Answer:
(x+5)(x-1)(x+1)
Step-by-step explanation:
Let's attempt factoring by grouping:
So what this means we first want to group the first two terms together and second two terms together, like so:
(x^3+5x^2)+(-x-5)
Now we factor what we can from each pair:
x^2(x+5)+1(-x-5)
Notice x+5 doesn't appear to be the same as -x-5 so we should factor out -1 instead of 1 in the second pair of terms:
x^2(x+5)-1(x+5)
You have two terms: x^2(x+5) and -1(x+5); they have a common factor of (x+5) so we can factor it out:
(x+5)(x^2-1)
You can actually factor this more because x^2-1 is a difference of squares.
The formula for factoring a difference of squares is u^2-v^2=(u-v)(u+v).
So the factored form of x^2-1 is (x-1)(x+1).
So the complete factored form of our expression we had initially is
(x+5)(x-1)(x+1).
Answer:
[tex]\large\boxed{x^3+5x^2-x-5=(x+5)(x-1)(x+1)}[/tex]
Step-by-step explanation:
[tex]x^3+5x^2-x-5\qquad\text{distributive}\\\\=x^2(x+5)-1(x+5)\\\\=(x+5)(x^2-1)\\\\=(x+5)(x^2-1^2)\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\\\=(x+5)(x-1)(x+1)[/tex]
(50 Points)
Drag each description to the correct location on the table. Each description can be used more than once.
Some systems of equations and their graphs are given in the table. For each system, place the description(s) in the box that correctly describe the type of system shown.
Please helppppp :((((
Answer:3x+y=3 is the red line.
6x+y=-4 is the blue line.
Step-by-step explanation:I answer it on the test it is right..
graph the line with slope -2/3 passing through the point (-3,5)
Answer:
[tex]\large\boxed{y-5=-\dfrac{2}{3}(x+3)}[/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
(x₁, y₁) - point on a line
We have the slope [tex]m=-\dfrac{2}{3}[/tex] and the point [tex](-3,\ 5)[/tex].
Substitute:
[tex]y-5=-\dfrac{2}{3}(x-(-3))\\\\y-5=-\dfrac{2}{3}(x+3)[/tex]
Which is a perfect square?
Answer:
121
Step-by-step explanation:
THIS IS BECAUSE 11*11 = 121
Answer:
121
Step-by-step explanation:
121= 11x11, that is the only option
140 has no square
168 is close, but still isn't a square
195 is 1 away from a square, but not a square
Given the system of equations, match the following items.
x + 3y = 5
x - 3y = -1
To solve the system of equations x + 3y = 5 and x - 3y = -1, we add both equations to get 2x = 4, solve for x to find x = 2, and then substitute x back into one of the equations to find y = 1, resulting in the solution (2, 1).
The solution of the system of linear equations given by x + 3y = 5 and x - 3y = -1 involves manipulating the equations to find the values of x and y that satisfy both equations simultaneously. One common method to solve these is to add or subtract the equations, which eliminates one variable, making it possible to solve for the other.
Starting with the addition method, we align the equations and add them together:
x + 3y = 5
x - 3y = -1
Adding these equations, we get 2x = 4, and solving for x gives us x = 2. We can substitute x = 2 back into one of the original equations to find the value of y, yielding y = 1.
The solution to the system is the intersection point of the two lines represented by the equations, which is the point (2, 1).
Simplify this algebraic expression completely.
7x-5(x+6)
Answer:
8x+1
Step-by-step explanation:
Answer:
x=15
Step-by-step explanation:
7x−5(x+6)
=7x+(−5)(x)+(−5)(6)
=7x+−5x+−30
=7x+−5x+−30
=(7x+−5x)+(−30)
=2x+−30
-2x=-30
x=15
The altitude of an isosceles triangle is the same segment in the triangle as
the
A. hypotenuse
B. median
c. bisector
D. leg
B -median
Hypotenuse is only right triangles and legs are sides of a triangle. A bisector divides something in half evenly . Altitude is height of a triangle and median is the same segment
:
The altitude of an isosceles triangle is the same segment in the triangle as the bisector.
What is a bisector?The bisector is a line that divides a line or an angle into two equivalent parts. The bisector of a segment always contains the midpoint of the segment.
In an isosceles triangle,
Bisector of vertex angle = midline of base side = altitude
The altitude of an isosceles triangle is the same segment in the triangle as the bisector.
Option C is correct.
Find out more information about bisector here
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can someone help with this question?
Answer:
y ≤ ¼x + 1
Step-by-step explanation:
Starting from the y-intercept of course, use rise\run until you hit another endpoint [finding the rate of change (slope)]. That means me we go up north one block, then go over four blocks east, and since the slope is already simplified, we do not need to go any further. Now all we have left is to determine the correct inequality symbol, and since we know that the bottom portion of the graph is shared, we automatically know it is less than, but to check this, we need to do what is called a zero-interval test [do not recall the actual term], meaning that we plug in 0 for both y and x, getting 0 < 1, which is a GENUINE statement, so the bottom portion stays shaded, otherwise we would have had to shade the top portion if it were a false statement. Finally, we have to determine if we have to add an equivalence line under the inequality symbol, and we DO because as you can see, the line is SOLID BLACK. If it were DASHED BLACK, then it would stay "<" instead of "≤".
I am joyous to assist you anytime.
Find the length of the side labeled x. Round intermediate values to the nearest tenth. Use the rounded values to calculate the next value. Round your final answer to the nearest tenth.
A. 69.4
B. 61.1
C. 57.9
D. 36.9
Answer:
Step-by-step explanation:
Givens
Tan(60) = opposite / adjacent
adjacent = 26
Cos(39) = adjacent / hypotenuse
Solution
Tan(60) = opposite (which is the height) / 26 Multiply both sides by 26
26*tan(60) = opposite Multiply the left.
tan60 = 1.732
26 * 1.732 = opposite
45.033
====================
Cos(39) = adjacent / hypotenuse
cos(39) = 0.7771
0.7771 = 45.0333 / x Multiply both sides by x
0.7771*x = 45.0333 Divide by 0.7771
x = 45.0333 / 0.7771
x = 57.94
Answer:
option C
Step-by-step explanation:
We have to find the value of x
[tex]tan\theta=\frac{perpendicular side}{base}[/tex]
[tex]tan60^{\circ}=\frac{height}{26}[/tex]
We know that [tex] tan60^{\circ}=\sqrt3[/tex]
[tex]\sqrt3=\frac{height}{26}[/tex]
[tex]height=1.732\times 26[/tex]
Where [tex]\sqrt3=1.732[/tex]
Height=45.032
Height=45.0
[tex]cos\theta=\frac{bas}{hypotenuse}[/tex]
[tex] cos 39^{\circ}=\frac{45}{x}[/tex]
[tex]0.777=\frac{45}{x}[/tex]
[tex]x=\frac{45}{0.777}[/tex]
x=57.9
Hence, option C is true.
About 95% of sixth-grade students will have heights between ______ inches and ______inches.
Answer:
53.4 and 62.6
Step-by-step explanation:
Answer:
53.4 and 62.6
Step-by-step explanation:
Got it right :/
Find the slope of the line that passes through the points (-2,3) and (2,7)
Answer:
[tex]\large\boxed{\frac{1}{1}\,\text{or}\,1}[/tex]
Step-by-step explanation:
In this question, we're trying to find the slope with the given points.
To find the slope, we're going to need to sue the slope formula.
Slope formula:
[tex]\text{Slope}=\frac{y2-y1}{x2-x1}[/tex]
You would plug in the coordinates to its right spot.
Plug in -2 to x1, 3 in y1, 2 in x2, and 7 in y2.
Your equation should look like this:
[tex]\text{Slope}=\frac{7-3}{2-(-2)}[/tex]
Now, you will solve:
[tex]\text{Slope}=\frac{7-3}{2-(-2)}\\\\\text{Slope}=\frac{4}{2-(-2)}\\\\\text{Carry the minus sign over to the -2, turning it to a positive 2}\\\\\text{Slope}=\frac{4}{2+2}\\\\\text{Slope}=\frac{4}{4}\\\\\text{Divide}\\\\\text{Slope}=\frac{1}{1}=1[/tex]
When you're done solving, you should get 1.
This means that the slope of the line is 1/1 or 1
I hope this helped you out.Good luck on your academics.Have a fantastic day!Finding the slope using two points:
The formula for slope is
[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
In this case...
[tex]y_{2} =7\\y_{1} =3\\x_{2} =2\\x_{1} =-2[/tex]
^^^Plug these numbers into the formula for slope...
[tex]\frac{7-3}{2 - (-2)}[/tex]
[tex]\frac{4}{4}[/tex]
^^^This can be further simplified down to...
1
^^^This is your slope
Hope this helped!
