Step-by-step explanation:
Using squares of integers numbers, it is found that the solution of the equation is located between the integers x = 1 and x = 2.
The equation given is:
x^2=3
The solution of the equation given is:
X=√3
The squares of the integers numbers until the square root of 3 are:
1^2=1
2^2=4
Since , the square root of 3, which is the solution to the equation, is located between the integers x = 1 and x = 2.
Use the method of completing the square to write the equation of the given parabola in this form:
(y-k)=a(x-h)²
where a≠ 0,(b, k) is the vertex, and x=h is the axis of symmetry.
Find the x-intercepts of the parabola with vertex (6,-5) and y-intercept (0,175). Write your answer in this form: x₁, y₁),(x₂, y₂). If necessary, round to the nearest hundredth.
The x-intercepts of the parabola are (x₁, y₁) = (6.67, 0) and (x₂, y₂) = (5.33, 0).
What is the equation of a parabola?
The general equation of a parabola is given by y = a(x – h)2 + k or x = a(y – k)2 +h. Here (h, k) denotes the vertex.
To write the equation of the given parabola in the desired form, we can complete the square.
The equation of a parabola with vertex at (h, k) and axis of symmetry x = h is given by:
y = a(x - h)^2 + k
where a is a nonzero constant.
In this case, the vertex is (6, -5) and the y-intercept is (0, 175), so the equation of the parabola is of the form:
y = a(x - 6)^2 - 5
Substituting the y-intercept, we have:
175 = a(0 - 6)^2 - 5
Solving for a, we find that a = 15/4.
Thus, the equation of the parabola is:
y = 15/4(x - 6)^2 - 5
To find the x-intercepts, we need to find the values of x such that y = 0. Substituting y = 0 into the equation of the parabola, we have:
0 = 15/4(x - 6)^2 - 5
Adding 5 to both sides, we have:
5 = 15/4(x - 6)^2
Dividing both sides by 15/4, we have:
4/15 = (x - 6)^2
Taking the square root of both sides, we have:
x - 6 = +/- 2/3
Thus, the x-intercepts are at x = 6 +/- 2/3.
Therefore, the x-intercepts of the parabola are (x₁, y₁) = (6 + 2/3, 0) and (x₂, y₂) = (6 - 2/3, 0).
Rounded to the nearest hundredth, the x-intercepts are (x₁, y₁) = (6.67, 0) and (x₂, y₂) = (5.33, 0).
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Tamala’s school day is 7 1/2 hours. She has six classes that are 7/6 of an hour long each. How many hours is Tamala not in class while she is at school?
By simplifying and solving, Tamala is not in class while she is at school is 0.5 hour.
What is Algebraic simplification?Algebraic simplification is the process of rewriting an algebraic expression in a simpler form, without changing its value.
What is algebra?Algebra is a branch of mathematics that involves the use of letters and symbols to represent unknown quantities, known as variables, in equations and formulas.
Tamala is in class for 6 * (7/6) = 7 hours.
Tamala is not in class for 7(1/2) - 7 = 1/2 hours.
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Johnny oeders 5 cheese pizzas and 6 pepperoni pizzas for his son's birthday party. He paid $136. Mid party he realized he was going to run out of pizzaz, so he decided to place a second order. This time johnny ordered 2 cheese pizzas and 2 pepperoni pizzas and paid $49.00. Write a linear system that could be used to find the cost of each type of pizza?
Step-by-step explanation:
Let x = cost of cheese pizza
Let y = cost of pepperoni pizza
x + 6y = 136
2x + 2y = 49
Solve the system:
x = $14
y = $15
You volunteer to help drive children at a charity event to the zoo, but you
can fit only 6 of the 18 children present in your van. How many different
groups of 6 children can
you
drive?
18,564 different groups of 6 children can be driven.
Here we are given 18 Children in total and we can fit Only 6 Children out of them.
