Step 1
From the question;
[tex]\begin{gathered} Bobby\text{ reads 20 books in 2 months} \\ \end{gathered}[/tex]We are required to find how many months it will take him to read 90 books
Step 2
We will use the ratio below to solve the problem.
[tex]\begin{gathered} \frac{20\text{ books}}{90\text{ books}}=\frac{2months}{x} \\ x=months\text{ to read 90books} \\ x=\frac{90\times2}{20} \\ x=9\text{ months} \end{gathered}[/tex]Answer; It will take Bobby 9months to read 90 booj
[tex]9\text{ months}[/tex]px+5=7x–q please help me
Answer:
Step-by-step explanation:
Simplifying
px + 5 = -4x + q
Reorder the terms:
5 + px = -4x + q
Reorder the terms:
5 + px = q + -4x
Solving
5 + px = q + -4x
Solving for variable 'p'.
Move all terms containing p to the left, all other terms to the right.
Add '-5' to each side of the equation.
5 + -5 + px = q + -5 + -4x
Combine like terms: 5 + -5 = 0
0 + px = q + -5 + -4x
px = q + -5 + -4x
Reorder the terms:
px = -5 + q + -4x
Divide each side by 'x'.
p = -5x-1 + qx-1 + -4
Simplifying
p = -5x-1 + qx-1 + -4
Reorder the terms:
p = -4 + qx-1 + -5x-1
Write the equation, in standard form, of the parabola containing the following points: (0, 1), (1, 5), (2, 3). You must set up a system of three equations to get credit for this question.
The equation of the parabola for the given points is y = -3x² + 7x + 1
Equation of the parabola
The standard form of the equation of a parabola is expressed as
y = f(x) = ax² + bx + c
where a, b, and c are constants and a ≠ 0.
Given,
Here we have the points (0, 1), (1, 5), (2, 3).
Now, we have to find the equation of the parabola.
Here we are given three coordinates (0, 1), (1, 5), and (2, 3) which lie on the parabola and which means that it satisfies the parabolic equation.
In order to find the values of a, b and c we need to formulate three equations using the three given points.
Since for the three unknowns a, b, and c, we will require three equations.
For that we have to take the Point (0,1) i.e. x = 0 and y = 1
Substituting the values of x and y in the standard parabola equation, then we get,
1 = a(0)² + b(0) + c
1 = 0 + 0 + c
c = 1 -------------------(1)
Next, we have to take the Point (1, 5) i.e. x = 1 and y = 5
Substituting the values of x and y in the standard parabola equation, then we get,
5 = a(1)² + b(1) + c
5 = a + b + c
It can be written as,
a + b + c = 5 -----------------------------(2)
Finally, we have to take the Point (2, 3) i.e. x = 2 and y = 3
Substituting the values of x and y in the standard parabola equation, then we get,
3 = a(2)² + b(2) + c
3 = 4a + 2b + c
It can be written as,
4a + 2b + c = 3 -----------------------------(2)
Apply the value of c as 1 in equation (2), then we get,
a + b + 1 = 5
a + b = 4 ---------------------(4)
Similarly, apply the value of c on the equation (3), then we get,
4a + 2b + 1 = 3
4a + 2b = 2
Divide the equation by 2 on both sides, then we get,
2a + b = 1 --------------------(5)
Subtract equation (5) from equation (4),
(2a - a) +(b - b) = 1 - 4
a = -3
Apply the value of a in the equation (4) to get the value of b,
(-3) + b = 4
b = 7
Therefore, the equation of the parabola is
y = -3x² + 7x + 1
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If f(x) = 2x +1 and g(x) = -x2,
The value of (f·g)(x) from the given function is -2x³ - x².
The given functions are f(x) = 2x +1 and g(x) = -x².
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
Here,
(f·g)(x) = f(x) × g(x)
= (2x +1) × (-x²)
= 2x × (-x²) + 1 × (-x²)
= -2x³ - x²
Therefore, the value of (f·g)(x) from the given function is -2x³ - x².
