Answer:
[tex]x^{3} -12[/tex]
Step-by-step explanation:
[tex]y=\sqrt[3]{x+12}[/tex]
Replace x with y to get
[tex]x=\sqrt[3]{y+12}[/tex]
Cube both side
[tex]x^{3}=y+12[/tex]
Subract 12 from both sides
[tex]x^3-12=y[/tex]
Find three rational numbers between -2 and 1 ?
Answer:
-19/10,-18/10,-17/10
Step-by-step explanation:
multiply the both numbers up and down by 10.
then find the numbers
Answer:-1, 0, -1.33
Step-by-step explanation: Rational numbers include those with repeating decimals, natural, counting, etc.
Consider the polynomial:
x/4 -2x^5 +x^3/2+1
Which polynomial represents the standard form of the original polynomial?
A. x^3/2– 2x5 +x/4 + 1
B.–2x5 +x^3/2 +x/4 + 1
C.–2x5 +x/4 + x^3/2 + 1
D.1 – 2x5 + x^3/2 + x/4
Answer:
Step-by-step explanation:
Remember that polynomials involve ONLY integer powers of x. x^(3/2) does not satisfy that criterion.
Answer: OPTION B.
Step-by-step explanation:
In order to write a polynomial in Standard form you must arrange the terms by decreasing order of degree.
Then, given the polynomial:
[tex]\frac{x}{4} -2x^5 +\frac{x^3}{2}+1[/tex]
You must observe the exponent of each term of the polynomial and then arrange them from highest degree to lowest degree. Then, this polynomial written in Standard form is:
[tex]-2x^5 +\frac{x^3}{2}+\frac{x}{4}+1[/tex]
Select the graph for the solution of the open sentence. Click until the correct graph appears. |x| > 4
Answer:
***********o o**************
<----------(-4)--------(-2)--------(0)--------(-2)----------(4)-------------->
x>4 or x<-4
Step-by-step explanation:
You are looking for numbers that give you a distance, x, greater than 4 from 0. That wouldn't be anything between -4 and 4 because these would all give you a distance less than 4 from 0. So the answer would be to shade everything greater than 4 while also shading everything less than -4.
Here is a number line <-----|-----|-----|-----|-----|-----|-----|-----|-->
-6 -4 -2 0 2 4 6 8
Let's think about this more which of these numbers on this number line would satisfy |x|>4?
Numbers inside the numbers -4 and 4.
Or the numbers on the outside.
Let's try the inside numbers:
-2,02
|-2|>4
2>4 is false which means -2 doesn't satisfy |x|>4
|0|>4
0>4 is false which means 0 doesn't satisfy |x|>4
|2|>4
2>4 is false which means 2 doesn't satisfy |x|>4
We could also try -4 and 4... but these will both give you a distance equal to 4 from 0. And we are looking for greater than.
|-4|>4
4>4 is false which mean -4 doesn't satisfy |x|>4
|4|>4
4>4 is false which means 4 doesn't satisfy |x|>4
Now let's try the numbers on the outside:
-6,6,8
|-6|>4
6>4 is true so -6 does satisfy |x|>4
|6|>4
6>4 is true so 6 does satisfy |x|>4
|8|>4
8>4 is true so 8 does satisfy |x|>4
So what I'm trying to do is convince you more that the only numbers that would satisfy |x|>4 are numbers outside the interval from -4 to 4.
So x>4 or x<-4.
On a number line the solution would look like this:
***********o o**************
<----------(-4)--------(-2)--------(0)--------(-2)----------(4)-------------->
We have holes at -4 and 4 to mean we do not include those numbers. We would have if the inequality read [tex]|x| \ge 4[/tex]. The line underneath this inequality means to include or equals. We do not want to include; we did not have the equal sign. The only difference between the two solutions would be to fill the holes if you [tex]|x| \ge 4[/tex].
***********o o**************
<----------(-4)--------(-2)--------(0)--------(-2)----------(4)-------------->
What are the solutions of 3x^2 - x +7 =0?
