The GCF of the expression 6x+18/x^2-x-12 is (x+3)
How to find the GCF of the expression?The GCF (Greatest Common Factor) of two or more numbers or expressions is the greatest number or expression among all the common factors of the given numbers or expressions
Given 6x+18/x²-x-12
We can write 6x+18/x²-x-12 as:
6x+18/x²-x-12 = 6x+18/x²-4x+3x-12 By factorization:
= 6(x+3) / (x+3)(x-4)
Since (x+3) is common to both the numerator and the denominator. Therefore, the greatest common factor (GCF) is (x+3)
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Is x5 + x2 + x a polynomial? Explain why or why not.
A polynomial is a mathematical expression formed by variables and coefficients, that involves only the operations of addition, subtraction, multiplication and non-negative integer exponentiation of variables.
The expression:
[tex]x^5+x^2+x[/tex]Is formed by the addition of three terms, each consisting of the variable x raised to a positive integer quantity. Therefore, the given expression is a polynomial.
Sara has saved $500 and wants to buy a new computer. the computer she wants costs $1400. her current job pays $17.50 per hour after taxes . use an inequality to describe the situation , solve the inequality and write a sentence describing what the solution means to Sara
She has already 500
x hours woked
pund we got:
7.50 x >= 900
And inequality could be
fx:o
[tex]500+17.5x\ge1400[/tex]because we need to gain 1400 or more
hours in order to have enough money to buy the computer
Sara needs to work at least 52 00/17.5
x >= 5r t o
The equatu
1
And then we can solve for x a
500+17.5x>>= 1400
utioen x
For this50 case we can do this:
500+ 17.
can you please give me any examples on how to do this
we can take two numbers of the sequence and subtract them to see the difference
so
[tex]1.9-1.2=0.7[/tex]the sequence adds 0.7 each step
the next 3 terms are
[tex]3.3+0.7=4[/tex][tex]4+0.7=4.7[/tex][tex]4.7+0.7=5.4[/tex]The sum of 5 times a number and 7 equals 8. Find the number
Explanation
Let the number be x. Therefore, we will have
[tex]\begin{gathered} 5x+7=8 \\ 5x=8-7 \\ 5x=1 \\ x=\frac{1}{5} \end{gathered}[/tex]Which of the following numbers are greater than 6 and less than 8? Explainhow you know.
Let's analyze each case and see if they are less than 8 first:
[tex]7<8,therefore(7)^{\frac{1}{2}}<8[/tex][tex]\sqrt[]{64}=8[/tex]thus
[tex]\sqrt[]{60}<\sqrt[]{64}=8[/tex][tex]\sqrt[]{60}<8[/tex]Finally,
[tex]64<80[/tex][tex]\sqrt[]{64}<\sqrt[]{80}[/tex]thus
[tex]8<\sqrt[]{80}[/tex]In sumary, the first two options are less than 8, but not the third.
Now let's see if they are greater than 6
[tex]9>7[/tex][tex]\sqrt[]{9}>\sqrt[]{7}[/tex][tex]3>\sqrt[]{7}[/tex]and
[tex]6>3>\sqrt[]{7}[/tex]thus
[tex]6>\sqrt[]{7}[/tex]Now
[tex]36<60[/tex][tex]\sqrt[]{36}<\sqrt[]{60}[/tex]and so
[tex]6<\sqrt[]{60}[/tex]Finally
[tex]\sqrt[]{80}>\sqrt[]{60}>6[/tex]thus
[tex]\sqrt[]{80}>6[/tex]In conclussion, the second and third options are greater than 6, but not the first.
Describe a series of transformations that takes triangle ABC to triangle A’B’C’
Notice that if the triangle ABC is reflected over the X axis (red), and then reflected over the Y axis (green), we just would have to translate the triangle two units to the right (blue) to get A'B'C':
Give me a rhombus ABCD with BC =25 and BD= 30 find AC and the area of ABCD
300 u²
1) Let's start by sketching out this:
2) Since a Rhombus have 4 congruent sides, then we can state that 4 sides are 25 units, and we need to find out the other Diagonal (AC)
Applying the Pythagorean Theorem, to Triangle COD
a² =b² +c²
25² = 15² +c²
625 = 225 + c² subtract 225 from both sides
625-225 = c²
400 = c²
√c² =√400
c =20
2.2) Now, we can calculate the area, applying the formula for the area of a rhombus (the product of its diagonals).
