Answer:
15/56
Step-by-step explanation:
15 and 56 have a GCF of 1.
A farmer creates a rectangular pen using part of the wall of a barn for one side of the pen and a total of 130 feet of fencing for the remaining 3 sides, as shown in the diagram. Write and equation which gives the area of the pen, A, as a function of x, the length of fence parallel to the barn
The equation that describes the which gives the area of the pen, A, as a function of x, the length of fence parallel to the barn is A = 130x - x²
How to find area of a rectangle?The pen is rectangular. Therefore,
area of a rectangle = lw
where
l = lengthw = widthTherefore,
perimeter = 2w + l
perimeter = 2w + x
130 = 2w + x
130 - x = 2w
w = 65 - 1/ 2 x
A = xw
A = x(65 - 1/ 2 x)
A = 65x - 1 / 2 x²
Therefore, the function that represents A, the area of the pen is as follows:
A = 130x - x²
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Please help me I literally suck at algebra
Answer:
4
Step-by-step explanation:
Given :
f(x) = x² - 6x + 8
=============================================================
Solving :
Splitting the middle term :
⇒ f(x) = x² - 6x + 8
⇒ f(x) = x² - 2x - 4x + 8
⇒ f(x) = x (x - 2) - 4 (x - 2)
⇒ f(x) = (x - 4)(x - 2)
============================================================
Solutions :
⇒ x - 4 = 0 ⇒ x = 4
⇒ x - 2 = 0 ⇒ x = 2
3. What is the surface area of the triangular prism shown below?
Answer:
1233cm^2
Step-by-step explanation:
a of triangle = 1/2 bh
1/2 x 12 x 9 = 54
108 x 2 = 108
a of regtangle = l x w
25 x 15 = 375
375 x 3 = 1125
total surface area = 1125 + 108 = 1233cm^2
What are the roots of the polynomial equation x superscript 4 baseline x cubed = 4 x squared 4 x? use a graphing calculator and a system of equations. –2, –1, 0, 2 –2, 0, 1, 2 –1, 0 0, 1
Polynomial is an expression that consists of indeterminate(variable) and coefficients. The roots of the given polynomial are -2, -1, 0, and 2.
What are polynomials?Polynomial is an expression that consists of indeterminate(variable) and coefficient, it involves mathematical operations such as addition, subtraction, multiplication, etc, and non-negative integer exponential.
The roots of the given polynomial when plotted on graph are the point at which the graph intersect the x-axis. Therefore, the roots of the given polynomial is,
x = -2, -1, 0, 2
Hence, the roots of the given polynomial are -2, -1, 0, and 2.
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Answer:
It's A. -2, -1, 0, 2
Step-by-step explanation:
In triangle ABC, points D and E are on sides AB and BC, respectively,
such that DE | AC, and AD:DB = 3:5.
If DB = 6.3 and AC = 9.4, what is the length of DE, to the nearest
tenth?
The length of DE in the triangles is 5.9
How to determine the length of DE?The given parameters are:
DB = 6.3
AC = 9.4
AD : DB = 3 : 5
Substitute DB = 6.3 in AD : DB = 3 : 5
AD : 6.3 = 3 : 5
Express as fraction
AD / 6.3 = 3 / 5
Multiply both sides by 6.3
AD = 3.78
The length DE is then calculated using the following ratio:
BD : DE = BA : AC
Where:
BA = BD + AD
This gives
BD : DE = BD + AD : AC
Substitute known values
6.3 : DE = 6.3 + 3.78 : 9.4
Simplify
6.3 : DE = 10.08 : 9.4
Express as fraction
DE/6.3 = 9.4/10.08
Multiply both sides by 6.3
DE = 5.9
Hence, the length of DE is 5.9
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Please Help I Don't Understand!
Answer:
D) None of the choices are correct.
Explanation:
Given triangles AHL and NKG
Sides which are congruent:
AH and NKHL and KGAL and NGSo, AHL ≅ NKG. There are no such options.
On the set of axes below, graph f(x) = |x - 3| + 2.
