Answer:
x = 3
Step-by-step explanation:
Using alternate angles, these angles are congruent
20x + 9 = 27x - 12
27 - 20 = 7
12 + 9 = 21
21 / 7 = 3
x = 3
find the number of outfits a girl could wear if she has 7 skirts,4 shirts and 2 pairs of shoes
The number of outfits is 56
How to determine the number of outfits?The given parameters are:
Skirts = 7
Shirt = 4
Shoes = 2
The number of outfits is calculated as:
Number of outfits = Skirts * Shirt * Shoes
So, we have:
Number of outfits = 7 * 4 * 2
Evaluate
Number of outfits = 56
Hence, the number of outfits is 56
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Express with fractional exponents instead of radicals.
6√x² y³
Answer:
using of fractional exponents give us the value 6(x^2y^3)^1/2 or 6xy^3/2.
Please help gotta hand this in today
Actividades que te gusta hacer solo/a:
1. Leer en mi dormitorio.
2. Escuchar música en mi dormitorio.
3. Dibujar en mi dormitorio.
Actividades que te gusta hacer con amigos:
1. Jugar videojuegos en la casa de un amigo.
2. Ir al cine.
3. Comer comida nueva en diferentes restaurantes.
4. Jugar voleibol en el gimnasio.
Actividades que te gusta hacer con familia:
1. Ver películas en casa.
2. Visitar la casa de los abuelos.
3. Comprar ropa en el centro de la ciudad.
Activities that are on all three lists:
- Ver películas (watch movies)- Comprar ropa (go shopping for clothes)Step 2: Where could one go to do the following activities?
1. Ver películas → al cine, a mi casa, a la casa de un amigo.
2. Estudiar para los regents → a la biblioteca, a mi casa.
3. Dibujar → a mi dormitorio, a la escuela.
4. Comer comida nueva → a diferentes restaurantes, al centro de la ciudad.
5. Jugar videojuegos → a la casa de un amigo, a mi casa.
6. Jugar voleibol → al gimnasio, a la escuela.
7. Practicar español → a la escuela, a mi casa.
8. Comprar ropa → al centro de la ciudad, a diferentes tiendas de ropa.
\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)
♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)
Use the graph to write a formula for the polynomial function of the least degree
Answer:
0.5 degrees is the answer you divided the quotion by 5 then get your answer (this isnt actually the answer lol)
Step-by-step explanation:
What is the constant up a proportionally in a equation y=x/g
Answer:
Step-by-step explanation:
\(y=(\frac{1}{g} )x\)
Constant up a proportionally is \(\frac{1}{g}\).
What is the effect on the graph of f(x)=1xf(x) = \frac{1}{x}f(x)=x
1 when it is transformed to g(x)=1x−7g(x) = \frac{1}{x} - 7g(x)=x
1−7?
A.
The graph of f(x) is shifted 7 units down.
B.
The graph of f(x) is shifted 7 units to the left.
C.
The graph of f(x) is shifted 7 units to the right.
D.
The graph of f(x) is shifted 7 units up.
Answer:
A
Step-by-step explanation:
10,946 divided by 115
Answer:
95.18
Step-by-step explanation:
Answer:
95.20 simplified nearest tenth
Step-by-step explanation:
95.1826086957
don’t mind the pencil writing
Answer:
Length = 22 cm
Width = 4 cm
Step-by-step explanation:
Area = 88 cm²
Length = x + 7
Width = x - 11
Area of rectangle = length*width
Therefore:
(x + 7)(x - 11) = 88
x(x - 11) +7(x - 11) = 88
x² - 11x + 7x - 77 = 88
Add like terms
x² - 4x - 77 = 88
x² - 4x - 77 - 88 = 88 - 88
x² - 4x - 165 = 0
Factorize
x² - 15x + 11x - 165 = 0
x(x - 15) +11(x - 15) = 0
(x + 11)(x - 15) = 0
x = -11 or x = 15
Let's use the positive number.
Therefore:
Length = x + 7
Plug in the value of x
Length = 15 + 7 = 22 cm
Width = x - 11 = 15 - 11 = 4 cm
25 pts - 37.5 if brainliest
Find the equation of the trend line (line of best fit)
Based on the given points on the graph, the equation for the line of best fit or the trend line is y = 1.874x + 3.656
What is the trend line?Due to the fact that the points on the graph are not on a straight line, the least squares method can be used to find the line of best fit equation.