The number of different groups of 6 children that can fit into the van ca be calculated with a simple formula
The formula used will be -
n! = n(n-1)(n-2)(n-3).......1
n!= (18 x 17 x 16 x 15 x 14 x 13) / (6 x 5 x 4 x 3 x 2)
= 18,564
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Find the equation of the line joining the points (2,-8) and (5,6)
The equation of the line joining the points (2,-8) and (5,6) is y = 14 / 3 x - 52 / 3
How to find the equation of a line?The equation of a line in slope intercept form can be represented as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, the equation of the line passes through the points (2,-8) and (5,6). Let's find the slope.
m = 6 + 8 / 5 - 2
m = 14 / 3
Let's find the y-intercept using (5, 6).
y = 14 / 3 x + b
6 = 14 / 3 (5) + b
6 = 70 / 3 + b
b = 6 - 70 / 3
b = 18 - 70/ 3
b = -52 / 3
Therefore, the equation is y = 14 / 3 x - 52 / 3
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A superball is dropped from a height of h feet and left to bounce forever. The rebound ratio of the ball is r. In terms of r and h. find the formula for the total time needed for all this bouncing to take place.
Answer:
a b c or d?
Step-by-step explanation:
Answer: If a superball is dropped from a height of h feet and left to bounce forever, the total time needed for all this bouncing to take place can be represented by the formula:
t = h / (r - 1)
where t is the total time, h is the height from which the ball is dropped, and r is the rebound ratio of the ball.
The rebound ratio of the ball is the fraction of the ball's initial height that it bounces back up after each bounce. For example, if a ball has a rebound ratio of 0.5, it will bounce back up to half its initial height after each bounce.
The total time needed for the ball to bounce forever is equal to the height from which the ball is dropped divided by the difference between the rebound ratio and 1. This is because the ball will bounce back up a fraction of its initial height after each bounce, and the total time needed for all the bounces to take place is determined by the difference between the height of the ball and the fraction of the height that it bounces back up.
Hi i need this for noooow please
The y-intercept is the point the graph intersects the y-axis. It is represented by the constant c in the equation of a straight line graph, y = m·x + c
6. The y-intercept is 7
8. The y-intercept is 0
12 a. The error is taking the x-intercept as the y-intercept
b. Please find attached the graph of line with a y-intercept of 3 drawn with MS Excel
What is a straight line graph?A straight line graph is the graph of a linear equation.
The slope-intercept form of the equation of a straight line graph is y = m·x + c, where;
m = The slope of the graph
c = The y-intercept
6 The y-intercept is the point the graph crosses the y-axis.
The line crosses the y-axis at the point (0, 7)
The y-intercept is 78. The point at which the graph crosses the y-axis is (0, 0)
The y-intercept, which is the point at which the graph crosses the y-axis, from the graph of question 8 is 012. The graph in the question is a straight line graph that passes through the points (3, 0), and (0, -4)
The x-intercept of the graph is 3
The y-intercept of the graph is -4
a. The possible error of the graph that is an example of a line with a y-intercept of 3 is therefore, mistaking the y-intercept for the x-intercept
b. Please find attached the graph of the line y = x + 3 that has a y-intercept of 3 drawn with MS Excel on the graph of the question with equation y = (4/3)·x - 4
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mathe help needed easy graphing
Answer:
y = 2.5x
Step-by-step explanation:
When the relationship is proportional you can find the slope (or unit rate) by taking any point in the form y/x
20/8 = 2.5
30/12 = 2.5
This will work of every point n the line.
which of the following two pairs of sets have the same cardinality? question 9 options: natural numbers and irrational numbers integers and natural numbers real numbers and rational numbers irrational numbers and rational numbers
Natural numbers and irrational numbers are two pairs of sets that have the same cardinality.
It is sufficient to demonstrate the existence of a bijection between the set of real numbers R and the set of irrational numbers RQ in order to demonstrate that both have the same cardinality:
For each positive integer n, map n to 2n to produce a countable number of holes in R. Be aware that these countable holes are located at all irrational locations (2n-1), as well. R should be mapped to itself. R should be mapped to itself. Feel free to use your preferred irrational number in the above in place of [tex]\pi[/tex].
