The value of n is 3, value of m is 2 and the value de m + n + p is -2.
How to identify a null polynomialIn this question we must analyze a null polynomial and determine three unknown variables. A null polynomial is those whose coefficients are equal to zero.
Therefore, we must resolve the following system of linear equations:
3 · n - 9 = 0 (1)
m - 2 = 0 (2)
p + 7 = 0 (3)
The solution of this system of linear equations is: n = 3, m = 2, p = -7. The value of n is 3, value of m is 2 and the value de m + n + p is -2. [tex]\blacksquare[/tex]
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What is the area of the parallelogram shown? A) 60in B) 120in C) 140in D) 180in. + What is the area of a parallelogram that has a base 5 inches longer and the height 5 inches taller than a parallelogram shown? A) 230in B) 260in C) 290in D) 310in.
Answer:
B and B
Step-by-step explanation:
A = bh
A = 15 × 8
A = 120 in²
A = bh
A = 20 × 13
A = 260 in²
The area of the parallelogram shown are 120 in² and 260 in².
What is the area of a parallelogram?The area of a parallelogram is the product of the base and the height of the figure.
The area of a parallelogram = Base x Height
We are given that parallelogram that has a base 5 inches longer and the height 5 inches taller than a parallelogram
A = bh
A = 15 × 8
A = 120 in²
Now,
A = bh
A = 20 × 13
A = 260 in²
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u( w f +u ) = m + j
solve for u : u=
solve for f :F=
[tex]\textbf{Solve for u:}\\\\u(wf+v)=m+j\\\\\implies u = \dfrac{m+j}{wf+v}\\\\\textbf{Solve for f:}\\\\u(wf+v) = m+j\\\\\implies uwf+uv = m+j\\\\\implies uwf = m+j-uv\\\\\implies f=\dfrac{m+j-uv}{uw}[/tex]
Find the length of the ramp. ?
35 ft
12 ft
The length of the ramp is_____ ft.
Answer:
37 Feet
Step-by-step explanation:
We can use Pythagoras Theorem to solve this:
[tex]a^{2} +b^{2} =c^{2}[/tex]
[tex]35^{2} +12^{2} =c^{2}[/tex]
[tex]1225+144=c^{2}[/tex]
[tex]1369=c^{2}[/tex]
[tex]\sqrt{1369} =c[/tex]
37 = c
Answer:
37 ft
Step-by-step explanation:
Use Pythagorean Theorem for right triangles to find the hypotenuse
35^2 + 12^2 = Ramp^2 ramp = 37 ft
What is the length for X
Answer:
x = 5
Step-by-step explanation:
3^2 + 4^2 = x^2
9 + 16 = x^2
25
Now we need to find the square root of 25 :)
The answer is 5
X = 5
Have a great day!!
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(3√7 +5)^2
simplify the problem to its simplest form.
Answer:
88 + 30[tex]\sqrt{7} \\[/tex]
Step-by-step explanation:
Expand to make easier:
(3[tex]\sqrt{7} \\[/tex] + 5) x (3[tex]\sqrt{7} \\[/tex] + 5)
FOIL:
9(7) + 15 [tex]\sqrt{7}[/tex] + 15[tex]\sqrt{7}[/tex] + 25
Simplify:
63 + 30[tex]\sqrt{7}[/tex] + 25
88 + 30[tex]\sqrt{7}[/tex]
what is the measure of the space occupied by a solid. (Measured in cubic units)
write and solve an equation twice a number is 26
Answer:
2x = 26, x = 13
Step-by-step explanation:
Write and solve an equation twice a number is 26
x = unknown number
Equation: 2x = 26
Solve:
2x = 26
/2 /2 <== divide both sides by 2
x = 13
Check your answer:
2x = 26
2(13) = 26
26 = 26
This stament is correct
Hope this helps!
You spin the spinner, flip a coin, then spin the spinner again. Find the probability of the compound event. Write your answer as a fraction or percent rounded to the nearest hundredth. (the spinner is 1-9)
The probability of spinning a 4, flipping heads, then spinning a 7 is
Answer:
1/162
Step-by-step explanation:
first spin 1/9
land heads 50/50
second spin 1/9
so (9 x 2) x 9
= 162
1
Answer:
1/162 or 0.62 % to the nearest hundredth.
