Answer: 6x + 8 = 32
Explanation:
Let x represent the number
6 times the number = 6 * x = 6x
If we add 6x to 8, it becomes
6x + 8
Given that the result is 32, the equation could be used to solve the problem is
6x + 8 = 32
solve the equations. 13x - 6y = 22x= y + 6x=y=
Question 4 (5 points)
In Brock's class of 24 students, 10 students report that math is their favorite class, 25% of the students report that science is
their favorite, and 1/3 prefer reading.. Show your work and/or explain your answer: Which subject is favored by the greatest
number of students? (5 points)
Mathi is favored by the greatest i.e 10 students, using percentage
What is percentage?
A percentage that represents a tenth of a quantity. One percent, denoted by the symbol 1%, is equal to one-hundredth of something; hence, 100 percent denotes the full thing, and 200 percent designates twice the amount specified. A portion per hundred is what the percentage denotes. Percentage refers to one in a hundred. The % sign is used to denote it.
There are 24 students in Brock's class
10 students say math is their favorite class , 25% say that science is their favorite class and 1/3 prefer reading.
Now you have to find out if more students prefer math or science. Well since the information tells you that 10 students prefer math, you need to find out that 25% of students prefer science and 1/3 prefer reading.
For 1st case, math favorite have 10 students,
For 2nd case, 25% of 24 is 24*25/100
=24*1/4
=6
And for 3rd case, who prefer reading is 1/3rd of students which is 24*1/3
=8
So Most students like math.
Hence, Mathi is favored by the greatest i.e 10 students.
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solve the following for x 13 over8 = x over 9
ANSWER:
[tex]x=14\frac{5}{8}=14.625[/tex]STEP-BY-STEP EXPLANATION:
We have the following proportion:
[tex]\frac{13}{8}=\frac{x}{9}[/tex]We solve for x:
[tex]\begin{gathered} \frac{x}{9}=\frac{13}{8} \\ \\ x=\frac{13*9}{8} \\ \\ x=\frac{117}{8}=14\frac{5}{8}=14.625 \end{gathered}[/tex]2 4/7 divided by 2 3/5
Find the quotient. If possible, rename the quotient as a mixed number or a whole number. Write your answer in simplest form, using only the blanks needed.
Answer:
1 17/28
Step-by-step explanation:
2 4/7=18/17
2 3/5=8/5
18/17÷8/5=90/56=45/28=1 17/28
26. Find the perimeter of the polygon.3 ina. 15 inb. 21 inc. 9 in
To find the perimeter of the regular polygon, that in this case is a pentagon, multiply 5 by the sidelength of the pentagon, it means 5 times 3.
[tex]\begin{gathered} P=5\cdot3 \\ P=15 \end{gathered}[/tex]The perimeter of the polygon is 15in
23.35 in.43 in.36 in.A.1505 in.2B.142 in.2C. 71 in.2D. 1260 in.2
TIP
This parallelogram
The area of a parallelogram =BH
The area of a parallelogram
[tex]\begin{gathered} =35\text{ in }\times36in \\ =1,260in^2 \end{gathered}[/tex]The final answer is the last option
option D
Let f(x) = -2x^2– 7 and g(x) = 4x – 7.(fog)(x) =(gof)(x) =(fog)(1) =
Part 1.
The compositon fog is given by
[tex](f\circ g)(x)=-2(4x-7)^2-7[/tex]which gives
[tex]\begin{gathered} (f\circ g)(x)=-2(16x^2-56x+49)^{}-7 \\ (f\circ g)(x)=-32x^2+112x-98^{}-7 \\ (f\circ g)(x)=-32x^2+112x-105 \end{gathered}[/tex]Then, the answer is:
[tex](f\circ g)(x)=-32x^2+112x-105[/tex]Part 2.
The composition gof is given by
[tex](g\circ f)(x)=4(-2x^2-7)-7[/tex]Then, the answer is:
[tex](g\circ f)(x)=-8x^2-35[/tex]Part 3.
In this case, we need to substitute x=1 into the answer of Part 1, that is,
[tex]\begin{gathered} (f\circ g)(1)=-32(1)^2+112(1)-105 \\ (f\circ g)(1)=-32^{}+112-105 \end{gathered}[/tex]Therefore, the answer is:
[tex](f\circ g)(1)=-25[/tex]The graph below represents compound interest over time with an initial investment of $600 at in interest rate of 6% compounded annually. Which of these statements describes the situation?-it will take less than 10 years to double the initial investment-it will take less than 20 years to triple the initial investment-it will take more than 15 years to double the investment-it will take more than 30 years to triple the initial investment
ANSWER
It will take less than 20 years to triple the investment.
EXPLANATION
We want to identify the statement that best describes the situation represented by the graph of the compound interest over time.
To do this, let us find at what point the compound amount doubles and triples.