[tex]\begin{gathered} A=\frac{D\cdot d}{2} \\ A=\frac{40\cdot30}{2} \\ A=\frac{1200}{2} \\ A\text{ = 600} \end{gathered}[/tex]3) Hence, the answer is 300 u²
Fowler has a collection of marbles of different sizes and colors. Big Small Red 9 9 Green 14 9 Purple 9 6 Blue 0 10 What is the probability that a randomly selected marble is not red or is not small? Simplify any fractions.
From the given table, the following are observed:
No. of marbles that are not red and not small = No. of Big Green and Big Purple
= 14 + 9
= 23 Marbles
Total number of marbles = 9 + 14 + 9 + 9 + 9 + 6 + 10 = 66 Marbles
We get,
[tex]\text{ Probability of getting a marble that is not red or not small = }\frac{\text{ 23 Marbles}}{66\text{ Marbles}}[/tex][tex]\text{ = }\frac{23}{66}[/tex]We can no longer simplify 23/66. Therefore, 23/66 is the answer.
xyx2xy1645256720 2258 484 1,2762873 7842,044 3294 1,0243,008 45141 2,025 6,345 ∑x=143 ∑y=411 ∑x2=4,573 ∑xy=13,393 Which regression equation correctly models the data?y = 2.87x + 0.12y = 2.87x + 11.85y = 3.39x – 14.75y = 3.39x – 9.24
We are asked to identify the correct regression equation.
The regression equation is given by
[tex]y=bx+a[/tex]Where the coefficients a and b are
[tex]a=\frac{\sum y\cdot\sum x^2-\sum x\cdot\sum xy}{n\cdot\sum x^2-(\sum x)^2}[/tex][tex]b=\frac{n\cdot\sum xy-\sum x\cdot\sum y}{n\cdot\sum x^2-(\sum x)^2}[/tex]Where n is the number of observations that is 5.
Let us substitute the following into the above formula.
∑x=143
∑y=411
∑x^2=4,573
∑xy=13,393
[tex]a=\frac{411\cdot4573-143\cdot13393}{5\cdot4573-(143)^2}=-14.75[/tex][tex]b=\frac{5\cdot13393-143\cdot411}{5\cdot4573-(143)^2}=3.39[/tex]So, the coefficients are
a = -14.75
b = 3.39
Therefore, the correct regression equation is
[tex]y=3.39x-14.75[/tex]Mike is shopping for new clothes. He has a coupon for 20% off of his total purchase. His purchase price before the discount is $68. Let T represent the total cost after the discount. Which equation can be written to model this scenario? Select all that apply.68-0.2(68) = T68 - .20 =T68-20 = T0.8(68) = T0.2(68) =T
ANSWER
68 - 0.2(68) = T
0.8(68) = T
EXPLANATION
The coupon allows for 20% off of his total purchase.
His purchase price before the discount is $68.
To find the price after the discount, we can use two methods:
=> Find 20% of $68 and then subtract from $68 to get T.
That is:
[tex]\begin{gathered} 68\text{ - (}\frac{20}{100}\cdot\text{ 68) = T} \\ \Rightarrow\text{ 68 - 0.2(68) = T} \end{gathered}[/tex]=> Subract 20% from a total of 100% and then multiply by $68 to get T.
That is:
[tex]\begin{gathered} (100\text{ - 20)\% }\cdot\text{ 68 = T} \\ \Rightarrow\text{ 80\% }\cdot\text{ 68 = T} \\ \Rightarrow\text{ 0.8(68) = T} \end{gathered}[/tex]Those are the two answers.
clinical trial was conducted to test the effectiveness of a drug for treating insomnia in older subjects. before treatment 19 subjects had a mean wake time of 100.0 min after treatment the 19 subjects had a mean wake time of 71.6 min and a standard deviation of 20.4 min assume that the 19 sample value appears to be from a normally distributed population and construct a 99% confidence interval estimate of the mean wake time for a population with drug treatment what does the result suggest about the wake time of 100.0 min before the treatment does the drug appears to be effective
We have to calculate a 99% confidence interval for the mean.
