Answer:
[tex] \sf \large \: a = \frac{ - 1}{4} [/tex]
Step-by-step explanation:
Let's solve your equation step-by-step.
3/a(−2)−4=20
−4a−6/a=20
Step 1: Multiply both sides by a.
−4a−6=20a
−4a−6−20a=20a−20a(Subtract 20a from both sides)
−24a−6=0
−24a−6+6=0+6(Add 6 to both sides)
−24a=6
−24a/−24=6/−24
(Divide both sides by -24)
a=−1/4
Check answers. (Plug them in to make sure they work.)
a=−1/4
(Works in original equation)
a wire rope sling with a strength of 10,000 pounds and a total working load of 2,000 pounds has a design factor (multiplier) of .
According to the given statement the a wire rope sling with a strength of 10,000 pounds and a total working load of 2,000 pounds has a design factor of 5.
How is the design factor determined?Dividing the ultimate (or maximum) stress by both the normal (or working) stress yields a relatively simple equation to determine FoS. A structure but rather component with an FoS of 1 will fail precisely when it meets the design load and is unable to support any extra load.
Briefing:A wire rope sling, for example, with such a strength exceeding 10,000 pounds (4,545 kilograms) and a total process load of 2,000 pounds (909 kilograms), has a design factor (multiplier) of 5. Currently available wire rope slings have a design factor of 5.
In order to take into account uncertainty regarding the load, the structural qualities, or both, a design factor1 is a tolerance added to a load and structural strength. Design considerations have typically been applied to the size of the load while designing oilfield casing.
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8|x-2|=2 solve for x
Answer:
Step-by-step explanation:
on a straight highway, the distance from loretta’s house to a park is 43 miles. her friend jamal lives along this same highway between loretta’s house and the park. the distance from loretta’s house to jamal’s house is 31 miles. how many miles is it from jamal’s house to the park? miles
Distance between Jamal's house and the park = 12 miles
Given distance from Loretta's house to the park = 43 miles
Distance from Loretta's house to Jamal's house = 31 miles.
Jamal's house is in between Loretta's house and the park.
Let 'x' be the distance from Jamal's house to the park.
So the distance between Loretta's house and the park is more than the distance from Jamal's house and the park.
Also the distance from Loretta's house to the park is the sum of the distance from Loretta's house to Jamal's house and the distance from Jamal's house to the park.
i.e., 43 = x + 31
Therefore, x = 43 - 31
= 12 miles
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Find x from this parallelogram
The value of x in the given parallelogram is: x = 90°.
What is a Parallelogram?A parallelogram is a quadrilateral with four interior angles and four sides, whose opposite angles are equal to each other.
In the image given:
Angle A = 120°
Since ABCD is a parallelogram, therefore, the angle that is opposite to angle A would also be 120°. Therefore:
Angle C = 120°
Angle D = 180 - 120 = 60°.
Angle DCO = 1/2(angle C) = 1/2(120) = 60°
Angle CDO = 1/2(angle D) = 1/2(60) = 30°
x = 180 - m<DCO - m<CDO [triangle sum theorem]
Substitute
x = 180 - 60 - 30
x = 90°
Therefore, the value of x in the given parallelogram is: 90°.
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of the following integers, which is the closest approximation to open paren the square root of 2 plus the square root of 5 close paren squared ?
The closest approximation of (√2 + √5)² is 13.
What is the rule of approximation?If you want to round to one or two decimal places, look at the digit immediately after the decimal point. To the right of the necessary place value digit, draw a vertical line. Observe the following digit. Increase the preceding digit by one if the next digit is 5 or higher.
According to the question, we are Given,
(√2 + √5)²
⇒ 2 + 5 + 2(√2)(√5) (using (a+b)² = a² + b² + 2ab)
⇒ 7 + 2√10
⇒ 7 + 2 × 3.16
⇒ 7 + 6.3
⇒13.3
So, our answer is closest to 13.
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In the circle, BC is a diameter. What is the measure of x?
The measure of the angle x is 22.5 degrees
Circle geometryCircle theorem includes the concept of tangents, sectors, angles, the chord of a circle and proofs.
A circle is the locus of all points in a plane which are equidistant from a fixed point
From the given diagram
arc AC = 180 - 135
arcAC = 45 degrees
Since the angle at the vertex is half the intercepted arc, hence;
x = 1/2(arc AC)
x = 1/2(45)
x = 22.5 degrees
Hence the measure of the angle x is 22.5 degrees
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A bank offered a money market account with an APY of 3.227%.
A) If interest is compounded monthly, what is the equivalent annual nominal rate?
B) If you wish to have $10,000 in this account after 6 years, what equal deposit should
you make each month?
Step-by-step explanation:
A bank offered a money market account with an APY of 3.227%.
A) If interest is compounded monthly, what is the equivalent annual nominal rate?
