Find the sides of a rectangle whose area is given as x2 +15x +56.
Answers
x^2 + 15x + 56
Good way to factor quadratic functions:
In a function x^2 +bx + c
Find two number that when multiplied together will form c (in our case 56) and that when added together form b (in our case 15)
Number 1 x Number 2 = 56
Number 1 + Number 2 = 15
Number 1 = 8
Number 2 = 7
(It'll be easier to find these numbers with practice)
Now in the function instead of bx, split it and use (number 1)x + (number 2)x
It's allowed because it's the same value since N1 + N2 = bx already
x^2 + 15x + 56
Now is:
x^2 + 8x + 7x + 56
Now you can factor this function much easily because it can transformed into:
(x + 8)(x) + (x + 8)(7)
x + 8 is the common factor
it can become:
(x + 8) (x + 7)
The sides of the rectangle are 8 and 7
Hope this helps you with factoring :)
Related Questions
Hoang spends $10 on movie tickets, $50 on rent, and $3 on snacks. How much money did Hoang spend on variable expenses?
Answers
Answer:
63
Step-by-step explanation:
50+10=60 60+3=63 dollars
he spends 63$ on variable expenses
Together, kamela and Leo have 198 stamps. Kamela’s collection has 62 more stamps Thant Leon’s collection. How many stamps does Leo have?
Answers
((8x+5)/6)-((x-5)/6)=1/9
Answers
Answer:
x=-4/3
Step-by-step explanation:
(8x+5-(x-5))/6 = 1/9
(7x+10)/6=1/9
7x+10=2/3
7x=-28/3
x=-4/3
math project : I need an interesting project idea for mathematics that can relate 3 different topics, I should write a full research paper related on the topic this are some examples related to the project
You must state a question that you would like to answer. This must be a specific question within your topic and should be explored thoroughly to create a complete paper.
Examples:
(i) How can we use Mathematical/Calculus-based tools to study the spread of COVID-19?
(ii) Designing a new Mathematical/Calculus-based model to analyze the spread of COVID-19
(iii) How many entrances should there be at Expo to accommodate all visitors?
(iv) How much water does the UAE need in order to sustain its ever changing population? (i.e. comparing water usage vs. water production)
Literature review:
You must show using multiple references and sources of the current literature on your given topic. This does NOT imply that information is simply copied from the internet but rather you must present a comprehensive review and summary of the latest research on your topic. It is suggested that you chose a specific aspect of your topic in order to include all required elements.
Examples:
(i) Review of the existing Mathematical/Calculus-based models used to analyze the spread of COVID-19
(ii) Review of existing Mathematical/Calculus-based models and calculations regarding risk insurance.
Answers
A mathematics topic that van be looked into is how linear algebra, graph theory and optimization can be used on the airline industry.
How to explain the informationIn this case, to solve the scheduling issues faced by airlines such as planning flights, assigning planes and crews to routes - mathematical techniques can be employed.
By leveraging Linear Algebra, operators can simulate the flow of aircrafts and passengers while Graph Theory can help model flight schedules and aircraft routes.
Simultaneously using Optimization techniques in the problem-solving process can work to streamline various operations resulting in reduced costs and improved efficiency which can increase profit margins.
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I need to know this answer
Answers
The equation of the line is y = (3/2)x - 1/2.
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
Let's say you need to know the answer about the equation of a line that passes through points (3, 4) and (5, 7).
Now,
The equation of a line.
y = mx + c
The line passes through points (3, 4) and (5, 7).
m = (7 - 4) / (5 - 3)
m = 3/2
Slope = 3/2 _____(1)
Now,
(3, 4) = (x, y)
4 = 3/2 x 3 + c
4 = 9/2 + c
c = 4 - 9/2
c = (8 - 9) / 2
c = -1/2
y-intercept = -1/2 ____(2)
Now,
y = mx + c
From (1) and (2),
y = (3/2)x - 1/2
Thus,
The equation of the line is y = (3/2)x - 1/2.
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The complete question.
Find the equation of a line that [passes through the point (2, 4), and (5, 7).
