Step-by-step explanation:
simple x×x×y×z=x^2×yz=x^2yz
Step 5: to isolate x, multiply both sides by:
To isolate x , multiply both the sides by ( 5/23 )
What is an Equation ?An equation is formed when two algebraic expressions are equated using an equal sign.
The given equation is
(3/5)(x-10) = 18-4x-1
(3/5)x - 6 = 18-4x-1
(3/5)x - 6 = 17-4x
(3/5)x = 23 -4x
(23/5)x = 23
Step 5 says To isolate x , multiply both the sides by (5/23)
x = 5
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Fred's teacher gave the class the
quadratic function f(x) = 4x² + 16x+9
State two different methods Fred could use to solve the equation f(x) = 0.
Using one of the methods stated in part a, solve f(x) = 0 for x, to the nearest
tenth.
Two methods Fred could use to solve the equation are
The completing the square method The formula methodThe solution for the function is x ≅ -0.7 OR x ≅ - 3.3
Solving quadratic equationsFrom the question, we are to solve the given quadratic equation
Two methods Fred could use to solve the equation are
The completing the square method The formula methodThe given quadratic function is
f(x) = 4x² + 16x+9
Now, we are to solve f(x) = 0 for x
That is,
4x² + 16x+9 = 0
Using the formula method to solve the equation
[tex]x =\frac{-b \pm \sqrt{b^{2}-4ac } }{2a}[/tex]
In the equation,
a = 4, b = 16, and c = 9
∴ [tex]x =\frac{-16 \pm \sqrt{16^{2}-4(4)(9) } }{2(4)}[/tex]
[tex]x =\frac{-16 \pm \sqrt{256-144 } }{8}[/tex]
[tex]x =\frac{-16 \pm \sqrt{112 } }{8}[/tex]
[tex]x =\frac{-16 \pm 10.58 }{8}[/tex]
[tex]x =\frac{-16+ 10.58 }{8}[/tex] OR [tex]x =\frac{-16- 10.58 }{8}[/tex]
[tex]x =\frac{-5.42 }{8}[/tex] OR [tex]x =\frac{-26.58 }{8}[/tex]
x = -0.6771 OR x = - 3.3229
x ≅ -0.7 OR x ≅ - 3.3
Hence, the solution for the function is x ≅ -0.7 OR x ≅ - 3.3
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Question 9 of 10
If you vertically compress the absolute value parent function, F(x) = |x|, by
multiplying by 3/4 what is the equation of the new function?
A: G(x)= |x+3/4|
B: G(x)= 3/4 |x|
C: G(x)= |x|-3/4
D: G(x)= |3/4 x|
Answer:
B. g(x) = 3/4|x|
Step-by-step explanation:
Multiplying the function by a number in front will stretch, compress, and/or reflect the function over the x-axis.
So if the number in front is negative that will flip it upside down, over the x-axis.
If the number is greater than 1, the function will be vertically stretched, narrower, slimmer, skinnier, taller.
In this case, the graph is vertically compressed, making it flatter, fatter, wider smashed. In this case is where the number multiplied in front of the parent function is LESS than one.
g(x) = 3/4 |x|
Which equation represents a line that is parallel to the line that passes through the points (-6,9) and (7,-17)?
Answer:
y = -2x-3
Step-by-step explanation:
Slope = - 2 C = - 3y =-2x-313. What is the surface area of the rectangular solid below using its net?
90 square units
108 square units
72 square units
84 square units
Answer:
108 square units
Step-by-step explanation:3 x 4 = 12
3 x 4 = 12
6 x 3 = 18
6 x 3 = 18
6 x 4 = 24
6 x 4 = 24
24(2) + 18(2) + 12(2) = 108 square units
Therefore, the surface area of the rectangular solid below using its net is 108 square units
A candy is in the shape of a sphere. The candy has a radius of 1.5 centimeters. Which of the following is closest to the volume of the candy? (Use 3.14 for π.)
