The composition of functions evaluated in x = 3 is equal to -8.
t(3) = -8.
How to evaluate the composition of functions?Here we have the two functions g(x) and f(x), and the composition:
(g°f)(x) = t(x).
This is equal to:
t(x) = g(f(x))
Then:
t(3) = g( f(3) )
Evaluating f(x) in 3 we get:
f(3) = 4*3- 6 = 12 - 6 = 6
Then:
t(3) = g( f(3)) =g(6)
And we know that g(6) = -8, then:
t(3) = -8.
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Write a problem that could be solved by finding 5/8 divided by 2/5.
Answer:107/56 is the answer
look at the image
answer options are:
(a) and (b)
Neither
Only (a)
Only (b)
Answer: (a) only
Step-by-step explanation:
For there to be inverse proportion, the product of x and y must be constant.
hey what is 159 x 26
Question - For the functions f(x) = 5x and g(x) = 4x − 5, find (f o g)(x) and (g o f)(x)
provide your answer.
(f o g)(x)= , (g o f)(x)=
Which pair of angels are alternate exterior angles
○ <1and <2
○ <1and<7
○ <2and<7
○ <2and<5
∠2 and ∠7 are a pair of angels are alternate exterior angles .
A transversal that crosses two parallel lines results in alternate exterior angles.
They form two pairs of alternate outside angles since they are situated "outside" the two parallel lines but on different sides of the transversal (four total angles).When a third line, a transversal, separates two lines, the expression "alternating exterior angles" is frequently used. The alternate exterior angles theorem states that pairs of alternate exterior angles are congruent if k and l are parallel. A: One of two internal angles inside the two intersecting lines, also known as an alternate internal angle. B: One of two angles with distinct vertices that are on opposite sides of a transversal at the intersection of two other lines.So from the given figure the pairs of external alternate angles are:
∠1 and ∠8
∠2 and ∠7
Hence of the given options , ∠2 and ∠7 is the required external alternate angles .
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what are all the subsets of the set {-3,6}
The subsets of the set {-3, 6}, which are proper subsets is the option;
∅, {-3}, {6}What is a set in mathematics?A set is a model that represents a collection of mathematical objects such as numbers, lines, symbols, points, other sets, variables, or shapes.
In set theory, a set A is a subset of the set B if all the elements or members present in set A can be found in set B. Therefore, set B is said to contain set A or set A is contained in set B.
The above relationships can be expressed using examples as follows;
Let set A = {X, Y} and let set B = {X, Y, Z}, then set A is a subset of set B because the elements, X, Y, contained in set A, are also contained in set B,
Generally, the number of proper subsets of a set that contains n elements is [tex] {2}^{n} - 1[/tex]
Given that the subset of a set which is not a proper subset is the set of itself.
The given set is; {-3, 6}
The number of elements in the set, n = 2
Therefore;
The number of proper subsets = 2² - 1 = 3
All the subsets of {-3, 6} are therefore;
∅, {-3}, {6}
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1. evaluate (a-2b)^3 when a = -3 and b = - 1/2 enter the answer
2. evaluate (jk - 1) ÷ j when j = -4 and k = -0.9 enter as a decimal
3. evaluate -|a+b| /fraction line/ 2-c when a =1 7/8 , b = -1 , and c = -4 enter as a simplified fraction
4. evaluate (w^2 /fraction line/ x - 3) ÷ 10 multiplied by z when w = -9 , x = 2.7 , and z= -2/5 enter as simplified mixed number
5. evaluate (2a - 1/3) ÷ b/15 when a = -2/5 and b = -8.25 enter as simplified mixed number
The corresponding values of expressions 1, 2,3,4 and 5 when evaluated are -2, -0.65, -7/48, 67 1/2 and 2 2/33
How to evaluate algebraic expressions?1. To evaluate (a-2b)^3 when a = -3 and b = - 1/2, put a = -3 and b = - 1/2 into the expression (a-2b)^3:
(a-2b)^3 = ( -3 - 2(-1/2) )
= (-3 + 1) = -2
2. To evaluate (jk - 1) ÷ j when j = -4 and k = -0.9, put j = -4 and k = -0.9 into the expression (jk - 1) ÷ j:
(jk - 1) ÷ j = ( -4(-0.9) - 1) ÷ (-4)
= (3.6 -1) ÷ (-4) = (2.6) ÷ (-4) = -0.65
3. To evaluate -|a+b| / 2-c when a =1 7/8 , b = -1 , and c = -4 , put b = -1 , and c = -4 into the expression -|a+b| / 2-c:
-|a+b| / 2-c = -|1 7/8 + (-1)|/ 2 -(-4)
= -| 7/8 | / 6 = -7/48
4. To evaluate (w^2 / x - 3) ÷ 10 multiplied by z when w = -9 , x = 2.7 , and z= -2/5:
(w^2 / x - 3) ÷ 10z = ((-9)²/ 2.7 -3) ÷ 10(-2/5)
= (81/(-0.3)) ÷ (-4) = -270/-4 = 67 1/2
5. To evaluate (2a - 1/3) ÷ b/15 when a = -2/5 and b = -8.25:
(2a - 1/3) ÷ b/15 = (2(-2/5) - 1/3) ÷ -8.25/15
= (-4/5 - 1/3) ÷ (-11/20) = -17/5 ÷ (-11/20) = 2 2/33
Therefore, the expressions 1, 2,3,4 and 5 evaluate to -2, -0.65, -7/48, 67 1/2 and 2 2/33 respectively
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Find the x intercepts of the graph of the function.
