The equation of the line in point-slope form is; y=1.25 x+12.5 The slope of the line is 1.25.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let y is the total cost at the county fair and x is the number of tickets per ride
The variable in the linear equation;
y=mx+c
m=Cost per ticket ride
c= fair admission price
Given that;
y=$43.75
m=$1.25 per ticket ride
x=25 tickets
c=unknown
Now replacing;
43.75=(1.25×25)+c
c=43.75-31.25
c=12.5
The fair admission price will be; 12.5 dollar
The equation of the line in point-slope form is; y=1.25 x+12.5
The slope of the line is 1.25.
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I need help on in the answer to this question
To find out the value of z we can use the formula
[tex]z=\frac{w+79}{2}[/tex]But we also have to find out the value of w, which be found using the equation
[tex]360=x+79+w+60[/tex]Which needs the value of x, which be found using
[tex]\frac{x+60}{2}=70[/tex]But instead of doing all that and finding the value of x, w and z. We can directly find z using the fact that
Because it's all angles opposite by a vertex, and the sum of them all will be 360º, then we can say that
[tex]\begin{gathered} z+70+z+70=360 \\ \\ 2z+2\cdot70=360 \\ \\ 2z+140=360 \\ \\ 2z=360-140 \\ \\ 2z=220 \\ \\ z=\frac{220}{2} \\ \\ z=110 \end{gathered}[/tex]Therefore, z = 110º.
Which set of ordered pairs does not represent a function?
O {(-6, -1), (-4, 6), (-8, 2), (3, -1)}
O {(7,4), (9,-8), (-5, -7), (-2,4)}
O {(-3,-3), (4, 5), (8,9), (0,5)}
O {(-1,8), (8,-4), (8, 3), (-5, -6)}
▸
Set of ordered pairs does not represent a function i
= {(2, 2), (0, -8), (2, 7), (-3, 8)}
What is a function?A function relates an input to an output. A function is generally denoted by f(x) where x is the input.
What is a set?
Any collection of objects , which are mathematical or not
Ordered pair are a composition of the x coordinate (abscissa) and the y coordinate (ordinate), having two values written in a fixed order within parentheses.
From question given data is
{(4, 6), (9, -2), (3, -5), (6, 6)}
{(−1,−2),(−4,9),(8,−9),(1,2)}
{(-1, 9), (-7, 8), (3, -1), (4, -1)}
{(2, 2), (0, -8), (2, 7), (-3, 8)}
From the above options we can see that last option has same number in the x axis coordinate. Thus it does not represents a function.
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10. A square pyramid is shown. The height of the pyramid is 14 centimeters. The area of the base of the square pyramid, B, is 64 square centimeters. 8 64 cm Which measurement is closest to the volume of the pyramid in cubic centimeters? F 900 cm G 450 cm M 300 cm ) 150 cm
ANSWER
The closest measurement is 300cm³
EXPLANATION
The volume of a pyramid is:
[tex]V=\frac{1}{3}Bh[/tex]where B is the ares of the base and h is the height.
In this problem, B = 64cm² and h = 14cm. The volume is:
[tex]V=\frac{1}{3}\cdot64\operatorname{cm}^2\cdot14\operatorname{cm}=298.\bar{6}cm^3[/tex]The one that's closest is 300cm³
Write an equation for the line that passes through (3,-14) having slope 0. Give the answer in standard form
Slope intercept form:
y= mx + b
where:
m= slope
b= y intercept
m= 0
Replace (x,y) by the given point (3,-14) and solve for b
-14 = 0 (3)+ b
-14 = b
Slope intercept form:
y= - 14
Standard form:
Ax+BY = C
y = -14
Ben paid $1200 for a sofa. The price of the sofa Juana purchased was ⅔ the price that Ben paid. How much did Juana pay for her sofa?
Answer:
800
Step-by-step explanation:
y= ^2 -4x +6 y= -5^2 + 20x - 12 solve by elimination
The required solutions are x = 15/8 and y = 1/2 which is determined by the elimination method.
