Answer:
-103/5Step-by-step explanation:
-5x-25=78
-5x-25+25=78+25
-5x=103
divide both sides by -5
-5x/-5 = 103/-5
x=-103/5
write the equation of a line that is parallel to y=1/2x+4 and goes thru the point(-3,4)
The standard form equation for a line passing through the point (-3, 4) and parallel to the line denoted by y = 1/2x+4 is 2y - x = 11.
The standard form equation
ax + by = c
Here a, b, and c are constants and therefore use the slope-intercept form.
y = mx + c ...... (1)
where m is the slope, b = y-intercept
y = 1/2x + 4
Slope (m) = 1/2
It passes through a line that has points (-3,4)
Let's find c by putting the value of x = -3 and y = 4 in equation (1).
4 = 1/2 (-3) + c
4 = -3/2 + c
c = 4 + 3/2
=> c = (8+3)/2
=> c = 11/2
Therefore,
y = 1/2x + 11/2
y = (x+11)/2
=> 2y - x = 11
2y - x = 11 is the standard form of the line that passes through (-3,4) and is parallel to the line represented by y = 1/2x+4.
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A bicycle wheel has diameter 66 cm. Find how many turns the wheel makes when the bicycle travels 400 metres.
The number of turns the wheel makes is 1.93 ≈ 2.
What is Turns?
This is referred to as a cycle. It is a unit of plane angle measurement that is equivalent to 2π radians, 360 degrees, or 400 gradians.
formular for calculating Turns:
Turns = Lenght
Circumference
Circumference of a circle, C= πD
Where,
Diameter=D
π =22/7
Calculating Circumference;
C= 22 * 66
7
=207.4
From the question:
D= 66cm
L =400m
Calculating Turns:
Turns = Lenght
Circumference
= 400m
207.4
Turns =1.93
Turns =1.93≈ 2
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PLEASE HELP find the measure of each marked angle
Step-by-step explanation:
When dealing with transversals, most angles either add to 180 or equal to each other. These angles form a linear pair so they add to 180
[tex](x + 1) + 4x - 36 = 180[/tex]
[tex]5x - 35 = 180[/tex]
[tex]5x = 215[/tex]
[tex]x = 43[/tex]
So
[tex]x + 1 = 43+ 1 = 44[/tex]
[tex]4(43) - 36 = 136[/tex]
Answer:
x + 1 = 44 degrees
4x - 36 = 136 degrees
Step-by-step explanation:
Since the lines are parallel, the angles are same-side-interior angles, which means they are supplementary and add up to 180:
x + 1 + 4x - 36 = 180
5x - 35 = 180
5x = 180 + 35
5x = 215
x = 43
x + 1 = 43 + 1 = 44 degrees
4x - 36 = 4(43) - 36 = 136 degrees
-8(1+4p) +7p =-25-8p
Answer:
p = 1
Step-by-step explanation:
Given equation,
→ -8(1 + 4p) + 7p = -25 - 8p
Let's solve for the value of p,
→ -8(1 + 4p) + 7p = -25 - 8p
→ -8 - 32p + 7p = -25 - 8p
→ -32p + 7p + 8p = -25 + 8
→ -17p = -17
→ p = (-17)/(-17)
→ [ p = 1 ]
Hence, the value of p is 1.
The coordinates of the vertices of a polygon are shown on the graph below.
What is the name of the polygon?
octagon
pentagon
quadrilateral
triangle
Answer:
Triangle
Step-by-step explanation:
It has three side unlike the others can't have three sides
Let a and b be real numbers where a b 0. Which of the following functions could represent the graph below?
O f(x) = x(x-a)³(x-b)³
f(x) = (x-a)²(x-b)4
f(x) = x(x-a)(x-b)²
The function that can represent the graph is the option;
f(x) = x²·(x - a)²·(x - b)⁴·(x - c)
What is Polynomial Function?A function that only uses non-negative integer powers or only positive integer exponents of a variable in an equation is referred to as a polynomial function.
As, the graph touches the at x axis by 3 points.
So, the graph has an even multiplicity at three points as x², (x - a)², and (x - b)⁴ .
