Answer: =38x+16.
a_{\color{red}{8}}=(\color{blue}{3x-5}) + (\color{red}{8}-1)(\color{green}{5x+3})
a
8
=(3x−5)+(8−1)(5x+3)
a_{8}=3x-5+ 7(5x+3)
a
8
=3x−5+7(5x+3)
a_{8}=3x-5+35x+21
a
8
=3x−5+35x+21
Find the midpoint of the segment with the given endpoints.
(-2,2) and (10,0)
Answer:
I think it’s (4,1)
Solve system of equations.
1/2x-y=-1
x-2 y=5
Answer:
No solution the lines are parallel
Step-by-step explanation:
see picture for reference.
Determine the total number of roots f(x) = (3x^4 + 1)^2
[tex]f(x) = (3 {x}^{4} + 1) {}^{2} \\ f(x) = 0 \\ (3 {x}^{4} + 1) {}^{2} = 0 \\ 3x {}^{4} + 1 = 0 \\ 3x {}^{4} = -1 \\ x {}^{4} = \frac{ - 1}{3} [/tex]
[tex]f(x) \: admits \: no \: real \: roots[/tex]
Write the equation of the line that is perpendicular to y = 2x+4 and passes through the
point (-4,-1).
y =____________ X+
Answer: (Likely) y = -2x
Step-by-step explanation:
1. We know the line y = 2x + 4, it intersects 4 and it's rate of change is 2. We also know the point it is passing, (-4,-1).
2. With this info, It is best to confirm the slope is likely -2, since it is likely that lines when perpendicular are likely to be congruent.
3. So, how about the y intercept? Well, it's simple as well, we will substitute x for 0, and 2 times 0 equals 0, and y = 0, so the perpendicular line is y = -2x
richard cuts a $ 4\frac{1}{2} ~\text{ft} \times 7\frac{1}{2} ~\text{ft} \times 11\frac{1}{4}~ \text{ft}$ rectangular prism into congruent cubes without any part of the prism leftover. if he makes the cubes as large as possible, how many will he produce?
If he makes the cubes as large as possible, the maximum number of cubes is equal to 900 cubes.
How to determine the number of cubes?In order to determine the number of cubes that would be produced by Richard when the rectangular prism is cut into congruent cubes without any part of the rectangular prism leftover, we would make the edges of the cube 100 times larger and then evaluate:
Length of cube = 4 1/2 ft × 100 = 450 feet.Breadth of cube = 7 1/2 ft × 100 = 750 feet.Height of cube = 11 1/4 ft × 100 = 1125 feet.Note: The greatest common factor (GCF) of the dimensions above is 75.
Next, we would divide each of the dimension by 75:
Length of cube = = 450/75 = 6 feet.
Breadth of cube = 750/75 = 10 feet.
Height of cube = 1125/75 = 15 feet.
Therefore, the maximum number of cubes is given by:
Maximum number of cubes = 6 × 10 × 15
Maximum number of cubes = 900 cubes.
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Complete Question:
Richard cuts a 4 1/2 ft × 7 1/2 ft × 11 1/4 ft rectangular prism into congruent cubes without any part of the prism leftover. If he makes the cubes as large as possible, how many will he produce?
Find each quotient a7/12÷1/7b -0.05÷(5/8÷1/2) c6 1/4÷(-5/16) d-1÷-(10/13)
The quotient of the problem given are 49/12, -1/25, -20 and 13/10 respectively
These are the simple problems of fractions
A) 7/12 ÷ 1/7
7/12×7/1
49/12
B) -0.05 ÷(5/8 ÷ 1/2)
- 5/100 ÷ ( 5/8 ×2/1)
-5/100÷ (5/4)
-5/100 ×4/5
-1/25
C) 6 1/4 ÷(-5/16)
25/4 × (-16/5)
-20
D) -1 ÷(-10/13)
-1 ×(-13/10)
13/10
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2. Write an expression for the perimeter of a rectangle with a length of
(3x² + x + 2) and a width of (-x² – 5x + 1).
Answer:
2 × [(3x² + x + 2) + (-x² – 5x + 1)] =Step-by-step explanation:
Write an expression for the perimeter of a rectangle with a length of
(3x² + x + 2) and a width of (-x² – 5x + 1).
P = 2 × (L + W)
2 × [(3x² + x + 2) + (-x² – 5x + 1)] =
if you want the result:
4x²−8x+6
A triangle has an area of 15 square inches.
If the base is 5 inches, what is the height?
Draw the triangle and label its base and height with units
Answer:
The height is 5.
Step-by-step explanation:
Find this answer here in this link!