Step-by-step explanation:
Prob(spinning a 4) = 1/9
Prob(spinning a 7) = 1/9
Prob(flipping a head) = 1/2
Required Probability = 1/9 * 1/2 * 1/9
1/162.
Peter is buying a circular rug for his bedroom. The rug has an area of 40 square feet. What is the approximate diameter of the rug? Show your work or explain your answer.
The approximate diameter of the rug with an area of 40 ft² is 7.14 feet.
What is area?Area is the amount of space occupied by a two dimensional shape or object.
The area of a circle is given by:
Area = π * diameter²/4
The rug has an area of 40 square feet. Hence:
40 = π * diameter²/4
Diameter = 7.14 feet
The approximate diameter of the rug with an area of 40 ft² is 7.14 feet.
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Quadrilateral A B C D is shown. Sides A D and B C are parallel. Sides A B and C D are congruent. Angle A is 115 degrees.
What is the measure of ADC in quadrilateral ABCD?
45°
65°
115°
135°
Since no diagram attached there are two possible options.
Option 1
The quadrilateral is parallelogram.
In this case ∠A and ∠D sum up to 180°, therefore:
∠ADC = 180° - 115° = 65°Option 2
The quadrilateral is isosceles trapezoid.
In this case ∠A is congruent with ∠D, therefore:
∠ADC = ∠A = 115°Answer:
115
Step-by-step explanation:
[tex]\large \rm \sum \limits_{n = 0}^ \infty \frac{( { - 1)}^{1 + 2 + 3 + \dots + n} }{(2n + 1 {)}^{2} }[/tex]
The sum we want is
[tex]\displaystyle \sum_{n=0}^\infty \frac{(-1)^{T_n}}{(2n+1)^2} = 1 - \frac1{3^2} - \frac1{5^2} + \frac1{7^2} + \cdots[/tex]
where [tex]T_n=\frac{n(n+1)}2[/tex] is the n-th triangular number, with a repeating sign pattern (+, -, -, +). We can rewrite this sum as
[tex]\displaystyle \sum_{k=0}^\infty \left(\frac1{(8k+1)^2} - \frac1{(8k+3)^2} - \frac1{(8k+7)^2} + \frac1{(8k+7)^2}\right)[/tex]
For convenience, I'll use the abbreviations
[tex]S_m = \displaystyle \sum_{k=0}^\infty \frac1{(8k+m)^2}[/tex]
[tex]{S_m}' = \displaystyle \sum_{k=0}^\infty \frac{(-1)^k}{(8k+m)^2}[/tex]
for m ∈ {1, 2, 3, …, 7}, as well as the well-known series
[tex]\displaystyle \sum_{k=1}^\infty \frac{(-1)^k}{k^2} = -\frac{\pi^2}{12}[/tex]
We want to find [tex]S_1-S_3-S_5+S_7[/tex].
Consider the periodic function [tex]f(x) = \left(x-\frac12\right)^2[/tex] on the interval [0, 1], which has the Fourier expansion
[tex]f(x) = \frac1{12} + \frac1{\pi^2} \sum_{n=1}^\infty \frac{\cos(2\pi nx)}{n^2}[/tex]
That is, since f(x) is even,
[tex]f(x) = a_0 + \displaystyle \sum_{n=1}^\infty a_n \cos(2\pi nx)[/tex]
where
[tex]a_0 = \displaystyle \int_0^1 f(x) \, dx = \frac1{12}[/tex]
[tex]a_n = \displaystyle 2 \int_0^1 f(x) \cos(2\pi nx) \, dx = \frac1{n^2\pi^2}[/tex]
(See attached for a plot of f(x) along with its Fourier expansion up to order n = 10.)
