The product of the two binomials is (y + 1)(y - 5)
Step-by-step explanation:
To write a polynomial as a product of two binomials
At first simplify the polynomialAdd the like terms if necessaryFactorize it using any type of factorization to get a product of two binomials∵ The polynomial is (y - 5) - y(5 - y)
- Multiply y by the bracket (5 - y)
∵ y(5 - y) = y(5) - y(y)
∴ y(5 - y) = 5y - y²
- Substitute 5(5 - y) by (5y - y²)
∴ (y - 5) - y(5 - y) = (y - 5) - (5y - y²)
- Multiply (-) by the bracket (5y - y²)
∵ (-)(5y) = -5y
∵ (-)(-y²) = y²
∴ (y - 5) - y(5 - y) = y - 5 - 5y + y²
- Add the like terms
∴ (y - 5) - y(5 - y) = -4y - 5 + y²
- Arrange the terms from greatest power of y
∴ (y - 5) - y(5 - y) = y² - 4y - 5
Now let us factorize y² - 4y - 5 into two factors
∵ y² = y × y
∵ -5 = -5 × 1
- Multiply y by 1 and y by -5, then add the product the sum
must be equal the middle term of the polynomial above
∵ y(1) + y(-5) = y - 5y = -4y ⇒ as the middle term
- Now write the two bracts
∴ y² - 4y - 5 = (y + 1)(y - 5)
The product of the two binomials is (y + 1)(y - 5)
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How do you write the difference of a number and eight, divided by ten
Answer:
(x-8)/10
Step-by-step explanation:
-------
(X - 8)/10 or (8 -X)/10
The unknown number can be given as X
The difference between the number and 8 can be given as 8 -X or X - 8
The dividing it by 10 will give (x-8)/10 or (8-x)/10 depending on the value of the unknown number X
Rewrite the equation 2x + 3y = 6 in slope-intercept form.
y = -2 x + 6
y = - (fraction)x + 2
y = 2 x + 6
3 y = -2 x + 6
Answer:
y = - [tex]\frac{2}{3}[/tex] x + 2
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c
Rearrange 2x + 3y = 6 into this form
Subtract 2x from both sides
3y = - 2x + 6 ( divide all 3 terms by 3 )
y = - [tex]\frac{2}{3}[/tex] x + 2 ← in slope- intercept form
Decide which story can be represented by the system of equations y = x + 6 and
x + y = 100. Explain your reasoning.
a. Diego's teacher writes a test worth 100 points. There are 6 more multiple
choice questions than short answer questions.
b. Lin and her younger cousin measure their heights. They notice that Lin is 6
inches taller, and their heights add up to exactly 100 inches.
Option A and Option B are correct answers.
Step-by-step explanation:
Option a: Diego's teacher writes a test worth 100 points. There are 6 more multiple choice questions than short answer questions.
Reason:
Let x denote the multiple choice questions.
Let y denote the short answer questions.
It is given that there are 6 more multiple choice questions than short answer questions and writing it as equations,
[tex]y=x+6[/tex]
Also, given that Diego's teacher writes a test worth 100 points and writing it as equations,
[tex]x+y=100[/tex]
Option b: Lin and her younger cousin measure their heights. They notice that Lin is 6 inches taller, and their heights add up to exactly 100 inches.
Reason:
Lin is represented by the variable y.
Her younger cousin is represented by the variable x.
It is given that Lin is 6 inches taller and writing it as equation, we get,
[tex]y=x+6[/tex]
Also, given that their heights add up to exactly 100 inches and thus, writing it as equation, we get,
[tex]x+y=100[/tex]
Thus, Option a and Option b represent the same system of equations. Hence, both story can be represented by the system of equations.
The story that can be represented with the system of equations is story B.
Description of simultaneous equations
Simultaneous equations are a set of two or more equations that have to be solved together in order to determine the needed values.
Explanation of story B.If Lin is 6 inches taller than her cousin, if Lin's height is represented with y and her cousin's height is represented with x, then the equation is: y = x + 6. If the sum of their ages is 100, this can be represented with: x + y = 100.
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Solve for x. 11x+4< 15 OR 12x–7>-25
What are the zeros of f(x) = x2 + x - 30?
Ο
A. X = -5 and x = 6
B. X = -6 and x = 5
Ο.
O
C. x = -2 and x = 15
O
D. x = -15 and x = 2
Answer:
the zeros as x = 5 or x = -6 . SO the correct option is Option B.
