Step-by-step explanation:
[tex] = \frac{ {p}^{2} - p - 12 }{ {p}^{2} - 10 + 24} \\ [/tex]
[tex] = \frac{ {p}^{2} - (4 - 3)p - 12 }{ {p }^{2} - (6 + 4)p + 6 \times 4} \\ [/tex]
[tex] = \frac{ {p}^{2} - 4p + 3p - 4 \times 3 }{ {p}^{2} - 6p - 4p + 6 \times 4 } \\ [/tex]
[tex] = \frac{p(p - 4) + 3(p - 4)}{p(p - 6) - 4(p - 6)} \\ [/tex]
[tex] = \frac{(p + 3)(p - 4)}{(p - 4)(p - 6)} \\ [/tex]
[tex] = \frac{p + 3}{p - 6} \\ [/tex]
☘️☘️☘️...
Solve the equation and determine the solution(s) or any extraneous solution.
Answer:
Solution: x = 9 Extraneous solution: x = 1
Step-by-step explanation:
Given equation:
[tex]\sqrt{4x}=x-3[/tex]
Square both sides:
[tex]\implies \left(\sqrt{4x}\right)^2=\left(x-3\right)^2[/tex]
[tex]\implies 4x=x^2-6x+9[/tex]
Subtract 4x from both sides:
[tex]\implies 4x-4x=x^2-6x+9-4x[/tex]
[tex]\implies 0=x^2-10x+9[/tex]
[tex]\implies x^2-10x+9=0[/tex]
Split the term in x:
[tex]\implies x^2-x-9x+9=0[/tex]
Factor the first two terms and the last two terms separately:
[tex]\implies x(x-1)-9(x-1)=0[/tex]
Factor out the common term (x - 1):
[tex]\implies (x-9)(x-1)=0[/tex]
Apply the zero-product property:
[tex](x-9)=0 \implies x = 9[/tex]
[tex](x-1)=0 \implies x=1[/tex]
Substitute the found values of x into the original equation to verify the solutions:
[tex]\begin{aligned}x=9 \implies \sqrt{4 \cdot 9} & = 9-3\\\sqrt{36} & = 6\\6 & = 6\end{aligned}[/tex]
[tex]\begin{aligned}x=1 \implies \sqrt{4 \cdot 1} & = 1-3\\\sqrt{4} & = -2\\ 2 & = -2\end{aligned}[/tex]
Therefore, the only valid solution is x = 9:
Solution: x = 9Extraneous solution: x = 1Extraneous solution: A solution from the process of solving the equation that is not a valid solution to the original equation.
If you only have a 1/3 measuring cup and a recipe calls for 12 2/3 cups of flour, how many 1/3 cups would you need to use? 1/3 * t th cups
If we have a 1/3 measuring cup and a recipe calls for 12 and 2/3 cups of flour,then we would need 38 number of cups.
Given that we have a 1/3 measuring cup and a recipe calls for 12 and 2/3 cups of flour.
We are required to find the number of cups that are needed.
Fraction is the combination of two numbers,one above the division sign and other one below the division sign. The number which is above the division sign is known as numerator and the number which is below the division sign is known as denominator.
Measuring cup=1/3
Number of cups needed in recipe=12+2/3=38/3
Number of cups needed=38/3/1/3
=38 cups
Hence if we have a 1/3 measuring cup and a recipe calls for 12 and 2/3 cups of flour,then we would need 38 number of cups.
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If anyone can help me to solve this!!
What is the solution of −|t+3| + 3 ≥ −4?
Answer:
[tex]-1t+31 +3 \geq -4[/tex]
[tex]-1t +34 \geq -4[/tex]
[tex]-1t \geq 30[/tex]
[tex]t \geq -30[/tex]
Evaluate the expression when x=10, y=−2, and z=−5.
|xz−y|=
Answer:
it would be 52
Step-by-step explanation:
if x = 10 y = -2 and z= -5
x * z = 10 * -5 = -50
-50 - (-2) = -52
|-52| this would make it positive so the answer is 52
f(x)=x+2
g(x) = 3x² - 5
Find (f ·g)(x).