Given the linear system of equations as
y = 2 - 4x +6 or
4x + y = 8 …(i)
y= - 5² + 20x - 12 or
20x - y = 37 …(ii)
Equations (i) and (ii) constitute a system of two first-degree equations in the two variables x and y.
So, we have to find out the value of 'x’ and 'y’.
Add equation (i) and equation (ii), we get
4x + y + 20x - y = 8 + 37
24x = 45
x = 45/24
x = 15/8
Substitute the value of 'x’ into equation (i) and we get
4(15/8) + y = 8
60/8 + y = 8
y = 8 - 15/2
y = 1/2
Hence, the required solutions are x = 15/8 and y = 1/2.
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Help
Which statement is true?
Answer:
This table does not show a probability distribution because probabilities cannot be negative, and they cannot be greater than 1.
Can y’all help me plssss
(a) Solve the inequality: n > 12
(b) The greatest amount of trips that Edwin can take up the mountain and still pay less than Rhea would be 63
What is Inequality?
Inequality of wealth in major cities Economic inequality comes in many forms, but two stand out above the rest: wealth inequality as measured by the distribution of wealth and income inequality as measured by the distribution of income.
Edwin and Rhea, two siblings, decide on distinct payment arrangements even though they are both going skiing.
In Edwin's proposal, rentals cost $45 and each lift up the mountain costs $5.25.
Rhea had an arrangement whereby her whole day would cost $108.
An inequaity that simulates the n trips up the mountain that Edwin will pay for out of pocket and Rhea won't.
45 + 5.25n > 108
45 is deducted from both sides.
-45 + 45 + 5.25n > 108 -45
5.25n > 63
5.25 times both sides.
n > 12
Also,
5.25 x 12
= 63
The most trips Edwin could make up the mountain and still make less money than Rhea is 63.
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If 6x=30, then x=5. If x=5, then 2x=10. Make a conclusion using the law of syllogism
Given:
[tex]\begin{gathered} \text{If 6x=30 then x=5} \\ \text{If x=5 then 2x=10} \end{gathered}[/tex]The law of syllogism states that,
[tex]\text{ If a=}b\text{ and b=c then a=c}[/tex]For the given data,
[tex]\begin{gathered} a\colon\text{ 6x=30} \\ b\colon x=5 \\ c\colon2x=10 \\ By\text{ the law of syllogism,} \\ 6x=30 \\ 3\cdot2x=3\cdot10 \\ \Rightarrow2x=10 \\ Therefore, \\ \text{If 6x=30 then 2x=10} \end{gathered}[/tex]Find the value of k so that the remainder is 3(x^2-x+k) divided by (x-1)
Okay, here we have this:
Considering the provided polynomials, we are going to calculate the requested value, so we obtain the following:
So first we will perform the division assuming that k=0 to see what is the remainder that is obtained:
[tex]\begin{gathered} \frac{x^2-x}{x-1} \\ =\frac{x(x-1)}{x-1} \\ =x \end{gathered}[/tex]We obtain that the remainder when taking k=0, is zero, then it will mean that the k must be equal to the residue that we want:
In other words, if we want the remainder to be 3, k must be equal to 3, replacing:
[tex]\begin{gathered} \frac{x^2-x+k}{x-1} \\ \frac{x^2-x+3}{x-1} \\ =x+\frac{3}{x-1} \end{gathered}[/tex]Finally we confirm that for the remainder to be 3, the value of k must be equal to 3.
i need help with this question parts 3 - 7
Explanation
Question 3 wants us to determine the range of the function
The range will be
[tex](-\infty,1]\text{ U \lparen2,}\infty)[/tex]This is
∞
What operation do they use? Whats the total amount they collected.
What operation is used. Is a multiplicarion between irrational numbers.
What is the amount collected
It must be multiplied 15.5 x 3.98
Replace 15.5 = 15+ 0.5
3.98 = 4-0.02
then 15x 4 + 0.5x4 - 15x(0.02) - 0.5x(0.02)
Then result 60 + 2 - 0.30 - 0.01
62 - 0.31 = 61.69
A bike rental company charges $10 plus a charge per for the distance ridden. the total cost, t, can be represented by the equation t=10+cm , where c is the additional cost per mile and m is the number of miles ridden. solve the equation for c.
