The value of f(x) + h(x) when f(x) = 2x - 1 and h(x) = x² + 1 is x² + 2x.
Addition of linear functions:
Addition of two individual functions, a(x) and b(x); linearly, results in the formation of the functional addition, c(x) of the two functions, such as:
c(x) = a(x) + b(x) = (a+b)(x) – (i)
The addition of the functions strictly restricts to simple linear addition without any pre-defined constraints.
Given, f(x) = 2x - 1, g(x) = 3x and h(x) = x² + 1
Using the available formula in (i), we get
f(x) + h(x) = (f + h)(x) = (2x - 1) + (x² + 1) = x² + 2x = x(x + 2), which is a quadratic equation.
Thus, the required value of f(x) + h(x) is x² + 2x.
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A triangular boat's sail has a total area of 7 square inches.
If the height of the sail is 3 inches less than twice the
length of its base, then find the length of the base and
height.
Answer: b = 3.5, h = 4
Step-by-step explanation: a = 1/2bh, area of a triangle formula
7 = 1/2((b)(2b-3)) state h in terms of b
7 = 1/2(2b^2-3b) simplify
7 = b^2 - 1.5b simplify
b = 3.5 final answer
Then, solve for h.
h = 7 - 3 substitute
h = 4 final answer
hope this helps!
Step-by-step explanation:
area of a triangle
base × height / 2
in our case
base × height / 2 = 7
base × height = 14
height = 2×base - 3
we can use the last identity in the area equation and get
base × (2×base - 3) = 14
2×base² - 3×base - 14 = 0
the solution to a quadratic equation like
ax² + bx + c = 0
is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
base = (3 ± sqrt((-3)² - 4×2×-14))/(2×2) =
= (3 ± sqrt(9 + 112))/4 = (3 ± sqrt(121))/4 =
= (3 ± 11)/4
base1 = (3 + 11)/4 = 14/4 = 7/2 = 3.5 in
base2 = (3 - 11)/4 = -8/4 = -2
negative numbers for sizes of physical objects don't make sense, so, base = 3.5 in is our solution.
height = 2×base - 3 = 2×3.5 - 3 = 7 - 3 = 4 in
base length = 3.5 in
height = 4 in
ABCD is a quadrilateral.
Work out angle x.
В.
B
8 cm
A
X
6 cm
D
FIND x (
ABCD IS A QUADRILATERAL)
29%
13 cm
C
M= 19.7t² + 310.5t +7539.6
F= 28t² + 368t + 10127.8
modeling with mathematics during a recent period of time, the number (in thousands) of males M and females F that attend degree-granting institutions in the United States can be modeled by M= and F=
where t is time in years. Write a polynomial in standard form to model the total number of people attending degree-granting institutions. The polynomial is P=
Using addition of polynomials, the function modeling the number of people attending degree-granting institutions is:
P(t) = 48.7t² + 678.5t + 17667.4.
What is the function for the total number of people attending the institutions?The number of males is given by:
M(t) = 19.7t² + 310.5t + 7539.6.
The number of females is given by:
F(t) = 28t² + 368t + 10127.8.
The total number is given by the addition of the number of males and of females, that is:
P(t) = M(t) + F(t).
Which is an addition of polynomials. To add the polynomials, we combine the like terms, that is, adding the terms that have the same variable and exponent. Hence:
P(t) = M(t) + F(t).
P(t) = 19.7t² + 310.5t + 7539.6 + 28t² + 368t + 10127.8.
P(t) = 48.7t² + 678.5t + 17667.4.
Which is the desired function.
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Mohal has a loyalty card good for a discount at his local pharmacy. To find the total he has to pay, before tax, he multiplies the prices by 0.96. What percent discount does the card give?
The percent discount the card gives can be:
4% or 96%.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
We have,
Royal card for discount.
Multiplying the total price to pay with 0.96 means two cases.
0.96 = 96/100 = 96%
Cases 1:
If the percent discount is 96% we will multiply the total prices to pay by 0.96 and subtract the value from the total price.
Example:
Total price to pay = 100
0.96 x 100 = 96
Total price to pay = 100 - 96 = 4
Cases 2:
If the percent discount is 4% we will multiply the total prices to pay by 0.96 after subtracting 4% from 100%.
Example:
Total price to pay = 100
Discount = 4%
100% - 4% = 96%
96% = 0.96
Total price to pay = 0.96 x 100 = 96
Thus,
The percent discount the card gives can be:
4% or 96%.
