The area of a parallelogram when the dimensions are a base of 440 miles and a height of 120 miles is 52800 miles²
How to calculate the value?It should be noted that the area of a parallelogram is calculated by multiplying the base by the height.
The dimensions are a base of 440 miles and a height of 120 miles.
The area of the parallelogram will be:
= Base × Height
= 440 × 120
= 52800 miles²
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A student states that a triangle can be formed with side lengths 2 in, 3 in, and 6 in. is the student correct? why, or why not? yes, because 2 3 < 6 yes, because 6 2 > 3 no, because 2 3 < 6 no, because 6 2 > 3
A student is not correct when he stated that a triangle can be formed with side lengths 2 in, 3 in, and 6 in because 2 + 3 < 6.
A triangle is a polygon with three sides and three vertices.
To know if a set of numbers is a valid measure of the sides of a triangle, it must follow the Triangle Inequality Theorem which states that the sum of any two sides must be greater than the third side, such that a + b > c, a + c > b, and b + c > a.
Let a = 2, b = 3 , c = 6
a + b > c : 2 + 3 > 6 5 > 6 False
a + c > b : 2 + 6 > 3 8 > 3 True
b + c > a : 3 + 6 > 2 9 > 2 True
If at least one of these statements does not hold true, the measurements can't be the sides of a triangle.
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? 4 cm Area = 20 cm² 6 cm
The height of the triangle whose base is 4 cm and area is 20 cm² is 10 cm .
The area of a triangle is defined as the total space occupied by the three sides of the triangle in a two-dimensional plane. The basic formula for the area of a triangle is half the product of the base and the height, or A = 1/2 × b × h.It is given that base is 4 cm and area is 20 cm² .
Putting above values in area formula , we get
Area = 1 / 2 × base × height
20 = 1 / 2 × 4 × height
20 = 2 × height
10 cm = height
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The complete question is given below :
Find the height of the triangle whose base is 4cm and area is 20 cm².
WILL GIVE BRAINLIST TO BEST ANSWER
Julia drove a car 10 miles in 30 minutes. Jasmine drove a motorcycle 3 miles in 12 minutes. who drove faster? show work!
What’s the algebraic expression of:
Six times the sum of a and b squared minus four times the product of a and b squared
Answer:
6(a+b)^2 + 4ab^2
Step-by-step explanation:
sum is addition (a+b)
product is multiplication (ab)
6(a+b)^2 + 4ab^2
you will get 100 points if you get this right
Answer:12.5 Km/L
Step-by-step explanation:[tex]\frac{100km}{8L}[/tex]
=12.5Km/L
Answer: 12.5
100 / 8 = 12.5
CHECK
12.5 x 8 = 100
Hope this helps 0v0
A triangle has side lengths of (8w + 8x) centimeters, (3w+10y) centimeters, and
(4y + 8x) centimeters. Which expression represents the perimeter, in centimeters,
of the triangle?
Answer:
(8w+8x)(8w+8x)+(3w+10y)(3w+10y)+(4y+8x)(4y+8x)
Step-by-step explanation:
Find the inverse of each function. Is the inverse a function? f(x)=4 x-1
We need to know about inverse of a function to solve this problem. The inverse of the given function is (x+1)/4.
The inverse of a function is a function for whom the range of the function becomes it's domain. The domain of a function is the set of values that the function can take as input. The range of a function is the set of values that the function can have as possible output. The inverse of a function is a function that finds the pre-image of it's function. If the function is in terms of x, then the inverse of the function will be in terms of y. The inverse of a function can be found by making y the independant variable and expressing x in terms of y.
f(x)=4x-1
write this function in terms of y and wquating to x
x=4y-1
x+1=4y
y=(x+1)/4
[tex]f^{-1} (x)[/tex]=(x+1)/4
Therefore we found the inverse of the function to be (x+1)/4.
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Find an equation of the line passing through the point (6,-1) that is parallel to the line y = -3/2x- 3
Step-by-step explanation:
parallel means it has the same slope.
the slope is always the factor of x : -3/2
I guess the needed equation is in slope-intercept form :
y = ax + b
"a" being the slope, "b" being the y intercept (the y value when x = 0).
but since we have a point on the line and its slope, we can start with the point-slope form
y - y1 = a(x - x1)
"a"is again the slope, (x1, y1) is the given point.
and then we transform this into the slope-intercept form.
in our case we have
y - -1 = -3/2 × (x - 6)
y + 1 = -3x/2 + 18/2 = -3x/2 + 9
y = -3x/2 + 8
or
y = -3/2 x + 8
or
y = -1/2 × (3x - 16)
y varies directly with x .
