Answer:
g(x) = 3x + 2Step-by-step explanation:
[tex]f(x)=2x;\ g(x)=?\\\\(g\circ f)(x)=6x+2=3(2x)+2=3\bigg(f(x)\bigg)+2\to g(x)=3x+2\\\\Check:\\\\f(x)=2x,\ g(x)=3x+2\\\\(g\circ f)(x)\to\text{instead of x in g (x), put}\ 2x:\\\\(g\circ f)(x)=3(2x)+2=6x+2\qquad\bold{CORRECT :)}[/tex]
7 people share 3 cookies what part of a cookie does each person get
If 7 people share 3 cookies, a part of a cookie that each person gets is 3/7 cookies.
In Mathematics and Euclidean Geometry, a unit rate refers to the quantity of material that is equivalent to a single unit of product or quantity.
In this context, the unit rate can be calculated by using the following formula;
Unit rate = Total cookies/Total number of people
Unit rate = 3/7 cookies.
In this context, we can reasonably infer and logically deduce that the unit rate indicates 3/7 cookies per person.
Complete Question:
7 people share 3 cookies, what part of a cookie does each person get?
Which expression is equivalent to the algebraic expression below?
3(–2x – 1)
a x – 1
b –6x – 3
c x + 2
d –6x – 1
Answer:
b) -6x - 3
Step-by-step explanation:
3(-2x-1)=3*(-2x)+3*(-1)= -6x - 3
B. -6x - 3
Distribute the 3, or multiply it by everything in the parentheses.
You multiply 3 times -2x to get -6x, and you multiply 3 times -1 to get -3.
Put these together to get -6x-3.
Write the equation of the circle shown here.
Answer:
(x − 7)² + (y + 2)² = 52
Step-by-step explanation:
The equation of a circle is:
(x − h)² + (y − k)² = r²
where (h, k) is the center and r is the radius.
We know that (h, k) = (7, -2). But we need to find the radius. To do that, find the distance from the center to a point on the edge:
r² = (x₁ − x₂)² + (y₁ − y₂)²
r² = (7 − 1)² + (-2 − -6)²
r² = 6² + 4²
r² = 36 + 16
r² = 52
So the equation of the circle is:
(x − 7)² + (y + 2)² = 52
The equation of the circle is (x-2)^2 + (y-(-3))^2 = 5^2.
Explanation:To write the equation of a circle, we need to know the center and the radius of the circle. We can see from the diagram that the center of the circle is the point (2, -3), and the radius is 5 units.
The equation of a circle is given by the formula (x-h)^2 + (y-k)^2 = r^2,
where (h, k) is the center and r is the radius. Therefore, the equation of the circle is (x-2)^2 + (y-(-3))^2 = 5^2.
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What’s this answer ?
Answer:
the radius is 13
the diameter is 40.82 inches squared
the area is 530.66
Step-by-step explanation:
well, the radius is 13
Simplify 2x+x+x+2y x 3y x y
Answer:
3x+6y^3
Step-by-step explanation:
-First you add all the Xs
2x+x+x
-Then you multiply all the Ys
2y * 3y * y
* the Y has a 1 as an exponent by multiplying the Ys the exponents are added making the Y a Y^3
*the numbers are multiplied making it a 6
Together it forms 6y^3
-Ys and Xs cannot be added because they are different values so your answer would be 3x+ 6y^3
The simplification of the given algebraic expression 2x+x+x+(2y × 3y × y) is 4x + 6y³.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The simplification of 2x+x+x+(2y × 3y × y) can be done as,
2x + x + x + (2y × 3y × y)
= 4x + (2y × 3y × y)
= 4x + 6y³
Hence, the simplification of the given algebraic expression 2x+x+x+(2y × 3y × y) is 4x + 6y³.
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Use the properties of logarithms to expand log(zy8).
(By 8, they mean the exponent of 8, or the eighth power.)
Each logarithm should involve only one variable and should not have any exponents. Assume that all variables are positive.
Answer:
log (y)+ 8 log (z)
Step-by-step explanation:
use the rules of logarithm
The expanded form of the given function is log (x)+ 8 log (y).