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The time married men with children spend on child care averages 6.0 hours per week. You belong to a professional group on family practices that would like to do its own study to determine if the time married men in your area spend on child care per week differs from the reported mean of 6.0 hours per week. A sample of 40 married couples will be used with the data collected showing the hours per week the husband spends on child care. The sample data are contained in the table below. 1.4 4.9 8.5 5.2 10.2 2.6 7.2 2.6 11.1 10.6 2.3 7.8 1.8 8.7 2.1 4.5 5.3 3.5 8.8 6.7 2.9 10.8 8.4 4.9 5.7 9.8 0.9 11.9 3.5 8.7 6.5 6.5 2.0 9.7 a. What are the hypotheses if your group would like to determine if the population mean number of hours married men are spending in child care differs from the mean reported in your area? H : HA: # Ag b. What is the sample mean (to 1 decimal)? Calculate the value of the test statistic (to 2 decimals). What is the p-value? greater than .207 c. Select your own level of significance. What is your conclusion? Do not reject the null. We don't have enough evidence to disprove the reported time.
The null hypothesis (H0) would be that the population mean number of hours married men in your area spend on child care per week is equal to the reported mean of 6.0 hours per week.
The population mean number is equal to the reported mean according to null hypothesis. The alternative hypothesis (HA) would be that the population mean differs from the reported mean.
H0: μ = 6.0 hours/week
HA: μ ≠ 6.0 hours/week
b. To find the sample mean, we need to add up all of the values in the sample and divide by the number of values. The sample mean is 6.34 hours/week.
To calculate the test statistic, we can use the formula:
t = (x' - μ0) / (s / √n)
where x' is the sample mean, μ0 is the hypothesized mean (in this case, 6.0 hours/week), s is the sample standard deviation, and n is the sample size.
Plugging in the values, we get:
t = (6.34 - 6.0) / (3.23 / √40) = 0.34 / (0.53 / 6.32) = 0.34 / 0.08 = 4.25
The p-value is the probability of getting a result as extreme as the one we observed, given that the null hypothesis is true. In this case, we would need to use a t-distribution table or a computer program to find the p-value, since the sample size is small and the population standard deviation is unknown.
c. If we select a level of significance of 0.05, then we can use the p-value to make a decision about the null hypothesis. If the p-value is less than 0.05, we would reject the null hypothesis and conclude that the population mean differs from the reported mean. If the p-value is greater than 0.05, we do not have enough evidence to reject the null hypothesis and would conclude that the population mean is likely to be the same as the reported mean.
In this case, the p-value is greater than 0.207, so we do not have enough evidence to reject the null hypothesis. We would conclude that the population mean number of hours married men in your area spend on child care per week is likely to be the same as the reported mean of 6.0 hours per week.
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Question 1 of 10
What is the value of x ?
A. 160°
B. 50°
C. 55°
D. 20°
Answer:
it is B
Eplanation:
180-155=75 (straight line add up 180 degrees)
75+55+x=180
130+x=180(angles in triangle also add up 180 degrees)
x=180-130(rearranging formula)
x=50, which is option letter B
4. An equilateral triangle and an isosceles triangle share a common side. What is the measure of ∠ A B C?
Answer:
∠ABC = 98°
Step-by-step explanation:
an isosceles triangles base angles have the same angle measures
so both are 71
add them and then subtract that from 180 to find ∠ABD
180 - (71 + 71)
180 - 142 = 38
that is ∠ABD
to find ∠ABC you must add ∠DBC to ∠ABD
all angles of an equilateral triangle are equivalent
they are also 60 degrees
so add 60 to 38
38 + 60 = 98
that is your answer
What is the remainder that the number 10^2023 leaves after division by 13?
Applying the property of exponents, the remainder that the number 10^2023 leaves after division by 13 is 9.
What is remainder?The remainder is the amount left over after a division operation.
What is exponent?An exponent is a number that indicates how many times a base number is used as a factor in a multiplication expression.
From the property of exponent:
We can rewrite 10^2023 as (10^13)^155 * 10^8:
10^2023 = (10^13)^155 * 10^8
We can then use the property of exponents to simplify:
10^2023 = (10^(13*155)) * 10^8
Since 10^13 is congruent to 1 mod 13, 10^(13*155) is congruent to 1 mod 13 as well. Therefore, 10^2023 is congruent to 10^8 mod 13.
