Answers
Answer:
The first table.Step-by-step explanation:
If from a table a ratio
[tex]\dfrac{y_2-y1}{x_2-x_1}[/tex]
is constant, then a table represents a linear function.[tex]\begin{array}{c|c}x&y\\1&-2\\2&-10\\3&-18\\4&-26\end{array}\\\\\dfrac{-10-(-2)}{2-1}=\dfrac{-8}{1}=-8\\\dfrac{-18-(-10)}{3-2}=\dfrac{-8}{1}=-8\\\dfrac{-26-(-18)}{4-3}=\dfrac{-8}{1}=-8[/tex]
[tex]\begin{array}{c|c}x&y\\1&-2\\2&-4\\3&-8\\4&-16\end{array}\\\\\dfrac{-4-(-2)}{2-1}=\dfrac{-2}{1}=-2\\\dfrac{-8-(-4)}{3-2}=\dfrac{-4}{1}=-4[/tex]
Related Questions
Slope-intercept form of the equation for the line?
Answers
Answer:
[tex]\large\boxed{y=-\dfrac{3}{10}x+\dfrac{1}{2}}[/tex]
Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points from the graph (-5, 2) and (5, -1).
Substitute:
[tex]m=\dfrac{-1-2}{5-(-5)}=\dfrac{-3}{10}=-\dfrac{3}{10}[/tex]
We have the equation in form:
[tex]y=-\dfrac{3}{10}x+b[/tex]
Put the coordinates of the point (5, -1) to the equation:
[tex]-1=-\dfrac{3}{10}(5)+b[/tex]
[tex]-1=-\dfrac{3}{2}+b[/tex]
[tex]-\dfrac{2}{2}=-\dfrac{3}{2}+b[/tex] add 3/2 to both sides
[tex]\dfrac{1}{2}=b\to b=\dfrac{1}{2}[/tex]
For the straight line y=-
-4, what are the slope and y-intercept?
slope = 5, y-intercept = 4
slope = -
y-intercept = 4
slope =
y-intercept = -4
slope =
y-intercept = 4
Answers
Answer:
y-intercept is [0, -4]
Step-by-step explanation:
Straight lines NEVER have rate of changes [slopes].
What is the following product? Assume x ≥ 0
\sqrt[3]{x^{2} } . \sqrt[4]{x^{3} }
A. x\sqrt{x}
B. \sqrt[12]{x^{5} }
C. x(\sqrt[12]{x^{5} } )
D. x6
Answers
For this case we must multiply the following expression:
[tex]\sqrt [3] {x ^ 2} * \sqrt [4] {x ^ 3}[/tex]
By definition of properties of otencias and roots we have:
[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]
We rewrite the terms of the expression:
[tex]\sqrt [3] {x ^ 2} = (x ^ 2) ^ {\frac {1} {3}} = (x ^ 2) ^ {\frac {4} {12}}\\\sqrt [4] {x ^ 3} = (x ^ 3) ^ {\frac {1} {4}} = (x ^ 3) ^ {\frac {3} {12}}[/tex]
So, we have:
[tex](x ^ 2) ^ {\frac {4} {12}} * (x ^ 3) ^ {\frac {3} {12}} =[/tex]
Applying the above definition we have:
[tex]\sqrt [12] {(x ^ 2) ^ 4} * \sqrt [12] {(x ^ 3) ^ 3} =[/tex]
We multiply the exponents:
[tex]\sqrt [12] {x ^ 8} * \sqrt [12] {x ^ 9} =[/tex]
We combine using the product rule for radicals.