If x=1 when y=5 , find y when x=3 .
After direct variation y = 15 when x = 3.
What exactly do we mean when we say "direct variation"?To give the reader a hint, direct variation equations use the same phrase.Either "directly proportional" or "directly varies" is the phrase.For example, the area of a square is proportional to the square of its side.The variational constant is k = 3 if y varies directly as x and y = 6 when x = 2.As a result, y = 3x is the direct variation equation.So,
The initial statement is y = kx
Then to find y when x = 3.
K constant will be y/x ⇒ 5/1That is y = kx ⇒ y = 5/1 × xWhen x = 3:
y = 5/1 × 3 ⇒ y = 15Therefore, after direct variation y =15 when x = 3.
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Determine if each statement is true or false. Justify your answer.
log₃3/2 = 1/2 log₃3
The logarithm statement log₃ 3 / 2 = 1 / 2 log₃ 3 is a false statement as 1 / 2 log₃ 3 is equal to log₃ √3 and not log₃ 3 / 2.
We are given the logarithm as:
log₃ 3 / 2 = 1 / 2 log₃ 3
We need to tell if it is true of not.
We get that, it is false as 1 / 2 log₃ 3 is equal to log₃ √3 and not log₃ 3 / 2.
So, the statement given will be a false statement.
Therefore, we get that, the logarithm statement log₃ 3 / 2 = 1 / 2 log₃ 3 is a false statement as 1 / 2 log₃ 3 is equal to log₃ √3 and not log₃ 3 / 2.
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quadrilateral A'B'C'D. Describe a sequence F. Quadrilateral ABCD is congruent to of rigid motions that takes A to A, B to B, C to C, and D to D. (Lesson 1-17) A' B' C' A D C B
The sequence of transformations that take quadrilateral ABCD to quadrilateral A'B'C'D' is given by:
Rotation 90º clockwise.Translation left.What are examples of transformations in the graph of a function?Examples of transformations are given as follows, along with explanations on the changes caused by the transformations.
Translation: Can be either left/right or down/up, changing the position of the figure.Reflections: Can be over one of the axes or over a line, changing the orientation of the figure.Rotations: Happens over a degree measure, changing the inclination, along with the orientation, of the figure.Dilation: Happens when the coordinates of the vertices of the original figure are multiplied by the scale factor, changing the side lengths of the figure.As a dilation changes the side lengths the figure, a dilated figure is not congruent to the original figure, hence a dilation does not happen for this problem.
The first change was in the inclination and orientation of the figure, hence it underwent a rotation. From the movement of the vertices, for example, A to the bottom to the top, B from right to left, the rotation was of 90º clockwise.
Then, the function had the base at the same position, however it moved left, hence the second transformation was a translation left.
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Given a term in the sequence and the common ratio find the first term:
Please show work!! ASAP!! I’m desperate
============================================================
Explanation:
[tex]g_3 = 6.25[/tex] tells us that the third term is 6.25
The common ratio r = 5/4 = 1.25 tells us how to get the next term. We multiply the third term by 1.25 to get the next term
4th term = (3rd term)*(r) = (6.25)*(1.25) = 7.8125
--------------
To go backwards and find the second term, we will divide by r, which is the inverse operation of multiplication.
2nd term = (3rd term)/r = (6.25)/(1.25) = 5
Use the same idea to find the 1st term
1st term = (2nd term)/r = 5/(1.25) = 4 is the final answer
The job paid 25$ for every 2 hours of work.
Write an equation that represents how much the job pays, y, for x hours of work
Answer:
$12.5xy
Step-by-step explanation:
y = how much the jobs pays
x = hours of work
25/2
= 12.5xy
Please help I will give brainliest
The congruent figures are given as follows:
LMNOP and YAHFS.EFCD and XUYW.MON and TUE.What are congruent figures?Congruent figures are figures whose outer side lengths have the same measures. They may have different orientations, but the outer side lengths have to be the same.
Hence the congruent figures in this problem are given as follows:
LMNOP and YAHFS.EFCD and XUYW.MON and TUE.They have different orientations(rotated), but same side lengths.
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Add or subtract if possible. 10√27 - 4√12
The subtraction of the expression 10√27 - 4√12 is 22√3.
Combining things and counting them as one big group is done through addition. In math, addition is the process of adding two or more integers together.
In mathematics, subtraction involves removing anything from a group or a number of objects. What is left in the group gets smaller when you subtract.