Answer:
[tex]c=\frac{t-10}{m}[/tex]
Step-by-step explanation:
[tex]t=10+cm[/tex]
Subtract 10 from both sides:
[tex]t-10=cm[/tex]
Divide both sides by [tex]m[/tex]:
[tex]\frac{t-10}{m}=c[/tex]
Placing [tex]c[/tex] on the left:
[tex]c=\frac{t-10}{m}[/tex]
For example, if the total charge is $27.50 and the distance ridden is 250 mi, we can calculate the additional cost per mile, as such:
[tex]c=\frac{27.50-10}{250}[/tex]
[tex]c=0.07[/tex]
PLS HELP ASAP THIS IS DUE TODAY!!!!!!
Are lines L1 and L2 Parallel? Are lines L1 and L4 perpendicular? Explain your thinking.
The lines L1 and L2 are parallel and the Line L1 and L4 are not perpendicular .
In the question ,
it is given that ,
there are four line on the graph ,
to check whether lines are parallel or perpendicular , we need slope,
the Line L4 passes through the points , (0,-5) and (-2,-5),
slope = (-5+5)/(-2)
= 0
the Line L1 passes through the points (-3,-2) and (-6,-8) ,
slope = (-8+2)/(-6+3)
= -6/(-3)
= 2 ,
for the lines to be perpendicular the product of slope should be -1,
but the product of slope of Line1 and Line 4 is 0 .
So , they are not perpendicular .
the line L2 passes through the points (3 , 3.5) and (0 , -2.5) ,
slope = (3.5+2.5)/3
= 6/3
= 2 ,
Since the slope of Line1 and Line2 are equal ,
So , they are parallel .
Therefore , The lines L1 and L2 are parallel and the Line L1 and L4 are not perpendicular .
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You are at a grocery store and the cost of your groceries is $32.75. You need to add the sales tax, which is 6%. You have one $20 bill, two $10 bills, one $5 bill, five $1 bills, and some pennies.
How much is your total bill including tax?
How much should you give the cashier so you do not get back any pennies?
What denominations will you use for this?
1. The total bill including sales tax is $34.72.
2. The amount the purchaser should pay the cashier is $34.72.
3. The denominations for the payment should be one $20 bill, one $10 bill, four $1 bills, and 72 cents (pennies).
How is the total cost determined?The total cost payable to the grocery store cashier is the cost of the groceries plus the sales tax.
The cost for groceries = $32.75
Sales tax = 6%
Total cost = cost plus sales tax
= $34.72 ($32.75 x 1.06)
We can check the sum as follows:
Unit Bill Amount
1 $20 $20
1 $10 10
4 $1 4
Cents 0.72
Total $34.72
Thus, the grocery purchaser will be spending $34.72, including the sales tax.
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the sun of a first and second number is 184 three times the first number decreased by 212 is equal to the second number find the two numbers let x represent the first number and y represent the second number write the system of equations used to solve this problem
Answer:
B.is the answer.
Step-by-step explanation:
In the equation IX=b, if b<0, then how many solutions are there for x? Think about this: b is a number less than 0
If we assume x and b are real numbers:
|x| = √(x²)
So:
√(x²) = b
Where b<0
x will be always positive, because every number squared is positive
So, the left hand side of the equation will be positive. And since the right hand side of the equation will be always negative, because they tell us that b<0, we can conclude that it is absurd:
√(x²) ≠ b
Therefore, no solutions exist
The answer is Zero
$15,000 to invest and want to keep your money invested for 5 years. You are considering the following investment options. Choose the investment option that will earn you the most money.
A. 1.89% compounded monthly
B. 1.975% compounded quarterly
C. 1.99% compounded annually d.
D. 3.25% simple interest
Answer:
1) 15000*(1+0.0189)^(5*12) = 46130.16346
2) 15000*(1+0.01975)^(5*3) = 20113.9316
3) 15000*(1+0.0199)^5 = 16553.0954
4) 15000*(1+0.0325*5) = 17437.5
The first one is the best option.
what's the length and width of the actual flower bed.
