Answer:
Step-by-step explanation:
Part A, the system of equation is, presented here as follows;
(1) 2·y = 3·x + 2
(2) y = 2·x² - 3·x + 2
Part B; The graph of the system of equation is attached
The reason for the above answers is as follows;
Part A
A system of equations are a given number of equations from which a common solution of the system can be found
A linear equation is an algebraic equation in which the maximum exponent of the variables is one and the graph of the equation is a straight line which is of the form y = m·x + c
A maximum value of the exponents of the variable quadratic equation is 2, and the general form of the quadratic equation is y = a·x² + b·x + c, where a, b, and c are real numbers
Therefore, the system of equation that can be created is as follows;
(1) 2·y = 3·x + 2
(2) y = 2·x² - 3·x + 2
Method for solving;
Divide equation (1) by 2, and equate both values of y to find the common solution as follows;
2·y/2 = (3·x + 2)/2 = 1.5·x + 1
∴ y = 1.5·x + 1
Equating both values of y gives;
y = 1.5·x + 1
y = 2·x² - 3·x + 2
Therefore;
1.5·x + 1 = 2·x² - 3·x + 2
2·x² - 3·x - 1.5·x + 2 - 1 = 0
2·x² - 4.5·x + 1 = 0
Using the quadratic formula, we get;
x = (4.5 ± √((-4.5)² - 4×2×1))/(2 × 2)
x = 2, or x = 0.25
From which we get;
y = 1.5 × 2 + 1 = 4, or y = 1.5 × 0.25 + 1 = 1.375
The points where the line graph and the quadratic graph intersect are;
(2, 4), and (0.25, 1.375)
Part 2
The diagram shows the curve with equation y = ( 1 + x ) cosx.
Complete the table below for points on the curve, giving the y values correct to 3 decimal places where appropriate.
Answer:
y = 1, 1.319, 1.024, 0
Step-by-step explanation:
Given equation:
[tex]y=(1+x)\cos x[/tex]
[tex]\textsf{when}\:x=0:[/tex]
[tex]\begin{aligned} \implies y & =(1+0)\cos 0\\\implies y & = 1\end{aligned}[/tex]
[tex]\textsf{when}\:x=\dfrac{\pi}{6}:[/tex]
[tex]\begin{aligned} \implies y & =\left(1+\frac{\pi}{6}\right)\cos \left(\frac{\pi}{6}\right)\\\implies y & = 1.319\: \sf (3\:dp)\end{aligned}[/tex]
[tex]\textsf{when}\:x=\dfrac{\pi}{3}:[/tex]
[tex]\begin{aligned} \implies y & =\left(1+\frac{\pi}{3}\right)\cos \left(\frac{\pi}{3}\right)\\\implies y & = 1.024\: \sf (3\:dp)\end{aligned}[/tex]
[tex]\textsf{when}\:x=\dfrac{\pi}{2}:[/tex]
[tex]\begin{aligned} \implies y & =\left(1+\frac{\pi}{2}\right)\cos \left(\frac{\pi}{2}\right)\\\implies y & = 0\end{aligned}[/tex]
please help if you can xx
Answer:
Below in bold.
Step-by-step explanation:
The angle in a regular octagon = 180 - (360/8) = 135.
Using trigonometry sin (135/2) = k/2 / EF
sin 67.5 = k / 2EF
2EF = k / sin 67.5
EF = k / 2 sin 67.5 = k/1.8478
Perimeter of octagon = 8 * k/1.8478
= 4.33k to the nearest hundredth.
Can you pls answer the question
Answer:8
Step-by-step explanation: behind the x value (5) there are 2 ages that had a value. You add the two values (5+3) and you get 8.
Final answer is 8.
Consider the following system of equations.
1. 75x + 1. 25y = 2. 75
7x + 5y = 9
What is the solution to the system?
Since 11 ≠ 9, there is no solution.
Since 0 = 0, there are infinitely many solutions.
There is one solution, x = 0 and y = 0.
There are two solutions (11, 0) and (0, 9)
Multiply the upper system by -4:
[tex] - 7x - 5y = - 11[/tex]
[tex]7x + 5y = 7[/tex]
[tex]0 = - 3[/tex]
[tex]this \: system \: admits \: no \: solutions[/tex]
What is the mean of the data set?
{7, 9, 5, 4, 3, 6, 8}
Enter your answer in the box.
Kiwi fruit contains roughly two and a half times as much vitamin C as the same weight of oranges.
