Answer:
[tex]k=\frac{21}{2}[/tex]Explanation:
Given the equation:
[tex]\frac{8}{7}=\frac{12}{k}[/tex]To solve for k, let us take the reciprocal of both sides, so that k is a numerator.
[tex]\frac{7}{8}=\frac{k}{12}[/tex]Multiply both sides by 12
[tex]\begin{gathered} k=\frac{7}{8}\times12 \\ \\ =\frac{7\times12}{8} \\ \\ =\frac{84}{8} \\ \\ =\frac{21}{2} \end{gathered}[/tex]If a given set has nine elements, how many of its subsets have more than two elements ?
Total subsets of a set containing 9 elements having more than 2 elements = 466
What is a set?
A set comprises elements or members that can be mathematical objects of any sort, including numbers, symbols, points in space, lines, other geometric forms, variables, or even other sets. A set is the mathematical model for a collection of various things. A set with a single element is a singleton, while a set with no elements is an empty set. A set can either be infinite or have a finite number of items. If all of the items in two sets are identical, then the sets are equal. Modern mathematics is rife with sets. In fact, since the first part of the 20th century, Zermelo-Fraenkel set theory has been the de facto method for constructing solid foundations for all areas of mathematics.
C₉³+C₉⁴+C₉⁵+C₉⁶+C₉⁷+C₉⁸+C₉⁹
C₉³ = 84 subsets consisting of 3 elements
C₉⁴ = 126 subsets consisting of 4 elements
C₉⁵ = 126 subsets consisting of 5 elements
C₉⁶ = 84 subsets consisting of 6 elements
C₉⁷ = 36 subsets consisting of 7 elements
C₉⁸ = 9 subsets consisting of 8 elements
C₉⁹ = 1 subsets consisting of 9 elements
Total subsets of the set having 9 elements containing more than 2 elements = 84+126+126+84+36+9+1
= 466
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I need help & I need to know what the equation is at the bottom too
Given the following question:
Filling a table of values is very simple when we are already given the values of x, so what we need to do to fill in the rest of the table for f(x) and g(x) is substitute x for each of the table values given for x.
To start off we are given 1 so we substitute 1 in for x in both f(x) and g(x) and solve.
[tex]\begin{gathered} f(x)=6x+3 \\ g(x)=5x^2-x \\ x=1 \\ f(x)=6(1)+3 \\ 6\times1=6 \\ 6+3=9 \\ f(x)=9\text{ \lparen first table of values for f\lparen x\rparen\rparen} \\ g(x)=5x^2-x \\ 5(1)^2-x \\ 1^2=1 \\ 5\times1=5 \\ 5-1=4 \\ g(x)=4 \end{gathered}[/tex]Second table of values:
[tex]\begin{gathered} f(x)=6x+3 \\ g(x)=5x^2-x \\ x=2 \\ f(x)=6(2)+3 \\ 6\times2=12 \\ 12+3=15 \\ f(x)=15 \\ g(x)=5(2)^2-2 \\ (2)^2=4 \\ 5\times4=20 \\ 20-2=18 \\ g(x)=18 \end{gathered}[/tex]Third table of values:
[tex]\begin{gathered} f(x)=6x+3 \\ g(x)=5x^2-x \\ x=3 \\ f(x)=6(3)+3 \\ 6\times3=18+3=21 \\ f(x)=21 \\ g(x)=5(3)^2-3 \\ 3^2=9 \\ 5\times9=45 \\ 45-3=42 \\ g(x)=42 \end{gathered}[/tex]Final table of values:
[tex]\begin{gathered} f(x)=6x+3 \\ g(x)=5x^2-x \\ x=4 \\ f(x)=6(4)+3 \\ 6\times4=24 \\ 24+3=27 \\ f(x)=27 \\ g(x)=5(4)^2-4 \\ 4^2=16 \\ 5\times16=80 \\ 80-4=76 \\ g(x)=76 \end{gathered}[/tex]g(x)=5x^2-x eventually exceeds f(x) given the table of values.
Which of the following sets is considered a null set
The null set is the set containing weeks with eight days.
We are given four statements that describe a set of elements. We need to find the null set. The null set is one that does not have even a single element present in it.
