The mid point of the segment with the following endpoints. (-9, 8) and (-4, -2) is (-6.5, 3)
How to find mid point ?The mid point of the segment can be found as follows;
The endpoint is a follows:
(-9, 8) and (-4, -2)
Therefore,
mid point = (x₁ + x₂ / 2, y₁ + y₂ / 2)
hence,
mid point = (-9 - 4 / 2, 8 - 2 / 2)
mid point = (-13 / 2 , 6 / 2)
mid point = (-6.5, 3)
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Determine the equation of a cubic polynomial function with roots at (3,0), (2,0) and (-4,0) that also passes through the point (1,30).
Step-by-step explanation:
Step 1: Setting Up the Factors
Our roots are 3, 2, and -4 so
our factors are
[tex](x - 3)(x - 2)(x + 4)[/tex]
Step 2: Initial Test to see if the result equal 30
Let a be a constant, such we have
[tex]a(x - 3)(x - 2)(x + 4) = 30[/tex]
Plug in. 1 for x.
[tex]a(1 - 3)(1 - 2)(1 + 4) = 30[/tex]
[tex]a( - 2)( - 1)(5) = 30[/tex]
[tex]a(10) = 30[/tex]
[tex]a = 3[/tex]
So our equation is
[tex]3(x - 3)(x - 2)(x + 4)[/tex]
Or if you want it simplifed
[tex]3( {x}^{2} - 5x + 6)(x + 4) = 3( {x}^{3} + - {x}^{2} - 14x + 24) = 3 {x}^{3} - 3 {x}^{2} - 42x + 72[/tex]
Answer:
[tex]f(x)=3(x-3)(x-2)(x+4)[/tex]
Step-by-step explanation:
General form of a cubic polynomial function with 3 roots:
[tex]f(x)=a(x-b)(x-c)(x-d)[/tex]
where:
a is some constant to be foundb, c and d are the roots of the functionGiven roots:
(3, 0)(2, 0)(-4, 0)Substitute the given roots into the general form of the function:
[tex]\implies f(x)=a(x-3)(x-2)(x-(-4))[/tex]
[tex]\implies f(x)=a(x-3)(x-2)(x+4)[/tex]
To find the value of a, substitute the given point (1, 30) into the equation:
[tex]\begin{aligned} f(1) & = 30\\\implies a(1-3)(1-2)(1+4) & =30\\a(-2)(-1)(5) & = 30 \\10a & = 30\\\implies a & = 3 \end{aligned}[/tex]
Therefore, the equation of the cubic polynomial function is:
[tex]f(x)=3(x-3)(x-2)(x+4)[/tex]
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Solve the following simultaneous equations. x + y = 3
x -y = 1
Answer:
x = 2, y = 1 or (2, 1)
Step-by-step explanation:
Solving by elimination method :
x + y + (x - y) = 3 + 12x = 4x = 22 - y = 1y = 1The solution is : x = 2, y = 1 or (2, 1)
use your calc to work this out
Write down in terms of n, an expression for the nth term of the following sequences:
a) 12 10 8 6 4
b) 25 20 15 10 5
Answer:
The formula for an arithmetic sequence is:
an = a1 + (n - 1)d
In which a1 is the first term and d is the common difference.
a) 12, 10, 8, 6, 4
an = 12 + (n - 1)-2
an = 12 -2n + 2
an = -2n + 14
b) 25, 20, 15, 10, 5
an = 25 + (n - 1)-5
an = 25 -5n + 5
an = -5n + 30
What is the inverse of this function?
f(x) = -√x +3₁ x ≥ −3
f-¹(x) =
2-
-
for x ≤
Answer:
f(x)^-1=x^2-3
Step-by-step explanation:
So I'm assuming you meant to include the 3 in the radical as well which would make sense given the domain restriction. To find the inverse you simply swap the x and y since the inverse function is when the domain and range are swapped.
[tex]y=-\sqrt{x+3}\\x=-\sqrt{y+3}\\-x=\sqrt{y+3}\\(-x)^2=y+3\\x^2-3=y\\f(x)^{-1}=x^2-3[/tex]
can someone please help me?
