Answer:
[tex]x = \sqrt{-2} = 2i[/tex]
Step-by-step explanation:
[tex]5x^2-2=-12[/tex]
[tex]5x^2 =-10[/tex]
[tex]x^2 =-2[/tex]
[tex]x = \sqrt{-2} = 2i[/tex]
Write the equation of the line shown in the graph above in slope intercept form
A) y=2/3x+1
B) y=-x+2/3
C) y=-2/3x+1
D) 2x+3y=3
Answer:
C, y=-2/3x+1
Step-by-step explanation:
using points (0, 1) and (3, -1) obtained from the graph:
slope = -1-1/3-0 = -2/3
use one of the points above lets take (1, 0) and another point (x,y)
slope = y-0/x-1 = -2/3
y=-2/3x+1
Find area and perimeter of shaded regions below
Answer:
Step-by-step explanation:
ABCD is a square.
side = 24 cm
Area of square = side * side = 24 * 24 = 576 cm²
Semicircle:
d = 24 cm
r = 24/2 = 12 cm
Area of semi circle =πr²
= 3.14 * 12 * 12
= 452.16 cm²
Area of shaded region = area of square - area of semicircle + area of semicircle
= 576 - 452.16 + 452.16
= 576 cm²
Perimeter:
Circumference of semicircle = 2πr
= 2 * 3.14 * 12
= 75.36
Perimeter = 2* circumference of semicircle + 24 + 24
= 2 * 75.36 + 24 + 24
= 150.72 + 24 + 24
= 198.72 cm
A family has two cars. The first car has a fuel efficiency of 35 miles per gallon of gas and the second has a fuel efficiency of 15 miles per gallon of gas. During one particular week, the two cars went a combined total of 1825 miles, for a total gas consumption of 75 gallons. How many gallons were consumed by each of the two cars that week?
Answer:
1) 35 gallons by the first car 2) 40 gallons by the second car
Step-by-step explanation:
Suppose the first car used x gallons, when the second car used the rest- 75-x
If the first car's efficiency is 35 miles per galon, its milleage is 35*x, the second car's milleage is 15*(75-x). And the summary milleage is equal to 1825.
35x+15(75-x)=1825
35x+1125-15x= 1825
20x=700
x=35- gallons consumed by the first car,
75-35=40- gallons consumed by the second one
Please Help!
Use the function f(x) to answer the questions
f(x) = 5x^2 + 2x - 3
Part A: What are the x-intercepts of the graph of f(x)? Show your work (5 points)
Part B: Is the vertex of the graph of f(x) going to be a maximum or a minimum? What are the coordinates of the vertex? Justify your answers and show
your work (5 points)
Part 2: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part A and Part B to draw the graph (5 points)
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Answer:
A: -1, 3/5
B: (-1/5, -3 1/5)
2: plot the given points and draw a curve through them.
Step-by-step explanation:
Part AThe x-intercepts are most easily found from a graph of the function. I like the Desmos graphing calculator for this purpose. The x-intercepts are -1 and 3/5.
You can also find the x-intercepts by factoring the function.
f(x) = 5x^2 +5x -3x -3 = 5x(x +1) -3(x +1) = (5x -3)(x +1)
The x-intercepts are the values of x that make the factors zero:
5x -3 = 0 ⇒ x = 3/5
x +1 = 0 ⇒ x = -1
__
Part BThe vertex is on the axis of symmetry, which is the vertical line at the value of x halfway between the zeros. (-1 +3/5)/2 = (-2/5)/2 = -1/5
The value of f(x) there is ...
f(-1/5) = (5(-1/5) +2)(-1/5) -3 = (-1 +2)(-1/5) -3 = -1/5 -3 = -3 1/5
The vertex is (-1/5, -3 1/5).
__
Part 2The easiest step to take to graph the function is to type it into a graphing calculator (see attached).
If you're graphing this by hand, the three points given in parts A and B will be on the graph. The leading coefficient in the function is 3, so the x^2 parent function is vertically stretched by a factor of 3. This can make it a little more difficult to find points that lie on the graph.
Recognizing that the vertex form equation is ...
f(x) = 3(x +1/5) -3 1/5
I might choose x-values that are -1/5 ± 1/2 to get y-values that are -3 1/5 + 3/4. And, x = -1/5 ± 1 ⇒ y = -3 1/5 +3.
rewrite -4<x<-1 using absolute value sign
[tex] - | 4 | < x < - |1| [/tex]
dunno if that's the desired form tough, but it states the same definition
The given inequality rewritten using absolute value sign as |-4|<x<|-1|.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
The given inequality is -4<x<-1.
An absolute value inequality is an expression with absolute functions as well as inequality signs.
Here, using absolute value sign we get
|-4|<x<|-1|
Therefore, the given inequality rewritten using absolute value sign as |-4|<x<|-1|.
