Answers
Consider a quadratic expression, let "m" and "n" represent the factors.
The diamond method of factoring is the following:
On the left of the diamond, there is one of the factors, for example, "m", of the right of the diamond you will find the other factor "n".
On the top of the diamond, you will find the product of both factors, on the bottom of the diamond you will find the sum of the factors.
Looking at the given diamond, you know the result of the product and the sum of both factors:
\(m*n=-15\)\(m+n=14\)Using these expressions, you can find both factors.
- First, write the second expression for one of the variables, for example, for "n"
\(\begin{gathered} m+n=14 \\ m=14-n \end{gathered}\)- Second, replace the expression obtained on the second equation:
\(\begin{gathered} m*n=-15 \\ (14-n)n=-15 \end{gathered}\)Distribute the multiplication
\(14n-n^2=-15\)Zero the expression and order the terms from greatest to least:
\(\begin{gathered} 14n-n^2+15=-15+15 \\ 14n-n^2+15=0 \\ -n^2+14n+15=0 \end{gathered}\)- Third, use the quadratic expression to determine the possible values of n:
\(x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\)Where
a is the coefficient of the quadratic term
b is the coefficient of the x-term
c is the constant
For the quadratic expression obtained, where "n" represents the x-variable.
\(-n^2+14n+15=0\)The coefficients are:
a= -1
b=14
c=15
\(\begin{gathered} x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ n=\frac{-14\pm\sqrt{14^2-4*(-1)*15}}{2*(-1)} \\ n=\frac{-14\pm\sqrt{196+60}}{-2} \\ n=\frac{-14\pm\sqrt{256}}{-2} \\ n=\frac{-14\pm16}{-2} \end{gathered}\)Solve the sum and difference separately to determine both possible values for "n"
→Sum:
\(\begin{gathered} n=\frac{-14+16}{-2} \\ n=\frac{2}{-2} \\ n=-1 \end{gathered}\)→Difference:
\(\begin{gathered} n=\frac{-14-16}{-2} \\ n=\frac{-30}{-2} \\ n=15 \end{gathered}\)- Finally, determine the possible value/s of m:
For n=-1
\(\begin{gathered} m+n=14 \\ m+(-1)=14 \\ m-1=14 \\ m=14+1 \\ m=15 \end{gathered}\)For n=15
\(\begin{gathered} m+n=14 \\ m+15=14 \\ m=14-15 \\ m=-1 \end{gathered}\)So, the factors are -1 and 15 and the diamond is:
Related Questions
A quadrilateral has 4 sides. One angle of a regular quadrilateral measures (6w+13) Determine the value of w. Round to the nearest whole number.
Ow=13
Ow=23
Ow=59
Ow=90
Answers
The value of w for the expression of angle 6w + 13 will be 13. The correct option is A.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that a quadrilateral has 4 sides. One angle of regular quadrilateral measures (6w+13).
The value of 'w' will be calculated as,
6w + 13 = 90
6w = 90 - 13
6w = 77
w = 12.83 or 13
Therefore, the value of w for the expression of angle 6w + 13 will be 13. The correct option is A.
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It's in the picture !
Answers
The position of √17 between 4 and 5, which is nearer 5, and the location of 6, which is between 2 and 3, which is nearer 2.
What is Number line?A visual representation of real numbers in a linear manner is a number line. It is a straight line that is divided into intervals or segments, each of which stands for a distinct real number value.
Number lines can be vertical or horizontally oriented, and they can also have a positive or negative orientation. Positive numbers often extend to the right or up, whereas negative numbers typically extend to the left or down. The origin of the number line, or zero, is typically situated in the middle of the line.
The number line is a crucial tool in mathematics since it offers a means of representing numerical relationships visually and carrying out fundamental arithmetic operations. For instance, positive and negative motions along a number line can be used to depict addition and subtraction, respectively, with positive movements denoting addition and negative movements denoting subtraction. On a number line, multiplication and division can alternatively be shown as repeated addition or subtraction.
If we have a number line with the proper markings, we may indicate where the square roots of 17 and 6 are located as follows:
To begin, determine the approximate square root values:
√17 is between 4 and 5, since 4² = 16 and 5² = 25.
