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Related Questions
write the slope-intercept equation of the function f whose graph satisfies the given conditions. The graph of f passes through (-6,6) and is perpendicular to the line that has an x-intercept of 5 and a y-intercept of -15
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Answer:
[tex]y=-\dfrac{1}{3}x+4[/tex]
Step-by-step explanation:
Slope of line with given x and y intercepts
The x-intercept is when y = 0.
Therefore, if the x-intercept is 5 ⇒ (5, 0).
The y-intercept is when x = 0.
Therefore, the y-intercept is -15 ⇒ (0, -15).
Inputting these two points into the slope formula to find the slope of this line:
[tex]\sf slope\:(m)=\dfrac{change\:in\:y}{change\:in\:x}=\dfrac{-15-0}{0-5}=3[/tex]
Slope of function f(x)
If the function f(x) is perpendicular to the above line, then the slope of function f(x) is the negative reciprocal of the slope of the line.
[tex]\implies \sf slope\:of\:f(x)=-\dfrac{1}{3}[/tex]
Equation of f(x) in point-slope form
Use the found slope and the point (-6, 6) with the point-slope form of a linear equation to find the equation of function f(x):
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-6=-\dfrac{1}{3}(x-(-6))[/tex]
[tex]\implies y-6=-\dfrac{1}{3}(x+6)[/tex]
Expand and rearrange so that the equation is in the slope-intercept form of y=mx+b:
[tex]\implies y-6=-\dfrac{1}{3}x-2[/tex]
[tex]\implies y=-\dfrac{1}{3}x+4[/tex]
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The equation y = 1000x - 5000 represents the monthly profits of a start-up dry cleaning company. Time in months is x and profit in dollars is y. The first date of operation is when time is zero. However, preparation for opening the business began 3 months earlier with the purchase of equipment and supplies. Graph the linear function for x-values from -3 to 8
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The attached graph represents the graph of the linear equation y = 1000x - 5000 on a scale of 1 to 1000 units on both axes
What are linear equations?Linear equations are equations that have constant average rates of change, slope or gradient
How to graph the linear function?The equation of the linear function is given as:
y = 1000x - 5000
The x values are given as:
x = -3 to 8
This means that the domain of the function is [-3, 8] or -3 <= x <= 8
So, we set x = -3 and x = 8, and we calculate the y values.
So, we have:
y = 1000 * -3 - 5000 = -8000
y = 1000 * 8 - 5000 = 3000
So, we draw two points at (-3, -8000) and (8, 3000) and connect the dots
See attachment for the graph of the function
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Marissa is painting her rectangular patio, with the exception of a bench that does not need to be painted: rectangle with a length of x plus 25 and width of x plus 15 with a rectangle in the bottom right corner labeled bench that has a length of 10 and width of 3 write an equation to determine the area, a, of the patio that will be painted. a = (x 18)(x 35) a = (x 15)(x 25) 30 a = (x 5)(x 22) a = (x 25)(x 15) − 30
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The correct option is D.
An equation to determine the area, a, of the patio that will be painted :
a = (x + 25)(x + 15) - 30
What is Geometrical figure?Geometric shapes are the mathematical figures that show how ordinary objects in our world are shaped. Shapes in geometry are the configurations of things with boundary lines, angles, and surfaces.
According to the given Information:Length of the rectangular patio is (x+25).
Width of the rectangular patio is (x+15).
Length of bench is 5.
Width of the bench is 1.
Area of rectangle:Area of a rectangle is:
A = Length x Width
Area of rectangular patio is:
A[tex]_1[/tex] = (x + 25)(x + 15)
Area of bench is:
A[tex]_2[/tex] = 10 x 3
= 30
The painting area is:
A = A[tex]_1[/tex] - A[tex]_2[/tex]
A = (x + 25)(x + 15) - 30
Therefore, the correct option is D.