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"Your question is incomplete, probably the complete question/missing part is:"
If f(x) = 2x +1 and g(x) = -x², then find (f·g)(x).
I only need the answer
THANK YOU!!
Cartesian coordinates are- 4.2426
The horizontal component of the Cartesian coordinate system is denoted by the letter x, whereas the vertical component is denoted by the letter y. In this coordinate system, equations for lines will need to include both the x and y variables.
Given
(r,θ) = (6,π/4)
x= r cosθ =6 x cos(π/4)
= 6√2 = 3√2
≈ 4.2426
y= r sinθ = 6 x sin(π/4)
= 6√2 = 3√2
≈ 4.2426
Hence the answer is 4.2426
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please show me how to graph 4x + 5y = -40
Plot the points (0, -8), (1, -8.8) and (2, -9.6) on the graph. Therefore, the graph for the given equation is plotted below.
The given equation is 4x + 5y = -40.
What is the graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter.
Put x=0, 1, 2, 3, 4, 5,.....in the given equation and solve for y
When x=0, 4(0)+5y=-40
⇒ 5y=-40
⇒ y=-8
When x=1, 4(1)+5y=-40
⇒ 5y=-44
⇒ y=-8.8
When x=2, 4(2)+5y=-40
⇒ 5y=-48
⇒ y=-9.6
Plot the points (0, -8), (1, -8.8) and (2, -9.6) on the graph
Therefore, the graph for the given equation is plotted below.
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Select the table that represents a linear function. (Graph them if necessary.)
Step-by-step explanation:
any linear function represents a straight line (hence the name) and is therefore of the structure
y = f(x) = ax + b
"a" is the slope of the line, and it is represented by the ratio (y coordinate difference / x coordinate difference) when going from one point on the line to another point.
"b" is the y-intercept (the y-value when x = 0).
so, let's look at the answer options :
A.
x = 0 gives us b (the y value) : 2
so, then for x = 1, y = 3 ?
3 = a×1 + 2
a = 1
now, the next point must be also on the same line for the whole function to be linear (and that means the equation has to be true for all numbers involved) :
x = 2, y = 6
6 = 1×2 + 2 = 4
6 is for sure NOT 4, so this is not a linear function.
it is actually y = x² + 2
B.
x = 0 gives us b : 1
for x = 1, y = 3 ?
3 = a×1 + 1
a = 2
again, the next point must be on the same line :
x = 2, y = 9
9 = 2×2 + 1 = 5
9 is for sure NOT 5, so this is not a linear function.
it is actuality y = 3^x.
C.
x = 0 gives us b : 0
for x = 1, y = 1 ?
1 = a×1 + 0 = a
a = 1
the next point :
x = 2, y = 4
4 = 1×2 = 2
4 is for sure NOT 2, so this is not a linear function.
it is actually y = x².
D.
x = 0 gives us b : 3
for x = 1, y = 9
9 = a×1 + 3
a = 6
the next point(s) must fit :
x = 2, y = 15
15 = 6×2 + 3 = 12 + 3 = 15
correct
x = 3, y = 21
21 = 6×3 + 3 = 18 + 3 = 21
correct
yes, this is a linear function.
it is y = 6x + 3
Taylor works on an art project that uses rectangular pieces of paper the first rectangle has length 3/8 inches in width 3 in.
The weights of four puppies are shown in pounds. 9.5, 9 3/8, 9.125, 9 3/4 Which list shows these weights in order from greatest to least?
The data from greatest to least is 9 3/4 > 9.5> 9 3/8> 9.125.
What is Descending order?Any data, including numbers, alphabets, amounts, lengths, etc., are arranged in descending order from highest to lowest.
In other terms, anything is considered to be in descending order when it is arranged from a higher value to a lower value. It is possible to arrange numbers in descending order, including whole numbers, natural numbers, integers, fractions, and decimals.
For example 7, 3, 9, 2 in decreasing order, for instance. Starting with the biggest number, we'll work our way down to the lesser ones one at a time. When these numbers are listed in descending sequence, they are written as 9, 7, 3, and then 2.