The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.
The sample mean is M=71.6.
The sample size is N=19.
When σ is not known, s divided by the square root of N is used as an estimate of σM:
[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{20.4}{\sqrt{19}}=\dfrac{20.4}{4.359}=4.68[/tex]The degrees of freedom for this sample size are:
[tex]df=n-1=19-1=18[/tex]The t-value for a 99% confidence interval and 18 degrees of freedom is t=2.878.
The margin of error (MOE) can be calculated as:
[tex]MOE=t\cdot s_M=2.878\cdot4.68=13.471[/tex]Then, the lower and upper bounds of the confidence interval are:
[tex]\begin{gathered} LL=M-t\cdot s_M=71.6-13.471=58.129 \\ UL=M+t\cdot s_M=71.6+13.471=85.071 \end{gathered}[/tex]The 99% confidence interval for the mean is (58.129, 85.071). This interval does not include the value 100, so we can conclude that there is statistical evidence that the treatment reduces the mean wake time.
Find the slope, if it exists, of the line containing the pair of points. (−2,−6) and (−15,−7)
The linear regression for a given data set has the form
[tex]y=a+bx[/tex]where the values a and b can be solved using the equation
[tex]\begin{gathered} a=\frac{(\sum y)(\sum x^2)-(\sum x)(\sum xy)}{n(\sum x^2)-(\sum x)^2} \\ b=\frac{n(\sum xy)-(\sum x)(\sum y)}{n(\sum x^2)-(\sum x)^2} \end{gathered}[/tex]Based on the given data set, we have n equals 5. We will solve for the values of the summation first. We have the following
[tex]\begin{gathered} \sum y=4+4+6+6+8=28 \\ \sum x=1+3+5+7+9=25 \\ \sum xy=(1\cdot4)+(3\cdot4)+(5\cdot6)+(7\cdot6)+(8\cdot9)=160 \\ \sum x^2=1^2+3^2+5^2+7^2+9^2=165^{} \\ (\sum x)^2=25^2=625 \end{gathered}[/tex]Using these values to compute for the values of a and b, we get
[tex]\begin{gathered} a=\frac{(28\cdot165)-(25\cdot160)}{5(165)-625}=\frac{31}{10}=3.1 \\ b=\frac{5(160)-(28\cdot25)}{5(165)-625}=\frac{1}{2}=0.5 \end{gathered}[/tex]Take note that the problem wants us to reduce the numbers to the nearest tenth. Hence, the linear regression for the given data set is written as
[tex]y=3.1+0.5x[/tex]A tutoring service charges an initial consultation fee of $50 plus $25 for each tutoringsession.A. Write an equation that determines the total cost of tutoring services (y) based on thenumber of tutoring sessions (x).B. If a student decides to purchase 8 tutoring sessions, what will be his total cost?c. If a student had a total cost of $200, how many tutoring sessions did he attend?EditVioInsertFormatThols Table
A. y = 50 + 25x
B. number of session (x) = 8
Substitute x= 8 in the equation y= 50 + 25x
y = 50 + 25( 8 )= 50 + 200 = $250
The total cost for 8 tutoring sessions is $250
C. y = $200
x= ?
y = 50 + 25x
200 = 50 + 25x
200 - 50 = 25x
150 = 25x
Dividing through by 25
x = 150/25 =6
He attended 6 tutoring sessions
Determine whether the ratios are equivalent.
2:3 and 24:36
O Not equivalent O Not equivalent
We can conclude that the given ratios 2:3 and 24:36 are equivalent.
What are ratios?A ratio in math displays how many times one number is contained in another. The ratio of oranges to lemons, for instance, is eight to six if there are eight oranges and six lemons in a bowl of fruit. The proportions of oranges to the total amount of fruit are 8:14 for oranges and 6:8 for lemons, respectively.So, ratios are equivalent or not:
2:3 and 24:362/3 = 24/362/3 = 2/3 (Divide by 12)Then, 2:3 :: 2:3
Therefore, we can conclude that the given ratios 2:3 and 24:36 are equivalent.
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Which equation has at least one solution? Mark all that app A. 2x-1= 2 B. 3 y + 1) = 3y 1 C. 5p - (3 + p) = 6p + 1 D. 4/5m=1-1/5m E. 10 +0.5w =1/2w - 10 F. 4a + 3(a - 2) = 8a - (6 + a) Answer Choices:
Let's check the options
A.
2x - 1 = 2
2x= 3
x= 3/2=1.5
option A has atleast one solution
B
3y+ 1 = 3y
option B has no solution
C.
5p - (3 + p) = 6p + 1
5p - 3 - p = 6p + 1
4p - 6p = 1 + 3
-2p = 4
p =-2
option C has atleast one solution
D.
4/5 m = 1- 1/5 m
4/5 m + 1/5m = 1
1m = 1
m = 1
Option D has atleast one solution
E.
10 + 0.5w = 1/2w - 10
0.5 w - 1/2 w = -10 - 10
option E has no solution
F.
4a + 3(a-2) = 8a - (6+a)
4a +3a - 6 = 8a -6 - a
7a -6 = 7a - 6
option F has many solution. Hence it also has atleast one solution
Therefore;
option A, C, D and F has atleast one solution
Eddie brought his DVD set to the secondhand store to sell he was paid for all three DVDs in the set before he left Eddie used $15.70 of his earnings to purchase a pair of headphones had $2.30 remaining which equation can you use to find the amount of money Eddie received for each DVD
15.70(d-3)=2.30
3d-15.70=2.30
15.70d-3=2.30
3(d-15.70)=2.30
Answer:
3d - 15.70 = 2.30
Step-by-step explanation:
We don't know the cost of one DVD, so let's use d to represent this unknown variable. Eddie sold 3 DVDs, so 3 multiplied by d equals his total earnings.
Eddie then used $15.70 of his earnings to buy a pair of headphones. We can represent this by subtracting 15.70 from the total earnings (3d).
After buying/subtracting the price of the headphones from his total earnings, Eddie had $2.30 left over, which can be represented by making 3d - 15.70 equal 2.30.
So, the final equation turns out to be: 3d - 25.70 = 2.30
:)
The area of Bryce is 71.5 sq units.what is the area of abcd?
Solution
Step 1:
Area of BXYC = 71.5 square units
Step 2:
The area of ABCD is twice the area of BXYC
Step 3:
[tex]\begin{gathered} \text{Area of ABCD = 2 }\times\text{ Area of BXYC} \\ Area\text{ of ABCD = 2 }\times\text{ 71.5} \\ Area\text{ of ABCD = 143 square units} \end{gathered}[/tex]at Kelly's school, 2/3 of the play ground is covered by grass, and 3/5 of the grassy area is a baseball field. how much of the school playground is baseball feild?
At Kelly's school, 2/3 of the playground is covered by grass, and 3/5 of the grassy area is a baseball field.
How much of the school playground is the baseball field?
SOLUTION
2/3 of the playground is covered by grass and 3/5 of the grassy area is a baseball field.
The area of the school playground which is baseball field =
[tex]\frac{2}{3}\text{ x }\frac{3}{5}\text{ = }\frac{6}{15\text{ }}\text{ = }\frac{2}{5}[/tex]CONCLUSION :
[tex]\frac{2}{5}\text{ of the school field = Area of the Basket Ball Field.}[/tex]
Rewrite y + 1 = -2x – 3 in standard form
The algebraic expressions can be written as
[tex]a+b+c=0[/tex]The given expression is,
[tex]\begin{gathered} y+1=-2x-3 \\ -2x-y=1+3 \\ -2x-y=4 \\ -2x-y-4=0 \\ 2x+y+4=0 \end{gathered}[/tex]A retail clothing store offers customers an opportunity to open up a credit card during checkout. One location of the retail clothing store states that the number of credit cards, A, that are opened t months since January can be modeled by the function A(t) = 15 + 3t. The number of credit cards opened at another location, B, is defined by the function B(t) = 25 − t. What is an expression that can be used to determine the total amount of credit cards opened at the two locations?