We can find the remainder by calculating 10^8 mod 13:
10^8 = 100000000
After dividing 100000000 by 13, we get a remainder of 9.
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Jai and Keilantra are both driving along the same highway in two different cars to a
stadium in a distant city. At noon, Jai is 254 miles away from the stadium and
Keilantra is 293 miles away from the stadium. Jai is driving along the highway at a
speed of 41 miles per hour and Keilantra is driving at speed of 54 miles per hour. Let
J represent Jai's distance, in miles, away from the stadium & hours after noon. Let K
represent Keilantra's distance, in miles, away from the stadium t hours after noon.
Write an equation for each situation, in terms of t, and determine the number hours
after noon, t, when Jai and Keilantra are the same distance from the stadium.
The number of hours when Jai and Keilantra are the same distance from the stadium is 3 hours.
How to calculate the equation?Jai is 254 miles away from the stadium. Jai is driving along the highway at a speed of 41 miles per hour. This will be:
254 - 41h
Keilantra is 293 miles away from the stadium. Keilantra is driving at speed of 54 miles per hour. This will be:
293 - 54h
The equations will be:
254 - 41h = 293 - 54h
54h - 41h = 293 - 254
13h = 39
Divide
h = 39/13
h = 3
The number of hours is 3 hours.
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Deandre has a large collection of movies on DVD. In the past month, he has bought 11 DVDs that cost $27.95 each, 7 that cost $17.95 each, and
one that cost $7.95. How much has he spent on DVDs in the past month?
Answer:$441.05
Step-by-step explanation:
For this question you would multiply the amount of each DVD by the price and add them all up
like this:
11(27.95) +7(17.95)+1(7.95)=$441.05
WIL GIVE BRAINLIEST!!!!
What is the value of x in simplest radical form?
Look at the provided picture!!!
Answer: b
Step-by-step explanation:
3^2 + x^2 = 9^2
9 + x^2 = 81
x^2 = 72
x = sqrt(72)
Describe the composition of translations.
translation: (x, y)__
translation: {x, y)__
The composition of translations for the first image is (x+1, y+5) and for the second image is (x-4, y).
What is a translation?
A transformation that moves a figure through its points using a given ruler—a translation vector—is referred to as a translation. Without altering the original geometry, this process moves each point in a picture both horizontally and vertically.
Given a graph of translation
The first image is translated as 1 unit upward and 5 units right side.
Then, translation (x,y) → (x+1, y+5)
And,
The second image is translated as 4 units downward only.
Then, translation (x,y) → (x-4, y)
Hence, the above is the required composition of translations.
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-6.05+(-3.611) srrrrgggggggggggg
Answer:
-9.661
Step-by-step explanation:
Adding a negative is the same as subtracting a positive and you started with a negative number so:
-6.05
-3.611
------------
-9.661
Answer: -9.661
Step-by-step explanation:
A negative plus a negative will ALWAYS equal a negative. If you have an addition with two negatives, just add them normally and add the negative sign:
-6.05+(-3.611) = 6.05 + 3.611
6.05 + 3.611 = 9.661
Now add the negative sign:
9.661 = -9.661
Hope this helps!!
The entrance fee for a theme park is $20. Tickets for each ride and attraction are $3 a piece. Which of the following equations describes the relation between the total cost (Y) and the number of tickets purchased (X) in a single visit to the park?
a. Y = 3+ 20X
b. Y = 60X
c. Y = 20 +3X
d. X = 20 +3Y
Answer: c. Y = 20 +3X
The system of equation that describes the relation between the total cost (Y) and the number of tickets purchased (X) in a single visit to the park is Y = 3X + 20 i.e, option (C)
Define System of Equation
A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.
Given,
Cost of theme park is = $20
Tickets for each ride and attraction are = $3 a piece
Number of tickets purchased = X
So, total cost of tickets is = 3 * X
Total cost of visit to the theme park is = Y
So, the equation we get
Y = 3X + 20
Hence, the system of equation that describes the relation between the total cost (Y) and the number of tickets purchased (X) in a single visit to the park is Y = 3X + 20 i.e, option (C).
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Given x=a+b. Use the Pythagorean Theorem to find the value of x.
