The first step is to collect like terms:
This is done by adding 6 to both sides of the equation
1) add 6 to both sides (option D)
2x/3 -6+6 = 2+6
2x/3 = 8
The second step is to cross multiply OR
multiply both sides of the equation by 3
2x = 8(3)
2x = 24
2) Multiply both sides by 3 (option A)
The third step is to divide both sides by 2
2x/2 = 24/2
3) Divide both sides by 2 (option B)
x = 24/2
4) x = 12 (option C)
Which answer choice identifies the relevant information in the problem?
Sarah left the house at 12:15 p.m. to go to the store. She spent $42.20 on 2 books for her children and she spent $5.67 on a toys for her dog, Rover. Sarah arrived home at 1:00 p.m. How much did Sarah spend on each book?
Answer:
$18.26
Step-by-step explanation:
The total price is $42.20
We want to know how much 1 of those books cost
We know that $5.67 were for her dog
So we are gonna subtract that from $42.20
$42.20-$5.67=36.53
Now your gonna divide that by 2 because she got 2 books
So 36.53/2=$18.26
1 book=$18.26
Mary's dog weighs 25 pounds. How many ounces does the dog weigh? Remember, there are 16 ounces in a pound.
Answer:
400
Step-by-step explanation:
4 x 10^, 20^2
Answer:
25 pounds 16 ounces = 6400
Step-by-step explanation:
An item on sale costs 40% of the original price if the original price was $45 what is the sale price
Answer:
$18
Step-by-step explanation:
Finding 40% of something is the same as multiplying it by 0.4.
If we do this to 45 we get:
45 x 0.4 = 18
So, the sale price would be $18.
What are the values of X where f(x)=g(x)Round to the nearest hundredth’s place if necessary.select all that apply
Given:
The functions
[tex]\begin{gathered} f(x)=2Cos(x) \\ g(x)=(x+0.5)^2+1 \end{gathered}[/tex]Required:
What are the values of x where f(x)=g(x).
Explanation:
From graph we can see that function equals at x value (-0.934) and (0.412)
Answer:
The x values are (-0.93) and (0.41)
The instructor’s friend also plans to rent an apartment in the same complex. Use the graph to identify the y-intercept and the slope used to write the equation in slope intercept form.
y-intercept =
Slope =
Linear equation =
The y-intercept of the graph is: 3,000
The slope is: -2.75
The linear equation of the graph is: y = -2.75x + 3,000.
What is the Linear Equation of a Graph?The linear equation that represents a linear graph shows the slope (m) and y-intercept (b) of the graph and is expressed in slope-intercept form as, y = mx + b.
In the given graph:
The y-intercept (b) is the starting value, which is the point on the y-axis where the line intercepts, and it is equal to: 3,000.
Using two points on the graph, (0, 3,000) and (2, 2,450), the slope of the graph = change in y / change in x = (3,000 - 2,450)/(0 - 2) = 550/-2 = -2.75.
To write the linear equation, substitute m = -2.75 and b = 3,000 into y = mx + b:
y = -2.75x + 3,000.
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Circle A has center (0, 0) and radius 3. Circle B has center (-5, 0) and radius 1. What sequence of transformations could be used to show that Circle A is similar to Circle B?
A translation of T(x, y) = (- 5, 2) and a dilation with center (- 5, 2) with a scale factor of 1 / 3 are necessary to transform circle A into circle B. (Correct choice: D)
What sequence of rigid transformations can be done on a circle
In this problem we must determine the sequence of transformations require to transform circle A into circle B. From analytical geometry we know that the equation of the circle in standard form is:
(x - h)² + (y - k)² = r²
Where:
(h, k) - Coordinates of the center.r - Radius of the circle.Then, we need to apply the following rigid transformations:
Translation
f(x, y) → f(x - h, y - k), where (h, k) is the translation vector.
Dilation with center at the center of the circle
r → k · r, where k is the scale factor.
The circle A is represented by x² + y² = 3, then we derive the expression for the circle B:
f(x, y) → f(x + 5, y - 2)
(x + 5)² + (y - 2)² = 9
r → k · r
(x + 5)² + (y - 2)² = (1 / 3)² · 9
(x + 5)² + (y - 2)² = 1
Then, a translation of T(x, y) = (- 5, 2) and a dilation with center (- 5, 2) are necessary to transform circle A into circle B.
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Let f (2) = x? and g(2) r” and g(2) = 77 - 2. What is (fog)(x)? What is (fog)(0)?
