertex:
x: 40
y: 4000
This means that when the x-value is 40, the y-value is 4000. In this case, it means 40 minutes in, the altitude of the plane is 4000 meters.
On a graph, draw a point at x-value 40 and y-value 4000. This will be needed when we draw the graph.
We need at least 3 points to graph a quadratic equation (this applies to all parabolas.)
This part is a bit hard to explain, but you will get it with this example. Since we need 3 points, we need to solve for 2 more points like we just did. But what x-values do we use? For the vertex, we knew the x value was -b/2a!
Solve for x-values that have an equivalent absolute distance from the x value of the vertex.
For example, in this case, the x value of the vertex is 40.
If we were to pick the x value of 38 for the 2nd point, we would have to use the 42 for the 3rd point as they are both 2 away from 40.
|40-38| = 2
|40-42| = 2
I will use the x values of 38 and 42 to graph this. Lets do the same thing we did to find the y value of the vertex. Plug the x values into the equation individually.
Equation:
[tex]h=-2.5t^2+200t[/tex]
Plug in 38 to the x values (in this case its called t.)
[tex]h = -2.5(38)^2 + 200(38)[/tex]
Simplify.
h = -3610 + 7600
Add.
h = 3990
This means when the x value of the parabola is 38, the y value is 3990. In this case, it means after the plane has flown for 38 minutes, the altitude of the plane is 3990.
Now lets find what the y-value of the parabola would be when the x-value is 42 (when we've did this, we can graph it.)
But here is a little trick to speeden things up. If the absolute value of the difference of the x-value of the vertex (40 in this case) and the x value of the point we just found (38 in this case) is the same as the absolute value of the difference of the 3rd point we need to graph (42 in this case), which is always true if you followed the steps above, the y value is the same!
So, this means, when:
Point 2:
x: 38
y: 3990
Point 3:
x: 42
y: 3990
The y-value of the 3rd point we need to find is 3990.
Now we can graph it using our points.
Point 1 (Vertex):
x: 40
y: 4000
Point 2:
x: 38
y: 3990
Point 3:
x: 42
y: 3990
I'll just use paint to draw this, draw the points, label them, and connect the points with a parabola.
Now lets answer b using the definitions.
Because we need to find the x intercepts, lets use the quadratic formula.
[tex]\frac{ -b± \sqrt{b^2-4ac}}{2a}[/tex]
Ignore the A's, its a bug.
If you need to know how to use the quadratic equation, DM me. Otherwise, I will just write the x-intercepts.
x-intercepts:
0,80
Because it is asking for the distance between Toronto and Montreal in minutes, subtract 0 from 80.
80-0=80
B) 80 minutes
The maximum height of the aircraft is the y value of the vertex and the time that the aircraft reaches this height is the x-value of the intercept.
(Vertex):
x: 40
y: 4000
C) 4000 meters, 40 minutes
Answer:
a) See attached.
b) 80 minutes
c) Maximum height = 4000 m
Time = 40 minutes
Step-by-step explanation:
Given function:
[tex]h=-2.5t^2+200t[/tex]
where:
h is the height of the aircraft, in metres.t is the time, in minutes.Part a)The function is quadratic, which means the graph of the function is a parabola.
Axis of Symmetry
A parabola has perfect symmetry.
For a quadratic in the form [tex]ax^2+bx+c[/tex], its axis of symmetry is:
[tex]\boxed{x=-\dfrac{b}{2a}}[/tex]
Therefore, the axis of symmetry for the given function is:
[tex]x=-\dfrac{200}{2(-2.5)}=40[/tex]
Vertex
As the leading coefficient is negative, the parabola opens downwards.
Therefore, the vertex is the maximum point of the parabola.
The axis of symmetry is the x-value of the vertex.
Substitute t = 40 into the given function to find the y-value of the vertex:
[tex]\implies h(40)=-2.5(40)^2+200(40)[/tex]
[tex]\implies h(40)=4000[/tex]
Therefore, the vertex of the function is (40, 4000).
x-intercepts
To find the x-intercepts of the function, set the function to zero and solve for t:
[tex]\implies -2.5t^2+200t=0[/tex]
[tex]\implies -2.5t(t-80)=0[/tex]
Therefore:
[tex]\implies -2.5t=0 \implies t=0[/tex]
[tex]\implies t-80=0 \implies t=80[/tex]
Therefore, the x-intercepts are (0, 0) and (0, 80).