To learn more about the inequalities visit:
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Annie is opening a savings account which earns 5.2% interest, compounded continuously.
How much will she need to deposit in the account so that she has $2300 after 7 years?
Round your answer to the nearest dollar.
Do NOT round until you have calculated the final answer.
Answer:
1686.22
Step-by-step explanation:
2300=P(1+(0.052x7))
2300=P1.364
P=2300/1.364
=1686.217...
=1686.22...
=1686 FOR THE NEAREST DOLLAR
Which of the two functions below has the smallest minimum y-value?
f(x) = 4(x - 6)4 + 1
g(x) = 2x3 + 28
O A. g(x)
B. f(x).
C. The extreme minimum y-value for f(x) and g(x) is --
D. There is not enough information to determine
Answer:
Answer A
Step-by-step explanation:
[tex]\displaystyle \lim_{n \to -\infty} (3x^3+28)=-\infty\\\\minimum\ of \ f(x)=6\\\\Answer\ A[/tex]
Complete the equation describing how
x and y are related.
5
1 2 3 4
8 13 18
-2
3
23
28
y = 5x + [?]
Enter the answer that belongs in [?].
Answer:
y=5x+3
Step-by-step explanation:
The equation of line is y=5x+3 since the y intercept is 3
Which statements can be used to compare the characteristics of the functions? Select three options.
Answer:
Step-by-step explanation:
g(x) has the smallest minimum value. All three functions share the same domain and the y-intercept is also the same for all three thus options (C),(D), and (E) is correct.
What is a graph?A graph is a diametrical representation of any function between the dependent and independent variables.
For example y = x² form a parabola now by looking at only the graph we can predict that it has only a positive value irrespective of the interval of x.
As per the given table,
The minimum value among all functions is -204 which is for g(x).
The domain is the set of x since all function defines the same x thus they have the same domain.
At y-intercept x = 0
Since at x = 0 all function is 3 thus all three will have the same y-intercept.
Hence "The smallest minimal value is for g(x). The y-intercept for all three functions is the same, and all three functions have the same domain".
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11. Find the 5th term of the sequence defined by the given rule. (1/2 point)
f(n) = 6n + 4
Answer:
34
Step-by-step explanation:
n = 5
f(5) = 6(5)+4
f(5)=34
The fifth term of the sequence is equal to 34.
What is arithmetic progression?The sequence in which every next number is the addition of the constant quantity in the series is termed the arithmetic progression.
The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given expression is f(n) = 6n + 4. The value of the fifth term will be calculated as,
n = 5
f(5) = 6(5)+4
f(5)=34
Therefore, the fifth term of the sequence is equal to 34.
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2x + 5y = 10 into slope- intercept form
Answer:
y=-2x+10
Step-by-step explanation
Hope this helped
It used to take 20 hours to get to Los Angeles, now it takes 12 hours, how much shorter was it?
Step-by-step explanation:
It takes 20 Hours to get to Los Angeles
Now it takes 12 hours....
Therefore we subtract 20 from 12
which becomes
20 - 12= 8.
So it's 8 hours shorter
I’m the triangle shown we can find the angle theta as follows.
Answer:
sin = opp/hyp
cos = adj/hyp
tan = opp/adj
When it was built, the given stadium held 31,080 fans per game. Today, it holds 86,047. How many more fans could attend per year (12 games) compared to the year it was built?
Answer:
659604 students
Step-by-step explanation:
86047-31080=54967 more students per game
54967 students per game x 12 games = 659,604 students
Given the function f(x) = 3x - 1, explain how to find the average rate of change between x = 1 and x = 4.
Step-by-step explanation:
f(1) = 3×1 - 1 = 2
f(4) = 3×4 - 1 = 12-1 = 11
so, the functional value changes 11-2=9 units on an x interval of 4-1=3 units length.
the average change rate is the total change across the x interval relative to the interval length.
that is
9/3 = 3
which is the slope (= the factor of x) in the line equation.
for a line its change rate for any point is the same constant. and that is therefore automatically also the average change rate across an interval of x values.
if the change rate would be different for different parts of the function, it would not be a straight line.
Answer:
3
Step-by-step explanation:
The average rate of f(x) in the closed interval [ a, b ] is
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
Here [ a, b ] = [ 1, 4 ] , then
f(b) = f(4) = 3(4) - 1 = 12 - 1 = 11
f(a) = f(1) = 3(1) - 1 = 3 - 1 = 2
average rate of change = [tex]\frac{11-2}{4-1}[/tex] = [tex]\frac{9}{3}[/tex] = 3
Please figure this out and find the measure
Answer: ME
Step-by-step explanation:
Answer:
166
Step-by-step explanation:
Since the lines are parallel, A=B. 7x+40=3x+112, 4x=72, x=18. A=166
A circle P is circumscribed about a regular hexagon ABCDEF
If segment AE is drawn, triangle AEF is a/n ____________ triangle. Select one:
a. isosceles
b. scalene
c. equilateral
d. right
i’ll mark u as brainliest:))
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Answer:
a. isosceles
Step-by-step explanation:
Segments EF and FA of the hexagon are the same length, so the triangle is an isosceles triangle.