Since the initial investment is $600, it implies that double this investment is $1200, and triple this investment is $1800.
Hence, we have to identify what happens at these points on the graph.
Notice that when y approaches $1200 on the vertical axis, x is greater than 10 and less than 15. It occurs at about x = 12 years.
Also, notice that when y approaches $1800 on the vertical axis, x is less than 20 years (also less than 30 years). It occurs at about x = 19 years.
Hence, the only correct statement that describes the situation is that it will take less than 20 years to triple the investment.
The correct answer is the second option.
Calculate the volume of the composite solid . 2 cm 3 cm 2 cm 4 cm 3 cm 4 cm 8 cm
Notice that the solid consists of an 8x4x4cm rectangular prism minus a 3x4x2cm rectangular prism (the gap shown in the image).
Therefore, the volume of the solid is
[tex]V_{solid}=(8*4*4)-(3*4*2)=128-24=104[/tex]The answer is 104cm^3If $7025 is invested at a rate of 10% compounded continuously, what will be the balance after 12 years? Round your answer to two decimal places.
p = $7025
r = 10% = 10/100 = 0.1
t = 12
[tex]A=pe^{rt}[/tex]Therefore,
[tex]\begin{gathered} A=7025\times e^{0.1\times12} \\ A=7025\times e^{1.2} \\ A=7025\times3.32011692274 \\ A=23323.8213822 \\ A=\text{ \$}23323.82 \end{gathered}[/tex]Balance after 12 years = $23,323.82
Can I please get some help on this Graph y=1
the given expression is,
y = 1
the given expression is the equation of the line,
that is passing through y = 1 and parallel to x- axis,
so, the graph will be,
The perimeter of a square is (4x - 44). What is the length of each side?
The perimeter of square is given as,
[tex](4x-44)[/tex]Let length of side is denoted as S.
The formula for the perimeter of square is,
[tex]P=4\times S[/tex]To calculate the side of square , substitute the value of perimeter in the above formula.
[tex](4x-44)=4\times S\text{.}[/tex]Solving the equation we get,
[tex]4(x-11)=4\times S\text{.}[/tex][tex](x-11)=S.[/tex]The length of the square obtained is ,
[tex]S=(x-11).[/tex]Identify the points in figure 1 that correspond to the points Q and S . Label them B and D . What is the distance between b and d
what is the distance between P and R?
Step 1
the easiest way to find the distance is by using the grid, just count the division, one division in an unit, so
between P and R, there are six units, so the distance is 6
(1a) Clare drew a dashed line as shown in the diagram. She said the thattwo resulting shapes have the same area. Do you agree? *
The area of a rectangle is given by the formula:
[tex]A=b\times h[/tex]Where b is the length of the base and h is the height of the rectangle.
The area of a triangle is given by the formula:
[tex]A=\frac{b\times h}{2}[/tex]Where b is the length of the base of the triangle and h is its height.
The resulting shape on the right is a rectangle, whose base is 2 and its height is 4, then the area of this part of the shape is:
[tex]\begin{gathered} A=b\times h \\ A=2\times4=8 \end{gathered}[/tex]The area of the triangle resulting on the left side is:
[tex]\begin{gathered} A=\frac{b\times h}{2} \\ A=\frac{4\times4}{2}=\frac{16}{2}=8 \end{gathered}[/tex]Since the area of both shapes is 8, Clare is right.
Below, the function f(x) =3x-2 f(x)=3x-2 and the function f(x)= 3x+1f(x)=3x+1 are graphed. Compare and contrast the lines. What is similar about the equations and graphs? What is different?
You have the lines associated to the following functions:
f(x) = 3x - 2
f(x) = 3x + 1
The general equation of a line is given by:
y = mx + b
where m is the slope and b the y-intercept.
By comparing the given functions with the general form, you can notice that the slope of the lines are equal (m = 3) and the y-intercept are different, b=-2 and
b = 1.
Due to the slopes are the same you have two parallel lines.
What is the equation of a circle with center (2,-3) and radius 3?O -A. (x - 2)2 +(y +37- 3B. (x + 2)2 + (y - 3y - 9O C. (x - 2)2 +(y +3j? = 9x 2 2D. (x - 2) - (+31° - 9
The Equation of a Circle
Given a circle of radius r and centered at the point (h, k), the equation of the circle is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]Please, note the value of the coordinates of the center appear with its signs changed.
We have to find the equation of this circle by substituting the values of r = 3 and (h, k) = (2, -3). Substituting:
[tex]\begin{gathered} (x-2)^2+(y+3)^2=3^2 \\ \text{Operating:} \\ (x-2)^2+(y+3)^2=9 \end{gathered}[/tex]Choice C.
