Part A: The greatest common factor of [tex]10x2 + 25x − 15[/tex] is 5.
Part B:[tex]10x2 + 25x − 15[/tex] can be factored as [tex]5(2x2 + 5x − 3)[/tex].
Part C: The factoring from Part B is correct, as multiplying the two binomials in the parentheses yields [tex]2x2 + 5x − 3[/tex].
Part A: The greatest common factor of [tex]10x2 + 25x − 15[/tex] is 5. The greatest common factor (GCF) of a set of numbers is the largest number that is a factor of all numbers in the set. To find the GCF, first list all the factors of each number. The common factors among the numbers are the ones that are found in each list of factors. The largest number in the list of common factors is the GCF.
Part B:[tex]10x2 + 25x − 15[/tex] can be factored as [tex]5(2x2 + 5x − 3)[/tex]. To factor this expression, first identify the GCF, which is 5. Then divide the expression by 5 and factor the result. Since the result is a binomial, use the difference of squares formula, (x + a)(x − a). The resulting expression is then[tex]5(2x2 + 5x − 3[/tex]).
Part C: To check the factoring from Part B, multiply the two binomials in the parentheses. The result is [tex]2x2 + 5x − 3[/tex], which is the same as the original expression. To multiply, use the FOIL method. Multiply the First terms [tex](2x2 and 2x2)[/tex], the Outer terms[tex](2x2 and -3)[/tex], the Inner terms (5x and 2x), and the Last terms [tex](5x and -3)[/tex]. The resulting expression is [tex]2x2 + 5x − 3.[/tex]
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Select the correct answer.
What is the justification for step 3 in the solution process?
0.8a - 0.1a = a - 2.5
Step 1: 0.7a = a - 2.5
Step 2: -0.3a = -2.5
Step 3:
a =8.3
O A.
the addition property of equality
O B. the subtraction property of equality
О C.
combining like terms
O D. the division property of equality
Answer: D. the division property of equality
Step-by-step explanation:
In step three you will be dividing -2.5 divided by -0.3 to get a.
1) A function f(x), which contained the point (5,4) was transformed with the rule 2f (x-3) + 4. What would
be the new coordinates of that point?
(2,-2)
The solution is, point (5,4) will correspond to (5,8).
What is transformation?A transformation is a dramatic change in form or appearance. An important event like getting your driver's license, going to college, or getting married can cause a transformation in your life. A transformation is an extreme, radical change.
here, we have,
1) To find that the corresponding points, let'-s plug it into that formula:
(5,4)
If we plug 5 and we have output the number 4,
then f(x) is y=x-1
now,
2f(x-3)+4 is the function f(x) with a horizontal shift of 3 units to right, a vertical stretch 4, a reflection.
2) y=2(5-3)+4 then y=2(2)+4
y=8
So point (5,4) will correspond to (5,8)
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Estelle is having her birthday party at Gold Frames Art
costs $265
Museum this year. A party package
and covers the entrance fee for guests, a private party room, and an activity
guide. Estelle
upgraded her package to include a favor for each of her 8 guests, bringing the
total to $305.
Answer:
Step-by-step explanation:
im guessing youre finding the price of the favour.
(305-265)/8=answer
"/" means divide.
A container of laundry detergent holds 100 fluid ounces. You use 9 fluid ounces each week. The table shows the amount of laundry detergent that remains after a certain number of weeks. Complete the table Number of Weeks Fluid Ounces Remaining in the Container
The number of fluids remaining after x weeks is given by the following equation:
y = 100 - 9x.
Hence the number of fluids remaining after week x is found replacing x by the week at the above equation.
How to define the linear function?
The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
The slope m represents the rate of change.The intercept b represents the value of y when x = 0.For this problem, the parameters are given as follows:
b = 100, which is the capacity of the container.m = -9, as each week, the number of fluid ounces in the container is decreased by 9.Hence the function is given as follows:
y = 100 - 9x.
Missing InformationThe problem is incomplete, hence the function used to obtain the amounts is presented.
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I get 64% off a table the sale price is $72, what is the original price?
The original price of the table was $200 before the 64% discount was applied.
What is the percentage?
Percentage is a way of expressing a fraction or proportion out of 100. It is commonly used to compare two quantities, indicate the change or growth of a quantity over time, or express the probability or chance of an event occurring.
If you received a 64% discount on the sale price of a table, and the sale price is $72, we can calculate the original price of the table as follows:
Determine the percentage of the original price that corresponds to the sale price after the discount:
If the sale price is 100% - 64% = 36% of the original price, after the 64% discount.