Now, The function has a single zero or factor such as (x - c) in the first equation
So, The function that could represent the graph is the function
f(x) = x²·(x - a)²·(x - b)⁴·(x - c)
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Increase £16470.45 by 3.5%
Give your answer rounded to 2 DP
Answer:
it is £16490.36
Step-by-step explanation:
since £156.78 is 100%, £16470.45 by 3.5 is £16490.36
Answer:
it's 17,046.92
Step-by-step explanation:
that's what my calculations said
Which equations are true? Select all that apply. A. 66 ÷ 10 1 = 6 . 6 B. 660 ÷ 10 0 = 66 C. 6 , 600 ÷ 1 , 000 = 0 . 66 D. 0 . 66 ÷ 10 1 = 0 . 066 E. 6 ÷ 100 = 0 . 06
The equations 66 ÷ 10 = 6.6, 660 ÷ 10 = 66, 0.66 ÷ 10 = 0.066, and 6 ÷ 100 = 0.06 are true. which is the correct answer would be options (A), (B), (D), and (E).
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
A. 66 ÷ 10 = 6.6
66/10 = 6.6
This is the true equation.
B. 660 ÷ 10 = 66
660/10 = 66
This is the true equation.
C. 6,600 ÷ 1,000 = 0.66
This is not the true equation.
D. 0.66 ÷ 10 = 0.066
This is the true equation.
E. 6 ÷ 100 = 0.06
This is the true equation.
Thus, the equations 66 ÷ 10 = 6.6, 660 ÷ 10 = 66, 0.66 ÷ 10 = 0.066, and 6 ÷ 100 = 0.06 are true.
Hence, the correct answer would be options (A), (B), (D), and (E).
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Identify the graph of the equation of the form y=ax²+bx+c with a<0 and having two x-intercepts.
Choose the correct answer below.
E B
D A
C F
In the graphs given, only graph F has two x - intercepts and a < 0 i.e the graph is facing downwards or opens downwards
Graph of Quadratic FunctionThe graph of a quadratic function is called a parabola and has a curved shape. One of the main points of a parabola is its vertex. It is the highest or the lowest point on its graph. You can think of like an endpoint of a parabola.
In this question, we have to find the graph of a function f(x) that a < 0 and has two intercepts.
The easy features of this graph are
The graph must touch two opposite side on the x-axisThe graph must be facing downwardsIn the options given, only graph F has such features and it is the answer to the question.
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Solve ex = e2x + 5. Answers: A.) x = 10 B.) x = -5 C.) x = 5 D.) x = -2
The value of ex = e2x + 5 is -5.
What is mean by exponential function ?The mathematical expression f(x)=exp or ex denotes the exponential function. Unless otherwise stated, the term typically refers to the positive-valued function of a real variable. it can be extended to the complex numbers or adapted to other mathematical objects like matrices or Lie algebras.
A mathematical function with the formula f (x) = an x is an exponential function. where an is a constant known as the function's base and x is a variable. The transcendental number e, or roughly 2.71828, is the exponential-function base that is most frequently encountered.
Given ,
[tex]e^x=e^{2 x}+5[/tex]
By simplifying the exponential rule we get
x= -5
Therefore the value of [tex]e^x=e^{2 x}+5[/tex] is -5
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What value is needed to complete the square? Show all steps.
x^2 - 2x +__
In completing the square method, considering the equation X^2 - 2x + the number to be added should be 1 to make it a perfect square
How to know term that should addedThe standard quadratic equation is of the form
ax^2 + bx + c
The completing the square method is one of the methods of solving quadratic equations
The factor to be added to the equation while using the completing the square method is of the formula
(b / 2a)^2
compared to the equation in the problem X^2 - 2x +
= (b / 2a)^2
= (2 / 2)^2
= (1)^2
= 1
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When a number is decreased by 53%, the result is 30
f(x)=6x/5+3
Find the inverse of f(x)
f(x) can be written as y
y=6x/8
make x the subject
8y=6x
x= 8y/6
replace y with x and x with f(x)
answer:
f(x)-1 = 8x/6
"A toy rocket is shot vertically into the air from a launching pad 7 feet above the ground with an initial velocity of 72 feet per second. The height in feet, of the rocket above the ground at t seconds after launch is given by the function h(t)=-16 t²+72 t+7. How long will it take the rocket to reach its maximum height? What is the maximum height?
The rocket reaches its maximum height at second(s) after launch.
(Simplify your answer.)
The maximum height reached by the object is feet.
(Simplify your answer.)"
The time taken for the rocket to reach its maximum height by virtue of the information given is; 2.25 seconds.