We have the equation of a line:
[tex]y=-\dfrac{5}{4}x-1[/tex]
The formula of a slope of a line passes through points A, B:
[tex]A(x_A,\ y_A),\ B(x_B,\ y_B)\\\\m=\dfrac{y_B-y_A}{x_B-x_A}[/tex]
Complete the table:
Put the values of x to the equation of a line and calculate the value of y:
[tex]x=0\\\\y=-\dfrac{5}{4}\cdot0-1\\\\y=-1\\\\\\x=4\\\\y=-\dfrac{5}{4}\cdot4-1\\\\y=-6[/tex]
Substitute to the formula of a slope:
[tex]m=\dfrac{-6-(-1)}{4-0}\\\\m=\dfrac{-6+1}{4}\\\\\huge\boxed{m=-\dfrac{5}{4}}[/tex]
A delivery of 5 large boxes and 3 small boxes has a total mass of 137 kilograms. A delivery of 2 large boxes and 6 small boxes has a total mass of 128 kilograms. What is the mass of each type of box?
Answer:
Large boxes are 18.25 kg
Small boxes are 15.25 kg
Step-by-step explanation:
This is a system of equations. You need to set up each equation first.
I am assigning x to be big boxes and y to be small boxes.
5x + 3y = 137
2x + 6y = 128
To solve, you will need to eliminate a variable. That means you will have to multiply one of the equations by a number to make it so a variable will be eliminated. I will be multiplying the top equation by -2.
-2 ( 5x + 3y = 137)
2x + 6y = 128
Distribute the -2 to everything in the parentheses in the first equation.
-10x - 6y = -274
2x + 6y = 128
Notice the 6y will go away because -6y + 6y = 0. Now add the equations together. The remaining equation is:
-8x = -146
Solve for x by dividing by -8.
x = 18.25
Now plug that into one of the original equations.
2(18.25) + 6y = 128.
36.5 + 6y = 128 Subtract 36.5 from each side
-36.5 -36.5
6y = 91.5 Divide by 6 to solve
y = 15.25
K'L'M'N' is a dilation image of KLMN. Which is the correct description of the dilation?
Answer:
d
Step-by-step explanation:
Write an equation in slope intercept form with the given information.
Slope = 4 and goes through point (3,0)
Answer:
y = 4x - 12
Step-by-step explanation:
If f(x) = 2x² + 3x and g(x)= x - 2, what is (f+ g)(2)?
Answer:
14.
Step-by-step explanation:
If f(x) = 2x2 + 3x and g(x) = x - 2, (f + g)(2) is 14.
Answer:
14
Step-by-step explanation:
f(x) = 2x² + 3x
f(2) = 2 * 2^2 + 3(2) = 2*4 + 6 = 8+6 = 14
g(x)= x - 2
g(2) = 2-2 = 0
(f+ g)(2) = 14+0 = 14
What is 2 1/2 x 1 3/4 x 3/4
Answer:
45/32 or 1.40
Step-by-step explanation:
Answer:
3 9/32 or 105/32
Step-by-step explanation:
2 1/2 = 5/2, 1 3/4 = 7/4
5/2 * 7/4 = 35/8
35/8 * 3/4 = 105/32
105/32 = 3 9/32
Brainliest, please :)
can someone please do this for me
The range is from the maximum point into infinity that is [4, infty) and the vertex is at (0, 4)
Vertex, domain and range of a functionThe given graph is a parabola. It represents the graph of a quadratic equation.
From the shown graph, the parabola has a maximum point at (0, 4). This is also the vertex of the graph
The domain area values along the x-axis while the range lies on the y-axis. From the graph shown, the domain is [-2, 2] (x lies between -2 and 2)
The range is from the maximum point into infinity that is [4, infty)
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Find the total surface area of a regular pyramid with a square base if each edge of the base is 16 inches, the slant height of one side is 17 inches, and the altitude is 15 inches.
Answer:
the answer you're looking for is 60 inches
The perimeter of the base is 4 s since it is a square.
p = 4(16) = 64 inchesThe area of the base is s².
