slope = (change in y)/ change in x
[tex]undefined[/tex]use the method of dividing by prime factors to find the greatest common factor of the following numbers 574 and 532
The greatest common factor is the greatest number that divides both numbers.
The given numbers are 574 and 532.
First, let's decompose each number into their prime factors.
574 | 2
287 | 7
41 | 41
1
574 = 2*7*41
532 | 2
266 | 2
133 | 7
19 | 19
1
532 = 2*2*7*19
As you can observe, the common factors are 2 and 7, so the greatest common factor is 14 since that's the product between 2 and 7.
Therefore, the greatest common factor between 574 and 532 is 14.Adam leases a truck with an upfront payment of $3100 and monthly payments of $154. Assuming there are no additional charges, what will be the total cost of a 3-year lease?
State your answer in terms of dollars, rounded to the nearest cent, but do not include a $ sign or the word "dollars" with your response.
The total cost of leasing the truck for 3 years is $8644.
What is an equation?An equation is an expression that can be used to show the relationship between numbers and variables.
Let y represent the total cost of leasing the truck for x months.
Adam leases a truck with an upfront payment of $3100Monthly payments are $154y = 154x + 3100
In 3 years, number of months (x) = 3 * 12 months = 36 months
Total cost in 3 years is:
y = 3100 + 154(36) = 8644
Total cost is $8644
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Allen wanted to find the height of a tree in his yard. He knew that the fence surrounding his yard was 4 feet
high. At 3 pm the shadow of the fence was 2.5 feet long. The shadow of the tree was 11.3 feet long. What
was the height of the tree?
The graph of the following is graph of the following function is given below, apply the given transformations and graph the new function Y= f(x-1)+2
f(x-1) + 2 translates f(x) 1 unit to the right and 2 units up. Then, the graph of the new function is:
Find the value of b that makes quadrilateral RSTU a parallelogram.
We are asked to find the value of b that makes quadrilateral RSTU a parallelogram.
We know from the properties of a parallelogram that the opposite angles are always equal.
[tex]\begin{gathered} \angle S=\angle U \\ \angle T=\angle R \end{gathered}[/tex]Let us equate the angles and solve the equation for b.
[tex]\begin{gathered} \angle S=\angle U \\ 11b-6=12b-18 \\ 11b-12b=-18+6 \\ -b=-12 \\ b=12 \end{gathered}[/tex]Similarly,
[tex]undefined[/tex]Let f(x) = 2x - 1 and g(x) = x² + 1. Find and simplify: (g ° ƒ) (1/2)
To find the composition we need, let's first find the general expression:
[tex]\begin{gathered} (g\circ f)(x)=g(f(x)) \\ =g(2x-1) \\ =(2x-1)^2+1 \\ =4x^2-4x+1+1 \\ =4x^2-4x+2 \end{gathered}[/tex]Hence:
[tex](g\circ f)(x)=4x^2-4x+2[/tex]Now we can evaluate when x=1/2:
[tex]\begin{gathered} (g\circ f)(\frac{1}{2})=4(\frac{1}{2})^2-4(\frac{1}{2})+2 \\ =4(\frac{1}{4})-2+2 \\ =1-2+2 \\ =1 \end{gathered}[/tex]Therefore:
[tex](g\circ f)(\frac{1}{2})=1[/tex]1ptWhat value of c would make x2 – 14.c +ca perfect square?C=What is the factored form of this expression for this value of c?(.)?
The value of c would be 49 and the factored form will be;
[tex](x-7)^2[/tex]Here, we want to get the value of c that will make the expression a perfect square
We proceed as follows;
Divide the coefficient of x by 2 ;
That would be; -14/2 = -7
Now, square this value; that would be (-7)^2 = 49
The value 49 would make the expression a perfect square
Thus, we have the factored form as follows;
[tex](x^2-14x+49)\text{ = (x-7)(x-7)}[/tex]Simplify 6x(9-2)-6 divided by 2
i don't have any idea but ok JQJAJDJDJKSBA
Determine whether the graph represents a linear, quadratic, or exponential function.o Exponentialo Linearo Quadratic
When we graph a linear equation we draw a line. When we want to graph a quadratic equation we draw a parabola, a parabola is a U-shaped curve. The graph of an exponential function grows or decays and has asymptotic values.
In this case, the first graph is a line, so it represents a linear equation.
The second graph is a U-shaped curve, then it represents a quadratic equation.
The third graph decays, then it represents an exponential equation.
A college basketball team offers season passes for $85, but you pay $4.45 for a program
at each game. Non-season-pass holders pay $9.45 for admission to each game, but the
game program is free. For what number of games is the cost of these plans the same?
For 9 of games is the cost of these plans the same.
What are basic linear equations?Moving the variables to one side of the equation and the numeric portion to the other allows us to solve a linear equation with one variable. As an illustration, the equation x - 1 = 5 - 2x can be resolved by transferring the numerical components to the right side of the equation while leaving the variables on the left. Therefore, we receive x + 2x = 5 + 1. Thus, 3x Equals 6. As a result, x = 2. The formula for a two-variable linear equation is Ax + By + C = 0, where A and B are the coefficients, C is a constant term, and x and y are the two independent variables, each with a degree of 1. A linear equation involving two variables, for illustration, is 7x + 9y + 4 = 0.
Consequently, you would multiply $9.45 and $4.45 by the same number (I selected 9 because there are only one or two possible answers), then add $85 to the result for the $4.45 amount.
9.45 x 9
= 85.05
4.45 x 9
= 40.05 +85
= 125.05
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#15If you do not know college algebra, please say so and let me move on.
In order to graph the functiom we need to identify the parent function and the vertical and horizontal shifts that might be done to the function.
In this case we see that the parent function is a cubic function since the greater degree is 3
[tex]g(x)=x^3[/tex]this means that f(x) is a transformation of g(x)
then
the horizontal shifts since there is sum inside the parentheses the shift will be 1 unit to the left.
the vertical shift will be 1 unit up since there is a sum outside the parentheses.
and finally since there is a - it means that the function is reflected over the x-axis
the parent function will be the red line and the function #15 is the blue line.
In order to find points we can tabulate the values for given xs' and construct the graph.
Start by making a table like this:
now since the function is given we can replace x with the values and find y
[tex]\begin{gathered} y=-(x+1)^3+1 \\ y=-(-6+1)^3+1 \\ y=-(-5)^3+1 \\ y=-(-125)+1 \\ y=125+1 \\ y=126 \end{gathered}[/tex]then after tabulating values should look like this
Now looking at the graph on the blue function we can see that the function is decreasing until reaching x=-1, however after that the function will continue to decrease but at a different rate, which means that over the interval
[tex](-\infty,\infty)[/tex]the function will be decreasing
Scenario: I am interested in selling cookies in my online bakery store. But before that, I need to find out how much I should price it to maximize revenue. I surveyed 1500 people and found out that if I price it at $2.00 a cookie then 800 people would buy it. If I price it at a dollar more at $3.00. a cookie, then 600 people would buy it. On the other hand, if I price it at a dollar less at $1.00 a cookie, then 1000 people would buy it. Based on this information, I noticed that for every one dollar increase in price, 200 fewer people would buy it. 1. Solve the scenario problem above for the optimal item price that maximizesrevenue. Be sure to show all your work and reflect on your findings.
the Let number of people = y
Let price = x
Gradient = -200
[tex]\begin{gathered} -200\text{ = }\frac{y\text{ - 800}}{x\text{ - 2}} \\ y\text{ - 800 = -200(x - 2)} \\ y\text{ - 800 = -200x + 400} \\ y\text{ = -200x + 400 + 800} \\ y\text{ = -200x + 1200} \end{gathered}[/tex]Revenue = price X number of people
[tex]\begin{gathered} R(x)\text{ = x }\times\text{ y} \\ R(x)\text{ = x(-200x + 1200)} \\ R(x)=-200x^2\text{ + 1200x} \\ R^{\prime}(x)\text{ = -400x + 1200} \\ To\text{ maximize , R(x) = 0} \\ -400x\text{ + 1200 = 0} \\ 400x\text{ = 1200} \\ x\text{ = }\frac{1200}{400} \\ \text{x = 3} \end{gathered}[/tex]Optimal item price = $3
one integer is 7 less than 5 times another. Their product is 24. Find the integers.
Answer:
3, 8
Step-by-step explanation:
Let's make the first integer x and the second integer y.