Answer: Option A
[tex]x=\frac{1+\sqrt{83}i}{6}[/tex] or [tex]x=\frac{1-\sqrt{83}i}{6}[/tex]
Step-by-step explanation:
Use the quadratic formula to find the zeros of the function.
For a function of the form
[tex]ax ^ 2 + bx + c = 0[/tex]
The quadratic formula is:
[tex]x=\frac{-b\±\sqrt{b^2-4ac}}{2a}[/tex]
In this case the function is:
[tex]3x^2-x+7=0[/tex]
So
[tex]a=3\\b=-1\\c=7[/tex]
Then using the quadratic formula we have that:
[tex]x=\frac{-(-1)\±\sqrt{(-1)^2-4(3)(7)}}{2(3)}[/tex]
[tex]x=\frac{1\±\sqrt{1-84}}{6}[/tex]
[tex]x=\frac{1\±\sqrt{-83}}{6}[/tex]
Remember that [tex]\sqrt{-1}=i[/tex]
[tex]x=\frac{1\±\sqrt{83}*\sqrt{-1}}{6}[/tex]
[tex]x=\frac{1\±\sqrt{83}i}{6}[/tex]
[tex]x=\frac{1+\sqrt{83}i}{6}[/tex] or [tex]x=\frac{1-\sqrt{83}i}{6}[/tex]
Final answer:
The solutions to the equation 3x² - x + 7 = 0 are complex numbers. Using the quadratic formula, we find the solutions to be x = (1 + i√83) / 6 and x = (1 - i√83) / 6.
Explanation:
The solutions of the quadratic equation 3x² - x + 7 = 0 cannot be real numbers because the discriminant (b² - 4ac), in this case, is negative ((-1)² - 4(3)(7) = 1 - 84 = -83). Therefore, we need to use the quadratic formula to find the complex solutions. This formula is given by x = (-b ± √(b² - 4ac)) / (2a). By substituting the values from the equation into the quadratic formula, we obtain the complex solutions.
Quadratic formula application:
x = (-(-1) ± √((-1)² - 4(3)(7))) / (2(3))
x = (1 ± √(-83)) / 6
Therefore, the two complex solutions are x = (1 + i√83) / 6 and x = (1 - i√83) / 6, where i is the imaginary unit.
To confirm these answers, we can substitute each value back into the original equation and verify by simplification that each results in an identity.
slope intercept form of equation of a line that passes through (-3,8) y=-2/3x+6 what is the point slope equation for this line???
Answer:
[tex]\large\boxed{y-8=-\dfrac{2}{3}(x+3)}[/tex]
Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
We have the equation of a line in the slope-intercept form
[tex]y=-\dfrac{2}{3}x+6\Rightarrow m=-\dfrac{2}{3}[/tex]
and the point (-3, 8).
Substitute:
[tex]y-8=-\dfrac{2}{3}(x-(-3))\\\\y-8=-\dfrac{2}{3}(x+3)[/tex]
what is the ratio of 8 to 8
Answer:
1 to 1
Step-by-step explanation:
8 to 8 = 8:8 = 8/8
You can treat a ratio as a fraction. Reduce the fraction 8/8 by dividing the numerator and denominator by 8.
8/8 = 1/1
8 to 8 = 1 to 1
Answer:
1:1
Step-by-step explanation:
A ratio says that "for every _ of this quantity, you have _ of another quantity". This is just saying for every 8 of one thing, you have 8 of another. And then you can simplify, just like a fraction.