[tex]\sqrt [12] {x ^ 8 * x ^ 9} =[/tex]
By definition of multiplication properties of powers of the same base, we put the same base and add the exponents:
[tex]\sqrt [12] {x ^ {8 + 9}} =\\\sqrt [12] {x ^ {17}} =\\\sqrt [12] {x ^ {12} * x ^ 5} =\\x \sqrt [12] {x ^ 5}[/tex]
Answer:
Option C
Answer:
its c
Step-by-step explanation:
Which expresión is equivalente to (4g3 h2 k4)3
Answers
Answer: [tex]\bold{64g^9h^6k^{12}}[/tex]
Step-by-step explanation:
[tex]\text{Apply the product rule:} (a^b)^c=a^{b*c}\\\\(4g^3h^2k^4)^3\\\\=4^{(1*3)}g^{(3*3)}h^{(2*3)}k^{(4*3)}\\\\=4^3g^9h^6k^{12}\\\\=64g^9h^6k^{12}[/tex]
The lines shown below are parallel. If the green line has a slope of --, what is
the slope of the red line?
Answers
Answer: the answer would be -1/11
Step-by-step explanation: the reason being the slope of the green is a negative slope because it is going down ward not upwards therefore it is negative and because the the lines are parallel they are equal so the slope of both lines are -1/11
Use the net to find the surface area of the cylinder
give your answer in terms of pi
A 25pi yd2
B 70pi yd2
C 50pi yd2
D 120pi yd2
Answers
Answer:
D) 120pi yd2
Step-by-step explanation:
Order these values given in scientific notation from least to greatest.
1.49 x 10^5
1.05 x 10^-6
3.81 x 10^8
2.44 x 10^-9
3.75 X 10^4
Answers
Answer:
2.44x10^-9
1.05x10^-6
3.75x10^4
1.49x10^5
3.81x10^8
Final answer:
Values in scientific notation are ordered by their exponent values. First, compare the sign and size of the exponents, and then compare the coefficients if necessary. The ordered values from least to greatest are: 2.44 x 10^-9, 1.05 x 10^-6, 3.75 x 10^4, 1.49 x 10^5, 3.81 x 10^8.
Explanation:
To order the given values in scientific notation from least to greatest, we look at the exponent to determine their relative sizes. The values with negative exponents will be smaller than those with positive exponents, and among those with the same sign exponents, the one with the smaller absolute value of exponent is smaller. Then we compare the coefficients if necessary, that is if the exponents are the same.
[tex]2.44 x 10^-9[/tex]
[tex]1.05 x 10^-6[/tex]
[tex]3.75 x 10^4[/tex]
[tex]1.49 x 10^5[/tex]
[tex]3.81 x 10^8[/tex]
What is the solution to the equation
Answers
Answer:
x = 12
Step-by-step explanation:
5(x - 6) = 2(x + 3)
Distribute
5x - 30 = 2x + 6
Put like terms on each side by subtracting both sides by -2x and adding 30 on each side
3x = 36
Simplify
3x/3 = 36/3
x = 36/3
x = 12
Plug is back in to check
5(12) - 30 = 2(12) + 6
60 - 30 = 24 + 6
30 = 30
Answer:
x=12
Step-by-step explanation:
5(x-6) = 2(x+3)
Distribute
5x-30 = 2x+6
Subtract 2x from each side
5x-2x -30 = 2x-2x+6
3x-30 =6
Add 30 to each side
3x-30+30 = 6+30
3x=36
Divide each side by 3
3x/3 = 36/3
x =12
How do we express one-half of the difference of a number cubed and one?
Answers
Answer:
1/2(x^3 - 1) or we could write it as (x^3 - 1) / 2.
Step-by-step explanation:
A number cubed is x^3. Difference of this and 1 is x^3 - 1.
Finall we have 1/2 of this:
= 1/2(x^3 - 1) or we could write it as (x^3 - 1) / 2.
Answer:
[tex]\frac{x^3-1}{2}[/tex]
Step-by-step explanation:
We must follow what the statement asks us, starting from the last thing and going forward from there.
A number cubed: [tex]x^3[/tex]
The difference of a number cubed and one: [tex]x^3-1[/tex]
And finally:
one-half of the difference of a number cubed and one, this would be one half of the expression we already found:
[tex]\frac{x^3-1}{2}[/tex]
Factor completely. 81x^4 − 1
Answers
=(3x-1)(3x+1)(9x^2+1)
The expression 81x⁴ - 1 can be factored completely by identifying it as a difference of squares. First, factor it into (9x² + 1)(9x² - 1) and then further factor (9x² - 1) into (3x + 1)(3x - 1). The final factored form is (9x² + 1)(3x + 1)(3x - 1).