Consider the expression,
y = 10√27 - 4√12
Now, the number in the root can also be written as:
27 = 3 × 3 × 3
12 = 2 × 2 × 3
Therefore,
y = 10√27 - 4√12
y = 10[ √(3 × 3 × 3) ] - 4[ √( 2 × 2 × 3 ) ]
y = 10 × 3√3 - 4 × 2√3
y = √3 ( 10 × 3 - 4 × 2 )
y = √3 ( 30 - 8 )
y = 22√3
The value of the expression 10√27 - 4√12 is 22√3.
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Hi please help me!!!!!!
The slope and y-intercept of the line are -3 and -6 respectively.
How to find the slope and y-intercept of a line?The graph is a linear function.
The graph can be represented in a slope intercept form as follows;
y = mx + b
where
m = slopeb = y-interceptTherefore, using (1, -9)(-4, 6)
m = 6 - (-9) / -4 - 1
m = 6 + 9 / -5
m = 15 / -5
m = -3
Therefore,
slope = -3
Let's find the y-intercept as follows;
(1, -9)
y = -3x + b
-9 = -3(1) + b
b = -9 + 3
b = -6
Therefore, the slope and y-intercept of the line are -3 and -6 respectively.
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3 A trader buys some goods for $820. When he sells them, he makes a profit of 35%.
a Work out the profit, in dollars.
b Work out how much he sells them for
Based on the amount that the trader bought the goods for, when he sells them, he would make a profit of $287
The amount that the trader will sell the goods for is $1,107
How to find the dollar profit?The dollar profit that the trader will make from selling the goods is:
= Cost of the goods x Percentage profit
= 820 x 35%
= 820 x 0.35
= $287
The amount that the trader will sell the goods for is:
= Cost of the goods + Profit on the goods
= 820 + 287
= $1,107
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3(4x - 5) - 2 (x - 3) = 7
Can you please simplify this for me?
Step-by-step explanation:
12x - 15 - 2x + 6 = 7
10x - 9 = 7
10x = 16
x = 16/10
x = 8/5
Solve by substitution
3x-y=12
Y=4x-14
The value of x is 2 and the value of y is -6.
What is the solution of the equations?The substitution method is one of the methods used to solve simultaneous equations. It entails making one of the variables the subject of the equation in one of the equations.
Then the variable is substituted for in the first equation:
3x-y=12
Second equation :
1Y=4x-14
Substitute for y in equation 1 using equation 2 :
3x - (4x - 14) = 12 3x -4x + 14 = 12
Combine similar terms:
14 - 12 = 4x -3x
Add similar terms;
2 = x
Substitute for x in equation:
2y = 4(2) - 14 y = 8 - 14 y = -6
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The value of x is 2 and the value of y is -6.
What is the value of x and y?The substitution method is one of the methods that is used to solve for simultaneous equations. It entails making either of the variables the subject of the formula and then replacing for the variable in the other equation.
Other methods that can be used to solve simultaneous equations are the graph method and the elimination method.
3x - y = 12 equation 1
Y= 4x - 14 equation 2
y is the subject of the formula in equation 2
Substitute for y in equation 1
3x - (4x - 14) = 12
3x -4x + 14 = 12
Combine similar terms together:
14 - 12 = 4x -3x
Add similar terms together
2 = x
In order to determine the value of y, take the following steps
Substitute for x in equation 2
y = 4(2) - 14
8 - 14
y = -6
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Divide using long division or synthetic division:
(10x^3-x^2-29x-30)/(x^2-x-2)
Answer:
10 x^3 - x^2 - 29 x - 30 = (10 x + 9)(x^2 - x - 2) + -12
Step-by-step explanation:
Compute (10 x^3 - x^2 - 29 x - 30) ÷ (x^2 - x - 2) using polynomial long division:
x^2 - x - 2 | 10 x^3 | - | x^2 | - | 29 x | - | 30
To eliminate the leading term of the numerator, 10 x^3, multiply x^2 - x - 2 by 10 x to get 10 x^3 - 10 x^2 - 20 x. Write 10 x on top of the division bracket and subtract 10 x^3 - 10 x^2 - 20 x from 10 x^3 - x^2 - 29 x - 30 to get 9 x^2 - 9 x - 30:
| | | | | 10 x | |
x^2 - x - 2 | 10 x^3 | - | x^2 | - | 29 x | - | 30
| -(10 x^3 | - | 10 x^2 | - | 20 x) | |
| | | 9 x^2 | - | 9 x | - | 30
To eliminate the leading term of the remainder of the previous step, 9 x^2, multiply x^2 - x - 2 by 9 to get 9 x^2 - 9 x - 18. Write 9 on top of the division bracket and subtract 9 x^2 - 9 x - 18 from 9 x^2 - 9 x - 30 to get -12:
| | | | | 10 x | + | 9
x^2 - x - 2 | 10 x^3 | - | x^2 | - | 29 x | - | 30
| -(10 x^3 | - | 10 x^2 | - | 20 x) | |
| | | 9 x^2 | - | 9 x | - | 30
| | | -(9 x^2 | - | 9 x | - | 18)
| | | | | | | -12
The quotient of (10 x^3 - x^2 - 29 x - 30)/(x^2 - x - 2) is the sum of the terms on top of the division bracket. The remainder is the expression that remains after the final subtraction step.