The first set consists of mugs with handles. It is not a null set because most mugs have handles.
The second set is of dogs with four legs. It is not a null set because most dogs have four legs.
The third set consists of weeks with eight days. It is a null set because each week has only seven days.
The fourth set is of books with pages. It is not a null set because most books have pages.
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Today a new Explorer costs $39,900. In 1990, Explorers cost $24,000. What is the price relative?
The price relative of a new Explorer compared to the cost of Explorer in 1990 is 1.66.
What is the price relative?The price relative is the ratio of the price of the Explorer today to the price of the Explorer in 1990. In order to determine the price relative, divide the price of the Explorer today to the price of the Explorer in 1990.
Division is the operation that is used to determine the quotient of two or more numbers. The sign that is used to represent division is ÷.
Price relative = price of the Explorer now / price of the Explorer in 1990
$39,900 / $24,00 = 1.66
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The citizens of a certain community were ask to choose their favorite pet. The pie chart below shows the distribution of the citizens answers. If there are 140.000 citizens in the community, how many chose Cats, Fish, or Dogs
The number of citizens choosing cats, fish and dogs are 3360, 1820 and 3500 respectively.
Given, from the data which is represented by the pie chart, the percentage of citizens of a certain community choosing their favorite pet is listed below:
Fish = 13%
Dogs = 25%
Birds = 21%
Cats = 24%
Hamsters = 9%
Snakes = 8%
Altogether there are 14,000 citizens in the community.
we are asked to determine how many citizens have chosen cats, fish or dogs.
we use the method of percentage over here:
total citizens = 14000
percentage of citizens choosing cats = 24%
hence 24% of 14000 = 24/100 × 14000
= 24×140
= 3360
now, percentage of citizens choosing fish = 13%
hence 13% of 14000 = 13/100 × 14000
= 13×140
= 1820
And, percentage of citizens choosing dogs = 25%
hence 25% of 14000 = 25/100 × 14000
= 25 × 140
= 3500
hence the number of citizens choosing cats, fish and dogs are 3360, 1820 and 3500 respectively.
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If angleA and angleB are supplementary, and angleA = (3x - 9)°, and angleB = (2x + 14)degree, find x.
The values of x in the supplementary angles is 35.
What are supplementary angles?Supplementary angles refer to the pair of angles that always sum up to 180°.
Two angles are Supplementary when they add up to 180 degrees.
Therefore, for angle A and angle B to be supplementary they must add up to 180 degrees.
Hence,
∠A + ∠B = 180°
∠A = 3x - 9
∠B = 2x + 14
Therefore,
3x - 9 + 2x + 14 = 180
5x - 9 + 14 = 180
5x + 5 = 180
5x = 180 - 5
5x = 175
x = 175 / 5
x = 35
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The required value of x would be 35 degrees which are supplementary angles
We have been given that angle A and angle B are supplementary angles
∠A = 3x - 9 and ∠B = 2x + 14
Whenever two angles are supplementary, their sum is 180 degrees.
As per the property of supplementary angles,
The given angles add up to 180 degrees.
Thus, ∠A + ∠B = 180°
Substitute the values of ∠A and ∠B in the above equation,
3x - 9 + 2x + 14 = 180
5x - 9 + 14 = 180
5x + 5 = 180
5x = 180 - 5
5x = 175
x = 35
Hence, the supplementary angles have a value of 35 for x.
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A(n)= 3+(n -1)(5)A(2) = 8A(4) = ?I understand how to do the steps however it's still hard for me to do.The example, I looked at was A(n)= A(1) + (n -1)dA(n)=15+(n-1)(4)A(4)=15+(4-1)(4)A(4)=15+(3)(4)A(4)=15+12A(4)=27Still a bit tough.
