Learning Target #1: Creating and Solving Linear Equations11. Short Response #1: The perimeter of a rectangle is 130 ft. The length of the rectangle is 9 feetshorter than it is wide. What are the dimensions of the rectangle? (Hint: P = 2w + 2L) (4 points)Length:Width:
Answers
P = 2w + 2L
w = L - 9
Related Questions
Given:• 1 cm^3= 1 mL• 1 dm^3 = 1 L• 1L = 1,000 mLIf a health person's kidneys can filter 125 mL of blood per minute, then how long will it take for the kidneys to filter 4.5 L of blood?
Answers
-2. The sum of two cubes can be factored by using the formula o’ + b3 (a + b)(c? ab + b?).(a) Verify the formula by multiplying the right side of the equation.(b) Factor the expression 8x2 + 27.(C) One of the factors of q? - bºis a - b. Find a quadratic factor of q? - bº. Show your work.(d) Factor the expression x - 1.
Answers
Given that the sum of two cubes can be factored by using the formula
[tex]a^3+b^3=(a+b)(a^2-ab+b^2)[/tex]a) To verify the formula by multiplying the right side equation
[tex]\begin{gathered} (a+b)(a^2-ab+b^2) \\ =a(a^2-ab+b^2)+b(a^2-ab+b^2) \\ =a^3-a^2b+ab^2+a^2b-ab^2+b^3 \\ \text{Collect like terms} \\ =a^3-a^2b+a^2b+ab^2-ab^2+b^3 \\ \text{Simplify} \\ =a^3+b^3 \end{gathered}[/tex]Hence,
[tex](a+b)(a^2-ab+b^2)=a^3+b^3[/tex]b) To factor
[tex]8x^3+27[/tex]Using the sum of two cubes formula, i.e
[tex]a^3+b^3=(a+b)(a^2-ab+b^2)[/tex]Factorizing the expression gives
[tex]\begin{gathered} (2x)^3+(3)^3=(2x+3)((2x)^2-(2x)(3)+(3)^2)_{} \\ (2x)^3+(3)^3=(2x+3)(4x^2-6x+9) \end{gathered}[/tex]Hence, the answer is
[tex](2x+3)(4x^2-6x+9)[/tex]c) Given that one of the factors of a³ - b³ is a- b, the quadratic factor of a³ - b³ can be deduced by applying the differences of cubes formula below
[tex]a^3-b^3=(a-b)(a^2+ab+b^2)^{}_{}[/tex]Expanding the right side equations
[tex]\begin{gathered} (a-b)(a^2+ab+b^2)^{}_{}=a(a^2+ab+b^2)-b(a^2+ab+b^2) \\ =a^3+a^2b+ab^2-a^2b-ab^2-b^3 \\ \text{Collect like terms} \\ =a^3+a^2b-a^2b+ab^2-ab^2-b^3 \\ \text{Simplify} \\ =a^3-b^3 \end{gathered}[/tex]Hence, the quadratic factor is
[tex]a^3-b^3=(a-b)(a^2+ab+b^2)[/tex]d) To factor the expression
[tex]x^3-1[/tex]By applying the differences of cubes formula
[tex]a^3-b^3=(a-b)(a^2+ab+b^2)[/tex]Factorizing the expression gives
[tex]\begin{gathered} (x)^3-(1)^3=(x-1)(x^2+(x)(1)+1^2)^{}_{} \\ x^3-1^3=(x-1)(x^2+x+1) \end{gathered}[/tex]Hence, the answer is
[tex](x-1)(x^2+x+1)[/tex]
how do you find 18.84 20.91 19.5 on a number line 14-22
Answers
In order to find the given numbers on a number line thats moves between 14 and 22, we shall illustrate with a number line.
The number line illustrated above shows the numbers arranged in order from 14 to 22.
The numbers indicated in the question are printed in blue.
The position of the numbers are also indicated with a black "stroke" in relation to the position of the numbers 14 to 22.
simplify (6r+5)(r-8)
Answers
To solve, first open the parenthesis
6r(r-8) + 5(r-8)
6r² - 48r + 5r - 40
Re-arrange
6r² + 5r -48r-40
6r² -43r - 40
Please help me solve question 6 on my algebra homework
Answers
We have the following equation:
[tex]y-5=2(x-2)[/tex]First, we leave the equation in the slope-intercept form.
