The value of (fxg)(-3) if f(x)=5x-1 and g(x) =2x^2+1 will be 94.
What is a function?A function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. Let A & B be any two non-empty sets; mapping from A to B will be a function only when every element in set A has one end, only one image in set B. It is a relation “f” in which each element of set “A” is mapped with only one element belonging to set “B”. Also in a function, there can’t be two pairs with the same first element.
f(x)=5x-1
g(x) =2x^2+1
fxg = 5(2x^2+1) - 1
fxg = 10x^2 + 5 - 1
fxg = 10x^2 + 4
fxg(-3) = 10(-3)^2 + 4
fxg(-3) = 10(9) + 4
fxg(-3) = 90 + 4
fxg(-3) = 94
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Edgar works in the shipping department of a toy manufacturer. Toy cars weigh 6 pounds apiece and are shipped in a container that weighs 5 pounds when empty. Toy trucks, which weigh 3 pounds apiece, are shipped in a container weighing 20 pounds. When packed with toys and ready for shipment, both kinds of containers have the same number of toys and the same weight. What is the number of toys?
The number of toys is 5 in each container.
What is an Equation?An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.
Let x be the number of toys in each container.
Weight of one toy car = 6 pounds
Weight of the container in which toy cars shipped = 5 pounds
Weight of x toy cars = 6x
Total weight of the container when toy cars are placed = 6x + 5
Weight of one toy truck = 3 pounds
Container weight = 20 pounds
Weight of x toy trucks = 3x
Total weight of the container when toy trucks are place = 3x + 20
Given that both containers have same weight.
6x + 5 = 3x + 20
6x - 3x = 20 - 5
3x = 15
x = 5
Hence the number of toys in each container is 5.
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please help quickly!!!A shuffled deck of cards is placed face-down on the table. It contains 5 hearts, 6 diamonds, 4 clubs and 3 spades. What is the probability that the top two cards are both spades?.
The probability of getting two spades when two cards are drawn from the deck is 1/17.
What is probability?Probability branch of mathematics the deal with the likewood of an event occouring. It is the measure of how likely it is something will happen or be the case. Probabilities expressed as a number between zero and one 00 indicates impossibility and one indicus certainity. Probability can be used to calculate the chances of certain outcome based on a state condition or data. Probability can also be used to make decision and prediction about the future.
The probability of getting two spades when two cards are drawn from a shuffled deck of cards is 3/52 x 2/51, or 1/17.
This is because there is a 3/52 chance of getting the first spade and a 2/51 chance of getting the second spade (since there is one less card in the deck).
Therefore, the probability of getting two spades when two cards are drawn from the deck is 1/17.
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Translate the following phrase into an algebraic expression. Do not simplify. Use the variable name x or y to describe the unknowns
5 times a number, divided by 6
Answer: The phrase "5 times a number, divided by 6" can be translated into the algebraic expression:
(5/6)x
This expression represents "5 times a number, divided by 6", where x is the unknown number.
Step-by-step explanation:
A baker makes 60 muffins. He sells 24 of the muffins.
He put the rest of the muffins in boxes. Each box can hold 4 muffins.
Which equation can be used to find b, the number of boxes the baker will need?
OA.
B.
OC.
OD. (60
60+ 24 ÷ 4 = b
60 24 ÷ 4 = b
-
(60+24) ÷ 4 = b
24) = 4 = b
-
Answer:c
Step-by-step explanation:
c
Answer:b
Step-by-step explanation:
write an equation of the line that passes through (4,3) and is parallel to the line y=1/4x+10
keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above
[tex]y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{1}{4}}x+10\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
so we're really looking for the equation of a line whose slope is 1/4 and that it passes through (4 , 3)
[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{3})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{4} \\\\\\ \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-\stackrel{y_1}{3}=\stackrel{m}{ \cfrac{1}{4}}(x-\stackrel{x_1}{4}) \\\\\\ y-3=\cfrac{1}{4}x-1\implies {\Large \begin{array}{llll} y=\cfrac{1}{4}x+2 \end{array}}[/tex]
1. The flight of Jae and Miguel's rocket t seconds after launch is modeled by
h(t) = -5t² + 40t + 1, where h(t) is their rocket's height in meters.