This is the correct answer
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A rectangular mat has an area of 7/12. the length of the mat is 5/6. what is the width of the mat
The width of the rectangular mat is 7/10 units.
We know that the area of rectangle is A = length × width
For given question,
Let w be the width of the rectangular mat and l be the length of the rectangular mat.
The length of the mat is 5/6.
⇒ l = 5/6
A rectangular mat has an area of 7/12.
⇒ A = l × w
⇒ 7/12 = 5/6 × w
⇒ w = 7/12 × 6/5
⇒ w = 7/10
Therefore, the width of the rectangular mat is 7/10 units.
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A television transmitter tower is 600 ft high. If the angle between the guy wire (attached at the
top) and the tower is 55.4°, how long is the guy wire?
Using trigonometric relations, we can see that the length of the wire is 1,454.5 ft.
How can we find the length of the wire?
We can think of this as a right triangle, such that the height of the tower is one of the legs, and the wire is the hypotenuse.
In this case, we know that the angle between the tower and the wire measures 55.4°, and the height is the adjacent cathetus to this angle.
Then we can use the relation:
cos(a) = (adjacent cathetus)/(hypotenuse)
Where:
a = 55.4°
adjacent cathetus = 600ft
hypotenuse = L = length of the wire.
Replacing that we get:
cos(55.4°) = 600ft/L
L = 600ft/cos(55.4°) = 1,454.5 ft
We conclude that the length of the wire is 1,454.5 ft.
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if <1 and <2 form a linear pair and m<1 is 18 degrees less than five times the measure of <2 find m<1
∠1 and ∠2 will have the values 33° and 147° respectively when they form a Linear Pair.
In the question, It is given that ∠1 and ∠2 form a Linear Pair.
So, ∠1 and ∠2 = 180°, Also it is stated that ∠1 is 18° lesser than 5 times ∠2.
Taking ∠2 = x we get ∠1 = 5x-18
Now for Linear Pair, we have ∠1 + ∠2 = 180°
putting values of ∠1 and ∠2 we get : (5x-18) + x = 180
Solving the equation => (5x-18) + x = 180 => 6x = 198
=> x = 33
Putting the value of x in both ∠1 and ∠2 we get :
∠2 = 33° and ∠1 = 5(33) - 18 => ∠1 = 147°
Hence, we get ∠1 and ∠2 measures 147° and 33° respectively.
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Please help with my math
Answer:
(0,-5)
(2,1)
5,3
Step-by-step explanation:
Salome's house went from a valuation of 4.5 million ZAR (South African Rand) on 1st January
2011, to 6 million ZAR on 1st January 2020.
If the value of the house compounded monthly, what was the annual rate of increase?
Give your answer as a percentage, correct to 1 decimal place.
Using compound interest, it is found that the annual rate of increase was of 3.10%.
What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which:
A(t) is the amount of money after t years. P is the principal(the initial sum of money). r is the interest rate(as a decimal value). n is the number of times that interest is compounded per year.For this problem, the parameters are given as follows:
t = 9, A(t) = 6, A(0) = 4.5, n = 12.
Hence we solve for r to find the interest rate as follows:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
[tex]6 = 4.5\left(1 + \frac{r}{12}\right)^{12 \times 9}[/tex]
[tex]1 + \frac{r}{12}\right)^{108} = 1.33[/tex]
[tex]\sqrt[108]{1 + \frac{r}{12}\right)^{108}} = \sqrt[108]{1.33}[/tex]
[tex]1 + \frac{r}{12} = (1.33)^{\frac{1}{108}}[/tex]
1 + r/12 = 1.0026.
r/12 = 0.0026
r = 12 x 0.0026
r = 0.031.
The annual rate of increase was of 3.10%.
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(1 + 2 × 3)² + 7
please helppppooppppppppp
Answer:
56
Step-by-step explanation:
(1+2*3)^2+7
(1+6)^2+7
7^2+7
49+7
56
Answer:
Step-by-step explanation:
Using PEMDAS, first find the product of the parentheses. 2*3=6. 1+6=7. 7² is 49. 49+7=56.
what three numbers come next in the sequence 1458,486,162,54? and how do you get these numbers?
Answer:
18,6,2
Step-by-step explanation:
To get from the first term to the second term we divide by 3 .
To get from the second term to the third term we divide by 3 .
So we continue this pattern to find the next 3 terms :
So 54 ÷ 3 = 18
18 ÷ 3 = 6
6 ÷ 3 = 2
Hope this helped and have a good day
16. SHORT RESPONSE The first story of a building is 24 feet high, and each
additional story is 18 feet high. Write an expression for the height to the top
of the nth story. Explain the meaning of each term in the expression
The height to the top of the nth story of the building is ( 24 + 18(n-1) ).
