The number (2x)(3x) in the word will be two time the variable multiplied the three times the variable.
What is termed as the variable?A variable is a property that can be assessed and has multiple values. Variables can be divided into two types: categorical and numeric. The categories are further subdivided into two subgroups: ordinal or nominal for categorical variables and discrete as well as continuous for numeric variables.For the given question,
The number in digits is given as (2x)(3x).
The 'x' is the variable part who value is not defined for the question.
Thus, twice the variable will be 2x.
Thrice the variable will be 3x.
The multiplication of both the numbers will be (2x)(3x).
Therefore, in words the number will be written as two time the variable multiplied the three times the variable.
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What is the equation for a line transforming from y= x with a slope 5/6?
The equation of the transformed function is y' = 5/6x
How to determine the equation of the transformed function?From the question, we have the following equation that can be used in our computation:
y = x
Also, we have the slope of the linear function to be
Slope = 5/6
This can be rewritten as:
m = 5/6
When the function is transformed, we have the following representation:
y' = m * y
Substitute the known values in the above equation
y' = 5/6 * x
Evaluate
y' = 5/6x
Hence, the equation is y' = 5/6x
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Find the solution set of the inequality
\qquad5x + 13 \geq -37.5x+13≥−37.
5x + 13 ≥ -37
The solution set of the inequality 5x + 13 ≥ -37 is represented by x≥-10
and internal notation is [-10,∞).
Given the inequality equation is 5x + 13 ≥ -37.
Now solve the equation.
⇒ 5x + 13 ≥ -37
Arrange the constant terms on one side.
⇒ 5x ≥ -37 - 13
Subtract the terms.
⇒ 5x ≥ -50
Now solve for x.
⇒ x ≥ -50/5
⇒ x ≥ -10
Hence the solution set is x ≥ -10.
So, the internal notation is [-10,∞).
Therefore, the solution set of the inequality is x ≥ -10.
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(Laws of Exponents with Integer Exponents LC) Create an equivalent expression for 9−7 • 95.
The expression 9⁻⁷ • 9⁵ when simplified is 9⁻²
How to evaluate the expression?The expression is given as
9−7 • 95.
Rewrite properly
9⁻⁷ • 9⁵
The base of the above expression are the same
i.e. Base = 9
This means that we can apply the law of indices
When the law of indices is applied, we have the following equation:
9⁻⁷ • 9⁵ = 9⁻⁷ ⁺ ⁵
Evaluate the sum in the above equation
So, we have
9⁻⁷ • 9⁵ = 9⁻²
Hence, the simplified expression of the expression given as 9⁻⁷ • 9⁵ is 9⁻²
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A train leaves Little Rock, Arkansas, and travels north at 90 kilometers per
hour. Another train leaves at the same time and travels south at 60 kilometers
per hour. How long will it take before they are 300 kilometers apart?
Answer: 240 ft to be sure
Step-by-step explanation:
She earns $12 per hour working at a store.
She earns $30 per lawn mowed working for a landscaper.
Her goal is to earn $1,800 to pay her monthly expenses.
The situation can be modeled by the formula below, where represents the hours Tina works in the grocery store and represents the number of lawns mowed.
Answer:
Change Mixed fraction to improper fraction 2/9
someone help me thanks! it's on pythagoras theorem btw
Answer:
y = 3
Step-by-step explanation:
Pythag theorem : ( only applies to RIGHT triangles)
Hypotenuse ^2 = leg1 ^2 + leg 2^2
(7y-1)^2 = (5y-3)^2 + (5y+1)^2
49 y^2 - 14y +1 = 25y^2 -30 y + 9 + 25y^2 + 10y + 1
-y^2 + 6y -9 = 0
or y^2 -6y + 9 = 0 solve by factoring or using Quadratic Formula
( y -3)(y-3) = 0 shows y = 3
The display shows the data set from a survey about time spent on social media in a day. Vertical box plot titled average time spent on social media in a day, with minutes labeled on the vertical axis. The minimum is at 5, and the maximum is at 80. The lower quartile is at 30, the median is at 50, and the upper quartile is at 60. Which of the following describes the data set? Categorical and bivariate Categorical and univariate Numerical and bivariate Numerical and univariate
The data-set in this problem is classified as follows:
Numerical and univariate.