What was their rocket's height in meters 0.5 seconds after launch?
19.75 meters is the rocket's height when it has 0.5 seconds after launch
What is a function?A relation is a function if it has only One y-value for each x-value.
Given that The flight of Jae and Miguel's rocket t seconds after launch is modeled by
h(t) = -5t² + 40t + 1
h(t) is their rocket's height in meters.
we have to find the rocket's height in meters 0.5 seconds after launch
Put t=0.5 in the above function.
h(0.5)=-5(0.5)² + 40(0.5)+ 1
=-5(0.25)+20+1
=-1.25+20+1
=19.75
Hence, 19.75 meters is the rocket's height when it has 0.5 seconds after launch
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????What’s the answer??
Answer: d
Step-by-step explanation: -5 is the intercept since x is 0 above it.
using the y2-y1 / x2-x1 we will get 2/4 (1/2 when simplified).
Question 4(Multiple Choice Worth 2 points)
(Slope LC)
What is the slope of the line that contains the points (2, -8) and (-4,4)?
2
1/2
-1/2
-2
Answer:
the slope is -2
Step-by-step explanation:
hope this helps!!
x
A
B
C
Number of Cars
4x D
300
Based on the information in this chart, which statement is true?
200
100
0
li
8-10am 10am-12pm 12-2pm
2-4pm
Time of Day
6-8pm
8-10pm
Around the same number of cars are on the busy street between 10 am -12 pm and 6-8 pm.
Around the same number of cars are on the busy street between 10 am - 12 pm and 2-4 pm.
Around the same number of cars are on the busy street between 10 am - 12 pm and 2 - 6 pm.
Around the same number of cars are on the busy street between 10 am- 12 pm and 12 - 2 pm.
Answer:
between 10 am - 12 pm and 2-4 pm.
Let f(x) and g(x) be polynomials as shown below f(x)=a 0 +a 1 x+a 2 x^ 2 ...+a n x^ n; g(x)=b 0 +b 1 x+b 2 x^ 2 ...+b m x^ m Which of the following is true about f(x) and g(x) ? . f(x) and g(x) are not closed under addition because when added, the result will be a polynomial B. f(x) and g(x) are not closed under addition because when added, the result will not be a polynomial_ f(x) and g(x) are closed under addition because when added, the result will not be a polynomial . D. f(x) and g(x) are closed under addition because when added , the result will be a polynomial
Considering the closure under property the polynomials f(x) = a 0 + a 1 x + a 2 x^ 2 ... + a n x^ n; and g(x) = b 0 + b 1 x + b 2 x^ 2 ... + b m x^ m
D. f(x) and g(x) are closed under addition because when added , the result will be a polynomialWhat is closure under property?In mathematics, a set is considered closed if we are able to apply and complete an operation on its components while consistently receiving a component from the same set.
A set therefore either possesses closure for a given mathematical operation or it does not.
Use of real numbers is the closure property of addition. Addition of two real numbers results in areal number
In the given problem, the set considered is polynomial addition and the addition of the two polynomial will give a sum which is a polynomial hence we say it is closed under addition.
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Which graph matches the inequality y is greater than or equal to negative one third times x plus 1? The graph shows a solid line, which crosses the y-axis at 1 and the x-axis at 3, with shading above the line. The graph shows a dashed line, which crosses the y-axis at 1 and the x-axis at 3, with shading above the line. The graph shows a solid line, which crosses the y-axis at 1 and the x-axis at 3, with shading below the line. The graph shows a dashed line, which crosses the y-axis at 1 and the x-axis at 3, with shading below the line.
The graph shows a solid line, which crosses the y-axis at 1 and the x-axis at 3, with shading above the line.
What is the slope-intercept form of a line?The slope-intercept form of a line is represented by y=mx+c where m=slope and c is the y-intercept of the line
Given here: The inequality y≥ -x/3 +1
Now, To graph an inequality, treat the <, ≤, >, or ≥ sign as an = sign, and graph the equation. If the inequality is < or >, graph the equation as a dotted line. If the inequality is ≤ or ≥, graph the equation as a solid line.
