Answer:
x = -12.42 or x = 2.42
Step-by-step explanation:
x^2 + 10x - 13 = 17
To solve this using the completing the square method, we will follow the steps below;
First, we will add 13 to both side of the equation, we want only the x variable to be on the left-hand side of the equation
x^2 + 10x - 13 + 13 = 17 + 13
x^2 + 10x = 30
The next step is to add both-side of the equation by square of half of the coefficient of x (that is ; half of 10 is 5, then we will add 5² to both-side of the equation)
x^2 + 10x + 5² = 30 + 5²
Then we can now factorize the left-hand side of the equation and at the same time simplify the right-hand side of the equation
(x + 5)² = 30 + 25
(x + 5)² = 55
We will then take the square root of both-side of the equation
√(x + 5)² = ±√55
x + 5 = ±√55
To get the value of x, we will subtract 5 from both-side of the equation
x + 5 - 5 = ±√55 - 5
x = ±√55 - 5
Either x = + √55 -5 = 7.42 -5 = 2.42
OR
x = -√55 - 5 = -7.42 - 5 = -12.42
Therefore either x = -12.42 or x = 2.42
x = -12.42 or 2.42
Given the functions f(x) = 2x + 5 and g(x) = x2 + 8, which of the following functions represents f(g(x)] correctly?
1. f[g(x)] = 4x2 + 20x + 32
2. f(g(x)] = 4x2 + 20x + 25
3. f[g(x)) = 2x2 + 16
4. f(g(x)) = 2x2 + 21
Answer:
Choice 4.
Step-by-step explanation:
f(g(x))
Replace g(x) with x^2+8 since g(x)=x^2+8.
f(g(x))
f(x^2+8)
Replace old input,x, in f with new input, (x^2+8).
f(g(x))
f(x^2+8)
2(x^2+8)+5
Distribute:
f(g(x))
f(x^2+8)
2(x^2+8)+5
2x^2+16+5
Combine like terms:
f(g(x))
f(x^2+8)
2(x^2+8)+5
2x^2+16+5
2x^2+21
Answer:
D
Step-by-step explanation:
Took the test
What is the area of a rectangle with a length of 27 and a height of 56?
Answer:
A=1512
Step-by-step explanation:
The area of a rectangle with a length of 27 and a height of 56 is 1512.
Formula: A=wl
A=wl=56·27=1512
Answer: 1,512 units^2
Step-by-step explanation: To find the area of a rectangle, multiply the length by the width. 27 x 56 =1512. Since you are finding the area, the answer would be squared.
Which statements accurately describe the function f(x) = 3 sqrt 18?
algebra II engenuity
Answer:
The statements which accurately describe f(x) are
The domain is all real numbers ⇒ 1st answer
The initial value of 3 ⇒ 3rd answer
The simplified base is 3√2 ⇒ last answer
Step-by-step explanation:
* Lets explain how to solve the problem
- The form of the exponential function is f(x) = a(b)^x, where a is the
initial value , b is the base and x is the exponent
- The values of a and b are constant
- The domain of the function is the values of x which make the function
defined
- The range of the function is the set of values of y that correspond
with the domain
* Lets solve the problem
∵ [tex]f(x)=3(\sqrt{18}) ^{x}[/tex]
- The simplest form of is :
∵ √18 = √(9 × 2) = √9 × √2
∵ √9 = 3
∴ √18 = 3√2
∴ [tex]f(x)=3(3\sqrt{2})^{x}[/tex]
∵ [tex]f(x)=a(b)^{x}[/tex]
∴ a = 3 , b = 3√2
∴ The initial value is 3
∴ The simplified base is 3√2
- The exponent x can be any number
∴ The domain of the function is x = (-∞ , ∞) or {x : x ∈ R}
- There is no value of x makes y = 0 or negative number
∴ The range is y = (0 , ∞) or {y : y > 0}
* Lets find the statements which accurately describe f(x)
# The domain is all real numbers
∵ The domain is {x : x ∈ R}
∴ The domain is all real numbers
# The initial value is 3
∵ a = 3
∵ a is the initial value
∴ The initial value of 3
# The simplified base is 3√2
∵ b = √18
∵ b is the base
∵ The simplified of √18 is 3√2
∴ The simplified base is 3√2
- For more understand look to the attached graph
Drag steps in the given order to evaluate this expression. -3(-3+2)-6
Answer:
The answer is -3.