B = 16² = 256 inches ²[tex]\boldsymbol{CST=\dfrac{1}{2}(64)(17)+256=544+256=800 \ inches^{2} }[/tex]
[tex]\red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}[/tex]
Which of the following inequalities matches the graph?
graph of an inequality with a solid line through the points 0, negative 2 and 2, 1 with shading above the line
3x − 2y ≥ 4
3x − 4y ≤ 2
3x − 2y ≤ 4
The correct inequality is not listed.
Answer:
The correct option is 3.
Step-by-step explanation:
It is given a graph of an inequality with a solid line through the points (0, −2) and (2, 1) with shading above the line.
The equation of a solid line is:
[tex]y-y_{1} = \frac{y_{2}- y_{1} }{x_{2}- x_{1} } (x-x_{1})\\ y+2= \frac{1+2}{2-0}(x-0)\\ y+2= \frac{3}{2} x[/tex]
The y-intercept of the line is -2 and the shaded region is shading above the line. So, (0,0) must be lies in the shaded region.
Check the related equation by point (0,0).
0+2 =[tex]\frac{3}{2}(0)[/tex]
2 = 0
The statement is true if and only if the sign is greater than or equal instead of equal.
The required inequality is
[tex]y+2 \geq \frac{3}{2}x[/tex]
Multiply both sides by 2.
[tex]2y + 4 \geq 3x\\4\geq 3x-2y\\3x-2y \leq 4[/tex]
Therefore option 3 is correct.
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How would i work this out?
BD is the bisector of angle ABC Determine the measure of angle ABD
Answer:
45 degrees
Step-by-step explanation:
A bisector divides an angle into two equal parts. Since we are dividing a 90 degree angle by 2, we get a resulting value of 45 degrees.
Which of the following is a like radical to 3/7x?
4 (3√√7x)
O
O √Tx
0 x(³√7)
0 7√√√x
Answer:
Like radicals are those terms that are similar, just like like terms. From this concept we find that option A is correct. 4[∛(7x)] and ∛(7x) are like radicals.
Step-by-step explanation:
Mathematically, like radicals are just like like terms. For example,
x, 2x, -10x, , 7.3x are like terms because the power of x in each case is 1.
xy², -9xy², 13y²x are like terms because the total power of each expression is 3.
Similarly, like radicals are:
√2, -5√2, 1.1√2, etc.
Hence, from the given options, like radical to ∛(7x) is: 4[(7x)].
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What else would need to be congruent to show that ABC = XYZ by ASA
Answer:
Option d
Step-by-step explanation:
BC = YZ
AC cannot be equal to XZ else it will be SAA congruency
Find the value of x
Answer:
3
Step-by-step explanation:
11(3)+2 = 6
also,
33-29 =
and
29 - 23 = 6
I take a guss, but I think its 3
PLEASE HELP. DON’T NEED DEEP EXPLANATION JUST ANSWERS.
Which of the following are solutions to the equations below?
x^2 + 6x + 9= 20
Check all that apply.
Answer:
[tex]\large {\textsf{B and E}}\ \implies x_1=-2\sqrt{5}-3,\ x_2=+2\sqrt{5}-3[/tex]
Step-by-step explanation:
Quadratic Formula: [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Quadratic Equation: ax² + bx + x = 0, where a ≠ 0
Given equation: x² + 6x + 9 = 20
Step 1: Subtract 20 from both sides.
x² + 6x + 9 - 20 = 20 - 20
⇒ x² + 6x - 11 = 0
Step 2: Identify the values of a, b, and c and substitute them in the formula.
⇒ a = 1, b = 6, c = -11
[tex]x=\dfrac{-6\pm\sqrt{\bold{6^2}-4(1)(-11)}}{\bold{2(1)}}\\\\x=\dfrac{-6\pm\sqrt{36\bold{\ - \ 4(-11)}}}{2}\\\\x=\dfrac{-6\pm\sqrt{\bold{36+44}}}{2}\\\\x=\dfrac{-6\pm\sqrt{80}}{2}\\\\x=\dfrac{-6\pm\sqrt{16\times5}}{2}\implies \dfrac{-6\pm\sqrt{\bold{16}}\times\sqrt{5}}{2} \\\\x=\dfrac{-6\pm4\sqrt{5}}{2}[/tex]
Step 3: Separate into possible cases.
