Parallelograms are quadrilaterals with two sets of parallel sides
Slope Formula: y2-y1/x2-x1
A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles are additional to the transversal on the same side. 360 degrees is the sum of all interior angles.
KL: 12-7/6-2 = 5/4
LM; 13-12/13-6 = 1/7
MN: 8-13/9-13 = 5/4
KN: 7-8/9-2 = 1/7
We can identify this as a parallelogram since it has congruent angles and sides, which are found on a parallelogram.
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(−4x + 3)(−2x2 − 8x + 2)
On solving the expression, the standard form is obtained as 8x³ + 26x² - 32x + 6.
What is an expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
The given expression is - (−4x + 3)(−2x² − 8x + 2)
To solve this expression first expand the equation using arithmetic operation of multiplication.
(−4x + 3)(−2x² − 8x + 2)
-4x(−2x² − 8x + 2) + 3(−2x² − 8x + 2)
8x³ + 32x² - 8x - 6x² - 24x + 6
Collect the like terms together -
8x³ + 32x² - 6x² - 8x - 24x + 6
Perform the arithmetic operation of addition and subtraction -
8x³ + 26x² - 32x + 6
Therefore, the standard form is 8x³ + 26x² - 32x + 6.
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please help me with my homework!
Answer:
The machine makes 45 bottles per minute.
Step-by-step explanation:
We can first find the slope through this equation: [tex]\frac{y2-y1}{x2-x1}[/tex]
Since we are given two points, (2,90) and (7,315), we can plug those two points into the formula given above:
[tex]\frac{315-90}{7-2}[/tex]
= 45
Therefore, m = 45.
Now, we can pick one of the two points given--in this case, I'll use (2,90)--to find the equation of the line: [tex]y-y1 = m(x-x1)[/tex]
For (2,90), y1 will be 90, and x1 will be 2. Let's also plug in m:
y - (90) = 45(x - 2)
We can solve for y now to find what y=mx+b is:
y = 45(x-2) + 90
y = 45x
Since the problem asks how many bottles the machine can make per minute, we can plug x = 1: 45(1) = 45
The machine makes 45 bottles per minute.
Terra argues that is not a function because two different inputs produce the same output, as shown in the table.
Is Terra correct in claiming that is not a function?
Input Output
-1 2
0 0
1 2
Terra is
correct/incorrect
. In order for a relationship to be a function, each input value must result in
only one input/ multiple outputs
. In this equation, each input value does result in only one output value. It is
allowed/not allowed
for more than one input to have the same out. This does not mean that the relationship is not a function.
Terra is correct. In order for a relationship to be a function, each input value must result in only one input.
What is a function?A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a connection between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is often represented as y = f. (x).
We know that for a function each input value must result in a unique output value. Terra claims this statement, and hence she is correct.
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For the following right traingle, find the side length x. Round your answer to the nearest hundredth
7.21
Step-by-step explanation:The Pythagoras theorem allows us to solve for unknown sides of right triangles.
Right Triangles
Right triangles are triangles that have one 90-degree angle (aka a right angle). The side directly across from the right angle is called the hypotenuse. The hypotenuse is always the longest side of a triangle. The other 2 sides of a right triangle are called the legs of the triangle.
Pythagorean Theorem
The Pythagorean theorem states that a² + b² = c², where a and b are the legs of the triangle and c is the hypotenuse. To find the missing side we can plug in the values we know and solve for b.
12² + b² = 14²Then, subtract 12² from both sides.
14² - 12² = b²52 = b²Finally, take the square root of both sides. When you square root a number, the resulting value is plus or minus, but since we are finding a distance, we will only take the positive answer.
7.21 ≈ bI believe A and C are part of the answer but I am unsure of the rest
Please find attached the image of the enlargement of the shape X by a scale factor of -1 created using MS Word, which is a drawing equivalent to option B. The correct option is therefore;
B.
What is an enlargement transformation?An enlargement transformation is one in which the pri-image object size is scaled about a center of enlargement, using a scale factor, with the sign of the scale factor indicating the direction of the enlargement, which for a +ve sign is on the same side, and for a -ve sign is on the other side of the center of enlargement.
An enlargement by a scale factor of -1, can be obtained by producing the image on the alternate side of the center of enlargement, which with a scale factor of -1, is the same size as the size of the image.
Therefore, the dilation by a scale factor of -1, with the center at the origin, produces an image which is equivalent to a reflection of the original object (pre-image), across the y-axis followed by a reflection across the y-axis.
The image of the object following the dilation will therefore be the mirror image of the mirror image of the object reflected across the y-axis, which takes the shape of a vertically flipped, left flipped F, which is option B
Please find attached a drawing of the shape of the image of the enlargement of shape X by a scale factor of -1, created with MS Word
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Help please help please
Answer:
x = 60.4
Step-by-step explanation:
First, let's remember the three different trigonometric functions: sine, cosine, and tangent. In this case, we would use cosine because the adjacent side to the angle and hypothenuse are used/given.
[tex]cos(22) = \frac{56}{x}[/tex]
We need to set up a proportion because there is not much else you could do here.
[tex]\frac{cos(22)}{1} =\frac{56}{x}[/tex]
Then, cross-multiply.
[tex]cos(22) * x = 56[/tex]
Finally, divide both sides by cos(22). You'll probably need your calculator and make sure it's in degrees mode and not radians!
[tex]\frac{cos(22) * x}{cos(22)} = \frac{56}{cos(22)}[/tex]
[tex]x = 60.4[/tex]
Rounded to the nearest tenth, x = 60.4.
I Need help with this I’ve tried stuff and stuff but it’s not working
Answer:
y= -2x + 0
Step-by-step explanation:
to get to y you need to multiply by -2 and add 0 to that to get the final y answer
e
5 Louay wants a cap with less than white
stars. Which cap could Louay buy?
Cap 1
Cap 1 only
Cap 2 only
C
Cap 2 or 3
D Cap 1 or 3
A
B
Cap 2
Cap 3
The correct option regarding which cap Louay can buy is given as follows:
D. Cap 1 or 3.
How to obtain the fraction of white stars?The fraction of white stars is obtained using a proportion, dividing the number of white stars by the total number of stars.
Hence the fractions for each cap are given as follows:
Cap 1: 1/3 = 0.33 < 1/2 = 0.5.Cap 2: 2/4 = 0.5 = 0.5.Cap 3: 2/5 = 0.4 < 1/2 = 0.5.Meaning that Cap 1 and Cap 3 have the desired ratio of white stars relative to total stars, and thus the correct option is given by option D.
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What is the equation of the line that passes through the point (-3,-8) and has a slope of 0
Answer:
The equation of a line in the form of y = mx + b, where m is the slope, x is the variable and b is the y-intercept.
Given a point and the slope, we can find the equation of the line that passes through that point. We know that the slope of the line is 0, so we can write the equation of the line as:
y = 0x + b
We also know that the line passes through the point (-3,-8), so we can substitute these values into the equation and solve for b, the y-intercept:
-8 = 0(-3) + b
-8 = 0 + b
b = -8
So the equation of the line that passes through the point (-3,-8) and has a slope of 0 is:
y = 0x - 8
This line is a horizontal line with y-intercept -8, which means that the line passes through the point (0,-8)
i need a help with graphing
A graph of the line that passes through the two points (-3/2, -3/2) and (3/2, 3/2) is shown in the image attached below.
How to calculate the slope of any straight line?In Mathematics and Geometry, the slope of any straight line can be calculated by using this mathematical equation (expression);
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
From the information provided above, we have the following data points located on the line:
Points on the x-coordinate = (-3/2, 3/2).
Points on the y-coordinate = (-3/2, 3/2).
Substituting the given data points into the slope formula, we have the following;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (3/2 + 3/2)/(3/2 + 3/2)
Slope (m) = 3/3 = 1
At point (-3/2, -3/2), an equation of this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
Where:
m represents the slope.x and y are the data points.c represents the intercept.y - (-3/2) = 1(x - (-3/2))
y + 1.5 = x + 1.5
y = x
Next, we would use an online graphing calculator to plot the linear equation as shown in the graph attached below.
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Find the selling price.
Cost to store: $65
Markup: 80%
The selling price for the article if it is equal to marked price will be $117
using profit and loss formulas.
What is profit and loss formula?
Profit and Loss formula is used in mathematics to determine the price of a commodity in the market and understand how profitable a business is. Every product has a cost price and a selling price. Based on the values of these prices, we can calculate the profit gained or the loss incurred for a particular product. The important terms covered under this are cost price, fixed, variable and semi-variable cost, selling price, marked price, list price, margin, etc.