g(x)=1/4(x-6)(x-3). Hint x intercepts happen when g(x)=0.
The x intercepts of the function given in the question will be equal to x = 6 and x = 3.
A function may be defined as an entity in which for one value of input there is only one value of output. The input value is the value of x variable, or the independent variable and the output value is the value of y variable or the dependent variable. For example, f(x) = y = x + 2, in this function for the value of input x = 1 the value of output is y = 3. The x intercept of a function may be defined as the point on the graph at which the line of function crosses the x axis. For finding the x intercept the y value or the value becomes zero. We are given the function g(x) = (1/4) (x - 6) (x - 3)
Now, g(x) = 0
(1/4) (x - 6) (x - 3) = 0
=> (x - 6) (x - 3) = 0
=> x = 6 and x = 3
Therefore, x intercepts are x = 6 and x = 3.
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question linked in pic
iven:
heere are given that the population in the year 2000 was 12000 and the growth rate is 7% per year.
xplanation:
ccording to the question:
For t =0 which is the year 2000:
[tex]P(0)=12000[/tex]For t = 1:
[tex]P(1)=12000+7\%(12000)[/tex]If we say r is the rate, then:
[tex]\begin{gathered} P(1)=12000+r(12000) \\ P(1)=12000(1+r) \end{gathered}[/tex]Then,
For t = 2:
[tex]\begin{gathered} P(2)=12000(1+r)(1+r) \\ P(2)=12000(1+r)^2 \end{gathered}[/tex]And,
For t = 3:
[tex]P(3)=12000(1+r)^3[/tex]Therefore our function should be:
(a):
he population function:
[tex]P(t)=12000(1.07)^t[/tex]Now,
(b):
ccording to the question:
2008 is 8 year from year 2000:
Therefore, t = 8:
Then,
Put the value 8 for t into the function (a):
[tex]\begin{gathered} P(8)=12000(1.07)^t \\ P(8)=12000(1.07)^8 \\ P(8)=12000(1.718) \\ P(8)=20616 \end{gathered}[/tex]inal answer:
[tex]P(t)=12000\times(1.07)^{t-2000}[/tex]which equation are correct select each other answer
Answer:
A and D (the top one and the bottom one)
Step-by-step explanation:
You do not multiply the exponents when the two terms are be multiplied. Instead, you add the exponents. For example, in the first problem, the terms being multiplied are [tex]5y^4[/tex] and [tex]2y^5[/tex]. The exponents are 4 and 5, and when you add them together, that is the exponent that y should carry in the answer.
Hope this helps you! May I please get a brainliest?
How to find the slope of a graph? 9 and 10
9. To draw the rise, you can follow these steps:
- Identify a point on the line. In this case, this can be:
[tex](-3,1)[/tex]- Draw a vertical line that rises from that point. See the picture below:
10. To draw the line that represents the run, you need to Draw a horizontal line that goes from the endpoint of the line that represents the rise and extend it until it touches the function. See the picture below:
Therefore, the answers are (See the picture):
Trey buys a bag of cookies that contains 4 chocolate chip cookies, 6 peanut butter cookies, 7 sugar cookies and 7 oatmeal cookies.What is the probability that Trey reaches in the bag and randomly selects a sugar cookie from the bag, eats it, then reaches back in the bag and randomly selects an oatmeal cookie? Give your answer as a fraction, or accurate to at least 4 decimal places.