What is a logarithm?When you raise a number with an exponent, there comes a result.
Let's say you get
a^b = c
Then, you can write 'b' in terms of 'a' and 'c' using a logarithm as follows
[tex]b = \log_a(c)[/tex]
'a' is called base of this log function. We say that 'b' is the logarithm of 'c' to base 'a'
Given;
[tex]log(xy^8)[/tex]
use the rules of the logarithm;
log (x)+ 8 log (y)
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spining an odd number, not fliping heads, then not spining at 6
Answer:
1/8
Step-by-step explanation:
trust me
How many solutions does the following equation have?
Answer:
Answer choice D, Infinitely many solutions.
Step-by-step explanation:
6x-24=6x-24
these figures are similiar. the area of one is given. find the area of the other
Answer:
18 in²
Step-by-step explanation:
Given 2 similar figures then
linear ratio = 9 : 12 = 3 : 4
area ratio = 3² : 4² = 9 : 16
let the area of the other figure be x
[tex]\frac{9}{x}[/tex] = [tex]\frac{16}{32}[/tex] [ [tex]\frac{ratio}{corresponding area}[/tex] ]
cross- multiply
16x = 288 ( divide both sides by 16 )
x = 18
Area of other figure is 18 in²
The area of two similar figures is related by the square of the ratio of their corresponding sides. Once you know the ratio of their sides, you can find the area of the second figure by squaring this ratio and multiplying it by the area of the first figure.
Explanation:To figure out the area of the second figure, first you need to understand the concept of similarity. Two figures are similar if their corresponding sides are proportional. When two figures are similar, the ratio of their areas is the square of the ratio of their corresponding sides. If we let's say the ratio of their corresponding sides are in the ratio 1:R, then the ratio of their areas would be 1:R^2.
Suppose the area of the first figure is A and you're looking for the area of the second figure (let's call it A'). If the sides are in ratio 1:R, then A/A' = (1/R)^2. Or conversely, A' = A * R^2.
Once you find R (the ratio of their corresponding sides), you can find the area of the second figure by multiplying the area of the first figure by R^2.
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Louise completed the work shown below.
(5x3 + 3)2 = (5x3)2 + (3)2 = 25x6 + 9
Determine if Louise’s answer is correct. Explain.
Sample Response: Louise’s answer is not correct. She is missing the term 30x3. When squaring a binomial, it is best to write the product of the binomial times itself. Then you can use the distributive property to multiply each term in the first binomial by each term in the second binomial. Louise also could have used the formula for a perfect square trinomial, which is found by squaring a binomial.
Answer:
Louise is missing the term [tex]30x^3[/tex]
Step-by-step explanation:
Remember that the formula for squaring a binomial is:
[tex](a+b)^2=a^2+2ab+b^2[/tex]
Where
[tex]a[/tex] is the first term of the binomial
[tex]b[/tex] is the second term of the binomial
Our binomial is [tex](5x^3+3)^2[/tex], so [tex]a=5x^3[/tex] and [tex]b=3[/tex].
Replacing values
[tex](5x^3+3)^2=(5x^3)^2+2(5x^3)(3)+3^2[/tex]
[tex](5x^3+3)^2=5^2x^6+6(5x^3)+9[/tex]
[tex](5x^3+3)^2=25x^6+30x^3+9[/tex]
Since Louise’s answer is [tex](5x^3+3)^2=25x^6+9[/tex], we can conclude that she is missing the term [tex]30x^3[/tex]
Answer:
Louise’s answer is not correct. She is missing the term 30x3. When squaring a binomial, it is best to write the product of the binomial times itself. Then you can use the distributive property to multiply each term in the first binomial by each term in the second binomial. Louise also could have used the formula for a perfect square trinomial, which is found by squaring a binomial.