Step-by-step explanation:
f(x) = x + 2
g(x) = 3x² - 5
= (f.g)(x)
= (x + 2).(3x² - 5)
= 3x³ - 5x + 6x² - 10
= 3x³ + 6x² - 5x - 10
Solve for X
A- 68
B- 2
C- 17
D- 34
Answer:
The value of x = 17
Step-by-step explanation:
=> 4x + 2 = 70°
=> 4x = 70 - 2
=> 4x = 68
=> x = 68/4
=> x = 17
There were 256 farmers in the county 30 years ago 5/8 of those farmers have changed occupations how many of the 256 farmers changed occupations
The answer is 27 for your math
Step-by-step explanation:
In the addition problems below A, B, and C are digits. If C is placed in the tens
column instead of the ones column as shown at the right, the sum is 97. What are
the values of A, B, and C?
AB + C = 52
AB+ (C x 10) = 97
The values of A, B, and C are mathematically given as
A=48/BB=48/AC=5This is further explained below.
What are the values of A, B, and C?Generally, the equation for the statement is mathematically given as
AB + C = 52
AB+ (C x 10) = 97....1
Using the substitution technique we have
AB = 52- C ....2
Subbing 2 in 1
AB+ (C x 10) = 97
Therefore
52- C + 10C = 97
9C=97-52
9C=45
C=5
In conclusion,
AB = 52- C
AB = 52- 5
AB=48
A=48/B
Hence
B=48/A
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4x-6*x=238
solve for x
Answer:
x=-119
Step-by-step explanation:
[tex]4x-6x=238[/tex]
[tex]-2x=238[/tex]
[tex]\frac{-2x}{-2}=\frac{238}{-2}[/tex]
[tex]x=-119[/tex]
what is the value of 10 to the power of -16 written as a fraction
Answer: 1e-16
Step-by-step explanation:
Steps
(x)n = (10)-16
=
1
10 x 10 x .... x 10
=
1
10000000000000000
= 1e-16
The base rate for workers compensation insurance for roofers in one state is $16.95 per $100 paid to employees. The total monthly payroll for Certified Roofing Contractors is $15,738. What is the monthly premium for workers compensation insurance?
Answer:
3.3972 repeating dbbdeebebbbebe
Step-by-step explanation:
wvehhww3g33gg3g33vv3hh333h33hhh3
Answer:
C. not covered by workers' compensation and could recover damages from the employer.
Step-by-step explanation:
What is 6.4% written as a decimal number? 64.0 6.4 0.64 0.064
Answer:
0.064
Step-by-step explanation:
To convert just muiltiply the percent by 100.
Angle DFG and angleJKL are complementary angles. If the measure if the angle DFG=x+2 and the measure of the angle JKL =x+9 then find x.
complementary angles m < DFG = 48, m < JKL = 42 is value of x .
What is the opposing angle to the above example?
Complementary angles are those whose combined angle is exactly 90 degrees. 30 degrees and 60 degrees, for instance, are complimentary angles.
∠DFG and ∠JKL are complementary angles. m∠DFG = x + 5,
and m∠JKL = x − 1
When two angles are complementary then the sum of angles is 90 degrees
∠DFG and ∠JKL are complementary angles.
So m < DFG < + m < JKL = 90
Now replace the expressions and solve for x
x + 5 +x - 1 =90
2x + 4 = 90
2x = 90 - 4
2x = 86
x = 43
Now replace x with 43 and find out each angle
m < DFG = x + 5
m < DFG = 43 + 5 = 48
m < DFG = 48
m < JKL = x - 1 = 43 - 1 = 42
m < DFG = 48
m < JKL = 42
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A recipe calls for the following spices:1/4 teaspoon of turmeric,1/8 teaspoon of ginger, and 1/4 teaspoon of cumin. What is the total quantity of these three spices?
Given that the curves are formed from
quarter circles,
find the area of the shaded region.
Give your answer in terms of TT.
4m
4m
The diagram is not drawn to scale
The area of the shaded region is 8π-16.