Step-by-step explanation:
i) the zeros of any expression of f(x) is found by equating f(x) to zero and then solving for x.
ii) therefore to find the zeros ( or roots) of the given expression we can write f(x) = [tex]x^{2} + x - 30 = 0[/tex]
iii) therefore [tex]x^{2} + x - 30 = 0[/tex] ⇒ [tex]x^{2} + 6x - 5x - 30 = 0[/tex] .... from visual observation
therefore we can write [tex]x( x + 6) -5(x + 6) = 0[/tex] ⇒ [tex](x - 5)(x + 6) = 0[/tex]
therefore either x - 5 = 0, or, x + 6 = 0 if the above equation is to be true.
iv) therefore solving for x we get the zeros as x = 5 or x = -6. So the correct option is Option B.
Answer:
Therefore the zeros of
[tex]f(x)=x^{2}+x-30[/tex]
are
[tex]x=-6\ and\ x= 5[/tex]
Step-by-step explanation:
Given:
[tex]f(x)=x^{2}+x-30[/tex]
To Find:
Zeros of the function.
Solution:
Zeros of Polynomial or function:
Zeros of the polynomial means while substituting the value of X in the polynomial you will get the value of the polynomial or function equals to Zero.
Hence to find a value of zeros , the value of function should be zero.
Therefore,
f(x) =0
[tex]x^{2}+x-30=0[/tex]
To find the value of 'x' we need to factorize the above quadratic equation.
First is to remove the factor of -30 such that when you add the factors you should get one.
-30 = 6 × -5
6 - 5 = 1
Hence by splitting the middle term we get
[tex]x^{2}+6x-5x-30=0\\x(x+6)-5(x+6)=0\\(x+6)(x-5)=0\\x+6=0\ or\ x-5=0\\x=-6\ or\ x=5[/tex]
Therefore the zeros of
[tex]f(x)=x^{2}+x-30[/tex]
are
[tex]x=-6\ and\ x= 5[/tex]
Anna wants to buy a house at $67,000. She will need at down payment of 15%. What is the down payment amount
Answer:
67000*.15=10,050
Step-by-step explanation:
The required down payment would be the amount of $10,050.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
Anna wants to buy a house for $67,000.
She will need a down payment of 15%.
We have to determine the evaluation of 15% of $67,000.
⇒ 15% of 67,000
15% is expressed as 15/100 in fractional form
⇒ (15/100)(67,000)
15/100 is expressed as 0.15 in decimal form
⇒ (0.15)(67,000)
Apply the multiplication operation, and we get
⇒ 10,050
Therefore, the down payment would be $10,050.
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Find the average rate of change for f(x) = x2 + 9x + 18 from x = −8 to x = −2.
A) −1
B) −3
C) 1
D) 3
Answer:
c
Step-by-step explanation:
c
Here are the heights (in inches) of 12 students in a seminar.
69, 62, 73, 67, 63, 65, 73, 71, 70, 66, 59, 75
What is the percentage of these students who are shorter than 73 inches?
Answer: 75%
Step-by-step explanation:
Height given :
69, 62, 73, 67, 63, 65, 73, 71, 70, 66, 59, 75
The total number of height given = 12
The height less than 73 are 69 , 62, 67 ,63 , 65 , 71 , 70 , 66 , 59
The total number of heights less than 73 = 9
Therefore : the percentage of these students who are shorter than 73 inches = total number of students shorter than 73/ total number of height x 100
= 9/12 x 100
= 75%
About 75% of the students are shorter than 73 inches. This was determined by counting the number of students shorter than 73 inches (9 students) and dividing by the total number of students (12 students), then multiplying by 100%
Explanation:To calculate the percentage of students shorter than 73 inches, you first need to count how many students are shorter than 73 inches. From the given data, the heights of the students shorter than 73 inches are 69, 62, 67, 63, 65, 71, 70, 66, and 59. Thus, there are 9 students out of 12 who are shorter than 73 inches.
Now, to get the percentage, you divide the number of shorter students by the total number of students, and then multiply the result by 100. This is how it looks: (9/12)*100% = 75%. Thus, 75% of these students are shorter than 73 inches.
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you deposit $3,000 in an account that pays 5% annual interest compounded continuously. what is the balance after 2 years
Answer:
Step-by-step explanation:
$3307.50
During bowling practice, Marley rolled 14 strikes out of 70 attempts. What percent of Marley’s attempts were strikes?
|
|
fractions btw
Answer:
Step-by-step explanation:
14 strikes out of 70 attempts.....what percent were strikes ?
14/70 = 0.2
to turn a decimal to a percent, either multiply by 100 or move the decimal point 2 spaces to the right.
