So we are provided with the equation,
x2 + 10x + 40 = 5
To simplify it, we will first reorder the terms,
40 + 10x + x2 = 5
Now we will solve the equation to find the value of the unknown variable that we declared here as x.
40 + 10x + x2 = 5
Solving for variable 'x.'
40 + -5 + 10x + x2 = 5 + -5
We will combine similar terms; the variables and the constants.
40 + -5 = 35
35 + 10x + x2 = 5 + -5
Combine the like terms again:
5 + -5 = 0
35 + 10x + x2 = 0
Adding -35 on both sides
35 + 10x + -35 + x2 = 0 + -35
35 + -35 + 10x + x2 = 0 + -35
35 + -35 = 0
0 + 10x + x2 = 0 + -35
10x + x2 = 0 + -35
0 + -35 = -35
10x + x2 = -35
The x term is 10x.
Take half its coefficient (5) to make it a perfect square.
Square it (25) and add it to both sides.
10x + 25 + x2 = -35 + 25
25 + 10x + x2 = -35 + 25
-35 + 25 = -10
25 + 10x + x2 = -10
Perfect square on the left side:
(x + 5) (x + 5) = -10
We can see that the Square root of the right side can’t be calculated.
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Which angles of rotation will map the figure onto itself? Explain your reasoning
and/or show your work.
The standard normal probability density function is a bell-shaped curve that can be represented as?
The standard normal probability density function is represented by its formula, 1 /σ√2π(e^(-z²/2))
What is standard normal variate?
A standard normal variate is defined as a variate whose mean is equal to 0, i.e. µ=0 and standard deviation is equal to 1, σ =1. Its probability density function is given by:
f(x) = 1/√2π(e^(-z²/2))
Explanation
The standard normal probability density function is a bell-shaped curve that can be represented by using the given formula:
1 /σ√2π(e^(-z²/2))
Hence, the standard normal probability density function is represented by using its formula..
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Simplify each expression. 3[2(x-3)+2]+5(x-3)
The simplified form of the given expression 3[2(x - 3) + 2] + 5(x - 3) is 12x - 63.
According to the given question.
We have an expression 3[2(x - 3) + 2] + 5(x - 3).
To simplify the above expression we will use the distributive law and add and subtract the like terms.
Therefore,
3[2(x - 3) + 2] + 5(x - 3)
= 3[2x - 6 + 5x - 15] (distributive rule)
= 3[7x - 21] (adding the like terms)
= 21x - 63
Therefore, the simplified form of the given expression 3[2(x - 3) + 2] + 5(x - 3) is 12x - 63.
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For each rational function, find any points of discontinuity.
y=2x-1 / x²+4
In rational functions, the discontinuities are caused by the denominator terms. Since the denominator of a fraction is non-zero, any term multiplied by the denominator is also non-zero.
To find the discontinuities, we need to factor the polynomial below. Once we have the two binomials, we set each to 0. This way, you can find the value that produces 0 in the denominator.
If x = -2 then (x^2) + 4 is 0.
So, the discontinuities are shown as x = -2
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A certain species of fish costs $3.49 each. You can spend at most $30: How many of this type of fish can you buy for your aquarium?
Answers please help me
Answer:
Rita: r - 5= 2c, or r - 5= 2(36), or r - 5 = 72
Cora: (r - 5)/2 = 36
Step-by-step explanation:
Rita had r apps (let r = Rita original apps)She deleted 5 of them so r-5 She now has twice the number of apps as Cora so r-5 = 2c (let c = Cora's total apps) Cora's total apps are 36 so Rita's equation is r-5= 2(36) which means Rita equation for her number of apps is r-5= 72. As for Cora her equation is c= 36 but in relation to Rita's number of apps it's (r-5)/2 = 36Wayne bought ______ ounces of blueberries.
Wayne bought 72 ounces of blueberries.
How many ounces did he buy?
A fraction is a non-integer that is made up of a numerator that is divided by a line from the denominator. An example of a fraction is 1/2. 1 is the numerator and 2 is the denominator.