Expand the Fourier series to get sums resembling the [tex]S'[/tex]-s :
[tex]\displaystyle f(x) = \frac1{12} + \frac1{\pi^2} \left(\sum_{k=0}^\infty \frac{\cos(2\pi(8k+1) x)}{(8k+1)^2} + \sum_{k=0}^\infty \frac{\cos(2\pi(8k+2) x)}{(8k+2)^2} + \cdots \right. \\ \,\,\,\, \left. + \sum_{k=0}^\infty \frac{\cos(2\pi(8k+7) x)}{(8k+7)^2} + \sum_{k=1}^\infty \frac{\cos(2\pi(8k) x)}{(8k)^2}\right)[/tex]
which reduces to the identity
[tex]\pi^2\left(\left(x-\dfrac12\right)^2-\dfrac{21}{256}\right) = \\\\ \cos(2\pi x) {S_1}' + \cos(4\pi x) {S_2}' + \cos(6\pi x) {S_3}' + \cos(8\pi x) {S_4}' \\\\ \,\,\,\, + \cos(10\pi x) {S_5}' + \cos(12\pi x) {S_6}' + \cos(14\pi x) {S_7}'[/tex]
Evaluating both sides at x for x ∈ {1/8, 3/8, 5/8, 7/8} and solving the system of equations yields the dependent solution
[tex]\begin{cases}{S_4}' = \dfrac{\pi^2}{256} \\\\ {S_1}' - {S_3}' - {S_5}' + {S_7}' = \dfrac{\pi^2}{8\sqrt 2}\end{cases}[/tex]
It turns out that
[tex]{S_1}' - {S_3}' - {S_5}' + {S_7}' = S_1 - S_3 - S_5 + S_7[/tex]
so we're done, and the sum's value is [tex]\boxed{\dfrac{\pi^2}{8\sqrt2}}[/tex].
Hello, can someone help me with the working out to this problem
[tex]\text{If}~ \alpha ~\text{and}~ \beta~ \text{are the roots,}\\ \\x^2 -(\alpha + \beta)x +\alpha\beta = 0\\\\\text{For}~ x^2+3x-2=0\\\\\alpha +\beta=-\dfrac ba=-3\\ \\\alpha \beta = \dfrac ca = -2\\\\[/tex]
[tex]\text{So,~} \alpha^3+\beta^3 = (\alpha + \beta)(\alpha^2 + \beta^2 -\alpha \beta)\\ \\~~~~~~~~~~~~~~~~=(\alpha+\beta)\left[(\alpha +\beta)^2 -2\alpha \beta - \alpha \beta\right]\\\\~~~~~~~~~~~~~~~~=(\alpha+\beta)\left[(\alpha +\beta)^2 -3\alpha \beta \right]\\\\~~~~~~~~~~~~~~~~=-3\left[(-3)^2-3(-2)\right]\\\\~~~~~~~~~~~~~~~~=-3(15)\\\\~~~~~~~~~~~~~~~~=-45\\\\\text{And}~~~\alpha^3 \beta^3= (\alpha \beta )^3 = (-2)^3 = -8\\\\[/tex]
[tex]\text{Hence the equation whose roots are}~ \alpha^3 ~\text{and}~ \beta^3~ \text{is:}\\ \\ x^2-(\alpha^3 + \beta^3)x +\alpha^3 \beta^3 =0\\\\\implies x^2 -(-45)x+(-8)=0\\\\\implies x^2 +45x -8=0[/tex]
How large a sample must a pollster take in order to estimate with 95% confidence and to within 3 percentage points, the proportion of voters who are in favor of a certain measure
========================================================
Work Shown:
[tex]n = \hat{p}*(1-\hat{p})\left(\frac{z}{E}\right)^2\\\\n \approx 0.5*(1-0.5)\left(\frac{1.96}{0.03}\right)^2\\\\n \approx 1067.111\\\\n \approx \boldsymbol{1068}\\\\[/tex]
Notes:
At 95% confidence, the z critical value is roughly z = 1.96 which is determined using a Z table.E = 0.03 to represent the 3% error. We're not told the value of [tex]\hat{p}[/tex], so we assume the most conservative estimate of 0.5Always round up to the nearest integer. The value 1067.111 is closer to 1067, but we round up to 1068 to clear the hurdle needed.PLSSS HEELPPP A line passes through (3, -2) and (6, 2).
a. Write an equation for the line in point-slope form.
b. Rewrite the equation in standard form using integers.