Height of first story of a building = 24 feet
Height of each additional story = 18 feet
Total number of stories in a building = n
The Height of first story of a building is fixed to be 24 feet and Height of each additional story is 18 feet. We first need to calculate total number of additional stories to write an equation.
The total number of additional stories = ( total number of stories in a building - 1) = (n-1)
The height of total additional stories = 18 (n-1)
Total height of the building = (Height of first story of a building + height of total additional stories) = ( 24 + 18(n-1) ).
The height to the top of the nth story of the building is ( 24 + 18(n-1) ).
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If two pounds of meat will serve 5 people, how many pounds will be needed to serve 13
people?
Answer:
Step-by-step explanation:
2 pounds / 5 people
x pounds / 13 people
2/5 pounds per person so 2/5 * 13 = 26/5
5 1/5 i think
sorry if its wrong
Answer: The answer of the question is 2 and 3/5.
Step-by-step explanation: Every pound of meat serves one person, because 10 divided by 2 people is 5. Then, there are 3 pieces of meat left over, and since every person eats 5/5, or 1 whole, then there are 3/5 pieces left over. You then add 2 and 3/5 together, getting your answer 2 3/5.
use vectors to prove that the line joining the midpoints of two sides of a triangle is parallel to the third side and half its length.
We have proved that the line joining the midpoints of two sides of a triangle is parallel to the third side and half its length by using a vector.
What do you mean by vector?A quantity or phenomenon with independent qualities for both magnitude and direction is called a vector. The term can also refer to a quantity's mathematical or geometrical representation. Velocity, momentum, force, electromagnetic fields, and weight are a few examples of vectors in nature. A quantity or phenomenon that just exhibits magnitude and no specific direction is referred to as a scalar. (Weight is the force produced by the acceleration of gravity acting on a mass.) Scalars include things like velocity, mass, electrical resistance, and hard disk storage space.
In the triangle ABC, D is the midpoint of AB, and E is the midpoint of AC.
Now, using the triangle rule for triangle ADE,
AE+AD = ED
And for triangle ABC,
CA+AB = CB
2AE+2AD = CB [as AD = 1/2AB and AE=1/2AC]
=> 2(AE+AD) = CB
=> 2ED = CB
=> ED = CB/2
We can write two vectors equal to each other with only difference in magnitude only when they are parallel, i.e., the angle between ED and CB is 0.
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A sample of n=225 scores has =103 and s2 =16. what is the sample standard deviation?
Based on the calculations, the sample standard deviation is equal to 4.
What is a z-value?A z-value is also referred to as a z-score or standard score and it can be defined as a measure of the distance between a raw score and the mean, when standard deviation units are used.
In Statistics, z-values can either be positive or negative and it can be calculated by using this formula:
[tex]Z=\frac{\bar x\;-\;u}{\delta}[/tex]
Where:
x is the sample mean or observed data.u is the mean.δ is the standard deviation.In Statistics, the standard deviation of a data sample is the square root of the variance and as such, this given by:
Note: Variance, δ² = 16
Taking the square root of the variance, we have:
Standard deviation, δ = √16
Standard deviation, δ = 4.
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Complete Question:
A sample of n=225 scores has [tex]\bar x[/tex] = 103 and δ² = 16. What is the sample standard deviation?
Marcie cooked dinner for herself. the original recipe has a serving size of 4 and requires four and four fifths pounds of chicken. how many pounds of chicken will be needed for a single serving? four fifths pounds three twenty fifths pounds one and one fifth pounds sixteen and four fifths pounds
One and one fifth pounds of chicken will be needed for a single serving.
What is Converting and Adjusting Recipes and Formulas?Adapting recipes to fit the requirements of various contexts is common. Changing the amount of individual servings a recipe yields is the most frequent cause for recipe modifications. A typical recipe, for instance, might be written to make 25 pieces. The recipe must be properly altered if a circumstance develops when 60 servings of the item are required.
Changes in portion sizes (which may entail adjusting the recipe's batch size) and improved use of the preparation tools available are two additional reasons to modify recipes (for example, you need to divide a recipe to make two half batches due to a lack of oven space).
4 servings requires 4 and 4/5th pounds = 4+4/5= 24/5 pounds
1 serving will require = 24/5 pounds / 4 = 6/5 = (1+1/5) pounds
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Answer: 1 1/5
Step-by-step explanation: I took the test
On a road map, the distance from City A to City B is 4 inches. The map scale is 1 inch = 20 miles. What is the actual distance, in miles, between City A and City B?