[tex]\begin{gathered} y=2x-4+5 \\ y=2x+1 \end{gathered}[/tex]First, we leave the equation in the slope-intercept form.
Domain
The domain of a function is the set of the existence of itself, that is, the values for which the function is defined.
In this case, the solution is:
[tex]-\inftyIn interval notation[tex](-\infty,\infty)[/tex]Range
The range of the function is the set of all the values that the function takes in the existing interval of the domain.
In this case, the solution is:
[tex]-\inftyIn interval notation[tex](-\infty,\infty)[/tex]Zero
The zeros of a function are the points where the graph cuts the x-axis.
To find this, we equate the function to zero.
[tex]\begin{gathered} 2x+1=0 \\ x=-\frac{1}{2}=-0.5 \end{gathered}[/tex]In this case, the zero is in -0.5.
Y-intercept
To find the y-axis intercept, we solve the equation when x=0.
[tex]\begin{gathered} y=2\cdot0+1 \\ y=1 \end{gathered}[/tex]In conclusion, the y-axis intercept is in the coordinate (0,1)
Slope
Looking at the equation of the form y = mx+b we can easily tell what the slope is, remembering that "k" is the slope of the function.
[tex]\begin{gathered} y=2x+1 \\ k=2 \end{gathered}[/tex]In conclusion, the slope is k=2
Type of slope
There are four different types of slopes: negative, zero, positive and undefined.
In this case, the slope is positive, because the angle of the slope is greater than zero and less than 90 degrees.
In conclusion, the slope is positive
f(3)
We will solve the function when x=3
[tex]\begin{gathered} f(3)=2x+1 \\ f(3)=2\cdot3+1 \\ f(3)=6+1 \\ f(3)=7 \end{gathered}[/tex]Value of x, where f(x)=7
We must equal the function to 7 and clear "x".
[tex]\begin{gathered} 2x+1=7 \\ x=\frac{7-1}{2} \\ x=\frac{6}{2} \\ x=3 \end{gathered}[/tex]In conclusion, the value of "x" is x=3
I don't understand if this equation is a linear equation or not. Can you please help me?
Answers
we have the equation
[tex]\frac{x}{4}-\frac{y}{3}=1[/tex]To remove the fractions, multiply both sides by (4*3=12)
[tex]\begin{gathered} \frac{12x}{4}-\frac{12y}{3}=12 \\ 3x-4y=12 \\ 4y=3x-12 \\ y=\frac{3}{4}x-3 \end{gathered}[/tex]this is the equation of a line
that means
is a linear equation
What is the linear equation ( slope intercept equation ) for the line that passes through points (0,4) and (2,8) ?
Answers
The equation of a line in the slope intercept form is expressed as
y = mx + c
where
m represents slope
c represents y intercept
The formula for determining slope is expressed as
m = (y2 - y1)/(x2 - x1)
Consideing the given points,
x1 = 0, y1 = 4
x2 = 2, y2 = 8
m = (8 - 4)/(2 - 0) = 4/2
m = 2
We would find the y intercept, c by substituting m = 2, x = 0 and y = 4 into the slope intercept equation. It becomes
4 = 2 * 0 + c
c = 4
Substituting m = 2 and c = 4 into the slope intercept equation, it becomes
y = 2x + 4
The last option is correct
find the length of arc FH. Round to the nearest hundredth.(Degrees)
Answers
Given the circle G
As shown, m∠FGH = 36
And the radius of the circle = r = FG = 10 units
we will find the length of the arc FH using the formula:
[tex]\text{Arc}=\theta\cdot r[/tex]The given angle measured in degree, we will convert it to radian
So,
[tex]\theta=36\cdot\frac{\pi}{180}=\frac{\pi}{5}[/tex]So, the length of the arc =
[tex]\frac{\pi}{5}\cdot10=2\pi\approx6.283185[/tex]Round to the nearest hundredth.