This is function composition, so:
[tex]\begin{gathered} f(x)=x^2,g(x)=\sqrt[]{7-x}\text{ } \\ (f\circ g)(x)=f(g(x))=g(x)^2=(\sqrt[]{7-x})^2 \\ (f\circ g)(x)=(\sqrt[]{7-x})^2 \end{gathered}[/tex]And (f o g)(0) is:
[tex]\begin{gathered} (f\circ g)(0)=(\sqrt[]{7-0})^2 \\ (f\circ g)(0)=(\sqrt[]{7})^2=7^{} \end{gathered}[/tex]The answer is (f o g)(0) = 7
Simplify (z9z−3)−2.
1 over z raised to the twelfth power
1 over z raised to the sixth power
−z^12
−z^6
Answer:
A. 1 over z raised to the twelfth power
Step-by-step explanation:
Hope this helps! :))
Please tell me if this is incorrect
Answer:
1 over z raised to the twelfth power
Step-by-step explanation:
If the area of a parallelogram is 36 cm^2 and has a height of 4 cm, what is the basea cm
Given, the area of the parallelogram, A=36 cm^2.
The height of the parallelogram, h=4 cm.
The area of a parallelogram is,
[tex]A=bh[/tex]Here, b is the base length and h is the height of the parallelogram.
Put values of A and h in the above equation to find base b.
[tex]\begin{gathered} 36=b\times4 \\ \frac{36}{4}=b \\ 9cm=b \end{gathered}[/tex]Therefore, the base of the parallelogram is 9 cm.
Is 5 ft, 6 ft, 11 ft a right triangle
Answer:
No, not right or a triangle lol
Step-by-step explanation:
This is not a triangle.
5+6=11, it has to be greater :)
your triangle is a straight line.
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A group of 175 college students who took math last term were interviewed. They were asked whether they passed their math course and whether they live on campus. Their responses are summarized in the following table. Passed math Failed math Live on campus 49 21 Live off campus 28 77 Х x $ ? (a) What percentage of the students passed math? [% (b) What percentage of the students live on campus? % (C) What percentage of the students who live on campus passed math? []% (d) Is there evidence that students who live on campus tend to pass math more often than average? O No, because the percentage found in part (c) is about the same as the percentage found in part (a). O No, because the percentage found in part (c) is about the same as the percentage found in part (b). ○Yes, because the percentage found in part (C) is much greater than the percentage found in part (a).○yes because the percentage found in part C is much greater than the percent is found in Part B
Given the group of 175 college students who took math last term:
(a) You can identify in the table that the total number of students that passed math is:
[tex]49+28=77[/tex]Therefore, knowing the total number of students that were interviewed, you can determine that the percentage of the students who passed math is:
[tex]\frac{77}{175}\cdot100=44\text{ \%}[/tex](b) Based on the data shown in the table, the total number of students who live on campus is:
[tex]49+21=70[/tex]Therefore, you can determine that the percentage of the students who live on campus is:
[tex]\frac{70}{175}\cdot100=40\text{ \%}[/tex](c) You can identify that 49 students live on campus and passed math. Therefore, the percentage of the students who live on campus and passed math is:
[tex]\frac{49}{49+28}\cdot100\approx63.6\text{ \%}[/tex](d) Knowing that 63.6% of the students who live on campus passed math, 40% of the student who live on campus, and 44% of the students interviewed passed math, you can identify that students who live on campus tend to pass math more often than average, because:
[tex]63.6\text{ \%}>40\text{ \%}[/tex]Hence, the answers are:
(a)
[tex]44\text{ \%}[/tex](b)
[tex]40\text{ \%}[/tex](c)
[tex]63.6\text{ \%}[/tex](d) Last option.
find the X and the Y intercepts of the graph of the equation below 8x + 2y equals negative 16
The expresion is:
[tex]8x+2y=-16[/tex]to find the intercepts with the x axis we have to rplace in the equation y = 0, so:
[tex]\begin{gathered} 8x+2(0)=-16 \\ 8x=-16 \end{gathered}[/tex]and we solve for x
[tex]x=-\frac{16}{8}=-2[/tex]the intersection with the x axis is -2
And for the itercepts with the y axis we replace x = 0
[tex]\begin{gathered} 8(0)+2y=-16 \\ 2y=-16 \end{gathered}[/tex]and we solve for y
[tex]y=-\frac{16}{2}=-8[/tex]This means that the intersepts with the y axis is -8
1. Write the other side of this equation so that this equation is true for all values of u.2. Write the other side of this equation so that this equation is true for no values of u6(u-2)+2
SOLUTION
Given the question in the question tab, the following are the solution steps for the answer
Step 1: Write out the equation
[tex]6(u-2)+2[/tex]Step 2
PLEASE HURRY IM SO CONFUSED
What is the product of (−4)(23)(−7)?