11. Put brackets into each of the following expressions to make it correct:
(a) 3+9/5-2x5=20
Answer:
(3+9)/(5-2)x5 = 20
Step-by-step explanation:
It's a rather tedious type of task, because there's no simple way to solve them, except kind of by brute force or by trial and error. Here we can start by noticing x5 at the end, so if we can force everything before to be 4 it's gonna be dandy:
can we add brackets to 3+9/5-2 to be equal to 4 (because 20 / 5)?
fortunately, 3+9 is 4 times more than 5-2, so (3+9)/(5-2) = 4
so (3+9)/(5-2)x5=20 is a correct solution
The diagram shows three lines with some marked angle measures.
?
?
70°
?
?
53°
?
Find the missing angle
measures marked with
question marks.
The first intersection of the geometric system generates two vertical angles of 70° and two vertical angles of 110° and the second intersection of the geometric system generates two vertical angles of 53° and two vertical angles of 127°.
How to determine the measures of the missing angles of a geometric system
In this question we have a geometric system generated by three lines, where two lines pass through the first lines and four angles are generated on each intersection. The measures of the missing angles can be found by the following concepts:
Vertical angles - Two angles opposite to each other have the same measure.Supplementary angles - Two angles adjacent to each other that a total measure of 180°.The first intersection of the geometric system generates two vertical angles of 70° and two vertical angles of 110° and the second intersection of the geometric system generates two vertical angles of 53° and two vertical angles of 127°.
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9. The table shows the relationship between the number of targets a person
hits in a game of laser tag and that person's score.
Targets hit
3
4 5 6
Score
8 16 24 32 40 48
0 1 2
0
The table shows relationship between the number of targets a person
hits in a game of laser tag and that score of that person. The table shows is a continuous graph.
What is a continuous function in a graph?As the name implies, a continuous function is one whose graph is continuous throughout without any pauses or leaps. To put it another way, we say that a function is continuous if we can draw the curve (graph) of the function without ever picking up the pencil. In calculus, learning about a function's continuity is crucial since without it, a function cannot be differentiated.
If a function's graph is a continuous curve without any holes, gaps, or breaks, it is said to be continuous.
Now,
x-axis on the graph show "Target hit" and y-axis shows "Score"
Graph the points using a graphing calculator.
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The complete question is:
"The table shows the relationship between the number of targets a person
hits in a game of laser tag and that person's score.
Target hit 0 1 2 3 4 5 6
Score 0 8 16 24 32 40 48"
I need help asap!!!!
Answer: The first one is correct.
Step-by-step explanation:
x = 3
y = -2
So: 2 x 3 + 2 x (-2) = 6 + (-12) = -6
The probability that Bob will make a free throw is 3/4 . What is the probability that Bob will make his next 2 free throws.
Answer:
9/16
Step-by-step explanation:
NEED HELP ASAP!!!!!!
Which inequality represents all the solutions of -2(3x + 6) ≥ 4(x + 7)?
A.
[tex]x > - 4[/tex]
B.
[tex]x \leqslant - 4[/tex]
C.
[tex]x \geqslant 8[/tex]
D.
[tex]x \leqslant 8[/tex]
THE ANSWER IS B.
Answer: Hope it helps!!
I believe it is B. as well
Desmos Graphing calculator is great for problems as well!
W X Y Z is a square. If W T=3 , find each measure. m∠WTZ
Step-by-step explanation:
In this exercise we have to use the knowledge of quadrilaterals to calculate the measures of each side of the square, in this way we can say that it will be valid:
Given in the exercise that each the value of:
WT=3
The diagonals of a square are congruent, and bisect each other, that will help to find:
Solve system of equations.
x+y=-6
2 x-y=3
The system of equations involving x + y = -6 and 2x - y = 3 has the solution x = -1 and y = -5.
A system of linear equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.
There are three methods that can be used to solve system of linear equations.
1. Elimination
2. Substitution
3. Graphing
Using substitution method, given two linear equations in x and y,
x + y = -6 (equation 1)
2x - y = 3 (equation 2)
Express y in terms of x in one of the equations,
x + y = -6 (equation 1)
y = -x - 6
and then substitute it in the 2nd equation.
2x - y = 3 (equation 2)
2x - (-x - 6) = 3
2x + x + 6 = 3
3x = 3 - 6
3x = -3
x = -1
Substituting the value of x in the equation of y,
y = -x - 6
y = -(-1) - 6
y = 1 - 6
y = -5
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Number 13 and 9 please
Answer:
9.5>6 41.8>0
Step-by-step explanation: