Answer:
Symmetric Property of Equality
Step-by-step explanation:
The symmetric property of equality is a simple property that says we can interchange the sides of an equation without changing the truth-value of the equation. That is, if a = b, then b = a. Each side of the equation can be thought of as the mirror image of the other side.
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Please help me solve this short problem guys
Answer:
Step-by-step explanation:
Given equation of the quadratic function is,
y = x² + 5x - 7
Convert this equation into vertex form,
y = x² + 2(2.5x) - 7
= x² + 2(2.5x) + (2.5)² - (2.5)² - 7
= (x + 2.5)²- 6.25 - 7
= (x + 2.5)² - 13.25
Therefore, vertex of the function is → (-2.5, -13.25)
For the solutions,
y = 0
(x + 2.5)² - 13.25 = 0
x = (±√13.25) - 2.5
x = (±3.64) - 2.5
x = 1.14, -6.14
Solutions → (-6.14, 0) and (1.14, 0)
Need help on this activity!!
In this activity, you will rearrange and solve a rational equation and find and use the inverse of a rational equation.
As we’ve seen, for a circuit with two resistors arranged in parallel, we can calculate the total resistance in the circuit, , in ohms, with this equation.
Question 1
Part A
Question
Rewrite the equation to represent the resistance of resistor 2, , in terms of and .
Answer:
My best guess rn is the first option
Step-by-step explanation:
the last dude had it close but it was basically flipped as you can tell.
The answer is (C) [tex]R_2=\frac{R_TR_1}{(R_1-R_T)}[/tex]
We need to make [tex]R_2[/tex] the subject of the formula [tex]R_T=\frac{R_1R_2}{R_1+R_2}[/tex]
First remove the denominator by multiplying both sides by the binomial [tex](R_1+R_2)[/tex]
[tex]R_T\times (R_1+R_2)=\frac{R_1R_2}{R_1+R_2}\times(R_1+R_2)\\\\R_TR_1+R_TR_2=R_1R_2[/tex]
Arrange all terms containing [tex]R_2[/tex] on one side
[tex]R_1R_2-R_TR_2=R_TR_1[/tex]
Factor out [tex]R_2[/tex] from the LHS
[tex]R_2(R_1-R_T)=R_TR_1[/tex]
Finally, divide both sides by the binomial [tex](R_1-R_T)[/tex] to leave [tex]R_2[/tex]
[tex]R_2(R_1-R_T)\times\frac{1}{(R_1-R_T)}=R_TR_1\times\frac{1}{(R_1-R_T)}\\\\R_2=\frac{R_TR_1}{(R_1-R_T)}[/tex]
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Factor 15x3 – 5x² + 6x – 2 by grouping. What is the resulting expression?
Monica took a survey of her classmates' hair and eye color. The results are in the table below.
The focus of a parabola is located at (0,–2). The directrix of the parabola is represented by y = 2. Which equation represents the parabola? y2 = –2x x2 = –2y y2 = –8x x2 = –8y
Answer:
[tex]\boxed{x^2=-8y}[/tex]
Step-by-step explanation:
[tex](a,b)\ is \ the\ focus\\y=k\ is \ the\ directrice\\\\Formula\ to\ use:\ y=\dfrac{(x-a)^2}{2(b-k)} +\dfrac{b+k}{2} \\\\Here: \ a=0,\ b=-2, \ k=2\\\\y=\dfrac{(x-0)^2}{2(-2-2)} +\dfrac{-2+2}{2} \\\\so\ y=-\dfrac{x^2}{8} \\\\or\ x^2=-8y[/tex]
The equation which represents the parabola is x^2 = 8y, the correct option is C.
What is vertex form of a quadratic equation?
If a quadratic equation is written in the form
y=a(x-h)^2 + k
then it is called to be in vertex form. It is called so because when you plot this equation's graph, you will see vertex point(peak point) is on (h,k)
First of all, i used this vertex formula thing since it is visible that there are quadratic functions. Otherwise, you had to use calculus to get critical points, then second derivative of functions to find the character of critical points as minima or maxima or saddle etc to get the location of vertex point.
This point (h,k) is called the vertex of the parabola that quadratic equation represents.
We are given that;
Focus of parabola= (0,–2)
Now,
The vertex is halfway between the focus and the directrix on a line perpendicular to them. Since the focus is at (0,-2) and the directrix is y = 2, we can find that:
The vertex is at (0,0), because it has an x-coordinate of 0 (same as the focus) and a y-coordinate of 0 (the average of -2 and 2).
p is equal to 2, because it is half of the distance between -2 and 2.
Now we can plug in these values into the formula:
(x - 0)^2 = 4(2)(y - 0)
Simplifying, we get:
x^2 = 8y
Therefore, the equation of the parabola will be x^2 = 8y.
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Find a and b. PLS HURRY!
Answer:
[tex]a \: and \: b = \frac{5}{ \sqrt{2} } [/tex]
Step-by-step explanation:
[tex] \sin(45) = \frac{a}{5} \\ \frac{1}{ \sqrt{2} } = \frac{a}{5} \\ a = \frac{5}{ \sqrt{2} } \\ \\ \\ \\ \sin(45) = \frac{b}{5} \\ b = \frac{5}{ \sqrt{2} } [/tex]
I hope I helped you^_^
What is the solution for z?
24=z/0.6?
Answer:
[tex]z=14.4[/tex]
Step-by-step explanation:
One is given the following equation:
[tex]24=\frac{z}{0.6}[/tex]
Use inverse operations to solve this equation. Multiply both sides of the equation by (0.6) to undo the division of (0.6).
[tex]24=\frac{z}{0.6}[/tex]
[tex](0.6)(24)=z[/tex]
Simplify,
[tex](0.6)(24)=z[/tex]
[tex]z=14.4[/tex]
For each question circle the best choice.
Which of the following is an algebraic expression?
x + 5 = 7
5 - 2x = 3
5x + 4- 2x
-2 = 3x +1
5x+4-2x là biểu thức đại số
x3 + (y +z) factorize
What value of x is in the solution set of -2(3x + 2) >-8x + 6
Answer:
x >5
Step-by-step explanation:
-2(3x + 2) >-8x + 6
Distribute
-6x-4 > -8x+6
Add 8x to each side
-6x-4+8x > -8x+8x+6
2x-4 > 6
Add 4 to each side
2x-4+4 > 6+4
2x> 10
Divide by 2
2x/2 >10/2
x >5
Step-by-step:
-2(3x+2)>-8x+6. divided by 2,-3x-2>-4x+3. the solution set of -2(3x+3)>-8x+6 is {x/x>5}
Answer:
6
The function (1) describes the height, in feet, of an object at time, in seconds, when it is launched upward from the ground at an initial speed of 112 feet per second.
a. Find the domain.
b. What does the domain mean in this context?
Answer:
see below
Step-by-step explanation:
The domain is the values that the input takes
The values go from 0 to 7
0≤x≤7
This is the time from the initial launch until the object hits the ground
The velocity of a particle moving along a straight line is given by v(t)=6t2+4t−5 cm/sec at time t seconds with initial position s(0)=3 cm. What is the position of the particle at t=2 seconds, in cm?
Answer:
s(2) = 17 cm
Step-by-step explanation:
We are told that the velocity function is;
v(t) = 6t² + 4t − 5 cm/sec
Integral of velocity gives distance.
Thus;
s(t) = ∫v(t) = ∫6t² + 4t − 5
s(t) = 2t³ + 2t² - 5t + c
We are told that s(0)=3 cm
Thus;
s(0) = 2(0)³ + 2(0)² - 5(0) + c = 3
Thus; c = 3
Thus;
s(t) = 2t³ + 2t² - 5t + 3
At t = 2 secs
s(2) = 2(2)³ + 2(2)² - 5(2) + 3
s(2) = 17 cm
According to the graph what is the value of the constant in the equation below
Answer:
C. 1.5
Step-by-step explanation:
Step-by-step explanation:
Answer:
What is the median for the set of data? 6, 7, 10, 12, 12, 13
Answer choices:
6
7
10
12
12
13
Answer:
11
Step-by-step explanation:
If the set of numbers are not in least to greatest first set them up into their positions. But since this set is already in least to greatest we can go to the next step.
6, 7, 10, 12, 12, 13
Cross off all numbers until you get to the middle:
6, 7, 10, 12, 12, 13
Find the mean of the numbers in the middle:
10 + 12 = 22
22 / 2 = 11
The answer is 11
Hope this helped.