The first step is to determine the total fraction of blueberries that was used.
[tex]\frac{3}{8} + \frac{1}{6} + \frac{5}{12}[/tex]
[tex]\frac{27 + 12 + 30}{72}[/tex] = [tex]\frac{69}{72}[/tex]
Ounces of blueberries he bought = (ounces used ÷ fraction of blueberries used)
69 ÷ [tex]\frac{69}{72}[/tex]
69 x 72/69 = 72 ounces
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Please help very important!
Solve each system by substitution.
4y - 6 = 2x , y - 3x = 9
Using substitution method, the solution of the given system of equations is (-3,0)
A system of equation can be solved using:
graphical methodsubstitution methodelimination methodThe given system of equations:
4y - 6 = 2x ............ (1)
y - 3x = 9 .............. (2)
We need to find the solution using substitution method.
In equation (2), add 3x to both sides:
y - 3x + 3x = 9 + 3x
y = 9 + 3x ........ (3)
Substitute y = 9 + 3x into equation (1):
4y - 6 = 2x
4.(9 + 3x) - 6 = 2x
36 + 12x - 6 = 2x
12x - 2x = 6 - 36
10x = -30
x = -3
Substitute back x = -3 into equation (3)
y = 9 + 3x
= 9 + 3.(-3)
= 9 + (-9) = 0
Hence, the solution is (-3, 0)
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word problem :
answers: 10 plants, 18 plants, 14 plants, and 7 plants
Answer:
10
Step-by-step explanation:
10 because there is 40 squares
40/4=10
Solve z3 = 27.
please help due in 1 hour
whoever gets it right gets a crown
Answer:
z = 9
Step-by-step explanation:
Divide both sides by 3 to get z by itself
What is 6(2a-3)-2a=7(a-1)+3a
answer:
this is the solution
36. Where's the bus? Sally takes the same bus to work every morning. The amount of
time (in minutes) that she has to wait for the bus to arrive is described by the
uniform distribution below.
0
10
1
Height =
10
(a) Explain why this curve satisfies the two requirements for a density curve.
(b) On what percent of days does Sally have to wait more than 8 minutes for
the bus?
(c) On what percent of days does Sally wait between 2.5 and 5.3 minutes for
the bus?
According to the question, every morning Sally takes same bus and she has to wait to arrive with the used method called as uniform distribution.
And the range of the interval is as: min = 0 and max = 10.
For the calculation of the uniform distribution, the height some be constant.
Now, using standard uniform distribution formula:
Mathematically, the function f(x) can be written as:
f(x) = 1/(b - a)
where, 'a' and 'b' are defined intervals. Here, a = 0; b = 10.
Now, to calculate the percentage form the area as a rectangular grid which means:
f(x) = 1/10(5.3 - 2.5) = 2.8/10 = 0.28 = 28 percent.
Now, to know the percentile using above data:
f(x) = 1/(b - a) = 7/10 = 0.7 = 70 percent.
What is uniform distribution?
The uniform distribution is also called as density function which the nature of the two or more than two function should be equal or same.
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A student walked 100 meters north, then 100 meters west. How many more meters did the student walk compared to their total displacement from their starting point?.
Using Pythagorean theorem, the student walked 53.58 meters more compared to the total displacement from the starting point.
If a student walks 100 meters north, then 100 meters west, then the path he travels resembles the sides of a right triangle (see attached photo).
Using Pythagorean theorem, we can solve for the total displacement from the starting point to the end point.
c^2 = a^2 + b^2
where c is the total displacement from the starting point to the end point
a is the distance he walks up north
b is the distance he walks to the west
c^2 = 100^2 + 100^2
c^2 = 10,000 + 10,000
c^2 = 20,000
c = 141.42 meters
Comparing the total distance the student walked and the total displacement from the starting point to the end point by subtraction.
100 meters + 100 meters - 141.42 meters = 53.58 meters
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What is the probability that a randomly chosen diameter is greater than or equal to 10?
probability that a randomly chosen colony diameter is greater than or equal to 10 =P(10<X<12)+P(12<X<14)
=0.14+0.02 = 0.16
What is probability?