So, the answer will be the length of the arc FH = 6.28
4. Jill wants to buy $70,000 worth of insurance for her new house. If therate is $8.00 per $1000 of value, what will her insurance premium be?a. $590b. $560C. $530
Answers
Let's calculate the insurance premium Jill will have to pay for her insurance of her new home:
Insurance premium = 70,000 / 1,000 * 8
Insurance premium = 70 * 8
Now you can calculate easily the payment Jill will have to afford.
Triangle ACD is dilated about the origin.10D'987-854DC92СA-5-4-3-2-102- 1-2Which is most likely the scale factor?0 1 / 3OOo
Answers
Step 1
Find the length of any two sides of both figures
[tex]\begin{gathered} In\text{ the original image} \\ AC=3\text{ units} \\ CD=2\text{ units} \\ In\text{ the dilated image} \\ A^{\prime}C^{\prime}=9\text{ units} \\ C^{\prime}D^{\prime}=6\text{ units} \end{gathered}[/tex]Step 2
Write the ratio that will be used to get the dilation factor.
[tex]\begin{gathered} \frac{C^{\prime}D^{\prime}}{CD}=\frac{A^{\prime}C^{\prime}}{AC} \\ \frac{6}{2}=\frac{9}{3} \\ 3=3 \\ \text{Therefore, the scale factor = 3} \end{gathered}[/tex]A total of 5000 tickets were sold for a raffle. the prizes are $1000, $500, $200, and $100. what price should be charged so there is a 60% profit per ticket?
Answers
Answer: $0.576
Step-by-step explanation:
The total amount in prizes is $1800.
For there to be 60% profit, the total cost of the tickets need to be [tex]1800(1.6)=\$ 2880[/tex].
Thus, each ticket must sell for [tex]\frac{2880}{5000}=\$ 0.576[/tex]
$0.576 should be charged so there is a 60% profit per ticket.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
The prizes are $1000, $500, $200, and $100.
So, total prize = 1000+ 500+ 200+ 100 = $1800.
The, the price of ticket to break
= 1800 / 5000
= $0.36
Now, the price for 60% ticket = 0.36 (1 + 0.6)
= 0.36 x 1.6
= $0.576
Learn more about unitary method here:
https://brainly.com/question/22056199
#SPJ2
I need help with geometry. I am supposed to solve for x in this diagram and assume lines marked with interior arrowheads are parallel :)
Answers
ANSWER:
40°
STEP-BY-STEP EXPLANATION:
We can make the following equality thanks to the properties of these angles:
[tex]\begin{gathered} 3x=120 \\ \text{ solving for x} \\ x=\frac{120}{3} \\ x=40\text{\degree} \end{gathered}[/tex]The value of x is 40°
A vase can be modeled using x squared over 6 and twenty five hundredths minus quantity y minus 4 end quantity squared over 56 and 77 hundredths equals 1 and the x-axis, for 0 ≤ y ≤ 20, where the measurements are in inches. Using the graph, what is the distance across the base of the vase, and how does it relate to the hyperbola? Round the answer to the hundredths place.
Answers
We are given that a vase is modeled by the following hyperbola:
[tex]\frac{x^{2}}{6.25}-\frac{\left(y-4\right)^{2}}{56.77}=1[/tex]we are asked to determine the distance across the base. To do that we will first look at the graph of the equation:
Therefore, the base of the vase is the distance between the x-intercepts of the graph. To determine the x-intercepts we will set y = 0 in the equation. We get:
[tex]\frac{x^2}{6.25}-\frac{(0-4)^2}{56.77}=1[/tex]Solving the operation on the parenthesis we get:
[tex]\frac{x^2}{6.25}-\frac{16}{56.77}=1[/tex]Now we solve the fraction:
[tex]\frac{x^2}{6.25}-0.28=1[/tex]Now we add 0.28 to both sides:
[tex]\begin{gathered} \frac{x^2}{6.25}=1+0.25 \\ \\ \frac{x^2}{6.25}=1.25 \end{gathered}[/tex]Now we will multiply 6.25:
[tex]\begin{gathered} x^2=1.25(6.25) \\ x^2=7.81 \end{gathered}[/tex]Taking square root to both sides:
[tex]\begin{gathered} x=\sqrt[]{7.81} \\ x=\pm2.8 \end{gathered}[/tex]Therefore, the x-intercepts are -2.8 and 2.8.