What are the classification of variables?The variables can be classified as categorical or numerical as follows:
Categorical: The possible values assumed by the variable are labels, such as yes/no, good/bad, and so on...Numerical: The values assumed by the variable are numbers.In the context of this problem, the minimum, the maximum and the quartiles of the variable all assume numeric values, hence the variable is classified as numerical.
From the text, the variable under study is the time spent on social media in a day, as a function of minutes. Since the output of the study is a single variable, the study is called univariate.
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Answer:
Numerical and univariate.
Step-by-step explanation:
f(x) = 2x2 + 6x - 4 9(2) = 573 – 6x2 – 3 Find (f +9)(2). O A. (f +g)(x) = -523 + 8x2 + 6x – 1 O B. (f +9)(x) = 5x3 + 2x2 – 7 O C. (f+g)(x) =1723 – 7 O D. (f + g)(x) = 5x3 - 4x2 + 6x - 7
Answer:
The function (f+g)(x) is:
[tex](f+g)(x)=5x^3-4x^2+6x-7[/tex]Explanation:
Given the functions;
[tex]\begin{gathered} f(x)=2x^2+6x-4 \\ g(x)=5x^3-6x^2-3 \end{gathered}[/tex]We want to find the function (f+g)(x);
[tex]\begin{gathered} (f+g)(x)=f(x)+g(x) \\ (f+g)(x)=(2x^2+6x-4)+(5x^3-6x^2-3) \\ (f+g)(x)=5x^3+2x^2-6x^2+6x-4-3 \\ (f+g)(x)=5x^3-4x^2+6x-7 \end{gathered}[/tex]Therefore, the function (f+g)(x) is:
[tex](f+g)(x)=5x^3-4x^2+6x-7[/tex]What is 13^c^11?
O A. 91
OB. 105
C. 78
D. 120
78
1) Since we have a Combination, we can write out the following formula:
[tex]_{13}C_{11}=\frac{13!}{11!(13-11)!}=\frac{13\times12\times11!}{11!\text{ 2!}}=\frac{13\times12}{2}=78[/tex]Note that we canceled 11! on the numerator by the factorial of 11! on the denominator. And notice this is only possible when the order does not matter.
2) Hence, the answer is 78 because there are 78 combinations of 13 choosing 11.
Zak jogs from his house to a lake. He then jogs 5 laps around the lake at a constant speed. The table shows thetotal amount of time, in minutes, Zak has been jogging after completing x laps.Which equation represents the time, m, in minutes, Zak has been jogging after completing x laps?A m = 12x + 5B m = 5x + 12C m = 24x + 5D m = 5x + 24
We are given Zak's laps jogged along with the minutes elapsed.
If the equation of a line is:
m = kx + b
Where m is the number of minutes.
k is the slope of the line
x is the Laps
b is the y-intercept (or where the line crosses the y-axis)
In order to get the equation of the relationship between Laps (x) and Minutes (m),
we need to calculate the slope k and intercept b.
The formulas for doing these are given below:
[tex]\begin{gathered} m=\frac{\sum(x_i-X)(y_i-Y)}{(x_i-X)^2} \\ \text{where,} \\ x_i=\text{data points of Laps x} \\ X=\text{ Average of the Laps x} \\ y_i=\text{data points of Minutes m} \\ Y=\text{Average of Minutes m} \end{gathered}[/tex]The formula for intercept (b) is;
[tex]b=Y-kX[/tex]where Y and X are the averages of m and x values from the table.
[tex]\begin{gathered} Y=\frac{\sum m}{n}\text{ (n is the number of data values of Y)} \\ Y=\frac{17+41+65}{3} \\ \\ Y=41 \\ \\ X=\frac{\sum x}{n}\text{ (n is the number of data values of X)} \\ X=\frac{1+3+5}{3} \\ \\ X=3 \end{gathered}[/tex]In order to be tidy and quick, a table is used to solve.
This table is shown in the image below:
Therefore, we can now calculate slope (m):
[tex]\begin{gathered} m=\frac{\sum(x_i-X)(y_i-Y)}{(x_i-X)^2} \\ \\ m=\frac{\mleft(-24\mright)\mleft(-2\mright)+0\mleft(0\mright)+\mleft(24\mright)\mleft(2\mright)}{4+0+4} \\ m=\frac{96}{8} \\ \\ m=12 \end{gathered}[/tex]Now that we have slope (k) = 12, we can get the intercept b
[tex]\begin{gathered} b=Y-kX \\ Y=41-12(3) \\ Y=41-36 \\ Y=5 \end{gathered}[/tex]Therefore, the equation is:
m = 12x + 5
What is the total volume of all four gum balls?