Answer:
644
Step-by-step explanation:
-4x23=-92
-92x-7=644
i hope this helped :)
based off of this table, what would be the best guess for the domain and range of the composition?? i cant figure this out. PLEASE HELP
The composite function is:
[tex]y=\lvert-x^2\rvert[/tex]The domain (D) is:
The domain is the set of all possible x values. Since there are no limitations for the x-values, the domain is all real numbers.
D = (-∞, ∞).
The Range (R) is:
The range is the set of all possible y values (output values). As you can see in your table, there are no negative output values. So, the range is the positive real numbers and the zero.
R = [0, ∞).
Clarissa's division test was a 60% the first six weeks and a 72% the second six weeks. find the percent change. also, label it as increase or decrease.
The percentage change of the division test is 12%.
There is a percentage increase.
How to find percentage change?Percentage change is the difference in values and the percent change from the original value to the new value.
In other words, percentage change can be defined as a percentage change in value due to changes in the old number and new number, and the values can either increase or decrease.
Percentage change is all about comparing old to new values.
The division test was 60% in the first six week.
The division test was 72% in the second six week.
Therefore,
percentage change = 72% - 60%
percentage change = 12%
Therefore, there is a percentage increase by 12%.
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Write the correct expression for the following statement.
x six times
Use / for division
do not put any spaces
The vertical height in feet of a projectile on a planet in our solar system at a given time t in seconds is represented by the function h(t)=−6t2+24t . Re-write h(t) in the form h(t)=a(t-h)^2+k and determine the maximum height of the projectile. Show all work.
We are given the following function:
[tex]h(t)=-6t^2+24t[/tex]We will take "-6" as a common factor:
[tex]h(t)=-6(t^2-4t)[/tex]Now, we will complete the square in the expression inside the parenthesis by adding and subtracting the following term:
[tex]undefined[/tex]The graph shows the mass of the bucket containing liquid depends on the volume of liquid in the bucket. Use the graph to find the range of the function.
The range of the graph is 0 <= M <= 5.5
How to find the range of the function?The range of a function is the set of output values of the graph.
This in other words mean the range of a function is the set of y values of the graph.
How to determine the domain and the range?The domain
On the graph of the function, we can see that:
The x values start from 0 and it ends at 7.5
This means that the domain is 0 <= x <= 7.5
The range
On the graph of the function, we can see that:
The x values start from 0 and it ends at 5.5
This means that the range is 0 <= M <= 5.5
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Answer:
0 <= M <= 5.5
Step-by-step explanation:
HELP!
For triangle XYZ, m∠X = 38°, m∠Y = (5x − 11)°, and m∠Z = (4x − 45)°. Find m∠Y.
m∠Y = 22°
m∠Y = 43°
m∠Y = 99°
m∠Y = 158°
The value of m∠Y in triangle XYZ is 99°
How to solve an equationAn equation is used to show the relationship between two or more numbers and variables.
In triangle XYZ, the angles are angle x, y and z. Hence:
∠X + ∠Y + ∠Z = 180° (sum of angles in a triangle)
Substituting:
38 + (5x -11) + (4x -45) = 180
Collecting like terms:
9x - 18 = 180
9x = 198
x = 22
m∠Y = 5(22) - 11 = 99°
m∠Y is 99°
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What is the result when 4x3 19x2 + 19x + 13 is divided by 4x + 1? If there is a remainder, express the result in the form q(x) + 6(2):
Answer:
[tex]\frac{4x^3-19x^2+19x+13}{4x+1}=(x^2-5x+6)+7[/tex]1. Given the following table and graph, write the equation to representthe exponential function.уy43-1-4210-2-4-20х1-12-0.5
In order to find the equation of this exponential function, let's use this model for an exponential equation:
[tex]y=a\cdot b^x[/tex]Now, using some of the points given, we can find the values of the coefficients 'a' and 'b':
[tex]\begin{gathered} x=0,y=-2 \\ -2=a\cdot b^0 \\ a=-2 \\ \\ x=1,y=-1 \\ -1=-2\cdot b^1 \\ b=\frac{-1}{-2}=0.5 \end{gathered}[/tex]So our function is:
[tex]y=-2\cdot0.5^x[/tex]How do you use the z- tables for continuous normal distribution
The z-score table can be used by starting on the left side of the table, going down to 1.0, and then moving up to 0.00 (which corresponds to the value of 1.0 +.00 = 1.00). A mathematical table for the values of, which are the values of the cumulative distribution function of the normal distribution, is known as a standard normal table.