| | | | | 10 x | + | 9 | (quotient)
x^2 - x - 2 | 10 x^3 | - | x^2 | - | 29 x | - | 30 |
| -(10 x^3 | - | 10 x^2 | - | 20 x) | | |
| | | 9 x^2 | - | 9 x | - | 30 |
| | | -(9 x^2 | - | 9 x | - | 18) |
| | | | | | | -12 | (remainder) invisible comma
(10 x^3 - x^2 - 29 x - 30)/(x^2 - x - 2) = (10 x + 9) - 12/(x^2 - x - 2)
Write the result in quotient and remainder form:
Answer: 10 x^3 - x^2 - 29 x - 30 = (10 x + 9)(x^2 - x - 2) + -12
An angle measures 138° less than the measure of its supplementary angle. What is the
measure of each angle?
The measure of each angle is 159° and 21°.
What are supplementary angles?When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together. The Latin word "angulus," which means "corner," is where the word "angle" originates.Two angles are considered to be supplementary if their sums total 180 degrees. For instance, angle 130° and angle 50° are complementary angles since the sum of these two angles is 180°.So, supplementary angles = 180
Then,
2x + 138 = 1802x = 180 - 1382x = 42x = 2121 + 138 = 159Therefore, the measure of each angle is 159° and 21°.
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Your friend invested $1000 in an account that pays 6% annual interest. How much interest will your friend have after her college graduation in 4 years?
c. Is the solution of the equation the final answer to the problem?
The solution of the equation is the final answer to the problem , $ 240 .
Calculating Simple Interest :
Simple Interest = ( P * R * N ) / 100
where P = Principal Amount
R = Rate of Interest
and N = No. of years for which investment is done
According to question :
P = 1000
R = 6
N = 4
Hence ,
Simple Interest = ( 1000 * 6 * 4 ) / 100
= 240
Therefore , after college graduation in 4 years the interest received would be $240 .
The solution of the equation is the final answer to the problem .
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please help im giving 60 points on my most recent question earn another 10 here :D
Find the midpoint given the endpoints:
(___),(___)
Note: 1.5 = 3/2
=======================================================
Explanation:
The two points shown on the graph are located at (-3, -2) and (1, 5)
Let's focus on the x coordinates for now.
To find the midpoint of -3 and 1, we do two things in the order shown
Add up the values: -3+1 = -2Divide in half: -2/2 = -1Therefore, -1 is the midpoint of -3 and 1 on the number line.
It is also the x coordinate of the midpoint.
------------
Repeat these steps for the y coordinates of the given points.
Add: -2+5 = 3Divide in half: 3/2 = 1.5This is the y coordinate of the midpoint.
-------------
The midpoint overall is located at (-1, 1.5)
I used GeoGebra to confirm the answer as correct.
Please help!!! 4(3x + 2)= -76, show your work pleaseee!!!
Answer:
x=-7
Step-by-step explanation:
Divide both sides by 4: 4(3x+2)/4=-76/4
Simplify; 3x+2=-19
Subtract 2 from both sides: 3x+2-2=-19-2
Solve:3x=-21
divide side by 3: 3x/3=-21/3
simplify: x=-7 B)
Answer:
x = -7
Step-by-step explanation:
Given equation:
[tex]4(3x+2)=-76[/tex]
Distribute:
[tex]\implies 4 \cdot 3x+4 \cdot 2=-76[/tex]
[tex]\implies 12x+8=-76[/tex]
Subtract 8 from both sides:
[tex]\implies 12x+8-8=-76-8[/tex]
[tex]\implies 12x=-84[/tex]
Divide both sides by 12:
[tex]\implies \dfrac{12x}{12}=\dfrac{-84}{12}[/tex]
[tex]\implies x=-7[/tex]
Determine if each statement is true or false. Justify your answer.
log₂4+log₂8=5
The statement [tex]log_{2} 4 + log_{2} 8 = 5[/tex] is true.