Now, you take the information given and convert it into a system of equations:
xy = 24
x = 5y - 7
y = 24 / x
Now, we substitute:
(5y - 7) · y = 24
Distribute y
5y² - 7y = 24
Rearrange it into a quadratic equation:
ax² + bx + c = 0
5y² - y - 24 = 0
Use the quadratic formula (shown in image) and plug in the values:
x = (- (7) ± [tex]\sqrt{(-7^})^{2} -4(5)(-24)}[/tex] ) / 2(5)
[tex]\sqrt{(-7)^{2} -4(5)(-24)}[/tex] = [tex]\sqrt{49 - (-480)} = \sqrt{529} = 23[/tex]
Remember that ± means there are two y values
[tex]x = \frac{7+23}{10} = \frac{30}{10} = 3[/tex]
and
[tex]x = \frac{7-23}{10} = \frac{-16}{10} = -1.6[/tex]
Since y must be an integer, we know that y = 3
Now, plug in y:
5(3) - y = 24
15 - y = 24
- y = -24
y = 8
Let's check to see if we are right:
5y - 7 = 5(3) - 7 = 15 - 7 = 8
It works!
A car travels about 32 miles on 1 gallon of gas. While a truck drives about 260 miles on 9.75 gallons of gas. Which gets better gas mileage?
In order to determine which vehicle gets better gas mileage, we need to determine which of the two vehicles consumes less gas for each mile travelled. The car consumes 1 gallon of gas for every 32 miles. We shall now determine how many miles the truck covers to consume 1 gallon of gas.
[tex]\begin{gathered} \text{Truck} \\ 9.75gl=260\text{miles} \\ 1gl=\frac{260}{9.75}\text{miles} \\ 1gl=26.67miles \end{gathered}[/tex][tex]\begin{gathered} \text{Car} \\ 1gl=32\text{miles} \end{gathered}[/tex]Therefore, the results shows that the truck gets better gas mileage
Describe a series of transformations Matt can perform to decide if the two windows are congruent
The three transformations—rotations, reflections, and translations—can be combined to produce congruent shapes. The truth is that any pair of congruent shapes can be matched to one another by combining one or more of these three transformations.
Explain transformations.
A point, line, or geometric figure has four different transformations that can be applied to alter its appearance. While the term "Image" refers to the position and final shape of the object, "Pre-Image" refers to the object's shape before transformation.
Given Information
The size and shape of the figures are preserved during stiff transformations, as we already know (reflections, translations, and rotations). Always in harmony with one another is the pre-image.
These transformational skills are all possessed by Matt:
Reflection
The reason a reflection maintains its original form Comparable locations between the pre-image and the picture remain apart from the line of reflection.
Rotations as a Transformation of Congruence
When a figure rotates, it twists. Despite being the same size and shape, the figurine appears to have toppled over. A clock is an excellent example of how the globe rotates in reality. Every hour or every day, the connecting arms of a clock revolve around its axis. The degree of a rotation determines what kind of rotation it is; popular rotations include 90, 180, and 270 degrees. Before spinning around completely and going back to where it started, the figure rotates 360 degrees. the clockwise or counterclockwise direction in which a rotation is made. This data can be used to determine the degree, amount, a revolution's speed and direction.
Congruence translational transformation
When an object or shape is transferred from one location to another without altering its size, shape, or orientation, we refer to the transfer as a movement. A translation, often known as a slide, involves moving every point on an object or shape uniformly and in one direction.
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What is 14.481 rounded to the nearest tenth?A) 14B) 14.4C) 14.5D) 15
To round to the nearest tenth, we must round it to the nearest hundredth first, we have
[tex]14.481[/tex]See that we have 1 at the last decimal, then we will keep the hundredth value, it means that we will round to
[tex]14.481\rightarrow14.48[/tex]Now the last decimal is 8, it's above 5, then we must add one at the tenth and remove the hundredth
[tex]14.48\rightarrow14.5[/tex]Therefore the nearest tenth is the letter C, 14.5
Answer:c
Step-by-step explanation:THIS SOOO CORRECT!
help i just want to know if it's right or wrong
We consider a vector with:
• initial point (x₁, y₁) = (4, 3),
,• final point (x₂, y₂) = (-4, -1).