Now we need to determine the distance between these two points. We will use the distance between two points in a line:
[tex]d=\lvert x_2-x_1\rvert[/tex]Substituting the points we get:
[tex]d=\lvert2.8-(-2.8)\rvert=\lvert2.8+2.8\rvert=5.6[/tex]Therefore, the distance is 5.6 inches and is related to the hyperbola in the sense that it is the distance between the x-intercepts.
brainstorm some real-world applications where integration could be helpful, then describe your examples and explain how integration fits in
Answers
Given
Integration
Find
some real-world applications where integration could be helpful
Explanation
In real life , integrations are used in vaarious fields such as engineering , where engineers use integrals to find the slope of the building
In physics , it is used in the centre of gravity .
In field of graphical representation , where three- dimensional models are demonstrated.
Final Answer
Hence , above are the some real world applications.
4+(6x2²)-9 use pemdas
Answers
Given:
[tex]4+(6\times2^2)-9[/tex]Required:
To solve the given expression.
Explanation:
Consider
[tex]\begin{gathered} =4+(6\times2^2)-9 \\ \\ =4+(6\times4)-9 \\ \\ =4+24-9 \\ \\ =28-9 \\ \\ =19 \end{gathered}[/tex]Final Answer:
[tex]4+(6\times2^2)-9=19[/tex]7)Which table of values BEST represents a model of exponential decay?х012.34-12a(x)1a.251017-1012.34b.b(x)97531- 1х-101234cfx)346101834c.х-101234d.dx)191954723115
Answers
Answer:
the one that represents a model of experimental decay is d.
Step-by-step explanation:
In mathematics, exponential decay describes the process of REDUCING an amount by a consistent percentage rate over a period of time, it is different from linear decay because in linear decay factor relies on a percentage of the original amount, there is a constant rate of decay.
Therefore,
As we can see on the graphs, the only table of values that represent DECAYS is options b and d. But, notice option B is a linear decay since it has a constant rate of decay.
So, the one that represents a model of experimental decay is d.
14. In your rectangular backyard, you knowthe width of the yard is three lessthan four times the length. If the perimeterof your yard is 24 yards, what isthe width?18 3/5yards3 yards9 yards15 yards
Answers
ANSWER:
3rd option: 9 yards
STEP-BY-STEP EXPLANATION:
Given that:
Length = L
Width = W = 4L - 3
The perimeter is the sum of all the sides, therefore:
[tex]\begin{gathered} p=L+L+W+W \\ \\ \text{ We replacing:} \\ \\ 24=L+L+4L-3+4L-3 \\ \\ \text{ We solve for L} \\ \\ 24+3+3=10L \\ \\ L=\frac{30}{10} \\ \\ L=3\text{ yd} \\ \\ \text{ Therefore:} \\ \\ W=4L-3=4(3)-3=9\text{ yd} \end{gathered}[/tex]So the correct answer is 3rd option: 9 yards
69 is _________% more than 60
Answers
To find the solution we can use the rule of three:
[tex]\begin{gathered} 60\rightarrow100 \\ 69\rightarrow x \end{gathered}[/tex]then:
[tex]\begin{gathered} x=\frac{69\cdot100}{60} \\ x=115 \end{gathered}[/tex]This means that 69 is 115% of 60.
Therefore 69 is 15% more than 60.
Complete the following tables 1 and 3 only.