(A + B)(t) = 40 + 4t
(A + B)(t) = 40 + 2t
(A − B)(t) = −10 + 2t
(A − B)(t) = −10 + 4t
The expression that is useful to determine the total amount of credit cards opened at the two locations is (A + B)(t) = 40 + 2t so option (B) is correct.
What is an expression?A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.
A statement expressing the equality of two mathematical expressions is known as an equation.
As per the given,
The amount in location A is given as
A(t) = 15 + 3t
The amount in location B is given as
B(t) = 25 − t
The total amount combined between A and B is given as,
(A + B)(t) = 15 + 3t + 25 - t
(A + B)(t) = 15 + 25 + 3t - t
(A + B)(t) = 40 + 2t
Hence "The expression that is useful to determine the total amount of credit cards opened at the two locations is (A + B)(t) = 40 + 2t".
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Which recipe makes more cookies per cup of chocolate chips?
We are given the recipes of Grandma and Betty Potter box.
We are asked to find out which of them makes more cookies per cup of chocolate chips.
Let us find the unit rate for both of them and compare which is greater.
Grandma:
She uses 1 1/2 cups of chocolate chips to make 24 cookies.
The unit rate is
[tex]\frac{24}{1\frac{1}{2}}=\frac{24}{\frac{3}{2}}=24\times\frac{2}{3}=16[/tex]So the unit rate is 16 cookies per chocolate chip.
Betty Potter box:
60 cookies are made using 3 chocolate chips.
80 cookies are made using 4 chocolate chips.
200 cookies are made using 10 chocolate chips.
The unit rate is
[tex]\begin{gathered} \frac{60}{3}=20 \\ \frac{80}{4}=20 \\ \frac{200}{10}=20 \end{gathered}[/tex]So the unit rate is 20 cookies per chocolate chip.
As you can see, the recipe of Better Potter box makes more cookies per cup of chocolate chip.
x^2 = 16, therefore x = 4.
Is this a valid conclusion? If not, give a counterexample.
A straight line l1 with equation 5x - 7 = 0 cuts the x axis at point A. Straight line l2 is perpendicular to straight line l1 and passes through point A. What is the coordinates of point A and the equation of the straight line l2?
Point A has a coordinate of (7/5, 0) while the straight line l2 is represented by the equation y = 0
The coordinates of point AThe equation of line l1 is given as
5x - 7 = 0
It cuts the x-axis at point A
This means that
5A - 7 = 0
Solve for A
5A = 7
So, we have
A = 7/5
Rewrite as
A = (7/5, 0)
The equation of the straight line l2From the question, we have
Lines l1 and l2 are perpendicular lines
The equation 5x - 7 = 0 has no y variable
So, the slope is undefined
The slopes of perpendicular lines are represented as follows
Slope 1 * Slope 2 = -1
So, we have
Slope 2 = -1/Slope 1
This gives
Slope 2 = -1/undefined
Evaluate
Slope 2 = 0
This means that l2 has a slope of 0
The equation of l2 is calculated as
y = m(x - x₁) + y₁
In this case,
A = x₁ and y₁ = 0
So, we have
y = m(x - A)
This gives
y = 0 * (x - 7/5)
Evaluate
y = 0
Hence, the equation of the straight line l2 is y = 0
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Illustrate the ratio 7:3 using 'X' for 7 and 'y for 3
Given the ratio:
7:3
To illustrate the ratio above using x for 7 and y for 3, we have:
All you need to do is to replace 7 with x and replace 3 with y
7 : 3 ==> x : y
ANSWER:
x : y
At 3:00 PM a man 138 cm tall casts a shadow 145 cm long. At the same time, a tall building nearby casts a shadow 188 m long. How tall is the building? Give your answer in meters. (You may need the fact that 100 cm = 1 m.)
A tall man(138cm) casts a shadow of 145cm
A building nearby casts a shadow of 188m
Using the information you have to determine the height of the building.