0.2 * 100 = 20% <==== strikes
Answer:
20%
Step-by-step explanation:
Jane had to draw a triangle given the measure of three sides. Which if these measures would give a triangle? A 2cm, 4cm, 8cm. B. 3cm, 4cm, 6cm C 4cm 5cm 10cm D. 5cm 6cm 12cm. Help
Final answer:
To determine if a triangle can be formed given three side lengths, apply the triangle inequality theorem by comparing the sum of any two sides to the length of the remaining side. Option B and option D would give triangles.
Explanation:
To determine if a triangle can be formed given the measures of three sides, we need to apply the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side.
Let's examine each given set of side lengths:
A. 2cm, 4cm, 8cm: In this case, 2cm + 4cm = 6cm, which is less than 8cm. So, a triangle cannot be formed with these side lengths.
B. 3cm, 4cm, 6cm: Here, 3cm + 4cm = 7cm, which is greater than 6cm. The sum of any two sides is always greater than the third side, so a triangle can be formed with these side lengths.
C. 4cm, 5cm, 10cm: In this case, 4cm + 5cm = 9cm, which is less than 10cm. So, a triangle cannot be formed with these side lengths.
D. 5cm, 6cm, 12cm: Here, 5cm + 6cm = 11cm, which is greater than 12cm. The sum of any two sides is always greater than the third side, so a triangle can be formed with these side lengths.
Therefore, option B (3cm, 4cm, 6cm) and option D (5cm, 6cm, 12cm) would give triangles.
The radius of a sphere is 3 inches. Which represents the volume of the sphere?
12 cubic inches
The volume of a sphere with a radius of 3 inches is [tex]\(36 \pi\)[/tex] cubic inches. Therefore, the correct option is [tex]\(36 \pi\)[/tex] cubic inches.
The volume V of a sphere with radius r is given by the formula:
[tex]\[ V = \frac{4}{3} \pi r^3 \][/tex]
Given that the radius r is 3 inches, we can substitute this value into the formula:
[tex]\[ V = \frac{4}{3} \pi (3)^3 \]\[ V = \frac{4}{3} \pi (27) \]\[ V = \frac{4}{3} \times 27 \times \pi \]\[ V = 36 \pi \][/tex]
So, the volume of the sphere is [tex]\( 36 \pi \)[/tex] cubic inches.
Therefore, the correct option is: [tex]\( 36 \pi \)[/tex] cubic inches.
Complete Question:
The radius of a sphere is 3 inches. Which represents the volume of the sphere?
[tex]$12 \pi$[/tex] cubic inches
[tex]$36 \pi$[/tex] cubic inches
[tex]$64 \pi$[/tex] cubic inches
[tex]$81 \pi$[/tex] cubic inches
On average shawnte drinks 1/2 of a 6-ounce glass of water in 2/3 hour how much watee does she drink in a hour
she drinks 9/2 ounces of water in 1 hour
Step-by-step explanation:
On average, the person drinks 1/2 of a 6-ounce glass of water in 2/3 hour.
First of all, we have to rewrite the amount of water in a single fraction: we have
[tex]\frac{1}{2}\cdot 6 = \frac{6}{2}=3[/tex]
This means that the person drinks 3 ounces of water every 2/3 hours.
In order to find how much water she drinks in one hour, we use the following proportion:
[tex]\frac{3}{2/3}=\frac{x}{1}[/tex]
where
x is the amount of water she drinks in one hour.
Solving the equation for x,
[tex]x=\frac{3\cdot 1}{2/3}=\frac{3\cdot 1 \cdot 3}{2}=\frac{9}{2}[/tex]
Therefore, she drinks 9/2 ounces of water in 1 hour.
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25h to the power of 10 +18
Answer:
1.509909034 x10 ^36
Step-by-step explanation:
10 plus 18 is 28
Then you would multiply 28 by 25 numbers of itself.
4% of what amount of money is $19?
how many soulutions does the system of equations have x-3y=15. and 3x-9y=45
Answer:
Infinitely many solutionsStep-by-step explanation:
[tex]\left\{\begin{array}{ccc}x-3y=15\\3x-9y=45\end{array}\right\\\\\text{Divide both sides of the second equation by 3}\\\\\dfrac{3x}{3}-\dfrac{9y}{3}=\dfrac{45}{3}\\\\x-3y=15\\\\\text{We received the same equation as the first.}\\\\\bold{CONCLUSION}\\\\\text{The system of equations has infinitely many solutions.}[/tex]
[tex]\left\{\begin{array}{ccc}a_1x+b_1y=c_1\\a_2x+b_2x=c_2\end{array}\right\\\\\text{If}\ a_1=a_2,\ b_2=b_2,\ c_1=c_2,\ \text{then the system of equations}\\\text{ has infinitely many solutions}\\\\\text{If}\ a_1=a_2,\ b_1=b_2,\ c_1\neq c_2,\ \text{then the system of equations}\\\text{has no solutions}\\\\\text{Other the system of equations has one solution.}[/tex]
Two passenger trains traveling in opposite directions meet and pass each other. Each train is 1/12 miles long and is traveling 50 mph. How many seconds after the front cars of the trains meet will their rear cars pass each other?