Using a linear regression calculator, you can find the equation of the trend line by inputting the values of y and x in the graph.
When run through a linear regression calculator, the result will be:
y = 1.874x + 3.656
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Use the image to determine the direction and angle of rotation. Graph of triangle ABC in quadrant 1 with point A at 1 comma 3. A second polygon A prime B prime C prime in quadrant 4 with point A prime at 3 comma negative 1. 90° clockwise rotation 180° clockwise rotation 180° counterclockwise rotation 90° counterclockwise rotation
will give brainly if you help me thx
Answer:
A
Step-by-step explanation:
The answer is A because is it asking for a 3 in the hundredths place of the difference. Difference means subtraction. And you can find the hundredth spot in the second place over from the decimal
(ex. 1.23, hundredth place is a 3)
So then you do the math and find the differences.
14.56-9.33=5.23, which has a 3 in the hundredth place.
given , which of the following is true? f(x) is decreasing for all x < 6 f(x) is increasing for all x > 6 f(x) is decreasing for all x < 3 f(x) is increasing for all x < 3
The given function f(x) = (x + 6)/(x² - 9x + 18) is
(a) increasing on: (-6 - 6√3, 3), (3, -6 + 6√3)
(b) decreasing on: (-∞, -6-6√3), (-6+6√3,6), (6, ∞)
How to find the increase or decrease of a function?To find the increase in a function, the function f(x) is to be derivated and the derivative must be greater than 0. I.e,
f'(x) > 0
To find the decrease in a function, the function f(x) is to be derivated and the derivative must be less than 0. i.e.,
f'(x) < 0
Calculation:The given function is f(x) = (x + 6)/(x² - 9x + 18).
Its graph is shown below.
To find the increase or decrease in the function, we need to derivate it.
So,
f'(x) = d/dx{(x + 6)/(x² - 9x + 18)}
Applying d/dx(u/v) = (vu'-uv')/v²
So, on derivating the given function, we get
f'(x) = (x²+12x+72)/(x²-9x+18)²
= (x - (-6 + 6√3)) (x- (-6 - 6√3))/(x - 3)²(x - 6)²
For f'(x) > 0
The intervals that satisfy the given function for increasing are
(-6 - 6√3, 3), (3, -6 + 6√3)
For f'(x) < 0
The intervals that satisfy the given function for decreasing are
(-∞, -6-6√3), (-6+6√3,6), (6, ∞)
So, from the graph and the roots obtained, we can write,
The function f(x) decreases on: (-∞, -6-6√3), (-6+6√3,6), (6, ∞) and increases on (-6 - 6√3, 3), (3, -6 + 6√3).
Of the options none of them are correct.
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What is the solution to the equation?
4q + 4 = 20
Question 4 options:
q = 4
q = 6
q = 16
q = 24
Answer:
q = 4
Step-by-step explanation:
4q + 4 = 20
or, 4q = 20 - 4
or, q = 16/4
or, q = 4
Pre - Calculus evaluate exponential derivative at a point !
Answer:
\(\displaystyle\)\(\displaystyle f'(1)=-\frac{9}{e^3}\)
Step-by-step explanation:
Use Quotient Rule to find f'(x)
\(\displaystyle f(x)=\frac{3x^2+2}{e^{3x}}\\\\f'(x)=\frac{e^{3x}(6x)-(3x^2+2)(3e^{3x})}{(e^{3x})^2}\\\\f'(x)=\frac{6xe^{3x}-(9x^2+6)(e^{3x})}{e^{6x}}\\\\f'(x)=\frac{6x-(9x^2+6)}{e^{3x}}\\\\f'(x)=\frac{-9x^2+6x-6}{e^{3x}}\)
Find f'(1) using f'(x)
\(\displaystyle f'(1)=\frac{-9(1)^2+6(1)-6}{e^{3(1)}}\\\\f'(1)=\frac{-9+6-6}{e^3}\\\\f'(1)=\frac{-9}{e^3}\)
Answer:
\(f'(1)=-\dfrac{9}{e^{3}}\)
Step-by-step explanation:
Given rational function:
\(f(x)=\dfrac{3x^2+2}{e^{3x}}\)
To find the value of f'(1), we first need to differentiate the rational function to find f'(x). To do this, we can use the quotient rule.