[tex]x_1=\dfrac{-6-4\sqrt{5}}{2}\implies \dfrac{-6}{2}+\dfrac{-4\sqrt{5}}{2}\implies \boxed{-3-2\sqrt{5}\ \ \textsf{or}\ -2\sqrt{5}-3}\\\\x_2=\dfrac{-6+4\sqrt{5}}{2}\implies \dfrac{-6}{2}+\dfrac{4\sqrt{5}}{2}\implies \boxed{-3+2\sqrt{5}\ \ \textsf{or}\ \ 2\sqrt{5}-3}[/tex]
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may I have some assistance please
What method can be used to write the equation of a line in slope-intercept form given two points? Find the slope using the formula m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction, and then substitute one point and the slope into the equation y = m x + b to find the y-intercept. Find the slope using the formula m = StartFraction x 2 minus x 1 Over y 2 minus y 1 EndFraction, and then substitute one point and the slope into the equation y = m x + b to find the y-intercept. Find the y-intercept using the formula m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction, and then substitute one point and the y-intercept into the equation y = m x + b to find the slope. Find the y-intercept using the formula m = StartFraction x 2 minus x 1 Over y 2 minus y 1 EndFraction, and then substitute one point and the y-intercept into the equation y = m x + b to find the slope.
The method that can be used to write the equation of a line in slope-intercept form given two points is option A.
Calculations and ParametersWhen a person wants to write the equation of a line in slope-intercept form given two points, he would have to:
Know the two pointsUse them to find the slopeYou would get the value of mUse it to solve the equation y= mx + bFind the y-interceptTherefore, the answer is option A.
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Chris lost $8.59 playing poker in one week. If this continued, what would be his net
winnings or losses after five weeks?
Answer:
$42.95
Step-by-step explanation:
If Chris lost $8.59 playing poker in one week, in five weeks he would lose $42.95.
$8.59 lost per week.
5 weeks.
$8.59 x 5 = $42.95.
Hope this helps!
If not, I am sorry.
What is the difference between the answers when numbers are switched in a subtraction?
HELPPP PLEASE!!!!!!!!!!!
Answer:
C
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 2) and (x₂, y₂ ) = (4, 0) ← 2 points on the line
m = [tex]\frac{0-2}{4-0}[/tex] = [tex]\frac{-2}{4}[/tex] = - [tex]\frac{1}{2}[/tex]
the y- intercept is the value of y where the line crosses the y- axis , then
y- intercept = 2
Sahil chooses a number, divides it by 8 , adds 8 to the answer. Then multiples the answer with 8 . He obtains the result as 952 . The number he chooses in the beginning was
USER IS DEAD
TAKE POINTS
Answer:
888
Step-by-step explanation:
Sahil chooses a number, [We'll call it x]
divides it by 8 , [x/8]
adds 8 to the answer. [(x/8) + 8]
Then multiples the answer with 8 . [((x/8) + 8)*8]
He obtains the result as 952 . [((x/8) + 8)*8 = 952]
The number he chooses in the beginning was
((x/8) + 8)*8 = 952
x + 64 = 952
x = 888
CHECK:
Does (888/8 + 8)*8 = 952?
(119)*8 = 952? YES
The number is 888
table shows the travelling time to work of 50 people.
Travelling time (t) in minutes
Frequency
0 < t < 10
5
10 < t < 20
15
20 < t < 30
13
30 < t < 40
10
40 < t < 50
Calculate an estimate of the mean travelling time.
An estimate of the mean travelling time will be 24.8 mins.