Use the percentage found in step 1 to calculate the original price:
Let x be the original price
x * 36% = $72
0.36x = $72
x = $72 / 0.36
x = $200
Therefore, the original price of the table was $200 before the 64% discount was applied.
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what is the surface area of a right cylinder with a radius of 6 units and a height of 14 units?
The surface area of a right cylinder with a radius of 6 units and a height of 14 units is equal to 753.6 square units.
How to calculate surface area of a cylinder?Mathematically, the surface area (SA) of a right cylinder can be calculated by using this formula:
SA = 2πrh + 2πr²
Where:
h represents the height.r represents the radius.By substituting the given parameters into the surface area of a right cylinder formula, we have;
Surface area (SA) of cylinder = (2 × 3.14 × 6 × 14) + 2 × 3.14 × 6²
Surface area (SA) of cylinder = 527.52 + 226.08
Surface area (SA) of cylinder = 753.6 square units.
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The length of a rectangle is shown below:
On a coordinate grid from negative 6 to positive 6 on the x-axis and on the y-axis, two points A and B are shown. The point A is on ordered pair 1, 2, and the point B is on ordered pair negative 2, 2. A straight line joins the points A and B.
If the area of the rectangle to be drawn is 12 square units, where should points C and D be located, if they lie vertically below the line that connects B and A, to make this rectangle? (5 points)
C(−2, −1), D(1, −1)
C(−2, −4), D(1, −4)
C(−2, −2), D(1, −2)
C(−2, −5), D(1, −5
I NEEP HELP WITH THIS ONE LISTED BELOW:A solid is composed of squares and equilateral triangles. Its net is shown below:
A triangular prism and its net are shown. The net is three squares with side length 4 units. Attached above and below the middle square are equal sized triangles.
The area of each triangle is 7 square units. The surface area of the triangular prism is
square units. (Input whole number only.) (5 points)
PLEASE
The surface area of the triangular prism is 62 square units.
What is surface area?The area is the area occupied by a two-dimensional flat surface. It has a square unit of measurement. The surface area of a three-dimensional object is the space taken up by its outer surface.
For each three-dimensional geometrical shape, surface area and volume are determined. The area or region that an object's surface occupies is known as its surface area. Volume, on the other hand, refers to how much room an object has.
The side length of each of the three squares is 4 units.
The area of each would be:
4² = 16 sq. units.
For the three squares we have:
16(3) = 48 sq. units.
The area of each triangle is 7 sq. units.
This means together the area of the two triangles is 2(7) = 14 sq. units.
The surface area of the prism is:
14 + 48 = 62 sq. units.
Hence, the surface area of the triangular prism is 62 square units.
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*HELP ASAP*
Mr. Mackinson has to choose 2 students to lead the class field trip. If he draws from a list of 6 boys and 6 girls, what is the probabilty of 2 girls getting drawn?
Answer:
The probability of choosing 2 girls from a list of 6 girls and 6 boys can be calculated using combinations.
The number of combinations of choosing 2 girls out of 6 girls is given by the formula: C(6,2) = 6! / (6-2)!2! = 15.
So, the probability of choosing 2 girls is 15 / (C(12,2) = 66) = 15/66 = 5/22.
Therefore, the probability of Mr. Mackinson choosing 2 girls to lead the class field trip is 5/22 or approximately 0.227.
Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.
The owner of two hotels is ordering towels. He bought 6 hand towels and 27 bath towels for his hotel in Campbell, spending a total of $255. He also ordered 50 hand towels and 27 bath towels for his hotel in Lowell, spending $343. How much does each towel cost?
A hand towel costs $ ----------, and a bath towel costs $ --------.
Answer:
A handtowel costs $2.00 and a bathtowel is $9.00
Step-by-step explanation:
Let h equal the cost of a handtowel. And let b equal the cost of a bathtowel.
In Campbell, they spent:
255 = 6h + 27b
In Lowell, they spent:
343 = 50h + 27b
Solve the system.
see image.
In the U.S., shoe sizes are defined differently for men and women, but in Europe, both genders use the same shoe size scale. The accompanying histograrn shows the European shoe sizes of 269 male and female college students, converted from their reported U.S. shoe sizes. a) Describe the shape. b) How many modes does the histogram have? What might explain that? Click the icon to view the histogram of shoe sizes. a) The distribution is roughly symmetric and bimodal. b) Choose the correct answer below.
a) The distribution is roughly symmetric and bimodal. b) The histogram has two modes, which may be due to the different shoe size scales used for men and women in the U.S. but not in Europe.
