Answer:
Part A ----> 2
Part B ----> 2 (2x - 1) (x + 5)
Part C -----> See explanation below
Step-by-step explanation:
Given expression is
4x² + 18x - 10
Part A
The greatest common factor (GCF) of the terms 4x², 18x and 10 is the largest number that divides into all three numbers without a remainder
To find this
Find the prime factors of each of the terms
4x² = 2 · 2 · x · x
18x = 2 · 3 · 3 · x
10 = 2 · 5
The prime factor common to all 3 is 2
Therefore the GCF of the expression is 2
Part B
The factored expression can be obtained by factoring out the GCF
4x² + 18x - 10 = 2(2x² + 9x - 5)
We can further factor the term in parentheses:
2x² + 9x - 5
To do this,
Break the expression into groups:
= (2x² - x) + (10x - 5)
Factor x from 2x² - x: x(2x - 1)
Factor 5 from 10x - 5: 5(2x - 1)
Therefore
(2x² - x) + (10x - 5) = x(2x - 1) + 5(2x - 1)
Factor out the common term 2x -1 to get
(2x - 1)(x + 5)
Therefore
4x² + 18x + 10 = 2 (2x - 1) (x + 5)
Part C
Checking if factorization is correct
Multiply (2x - 1)(x + 5) using the FOIL method
= 2x ·x + 2x · 5 + (-1) · x + (-1) · 5
= 2x² + 10x -1x -5
= 2x² + 9x - 5
Multiply the whole expression by 2
2 · 2x² + ² · 9x - 2 · 5
= 4x² + 18x + 10
which is the original expression
So the factorization is correct
A washer and a dryer cost $770 combined. The washer costs $70 more than the dryer. What is the cost of the dryer?
Answer:
d = $350
Step-by-step explanation:
If we allow d to represent the cost of the dryer and w to represent the cost of the washer, we know that the total cost of the washer and dryer is
d + w = 770.
Since we're told that the washer costs $70 more than the dryer, we know that
w = d + 70
We can substitute equation for w in the original equation to find d:
d + d + 70 = 770
2d + 70 = 770
2d = 700
d = 350
If you went on to find w, you'd see that it'd be 420 since 770 - d = w and 770 - 350 = 420
We know that the dryer costs $350 and the washer costs $420. 420 is indeed $70 more than $350 so our answer for the cost of the dryer is correct.
Question is in the image. Please help me solve these
Answer:
Step-by-step explanation:
Which one of the following examples represents a proper
fraction?
A. 15/22
B. 12/9
C. 3/2
O D. 8/8
A.15/22 is the correct answer.
The correct answer is:
A. 15/22, represents a proper fraction.
Here, we have,
A proper fraction is a fraction where the numerator (the top number) is smaller than the denominator (the bottom number).
Out of the given options, only option A,
15/22, represents a proper fraction because 15 is smaller than 22.
Therefore, the correct answer is:
A. 15/22, represents a proper fraction.
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The number of lattes sold daily by two coffee shops is shown in the table.
Shop A Shop B
55 45
52 42
56 57
48 48
57 11
40 10
45 46
41 43
Based on these data, is it better to describe the centers of distribution in terms of the mean or the median? Explain.
A. Mean for both coffee shops because the data distribution is symmetric
B. Median for both coffee shops because the data distribution is not symmetric
C. Mean for shop B because the data distribution is symmetric; median for shop A because the data distribution is not symmetric
D. Mean for shop A because the data distribution is symmetric; median for shop B because the data distribution is not symmetric
Based on the data given in the table, B. Median for both coffee shops because the data distribution is not symmetric
Why is the median better ?It is better to describe the centers of distribution in terms of the median rather than the mean for both coffee shops because the data distribution is not symmetric.
The median is a better measure of central tendency in this case because it is not influenced by outliers or extreme values, which may exist in the data.
The mean, on the other hand, is sensitive to outliers and may not provide an accurate representation of the data distribution.