The maximum height reached by the toy rocket is; 88 feet.
What is the maximum height reached by the rocket?It follows from the task content that the maximum height reached by the rocket is to be determined.
The given function is; h (t) = -16 t² + 72t + 7.
Since it follows from evaluation that; at maximum height, the rate of change of height to time is equal to 0.
Therefore; at maximum height;
h'(t) = 0
h'(t) = -32t + 72 = 0
-32t = -72
t = -72/-32
t = 2.25 seconds.
Therefore, the time taken for the rocket to reach its maximum height is; 2.25 seconds.
Also, the maximum height reached by the rocket is at; h (2.25);
h(2.25) = -16(2.25)² + 72 (2.25) + 7
= -81 + 162 + 7
= 88.
The maximum height reached is; 88 feet.
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6 times a numbeer is 7 less than the square of that number. find the positive solution?
The positive solution of the given condition is 7.
What is a quadratic equation?
A second-order polynomial equation with a single variable, x, is known as a quadratic equation.
i.e. [tex]ax^{2} +bx+c=0[/tex]
Let '[tex]x[/tex]' be a number, then
The six-times a number= [tex]6x[/tex]
&, the square of a number= [tex]x^{2}[/tex]
Now, according to the question,
or, [tex]6x = x^{2} -7[/tex]
or, [tex]x^{2} -6x-7=0[/tex]
or, [tex]x^{2} -7x+x-7=0[/tex]
or, [tex]x(x -7)+1(x-7)=0[/tex]
or, [tex](x -7)(x+1)=0[/tex]
Either, [tex](x -7)=0[/tex] or, [tex](x+1)=0[/tex]
[tex]x=7[/tex] [tex]x=-1[/tex]
Therefore, the positive solution is x = 7.
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Mindy owns 20 pairs of shoes and every week he purchases two more but destroys one. How long will it take for her closet to have 50 pairs of shoes.
Solve and write an equation.
Answer:
29 weeks---------------------
Initial number of pairs of shoes is 20.
To achieve 50 pairs Mindy needs 30 more pairs.
Each week 2 pairs added but 1 removed. It makes total of 1 pairs addition.
After 28 weeks Mindy will have 20 + 28 = 48 pairs of shoes.
The next week he will purchase 2 more pairs and get 50 pairs in total.
The number of weeks it will take for her closet to have 50 pairs of shoes would be = 30 weeks.
What is purchase price?A purchase price is the amount of money that was use to obtain a valuable.
The number of shoes owned by Mindy = 20 pairs
The number of shoes Mindy purchases per week = 2 pairs
The number of shoes Mindy destroys = 1 pair.
Therefore, in a week Mindy has an additional 1 pair of shoe.
The number of pairs she needs extra = 50-20 = 30
Since 1 pair of shoe = 1 week, she will require 30 weeks to purchase additional 30 pairs making it up to 50 pairs of shoes she owns.
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Based on a poll, 50% of adults believe in reincarnation. Assume that 7 adults are randomly selected, and find the indicated probability. Complete parts (a) through
(d) below.
a. What is the probability that exactly 6 of the selected adults believe in reincarnation?
The probability that exactly 6 of the 7 adults believe in reincarnation is
(Round to three decimal places as needed.)
The probability that exactly 6 of the selected adults believe in reincarnation is 0.055
What is binomial distribution?The binomial distribution is the discrete probability distribution used in probability theory and statistics that only allows for Success or Failure as the possible outcomes of an experiment. For instance, if we flip a coin, there are only two conceivable results: heads or tails, and if we take a test, there are only two possible outcomes: pass or fail. A binomial probability distribution is another name for this distribution.Here, a binomial distribution uses the two parameters n and p. The number of times the experiment is run is indicated by the variable "n," and the probability of each possible outcome is indicated by the variable "p."This will be a binomial distribution with parameters:
n = 7, p = 0.50
Hence,
a) P (Exactly 6)
= ⁷C₆(0.50)⁶ (0.50)¹
= 0.055
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Bro please help. Im so lost
Answer:
D: x≤-4
Step-by-step explanation:
If its not just reply to me and i will re asses
Answer:
3
Step-by-step explanation:
A group of 16 people is choosing a chairperson and vice-chairperson. They put all 16 people's names into a hat. The first name drawn becomes chair. The second name drawn becomes vice-chair. How many possible combinations of chair and vice-chair are there?