Given data:
9.5, 9 3/8, 9.125, 9 3/4
Now, simplifying the mixed fraction as
9 3/8
=75/8
= 9.375
9 3/4
=39/4
= 9.75
Thus, we have the data in decimal form
9.5, 9.375, 9.125, 9.75
Hence, the data from greatest to least is 9 3/4 > 9.5> 9 3/8> 9.125.
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Find the value of x. Then find the measure of each labeled angle.
x= ____° (Simplify your answer.)
13x°= _____° (Simplify your answer.)
7x°= ____° (Simplify your answer.)
Answer:
13x + 7x = 180 (corresponding angles, sum of adjacent angles on a straight line=180)
20x = 180
x = 9
Substitute x into angle measures to find values.
13x° = 13(9)
= 117°
7x° = 7(9)
= 63°
Find the indicated value. (Round your answer to eight decimal places.) 26!
The factorial expression 26! has a value of 4.032914600e+26
How to evaluate the expression?The expression is given as
26!
The above expression is a factorial expression
And the factorial of a number n where n >= 0 and n is not a decimal number is calculated using
n! = n x (n - 1) x (n - 2) x ..... x 1
This means that
n = 26
So, we have
26! = 26 x 25 x 24 x 23 x ..... x 1
Evaluate the products
26! = 4.0329146e+26
Approximate
26! = 4.032914600e+26
Hence, the value of the expression is 4.032914600e+26
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5. Refer to Table 1. Suppose the government imposes a price ceiling of $5 on this market. What will be the size of
the shortage in this market?
0 units
2 units
8 units
10 units
There is no shortage of units in this market with a $5 price ceiling and the size of shortage is 0 units.
In mathematics, what is a data table?Tables are a good way to organize data by using rows and columns. Tables are a versatile organizational tool that can be used to communicate information on their own or in conjunction with another type of data representation (like a graph).Given: On this market, the government imposes a $5 price ceiling.
We need to find the size of the shortage in this market.
From the given table, we can see that the quantity demanded for $5 price ceiling is 4 units and the quantity supplied is 8 units.
So, the demand is satisfied and an extra 4 units are also provided.
Therefore, there is no shortage of units in this market a $5 price ceiling and the size of shortage = 0 units.
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You borrow $90,000 for college at an APR of 6.25%. You plan to elect 25-year repayment. How much more must you repay in total if your loan is unsubsidized, as opposed to being subsidized?
The amount which needs to be replayed if the loan is unsubsidized, as opposed to being subsidized is $59,295.86.
The monthly payment amount formula on a loan of P at rate r for t years is A = P(r ÷ 12) ÷ (1 -[tex]\frac{(1 +r)}{12} ^{-12t}[/tex])
For the normal compensation plan, T = 25. The P = $90,000 and r = 0.625, so the formula is,
A = $90,000(0.625 ÷ 12) ÷ (1 - (1 +[tex](\frac{1 +0.625}{12} )^{(-300)}[/tex])
A = $90,000(0.625) ÷ (1 - [tex](1.135)^{(-300)}[/tex])
A = $90,000(0.625) ÷ (1.832)
A = $(90,000 × 0.625) ÷ (1.832)
A = $30704.14
Payments under the extended repayment plan last for 25 years. The amount which needs to be replayed is $90,000 - $30704.14 = $59,295.86.
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Kevin, Mika, and Cheryl have a total of 45 people sponsoring them for a fun-raiser. Kevin has p people sponsoring him, MIka has one more than Kevin, and Cheryl has one more than MIka. Write and solve and equation to find the number of people sponsoring each person
The equation for the number of people sponsoring each person are; m = c + 3, p = c + 2.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given that Kevin, Mika, and Cheryl have a total of 45 people sponsoring them for a fun-raiser.
Consider that Kevin has p people sponsoring him, Mika has one more than Kevin, and Cheryl has one more than Mika.
Kevin = p
MIka = m
Cheryl = c
Then m = 1 + p
c = 1 + m
Or
m = c - 1
Now solve both equation;
m = 1 + p = c - 1
p = c - 1 -1
p = c + 2
p = m -1
p = c + 2
Then m - 1 = c + 2
m = c + 3
Hence, the equation for the number of people sponsoring each person are; m = c + 3, p = c + 2.
