4x -2 = 3(x-3)
4x - 2 = 3x - 9
bring like terms together
4x-3x = -9 +2
x = -7
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!
Ally has a square backyard with an area of 169 square feet. What is the length of one side of thebackyard?Sut
Ally has a square backyard with an area of 169 square feet.
Given a square of side length, s
[tex]\text{Area of a Square}=s^2[/tex]Therefore:
[tex]\begin{gathered} s^2=169\text{ square feet} \\ \text{Take the square root of both sides} \\ \sqrt{s^2}=\sqrt{169} \\ s=13\text{ feet} \end{gathered}[/tex]Therefore, the length of one side of the backyard is 13 feet.
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?
Jonah saw a news report that stated that 72% of children in his town played a sport last year. If there are 4,000 children in his town, how many children in his town played a sport last year?(1 point) children in his town played a sport last year.
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
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)
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°
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]In ATUV, the measure of ZV=90°, VU = 7, UT = 25, and TV = 24. What ratiorepresents the sine of ZU?U25NVT24Answer:Submit Answer
1) Since the sine is the ratio between the opposite leg and the hypotenuse.
And the hypotenuse is always opposite to the right angle
Then we can write
2) The sine of ∠ U can be written as the following ratio
sine (∠U) = 24/25
sine(∠U)= 0.96
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)
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
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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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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What are two ordered pairs that the midpoints (4, -10)? Please show that your points work.
In order to find any pair of points that have a midpoint of (4, -10), we can choose any two values p and q. Then, one of the endpoints will be (4+p, -10+q) and the other endpoint will be (4-p, -10-q).
For example, let's choose p = q = 2, so we have:
[tex]\begin{gathered} midpoint\text{ \lparen4,-10\rparen}\\ \\ \\ \\ 1st\text{ endpoint:}\\ \\ (4+2,-10+2)=(6,-8)\\ \\ \\ \\ 2nd\text{ endpoint:}\\ \\ (4-2,-10-2)=(2,-12) \end{gathered}[/tex]Therefore the ordered pairs (6, -8) and (2, -12) have a midpoint of (4, -10).
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]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.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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find the distance the points (-3,-5) and (9,-10). Enter the exact value of the answer.
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:
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.
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
#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
Solve the system by using the substitution method.y = 2x + 184x + 5y = 20
Let:
y=2x+18 (1)
4x+5y=20 (2)
replace (1) into (2)
4x+5(2x+18)=20
Using distributive property:
4x+10x+90=20
Add like terms:
(4x+10x)+90=20
14x+90=20
subtract 90 from both sides:
14x+90-90=20-90
14x=-70
Divide both sides by 14:
14x/14=-70/14
x=-5
Finally, replace the value of x into (1)
y=2(-5)+18
y=-10+18
y=8
Let:
2x+2y=6 (1)
3x-5y=25 (2)
From (1) let's solve for x:
subtract 2y from both sides:
2x+2y-2y=6-2y
2x=6-2y
Divide both sides by 2:
x=(6-2y)/2
x=3-y (3)
Replace (3) into (2)
3(3-y)-5y=25
Using distributive property:
9-3y-5y=25
Add like terms:
9+(-3y-5y)=25
9-8y=25
subtract 9 from both sides:
9-8y-9=25-9
-8y=16
Divide both sides by -8:
(-8y)/(-8)=(16)/(-8)
y=-2
Finally, replace the value of y into (3)
x=3-(-2)
x=3+2
x=5
a person weighs 140 pounds has 4 quarts if blood. estimate the number of quarts of blood in a person who weighs 120 pounds
The number of quarts of blood in a person who weighs 120 pounds is 3.4
How to calculate the number of quarts of blood ?The expression can be written as
W= kV
W represents the weight in pounds
V= number of quarts
k= 140/4
= 35
The number of quarts of blood in a person that weighs 120 pounds can be calculated as follows
= 120/35
= 3.4
Hence 3.4 quarts of blood is gotten from a person who weighs 120 pounds. This was done by dividing 120 by 35
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PLEASE HELP ITS DUE SOON! I DONT GET ANY OF THIS! HELP WOULD BE MUCH APPRECIATED! NEED THIS DONE BEEN STUCK ON THIS FOR WAY TO LONG!
YOU WILL GET 100 POINTS IF YOU HELP! QUESTION DOWN BELOW!!!!!
THIS IS MY LAST QUESTION!!
Answer:
See below.
Step-by-step explanation:
Vertical Angles Theorem
When two straight lines intersect, the opposite vertical angles are congruent.
Alternate Interior Angles Theorem
If a line intersects a set of parallel lines in the same plane at two distinct points, the alternate interior angles that are formed are congruent.
Transitive Property of Equality
If a=b and c=b, then a=c.
Proof that ∠1=∠2
∠3 is equal to ∠4 (Vertical Angle Theorem).As BC intersects the set of parallel lines AB and CD (given), ∠3 is equal to ∠2 (Alternate Interior Angles Theorem).If ∠3=∠4 and ∠3=∠2 then ∠2=∠4 (Transitive Property of Equality).Given that ∠1=∠4 and ∠2=∠4 then ∠1=∠2 (Transitive Property of Equality).[tex]\begin{array}{c|c}\sf Statement & \sf Reason\\\cline{1-2}\\ \angle 3 = \angle 4 & \textsf{Vertical Angle Theorem}\\\\AB \parallel CD & \textsf{Given}\\\\\angle 3 = \angle 2 & \textsf{Alternate Interior Angles Theorem}\\\\\angle 2 = \angle 4 & \textsf{Transitive Property of Equality}\\\\\angle 1 = \angle 4 & \textsf{Given}\\\\\angle 1 = \angle 2 & \textsf{Transitive Property of Equality}\\\\\end{array}[/tex]
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
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
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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x 0 1 9
P(X = x) 0.14 0.35 0.51
Answer:
Step-by-step explanation:
k = 0.2
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!