What is the first step to solving the following equation?5x – 11 = 42
Answer:
add 11 on both sides
Step-by-step explanation:
to solve this, you want x alone on one side. To achieve this, you first add 11 on both sides, so you only have the 5x alone.
Second step then is something to get only one x on the left side ;-)
(divide both sides by 5)
Answer:
the first step is to get the x term by itself on one side
Liza hired a cleaning service to clean her house. To find C, the total cost of cleaning her house, she used the following formulaC=7.5x +25What is the dependent variable of the formula
The dependent variable of the formula
[tex]C=7.5x+25[/tex]is x
I need to know the system of equation in the photo
Solution:
The graph has a solution (4,-1);
That is, the system of equation must satisfy x=4 as y=-1.
LINE 1 has its y-intercept;
[tex]\begin{gathered} (0,1) \\ \end{gathered}[/tex]LINE 2 has its y-intercept as;
[tex](0,-5)[/tex][tex]\begin{gathered} x+2y=2 \\ 2y=-x+2 \\ y=-\frac{1}{2}x+\frac{2}{2} \\ y=-\frac{1}{2}x+1 \\ \\ x-y=5 \\ y=x-5 \end{gathered}[/tex]Thus, the system of equation that satisfy the graph is;
[tex]\begin{gathered} x-y=5 \\ x+2y=2 \end{gathered}[/tex]Using long division divide y cubed + 0y squared minus 1 by y +4
Given the expression:
[tex]\frac{y^3+0y^2-1}{y+4}[/tex]Step 1:
Divide the leading term of the dividend by the leading term of the divisor. Multiply the result by the divisor and subtract the final result from the dividend as follows:
[tex]\begin{gathered} \frac{y^3}{y}=y^2 \\ \\ \\ y^2(y+4)=y^3+4y^2 \\ \\ \\ (y^3-1)-(y^3+4y^2)=-4y^2-1 \end{gathered}[/tex]Step 2: Divide the leading term of the obtained remainder by the leading term of the divisor, multiply it by the divisor, and subtract the remainder from the obtained result:
[tex]\begin{gathered} \frac{-4y^2}{y}=-4y \\ \\ \\ -4y(y+4)=-4y^2-16y \\ \\ \\ (-4y^2-1)-(-4y^2-16y)=16y-1 \end{gathered}[/tex]Step 3: Divide the leading term of the obtained remainder by the leading term of the divisor, multiply it by the divisor, and subtract the remainder from the obtained result:
[tex]\begin{gathered} \frac{16y}{y}=16 \\ \\ \\ 16(y+4)=16y+64 \\ \\ \\ (16y-1)-(16y+64)=-65 \end{gathered}[/tex]Since the degree of the remainder is less than the degree of the divisor, we would stop.
Therefore, the answer is:
[tex]\frac{y^3-1}{y+4}=y^2-4y+16+\frac{-65}{y+4}[/tex]Taylor wants four different pairs of sneakers, but can only afford to buy three of thepairs? How many sets of three pairs of sneakers can she possibly choose?
We have a set of four pairs of sneakers {A; B; C; D} and want to know how many sub-sets of three pairs of sneakers can be made with this.
To calculate that, we just need to have in mind that, for the first pair which Taylor will choose, there are four possibilities. After Taylor chooses the first pair, will be three possibilities for the second pair. And, for the third pair, we will have only the las two possibilities.
So, to gete the total number of sets of three pairs of sneakers that can be made, we just multiply the three correspondent possibilities for each choose: 4*3*2 = 24
The first bar is what percent as long as the second bar?
To find the how much the first bar represents from the second bar, we need to calculate the ratio between them.
[tex]\frac{2}{5}[/tex]To convert this ratio to a percentage, we just need to convert the denominator to 100, and the numerator will be the percentual value. We can convert by multiplying both the numerator and denominator by 20.
[tex]\frac{2}{5}\times\frac{20}{20}=\frac{2\times20}{5\times20}=\frac{40}{100}=40\%[/tex]The first bar is 40% as long as the second bar.
which of the following number is rationalA
A rational number is any number that can be expressed as a ratio of two integers, in the form p/q.
We can say that root(16) is a rational number:
[tex]\sqrt[]{16}=4=\frac{4}{1}[/tex]Find the quotient. 1 5 – 2. + 3 1 55+3= 2 (Type a whole number, fraction, or mixed number.)
we have
[tex]5\frac{1}{2}\colon3[/tex]Convert mixed number to an improper fraction
5 1/2=5+1/2=11/2
substitute
(11/2):3=11/(3*2)=11/6
convert to mixed number
11/6=6/6+5/6=1+5/6=1 5/6
answer is
11/6 or 1 5/6
8 / 1/3 and 2 / 1/9 what's the generalizations can make about the equations
The generalization about the terms is that one is the cube root of the other
∛(8/9) = 2/3
What is generalizations in mathematics?Generalization can be viewed as a statement that holds true for a broad category of objects or numbers, as the method by which we arrive at a general statement, or as a means of transferring information from one context to another in the mathematics.