Answer:
length: 16ft
breadth:- 12ft
Question #6 Which scenario represents a unit rate of $2? A A 6-pack of hair bows costs $6. How much does 1 hair bow cost? B A 12-pound bag of cat food costs $24. How much does 1 pound of cat food cost? C A 24-pack of water bottles costs $12. How much does 1 water bottle cost? A 42-pound bag of fertilizer costs $21. How much does 1 pound of fertilizer cost ?
We will have that the $12 rate is given by:
B. A 12-pound bag of cat food cost $24, that is:
$24/12 = $2 per pound of food.
D what is the image pointof (3-4) after a translationleft 2 units and up 2 units?
Point = (3,-4)
After a translation left 2 units(-2) and 2 units up
(3-2,-4+2) = (1,-2)
which of the points plotted below satisfy the equation in the box? check all that apply point Apoint Bpoint Cpoint Dpoint Epoint F
The equation is:
[tex]y=-3x[/tex]so is in the form y = mx + c
this means that C = 0 so the intersection when x = 0 y = 0 so the first point is (0,0)
we also know that the slope is negative, so only points in the II and IV cuadrant can be part of the line so we evaluate them:
For point A
[tex]\begin{gathered} 9=-3(-3) \\ 9=9 \end{gathered}[/tex]point A is part of the line (-3,9)
For point D
[tex]\begin{gathered} -6=-3(2) \\ -6=-2 \end{gathered}[/tex]So D is part of the line
So the solution is: PointsIf you don’t need further explanation on this question, we can end the session. I’d really appreciate you letting me know how I did by rating our session after you exit. Thanks and have a great day! A, B, D
Answer:
correct answer: B and F
Step-by-step explanation:
I would like to know the formula that was used to get 120 cm
The given figure is a 2d representation of a 3d figure. If we wrap this figure, we get a building block.
In the figure below, the unknown edges are written:
Now, we have to find the area of all the polygons given in the figure. It consists of two same triangles and three different rectangles.
The area of the two triangles is given below:
[tex]\begin{gathered} A=2\times\frac{1}{2}\times\text{base}\times\text{height} \\ =\text{base}\times\text{height} \\ =3\times4 \\ =12 \end{gathered}[/tex]Thus, the area of two triangles is 12 cm^2.
We know that the area of a rectangle is length times width. Now, the area of three rectangles is given below:
[tex]\begin{gathered} A=9\times5+9\times4+9\times3 \\ =45+36+27 \\ =108 \end{gathered}[/tex]Thus, the area of three rectangles is 108 cm^2.
So, the total area is 12 + 108 = 120 cm^2.
ƒ (4) = -8, ƒ (-3) = 1
write a linear function
f(4) = -8 is another way of saying the point is (4 , -8)
f(-3) = 1 is another way of saying the point is (-3 , 1)
to get the equation of any straight line, we simply need two points off of it, so let's use those two provided
[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{-8})\qquad (\stackrel{x_2}{-3}~,~\stackrel{y_2}{1}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{(-8)}}}{\underset{run} {\underset{x_2}{-3}-\underset{x_1}{4}}} \implies \cfrac{1 +8}{-7} \implies \cfrac{ 9 }{ -7 } \implies - \cfrac{9 }{ 7 }[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-8)}=\stackrel{m}{- \cfrac{9 }{ 7 }}(x-\stackrel{x_1}{4}) \implies y +8 = - \cfrac{9 }{ 7 } ( x -4) \\\\\\ y+8=- \cfrac{9 }{ 7 }x+\cfrac{36}{7}\implies y=- \cfrac{9 }{ 7 }x+\cfrac{36}{7}-8\implies {\Large \begin{array}{llll} y=- \cfrac{9 }{ 7 }x-\cfrac{20}{7} \end{array}}[/tex]
Find the distance between the points (20, 15) and (20, 6).