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write four cubed in expanded form and then evaluate
Answer:
64
Step-by-step explanation:
4^3 = 4 x 4 x 4 which can be written as 2^6 which is equivalent to 64 too
(If this is what you're asking)
Two parallel lines are cut by a transversal as shown belc
Suppose m 8 =107 Find m2 1and m2 3
1
2
4
3
5
6
8
7
The values of the angles m∠1 and m∠3 is equal to 73°.
A transversal may be defined as a line which cuts a pair of parallel lines and forms several angles. When transversal cuts parallel lines the alternate interior angles are equal as well as the corresponding angles are equal. Also, the pair of vertically opposite angles are equal. From the figure attached. ∠4 = ∠8 as they are corresponding angles. So, m∠8 = m∠4 = 107°. Now, we know that ∠1 and ∠4 formed a pair of linear angles and the sum of the measures of the linear angles is 180°. So,
m∠1 + m∠4 = 180°
We know, m∠4 = 107°
m∠1 = 180° - 107°
m∠1 = 73°
Now, ∠1 and ∠3 are vertically opposite angles, so they are equal as the parallel lines are cut by transversal. Therefore, m∠1 = m∠3
=> m∠1 = 73°
=> m∠3 = 73°
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Marybeth rides her skateboard 5 miles in 30 minutes. If she maintains this rate, how far will she ride her skateboard in 4 hours?
Using the SSS congruence is criterion what additional information is needed to show that triangle RST is congruent to triangle UTS?
The additional information you will need to show that triangles RST and UTS are congruent by SSS congruence is: c. RT ≅ US.
How to Prove Two Triangles are Congruent by SSS Congruence Postulate?To prove that two triangles are congruent to each other using the SSS congruence as a criteria, we need to know or be able to show that the three sides of one triangle are congruent to the corresponding 3 sides of the other triangle.
If this criterion is met, then we have enough information needed to show the two instruments are congruent by the SSS congruence.
RS ≅ UT as marked in the diagram shown. Also, by the reflexive property, we ST ≅ TS.
We already know two pairs of sides are congruent to each other in both triangles.
In other to prove the triangles are congruent by SSS congruence, the additional information needed is: c. RT ≅ US.
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Answer:
Step-by-step explanation:The additional information you will need to show that triangles RST and UTS are congruent by SSS congruence is: c. RT ≅ US.
How to Prove Two Triangles are Congruent by SSS Congruence Postulate?
To prove that two triangles are congruent to each other using the SSS congruence as a criteria, we need to know or be able to show that the three sides of one triangle are congruent to the corresponding 3 sides of the other triangle.
If this criterion is met, then we have enough information needed to show the two instruments are congruent by the SSS congruence.
RS ≅ UT as marked in the diagram shown. Also, by the reflexive property, we ST ≅ TS.
We already know two pairs of sides are congruent to each other in both triangles.
In other to prove the triangles are congruent by SSS congruence, the additional information needed is: c. RT ≅ US.
3x = 0Graph the line by plotting any two ordered pairs with integer value coordinates that satisfy the equation
we have the equation
3x=0
is the same that
x=0
This is a vertical line (is the equation of the y-axis)
two ordered pairs that lies in this line are
(0,4) and (0,10)
graph the line
plot the points and join them
see the attached figure
A car’s velocity increases from 4.2m/s to 14.8 m/s, E, in 2.5 sec. What is its acceleration?
The acceleration is 4.24 m^2/s
What is acceleration?
They are accelerations and vector quantities. The direction of an object's acceleration is determined by the direction of the net force acting on it. Acceleration describes the rate at which a speed changes over time.
The velocity is changing over time. The velocity is actually changing at a constant rate of 10 m/s per second. If an object's velocity is changing, it is said to be accelerating; it has acceleration.
According to question,
Acceleration = final velocity- initial velocity/ time
Final velocity = 14.8 and initial velocity = 4.2
Hence, acceleration = 14.8-4.2/2.5
=10.6/2.5
=4.24.
The acceleration is 4.24 m^2/s.
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Yall please help i need to turn this in i have too many demerits
The answers to all the subparts are:
(A) 5 cups of yellow paint will be needed with 1 cup of blue paint to make the same green shade.(B) The new pair to make the same shade of green will be 4 cups of blue paint and 20 cups of yellow paint.(C) The proportional relationship of the table will be x : 5y.(D) According to part (C), the Constant of proportionality will be x : 5y.What is constant proportionality?The ratio of two proportional values at a constant value is known as the constant of proportionality. When either their ratio or product results in a constant, two variables' values are said to be proportionally related. The ratio between the two specified quantities determines the value of the proportionality constant.So, (A) To make the same shade of green:
Cups of blue paint: 2Cups of yellow paint: 10Then, cups of yellow paint when blue paint is just 1 cup:
10/2 = 5/1 = 5
Therefore, 5 cups of yellow paint will be needed with 1 cup of blue paint to make the same green shade.