Therefore y=-x/3 +1 is a line in slope-intercept form with slope=-1/3 and y-intercept 1
Thus the line should intersect the y-axis at y=1 and the x-axis at x=3
∴ The graph of this equation is plotted in attached file.
Hence, The graph shows a solid line, which crosses the y-axis at 1 and the x-axis at 3, with shading above the line.
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Answer:
A
Step-by-step explanation:
i took the test xx
how much did bleep blair receive in royalties last year
Which of the following is an equivalent expression to 7.5+s using commutative property?
An equivalent expression to 7.5 + s using commutative property is; s + 7.5
How to use the commutative property of algebra?
The commutative property under addition is an algebra property that states that the change in the order of numbers in an addition operation does not change the sum.
This means that for any real numbers x, y, we have;
x + y = y + x
The commutative property under multiplication states that the change in the order of numbers in multiplication operation does not change the product.
This means that for any real numbers c, d we have;
c × d = d × c
We want to find n equivalent expression to 7.5 + s using commutative property. Thus, we will apply the commutative property of addition as followd; 7.5 + s = s + 7.5
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Ravi and Susan each opened a savings account today. Ravi opened his account with a starting amount of $650, and he is going to take out $40 dollars per month. Susan opened her account with a starting amount of $850 dollars, and she is going to take out $65 per month. Write an expression to show how much money will be in each account after 6 months, and also another to show when the two accounts would have the same amount of money.
The amount in Ravi account after 6 months will be $410.
The amount in Susan account after 6 months will be $460
How to illustrate the expression?From the information, Ravi and Susan each opened a savings account today. Ravi opened his account with a starting amount of $650, and he is going to take out $40 dollars per month. This will be:
650 - 40m
Susan opened her account with a starting amount of $850 dollars, and she is going to take out $65 per month. This will be:
850 - 65m
The amount in Ravi account after 6 months will be;
= 650 - 40(6)
= 410
The amount in Susan account after 6 months will be:
= 850 - 65(6)
= $460
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there is a line that includes the point(1,17) and has a slope of 1. What is its equation in slope-intercept form
An equation of the line in slope-intercept form that passes through the point (1, 17) and has a slope of 1 is equal to y = x + 16.
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁)
Where:
m represents the slope.x and y are the points.Given the following parameters:
Point (x, y) = (1, 17)Slope = 1Substituting the given parameters into the point-slope formula, the equation of the line in is slope-intercept form given by;
y - y₁ = m(x - x₁)
y - 17 = 1(x - 1)
y = x - 1 + 17
y = x + 16
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Please help. I'm really confused on how to solve this.
One batch of brownies calls for 1 box of brownie mix and the ingredients shown.
Fudge-like brownie
2 eggs
1/4 cup of water
1/2 cup of oil
Cake-like brownie
3 eggs
1/4 cup of water
1/2 cup of oil
a. What amounts of eggs, water, and oil would you need for 2 batches of fudge-like brownies?
b. What amounts of eggs, water, and oil would you need for 3 batches of cake-like brownies?
Sorry if it's all confusing. If you don't know, then don't answer. Please answer if you know ASAP.
a) The amounts needed for 2 batches of fudge-like brownies are of:
Eggs: 4.Water: 1/2 cup.Oil: 1 cup.b) The amounts needed for 3 batches of cake-like brownies are of:
Eggs: 9.Water: 0.75 cups.Oil: 1.5 cups.How to obtain the needed amounts?The needed amounts for each case are obtained applying the proportions in the context of this problem.
Hence:
The amounts needed for 2 batches of fudge-like brownies are obtained multiplying the amounts given for 1 box of fudge-like brownie (2 eggs, 1/4 of a cup of water and 1/2 of a cup of oil) by 2.The amounts needed for 3 batches of cake-like brownies are obtained multiplying the amounts given for 1 box of cake-like brownie (3 eggs, 1/4 of a cup of water and 1/2 of a cup of oil) by 3.More can be learned about proportions at https://brainly.com/question/24372153
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The amounts of eggs, water, and oil needed for 2 batches of fudge-like brownies are:
eggs = 4cup of water = 2/4cup of oil = 1The amounts of eggs, water, and oil needed for 3 batches of cake-like brownies are:
eggs = 9cup of water = 3/4cup of oil = 3/2What is the ingredients needed for 2 batches?One batch of Fudge-like brownies:
2 eggs
1/4 cup of water
1/2 cup of oil
One batch of Cake-like brownie
3 eggs
1/4 cup of water
1/2 cup of oil
The amounts of eggs, water, and oil needed for 2 batches of fudge-like brownies can be determined by multiplying each ingredients by 2
eggs = 4
cup of water = 2/4
cup of oil = 1
The amounts of eggs, water, and oil needed for 3 batches of cake-like brownies can be determined by multiplying each ingredients by 3
eggs = 9
cup of water = 3/4
cup of oil = 3/2
Therefore, the ingredients needed for the other batches is determined by multiplying each ingredients by the number of required batches.