An equation to determine the area, a, of the patio that will be painted :
a = (x + 25)(x + 15) - 30
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A company did a quality check on all the packs of trail mix it manufactured. each pack of trail mix is targeted to weigh 9.25 oz. a pack must weigh within 0.23 oz of the target weight to be accepted. what is the range of rejected masses, ×, for the manufactured trail mixes? (1 point) 0 x<9.02 or x> 9.48 because lx - 9.251 > 0.23 o x<9.25 or x > 9,48 because ix - 0.231 9.25 > 0 0 x€ 9.02 or x> 9.48 because ix - 0.231 9.25 > 0 o x< 9.25 or x> 9.48 because ix - 9.25| > 0.23
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Rejected masses x are those that weigh less than 9.02 oz or more than 9.48 oz.
What is the range?In mathematics, the range of a function can refer to one of two notions that are closely related.The function's codomain, the function's visual representation.A binary relation f between two sets X and Y is a function if for every x in X there is exactly one y in Y such that f relates x to y.To find the rejected masses:
If each pack of trail mixes is supposed to weigh 9.25 oz and must be within 0.23 oz of that weight to be accepted, then rejected masses x are those that weigh less than 9.02 oz or more than 9.48 oz.Therefore, rejected masses x are those that weigh less than 9.02 oz or more than 9.48 oz.
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The correct question is given below:
A company did a quality check on all the packs of trail mix it manufactured. each pack of trail mix is targeted to weigh 9.25 oz. a pack must weigh within 0.23 oz of the target weight to be accepted. what is the range of rejected masses, ×, for the manufactured trail mixes?
20. A trader took a loan of 1,800.00 at an interest of 12 percent per annum. It was agreed that the loan and the interest must be paid in one year equal monthly instalments.
a) Calculate
i) the interest on the loan.
ii) the amount to be paid at the end of the year.
iii) the monthly instalment.
b) Another trader took a loan at the same rate interest and conditions. If she had to pay $200.00 monthly instalment, find to the nearest cedi, how much she took.
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Step-by-step explanation:
i)I=PRT/100
I=1800*12*1/100
I=$216
ii) amount to be paid =1800+216
=$2016
iii) monthly installments=2016/12
=$168
b)I=PRT/100
I=
If a trader took a loan of 1,800.00 at an interest of 12 percent per annum
a. Interest on the loan is $216.
Amount to be paid at the end of the year is $2016
Monthly Installment is $168
b. She took $2184 to the nearest dollar.
What is the Interest?a) i) Interest on the loan:
Interest = Principal × Rate × Time
Interest = $1800 × 0.12 × 1
Interest = $216
ii) Amount to be paid at the end of the year:
Amount = Principal + Interest
Amount = $1800 + $216
Amount = $2016
iii) Monthly installment:
Number of monthly installments = 12
Monthly Installment = Total Amount / Number of Installments
Monthly Installment = $2016 / 12
Monthly Installment ≈ $168
b) Let's X represent the amount she took
Total Payment = Monthly Installment × Number of Months
Total Payment = $200 × 12
Total Payment = $2400
So
Total Payment = X + $216
$2400 = X + $216
Subtract $216 from both sides:
$2400 - $216 = X
$2184 = X
Therefore she took approximately $2184 to the nearest dollar.
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From the diagram below, we can tell that ___.
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Answer: b. the two triangles are similar by SAS
Step-by-step explanation:
These two triangles (ABC and ADE) both share angle A. This means that one angle is congruent.
Next, we will look at the sides. Triangle ADE has side lengths of 6, 9, and x. Triangle ABC has side lengths of 8+6, 12+9, y. Let us see how these side lengths compare.
[tex]\frac{8+6}{12+9} =\frac{14}{21} =0.6666[/tex]
[tex]\frac{6}{9} = 0.6666[/tex]
THey are similar. This means the triangles can be prooven similar with SAS.