We have been given two logarithm terms that is the first term is [tex]log_{2} 4[/tex] and second term is [tex]log_{2} 8[/tex].
The properties of logarithm that we are going to use are
[tex]log a^{m} = m *log a[/tex] and [tex]log_{a} a = 1[/tex]
First we will find the value of the two terms by operating the above mentioned properties of logarithm to obtained the values of the logarithm.
Thus,
[tex]log_{2} 4 = log_{2} 2^{2} \\ = 2* log_{2} 2\\ = 2*1\\ = 2[/tex]
Similarly,
[tex]log_{2} 8 = log_{2} 2^{3} \\ = 3* log_{2} 2\\ = 3*1\\ = 3[/tex]
Now adding both the terms by substituting its respective values which we have calculated above, we get
[tex]log_{2} 4 + log_{2} 8 = 2+3 = 5[/tex]
Thus, we have proved that R.H.S = L.H.S
Hence the statement is [tex]log_{2} 4 + log_{2} 8 = 5[/tex] is true.
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help me out asap pls
Answer:
I don't think any are parrallel.
Step-by-step explanation:
If you look at the angles, they are different. Just slightly. So the rays making the angles would be at different angles. If they were the same angles the rays making the angles would be the same not allowing them to touch making them parallel. But since they are not I don't think they are parallel.
Simplify each expression. Rationalize all denominators. 1-√3 x / √6 x
After simplifying and rationalizing the expression 1 - √ 3 x / √ 6 x, we get the result as - (√ 2 / 2) + (√6 / 6) x .
We are given the expression:
1 - √ 3 x / √ 6 x
We need to simplify each expression by rationalizing the denominator.
Multiply √ 6 in both numerator and denominator, we get that:
(1 - √ 3 x) / √ 6 x × ( √ 6 / √ 6)
We get that:
= (√ 6 - 3 √ 2 x) / 6 x
= - (√ 2 / 2) + (√6 / 6) x
Therefore, after simplifying and rationalizing the expression 1 - √ 3 x / √ 6 x, we get the result as - (√ 2 / 2) + (√6 / 6) x .
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An elementary school collected 1,705 bottles for a recycling program. A high school also collected some bottles. Both schools collected 3,627 bottles combined. How many bottles did the high school collect?
answer choices
5,332
5,333
2,122
1,922
The number of bottles collected by the high school is 1922 bottles since the total collected bottles is 3627.
What is total of all bottles collected by both groups?The total number of bottles collected by both elementary and high schools is 3627 bottles, which means that the number of bottles collected by the high school can be determined as the total bottles minus the ones collected by the elementary school:
bottles collected by high school = total bottes - bottles collected by elementary schoolbottles collected by high school = 3627 - 1705bottles collected by high school = 1922Find out more about subtraction on: brainly.com/question/134255
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Review the graph. A student spends 16.5 hours studying and receives a mark of 61.4%. Which statement describes this result?
Using the line of best fit, the correct statement that describes this result is given by:
D. The result is an outlier and there is no gap in the data.
What is the missing information?The statements are missing, and are given as follows:
A. The result is not an outlier and there is a gap in the data.
B. The result is not an outlier and there is no gap in the data.
C. The result is an outlier and there is a gap in the data.
D. The result is an outlier and there is no gap in the data.
What does the line of best fit mean?The line of best fit gives the expected exam score for a student that studies x hours. For example, for a student that studies 16 hours, the expected score is of 90.
The actual score is 61.4%, which is significantly less than the expected score, meaning that there is an outlier. However, there are no gaps in the data-set, as as the line considers students between 0 and 20 hours, and 16 is in this interval.
This means that option D is correct.
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What is the quotient of 1. 843\times 10^71. 843×10 7 and 4. 85 \times 10^44. 85×10 4 expressed in scientific notation?
The quotient of 1.843 × 10^7 and 4.85 × 10^4, expressed in scientific notation, is 3.8 × 10^2.
Scientific notation is a way of expressing a very large or a very small number that are too much to be written in decimal form. The scientific notation is represented as:
a × 10^b
where a is between 1 and 10 and b is an integer representing the number of zeros
To divide numbers in scientific notation,
1. Divide the decimal numbers.
1.843 ÷ 4.85 = 0.38
2. Subtract the exponents of your power of 10.
7 - 4 = 3
3. Place the new power of 10 with the decimal in scientific notation form.
0.38 × 10^3 = 3.8 × 10^2
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