B) If you wish to have $10,000 in this account after 6 years, what equal deposit should
you make each month?
If katya takes a trip of 600miles how many gallons of gas would be needed to make the trip
So Katya needs 21.42 gallons of gas for 600 miles.
A Linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.
Given we have Katya have to take a trip for 600 miles.
Let x be number of gallons of gas y be number of miles driven by Katya
We have an relation from table that 28X = Y and Y we have from table 600
So 28X = 600 and [tex]X = \frac{600}{28}[/tex]
X= 21.42 gallons .
Therefore Katya needs 21.42 gallons of gas for 600 miles.
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Mandisa draws a rectangle to represent the area of her yard. The area can be represented by 10x2 – 13x – 14.What expressions can Mandisa use to represent the length and width of her yard?
(2x + 2) and (5x – 7)
(5x – 2) and (2x + 7)
(x – 2) and (10x + 7)
(10x + 2) and (x – 7)
Answer: (x–2) and (10x+7)
Step-by-step explanation:
10x^2 – 13x – 14=
10x^2 – 20x + 7x – 14=
10x(x–2) + 7(x–2)=(x–2)(10x+7) ==> 3rd option
5t+3t=100
what is t?
Answer:
t=12.5
Step-by-step explanation:
First of you're going to combine liked terms, (5t+3t) to get 8t. You want to get t isolated so you're going to divide it by 8 to get t by itself, you are also going to do 100 divided by 8 because to remain equal you have to do the math on both sides.
34.
Match each equation with the corresponding equation solved for a.
A. a + 2b = 5
1.a=2/
B. 5a = 2b
2.a ==
C.a +5=2b
3. a = -2b
D. 5(a + 2b) = 0
4. a=2b-5
E. 5a + 2b =0
5. a=5-2b
Based on the solution below, we have:
A. a + 2b =5 corresponds to 5. a = 5 - 2b;
B. 5a = 2b corresponds to 1. a = 2b/5;
C. a + 5 = 2b corresponds to 4. a = 2b - 5;
D. 5(a + 2b) = 0 corresponds to 3. a = -2b; and
E. 5a + 2b=0 corresponds to 2. a = -2b/5.
How do we solve an equation for a variable?For clarity purposes, the equations in the question are restated as follows:
A. a + 2b = 5 1. a = 2b/5
B. 5a = 2b 2. a = -2b/5
C. a + 5 = 2b 3. a = -2b
D. 5(a + 2b) = 0 4. a = 2b-5
E. 5a + 2b =0 5. a = 5-2b
A. From the equation a + 2b = 5, a can be solved as follows:
a + 2b = 5
a = 5 - 2b
B. From the equation 5a = 2b, a can be solved as follows:
5a = 2b
a = 2b/5
C. From the equation a + 5 = 2b, a can be solved as follows:
a + 5 = 2b
a = 2b - 5
D. From the equation 5(a + 2b) = 0, a can be solved as follows:
5(a + 2b) = 0
5a + 10b = 0
5a = -10b
a = -10b/5
a = -2b
E. From the equation 5a + 2b =0, a can be solved as follows:
5a + 2b =0
5a = -2b
a = -2b/5
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Let f(x)=5x-6. Write a function g whose graph is horizontal shrink of the graph of f by a factor of 1/4
The transformed function is g(x)=
The transformed function is g(x) = 20x-6.
The graph of the function y=f(ax) represents a Horizontal Shrink by a factor of "1/a" of the graph y=f(x) .
To find the horizontal shrink by a factor of 1/a we multiply the input by a .
In the given question
f(x)=5x-6 , is horizontally shrink by a factor of 1/4.
So we multiply the inputs by 4 .
On multiplying the inputs by 4 , we get
f(4x)=5(4x)-6 (...as 5*4=20)
Let g(x) represents the horizontal shrink of f(x) by factor 1/4 , So
g(x)=20x-6
Therefore , the horizontal shrink of the graph of f by a factor of 1/4 is g(x)=20x-6.
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The population of the town Val lives in is about 8*10 to the power of 3.The population of the town that Vic lives in is about 6*10 tot he power of 4.Whose town has the greater population?By how many people?
The population of town Vic is greater than population of town Val by 52000 .
In the question ,
it is given that
the population of town Val = 8x10³
the population of town Vic = 6x10⁴
Rewriting both the numbers we get
population of town Val = 8x1000 = 8000
population of town Vic = 6x10000 = 60000
It can be clearly seen that 60000 > 8000
So the population of Vic > population of Val
To calculate the difference subtract the population of Val from population of Vic .
Substituting the values of population we get ,
difference = 60000 - 8000
= 52000
Therefore , the population of town Vic is greater than population of town Val by 52000 .