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PLEASE HELP I DON'T UNDERSTAND
Ten cards are numbered from 1 to 10 and placed in a box. One card is selected at random and replaced. Another card is randomly selected. What is the probability of selecting two even numbers?
P(two even numbers) _________
Answer:
30%
Step-by-step explanation:
if you increase your current quality score of 85% by 7%, you will have a score of?
Answer:
90.95%
Step-by-step explanation:
85 * 0.07 = 5.95 5.95 + 85= 90.95
Answer:
The answer to your problem is, 90.95%
Step-by-step explanation:
Calculation:
In order to find the answer we need to
= Old score + New Score
= 85 + 7% of 85
= 85 + ( [tex]\frac{7}{100}[/tex] x 85 )
= 85 + ( 0.07 x 85 )
= 85 + 5.95
= 90.95
Which 90.95% is our answer.
Thus the answer to your problem is, 90.95%
Suppose you have a 4 foot sub and you have to feed 10 people ,how many cuts will you make?
Answer: Cut 3 inch per person
Step-by-step explanation:
there is a 4 foot sub you take the quadrilatiral and divide it by 10 and you get 3 inches per person remember to multiply the reciprocal by 12 as there are 12 inches in a foot and you have 4 foot so the product of that reciprocal will be equal to 4 divided by your sum from adding the recriptorcal into the quadrilateral remember a quadrilateral not a duolateral or a triolatiral as there is 4 feet in the sub. >:)
Answer:
7 Cuts
Step-by-step explanation:
This is because if you do 48 inches / 6 inches = 8 sections Since each cut will create two sections, you need to make 7 cuts (one fewer than the number of sections) to get 8 equal portions.
PLEASE HELP!!!
A cylinder has a height of 15 inches. A similar cylinder has a height of 20 inches.
What is the ratio of the surface area of the larger cylinder to the surface area of the smaller cylinder?
Enter your answer by filling in the boxes.
The ratio of the surface area of the larger cylinder to the surface area of the smaller cylinder is 4:3, or 4/3.
How do you find the ratio of the surface area of the larger cylinder to the the smaller cylinder?To find the ratio of the surface areas of the two similar cylinders, we need to consider the ratio of their corresponding dimensions. Since the two cylinders are similar, their radii are proportional to their heights. Let's denote the height of the smaller cylinder as h1, the height of the larger cylinder as h2, the radius of the smaller cylinder as r1, and the radius of the larger cylinder as r2.
Given:
h1 = 15 inches
h2 = 20 inches
The ratio of the heights is:
h2 / h1 = 20 / 15 = 4 / 3
Since the cylinders are similar, the ratio of their radii is the same as the ratio of their heights:
r2 / r1 = 4 / 3
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Can someone help me please
The row operation is given as follows:
Division by 7 = multiplication by 1/7.
The matrix after the row operation is then given as follows:
[tex]\left[\begin{array}{ccc}1&-\frac{4}{7}&\frac{8}{7}\\-12&7&-13\end{array}\right][/tex]
How to do the row operation?The matrix in the context of this problem is defined as follows:
[tex]\left[\begin{array}{ccc}7&-4&8\\-12&7&-13\end{array}\right][/tex]
The element at row 1 and column 1 is given as follows:
7.
An example of a valid row operation is the multiplication of the row by a constant, and as the element has a value of 7, the constant to obtain a value of 1 is:
7/k = 1
k = 7.
The first row is given as follows:
7, -4 and 8.
Dividing every element of the first row by 7, the resulting matrix is then given as follows:
[tex]\left[\begin{array}{ccc}1&-\frac{4}{7}&\frac{8}{7}\\-12&7&-13\end{array}\right][/tex]
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Can the sides of a right triangle have lengths 7,9 and the square Root of 155
Answer:
No
Step-by-step explanation:
In order for a triangle to be a right angle, the sum of the squares of the two legs (a and b) must be equal the square of the longest side, known as the hypotenuse (c):
[tex]a^2+b^2=c^2[/tex]
The square root of 155 is the longest side as it is approximately 12.45. Thus, if the triangle is a right triangle, the square root of 155 must be the hypotenuse.