Step 1:
Write the equation
A(n) = 3 + (n - 1)5
Step 2:
To find A(2)
Compare A(2) with A(n)
You can see that n = 2 for A(2)
Next, substitute n = 2 in A(n) = 3 + (n-1)5 to find A(2)
[tex]\begin{gathered} A(n)\text{ = 3 + (n - 1)5} \\ A(2)\text{ = 3 + (2 - 1) }\times\text{ 5} \\ A(2)\text{ = 3 + 1}\times5 \\ A(2)\text{ = 3 + 5} \\ A(2)\text{ = 8} \end{gathered}[/tex]Step 3
Let find A(4)
[tex]\begin{gathered} A(n)\text{ = 3 + (n - 1)5} \\ \text{From A(4), n = 4} \\ A(4)\text{ = 3 + ( 4 - 1 ) }\times\text{ 5} \\ A(4)\text{ = 3 + 3}\times5 \\ A(4)\text{ = 3 + 15} \\ A(4)\text{ = 18} \end{gathered}[/tex]Final answer
A(4) = 18
Find the equation of the line:
a) with a gradient of ½ and a y-intercept of -2
b) with a gradient of 3 and passing through the point (-2:2)
c) passing through the points (1; -2) and (-2; 1)
d) parallel to the y-axis cutting the x-axis at -1
Step-by-step explanation:
gradient means slope.
the slope is anyways the factor a of x on the slope-intercept form
y = ax + b
and in the point-slope form
y - y1 = a(x - x1)
"a" is as mentioned the slope. b is the y-intercept (the y- value when x = 0).
(x1, y1) is a point on the line.
a)
y = (1/2)×x - 2
b)
y - 2 = 3(x - -2) = 3(x + 2) = 3x + 6
y = 3x + 8
c)
remember, the slope is defined as ratio (y coordinate change / x coordinate change) when going from one point on the line to another.
so, let's go from (1, -2) to (-2, 1)
x changes by -3 (from 1 to -2)
y charges by +3 (from -2 to 1)
the slope is +3/-3 = -1/1 = -1
so, we pick one point, e.g. (1, -2), and the line is
y - -2 = -(x - 1) = -x + 1
y + 2 = -x + 1
y = -x - 1
d)
x = -1
this is a vertical line (parallel to the y-axis) representing all points on the grid for which x = -1.
the slope is undefined, as it is y/0 (because x never changes at all). and there is no y-intercept, as x can never be 0, and the line is parallel to the y-axis, so, there cannot be any intersection point.
Answer:
[tex]\textsf{a) \quad $y=\dfrac{1}{2}x-2$}[/tex]
[tex]\textsf{b) \quad $y=3x+8$}[/tex]
[tex]\textsf{c) \quad $y=-x-1$}[/tex]
[tex]\textsf{d) \quad $x=-1$}[/tex]
Step-by-step explanation:
Part (a)Slope-intercept form of a linear equation:
[tex]y=mx+b[/tex]
where:
m is the slope.b is the y-intercept.Given values:
Slope = ¹/₂y-intercept = -2Substitute the given values into the formula to create the equation of the line:
[tex]\implies y=\dfrac{1}{2}x-2[/tex]
---------------------------------------------------------------------------
Part (b)Point-slope form of a linear equation:
[tex]y-y_1=m(x-x_1)[/tex]
where:
m is the slope.(x₁, y₁) is a point on the line.Given:
Slope = 3(x₁, y₁) = (-2, 2)Substitute the given values into the formula to create the equation of the line:
[tex]\implies y-2=3(x-(-2))[/tex]
[tex]\implies y-2=3(x+2)[/tex]
[tex]\implies y-2=3x+6[/tex]
[tex]\implies y=3x+8[/tex]
---------------------------------------------------------------------------
Part (c)Slope formula:
[tex]\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
where (x₁, y₁) and (x₂, y₂) are points on the line.
Given points:
(x₁, y₁) = (1, -2)(x₂, y₂) = (-2, 1)Substitute the points into the slope formula to calculate the slope of the line:
[tex]\implies m=\dfrac{1-(-2)}{-2-1}=\dfrac{3}{-3}=-1[/tex]
Substitute the found slope and one of the points into the point-slope formula to create the equation of the line:
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-(-2)=-1(x-1)[/tex]
[tex]\implies y+2=-x+1[/tex]
[tex]\implies y=-x-1[/tex]
---------------------------------------------------------------------------
Part (d)If the line is parallel to the y-axis, it is a vertical line.
The equation of a vertical line is x = c.