Answers
Answer:
(a) D = 5/8 in
(b) A = 31.2 cm
(c) B = 8 ft
(d) C = 3 m
Explanation:
If two triangles are similar, their corresponding sides are proportional, so we can always use the following equation:
[tex]\frac{A}{B}=\frac{C}{D}[/tex]Therefore, for row (a), we can write the following equation:
[tex]\frac{5\frac{1}{2}}{1\frac{1}{4}}=\frac{2\frac{3}{4}}{D}[/tex]So, changing the mixed number by decimals and solving for D, we get:
[tex]\begin{gathered} \frac{5.5}{1.25}=\frac{2.75}{D} \\ 5.5D=2.75(1.25) \\ 5.5D=3.4375 \\ \frac{5.5D}{5.5}=\frac{3.4375}{5.5} \\ D=0.625 \end{gathered}[/tex]Then, for row (a), D = 0.625 = 5/8
In the same way, we can write and solve the following equation for row (b)
[tex]\begin{gathered} \frac{A}{23.4}=\frac{20.8}{15.6} \\ \frac{A}{23.4}\times23.4=\frac{20.8}{15.6}\times23.4 \\ A=31.2 \end{gathered}[/tex]For row (c), we get:
[tex]\begin{gathered} \frac{12}{B}=\frac{9}{6} \\ 12(6)=9(B) \\ 72=9B \\ \frac{72}{9}=\frac{9B}{9} \\ 8=B \end{gathered}[/tex]For row (d), we get:
[tex]\begin{gathered} \frac{4.5}{3.6}=\frac{C}{2.4} \\ \frac{4.5}{3.6}\times2.4=\frac{C}{2.4}\times2.4 \\ 3=C \end{gathered}[/tex]Therefore, the answers are:
(a) D = 5/8 in
(b) A = 31.2 cm
(c) B = 8 ft
(d) C = 3 m
Aiden ipens a savings account with a deposit of 4500. The account pays 3% simple interest.3. If Aiden does not make any more deposits or withdrawals, how much will he have in the account at the end of two years?A 4527B 4635C 4680D 4774E 4905
Answers
Answer: $4, 770
Aiden deposit $4500 into her account with an interest rate of 3%
Time = 2 years
Using the Simple Interest
[tex]\begin{gathered} I\text{ = }\frac{P\text{ x R x T}}{100} \\ P\text{ = \$4500} \\ R\text{ = 3\%} \\ T\text{ = 2} \\ I\text{ = }\frac{4500\text{ x 3 x 2}}{100} \\ I\text{ = }\frac{4500\text{ x 6}}{100} \\ I\text{ = }\frac{27000}{100} \\ I\text{ = \$270} \\ \text{The total amount in her account is } \\ \text{Balance = Principal + Interest} \\ \text{Balance = \$4500 + \$270} \\ \text{Balance = \$4, 770} \end{gathered}[/tex]The portable basketball hoop shown is made so that BA = AS = AK. The measure of < BAK is 128 degrees. Calculate m < BSK.
Answers
The measure of ∠BSK is 64 degrees, that is the value of m∠BSK is 64 degrees.
We are given BA = AS = AK.
∠BAK = 128 degrees
From the linear pair concept:
∠BAK + ∠SAK = 180 degrees
128 degrees + ∠SAK = 180 degrees
∠SAK = 180 degrees - 128 degrees
∠SAK = 52 degrees
From the angle sum property of a triangle in triangle ASK, we will get;
∠SAK + ∠ASK + ∠AKS = 180 degrees
52 degrees + ∠ASK + ∠AKS = 180 degrees
2 ∠ASK = 180 degrees - 52 degrees (Since, AS = AK)
∠ASK = 128/2 degrees
∠ASK = 64 degrees
Thus, the measure of ∠BSK is 64 degrees, that is the value of m∠BSK is 64 degrees.
To learn more about the angle sum property visit:
https://brainly.com/question/8492819
#SPJ9
Identify the key features for the following equation: y=4sin(x)−5What kind of cyclic model is the equation?
Answers
Given,
The equation of the function is:
[tex]y=4sinx-5[/tex]The standard equation of wave is,
[tex]y=Asin\text{ \lparen Bx+C\rparen+D}[/tex]Here, A is the amplitude
B is the period.
C is the phase shift.
D is vertical shift.
As the given function have the sine function so, the cyclic model of the wave is sine.
Amplitude = 4.
