Compare the slope and length of segment EF with the slope and length of segment AB. What do you notice? What are you wondering?
The slope of segment EF and AB is same but the length of segment EF is half of the length of segment AB.
What is Line segment ?
An unmoving portion of a line is called a line segment. Two points serve as its ends. By the termination points, it is identified.
Let's assume the length of EF to be "x"
from the figure, we can clearly see that AB is made up of two segments which are of same length as EF.
So, we can say that AB = 2 times of the length of EF
i.e. AB = 2 x
Hence, By comparing, we conclude that AB's length is double of EF.
Now, if we look at slope,
Slope of EF = CE/CF
and, Slope of AB = BC/AC
But, we know that AC = 2 CF and BC = 2 CE
So, Slope of EF = CE/CF
and, Slope of AB = 2 CE / 2 CF
= CE/CF.
Hence, Both segments have same slope direction.
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Algebra tiles??
Please help!!
Answer:
(-x+2)(2x+1) — first option
Step-by-step explanation:
The rectangles represent an x, red means negative and yellow is positive.
The squares represent a unit (the number 1).
The diagram attached below demonstrates how this works.
Basically the top row of this tile equation is (-x + 2)And the column is (2x+1).
Expanding this makes -2x²+3x+2
Simplifying algebraic radicals. 14 sqrt 320
you can choose one of three boxes. box a has four $5 bills and a single $100 bill, box b has 400 $5 bills and 100 $100 bills, and box c has 24 $1 bills. you can have all of box c or blindly pick one bill out of either box a or box b. which offers the greatest expected winning?
find the difference between 307 and 188
the primary tool or measure for determining whether the assumed regression model is appropriate is .
The primary tool or measure for determining whether the assumed regression model is appropriate is the residual plot.
A residual plot is a graph that shows the residuals, or the differences between the observed values and the predicted values from the regression model, plotted against the predictor variable(s). If the residuals are randomly scattered around zero, with no discernible pattern, then the regression model is a good fit for the data.
However, if there is a pattern in the residuals, such as a curved or U-shaped relationship, then the regression model may not be appropriate and a different model may need to be considered.
In addition to the residual plot, other measures such as the coefficient of determination (R-squared), the p-values of the regression coefficients, and the normality of the residuals can also be used to evaluate the goodness of fit of a regression model.
However, the residual plot is often considered the primary tool for assessing the adequacy of a regression model.
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A large cheese pizza costs
$
18
$18dollar sign, 18. Each topping you add on costs
$
1.50 dollar sign, 1, point, 50.
How much would it cost to get a large cheese pizza with
cc toppings added?
Write your answer as an expression.
Answer:
A
=
1.50c + 18
where
A
is amount and
c
is toppings added
Step-by-step explanation:
The constant price is
18
dollars, which never changes and for every topping you get, it costs
$
1.50
. If you got no toppings, sub in
0
for
c
to get
$
18
.
a college student is preparing a course schedule of four classes for the next semester. the student can choose from the open sections shown in the table. (a) find the number of possible schedules that the student can create from the offerings. (b) find the number of possible schedules that the student can create from the offerings if two of the math 100 sections are closed. (c) find the number of possible schedules that the student can create from the offerings if two of the math 100 sections and four of the english 105 sections are closed.
(a) The number of possible schedules that the student can create from the offerings is 96.
(b) the number of possible schedules that the student can create from the offerings if two of the math 100 sections are closed is 48.
(c) the number of possible schedules that the student can create from the offerings if two of the math 100 sections and four of the English 105 sections are closed is 4.
(a) To find the total number of possible schedules, we need to multiply the number of choices for each class:
Number of schedules = 4 x 2 x 3 x 4 = 96
So, there are 96 possible schedules that the student can create from the offerings.
(b) If two of the math 100 sections are closed, then there are only two choices for that class. So, we have:
Number of schedules = 2 x 2 x 3 x 4 = 48
So, there are 48 possible schedules that the student can create from the offerings with two of the math 100 sections closed.