\(\boxed{\begin{minipage}{5.5 cm}\underline{Quotient Rule for Differentiation}\\\\If $f(x)=\dfrac{g(x)}{h(x)}$ then:\\\\\\$f'(x)=\dfrac{h(x) g'(x)-g(x)h'(x)}{(h(x))^2}$\\\end{minipage}}\)
\(\textsf{Let}\;g(x)=3x^2+2 \implies g'(x)=6x\)
\(\textsf{Let}\;h(x)=e^{3x} \implies h'(x)=3e^{3x}\)
Therefore:
\(f'(x)=\dfrac{e^{3x} \cdot 6x -(3x^2+2) \cdot 3e^{3x}}{\left(e^{3x}\right)^2}\)
\(f'(x)=\dfrac{6x -(3x^2+2) \cdot 3}{e^{3x}}\)
\(f'(x)=\dfrac{6x -9x^2-6}{e^{3x}}\)
To find f'(1), substitute x = 1 into f'(x):
\(f'(1)=\dfrac{6(1) -9(1)^2-6}{e^{3(1)}}\)
\(f'(1)=\dfrac{6 -9-6}{e^{3}}\)
\(f'(1)=-\dfrac{9}{e^{3}}\)
Kaylee owns a food truck that sells tacos and burritos. She only has enough supplies to make 120 tacos or burritos. She sells each taco for $3 and each burrito for $6. Kaylee must sell at least $480 worth of tacos and burritos each day. If xx represents the number of tacos sold and yy represents the number of burritos sold, write and solve a system of inequalities graphically and determine one possible solution.
The system of inequalities is:
x + y ≤ 120
x*3 + y*6 ≥ 480
And one possible solution to it is x = 20 and y = 80.
How to find the system of inequalities?
First, we need to define two variables, we will be using:
x = number of tacos.y = number of burritos.We know that she can make at most 120 units, then:
x + y ≤ 120
And she wants to win at leastt $480, then:
x*3 + y*6 ≥ 480
So our system of inequalities is:
x + y ≤ 120
x*3 + y*6 ≥ 480
And the graph can be seen in the image below, the solution set of the system is given by the region where both shaded areas intersect.
There we can see that one possible solution is x = 20 and y = 80, in that case the total number of items made is:
20 + 80 = 100, which is less than 120
And the income is:
20*3 + 80*6 = 540.
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What is the smallest positive integer $n$ such that $\sqrt[4]{56 \cdot n}$ is an integer?
The smallest positive integer n such that t \($\sqrt[4]{56 \cdot n}$\) is an integer is 686.
We have to find the smallest positive integer n such that \($\sqrt[4]{56 \cdot n}$\) is an integer
To find the smallest positive integer n such that \($\sqrt[4]{56 \cdot n}$\) is an integer, we need to determine the factors of 56 and find the smallest value of n that, when multiplied by 56, results in a perfect fourth power.
The prime factorization of 56 is:
56 = 2³ × 7
The prime factors of 56 need to be raised to multiples of 4.
Therefore, we need to determine the smallest value of n that includes additional factors of 2 and 7.
To make the expression a perfect fourth power, we need to raise 2 and 7 to the power of 4, which is 2⁴ × 7⁴
The smallest value of n that satisfies this condition is:
n = 2 × 7³ = 2× 343 = 686
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Which of the statements below is true for the following set of numbers?
20, 15, 50, 85, 75, 60
Answer:B
Step-by-step explanation:
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
20, 15, 50, 85, 75, 60
The range is the difference between the highest value and the lowest values in the given set of numbers.
Midrange = Range ÷ 2
Option D is the correct answer.
The range of the set of numbers is 70
The midrange of the set of numbers is 35
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
20, 15, 50, 85, 75, 60
The range is the difference between the highest value and the lowest values in the given set of numbers.
Now,
The lowest value is 15
The highest value is 85
Range = 85 - 15 = 70
Midrange = 70/2 = 35
Thus,
The range of the set of numbers is 70
The midrange of the set of numbers is 35
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PLEASE HELP FAST I NEED HELP WITH THIS!
Answer:
Step-by-step explanation:
13. Find the total number of coinsss
8+4+3+1
=16
First pick:
1/16
Second pick:
1/15
So I guess your chances are 1/16+1/15 ?
=31/240
hopefully
14.
add the sockss
3+4+3
= 10
First pick
1/10
Second Pick
1/9
Add them:
19/90
Forgive me if this is wrong
:,)
Out of 60 students, 31 are taking English, 34 are taking Math, and 16 are in both classes.
