An equation of the line that passes through the point (-3, -1) and is perpendicular to the line x - 2y = 6 is y = -2x - 7.
How to determine an equation of this line?Mathematically, the standard form of the equation of a straight line is given by this mathematical expression;
y = mx + c
Where:
m represents the slope.x and y are the points.c represents the intercept.Next, we would rewrite the given equation representing a line in standard form:
x - 2y = 6
2y = x - 6
y = x/2 - 6
Therefore, slope (m) = 1/2
In Mathematics, a condition that must be met for two lines to be perpendicular is given by:
m₁ × m₂ = -1
1/2 × m₂ = -1
m₂ = -2
At point (-3, -1), an equation of this line can be calculated by using the point-slope form:
y - y₁ = m(x - x₁)
y - (-1) = -2(x - (-3))
y + 1 = -2(x + 3)
y + 1 = -2x - 6
y = -2x - 6 - 1
y = -2x - 7
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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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Jerry watched 1 2 of a movie in the morning, and he watched ome more at night. By the end of the day, he till had 2 5 of the movie left to watch. How much of the movie did Jerry watch at night?
Jerry watched 1/10 part of the movie at night.
Given that,
Watched movie in morning = 1/2
Movie left to watch = 2/5
To find:
Movie she watch at night
Now,
Movie she watch at night= 1 - Watch movie in morning - Movie left to watch
= 1 - 1/2 - 2/5
solving the right hand side by taking LCM , we get,
= 10 - 5 - 4/10
= 1/10
∴ Movie she watch at night is 1/10.
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What is the slope of a line perpendicular to the line whose equation is x+y= 3. Fully simplify your answer.
The slope of the line perpendicular to the line whose equation is x+y = 3 is 1.
According to the question,
We have the following information:
The equation of the line:
x+y = 3
Now, we will convert this equation into the slope-intercept form:
y = -x+3
Now, slope of this line is -1.
Slope of the perpendicular line to this line = -1/m where m is the slope of the line
Slope of the perpendicular line to this line = -(-1)/1
Slope of the perpendicular line to this line = 1
Hence, the slope of the line perpendicular to the line whose equation is x+y = 3 is 1.
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38. The manufacturing cost for a certain automobile is n dollars. The manufacturer
sells the car to a retailer at 5 percent more than cost. If the retailer sells the car to a
consumer for 10 percent more than he paid for it, how many dollars does the car
cost the consumer?
(A)1.050n
(D)1.515n
(B)1. 150n
(E)1.555n
(C)1. 155n
Answer:
C) 1.155nStep-by-step explanation:
Cost price is n.
Add 5% n + 5% = n + 0.05n = 1.05nNow add 10%1.05n + 10% = 1.05n + 0.1*1.05n = 1.05n + 0.105n = 1.155nCorrect choice is C.
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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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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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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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
A student assigns a random number from 1 to 13 to simulate the value of a card drawn at random from a standard deck of playing cards. A. The simulation should model the real situation. B. The simulation might not model the real situation. The deck may not be shuffled, in which case the real situation may not be random C. The simulation will not model the real situation. The simulation must also account for the cards suit D. The simulation will not model the real situation. The simulation sould use random nubmers from 1 to 12
To simulate the value of a card drawn at random, then option A. the simulation should model the real situation.
The likelihood that something will happen is what is commonly referred to as probability. When we don't know how something will turn out, we can talk about the possibility of a few outcomes or the probability of one. A probability distribution's effect on events is the subject of statistics. Probability theory is the name of the branch of mathematics that studies probability. The concept of probability, which has many different interpretations, is formalized by probability theory through a set of axioms. The term "simple probability" refers to the process of calculating a result or the probability that an event will ever occur. By dividing one possible event by all other possible outcomes, a basic probability can be calculated.
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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.
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
please help!!!! tysm in advance
The least common denominator, LCD, for the given pair of fractions is x²- 25
Determining the least common denominatorFrom the question, we are to determine the least common denominators of the given fractions.
The given fractions are
3/x -5 and 3/x + 5
To determine the least common denominator of the fractions, we will determine the lowest common multiple of their denominators.
The denominators are x - 5 and x + 5
To do this, we will find the product of the expressions
(x -5)(x + 5)
Clear the parentheses by applying the distributive property
That is,
x(x + 5) -5(x + 5)
x² + 5x -5x - 25
x² - 25
Hence, the LCD is x² - 25
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The width of a rectangle is 7x - 1 feet and the length is 2x + 10 feet. Find the perimeter of the rectangle.
Answer:
18x +18
Step-by-step explanation:
We know the opposite sides of a rectangle are always equal, so all you need to do is double both sides and add them together.