a. y+2= 4/3(x+3); -4x+ 3y= -18
b. y+2= 4/3(x-3); -4x+3y= -18
c. y-2= 4/3(x-3); -4x+3y= 18
d. y-3= 4/3(x+2); -4x+3y= 17
Answer:
b)
Step-by-step explanation:
Question (a)
[tex]\sf let \ (x_1,y_1)=(3,-2)\\\\\sf let \ (x_2,y_2)=(6,2)[/tex]
[tex]\sf slope \ (m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{2-(-2)}{6-3}=\dfrac43[/tex]
Point-slope formula: [tex]\sf y-y_1=m(x-x_1)[/tex]
Substituting m and point (3, -2) into the formula:
[tex]\sf y-(-2)=\dfrac43(x-3)[/tex]
[tex]\sf y+2=\dfrac43(x-3)[/tex]
Question (b)
Rewrite in standard form:
[tex]\sf y+2=\dfrac43x-4[/tex]
[tex]\sf \implies y=\dfrac43x-6[/tex]
[tex]\sf \implies 3y=4x-18[/tex]
[tex]\sf \implies -4x+3y=-18[/tex]
AB is a diameter. 48° B A What is the measure of BC? 180° 84 42° 96°
Answer:
84°
Step-by-step explanation:
The central angle of a circle is twice any inscribed angle subtended by the same arc.
because AB is a diameter, we also know that the triangle angle at C is 90° (all the inscribed triangles with their baseline being a diameter are right-angled).
as always, the sum of all angles in a triangle is 180°.
so, we know the triangle angle at A is
180 - 90 - 48 = 42°.
this is also the inscribed angle of the arc BC.
the central angle for arc BC (that is what is requested here) is then twice that angle : 2×42 = 84°
What equation results from completing the square and then factoring?
x^2 + 4x = 5
A. (x + 2)^2 = 3
B. (x + 2)^2 = 7
C. (x + 2)^2 = 1
D. (x + 2)^2 = 9
Answer:
(x+2)^2 = 9
Step-by-step explanation:
To complete the square we need to add 4 to both sides of the equation,
Why we add 4 to both sides? Because if we add it to one side only, the equation will turn into an inequation
x^2 + 4x + 4 = 5 + 4
x^2 + 4x + 4 = 9 and the factor of the expression is (x+2)*(x+2) = 9
(x+2)^2 = 9
9
These lists show the ages of attendees in a yoga class and a dance dass
Yoga: 18, 31, 17, 14, 20, 33, 36
Dance: 20, 47, 23, 38, 26, 42, 30
Select from the drop-down menus to correctly complete each statement about the attendees in the two cases
The median age of the attendees in the yoga class is
the median age of the attendees in the dance
The range of ages of the attendees in the yoga class is
the range of ages of the attendees in the conce
Answer:
median is 20
Step-by-step explanation:
due to both of them having it in there 1 time
Answer:
The Median Age: Yoga Class (31) Dance Class (30)
The Range: Yoga Class (17-44) Dance Class (20-47)
Step-by-step explanation:
A laptop computer is purchased $1500. After each year , the resale value decreases by 25%. What will the resale value be after 5 years ? Round to the nearest dollar
Help me please with math for points
Answer:
The answer is 72
Step-by-step explanation:
because you take the 8 times it by the 9
9×8=72 square³
please help
me answer this question
Answer:
x ≥ 4
Step-by-step explanation:
Given:
[tex]\displaystyle \large{3x-1\geq 11}[/tex]
Add both sides by 1:
[tex]\displaystyle \large{3x-1+1\geq 11+1}\\\displaystyle \large{3x\geq 12}[/tex]
Divide both sides by 3:
[tex]\displaystyle \large{\dfrac{3x}{3} \geq \dfrac{12}{3}}\\\displaystyle \large{x\geq 4}[/tex]
Hence, the solution is x ≥ 4
what is the difference of 21 1/4 - 18 2/4
Answer: Difference between 21 1/4 - 18 2/4 =2 3/4
Step-by-step explanation:
Which is the graph of x2 − y2 = 16?
Answer:
see attached
Step-by-step explanation:
When the signs of the x^2 and y^2 terms of a relation quadratic in both x and y are different, the relation represents a hyperbola. The graph of the hyperbola is shown in the attachment.