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under which conditions does the commutative property apply to compositions of f(x) and g(x)?when f(g(x)) and g(f(x) are inverse functionswhen f(g(x)) and g(f(x) are equal for at least one value of xwhen f(g(x)) and g(f(x) are equal for all values of xwhen f(g(x)) and g(f(x) are not inverse functi
The commutative property apply to compositions of f(x) and g(x) when f(g(x)) and g(f(x)) are equal for all values of x.
The commutative property says that [tex]a*b=b*a[/tex] , for any binary operation [tex]'*'[/tex]. These binary operations can be addition, multiplication, function composition, etc. But subtraction and division does not follow commutative property.
Here the operation is composition of two functions defined as,
[tex](fog) (x)= f(g(x))[/tex] ,where f and g are two functions.
Then the function composition has commutative property when
[tex]fog = gof[/tex].
That is, when f(g(x)) = g(f(x))
This means that the commutative property apply to the composition of functions, f(x) and g(x) when f(g(x)) and g(f(x) are equal for all values of x.
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Find the 6th term of the arithmetic sequence x+2, -6x-3, -13x-8,...
Answer:
-21x-13
Step-by-step explanation:
That is all you need
An angle is 134.2 more than the measure of its supplementary angle
Supplementary angles are two angles whose measures add up to 180°. If An angle is 134.2 then other angles are 22.9.
What are supplementary Angles?Supplementary angles are two angles whose measures add up to 180°
Supplementary angles are those that add up to 180.
supplementary angle: x
an angle: x+134.2
and together they must measure 180:
x+x+134.2 = 180
2x+134.2=180
2x=180-134.2
2x=45.8
x=22.9
This is the supplementary angle the other angle is 22.9+134.2 = 157.1
Thus the the angle of each is 22.9.
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(x+7)+(3x-11)=180
what would be the answer
in a right triangle, the longest side opposite the right angle is called the hypotenuse and the other two sides are called ---select--- .
The right angle is called the hypotenuse and the other two sides are called adjacent and opposite.
Right angle triangleA right angled triangle is a triangle that has 3 sides and angles. For a right angled triangle, one of the angles is 90 degrees.
The longest side of the triangle is hypotenuse and the other two sides are known as the adjacent and opposite.
Hence in a right triangle, the longest side opposite the right angle is called the hypotenuse and the other two sides are called adjacent and opposite.
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Weighs 2 grams per milliliter of volume. Express this density in kilograms per pint. Round your answer to the nearest hundredth
This density in kilograms per pint is 0.946.
Important conversions:
1 gram = 0.001 kilogram
1 ml = 0.001 litres
1 pint = 0.473 litres
1 litre = 2.113 pints
Step 1 : Convert 2 grams per millilitre of volume (2 g/ml) into kilograms per litre (kg/l)
Divide 2 grams per millilitre (g/ml) by 0.001 and multiply with 1000 to get the density in kilograms per litre (kg/l)=> (2 x 1000)/ (0.001) = 2 kg / l
Therefore, we get the density in kilograms per litre (kg/l) as 2 kg/l.
Step 2 : Convert the density in kilogram per litre (kg/l) into kilograms per pint (kg/pint)
Multiply 2 kilograms per litre with 0.473 to get the density in kilograms per pint=> 2 x 0.473 = 0.946 kg/l
Therefore, by converting 2 grams per millilitre of volume into kilograms per pint, we get the density as 0.946 kg/pint.
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help me again now i will have a little more
Using the average rate of change, it is found that snow was falling at a rate of 0.1 inch an hour during the first period.
What is the missing information?This problem is incomplete, but researching it on a search engine, it asks the rate at which snow was falling during the first period.
What is the average rate of change of a function?The average rate of change of a function is given by the change in the output divided by the change in the input. Hence, over an interval [a,b], the rate is given as follows:
[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]
From the graph, the first period is until the 10th hour, hence:
f(0) = 1.f(10) = 2.The rate is:
r = (2 - 1)/(10 - 0) = 0.1.
Hence snow was falling at a rate of 0.1 inch an hour during the first period.
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At a local farmers market, Jose bought a watermelon that weighted 83.2 ounces.
Watermelon cost $1.35 per pound
There are 16 ounces in a pound
How much did Jose watermelon cost?
Answer:
The watermelon's price was $7.02
Step-by-step explanation:
83.2 ounces= 5.2 pound
The watermelon that Jose bought weights 5.2 pounds
If 1 pound= $1.35
5.2= $7.02
write a function of g whose graph represents the indicated transformation
f(x)=-|8x|-4 vertical shrink by 1/4
The function of g whose graph represents the indicated transformation is g(x) = -|2x| - 1
How to write a function of g whose graph represents the indicated transformation?The function is given as
f(x) = -|8x| - 4
The transformation is given as
A vertical shrink by 1/4
This is represented as
g(x) = 1/4f(x)
So, we have
g(x) = 1/4 * (-|8x| - 4)
Evaluate
g(x) = -|2x| - 1
Hence, the function of g whose graph represents the indicated transformation is g(x) = -|2x| - 1
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two numbers are 10 units away in different directions from their midpoint, m, on a number line. the product of the numbers is –99. which equation can be used to find m, the midpoint of the two numbers? (m – 5)(m 5)
The mid point of equation is [tex]m^{2} - 100 = -99[/tex].