Answer:
6 seconds
Step-by-step explanation:
1/12 mile * 5280 feet/mile = 440 feet per train
50 miles/hour * 1/3600 hr/sec * 5280 ft/mile = 73 1/3 ft/second
one train has to travel 440 feet to pass the other train
440 feet * 1/(73 1/3) sec/ft = 6 seconds
The time it will take for the two trains to pass each other's rear car is 6 seconds.
What is speed?The speed is the distance covered by an object at a particular time. Therefore, it is the ratio of distance and time.
[tex]\rm{Speed = \dfrac{Distance}{Time}[/tex]
Two passenger trains travelling in opposite directions meet and pass each other. Each train is 1/12 miles long and is traveling 50 mph.
Therefore, the total distance that the two train needs to cover is twice the size of a train.
Distance = 2 × 1/12miles = 1/6 miles
Also, the relative speed of the two trains moving in opposite directions is,
Speed = 50 mph + 50 mph = 100 mph
Now, the time that the two trains need to cover the entire distance is,
Time = (1/6 miles)/ 100mph = 1/600 hours
Converting the time to seconds,
Time = 1/600 hours × 3600 = 6 seconds
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The points (9,9) and (10,k) fall on a line with a slope of -1. What is the value of k?
The value of k is 8
Solution:
Given that, points (9, 9) and (10, k) fall on a line with a slope of -1
To find: value of "k"
The slope of a line with points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is given as:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Here given that,
slope = m = -1
[tex](x_1, y_1) = (9, 9)\\\\(x_2, y_2) = (10, k)[/tex]
Substitute the values in formula, and solve to get value of k
[tex]m = \frac{k-9}{10-9}\\\\-1 = \frac{k-9}{10-9}\\\\-1 = \frac{k-9}{1}\\\\k-9 = -1\\\\k = -1+9\\\\k = 8[/tex]
Thus the value of k is 8
Ernise evaluated the expression 10(3 + 5) like this:
Step 1: 10.3 + 10.5
Step 2: 30 + 50
Step 3: 80
Which mathematical property was she using?
Answer:
distributive property
Dist. can be identified by x(y+z)
x/5 = -10 What is the value of X
Answer:
[tex]x=-50[/tex]
Step-by-step explanation:
we have
[tex]\frac{x}{5} =-10[/tex]
Solve for x
That means ----> isolate the variable x
Multiply by 5 both sides to remove the fraction
[tex]\frac{x}{5}(5) =-10(5)[/tex]
Simplify
[tex]x=-50[/tex]
You work as a tailor. You are provided with 5 3/4 yards of cloth for making curtains. You use 4 1/4 yards of cloth for that purpose.
How many yards of cloth remain?
Final answer:
After using 4 1/4 yards out of 5 3/4 yards of cloth to make curtains, 1 1/2 yards of cloth remain.
Explanation:
You are provided with 5 3/4 yards of cloth and you use 4 1/4 yards for making curtains. To find out how much cloth remains, you need to subtract the amount used from the total amount provided. You perform the subtraction by converting the mixed numbers to improper fractions or by subtracting the whole numbers and fractions separately.
First, subtract whole numbers:
5 yards - 4 yards = 1 yardNext, subtract the fractions:
3/4 yard - 1/4 yard = 2/4 yard, which simplifies to 1/2 yard.Combine the whole number and the fraction for the final answer:
1 yard + 1/2 yard = 1 1/2 yards of cloth remain.on friday,718 peoole went to school play.on saturday,822 people went.about how many oeople saw the play altogether
Answer:
1540
Step-by-step explanation:
Add 718 and 822! Thanks
To find out how many people saw the play altogether, add the number of people who went on Friday and Saturday. The total number of people who saw the play is 1540.
To find out how many people saw the play altogether, we need to add the number of people who went on Friday and the number of people who went on Saturday.
On Friday, 718 people went to the school play. On Saturday, 822 people went.
