Answer:
14 = 2 * 7
15 = 3 * 5
LCM = 2 * 3 * 5 * 7 = 210
question 9 (10 points)
4
If ƒ (x) = 4 — x, evaluate f (2k + 4).
k=1
The value of f(2k+4) for k=1 and f(x)= 4-x is -2
What is the value of a function?
When the variables and constants in a mathematical expression are given values, the outcome of the computation it describes is the expression's value.
We are given a function f(x)= 4-x
We have to find f(2k+4).
[tex]f(2k+4)=4-2k-4[/tex]
Now substitute k=1
We get,
[tex]f(2+4)=4-2-4\\f(6)=-2[/tex]
Hence, The value of function f(2k+4) at k=1 for the function f(x)=4-x is -2
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Which statements must be true about two similar figures? Select all that apply.
Group of answer choices
-The ratio of the corresponding angles equals 1.
-One triangle can be mapped onto the other triangles through a sequence of transformations.
-The ratios of corresponding side lengths are equal.
-The two triangles share a common side.
-The two triangles have exactly one pair of corresponding angles.
The statements that are true concerning two similar figures include:
The ratio of the corresponding angles equals 1.
The ratio of corresponding side lengths are equal. That is option A and C.
What is ratio?Ratio is defined as the number of time a proportion is doing in another proportion.
The similarity that exists between figures or shapes such as a triangle is being proven using Congruence & Similarity. That is,
To say that figures are similar, they must be congruent that is similar when superimposed.All the angle of their sides must also be equal and identical. There the ratio of the angel = 1.The sides of the figure must be proportional.Learn more about angles here:
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100PT AND BRAINLIEST! Write a complete two-column proof for the following information.
Given: m∠1 = 62° and lines t and l intersect
Prove: m∠4 = 62°
I would greatly appreciate if every step were labeled with the property used, e.g. "subtraction property of equality," etc. Thanks in advance for any help you can give!
Answer:
Since Lines t and l are straight lines and are intersecting, Angle 1 and 4 are vertically opposite angles.
Angle 1 = Angle 4 (vertically opposite angles)
Angle 1 = 62 degrees
Therefore Angle 4 = 62 degrees
Step-by-step explanation:
A recipe calls for 1 1/4 cups of flour to make 1 dozen cupcakes. How many cups of flour are needed to
make 36 cupcakes?
Since 1 dozen = 12, 12 cupcakes = 1 1/4 cups of flour
36/12 = 3
36 = 1 1/4(3)
36 cupcakes = 3 3/4 cups of flour
Answer:
8 1/4 cups
Step-by-step explanation:
You multiple 11/4 by 3 and change the answer to a mixed fraction
(2,-5) and (-1,1) are in the line, put it in standard form. Please help me I don’t understand it
The points (2, - 5) and (- 1, 1) lie on the equation of the line - 2 · x - y = 1.
What is the equation of the line in standard form?
According to Euclidean geometry, a line can be constructed from two distinct points on a plane. Then, we can find the equation of the line based on the coordinates of two points set on Cartesian plane, whose standard form is shown below:
a · x + b · y = 1
In this question we have the coordinates of two points: (2, -5), (- 1, 1). If we substitute in the equation of the line, then we find the following system of linear equations:
2 · a - 5 · b = 1
- a + b = 1
Then, we find the solution to the system by using numerical methods:
(a, b) = (- 2, - 1)
The equation of the line - 2 · x - y = 1 contains the points (2, - 5) and (- 1, 1).
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AB and CD lie in plane Z. If EF bisects either AB CD or, does EF lie in plane Z? If EF bisects both AB and CD, does EF lie in plane Z? Explain
your reasoning.
Answer:
If a b and c d lie in plane, z, so my screen is a plane, so let's just think of that here's a b! Now I didn't say they were parallel. It just said a b and c d, so they lie in a plane.
