Answer
[tex]\begin{gathered} Given\text{ }x^2+4x-27=5 \\ x^2+4x-27-5=5-5 \\ x^2+4x-32=0 \end{gathered}[/tex]Using factorization method
[tex]\begin{gathered} x^2+8x-4x-32=0 \\ x(x+8)-4(x+8)=0 \\ (x+8)(x-4)=0 \end{gathered}[/tex][tex]\begin{gathered} x+8=0\text{ }or\text{ }x-4=0 \\ x=-8\text{ }or\text{ }x=4 \end{gathered}[/tex]Therefore, x = -8 or x = 4
y=-7/3x+5/2 what is they slope
Answer: -4.667/2.000 = -2.333
Step-by-step explanation:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : y-(-7/3*x+5/2)=0
Simplify [tex]\frac{5}{2}[/tex]
Equation at the end of step : y - ((0 - ([tex]\frac{7}{3}[/tex] • x)) + [tex]\frac{5}{2}[/tex]) = 0
The left denominator is : 3 The right denominator is : 2
Least Common Multiple: 6
y - [tex]\frac{(15-14x)}{6}[/tex] = 0
y • 6 - [tex]\frac{(15-14x)}{6}[/tex] [tex]\frac{6y + 14x - 15}{6}[/tex]
[tex]\frac{ 6y + 14x - 15}{6}[/tex]
Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 2.500 and for x=2.000, the value of y is -2.167. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of -2.167 - 2.500 = -4.667 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)
Slope = -4.667/2.000 = -2.333
x-intercept = 15/14 = 1.07143
y-intercept = 15/6 = 5/2 = 2.50000
(2/3)y + 1 = (1/6)y +8
Answer:
y=14
Step-by-step explanation:
have a good day
The parenthesis are been used just as the absolute value signs. * 2 points Given the parent function f(x) = r, the function g(x) = (x - 1)3 - 2 is the result of a shift of f(x) (1) 1 unit left and 2 units down (2) 1 unit left and 2 units up (3) 1 unit right and 2 units down (4) 1 unit right and 2 units up 0 1 2 3 O 4
We know that every equation expressed in terms of x can be graph in an x-y plane, in this case the equation is
[tex]f(x)=x^3[/tex]if we want to move it up or down we add or substract the quantity of unities we are moving it. If we want to move it down two unities we substract 2 on the whole equation:
[tex]x^3\Rightarrow x^3-2[/tex]If we want to move it to the left or to the right we add or substract the quantity of unities we are moving it to the x term. If we add it means it is going to the left and if we substract it means it is going to the right. If we want to move it one unity to the right then we substract 1 from the x :
[tex]x^3\Rightarrow x^3-2\Rightarrow(x-1)^3-2[/tex]Then, the function:
[tex]g(x)=(x-1)^3-2[/tex]is the result of moving
f(x) = x³
1 unit to the right and 2 units down
Answer: 3On a family camping trip, 5 backpacks can fit in the trailer for every 3 people. if 9 people are going on the trip, how many backpacks can fit? 12 backpacks 14 backpacks 15 backpacks 24 backpacks
15 bags are expected for the journey for 9 people to fit backpacks in the trailer.
The fundamental principle of multiplication
To calculate the sum of two or more numbers, utilize the mathematical operation of multiplication. If an event can happen in m different ways and a second event can happen in n different ways after it, then the two events that happen in succession can happen in m n distinct ways.
Given that 5 backpacks can fit in the trailer for every 3 people.
Then 3 people = 5 backpacks
1 people = [tex]\frac{5}{3}[/tex] backpacks
therefore If 9 people are going on the trip, then;
9 people = [tex]\frac{5}{3}*9[/tex] backpacks
= 5 x 3
= 15 backpacks
Hence, the trailer can fit 15 backpacks if 9 people go on the trip.
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Adrian buys a one-gallon bottle of juice for $17.92. What is the unit rate of the cost of
the juice per fluid ounce?
1 gallon = 4 quarts
1 quart = 2 pints
1 pint = 2 cups
1 cup 8 fluid ounces
=
Before you try that problem, answer the question below.
How many fluid ounces of juice did Adrian buy?
Answer:
128 fluid ounces per gallon.
Unit rate = $0.14 per fluid ounce of juice.
Step-by-step explanation:
Given:
1 gallon = 4 quarts1 quart = 2 pints1 pint = 2 cups1 cup = 8 fluid ouncesTherefore, the number of fluid ounces in 1 gallon is:
⇒ 4 × 2 × 2 × 8 = 128 fluid ounces
Therefore, Adrian bought 128 fluid ounces of juice.