~Just a girl in love with Shawn Mendes
PLEASE HELP!!!
The following table shows a proportional relationship between A and B.
A= 8, 24, 40 B= 3, 9, 15
Write an equation to describe the relationship between A and B.
Answer:
b=3/8a
Step-by-step explanation:
Have a good night/day<3
To find the equation describing the proportional relationship between A and B, we divide B by A and find that the constant of proportionality is 3/8. Thus, the equation is B = (3/8)A.
To find the equation that describes the proportional relationship between A and B, we can start by examining the given pairs of values. For A = 8, B = 3; for A = 24, B = 9; and for A = 40, B = 15. We observe that as A increases, B increases at a constant rate. This suggests a direct proportionality between A and B.
To determine the constant of proportionality (the rate at which B changes with respect to A), we can divide the values of B by the corresponding values of A. Doing so, we find:
B/A for (8, 3) = 3/8B/A for (24, 9) = 9/24B/A for (40, 15) = 15/40All these ratios reduce to 3/8, which is the constant of proportionality. Therefore, B is 3/8 times A, which we can express as:
B = (3/8)A
This equation represents the proportional relationship between A and B, with the constant of proportionality being 3/8.
Do you guys know the answer for number 4
Answer:
G !!! Have a good day BLOODY
Please help me, I Am getting-28 but I do t think it is correct
Answer:
-28
Step-by-step explanation:
[tex]-(2-2^3)^2-4 \cdot (-2)[/tex]
We going to use PE(MD)(AS).
So P means ( ).
We do have operations to perform in the ( ).
We have [tex]2-2^3[/tex] in the first set of ( ) and (-2) in the second set of ( ).
There are no operations in the second set containing -2.
So we are just focusing on the [tex]2-2^3[/tex] right now.
You have subtract and exponent here.
Exponents come first in PE(MD)(AS) so we will perform that first.
[tex]2-2^3=2-8=-6[/tex]
Let's go back to the original problem now.
[tex]-(2-2^3)^2-4 \cdot (-2)[/tex]
[tex]-(-6)^2-4 \cdot(-2)[/tex]
Now there are no longer any operations grouped together by use of ( ).
It on to the rest of PE(MD)(AS).
So now we are doing the E part, the exponents.
[tex]-(36)-4 \cdot(-2)[/tex]
Now there is multiplication and subtraction left.
(MD) comes before (AS) so we do the multiplication and then the subtraction. So I'm going to do 4(-2) now:
[tex]-(36)-(-8)[/tex]
Subtraction is addition of the opposite so you could write:
[tex]-(36)+8[/tex]
We don't really need ( ) around the first number:
[tex]-36+8[/tex]
36-8 is 28 but since 36>8 and 36 has a negative sign on it, the answer is -28.
A football coach is trying to decide: when a team ahead late in the game, which strategy is better?
A)
B)
C)
or D)
APEX
Answer: B
Step-by-step explanation:
Help me on this math question
Answer: A. 1.55 repeating.
Step-by-step explanation: Since 5/9 is not going to end as .5, the answer would be 1.55 repeating. 5/10 would make the answer be 1.5.
The mixed fraction number 1 5/9 is equal to the decimal number 1.55.... Then the correct option is A.
What is Algebra?Algebra is the study of algebraic expressions, while logic is the manipulation of those concepts.
The decimal number is the sum of a whole number and part of a fraction number. The fraction number is greater than zero but less than one.
The mixed fraction number is given below.
⇒ 1 5/9
Convert the mixed fraction number into the fraction number. Then we have
1 5/9 = 14 / 9
Convert the fraction number into a decimal number, then we have
⇒ 14/9
⇒ 1.55......
The mixed fraction number 1 5/9 is equal to the decimal number 1.55.... Then the correct option is A.
More about the Algebra link is given below.
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Find the equation in slope-intercept form that describes a line through (4, –2) with slope –3
Answer:
y = - 3x + 10
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here slope m = - 3, hence
y = - 3x + c ← is the partial equation
To find c substitute (4, - 2) into the partial equation
- 2 = - 12 + c ⇒ c = - 2 + 12 = 10
y = - 3x + 10 ← equation of line
Answer: [tex]y=-3x+10[/tex]
Step-by-step explanation:
The equation of a line in intercept form: [tex]y=mx+c[/tex]
The equation of a line passing through (a,b) and has slope m is given by :_
[tex](y-b)=m(x-a)[/tex]
Similarly, the equation in slope-intercept form that describes a line through (4, -2) with slope -3 will be :_
[tex](y-(-2))=-3(x-4)\\\\\Rightarrow\ y+2=-3x+12\\\\\Rightarrow\ y=-3x+12-2\\\\\Rightarrow\ y=-3x+10\ \ \text{In intercept form}[/tex]
Hence, the equation in slope-intercept form that describes a line through (4, -2) with slope -3 = [tex]y=-3x+10[/tex]
What does h(40)=1820 mean in terms of the problem ? Help please
Final answer:
The notation h(40)=1820 means that the function h produces an output of 1820 when the input is 40, although additional context is needed to determine what h represents specifically in this scenario.