√6 is between 2 and 3, since 2² = 4 and 3² = 9.
Place the number √17 closer to 5, between 4 and 5.
Place the number √6 between the numbers 2 and 3, closer to 2.
Since 6 and 17 are not integers and their values are not evenly spaced, it should be noted that their markings will not be evenly spaced on the number line.
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Number line attached below,
Audrey is growing basil. On February 1st, her plant was 5 inches tall. A week later, the plant was 9 inches tall. By what percent did the plant grow?
Answers
Answer:
80%
Step-by-step explanation:
We know that the plant was 5 inches and it grew 4 inches to become 9 inches, so now we just need to figure out what percentage 4 is of 5. An easy way to do this is by multiplying 5 by 2 to get 10 and since 4 is 40% of ten we know that 4 is 80% of 5 because we have to multiply 4 by 2 because we did 5.
the plant grew by 80%.
Step-by-step explanation:
Solve for the value of X.
-4x + 3 = 35
Answers
Answer:
-8
Step-by-step explanation:
To evaluate whether customers enjoy the barista’s new smoothie, a restaurant manager surveys every other customer who orders the new smoothie. The manager determines that customers enjoy the new smoothie. Select all the statements that are true about the sampling method.
Answers
The sampling method used by the restaurant manager allows for efficient data collection and a representative sample, it may introduce bias and lacks randomization.
Based on the information provided, we can identify the following statements that are true about the sampling method used by the restaurant manager to evaluate customer satisfaction with the new smoothie:
1. The manager uses systematic sampling: The manager surveys every other customer who orders the new smoothie. This systematic approach involves selecting every second customer, providing a consistent and organized sampling method.
2. The sample is representative: By surveying every other customer who orders the new smoothie, the manager ensures that the sample includes a variety of customers, reflecting the customer population as a whole.
3. The sample size may be smaller than the total customer base: Since the manager surveys every other customer, the sample size may be smaller compared to surveying every customer. This allows for efficient data collection and analysis.
4.The sampling method may introduce bias: The manager may inadvertently introduce bias by only surveying every other customer. Customers who are skipped in the survey may have different preferences or opinions, leading to a potential bias in the results.
5. The sampling method lacks randomization: Randomization is not employed in this sampling method, as the manager systematically selects customers. This could potentially introduce bias or exclude certain types of customers from the sample.
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Assume that a sample is used to estimate a population mean . Find the 99.5% confidence interval for a sample of size 353 with a mean of 75.7 and a standard deviation of 6.8. Enter your answer as a tri-linear inequality accurate to 3 decimal places.
Answers
The 99.5% confidence interval for a sample of size 353 with a mean of 75.7 and a standard deviation of 6.8 is: (74.94, 76.46)
Hope to calculate the valueTo calculate the confidence interval, we can use the following formula:
CI = x ± tα/2 * s / √n
In this case, the critical value of the t-distribution for a confidence level of 99.5% is 2.776. Plugging in the other values, we get the following confidence interval:
CI = 75.7 ± 2.776 * 6.8 / √353
CI = (74.94, 76.46)
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what unit should i use for this bar graph?
Answers
Answer: x (Subject), y (Number of books)
Step-by-step explanation: When using numbers in a bar graph, it is displayed on the Y-axis as its easily interpreted.
Answer:
In your bar graph, use one the bottom place written subjects, and the right side for Number of books.
Step-by-step explanation:
Here is where l
you write l
the numbers l
and ''number l
of books'' l the middle is now where you draw
l
l
l
_____________________
subjects are written bellow
A convex polyhedron has faces that consist of 30 squares, 20 triangles, and 12 pentagons. The polyhedron has 120 edges. How many vertices does it have?
Euler’s formula: V + F = E + 2
a:60
b:92
c:122
d:180
THE ANSWER IS A:60 ON EDGE 2021
Answers
Answer:
THE ANSWER IS D 180
Step-by-step explanation:
THE PERSON WHO MADE THIS QUESTION IS WRONG, PLS TRUST
If triangle ABC was reflected over the x-axis, what would be the coordinates of B’?
a(-3, 4)
b(3, -4)
c(4, -3)
d(-4, 3)
Answers
The coordinates of B’ is given by D. A'(2, -5)
Since point A is at (2, 5), and you are reflecting it across the x-axis, you take a look at the y-coordinate.