Step-by-step explanation:
factor completely x^3 + 1/8
Answer:
((2 x + 1) (4 x^2 - 2 x + 1))/8
Step-by-step explanation:
Factor the following:
x^3 + 1/8
Put each term in x^3 + 1/8 over the common denominator 8: x^3 + 1/8 = (8 x^3)/8 + 1/8:
(8 x^3)/8 + 1/8
(8 x^3)/8 + 1/8 = (8 x^3 + 1)/8:
(8 x^3 + 1)/8
8 x^3 + 1 = (2 x)^3 + 1^3:
((2 x)^3 + 1^3)/8
Factor the sum of two cubes. (2 x)^3 + 1^3 = (2 x + 1) ((2 x)^2 - 2 x + 1^2):
((2 x + 1) ((2 x)^2 - 2 x + 1^2))/8
1^2 = 1:
((2 x + 1) ((2 x)^2 - 2 x + 1))/8
Multiply each exponent in 2 x by 2:
((2 x + 1) (2^2 x^2 - 2 x + 1))/8
2^2 = 4:
Answer: ((2 x + 1) (4 x^2 - 2 x + 1))/8
[tex]x^3+\dfrac{1}{8}=\\ \\ =x^3+2^{-3} = \\ \\ =x^3+(2^{-1})^3 =\\ \\ = (x+2^{-1})(x^2-2^{-1}x+2^{-2}) = \\ \\ = \Big(x+\dfrac{1}{2}\Big)\Big(x^2-\dfrac{x}{2}+\dfrac{1}{4}\Big)\\ \\ \\ \boxed{a^3+b^3 = (a+b)(a^2-ab+b^2)}[/tex]
Derek's collection: 1950, 1952, 1908, 1902, 1955, 1954, 1901, 1910
Paul's collection: 1929, 1935, 1928, 1930, 1925, 1932, 1933, 1920
Find the indicated measures of center and the measures of variation for each data set. Round your answer to the nearest hundredth, if necessary.
Find the mean, median, range, IQR, MAD for Derek's collection and Paul's collection.
Answer:
Derek:
Mean:1929
Median: 1930
range: 54
IQR: 48
MAD: 23.75
Paul:
Mean: 1929
Median: 1929.5
range: 15
IQR: 6
MAD: 3.5
Step-by-step explanation:
For the Derek's collection:
1. Mean = 1930.375
2. Median = 1930
For the Paul's collection:
1. Mean = 1929.75
2. Median = 1931
For Derek's collection:
Mean:
Add up all the numbers and divide by the total number of numbers:
Mean = (1950 + 1952 + 1908 + 1902 + 1955 + 1954 + 1901 + 1910) / 8
= 1930.375
Median:
The median is the middle value of the set, so we first need to put the numbers in order:
1901, 1902, 1908, 1910, 1950, 1952, 1954, 1955
The median is the average of the middle two numbers, which are 1910 and 1950:
Median = (1910 + 1950) / 2
= 1930
For Paul's collection:
Mean:
Add up all the numbers and divide by the total number of numbers:
Mean = (1929 + 1935 + 1928 + 1930 + 1925 + 1932 + 1933 + 1920) / 8
= 1929.75
Median:
The median is the middle value of the set, so we first need to put the numbers in order:
1920, 1925, 1928, 1929, 1930, 1932, 1933, 1935
The median is the average of the middle two numbers, which are 1930 and 1932:
Median = (1930 + 1932) / 2
= 1931
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3x+1+5x=7+15+7x what is x?
Answer:
x = 21Step-by-step explanation:
3x + 1 + 5x = 7 + 15 + 7x combine like terms
(3x + 5x) + 1 = (7 + 15) + 7x
8x + 1 = 22 + 7x subtract 1 from both sides
8x = 21 + 7x subtract 7x from both sides
x = 21
Answer:
X= 21
Step-by-step explanation:
First you want to add alike terms which will get you 8x+1=22+7x. Next you want to get your x on one side so I subtracted 7x which you get x+1=22. Last you want to get rid of your 1 to get x alone so you subtract 1 from both sides and you get x=21.
A gas at 89°C occupies a volume of 0.67 L. At what Celsius temperature will the volume increase to 1.12 L?