We are given the expression 81x⁴ - 1 and need to factor it completely. This is a difference of squares, which can be written as:
81x⁴ - 1 = (9x²)² - 1²The difference of squares formula is a²- b² = (a + b)(a - b). Applying this formula, we get:
(9x²)² - 1² = (9x² + 1)(9x² - 1)Next, notice that 9x²- 1 is also a difference of squares:
9x² - 1 = (3x)²- 12Again using the difference of squares formula, we get:
(3x)² - 1 = (3x + 1)(3x - 1)Putting everything together, the complete factorization of 81x⁴ - 1 is:
81x⁴ - 1 = (9x² + 1)(3x + 1)(3x - 1)71, 92, 94, 93, 98, 85, 66, 70, 68, 93, 87, 71, 85, 52, 61, 62, 85, 69, 95, 79
Calculate the mean for the data list above.
ОА. 82
ОВ. 78.8
Ос. 93
Op. 87
Answers
To find the mean you must add all the numbers together then divide the sum by the total amount of numbers in the data set
71 + 92 + 94 + 93 + 98 + 85 + 66 + 70 + 68 + 93 + 87 + 71 + 85 + 52 + 61 + 62 + 85 + 69 + 95 + 79 = 1576
There are at total of 20 numbers in this data set so you must divide 1576 by 20
1576 / 20 = 78.8
Hope this helped!
~Just a girl in love with Shawn Mendes
2-digit numbers less than 91 which are 1 less than a multiple of 10
Answers
Answer:
{19, 29, ... , 79, 89}
Step-by-step explanation:
Multiples of 10 are {10, 20, 30, 40, ... , 90}
Numbers which are each 1 less than these multiples of 10 would be:
{9, 19, 29, ... , 79, 89}.
Note that the last number, 89, is less than 91.
We must omit 9 from this set, since 9 is not a 2-digit number. Then our final list is {19, 29, ... , 79, 89}.
Answer:
The numbers are 19,29,39,49,59,69,79,89
Step-by-step explanation:
2 digit numbers starts from 10 and ends on 99.
2 digit numbers less than 91 starts from 10 and ends at 90.
2 digit numbers less than 91 and multiple of 10 are 10,20,30,40,50,60,70,80,90.
2 digit numbers less than 91 and which are 1 less than a multiple of 10 are 19,29,39,49,59,69,79,89.
The numbers are 19,29,39,49,59,69,79,89
6a - 5b when a = -3 and b = 4
Answers
Given.
6a - 5b
Plug in values.
6(-3) - 5(4) =
-18 - 20 =
-38
For this case we have the following expression:
[tex]6a-5b[/tex]
We must evaluate the expression when:
[tex]a = -3\\b = 4[/tex]
Then, replacing the values we have:[tex]6 (-3) -5 (4)[/tex]
Taking into account that according to the law of the signs of multiplication, it is fulfilled that:
[tex]+ * - = -[/tex]
So:
[tex]-18-20 =[/tex]
Equal signs are added and the same sign is placed:
-38
Answer:
-38
gerard’s baby brother spends 7/8 of his day sleeping. How many hours does his baby brother sleep? i
Answers
[tex] \frac{7}{8} \times 24 = 21 \\ [/tex]
You multiply 7/8 to the number of hours in a day which 24
Gerard's baby brother sleeps for 7/8 of the day, which equals 21 hours when calculated (7/8 * 24 hours).
Explanation:Gerard's baby brother spends 7/8 of his day sleeping.
To calculate how many hours this is, we need to know how many hours there are in a full day.
A full day has 24 hours. So, we multiply 7/8 by 24 to find out the total hours spent sleeping.
Here's the step-by-step calculation:
Multiply the fraction of the day spent sleeping (7/8) by the total number of hours in a day (24).7/8 * 24 = 21 hours.Therefore, Gerard's baby brother sleeps for 21 hours a day.