(c) If two of the math 100 sections and four of the English 105 sections are closed, then there are only two choices for math 100 and one choice for English 105. So, we have:
Number of schedules = 2 x 2 x 1 x 1 = 4
So, there are 4 possible schedules that the student can create from the offerings with two of the math 100 sections and four of the English 105 sections closed.
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A dietician recommends 48 grams of protein each day for his patient. At the end of the day, the patient has only eaten 40 grams of protein. What percent of her daily intake has the patient eaten?
Answer:
83%
Step-by-step explanation:
To find the percentage divide 40 by 48
40/48 = 0.83333333333333
Round to 0.83
Multiply by 100
The patient has only eaten 83% of her daily intake.
There are approximately 1. 06 quarts per liter. There are 4 quarts per gallon. If gasoline cost $0. 50 per liter, how much does gasoline cost per gallon?
A. $1. 42/gal
B. $1. 75/gal
C. $1. 89/gal
D. $2. 12/gal
E. $4. 24/gal
Answer:
$1.89/gal
Step-by-step explanation:
Find an equation of the line of symmetry of triangle ABC.
Answer:
The equation of the line of symmetry of triangle ABC is:
3x + 2y = 86Step-by-step explanation:
The line of symmetry of an isosceles triangle bisects the vertex angle (the angle opposite the base) and is perpendicular to the base of the triangle.
As AB = AC, then angle A is the vertex angle of the isosceles triangle ABC.
If B and C lie on the line with equation 3y = 2x + 12, then the line of symmetry is the line that is perpendicular to this line and passes through A (4, 37).
Rearrange the given equation 3y = 2x + 12 to slope-intercept form by dividing both sides by 3:
[tex]\implies y=\dfrac{2}{3}x+4[/tex]
Perpendicular lines have slopes that are negative reciprocals of one another. Therefore, the slope of the perpendicular line is -³/₂.
Substitute the found slope and point A (4, 37) into the point-slope formula:
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-37=-\dfrac{3}{2}(x-4)[/tex]
Rearrange the equation to standard form:
[tex]\implies 2y-74=-3(x-4)[/tex]
[tex]\implies 2y-74=-3x+12[/tex]
[tex]\implies 3x+2y-74=12[/tex]
[tex]\implies 3x+2y=86[/tex]
Therefore, the equation of the line of symmetry of triangle ABC is:
3x + 2y = 86There are 15000 average passengers on domestic flights daily. 1/20 of the passengers are tourists and 1/15 of the tourists are travel bloggers. How many tourist passengers on domestic flights are travel bloggers
If there are 15000 average passengers on domestic flights daily, then 1/20 of the passengers are tourists, which means there are 15000 * (1/20) = 750 tourists daily.
And if 1/15 of the tourists are travel bloggers, then there would be 750 * (1/15) = 50 travel bloggers daily.
If there are 15000 average passengers on domestic flights daily, then 1/20 of the passengers are tourists, which means there are
15000 * (1/20) = 750 tourists daily
So, there would be a total of 50 tourist passengers on domestic flights who are travel bloggers.
It is important to note that these are average numbers and the actual number of tourists and travel bloggers on domestic flights can vary from day to day. However, this calculation provides a general idea of the proportion of tourist passengers who are travel bloggers on domestic flights.
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Harold lives 70 miles due south of his parents' house and 24 miles west of his grandparents' house. On his birthday, Harold drove from his house to his parents' house. From there, he drove in a straight line to his grandparents' house and then back home. How far did Harold drive on his birthday?
Approximately 70 miles separated Harold's home at his grandparents' home from his own home. Accordingly, Harold travelled the following distance overall on his birthday: 70 + 74.46 + 70 ≈ 214.46
How would you define distance in plain English?What is a distance? . Regardless of the start or end point, distance can be defined as the amount of space object has to cover.
How do you gauge a distance?The metre serves as the SI unit of distance (m). Centimeters (cm) are a common unit of measurement for short distances, whereas kilometres (km) are used for longer distances (km). You could measure a piece of paper's length in centimetres, for instance, by measuring from the bottom to the top.