For example, for a shopkeeper, if the value of the selling price is more than the cost price of a commodity, then it is a profit and if the cost price is more than the selling price, it becomes a loss.
Now,
Given Cost price=$65
Marked up price = 180%*$65
As
Marked up price = selling price
Therefore
selling price= 180%*$65
selling price =$117
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A mathematics teacher wanted to see the correlation between test scores and homework. The homework grade (x) and test grade (y) are given in the accompanying table. Write the linear regression equation that represents this set of data, rounding all coefficients to the nearest tenth. Using this equation, find the projected test grade, to the nearest integer, for a student with a homework grade of 37.
Regression equation:
Final Answer:
You can substitute a homework grade of 37 into the equation in place of x, to find the projected test grade.
What is linear regression?Linear regression is a statistical method that is used to study the relationship between two continuous variables, often referred to as the independent variable (x) and the dependent variable (y). The goal of linear regression is to find the best-fitting line that describes the relationship between these two variables. The best-fitting line is known as the regression line, and it is represented by the equation y = mx + b, where m is the slope of the line, and b is the y-intercept.
To find the linear regression equation, we need to use the least squares method to find the line of best fit that describes the relationship between the homework grade (x) and the test grade (y). The equation of the line is in the form of y = mx + b, where m is the slope and b is the y-intercept.
To find the slope (m) and y-intercept (b) we can use the following formulas:
m = (n(Σxy) - (Σx)(Σy)) / (n(Σx²) - (Σx)²)
b = (Σy - m(Σx)) / n
where n is the number of data points, Σx and Σy are the sum of x and y values, Σxy is the sum of the product of x and y values, and Σx² is the sum of the squares of x values.
Given the data points, we can use this information to calculate the slope and y-intercept, and write the linear regression equation.
Given the linear regression equation of the form y = mx + b
You can substitute a homework grade of 37 into the equation in place of x, to find the projected test grade.
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3
The teacher estimated that she would have 68 students this school year. She actually had 74.
What is the percent error?
A 2. 08%
B
6%
8. 11%
D 191. 89%
Answer:
Hi, I'm Za'Riah! I will gladly assist you with your problem. (see explanation)
Step-by-step explanation:
The answer is C
Hope this helped!
Roger received $200 for his birthday. He wants to use the money to buy new clothes for work. He can buy pants
for $30 and shirts for $20. He wants at least 6 new items. Determine the shirt and pants combination Roger
can buy.
From the inequalities 30x + 20y ≤ 200 and x + y ≥ 6, Roger can buy 3 pants and 3 shirts.
What is an equation?An equation is an expression that shows the relationship between numbers and variables.
Inequalities is used for the non equal comparison of these numbers and variables.
Let x represent the number of pants that Roger buys and y represent the number of shirts he buys.
He can buy pants for $30 and shirts for $20. Roger received $200 for his birthday, therefore:
30x + 20y ≤ 200 (1)
Also:
He wants at least 6 new items. hence:
x + y ≥ 6 (2)
From both equations, the solution to these equalities is (3, 3)
Roger can buy 3 pants and 3 shirts.
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Given p(x) = x^3+4x^2-3x+2 and p(x)/x-1= x^2+5x+2 R4 Which statement is true? Select all that apply. A.p(1)= 4 B.p(x)= (x - 1)(x^2 + 5x + 2) +4/x-1 C.p(x)= (x-1)-(x^2+5x+2)+4 D.p(-1)= 4
The correct statement relative to the polynomial function is given as follows:
A. p(1)= 4
B. p(x)= (x^2 + 5x + 2) +4/x-1
How to obtain the correct statement?The polynomial function for this problem is given as follows:
p(x) = x^3+4x^2-3x+2
Dividing the polynomial function by x - 1, the quotient and the remainder are given as follows:
Quotient: x² + 5x + 2Remainder: 4.Meaning that:
The function can be written as: p(x)= (x^2 + 5x + 2) +4/x-1.By the Remainder Theorem, p(1) = 4.Hence the correct options are given by option A and option B.
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Line segment SU is dilated to create S'U' using the dilation rule DQ,2. 5. What is the distance, x, between points U' and U?