What is the beat solution to the system? X-y+2z=-7
y+z=1
x-2y-3z=0
Answer:
(0, 3 , -2)
Step-by-step explanation:
X-y+2z=-7 ------------------ equ 1
y+z=1 ------------------ equ 2
x-2y-3z=0 ------------------ equ 3
equ 1 X - y + 2z = -7
equ 3 x - 2y - 3z = 0
- + __+_____
equ 1 - equ 3 ⇒ y + 5z = -7 -------------- equ 4
equ 2 y + z = 1
equ 4 y + 5z = -7
- - = +
equ 2 - equ 4 -4z =8
z = 8/ -4 = -2
z = -2Put z = -2 in equ 2,
y + z = 1
y - 2 = 1
y = 1 + 2 =3
y = 3
Put z = -2 & y = 3 in equ 1
X - y + 2z = -7
x - 3 + 2* (-2) = -7
x - 3 - 4 = -7
x -7 = -7
x = -7 + 7 =0
x = 0
To solve the system of equations, you can use the method of substitution or elimination. Let's use the method of substitution to find the solution. First, solve for y in the second equation and substitute this value into the other equations. Simplify and solve the resulting equations to find the values of x and z.
Explanation:To find the solution to the given system of equations:
x - y + 2z = -7
y + z = 1
x - 2y - 3z = 0
You can use the method of substitution or elimination to solve the system. Let's use the method of substitution.
From the second equation, solve for y: y = 1 - zSubstitute this value of y into the other equations to eliminate y:Plug y = 1 - z into the first equation: x - (1 - z) + 2z = -7Plug y = 1 - z into the third equation: x - 2(1 - z) - 3z = 0Simplify and solve the resulting equations:x + 3z = -6x + z = 2Subtract the second equation from the first equation: x + 3z - (x + z) = -6 - 2Simplify and solve for z:Learn more about Solving systems of equations here:https://brainly.com/question/29050831
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Classify the isometry.
a) glide reflection
b) reflection
c) rotation
d) translation
Answer:
A. glide reflection
Step-by-step explanation:
This is a glide reflection since the figure has been both reflected over a line and transported downwards.
Answer:
a) glide reflection
Step-by-step explanation:
An isometry is a transformation of a figure in the plane that preserves lenght, it could be reflections, rotations, or translations, in the figure you can se what is called a glide reflection, which is a reflection of the figure over a line, and then a translation of the same figure.
what is the midpoint of the line segment with endpoints ( 1,-6) (-3,4)
Answer:
(-1, -1)
Step-by-step explanation:
[tex]\boxed{midpoint=(\frac{x_{1} +x_{2} }{2} ,\frac{y_{1}+y_{2} }{2}) }[/tex]
Midpoint of line segment
[tex]= (\frac{1-3}{2},\frac{-6+4}{2} )\\= (\frac{-2}{2},\frac{-2}{2})\\= (-1, -1)[/tex]
A fancy rug in the shape of a trapezoid has an area of 800 square inches and the sum of the lengths of its parallel sides is 80 inches. What is the height of the rug?
A.
10 in.
B.
20 in.
C.
40 in.
D.
80 in.
Answer:
The answer is B. 20in.
Step-by-step explanation:
The parallel sides have to be the two bases (b1 and b2) = 80in.
h = height or altitude.
h = 2(800)/b1+b2
h = 1600/80
h = 20 in.
Answer:
The height of the Trapezoid is 20 inches
Step-by-step explanation:
Given Parameters
Shape: Trapezoid
Area of the Trapezoid = 800in²
Sum of opposite parallel sides = 80 in
Required: Height of the Trapezoid...
Are of trapezoid is calculated using the following formula:
A = ½(a + b) * h
Where a + b = sum of the opposite parallel sides
h = height.
A = Area.
By comparison, we have that
A = 800 in²
a + b = 80 in
By substituton, we have that
A = ½(a + b) * h becomes
800 = ½(80)h
800 = ½ * 80 * h
800 = 40 h---- divide through by 40
800/40 = 40h/40
20 = h --- reordsr
h = 20in
Hence, the height of the Trapezoid is 20 inches
Factor completely x2 + 25.
(x + 5)(x + 5)
(x + 5)(x − 5)
(x − 5)(x − 5)
Prime
Answer:
Prime
Step-by-step explanation:
x² + 25 is prime (unfactorable).