Solution
The total number nof cookies in the bag is:
[tex]4+6+7+7=24\text{ cookies}[/tex]- Thus, we can write the probabilities of choosing any of the cookies are given as:
[tex]\begin{gathered} P(\text{chocolate chip)}=\frac{4}{24} \\ \\ P(\text{Peanut Butter)}=\frac{6}{24} \\ \\ P(\text{Sugar Cookies)}=\frac{7}{24} \\ \\ P(\text{Oatmeal)}=\frac{7}{24} \end{gathered}[/tex]- Now, let us analyze Trey's random choices
Choice 1:
He chose a sugar cookie at first.
- Thus, the probability of this choice is
[tex]P(\text{Sugar Cookies})=\frac{7}{24}[/tex]Choice 2:
- He chose an oatmeal cookie in the second choice.
- But he already had one cookie before this choice, thus, the total number of cookies is one less. That is, 23 not 24.
- Thus, the probability of choosing the oatmeal cookie is given as:
[tex]P(\text{Oatmeal)}=\frac{7}{23}[/tex]- Because these choices do not interfere with one another (i.e. they are mutually exclusive), we can apply the AND probability formula to calculate the probability that Treys chose a Sugar Cookie first, and then an Oatmeal cookie next.
- The AND probability is given as
[tex]P(A\text{ AND }B)=P(A)\times P(B)[/tex]- Thus, we can find the probability that Trey chooses Sugar Cookies first and Oatmeal Cookie next as follows:
[tex]\begin{gathered} P(\text{Sugar Cookies AND Oatmeal)}=\frac{7}{24}\times\frac{7}{23} \\ \\ P(\text{Sugar Cookies AND Oatmeal)}==\frac{49}{552} \end{gathered}[/tex]Final Answer
The answer is
[tex]P(\text{Sugar Cookies AND Oatmeal)}==\frac{49}{552}[/tex]Ariya likes to play golf. The number of times per year that she plays depends on the price of playing a round of golf, Ariya's income, and the price of other types of entertainment-in particular, the price of going to a movie instead of playing golf. The three demand schedules in the following table show how many rounds of golf per year Ariya will demand at each price per round under three different scenarios. In scenario D1, Ariya's income is $50,000 per year and movies cost $9 each. In scenario D2, Ariya's income is also $50,000 per year, but the price of seeing a movie rises to $11. And in scenario D3, Ariya's income goes up to $70,000 per year, while movies cost $11.
Scenario
Income per year
Price of movie ticket
Price of Golf
$50
$35
$20
D1
$50,000
$9
15
25
40
D2
$50,000
$11
Quantity Demanded
10
15
20
D3
$70,000
$11
15
30
50
Answer:
Using the data under D1 and D2, calculate the cross elasticity of demand for golf at all three prices. (To do this, apply the midpoints approach to the cross elasticity of demand.) At $50, cross elasticity = -2.40 ± 0.05At $35, cross elasticity = -3.00 ± 0.05At $20, cross elasticity = -4.00 ± 0.05Is the cross elasticity the same at all three prices? No. Are movies and golf substitute goods, complementary goods, or independent goods? Complementary goods.b. Using the data under D2 and D3, calculate the income elasticity of demand for golf at all three prices. (To do this, apply the midpoints approach to the income elasticity of demand.) At $50, income elasticity of demand = 1.40 ± 0.05At $35, income elasticity of demand = 2.33 ± 0.05At $20, income elasticity of demand = 3.00 ± 0.05Is the income elasticity the same at all three prices? No. Is golf an inferior good? No, it is a normal good.
The required statement is given as the data tends to the normal good.
Statistics is the study of mathematics that deals with relations between comprehensive data.
Calculate the cross elasticity of demand for golf at each of the three prices using the information under D1 and D2.
At $50, the cross elasticity is equal to -2.40 ± 0.05;
At $35, it is - 3.00± 0.05;
At $20, it is - 4.00 ±0.05.
No golf and movies complementary, independent, or alternative goods complementing products b.
Calculate the income elasticity of demand for golf at each of the three prices using the information under D2 and D3.
At $50, the income elasticity of demand is equal to 1.40±0.05
At $35, it is 2.33± 0.05
At $20, it is 3.00± 0.05
Thus, the required statement is given as the data belong to the normal good.
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i need help plssssssssssddd
Answer:
see explanation
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
(a)
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 3, 0) and (x₂, y₂ ) = (0, - 2) ← 2 points on the line
m = [tex]\frac{-2-0}{0-(-3)}[/tex] = [tex]\frac{-2}{0+3}[/tex] = - [tex]\frac{2}{3}[/tex]
(b)
the y- intercept is the point on the y- axis where the line crosses, that is
y- intercept c = - 2
(c)
y = - [tex]\frac{2}{3}[/tex] x - 2 ← equation of line
Factor the following trinomial.
9x² + 30x + 25
The factor of the trinomial 9x² + 30x + 25 is (3x + 5).