Step-by-step explanation:
-3(-3+2)-6
First solve the parenthesis. -3+2= -1.
-3(-1)-6
-3 times -1 is 3. Two negatives always equal a positive.
3-6 = -3.
Determine what type of model best fits the given situation: A $500 raise in salary each year.
Answer:
A linear modelExplanation:
The type of model that best fits the situation of a $500 raise in a salary each year is a linear model.
In a linear model, the dependent variable changes a constant amount for constant increments of the independent variable.
In the given case, the dependent variable is the salary and the independent variable is the year.
You may build a table to show that for increments of 1 year the increments of the salary is $500:
Year Salary Change in year Change in salary
2010 A - -
2011 A + 500 2011 - 2010 = 1 A + 500 - 500 = 500
2012 A + 1,000 2012 - 2011 = 1 A + 1,000 - (A + 500) = 500
So, you can see that every year the salary increases the same amount ($500).
In general, a linear model is represented by the general equation y = mx + b, where x is the change of y per unit change of x, and b is the initial value (y-intercept).
In this case m = $500 and b is the starting salary: y = 500x + b.
A customer cash a 1000.00 check at 3 percent how much does he receive back?
Let r = amount customer gets back
r = 1000 - (1000)(0.03)
r = 1000 - 30
r = $970
Raina brought a table for 627 the price was 35%less than the original price
Answer:
964.62
Step-by-step explanation:
Let x = the original price
35% less than means we pay 65% of the original price
627 = 65% x
Changing to decimal form
627 = .65x
Divide each side by .65
627/.65 = .65x/.65
964.6153846 =x
Rounding to the near cent
964.62
a cars fuel efficiency is no less the 45 mpg use F to find the cars fuel efficiency. how do i turn this into an inequality math problem
Answer:
F ≥ 45
Step-by-step explanation:
"No less than" means "greater than or equal to", so you can write the expression as ...
F ≥ 45 . . . . . miles per gallon
The price of an iPod dropped from $210.95 to $165.88.
What was the percent decrease in prices? (round to the
nearest hundredth)
o 21.37%
o 21.34%
O 21.38%
O none of the above
Answer:
The correct answer would be option A, 21.37
Step-by-step explanation:
In order to find out the percentage change of price of a product, either increase of decrease, that is found by finding the change in the price and then divide it by the base price and then finding the percentage of that price. The whole process is as follows:
Original price of iPod: $210.95
New Price of iPod: $165.88
Decrease in the price of iPod: 210.95-165.88= 45.07
Now dividing decreased price with the original price we get:
45.07/210.95=0.213652
Now to find the percentage, we need to multiply it with 100
0.213652*100=21.3652% which is approximately 21.37%
Use the figure to decide the type of angle pair that describes
<5 and <6
Answer:
corresponding angles
Step-by-step explanation:
Corresponding angles are in matching corners .
Both 5 and 6 are in the lower left corner
write an inequality to represent the graph?
[tex]y > \frac{2}{5}x - 3 [/tex]
[tex]y < \frac{2}{5}x - 3[/tex]
[tex]y > \frac{5}{2}x - 3[/tex]
[tex]y < \frac{5}{2}x - 3[/tex]
which one is it 1,2,3,or 4 one
Answer:
[tex]\large\boxed{y>\dfrac{5}{2}x-3}[/tex]
Step-by-step explanation:
<, > - dotted line
≤, ≥ - solid line
<, ≤ - shaded region below the line
>, ≥ - shaded region above the line
We have dotted line (<, >) and shaded region above the line (>, ≥).
Therefore your answer is:
[tex]y>\dfrac{2}{5}x-3[/tex] or [tex]y>\dfrac{5}{2}x-3[/tex]
Calculate the slope.