Therefore, as the line intersects the x-axis at -1, the equation of the line is:
[tex]\implies x=-1[/tex]
Determine the end (long run) behavior for: f(x)=−2(x−1)3(x+2)2
The end behavior of the function f(x) = −2(x−1) * 3(x+2) * 2 is
as x tends to ∞, f(x) tends to -∞as x tends to -∞, f(x) tends to -∞What is end behavior?The end behavior of function typically says the characteristics of the function at the ends
How to find the end behaviorThe given function is:
f(x) = −2(x−1) * 3(x+2) * 2
The given function is first expanded
= −2(x−1) * 3(x+2) * 2
= (-2x + 2) * (3x + 6) * 2
= (-4x + 4) * (3x + 6)
= -12x² - 36x + 24
The end behavior is determined by the leading term = -12x²and it is described as
x ⇒ ∞ f(x) ⇒ -∞
x ⇒ -∞ f(x) ⇒ -∞
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Did I correctly or incorrectly solve the equations below?From the information given, find the quadrant in which the terminal point determined by t lies. Input I, II, III, or IV.(a) sin(t)<0 and cos(t)<0 , quadrant_____III_____ ;(b) sin(t)>0 and cos(t)<0 , quadrant____II______ ;(c) sin(t)>0 and cos(t)>0, quadrant______I_____;(d) sin(t)<0 and cos(t)>0, quadrant____IV_______ ;
We know that the sine function is positive in the first and second quadrant; we also know that the cosine function is positive in the first and fourth quadrant.
Pls help me answer these 2 questions
Answer:
Step-by-step explanation:
A = 1 plus negatives out be minusing positive
B= -8 minus negatives would be nega tive plus negatives
rules
If you love to love your a lover
if you hate to hate your a lover
if you love to have ur a hater
if you hate to love ur a hater
this all relates to positive and negative addition and subtraction
Answer:
4+(-3) = 1
-6-2= -8
Step-by-step explanation:
Same sign add
Different sign subtract
Keep the sign of the bigger number
How to go from radians to degrees
Answer:
Recall that:
[tex]360^{\circ}=2\pi\text{ radians.}[/tex]Therefore:
[tex]1^{\circ}=\frac{2\pi}{360}radians,[/tex]or
[tex]1\text{ radian=}\frac{360^{\circ}}{2\pi}degrees.[/tex]A kitten weighs 5 pounds what is the kilograms
Nelson, this is the solution:
Let's recall that 1 pound = 0.4536 kg, therefore:
• 5 pounds = 0.4536 * 5
,• 5 pounds = 2.268 kilograms
how to find point-slope form off a graph
Solution
For this case we need to remember that the point-slope formula is given by:
y= mx+b
And in order to find the slope we just need to have two points (x1,y1) and (x2,y2) and we can find m like this:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Then if we look at the graph we have two points:
x1= -2, y1= 3
x2= 0, y2= -1
And replacing we got:
[tex]m=\frac{-1-3}{0+2}=-2[/tex]And using the second point we can find the intercept
3= -2(-2)+b
b= 1
Our solution for this case :
y-3=-2(x+2)
During the worst periods of hyperinflation in a certain country, the price of food increased at a rate of 15% per month. State whether this increase was linear or exponential. If your food bill was $130 in one month during this period, what was it three months later?What was the monthly food bill after three months?$ enter your response here
Given:
Increased rate = 15%
One month bill = $130
Find-:
What was the monthly food bill after three months?
Explanation-:
Formula:
[tex]A=P(1+\frac{r}{100})^n[/tex]Where,
[tex]\begin{gathered} A=\text{ Amount after time} \\ \\ P=\text{ Initial amount} \\ \\ r=\text{ Rate} \\ \\ n=\text{ Time period } \end{gathered}[/tex]The given value is:
[tex]\begin{gathered} P=130 \\ \\ r=15 \\ \\ n=3 \end{gathered}[/tex]Amount after 3 months.