Geometry: complete this proof (ASAP!!! It’s urgent)
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Answer:
1. BD bisects <CBE, AE || BD (Given)
2. <EBD ~= <CBD (Definition of < Bisectors)
3. <AEB ~= <EBD (Alternate Interior Angles Theorem)
4. <CAE ~= <CBD (Corresponding Angles Postulate)
5. <CAE ~= <AEB (Transitive Property of Congruence)
6. AB ~= BE (Converse of Isosceles Triangles Theorem)
(08.07 HC)
An expression is shown below:
f(x) = 2x²-3x - 5
Part A: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)
Part B: Is the vertex of the graph of f(x) going to be a maximum or minimum? What are the
coordinates of the vertex? Justify your answers and show your work. (3 points)
Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers
obtained in Part A and Part B to draw the graph. (5 points)
(10 points)
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Answer:
Below in bold.
Step-by-step explanation:
Part A
At the x-intercepts f(x) = 0, therefore:
2x^2 - 3x - 5 = 0
(2x - 5)(x + 1) = 0
x = 5/2, -1)
So the x intercepts are (-1, 0) and (5/2, 0).
Part B
The Coefficient of x^2 is positive ( it is 2) So the graph opens upwards and the vertex will be a minimum.
Convert f(x) to vertex form, by completing the square:
f(x) = 2x^2 - 3x - 5
= 2(x^2 - 3/2x) - 5
= 2[(x - 3/4)^2 - 9/16] - 5
= 2(x - 3/4)^2 -18/16 - 80/16
= 2(x - 3/4)^2 - 49/8
So the coordinates of the vertex are
(3/4, -49/8) or
(0.75, -6.125) in decimal form.
Part C
To graph f(x) you would first mark the points on the x axis which we found in Part 1 and the vertex found in Part 2. This vertex will be the bottom of the 'U'.
The graph is a parabola shaped roughly like a U, and will be symmetrical about the line x = 0.75 (which passes through the vertex).
You would also plot 2 more points above the x axis so as to get an accurate graph. 1 would be to the left of the line of symmetry and 1 to its right.
Suggest x = - 2 and calculate f(-2) = 2(-2)^2 - 3(-2) - 5 = 11.
- that is the point (-2,11) and the other would be x = 4, f(x) = 15. (4, 15)
Once you have plotted these points draw a smooth u shaped curve through them.
Rick runs 5 miles which burns approximately 500 calories. how many miles would rick have to run to burn one pound of adipose tissue?
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35miles Rick have to run to burn one pound of adipose tissue.
According to the given question.
Rick runs 5miles to burn 500 calories.
⇒ 1 mile burns the amount of calories = 500/5 = 100 calories.
As we know that
1 pound = 3,500 calories.
So the number of miles Rick needed to run to burn 1 pound of adipose tissue = 3500/100 = 35miles
Hence, 35miles Rick have to run to burn one pound of adipose tissue.
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can someone please help mee ( will give brainliest 20 points!!!)
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The piecewise function graphed below is given as follows:
[tex]f(x) = 3, -4 \leq x \leq -2[/tex][tex]f(x) = x + 2, -2 < x \leq 3[/tex][tex]f(x) = -1, 3 < x \leq 5[/tex]What is a piecewise function?A piecewise function is a function that has different definitions, depending on the input.
For x between -4 and -2, inclusive, the function is constant at 3, hence the definition is:
[tex]f(x) = 3, -4 \leq x \leq -2[/tex]
For x greater than -2 until 3, the function is a line with slope 1 and y-intercept 2, hence the definiton is:
[tex]f(x) = x + 2, -2 < x \leq 3[/tex]
For x greater than 3 until 5, the function is constant at -1, hence the definition is:
[tex]f(x) = -1, 3 < x \leq 5[/tex]
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When a number increases by 10 % it become 22, Find the number.
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what expression is equivalent to 6+3(n-4)-8+2n
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Answer:
Step-by-step explanation:
Comment
Begin by removing the brackets.