The histogram of European shoe sizes of 269 male and female college students converted from their reported US shoe sizes is not visible based on the information provided, but the questions are clear.
a) The shape of the distribution is not visible, but it is mentioned that it is "roughly symmetric and bimodal".
b) There are two modes in the histogram. This could be because shoe sizes in the United States are defined differently for men and women, but not in Europe. As a result, the histogram of the distribution of European shoe sizes for both men and women may show two distinct peaks.
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In order to keep the numbers in the proper place-value column
The order of the place value in increasing order is equal to units , tens , hundreds , thousands , ten-thousand and so on.
The value of every digit present in any number depends on the position of the digit in a number.The place of the digit in the number represents its place value of the digit in a number.Starting position of a digit is ones or units.After unit the place value is tens.In ascending order the place value of all the digit in any given number is represented as units , tens , hundreds , thousands , ten- thousands, so on.Therefore, the order of the place value in ascending order of the place of the digit is given by units , tens , hundreds , thousands , ten-thousand and so on.
The given question is incomplete, I answer the question in general according to my knowledge:
What is the order of the place value ?
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4)
Slope:
2
y
(0, 1)
1
Y-Intercept:
Equa
5.) DO THE MATH: In 1921, $1,500,000 in real estate and $750,000 in personal property
was lost. Add both numbers and subtract them rom $32, 250,000 from 2019. What is the
difference? (10 points)
The difference between 2019 and 1921 is given by $30,000,000
What is the difference?Difference refers to the subtraction of two or more values.
1921 loss:
Real estate= $1,500,000
Personal property = $750,000
Total loss = $1,500,000 + $750,000
= $2,250,000
2019:
$32, 250,000
The difference between 2019 and 1921
= $32, 250,000 - $2,250,000
= $30,000,000
Therefore, there is a difference of $30,000,000
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Determine if the two are equivalent.choose 3 different values for x and complete the table.Explain your reasoning.X
2(x + 5) + 3x
5x + 10
Answer:
The expressions are identical, as shown by two methods: 1) equation rearrangement and 2) mathematical calculations.
Step-by-step explanation:
2(x + 5) + 3x
Let's simplify this expression.
2(x + 5) + 3x
2x + 10 + 3x [remove parentheses]
5x + 10 [combine like terms]
This matches the other expression.
5x + 10
Several values of x are calculated for both expressions and are shown on the attached table. Each expression results in the same value for a given value of x. This comparison also holds for negative numbers.
What is the length of each leg of a 45-45-90 triangle if the hypotenuse has a length of 4√2?
Answer:
The length of each leg would be 4 units
Step-by-step explanation:
The hypotenuse of a 45-45-90 is √2 times bigger than either side length since they're the same lengths.
pls help asap it’s annoying me
Answer:
b. 53.1°
c. 126.9⁰
Step-by-step explanation:
These are SSA triangles; use Law of Sines to find the unknown angle:
b) sin30/15 = sinA/24
sinA(15) = sin30(24)
sinA = sin30(24)/15 = 0.80
m∠A = sin⁻1(0.80) = 53.1°
c) m∠A = 180 - 53.1 = 126.9⁰
Answer:
∠ BAC = 53.13° , ∠ BAC = 126.87°
Step-by-step explanation:
using the Sine rule in Δ ABC
[tex]\frac{a}{sinA}[/tex] = [tex]\frac{c}{sinC}[/tex]
where a is the side opposite ∠ A and c is the side opposite ∠ C
here a = BC = 24 and c = AB = 15 , then
[tex]\frac{24}{sinA}[/tex] = [tex]\frac{15}{sin30}[/tex] ( cross- multiply )
15 sinA = 24 sin30° ( divide both sides by 15 )
sin A = [tex]\frac{24sin30}{15}[/tex] , then
A = [tex]sin^{-1}[/tex] ( [tex]\frac{24sin30}{15}[/tex] ) = 53.13°
(b)
acute angle BAC = 53.13°
(c)
the sine of an angle is positive in both the first and second quadrant , so
obtuse angle BAC = 180° - 53.13° = 126.87°
Jody is picking a movie to watch this evening.
Of the movies in her cabinet, 9 are romantic
comedies. She will pick one movie at random.
If the probability of the selected movie being
a romantic comedy is 25%, how many movies
are on the shelf?
The number of movies on the shelf is given as follows:
36 movies.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.
For this problem, the parameters are given as follows:
Probability of 25% = 1/4.Number of desired outcomes is of 9.Hence the total number of outcomes, representing the number of movies on the shelf, is obtained as follows:
1/4 = 9/x
x = 9 x 4
x = 36 movies.