To find the unit rate of the cost of the juice per fluid ounce, divide the cost per gallon by 128:
[tex]\implies \dfrac{17.92}{128}=0.14[/tex]
Therefore, the unit rate of the cost of the juice per fluid ounce is $0.14.
how do your graph questions like y= 1/2+7
Answer:
so basically Write a factor
Step-by-step explanation:
1 - write a factor and then multiply then divide that's all hopefully this is helpful:)
.
Which is the best approximation of 110
Step-by-step explanation:
We can find the square root of a number by using scientific notations, specifically the one listed below.[tex]110 \times 10^{-1}[/tex]
When dealing with negative exponents to base 10, the answer will move left. To our surprise, though, the number does not become negative. Instead, the answer would be 11, because 110 × 10⁻¹ is like saying 110 ÷ 10, which is 11.[tex]= 11[/tex]
Answer:
Given the answer is 11, we can round that down to 10.5
Hope this helps!
You put some money in an investment account with an interest rate 2.82.8% compounded annually for 11 years. Your initial investment is $ 12130.0012130.00. How much is your account worth in 11 years?
Answer:
g× $12130.0012130.00.
How many meters are in 18200 millimeters
Answer:
18.2
Step-by-step explanation:
18200/1000 becuase their are 1000 millimeters in a meter
apply the law of syllogism form a mew statement based on the following
Okay, here we have this:
Considering the provided sentences, we are going to apply the law of syllogism, so we obtain the following:
Let us remember that the law of Syllogism says that:
(1) If p , then q . And (2) If q , then r .
Then we can derive that: (3) If p , then r .
Applying:
(1) If the dog jumps in the lake, then it gets wet. (R->S)
(2) If the dog gets wet, then it can't come in the house. (S->T)
We can derive that:
(3) If the dog jumps in the lake, then it can't come in the house. (R -> T)
What is halfway between 242 and 263?
Answer:252.5
Step-by-step explanation:
263-242=21
21/2=10.5
242+10.5=252.5
The halfway between 242 and 263 is 252.5
what is 49.6 divided by 7.8?
Answer: 6.4
Step-by-step explanation: If rounding to one decimal place, your answer would be 6.4.
49.6 divided by 7.8 = 6.35897435...
Now, we see that after the 3 (The first decimal place) there is a five. Because we are rounding to the first decimal place the second decimal place will tell us to round up or down. In this case because it's a five, we would round up.
2 1/2 - 3/4 / (3/5 + 1 2/5) times 4
please answer! thank you so much! :)
Answer is: 1
Explaination:
2 · 2 + 1/2 = 4 + 1/
2= 5/2
To find a new numerator:
a) Multiply the whole number 2 by the denominator 2. Whole number 2 equally 2 * 2/2
= 4/2
b) Add the answer from previous step 4 to the numerator 1. New numerator is 4 + 1 = 5
c) Write a previous answer (new numerator 5) over the denominator 2.
Two and one half is five halfs
Subtract: 5/2
- the result of step No. 4 = 5/2
- 3/2
= 5 - 3/2
= 2/2
= 2 · 1/2 · 1
= 1
It is suitable to adjust both fractions to a common (equal, identical) denominator for adding, subtracting, and comparing fractions. The common denominator you can calculate as the least common multiple of both denominators - LCM(2, 2) = 2. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 2 × 2 = 4. In the following intermediate step, cancel by a common factor of 2 gives 1/1.
In other words - five halfs minus three halfs is one.
If you get paid $450 for 20 h work, what is your hourly rate?
As per the division operation, the hourly pay rate is $37.5
Division operation:
The division is a process of splitting a specific amount into equal parts.
Given,
You get paid $450 for 20 hours.
Here we need to calculate the hourly pay for us.
To find the hourly pay we have to perform the division operation.
The process of doing long division is,
If the number you're dividing by has a decimal, move the decimal point all the way to the right counting the number of places you've moved it to. Then move the decimal point in the number you're dividing the same number of places to the right.Insert a decimal point in the quotient (answer) space, exactly above the decimal point in the number under the division bar.Divide until the remainder is zero, or until you have enough decimal places in your answer. You can also stop if the remainder repeats because this indicates that your answer is a repeating decimal.Such that, we have to divide 450 by 12, then we get,
And the process of division is shown below.
So, the hourly pay for us is $37.5.
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Indicate which property is illustrated in Step 1.
Step 1 2 • 6 • 5 • 1 = (2 • 6) • (5 • 1)
Step 2 = (6 • 2) • (1 • 5)
Step 3 = 12 • (1 • 5)
Step 4 = 12 • 5
A.
associative property of multiplication
B.
commutative property of multiplication
C.
commutative property of addition
D.
associative property of addition
As per the properties of numbers, Step 1) 2 • 6 • 5 • 1 = (2 • 6) • (5 • 1) uses the option A. associative property of multiplication
Properties of numbers:
The properties of numbers are stated for real numbers.