6+3(n-4)-8+2n
6 + 3n - 12 - 8 + 2n Collect like terms
3n + 2n + 6 - 12 - 8 Combine
5n - 14
Answer
5n - 14
Select the correct answer what are the solutions to this quadratic equation 4x^2-10=10-20x
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Answer:
x1 = 5-3squareroot 5/2 x2= -5+3 squareroot 5 / 2
Step-by-step explanation:
Find the midpoint of the line segment joining points A and B.
A(6-7); B(4,3)
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Answer: [tex]\Large\boxed{Midpoint=(5,~-2 )}[/tex]
Step-by-step explanation:
Given information
[tex](x_1,~y_1)=(6,~-7)[/tex]
[tex](x_2,~y_2)=(4,~3)[/tex]
Given the midpoint formula
[tex]Midpoint=(\dfrac{x_1+x_2}{2} ,~\dfrac{y_1+y_2}{2} )[/tex]
Substitute values into the given formula
[tex]Midpoint=(\dfrac{(6)+(4)}{2} ,~\dfrac{(-7)+(3)}{2} )[/tex]
Simplify values on the numerator
[tex]Midpoint=(\dfrac{10}{2} ,~\dfrac{-4}{2} )[/tex]
Simplify the fractions
[tex]\Large\boxed{Midpoint=(5,~-2 )}[/tex]
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To eliminate the y terms and solve for x in the fewest steps, by which constants should the equations be multiplied by before adding the equations together?
First equation: 4x − 3y = 34
Second equation: 3x + 2y = 17
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Answer:
Multiply both sides of the first equation by 2.
Multiply both sides of the second equation by 3.
Step-by-step explanation:
The y terms are
-3y
2y
The LCM of 2 and 3 is 6.
We need the y terms to add to zero.
Multiply both sides of the first equation by 2 to get -6y.
Multiply both sides of the second equation by 3 to get 6y.
Then -6y + 6y = 0 eliminating the y terms after adding the equations.
PLSSS HELP ASAP!! ty
On a graph, sketch f(x)=x+3 and g(x)=x. Is there a way of determining the graph of f(x)+g(x) without solving it algebraically? Explain your thinking below.
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From the graph, the equation of f(x) + g(x) is f(x) + g(x) = 2x + 3
How to determine the graph of f(x) + g(x)?The functions are given as:
f(x) = x + 3
g(x) = x
From the above functions, we can see that the function g(x) is the parent function of a linear function.
When the parent function of a linear function is added to another function to form a composite function, the new function would pass through the following points
(x, y)= (0, b) and (-b, -b)
Where b is the y-intercept of the other function
i.e b = 3 from f(x) = x + 3
So, we have the following points
(0, 3) and (-3, -3)
Next, we draw the points and we connect the points
When the equation of f(x) + g(x) is calculated, we have
f(x) + g(x) = 2x + 3
See attachment for the graph of the functions
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Perfect pizza has 16 toppings listed on their menu. how many ways could a customer choose a pizza that contains 5 different toppings?
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Answer:
4368 ways
Step-by-step explanation:
Use nCk for this. 16C5. This is [tex]\frac{n!}{(n-k)!(k!)}[/tex]. This becomes[tex]\frac{16!}{(11!)(5!)}[/tex]. This is [tex]\frac{16*15*14*13*12}{5*4*3*2*1}[/tex] due to 16! and 5! canceling out. This becomes 4368.
Solve the equation in the image (yr 8 maths, 50pts)
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4x - 20 = -x
5x -20 = 0
5x = 20
x = 4
Answer: x = 4
Step-by-step explanation:
Given equation
4x - 20 = -x
Add x on both sides
4x - 20 + x = -x + x
5x - 20 = 0
Add 20 on both sides
5x - 20 + 20 = 0 + 20
5x = 20
Divide 5 on both sides
5x / 5 = 20 / 5
[tex]\Large\boxed{x=4}[/tex]
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whats the surface area of the rectangular prism
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The surface area of the rectangular prism is 2(lw + wh + lh). A rectangular prism has six rectangular faces.