The attached graph represents the graph of the function f(x) = |x - 3| + 2
How to graph the function?The equation of the function is given as:
f(x) = |x - 3| + 2
The above equation is an absolute value function, and it has the following parameter:
Vertex = (3,2)
Next, we plot the graph of the function (see attachment)
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80% of the sixth-grade students and 20% of the fifth-grade
students at a school went on a field trip. If there are 20 sixth-grade
students and 80 fifth-grade students, what percent of all the fifthgrade and sixth-grade students from this school went on the field
trip? I WILL MAKE U BRAINLISET
Write the equation in slope-intercept form for the line with the given slope that contains the given point.
slope = 1; (3,5)
A) y=2x+1
B) y=3x+5
C) y=5x+3
D) y=1x+2
Answer:
D) y = 1x + 2
Step-by-step explanation:
The general structure of an equation in slope-intercept form is:
y = mx + b
In this equation, "m" stands for the slope and "b" stands for the y-intercept. You can substitute the given value of the slope into the equation. Since you are not given "b", you can plug the value of the points into the half-completed equation (with the slope) and isolate "b".
slope = m = 1
y = (1)x + b
(3,5) ------> y = 5 and x = 3
5 = 1(3) + b
5 = 3 + b
2 = b
Final Equation:
y = 1x + 2
Graph the functions on the same coordinate plane.
f(x)=−x+4
g(x)=x2−2
What are the solutions to the equation f(x)=g(x) ?
Select each correct answer.
3
−3
−2
2
0
Answer:
[tex]x = 2~\text{and} ~x = -3[/tex]
Step-by-step explanation:
[tex]~~~~~~f(x) = g(x)\\\\\implies -x +4 =x^2 -2\\\\\implies x^2 -2+x -4=0\\\\\implies x^2 +x -6 = 0\\\\\implies x^2 +3x -2x -6 =0\\\\\implies x(x+3) - 2(x+3) = 0\\\\\implies (x-2)(x+3) = 0\\\\\implies x = 2,~ x = -3[/tex]
Answer:
x = -3 and x = 2
Step-by-step explanation:
Plotting the graphs :
f(x)
⇒ Find two points (preferably the x and y intercepts)
⇒ 0 = -x + 4
⇒ x = 4
⇒ Point 1 : (4, 0)
⇒ f(x) = 0 + 4
⇒ f(x) = 4
⇒ Point 2 : (0, 4)
g(x)
⇒ g(x) = 0 - 2
⇒ g(x) = -2
⇒ Point 1 : (0, -2)
⇒ g(x) = 2² - 2
⇒ g(x) = 2
⇒ Point 2 : (2, 2)
* Graph with both functions is attached below *
=============================================================
Finding the solutions :
⇒ Equate f(x) and g(x)
⇒ -x + 4 = x² - 2
⇒ x² + x - 6 = 0
⇒ x² + 3x - 2x - 6 = 0
⇒ (x + 3)(x - 2) = 0
⇒ x = -3 and x = 2
In brianna's homeroom class, 9% of the students were born in march and 40% of the students have a blood type of o+.
what is the probability of a student chosen at random from tania's homeroom class being born in march and having a blood type of o+?
(enter the answer as a percent)
Answer:
3.6%
Step-by-step explanation:
Because the two events are independent, their probabilities are multiplied, so the probability of a student being born in March and having a blood type of O+ is 9% * 40% = 0.09 * 0.40 = 0.036 = 3.6%
need help pls
thank you in advance
Answer:
Mean[tex]\textsf{Mean}\:\overline{X}=\sf \dfrac{\textsf{sum of all the data values}}{\textsf{total number of data values}}[/tex]
[tex]\implies \sf Mean\:(Nilo)=\dfrac{5+6+14+15}{4}=\dfrac{40}{4}=10[/tex]
[tex]\implies \sf Mean\:(Lisa)=\dfrac{8+9+11+12}{4}=\dfrac{40}{4}=10[/tex]
Standard Deviation[tex]\displaystyle \textsf{Standard Deviation }s=\sqrt{\dfrac{\sum X^2-\dfrac{(\sum X)^2}{n}}{n-1}}[/tex]
[tex]\begin{aligned}\displaystyle \textsf{Standard Deviation (Nilo)} & =\sqrt{\dfrac{(5^2+6^2+14^2+15^2)-\dfrac{(5+6+14+15)^2}{4}}{4-1}}\\\\& = \sqrt{\dfrac{482-\dfrac{40^2}{4}}{3}}\\\\& = \sqrt{\dfrac{82}{3}}\\\\& = 5.23\end{aligned}[/tex]
[tex]\begin{aligned}\displaystyle \textsf{Standard Deviation (Lisa)} & =\sqrt{\dfrac{(8^2+9^2+11^2+12^2)-\dfrac{(8+9+11+12)^2}{4}}{4-1}}\\\\& = \sqrt{\dfrac{410-\dfrac{40^2}{4}}{3}}\\\\& = \sqrt{\dfrac{10}{3}}\\\\& = 1.83\end{aligned}[/tex]
SummaryNilo has a mean score of 10 and a standard deviation of 5.23.