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monique is 2 years older than vanessa. the sum of their ages is 32.let v represent vanessas age.which of the following equations can be used to find vanessas age?
a.v+2=32
b.2v -2=32
c.v+(v-2)=32
d.v+(v+2)=32
The correct option is a. The equation used to find Vanessa's age is v + 2 = 32.
What is an equation?A mathematical statement known as an equation utilises the equals sign to demonstrate the equality of two expressions. It may be used to address a variety of issues and can contain both numbers and variables. Algebraic operations including addition, subtraction, multiplication, division, and exponentiation are frequently used in equations.
In the given question, Vanessa's age may be calculated using the equation a. v+2=32. This equation shows that Vanessa's age plus 2 equals 32, implying that Vanessa's age is 30. We may solve this equation by removing 2 from both sides, yielding v=30. This equation is valid for determining Vanessa's age because it specifies that Vanessa's age plus Monique's age equals 32.
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3²ˣ -3ˣ⁺² = 3ˣ⁺¹ - 3³.
Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 3\le x \le 43≤x≤4.
The average rate of change of f(x) over the interval 3≤x≤4 is 15
What is the average rate of change of f(x) over the intervalFrom the question, we have the following parameters that can be used in our computation:
The table of values
On the table, we have
f(3) = -4
f(4) = 11
The average rate is then calculated as
Average rate = [f(4) - f(3)]/[4 - 3]
Substitute the known values in the above equation, so, we have the following representation
Average rate = (11 + 4)/(4 - 3)
Evaluate
Average rate = 15
Hence, the average rate is 15
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Complete question
Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 3\le x \le 43≤x≤4.
X f(x)
3 -4
4 11
5 8
6 10
7 11
8 14
3-83. Challenge Problem! Find the dimensions of the generic rectangle below. Then write an equivalency
statement (length width = area) of the area as a product and as a sum.
x²
3x
-5x
-15
The dimensions are 5 units each
The area of the rectangle is 25 units
How to determine the dimensions
It is important to note that algebraic expressions are defined as expressions that are composed of variables, terms, cofficients, constants and factors.
They are also described as expressions with mathematical operations.
From the information given, we have that;
x² - 5x + 3x - 15
To solve the quadratic equation, let us use the factorization method
Group the values in pairs
(x² - 5x) + (3x - 15)
factor the terms
x(x -5) +3(x - 5)
Then, x + 3 = 0
x = -3
And x - 5 = 0
x =5
But area of a rectangle is;
= Length× width
= 5 × 5
= 25 square units
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5843 divided by 11 whth remainders
Answer:
Remainder:
Step-by-step explanation:
Step 1: Divide 5843 by 11.
5843/11 = 530.272727
Step 2: Find the quotient.
Quotient = 530
Step 3: Find the remainder.
Remainder = 3
At its earliest stages, a logistic growth curve closely resembles an exponential growth curve. False/True.
At its earliest stages, a logistic growth curve closely resembles an exponential growth curve - True
It is true that at its earliest stages, a logistic growth curve closely resembles an exponential growth curve.
The logistic growth curve shows the logistic population growth rate, the logistic growth curve on a line graph is similar to a S-shaped and it's observed that there is a slow increase, rapid population growth, and finally, the reduction in the growth.
On the other hand, the exponential growth curve is a J-shaped curve that shows us that there is a rapid and consistent or steady growth in the population over the duration of a specific period.
It could be said that an exponential growth curve is opposite of a slow and steady success.
Both the curve start along with the same pattern but with time gradually change their constrain over the graph.
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Mr. Stanley owns a farm measuring 24m long and 40m wide. If he wants to plant in squares, what is the largest sized square he can use?
The largest square that Mr. Stanley can use to plant in his farm is a square with a side length of 8 meters.
To find the greatest common factor of 24 and 40, we can list the factors of both numbers and find the highest factor that they have in common:
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
The highest factor that 24 and 40 have in common is 8.
Factors are numbers that can be multiplied together to get a given number. For example, the factors of 6 are 1, 2, 3, and 6 because 1 x 6 = 6 and 2 x 3 = 6. Factors can be prime or composite. Prime factors are those that are only divisible by 1 and themselves. Composite factors are those that have more than two factors.