First step is to convert the units of the height of the man and the length of his shadow from cm to meters:
100cm=1m
So 145cm=1.45m
And 138co=1.38m
Now that the measurements are expressed in the same units you can determine the height shadow ratio of the man and use it to calculate the height of the bulding.
[tex]\frac{\text{height}}{\text{shadow}}=\frac{1.38}{1.45}[/tex]Compare this ratio with the ratio between the heigth/shadow ratio of the building to determine the heigth of the building.
Said height will be symbolized as "x"
[tex]\begin{gathered} \frac{1.38}{1.45}=\frac{x}{188} \\ x=(\frac{1.38}{1.45})188 \\ x=178.92m \end{gathered}[/tex]The building is 178.92m
the discriminant equation How many real solution 4x^2-8x+10=-x^2-5 have?
Answer:
0 real solutions
Explanation:
First, we need to transform the equation into the form:
[tex]ax^2+bx+c=0[/tex]So, the initial equation is equivalent to:
[tex]\begin{gathered} 4x^2-8x+10=-x^2-5 \\ 4x^2-8x+10+x^2+5=-x^2-5+x^2+5 \\ 5x^2-8x+15=0 \end{gathered}[/tex]Now, the discriminant can be calculated as:
[tex]b^2-4ac[/tex]If the discriminant is greater than 0, the equation has 2 real solutions.
If the discriminant is equal to 0, the equation has 1 real solution
If the discriminant is less than 0, the equation has 0 real solutions
So, in this case, a is 5, b is -8 and c is 15. Then, the discriminant is equal to:
[tex](-8)^2-4\cdot5\cdot15=84-300=-236[/tex]Since the discriminant is less than zero, the equation has 0 real solutions
Absolute risk is defined as the proportion or percentage of people in a group for whom an undesirable event occurs. In college classrooms, students typically can choose their own seats. Professors have noticed a difference in grades between students who choose to sit in the front and those who choose to sit in the back. For example, in one math class, 9 of the 20 students who sat in the back failed the class, but only 3 of the 20 students who sat in the front failed the class. What was the absolute risk of failing the class for students who sat in the back? For students who sat in the front? Give your answers as fractions, proportions, and percents.
Given in the scenario:
a.) 9 of the 20 students who sat in the back failed the class.
b.) 3 of the 20 students who sat in the front failed the class.
A.) The absolute risk of failing the class for students who sat in the back.
In the back, 9 of the 20 students who sat in the back failed the class.
The absolute risk in proportion = 9:20
The absolute risk in fraction = 9/20
The absolute risk in percentage = (9 ÷ 20) x 100 = 0.45 x 100 = 45%
B.) The absolute risk of failing the class for students who sat in the front.
In the front, 3 of the 20 students who sat in the front failed the class.
The absolute risk in proportion = 3:20
The absolute risk in fraction = 3/20
The absolute risk in percentage = (3 ÷ 20) x 100 = 0.15 x 100 = 15%
Describe the association in the scatter plot below.----------------The scatter plot shows (positive linear, positive linear with one outlier, negative linear, negative linear with one outlier, nonlinear, or no) association because as the plotted values of x increase, the values of y generally (decrease, increase, show no pattern or follow a nonlinear pattern).
From the given figure
The given point can form a line with a negative slope, because when
the values of x increase the values of y decrease
Then the scatter plot shows a negative linear association because
as the values of x increase, the values of y generally decrease
Line AB and line DA are?
Answer:
perpendicular
Step-by-step explanation:
Square
Rectangle
Right triangle
Cube
Rectangular prism
are all examples of perpendicular shapes
i hope this helped
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4y - 6 = 2y + 8how to solve this equation
To solve this equation, we need to collect like terms
To collect like terms, we bring the terms similar to each other to the same side
In this case, the value having y will be brought to same side of the equation
Kindly note that if we are bringing a particular value over the equality sign, then the sign of the value has to change
This means if negative, it becomes positive and if positive, it becomes negative
Proceeding, we have
4y - 2y = 8 + 6
2y = 14
divide both sides by 2
2y/2 = 14/2
y = 7
The value of y in this equation is 7