What is the reflecting axis?A reflection of a point, a line, or a figure in the X-axis involved reflecting the image over the x-axis to create a mirror image. In this case, the x-axis would be called the axis of reflection.
Since it is five above the x-axis, you go five below the x-axis, or just give the opposite of 5, which is -5.
So, A' is at (2, -5).
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Answer:
c (4, -3)
Step-by-step explanation:
took the quiz
Find the value of x
55’. x
Answers
Answer:
x = 35
Step-by-step explanation:
The sum of the angles of a triangle is 180°.
\(x+55+90=180\\x+145=180\\x=35\)
Answer:
\({ \boxed{ \mathfrak{ \: answer : \: { \rm{35\degree}}}}}\)
Step-by-step explanation:
\({ \rm{55 \degree + 90\degree + x = 180\degree}} \\ { \tt{ \{angle \: sum \: of \: a \: triangle \}}} \\ { \rm{145\degree + x = 180\degree}} \\ { \rm{x = 35\degree}}\)
Here is another question DUE SOON PLEASE ASAP
Question 5(Multiple Choice Worth 1 points)
(08.07 MC)
The table describes the quadratic function p(x).
x p(x)
−1 10
0 1
1 −2
2 1
3 10
4 25
5 46
What is the equation of p(x) in vertex form?
p(x) = 2(x − 1)2 − 2
p(x) = 2(x + 1)2 − 2
p(x) = 3(x − 1)2 − 2
p(x) = 3(x + 1)2 − 2
Answers
The equation of p(x) in vertex form is;
p(x) = 9.67(x + 1.04)² - 10.25
The closest answer choice is:
p(x) = 3(x - 1)² - 2, which is not correct.
What is vertex?In the context of a quadratic function, the vertex is the highest or lowest point on the graph of the function. It is the point where the parabola changes direction. The vertex is also the point where the axis of symmetry intersects the parabola.
To find the vertex form of the quadratic function p(x), we need to first find the vertex, which is the point where the function reaches its maximum or minimum value.
To find the vertex, we can use the formula:
x = -b/2a, where a is the coefficient of the x² term, b is the coefficient of the x term, and c is the constant term.
Using the table, we can see that the highest value of p(x) occurs at x = 5, and the value is 46.
We can then use the formula to find the vertex:
x = -b/2a = -5/2a
Using the values from the table, we can set up two equations:
46 = a(5)² + b(5) + c
1 = a(0)² + b(0) + c
Simplifying the second equation, we get:
1 = c
Substituting c = 1 into the first equation and solving for a and b, we get:
46 = 25a + 5b + 1
-20 = 5a + b
Solving for b, we get:
b = -20 - 5a
Substituting b = -20 - 5a into the first equation and solving for a, we get:
46 = 25a + 5(-20 - 5a) + 1
46 = 15a - 99
145 = 15a
a = 9.67
Substituting a = 9.67 and c = 1 into b = -20 - 5a, we get:
b = -20 - 5(9.67) = -71.35
Therefore, the equation of p(x) in vertex form is:
p(x) = 9.67(x - 5)² + 1
Simplifying, we get:
p(x) = 9.67(x² - 10x + 25) + 1
p(x) = 9.67x² - 96.7x + 250.85 + 1
p(x) = 9.67x² - 96.7x + 251.85
Rounding to the nearest hundredth, we get:
p(x) = 9.67(x - 5² + 1 = 9.67(x + 1.04)² - 10.25
Therefore, the answer is:
p(x) = 9.67(x + 1.04)² - 10.25
The closest answer choice is:
p(x) = 3(x - 1)² - 2, which is not correct.
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A tailor has 100 square yards of cotton and 120 square yards of wool material. it takes 2 square yards of each type to make a sports coat. It takes 1 square yard of cotton and 3 square yards of wool to make a pleated skirt. The tailor already has orders for at least 15 sport coats and 5 skirts. If the tailor sells each coat for $40 and each skirt for $45, how many of each garment should be made in order to fill the orders and maximize profit.
Answers
Answer:t
Takes 2 Square Yards Of Each Type To Make A Sports Coat. It Takes 1 Square Yard Of Cotton And 3 Square Yards Of Wool To Make A Pleated Skirt.