PLEASE SOMEONE HELP I NEED IT LIKE RN
1. Write a linear equation with the given information
Through (4,-5), parallel to y = -x + 1(4 Points)
2. Write a linear equation with the given information
Through (2,-1), perpendicular to y = -2/3x + 5(4 Points)
Answers
\((d) \: \: y = - x - 1\)
(2)Slopes of 2 perpendicular lines multiply to -1\(a \times \frac{ - 2}{3} = - 1 \\ a = \frac{3}{2} \)
(D): y=(3/2)x+bPasses through (2,-1)-1=(3/2)(2)+bb=-1-3=-4\((d) \: \: \: \: y = \frac{3}{2} x - 4\)
Answer:
1. y = -x - 1
2. y = (3/2)x - 4
Step-by-step explanation:
1. Let y = ax + b be the equation of the line
that passes Through (4,-5) and parallel to y = -x + 1
Where ‘a’ is the slope and b the y value of the y-intercept point.
The lines are parallel
then
they have the same slope
then
a = -1
we get :
y = -x + b and the point (4 , -5) lies on the line
then
-5 = -(4) + b
Then
b = -5 + 4 = -1
Conclusion:
y = -x - 1
………………………………………
2. Let y = mx + p be the equation of the line
that passes Through (2,-1) and perpendicular to y = -2/3x + 5
Where ‘m’ is the slope and p the y value of the y-intercept point.
The lines are perpendicular
then
The product of their slopes = -1
Then
m × (-2/3) = -1
Then
m = 3/2
we get :
y = 3/2x + p and the point (2 , -1) lies on the line
then
-1 = (3/2)×(2) + p
Then
p = -1 - 3 = -4
Conclusion:
y = (3/2)x - 4
On Saturday, many tickets for a hockey game were sold. Children and adult tickets were sold in the ratio of 4:7. There are 88 tickets in total.
How many adult tickets were sold?
Answers
Answer:
49 tickets
Step-by-step explanation:
THis is pretty straight forward
So we have the ratio 4:7
We know there were 88 tickets in total but we don’t know the exact amount of adult and kids
So we can Add up the ratio
4+7=11
Now we can divide 88 by 11
you’ll get 7
So by doing this we know there are 7 groups of the ratio for child to adults 4:7
So we just multiply the 7 to each
4*7
7*7
you’ll get 28:49
Now we know there are 28 kid tickets and 49 adult tickets
We know this is correct becuase if you add up the ratio, it’ll be 88
Which is the same as the amount fo people at the hockey game
after spending 5/6 of his January salary on paying school fees, Bikila was left with ksh 1500. how much money did he earn that month?
Answers
Answer:
9000
Step-by-step explanation:
Al lanzar un dado determinar la probabilidad de que salga un número primo o un número mayor que 3
Answers
The probability of a prime number or a number greater than 3 coming up is given as follows:
5/6.
How to calculate a probability?The parameters that are needed to calculate a probability are listed as follows:
Number of desired outcomes in the context of a problem or experiment.Number of total outcomes in the context of a problem or experiment.Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.
When a dice is thrown, there are six possible outcomes, ranging from 1 to 6, and the desired outcomes are given as follows:
Prime numbers: 2, 3, 5.Non-prime greater than 3: 4 and 6.Hence the probability is given as follows:
5/6.
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ADD TEXT Find the 14th term of the sequence: 2, 4, 8, 16...
a.4096
b.8192
c.16384
d.65536
Answers
Answer:
it's actually 32,768 so yeah
but choose either c or d
Consider the polynomial
(4mn^2n - 2mn + 6) + (6mn^2 - 1) - (mn^2 - 2 + 9mn)
Combine all like terms and enter the coefficients for each term into the blanks below
Answers
The required coefficients are:4, -1, -11, and 7.
Coefficients refer to the numerical values that are assigned to variables in mathematical equations, models, or formulas. They indicate the relative importance or contribution of each variable in the equation. Coefficients are used to determine the relationship between variables and are often estimated through statistical analysis or optimization techniques.