Answer:
V1 / T1 = V2 / T2
0.67 / (273 + 89) = 1.12 / (273 + t )
t = 332 °C
Given values:
Volume,
[tex]V_1 = 0.67 \ L[/tex][tex]V_2 = 1.12 \ L[/tex]Temperature,
[tex]T_1 = 89^{\circ} C \ or \ 362 \ K[/tex][tex]T_2 = \ ?[/tex]We know the relation,
→ [tex]\frac{V_1}{T_1} = \frac{V_2}{T_2}[/tex]
By substituting the values, we get
→ [tex]\frac{0.67}{362} = \frac{1.12}{T_2}[/tex]
→ [tex]T_2 = \frac{1.12\times 362}{0.67}[/tex]
[tex]= 332^{\circ} C[/tex]
Thus the answer above is right.
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A house worth $70,000 when purchased was worth $67,000 after the first year and $64,000 after the second year. If the economy does not improve and this trend continues, what will be the value of the house after 7 years? a) Write an explicit formula for the sequence. Explain where you found the numbers you are putting in the formula. b) Identify the value of n and explain where you found it. Use the explicit formula to solve the problem.
Answer:
a) The formula for the sequence is
[tex]a_n = 67,000 -3,000(n-1)[/tex]
b) [tex]a_7 = 49,000[/tex]
Step-by-step explanation:
Note that the difference between any two consecutive terms in the sequence is always equal to $3,000
[tex]67,000-70,000= -3,000\\\\64,000-67,000=-3,000[/tex]
Then we have an arithmetic sequence where each term increases by a magnitude of 3,000 with respect to the previous term.
The explicit formula for an arithmetic sequence is:
[tex]a_n = a_1 +d(n-1)[/tex]
Where d is the common difference between the consecutive terms of the sequence
[tex]d = -3,000[/tex]
[tex]a_1[/tex] is the first term, or the value of the house after year 1 [tex]a_1= 67,000[/tex]
n represents the number of years since the house was purchased
With
n={0, 1, 2, 3, 4, 5, 6, 7,.., n}
a) Then the formula for the sequence is
[tex]a_n = 67,000 -3,000(n-1)[/tex]
With
n={0, 1, 2, 3, 4, 5, 6, 7,.., n}
---------------------------------------------------------------------------------------------
b) Now we can use the formula to find the price of the house after 7 years
[tex]a_7 = 67,000 -3,000(7-1)[/tex]
[tex]a_7 = 67,000 -3,000(6)[/tex]
[tex]a_7 = 49,000[/tex]
In which step did his first error occur?
Anani used 10 as an anchor to find the difference of 16 and
7. His steps are shown.
Step 1: The phrase "difference of" means subtraction.
Step 2: 16-6 = 10
Step 3: Since 7 is 1 more than 6, 1 more needs to be added
to 10.
Step 4: Therefore, 16 - 7 = 11.
OOOO
Step 1
Step 2
Step 3
Step 4
Answer:
Step 3
Step-by-step explanation:
16-7=9 he just miscalculated this equation
Answer:
Option 3.
Step-by-step explanation:
It is given that Anani used 10 as an anchor to find the difference of 16 and 7.
The correct steps are
Step 1: The phrase "difference of" means subtraction.
Step 2: 16-6 = 10
Step 3: Since 7 is 1 more than 6, 1 more needs to be subtracted
to 10.
16-6-1 = 10-1
Step 4: Therefore, 16 - 7 = 9.
Anani did his first error in step 3.
Therefore, the correct option is 3.
Bert is planning to open a savings account that earns 1.6% simple interest yearly. He wants to earn exactly $192 in interest after 2 years. How much money should be deposit?
Answers:
A: $6,000
B: $600
C: $60
D: $3,072
B is correct. Hope I helped yah.
2y-9x= 14 what’s y??
Answer:
the answer is y= 9/2 x+7
Did you mean the interception or solve for? Anyway I'll do both.
Solve for y:
[tex]
2y-9x=14\Longrightarrow 2y=14+9x \\
2y=14+9x\Longrightarrow y=\frac{14+9x}{2} \\ \boxed{y=7+\frac{9x}{2}, x\in\mathbb{R}}
[/tex]
Intercept: [tex]2y-9x=14\Longrightarrow2y=14\Longrightarrow y=7[/tex]
solve for x cos90=4/x
Final answer:
The equation cos(90°) = 4/x has no solution because cos(90°) is 0, and no value of x would satisfy the equation 0 = 4/x.