3. Is there another method to determine this value besides a calculator? What are the pros and cons to using the nCr function on yourgraphing calculator in comparison to the other method(s) you mentioned?
Given:
The expression is:
[tex]_{12}C_5[/tex]Find-:
The value of the expression
Explanation-:
The formula of:
[tex]_nC_r[/tex]Combination formula:
[tex]_nC_r=\frac{n!}{(n-r)!r!}[/tex]The given expression is:
[tex]\begin{gathered} n=12 \\ \\ r=5 \end{gathered}[/tex]So, the value is:
[tex]\begin{gathered} _{12}C_5=\frac{12!}{(12-5)!5!} \\ \\ =\frac{12\times11\times10\times9\times8\times7!}{7!\times5!} \\ \\ =\frac{12\times11\times10\times9\times8}{5!} \\ \\ =\frac{12\times11\times10\times9\times8}{5\times4\times3\times2\times1} \\ \\ =792 \end{gathered}[/tex]The value is 792.
If 3m+5=27, then the value of m is
Answer:
m=7 1/3 in mixed number or 22/3 in improper fraction
Step-by-step explanation:
3m+5=27 is your equation
You will have to subtract 5 on both sides and you will be left with
3m=22
After that you will divide three on both sides
Therefore the answer is m=7 1/3 or 22/3
1. Anna is saving up for a new laptop. She currently has 2x² - 2x dollars saved in her bank account. After working at her part-time job, she is able to deposit another 11x + 15 dollars. She finally has enough money to buy the laptop, and so she withdraws x²- 5x + 3 dollars. How much money does she have left in her bank account after buying her laptop? SHOW ALL WORK!
1) Gathering the data
Anna currently has 2x² -2x dollars
Then She adds: 11x +15 dollars
And withdraw x²-5x +3 dollars
2) Let's rewrite that
2x² -2x
+11x +15
---------------------
2x² +9x +15 - (x² -5x +3)
2x² +9x +15
-x² +5x -3
---------------------
x² +14x +12
That's the amount of money Anna has left for her laptop: x² +14x +12 dollars
A planner at Barnes and Noble originally cost $10. During the weekend, the planner went on sale for $9. What is the price markdown (percent of change)?
new cost = $9
original cost = $10
Substitute the value into the formula;
[tex]\text{percentage change =}\frac{10-9}{10}\times100^{}[/tex]
= 1/10 x 100%
= 10%
John's bank account was overdrawn. The status of his account was − $162. He did not realize the problem and wrote another check for $78. The bank charged him a $24 fee for being overdrawn.What was the new status of John's account at this point?
The initial status of John's bank account was -$162.
After he wrote a check for $78 and being charged in $24 for being overdrawn, the new status is - 162 - 78 - 24 = -$264
What’s the equation passing threw the points? And is parallel to the line 3x+y=3
The parallel line 3x + y =3, can be write on y-intercept form:
Solve for y the equation:
3x + y = 3
y = 3 -3x
Now, two lines are parallel when they have the same slope. In this case for line y= 3 -3x, the slope is the number with the x.
Therefore, the slope is -3.
Use the slope intercept-form using slope=m=3 and the point (1,-7):
[tex]y-y_1=m(x-x_1)[/tex]Replace these values and solve for y:
[tex]y-(-7)=-3(x-1)[/tex][tex]y+7=-3x+3[/tex]Solving for x:
[tex]y=3x+3-7[/tex]The equation that passes through the point (1,-7) and is parallel to the line3x + y =3 is :
[tex]y=-3x-4[/tex]solve the following equation. express your answer as both an exact expression and a decimal approximation rounded to two decimal places. use e = 2.71828182845905.
SOLUTION:
Case: Exponential equations
Given:
[tex]e^{3x-8}=102^{5x+5}[/tex]Required: To solve for x
[tex]\begin{gathered} e^{3x-8}=102^{5x+5} \\ Take\text{ }natural\text{ }logarithm\text{ }of\text{ }both\text{ }sides \\ ln(e^{3x-8})=ln(102^{5x+5}) \\ (3x-8)lne^=(5x+5)ln(102) \\ 3x-8=(5x+5)4.624972 \\ 3x-8=23.12x+23.12 \\ Collecting\text{ }like\text{ }terms \\ -23.12-8=23.12x-3x \\ -31.12=20.12x \\ x=-\frac{31.12}{20.12} \\ x=-1.54658754284 \end{gathered}[/tex]Final answer:
Exact value
[tex]x=-1.54658754284[/tex]To 2 decimal places
[tex]x\approx-1.55[/tex]Suppose Latoya borrows$4000.00 at an interest rate of 18% compounded each year.Assume that no payments are made on the loan.Find the amount owed at the end of 1 year.Find the amount owed at the end of 2 years.