To find the total number of people who saw the play, we add 718 and 822:
Total number of people = 718 + 822 = 1540
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Help ASAP
What is the 5th term in the geometric sequence described by this explicit
formula?
an=40 • (-2)^(n-1)
A. 1280
B. -640
c. -1280
D. 640
The fifth term of the geometric sequence is 640, so the correct option is D.
How to get the fifth term of the given geometric sequence?
Here we have a geometric sequence, such that the terms are given by:
[tex]A_n = 40*(-2)^{(n-1)}[/tex]
To get the 5-th term, we just need to replace n by 5 on the above rule, so we can write:
[tex]A_5 = 40*(-2)^{(5-1)} = 40*(-2)^4 = 640[/tex]
Then the value of the 5-th term is 640, which means that the correct option is D.
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What percent of 18 is 24?
Answer:
133%
Step-by-step explanation:
24/18=4/3=1.33...=133%
Answer:
75%
Step-by-step explanation:
because it = 18/24 or 75%
The world record for the 100 meter sprint is 9.77 seconds. How long would it take to run 1 meter at the speed
Answer:
Step-by-step explanation:
Time taken = 9.77/100 = 0.0977 seconds
helpppppp pleaseeee!!!!! like the north pole the south pole receives little solar radiation during the winter. unlike the north pole, however, the south pole does not send outbreaks as far as the subtropics. Why? (Hint: you may want to study a world map to answer this question.)
Step-by-step explanation:
firstly there is hole in the ozone
secondly i believe it is because of the axis of the earth and that the raidiation to coming to the equator not the poles
Three bags of sweets weigh 6 3/4 kg. Two of them have the same weight and the third bag is heavier than each of the bags of equal weight by 1 1/5 kg. Find the weight of each bag.
Final answer:
The weight of each bag of equal weight is 1 17/20 kg and the weight of the third bag is 1 41/20 kg.
Explanation:
Let's assume the weight of each bag of equal weight is x kg. According to the question, the third bag is heavier than each of the equal bags by 1 1/5 kg, which can be written as 6/5 kg.
So, the weight of the third bag is x + 6/5 kg.
Now, we can set up an equation based on the given information:
2x + (x + 6/5) = 6 3/4
Simplifying the equation, we get:
3x + 6/5 = 27/4
Now, we can solve for x by multiplying both sides of the equation by 5 to get rid of the fraction:
15x + 6 = 135/4
15x = 135/4 - 6
15x = 135/4 - 24/4
15x = 111/4
Now, divide both sides of the equation by 15 to solve for x:
x = (111/4) / 15 = 111/60 = 37/20 = 1 17/20
Hence, the weight of each bag of equal weight is 1 17/20 kg and the weight of the third bag is 1 17/20 + 6/5 = 1 17/20 + 24/20 = 1 41/20 kg.
A fraction that is a terminating decimal between 1.25 and 1.5
Answer:
13/10
Step-by-step explanation:
13/10 = 1.30 is a number between 1.25 and 1.50.
If 1 inch represents 85 miles on a map, then how many inches will represent 800 miles
800/85 = 9.411764705882353 inches
ans = 9.411764705882353 inches
Answer:
9.41 inches to the nearest hundredth.
Step-by-step explanation:
By proportion it is 800 / 85
= 9.41 inches.
Can someone please help me with this? Thank you!
Answer:
[tex]\left[\begin{array}{ccc}-25&\dfrac{75}{2}&-\dfrac{25}{2}\end{array}\right][/tex]
Step-by-step explanation:
In the first equality
[tex]5\times \left[\begin{array}{cc}-1&2\\4&8\end{array}\right] =\dfrac{2}{5}m\times \left[\begin{array}{cc}-1&2\\4&8\end{array}\right],[/tex]
the matrices in both parts are the saem. The equality will be true if the same matrices are multiplied by the same numbers, so
[tex]5=\dfrac{2}{5}m\Rightarrow m=5\times \dfrac{5}{2}=\dfrac{25}{2}[/tex]
For the second equality
[tex](H+[1\ 4\ -2])+[3\ 2\ -6]=[-2\ 3\ -1]+([1\ 4\ -2]+[3\ 2\ -6]),[/tex]
if [tex]H=[-2\ 3\ -1][/tex], then this equality represents the assotiative property of matrix addition.
Hence,
[tex]m\times H=\dfrac{25}{2}\times [-2\ 3\ -1]=\left[\begin{array}{ccc}-25&\dfrac{75}{2}&-\dfrac{25}{2}\end{array}\right][/tex]