Explanation:
The student's equation is cos(90°) = 4/x. Knowing that the cosine of 90 degrees (or π/2 radians) is 0, we can substitute that into the equation, which simplifies to 0 = 4/x. This indicates that there is no value of x that would satisfy this equation, as no number multiplied by 0 can result in 4. Therefore, the solution is that there is no solution for x in this equation.
how do i turn 1 and 1 fith in a decimal
Answer:
The answer is 1.2
Step-by-step explanation:
1/5 it basicly stands for 1 ÷ 5
1 ÷ 5 = 0.2
plus the one you already have
1 + 0.2 = 1.2
1.2
Hope this helped!
~Lunar Rose. Moon
Answer:
1.2
Step-by-step explanation:
Take 1/5, or make it larger into 2/10 and divide those.
2/10 is obviously .2, while 1/5 is also .2.
now take the .2+ the 1 we had and you get 1.2
Witch expression is equivalent to (cd)5?
Answer:
Step-by-step explanation:
the expression is equivalent to (cd)5 : c^5×d^5
Find the area of the circle r=6ft
[tex]\text{Hey there!}[/tex]
[tex]\text{Find the area of the circle}[/tex]
[tex]\text{r = 6ft}[/tex]
[tex]\text{Use the pi formula to find it\ } (\bf{\pi})[/tex]
[tex]\text{Pi equals 3.14}[/tex]
[tex]\text{A =\ }\pi r^2 \approx \text{3.14}\times (6)^2[/tex]
[tex]\text{6}^2 =6\times6=36[/tex][tex]\text{3.14}\times\text{36 = 113.04}[/tex]
[tex]\approx\text{Which is rounded to 113}[/tex]
[tex]\boxed{\boxed{\text{Answer: A. 113.04 ft}^2}}\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
Please help and thank you
Answer:
D. The equation represents an arithmetic sequence because the successive y-values have a common difference of 6.Step-by-step explanation:
y = 6x - 1
f(n) = 6n - 1
f(n + 1) = 6(n + 1) - 1 = 6n + 6 - 1 = 6n + 5
f(n + 1) - f(n) = (6n + 5) - (6n - 1) = 6n + 5 - 6n + 1 = 6 = constant
50 POINTS! HELP! A restaurant manager is planning a new layout for the tables in his store. He will be placing tables of 2, tables of 4, and tables of 6 throughout the dining room. To help him decide how many of each he needs, he decides to keep track of all table requests by customers during a 2-week period. Which measure of central tendency would BEST indicate the typical table size needed?
A) mean
B) median
C) mode
D) range
Answer:
The best possible answer for this would be: D. Mode.
This is because mode measures how many times each number appears.
Answer:
mine said c is the correct answer
Step-by-step explanation:
triangle ABC is congruent to triangle DEF
Answer:
m<A = m<D
Step-by-step explanation:
This is the correct answer to your question.
Hope this helps!!!
Kyle.
a building casts a shadow that is 348 meters long at the same time a person who is 2 meters tall casts a shadow that is 6 meters long how tall is the building A.) 1044m B.) 116m C.) 64 m D) 100n
Answer:
Option B. [tex]116\ m[/tex]
Step-by-step explanation:
Let
x------> the height of the building
we know that
using proportion
[tex]\frac{2}{6}=\frac{x}{348} \\ \\x=348*2/6\\ \\x=116\ m[/tex]
Which of the following statements a true of the following f(x)=(x+5)(x-3)
Oodoososososo o mi o mi o mi o my ha
In a bus there is, A pregnant lady 24 years old A security guard 37 years old A random woman 56 years old Driver 68 years old Who is the youngest?
Answer:
The baby
Step-by-step explanation:
If you count the baby inside the pregnant woman, then he is the youngest.
hahha funny the baby of course
I need help please.
Answer:
No
Step-by-step explanation:
No it is not the correct answer.
PLEASE ANSWERRRRRRR! THANKS!!!!!!!!!!!!!!!!!!!!!!
Solve for x.
57 = 3x + 12
57-12= 3x+12-12
45=3x
Divide by 3
x=15
Check answer
57= 3(15)+12
57=57
Answer is correct.
x= 15