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Put the coordinates of the given points from the graph:
(0, -3) and (2, 2):
[tex]m=\dfrac{2-(-3)}{2-0}=\dfrac{5}{2}[/tex]
Find the complete factored form of the polynomial -24a6b4-40a3
For this case we have the following polynomial:
[tex]-24a ^ 6b ^ 4-40a ^ 3[/tex]
We must find the greatest common factor of the terms of the polynomial.
The GCF of the coefficients is given by:
[tex]24 = 3 * 8\\40 = 5 * 8[/tex]
Then we look for the GFC of the variables:
We have then:
[tex]a ^ 6 = a ^ 3a ^ 3\\a ^ 3 = a ^ 3[/tex]
Finally rewriting we have: [tex]-24a ^ 6b ^ 4-40a ^ 3 = -8a ^ 3 (3a ^ 3b ^ 4 + 5)[/tex]
Answer:
the complete factored form of the polynomial is:
[tex]-8a ^ 3 (3a ^ 3b ^ 4 + 5)[/tex]
PLEASE DO 41 AND 45!!!!!!
Answer:
see below
Step-by-step explanation:
41
-4 ≤2+4x<0
Subtract 2 from all sides
-4-2 ≤2-2+4x<0-2
-4 ≤2+4x<0
Divide all sides by 4
-6/4 ≤4x/4<-2/4
-3/2 ≤x <-1/2
graph is attached
45
2x-3 ≤-4 or 3x+1 ≥4
Lets solve the left side first
2x-3≤-4
Add 3 to each side
2x-3+3 ≤-4+3
2x ≤-1
Divide by 2
2x/2 ≤-1/2
x ≤-1/2
Now solve the right inequality
3x+1 ≥4
Subtract 1 from each side
3x+1-1 ≥4-1
3x ≥3
Divide by 3
3x/3 ≥3/3
x≥1
So we have
x ≤-1/2 or x≥1
see attached
Notice closed circles where there is a greater than equal to or less than equal to
7hr= how many minutes
Answer:
420 minutes
Step-by-step explanation:
1 hour = 60 minutes
7 * 1 hour = 7 * 60 minutes
7 hours = 420 minutes
We know that 1 hour = 60 minutes
To find how many minutes is in seven hours, we can multiply 60 by 7 and we will get a product of 420.
1 hour = 60 minutes
2 hours = 120 minutes
3 hours = 180 minutes
4 hours = 240 minutes
5 hours = 300 minutes
6 hours = 360 minutes
7 hours = 420 minutes
what is 240,567 divided by 67 is 3590
Answer:
Step-by-step explanation:
_____
Good evening ,
_______________
Look at the photo below for the answer.
___
:)
(1 point) Solve the equation in the interval [0,2π]. If there is more than one solution write them separated by commas. (sin(x))2=1/36
To solve (sin(x))^2 = 1/36, we find the arcsine of ±1/6. The solutions are sin⁻¹(1/6), π - sin⁻¹(1/6), 2π - sin⁻¹(1/6), and π + sin⁻¹(1/6) within the interval [0,2π].
Explanation:To solve the equation (sin(x))^2 = 1/36 in the interval [0,2π], we first take the square root of both sides to get sin(x) = ±1/6. The sine function oscillates between -1 and 1 every 2π radians, which means that we are looking for angles where the sine value is ±1/6.
To find the specific angles, we use the arcsine function or inverse sine function. The principal value of sin⁻¹(1/6) gives us one of the solutions, and considering the symmetry of the sine function, the other solutions can be found in the second and fourth quadrants, where the sine function is positive and negative, respectively.
The solutions to sin(x) = 1/6 in the interval [0,2π] are x = sin⁻¹(1/6) and x = π - sin⁻¹(1/6). For sin(x) = -1/6, the solutions are x = 2π - sin⁻¹(1/6) and x = π + sin⁻¹(1/6). Thus, the solutions to the original equation (sin(x))^2 = 1/36 within [0,2π] are sin⁻¹(1/6), π - sin⁻¹(1/6), 2π - sin⁻¹(1/6), and π + sin⁻¹(1/6), all of which can be calculated to find the exact values.
place parenthesis in the expression below to make it a true statement.