We can now check to see whether the sum of the squares of 7 and 9 equal the square of the square root of 155:
[tex]7^2+9^2=(\sqrt{155})^2\\ 49+81=155\\130=155[/tex]
The equation is not true since 130 is less than and not equal to 155. Therefore, a triangle with side lengths 7, 9, and the square root of 155 cannot be a right triangle.
The high school basketball team is selling donuts to raise money for the new uniforms. This team Mexico to sell at least $1000 in donuts. They are selling a half dozen box of donuts for eight dollars and a full dozen box of donuts for $12. They write the inequality 8X +12 Y is greater than or equal to 1000 to determine how many boxes they need to sell where X is the number of half dozen boxes and why is the number of four dozen boxes they sell which of the following solutions available in terms of the given context select all that apply.
The team can sell 50 half dozen boxes and 50 full dozen boxes to raise at least $1000.
Understanding Word Problem in Solving MathsWe can derive an inequality from the problem statement which is:
8X + 12Y >= 1000
This inequality represents the amount of money the basketball team needs to raise by selling donuts.
X is the number of half dozen boxes sold
Y is the number of full dozen boxes sold.
To find a solution in terms of the given context, we can plug in different values for X and Y that satisfy the inequality. For example:
If the team sells 50 half dozen boxes and 50 full dozen boxes, they will make:
8(50) + 12(50) = $400 + $600 = $1000
So this is a valid solution that meets the fundraising goal.
If the team sells 100 half dozen boxes and 0 full dozen boxes, they will make:
8(100) + 12(0) = $800
This is not enough to meet the fundraising goal, so it is not a valid solution.
If the team sells 0 half dozen boxes and 100 full dozen boxes, they will make:
8(0) + 12(100) = $1200
This is more than the fundraising goal, so it is a valid solution, but the team may not want to sell so many full dozen boxes.
Therefore, one solution in terms of the given context is that the team can sell 50 half dozen boxes and 50 full dozen boxes to raise at least $1000.
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Which of the following equations are equivalent? Select three options. 2 + x = 5 x + 1 = 4 9 + x = 6 x + (negative 4) = 7 Negative 5 + x = negative 2
In a lottery game, a player picks six numbers from 1 to 22. If the player matches all six numbers, they win 40,000 dollars. Otherwise, they lose $1.
To find the probability of winning the lottery game, we can use the formula for combinations:
nCk = n! / (k! * (n - k)!)
where n is the total number of choices (22 in this case) and k is the number of choices we make (6 in this case).
So, the number of possible combinations of six numbers from 22 is:
22C6 = 22! / (6! * 16!) = 13,983,816
Therefore, the probability of winning the lottery game is 1 in 13,983,816.
The expected value of playing the lottery game can be calculated as follows:
Expected value = (Probability of winning * Amount won) - (Probability of losing * Amount lost)
Expected value = (1/13,983,816 * $40,000) - (13,983,815/13,983,816 * $1)
Expected value = $0.5709
This means that on average, the player can expect to win about 57 cents per game played. However, it is important to note that this is just an average and the actual outcome of any single game can vary widely.
Please help quickly I'm begging!
Assignment details: In this assignment, you will create two graphs and answer questions about Bond's Gym, the business you are supporting.
The functions are f(x) = 600 - 10x & g(x) = 20/3x, and the graphs are added as attachments
Creating the functions of the Bond's GymFrom the question, we have the following parameters that can be used in our computation:
The table of values
For the membership application, we have the following features
Initial value = 600Constant rate of change = (450 - 600)/(15 - 0) = -10So, the function is
f(x) = 600 - 10x
For the membership available, we have the following features
Initial value = 0Constant rate of change = (100 - 0)/(15 - 0) = 20/3So, the function is
g(x) = 20/3x
So, the functions are f(x) = 600 - 10x & g(x) = 20/3x
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write the opposite of loss of 700
Answer:
gain of 700 or 700
Step-by-step explanation:
A loss of 700 would be -700 and the opposite of that is 700.