Use Venn diagram below to organize the information.
English
II.
Submit Question
Region | =
Region II =
Region III =
Region IV =
How many students are in English or Math?
How many students are not in English?
How many students are in English and not in Math?
Math
III.
Complete the Venn diagram by entering the number of elements in each region and answer the questions
below:
IV.
Region I's value is 15. Region II is valued at 16. 18 is the value of Region III. 33 pupils are enrolled in math or English classes. There are 18 students that do not speak English. There are 15 pupils in English classes who do not take math.
What is Venn diagram?The Venn diagram uses circles to represent the relationships between sets and the region that they overlap. Set operations such as set intersection, set union, and set difference are shown in a Venn diagram, also called a set diagram. It may also be used to symbolize parts of a set. The diagrammatic depiction of two or more sets is called a Venn diagram.
Here,
Region I,
=31-16
=15
Region II,
=16
Region III,
=34-16
=18
Students in English or Math,
=15+18
=33
Students not in English,
=18
Students in English and not in Math,
=15
The value of Region I is 15. The value of Region II is 16. The value of Region III is 18. Number of students in English or Math is 33. Number of student not in English is 18. Number of students in English and not in Math is 15.
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A bag contains three red marbles, five blue marbles, and five yellow marbles. You randomly pick a marble. The marble is red or blue
Answer:
Blue
Step-by-step explanation:
The answer is blue because there is more blue marble than red.
Ronald is walking at a rate of 3 miles per hour. If he walks for 2 hours and then runs at a rate of 6 miles per hour for another 1 hour, how far did Ronald travel in total?
Answer:
12Step-by-step explanation:
Ronald's walking speed is 3 miles per hour, and he walks for 2 hours, so he covers 3 * 2 = 6 miles. In the next hour, he runs at a speed of 6 miles per hour, covering an additional 6 miles. Therefore, Ronald traveled a total of 6 + 6 = 12 miles.
(x−5)÷3=21 HELP ME PLZ PEOPLE
Answer:
x=68
Step-by-step explanation:
(x-5)/3=21
x-5=63 (multiplied by 3)
x=68 (added 5)
Rationalize the denominator and simplify.
7
3
Answer:
\(\frac{\sqrt{21}}{3}\) is the answer.
Step-by-step explanation:
To rationalize the denominator of \(\sqrt{\frac{7}{3}}\) we will remove the square root or cube root from the denominator.
For which we multiply with the same value given in the denominator to numerator and denominator both.
\(\sqrt{\frac{7}{3}}=\frac{\sqrt{7} }{\sqrt{3} }\)
\(\frac{\sqrt{7}}{\sqrt{3}}=\frac{\sqrt{7}}{\sqrt{3}}\times \frac{\sqrt{3}}{\sqrt{3}}\)
\(=\frac{\sqrt{7\times 3}}{(\sqrt{3})^2}\)
\(=\frac{\sqrt{21}}{3}\)
\(\frac{\sqrt{21}}{3}\) is the rationalized form.
Therefore, \(\frac{\sqrt{21}}{3}\) will be the answer.
Solve the equation. Then check your solution.
1. 1/4 = a +3/8
as – 16a,
as – 4a3,
2a3 + 8a - 4a2 - 16
Answer:
1) as-16a
taknig a as common
=a(s-16)
2)as-4a³
taking a as common
=a(s-4a²)
3)2a³+8a-4a²-16
taking common terms
=2a(a²+4)-4(a²+4)
=(2a-4)(a²+4)
again taking common
=2(a-2)(a²+4)
i hope this will help you :)
(as a unit rate simplified) 24 bottles for $2.95
Answer:
Bottle unit: 8.14
Dollar unit: $0.12
Step-by-step explanation:
Dividing the equation, bottle on top for bottle and dollars on top for dollar.
Right triangle EFG has its right angle at F, EG = 6 , and FG = 4 What is the value of the trigonometric ratio of an angle of the triangle? Drag a value to each box to match the trigonometric ratio with its value .
Answer:
\(\cos G=\dfrac{2}{3}\)
\(\csc E=\dfrac{3}{2}\)
\(\cot G=\dfrac{2}{\sqrt{5}}\)
Step-by-step explanation:
If the right angle of right triangle EFG is ∠F, then EG is the hypotenuse, and EF and FG are the legs of the triangle. (Refer to attached diagram).