5+5÷5X5=0
Help on 10 and 11 and give me the answers for the blank ones
Answer:
10) Exact Answer: 36
Estimate: 36
11) Exact Answer: 2001
Estimate: 1900
Step-by-step explanation:
10a) To find the exact answer, simply divide the given numbers.
10b) To find the estimated answer, use compatible numbers. We know that any "hundred" number is easily divisible by 5. Therefore, 900/5 = 36.
It is possible for the estimate to be the same as the exact answer.
10a) To find the exact answer, simply divide the given numbers.
10b) To find the estimated answer, use compatible numbers. There is no pattern we can look for, so round to the nearest whole number.
We know that if we rounded .38 to 0 or 1, the answer would not be nearly as close as if we rounded .38 to .4.
Therefore, 760/.4 = 1900
Please mark as Brainliest, hope this helps!
A video game requires at least 4 points to advance. Each solved puzzle is worth two points. Each solved riddle is worth 1 point. If x is the number of solved puzzles and y is the number of solved riddles, which graph represents this scenario?
Answer:
The graph that representss this scenario is attached.Explanation:
You can create the graph by determining the expression that shows the relationship between the variables and then drawing the graph in a coordinate system.
1. Determine the expression that relates the variables.
a) The name of the variables is given:
x: number of solved puzzlesy: number of solved riddlesb) Point rules:
Each solved puzzle is worth two points: 2x Each solved riddle is worth 1 point: 1y = ySum of points: 2x + yThe video game requires at least 4 points to advance: this means that the number of points must grater than or equal to 4 ⇒ 2x + y ≥ 4 .In conclusion, it has been determined that the expression that rules the system of points is the inequality 2x + y ≥ 4.
2) Building the graph
Solve algebraically for y: y ≥ 4 - 2xYou want to draw the border line of the function, that is y = 4 - 2xYou have a linear function, so you need only two points to draw it. It is generally easier to work with the intercepts.x-intercept (y = 0) ⇒ 2x + 0 = 4 ⇒ 2x = 4 ⇒ x = 2 ⇒ point (2, 0)y-intercept (x = 0) ⇒ 2(0) + y = 4 ⇒ y = 4 ⇒ point (0, 4).In conclusion, you can use the points (2,0) and (0,4) to draw the line that is the border of your graph.
Addtional constrains: x and y cannot be negative, so add the constrains:x ≥ 0 and y ≥ 0
The set of solutions of y ≥ 4 - 2x is the same line y = 4 - 2x and the region over the line, so you have to shade that portion of the graph, but only in the first quadrant (since x and are greater than or equal to zero).The resulting graph is attached.
Answer:
D
Thank me later!! Just did the test on edge
30 POINTS! Consider the system of linear equations and the matrix equations below.
What is the value of x in the equation?
Answer:
Option C is correct.
Step-by-step explanation:
-x+3y=2
4x-2y=22
In matrix form is represented as:
[tex]\left[\begin{array}{cc}-1&3\\4&-2\end{array}\right] \left[\begin{array}{c}x&y\end{array}\right] =\left[\begin{array}{c}2&22\end{array}\right][/tex]
AX=B
[tex]X = A^{-1}B[/tex]
[tex]A^{-1} = |A|/Adj A[/tex]
|A| = (-1)(-2)-(3)(4)
|A| = 2-12
|A| = -10
Adj A = [tex]\left[\begin{array}{cc}-2&-3\\-4&-1\end{array}\right][/tex]
A^-1 = -1/10[tex]\left[\begin{array}{cc}-2&-3\\-4&-1\end{array}\right][/tex]
A^-1 = 1/10[tex]\left[\begin{array}{cc}2&3\\4&1\end{array}\right][/tex]
X= A^-1 B
X = 1/10[tex]\left[\begin{array}{cc}2&3\\4&1\end{array}\right][/tex][tex]\left[\begin{array}{c}2&22\end{array}\right][/tex]
X=1/10[tex]X=1/10\left[\begin{array}{c}2*2+3*22\\4*2+1*22\end{array}\right]\\X=1/10\left[\begin{array}{c}4+66\\8+22\end{array}\right]\\X=1/10\left[\begin{array}{c}70\\30\end{array}\right]\\X=\left[\begin{array}{c}70/10\\30/10\end{array}\right]\\X=\left[\begin{array}{c}7\\3\end{array}\right][/tex]
So, x = 7 and y =3
Hence Option C is correct.