(7x-1) + (7x-1) + (2x+10) + (2x+10) = 18x +18
What is the answer to 4r - 9r - 11r + 7r
Answer:
-11r
Step-by-step explanation:
4r - 9r = -5r
-5r - 11r = -16r
-16r + 7r = -11r
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:
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
5 cards are drawn from a standard deck without replacement. What is the probability that at least one of the cards drawn is a 3? Express your answer as a fraction or a decimal number rounded to four decimal places.
The Probability that at least one of the cards drawn is 3 is 0.3412 .
In the question ,
it is given that ,
number of cards drawn from the deck [tex]=[/tex] 5 .
total cards in the deck is [tex]=[/tex] 52 .
number of "3" cards in the deck = 4
number of cards that are not "3" = 48 .
Number of ways to draw cards that are not 3 = ⁴⁸C₅
Total number of ways to draw 5 cards from the deck = ⁵²C₅
the probability that card dawn is not 3 = ⁴⁸C₅/⁵²C₅
as the value of ⁴⁸C₅ = 1712304 and ⁵²C₅ = 2598960
= 1712304/2598960
= 0.65885
So , the probability that at least one card is 3 = 1 - (probability that no card is 3)
= 1 - 0.65885
= 0.34115
≈ 0.3412
Therefore , The Probability that at least one of the cards drawn is 3 is 0.3412 .
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HWLP ASPP PLEASE SHOW UR WORK
Answer: 1. 3
5. -3
Step-by-step explanation:
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:
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?
The diameter of a regulation soccer ball is about 8 3/5 inches. This number was graphed on a number line. Which point could he be the point representing the graph of the diameter of the ball
The number is in between 8 and 9 on the right side of the line.
The number line is a line composed of numbers from negative infinity to positive infinity.
This means all kinds of numbers, except imaginary numbers, are included including integers (whole numbers), rational and irrational numbers.
Positive numbers lie on the right side while negative numbers lie on the left side.
In this case, the first thing to do is to convert the fraction part of 8 3/5 to estimate its location in the number line.
So, 3/5 is equal to 0.6.
Thus, 8 3/5 = 8.6.
The number is thus in between 8 and 9 on the right side of the line that is a little more than the half between these numbers.
Hence the answer is the number is thus in between 8 and 9 on the right side of the line.
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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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5x+7
i need answer pls
Answer:
if all this equals with zero the answer is x= - 5/7
Step-by-step explanation:
IF it is 5x+7=0 =} 5x= -7=} x= - 5/7
Adela has 24 bracelets. She makes 3 more
each day.
Isaiah has 10 bracelets. He makes
5 more each day.
The equations represent
the number of bracelets y each person has after x days.
Adela: y = 3x + 24
Isaiah: y = 5x + 10
Use elimination to solve the system of equations.
What does the solution mean in the situation?
The solution of the system of equations is; (7, 45).
The solution in this situation means that after 7 days, Adela and Isaiah would each have 45 bracelets.
What is the solution of the system of equations?It follows from the task content that the solution to the system of equations is to be determined and interpreted accordingly.
Since the given equations are;
Adela: y = 3x + 24Isaiah: y = 5x + 10By elimination, we must subtract Isaiah's equation from Adela's so that we have;
(y - y) = (3x - 5x) + (24 - 10)
0 = -2x + 14
2x = 14; x = 7.
Consequently, y = 3 (7) + 24
y = 21 + 24; y = 45.
Consequently, the solution to the system of equations as given in the task content is; (7, 45).
This means that after 7 days, Adela and Isaiah would both have; 45 bracelets.
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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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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.
Your store cost on a loaf of bread is $0. 75, and your retail price is $3. 85. You are having a promotion which discounts the bread 20%. What is your margin on the discounted bread?.
The margin on the discounted bread is $2.33
Given,
In the question:
Your store cost on a loaf of bread is $0. 75,
and your retail price is $3. 85.
You are having a promotion which discounts the bread 20%.
To find the margin on the discounted bread.
Now, According to the question:
Given store cost on a loaf of bread is $0.75 and retail price is $3.85.
Discount is always given on retail price.
The amount of discount is 20%
Discount given on $3.85 = 20% of 3.85= .20(3.85)= 0.77.
Cost of bread after discount =3.85-0.77= 3.08
The discounted bread costs $3.08.
The difference in store cost and discounted cost = 3.08-0.75=$2.33
Hence, the margin on the discounted bread is $2.33
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Martin wants to join a book club to get discount books. Store A charges a joining fee of $75 plus $10 per book. Store B does not have a joining fee and charges $15 per book. What is the greatest number of books Martin can buy so that the total cost at Store A is less than the total cost at Store B?
Step-by-step explanation:
cost at store A :
cost(b) = 10b + 75
cost at store B :
cosr(b) = 15b
b = the number of books bought.
to answer the question find for what b both functions deliver the same result :
10b + 75 = 15b
75 = 5b
b = 15
when buying the 15th book both costs are the same.
to keep the costs of store A truly less than the costs of store B the limit is therefore 14 books.
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