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HELP!
Match the following.
1 .
alternate interior angles
outside angles
2 .
corresponding angles
two inside angles that lie on different sides of a transversal
3 .
interior angles
two outside angles that lie on different sides of a transversal
4 .
parallel lines
inside angles
5 .
alternate exterior angles
lines that intersect two or more lines to create angles
6 .
perpendicular lines
lines that intersect and create right angles
7 .
exterior angles
lines that share one point
8 .
intersecting lines
lines that never cross one another and are the same distance apart at all times
9 .
transversals
two angles in the same position on different lines
The answers include the following below:
alternate interior angles - two inside angles that lie on different sides of a transversal.alternate exterior angles - two outside angles that lie on different sides of a transversal.transversals - lines that intersect two or more lines to create angles.perpendicular lines - lines that intersect and create right angles.intersecting lines - lines that share one point.parallel lines - lines that never cross one another and are the same distance apart at all times.corresponding angles - two angles in the same position on different lines.interior angles - inside anglesexterior angles - outside angles.What is an Angle?This is referred to as the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.
Parallel lines refers to the type of lines that never cross one another and are the same distance apart at all times.
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Yuki Says that 43 is a 2 digit odd number that is composite is she correct explain
No. The statement given by Yuki that 43 is a 2 digit odd number that is composite is not correct.
A composite number is a positive integer greater than 1 that has more than two positive divisors. In other words, a composite number is a number that can be divided by more than just 1 and itself. For example, 4 is a composite number because it can be divided by 1, 2, and 4.
On the other hand, a prime number is a positive integer greater than 1 that has exactly two positive divisors, 1 and itself. For example, 5 is a prime number because it can be divided only by 1 and 5.
Now, let's consider the number 43. 43 is a two-digit odd number, which means it has two digits and is not divisible by 2. However, 43 is a prime number, which means it has exactly two positive divisors, 1 and 43. Therefore, 43 is not a composite number.
To further verify this, we can check the divisors of 43. The divisors of 43 are 1 and 43, because 43 is not divisible by any other positive integer. Therefore, we can conclude that 43 is a prime number and not a composite number.
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An observer in watertown, new york, would see the star polaris at an altitude of approximately. ?
44°
45°
75°
76°
Answer:
44
Step-by-step explanation:
There are 150 employees in a factory.（2/3）of the employees are males. Then, 20 male employees and 10 female employees are resigned. A employee is chosen at random from the remaining employees. Find the probability of choosing a female employee.
===================================================
Explanation:
2/3 of 150 = (2/3)*150 = 100 employees are male and 150-100 = 50 employees are female. This is before the resignations.
After the resignations happen, we would have:
100-20 = 80 males remain50-10 = 40 females remain80+40 = 120 employees remain.The chances of picking a female employee at random would be 40/120 = 1/3 which is the final answer.
Notice how the chances haven't changed from earlier (male = 2/3 chance, so 1-2/3 = 1/3 are the chances of picking a woman). Why is this? Well notice the ratio of 20 men to 10 women resigning. This ratio is 2:1, meaning twice as many men resigned. Furthermore, notice how 2/3 is twice that of 1/3.
This keeps the same proportion of men to women. Therefore, the odds haven't changed.
Greta has two pet lizards, Draco and Lizzy. For every 11 crickets Greta feeds Draco, she always feeds Lizzy 8 crickets. Last week, Greta fed Draco 77 crickets.
Answer:
56 crickets
Step-by-step explanation:
Angle QRS is an equilateral triangle. If QR is seven less than twice x, RS is 61 less than five times x, and QS is 11 more than x, find the value of x and the measure of each side
The value of x is 18 and the measure of each side is:
QR = RS = QS = 29
What is called equilateral?An equilateral triangle is a triangle that has all its sides equal in length. Since the three sides are equal therefore the three angles, opposite to the equal sides, are equal in measure. Therefore, it is also called an equiangular triangle, where each angle measure 60 degrees.
Now, According to the question:
Angle QRS is an equilateral triangle.
QRS is an equilateral triangle, thus all the three sides of the given triangle will be equal.
we have
QR = 2x - 7___(1)
RS = 5x - 61 ___(2)
QS = 11 + x_____(3)
Now, As all the sides of the triangle are equal, therefore
QR = RS = QS
⇒QR = RS
⇒2x - 7 = 5x - 61
⇒ -7 + 61 = 5x - 2x
⇒ 54 = 3x
⇒ x = 18
Put the value of x in above equations:
Thus, the measure of
QR = 2(18) - 7=29,
RS = 5(18) - 61 = 29 and
QS = 11 + 18 = 29.