In algebraic equations, coefficients are the numbers multiplied by variables. For example, in the equation 2x + 3y = 5, the coefficients are 2 and 3.
In statistical models, such as linear regression, coefficients represent the slopes or weights assigned to the predictor variables. These coefficients indicate how much the response variable is expected to change for a unit change in the corresponding predictor variable, assuming all other variables are held constant.
We need to consider the polynomial:
(4mn^2n - 2mn + 6) + (6mn^2 - 1) - (mn^2 - 2 + 9mn)
To combine the like terms and find the coefficients of each term, we can write the polynomial in the following form:
4mn^2n - 2mn + 6 + 6mn^2 - 1 - mn^2 + 2 - 9mn
Taking the coefficients of the terms with "mn^2"4mn^2n - mn^2
Taking the coefficients of the terms with "mn"-2mn - 9mn = -11mn
Taking the coefficients of the constant terms6 + 2 - 1 = 7
Therefore, the required coefficients are:4, -1, -11, and 7.
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-32 > +32? True or false?
Answers
Answer:
False
Step-by-step explanation:
+32 is greater than -32
Answer:
false it is less than
Step-by-step explanation:
-32<+32
2 Mabaso has R140, Thabo has R70 and Ally has R35. What is the ratio of the amount of money Mabaso has, to the amount of money Thabo has and to the amount of money Ally has? Write the ratios in simplest form. The price of a steel table is R750. On Black Friday the table could be bought for R600. Calculate the percentage discount? Show ALL your calculations. Convert 125 g to kilograms. (1 kg = 1 000 grams) A green grocer packs 12 apples in a plastic bag. Calculate the number of bags he w need if he has 285 apples. The scale of a map is 1 500 000. Determine the actual distance in km if measurement on the map is 23,7 cm. Hint: 1 km = 100 000 cm
Answers
The actual distance represented by 23.7 cm on the map is 355.5 km.
To find the ratio of the amount of money Mabaso has to the amount of money Thabo has and the amount of money Ally has, we can divide each amount by the smallest amount (which is R35) to simplify the ratio.
Mabaso has R140, Thabo has R70, and Ally has R35.
The ratio of Mabaso's money to Thabo's money is:
R140 ÷ R35 = 4
The ratio of Mabaso's money to Ally's money is:
R140 ÷ R35 = 4
Therefore, the ratio of the amount of money Mabaso has to the amount of money Thabo has and to the amount of money Ally has is 4:1:1.
To calculate the percentage discount of a steel table, we need to find the difference between the original price and the discounted price, and then divide it by the original price. Finally, we multiply the result by 100 to get the percentage.
Original price: R750
Discounted price: R600
Discount: R750 - R600 = R150
Percentage discount: (R150 ÷ R750) × 100 = 20%
So, the table has a 20% discount on Black Friday.
To convert 125 grams to kilograms, we divide the amount in grams by 1,000 (since there are 1,000 grams in a kilogram).
125 g ÷ 1,000 = 0.125 kg
Therefore, 125 grams is equal to 0.125 kilograms.
If a green grocer packs 12 apples in a plastic bag and has 285 apples, we divide the total number of apples by the number of apples per bag to determine the number of bags needed.
Number of bags needed: 285 apples ÷ 12 apples/bag = 23.75 bags
Since we can't have a fraction of a bag, we round up to the nearest whole number. Therefore, the green grocer would need 24 bags.
If the scale of a map is 1,500,000 and the measurement on the map is 23.7 cm, we can use the scale to determine the actual distance.
1 cm on the map represents 1,500,000 cm in reality.
23.7 cm on the map represents x cm in reality.
x = 23.7 cm × 1,500,000 cm = 35,550,000 cm
To convert cm to km, we divide by 100,000 (since there are 100,000 cm in a kilometer).
35,550,000 cm ÷ 100,000 = 355.5 km
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the simple formula for price elasicity of demand is
Answers
Answer:
The price elasticity of demand is calculated as the percentage change in quantity divided by the percentage change in price.
