Answers
Given:
The coordinates of the figure ABC are,
A(-2,0)
B(-3,-4)
C(-1,-4)
To find the correct statement:
Let us find the coordinates after rotating the figure 90 degree clockwise direction.
As we know,
In a rotation of 90 degrees clockwise, every point (x,y) will be changed to (y, -x).
So, we get,
D(0,2)
E(-4, 3)
F(-4,1)
It perfectly matches with given graph.
So, Betty's statement is correct.
If we translate the figure two units up and two units right, the given point B (-3,-4) will be changed to (-1,-2) and its reflected point over the y-axis will be (1,-2).
But, this does not match with E(-4,3).
So, Veronica's statement is wrong.
Hence, Betty's statement alone is the correct one.
Related Questions
A principal of $600 earns 3.2% interest compounded monthly. What is the effective interest (growth) rate? (Hint: make the equation look like abt.) About how long does it take to reach $1000?
Answers
Answer:
Explanation:
The formula for calculating the effective interest rate is expressed as
R = (1 + i/n)^n - 1
where
R is the effective interest rate
i is the nominal rate
n is the number of compounding periods in a year
From the information given,
n = 12 because it was compounded monthly
i = 3.2% = 3.2/100 = 0.032
Thus,
R = (1 + 0.032/12)^12 - 1
R = 0.03247
Multiplying by 100, it becomes 0.03247 x 100
Effective interest rate = 3.25%
We would apply the formula for calculating compound interest which is expressed as
A = a(1 + r/n)^nt
where
a is the principal or initial amount
t is the number of years
A is the final amount after t years
From the information given,
A = 1000
a = 600
n = 12
We want to find t
By substituting these values into the formula, we have
1000 = 600(1 + 0.032/12)^12t
1000/600 = (1.00267)^12t
Taking natural log of both sides, we have
ln (1000/600) = ln (1.00267)^12t = 12tln(1.00267)
12t = [ln (1000/600)]/ln (1.00267) = 191.5758
t = 191.5758/12
t = 16
It takes 16 years for the amount to reach $1000
the line L3 is perpendicular to 3x-y+2=0 .find the gradient of L3
Answers
Answer:
[tex]-\frac{1}{3}[/tex]Explanation:
Here, we want to get the gradient of the line L3
The equation of a straight line can be expressed as:
[tex]y\text{ = mx + b}[/tex]where m is the gradient (slope) and b is the y-intercept (the y-value when x = 0)
Now,let us write the equation of the first line in the slope-intercept form
Mathematically, we have this as:
[tex]\begin{gathered} 3x-y\text{ + 2 = 0} \\ y\text{ = 3x + 2} \end{gathered}[/tex]The gradient of the first line is 3
Now,let us get the gradient of the second line L3
Mathematically, when two lines ae perpendicular, the product of their gradients (slopes) equal -1
Thus, we have it that:
[tex]\begin{gathered} m_1\text{ }\times m_2\text{ = -1} \\ 3\text{ }\times m_2\text{ = -1} \\ m_2\text{ = -}\frac{1}{3} \end{gathered}[/tex]A spinner with 10 equally sized slices has 10 yellow slices. The dial is spun and stops on a slice at random. What is the probability that the dial stops on a yellow slice? Write your answer as a fraction in simplest form. Explanation Check U 00 00 X. S ? Esp E D 5 E [2]
Answers
Step 1
Given;
Step 2
The probability of an event is given as;
[tex]P(event)=\frac{Required\text{ number of events }}{Total\text{ number of events}}[/tex][tex]\begin{gathered} Required\text{ number of events=Yellow slice=10} \\ Total\text{ number of events= 10 slices} \end{gathered}[/tex]Thus,
[tex]P(yellow\text{ slice\rparen=}\frac{10}{10}=1[/tex]Answer;
[tex][/tex]Suppose the booster club is raising money to help offset the cost of a trip.You make $10 per door wreath sold and $2 per candy bar sold. The clubwants to raise at least $400.00. Write an inequality to represent thissituation.
Answers
Let the number of door wreath sold is x.
Let the number of candy bar sold is y.