What is Factoring Trinomials?When you factor a trinomial, you change an algebraic expression from a trinomial to a binomial. ax² + bx + c, where a and b are coefficients and c is a constant, is the general expression for a trinomial, which is a polynomial with three terms.
Given trinomial: 9x² + 30x + 25
Factoring the trinomial, we get
9x² + 30x + 25
9x² + 15x + 15x + 25
3x(3x + 5) + 5(3x + 5)
(3x + 5)²
Therefore, (3x + 5) is the factor of the given trinomial.
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Please help I’ll mark you as brainliest if correct!!
Answer:
14, 9, 16
Step-by-step explanation:
from 3 to 10, you add 7
from 10 to 5, you minus 5
from 5 to 12, you add 7
from 12 to 7, you minus 5
so the pattern is add 7, minus 5
7 plus 7 is 14
14 minus 5 is 9
9 plus 7 is 16
A chef needs 3/4 of a cup of flour for her recipe, but her 1/4 cup measure is missing. Which method could she use to measure an equivalent amount?
The method that she could use to measure an equivalent amount is to remove 25% from the measurement used.
How to calculate the fraction?From the information, the chef needs 3/4 of a cup of flour for her recipe, but her 1/4 cup measure is missing.
Therefore, the method that she could she use to measure an equivalent amount will be to subtract 25% from whatever value that she is using.
It should be noted that 3/4 to percentage will be:
= 3/4 × 100.
= 75%
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Let f(x) =[tex]2x^2-2x-1[/tex]. At which points does the graph of the f(x) have a horizontal tangent line?
The graph has the horizontal tangent line at the the turning point(stationary point) And we know that at the turning point the gradient is 0. We can find the gradient of f(x0 by the first derivative. As I said the gradient a the turning point is 0 meaning since f'(x) =m and m=0 ∴f'(x)=0
[tex]f'(x)=4x-2\\0=4x-2\\4x=2\\\frac{4x}{4}=\frac{2}{4} \\x=\frac{1}{2}[/tex]
Now we know that in order to find the point where x = [tex]\frac{1}{2}[/tex] we can substitute the value of x in the original equation
[tex]f(\frac{1}{2})=2(\frac{1}{2} )^{2} -2(\frac{1}{2} )-1\\f(\frac{1}{2} )=-\frac{3}{2}[/tex]
The answer is [tex](\frac{1}{2} ,-\frac{3}{2} )[/tex]
Hope I helped.
Lines A and B are parallelA155°34fB5 67 8m 27 = [ ? ]°
From the diagram we notice that the angle of 55° is vertical opposite to angle 3, hence they are equal.
Also from the diagram we notice that angles 3 and 6 are alternate interior angles and since lines A and B are parallel then they are equal.
Finally angle 6 and angle 7 are vertical opposite, which means they are equal.
Therefore, the value of angle 7 is 55°
Using the DMS method to describe an angle, one degree of angle measurement can be divided into how many minutes?
A.100'
B.360'
C.60'
D.90'
Answer: I am 97% sure it's D
Step-by-step explanation:
If the ratio of girls to boys on the trackteam is 5 to 6, which of these showspossible numbers of girls to boys onthe track team?A 24 girls, 20 boysB 50 girls, 56 boysC 60 girls, 50 boysD 20 girls, 24 boys
The ratio of 5 to 6 means that for every 5 girls on the track team there are 6 boys.
So, if there are n groups of 5 girls, there should be also n groups of 6 boys. Thus, we have the proportion:
[tex]\frac{\text{ number of girls}}{\text{ number of boys}}=\frac{5}{6}[/tex]Then, let's check each item to find out which one shows possible numbers of girls to boys on the track team.
A. 24 girls, 20 boys
[tex]\frac{\text{ number of girls}}{\text{ number of boys}}=\frac{24}{20}=\frac{24\colon4}{20\colon4}=\frac{6}{5}\ne\frac{5}{6}[/tex]B. 50 girls, 56 boys
[tex]\frac{\text{ number of girls}}{\text{ number of boys}}=\frac{50}{56}=\frac{50\colon10}{56\colon10}=\frac{5}{5.6}\ne\frac{5}{6}[/tex]C. 60 girls, 50 boys
[tex]\frac{\text{ number of girls}}{\text{ number of boys}}=\frac{60}{50}=\frac{60\colon10}{50\colon10}=\frac{6}{5}\ne\frac{5}{6}[/tex]D. 20 girls, 24 boys
[tex]\frac{\text{ number of girls}}{\text{ number of boys}}=\frac{20}{24}=\frac{20\colon4}{24\colon4}=\frac{5}{6}[/tex]Therefore, option D is correct.