What is the area of a rectangle?The area of a rectangle with length and width is
Area = length × width
I.e., A = l × w sq. units
How to calculate the area of the rectangular prism?A rectangular prism has six rectangular faces and the length 'l', width 'w', and height 'h'.
So, the areas of each face are as follows:
A(R1) = l × w
A(R2) = l × h
A(R3) = w × h
A(R4) = l × w
A(R5) = l × h
A(R6) = w × h
Thus, the area of the prism = sum of areas of all the faces
⇒ Area of the prism = lw + lh + wh + lw + lh + wh
⇒ A = 2lw + 2lh + 2wh
⇒ A = 2(lw + lh + wh)
Therefore, the area of the rectangular prism is A = 2(lw + lh + wh).
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The function f(x) = –Two-sevenths (five-thirds)x is reflected over the y-axis to create g(x). Which points represent ordered pairs on g(x)? Check all that apply.
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The values of the function if the function f(x) is reflected over y-axis is g(x) = 10/21x
Reflection of coordinatesReflection is a transformation technique that changes the position of an object on an xy-plane.
If the function f(x) is reflected over y-axis, the resulting function is y = f(-x). Given the following function;
f(x) = -2/7(5/3)x
This can also be written as;
f(x) = -10/21 x
Replace x as -x
f(-x) = -10/21(-x)
f(-x) = g(x) = 10/21x
Hence the values of the function if the function f(x) is reflected over y-axis is g(x) = 10/21x
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1.** Mr. Jokinen is complaining about his heavy backpack. He removed a few books which decreased the weight of his backpack by 20%, but it still weighs 20 pounds. How much did his backpack weigh before he removed the books?
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Answer: 25 pounds
Step-by-step explanation: 100% - 20% = 80%
20 divided by 80% = 25
A jar contains 5 orange marbles, 3 black marbles, and 6 brown marbles. event a = drawing a brown marble on the first draw event b = drawing an orange marble on the second draw if two marbles are drawn from the jar, one after the other and not replaced, what is p(b|a) expressed in simplest form?
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The probability of event A and event B IS 15/91.
What is the probability?
Probability determines the odds that a random event would occur. The odds lie between 0 and 1.
The probability of event A = number of brown marbles / total number of marbles
= 6/14
The probability of event B = number of orange marbles / total number of marbles -1
= 5/13
P(A and B) =6/14 x 5/13
= 30/182
= 15/91
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Answer:
B.) 5/13
Step-by-step explanation:
15/3=5
91/7=13
5/13
BRAINEST IS VERYYYY APPRECATED
Given that a randomly chosen flight arrives in los angeles (lax), what is the probability that the carrier is american airlines (aa)?
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Using concepts of probability, it exists found that there exists a 4.7% probability that it arrives at American airlines (aa).
What is probability?A probability exists given by the number of expected outcomes divided by the number of total outcomes.
Over a large number of trials, a percentage can also define the probability of a single event.
In this question, analyzing the problem on the internet, we have that over a considerable number of flights, of those which came on time, 4.7% of them were in American airlines.
There exists a 4.7% probability that it arrives on American airlines(aa).
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Answer: 2316/16924 = 0.137 = 13.7%
Step-by-step explanation:
In using the multiple regression method, we can model the effects of the different levels of a qualitative independent variable by using a(n) ____________
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For the levels of qualitative, the variable called dummy variables is used in the multiple regression method.
According to the statement
we have given that the by which method we use the different levels of a qualitative independent variable and we have to explain about it.
So, For his purpose, we know that the
A dummy variable is a variable that takes values of 0 and 1, where the values indicate the presence or absence of something.
And in the multiple regression method there are a lot of different variables which are used for a qualitative and for this a variable is used which is called the dummy variables.
By this variables we show the analysis between the given data. it gives the output in the 0 and 1 numbers.
So, For the levels of qualitative, the variable called dummy variables is used in the multiple regression method.