(B) New pair of numbers to make the same green shade:
Old pair:
Cups of blue paint: 2Cups of yellow paint: 10Another pair:
Cups of blue paint: 1Cups of yellow paint: 5The new pair would be:
Cups of blue paint: 2 × 2 = 4Cups of yellow paint: 10 × 2 = 20Therefore, the new pair to make the same shade of green will be 4 cups of blue paint and 20 cups of yellow paint.
(C) Proportional relationship:
Let cups of blue paint be: xCups of yellow paint be: yOld pair:
Cups of blue paint: 2Cups of yellow paint: 10Proportional relationship will be:
2x/10y = x/5y ⇒ x : 5yTherefore, the proportional relationship of the table will be x : 5y.
(D) Constant of proportionality:
According to part (C), the Constant of proportionality will be x : 5y.
Therefore, the answers to all the subparts are:
(A) 5 cups of yellow paint will be needed with 1 cup of blue paint to make the same green shade.(B) The new pair to make the same shade of green will be 4 cups of blue paint and 20 cups of yellow paint.(C) The proportional relationship of the table will be x : 5y.(D) According to part (C), the Constant of proportionality will be x : 5y.Know more about constant proportionality here:
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The animals at a safari park include crocodiles, deer and penguins.
There are 16 more deer than there are crocodiles. 4 There are 3 times as many penguins as there are crocodiles. There are the same number of deer as there are penguins.
How many crocodiles are there at the safari park?
Answer:
8
Step-by-step explanation:
8x3 = 24
8+ 16 = 24
MEAN The mean A of two numbers, x and y, is given by A =*+. Solve for y.
The mean can be written as mean A= x+ y/2
What is Mean?A data set's mean (average) is calculated by summing all of the numbers in the set, then dividing by the total number of values in the set.
Only numerical variables—regardless of whether they are discrete or continuous—can be used to determine the mean. Simply dividing the total number of values in a data set by the sum of all of the values yields it.
The mean formula is
= {Sum of Observation} ÷ {Total numbers of Observations}
Given:
mean A of two numbers, x and y
So, the mean can be written as
mean A= x+ y/2
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Please help or answer questions 2, 3, and 4. You may answer question 1 if you’d like but I do not need it. I have already done question 2 but confirming my answers would be nice. I will give out brainliest.
The ratios that can be used to compare the soda and punch recipes are as follows;
1. Emily:
Mason's recipe for soda is y = (1/2)•x
Tyler's recipe; y = (3/5)•x
Julio's
Mason's recipe; y = (1/3)•x
Tyler's recipe; y = (3/8)•x
2. Please see the completed values in the table in the elucidation that follows
3. The equivalent ratio relationship in each graph is given by the constant ratio of each coordinate pair.
4. The recipe that has the strongest lemon lime taste is given by the graph that has the steepest slope
What is the slope of a graph?The slope of a graph is given by the ratio of the rise to the run of a graph
1. The unit rate for Mason's recipe is (1/2) cup of lemon–lime per cup of club
While the unit rate for Tyler's recipe for club soda is (3/5) cup of lemon and lime per cup of club
Mathematically, we have
Emily;
Mason's recipe; y = (1/2)•x
Tyler's recipe; y = (3/5)•x
Julio;
Mason's recipe; y = (1/3)•x
Tyler's recipe; y = (3/8)•x
Carlos's recipe; y = (2/5)•x
Zeb's recipe; y = (1/5)•x
2. The values in the table becomes;
MasonLemon–lime; 1/3, 2/3, 1, 4/3, 5/3, 6/3
Total punch; 1, 2, 3, 4, 5, 6
Tyler'sLemon–lime; 3/8, 3/4, 9/8, 3/2, 15/8, 9/4
Total punch; 1, 2, 3, 4, 5, 6
Carlos'sLemon–lime; 2/5, 4/5, 6/5, 8/5, 2, 12/5
Total punch; 1, 2, 3, 4, 5, 6
Zeb'sLemon–lime; 1/5, 2/5, 3/5, 4/5, 1, 6/5
Total punch; 1, 2, 3, 4, 5, 6
3. Each graph represents equivalent ratios given that the value of the ratio of data point is a constant, that is, we have;
For Mason, 1:(1/3) = 2:(2/3) = 3:1...