Answer:
The answer would be 14 cm
[tex]V = \frac{4pi(1.5)^3}{3}[/tex]
[tex]4.5pi = 14.3[/tex]
(pi = π)
Your welcome :)
Answer:
14 cm
Step-by-step explanation:
THE SIMPLE ANSWER
find the area of the shaded part.
Answer:
Step-by-step explanation:
For part a :
The circumference of the circle is given by the formula 2πr. We are given r so we double r and put it next to pi :
C = 2×π×r = 2×π×8 = 16π
For part b :
The area of a circle is given by the formula πr². We are given r so we square r and put it next to pi :
A = π×r² = π×8² = 64π
For part c :
The area of a square is given by the formula a² where a is the side length. This question requires an extra step as we don't have the length of the square. But we know that the diameter of the circle will be equal to the side of the length. The diameter of a circle is given by the formula 2r : so
D = 2r = 2×8 = 16
So the area of the square will equal :
A = 16² = 256
Hope this helped and brainliest and hearts please.
I'm on my road to genius rank
You wish to take a flight from Nevada to New York. Use the point (-4, 0) to represent Nevada, and the (5, 2) to represent New York. The airline has partitioned the flight so that you have a layover. The flight distance is partitioned in a ratio of 3:1. Determine the ordered pair that represents the location of the layover.
Using proportions, it is found that the ordered pair that represents the location of the layover is (3.75, 1.5).
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The flight distance is partitioned in a ratio of 3:1, hence, for both the x and y coordinates, we have that:
L - Nv = 3/4(Ny - Nv)
For the x-coordinate, we have that:
[tex]x + 4 = \frac{3}{4}(5 + 4)[/tex]
[tex]x = \frac{27}{4} - \frac{16}{4}[/tex]
[tex]x = \frac{11}{4}[/tex]
x = 3.75
For the y-coordinate, we have that:
[tex]y = \frac{3}{4}(2)[/tex]
[tex]y = \frac{6}{4}[/tex]
y = 1.5.
The ordered pair that represents the location of the layover is (3.75, 1.5).
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If f(x) = 6x³ + 5x, g(x) = 3x² +5, and h(x) = 9x² - 8, What is the degree of f(g(h(x)))?
a)2
b)3
c)7
d) 12
Degree of f(x)=3
Degree of g(x)=2
Degree of h(x)=2
Degree of f(g(h(x)))
3(2)(2)12Option D
Answer:
d) 12
Step-by-step explanation:
Given functions:
[tex]f(x)=6x^3+5x[/tex]
[tex]g(x)=3x^2+5[/tex]
[tex]h(x)=9x^2-8[/tex]
As we are only interested in the degrees of the function, we can eliminate the coefficients of each variable and the constants:
[tex]f(x)=x^3+x[/tex][tex]g(x)=x^2[/tex][tex]h(x)=x^2[/tex]Therefore:
[tex]\begin{aligned}g[h(x)]& =(x^2)^2\\& =x^4\end{aligned}[/tex]
[tex]\begin{aligned}f[g[h(x)]] & = (x^4)^3+x^4\\& = x^{12}+x^4\end{aligned}[/tex]
Therefore, the degree of f[g[h(x)]] is 12
Please show work! Factor sin^2Θ + sin^2Θ cos^2Θ
Factorization of sin²θ + sin²θ cos²θ gives us; 2sin²θ - sin⁴θ
How to simplify Trigonometric Functions?