Answer: 240 combinations
Step-by-step explanation: So basically because you can have a possibility of 16 people being chairperson and 15 vice chairpersons, so all you have to do is multiple 16x15 which is 240.
(12x)
D
A
E
(17x - 14)°
В
(2x + 5)°
с
The value of x for the given equation (2x+5)=(17x-14) will be 19/15.
What is the equation?An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.
It is given that,
(2x+5)=(17x-14)
We have to rearrange the equation by applying the arithmetic operation for the like term, the terms which are similar, and we can perform arithmetic operations on it like addition and subtraction.
17x-2x=5+14
15x=19
x=19/15
Thus, the value of x for the given equation (2x+5)=(17x-14) will be 19/15.
The question is incomplete, the complete question is"solve the value of x for the given equation,
(2x+5)=(17x-14)
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Find m and c for this line
Y+3x=1
Answer:
m = -3 ; c = 1
Step-by-step explanation:
y = -3x + 1
y = mx + c
m = -3
c = 1
Really quick! Need help...and will give brainliest to the first correct answer.
Answer:
[tex]x + 3y = -30:[/tex] Perpendicular to line a
[tex]y = \frac{1}{3} x + 1 :[/tex] Neither Parallel nor Perpendicular to line a
[tex]-3x + y = -2 :[/tex] Parallel to line a
Explanation:
[tex]-3x + y = -4\\y = 3x - 4[/tex]
[tex]x + 3y = -30\\3y = x - 30\\y = \frac{1}{3} x - 10[/tex]
[tex]y = \frac{1}{3} x + 1[/tex]
[tex]-3x + y = -2\\y = 3x - 2[/tex]
Using the declining-balance method, complete the table as shown (twice the straight-line rate): (Enter your answers as a whole dollar amount.) Auto $29,000 5 years Residual $2,000 Year Cost Accumulated Depreciation B.O.Y Book Value B.O.Y Depreciation Expense Accumulated Depreciation E.O.Y Book Value E.O.Y 1 A B C D E F 2 G H I J K L 3 M N O P Q R
Using the double-declining-balance method of depreciation, the completion of the table as shown is as follows:
Year Cost Accumulated Book Value Depreciation Accumulated Book
Depreciation B.O.Y Expense Depreciation Value
B.O.Y E.O.Y E.O.Y
1 $29,000 $0 $29,000 $11,600 $11,600 $17,400
2 $29,000 $11,600 $17,400 $6,960 $18,560 $10,440
3 $29,000 $18,560 $10,440 $4,176 $22,736 $6,264
What is the double-declining-balance method?
The double-declining-balance method is one of the depreciation methods in use, but it allocates more cost to the earlier years of the asset's life.
This depreciation method uses twice the straight-line rate, which is computed as the product of 100/estimated useful life multiplied by 2.
For each year's depreciation expense, the double rate is applied at the end of the year's balance.
For the last year, the difference between the previous year's ending balance and the residual value is taken as the depreciation expense.
Auto = $29,000
Estimated useful life = 5 years
Residual = $2,000
Depreciable amount = $27,000 ($29,000 - $2,000)
Straight-line depreciation rate = 20% (100/5)
Double-declining depreciation rate = 40% (20% x 2)
Depreciation Expense:
1st year = $11,600 ($29,000 x 40%)
2nd year = $6,960 ($17,400 x 40%)
3rd year = $4,176 ($10,440 x 40%)
4th year = $2,506 ($6,264 x 40%)
5th year = $1,758 ($3,758 - $2,000)
Year Cost Accumulated Book Value Depreciation Accumulated Book
Depreciation B.O.Y Expense Depreciation Value
B.O.Y E.O.Y E.O.Y
1 $29,000 $0 $29,000 $11,600 $11,600 $17,400
2 $29,000 $11,600 $17,400 $6,960 $18,560 $10,440
3 $29,000 $18,560 $10,440 $4,176 $22,736 $6,264
4 $29,000 $22,736 $6,264 $2,506 $25,242 $3,758
5 $29,000 $25,242 $3,758 $1,758 $27,000 $2,000
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Solve the equation 42 = v + 35 for v.
A. −77
B. 77
C. −7
D. 7
Answer:
v = 7
Step-by-step explanation:
42 = v + 35
-35 -35
7 = v
The answer is D. 7
I took the quiz and got it right
7 is what percent of 77? please with work!!!