Helping in the name of Jesus.
Georgia has 322 beads. She buys 38 more beads. She will use a 120 beats to make bracelets and use the rest of the beads to make necklaces. Each necklace has 9 beads. What is the greatest number of necklacea georgia can make?
Applying mathematical operations, the greatest number of necklaces Georgia can make is 26.
How the mathematical operations are applied:The total number of beads available for making bracelets and necklaces is an addition operation between the beginning inventory of beads and the additional units purchased.
A subtraction operation is performed to determine the remainder after making bracelets.
Finally, a division operation determines the greatest number of necklaces to make.
The beginning inventory of beads = 322
The units purchased = 38 beads
The total number of beads that Georgia has = 360 (322 + 38)
The number of beads required to make bracelets = 120
The remainder after making bracelets = 240 (360 - 120)
The number of beads required for each necklace = 9
The greatest number of necklaces Georgia can make = 26 (240 ÷ 9)
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Julie was testing how far two new electric cars—model A and model B—could drive on a full charge. She obtained a sample of 5 55 new cars of each model, charged them fully, and drove them as far as she could along a controlled route. Here is a summary of the distances: Distance Model A Model B Mean 168 km 168 km168, start text, space, k, m, end text 172 km 172 km172, start text, space, k, m, end text Standard deviation 5.4 km 5.4 km5, point, 4, start text, space, k, m, end text 7.5 km 7.5 km7, point, 5, start text, space, k, m, end text Number of cars 5 55 5 55 Julie wants to use these results to test H 0 : μ A − μ B = 0 H 0 : μ A −μ B =0start text, H, end text, start subscript, 0, end subscript, start text, colon, space, end text, mu, start subscript, start text, A, end text, end subscript, minus, mu, start subscript, start text, B, end text, end subscript, equals, 0 versus H a : μ A − μ B ≠ 0 H a : μ A −μ B =0start text, H, end text, start subscript, start text, a, end text, end subscript, start text, colon, space, end text, mu, start subscript, start text, A, end text, end subscript, minus, mu, start subscript, start text, B, end text, end subscript, does not equal, 0. Assume that these are representative samples and all other conditions have been met. What is the P-value associated with these sample results? Choose 1 answer: Choose 1 answer: (Choice A) P -value < 0.01 P-value<0.01P, start text, negative, v, a, l, u, e, end text, is less than, 0, point, 01 A P -value < 0.01 P-value<0.01P, start text, negative, v, a, l, u, e, end text, is less than, 0, point, 01 (Choice B) 0.01 ≤ P -value < 0.05 0.01≤P-value<0.050, point, 01, is less than or equal to, P, start text, negative, v, a, l, u, e, end text, is less than, 0, point, 05 B 0.01 ≤ P -value < 0.05 0.01≤P-value<0.050, point, 01, is less than or equal to, P, start text, negative, v, a, l, u, e, end text, is less than, 0, point, 05 (Choice C) 0.05 ≤ P -value < 0.10 0.05≤P-value<0.100, point, 05, is le
The p value based on the information will be E. P - value ≥ 0.20
How to compute the valueOpen Minitab 17. Select 'Stat' -> 'Basic Statistics' -> '2 - Sample t... Select 'Summarized data' from the dropdown menu.
Enter 5 in both Sample size of sample 1 and sample 2, 168 and 172 in Sample mean of Sample 1 and Sample 2. 5.4 and 7.5 in Standard deviation of Sample 1 and Sample 2.
Click on 'Options' and Enter 'Confidence level' 95.0(or the given Cofidence level) , 'Hypothesized difference' 0.0 , 'Alternative hypothesis' 'Difference \\neq Hypothesized difference'. Also the box 'Assume equal variance' can be ticked as requirement.
Click on 'Ok' -> 'Ok'.