The equation represented as 8 / 1/3 and 2 / 1/9
is made an equated to each other and rearranged as follows
8 / 1/3 ⇔ 2 / 1/9
cross multiplying
8 * 1/9 ⇔ 2 * 1/3
8/9 ⇔ 2/3
the equation only holds true when the cube root sign is there then we have
∛(8/9) = 2/3
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Find the volume for the solid picture. ROUND TO THE NEAREST HUNDREDTH
The given picture is in the shape of the cuboid
The general expression for the voulme of cuboid is : Length x Breadth x Height
In the given picture of cuboid we have :
Length = 9.6 in
Breadth = 6.75 in
Height = 2 in
So, the volume of given picture is :
[tex]\begin{gathered} \text{ Volume of Cuboid = Length}\times Breadth\times Height \\ \text{ Volume of Cuboid = 9.6}\times6.75\times2 \\ \text{Volume of Cuboid = }129.6in^3 \end{gathered}[/tex]To round off to the nearest hunredth : 129.6 will become 129.60
So, the volume of given solid picture is 129.60 in³
Answer : The volume of given solid picture is 129.60 in³
need help with hw I'm stuck
The quadratic formula is:
[tex]\begin{gathered} \frac{\text{ -}b\pm\sqrt[2]{b^2\text{ -4ac}}}{2a} \\ The\text{ }equation\text{ }is: \\ 2x^2+3x\text{ -}5=4 \\ 2x^2+3x\text{ -}5\text{ -4=0} \end{gathered}[/tex]We need to equal to zero before using the formula.
Noah's mistake was that he stated c=-5 when c= -9
[tex]\begin{gathered} \frac{\text{ -}b\pm\sqrt{b^2\text{ -4ac}}}{2a} \\ =\frac{-3\pm\sqrt{(\text{ -3\rparen}^2\text{ -4\lparen2\rparen\lparen-9\rparen}}}{2(2)} \\ =\frac{-3\pm\sqrt{9\text{ +72}}}{4} \\ =\frac{-3\pm\sqrt{81}}{4} \\ =\frac{-3\pm9}{4} \\ \\ x1=\frac{-3+9}{4} \\ =\frac{6}{4}=\frac{3}{2}=1.5 \\ \\ x2=\frac{-3-9}{4} \\ =\frac{-12}{4} \\ =\text{ -3} \end{gathered}[/tex]x = 1.5 or x = -3
I need some help with this I don’t understand how I would do it can I have some help
from the graph shown in the question,
we could deduce that:
x = -3,
which means x + 3 = y,
we can also deduce that x = 4,
which means that, x - 4 = y
so, the eqaution of the graph could be
y = (x - 2) (x + 3) (x - 4)
since the graph is a cubic graph
therefore the correct option is B
Suppose that f is a one-to-one function, and f^-1 is its inverse. Suppose also that h(x) = 4 and g(x) = x^2 +xsecx. Then which of the following do we NOT know to be true?
Given:
The functions are,
h(x) = 4,
g(x) = x²+xsecx
The objective is to find which of the following is not known to be true.
Let's consider option (A).
[tex]\begin{gathered} (f\circ f^{-1}\circ h)(x)=(f(f^{-1})\circ h)(x) \\ =h(x) \\ =4 \end{gathered}[/tex]Thus, option (A) is true.
Let's consider option (B).
[tex]\begin{gathered} (g\circ h\circ f^{-1})(x)=(g(h(x))f^{-1})(x) \\ =(g(4))f^{-1})(x) \\ =((4^2+4\sec 4)f^{-1})(x) \\ =((16+4\sec 4)f^{-1}(x)) \end{gathered}[/tex]Since, the obtiaed answe doesn't matches with the given options.
Hence, option (B) is not true.
A circle has a diameter of 300m. What is his circumference using pi?
To find the circumference using π = 3.14, we can proceed as follows:
1. The formula to find the circumference of a circle is:
[tex]C=2\pi r\Rightarrow D=2r\Rightarrow C=D\pi[/tex]2. That is, given the diameter, we can use it directly into the answer, since twice the value of the radius is the diameter of the circle:
[tex]C=300m\cdot3.14=942m[/tex]If we find the radius as:
[tex]D=2r\Rightarrow r=\frac{D}{2}=\frac{300m}{2}=150m[/tex]And If we use the next formula:
[tex]C=2\pi r=2\cdot3.14\cdot150m=942m[/tex]As we can see, in both cases, we found that the value for the circumference is equal to 942 meters (if we use π = 3.14).
In summary, the circumference of a circle that has a diameter of 300 meters is equal to 942 meters (C = 942m) (using π = 3.14).