[tex]a=\sqrt{5^2-4^2}=3 \\ \\ b=\sqrt{5^2-4^2}=3 \\ \\ \therefore x=3+3=\boxed{6}[/tex]
A school dance committee is to consist of 2 freshmen, 3 sophomores, 4 juniors, and 5 seniors. If 7 freshmen, 9 sophomores, 7 juniors, and 7 seniors are eligible to be on the committee, in how many ways can the committee be chosen?
There are 3457440 ways combination in which this dance committee can be formed.
What is permutation and combination?
A set of items can be divided into subsets in two different ways: combination and permutation. The subset's components can be listed in any order when combined. The components of the subset are arranged in a particular order in a permutation.
2 freshmen out of 7 freshmen can be chosen in ⁷C₂ ways.
3 sophomores out of 9 sophomores can be chosen in ⁹C₃ ways.
4 juniors out of 7 juniors can be chosen in ⁷C₄ ways.
5 seniors out of 8 seniors can be chosen in ⁸C₅ ways.
⁷C₂ × ⁹C₃ × ⁷C₄ × ⁸C₅ ways, the dance committee of 2 freshmen, 3 sophomores, 4 juniors, and 5 seniors can be chosen.
= 7!/(7-2)!2! × 9!/(9-3)!3! × 7!/(7-4)!4! × 8!/(8-5)!5!
= 7!/5!2! × 9!/6!3! × 7!/3!4! × 8!/3!5!
= 21×84×35×56.
= 3457440 ways.
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Ron and Annie have $1,571.13 in their checking account. During the week Annie goes to an ATM and withdraws
$80. The following week Ron deposits his paycheck of $456.82. Annie then pays bills online in the amounts of:
179.48, $74.73, $82.70, and $139.55. What is the current balance in their checking account?
Answer:
$1471.49
Step-by-step explanation:
1571.13-80=1491.13
1491.13+456.82=1947.95
179.48+74.73+82.70+139.55=476.46
1947.95-476.46=1471.49
Cab companies often charge a flat fee for picking someone up and then charge an additional fee per mile driven.
The city of Raleigh, NC charges $ 1.95 fee and $ 2.70 per mile for each cab ride.
The equation of Total Charges will be $1.95 + ($2.7 * x)
What is Linear Equation in One Variable?
A linear equation is a one-variable equation of a straight line. The variable's only power is 1. Linear equations in one variable have the form ax + b = 0 and are solved using simple algebraic techniques.
Solution:
The equation of Total Charges will be
Let, the total distance in miles be x
Then,
Total Charges = $1.95 + ($2.7 * x)
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transform the linear equation 12-4y=5x to slope and y-intercept form
Step-by-step explanation:
-4y = 5x - 12
4y = -5x + 12
y = -5/4x + 3
Your family plans to start a small business in your neighborhood. Your father borrows
$10, 000 from the bank at an annual interest rate of 8% rate for 36 months. What is the
amount of interest he will pay on this loan?
The amount of interest he will pay on this loan is $12,400.
Principal = $10,000
Rate = 8%
Time = 36 months, 1 year - 12 months
36 months - 36/12= 3 years
S.I. = PRT/100
10,000*8*3/100
240,000/100 = $2,400
A = P+I = 10,000+2,400= $12,400
The amount of interest he will pay on this loan $12,400.
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Write the slope-intercept form of the equation of the line through the given point with the given slope.
The slope-intercept form of the equation of the line through the given point with the given slope is y=-4x+1.
The given coordinate point is (-1, 5) and slope=-4.
What is the slope intercept form?The slope intercept form of a straight line is one of the most common forms used to represent the equation of a line. The slope intercept formula can be used to find the equation of a line when given the slope of the straight line and the y-intercept.
The standard form of the slope intercept form is y=mx+c.
Substitute (x, y)=(-1, 5) and m=-4 in standard form of the slope intercept form, we get
5=-4×(-1)+c
⇒ c=5-4
⇒ c=1
Substitute m=-4 and c=1 in y=mx+c, we get
y=-4x+1
Therefore, the slope-intercept form of the equation of the line through the given point with the given slope is y=-4x+1.