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10. Which of the following must be true?
Note that in the above mathematical scenario involving two similar triangles, the option that MUST be correct is AC < FH (Option C) This solution is arrived at using the Open Mouth Theorem.
What does the Open Mouth Theorem state?The above-stated Theorem in Geometry asserts that if two sides of two triangles are congruent and the included angle differs, then the greater angle is opposite the longer side.
This theorem is known as the Open Mouth Theorem because it is based on the idea that the two sides of a triangle are "pivoted" at their common vertex.
Please keep in mind that this theorem only works if we know two pairs of sides are congruent like this.
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Classify the variables in the data if it’s (qualitative, nominal, ordinal, quantitative, discrete, or continuous etc)
Answer:
Like
Step-by-step explanation:
1. Nominal
2. Discrete
3. Quantitative
4. discrete
5. discrete
6. Qualitative
The surface area of an open-top box with length
L
, width
W
, and height
H
can be found using the formula:
A
=
2
L
H
+
2
W
H
+
L
W
Find the surface area of an open-top box with length 3 cm, width 5 cm, and height 7 cm.
The surface area of the open top box is 127 cm².
What is Surface Area?The area of a three dimensional object on it's outer surface is called the surface area of the object.
Given that,
Surface area of the open-top box = 2LH + 2WH + LW, where L is the length, W is the width and H is the height.
L = 3 cm
W = 5 cm
H = 7 cm
Surface area = (2 × 3 × 7) + (2 × 5 × 7) + (3 × 5)
= 42 + 70 + 15
= 127 cm²
Hence the surface area of the given open top box is 127 cm².
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Unsure how to do my Algebra homework!
On solving the exponential function 16000 = P(0.9455)^t, the original value of the car is obtained as $18,930.
What is an exponential function?
The formula for an exponential function is f(x) = a^x, where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.
The value of car in amount is A(t) = $16,000.
The rate of depreciation is x = 5.45% per year.
Rewriting the rate in exponential form - (1 - 0.0545) = 0.9455
The car is t = 3 years old.
Let P be the model that depicts the original cost of the car.
Then the exponential function will be -
16000 = P(0.9455)^t
Substituting the value of t in the equation -
16000 = P(0.9455)³
16000 = 0.8452P
P = 16000/0.8452486
P = 18,929.34 ≈ 18,930
Therefore, the original value of car was $18,930.
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A contractor bought 8.2^2 ft of sheet metal. has used 3.7^2 ft so far and has $90 worth of sheet metal remaining. The equation 8.2x - 3.7x = 90 represents how much sheet metal is remaining and the cost of the remaining amount. How much does sheet metal cost per square foot?
Answer:
$20 per square foot
Step-by-step explanation:
[tex]8.2x-3.7x=90 \\ \\ 4.5x=90 \\ \\ x=20[/tex]
Multiply.
8×35
Enter your answer as a mixed number in simplest form by filling in the boxes
PLS HELP
Answer:
280
Step-by-step explanation:
Answer:
8×35=280.
This is the best I can give to you
An animal shelter has 1008 cats, dogs and rabbits. The ratio of the number of dogs to the number of cats in the animal shelter is 3:7. The ratio of the number rabbits to the number of dogs is 2:5. How many rabbits are in the shelter
There are 108 rabbits in the shelter.
What is mean by Ratio?A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y. Where, x and y are individual amount of two quantities. And, Total quantity gives after combine as x + y.
We have to given that;
An animal shelter has 1008 cats, dogs and rabbits.