Lisa has a mean score of 10 and a standard deviation of 1.83.
The mean scores are the same.
Nilo's standard deviation is higher than Lisa's. Therefore, Nilo's test scores are more spread out that Lisa's, which means Lisa's test scores are more consistent.
Answer gets brainlist
If x=3 and y=-2, the value of -2xy³ is
A 10
B -48
C -96
D 40
Answer:
B
Step-by-step explanation:
if
x=3
y=2
-2xy²
3
2³=8
-2×3×8
= -48
I need help asap please? and this is for the math question? what is 77x+93=360? put in a fraction and decimal and you can round to nearest tenths, plus I will give out brainlists to whom ever answers first
[tex]\\ \rm\Rrightarrow 77x+93=360[/tex]
[tex]\\ \rm\Rrightarrow 77x=360-93[/tex]
[tex]\\ \rm\Rrightarrow 77x=367[/tex]
[tex]\\ \rm\Rrightarrow x=4.77[/tex]
[tex]\\ \rm\Rrightarrow x=4.8[/tex]
Aswer with Nina ^-^
Don't report my answer ✅
Write the equation in slope - point form using the following information.
m = [tex]\frac{2}{5}[/tex] and point (-10, 1). Then, convert it to general form.
Answer:
[tex]\sf 2 x-5y +25=0[/tex]
Explanation:
Given points: (-10, 1)slope: 2/5Equation:
[tex]\dashrightarrow \sf y - y_1 =m(x - x_1)[/tex]
[tex]\dashrightarrow \sf y - 1 = \dfrac{2}{5} (x - (-10))[/tex]
[tex]\dashrightarrow \sf y = \dfrac{2}{5} x +4 + 1[/tex]
[tex]\dashrightarrow \sf y = \dfrac{2}{5} x +5[/tex]
[tex]\dashrightarrow \sf 5y = 2 x +25[/tex]
[tex]\dashrightarrow \sf 2 x-5y +25=0[/tex] General form: ax + by + c = 03. Jean rides her horse twice a week at Free-
and-Bold Stables. One Monday, she goes
for a horseback ride. She leaves the barn
on her horse at 2:10 PM, and comes back at 2:50 PM. How long was her ride?
the answer is 40 minute's 250-210 is 40
You have an account with a principal of $200. it pays 8% at the end of every year. calculate the principal at the end of 3 years.
Simple interest is a method of calculating interest on an amount for n period of time with a rate of interest of r. The principal at the end of 3 years is $248.
What is simple interest?Simple interest is a method of calculating interest on an amount for n period of time with a rate of interest of r. It is calculated with the help of the formula,
SI = (P × R × T)/100
where SI is the simple interest, P is the principal amount, R is the rate of interest, and T is the time period.
The principal at the end of 3 years is,
Principal after 3 years = P + (P × R × T)
= $200 + ($200 × 0.08 × 3)
= $200 + $48
= $248
Hence, the principal at the end of 3 years is $248.
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Use the information below for 6 and 7. Data was collected on hours per week spent doing homework by the students in two classes.
Answer:
A its becuase im rewlly smart
8x+72.8=5x+84.5 solve for x
8x+72.8=5x+84.5
8x-5x = 84.5-72.8
3x = 11.7
x = 3.9
x = {3.9}
For the function h defined by h(x) = 2x² - 2, find h(-1/2).
Answer:
-1.5
Step-by-step explanation:
h(-1/2)=2 [tex](\frac{-1}{2})^{2}[/tex] -2
h(-1/2)= [tex]\frac{1}{2} -2\\[/tex]
h(-1/2)=-1.5
Which segment does NOT intersect line AG? Please help.
Answer:
line BC
Step-by-step explanation:
Line BC is the only line that doesn’t touch line AG
Please Help I Don't Understand
Step-by-step explanation:
please Mark me brainlist!!
15c² - 5c. Factorise completely
Looking at the problem, what we must do to complete this question is to completely factor the expression that was provided. The expression that was provided is [tex]15c^2 - 5c[/tex].
The first step that we must do is to take a look at the expression and see what the two pieces of the expression have in common. We can see that both [tex]15c^2[/tex] and [tex]-5c[/tex] have the number 5 and the variable c associated with them so we can factor out those two.
Factor out 5c
[tex]15c^2 - 5c[/tex][tex]5c(\frac{15c^2}{5c}) - 5c(\frac{5c}{5c})[/tex][tex]5c(3c) - 5c(1)[/tex][tex]5c(3c - 1)[/tex]Now we have completely factored out the expression that was provided in the problem statement and we came to final answer of [tex]5c(3c - 1)[/tex].