What weight of kiwi fruit contains approximately the same amount of Vitamin C as 1kg of oranges
Using proportions, it is found that 400g = 0.4kg of kiwi fruit contains approximately the same amount of Vitamin C as 1kg of oranges.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
Kiwi fruit contains roughly two and a half times as much vitamin C as the same weight of oranges. Hence, if there is 1 kg = 1000g of oranges, the weight of kiwi fruit is given by:
1000/2.5 = 400g = 0.4kg.
More can be learned about proportions at https://brainly.com/question/24372153
Find the volume of the cone. Round your answer to the nearest tenth.
we know the base of the cone has a diameter of 6, thus its radius must be half that or 3.
[tex]\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=3\\ h=8 \end{cases}\implies \begin{array}{llll} V=\cfrac{\pi (3)^2(8)}{3}\implies V=24\pi \\\\\\ V\approx 75.4~in^2 \end{array}[/tex]
find the angle between the pair of vectors to the nearest tenth of a degree
6i-4j, 2i-6j
[tex]~~~~~~~~~~~~\textit{angle between two vectors } \\\\ cos(\theta)=\cfrac{\stackrel{\textit{dot product}}{u \cdot v}}{\underset{\textit{magnitude product}}{||u||~||v||}} \implies \measuredangle \theta = cos^{-1}\left(\cfrac{u \cdot v}{||u||~||v||}\right) \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} 6i-4j\\ 2i-6j \end{cases}\implies \stackrel{\qquad a~\hfill b\qquad }{\begin{array}{llll} < 6~~,~~-4 > \\ < 2~~,~~-6 > \end{array}}[/tex]
[tex]\stackrel{\textit{\Large dot product}}{ < 6~~,~~-4 > \cdot < 2~~,~~-6 > \implies (6\cdot 2)+(-4\cdot -6)}\implies 12+24\implies 36 \\\\\\ \stackrel{\textit{\Large magnitudes}}{|| < 6~~,~~-4 > ||\implies \sqrt{6^2+(-4)^2}\implies \sqrt{52}} \\\\\\ || < 2~~,~~-6 > ||\implies \sqrt{2^2+(-6)^2}\implies \sqrt{40} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\measuredangle \theta =cos^{-1}\left( \cfrac{36}{\sqrt{52}\cdot \sqrt{40}} \right)\implies \measuredangle \theta =cos^{-1}\left( \cfrac{36}{\sqrt{52}\cdot \sqrt{40}} \right) \\\\\\ \measuredangle \theta =cos^{-1}\left( \cfrac{36}{\sqrt{2080}} \right)\implies \measuredangle \theta \approx 37.9^o[/tex]
If the slope of a line is -4 find y when (2,y) and (3,8)
(Someone please explain I'm so confused)
Answer:
y=12
Step-by-step explanation:
[tex]slope=\frac{y2-y1}{x2-x1} \\-4=\frac{8-y}{3-2} \\-4=8-y\\y=8+4=12[/tex]
Find the surface area of each solid.
Answer:
232 in^2
Step-by-step explanation:
This rectangle has 6 surfaces:
Front: 10 x 8 = 80
Back: 10 x 8 = 80
Top: 10 x 2 = 20
Bottom: 10 x 2 = 20
Side: 8 x 2 = 16
Side: 8 x 2 = 16
Total surface area: 232 in^2
How can you decompose the composite figure to determine its area? as a pentagon and four semicircles as two rectangles and four circles as a square and four semicircles as two triangles and four circles
Answer: as a square and four semicircles
Step-by-step explanation:
The composite shape area can be found by first decomposing the figure as: a square and four semicircles.
What is area ?Area is the measure of a region's size on a surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.
here, we have,
to Find the Area of a Composite Figure:
To find the area of a composite figure, the first thing to do is to identify the individual shapes that make up the figure, then find the area of each shape before adding all the areas together.
For a composite figure that is comprised of a square and 4 semicircles, the composite figure would be decomposed into: a square and four semicircles.
Hence, The composite shape area can be found by first decomposing the figure as: a square and four semicircles.
Learn more about composite figures on:
brainly.com/question/15981553
#SPJ5
Pleaseeeee helppppp meeeee
Answer:
NY or MZ
Step-by-step explanation:
they are both outside of the parallel lines and on opposite sides of the transverse line
using the rule y= 7 x-5,find the value of y when x is 3
Answer:
16
Step-by-step explanation:
If x = 3, then all we must do is substitute.
y=7(3)-5
y= 21 -5
y= 16
---
Hope I helped :)
A bookshelf contains 9 mysteries and 7 biographies books. A book is randomly selected and not replaced.
What is the probability that the first book is mystery and the second is the biography?