Given ΔEFG is a right triangle, and EG = 6 and FG = 4, we can use Pythagoras Theorem to calculate the length of EF.
\(\begin{aligned}EF^2+FG^2&=EG^2\\EF^2+4^2&=6^2\\EF^2+16&=36\\EF^2&=20\\\sqrt{EF^2}&=\sqrt{20}\\EF&=2\sqrt{5}\end{aligned}\)
Therefore:
EF = 2√5FG = 4EG = 6\(\hrulefill\)
To find cos G, use the cosine trigonometric ratio:
\(\boxed{\begin{minipage}{9 cm}\underline{Cosine trigonometric ratio} \\\\$\sf \cos(\theta)=\dfrac{A}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)
For angle G, the adjacent side is FG and the hypotenuse is EG.
Therefore:
\(\cos G=\dfrac{FG}{EG}=\dfrac{4}{6}=\dfrac{2}{3}\)
\(\hrulefill\)
To find csc E, use the cosecant trigonometric ratio:
\(\boxed{\begin{minipage}{9 cm}\underline{Cosecant trigonometric ratio} \\\\$\sf \csc(\theta)=\dfrac{H}{O}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)
For angle E, the hypotenuse is EG and the opposite side is FG.
Therefore:
\(\csc E=\dfrac{EG}{FG}=\dfrac{6}{4}=\dfrac{3}{2}\)
\(\hrulefill\)
To find cot G, use the cotangent trigonometric ratio:
\(\boxed{\begin{minipage}{9 cm}\underline{Cotangent trigonometric ratio} \\\\$\sf \cot(\theta)=\dfrac{A}{O}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)
For angle G, the adjacent side is FG and the opposite side is EF.
Therefore:
\(\cot G=\dfrac{FG}{EF}=\dfrac{4}{2\sqrt{5}}=\dfrac{2}{\sqrt{5}}\)
HELP!!!!!!!! Which system of linear equations can be solved using the information below?
The system of linear equations that can be solved from the matrices is given as follows:
-5x + 4y = 3.-8x + y = -6.How to obtain the system of equations?Considering that the row [3, -6] is common to matrices Ax and Ay, the matrix A is given as follows:
A = [-5 4; -8 1]
Hence the multiplication of matrices representing the system is given as follows:
[-5 4; -8 1][x; y] = [3; -6]
Applying the multiplication of matrices, the system of equations is given as follows:
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Given the function f(x) = 72²+3x+3.
Find the average rate of change of f from z = -7 to z=6
Give your answer as an integer or reduced fraction.
I
Average rate of change:
the average rate οf change οf f frοm z = -7 tο z = 6 is 50/13 οr apprοximately 3.846 (rοunded tο three decimal places).
What is average?In mathematics, average refers tο a measure that represents the central οr typical value οf a set οf numbers. There are several types οf averages, including mean, median, and mοde.
The mean, alsο called the arithmetic mean, is the sum οf all the numbers in a set divided by the tοtal number οf values in the set. It is the mοst cοmmοnly used type οf average.
Tο find the average rate οf change οf f frοm z = -7 tο z = 6, we need tο calculate the change in f οver the change in z and then take the average.
First, we calculate f(6) and f(-7):
f(6) = 72² + 3(6) + 3
= 5184 + 18 + 3
= 5,191
f(-7) = 72² + 3(-7) + 3
= 5184 − 21 + 3
= 5,141
The change in f over the change in z is:
\($\frac{5,191 - 5,141}{6 - (-7)} = \frac{50}{6 - (-7)} = \frac{50}{13}\)
Therefore, the average rate of change of f from z = -7 to z = 6 is 50/13 or approximately 3.846 (rounded to three decimal places).
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Here's a graph of a linear function. Write the
equation that describes that function.
xpress it in slope-intercept form.
Answer:
the slope intercept form is y = (1/2)x - 1
Step-by-step explanation:
The slope-intercept form is, y = mx + b
We see from looking at the graph that,
at x = 0, y = -1
So, from this we find that b = -1
at x = 2, y = 0,
now, we find the slope m,
using,
\(m = \frac{y_{2} -y_1}{x_2-x_1}\)
Using x_2 = 2, y_2 = 0,
x_1 = 0, y_1 = -1, we get,
m = (0-(-1))/(2-0)
m = 1/2
So, the slope intercept form is,
y = (1/2)x - 1