Probability is basically how likely something is to happen. Whenever we're uncertain around the outcome of an occasion, ready to talk approximately the probabilities of certain outcomes—how likely they are. The analysis of occasions administered by probability is called statistics.
Probability may be a measure of the probability of an event to occur. Numerous events cannot be predicted with add up to certainty. Able to predict as it were the chance of an occasion to happen i.e. how likely they are to happen, using it.
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Some people think that the Spaceship Earth geosphere at Epcot in Disney World in Orlando, Florida, resembles a golf ball. The building is a sphere measuring 165 feet in diameter. A typical golf ball has a diameter of approximately 1.5 inches.
d. What is the ratio of the volumes of Spaceship Earth to a golf ball?
The ratio of the volumes of the Spaceship Earth to a golf ball = 1926949795 : 1
We need to find the volumes of the Spaceship Earth and a golf ball.
Spaceship Earth
Radius, R = 165/2 ft = 82.5 ft
Volume of the Spaceship Earth = [tex]\frac{4\pi R^3}{3}[/tex] = (4 x 3.14 x 561515.625)/3
= 2350878.75 cubic ft.
A golf ball
Radius = 1.5/2 inches = 0.75 inches
1 ft = 12 inches
So 0.75 inches = 0.75/12 = 0.0625 ft.
So radius, r = 0.0625 ft
Volume of a golf ball = [tex]\frac{4\pi r^3}{3}[/tex] = (4 x 3.14 x [tex]0.0625^3[/tex])/3
= 0.00122 cubic ft.
Ratio of the volumes of Spaceship Earth to a golf ball
= 2350878.75:0.00122
= 1926949795 : 1
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i think i know it but i’m not sure
Answer: (3, 5]
Step-by-step explanation:
3w-3<=12 and 2w-1>5
3w-3+3<=12+3 and 2w-1+1>5+1
3w<=15 and 2w>6
3w/3<=15/3 and 2w/2>6/2
w<=5 and w>3
3<w<=5 ==> (3, 5]
Parentheses are notated for non-inclusion(3 isn't included in the solution) and brackets are notated for inclusion(5 is included in the solution).
ndclhdabcDC.sbdcb.dschsd
Answer:
I agree thanks for the points
Step-by-step explanation:
Simplify.
√6 / √3 . √8 / √3
The simplified value of the given expression is √6√8 / 3.
What is rationalization?Rationalization is a mathematical operation that allows us to determine or eliminate a root of the denominator of a fraction, so that it can be expressed in linear form, either decimal or integer, by the product of a root.
As defined above, we must perform a mathematical operation to eliminate the root of the denominator without altering the value.
(√6 / √3) (√8 / √3) we have a common denominator.
√6 √8/(√3)²
√6√8 / 3 is the result.
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Mohammad leaves home walks 5 blocks to the library. he then walks 2 blocks toward home to meet up with his friend. together, he and his friend walk to the library together. how far did mohammad walk?
If Mohammad leaves home walks 5 blocks to the library and he then walks 2 blocks toward home to meet up with his friend and then together, he and his friend walk to the library together, then Mohammad walked for 9 blocks.
To calculate how far Mohammad walked we use addition.
Total blocks Mohammad walked = blocks to the library + blocks towards home to meet up with friend + blocks back to the library together
blocks to the library = 5
blocks towards the home to meet up with friend = 2
blocks back to the library together = 2 (As he walked 2 blocks towards home from the library, he will walk the same number of blocks again to reach the library)
Therefore,
total blocks Mohammad walked = 5 + 2 + 2
total blocks Mohammad walked = 9
Hence, the number of blocks Mohammad walked for is calculated to be 9.
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Determine if each function is a vertical stretch or vertical compression of the parent function y=|x| .
y= 3/2|x|
Vertically Stretching and Compressing
Multiplying a function by positive constant yields a function whose graph is vertically stretched or compressed relative to the original function's graph. If the constant is greater than 1, it will stretch vertically. If the constant is between 0 and 1, vertical compression is done. You get vertical compression.