Step-by-step explanation:
I just did this on edge
302)+5)-1+4 (202)- 3) ≤125
True or False
The inequality (302+5)-1+4 (202)- 3) ≤ 125 is false for the given question.
What is inequality?A mathematical statement known as an inequality in algebra uses the inequality symbol to show the relationship between two expressions. An inequality symbol denotes that the expressions on either side are not equal.
It indicates that the expressions on the left and right should be greater or less than one another, or vice versa. Literal inequalities are those where the relationship between two algebraic expressions is defined by the inequality symbols '≠'.
We have given the inequality
(302+5)-1+4 (202)- 3) ≤ 125
Lets simplify
(302+5)-1+4 (202)- 3) ≤ 125
1111 ≤ 125
Thus, The inequality is false.
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Aaden signed up for a streaming music service where there's a fixed cost for monthly membership and a cost per song downloaded. His total cost per month is given by the equation c=2.99+1.75xc=2.99+1.75x, where xx represents the number of songs he downloads and cc represents the total cost, in dollars and cents. What could the number 2.99 represent in the equation?
Answer:
2.99 is the fixed monthly membership fee
Step-by-step explanation:
Solve the inequality x(2x+3) > 20
The inequality of the equation x(2x+3) > 20 is x<-4 or x>5/2.
Given, the expression is x(2x+3) > 20
open the brackets.
⇒ 2x²+3x>20
⇒ 2x²+3x-20>0
Factorize the equation.
⇒ 2x²+8x-5x-20>0
⇒ 2x(x+4)-5(x+4)>0
⇒ (x+4)(2x-5)>0
hence, (x+4)>0 or (2x-5)>0
(x+4)>0
⇒ x<-4
(2x-5)>0
⇒ 2x > 5
⇒ x >5/2
Hence we get the required inequality for the given equation.
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Please help now need it soon!! :) Please and thank you!!
Zach spent 2/6 of his paycheck on a new video game the cost of the videogame was $58 what was the total amount of his paycheck?
The total amount of Zach's paycheck was $174.
The fraction of the paycheck spent by Zach on the new video game is 2/6. The cost of the video game is $58. We need to find the total amount that Zach had in the paycheck.
A fraction is a portion of a whole or, more broadly, any number of equal pieces. An equation is a formula in mathematics that expresses the equivalence of two expressions by linking them with the equal sign.
Let the total amount of the paycheck be "x". Using the information above, we can form an equation as given below :
(2/6)*x = 58
x = (6/2)*58
x = 174
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Cannon wants to put as much as he can into a retirement account as soon as he starts working. He deposits $25,000 at then end of each year for 5 years in an account paying 6% interest compounded annually. How much will he have in the account at the start of the 6th year? A) $140,927.34 B) $174,382.96 C) $395,240 D) $557,593.99
The compound interest formula is given by the formula
[tex]A\text{ = }p(1+\frac{r}{100})t[/tex]Where A = Amount after t years
r = rate = 6
t = time = 5
p = $ 25000
For the first year
[tex]\begin{gathered} A=\text{ 25000(1+0.06)} \\ =25000\times1.06=26500 \end{gathered}[/tex]For the second year
P=26500+25000=51500
[tex]\begin{gathered} A=51500(1+0.06) \\ =515000\times1.06=54590 \end{gathered}[/tex]For the third year
P=54590 + 25000=79590
[tex]\begin{gathered} A=79590\text{ }\times1.06 \\ =84365.4 \end{gathered}[/tex]For the fourth year
P=84365.4 + 25000=109365.4
[tex]\begin{gathered} A=\text{ 109365.4}\times1.06 \\ =115927.324 \end{gathered}[/tex]For the fifth year
P= 115927.324 + 25000 =140927.324
[tex]\begin{gathered} A=\text{ 140927.324}\times1.06 \\ =149382.962 \end{gathered}[/tex]At the start of the 6th year
P= 149382.962+25000= 174382.96
Answer = $174382.96
Option B is correct
HELP ME PLEASE AND THANK U
Find the slope if it exist of the line containing the pair of points
(5,-10) and (-3,-10)
The slope m=
The slope of the line containing the pair of points (5,-10) and (-3,-10) = m = 0.