Step-by-step explanation:
hope that is what you were needing
5.18 × 10¹ = write in standard format
Answers
Answer:
51.8
Step-by-step explanation:
10¹ = 10
5.18 × 10 = 51.8
multiplying by 10 moves the decimal point once to the right
Answer:
51,8
Step-by-step explanation:
5.18 × 10¹
5.18 × 10
= 51,8
Suppose we want to choose 5 letters, without replacement, from 15 distinct letters
Answers
\(\text{order does not matter}\)
\(\text{sample space}= \text{15 letters}\)
\(\text{no repetition}\)
\(\text{P(A)}= \text{15C5}= \text{3003 ways}\)
what is the value of pi based on the equation for the best-fit line? (1pts) calculated value of pi: (1pts) question 5 determine the percent error using equation ex.1 and an actual value of 3.142 for pi. % e r r o r
Answers
Pi (π) is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The equation for the best-fit line does not provide any direct information about the value of pi. The best-fit line is used to model the relationship between two variables, and it can be used to make predictions or estimates based on that relationship.
Pi (π) is a mathematical constant that represents the ratio of the circumference of a circle to its diameter. Its value is approximately 3.14159. Pi is a fundamental constant in mathematics and appears in many different mathematical equations and formulas.
Hence, Pi (π) is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.
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how would someone use the cross product property on an equation with 3 different values instead of two? I provided an example image
Answers
Using the cross product for the proff of Pythagoras theorem, the correct step is
By the cross product property, AB² = BC multiplied by BD
What is cross product propertyThe cross product property is typically used to solve equations with two values, where the product of the extremes (the outer terms) is equal to the product of the means (the inner terms).
For the similar triangles, the ratio is as follows
BD / BA = BA / BC
BA² = BD * BC
and AB = BA, hence
BA² = BD * BC
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The theater was full when the movie began. Seventy-six people left
before the movie ended. One hundred twenty-four people remained.
How many people were in the theater when it was full?
Answers
The number of people were 200 in the theater when it was full.
What is a theater?
In architecture, a theatre, usually spelled theatre, is a structure or area where a play can be conducted in front of spectators. The term comes from the Greek theatron, which means "a place of seeing." The actual performance usually takes place on a stage in a theatre.
Given that, the theater was full when the movie began.
76 people leave the theater before end the movie. At the end of the movie, there is 124 people left.
Apply algebraical operation that is addition to find the required answer.
Therefore, the number of people that was present at the beginning of the movie is (76 + 124) = 200.
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Is 2 a solution of 3-p=1
Answers
Evaluate
(0.3)*4= plplpl
Answers
Answer:
1.2
Step-by-step explanation:
0.3 * 4
= 3 * 0.1 * 4
= 3 * 4 * 0.1
= 12 * 0.1
= 1.2
10 to the negative 3 + 10 to the 4th power
Answers
10000.001
You can search for any mathematical expression, using functions such as: sin, cos, sqrt, etc. You can find a complete list of functions here.
Ziba brought 4 bottles of water to the park. Each bottle held 6 ounces of water. Ziba drank an equal number of ounces of water each hour. If she was at the park 3 hours, how many ounces of water did she drink each hour
Answers
By taking the quotient between the total volume and the number of hours, we conclude that she drinks 8 ounces per hour.
How many ounces of water did she drink each hour?
We know that Ziba has 4 bottles, each one with 6 ounces, so the total volume of water is:
V = 4*6 ounces = 24 ounces.
We know that she drinks that in 3 hours, so the amount that she drinks each hour is:
24 oz/3 = 8 oz
She drinks 8 ounces of water each hour.
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Lucy buys 1200 of new stock from a wholesale
M
Answers
Answer:
so what should we do for it
Candace invests $636 in an investment that pays 7% interest compounded quarterly. What is her annual effective yield? Input answer as a percentage to two decimal places.
Answers
Answer:
7.19%
Step-by-step explanation:
let i be the effective rate
\((1+\frac{.07}{4})^4=(1+i)\\.071859031\)
The annual effective yield will be 7.19% for the investment.
What is compound interest?Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.