The common properties are:
Commutative Property: a + b = b + a
Associative Property: a . (b . c) = (a . b) .(a . c)
Distributive Property: a × (b + c) = a × b + a × c
Identity property: a.1 = a
Given,
Here we have the following steps.
Step 1 2 • 6 • 5 • 1 = (2 • 6) • (5 • 1)
Step 2 = (6 • 2) • (1 • 5)
Step 3 = 12 • (1 • 5)
Step 4 = 12 • 5
In this one, we have to identify the property used in step 1.
While we looking into the step 1), we have identified that the product is the same regardless of the way in which the numbers are grouped.
Based on this concept, we have identified that the step is used the associative property of multiplication.
Therefore, step 1 is uses the concept associative property of multiplication.
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A carpenter cuts lumber to a length of 36 inches. For her project, the lumber must be accurate
within 25 inches Write an inequality to represent the acceptable length of the lumber, then
solve the inequality.
The inequality to represent the acceptable length of the lumber is 11 ≥ x ≤ 61.
The minimum and maximum length is 11 and 61 inches.
What is an inequality?Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.
The minimum length will be:
= 36 - 25
= 11 inches
The maximum length will be:
= 36 + 25
= 61 inches
Therefore, the inequality is 11 ≥ x ≤ 61.
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What is the answer to this
Answer:
They can invite at most 133 people
Step-by-step explanation:
132.97 rounded to the nearest "whole person" is 133
Given f(x) = (1/4)^-x, evaluate f(-2), f(1), and f(2).
The evaluated functions are as follows:
f(-2) = 1 / 16f(1) = 4f(2) = 16How to evaluate functions?The functions can be evaluated as follows:
Therefore,
f(x) = (1 / 4)⁻ˣ
For we to evaluate the function we have to substitute each value of x in the function.
Hence, let's evaluate the following:
we will replace x in the function by -2
f(-2) = (1 / 4)⁻⁽⁻²⁾
f(-2) = (1 / 4)²
f(-2) = 1 / 16
we will replace x in the function by 1
f(1) = (1 / 4)⁻¹
f(1) = 4
we will replace x in the function by 2.
f(2) = (1 / 4)⁻²
f(2) = 16
Therefore,
f(-2) = 1 / 16f(1) = 4f(2) = 16learn more on evaluation and function here: https://brainly.com/question/15559220
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y2-y1m =X2-X1Find the slope of the line that passesthrough these two points.Simplify completely.(1,5)(4.6)[2]
Okay, here we have this:
Considering the provided points and information, we are going to calculate the requested slope, so we obtain the following:
m=(y2-y1)/(x2-x1)
m=(6-5)/(4-1)
m=1/3
Finally we obtain that the slope of the line is 1/3.
Jack had 333 bags of golf balls with bbb balls in each bag; then his friend gave him 666 more golf balls.
The number of golf ball after his friend gave him balls is y = 3b + b
How to find the number of balls Jack has?He has 3 bags of golf balls with b balls in each bag.
His friend gave him 6 more balls.
Therefore, the number of balls jack has can be represented with the following equation.
b balls are in each of the 3 bags.
Therefore,
the number of balls in the whole bags = 3b
Hence, the number of balls after the friend gave him 6 more balls is as follows;
y = 3b + b
where
y = number of total golf balls
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Graph the solution set of the inequality and write the solution using interval notation. Please give me a step by step explanation.
We have the inequality:
-4 < (3x - 2)/5 ≤ 6
We multiply all the sides by 5:
-4*5 < 5*(3x - 2)/5 ≤ 6*5
-20 < 3x - 2 ≤ 30
Now, we add 2 to all the sides of the inequality:
-20 + 2 < 3x - 2 + 2 ≤ 30 + 2
-18 < 3x ≤ 32
Finally, we divide by 3:
-18/3 < 3x/3 ≤ 32/3
-6 < x < 32/3
Now, using interval notation:
x = (-6, 32/3]
This means that x takes all the values greater than -6 and less or equal to 32/3. Graphically, this is:
Solve for the value of n
Answer: n = 17
Step-by-step explanation:
2n + 3n -5 = 90
5n - 5 = 90
5n = 85
n = 17
Answer:
n = 19°
Step-by-step explanation:
The tiny square in the corner of the big angle shows that it is a right angle. Right angles have a measure of 90°. So the two angles labelled added together make a 90° angle.
2n + 3n - 5 = 90
Combine like terms.
5n - 5 = 90
Add 5.
5n = 95
Divide by 5.
n = 19
Hello, please help.