__
If the signs are the same, the relation represents an ellipse. If the coefficients of the squared terms are also the same, then that ellipse is a circle.
The dimensions of triangle A are three times the dimensions of triangle B. The area of triangle B is 28 cm What is the area of triangle A?
Answer:
Below in bold.
Step-by-step explanation:
The ratio of theire areas is 1^2 : 3^2
= 1:9.
So the area of triangle A = 28 * 9
= 252 cm^2.
Answer:
[tex]252cm {}^{2} [/tex]
step by step explanation:
[tex]since \: \: dimension \: of \: traiangle \: a \: = 3 times \: dimension \: of \: triangle \: b \\ note \: that \: area \: is \: square \: of \: dimension \: \\ therefore \: area \: of \: triangle \: a \: = 3 {}^{2} \: area \: of \: triale \: \: b \\ area \: of \: trianle \: a = 9 \times 28 = 252cm {}^{2} [/tex]
A chemist has one solution that is 20% alcohol and another that is 60% alcohol.
How much of each solution must the chemist use to get 200 mL of a solution that is 52%
alcohol?
Answer:
solution 1= 40ml
solution 2= 160ml
Step-by-step explanation:
%alcohol= amount of alcohol/total solutionx100
0.52x200=104ml of alcohol present
0.2x L=0.2Lml of alcohol in solution one
0.6 x M=0.6Mml of alcohol in solution two
1st equation
0.2L+0.6M=104ml alcohol
times 10 to get whole
2L+6M=1040ml
2nd
same for this equation
10L+10M=2000ml
10L+10M=2000
2L+6M=1040
elimination method
=20L+20M=4000
-
=20L+60M=10400
-40M=-6400
M=160ml
2L+6 (160)=1040
2L=1040-960
2L=80
L=40ml
April is 19, Bryan is 20, Carla is 20, and Dave is 21, how old is Erica is the average of their given ages is 23?
Answer: 35
Step-by-step explanation:
The average can be found by adding their ages together and dividing by the number of ages.
Given:
[tex]\frac{19+20+20+21+x}{5}[/tex] = 23
Multiply both sides of the equation by 5:
19 + 20 + 20 + 21 + x = 115
Combine like terms:
80 + x = 115
Subtract 80 from both sides of the equation:
x = 35
Erica is 35.
PLEASE HELP ME WILL GIVE BRAINLIEST
Answer:
1 3/4, 0
Step-by-step explanation:
You have to go 1 3/4 to the right and 0 up.
Find the measure of the following arc.
mJH = ____
Step-by-step explanation:
the inner angle of 2 crossing segment lines is half of the sum of the 2 arc angles.
55 = (arc angle IG + arc angle JH)/2 = (76 + JH)/2
110 = 76 + JH
arc angle JH = 34°
The required arc angle JH measures 34 degrees.
What is a chord?In geometry, a chord is a line segment that connects two points on the circumference of a circle. The two endpoints of the chord lie on the circle, and the chord divides the circle into two segments - the major segment and the minor segment.
Given the problem, we are given that the inner angle measures 55 degrees. Thus, we can set up an equation using the formula and solve for the unknown value.
The equation is given as follows:
55 = (arc angle IG + arc angle JH)/2
We know that the arc angle IG measures 76 degrees, so we can substitute this value into the equation:
55 = (76 + arc angle JH)/2
Multiplying both sides of the equation by 2 yields:
110 = 76 + arc angle JH
Subtracting 76 from both sides of the equation gives:
arc angle JH = 34°
Therefore, the arc angle JH measures 34 degrees.
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How to solve 4 divided by 5
Answer: HELLO THERE! Here's what I found from study dot com "4 divided by 5 is equal to 0.8. This decimal can also be written as a fraction. 0.8 = eight tenths or 8/10 (4/5 in its reduced form)."
Step-by-step explanation:
Hope this helps, have a good day!
If line segment AB is 400%, what is the length of a line segment that is 100%?
the length of the line would be 1 inch
What is the perimeter of the pentagon below? 3.2 cm?
Answer:
You didn't attach a picture of the pentagon, but the perimiter can easily be found using one of the following formulae:
Step-by-step explanation:
P = 5s, where s is the length of a side
P = 2r × Sin(180/5), where r is the radius