Here's what the other options come out to:
(x + 5)(x + 5) = x² + 10x + 25
(x + 5)(x − 5) = x² − 25
(x − 5)(x − 5) = x² − 10x + 25
The correct option is option D: x²+25 is prime.
How to factorize the algebraic expression?The algebraic expressions are factorized by taking common factors from the terms and using algebraic properties like a²-b²=(a+b)(a-b), (a+b)²=a²+2ab+b², etc.
The expression which can not be factorized is called prime i.e. unfactorizable.
Here x²+25 is unfactorizable so it is prime.
Also by checking each option
(x + 5)(x + 5)=x²+10x+25≠x²+25 so this option is incorrect.(x + 5)(x − 5)=x²-25≠x²+25 so this option is incorrect.(x − 5)(x − 5)=x²-10x+25≠x²+25 so this option is incorrect.Prime: it is true as x²+25 is unfactorizable.Therefore x²+25 is prime.
Learn more about factorization
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A wire is tied from the top of one tower to the top of another. The angle of depression from the top
to the top of the taller tower to the top of the shorter tower is 37 degrees. If the wire is 100 feet long, find the
distance between the towers.
Check the picture below.
let's recall that the "gray" angle of depression is equals to its alternate interior angle of elevation in "blue".
make sure your calculator is in Degree mode.
Use the elimination method to solve the system of equations. Choose the correct ordered pair. 4x4y-27 5x-y-18
A. (6,9)
B. (2,8)
C. (3,6)
D. (5,7)
Answer:
(5,7)
Step-by-step explanation:
4x+y=27
5x-y=18
Since we want to solve this by elimination we need the lines to be in the same form, and a column with opposite variables or same variables. We actually have both of these.
Both equations are in the form ax+by=c.
The column that contains the y's, we have opposites there. That is the opposite of y is -y. When you add opposites, you get 0.
So we just add vertically now.
4x+y=27
5x-y=18
--------------Add
9x+0=45
9x =45
Divide both sides by 9:
x =45/9
Simplify:
x =5
Now to find y, you just need to use one of your equations (just pick one) along with x=5.
I guess I will choose 4x+y=27 with x=5.
4x+y=26 with x=5
4(5)+y=27
20+y=27
Subtract 20 on both sides:
y=27-20
y=7
So the solution (x,y) is (5,7).
Which method would you use to prove that the two triangles are congruent?
SAS
SSS
AAS
ASA
Answer: The correct option is (A) SAS.
Step-by-step explanation: We are given to select the method that would be used to prove that the two triangles are congruent.
Let us name the given triangles as ABC and EBD as shown in the attached figure below.
Then, according to the given information, we have
[tex]AB=BD\\\intertext{and}\\BC=EB.[/tex]
Also, ∠ABC and ∠EBD are vertically opposite angles, so they must have equal measures.
That is,
[tex]m\angle ABC=m\angle EBD.[/tex]
So, in triangles ABC and EBD, we have
[tex]AB=BD,\\\\BC=EB\\\\\intertext{and}\\m\angle ABC=m\angle BED.[/tex]
That is, two sides and the included angle of one triangle are congruent to the corresponding two sides and the included angle of the other triangle.
Therefore, by side-angle-angle postulate, the two triangles are congruent.
Thus,
ΔABC ≅ ΔEBD (SAS postulate).
Option (A) is CORRECT.
The variable z is directly proportional to x. When x is 15, z has the value 165. What is the value of z when x = 25?
Answer:
z=275
Step-by-step explanation:
it has a ratio 1:11
that must be it
Answer:
275
Step-by-step explanation:
z is directly proportional to x:
z = kx
When x is 15, z is 165.
165 = k × 15
k = 11
When x = 25:
z = 11 × 25
z = 275
A truck with 36-in.-diameter wheels is traveling at 55 mi/h.
How many revolutions per minute do the wheels make?