Answer:
[tex]\begin{gathered} A=\text{ \$4,720 at the end of 1 year} \\ A=\text{ \$5,570 at the end of 2 year} \end{gathered}[/tex]Step-by-step explanation:
The compound interest is represented by the following equation:
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ where, \\ P=\text{ principal borrowed} \\ r=\text{ rate} \\ n=\text{ number of times compounded per time ''t''} \\ t=\text{ time in years} \end{gathered}[/tex]Therefore, if Latoya borrows $4000 at an interest rate of 18% compounded each year;
[tex]\begin{gathered} A=4000(1+\frac{0.18}{1})^1 \\ A=\text{ \$4,720 at the end of 1 year} \end{gathered}[/tex]Now, at the end of 2 years:
[tex]\begin{gathered} A=4000(1+\frac{0.18}{2})^2 \\ A=\text{ \$5,569.6 at the end of 2 year} \end{gathered}[/tex]What is x?
-2 + 3x = 5x - 8
Answer:
x = 3
Step-by-step explanation:
-2 + 3x = 5x - 8
add 8 to both sides:
-2 + 3x + 8 = 5x - 8 + 8
6 + 3x = 5x
subtract 3x from both sides:
6 + 3x - 3x = 5x - 3x
6 = 2x
divide both sides by 2:
6/2 = 2x/2
x = 3
check: when x = 3
-2 + 3(3) = 5(3) - 8
-2 + 9 = 15 - 8
7 = 7
Answer:
X = 3
Step-by-step explanation:
-2 + 3x = 5x - 8
+8 Because -8 is lower then -2 we start by doing the opposite and +8 to -2
6 + 3x = 5x
-3x Because now we have to do the opposite on the variable too.
6 = 2x
/2 Because you have to divide the integer by the variable
x = 3
700 tickets were sold for a game for a total of $900.00 If adult tickets sold for $2.00 and children's tickets sold for $1.00 how many of each kind of ticket were sold?
Let x be the number of adult tickets and let y be the number of children.
We know that in total there were sold 700 tickets, that means:
[tex]x+y=700[/tex]Now we know that each adult ticket was $2 and the children's tickets was $1, and that the total was $900, this means that:
[tex]2x+y=900[/tex]Then we have the following system of equations:
[tex]\begin{gathered} x+y=700 \\ 2x+y=900 \end{gathered}[/tex]To solve it we substract the second equation from the first one, then we have:
[tex]\begin{gathered} x+y-2x-y=700-900 \\ -x=-200 \\ x=200 \end{gathered}[/tex]Now that we have the value of x we plug it in the first equation to find y:
[tex]\begin{gathered} 200+y=700 \\ y=700-200 \\ y=500 \end{gathered}[/tex]Therefore, there were 200 adult's tickets and 500 children's tickets sold.
For a right triangle ABC, you are told that cos A=X and sun A=y. Which option gives an expression that is equivalent to tan A? X/ x2+y2. X/y. Y/X. Y/x2+y2
For a right triangle ABC, the expression that is equivalent to tan A is y/x.
What is defined as the trigonometric functions?Trigonometric functions, also recognized as circular functions, are simply functions of a triangle's angle. These trig functions define the relationship between both the angles as well as sides of a triangle. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions. The sine, cosine, as well as tangent angles are the primary categorization of trigonometric functions. The primary functions can be used to derive the three functions cotangent, secant, and cosecant.For the given question,
In a right triangle ABC.
The cosine and sin functions are defined as;
cos A=X and sin A=y.
Then, we know that tan A function can be written in the form in the form of cos A and sin A as,
tan A = sin A/ cos A
Put the values,
tan A = y/x
Thus, the expression that is equivalent to tan A is y/x.
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hello I need on this hw question please thank you
Given:
The given equation is,
[tex]3x-19+(?)x=-5x-19[/tex]Required:
To find the missing value.