Answer:
The answer is 7/30
Step-by-step explanation:
According to counting rules, we use permutation when we want to choose successively and without replacement, as given in this problem
Rule of permutation: nPr = n! /(n-r)!
where: n:objects and r:sample
n of mysteries=9 ; r of mysteries=1 ; ⇒ 9P1
n of biographies=7 ; r of biographies=1 ; ⇒ 7P1
n of total books=9+7=15 ; r of total books=2 ; ⇒15P2
Probability=( 9P1 x 7P1 ) / 15P2 = 49/210 = 7/30
Hope this helps :)
1. Carol jogged 13 miles on 5 days last week.
She jogged 22 miles on 4 days this week.
Was her total distance greater last week or
this week? How much greater? Explain.
Find the area, no need to explain, need this quick!!
Answer:
A = 201.5 m2
Step-by-step explanation:
[tex]A=76.5+65+60=201.5[/tex]
Hope this helps
2. Draw what might be the missing figure in
the pattern below.
Please helps
Please I’m stuck in the answer
Answer:
PLEASE ATTACH THE FIGURE LIKE THIS.....
1. Find the value of X and Y:
2. Find the value of X:
Answer:
Step-by-step explanation:
Find the surface area of the prism:
Answer: the prism has a surface area with 920
Matthew collected different types of leaves for a science project. He measured the lengths of the leaves. This list shows his findings. 2, 2, 234, 214, 3, 234, 3, 234, 314, 312, 3, 234 Create a line plot to display the data.
Answer:
Place 2 X's above the 2 column, and Place 1 X above the 2 1/4 column, place 4 X's in the 2 3/4 column, place 2 X's in the 3 column, place 1 X in the 3 1/4 column, and 1 X in the 3 1/2 column.
Step-by-step explanation:
The key with Line plots is to count the amount of that number. As you can see, there are 2 2's in the 2 columns, 2 3's in the three-column, and so on. And the three main steps of making a line graph are these:
1. Count the Number of what you have
2. Always give your graph a title
3. Keep your graph organized. An unorganized graph can cause confusion.
And you're done! I hope this helped!
Traingle Congruence, FlowChart Proof Level2, 10th Grade
Answer:
Step-by-step explanation:
→1.
Statement : AB ≅AD (side)
Reason: Given
→2.
Statement : ∡BAC≅∡CAD (angle)
Reason: Given
→3.
Statement : AC ≅AC (side)
Reason: Reflexive Property -a side is congruent with itself
→
Statement : ΔABC ≅ΔADC
Reason: Side-Angle-Side Theorem of Congruency
(If two corresponding sides of two triangles are congruent and the corresponding angles between those two sides are congruent then the two triangles are congruent)
10 identical copies of a movie will be stored on 40 computers such that each computer has at most 1 copy. How many different ways can the 10 copies be stored
We will see that there are 847,660,528 different ways in which the copies can be stored.
In how many ways can the 10 copies be stored?
So, we know that the copies can be stored in any of 40 computers, such that each computer can get, at most, one copy.
Then what we need to do is find how many different combinations of 10 computers can we make with the set of 40 computers, this is given by using the combination formula:
[tex]C(40, 10) = \frac{40!}{(40 - 10)!*10!} = \frac{40*39*38*37*36*35*34*33*32*31}{10*9*8*7*6*5*4*3*2} = 847,660,528[/tex]
This means that the 10 computes can be selected in 847,660,528 different ways, so there are 847,660,528 different ways in which the copies can be stored.
If you want to learn more about combinations, you can read:
https://brainly.com/question/11732255
What value of x is the solution to the equation −3/2x−3/4=−1/5 ?
A
−19/30
B
33/40
C
−19/20
D
−11/30
Answer:
[tex]\Longrightarrow: \boxed{\sf{x=-\dfrac{11}{30} }}[/tex]
Step-by-step explanation:
Isolate the term of x from one side of the equation.
-3/2x-3/4=-1/5First, add by 3/4 from both sides.
[tex]\sf{-\dfrac{3}{2}x-\dfrac{3}{4}+\dfrac{3}{4}=-\dfrac{1}{5}+\dfrac{3}{4} }[/tex]
Solve.
⇒ = -3/2x=11/20
Then, you multiply by 2 from both sides.
2(-3/2x)=11*2/20
Solve.
11*2/20
11*2=22
22/20
Common factor of 2.
11/10
-3x=11/10
Divide by -3 from both sides.
[tex]\sf{\dfrac{-3x}{-3}=\dfrac{\dfrac{11}{10}}{-3}}[/tex]
Solve.