Answer:
11
Step-by-step explanation:
10+12=22
22÷2=11
median is equal to the middle number after being arranged in ascending order.
What is AE?
Enter your answer in the box?
Answer:
AE = 18 units
Step-by-step explanation:
Δ AEB and Δ DEC are similar , then corresponding sides are in proportion, that is
[tex]\frac{AE}{DE}[/tex] = [tex]\frac{AB}{DC}[/tex] , substitute values
[tex]\frac{2x+4}{x+8}[/tex] = [tex]\frac{12}{10}[/tex] ( cross- multiply )
10(2x + 4) = 12(x + 8) ← distribute parenthesis on both sides
20x + 40 = 12x + 96 ( subtract 12x from both sides )
8x + 40 = 96 ( subtract 40 from both sides )
8x = 56 ( divide both sides by 8 )
x = 7
Then
AE = 2x + 4 = 2(7) + 4 = 14 + 4 = 18 units
The height of a right cylinder is 3 times the radius of the base. The volume of the cylinder is 247 cubic units.
What is the height of the cylinder?
O 2 units
O 4 units
O 6 units
O 8 units
The height of the cylinder is 6 units.
What is cylinder?A cylinder has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes. In elementary geometry, it is considered a prism with a circle as its base.
Given that, the height of a right cylinder is 3 times the radius of the base. The volume of the cylinder is 24π cubic units.
Volume = π × radius² × height
Let the height of 3x then the radius will be x,
24π = π × x² × 3x
24 = 3x³
x = ∛8
x = 2
Therefore, height = 6
Hence, the height of the cylinder is 6 units.
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Rewrite the expression in the form z^n.
z^3/4 x z^2
Step-by-step explanation:
here's the answer to your question
Rewrite
4/10 : 1/25 as a unit rate.
A: 10:1
B: 25:4
C: 2:125
D: 100:1
Answer:
4/10 : 1/25
4/10 / 1/25 = 4/10 x 25/1 = 100/10 = 10.
10 can also be written as 10:1, so A is correct.
Hope this helps!
Find the 13th term of the arithmetic sequence -3x – 1,42 + 4,112 + 9, ...
Answer:
The 13th term is 81x + 59.
Step-by-step explanation:
We are given the arithmetic sequence:
[tex]\displaystle -3x -1, \, 4x +4, \, 11x + 9 \dots[/tex]
And we want to find the 13th term.
Recall that for an arithmetic sequence, each subsequent term only differ by a common difference d. In other words:
[tex]\displaystyle \underbrace{-3x - 1}_{x_1} + d = \underbrace{4x + 4} _ {x_2}[/tex]
Find the common difference by subtracting the first term from the second:
[tex]d = (4x+4) - (-3x - 1)[/tex]
Distribute:
[tex]d = (4x + 4) + (3x + 1)[/tex]
Combine like terms. Hence:
[tex]d = 7x + 5[/tex]
The common difference is (7x + 5).
To find the 13th term, we can write a direct formula. The direct formula for an arithmetic sequence has the form:
[tex]\displaystyle x_n = a + d(n-1)[/tex]
Where a is the initial term and d is the common difference.
The initial term is (-3x - 1) and the common difference is (7x + 5). Hence:
[tex]\displaystyle x_n = (-3x - 1) + (7x+5)(n-1)[/tex]
To find the 13th term, let n = 13. Hence:
[tex]\displaystyle x_{13} = (-3x - 1) + (7x + 5)((13)-1)[/tex]
Simplify:
[tex]\displaystyle \begin{aligned}x_{13} &= (-3x-1) + (7x+5)(12) \\ &= (-3x - 1) +(84x + 60) \\ &= 81x + 59 \end{aligned}[/tex]
The 13th term is 81x + 59.
In 2000, U.S. Airways burned about 115 litres of fuel per passenger. In 2014 that dropped
to 90 litres of fuel per passenger. What is the percentage reduction in fuel used? Give you
answer to the nearest whole percentage.
Answer:
22% reduction
Step-by-step explanation:
Find the percent decrease by dividing the difference in amounts by the original amount.