The American Population is living longer. Along with the longevity of life comes additional challenges with both medical and Psychiatric problems. Your patient is about to be discharged from a short-tern rehab center. You overhear the daughter confiding in the nursing student that she cannot handle her mother and will be looking for a Memory care unit to put her mother in. You also hear the student nurse who was raised in a foreign country state, " I would NEVER put my mother in a home. I would take care of her woth my two sisters junti she dies.
what considerations might you make withthis students. Address the cultural differneces in elder care and adress the conself od "Role Strain" in caring for special populations.
Answers
Cultural sensitivity is crucial in elder care. Cultural beliefs impact elderly care. A foreign-raised nursing student desires to care for her mother and sisters until her mother's passing.
What is the cultural Strain?Consider cultural values: Students from certain backgrounds may see caring for their elderly parents as a moral duty. Respecting elder beliefs is critical in discussing care options. Have open, non-judgmental communication with the nursing student. Show empathy and listen to her perspective.
Educate the nursing student about caring for a loved one with medical and psychiatric problems. Explain physical, emotional, and financial consequences, including effects on relationships and responsibilities.
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What number goes on top?
Answers
Answer:
16
Step-by-step explanation:
because if you can see 8+8= 16 so my correct answer is 16
The retail price of a television set is $4,500. If the buyer pays by cash, the price is 10% below the retail price. If the set is bought on higher purchase, the buyer pays a down payment of $675 and 24 monthly installments of $212.50. Calculate for the television the:
cash price to the buyer, if he pays by cash.
amount payable.
outstanding balance.
hire purchase price.
interest.
difference between the hire purchase and the cash price.
percentage interest charged.
Answers
Cash price to the buyer, if he pays by cash:
The cash price would be 10% less than the retail price of $4,500:
Cash price = $4,500 - (10% * $4,500)
Cash price = $4,500 - $450
Cash price = $4,050
Amount payable:
If the buyer chooses to purchase the TV on higher purchase, the amount payable would be the sum of the down payment and the total amount of monthly installments:
Amount payable = Down payment + (24 * Monthly installment)
Amount payable = $675 + (24 * $212.50)
Amount payable = $5,175
Outstanding balance:
The outstanding balance would be the difference between the amount payable and the down payment:
Outstanding balance = Amount payable - Down payment
Outstanding balance = $5,175 - $675
Outstanding balance = $4,500
Hire purchase price:
The hire purchase price would be the sum of the down payment and the outstanding balance:
Hire purchase price = Down payment + Outstanding balance
Hire purchase price = $675 + $4,500
Hire purchase price = $5,175
Interest:
The interest charged on the hire purchase would be the difference between the hire purchase price and the cash price:
Interest = Hire purchase price - Cash price
Interest = $5,175 - $4,050
Interest = $1,125
Difference between the hire purchase and the cash price:
The difference between the hire purchase price and the cash price would be the interest charged:
Difference = Interest
Difference = $1,125
Percentage interest charged:
To calculate the percentage interest charged, we can divide the interest by the hire purchase price and multiply by 100:
Percentage interest charged = (Interest / Hire purchase price) * 100
Percentage interest charged = ($1,125 / $5,175) * 100
Percentage interest charged = 21.74%
Therefore, the cash price to the buyer is $4,050, the amount payable is $5,175, the outstanding balance is $4,500, the hire purchase price is $5,175, the interest charged is $1,125, the difference between the hire purchase and the cash price is $1,125, and the percentage interest charged is 21.74%.
Translate to an equation please.
four less than thirteen times a number is equal to that number added to eight
Answers
Hi
let call "a number" X.
then we have: 4-13X = X + 8 ..
13x-x = 8+ 4
12x= 12
X= 1
Form a paragraph proof for the following. Make sure you include all the
explanations.
HELP ASAP PLS
Answers
Answer:
Line BD is Congruent to Line BD due to the Reflexive property. Angle Bad is congruent to angle BCD because of the third angle theorem therefore triangle ABD is congruent to triangle CBD because all angles and sides are congruent
I don't know if that will satisfy your teacher because some prefer different things but that leaves no ground to be inferred and explains everything word for word.
candy selling at $6. per pound will be mixed with candy $9. per pound. how many pounds of the more expensive candy are needed to produce a 15 pound mixture fbaf sales for $7. per pound
Answers
Let's use the variable x to represent the amount of $6 candy bought and y to represent the amount of $9 candy bought.