Output: -
P - value = 0.361 i.e., P - value ≥ 0.20
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find 15x2 2/3 using the distributive property
If cos(x) = -5/6, x in quadrant II, then find exact values (without finding x):
sin(2x)= ?
cos(2x)=?
tan (2x)=?
If cos(x) = -5/6, and x lies in quadrant"II", then exact values are:
sin(2x) = (-5√11)/(18);
cos(2x) = 7/18;
tan (2x) = -5√11/7.
We know that, Cos(x) = -5/6 and "x" is in quadrant II, so, we can use the Pythagorean identity to find sin(x):
sin(x) = √(1 - cos²(x)) = √(1 - (-5/6)²) = √(1 - 25/36) = √(11/36) = √11/6
Using the double angle trigonometry identities for sine and cosine, we find sin(2x) and cos(2x):
Substituting the value of Sin(x) and Cos(x),
We get,
sin(2x) = 2sin(x)cos(x) = 2(√11/6)(-5/6) = (-5√11)/(18);
cos(2x) = cos²(x) - sin²(x) = (-5/6)² - (11/6) = 25/36 - 11/36 = 14/36 = 7/18;
Finally, we find tan(2x) by using the identity:
tan(2x) = sin(2x)/cos(2x) = (-5√11/18) / (7/18) = -5√11/7.
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graph the cirlces (x+1)+(y+2)=9
Center :
Note that the graph of the function ((x+1)²+(y+2)²=9) is attached accordingly
What is a graph?A coordinate graph is one that has two axes that are perpendicular to each other. These two axes are known as the x- and y-axes. The y-axis is represented by the vertical line, while the x-axis is represented by the horizontal line. A coordinate plane, a Cartesian plane, and a Cartesian coordinate system are other names for it.
The given circle has a radius of 3 units and centre is (-1,-2).
This circle can thus be drawn by first plotting the point (-1,-2) and then with this point as centre draw a circle of radius 3.
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Full question:
graph the circle
((x+1)²+(y+2)²=9)
Solve for the missing side in each triangle
Answer:
6[tex]\sqrt{13}[/tex]
Step-by-step explanation:
a^2+b^2=c^2 c is hypotenuse, which is what we're looking for
12^2+18^2=c^2
144+324=c^2
c=[tex]\sqrt{468}[/tex]=[tex]\sqrt{36*13}[/tex]=6[tex]\sqrt{13}[/tex]
Ruth has a cylindrical cup that is filled with water. The cup has a diameter of 2 inches and a height of 6 inches. Select the containers that could hold all of the water in Ruth's cup
Since the containers were not given in the question, In a case whereby Ruth has a cylindrical cup that is filled with water where the cup has a diameter of 2 inches and a height of 6 inches, the volume of cylinder cup is 18.85inch^3.
How can the volume be calculated?Note that ; the container were not given in the question, so we will just need to calculate the volume of the cylindrical cup to know how much water it can hold .
The volume of a cylinder can be caluculated using te exppresion π r² h
Then from the question the diameter = 2 inches radius = 2/2 = 1 inches
height =6 inches
π r² h
=π * 1^2 * 6
=18.85inch^3
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What is the output for x = -1
Answer:
f(-1) = 16
Step-by-step explanation:
"output" and the f(x) setup just means to plug in -1 in place of x and calculate.
For the function f(x) = 12(3/4)ˣ you have to already know that once you put that -1 in place of x that the -1 power only goes to the 3/4, not the 12 and also what to do with a negative exponent.
Exponent rules are just shortcuts. The shortcut to know here is that the -1 exponent will flip the 3/4 over and make it 4/3 (there are math reasons for this, it's not random. But that's how it works)
So now you have
f(-1) = 12(3/4)⁻¹ which becomes
f(-1) = 12(4/3)
Now you need to know how to multiply with fractions. Here you have a whole, big number times a fraction, which is:
"big num×top all over bottom"
So multiply the 12 times the 4 and put it over the 3
f(-1) = 48/3 = 16
(or you can "cancel" the 12 with the 3 and get 4×4, which is 16, so it comes out the same)
[SKIP TO HERE IF YOU DON'T CARE WHY]
f(x) = 12(3/4)ˣ
f(-1) = 12(3/4)⁻¹
f(-1) = 12(4/3)
f(-1) = 16
Find the degree of the polynomial y = -3x^5 + 4x^4 + 2 + x^2
The degree of a polynomial is the highest exponent of the variable in the polynomial.