You bought 6 tickets for $40 and wanted to know how many tickets you could get for $200,
you would write the following proportion:
Answer:
30
Step-by-step explanation:
200/40=5
5x6=30
therefore there are 30 tickets you could get with 400$
hope this helped
have a great day ^^
Answer:
30 tickets
Explanation:
One ticket can be represented as variable t.
Using t, we can set up an equation (proportion) using the given information:
[tex]6t = \$ 40[/tex]
Then, we can multiply both sides of the equation (proportion) by something such that the number of dollars on the right side is $200.
[tex]6t \ = \ \$ 40 \\\times 5 \ \ \ \times 5[/tex]
[tex]30t = \$ 200[/tex]
So, we can get 30 tickets for $200.
If the price of cord of firewood starts at $255 with a quantity supplied of 300 cords, then rises to $348 per cord, what is the new quantity supplied at this price? Assume the slope of the supply curve is 0.75. Round your answer to the nearest cord. A cord of firewood is a stack of wood 4 feet high x 8 feet long x 4 feet deep.
The new quantity supplied when the price is $348 per cord is 424.
What is the new quantity supplied?The supply curve is a graph that shows the relationship between price and quantity supplied. The supply curve has a positive slope.
The slope of the supply curve is the ratio of the change in the value of price divided by the change in the value of the quantity supplied.
Slope = change in price / change in quantity supplied
0.75 = ($348 - $255) / change in quantity supplied
0.75 = $93 / change in quantity supplied
change in quantity supplied = 93 / 0.75 = 124
The new quantity supplied = 300 + 124 = 424
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Mr. Jackson earns $10 per hour working in an electronics store. In addition, he earns 5% commission on all of his computer sales. Last week, he worked 5 days from 9 am to 3 pm and sold $3,100 worth of computers. What was Mr. Jackson's total income for the week?
At a sale, shirts were sold for $15 each. This price was 20% off their original price. What was the original price?
Answer:
The original price was 18 dollars.
Step-by-step explanation:
Givens
Final price = 15 dollars
Discount = 20%
Original Price = x
Formula
x = 15 + 20/100 15
Solution
x = 15 + 300/100 Multiply 20 * 15. Divide by 100
x = 15 + 3
x = 18
An investment portfolio is shown below.
Investment Amount Invested ROR
Savings Account $3,200
2.1%
Municipal Bond $4,900
4.5%
Preferred Stock
$940
10.5%
Common Stock A $1,675
-3.5%
Using technology, calculate the weighted dollar amount of the savings account.
O-$58.63
$58.63
O-$67.20
O $67.20
The weighted dollar amount of the savings account as per the an investment portfolio given is equal to $67.20.
As given in the question,
An investment portfolio is shown below.
Investment Amount Invested ROR
Savings Account $3,200 2.1%
Municipal Bond $4,900 4.5%
Preferred Stock $940 10.5%
Common Stock A $1,675 -3.5%
The weighted dollar amount of the savings account is equal to :
= 2.1% of $3200
= ( 2.1 / 100) × $3200
= ($6720) /100
= $ 67.20
Therefore, the weighted dollar amount of the savings account as per the an investment portfolio given is equal to $67.20.
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Adam is baking 4 pizzas. Each pizza is a rectangle. It takes Adam 35 minutes to bake the pizzas. He divides each pizza into the equal-size square slices shown.
Answer:
Step-by-step explanation:
Incomplete question.
Can someone please help me with this, it’s geometry by the way
Answer:
congruent: a° and c°; d° and b°
Supplementary: c° and b°; a° and b°; a° and d°; c° and d°
Step-by-step explanation:
Please help I’ll mark you as brainliest if correct!!
Answer:
1, 7, 13, 19, 25, 31, 37, 43
Step-by-step explanation:
it is increasing by 6 each time so you add 6 three more times.
Chelsy wants to buy a new pair of jeans in one store the jeans are selling for 1/5 off the original price of $70 in second store the same jeans are selling for 1/3 off the original price $81 chelsy wants to buy the cheaper pair of jeans in which store should chelsy buy the jeans and how much will they cost
iN linear equations, store 1 jeans is cheaper than store 2.
What are instances of linear equations?
Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5.When an equation is given in this format, finding both intercepts is rather simple (x and y).When attempting to solve systems involving two linear equations, this form is also quite helpful.one store the jeans are selling for 1/5 off the original price of $70
$70 * 1/5 = 14
second store the same jeans are selling for 1/3 off the original price $81
$81 * 1/3 = 27
So, store 1 jeans is cheaper than store 2.
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