If the final mixture has 15 pounds, we have the equation:
\(x+y=15\)Then, the final price is $7 per pound, so we can write the equation:
\(x\cdot6+y\cdot9=15\cdot7\)Solving this system, we have:
\(\begin{gathered} \begin{cases}x+y=15 \\ 6x+9y=105\end{cases} \\ \begin{cases}-6x-6y=-90 \\ 6x+9y=105\end{cases} \\ -6x-6y+(6x+9y)=-90+105 \\ 3y=15 \\ y=5 \end{gathered}\)So the number of pounds of the expensive candy if 5, therefore the correct option is A.
70 points! Complete each proof using the most appropriate method.
Answers
All statements and reasons are shown below.
What is triangle?A triangle is a closed two-dimensional geometric shape that has three sides, three angles, and three vertices. Triangles are one of the basic shapes in geometry and can be classified according to the length of their sides (scalene, isosceles, or equilateral) or the size of their angles (acute, right, or obtuse). The sum of the angles of a triangle is always 180 degrees, and the Pythagorean theorem can be used to find the length of one side if the other two sides are known in a right triangle.
According to the given figure:
4. In ΔFGH and ΔFJH,
Statement Reason
GH = JH (Given)∠FGH = ∠FJH (each 90°)FH = FH (Common)ΔFGH ≅ ΔFJH (by R.H.S rule)5. In ΔTVY and ΔXWY,
Statement Reason
TY = XY (Given)∠TVY = ∠XWY (Given)∠VYT = ∠WYX (Vertically opposite angle)ΔTVY ≅ ΔXWY (by A.A.A rule) angle-angle-angle ruleTV = XW (by C.P.C.T)6. In ΔKML and ΔPMN,
Statement Reason
KL = PN (Given)∠KLM = ∠PNM (KL║NP and LN is transversal line, so this is alternate interior angle)∠LKM = ∠NPM (Alternate interior angle)ΔKML ≅ ΔPMN (by A.S.A rule) angle-side-angle ruleLM = NM (by C.P.C.T)To know more about types of triangle, visit:
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Find the equation of the line with slope 2/5 and y-intercept (0,−2).
Answers
Answer:
\(\boxed {\tt y=\frac{2}{5}x-2}\)
Step-by-step explanation:
If the slope and y-intercept is known, the equation of a line can be written using slope-intercept form.
\(y=mx+b\)
where m is the slope and b is the y-intercept.
We know that the slope is 2/5.
The y-intercept is (0,-2). For this form, we only need the y-coordinate, which is -2 in this case. Therefore, we can say the y-intercept is -2.
\(m=2/5 \\b= -2 \\\)
Substitute the values into the formula.
\(y=2/5x+ (-2)\)
\(y=2/5x-2\)
The equation of the line is y=2/5x-2
Find the vertex of the function given below.
y = 3x² + 6x +1
A. (1,7)
B. (-1,-2)
C. (-4,9)
D. (-1,-1)
Answers
\(\textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{3}x^2\stackrel{\stackrel{b}{\downarrow }}{+6}x\stackrel{\stackrel{c}{\downarrow }}{+1} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{ 6}{2(3)}~~~~ ,~~~~ 1-\cfrac{ (6)^2}{4(3)}\right) \implies \left( - \cfrac{ 6 }{ 6 }~~,~~1 - \cfrac{ 36 }{ 12 } \right) \\\\\\ (-1~~,~~1-3)\implies {\Large \begin{array}{llll} (-1~~,~~-2) \end{array}}\)
Quadrilateral A'B'C'D'A ′ B ′ C ′ D ′ A, prime, B, prime, C, prime, D, prime is the image of quadrilateral ABCDABCDA, B, C, D under a dilation with a scale factor of \dfrac{1}{3} 3 1 start fraction, 1, divided by, 3, end fraction.What is the length of segment \overline{CD} CD start overline, C, D, end overline?