Answer:
The wheels make 512 revolutions per minute
Step-by-step explanation:
Diameter of truck = 36 in
Speed = 55 mi/h
Revolutions per minute =?
Radius r = diameter / 2
r = 36/2
r = 18 inches
Speed = 55 mi/h
1 mile = 63360 inches
55 miles = 55*63360 inches
55 miles = 3484800 inches
1 hr = 60 minutes
Speed = 3484800 inches/60 minutes
Speed = 58,080 inches/min
The formula used to calculate the revolutions per minute is:
revolutions = speed/Circumference
revolutions = 58,080 / 2*3.14*18
revolutions = 58,080 /113.4
revolutions = 512.16
revolutions = 512 revolutions per minute
So, The wheels make 512 revolutions per minute
what number should be added to both sides of the equation to complete the square
xsquared2-10x=7
Answer:
subtract 2 from each side and o think u decide the last two numbers
Answer:
Step-by-step explanation:2-10x=7
First you have to subtract you 2 on both sides so it would 7-2= 5
You are left with -10x =5
Then you divide your -10x by -10 to get rid of your x
Last you divide 5/-10
Which of the following inequalities matches the graph?
A.3x - 2y \geqslant 4
B.3x - 4y \leqslant 2
C.3x - 2y \leqslant 4
D.the correct inequality is not listed
Answer:
C.Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept → (0, b)
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
From the graph we have the points (0, -2) and (6, 7).
(0, -2) → b = -2
Calculate the slope:
[tex]m=\dfrac{7-(-2)}{6-0}=\dfrac{9}{6}=\dfrac{9:3}{6:3}=\dfrac{3}{2}[/tex]
Put the value of b and m to the equation of the line in the slope-intercept form:
[tex]y=\dfrac{3}{2}x-2[/tex]
=====================================
<, > - dotted line
≤, ≥ - solid line
<, ≤ - shaded region below the line
>, ≥ - shaded region above the line
======================================
We have the soli line (≤ or ≥).
Shaded region is above the line (> or ≥)
Therefore we have the answer: [tex]y\geq\dfrac{3}{2}x-2[/tex]
Convert to the standard form: [tex]Ax+By=C[/tex]
[tex]y\geq\dfrac{3}{2}x-2[/tex] multiply both sides by 2
[tex]2y\geq3x-4[/tex] subtract 3x from both sides
[tex]-3x+2y\geq-4[/tex] change the signs
[tex]3x-2yleq4[/tex]
Solve -5x=30 (5points)
6
-6
25
35
Answer: -6
Step-by-step explanation:
-5x = 30
x = 30/-5
x = -6
Hope it helped!
Bryan is getting trained and licensed to be a truck driver. He only has $350 in his bank account. The training is free but gas costs 13 cents per mile. Write an equation where a is the amount of money in Bryan's bank account and m is the number of miles he travels.
A. a=0.13m−350
B. a=350−13m
C. a=13m−350
D. a=350−0.13m
Answer:
D
Step-by-step explanation:
a= 350 minus every 13 cents per mile
A ski club charges a $45 membership fee plus $18 to rent ski equipment per day. Which of the following equation can be used to find the total cost of membership at the club, when renting equipment for X days?
Answer:
[tex]y = 18x + 45[/tex]
Step-by-step explanation:
You can use a linear equation of the form
[tex]y = mx + b[/tex] to represent the situation.
where b is the constant amount represented by the intercept with the y-axis, in this case b e is the cost of membership.
m is the slope, and in this case it is the cost per day of renting a team for x days.
y is the total cost of membership at the club, when renting equipment for X days
So the linear equation is:
[tex]y = 18x + 45[/tex]
There are 42 boys and 48 girls in the sixth grade and each student must be assigned a homeroom. Each homeroom should have the same number of boys and the same number of girls.
What is the greatest possible number of sixth-grade homerooms?
A
8
B
6
C
4
The most significant number of homerooms that can be created with an equal number of boys and girls in each is 6.