The side of the square is 4 m. Imagine a diagonal of the given square, which divides the shaded region into two equal parts due to symmetry. The radius of the quarter circle formed by one of the arcs and the two sides of the square is 4 m. The area of the quarter circle = 1/4πr²The area of the quarter circle = 1/4π4²The area of the quarter circle is 4π m². The diagonal and the two adjacent sides of the square form a right-angled triangle with a base of 4 m and a height of 4 m. The area of the triangle is 1/2*base*height. The area of the triangle is 1/2*4*4. The area of the triangle is 8 m². The area of the shaded region bisected by the diagonal = Area of quarter circle - Area of triangleThe area of the shaded region bisected by the diagonal = 4π-8 m²The area of the shaded region is twice the area of the shaded region bisected by the diagonal. The area of the shaded region = 2 * (4π-8)The area of the shaded region is 8π-16 m².To learn more about area, visit :
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−12 + −9 = ? I need an answer!
Answer: -21
Step-by-step explanation:
Translate this phrase into an algebraic expression.
Three less than the product of 15 and Chrissy's score
Use the variable c to represent Chrissy's score.
Answer:
15c - 3
Step-by-step explanation:
Product means 'The answer when you Multiply' So we are working in multiplication ( x )
15 x c can also be written as 15c
'3 less than' means subtracting 3 off the answer.
So therefore the answer is:
15c - 3
just need the second one done please
Answer: 15
Step-by-step explanation:
order all the numbers from least to greatest and then find the one in the middle
A study was performed with a random sample of 5 people from a certain city. What population would be appropriate for generalizing conclusions from the study, assuming the data collection methods used did not introduce biases?
The standard deviation is a statistic that describes the degree of volatility or dispersion in a set of numerical values. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.
High sample size is typically crucial in order to be able to draw generalizations from a sample, aside from avoiding bias. Since the sample size is modest, it will thus be possible to draw general conclusions about the study utilizing a larger sample, in my opinion.
The size of the sample has a significant impact on whether an experiment is legitimate. The central limit theorem states that as sample size rises, the sample mean approaches the population means value.
Because of this, generalizing from just five samples regarding a population of city dwellers won't produce a result that can be generalized.
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PLEASE HELP!!! ASAP!! FIND THE DOMAIN AND RANGE OF THEESE GRAPHS
Answer:
Domain: [-2, infinity)
Range: [-4, infinity)
Step-by-step explanation:
There's only one graph I see.
Domain is how far the graph extends on the x axis.
Range is how far the graph extends on the y axis.
the class was required to draw plan for the foundation day. Mary and tess was assigned to draw buildings. mary draw buildings twice as much as tess. if the total buildings are 99, how many buildings was draw by mary and tess
Answer:
Mary drew 66 buildings and Tess drew 33 buildings.
Step-by-step explanation:
Let's label the number of buildings drawn by Mary as x and the number of buildings drawn by Tess as y.
We know there are 99 buildings drawn. This means
99=x+y
We also know that Mary drew twice as many buildings as Tess. We can represent this as
x=2y
Now, let's substitute x for 2y, since that would put us in common terms
99=2y+y
Add common variables together and you get
99=3y
Solve for y by dividing 99 by 3
y=33
We now know that Tess drew 33 buildings, as well as y=33. Substitute y in the equation for how many buildings Mary drew:
x=2(33)
Now we know that Mary drew 66 buildings.
To check our work,
99=x+y
99=66+33
99=99
Malcolm got his first job. His wage in his first year was $8.65 an hour. In year 2, it was raised to $10 an hour. What was the percent increase in his hourly wage between year 1 and year 2
O 15.61%
O 13.5%
O 1.35%
O 0.16%
The percentage increase is the ratio of value increased to the original value and multiplied by 100.
The percentage increase in his hourly wage between year 1 and year 2 is 15.61%.
Option A is the correct answer.
What is a percentage increase?The percentage increase is the ratio of value increased to the original value and multiplied by 100.
It is expressed in percentage.
If there is an increase in the value of anything, then there is an increase in percentage.
We have,
Wage in the first year per hour = $8.65
Wage in the second year per hour = $10
The percentage increase in hourly wage:
= [ (10 - 8.65) / 8.65 ] x 100
= ( 1.35 / 8.65 ) x 100
= 15.6069 %
= 15.61 %
Thus the percentage increase in his hourly wage between year 1 and year 2 is 15.61%.
Option A is the correct answer.
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What is the area?