Stefania pours 2 liters of orange juice and 1.5 liters of pineapple juice into a punch bowl. How many liters are in the punch bowl?
Answers
Answer:
3.5 liters
Step-by-step explanation:
2 liters + 1.5 liters = 3.5 liters
A shipping company charges $6 to ship a package that weighs up to 1 pound and $2 for each additional pound or portion of
a pound. Which equation represents this situation?
Of(x) = 8+2[x-1, where x > 0
Of(x) = 6+2Lx-1), where x > 0
O (x) = 6+2[x+1), where x > 0
Of(x) = 6+2x+1), where x > 0
Answers
Answer:
6 + 2[x - 1) , where x > 0. I think.
Answer:
f(x) = 6+2Lx-1), where x > 0
Step-by-step explanation:
To answer this you need to understand two things, variables and constants, the constant price of the shipping is $6 so that is a constant, now the company would charge you with $2 for every fraction or pound extra over the one pound that you are charged for the $6, so your variable is the weight of the package, and this will be expressed by X
So the function would look like this:
[tex]f(x)= 6+ 2(x-1) when x > 0[/tex]
If the weight of your package is less than oneyou´d just pay the 6 bucks, since when the weight is bigger than 1 pound you would pay 2 extra bucks, you just need yo know how many extra buck you´ll pay that´s why it´s expressed with the Lx-1)
Zed is making a centerpiece for his dining room table by putting sand in a cube-shaped vase. The vase is 0.25 meters in length, width, and height. He bought 25 kg of sand. Assume the density of dry sand is 1,602 kgm3. What is the volume of the sand that Zed purchased?
The volume of the sand is approximately __________ m3.
Enter your answer as the number that correctly fills in the blank in the previous sentence. If necessary, round your answer to six decimal places, like so: 42.536475
Answers
The answer is:
The volume of the sand is approximately 0.015605 m3
Why?To solve the problem, and find the volume of the sand that Zed purchased, we need to use the formula to calculate the density and isolate the volume from it.
So, solving we have:
[tex]density=\frac{mass}{volume}[/tex]
From the statement we know that:
The mass of the sand is 25 kg
The density of the dry sand is 1,602 kg/m3
So, substituting and solving we have:
[tex]density=\frac{mass}{volume}\\\\volume=\frac{mass}{density}\\\\volume=\frac{25kg}{1,602\frac{kg}{m^{3}}}=0.015605m^{3}[/tex]
Hence, the volume of the sand is approximately 0.015605 m3
Have a nice day!
The function s(V) = describes the side length, in units, of a cube with a volume of V cubic units. Jason wants to build a cube with a minimum of 64 cubic centimeters.
What is a reasonable range for s, the side length, in centimeters, of Jason’s cube?
s > 0
s 4
s 8
s 16
Answers
Answer:
[tex]s\geq 4\ cm[/tex]
Step-by-step explanation:
we know that
[tex]s(V)=\sqrt[3]{V}[/tex]
where
s is the side length, in units, of a cube
V is the volume of a cube in cubic units
For a [tex]V=64\ cm^{3}[/tex]
substitute in the formula
[tex]s=\sqrt[3]{64}[/tex]
[tex]s=4\ cms[/tex]
If Jason wants to build a cube with a minimum of 64 cubic centimeters
therefore
the minimum length side of the cube is 4 cm
[tex]s\geq 4\ cm[/tex]
What is the greatest common factor of 8 and 36
Answers
Answer:
4
Step-by-step explanation:
When multiplying, the greatest common factor of each is four.
8= 4 x 2
36= 4 x 9
The greatest common factor (GCF) of 8 and 36 is 4. The correct option is B.
GCF stands for "Greatest Common Factor." It refers to the largest positive integer that divides evenly into two or more given numbers. In other words, the GCF is the largest number that is a factor of all the given numbers.