We want to simplify;
sin²θ + sin²θ cos²θ
Let us factorize out sin²θ to get;
sin²θ(1 + cos²θ)
Now, we know that cos²θ = 1 - sin²θ
Thus;
sin²θ(1 + cos²θ) = sin²θ(1 + 1 - sin²θ)
⇒ sin²θ(2 - sin²θ)
⇒ 2sin²θ - sin⁴θ
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10 1. Use the image below to answer the following questions: Solve for the measurement of A. b. Solve for y. a. C. Solve for x. X 48 Y A
Answer:
see explanation
Step-by-step explanation:
(a)
the sum of the 3 angles in the triangle = 180° , then
∠ A = 180° - 90° - 48° = 180° - 138° = 42°
(b)
using the tangent ratio in the right triangle
tan48° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{y}{10}[/tex] ( multiply both sides by 10 )
10 × tan48° = y , then
y ≈ 11.1 units ( to the nearest tenth )
(c)
using the cosine ratio in the right triangle
cos48° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{10}{x}[/tex] ( multiply both sides by x )
x × cos48° = 10 ( divide both sides by cos48° )
x = [tex]\frac{10}{cos48}[/tex] ≈ 14.9 units ( to the nearest tenth )
guys help just with part b for number 2!
Answer:
22 8th graders
Step-by-step explanation:
if 25% of the 88 kids are 8th graders then do this.
88x.25=22
88x.75=66
there are 22 eighth graders
and 66 seventh graders.
URGENT
Find the area of the triangle. Round your answer to the nearest tenth.
A triangle A B C with side A C labeled 15 units and side B C as 7 units. The measure of angle A C B is 96 degrees.
The area of the triangle is about (blank) square units.
Answer:
hope you can understand
Find the length of side x in simplest radical form with a rational denominator.
Answer:
[tex]x =\sqrt 2[/tex]
Step-by-step explanation:
Given is a 30° - 60° - 90° triangle.side x lie opposite to 30° angle[tex]\implies x = \frac{1}{2}\times \sqrt 8[/tex][tex]\implies x = \frac{1}{2}\times 2\sqrt 2[/tex][tex]\implies x =\sqrt 2[/tex]
if the observed value is 69.4 and the predicted value is 70.4, what is the residual value? round your answer to the nearest hundredth.
The residual value will be equal to -1.
What is residual value?A residual is a difference between the observed y-value of a data point and the predicted y-value on a regression line for the x-coordinate of the data point. A residual is positive when the point is above the line, negative when it is below the line, and zero when the observed y-value equals the predicted y-value.
Take, for instance, we have the following data entry:
Observed value = 69.4
Predicted value = 70.4
The residual (r) would be:
Residual value = 69.4 - 70.4 = -1
Therefore the residual value will be -1
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How do you write y=mx+b for this equation 21-y-mx=34
Answer:
y = -mx - 13.
Step-by-step explanation:
21-y-mx=34
Add y to both sides
21 - mx = 34 + y
Subtract 34 from both sides
-13 - mx = y
Rearrange:
y = -mx - 13.
The nearest hundred to 83,752,245 is?
Answer:
83,752,000
Very positive with this answer
Answer:
83,752,200
Step-by-step explanation:
please give me brainlist
WILL GIVE BRAINLISEST AND 60 POINTS !!!!
Question 5(Multiple Choice Worth 4 points)
(04.04)
Which graph represents a linear function?
Answer:
3rd one
Step-by-step explanation:
it is the only one with a function and a straight line
Which of these can help you visualize data? Select all that apply.
bank statement
circle graph
spreadsheet
table
bar graph
Answer:
circle graph and bar graph
Step-by-step explanation:
they visualize because they are not simply just words, they make colorful graphs
Andy wrote the equation of a line that has a slope of Step 2: y plus 2 equals StartFraction 3 Over 4 EndFraction x minus StartFraction 9 Over 4 EndFraction. and passes through the point (3, –2) in function notation.
Andy's equation is incorrect and the correct equation of the line is y + 2= 3/4(x - 3)
How to determine the equation of the line?The given parameters are:
Slope, m = 3/4
Point, (x,y) = (3,-2)
The equation of the line is calculated using:
y - y1 = m(x - x1)
Substitute the known parameters
y + 2= 3/4(x - 3)
From the question;
Andy's equation is y + 2 = 3/4(x - 9/4)
The above equation is different from the actual equation y + 2= 3/4(x - 3)
Hence, Andy's equation is incorrect and the correct equation of the line is y + 2= 3/4(x - 3)
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Please help!! Need help asap.