4 units
4. 8 units
6 units
10 units
If Line segment SU is dilated to create S'U' using the dilation rule DQ₂.₅ , then the distance "x" between points U' and U is (c) 6 units .
The Scale Factor is written as ratio of the distance from center to image of a point and distance from center to corresponding point.
the scale factor from the figure can be written as : QU'/QU ;
From the figure , we can see that QU = 4 units and scale factor is = 2.5 ;
⇒ 2.5 = QU'/4 ;
On simplifying ,
we get ;
⇒ QU' = 2.5 × 4 = 10 ;
From the figure : UU' = QU' - QU ;
⇒ UU' = 10 - 4 = 6 .
Therefore , the distance between points U and U' denoted by "x" is 6 units .
The given question is incomplete , the complete question is
Line segment SU is dilated to create S'U' using the dilation rule DQ₂.₅ , What is the distance, x, between points U' and U?
(a) 4 units
(b) 4.8 units
(c) 6 units
(d) 10 units
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An item on sale costs 30% of the original price. If the original price was $90 what is the sale price
Combine like terms to create an equivalent expression.
3.4 2.8d +2.8d-1.3
Answer:
Step-by-step explanation:
If the problem was supposed to be "3.4 + 2.8d + 2.8d -1.3". Then the answer would be 5.6d + 2.1. you can combine the "d" terms because they have the same variable and you can combine the number terms because they are like. This result in 2.8d+2.8d + 3.4 - 1.3. This simplifies to the correct answer given above.
Think about what you know about breaking apart numbers with addition. Fill in each box. Use words, numbers. and picture. Show as many ideas as you can.
The breaking of number using addition is discussed above.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is the breaking apart of numbers with addition.
We can breaking apart the numbers with addition as follows. Assume the number to be 50. We can break the number 50 as follows -
50 = 25 + 25
50 = 15 + 10 + 15 + 10
50 = 10 + 10 + 10 + 10 + 10
50 = 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5
Therefore, the breaking of number using addition is discussed above.
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Please can somebody help me do this further maths gcse question in ‘transformations of graphs and functions’
Answer:
y=f(x)-6 is a vertical translation down by 6 units so draw the same graph but 6 units down with the point at which it crosses the y-axis as (0,-4)
(A)Find the length of the arc.
(B)Find the area of the sector.
r = 8 cm, Theta = 45°
a. The length of the arc is 6.28cm
b. The area of the sector is 25.12cm²
What are arc and sector?The arc of a circle is defined as the part or segment of the circumference of a circle. A sector is the space bounded by the arc and the radii of the circle. The smaller area is known as the minor sector and the bigger area is known as the major sector.
The length of an arc = tetha /360 ×2πr
= 45/360 × 2×3.14× 8
= 2×3.142 = 6.28cm
The area of a sector = tetha / 360 × πr²
= 45/360 × 3.14 × 8× 8
= 3.14× 8
= 25.12 cm²
Therefore, the length of the arc is 6.28cm and the area of the sector is 25.12cm²
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100 points Factor completely and then place the factors in the proper location on the grid. 4 y2 + 25 y + 6
The factored expression to the expression is (4y + 1)(y + 6)
How to determine the factor to the equationFrom the question, we have the following parameters that can be used in our computation:
4 y2 + 25 y + 6
Express properly
So, we have the following representation
4y² + 25 y + 6
Expand the expression
This gives
4y² + 24y + y + 6
Next, we factor the expression
4y(y + 6) + 1(y + 6)
Factor out y + 6
(4y + 1)(y + 6)
Hence, the solution is (4y + 1)(y + 6)
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I read a total of 42 books over 7 months. If Craig has read 48 books so far, how many months has he been with his book club? Solve using unit rates.
Answer:
8
Step-by-step explanation:
42/7 =
6..
Since +6 more to 42 = 48 =
42+6=
48.
Just add 1 more month =
7+1=
8
Need more explanation I am happy to help :)
If 3+x<5 and 8+x>5,What range of values of x satisfies both inequalities?
The range of values of x which satisifies both of the inequalities is:
(-3, 2)
What range of values of x satisfies both inequalities?Here we have two inequalities:
3 + x < 5
8 + x > 5
And we want to see which range of values of x satisfie both of these inequalities.