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6) What is the length of side x?
The given triangle is a right angled triangle. Therefore, by Pythagoras theoram,
[tex]\text{hypo}^2=base^2+altitude^2[/tex]From the figure,
[tex]\begin{gathered} x^2=2^2+5^2 \\ x^2=29 \\ x=\sqrt[]{29} \end{gathered}[/tex]Hence, Option D is the right answer.
Rosa uses 1/2 of a cup of vinegar in her salad dressing recipe. How
much vinegar would Rosa use to make 1/3 of a recipe?
Answer:
1/6
Step-by-step explanation:
1/2 1/3
lcd(least common denomitator)=6
there fore it is 1/6
32
3 ÷ (z -
5
2
-)=2=÷(z+
3
2
+
3
Step-by-step explanation:
Consider the Cartesian equation,
2
x+3
=
4
y−5
=
2
z+6
Now,
a
=−3
i
+5
j
−6
k
b
=2
i
+4
j
+2
k
Vector equation,
r
=
a
+λ.
b
=−3
i
+5
j
−6
k
+λ(2
i
+4
j
+2
k
)
This is the required equation
factor out 28p^5q^3+24p^3
Answer: 4p^3(7p^2q^3+6
Step-by-step explanation: Im pretty sure.
Identify two segments that are marked congruent to each other on the diagrambelow. (Diagram is not to scale.)
Step 1:
What are congruences?
Congruent triangles are triangles that have the same size and shape. This means that the corresponding sides are equal and the corresponding angles are equal.
Step 2:
JH is congruent to HI
Final answer
JH is congruent to HI
systems of equations
The solution to the system of equations in problem 13 is (0, -4).
The solution to the system of equations in problem 14 is (-6, -1).
In problem 13, the system of equations is:-5x-5y = 20x+6y = -24Simplify the first equation.x + y = -4x = -4-ySubstitute this value into the second equation.-4-y + 6y = -245y = -20y = -4x = -4-yx = -4-(-4)x = 0In problem 14, the system of equations is:-7x+12y = 30-3x+6y = 12Simplify the second equation.x-2y = -4x = 2y-4Substitute this value into the first equation.-7(2y-4)+12y = 30-14y + 28 + 12y = 30-2y = 2y = -1x = 2y-4x = 2(-1)-4x = -2-4x = -6To learn more about equations, visit :
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simplify 5/7 x + 2/7 y − 2 − 1/7 x + 7
The simplification of the given expression would be; 4x/7 + 2y /7 + 5.
What is a simplification of an expression?Simplification involves proceeding with the pending operations in the expression. Like, 5 + 2 is an expression whose simplified form can be obtained by doing the pending addition, which results in 7 as its simplified form. Simplification usually involves making the expression simple and easy to use later.
We have been given an expression as 5/7 x + 2/7 y − 2 − 1/7 x + 7
Thus,
5/7 x + 2/7 y − 2 − 1/7 x + 7
Combine the like terms first;
5/7 x − 1/7 x + 2/7 y − 2+ 7
Then solve the like terms;
(5 -1)x/7 + 2y /7 + 5
4x/7 + 2y /7 + 5
Therefore, the simplification of the given expression would be; 4x/7 + 2y /7 + 5.
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3 sailboats to 5 fan boatsHow many fan boats if therewere 54 sailboats?
