Answer:
The correct option is B:
Subtract 2 from both sides
Step-by-step explanation:
We have the equation x²-4x+16=2
The first step to solve this equation is:
Subtract 2 from both sides
We get;
x²-4x+16=2
x²-4x+16-2=2-2
x²-4x+14=0
Now this is the quadratic equation. You can use quadratic formula to solve this equation....
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]
Write an equation in a point-slope form that passes through the given point with the given slope (3, 5), m = -4 and-1, 8), m = ½
Answer:
[tex]\large\boxed{y-5=-4(x-3)}\\\boxed{y-8=\dfrac{1}{2}(x+1)}[/tex]
Step-by-step explanation:
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
[tex]m=-4,\ (3,\ 5)\\\\y-5=-4(x-3)[/tex]
[tex]m=\dfrac{1}{2},\ (-1,\ 8)\\\\y-8=\dfrac{1}{2}(x-(-1))\\\\y-8=\dfrac{1}{2}(x+1)[/tex]
Which function described below has the greatest rate of change? I WILL MARK BRAINLIEST
Answer:
C III
Step-by-step explanation:
The rate of change of a linear function is the slope.
f(x) = mx + b is the equation of a linear function whose graph is a straight line. m is the slope.
I f(x) = 4x - 3; m = slope = 4
II f(x) = 1/2 x + 5; m = slope = 1/2
III We can use two points to find the slope.
Let's use points (1, 6) and (2, 12).
m = slope = (y2 - y1)/(x2 x1) = (12 - 6)/(2 - 1) = 6/1 = 6
The three slopes are 4, 1/2, 6.
The greatest rate of change is 6, so the answer is C III.
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)-------------->
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
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]
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
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.
Rowena walks 3 kilometers a day. How many meters does she walk in three days?
[tex]\huge{\boxed{\text{9,000 meters}}}[/tex]
There are 1,000 meters in each kilometer, so multiply to find the daily number of meters. [tex]3*1000=3000[/tex]
Multiply this by 3 to find the number of meters Rowena walks in three days. [tex]3000*3=\boxed{9000}[/tex]
which two numbers have a mean of 10 and a range of 4
Answer:
12 and 8
Step-by-step explanation:
set two numbers as x and y
mean of 10 → x+y/2=10
range of 4 → x-y=4
x+y=20
+ x-y=4
____________
2x=24, x=12
12-y=4, y=8
Answer:
the answer is 8 and 12 hope it helps
Step-by-step explanation:
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}
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.
Solve -5x=30 (5points)
6
-6
25
35
Answer: -6
Step-by-step explanation:
-5x = 30
x = 30/-5
x = -6
Hope it helped!
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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PLEASE!!!! ASAP!!! Two airplanes leave the airport. Plane A departs at a 44° angle from the runway, and plane B departs at a 40° from the runway. Which plane was farther away from the airport when it was 22 miles from the ground? Round the solutions to the nearest hundredth.
Answer:
Plane B was farthest away from the airport
Step-by-step explanation:
This question requires you to visualize the run way as the horizontal distance to be covered, the height from the ground as the height gained by the plane after take of and the distance from the airport as the displacement due to the angle of take off.
In plane A
The take-off angle is 44° and the height gained is 22 ft.
Apply the relationship for sine of an angle;
Sine Ф°= opposite side length÷hypotenuse side length
The opposite side length is the height gained by plane which is 22 ft
The angle is 44° and the distance the plane will be away from the airport after take-off will be represented by the value of hypotenuse
Applying the formula
sin Ф=O/H where O=length of the side opposite to angle 44° and H is the hypotenuse
[tex]Sin44=\frac{O}{H} \\\\\\Sin44=\frac{22}{H} \\\\\\H=\frac{22}{sin44deg} \\\\\\H=31.67[/tex]
31.67 miles
In plane B
Angle of take-off =40°, height of plane=22miles finding the hypotenuse
[tex]sin40deg=\frac{O}{H} \\\\\\sin40deg=\frac{22}{H} \\\\\\H=\frac{22}{sin40deg} \\\\\\H=34.23miles[/tex]
34.23miles
Solution
After take-off and reaching a height of 22 ft from the ground, plane A will be 31.67 miles from the airport
After take-off and reaching a height of 22 ft from the ground, plane B will be 34.23 miles away from the airport.
Answer:
9.33 (flvs)
Step-by-step explanation:
i took the test
Let f(x) = 4x - 7 and g(x) = 2x - 3. Find (fog)(4).