[tex]\Longrightarrow:\boxed{\sf{x=-\dfrac{11}{30} }}[/tex]
Therefore, the correct answer is D. x=-11/30.I hope this helps! Let me know if you have any questions.
What is the volume of this pyramid? 32 cm 9 cm 15 cm
Answer:
720cm^3
Step-by-step explanation:
The volume of the pyramid with a = 9cm, b = 15cm and l = 32cm is 720cm^3.
Answer:
720³ cm
The formula for volume is...
length ×width ×heightWith that information, we should multiply the smaller numbers first.
[tex]B = \frac{1}{2} xy[/tex]
Replace the substituted parameters with 9 and 15, then multiply them and solve.[tex]B = \frac{1}{2}(9)(15) = \frac{135}{2}[/tex]
UseV for volume.[tex]V = \frac{1}{3} * \frac{135}{2} * 32 = 45 * 16[/tex]
Reducing the expression ↓[tex]V = 720^3~cm[/tex]
Hence, the volume is 720³ cm
Planet XX is in a stable circular orbit around a star, as shown in the figure. Which of the following graphs best predicts the angular momentum of the planet as a function of its horizontal position from point AA to point BB if the planet is moving counterclockwise as viewed in the figure above?
Answer:
option c iscorrect
Step-by-step explanation:
Speed
|
|~~~~~~~~~~~~
|
|________________ position
The volume of a cone-shaped hole is 147 pi ft3 If the hole is 9 ft deep, what is the radius of the hole?
Please help!!
radius : 3.95 ft
[tex]\sf volume \ of \ cone: \dfrac{1}{3} \pi r^2h[/tex]
[tex]\hookrightarrow \sf \dfrac{1}{3} \pi r^2(9) = 147[/tex]
[tex]\hookrightarrow \sf r^2 = \dfrac{147*3}{\pi (9)}[/tex]
[tex]\hookrightarrow \sf r = \sqrt{\dfrac{147*3}{\pi (9)}}[/tex]
[tex]\hookrightarrow \sf r = 3.95 \ ft[/tex]
Find the surface area of the figure. Be sure to show all of your work and steps in solving
for your answer.
Please show me the steps and solutions not just answers pls pls pls help me, tysm!!
The surface area of the figure which comprises two rectangular prisms is: 328 in.²
What is the Surface Area of a Rectangular Prism?Surface area = 2(wl+hl+hw)
Decompose the given figure into two.
Surface area of the figure = surface area of the top rectangular prism + surface area of the bottom rectangular prism - 2(area of base of the top rectangular prism)
Surface area of top rectangular prism:
l = 6 in.
w = 4 in.
h = 5 in.
Surface area = 2(wl+hl+hw) = 2(4×6 + 5×6 + 5×4) = 148 in.²
Surface area of bottom rectangular prism:
l = 6 in.
w = 9 in.
h = 4 in.
Surface area = 2(wl+hl+hw) = 2(9×6 + 4×6 + 4×9) = 228 in.²
Area of base of the top rectangular prism:
Area = (l)(w) = (6)(4) = 24 in.²
Surface area of the figure = 148 + 228 - 2(24)
Surface area of the figure = 328 in.²
Learn more about surface area of a rectangular prism on:
https://brainly.com/question/1310421
You have $5,000 to invest for ten years. Crown of The Sun bank pays compound interest at an annual rate of 4.5%. Calculate your balance after 10 years. Round to the nearest hundreth
Answer: $7,764.85
Step-by-step explanation:
Use the formula for Compound Interest: CI = P(1 + r/n)^nt
CI = 5000(1 + 0.045/1)^10
CI = 5000(1.045)^10
CI ≅ $7,764.85
After 10 years, the balance should be $7,764.85
Answer:
$7764.85
Step-by-step explanation:
Assume the compounding is annual.
F = P(1 + r/n)^(nt)
F = 5000(1 + 0.045/1)^10
F = 7764.85
Answer: $7764.85
Can someone please help me
Answer:
15
Step-by-step explanation:
f(X)= f(5)
meaning X= 5
x²-2x
5²-2(5) = 15
A store owner bought a grill for $180, then
marked it up 25% to sell in his store. If a
customer has a coupon for 25% off and
purchases the grill, which statement is true?
A. The customer paid the same
amount the store owner paid.
B. The customer paid $8.75 less
than the store owner paid.
C. The customer paid $11.25 less
than the store owner paid.
D. The customer paid $9.50 more
than the store owner paid.
Answer:
A. The customer paid the same
amount the store owner paid.
Step-by-step explanation:
its adding 25% of the original $180, then immediately decreasing 25% of the original $180, thus the customer paid the same amount the store owner paid.