Answer:
7
Step-by-step explanation:
right on edge
What is the solution to the equation 1/4x- 1/8=7/8+1/2x
Answer:
4
Step-by-step explanation:
Start by multiplying both sides by 4.
[tex]\frac{1}{4} x-\frac{1}{8} =\frac{7}{8} +\frac{1}{2} x\\x-\frac{1}{2} =\frac{7}{2}+2x[/tex]
Next, combine like terms.
[tex]x-\frac{1}{2} =\frac{7}{2}+2x\\-\frac{1}{2} =\frac{7}{2} +x\\x=\frac{8}{2} \\x=4[/tex]
ces
Question 8 of 20 :
Select the best answer for the question
8. Gina decided to order some clothes from a catalogue. She ordered 3 pairs of jeans at $39 each, 4 T-shirts at $15 each, and 2 skirts at
$27 each. What was her total bill?
A. $192
B. $231
C. $117
D. $177
-3 3/8 x -2/3 divided by(-1 3/4)
[tex]\bf \stackrel{mixed}{-3\frac{3}{8}}\implies -\cfrac{3\cdot 8+3}{8}\implies \stackrel{improper}{-\cfrac{27}{8}}~\hfill \stackrel{mixed}{-1\frac{3}{4}}\implies -\cfrac{1\cdot 4+3}{4}\implies \stackrel{improper}{-\cfrac{7}{4}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \stackrel{\textit{from left to right}}{-\cfrac{\stackrel{9}{~~\begin{matrix} 27 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}{\underset{4}{~~\begin{matrix} 8 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}\times -\cfrac{~~\begin{matrix} 2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{~~\begin{matrix} 3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\div -\cfrac{7}{4}}\implies \cfrac{9}{4}\div -\cfrac{7}{4}[/tex]
[tex]\bf \cfrac{9}{~~\begin{matrix} 4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\times-\cfrac{~~\begin{matrix} 4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{7}\implies -\cfrac{9}{7}[/tex]
perform the indicated operation 1 1/3 × 3 3/4
Answer:
5.
Step-by-step explanation:
1 1/3 * 3 3/4
= 4/3 * 15/4
= 60/12
= 5.
First we simplify,
[tex]1\dfrac{1}{3}\cdot3\dfrac{3}{4}[/tex]
to
[tex]\dfrac{4}{3}\cdot\dfrac{15}{4}[/tex]
Then we continue simplifying,
[tex]
\dfrac{4\cdot15}{4\cdot3}=\dfrac{15}{3}=\boxed{5}
[/tex]
Hope this helps.
r3t40
What is the solution to the system of equations below when graphed?
y=3x+1
y=4x-1
A. (3,4)
B. (1,-1)
C. (6,8)
D. (2,7)
Answer:
A
Step-by-step explanation:
Lets say x=1
y: 3(1)+1=4
x: 4(1)-1=3
Final answer:
The correct option is (D) (2,7). To solve the system of equations, set them equal to each other and solve for x, which is 2, and then substitute x back into either equation to find y, which is 7. Hence, the intersection point is (2, 7).
Explanation:
To find the solution to a system of equations when graphed, you look for the point where the two lines intersect. The given equations are y=3x+1 and y=4x-1.
Since both equations equal y, you can set them equal to each other to find the point of intersection:
3x + 1 = 4x - 1.