Answers
Answer:
The length of CD is 6
Step-by-step explanation:
Look at attachment:
Hope this helps! :)
Answer:
6 units.
Step-by-step explanation:
Got it correct on khan academy:
how do you solve this on the interval of [0,2pi)
Answers
Given:
\(\tan 3x=1,\lbrack0,2\pi)\)To find the value of x:
Solving we get,
\(\begin{gathered} \tan (3x)=1 \\ 3x=\frac{\pi}{4},\frac{5\pi}{4},\frac{9\pi}{4},\frac{13\pi}{4},\frac{17\pi}{4},\frac{21\pi}{4} \\ x=\frac{\pi}{12},\frac{5\pi}{12},\frac{3\pi}{4},\frac{13\pi}{12},\frac{17\pi}{12},\frac{7\pi}{4} \end{gathered}\)Hence, the answers are,
\(x=\frac{\pi}{12},\frac{5\pi}{12},\frac{3\pi}{4},\frac{13\pi}{12},\frac{17\pi}{12},\frac{7\pi}{4}\)1. Why should you plan for retirement now? Use 2-3 complete sentences
Answers
Which of the following sets of ordered pairs represents a function? PLEASE HELP
Answers
The set of ordered pairs that represents a function is (D) {(-6, -3), (-4, -3), (-3, -3), (-2, -3), (0, 0)}.
A set of ordered pairs represents a function if each unique input (x-value) is associated with only one output (y-value).
{(-4, -3), (-2, -1), (-2, 0), (0, -2), (0, 2)}
In this set, both (-2, -1) and (-2, 0) have the same x-value but different y-values. Therefore, this set does not represent a function.
{(-5, -5), (-5, -4), (-5, -3), (-5, -2), (-3,0)}
In this set, all the ordered pairs have the same x-value (-5). Since (-5, -5), (-5, -4), (-5, -3), and (-5, -2) have the same x-value but different y-values, this set does not represent a function.
{(-4, -5), (-4, 0), (-3, -4), (0, -3), (3, -2)}
In this set, (-4, -5) and (-4, 0) have the same x-value but different y-values. Therefore, this set does not represent a function.
{(-6, -3), (-4, -3), (-3, -3), (-2, -3), (0, 0)}
In this set, each unique x-value is associated with a single y-value. There are no repeated x-values. Therefore, this set represents a function.
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may someone please help me find the increasing and decreasing
Answers
Answer:
from [- infinity to (2, 0)] is when it is increasing. (both included).
from [(2, 0) to infinity ] is when it is decreasing. (both included).
By looking at the graph, we can determine this.
The slope of the increasing line is positive, and the slope of the decreasing line is negative.
Which diagram shows lines that must be parallel lines cut by a transversal?
Answers
The first diagram shows the parallel lines cut by a transversal.
According to the statement
We have to explain all about the parallel lines cut by a transversal.
So, For this purpose, we know that the
A transversal line is a line that passes through two lines in the same plane at two distinct points.
And
Parallel lines are lines in a plane that are always the same distance apart.
From the given information:
In the given pictures we see that there are the presence of the two parallel lines and a one line is passes through these lines and cut the two parallel lines and there is a formation of the some angles in it.
And by property and the behavior of the transversal line to the parallel lines.
The diagram in first option shows a perfect lines that must be parallel lines cut by a transversal.
So, The first diagram shows the parallel lines cut by a transversal.
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Vanessa runs 4 miles each week. Use the number line below to solve and represent the number of weeks it will take her to run 96 miles.
Answers
The number of weeks that Vanessa ran for the number of miles given would be = 24 weeks
How to calculate the number of weeks used by Vanessa for race?The amount of distance that Vanessa covers for a week = 4 miles
The amount of weeks it will take for her to cover 96 moles would be = ?
That is;
1 week = 4 miles
X weeks = 96 miles
Make X the subject of formula;
X = 96× 1/4
= 24 weeks
Therefore Vanessa will be able to cover 96 miles in only 24 weeks.
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