Slope of a line
In Mathematics, a slope of a line is the change in y coordinate with respect to the change in x coordinate. The net change in y-coordinate is represented by Δy and the net change in x-coordinate is represented by Δx.
Determine the difference in y-coordinates of these two points (rise). Determine the difference in x-coordinates for these two points (run). Divide the difference in y-coordinates by the difference in x-coordinates (rise/run or slope).
Given that the line containing the pair of points (5,-10) and (-3,-10).
Slope of a line = (y2 - y1)/ (x2 - x1)
Here
y1 = -10
x1 = 5
y2 = -10
x2 = -3
Therefore slope of a line = m = [-10 - (-10)]/ (-3 - 5)
= 0/ (-8)
= 0
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Xin owns a trucking company. for every truck that goes out, xin must pay the driver $20 per hour of driving and also has an expense of $2.25 per mile driven for gas and maintenance. on one particular day, the driver drove an average of 50 miles per hour and xin's total expenses for the driver, gas and truck maintenance were $1457.50. write a system of equations that could be used to determine the number of hours the driver worked and the number of miles the truck drove. define the variables that you use to write the system.
The number of miles that the truck drove is 550 miles.
How to illustrate the information?From the information, Xin must pay the driver $20 per hour of driving and also has an expense of $2.25 per mile. This can be illustrated as:
20x + 2.25y = 1457.50 ....... i
x = number of hours
y = number of miles driven
The driver drove an average of 50 miles per hour. This will be illustrated as:
y/x = 50
y = 50x
Substitute into equation i
20x + 2.25y = 1457.50
20x + 2.25(50x) = 1457.50
20x + 112.50x = 1457.50
Collect like terms
132.50x = 1457.50
Divide
x = 1457.50 / 132.50
x = 11
y = 50x = 50 × 11 = 550 miles
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A fish tank has 150 gallons of water and is being drained at a rate of 1/2 gallon each second. A second fish tank has 120 gallons of water and is being filled at a rate of 1/4 gallon each second. After how many seconds will the two fish tanks have the same amount of water?
Answer: 40 seconds
Step-by-step explanation:
This is basically a very simple algebra problem.
Let x be the number of seconds it takes for the statement to be true
120 + x/4 = 150 - x/2
Add x/2 to both sides:
120 + 3x/4 = 150
Subtract 120 from both sides:
3x/4 = 30
Therefore x = 40.
Solve similar problems with an equation, where the variable is the thing you need to find.
Help me! im not sure what to do!
The frequency of the heights are:
a = 15
b = 20
c = 40
d = 15
Histogram :
A histogram is a visual representation of statistical data that makes use of rectangles to illustrate the frequency of data points over a range of successive numerical intervals of equal width. The independent variable and dependent variable are plotted along the horizontal axis and the vertical axis, respectively, in the most typical type of histogram.
A common tool for graphing is the histogram. It is employed to summarise continuous or discrete data that is measured on an interval scale. It is frequently used to provide a convenient manner of illustration for the main characteristics of the data distribution.
Now Calculating the frequency by studying the given histogram.
By studying the given histogram, 1 division of the x-axis = 0.5
For height, [tex]0\leq h\leq 50[/tex], the histogram reaches up to 30 divisions which indicates that the frequency is 15.
For height,[tex]50\leq h\leq 75[/tex], the histogram reaches up to 40 divisions which indicate that the frequency is 20.
For height, [tex]75\leq h\leq 100[/tex], the histogram reaches up to 80 divisions which means the frequency is 40.
For height,[tex]100\leq h\leq 150[/tex], the histogram reaches up to 30 divisions which indicate that the frequency is 15
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Students on the soccer team and the rugby team at several high schools were surveyed to choose a vacation location: Aspen, Colorado, or New York, NewYork.
Which location would you most like to visit?
What is the joint frequency of soccer team students who would most like to visit New York?
•27
•35
•53
•62
Five mi is approximately equal to 8 km. Use mental math to estimate
the distance in kilometers to a town that is 30 mi away.
Using the conversion factor, we know that 30 miles are approximately 48 km.
What is the conversion factor?A conversion factor is a number that is used to multiply or divide one set of units into another. If a conversion is required, it must be done using the correct conversion factor to get an equal value. For instance, 12 inches equals one foot when converting between inches and feet.So, 30 miles is how many kilometers:
We know that 1 mile = 1.60934 kmThen, 5 miles:
1.60934 × 5 = 8.04672 kmSimilarly 30 miles:
1.60934 × 30 = 48.2803Rounding off: 48 km approximately
Therefore, using the conversion factor, we know that 30 miles are approximately 48 km.
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The greater of two numbers is 5 more than the smaller. If the
smaller is added to twice the greater, the result is 22. Find both
of the numbers.
Answer:
First number = 4
Second number = 9
Step-by-step explanation:
If the first number = x, the second number = x + 5.
The calculation can be expressed as follows:
x + 2(x + 5) = 22
First, expand the bracket 2(x + 5):
x + 2x + 10 = 22
Combine like terms:
3x + 10 = 22
Subtract 10 from both sides:
3x = 12
Divide both sides by 3:
x = 4
First number = 4
Second number = 4 + 5 = 9
The rectangle below has been drawn on a centimetre square grid.
What is the perimeter of the rectangle?
Give your answer in centimetres (cm).
4 cm
The equation for a rectangle's perimeter is P = length + breadth + length + breadth. Alternatively, P=2(length + breadth). The length of a shape's outline is its perimeter. You must add the lengths of all four sides of a rectangle or square to determine its perimeter.
What is the rectangle's perimeter? The complete distance that the rectangle's outside boundary covers is referred to as its perimeter. Its length is expressed in units. The perimeter is calculated using the formula: Perimeter, P = 2 (Length + Width).The perimeter of a form is the space surrounding its edge. Find the perimeter of various forms by summing the lengths of their sides.Simply add the lengths of the three sides to calculate the perimeter as all the sides are measured in cm. You may occasionally need to use what you already know about a polygon to determine its perimeter.The area of a rectangle is calculated using the formula A=LW A = L W, where A is the area and L and W are the length and breadth of the rectangle, respectively. The formula for a rectangle's perimeter is P=2(L+W), where P stands for the perimeter, L for length, and W for width.To know more about Perimeter refer to:
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A family used a professional decorator to help furnish their new home. The decorator selected $1,580 worth of furnishings. The family paid for the furnishings, plus 4.5% tax on the purchases. The decorator’s fee was 12% of the purchases, not including the tax. Question 1 Part A Write an equation in the form of y=kx, using x to represent the decorator’s fee. Then use the equation to calculate the amount of that fee.Part B Write an equation in the form of y=kx to represent the tax. Then use the equation to calculate the amount of tax.Part C What is the total cost that the family paid?
PLEASE HELP!!!THANK YOU!!
As per direct variation,
Part A) Decorators fee is $198.132
Part B) Tax for the purchase is $71.10
Part C) The total amount spend by the family is $1849.232.
Direct variation:
Direct variation depicts a simple relationship between two variables . We say y varies directly with x if:
y=kx
for some constant kk , called the constant of variation or constant of proportionality. Which means that as x increases, y increases and as x decreases, y decreases—and that the ratio between them always stays the same.
Given,
A family used a professional decorator to furnish their new home.
The decorator selected $1,580 worth of furnishings for their home.
The payment will be made by the family for the furnishings, plus 4.5% tax on the purchases.
The decorator’s fee was 12% of the furnishings , excluding the tax.
Here we need to find the following:
Part A) Decorator's fee
Part B) Tax amount
Part C) Total cost.
We know that, the decorator’s fee was 12% of the purchases.
So, the equation is then be calculated as:
y = kx
where,
y = decorators fee
k = percentage of decorators fee for the purchases
x = amount paid
y = 12% × $1651.10
= 0.12 × $1651.10
Therefore, the decorators fee is $198.132
Decorator selected furnishings cost = $1,580.
Tax = 4.5%
Decorator’s fee = 12% of the purchases.
So, it can be calculated as,
Tax = 4.5% × 1580
Tax = 0.045 × 1580
Therefore, the tax for the purchase is $71.10
Amount paid = 1580 + 71.10 = 1651.10
Now, the total amount paid by the family is,
=> purchase amount + decorator fee
=> 1651.10 + 198.132
=> 1849.232
Therefore, the total amount spend by the family is $1849.232.
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What is the product?
(3a^2b^7)(5a^3b^8)
===================================================
Explanation:
The coefficients of each term are 3 and 5. They are the first things mentioned in each parenthesis grouping. The coefficients multiply to 3*5 = 15. This is the coefficient of the final answer.
The 'a' terms are a^2 and a^3. They multiply to a^2*a^3 = a^(2+3) = a^5. Add the exponents because we're using the rule a^b*a^c = a^(b+c). The base must be the same for this rule to apply.
The b terms are b^7 and b^8. They multiply to b^7*b^8 = b^(7+8) = b^15
--------
To summarize
The coefficients multiply to 15. The 'a' terms multiply to a^5 The b terms multiply to b^15This is how we end up with 15a^5b^15 as the final answer
WRITE AN EQUATION TO REPRESENT YOUR ANSWER.
FORMAT: variable term + constant = total
Ginny is making cookies for a bake sale. The recipe she is using makes 24 cookies in a batch. Ginny took 198 cookies to the bake sale after 18 burned. How many batches of cookies did she make?
-2x + 6x – 9 = 15 solve for ex show your work that why i give so much
Answer:
x=6
Step-by-step explanation:
1. Combine like terms
2. Add 9 to both sides
3. Divide by 4 on both sides
4. Arrive at solution
5. Plug solution in to equation.
Answer:
-3
Step-by-step explanation:
first you start with by adding 9 to both sides to balance
-2x+6x-9=15
+9 +9
Giving you -2x+6x=24 now you start by dividing
I started by dividing -2
-2x+6x=24
÷(-2) ÷(-2)
Giving you x+6x=(-12) again divide
x+6x=(-12)
÷6 ÷6
Giving you x+x=(-6) we know that x+x is = to 2x next we divide agian
2x=(-6)
÷2 ÷2
Giving you the answr x=(-3)
Please help me it a test grade and it's do today
Answer:
[tex]x = 16[/tex]
Step-by-step explanation:
Because of the fact, the angle is ∠BCA = 10x - 10 and ∠ABC = 30 lies on a straight line and ∠BCA is obtuse while ∠ABC is acute, we can just set them equal to 180 to find the value of x.
So we will set up the equation:
10x - 10 + 30 = 180
1. Combine Like Terms (eg. -10 and 30)
[tex]10x - 10 + 30 = 180[/tex]
= [tex]10 x + 20 = 180[/tex]
2. Subtract 20 on both sides
[tex]10x + 20 = 180[/tex]
[tex]-20 -20[/tex]
= [tex]10x = 160[/tex]
3. Divide 10 into both sides
[tex]\frac{10x}{10} = \frac{160}{10}[/tex]
And we will get:
[tex]x = 16[/tex]
Check Your Work!
Now if we replace x in the equation for 16 like below we do in fact get 180:
[tex]10(16) - 10 + 30 = 180[/tex]
[tex]160 - 10 + 30 = 180[/tex]
[tex]150 + 30 = 180[/tex]
[tex]180 = 180[/tex]Two functions are given below: f(x) and h(x). State the axis of symmetry for each function and explain how to find it.
f(x)=3(x+4)²+1
Step-by-step explanation:
the axis of symmetry for a regular parabola (opens up or down) is a line parallel to the y-axis (vertical) going through the vertex of the parabola.
the standard form of a parabola is
y = a(x - h)² + k
with (h, k) being the vertex.
so, we see for f(x) the vertex is (-4, 1).
the axis of symmetry uses the x coordinate of the vertex and is
x = -4
for h(x) we see in the graphic that the vertex is (1, -3).
so, the axis of symmetry is
x = 1
FYI - based on what we see : vertex is (1, -3), h(0) = -1 the function here would be
h(x) = 2(x - 1)² - 3
A package of 5 pairs of insulated gloves costs $25.95. What is the unit price of the pairs of gloves
The unit price of the pair of gloves is $5.19.
Here, a package of 5 pairs of insulated gloves costs $25.95.
We have to find the unit price of the pairs of gloves.
5 pairs of insulted gloves = $25.95
So we have to find the value of 1 pair of gloves, so by dividing the value by 5 we will get the value of 1 pair of gloves.
Unitary method:
The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit.
So by using the unitary method we have:
1 pair of insulated gloves = 25.95/ 5
= 5.19
Therefore the unit price of the pair of gloves = is $5.19.
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The population of a city increases by 0.8% per year. if this year's population is 101,000, what will next year's population be, to the nearest individual?
The population of the city till next year will be 101,808.
Given, a population of a city increases by 0.8% per year.
Presently the population of the city is = 101,000
Next year's population will be = ?
population increases by 0.8% per year = 1+0.8%
Hence the expression can be written as:
present population of city × population increases by 0.8% per year
= 101,000 × (1+0.8%)
= 101,000 × (1+0.008)
= 101,000 × (1.008)
multiply the terms.
=101808
Hence when the population of the city increases by 0.8% per year, then next year's population will be 101,808.
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Edgar us using computer graphics to build the background images for a new animated film. He is using linear modeling, the process of using linear equations to describe real-world objects. Edgar had identified the functions needed to build an image in the graphics program.
A field of mathematics called linear equations is essential to computer graphics. It investigates matrices, linear transformations, and vectors. These subjects were covered in Subsection 2.3. 8 in a two-dimensional setting.
What is a linear model?A continuous response variable is described by a linear model as a function of one or more predictor variables. They can assist you in analyzing experimental, monetary, and biological data or in understanding and predicting the behavior of complex systems. A statistical technique used to build a linear model is called linear regression.
Depending on the context, the phrase "linear model" is used differently in statistics. The word is frequently used interchangeably with a linear regression model since it occurs most frequently in relation to regression models. The phrase has a different connotation when employed in time series analysis, though.
By using a linear combination of predictor variables, linear models can be used to describe a response variable. A continuous variable with a response that is at the very least roughly regularly distributed is required.
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need help with this pleaseee!!
The coordinate of B is option C (0,-2). A spherical or elliptical coordinate system known as the geographic coordinate system is used to measure and transmit positions on Earth as latitude and longitude. Of the several spatial reference systems in use, it is the most basic, traditional, and often utilized. It also serves as the foundation for the majority of others.
What is coordinates?Coordinates are numerical lengths or angles that uniquely identify locations on two-dimensional (2D) surfaces or in three-dimensional (3D) space. Mathematicses, scientists, and engineers frequently employ a variety of coordinate systems.
A coordinate system in geometry is a method for determining the location of points or other geometric objects on a manifold, such as Euclidean space, uniquely using one or more numbers, or coordinates.
the coordinates of B(-5,0)
the translation rule
(x,y)---------(x+5,y-2)
so
B(-5,0)-----B(-5+5,0-2)
(-5,0)--------(-5+5,0-2)----------(0,-2)
Hence, the correct answer is (0,-2)
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