The Midpoint is the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints. It bisects the segment.
We have been given that two numbers are 10 units away in different directions from their midpoint, m, on a number line.
The two numbers that are 10 units away indifferent directions would be (m - 10) and(m+10).
The product of both number would be(m -10)(m + 10) .
Since the product of both numbers is -99, so we can represent this information in an equations (m -10)(m + 10) = -99.
Let us simplify our equation using difference of squares[tex](a + b)(a - b) =a^{2} - b^{2}[/tex]
as: [tex]m^{2} - 10^2= -99[/tex]
[tex]m^{2} - 100 = -99[/tex]
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an ordered pair of real numbers can be represented in a plane called the rectangular coordinate system or the ---select--- plane.
Coordinate plane is the answer of this problem.
A Coordinate plane is a two-dimensional plane formed by the intersection of two number lines. One of these number lines is a horizontal number line called the x-axis and the other number line is a vertical number line called the y-axis
We have been given real numbers A number is real that has no imaginary part the set of all real numbers comprises the rational and the irrationals.
A Cartesian coordinate system in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in the same unit of length.
So therefore an ordered pair of real numbers can be represented in a plane called the rectangular coordinate system or the Coordinate plane.
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Use matrices A and B. Compute B - A, if you can. (1 point)
f(3)=4x-5 please solve for f(3) pleaseeeeeeeeeee
Answer:
7
Step-by-step explanation:
f(x)=4x-5
f(3)=4(3)-5
f(3)=12-5=7
When a company first started it had 85 employees. It was decided to increase the number of employees by the 10 at the beginning of each year. PLs help me with this question!!!
a. Find the number of employees during the second year and during the third year
b. How many employees will this company have during the 10th year?
c. After how many years will the company have 285 employees?
Answer:
a. 105 and 115 employees
b. 185 employees
c. 20 years
Step-by-step explanation:
The total of employees at any given year is y
x is the number of year
then y = 85 + 10x
a. 2nd year: y = 85 + 10(2) = 85 + 20 = 105
3rd year: y = 85 + 10(3) = 85 + 30 = 115
b. 10th year: y = 85 + 10(10) = 85 + 100 = 185
c: if y = 285
285 = 85 + 10x
10x = 285 - 85
10x = 200
x = 20
you have to round to the nearest cent (??)
The exponential functions to the nearest cent :
y = (500)(1.06)^3 is $595.51
y = (20,000)(0.088)^3 is 13,629,44
y = (15,000)(1.05)^5 = 19,144.22
How to round off to the nearest cent?Cent is hundredth value of the dollar. The hundredth term is the second digit to the right of the decimal point. For example, the cent in this amount, $100.11 is 0.01.
In order to round off to the nearest cent, look at the thousandth term, if the number is equal to 5 or greater than 5, add 1 to the hundredth term and the thousandth term becomes 0. For example, $100.527 to the nearest cent is $100.53
In order to round off to the nearest cent, look at the thousandth term, if the number is less than 5, the hundredth term does not change and thousandth term becomes 0. For example, $20. 124 becomes $20.12 to the nearest cent.
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what multiplication equation can you use to find 5 divided by 1/3
When 5 is divided by 1/3, we get 15.
What is multiplication?
Multiplication is an operation that represents the basic idea of repeated addition of the same number.
Given is 5 divided by 1/3.
Assume the result after 5 is divided by 1/3 is equal to [x]. Then, we can write -
x = 5/(1/3) = 15
Therefore, when 5 is divided by 1/3, we get 15.
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Financial statements are of prime importance to , who will use the information to buy or sell stocks of the company. These statements are also inspected by to look into any irregularities or fraud in the book of accounts.
Answer:
Lydia is preparing financial statements for her company. Who would be interested in the information provided in these financial statements? Financial statements are of prime importance to Investors who will use the information to buy or sell stocks of the company. These statements are also inspected by an auditor to look into any irregularities or fraud in the book of accounts.
Step-by-step explanation:
Investors
Investors are individuals or firms who offer capital to a business in exchange for a share in ownership and profits. They are external users of financial statements. Investors use financial statements to know what returns to expect from their investments. Existing and potential investors rely on financial reports to decide on whether to buy or sell their shares.
Auditor
An auditor is a skilled individual authorized to assess, evaluate, and validate financial statements' accuracy as prepared by a company. The auditor reviews and gives a professional and independent opinion on the company's financial affairs.