And, The ratio of the number of dogs to the number of cats in the animal shelter is 3 : 7. The ratio of the number rabbits to the number of dogs is 2 : 5.
Here, The ratio of the number of dogs to the number of cats in the animal shelter is 3:7. The ratio of the number rabbits to the number of dogs is 2:5.
So, We can formulate;
Number of dogs : Number of cats = 3 : 7
Number of rabbits : Number of dogs = 2 : 5
Hence, We get;
Number of rabbits : Number of dogs : Number of cats = 6 : 15 : 35
Since, An animal shelter has 1008 cats, dogs and rabbits.
Hence, We get;
⇒ 6x + 15x + 35x = 1008
⇒ 56x = 1008
⇒ x = 18
Thus, Number of rabbits = 6x
= 6 × 18
= 108
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Which of the following points satisfies y < 3x - 6?
(2, -4)
(1,0)
The point (2,-4) satisfies y < 3x - 6
MARKING BRAINLIEST!!!!! The Sea Dragon, a pendulum ride at an amusement park, moves from its central position at rest according to the trigonometric function below, where t represents time, in seconds. F(t) = 20cos (2pi/5)t, how many seconds does it take the pendulum to complete one full cycle?
According to the trigonometric function, F(t) = 20 cos (2π/5)t where t represents time, in seconds. representing the pendulum ride of the sea dragon. It will take the pendulum 5 seconds to complete one full cycle.
What is a period in math?A period on a graph function is the distance between two repeating points.
The graph repeats itself as it advances along the x-axis, as you can see.
Periods are the cycles of this predictable repetition. Every 6.28 units, or 2 pi radians, this graph repeats.
The equation is F(t) = 20 cos (2π/5)t
The amplitude of the equation is 20 and the graph makes 2π/5 oscillations at every t seconds
the period to complete an oscillation which is 2π
2π/5 * t = 2π
t = 2π * 5/2π
t = 5 seconds
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h is defined by the rule
h(x)=2x-3
The complete function table using the defined function rule is as shown below.
How to solve function tables?We are given the function rule as;
h(x) = 2x - 3
From the function table attached, we will need to find the value of the function h(x) at x = -3, -2, 1, 3, 5
Thus;
Plugging in the value of -3 for x in the given function rule gives us the output as;
h(-3) = 2(-3) - 3
h(-3) = -9
Plugging in the value of -2 for x in the given function rule gives us the output as;
h(-2) = 2(-2) - 3
h(-2) = -7
Plugging in the value of 1 for x in the given function rule gives us the output as;
h(1) = 2(1) - 3
h(1) = -1
Plugging in the value of 3 for x in the given function rule gives us the output as;
h(3) = 2(3) - 3
h(3) = 3
Plugging in the value of 5 for x in the given function rule gives us the output as;
h(5) = 2(5) - 3
h(5) = 7
Thus, the complete function table is;
x h(x)
-3 -9
-2 -7
1 -1
3 3
5 7
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Which ordered pairs are solutions to the system of equations (-2,1.6)(0,3 3/5)(2,5 3/5) y=-0.5x+0.6
Y=x+3 3/5
The ordered pairs are solutions to the system of equations are (-2,1.6)
How to determine which ordered pairs are solutions to the system of equations?In order to determine which ordered pairs are solutions to the system of equations, you need to equate the two equations and solve for x:
y = -0.5x+0.6 and y= x+3 3/5
-0.5x+0.6 = x+3 3/5
-0.5x+0.6 = x+3.6
x+3.6 + 0.5x-0.6 = 0
1.5x + 3 = 0
1.5x = -3
x = -3/1.5
x = -2
y =-0.5x+0.6
y = -0.5(-2) + 0.6
y = 1.6
y = x + 3.6
y = -2 + 3.6
y = 1.6
Thus, the ordered pairs are (-2, 1.6)
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What is the value of
Answer:
1
Step-by-step explanation:
[tex](\frac{2}{3} )^{0} =1[/tex]
[tex](1)^{-3} =1[/tex]
Hope this helps
Multiply: (x + 3) (x2 + x – 2)
Answer:
x3+4x2+x-6
Step-by-step explanation:
do it your selve