Find the difference:
115 - 90 = 25
Divide this by the original amount:
25/115
= 0.217
So, the percent decrease is 21.7%. Round this to the nearest whole percentage:
= 22
The percent reduction in fuel used was approx. 22%
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER PLS GIVE ME A STEP BY STEP EXPLANATION!!
Find the missing term in the proportion:
1/y = 4/11
y=?
Answer:
2.75, or 2 3/4
Step-by-step explanation:
Cross multiply first to get:
4y = 11
Divide by 4 on both sides
y = 2.75
Now, simplify to a mixed number or keep it as a decimal to get 2.75, or 2 3/4.
Hope this helps!
If there is something wrong, just let me know.
Answer:
2.75
Step-by-step explanation:
1/y = 4/11 cross multiply the expressions
4y = 11 divide both sides by 4
y = 2.75
What's 672 divided by 32
Answer:
the answer is 21
Step-by-step explanation:
If BC = 5, DE = 9, and AB = 4, what is the length of AD?
7
8
7.2
7.5
There are two triangles here: ABC and ADF. These triangles are similar, and thus proportional. So, we can set up a proportion between the left side of each triangle and the base of each triangle.
AB / AD = BC / DE
4 / (4 + BD) = 5 / 9
---AD is made up of AB and DB. We know AB, but not BD, so we need to find its value to find the length of AD.
5(4 + BD) = 9 x 4
20 + 5BD = 36
5BD = 16
BD = 3.2
AD = AB + BD
AD = 4 + 3.2
AD = 7.2
Hope this helps!
Can I please get help with these 2 questions about polygons
Answer:
a)139°
Step-by-step explanation:
two co interior angles make one opposite exterior angle
49+90=139°
Hey please help for 100 points! Has to be accurate and explained well though for brainiest!
Question: Identify the property of equality(addition, subtraction, multiplication, or division) that could isolate this variable:
k - 4.5 = 9.8
Answer:
addition property of equality
Step-by-step explanation:
k - 4.5 = 9.8
Add 4.5 to each side using the addition property of equality
k-4.5 +4.5 = 9.8+4.5
k = 14.3
Answer:
Addition Property of Equality
Step-by-step explanation:
k - 4.5 = 9.8
~Add 4.5 to both sides
k = 14.3
Best of Luck!
( a ) 2x + 3y − 5z ( ) 32
( b ) x + y + z ( ) 8
( c ) x
2 + 2xy + z
2
( ) 36
( d ) (x + y)(x + z) ( ) −1
( e ) −(x
2 − y
2
) ( ) −16
Answer:
Step-by-step explaWe are losing Earth's greatest biological treasures just as we are beginning to appreciate their true value. Rainforests once covered 14% of the earth's land surface; now they cover a mere 6% and experts estimate that the last remaining rainforests could be consumed in less than 40 years.
One and one-half acres of rainforest are lost every second with tragic consequences for both developing and industrial countries.
Rainforests are being destroyed because the value of rainforest land is perceived as only the value of its timber by short-sighted governments, multi-national logging companies, and land owners.
Nearly half of the world's species of plants, animals and microorganisms will be destroyed or severely threatened over the next quarter century due to rainforest deforestatioue to rainforest deforestation. That equates to. As the rainforest species of tesrees anddisappear, so do many possible that 1% plants have been tested by sciMost rainforests are cleared by chainsaws, bulldozers and fires for its timber value and then are followed by farming and ranching operations, onian Rainforest five centuries ago. Today there are less than 200,000.
In Brazil alone, European colonists have destroyed more than 90 indigenous tribes since the 1900's. With them have gone centuries of
nation:
Expand the following
(x+2x)(2s-2t)
(m-n)²
(k+9)²
(4a-3b)(c+6d)
please check the attachment for solutions
Find the y-intercept of the following equation. Simplify your answer.
y = -10x -3/7
Answer: (0, -3/7)
Step-by-step explanation:
The Y-intercept would be the value of y when x is at 0, which is when the Y axis is intercepted. -3/7 is the starting position of the function when the the X = 0.
2 + 16 + 48 factorizar
alguien que me ayude??
Answer:
2*6*11
Step-by-step explanation:
I am not sure what your question is because I think you are asking the factor of these numbers. so u do 2+16+48 which is 66 and if you prime factorize it then you get 2*6*11. so the answer is 2*6*11.