What are mean?The mean is the average value which can be calculated by dividing the sum of observations by the number of observations
Mean = Sum of observations/the number of observations
Given;
Time > timemark > frequency
0 – 10 > 10/2 = 5 > 5
10 – 20 > (10+20)/2 = 15 > 15
20 – 30 > (20+30)/2 = 25 > 13
30 – 40 > (30+40)/2 = 35 > 10
40 – 50 > (40+50)/2 = 45 > 7
The mean time for the 50 people can be calculated as;
Mean = Summation of (mid-time x frequency) / total frequency
Mean = [5x5 + 15x15 + 25x13 + 35x10 + 45x7] / 50
Mean = [25 + 225 + 325 + 350 + 315] / 50
Mean = 1240 / 50
Mean = 24.8 mins
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f(x)=(2x−3)(x+6)(5x+6)f, left parenthesis, x, right parenthesis, equals, left parenthesis, 2, x, minus, 3, right parenthesis, left parenthesis, x, plus, 6, right parenthesis, left parenthesis, 5, x, plus, 6, right parenthesis has zeros at x=-6x=−6x, equals, minus, 6, x=-\dfrac{6}{5}x=− 5 6 x, equals, minus, start fraction, 6, divided by, 5, end fraction, and x=\dfrac{3}{2}x= 2 3 x, equals, start fraction, 3, divided by, 2, end fraction. What is the sign of fff on the interval -6
Answer:
566
Step-by-step explanation:
I got it right..................
Hi pls help
1) -15+4r=-9
2) 5-y/3=-1
3) 42=-5x-8
1) -15+4r=-9
-15+4r=-9
We move all terms to the left:
-15+4r-(-9)=0
We add all the numbers together, and all the variables
4r-6=0
We move all terms containing r to the left, all other terms to the right
4r=6
r=6/4
r=1+1/2
2) 5-y/3=-1
5-y/3=-1
We move all terms to the left:
5-y/3-(-1)=0
We add all the numbers together, and all the variables
-y/3+6=0
We multiply all the terms by the denominator
-y+6*3=0
We add all the numbers together, and all the variables
-1y+18=0
We move all terms containing y to the left, all other terms to the right
-y=-18
y=-18/-1
y=+18
3) 42=-5x-8
42=-5x-8
We move all terms to the left:
42-(-5x-8)=0
We get rid of parentheses
5x+8+42=0
We add all the numbers together, and all the variables
5x+50=0
We move all terms containing x to the left, all other terms to the right
5x=-50
x=-50/5
x=-10
One way to prove this quadrilateral is a square is by calculating the slopes of its sides and the slopes of its diagonals.
If we can prove that it has 2 pairs of parallel sides, one pair of consecutive sides perpendicular and perpendicular diagonals, then the quadrilateral shown ab
By examining it we found that:
If your answer is a fraction enter is as a fraction. Example: To enter negative one fifth type: -1/5
a. Slope of CB is
b. Slope of DA is
so DA is parallel to CB
c. Slope of CD is
so CD is perpendicular to CB
d. Slope of BD is
e. Slope of CA is
so CA is perpendicular to BD
A slope is also known as the gradient of a line. Slope of a line or straight object is the ratio of how much amount of rise occurs in correspondence to the increment in the run.
What is Slope?A slope is also known as the gradient of a line is a number that helps to know both the direction and the steepness of the line.
How to find the slope?Slope of a line or straight object is the ratio of how much amount of rise occurs in correspondence to the increment in the run.
Thus, we get:
Slope = rise/ run
The slope of any line can found by finding the ratio of the vertical distance to horizontal distance between two ends. Therefore, the blanks can be filled as shown below.
The Slope of CB is 4/3,The Slope of DA is 4/3, so DA is parallel to CBThe Slope of CD is (-3/4), so CD is perpendicular to CBThe Slope of BD is -7The Slope of CA is 1/7, so CA is perpendicular to BD.Learn more about Slope of Line:
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Suppose y varies inversely as x, and y = 16 when x = 1/2. Find y when x = 17.
Finding the proportionality constant :
y = k/x16 = k/(1/2)k = 8Finding y when x = 17 :
y = 8/(17)y = 8/17The value of y is 8/17 when x = 17.