we can use cross multiplication
[tex]\begin{gathered} 3\text{sail}\longrightarrow5\text{fan} \\ 54\text{sail}\longrightarrow\text{xfan} \end{gathered}[/tex]where x is the number of fan boats
[tex]\begin{gathered} x=\frac{54\times5}{3} \\ \\ x=90 \end{gathered}[/tex]the number of fan boats to 54 sailboats is 90
Please help me. I know I’m solving for the principal but need help with the steps
Given: The information below
[tex]\begin{gathered} time(t)=5\text{years} \\ rate(r)=4\%=0.04 \\ Interest(I)=40 \end{gathered}[/tex]To Determine: How much Austine invested
Solution
Please note that the amount invested is the Principal
The formula combining principal, rate, time and interest for simple interest is
[tex]I=\text{Prt}[/tex]Make P the subject of the formula
[tex]P=\frac{I}{rt}[/tex]Substitute for I, r and t given into the formula as shown below
[tex]\begin{gathered} P=\frac{40}{0.04\times5} \\ P=\frac{40}{0.2} \\ P=200 \end{gathered}[/tex]Hence, the amount invested by Austine is $200
Use the factor theorem to find all real zeroes for the given polynomial function and one factor Enter your answer as a comma separated list
Given:
[tex]2x^3+5x^2-4x-10[/tex](2x+5) is one of the factor.
[tex]\begin{gathered} 2x^3+5x^2-4x-10=(2x+5)(2x^2-4) \\ =2(2x+5)(x^2-2) \end{gathered}[/tex]By taking the factors equal to zero then we get the values of x.
Therefore, the zeros of the polynomial are
[tex]-\frac{5}{2},\sqrt[]{2},-\sqrt[]{2}[/tex]Expand (x-3)^5 using the vi al theorem and Pascal’s triangle. Show all the steps
Given:
[tex](x\text{ - 3\rparen}^5[/tex]To find:
To expand the expression using binomial's theorem
To expand, we will apply the binomial theorem formula:
[tex](x\text{ + y\rparen}^n=\text{ }^nC_0x^n\text{ + }^nC_1x^{n-1}y\text{ + }^nC_2x^{n-2}y^2+.\text{ . . + }^nC_ny^n[/tex][tex]\begin{gathered} (x\text{ - 3\rparen}^5\text{ = }^5C_0x^5\text{ + }^5C_1x^{5-1}y\text{ + }^5C_2x^{5-2}y^2+\text{ }^5C_3x^{5-3}y^3\text{ + }^5C_4x^{5-4}y^4\text{ + }^5C_5y^5 \\ \\ We\text{ will use pascal's triangle to get the coefficient of the terms.} \\ The\text{ coefficients represents the value of the combinations} \\ \\ The\text{ pascals triangle coefficients for power of 5 = 1 5 10 10 5 1} \end{gathered}[/tex][tex]\begin{gathered} (x\text{ - 3\rparen}^5\text{ = \lparen1\rparen}x^5\text{ + \lparen5\rparen}x^{5-1}y\text{ + \lparen10\rparen}x^{5-2}y^2+\text{ \lparen10\rparen}x^{5-3}y^3\text{ + \lparen5\rparen}x^{5-4}y^4\text{ + \lparen1\rparen}y^5 \\ \\ y\text{ = -3} \\ (x\text{ - 3\rparen}^5\text{ = \lparen1\rparen}x^5\text{ + \lparen5\rparen}\times x^4\times(-3)\text{ + \lparen10\rparen}\times x^3\times(-3)^2+\text{ \lparen10\rparen}\times x^2\times(-3)^3\text{ + \lparen5\rparen}\times x^1\times(-3)^4\text{ + \lparen1\rparen\lparen-3\rparen}^5 \\ \\ (x\text{ - 3\rparen}^5\text{ = }x^5\text{ -15}x^4\text{ + 90}x^3-27\text{0}x^2\text{ + 405}x^1\text{ -243} \end{gathered}[/tex]The expansion becomes:
[tex](x\text{ - 3\rparen}^5\text{ = }x^5\text{ - 15}x^4\text{ + 90}x^3-27\text{0}x^2\text{ + 405x - 243}[/tex]in a class of 34 students 19 of them are girls what percentage of the class are girls give you answer to one decimal place
In class of 34 students, 19 of them are girls, then the percentage of girls in the class is 55.9%
The total number of students in the class = 34
Number of girls in the class = 19
The percentage is defined as the ratio that can be expressed as the fraction of 100. The percentage is often represented using the percentage sign "%"
The percentage of girls in the class = (Number of girls in the class/The total number of students in the class) ×100
Substitute the values in the equation
The percentage of girls in the class = (19/34)×100
= 0.559×100
= 55.9%
Hence, in class of 34 students, 19 of them are girls, then the percentage of girls in the class is 55.9%
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find the domain of (x). express your answer in interval notation.