Factors are important in math because they can be used to simplify fractions, find common denominators, and solve equations. They also play a crucial role in number theory and cryptography, where they are used to encrypt and decrypt messages. 150 is a composite number, which means it has factors other than 1 and itself. The factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150. To find these factors, you can divide 150 by each number smaller than it and see if the remainder is 0.
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HELPP PLSSS
Factor the polynomial.
x²+2x² +14x+7x²
Answer:
2x(5x+7)
Step-by-step explanation:
[tex]x^2+2x^2+14x+7x^2\\=10x^2+14x\\=2x(5x+7)[/tex]
How would you
write the name of a segment differently than the name of a line? What
symbols would you use?
The primary difference between writing the name of a segment and the name of a line is the use of symbols.
What is symbol?A symbol is an object, image, or action that stands for or represents something else. Symbols can be used to convey a wide variety of ideas and concepts, from the literal, such as a heart to represent love, to the abstract, such as a peace sign to represent a call for world peace. Symbols are often used to communicate complex ideas quickly and easily.
To denote a segment, a line is usually written with two arrows pointing in opposite directions, such as ↔. To denote a line, the line is usually written with a single arrow pointing in one direction, such as →.
For example, if you were writing the name of a segment called "AB", then you would use the symbol ↔ AB. If you were writing the name of a line called "AB", then you would use the symbol → AB.
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Use synthetic division to find the quotient and remainder when x³ + 9x² + 12x - 5 is divided by x+7 by completing the parts below.
(a) Complete this synthetic division table.
-7)
19 12 -5
000
OOOO
(b) Write your answer in the following form: Quotient +
3
x³ + 9x² +
+ 9x + 12x-5
x+7
=
x+7
Remainder
x+7
X
The division can be written as: x³ + 9x² + 12x - 5 = (x + 7)(x² + 7x + 10) - 75
What is synthetic division ?
Synthetic division is a simplified method of polynomial division that can be used to divide a polynomial by a linear binomial. It's used to find the quotient and remainder of a polynomial division without having to perform long division.
In synthetic division, the coefficients of the polynomial are arranged in a table along with the coefficients of the divisor, and then divided and multiplied using the same rules as in long division. The remainder of the division is the last entry in the table, and the quotient is the polynomial whose coefficients are the entries in the table, excluding the remainder.
To perform synthetic division, we divide x³ + 9x² + 12x - 5 by x + 7 by dividing each coefficient by x + 7 and then writing the result in a table with the dividend on top and the divisor on the bottom. Here's what the table would look like:
+ 7 | 1 9 12 -5
-------------------
x^3 | x^3 9 12 -5
x^2 | x^2 +7x 3 -35
x | x +7 10 -70
-------------------
10 43 -75
The quotient of the division is x² + 7x + 10, and the remainder is -75.
Therefore, the division can be written as: x³ + 9x² + 12x - 5 = (x + 7)(x² + 7x + 10) - 75
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3. a computer password consists of two lowercase letters followed by a capital letter and four digits. find the total number of possible passwords.
The total number of possible passwords is 17,576,000.
There are several steps involved in calculating the total number of possible passwords.
Step 1: Determine the number of possible choices for the first lowercase letter. Since there are 26 letters in the alphabet, and the password consists of lowercase letters, there are 26 choices for the first letter.
Step 2: Determine the number of possible choices for the second lowercase letter. Since there are 26 letters in the alphabet and repetition is allowed, there are 26 choices for the second letter.
Step 3: Determine the number of possible choices for the capital letter. Since the password requires a capital letter, there are 26 choices for this position.
Step 4: Determine the number of possible choices for the first digit. Since there are 10 digits (0-9), there are 10 choices for the first digit.
Step 5: Determine the number of possible choices for the second digit. Since there are 10 digits (0-9) and repetition is allowed, there are 10 choices for the second digit.
Step 6: Determine the number of possible choices for the third digit. Since there are 10 digits (0-9) and repetition is allowed, there are 10 choices for the third digit.