The inequality can be represented as,
[tex]10x+2y\ge400[/tex]Thus, the above inequation gives the required inequality.
solve the equation. check your solution 1/3 (2b+9) =2/3 (b+9/2)
Answers
The equation to solve is:
[tex]\frac{1}{3}(2b+9)=\frac{2}{3}(b+\frac{9}{2})[/tex]We use distributive property [a(b+c)=ab+ac], simplify and solve for b:
[tex]\begin{gathered} \frac{1}{3}(2b+9)=\frac{2}{3}(b+\frac{9}{2}) \\ \frac{2}{3}b+3=\frac{2}{3}b+3 \end{gathered}[/tex]From here, we can't solve.
It is the same equation.
No Solution.
A gift box for a shirt has a length of 60 centimeters, a width of 30 centimeters, anda height of 10 centimeters. Find the surface area of the gift box.
Answers
A rectangular box has six faces. The surface area is given by the sum of the area of those faces. Parallel faces have the same area, therefore, we just need to calculate the area of three of them and multiply by 2. The surface area of our gift box is:
[tex]\begin{gathered} S=2(60\times30+60\times10+30\times10) \\ =2(1800+600+300) \\ =2(2700) \\ =5400 \end{gathered}[/tex]The surface area of the box is 5400 cm².
Consider the following function. Complete parts (a) through (e) below.f(x)=x²-2x-8The vertex is.(Type an ordered pair.)c. Find the x-intercepts. The x-intercept(s) is/are(Type an integer or a fraction. Use a comma to separate answers as needed.)d. Find the y-intercept. The y-intercept is(Type an integer or a fraction.)e. Use the results from parts (a)-(d) to araph the quadratic function.
Answers
Given the function:
[tex]f(x)=x^2-2x-8[/tex]It is a quadratic function where:
a=1
b= -2
c= -8
The x-coordinate of the vertex is given by:
[tex]x=-\frac{b}{2a}[/tex]Substitute a and b:
[tex]x=-\frac{-2}{2(1)}=\frac{2}{2}=1[/tex]Substituting in the original equation to obtain the y-coordinate, we obtain:
[tex]y=(1)^2-2(1)-8=1-2-8=-9[/tex]So, the vertex is (0, -9)
c. For the intercept at x we make y = 0:
[tex]0=x^2-2x-8[/tex]And solve for x by factorization:
[tex]\begin{gathered} (x-4)(x+2)=0 \\ Separate\text{ the solutions} \\ x-4=0 \\ x-4+4=0+4 \\ x=4 \\ and \\ x+2=0 \\ x+2-2=0-2 \\ x=-2 \end{gathered}[/tex]So, the x-intercepts are:
(-2, 0) and (4,0)
Answer: (-2,0), (4,0)
d. For the intercept at y we make x = 0:
[tex]y=(0)^2-2(0)-8=-8[/tex]So the y-intercept is (0, -8)
Answer: (0, -8)
e. Graphing the function:
The midpoint of AB is M(5,1). If the coordinates of A are (3,6), what are thecoordinates of B?
Answers
We have a segment AB of which we know the coordinates of A(3,6) and the midpoint M(5,1).
We have to find the coordinates of B.
We know that the coordinates of the midpoint M are the average of the coordinates of the endpoints A and B, so we can write:
[tex]\begin{gathered} x_M=\frac{x_A+x_B}{2} \\ 2\cdot x_M=x_A+x_B \\ x_B=2x_M-x_A \end{gathered}[/tex]Now we have the x-coordinate of B in function of the x-coordinates of A and M.
The same can be calculated for the y-coordinate:
[tex]y_B=2y_M-y_A[/tex]Then, we can replace and calculate:
[tex]\begin{gathered} x_B=2x_M-x_A \\ x_B=2\cdot5-3 \\ x_B=10-3 \\ x_B=7 \end{gathered}[/tex][tex]\begin{gathered} y_B=2y_M-y_A \\ y_B=2\cdot1-6 \\ y_B=2-6 \\ y_B=-4 \end{gathered}[/tex]Then, the coordinates of B are (7,-4).
Answer: B = (7,-4)
I need this practice problem from my prep guide answered and explained
Answers
To rewrite the equation in the indicated form, isolate the variable terms on the left side of the equation.