Answer:
13
Step-by-step explanation:
(f∘g)(4) is another way of writing f(g(4)).
First, find g(4).
g(x) = 2x − 3
g(4) = 2(4) − 3
g(4) = 5
Now substitute into f(x).
f(x) = 4x − 7
f(g(4)) = 4g(4) − 7
f(g(4)) = 4(5) − 7
f(g(4)) = 13
[tex](f\circ g)(x)=4(2x-3)-7=8x-12-7=8x-19\\\\(f\circ g)(4)=8\cdot4-19=13[/tex]
4x – 9y = 7
–2x + 3y = 4
What number would you multiply the second equation by in order to eliminate the x-terms when adding to the first equation?
Answer:
By 2.
Step-by-step explanation:
You need to eliminated the x-terms, so the first step is to focus only in those terms.
So yo have 4x and -2x, since you are thinking in eliminate then you have this equation>
[tex]4-2*K=0[/tex]
Note that we dont put the x variable, since we are studying its coefficients in the equations system.
Solving for K, Gives us that K=2
So.
Multiplying the second equation by 2 results in
[tex]-4x+6y=8[/tex]
When you put them together, it gives you the following
[tex]4x-9y -4x+6y- 7+8[/tex]
and the final equation is
[tex]-3y=15\\[/tex]
giving you the answer for y, that is [tex]y=-5[/tex]
Answer: 2 and 3.
Step-by-step explanation:
Tabitha is trying to find the equation of a line perpendicular to y= 1/2x - 5 in slope-intercept form that passes through the point (2, -7). which of the following equations will she use.
1. y-(-7) = 1/2(x-2)
2.y-2=1/2(x-(-7))
3.y-(-7)=-2(x-2)
4.y-2=-2(x-(-7))
Answer:
[tex]\large\boxed{3.\ y-(-7)=-2(x-2)}[/tex]
Step-by-step explanation:
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
Let [tex]k:y=m_1x+b_1,\ l:y=m_2x_b_2[/tex].
[tex]l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\if m_1=m_2[/tex]
================================================
We have the equation of the line:
[tex]y=\dfrac{1}{2}x-5\to m_1=\dfrac{1}{2}[/tex]
Therefore
[tex]m_2=-\dfrac{1}{\frac{1}{2}}=-2[/tex]
Put it and coorinates of the point (2, -7) to the equation of a line
in the point-slope form:
[tex]y-(-7)=-2(x-2)\\\\y+7=-2(x-2)[/tex]
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
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.
(- 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
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.
Use the Counting Principle to find the probability.
rolling a 5 on each of 2 number cubes
Answer:
2/12
Step-by-step explanation:
Rolling a 5 on one die the probability is 1 out of 6 or 1/6 so when you add the second die the probability increases as well as the number of outcomes so you have 1/6+1/6 or 2/12. hope this helps
Answer:
1/36
Step-by-step explanation:
A cube has six sides. On number cubes (also called dice), the sides are numbered 1 through 6. So the probability of rolling a 5 on either cube is 1/6. The probability of rolling a 5 on both cubes is:
P(A and B) = P(A) × P(B)
P(A and B) = 1/6 × 1/6
P(A and B) = 1/36
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
here: https://brainly.com/question/25829061
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-8(5x+5)+9x(10x+9)=20
[tex]-8(5x+5)+9x(10x+9)=20\\-40x-40+90x^2+81x-20=0\\90x^2+41x-60=0\\\\\Delta=41^2-4\cdot90\cdot(-60)=1681+21600=23281\\\\x=\dfrac{-41\pm \sqrt{23281}}{2\cdot90}=\dfrac{-41\pm \sqrt{23281}}{180}[/tex]
18 divided 5236
[tex]18 \sqrt{5236} [/tex]
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]
Find the Inverse of this function f(x)={(3,4),(4,3),(-2,6)}
as you may already know, the inverse of a function has the same exact x,y pairs but backwards, namely f(x)'s domain is f⁻¹(x)'s range.
[tex]\bf \stackrel{f(x)}{\begin{array}{|cc|ll} \cline{1-2} \stackrel{domain}{x}&\stackrel{range}{y}\\ \cline{1-2} 3&4\\ 4&3\\ -2&6\\ \cline{1-2} \end{array}}~\hspace{10em} \stackrel{inverse~of~f(x)}{\begin{array}{|cc|ll} \cline{1-2} \stackrel{domain}{x}&\stackrel{range}{y}\\ \cline{1-2} 4&3\\ 3&4\\ 6&-2\\ \cline{1-2} \end{array}}[/tex]
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).
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]