Just answers
Answer:
B
Step-by-step explanation:
The exponent means to multiply x² by itself 3 times.
Which of the following are integer solutions to the inequality below?
−
2
≤
x
<
3
The integer solutions in the inequality expression given as − 2 ≤ x < 3 are -2, -1, 0, 1 and 2
What are inequalities?Inequalities are expressions that do not have equal value
As a general rule, inequalities are represented by the unequal symbols
How to determine the integer solutions?The inequality expression is given as
− 2 ≤ x < 3
The above inequality implies that
The values in the range or domain are values greater than -2, but less than 3
This means that
-2 is inclusive of the range, while 3 is not inclusive of the range
Using the above as a guide, the values in the range are
-2, -1, 0, 1 and 2
Hence, the integer solutions are -2, -1, 0, 1 and 2
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The sum of the squares of two consecutive positive even numbers is 340. Find the numbers.
The consecutive even numbers are
and
.
Answer:
12, 14
Step-by-step explanation:
Let x = smaller positive even integer.
Then x + 2 is the next greater even integer.
Add the squares of the numbers.
x² + (x + 2)²
Set the sum equal to 340.
x² + (x + 2)² = 340
x² + x² + 4x + 4 = 340
2x² + 4x - 336 = 0
x² + 2x - 168 = 0
We need to factor the left side. We need 2 factors of -168 that add to 2.
168 = 2³ × 3 × 7
2² × 3 = 12
2 × 7 = 14
14 × (-12) = -168
14 + (-12) = 2
The factors are 14 and -12.
x² + 2x - 168 = 0
(x - 12)(x + 14) = 0
x - 12 = 0 or x + 14 = 0
x = 12 or x = -14
x = 12
x + 2 = 12 + 2 = 14
Answer: 12, 14
Determine whether a triangle with the given side lengths is a right triangle. side lengths right triangle not a right triangle not enough information 5, 13, 14 18, 24, 30 8, 15, 17 22, 29, 36
Answer:
It is a right triangle
Step-by-step explanation:
The shortest side of a right triangle measures 9, and the longest side measures 15. Determine the measurement of the unknown side. A. 8 B. 11 C. 12 D. 15
Answer:
C
Step-by-step explanation:
the longest side in a right triangle is the hypotenuse.
using Pythagoras' identity in the right triangle
let the unknown side be x , then
x² + 9² = 15²
x² + 81 = 225 ( subtract 81 from both sides )
x² = 144 ( take square root of both sides )
x = [tex]\sqrt{144}[/tex] = 12
Answer:
12 is the answer
Step-by-step explanation:
what is the value of x
Answer:
X=6
Step-by-step explanation:
Simplify:
(2p^3x)^3 = 8p^54 into:
2p^3x = 2p^18
p^3x = p^18
3x = 18
x=6
What is the equation of the line that is parallel to the given line and passes through the point (â€"2, 2)? y = one-fifthx 4 y = one-fifthx twelve-fifths y = â€"5x 4 y = â€"5x twelve-fifths
The equation of the line that is parallel to the given line and passes through the point (–2, 2) is: B. y = 1/5(x) + 12/5
How to calculate the slope of a line?In order to determine the equation of this line, we would first of all calculate its slope. Mathematically, the slope of any straight line can be calculated by using this formula;
[tex]Slope,\;m = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope\;,m = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]
By critically observing the graph of the line, we can logically deduce the following points:
Point (x, y) = (0, -3)
Point (x, y) = (-5, -4)
Substituting the given points into the formula, we have;
Slope = (-4 - (-3))/(-5 - 0)
Slope = (-4 + 3)/(-5)
Slope = -1/-5
Slope = 1/5
In Geometry, two (2) lines are parallel under the following conditions:
m₁ = m₂
Note: m represents the slope.
Mathematically, the point-slope form of a line is given by this equation:
y - y₁ = m(x - x₁)
Where:
x and y are the points.m represents the slope.At point (-2, 2), we have:
y - 2 = 1/5(x - (-2))
y - 2 = 1/5(x + 2)
y - 2 = x/5 + 2/5
y = x/5 + 2/5 + 2
y = x/5 + 12/5
y = 1/5(x) + 12/5
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Complete Question:
What is the equation of the line that is parallel to the given line and passes through the point (–2, 2)?
y=1/5x+4
y=1/5x+12/5
y=-5x+4
y=-5x+12/5
Answer: B. y = 1/5x + 12/5
Step-by-step explanation: This is just a sum of what the person above me said.....and i can confirm this is the right answer bc i just did the quiz and scored 100% loll. Hope this helps! :D
Express 200g as a ratio of 5kg in it lowest terms
Answer:
1:25
Step-by-step explanation:
200/5000 (5kg = 5000g)
1/25
1:25