[tex]A=P(1+\frac{r}{100})^n[/tex][tex]\begin{gathered} A=130(1+\frac{15}{100})^3 \\ \\ A=130(1+0.15)^3 \\ \\ A=130(1.15)^3 \\ \\ A=130\times1.521 \\ \\ A=197.714 \end{gathered}[/tex]So, the food bill after three months is $197.714
WILL MARK BRAINLIEST IF CORRECT! the verticals of a triangle are A (2, 5), B (1, 2) and C (3, 1). Find the coordinates of the image after a reflection in the y-axis
the coordinates of the image after a reflection in the y- axis are =A (5,2), B (2,1) and C(1,3)
what is coordinates?A pair of number that describe the position of a point on a coordinate plane by using the horizontal and vertical distances from the two reference axes. Usually represented by (x ,y)the x-value and y- value
Firstly, we want to reflect across the x-axis When we reflect a point (x,y) over x-axis, we get (x,-y)
So;
A ( 2,5) becomes (2,-5)
B (1,2) becomes (1,-2)
C ( 3,1) becomes (3,-1)
Then we proceed to rotate 90 degrees counterclockwise about the origin
Here we have;
(x, y) becomes (-y ,x)
(2,-5) becomes (5,2)
(1,-2) becomes (2,1)
(3,-1) becomes (1,3)
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PLEASE HELP I WILL GIVE BRAINLYEST!! ALGEBRA 1 MATH HW
Answer: a. the weight of a burger with 0 patties is not 0 ounces because
the burger has to have weight, it cannot just be 0 ounces because you will not feel anything in your hand.
b. For patty 0 the weight is 0 oz, For patty 1 the weight is 6.6 oz, For patty 2 the weight is 22.2 oz, For patty 3 the weight is 46.8 oz.
Im sorry but I do not know what to do for C, I hope this helps. Sorry that I couldn't help you with c, but good luck!!
:)
Step-by-step explanation:
please write the value of x and the equation used.
Zachary pays $68 per month and $5 per months for gigabytes
X be the number of gifabytes
SO, price of x gigabytes = 5x
total budget = 5x + Amount paid :
So, y = 5x + 68
Answer: y = 5x + 68
|5-2x|+1≤10 absolute value equations or inequalities and graph the solution set on the number line
The given inequality is
[tex]|5-2x|+1\leq10[/tex]First, we subtract 1 on each side
[tex]\begin{gathered} |5-2x|+1-1\leq10-1 \\ |5-2x|\leq9 \end{gathered}[/tex]Now we use the property of inequalities with absolute values, which states
[tex]|x|\leq a\rightarrow-a\leq x\leq a[/tex]Using this property, we have
[tex]|5-2x|\leq9\rightarrow-9\leq5-2x\leq9[/tex]We solve the compound inequality now
[tex]\begin{gathered} -9\leq5-2x\leq9 \\ -9-5\leq-2x\leq9-5 \\ -14\leq-2x\leq4 \\ \frac{-14}{-2}\ge\frac{-2x}{-2}\ge\frac{4}{-2} \\ 7\ge x\ge-2 \\ -2\leq x\leq7 \end{gathered}[/tex]Therefore, the solution is the interval [-2,7], and the graph of it would be
help meeeeee pleaseee !!!!!!!!!
Answer:
74.52
Step-by-step explanation:
[tex]P(10)=0.018(10)^3-0.294(10)^2+3.074(10)+55.180 \\ \\ =74.52[/tex]
Unbounded Limits and Asymptotes Part B
Answer: -0
Step-by-step explanation: cause one is negative 0 and then the other is 0
Solve the system by the substitution method.
15x - y = 55
y = x² + 1
Answer:
Point Form: (8,65) , (7,50)
Equation Form:
x = 8, y = 65
x = 7, y = 50
Step-by-step explanation:
True or false. 3|48,025
Mr. barber used 5/6 yard of wire to put up a ceiling fan. he used 1/2 yard of wire to fix a switch pt 1 out of 2 complete the calculations below to write equivalent fraction with the least common denominator
Least common denominator is the smallest number that can be divided by both given denominators.
From the problem, we have :
[tex]\frac{5}{6}\quad \text{and}\quad \frac{1}{2}[/tex]The denominators are 6 and 2.
The smallest number that can be divided by 6 and 2 is 6.
6/6 = 1 and 6/2 = 3
So we need an equivalent fraction with a denominator of 6.