Answer:
5c(3c - 1)
Step-by-step explanation:
Take out the 5c to factor out completely
Jake owns stock in a high-tech firm. Each share is currently valued at $61 per share, which is 22% more than Jake paid to purchase it. What did Jake pay per share?
The price per share of the stock of the high-tech firm that was purchased by Jake is $50.
What is the price per share?Percentage is a measure of frequency that calculates the fraction of an amount out of hundred.
What is the price per share of the stock purchased by Jake = current value / ( 1 + percentage increase)
61 / 1.22 = $50
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Im Not Understanding!
Answer:
3/2 + 3/2 + 3/2 = 3/1
so 3 over 1 times 1 over 2
find the distance and displacement for the following figures :
The figure (i) have a distance of 15.996 meters and a displacement of 13.892 meters and (ii) a distance of 480 centimeters and a displacement of 339.411 centimeters
How to find the distance and displacement in each trajectory
The distance is the sum of the lengths that form a trajectory and the displacement is the distance between the initial and final point of a trajectory. Then, we have the following results for each case:
Case I
Distance
d = 5 m + 0.5π · (7 m)
d ≈ 15.996 m
Displacement
[tex]D = \sqrt{(12\,m)^{2}+(7 m)^{2}}[/tex]
D ≈ 13.892 m
Case II
Distance
d = 8 · (60 cm)
d = 480 cm
Displacement
[tex]D =\sqrt{(240\,cm)^{2}+(240\,cm)^{2}}[/tex]
D ≈ 339.411 cm
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Yusuf and some friends are going to the movies. At the theater, they sell a bag of popcorn for $4 and a drink for $3.25. How much would it cost if they bought 4 bags of popcorn and 8 drinks? How much would it cost if they bought p bags of popcorn and d drinks? Total cost, 4 bags of popcorn and 8 drinks: Total cost, p bags of popcorn and d drinks:
Answer:
$42 would be the correct answer.
100 PTS PLEASE ANSWER ASAP! <3
[tex]\\ \rm\Rrightarrow g(x)=6(\dfrac{3}{2})^x[/tex]
[tex]\\ \rm\Rrightarrow g(-1)=6(\dfrac{3}{2})^{-1}=6(\dfrac{2}{3})=2(2)=4[/tex]
[tex]\\ \rm\Rrightarrow g(0)=6[/tex]
[tex]\\ \rm\Rrightarrow g(1)=6(\dfrac{3}{2})=3(3)=9[/tex]
[tex]\\ \rm\Rrightarrow g(2)=6\times\dfrac{9}{4}=13.2[/tex]
Attached the graph
Answer:
Given function:
[tex]g(x)=6\left(\dfrac{3}{2}\right)^x[/tex]
To find each of the points, substitute the given values of x into the function:
[tex]x=-1 \implies g(-1)=6\left(\dfrac{3}{2}\right)^{-1}=4[/tex]
[tex]x=0 \implies g(0)=6\left(\dfrac{3}{2}\right)^{0}=6[/tex]
[tex]x=1 \implies g(1)=6\left(\dfrac{3}{2}\right)^{1}=9[/tex]
[tex]x=2 \implies g(2)=6\left(\dfrac{3}{2}\right)^{2}=13.5[/tex]
Therefore:
[tex]\large \begin{array}{| c | c | c | c | c |}\cline{1-5} x & -1 & 0 & 1 & 2 \\\cline{1-5} g(x) & 4 & 6 & 9 & 13.5 \\\cline{1-5} \end{array}[/tex]
As the function is exponential, there is a horizontal asymptote at [tex]y=0[/tex].
Therefore, as [tex]x[/tex] approaches -∞ the curve approaches [tex]y=0[/tex] but never crosses it.
So the end behaviors of the graph are:
[tex]\textsf{As }x \rightarrow - \infty, \:\:g(x) \rightarrow 0[/tex][tex]\textsf{As }x \rightarrow \infty, \:\:g(x) \rightarrow \infty[/tex]Plot the points on the graph and draw a curve through them.
The equation y= -3x7 describes a parabola. Which way does the parabola
open?
Answer:
See below
Step-by-step explanation:
y = -3 x^7 is NOT a parabola.... y = -3x^2 IS a parabola that opens downward due to the negative coefficient (-3)
What is the measure of angle B in the figure below?
A
3
B
D
3√√2
C
O 30°
O 45°
O 60°
O 90°