Finding the GCF is useful in various mathematical operations, such as simplifying fractions, finding equivalent fractions, or solving equations. It helps in identifying common factors and simplifying calculations.
To find the GCF, you can identify the common factors of both numbers and determine the largest one they share.
The factors of 8 are 1, 2, 4, and 8.
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
The largest factor that both 8 and 36 share is 4.
Therefore, the greatest common factor of 8 and 36 is 4.
To learn more about the greatest common factor click:
https://brainly.com/question/2352983
#SPJ6
Choose the required figure.
A right triangle circumscribed about a circle:
Answers
Answer:I think that in this problem you need a right angle with a circle in it
Yuto solved the equation below.
What is the solution to Yuto’s equation?
Answers
For this case we have the following equation:
[tex]-2 (x + 5) = - 2 (x-2) +5[/tex]
We apply distributive property to the terms within parentheses:
[tex]-2x-10 = -2x + 4 + 5[/tex]
We add similar terms to the right side of the equation:
[tex]-2x-10 = -2x + 9[/tex]
We add 2x to both sides of the equation:
[tex]-10 = 9[/tex]
Equality is not fulfilled, so the equation has no solution.
Answer:
It has no solution
Answer: Yuto's equation has no solution.
Step-by-step explanation:
To find the solution to Yuto’s equation, you need to solve for the variable "x":
Apply Distributive property:
[tex]-2(x+5)=-2(x-2)+5\\\\-2x-10=-2x+4+5\\\\-2x-10=-2x+9[/tex]
Add [tex]2x[/tex] to both sides of the equation:
[tex]-2x-10+2x=-2x+9+2x\\\\0x-10=9\\\\-10=9\ (False)[/tex]
Therefore, the equation has no solution.
The given line passes through the points (-4,-3) and (4,1) what is the equation in point-slop
e form, of the line that is perpendicular to the given line and passes through the point (-4,3)?
Answers
let's bear in mind that perpendicular lines have negative reciprocal slopes...... hmmmm what's the slope of the given line anyway?
[tex]\bf (\stackrel{x_1}{-4}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{1-(-3)}{4-(-4)}\implies \cfrac{1+3}{4+4}\implies \cfrac{4}{8}\implies \cfrac{1}{2} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{\cfrac{1}{2}}\qquad \qquad \qquad \stackrel{reciprocal}{\cfrac{2}{1}}\qquad \stackrel{negative~reciprocal}{-\cfrac{2}{1}\implies -2}}[/tex]
so, we're really looking for a line whose slope is -2 and runs through (-4 , 3)
[tex]\bf (\stackrel{x_1}{-4}~,~\stackrel{y_1}{-3})~\hspace{10em} slope = m\implies -2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-3)=-2[x-(-4)] \implies y+3=-2(x+4) \\\\\\ y+3=-2x-8\implies y=-2x-11[/tex]
Given f(x) = 17-X^2what is the average rate of change in f(x) over the interval [1, 5]?
Answers
Answer:
-6
Step-by-step explanation:
The formula for finding the rate of change is:
[tex]Rate\ of\ change=\frac{f(b)-f(a)}{b-a}[/tex]
The interval is [1,5]
So, a = 1 and b=5
[tex]f(1) = 17 - (1)^2\\ =17-1\\=16\\f(5) = 17-(5)^2\\=17-25\\=-8[/tex]
Putting in the values
[tex]Rate\ of\ change = \frac{f(5)-f(1)}{5-1} \\=\frac{-8-16}{5-1}\\= \frac{-24}{4}\\ =-6[/tex]
The average rate of change is -6 ..
Answer:
-6
Step-by-step explanation:
Dimetri says that a function that is made of terms
where the variable is raised only to an odd power
will be an odd function. Do you agree with
Dimetri?
Answers
Answer:
Dimetri says that a function that is made of terms
where the variable is raised only to an odd power
will be an odd function. Do you agree with
Dimetri?
Step-by-step explanation:
If g is an odd function and f is an odd function then g ◦ f is odd.
g ◦ f (x) = g (f (x)) = g (−f (−x)) = −g (- (- f (−x))) = −g (f (−x)) = - g ◦ f (−x)
The answer is: No, I am not agree with Dimetri, statement is false because there are so many counterexamples.