Graphing the function
Draw a coordinate plane where the axis scale is:
x-axis : y-axis = 1 : 100Plot:
Vertex = (40, 4000)Axis of symmetry: x = 40x-intercepts: (0, 0) and (0, 80)Draw a curve, symmetric about the axis of symmetry, that passes through the vertex and the x-intercepts.
Part b)When the aircraft is in Toronto and Montreal, the height of the aircraft is zero.
The time at which the height of the aircraft is zero is t = 0 and t = 80 (from part a). Therefore, the time it takes to fly from Toronto to Montreal is the difference between the two times:
[tex]\implies 80-0=80\; \sf minutes[/tex]
Part c)The maximum height of the aircraft is the y-value of the vertex of the parabola.
Therefore, as the vertex of the parabola is (40, 4000), the maximum height of the aircraft is 4000 m.
The maximum height is reached 40 minutes after the aircraft leaves Toronto.
find the middle side of each triangle. round your answers to the nearest tenth if necessary.
Step-by-step explanation:
using Pythagoras theorem.
37,
x² = 6² + 8²
x = √6²+8² = 10ft
38.
13²=12²+x²
169 = 144 + x²
√169 - 144 = x = 5cm
hope it helps. :)
Answer:
x = 10 and x = 5
Step-by-step explanation:
using Pythagoras' identity
the square on the hypotenuse is equal to the sum of the squares on the other 2 sides.
(36)
x² = 6² + 8² = 36 + 64 = 100 ( take square root of both sides )
x = [tex]\sqrt{100}[/tex] = 10
(38)
13² = x² + 12²
169 = x² + 144 ( subtract 144 from both sides )
25 = x² ( take square root of both sides )
[tex]\sqrt{25}[/tex] = 5 = x
x = 5
Please help F(-1/2)=1 and f(0)=-4
Question:
Write a linear function f with f (- 1/2) = 1 and f (0) = -4
The linear function f with f (- 1/2) = 1 and f (0) = -4 would be ; y = -5x -4.
What is a linear equation?
A linear equation is an equation in which each term has at max one degree. Linear equations in variables x and y can be written in the form
y = mx + c
Linear equation with two variables, when graphed on the cartesian plane with axes of those variables, give a straight line.
We are asked to write the linear function f with f (- 1/2) = 1 and f (0) = -4
Let the equation in variables x and y can be written in the form y = mx + c
So f (- 1/2) = 1
this gives, 1 = -1/2m+c -----------eq 1
Also f (0) = -4
This gives -4 = c. --------------eq2
Now Putting the value of c in the equation in eq1 we get m=0.
So 1 = -1/2m+c
1 = -1/2m - 4
m = -5
Then we get;
y = -5x -4.
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PLEASE HELP, QUESTION IN THE PICTURE
Step-by-step explanation:
AC is the combination of AB and BC.
so, AB + BC = AC
(2n - 1) + (4n + 5) = 10n - 12
2n - 1 + 4n + 5 = 10n - 12
6n + 4 = 10n - 12
4 = 4n - 12
16 = 4n
n = 4
What is the answer to this question
Answer:
soda: 97
Hot dogs: 56
Step-by-step explanation:
S-sodas
H- hot dogs
S+H=153
41+H=S
Substitute equation
(41+H)+H=153
41+2H=153
-41. -41
2H=112
/2. /2
H=56
S+56=153
-56. -56
S=97
Hopes this helps please mark brainliest
what's the slope of 6x+13y= -18
Answer:
slope is the coefficient of x
so it is 6
good luck!!
if a farm has 30 chickens and cows and there are 82 chicken and cows legs all together then how many chickens and how many cows could the farm have?
Answer: 11 cows and 19 chickens
Step-by-step explanation:
Point B' is the image of point B after a reflection in a line. Write an equation of the line.
B(2, -4), B'(6, -4)
Answer:
x = 4
Step-by-step explanation:
which of the following fractions is smaller 4/9 or 1/5
Answer:
1/5
Step-by-step explanation:
these fractions are proper fractions
Answer: 1/
Step-by-step explanation:
What is the answer to 4r - 9r - 11r + 7r
Answer:
-11r
Step-by-step explanation:
4r - 9r = -5r
-5r - 11r = -16r
-16r + 7r = -11r
algebra 2 please help :)!