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[tex]2\frac{5}{7}g+3\frac{3}{5} g[/tex]
The solution of the fraction is 6 11/35.
What is fractions?A fraction, such as one-half, eight-fifths, or three-quarters, indicates the number of components of a particular size as it is represented in common English. A common, vulgar, or simple fraction is one that has a non-zero denominator shown below (or after) the line that separates the numerator from the denominator. Compound fractions, complicated fractions, and mixed numeral fractions are examples of uncommon fractions that use numerators and denominators.The numerator and denominator of positive common fractions are both natural integers. The denominator shows how many of the numerator's equal parts make up a unit or whole, and the numerator reflects the number of equal parts. Since there can never be zero components in a whole, the denominator cannot be zero.Covert mixed numbers to improper fractions:
[tex]2\frac{5}{7}g=\frac{19}{7}g[/tex]
[tex]3\frac{3}{5}g=\frac{18}{5}g[/tex]
factor out common term g:
=[tex]g(\frac{19}{7} +\frac{18}{5})\\g(\frac{221}{35})[/tex]
Convert improper fractions to mixed numbers:
[tex]=\frac{221}{35}g \\\\=6\frac{11}{35} g[/tex]
Hence, The solution of the fraction is 6 11/35.
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A continuous probability distribution has density:
a) If the expected value is equal to 1, find the values of a and b.
b) What is the variance of X?
Therefore the solution to this question is expression a=3/5 & expression b=6/5 3a+b=3 , and 10a+5b=6+6=12 .
What is probability?Probability is the study of how likely it is for an event to occur or for a statement to be true, with numerical explanations of probability being a key component. An event's probability is represented by a number between 0 and 1, where, broadly speaking, 0 indicates that the event is impossible and 1 indicates that it is certain to occur.
Here,
Naturally, the total probability for x∉[0,1] is 0 and since the total probability must be 1, we have
∫01a+bx2dx=1
The left-hand side is
[ax+b[tex]x^{3}[/tex]/3] x=1 & x=0 => a+b3
3a+b=3
In general, for continuous probability distributions we have
E(x)=∫P(x)xdx
(If you have a sufficiently advanced version of integration, the restriction to continuous distributions may be lifted.)
In this case, it's
E(x)=[a[tex]x^{2}[/tex]/2+b[tex]x^{4}[/tex]/4]x=1 & x=0 => a/2+b/4
So,
a/2+b/4=3/5
10a+5b=12
Being shrewd with matrix inversion or anything of the sort is pointless. Just get rid of b:
15a+5b=15
5a=3
a=3/5
b=3(1−a)=6/5
and indeed 3a+b=3 , and 10a+5b=6+6=12 .
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The average ticket price for several NFL teams is listed below.
Seahawks =$84.60
Packers= 89.37
Jets= $105.66
Cowboys= 110.20
Lions = $79.16
how much more would it cost a family of 5 to get the jets game ($105.66) than a Lions game ($79.19?
It would cost a family of 5 $132.35 more to get the jets game than a Lions game
How to determine how much more it would cost a family of 5 to get the jets game than a Lions game?
Given that:
The average ticket price for Jets game = $105.66
The average ticket price for Lions game = $79.19
Jets game for a family of 5 will be:
Jet game cost = 5× $105.66 = $528.3
Lions game for a family of 5 will be:
Lions game cost = 5× $79.19 = $395.95
Difference = $528.3 - $395.95 = $132.35
Therefore, it would cost a family of 5 $132.35 more to get the jets game
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which equation in point-slope from is equivalent to y=-3/4x + 9?
A. y-9=-3/4(x-0)
B. y-1=-3/4(x-9)
C. y-3/4=9(x-0)
D. y-1=9(x+3/4)
Answer:
Step-by-step explanation:
I know that in point-slope form, the equation is y - y1 = m(x - x1)
Fill in y1 and x1 with the points given in the multiple choices.
If you look at Letter A, it shows the point (0,9). If you fill that in the formula. You solve the equation:
y - 9 = -3/4(x - 0)
y - 9 = -3/4x
+9. =. +9
y = -3/4x + 9
Therefore your answer is letter A.