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Which of the equations below represents
this ellipse?
a. x^2/4+y^2/20=1
b. x^2/2+y^2/10=1
c. x^2/100+y^2/4=1
d. x^2/4+y^2/100=1
Answers
The equation that represents the graph of the ellipse is x² / 4 + y² / 100 = 1. (Correct choice: D)
What is the equation of the ellipse represented in the graph?
Herein we have a representation of an ellipse in the image attached aside, ellipses are characterized by the following standard formula:
(x - h)² / a² + (y - k)² / b² = 1 (1)
Where:
(h, k) - Coordinates of the centera, b - Lengths of the semiaxesPlease notice that ellipse will be vertical if b > a, otherwise it will be horizontal. The graph exhibits a vertical ellipse centered at the origin and therefore we conclude that (h, k) = (0, 0) and b > a (b = 10, a = 2). Finally, the equation that represents the graph of the ellipse is x² / 4 + y² / 100 = 1. (Correct choice: D)
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HELP HELP PLEASEEE
Theo has 2.5k followers. He knows that if he posts daily, he will gain 1k followers each day.
In this scenario, identify the initial value and rate of change. Then, explain why this is or is not
proportional and/or a linear relationship.
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What are angles <3 and <4 ?alternate interior angles
alternate exterior angles
vertical angles
corresponding angles
Answers
An alternate exterior angle would be 2 and 4.
An alternate interior angle would be 1 and 3
A corresponding angle would be 1 and 4 or 2 and 3.
How many 5-digit numbers can be created
using the digits 2, 3, 5, 7, and 8 without
repeating any digits within that 5-digit
number?
Answers
Answer:
120.
Step-by-step explanation:
That would be factorial 5, written 5!.
That is 5*4*3*2*1
= 120.
Answer:
120
Step-by-step explanation:
We have 5 digits that can be used to create different 5 digit numbers. We are also not allowed to repeat any numbers. Let's say we have 5 boxes to put the 5 numbers in.
Box 1
Box 2
Box 3
Box 4
Box 5
In the first box, we have 5 different choices. Since we aren't allowed to repeat any digits, the second box only has 4 different choices. And so on...
Box 1 --> 5 choices
Box 2 --> 4 choices
Box 3 --> 3 choices
Box 4 --> 2 choices
Box 5 --> 1 choice
Therefore the amount of 5 digit numbers that can be created is:
[tex]5\times4\times3\times2\times1[/tex] or 5 factorial (a factorial is all the product of all the positive integers equal to and less than the number), which is equivalent to:
120 5-digit numbers
(b) Expand and simplify (x - 3) (2x + 3)(4x + 5)
Answers
Answer:
8x³ - 2x² - 51x - 45
Step-by-step explanation:
(x - 3)(2x + 3)(4x + 5) ← expand the 2nd/3rd factors using FOIL
= (x - 3)(8x² + 10x + 12x + 15)
= (x - 3)(8x² + 22x + 15)
multiply each term in the second factor by each term in the first factor.
x(8x² + 22x + 15) - 3(8x² + 22x + 15) ← distribute parenthesis
= 8x³ + 22x² + 15x - 24x² - 66x - 45 ← collect like terms
= 8x³ - 2x²- 51x - 45
Expand first 2 bracket first to get:
2x^2 + 3x - 6x - 9 & simplify, then expand with last bracket.
2x^2 - 3x - 9 (4x + 5)
2x^2 x 4x = 8x^4
2x^2 x 5 = 10x^2
Repeat for the next two numbers next to the bracket.
You get => 8x^3 + 10x^2 - 12x^2 - 15x - 36x - 45
Final simplified answer of:
8x^3 - 2x^2 - 51x - 45
Hope this helps!
Area=
Help me please!! Thanks so much-needed
Answers
First you have to figure out the side length of the triangle.
sin(60)= X/8
Let's call x the side length.
8 sin(60)=X
X=6.93
The multiply it by 4
The area is 27.72