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SOMEONE HELLPPPP IM SCAREDDDDD
Answer: AE
Step-by-step explanation:
if you look at the picture you can tell that Ae is a ray because rates tend to have 2 points and 2 sides one going on forever. that's why there's an arrow near "a"
One hundred people were asked about their favorite sport.
The statement that best describes the two - way frequency table is b. More females like soccer.
How to find the correct statement ?The number of females who like soccer are 31 females out of a total of fifty females who were interviewed.
This means that the number of females who like basketball are :
= 50 - 31 females for soccer
= 19 females
31 females like soccer while 19 females like basketball which shows that more females prefer soccer to basketball.
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3) we have 2 engineers and 10 computer scientists. we need to create a committee of 10 people with at least one engineer represented there. how many different ways are there to create such a committee? show at least 2 different ways to solve this problem.
Answer:
Step-by-step explanation:
Method 1: Counting the number of committees with exactly one engineer:
There are 2 ways to choose the engineer, and 10 ways to choose the remaining 9 computer scientists. Hence, there are 2 * 10 = 20 different committees with exactly one engineer.
Method 2: Using the combinations formula:
There are 12 people in total, and we need to choose 10 of them for the committee. We can use the combinations formula to calculate the number of different ways to choose 10 people from 12: C(12, 10) = (12!) / (10! * (12-10)!) = (12!) / (10! * 2!) = 66.
So, there are 66 different ways to create a committee of 10 people with at least one engineer represented.
a statistical method for identifying cost behavior is the:A. Scatter diagram methodB. High-low methodC. Composite methodD. CVP charting methodE. Least-squares regression method
The statistical method that is used for identifying the cost behavior is (e) Least Squares regression method .
The Least Squares Regression method is defined as a statistical technique that is used to determine the relationship between two variables, which are , "the cost" and its "corresponding activity level" .
This method also involves plotting data points on a scatter diagram and fitting a straight line to data points.
The line that best fits data is line that minimizes sum of squared vertical distances between the data points and the line, this is why it is called the Least Squares regression method.
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The given question is incomplete , the complete question is
A statistical method for identifying cost behavior is the:
(a) Scatter diagram method
(b) High low method
(c) Composite method
(d) CVP charting method
(e) Least Squares regression method
Gina's goal is to raise $160 for the school through her ticket sales. if she is selling the tickets for $3 each, what is the minimum number of tickets Gina needs to sell in order to earn $160?
Answer: All she needs to sell is 53 tickets
Step-by-step explanation: You divide 160 by 3 which gives you 53.3333 so you take the decimal place and get rid of it and it gives you 53. So she needs to sell at least 53 tickets to reach her goal
Let y represent the total cost of publishing a book (in dollars). Let x represent the number of the copies of the book printed. Suppose that x and y are related by the equation 15x+1100=y
a) What is the change in total cost for each book printed?
b) What is the cost to get started (Before any books are printed)?
a) The change in total cost for each book printed is $15.
b) The cost to get started (Before any books are printed) is $110
Overall, understanding the relationship between the number of copies printed and the total cost of publishing a book can help publishers and authors make important financial decisions.
a) The change in total cost for each book printed is represented by the slope of the equation.
In this case, the equation is in slope-intercept form
=> y = mx + b, where m is the slope and b is the y-intercept.
The slope of the equation 15x+1100=y is 15.
This means that for every additional book printed (x), the total cost (y) will increase by $15.
So, the change in total cost for each book printed is $15.
b) The cost to get started, before any books are printed, is represented by the y-intercept of the equation. In this case, the y-intercept is 1100.
This means that the cost to get started, before any books are printed, is $1100.
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Which kind of triangle is shown?
acute triangle
obtuse triangle
equilateral triangle
right triangle
The kind of triangle which is shown in the image is Obtuse triangle. The Option B is correct.
What is the features of Obtuse triangle?An obtuse-angled triangle is a triangle in which one of the interior angles measures more than 90° degrees. In an obtuse triangle, if one angle measures more than 90°, then the sum of the remaining two angles is less than 90°.
Characteristics of Obtuse Angled Triangle:
The sum of the two angles other than the obtuse angle is less than 90°.The side opposite the obtuse angle is the longest side of the triangle.An obtuse triangle will have one and only one obtuse angle. The other two angles are acute angles.Read more about Triangle
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