Explanation:
The expression h(40)=1820 typically means that a function h is being evaluated at the input value of 40, and the output is 1820. This could represent a variety of contexts, such as the height of a rocket in meters at 40 seconds after launch, the amount of money saved after 40 weeks, or any other situation described by a function where the variable h depends on the number 40. Without additional context, it's impossible to say precisely what 1820 refers to, but it is the result of the function h when the input is 40.
Lara is a 50% partner. She is guaranteed payment of no less than 20,000. The partnership's income before deducting guaranteed payment is 50,000 what is Lara's distributive share?
Answer:
Lara's share = 25000
Step-by-step explanation:
Partnership's income = 50,000
Lara's guaranteed payment = 20,000
As the Income 50,000 is larger than Lara's guaranteed payment i.e 20,000. Since Lara is 50% partner so she will receive half the amount of the partnership's income.
Partnership's Income = 50,000
Half of Partnership's income = 50,000/2
= 25,000
Therefore, Lara's distributive share is 25,000.
!!
Piecewise defined function.
f(x) = {-x^2+2x+2 if
[tex]x \leqslant - 5[/tex]
{-3/4x+3 if
[tex]x > 1[/tex]
find what f(-5) =
Answer:
f(-5) = -33
Step-by-step explanation:
f(x) = {-x^2+2x+2 if x ≤ - 5
{-3/4x+3 if x > 1
find what f(-5) =
If x=-5, we use the first equation
f(-5) = -x^2+2x+2 since it has the equal to part
= - (-5)^2 +2(-5) +2
= -25 -10+2
= -35+2
=-33
Martina begins a dive at sea level. She dives down 20 feet, and then rises 7 feet.
She dives again, going down 9 more feet. How far below sea level is Martina?
Answer:
22 feet below sea level
Step-by-step explanation:
If she goes down by 20 and back up by 7 the overall effect is going down by 13 and then going down 9 more feet makes it a total of 22 feet.
Answer:22
Step-by-step explanation:
-20+7-9= -22 ft, or 22 ft below sea level
What is the volume of a rectangular prism with a length of 2.2 cm, a width of 3.1 cm and a height of 1.2 cm
To find the volume of a rectangular prism, multiply the length by the width by the height.
Volume = 2.2 x 3.1 x 1.2 = 8.184 cm^3
All the dimensions are one decimal place, so if you round the answer to one decimal place it would be 8.2 cm^3
To find the volume of a rectangular prism, multiply the length by the width by the height.Volume = 2.2 x 3.1 x 1.2 = 8.184 cm^3All the dimensions are one decimal place, so if you round the answer to one decimal place it would be 8.2 cm^3
What is the measure of the radius of circle m? see picture
Answer:
10.5 units
Step-by-step explanation:
Since M is the centre of the circle. The measure to the edge is the radius.
Which in this case is 10.5 units
Answer: A. 10.5 units
Step-by-step explanation: The answer would be 10.5 units because the radius is equal to half the circle. MS is a radius, and MR is a radius. A radius has one point in the center, and one point on the circle.
which function represents exponential decay?
a)y=14(0.95)^x
b)y=14(1.95)^x
c)y=14x^1.95
d)y=14/0.95
Answer:
a
Step-by-step explanation:
We are looking for an exponential function [tex]y=a(r)^x[/tex] where r is less than 1.
a works because it is in the form [tex]y=a(r)^x[/tex] where r is less than 1.
b is in the form [tex]y=a(r)^x[/tex] but r is more than 1.
c. and d. are not even exponential functions.
c. is a polynomial
d. is a constant polynomial (no variable)
You graph the function f(x)=-|×|-12
in the
standard viewing window of -10 to 10. Will you be
able to see the graph? Explain.
Answer:
See attachment
Step-by-step explanation:
We want to graph [tex]f(x)=|x|-12[/tex] on the interval -10 to 10.