34 cm
39 cm
square centimeters
The area of the shape will be 1326 cm².
How to calculate the area?It should be noted that the area is calculated by multiplying the dimensions that are given.
Therefore the area will be:
= Length × Width
= 34 × 39.
= 1326 cm²
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Solve x/4>_-1 and -4x-4<_-3 and write the solution in interval notation. If there is no solution, type the no solution symbol.
The solution interval for x is x ∈ (-1/4 , ∞)
An inequality shows the relationship of a non-equal comparison between two numbers or mathematical expressions.
Here, we are given two inequalities
x/4 > -1 and -4x - 4 < -3
Let us take the first equation
x/4 > -1
⇒ x > 4(-1)
x > -4
Now, the second equation
-4x - 4 < -3
-4x < -3 + 4
-4x < 1
Now since we are dividing both sides by a negative number, that is 4, the sign of the inequality will be reversed,
x > 1/-4
x > -1/4
Thus, we get x > -4 and x > -1/4
This means that all values of x greater than -1/4 will satisfy.
Thus, x ∈ (-1/4 , ∞)
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How many milliliters of a 28% sugar Solution do we need to mix with 75 milliliters of a 10% sugar solution so that the resulting mixture is a 13% sugar solution?
We need to mix 15 ml of 28 % of solution to get the resulting mixture as a 13 % sugar mixture.
Let the amount of 28 % sugar solution be x ml.
We are given that:
10 % sugar solution = 75 ml
Total solution = 75 ml + x ml
We need the solution to be 13 % sugar solution.
So, we get that:
28 % x + 10 % ( 75 ) = 13 % ( 75 + x )
28 x + 750 = 13 ( 75 + x )
28 x + 750 = 975 + 13 x
28 x - 13 x = 975 - 750
15 x = 225
x = 225 / 15
x = 15
Therefore, we need to mix 15 ml of 28 % of solution to get the resulting mixture as a 13 % sugar mixture.
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A company asks an investor for an investment of $800,000 in exchange for 15% equity in the business. What is the implied valuation of the business?
If a company asks an investor for an investment of $800,000 in exchange for 15% equity in the business. The implied valuation of the business is: $4,533,333.
Implied valuationFirst step is to calculate the equity valuation
Using this formula
Equity valuation=Amount invested/Equity rate
Let plug in the formula
Equity valuation=$800,000/.15
Equity valuation=$5,333,333
Second step is to calculate the implied valuation
Implied valuation=Equity valuation-Amount invested
Let plug in the formula
Implied valuation=$5,333,333-$800,000
Implied valuation=$4,533,333
Therefore If a company asks an investor for an investment of $800,000 in exchange for 15% equity in the business. The implied valuation of the business is: $4,533,333.
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Directions: Write the following in set-builder notation. Input your answer inside the box provided for each given. Do not put a space in between symbols in your answer. Follow the format of the given example below.
1. A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
2. E is the set of letters in the word “notation”.
Answer:
1. A = {x:x is the set of natural number <= 10}
2. E = {x:x is the set of natural number <= 8}
List the interval(s) on which f is increasing.
The interval(s) in which f is increasing is/are: _____________.
(Type your answer in interval notation. Use a comma to separate answers as needed.)
The intervals on which the function f of x is increasing is:
(6, 0) U (2, 4) U (7, 9)
In which intervals is the function increasing?When we have the graph of a function, we can identify if it is increasing if, reading from left to right, we can see that the graph of the function goes upwards.
For the graphed function, we can see that it increases for the values:
-6 < x < 0
2 < x < 4
7 < x < 9
Writing this in interval notation, we have:
(6, 0) U (2, 4) U (7, 9)
This is the list of intervals on which the function f(x) is increasing.
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Please show me how to solve this: Katie and Tara are making crafts for their school's craft fair. For every 7 Tara makes, Katie makes 9. If they made a total of 240 crafts, how many did each girl
make?
Answer:
Tara makes 7x =7*15 = 105 crafts and Katie made 9x = 9*15 = 135 crafts.
Step-by-step explanation:
Crafts tara and katie make resoectively are in the ratiob 7:9. Let's say 7x and 9x.
Now,
7x + 9x = 240
so, x = 240/16
so, x = 15