In this case, the degree of the polynomial y = -3x^5 + 4x^4 + 2 + x^2 is 5, because the highest exponent of x is 5 (in the term -3x^5). Therefore, the answer is 5.
inverse statement of M implies N
The inverse statement of M implies N is a negation of both the conclusion and the hypothesis.
What is an inverse statement?An inverse statement is one in which both the hypothesis and the conclusion are negated. Let us assume a statement with the hypothesis and conclusion as follows: If they annul the law, we will drive carelessly.
The inverse of this statement will be: If they do not annul the law, we will not drive carelessly. So, both the hypothesis and the conclusion are rewritten in negative terms.
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NEED HELP ASAP PLS AND THX PIC IS ATTACHED
The trigonometry functions when evaluated are shown below
Evaluating the trigonometry functionsIn trigonometry, sine (sin), cosine (cos), and tangent (tan) are three basic functions that relate angles to the sides of a right triangle.
They are defined as follows:
sin A = opposite side/hypotenuse.
cos A = adjacent side/hypotenuse.
tan A = opposite side/adjacent side.
So, we have
Figure 1
sin A = 6/9cos A = √5/3tan A = 6/√5Figure 2
sin A = √2/2cos A = √2/2tan A = 1Figure 3
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What is the numerical expression that represents the sun of eight squared and thirty two
The numerical expression that represents the sum of eight squared and thirty two will be 96.
A numerical expression is a mathematical expression that consists of numbers and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation.
The numerical expression that represents the sum of eight squared and thirty two is
= 8² + 32
= 64 + 32
= 96.
The question is incomplete and the complete question is '' What is the numerical expression that represents the sum of eight squared and thirty two''.
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Which of these are statistical questions? Select ALL that Apply Question 1: How many minutes does it usually take each teacher to get from home to work? Question 2: During the past year did you work for more than 50 weeks? Question 3: During the past year how many hours did each teacher usually work each week? Question 4: How many extra hours did each doctor work each week?
The statistical questions are:
Question 1: How many minutes does it usually take each teacher to get from home to work?Question 3: During the past year how many hours did each teacher usually work each week?Question 4: How many extra hours did each doctor work each week?What is a statistical question?
A statistical question is a question that can be answered by collecting and analyzing data. It is a question that expects a variability in the response, meaning different individuals may give different answers. Statistical questions usually ask about a population, a group of individuals or objects that share a common characteristic or feature, and seek to understand a pattern or trend within that population.
In general, a statistical question is open-ended, does not have a single correct answer, and requires data analysis to arrive at a reasonable conclusion.
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Can someone help me with this pls
Write the equation of a line that is perpendicular and passes through the midpoint of AB with A(-3, 5) and B(1, -1).
The given line AB is having endpoints A(-3,5) & B(1,-1).
To find the equation of line AB it can be written as[tex]y-y_1=(x-x_1){(y_2-y_1)/(x_2-x_1)}\\[/tex]
Substituting the given points
[tex]y-(-1)=(x-1){(5-(-1))/(-3-1)}\\[/tex]
y=-(3/2)x+1/2
For two perpendicular lines [tex]m_1*m_2=-1[/tex]
Therefore, (-3/2)*[tex]m_2[/tex]=-1
or [tex]m_2[/tex] = 2/3
Also, the midpoint of AB will be [tex]{1-(-3)}/2, {5-(-1)}/2[/tex] = (2,3).
The line passing through (2,3) & perpendicular to y=-3/2x+1/2 will be given as follows
(y-3)=(2/3)(x-2)
3y-9=2x-4
3y=2x+5 is the required equation of the line.
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