Midline = -5
Minimum = -9
Hence, the key feature of the cyclic model is identified.
find the area of the semicircle round to the nearest tenth use 3.14 for pi do not include units with your answer to 22.5 in
Answers
Semicrcle area = π•Diameter^2 / 8
. = 3.14 • (2 R)^2/8
. = 3.14• (45)^2/8
. = 3.14• 2025/8= 794.81
Then answer is
Area of semicircle = 795 square inches
write 37,000,010 numbers using words
Answers
thirty-seven million ten
Explanation
Step 1
count the number of digits after 37
[tex]\begin{gathered} 37000010 \\ 6\text{ digits, it meas} \\ by\text{ now, we have} \end{gathered}[/tex]thirty-seven million
Step 2
the remaining number is
[tex]\begin{gathered} 000010 \\ it\text{ is , ten} \\ 10 \end{gathered}[/tex]ten
Step 3
combine
thirty-seven million ten
Christian and Lea are in charge of planning the school prom. They will spend $250 on decorations. Dinner will cost $12 per person (p) that attends theprom. Which equation represents the total cost (t) of the prom for any number of students attending?p = 250t + 12p = 12 + 250t=12p - 250t = 250p + 12
Answers
If one object costs $x then p objects will cost $px.
Given data:
It is given that they spend $250 on decorations and $12 per person for dinner.
Now the cost $250 is fixed.
Now, if cost od dinner for one person is $12.
So the cost of dinner for p persons will be $12p
Therefore, total cost 't' will be
[tex]t=12p+250[/tex]Convert the following measurement 19 quarts to cups
Answers
76 cups
Explanation:Note that:
1 quart = 4 cups
Therefore:
19 quarts = 4 x 19 cups
19 quarts = 76 cups
An equilateral triangle and an isosceles triangle share a common side. What is the measure of /_ABC?
Answers
The sum of all the angles in a triangle is equal to 180 degrees
For an equilateral triangle, all sides are equal
i.e 60 + 60 + 60= 180
For an isosceles triangle, two sides are equal
the first image is an isosceles triangle why the second image is an equilateral triangle
Function A Function B Tell whether each function is linear or nonlinear. х y 4 0 1 3 5 24 8 2 3 13 0 1 2 3 4 5 Function A is a function. Function B is a function.
Answers
Function A is NOT LINEAR
Function B is LINEAR
The slope (change in y over change in x) does not follow a linear pattern in function A. That is the increase/decrease in the y coordinates is not at the same rate as that of the x coordinate. Whereas, for the other function, function B, the slope follows a linear pattern, that is the rate of change in y over the rate of change in x is the same rate, that is why function B has a straight line graph
dominic is making meatballs. he uses 3/4 cup of breadcrumbs for every 1 1/4 pounds of ground beef. how many cups of bradecrumbs does he need when he uses 1 3/4 pounds of ground beef?
Answers
The number of cups of breadcrumbs he will need when he uses 3/4 pounds of ground beef would be = 1¹/20 cup.
What are breadcrumbs?Breadcrumbs is a type of food product that is produced from crumbling of dried bread which is used making dishes such as meatballs.
The number of cups of breadcrumbs for 1¼ of meat ball = ¾ cup
Therefore the number of cups of breadcrumbs for 1¾ = X cup.
That is ; 1¼ = ¾ cup
1¾ = X cup
Make X cup the subject of formula;
X cup = 1 ¾ × ¾ ÷ 1¼
X cup = 21/16 ÷ 5/4
X cup = 21/16 × 4/5
X cup = 21/20
X cup = 1 ¹/20 cup
Learn more about ratio here:
https://brainly.com/question/25927869
#SPJ1
4. Angelo gave 3 of a bag of pretzels to Ben. Ben ate a portion (x) of the pretzels and then gave 4 of the remaining pretzels in the bag to Connor. The expression below represents Connor's portion of the bag of pretzels. 2/3 314 Which expression is equivalent to Connor's portion of the bag of pretzels?
Answers
we have Connor's portion of the pretzels
[tex]\frac{2}{3}\times(\frac{3}{4}-x)[/tex]then simply the expression
[tex]\begin{gathered} \frac{2}{3}\times\frac{3}{4}-\frac{2}{3}x \\ \frac{2\times3}{3\times4}-\frac{2}{3}x \\ \frac{6}{12}-\frac{2}{3}x \\ \frac{1}{2}-\frac{2}{3}x \end{gathered}[/tex]answer: C