Help asap plss step by step maybe?
[tex] \frac{ - 9 + a}{15} > 1 \\ \\ - 9 + a > 1 \times 15 \\ - 9 + a > 15 \\ a - 9 + 9 > 15 + 9 \\ a > 24[/tex]
please solve the question in the picture
Answer with a step-by-step explanation:
Let us write answers to the questions using the given Venn diagram
1) 4 students
2) 3 students
3) 3 students
4) Face book ( 7 students are using Face book while only 6 students are using the other social media platform)
- More explanation is attached to the picture -
Help lolllllllllllll
Answer:
-5 or 5
Step-by-step explanation:
the absolute value of -5 is 5. The absolute value of 5 is also 5.
Hope this helps :)
-9y- 10 = x
5x +6y = -11
Answer: x = -1 , y = -1
A local television station sells time slots for programs in 303030-minute intervals. If the station operates 242424 hours per day, every day of the week, what is the total number of 303030-minute time slots the station can sell for Tuesday and Wednesday
Answer:
96
Step-by-step explanation:
Each day is 24 hours.
2 days = 2 × 24 hours = 48 hours
30-minute slot = 0.5-hour slot
48 hours / 0.5 hours = 96
Answer: 96
Answer:
96
Step-by-step explanation:
Seventy three percent of a town’s population own cars. What is the population of the town, if the number of cars owned is 112,420?
Fractions are written as a ratio of two integers. The total number of cars owned is 154000 cars
Fractions and percentagesFractions are written as a ratio of two integers.
Given the following
Total cars = 112,420 cars
If Seventy three percent of a town’s population own cars, then;
73% of x = 112,420
where x is the total population
0.73x = 112,420
x = 112,420/0.73
x = 154000
Hence the total number of cars owned is 154000 cars
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How many different sequences of 3 playing cards (from a single 52-card deck) exist?
22,100
140,608
132,600
24,804
There 1,32,600 possibilities to withdrawn 3 different sequence of playing cards from 52 cards.
What is Permutations?A permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements.
Here, total number of cards = 52
Number of Withdrawn cards = 3
Possibilities of different sequences of 3 playing cards = 52 X 51 X 50
= 132600
Thus, there 1,32,600 possibilities to withdrawn 3 different sequence of playing cards from 52 cards.
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Answer:
132,600
Step-by-step explanation:
To determine the number of different sequences of 3 playing cards from a 52-card deck, we can use the formula for permutations, which is given by:
P(n, k) = n! / (n-k)!
Where n is the total number of items (in this case, the number of cards in the deck) and k is the number of items chosen (in this case, 3 cards).
Plugging in the values:
n = 52 (total number of cards in the deck)
k = 3 (number of cards chosen)
P(52, 3) = 52! / (52-3)!
Calculating the factorial terms:
52! = 52 x 51 x 50 x ... x 3 x 2 x 1
(52-3)! = 49! = 49 x 48 x ... x 3 x 2 x 1
Simplifying the equation:
P(52, 3) = 52 x 51 x 50
P(52, 3) = 132,600
Therefore, there are 132,600 different sequences of 3 playing cards that can be formed from a single 52-card deck.
How many pairs of vertical angles are shown in the drawing?
Answer:
A.0
Step-by-step explanation:
Vertical angles are angles that are opposite of each other when two lines cross
Hope This Helped
Using synthetic division, find (2x4 − 3x3 − 20x − 21) ÷ (x − 3).
A.
2x3 + 3x2 + 9x + 7
B.
2x4 + 3x3 + 9x2 + 7x
C.
2x4 + 3x2 − 11x − 54
D.
2x3 + 3x2 − 11x − 54
The correct option for the synthetic division is A. 2x³ + 3x² + 9x + 7
How to solve the division?
Write down the first coefficient without changes and multiply the entry in the left part of the table by the last entry in the result.
Then, add the obtained result to the next coefficient of the dividend, and write the sum. All the coefficients are the coefficients of the quotient, and the last coefficient is the remainder.
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