For Tyler, 1:(3/8) = 2:(3/4) = 3:(9/8)...
For Carlos, 1:(2/5), 2:(4/5), 3:(6/5)...
For Zeb, 1:(1/5), 2:(2/5), 3:(3/5)...
4. The slope of each graph is given by the number of cups of lemon–lime per one cup of total punch,
The recipe that has the strongest lemon–lime taste is given by the recipe that has the most lemon–lime per each cup of total punch
Which gives;
The recipe that has the strongest lemon–lime can be found from the graph that has the largest slope, which is given by Carlos's recipe.
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Find the length of side x in simplest radical form with a rational denominator. I will give brainliest please help asap
Answer:
[tex]x=\frac{\sqrt{2}}{2}[/tex]
Step-by-step explanation:
x^2+x^2=1
x^2=1/2
x=1/sqrt2
x=sqrt2/2
:]
What calculation will give us the estimated volume of the Great Pyramid of Giza in cubic meters?
The option that would give the estimated volume of the Pyramid of Giza is = [tex]\frac{53,000 . 150 }{3}[/tex]
What is the volume?A pyramid is a 3-dimensional shape that is made up of a polygonal base and 4 triangular faces. The 4 triangular faces are joined at a vertex. Types of pyramids include a square pyramid, rectangle pyramid, triangle pyramid.
The volume of a pyramid is the amount of space that is a three-dimensional shape.
Volume of a pyramid = 1/3 x (base area x height)
1/3 x (53,000. 150)
= [tex]\frac{53,000 . 150 }{3}[/tex]
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By looking at the equation of the least-squares regression line, you can see that the correlation between height and arm span is.
Step-by-step explanation:
If the data shows a leaner relationship between two variables, the line that best fits this linear relationship is known as a least-squares regression line, which minimizes the vertical distance from the data points to the regression line.
help pls
1
3
144
432
The value of the given equation is 12.
What is the value of the equation?In order to solve this question, the BODMAS rule would be used. The BODMAS rule gives the order in which mathematical operations can be solved. The order is:
Bracket OfDivision Multiplication Addition SubtractionIn the numerator:
the addition would be done first: 3² + 1 = 9 + 1 = 10
Then the subtraction would be done next = 14 - 10 = 4
Now determine the square of the term in the bracket : 4²= 16
In the denominator:
The multiplication would be solved first: 3 x 1/4 = 3/4
The next step is to solve the division : 1 ÷ 3/4 = 1 x 4/3 = 4/3
The fraction becomes : 16 ÷ 4/3
16 x 3/4 = 12
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Answer:
The answer is 432
Step-by-step explanation:
I did the k 12 quiz and I got it right! good luck
Complete each statement with a number that makes the statement true.
A. __< 7°C.
B. __ <-3°C.
C. -0.8°C <___< -0.1°C
D. __> -2°C
Answer:
A. 6°C
B. -4°C
C. -0.7°C
D. -1°C
Answer:
A. 6°C < 7°C.
B. -4°C < -3°C.
C. -0.8°C < -0.7°C < -0.1°C
D. -1°C > -2°C
12/1-(2x+3)
How to simplify this fraction
Step-by-step explanation:
so, it is
12 / (1 - (2x + 3))
yes, that is
12 / (1 - 2x - 3) = 12 /(-2x -2) | divide both sides by -2
-6/(x + 1)
The blueprint for the moreno’s living room has a scale of 2 inches= 5 feet. The family wants to use a scale of 1 inch= 3 feet. What is the width of the living room on the new blueprint
The width of the living room on the new blueprint is 15 feet.
How to calculate the width?Based on the information, the scale of the original blueprint will be:
= 2 in / 5 ft
The width of the original blueprint is 6 inches, the actual width of the living room will be:
2/5 = 6/x
where x = width of living room
Cross multiply
x = 5 × 6 / 2
x = 15 feet.
The width is 15 feet.
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Determine which statement completes each open sentence:
32+8+1
15 (1+2)
4²
4.2
3(x - 4 + x)
when x = 4
111
3(x-4 + x)
when x = 2
32-1
15 +1 +2
3x4+x
3x4+x
1. is equal to
2. is NOT equal to
The statement which completes each of the open sentences are given below:
32 ÷ 8 + 1 is not equal to 3² - 1
15 ÷ ( 1 + 2) is not equal to 15 ÷ 1 +2
4² is not equal to 4 . 2
3 ( x - 4 + x) is not equal to 3x - 4 + x when x = 4
3 ( x - 4 + x) is not equal to 3x - 4 + x when x = 2
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Calculate the average rate of change of fover the interval -3≤x≤9. Show the calculations that lead to your answer.