Vertical compression occurs when you multiply the function by a rational scaling factor. The base of the function graph remains the same even when the graph is compressed vertically. Only initial values are affected.
Reflect across the x-axis Vertically stretch a factor of 3/2
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The expression 16t² models the distance in feet that an object falls during the first t seconds after being dropped. What is the distance the object falls during each time?
10 seconds
If the expression 16t² models the distance in feet that an object falls during the first t seconds after being dropped, then the distance the object falls during 10 seconds is 1600 foot
Given,
The algebraic expression of the distance in feet that an object falls = [tex]16t^{2}[/tex]
Where t is the time in seconds
Here,
time t = 10 seconds
Substitute the value in the expression
[tex]16t^{2}=16(10)^{2}[/tex]
=1600 foot
Hence, If the expression 16t² models the distance in feet that an object falls during the first t seconds after being dropped, then the distance the object falls during 10 seconds is 1600 foot
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(5x + 9) + (8x - 30) = 180
Hello and Good Morning Afternoon:
Let's take this problem step-by-step:
[tex](5x + 9) + (8x-30)=180\\\\\text{Take out the parentheses as they are unnecessary to solve this problem}\\5x + 9+8x-30=180\\\\\text{Combine like terms like variables to variables and constants to constants}\\5x + 8x + 9-30 = 180\\13x - 21=180\\13x = 201\\x = 15.46 \text{ or }\dfrac{201}{13}[/tex]
Answer: 15.46 or 201/13
Hope that helps!
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100 POINTS + BRAINLEIST ANSWER ASAP
Answer:
Ori's definition = incorrect
Daniella's definition = hip , hip hurray!!!
Kaori's definition= part of your definition is correct , but other part is
Answer:
daniel: second one
ori: third one
kaori: first one
Step-by-step explanation:
What 8.1+2.53 with shown work
Answer:
10.63
Step-by-step explanation:
Please can someone help me? It’s due trmw
Answer:
Yes OFC
Step-by-step explanation:
As you can see at the 12-second mark the graph shows 1466 wave length for air so the density of the mass will be subtracted from the height
Determine whether the given conclusion is based on inductive or deductive reasoning.
If Beth turns in her report early, she receives extra credit. Beth turned in her report early. She concludes that she will receive extra credit.
The given conclusion is deductive reasoning.
What are Inductive reasoning and Deductive Reasoning?Inductive reasoning is a bottom-up technique, whereas deductive reasoning is a top-down approach. Inductive thinking proceeds from the particular to the universal, whereas deductive reasoning proceeds from general premises to specific conclusions.
Given the statements; If Beth turns in her report early, she receives extra credit.
Beth turned in her report early.
She concludes that she will receive extra credit.
From the sentences, the first sentence is a general statement, the second statement is a specific statement. And, the third statement is a conclusion statement.
Therefore, the given conclusion is deductive reasoning.
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A(1,7), B(1,2), and C(5,2) area
Christopher is the oldest of three siblings whose ages are consecutive odd integers. If the sum of their ages is 63, find Christopher's age.
Answer: 50
Step-by-step explanation: because
What is the sum of each finite series?
b. Σ ⁴ n=1 n³
The sum of the given finite series is 100
The summation notation tells us how to sum each term in a series.
Example:
[tex]\sum\limits^5_{n=1} {3n+1}[/tex]
means we need to evaluate the sum of (3n+1) as n moves from 1 to 5. Here 1 is the lower limit, while 5 is the upper limit.
The given series is:
[tex]\sum\limits^4_{n=1} {n^{3}}[/tex]
Expand this series:
[tex]\sum\limits^4_{n=1} {n^{3}}=1^{3}+2^{3}+3^{3}+4^{3}[/tex]
1³ = 1
2³ = 8
3³ = 27
4³ = 64
Hence,
1³ + 2³ + 3³ + 4³ = 1 + 8 + 27 + 64 = 100
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