For 5/6, multiply this by 1/1 since the denominator is already 6.
[tex]\frac{5}{6}=\frac{5\times1}{6\times1}=\frac{5}{6}[/tex]For 1/2, multiply this by 3/3 to make the denominator equal to 6.
[tex]\frac{1}{2}=\frac{1\times3}{2\times3}=\frac{3}{6}[/tex]The second step in the process for factoring the trinomial x-5x - 36 is to:
There are several ways that you can follow to from two binomials from this trinomial, for example, you can do it by following these steps:
1.write two sets of parenthesis, both with the term x
2. write a list of all the factors of 36
3. find the sum of the factors of 36
4. choose the factors whose sum equals 7 and write them into the two parenthesis
Then, the second step in the process of factoring this trinomial is: option D, to write a list of all the factors of 36
4 Which expressions represent the area of the triangle in square feet? Select all that apply. A. 48.9 B 16 +8719 D 16119 318319 E 16)(9) 1889)
Answer
Options B, C and D are correct.
Area = ½ × 14 × 9 = (14)(9) ÷ 2
Area = ½ (6 + 8) (9)
= ½ (6)(9) + ½ (8)(9)
= 63 ft²
Explanation
We are asked to pick out the options that give the area of the triangle.
To do that, we need to first note that the area of a triangle is given as
Area = ½ × Base × Height
For the triangle in the question
Base = 6 + 8 = 14 ft
Height = 9 ft.
So, the area of the triangle is
Area = ½ × Base × Height
Area = ½ × 14 × 9
We can then break this down for the two triangles in the one big triangle as
Area = ½ × 14 × 9 = (14)(9) ÷ 2
Area = ½ (6 + 8) (9)
= ½ (6)(9) + ½ (8)(9)
= 63 ft²
Hope this Helps!!!
The size of a rectangular TV screen is given by the length of its diagnol. What is the width of the 27 TV screen with a height of 16.2 inches?
Given:
The size of a rectangular TV screen is given by the length of its diagnol.
THe diagonal length is 27 inches.
The height is 16.2 inches.
Required:
To find the width.
Explanation:
From the given data
Let x be the width.
From the above figure
[tex]\begin{gathered} 27^2=x^2+16.2^2 \\ \\ x^2=27^2-16.2^2 \\ \\ x^2=729-262.44 \\ \\ x^2=466.56 \\ \\ x=\sqrt{466.56} \\ \\ x=21.6 \end{gathered}[/tex]Final Answer:
The width of the TV screen is 21.6 inches.
What is the domain of f(x)= log7x-4
identify the vertical asymptotes, horizontal asymtope, domain, range. Sketch the graph
The given function is,
[tex]f(x)=-\frac{4}{x-2}+1[/tex]The domain can be determined as,
[tex]\begin{gathered} x-2\ne0 \\ x\ne2 \\ x\in R-\lbrace2\rbrace \end{gathered}[/tex]Thus, the domain is the set of real numbers excluding the number 2.
The graph can be drawn as,
The vertical asymtotes is x=2 as the fuction attains the value of infinty and negative infinity at x=2.
The horizontal asymtotes is y=1 as at this value of function the value of x is either infinity or negative of infinity.
The range of the function is,
[tex]y\in\in R-\lbrace1\rbrace[/tex]Thus, the required range of the function is set of all real numbers excluding 1.
2) Theodore inherited two different stocks whose yearly income was $2100. The total appraised value of the stocks was $40,000 and one was paying 4% and one 6% per year. What was the value of each stock? 3) Yi-fei Wang inherited $20,000 which she invested in stocks and bonds. The stocks returned 6% and the bonds 8%. if the return on the
Given data:
The value of the socks are x+y=$40,000.
The total interest is I=$2100.
The interest on first stock is,
i=x(4%)(1)/100
i=0.04x
The interest on second stock is,
i'=y(6%)(1)/100
=0.06x
0.04x+0.06y=2100
Substitute 40,000-x for y in the above expression.
0.04x+0.06(40,000-x)=2100
0.04x-0.06x=-300
-0.02x=-300
x=$15000
The value of second stock is,
y=40,000-15,000
=$25,000