so the domain is
[tex](0,\propto)[/tex]Mr. Stern owns an apartment building with 60 suites. He can rent all the suites if he charges a monthly rent of $200 per suite. At a higher rent, some suites will remain vacant. On the average, for each increase of $5, one suite remains vacant with no possibility of renting it. Determine the functional relationship between the total monthly revenue and the number of vacant units. What monthly rent will maximize the total revenue? What is the monthly revenue?
If Mr. Stern charges a monthly rent of $200, we still can rent all suites. An average increase of $5 in the monthly rent imply in the addition of one suite vacant.
Therefore, the total monthly revenue r in function of the number of vacant units v can be writen in the form:
[tex]\begin{gathered} r=(200+5v)\cdot(60-v) \\ r=-5v^2+100v+1200 \\ 0\leq v\leq60 \end{gathered}[/tex]The monthly rent m is given by:
[tex]m=200+5v[/tex]The value of v that maximize the total revenue r is the one found in the vertex of the parabola that represents r:
[tex]v_{\max }=-\frac{100}{2\cdot(-5)}=10[/tex]Therefore, the monthly rent that maximize the total revenue is m = 200 + 5*10 = $700
The monthly revenue with this monthly rent is:
[tex]r=-5\cdot10^2+100\cdot10+1200=\text{ \$1700}[/tex]
how do you write 4.501795324E^-6 in simpler form
Answer: you cant but here are some ways to practice:)
Find the greatest common divisor of both the numerator and the denominator. This can be done either with prime factor trees or another method.
Divide both the numerator and the denominator with the greatest common divisor.
The result is a simplified fraction. hope this helps and sorry.
Quadrilateral ARMY is rotated 90° about the origin.
Draw the image of this rotation.
A 3,3
Y 5,1
M 7,5
R 5,7
The quadrilateral's image points will be A(3, 3) A'(-3, 3) R(5, 7) R'(-7, 5) M(7, 5) M'(-5, 7) Y(5, 1) Y' (-1, 5).
What do math quadrilaterals mean?
A polygon called a quadrilateral has four sides, four angles, and four vertices. Quadrilateral is a derivative of the Latin words quadri, which means four, and latus, which means side. A quadrilateral is shown in the above image as an example. quadrilateral pieces.If a point (x, y) is rotated 90 degrees counterclockwise with respect to the origin, the rotational rule is:
(x, y) → (-y, x) (-y, x)
Consequently, the image point's coordinates following rotation will be (-y, x).
According to this rule, the quadrilateral's image points will be A(3, 3) A'(-3, 3) R(5, 7) R'(-7, 5) M(7, 5) M'(-5, 7) Y(5, 1) Y' (-1, 5)
We may obtain the graph of the picture quadrilateral A'R'M'Y' by graphing the image points.
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The two ways we can measure the SPREAD of a distribution:a. mean and quartilesb. median and standard deviationc. mean and mediand.quartiles and standard deviation
In statistics, there are ways of analyzing data and these include measures of "central tendency" and "measures of dispersion."
This question is focused on "measures of dispersion," that is, an analysis of how well the data set is being spread away from the centre. The centre is most commonly denoted as the mean (average), and the SPREAD is an analysis of how farther away the observed data is from the centre.
The Mean, Median and Mode are basically measures of "central tendency" and therefore, options A, B and C do not measure the SPREAD of a distribution.
The Quartiles and Standard deviation actually measure how well (either very close or very far) the data set move away from the distribution.
The Quartiles basically examine the data set from all four quarters of the entire set, the 1st, 2nd, 3rd and 4th quarters. This measure of spread measures how well the data is from the distribution depending on which quartile it falls. The Standard deviation measures how far the mean deviates (or drifts away) from the data set.
The correct answer therefore is option D.