What is a continuous normal distribution?Continuous probability distribution with a bell-shaped probability density function is known as a normal (or Gaussian) distribution. In terms of statistics, it is the most prominent probability distribution.
The z-score table can be used by starting on the left side of the table, going down to 1.0, and then moving up to 0.00 (which corresponds to the value of 1.0 +.00 = 1.00). The probability is represented by the value. 8413 in the table.
A z-table, also known as the standard normal table, is a mathematical table that enables us to determine the proportion of values in a standard normal distribution that fall below (to the left) a given z-score (SND).
A mathematical table for the values of, which are the values of the cumulative distribution function of the normal distribution, is known as a standard normal table. It is also known as the unit normal table or the Z table.
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Select the GCF for each pair of numbers. 9,15 12,18 15,27 30,54
The Greatest common factors for each pair of numbers are;
1, ( 9 , 15 ) = 3
2. ( 12 , 18 ) = 6
3. ( 15 , 27 ) = 3
4. (30, 54) = 6
What is Greatest common factors?
The highest number that divides exactly into two more numbers, is called Greatest common factors.
Given that;
The pairs of numbers are;
1, ( 9 , 15 )
2. ( 12 , 18 )
3. ( 15 , 27 )
4. (30, 54)
Now,
Find the Greatest common factors of the pairs of the numbers as;
1, ( 9 , 15 )
LCM of 9 = 3 x 3
LCM of 15 = 3 x 5
So, GCF of 9 and 15 = 3
2. ( 12 , 18 )
LCM of 12 = 2 x 3 x 2
LCM of 18 = 3 x 3 x 2
So, GCF of 12 and 18 = 3 x 2 = 6
3. ( 15 , 27 )
LCM of 15 = 3 x 5
LCM of 27 = 3 x 3 x 3
So, GCF of 15 and 27 = 3
4. (30, 54)
LCM of 30 = 2 x 3 x 5
LCM of 18 = 3 x 3 x 2
So, GCF of 30 and 54 = 3 x 2 = 6
Thus, The Greatest common factors for each pair of numbers are;
1, ( 9 , 15 ) = 3
2. ( 12 , 18 ) = 6
3. ( 15 , 27 ) = 3
4. (30, 54) = 6
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For each expression, select all equivalent from the list.
(a) 9x-5x+8x
(b) 9(1+7y)
Answer:
a)12x
b)9+63y
goodluck
Suppose the Rocky Mountains have 72 centimeters of snow. Warmer weather is melting the snow at a rate of
5.8 centimeters a day. If the snow continues to melt at this rate, after seven days of warm weather, how much
snow will be left?
Answer:
31.4 cm
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]
The y-intercept is the y-value when x is zero, so the initial value.
If the initial amount of snow is 72 cm, the y-intercept is 72.
The slope is the rate of change.
If the snow is melting at a rate of 5.8 cm per day, then the rate of change is -5.8.
Therefore, the equation that models the given word problem is:
[tex]\boxed{\begin{minipage}{5.4 cm}\phantom{w}\\$y=-5.8x+72$\\\\where:\\ \phantom{ww}$\bullet$ $y$ is height of the snow in cm. \\ \phantom{ww}$\bullet$ $x$ is the time in days.\\\end{minipage}}[/tex]
To find how much snow is left after 7 days, substitute x = 7 into the found equation:
[tex]\implies y=-5.8(7)+72[/tex]
[tex]\implies y=-40.6+72[/tex]
[tex]\implies y=31.4[/tex]
Therefore, there will be 31.4 cm of snow left after seven days of warm weather.
The top needs to know what type of triangle like sas ssa or the other types
From the parameters given, the triangle could be as shown below
a) From the above figures, the triangle can either be an acute triangle or a reflex triangle .
b) There are thus, 2 solutions
An item on sale costs 40% of the original price if the original price was $25 what is the sale price
Answer: $10
Step-by-step explanation:
original price = 25
40% = 0.4
25 * 0.4= 10
simply the (3x^2y^2)^2
Answer:
9x^4y^4
Step-by-step explanation:
Attachment below. :D
In the expression 7^4 = 2,401, the value of the____ is 7.A. BaseB. PowerC. exponent
The value of the base is 7 (option A)
Explanation:Given:
[tex]7^4\text{ = 2401}[/tex]To find:
To complefe the sentence by ill ingthe blanks
In powers and exponents:
[tex]For\text{ }a^b:\text{ a = base, b = exponent}[/tex][tex]\begin{gathered} Applying\text{ same principle:} \\ 7^4:\text{ Base = 7, exponent = 4} \end{gathered}[/tex]The value of the base is 7 (option A)