Step 7: Determine the number of possible choices for the fourth digit. Since there are 10 digits (0-9) and repetition is allowed, there are 10 choices for the fourth digit.
Step 8: Multiply the number of choices for each position together to get the total number of possible passwords.
Using the multiplication rule of counting, we get:
Total number of possible passwords = (Number of choices for the first lowercase letter) x (Number of choices for the second lowercase letter) x (Number of choices for the capital letter) x (Number of choices for the first digit) x (Number of choices for the second digit) x (Number of choices for the third digit) x (Number of choices for the fourth digit)
Total number of possible passwords = 26 x 26 x 26 x 10 x 10 x 10 x 10
Total number of possible passwords = 17,576,000
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A 13-foot ladder is leaning up against a building. The top of the ladder reaches the wall at a height of 12 feet. How far is the
bottom of the ladder from the building? Find the angle (2B) that the ladder makes with the ground?
A
12
C
building
13
ladder
X
ground
B
How far is the ladder from the building? Find x = ?
Keep the results to the nearest whole number.
feet
Find the angle that the ladder makes with the ground? LB =
Keep the results to the nearest whole number.
The angle that the ladder makes with the ground is ∠B = 67.38°.
The distance between the ladder from the building is 5 feet.
What is the right triangle?A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.
Given that a 13-foot ladder is placed up against a wall.
The ladder's top touches the wall at a height of 12 feet.
As per the given question, we have the right triangle ΔABC
Using sine ratio to find angle ∠B as:
sin ∠B = AC/ AB
sin ∠B = 12/13
∠B = sin ⁻¹(12/13)
∠B = 67.38°
Now, using Pythagoras's theorem to find distance x as:
AC² + BC² = AB²
12² + x² = 13²
144 + x² = 169
x² = 169 - 144
x² = 25
x = 5
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2x-y=9,4x+y=21
answer this equation for a bloody cookie mate
Answer:
x=5, y=1
Step-by-step explanation:
2x-y=9
2(5)=10
10-1=9
4x+y=21
4(5)=20
20+1=21
Hope this helps! Please give brainliest!
Represent and Connect Lennon has 3,330 toothpicks. He
wants to use them all to make a floor mat with 18 equal
rows. Use the bar diagram to write a division equation.
Then solve the equation to find how many toothpicks
Lennon should use in each row.
The toothpicks lennon should use in each row is 185.
What is Algebra?Algebra is the study of abstract symbols, and logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction also. This approach is used to answer the given problem correctly and completely.
We are given that;
Total number of toothpicks= 3330
Number of rows= 18
Now,
To find the number of toothpicks in each row
=3330/18
=1665/9
=185
Therefore, by algebra the answer will be 185.
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If 3 times a certain number is increased by 4 the result is 28. What is the number?
Answer:
8
Step-by-step explanation:
8x3 = 24
24 + 4 = 28
Secured loans are less costly than unsecured loans because _________.
They usually have a lower interest rate.
They require collateral.
They are less risky for the financial institution.
All of these are true.
Due to the fact that secured loans often have lower interest rates than unsecured loans, they are less expensive. They require collateral. They are less risky for the financial institution. The correct option is D.
What are secured loans?A secured loan is one in which the borrower pledges an asset as security for the loan, turning the pledged asset into a secured debt owing to the lender (the creditor).
Some loans may be backed by assets other than your house; for instance, they may be backed by your automobile, jewelry, or other possessions. Because lenders can collect the asset in the event of a default on a secured loan, secured loans often have lower interest rates than unsecured loans.
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Tanner is 2 years younger than his
brother. Tanner's age t in years is 2
less than his brother's age b.
dependent variable:
independent variable:
equation:
The equation will be:
t = b - 2
And we can see that:
independent variable = brother's age.dependent variable = Tanner's age.How to identify the variables?Here we have two variables:
t = taner's age
b = age of Tanner's brother.
The independent variable is the one that does not depend on the other, in this case (for how it is worded) is the brother's age.
The dependent variable depends on the other, on this case, Tanner's age.
Now let's write the equation, we know that Taner's age is 2 years less than his brother, then:
t = b - 2
That is the equation.
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