To solve for x, subtract 3x from both sides:
1 = x - 1.
Then, add 1 to both sides to isolate x:
x = 2.
To find the corresponding y value, substitute x into one of the original equations, let's use the first one:
y = 3(2) + 1,
which simplifies to y = 6 + 1 = 7.
Therefore, the solution to the system of equations and the point of intersection is (2, 7).
What is the solution to the linear equation?
4b + 6 = 2 - 6 + 4
Answer:
-1½ = b
Step-by-step explanation:
Combining all like-terms on the right side of the equivalence symbol will give you this:
4b + 6 = 0
- 6 -6
------------
4b = -6 [Divide by 4]
b = -1½ [OR -1,5]
I am joyous to assist you anytime.
In the pendulum formula, we use g=9.8 m/s^2 for the acceleration due to gravity on Earth. But what about on Venus? If an astronaut on the surface of Venus swings a 1-meter long pendulum, and it has a period of 2.11 seconds, what is the acceleration due to gravity, g, on Venus?
Answer:
Option A is the correct answer.
Step-by-step explanation:
Period of simple pendulum is given by the expression,
[tex]T=2\pi \sqrt{\frac{l}{g}}[/tex]
Where l is the length of pendulum, g is acceleration due to gravity.
Here given for Venus
Period, T = 2.11 s
Length of pendulum, l = 1 m
We need to find acceleration due to gravity, g
Substituting
[tex]2.11=2\pi \sqrt{\frac{1}{g}}\\\\\sqrt{g}=\frac{2\pi}{2.11}\\\\g=8.87m/s^2[/tex]
Acceleration due to gravity of Venus = 8.9 m/s²
Option A is the correct answer.
What is the product?
(4y - 3)(2y2 + 3y – 5)
8y3 + 3y + 15
8y3 – 23y + 15
8y3 - 6y2 - 17y + 15
O 8y2 + 6y2 - 29y + 15
Answer:
8y³ + 6y² - 29y + 15
Step-by-step explanation:
Take each separate term in the second set of parentheses and multiply it by the terms in the first set of parentheses. Put them altogether, and you will arrive at the above answer.
I am joyous to assist you anytime.
Hence, the product is [tex]8y^3+6y^2-29y+15[/tex]
What is product?The product of two numbers is the result you get when you multiply them together. So 12 is the product of 3 and 4, 20 is the product of 4 and 5, and so on.
How to solve?multiplying corresponding terms,
[tex](4y-3)(2y^2+3y-5)\\8y^3+12y^2-20y-6y^2-9y+15\\8y^3+6y^2-29y+15[/tex]
Hence, the product is [tex]8y^3+6y^2-29y+15[/tex]
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what is the answer for 2a x -a?
Answer:
-2a²
Step-by-step explanation:
The question is 2a × -a
This means 2a(-a)
= -2×(a×a)
=-2(a²)
=-2a²
Helpppppo!!!!!!!!!
The mean of the temperatures in the chart is 24° with standard deviation of 4º. How many years had temperatures within one
standard deviation of the mean?
20
25
28
35
Answer:
25
Step-by-step explanation:
If the mean of the temperatures in the chart is 24° with standard deviation of 4º, there has been 25 years within one standard deviation of the mean.
27° is the temperature value that is within one standard deviation of mean.
What is Mean?Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.
Given
Mean of the temperatures in the chart [tex]\mu[/tex] [tex]\mew[/tex]= 24°
Standard deviation [tex]\sigma[/tex] = 4º
The lower and upper bound for temperature within one standard deviation of the mean is given as:
Lower bound = [tex]\mu[/tex] - [tex]\sigma[/tex] = 24° - 4º = 20°
Thus, the lower bound is = 20°
Upper bound = [tex]\mu[/tex] + [tex]\sigma[/tex] = 24° + 4º = 28°
Thus, the upper bound is = 28°
Now, the temperature value between (Lower bound, Upper bound) that is (20°, 28°) is said to be within one standard deviation of the mean.
Hence, 27° is the temperature value that is within one standard deviation of mean.
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