Explanation:To answer this question, we need to find the greatest common divisor (GCD) for the number of boys and girls. The GCD is the most significant number that can divide both numbers equally. The GCD of 42 (number of boys) and 48 (number of girls) is 6.
Therefore, the sixth grade's most significant possible number of homerooms would be 6, with each homeroom having seven boys and eight girls.
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The function f(x)=−5x^2+3 is defined over the domain −4
Answer:
-77 if I understand correctly
Step-by-step explanation:
If the domain is really {-4} and you have the function f(x)=-5x^2+3.
The range is just whatever the result of f(-4) is...
f(-4)=-5(-4)^2+3
f(-4)=-5(16)+3
f(-4)=-80+3
f(-4)=-77
So again if the question is really "The function f(x)=-5x^2+3 is defined over the domain {-4}, what is the range?"... then the answer is just {-77}
(- 7x + 1) - (4x - 5)
Answer:-11x+6
Step-by-step explanation:
(-7x+1)-(4x-5)
collect the like terms and then calculate the sum
-7x+1-4x+5
-11x+1+5
-11x+6
Answer:
-11x +6
Step-by-step explanation:
(- 7x + 1) - (4x - 5)
Distribute the minus sign
(- 7x + 1) - 4x + 5
Combine like terms
-11x +6
m=
7/8 divided by m= 1/7
How do I solve for m?
Answer:
[tex]\large\boxed{m=\dfrac{49}{8}}[/tex]
Step-by-step explanation:
[tex]\dfrac{7}{8}:m=\dfrac{1}{7}\\\\\dfrac{7}{8}\cdot\dfrac{1}{m}=\dfrac{1}{7}\\\\\dfrac{7}{8m}=\dfrac{1}{7}\qquad\text{cross multiply}\\\\(8m)(1)=(7)(7)\\\\8m=49\qquad\text{divide both sides by 8}\\\\m=\dfrac{49}{8}[/tex]
The quotient of three times a number and 4 is at least -16
Quotient is division,
Writing the equation out you get:
3x/4 ≥ -16
Now we can solve by x.
First multiply both sides by 4:
3x ≥ -64
Now divide both sides by 3:
x ≥ -64/3
The original price of a game system was reduced by $99.
If p = the game system's original price in dollars, which algebraic expression
represents the reduced price?
Final answer:
The algebraic expression for the reduced price of the game system is p - $99, where p represents the original price in dollars.
Explanation:
To express the reduced price of the game system algebraically, we start with the original price, represented by the variable ( p ), and subtract the reduction amount of $99. Mathematically, this can be represented as p - $99.
This expression signifies that we are taking the original price ( p ) and reducing it by $99 to find the new price after the discount. It's essential to understand that algebraic expressions provide a concise and general way to represent mathematical relationships.
In this case, the expression p - $99 encapsulates the idea of reducing the original price by $99, allowing us to calculate the reduced price for any given original price represented by the variable ( p ). This algebraic representation is flexible and can be applied to various scenarios involving discounts or reductions.
18 divided 5236
[tex]18 \sqrt{5236} [/tex]
What is .7995 rounded to the nearest cent?
Answer:
.7995 rounded to the nearest cent is 0.80 cents
Answer:
.7995 rounded to the nearest cent is .80.
Step-by-step explanation:
Rounding with numbers higher than 4 makes them round up, lower than 5 makes them round down.
The compound probability of two events, E and F, is ; the probability of E is and of F is . In two or more complete sentences, explain why E and F are not independent.
Answer:
Events E and F are not independent if the probability of event E occurring is affecting the probability of event F occurring.
Step-by-step explanation:
Two events are independent when the probability of one event occurring has no connection with that of the other event.
Example, when you toss a coin and roll a six sided die, the probability of getting a head or a tail has no connection with the probability of getting any number face.A real life example will be the probability going to the mall and owning a cat at home.These two have no influence on one another.
Mathematically independent events can be calculated as;
P(E∩F)=P(E)-P(F)