Answer:
5,14
Step-by-step explanation:
help me..............
I need to find "S"
32 = s - 19
Add 19 in both sides
32 + 19 = s - 19 + 19
51 = s
Result
s = 51
200 students were asked to name their favorite science class. The results are shown in the two-wayfrequency table. Use the table to answer the following question.
Explanation:
We're told from the question that 200 students took part in the exercise, so if the total number of girls is 100 then the total number of boys will be;
[tex]\text{Total number of boys =}200-100=100[/tex][tex]\text{Total number of boys that chose Biology}=100-44-37=19[/tex][tex]\text{Total number of boys and girls that chose Biology}=40+19=59[/tex][tex]\text{Total number of boys and girls that chose Chemistry}=39+44=83[/tex][tex]\text{Total number of boys and girls that chose Physics}=21+37=58[/tex][tex]\text{Total of the total row}=59+83+58=200[/tex]To find how many more girls than boys chose Biology, we'll have;
[tex]40-19=21[/tex]So 21 more girls than boys chose Biology.
What are the coordinates of the vertex?What is the equation of the axis of symmetry?What is/are the x-intercept(s)?What is the y-intercept?
We will find the vertex of the parabola as follows:
*Given a quadratic function of the form:
[tex]y=ax^2+bx+c[/tex]We will have that the vertex is given by:
[tex](-\frac{b}{2a},\frac{b^2-4ac}{4a})[/tex]So, for the function given we will have the following vertex:
[tex](-\frac{(-8)}{2(-1)},\frac{(-8)^2-4(-1)(0)}{4(-1)})\to(-4,16)[/tex]So, the vertex for the function is given by the ordered pair (-4, 16).
We will have that the equation of the axis of symmetry is given by:
[tex]x=-4[/tex]So, the axis of symmetry is x = -4.
We will determine the x-intercepts as follows:
[tex]-x^2-8x=0\Rightarrow x=\frac{-(-8)\pm\sqrt[]{(-8)^2-4(-1)(0)}}{2(-1)}[/tex][tex]\Rightarrow\begin{cases}x=-8 \\ \\ x=0\end{cases}[/tex]So, we will have that the x-intercepts are located at x = -8 & x = 0.
From the previous point we can see that the point (0, 0) belongs to the parabola, thus the y-intercept is y = 0.
If f(x) = 2x - 9, which of the following are correct? Select all that apply. f(-1) = -11 f(2) = 5 f(3) = -3 f(0) = -9 f(-3) = 15
The correct options are f(-1) = -11, f(3) = -3 and f(0) = -9.
Given equation:-
f(x) = 2x - 9
We have to find which of the following are correct:-
f(-1) = -11 ,f(2) = 5 ,f(3) = -3 ,f(0) = -9 and, f(-3) = 15
Putting x = -1 in the given equation, we get:-
f(-1) = 2*(-1) - 9 = -2 - 9 = -11
Hence, this is true.
Putting x = 2 in the given equation, we get:-
f(2) = 2*(2) - 9 = 4 - 9 = -5
Hence, this is false.
Putting x = 3 in the given equation, we get:-
f(3) = 2*(3) - 9 = 6 - 9 = -3
Hence, this is true.
Putting x = 0 in the given equation, we get:-
f(0) = 2*(0) - 9 = 0 - 9 = -9
Hence, this is true.
Putting x = -3 in the given equation, we get:-
f(-3) = 2*(-3) - 9 = -6 - 9 = -15
Hence, this is false.
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The ratio of the heights of similar cones is 5:2. If the base area of the small cone is 64pi cm^2, find the base area of the large cone. Thanks!
Answer: 400π
Explanation:
From the information given, the ratio of the heights is 5:2. This means that the scale factor is 5:2. This means that the ratio of the areas is
(5/2)^2 = 25/4 = 25:4
Thus,
base area of large cone/base area of small cone = 25/4
Given that base area of small cone is 64π, it means that
base area of large cone/64π = 25/4
By cross multiplying,
base area of large cone = 25/4x 64π
base area of large cone = 400π