Answer:
The given equation is,
[tex]\begin{gathered} 3x-19+(?)x=-5x-19 \\ \end{gathered}[/tex]By putting (-8) in place of (?) in the given equation, we get,
[tex]\begin{gathered} 3x-19+(-8)x=-5x-19 \\ \Rightarrow3x-19-8x=-5x-19 \\ \Rightarrow-5x-19=-5x-19 \\ \Rightarrow-19=-19 \end{gathered}[/tex]This shows that the given equation has infinitely many solutions.
Final Answer:
The missing value is -8.
Use the information to find and compare ∆y and dy (Round your answers to three decimal places.)
y=4x^3 x=2 ∆x=dx=0.1
The values of derivatives Δy and dy are given as 0.48 and 4.8
The values of Δy and dy will be calculated using the formula Δy = f(x + Δx) - f(x) and dy = f'(x)dx. For calculating the values, we put the values which are given in the question that is
Δy = f(x + Δx) - f(x)
Δy = f(2 + 0.1) - f(2)
Δy = f(2.01) - f(2)
Δy = 4(2.01)³ - 4(2)³
Δy = 32.48 - 32
Δy = 0.48
Now, we have f(x) = 4x³, so we have f'(x) = 12x²
Now, dy = f'(x)dx
dy = 12x²dx
dy = 12(2)²(0.1)
dy = 4.8
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Our school district is sending two teachers to a 3-day training session on innovative teaching
strategies. Expenses per person: registration, $275; supplies, $40; breakfast, $8; lunch $15;
and dinner $20. Total transportation cost for the two people is $120. If our district has
budgeted $1,500 for the 2 to attend the training session, what is the most they can each pay
for their hotel per person per night?
Answer: Approximately $117.33
Step-by-step explanation:
1. Add all the Expenses per person to get $338
2. Multiply these expenses by 2 for each person to get $676
3. Add $120 for Transportation to get $796
4. Multiply the people going by the amount of days they are staying to get 6
5. Subtract the total expenses by the budget to get $704
7. Divide the answer of step 4 by the remaking budget to get the final answer of approximately $117.33
Yoshi has played in 6 basketball games so far this season. Her points in each game aredisplayed in the table below.GamePoints181234562420142224What is the median of Yoshi's points per game?O 21None of the other answers are correctO 221920
Let us revise how to find the median
At first you must arrange the numbers from small to big
Let us do that
14, 18, 20, 22, 24, 24
We have 6 numbers we need to find the middle one because the median means middle number in a set of data
But there are 6 numbers the middle numbers are 20 and 22
So the median will be the average of the two number
[tex]\text{Median}=\frac{20+22}{2}=\frac{42}{2}=21[/tex]There is a very important note for the median
If the number of data is even the median will be the average of the middle two numbers as our question, but if the number of data is odd then the median will be the middle number.
The answer is the first choice
Determine whether each pair of polygons is similar. OPTIONSSimilar, sides are proportional and angles are corresponding Similar, sides are proportional and angles are congruent Not similar, sides are not proportional and angles are congruent Not similar, sides are proportional and angles are not congruent
From the figure it can be observed that angles of both figure are equal to 90 degrees. So angles are congurent of polygons are conurent to each other.
Determine the ratio of corresponding sides of two polygon.
[tex]\frac{3}{4}[/tex]And
[tex]\frac{6}{9}=\frac{2}{3}[/tex]As sides of the polygons are not proportional to each other. So figure are not similar.
Thus correct option is,
Not similar, sides are not proportional and angles are congruent .
Simplity 24 ÷ (-2)(3) + 7
Nashia, this is the solution:
24 ÷ (-2)(3) + 7
• We use ,PEMDAS, for the order of operations, as follows:
Step 1: Solve the parenthesis
24 ÷ -6 + 7
Step 2: We solve the division
-4 + 7
Step 3: We solve the addition
3
The result is 3
The radius of a circle is 11ft. Find its area in terms of pi
Answer: A≈380.13ft²
Step-by-step explanation:
convert each fraction to its equivalent using the least common denominator 3/7 , 3/4
The least common denominator of 3/7 and 3/4 is 7*4=28, therefore:
[tex]\begin{gathered} \frac{3}{7}=\frac{3\cdot4}{7\cdot4}=\frac{12}{28}, \\ \frac{3}{4}=\frac{3\cdot7}{4\cdot7}=\frac{21}{28}. \end{gathered}[/tex]Answer:
3/7, option e.
3/4, option c.