If we isolate x on both inequalities, we will get:
3 + x < 5
x < 5 - 3
x < 2
And the other one is:
8 + x > 5
x > 5 - 8
x > -3
Then we havethe compound inequality:
x < 2
x > -3
Then the range of values that satisfies both inequalities is (-3, 2)
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A population of 1500 deer decreases by 1.5% per year. At the end of 10 years, there will be approximately
1290 deer in the population. Which function can be used to determine the number of deer, y, in this population
at the end of t years?
The function is y = 1500[tex](0.985)^t[/tex].
What is function?
A mathematical function , rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
Here initial population is 1500 .
Rate of decrease = 1.5%
Number of years = 10
After 10 years , the end population = 1290.
Now using formula,
=> P = [tex]P_0[/tex][tex](1-\frac{r}{100})^n[/tex]
Here number of deer, y, in this population at the end of t years then
=> y = 1500[tex](1-\frac{1.5}{100})^t[/tex]
=> y = 1500[tex](1-0.015)^t[/tex]
=> y = 1500[tex](0.985)^t[/tex]
Hence the function is y = 1500[tex](0.985)^t[/tex].
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-13, -17, -21, -25 write an equation for the nth term of the arithmetic sequence then find a10
The tenth term of the given arithmetic sequence is; -49
What is the nth term of an arithmetic sequence?The formula for the nth term of an arithmetic sequence is;
aₙ = a + (n - 1)d
where;
a is first term
d is common difference
From the given sequence, we see that;
a = -13
d = -17 - (-13)
d = -17 + 13
d = -4
Thus, the tenth term of the arithmetic sequence is;
a₁₀ = -13 + (10 - 1)-4
a₁₀ = -13 -36
a₁₀ = -49
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(9a^4-31a^3-21a^2+6a-13)/(a-4) Synthetic Division
The quotient from the synthetic division (9a^4-31a^3-21a^2+6a-13)/(a-4) is 9a⁴ - 22a³ - a² + 5a - 8/a -4
What is synthetic division?Synthetic division can be defined as a mathematical method of dividing a polynomial by a binomial x - c
Such that, c is a constant.
The steps to take in synthetic division;
Arrange the set up for synthetic divisionWrite down the leading coefficient in the bottom rowMultiply the value of c by the value written on the bottom rowAdd the column that was created in step 3Repeat until the process till the last coefficientGiven the polynomial;
(9a^4-31a^3-21a^2+6a-13)/(a-4)
[tex]\sqrt[a -4]{9a^4 -31a^3 +6a -13}[/tex]
c of divisor x-c
4 coefficients of dividend
9 -31 -21 6 -13
_____9__-22__-1___ 5_______
9 -22 -1 5 -8
The quotient is the;
9a⁴ - 22a³ - a² + 5a - 8/a-4
Hence, the expression is 9a⁴ - 22a³ - a² + 5a - 8/a-4
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!!! asap
Bryce graphs an arithmetic sequence and draws a line through the points. The line has a negative slope and a positive y-intercept. Write an arithmetic sequence that could represent Bryce's sequence
The possible equation of the sequence is f(x) = -2x + 5
How to determine the possible sequenceFrom the question, we have the following parameters that can be used in our computation:
Sequence type = arithmetic
Also, we have the following features
slope = negative
y-intercept = positive
A linear equation (or an arithmetic sequence) can be represented as
y = mx + c
Where
slope = m
y-intercept = c
Using the given features, we can use the following assumed values
m = -2
c = 5
So, the sequence is
f(x) = -2x + 5
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Jenny went for a drive in her new car. She drove for 198.4 miles at a speed of 62 miles per hour. For how many hours did she drive?
The number of hours that Jenny drove in her new car is 3.2 hours
How to calculate the number of hours that Jenny drove in her car?
The speed is 62 miles
The distance is 198.4 miles
The number of hours can be calculated as follows
speed= distance/time
62= 198.4/x
cross multiply both sides
62x= 198.4
x= 198.4/62
x= 3.2
Hence the number of hours that Jenny drove is 3.2 hours
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Your water hose leaking at a rate of 0.25 cups per hour. How many gallons did your hose leak in a full 24 hour day ?
well, let's first find out how many cups was that in 24 hours anyhow.
so in 1hr the hose leaks 0.25 cups, so in 24 hrs that'd be (24)(0.25) = 6 cups.
Since a gallon has 16 cups, that'd be 6/16 gallons or 3/8 = 0.375 of a gallon.