The volume of a gas with a pressure of 1.2 atm increases from 1.0 L to 4.0 L. What is the final pressure of the gas, assuming constant temperature?
(a) 1.2 atm
(b) 0.30 atm
(c) 3.3 atm
(d) 4.8 atm
(e) 1.0 atm
Answer:
(b) 0.30 atm
Step-by-step explanation:
Given data
Initial pressure= 1.2atm
Initial volume= 1.0L
Final volume= 4.0L
Final pressure= ???
Let us apply the gas formula to find the Final pressure
P1V1= P2V2
Substitute
1.2*1= x*4
Divide both sides by 4
1.2/4= x
x= 0.3atm
Hence the final pressure is 0.3 atm
- 18 = -3x + 6
Plz help
Answer:
8 =x
Step-by-step explanation:
- 18 = -3x + 6
Subtract 6 from each side
-18-6 = -3x+6-6
-24 = -3x
Divide each side by -3
-24/-3 = -3x/-3
8 =x
Answer:
x= 8
Step-by-step explanation:
[tex]\sf{}[/tex]
=> -3x+6 = -18
=> -3x+6-6= -8-6
=> -3x= -24
=> x= 8
Which graph represents the solution set for the quadratic inequality x2 + 2x + 1 > 0?
howdy!!
yr answer is the third graph!
HURRY WILL GIVE BRANLIEST
I believe that the answers in order are: Rational, Irrational, Irrational, Irrational. I think these answers are correct, but if not, please let me know. Thanks.
Answer:
I think 0.5 and 0/100 are rational
the others are irrational
Order the expressions from least to greatest.
Anwser
4 then 5 then 6
Answer:
This the right order:
4^2+2^2 = 20
5^2= 25
6^2-6 = 30
a group of workers can plant 3/5 acres in 5/6 days. what is the unit rate per day?
Answer:
Workers can plant 0.72 acres per day.
(a+b)^3=? hhihiihihihihih
Answer:
Step-by-step explanation:
Find the other endpoint of the line segment with the given endpoint (-2, -2) and midpoint (3,10)
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Answer:
(8, 22)
Step-by-step explanation:
For endpoints A and B, and midpoint M, the relationship of interest is ...
B = 2M -A
B = 2(3, 10) -(-2, -2) = (6+2, 20+2)
B = (8, 22)
The other end point is (8, 22).
Find Term 20 for the sequence a= 4 6 8 10......
4,6,8,10 are in A.P
a=4d=2[tex]\\ \rm\Rrightarrow a_n=a+(n-1)d[/tex]
[tex]\\ \rm\Rrightarrow a_20=4+(20-1)2[/tex]
[tex]\\ \rm\Rrightarrow a_20=4+19(2)[/tex]
[tex]\\ \rm\Rrightarrow a_20=4+38[/tex]
[tex]\\ \rm\Rrightarrow a_20=42[/tex]
Form a polynomial whose zeros and degree are given.
Zeros: - 2, 2, 6; degree: 3
Type a polynomial with intéger coefficients and a leading coefficient of 1 in the box below.
f(x)=(Simplify your answer.)
Answer:
[tex]f(x) = (x + 2)(x - 2)(x - 6)[/tex]
[tex]f(x) = ({x}^{2} + 4)(x - 6)[/tex]
[tex]f(x) = {x}^{3} - 6 {x}^{2} + 4x - 24[/tex]
Step-by-step explanation:
Multiply factors.
multiply 725base 9× 367base 9
Answer:
Hello,
Answer 303028
Step-by-step explanation:
Multiplication in base 9
[tex]\begin{array}{cccccc}9^5&9^4&9^3&9^2&9^1&9^0\\--&--&--&--&--&--\\&&&7&2&5\\&&&3&6&7\\--&--&--&--&--&--\\&&5&5&8&8\\&4&7&6&3&\\2&3&7&6&&\\--&--&--&--&--&--\\3&0&3&0&2&8\end{array}[/tex]
14% of all Americans live in poverty. If 35 Americans are randomly selected, find the probability that
a. Exactly 3 of them live in poverty.
b. At most 7 of them live in poverty.
c. At least 4 of them live in poverty.
d. Between 1 and 8 (including 1 and 8) of them live in poverty.
find x on the lines plz and thanks
Answer:
x = 9
this is a ratio problem. You can see that 12/6 = 2, so you can also take 18/2 to get 9.
Answer:
the answer is 6
Step-by-step explanation:
Because 6 and x are corresponding angle so that means no matter what ( if u want the answer to how long the line is or what degree the angle is ) the answer is always going to be the same as the one above ( which is 6 )
Hop this helpssss