Answer:
Sample Response: He is correct only if there is no constant term. −x to an odd power is −x, so the signs will change on the terms with the variable but not on the constant term.
Step-by-step explanation:
The mass of a small virus is 10^-20 kg. The mass of an average human cell is 10^-12 kg. Which of the two has lesser mass? how many less is it?
Answers
For this case we have:
[tex]10 ^ {- 20}[/tex], we must run the decimal point 20 spaces to the left.
[tex]0.00000000000000000010 \ kg[/tex]
[tex]10 ^ {- 12}[/tex], we must run the decimal point 12 spaces to the left.
[tex]0.000000000010 \ kg[/tex]
Thus, it is observed that the mass of a small virus is smaller!
We subtract and obtain:
[tex]10 ^ {-11}[/tex]
ANswer:
The mass of a small virus is less!
Answer: -10kg
Step-by-step explanation:
10-20 =-10
10-22 =-12
-10 is lesser
what is x and y when the right angle side is 7 and the angles are 90,45 and 45?
Answers
Answer:
x=7
Step-by-step explanation:
The other angle is equivalent to 45 degrees. According to the 45-45-90 triangle theorem, the hypotenuse is a times the square root of 2 and the legs are equivalent to a. In this scenario a is equivalent to 7. X is another leg and therefore is also 7.
PLEASE HELP PLEASE
Tricia has the same number of nickels and dimes in her pocket. The coins total $3.60. How many of each coin does she have?
A) 12 nickels and 12 dimes
B) 24 nickels and 24 dimes
C) 36 nickels and 36 dimes
D) 48 nickels and 48 dimes
Answers
Answer:
B
Step-by-step explanation:
Find out the total value of each option and see which one gives a total of $3.60
For A, 12 nickels + 12 dimes = 12 x $0.05 + 12 x $0.10 = $1.80 ≠ $3.60
For B, 24 nickels + 24 dimes = 24 x $0.05 + 24 x $0.10 = $3.60 (correct)
For C, 36 nickels + 36 dimes = 36 x $0.05 + 36 x $0.10 = $5.40 ≠ $3.60
For D, 48 nickels + 48 dimes = 48 x $0.05 + 48 x $0.10 = $7.20 ≠ $3.60
Answer:
For my opinion, the best option it B.
Solve the following equation for x: 2x + 5y = 8.
Answers
Answer:
x = -5/2 y +4
Step-by-step explanation:
2x+5y = 8
Subtract 5y from each side
2x+5y -5y = -5y+8
2x = -5y+8
Divide each side by 2
2x/2 = -5y/2 +8/2
x = -5/2 y +4
Determine the range of the function graphed above.
A. [4,∞)
B. [-4,0]
C. [0,4]
D. (-∞,4]
Answers
Answer:
D. (-∞,4]
Step-by-step explanation:
The range is the y values
The lowest y values is negative infinity
The highest y values is 4
( - inf, 4]
We use the parentheses since we cannot get to negative infinity, the bracket since we reach 4
Maria has three red dresses, 2 white dresses, and one blue dress . What is the probability she will wear a blue dress at her party?
Answers
Answer:
1/6
Step-by-step explanation:
there are 6 dresses altogether and 1 blue dress.
Answer:
[tex]\frac{1}{6}[/tex]
Step-by-step explanation:
We have been given that Maria has three red dresses, 2 white dresses, and one blue dress. We are asked to find the probability that Maria will wear a blue dress at her party.
[tex]\text{Probability}=\frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}[/tex]
We know that number of blue dresses is 1, so number of favorable outcomes is 1.
Total dresses = 3 Red dresses + 2 White dresses + 1 Blue dress = 6 dresses.
[tex]\text{Probability that Maria will wear a blue dress at her party}=\frac{1}{6}[/tex]
Therefore, our required probability is [tex]\frac{1}{6}[/tex].