Let [tex]g(x)=|x|[/tex] be the parent absolute value function.
We can easily graph [tex]f(x)=|x|-12[/tex], if we use translation.
When the parent function is shifted downwards by 12 units, we obtain the graph of [tex]f(x)=|x|-12[/tex].
The parent function is a v-shaped graph with vertex at the origin.
We shift the parent function down so that its vertex is now at (0,-12) to get the graph of [tex]f(x)=|x|-12[/tex] .
See attachment for the graph of [tex]f(x)=|x|-12[/tex] on the specified interval.
Answer:
Which of the following did you include in your response?
No, you will not see the graph.
When x is 0, y is –12, which is outside the viewing window.
Because the function has been reflected, it opens down.
From x = –10 to x =10, the y-values range from –22 to –12.
Step-by-step explanation:
Solve for x. Write the smaller solution first, and the larger solution second. (x-10)^2-1=0
Answer:
[tex]x_1 = 9[/tex] and [tex]x_2 = 11[/tex].
Step-by-step explanation:
Start by adding 1 to both sides of this equation.
[tex](x - 10)^{2} = 1[/tex].
The square of what number or numbers will lead to the number "1"? It turns out that not only [tex]1^{2} = 1[/tex], but [tex](-1)^{2}= 1[/tex] as well. In other words, the value [tex](x - 10)[/tex] can be either 1 or -1. Either way, the equation is still going to hold. That's the reason why there are two solutions to this equation.
Consider the case when [tex]x - 10 = 1[/tex]. Add 10 to both sides of the equation. [tex]x = 11[/tex].
Now, consider the case when [tex]x - 10 = -1[/tex]. Again, add 10 to both sides of the equation, [tex]x = 9[/tex].
Order the two solutions in an increasing order:
[tex]x_1 = 9[/tex],[tex]x_2 = 11[/tex].Which of the following is the equation of a line that passes through (-2,1) and (-4,-3)?
Points [tex]X(-2,1)[/tex] and [tex](-4,-3)[/tex] are defined therefore we have all data we need to construct equation.
Linear function has a form of,
[tex]y=ax+b[/tex]
First calculate the slope a.
[tex]a=\dfrac{dy}{dx}=\dfrac{-3-1}{-4-1}=\dfrac{-4}{-5}=\dfrac{4}{5}[/tex]
Now plug in the coordinates of either one of the points into the linear function. I'll pick point X.
[tex]y=ax+b\Longrightarrow1=\dfrac{4}{5}\cdot(-2)+b[/tex]
Now just solve for b.
[tex]1=-\dfrac{8}{5}+b\Longrightarrow b=\dfrac{13}{5}[/tex]
The equation is therefore,
[tex]\boxed{y=\dfrac{4}{5}x+\dfrac{13}{5}}[/tex]
Hope this helps.
r3t40
what is the slope of the line shown below? (4, 8) (2, 4)
Answer:
Slope = 2
Step-by-step explanation:
Slope is the change in y/change in x. So (8-4)/4-2)=2.
Answer: Using the formula below you will get -4/-2 which is slope of 2
Step-by-step explanation:
So you would use the slope formula which is y_{2}- y_{1} / x_{2}-x_{1}
All rhombuses are. Parallelograms square rectangules quadrilaterals
Step-by-step explanation:
Look at the picture.
All rhombuses are
parallelograms
quadrilaterals
Simplify the following algebraic expression: 6(2y + 8) - 2(3y - 2)
Answer:
[tex]\large\boxed{6y+52}[/tex]
Step-by-step explanation:
In this question, we're going to simplify the expression.
We would do this by distributing and solving after.
Solve:
[tex]6(2y + 8) - 2(3y - 2)\\\\\text{Distribute the 6 to the 2y and 8}\\\\12y+48- 2(3y - 2)\\\\\text{Distribute the -2 to the 3y and -2}\\\\12y+48-6y+4\\\\\text{Combine like terms}\\\\6y+48+4\\\\\boxed{6y+52}[/tex]
When you're done solving, you should get 6y+52
This means that the simplified version would be 6y+52
I hope this helped you out.Good luck on your academics.Have a fantastic day!The reciprocal of -7 is: -7 7 -1/7 1/7
Answer: -1/7
Step-by-step explanation: The reciprocal of -7 is -1/7. Flip -7 to get the answer. -7 is the same as -7/1, so flip the numbers to find the reciprocal.