The function has an average rate of change f is 1/2 over the interval
How to determine the average rate of change f?The possible graph that completes the question is added as an attachment
The interval is given as
-3 ≤ x ≤ 9
This can be rewritten as
x = -3 to x = 9
This can also be represented as
(a, b) = [-3, 9]
From the attached graph, we have
f(-3) = -1.5
Also, we have
f(9) = 0.5
The estimate (to one decimal place) of the average rate of change f is calculated as
Rate = [f(b) - f(a)]/[b - a]
This gives
Rate = [f(9) - f(-3)]/[9 + 3]
So, we have
Rate = [0.5 + 1.5]/[9 + 3]
Evaluate
Rate = 2/12
Simplify
Rate = 1/6
Hence, the average rate of change f is 1/6
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82.8 cm measured to the nearest tenth of a cm.
The water level will be 10 feet or lower by tomorrow.
The inequality written for the given statement is x≤10. Therefore, option A is the correct answer.
The given statement is "The water level will be 10 feet or lower by tomorrow."
What is a inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
The inequality for the given statement is x≤10
The inequality written for the given statement is x≤10. Therefore, option A is the correct answer.
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"Your question is incomplete, probably the complete question/missing part is:"
Choose the inequality that represents the statement.
The water level will be 10 feet or lower by tomorrow.
A. x≤10
B. x<10
C. x>10
D. x=10
Homework: Section 3.4HomeworkQuestion 6, 3.4.25 >HW Score: 50%, 5 of 10 pointsO Points: 0 of 1SaveFind an nth-degree polynomial function with real coefficients satisfying the given conditions. If you are using a graphing utility, use it to graph the function and verifythe real zeros and the given function value.n=3;3 and 4 i are zeros;f(2)=40f(x)=(Type an expression using x as the variable. Simplify your answer.)Clear allCheck answerHelp me solve thisView an example Get more help.
The roots are
[tex]\begin{gathered} x=3 \\ x=4i \\ x=-4i \end{gathered}[/tex]The polynomial can be modellled as ;
[tex]f(x)=a(x-3)(x-4i)(x+4i)[/tex][tex]f(x)=a(x-3)(x^2+16)[/tex]
Let us use f(2) to obtain a value for a
[tex]\begin{gathered} f(2)=a(2-3)(2^2+16) \\ 40=-20a \\ a=-2 \end{gathered}[/tex]The polynomal f(x) is given as
[tex]\begin{gathered} f(x)=-2(x-3)(x^2+16) \\ f(x)=-2x^3+6x^2-32x+96 \end{gathered}[/tex]Please answer quick i really need help
Answer:
( - 36, 24 )
Step-by-step explanation:
(- 9, 6)
( - 9×4, 6×4)
( - 36, 24 )
11) Translate the following phrases into algebraic expressions
a. The difference of a number k and four
b. Eight less than a number x
e. The sum of six and a number d
d. The product of a number and five
e The quotient of eight and a number
f. The product of two and a number increased by seven
g. Half of a number decreased by twelve
A number, a variable, or a mix of numbers, variables, and operation symbols make up an expression. The translation is as follows:
a) 4 - k
b) 8 - x
c) 6 + d
d) x + 5
e) 8 / x
f) 2 + x = 8
g) 1/2n-12
What is meant by algebraic expressions?A number, a variable, or a mix of numbers, variables, and operation symbols make up an expression. Two expressions joined by an equal sign form an equation.
Arithmetic operations like subtraction, addition, division, multiplication, and exponentiation are used to combine variables and integers to produce any algebraic expression. A variable, a number, or a variable and number with an exponent as a product can all be used as the phrase.
The translation is as follows:
a) 4 - k
b) 8 - x
c) 6 + d
d) x + 5
e) 8 / x
f) 2 + x = 8
g) 1/2n-12
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after the given information, at least how many more steps are necessary to solve this proof
The following steps would be:
• TP and TP (for both triangles) are congruent by the reflexive property.
,• The triangles are congruent by the SAS theorem.
,• Angle S and angle O are congruent.
equivalent to 6+12x?
Answer:
Step-by-step explanation:
6 + 12x
6 ( 1 + 2x )