Given that Candace invests $636 in an investment that pays 7% interest compounded quarterly.
The annual effective yield will be calculated as below:-
[ ( 1 + ( 0.07 / 4 )⁴ ] = ( 1 + i)
Solve the equation:-
i = 0.0718
i = 0.0718 x 100 = 7.19%
Therefore, the annual effective yield will be 7.19% for the investment.
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x-(-4x-(y + y)); use x = -4, and y = -3 evaluate
Answers
please mark this answer as brainlist
Find a vector function that represents the curve of intersection of the paraboloid z=5x^2+2y^2 and the cylinder y=4x^2. Use the variable t for the parameter.
Answers
The vector function that represents the curve of intersection is: r(t) = [x(t), y(t), z(t)] =\([t, 4t^2, 5t^2 + 32t^4]\)
How to determine the vector function that represents the curve of intersectionTo find a vector function that represents the curve of intersection between the paraboloid and the cylinder, we need to express the coordinates (x, y, z) in terms of a parameter t.
Let's start by expressing the cylinder equation in terms of x and y:
y = \(4x^2\):
We can rewrite this as:
y - 4x^2 = 0
Now, we'll substitute this expression for y in the equation of the paraboloid:
z =\(5x^2 + 2y^2\)
Replacing y with \(4x^2\):
\(z = 5x^2 + 2(4x^2)^2\\z = 5x^2 + 32x^4\)
Now we have the equations for x and z in terms of t:
x = t
z = 5t^2 + 32t^4
To obtain the y-coordinate, we substitute the x value into the equation of the cylinder:
y = \(4x^2\):
y =\(4t^2\)
Therefore, the vector function that represents the curve of intersection is: r(t) = [x(t), y(t), z(t)] =\([t, 4t^2, 5t^2 + 32t^4]\)
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Martha, Lee, Nancy, Paul, and Armando have all been invited to a dinner party. They arrive randomly, and each person arrives at a different time.
a. In how many ways can they arrive?
b. In how many ways can Martha arrive first and Armando last?
c. Find the probability that Martha will arrive first and Armando last.
Show your work
Answers
Answer:
a) 120
b) 6
c) 1/20
Step-by-step explanation:
a) 5! = 120
b) (5 - 2)! = 6
c) 6/120 = 1/20
what is (9x+8)^2-54x+48y
Answers
Answer:
81x² + 90x + 48y + 64
Step-by-step explanation:
(9x+8)² = (9x+8)(9x+8) = 9x*9x + 9x*8 + 8*9x + 8*8 = 81x² + 72x + 72x + 64
= 81x² + 144x + 64
then:
(9x+8)² -54x+48y = (81x² + 144x + 64) -54x + 48y = 81x² + 90x + 48y + 64
What is the solution to the system of equations
Answers
The solution of the given system of equations is (-1, -2).
Explain the method of substitution?Three steps make up the substitution technique: For each of the variables, solve one equation. Put this expression (or plug it in) into the other equation, then solve it. To identify the corresponding variable, rewrite the value's original equation.We are aware that a linear system of equations can be solved using a substitution method.
The intersection of the two lines represents the system's solution.
The given equations are-
y = 3x+1 ...eq 1
y = -2x-4 ...eq 2
Put the value of eq 1 in eq2 .
3x+1 = -2x-4
3x + 2x = -4 - 1
5x = -5
x = -5/5
x = -1
Put the x in eq 1.
y = 3(-1)+1
y = -2
Thus, the solution of the given system of equations is (-1, -2).
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The complete question is-
What is the solution to the system of equations-
y=3x+1 ;
y=-2x-4
a company was offering a special on cell phones for $3 each but only if you spent 5 dollars a month for 2 months how much would it end up costing you total if u bought 1 phone ?
Answers
Answer:
10 dollars
Step-by-step explanation:
5 + 5
Solve the exponential equation: 3- x = 1
OA) X=0
x
OB) x= 1
OC) x=-2
x=
OD) x= 2
Answers
\(~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ 3^{2-x}=1\implies 3^2\cdot 3^{-x}=1\implies 3^2\cdot \cfrac{1}{3^x}=1\implies \cfrac{3^2}{3^x}=1 \\\\\\ 3^2=3^x\implies 2=x\)