Answer:
5.39
Step-by-step explanation:
Answer: 9.09%
that is the answer
Jorani buys [tex]8\frac{1}{3}[/tex] bolts of fabric. Each bolt has 24m of fabric. The fabric costs $1.65/m. Determine the total cost of the fabric.
The total cost of the fabric Jorani bought is 330 dollars.
How to find the total cost of the fabric?Jorani buys [tex]8\frac{1}{3}[/tex] bolts of fabrics. Each bolt has 24m of fabric. The fabric costs $1.65 per metres. The total cost of the fabric can be calculated as follows:
1 bolt = 24 metres
25 / 3 bolt = ?
cross multiply
length of the fabrics = 25 / 3 × 24
length of the fabrics = 600 / 3
length of the fabrics = 200 metres
Therefore,
1 metres = 1.65 dollars
200 metres = ?
cross multiply
cost of the fabric = 200 × 1.65
cost of the fabric = 330 dollars
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20. To calculate your electric bill for your home, DTE uses the following equation: C = 5 + 4e where C is how much they charge you and e is the amount of electricity used measured in kilowatt-hours (kwh) used.
a. Does this situation represent a linear function? Explain.
b. Find the domain of the function. Is the domain discrete or continuous? Explain.
c. Graph the function using its domain.
Considering the function C = 5 + 4e, it is found that:
a. The situation represents a linear function, as the increase in the price is constant for each kwh hour used.
b. The continuous domain of the function is: e ≥ 0.
c. The graph of the function is given by the image shown at the end of the answer.
What is a linear function?A linear equation is a special function that has the format of the equation given as follows:
y = mx + b.
The coefficients of the equation y = mx + b are given as follows:
m is the slope, representing the rate of change of y relative to x.b is the y-intercept, representing the value of y when x = 0.For this problem, the function is:
C(e) = 5 + 4e.
Which is a linear function, as it follows the same format of the general linear function, with a constant cost of 4 per each kwh used.
The domain of the function contains the set of all possible input values of the function. Hence, in this problem, it is composed by the amounts of kwh used, which:
Is a continuous amount, as it can assume decimal values.Cannot assume decimal values.Hence the domain is:
e ≥ 0.
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from the package. What fraction shows what part of the package they have eaten? Sofia's family buys little boxes of cereal in a package containing 10 boxes. They have eaten 6 boxes of cereal from the package.What f fraction shows what part of the packages they have eaten .
The fraction which shows what part of packages they have eaten is 3/5.
What is fraction?
A fraction is characterized as a portion of something larger. Fractions make calculations quicker and easier by making it easier to distribute and judge numbers.
Main Body:
Total no. of boxes of cereals in a package = 10
Total no. of boxes eaten by family = 6
Fraction can be calculated by directly by diving the values.
Fraction ⇒ 6/10
dividing by 2 on both denominator and numerator
hence, Simple fraction is 3/5.
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The ratio of girls to boys in the school is 3 to 1. If there is a total of 400 students, how many are boys? The answer must be a whole number.
Step-by-step explanation:
girls:boys
3:1
total=400
1/3 × 400
400/3
=133.33
to whole number
=133 boys
Answer:
The correct answer is 100
Part A: Timothy said that AKLM was dilated by a scale factor of 1.5 centered at the origin. Is Timothy CORRECT? Explain your answer or show your work.
Yes Timothy is correct because triangle AKLM was dilated by a scale factor of 1.5 centered at the origin.
What is dilation?In Geometry, dilation simply refers to a type of transformation which changes the size of a geometric object based on the scale factor, but not its shape.
For the given vertices of triangle KLM, the dilation with a scale factor of 1.5 from the origin (0, 0) or center of dilation should be calculated as follows:
Point K (-1, 3) → Point K' (-1 × 1.5, 3 × 1.5) = Point K' (-1.5, 4.5).
Point L (8, 4) → Point L' (8 × 1.5, 4 × 1.5) = Point L' (12, 6).
Point M (10, -3) → Point M' (10 × 1.5, -3 × 1.5) = Point M' (15, -4.5).
In conclusion, the coordinates of the image triangle K'L'M after a dilation with a scale factor of 1.5 from the origin are (-1.5, 4.5), (12, 6), and (15, -4.5) as shown in the graph, and as such Timothy is correct.
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