The magnitude of the vector is given by:
[tex]||v||=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}=\sqrt{(-4-4)^2+(-1-3)^2}\cong8.944.[/tex]The angle of the vector is given by:
[tex]\tan\theta^{\prime}=\frac{y_2-y_1}{x_2-x_1}=\frac{-1-3}{-4-4}=\frac{-4}{-8}=\frac{1}{2}\Rightarrow\theta^{\prime}=\tan^{-1}(\frac{1}{2})\cong26.565.[/tex]We have obtained a positive value of the angle θ'. But we see that our vector points in the negative direction. To take into account this, we must sum 180° to this result:
[tex]θ\cong26.565\degree+180\degree=206.565\degree.[/tex]Answer||v|| = 8.944, θ = 206.565°
please help- I’m failing math. an explanation would help too
Answer:
11
Step-by-step explanation:
The answer would be 11, because when you add 5 and 6 together, you get 11. Pretend you had 5 cookies, and you got 6 more.
5 Cookies- O,O,O,O,O
6 More Cookies- O,O,O,O,O,O
If you add the cookies up, you get 11.
A group of friends wants to go to the amusement park tey have no more than $115 to spend on parking and admission parking is $15 and the tickets cst $25 per person including tax wrote and solve an inequality which can be used to determine x the number of people who can go to the amuement park
An inequality which can be used to determine x the number of people who can go to the amusement park is: 15 + 25x ≤ 115
Also, approximately 4 people can go to the amusement park.
In the given question,
cost for admission parking = $15
Tickets = $25 per person
Let x be the number of people those who go to the amusement park.
On parking and admission spent not more than $115
So we get an inequality,
15 + 25x ≤ 115
We solve above inequality.
25x ≤ 115 - 15
25x ≤ 100
25x / 25 ≤ 100/25
x ≤ 4
This means that approximately 4people can go to the amusement park.
Therefore, an inequality which can be used to determine x the number of people who can go to the amusement park is: 15 + 25x ≤ 115
Also, approximately 4 people can go to the amusement park.
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Can someone help me with this? Please and thank you
Given the line shown in the figure passes through the points (-3, -4) and (1, 2)
We will write the equation of the line.
First, we will find the slope of the line using the following formula:
[tex]slope=m=\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}[/tex]Substitute with the given points:
[tex]m=\frac{2-(-4)}{1-(-3)}=\frac{2+4}{1+3}=\frac{6}{4}=\frac{3}{2}=1.5[/tex]The equation of the line in point-slope form will be as follows:
[tex]\begin{gathered} y+4=1.5(x+3) \\ or \\ y-2=1.5(x-1) \end{gathered}[/tex]Convert tot he slope-intercept form, so, the equation will be:
[tex]\begin{gathered} y=1.5(x+3)-4 \\ y=1.5x+4.5-4 \\ \\ y=1.5x+0.5 \end{gathered}[/tex]Now, we will check the options to see the correct equations.
So, the answer will be, we will select the options:
A. y+4 = 1.5 (x+3)
B. y = 1.5x + 0.5
C. y - 2 = 1.5 (x - 1)
What’s the correct answer answer asap
Answer:
Serbia
Step-by-step explanation:
Austria-Hungary declares war on Serbia, effectively beggining the first world war
What is the solution set for: 4x - 3>29 *X> 4OX >8OX8OX > 3
Let us first solve the inequality
[tex]\begin{gathered} 4x-3>29\rightarrow \\ 4x>29+3=32 \\ 4x>32 \\ x>\frac{32}{4}=8 \\ x>8 \end{gathered}[/tex]So the answer is x>8
help meeeeeeeeee pleaseeeeeeeeeee!!!
thank youu
For the given ques, the graph is mention in the question.
As, domain are the all set of values lying on the x-axis.
Thus,
A. Domain {-1 to infinity} (In integer or fraction form.)
B. Domain [-1, ∞), (interval notation; half closed half open)
Range of the relation of function are-
A. Range {- infinity to infinity} (In integer or fraction form.)
B. Range (- ∞, ∞), (interval notation open interval both sides)
Thus, the value of domain and range of the function are found.
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Pls help I don’t get what dis teacher even wants bro
Answer:
5 cups of flour.
Step-by-step explanation:
I know the wording of the problem may be confusing at first, but if you look at it a little bit, it's just multiplication and division.
To start,
12 biscuits require 2 cups of flour,
meaning that 6 biscuits (half of the original) only require 1 cup.
(12/2 = 6)
Next,
We need to find how much flour is in 30 biscuits.
We know that 1 cup is in 6 biscuits, and if you were to find how much was in 30 biscuits, you would just need to divide 30 by 6.
(30/6 = 5)
5 cups of flour would be your answer.
To put it mathematically,
(12/2 = 6), (30/6 = 5)
4. Which function will translate f(x) = x2 right 3 units and down 2 units?a. f(x) = (x - 2)2 – 3b. B. f(x) = (x - 3)2 – 2c. C. f(x) = (x - 3)2 + 2d. D. f(x) = (x + 3)2 – 2
f(x) = x^2
To translate the function 2 units down (along the y axis) subtract 2
F(x) = x^2 -2
To translate the function 3 units to the right (along the x-axis) subtract 3 units inside the parentheses.
f(x) = (x-3)^2 - 2
Brian split 4/5 pounds of candy among 5 people. What is the unit rate in pounds per person. Write the answer in simplest form.
SOLUTION:
Case: Unit rates
Given: Brian split 4/5 pounds of candy among 5 people
Method:
The unit rate in pounds per person
[tex]\begin{gathered} rate=\frac{4}{5}\div5 \\ rate=\frac{4}{5}\times\frac{1}{5} \\ rate=\frac{4}{25} \end{gathered}[/tex]Final answer:
The rate in pounds per person is:
4/25 pounds
Find the cosecant for the angle whose measure is 7pi/4....7pi divided by 4.
cosecant = hypotenuse / opposite side
Angle = 7pi/4
I suggest to convert radians into angles
180° ------------------------- pi rad
x ------------------------ 7pi/4
x = 315°
Use the calculator to find this value
Cosecant 315° = -1.41
This is the answer
[tex]-\frac{\sqrt[]{2}}{2}[/tex]The midpoint of overline PQ is M = (- 2, 1) . One endpoint is P = (- 5, - 1) Find the coordinates of the other endpoint , Q.
Answer;
The coordiantes of the point Q is;
[tex](1,3)[/tex]Explanation;
Here, we want to get the coordinates of the other endpoint
Mathematically, we can find the midpoint of two endpoints using the formula below;
[tex](x,y)\text{ = (}\frac{(x_1+x_2)}{2},\frac{(y_1+y_2)}{2})[/tex]The notation 1 and 2 represents the coordinates of the two end points
Now, by replacing the values given in the question, we have it that;
(x,y) is the coordinate of the point m which is (-2,1)
Now the first end point has the coordinates (-5,-1)
The second endpoint Q has the endpoint (x2,y2) which we want to calculate
We proceed to make the substitutions as follows;
[tex](-2,1)\text{ =}\frac{(-5+x_2)}{2},\frac{(-1+y_2)}{2}[/tex]We proceed to susbtitute the individual branches as follows;
[tex]\begin{gathered} -2\text{ = }\frac{-5+x_2}{2} \\ 2(-2)=-5+x_2 \\ -4=-5+x_2 \\ x_2=-4+5 \\ x_2\text{ = 1} \end{gathered}[/tex]Finally, we have;
[tex]\begin{gathered} 1=\frac{-1+y_2}{2} \\ 2(1)=-1+y_2 \\ 2+1=y_2 \\ y_2\text{ = }3 \end{gathered}[/tex]There were 20 baby devils 4 born in 2013 on Maria Island. In 2014, the number born was 200% of the 2013 devils. How many were born in 2014?
There are 20 baby devils in 2013 on Maria Island
in 2014 200 % where born
the number of baby devils born in 2014 can be gotten by
20 -------- 100
x -----------200
by proper analysis x = (200 x 20)/100 = 4000/100 = 40
40 baby devils were born in 2014
Three clocks exist in a room:
The round clock is 10 minutes behind the actual time
The rectangular clock is 5 minutes after the actual time
The squared clock is 5 minutes slower than the round clock
The time now on the squared clock is 08:05, what is the time now on the rectangular clock?
08:25
08:20
08:15
08:30
Answer:
First choice: 08:25
Step-by-step explanation:
Squared Clock is 5 minutes slower than the round clock
since the round clock is 10 minutes behind actual time, square clod is 15 minutes behind actual time
Time on square clock = 8:05
So actual time = 8:05 + 15 = 8:20
Rectangular clock is 5 minutes ahead of actual time
So time on rectangular clock is 8:20 + 05 = 8:25
Answer: First choice: 08:25