[tex]8x^2+9y^2-16x-9y=-2[/tex]Group the variable terms and then complete the squares. Add the same terms on the right side of the equation to make it balance.
[tex]\begin{gathered} (8x^2-16x)+(9y^2-9y)=-2 \\ 8(x^2-2x)+9(y^2-y)=-2 \\ 8(x^2-2x+1)+9(y^2-y+\frac{1}{4})=-2+8+9(\frac{1}{4}) \end{gathered}[/tex]Rewrite the trinomials as squares of binomials and then simplify the right side of the equation.
[tex]8(x-1)^2+9(y-\frac{1}{2})=\frac{33}{4}[/tex]To make the right side of the equation equal to 1, multiply both sides of the equation by 4/33.
[tex]\begin{gathered} \mleft(\frac{4}{33}\mright)(8)(x-1)^2+\mleft(\frac{4}{33}\mright)(9)(y-\frac{1}{2})=\mleft(\frac{4}{33}\mright)\mleft(\frac{33}{4}\mright) \\ \frac{32\mleft(x-1\mright)^2}{33}+\frac{12(y-\frac{1}{2})}{11}=1 \end{gathered}[/tex]Can anyone help me? I don't know the answer.
Answers
Hence, the area of the rectangle is [tex]\frac{21}{32}m^2[/tex].
What is the rectangle?
A rectangle is a two-dimensional flat shape. In an [tex]XY[/tex] plane, we can easily represent a rectangle, where the arms of x-axis and y-axis show the length and width of the rectangle, respectively.
Area of rectangle = Length × Width
Here given that,
[tex]L=\frac{7}{8}m[/tex]
[tex]W=\frac{3}{4}m[/tex]
So,
Area of rectangle = [tex](\frac{7}{8}m)*(\frac{3}{4}m)\\[/tex]
[tex]=\frac{21}{32}m^2[/tex]
Hence, the area of the rectangle is [tex]\frac{21}{32}m^2[/tex].
To know more about the rectangle
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Need help with solving equations and also need help understanding what moves to the lowest variable term mean.
Answers
An equation is a mathematical expression that contains an equal sign. The objective of an equation is usually to determine the value of an unkown variable, commonly referred to x or y. In order to do that, however, we need to isolate the variable on the left side and this has to be done in a way that mantains the balance in the equation. This means that whatever operation we do on one side we have to perform the same exact operation on the other side. Let's take a look at an example.
[tex]3x+9=x+40[/tex]For this equation we have the unknown variable x, which is the value we want to find. Our goal is to isolate the variable on the left side, however we can see that there is one x on the right side, the first step will be to move this to the left side, this is what means to move the lowest variablem term first, because if we were to move "3x", which is the highest variable term, we would have to perform more steps to solve the equation.
To move the term "x" from the right to the left we need to subtract both sides by "x", this is because when we subtract "x-x" on the right side, the result will be 0 and we will be left with unkown variables only on the left. Let's check this out:
[tex]\begin{gathered} 3x+9-x=x+40-x \\ 3x-x+9=x-x+40 \\ 2x+9=40 \end{gathered}[/tex]As we can see by doing so we eliminated the variable on the right side. Now we want to remove the 9 from the left side, we will have to perform a similar operation by subtracting 9 from both sides.
[tex]\begin{gathered} 2x+9-9=40-9 \\ 2x=31 \end{gathered}[/tex]Now we have only a variable term on the left side, but it still being multiplied by 2 and we don't want that, so we have to divide both sides by 2.
[tex]\begin{gathered} \frac{2x}{2}=\frac{31}{2} \\ x=\frac{31}{2} \end{gathered}[/tex]With this we achieved the goal of the equation, which was to find the value of x. In short we always want to isolate the variable on the left side and to do that we will have to perform the inverse operation of the other terms in both sides of the equation, if a term is adding we need to subtract on both sides, if it is multiplying we need to divide on both sides and so on. We have to do that first with the term that contains the letter of lowest value, like we did with this one.
7/5-6/5+3/2=17/10=1 7/10
Answers
Question:
Solution:
Let us denote by x the blank space in the given equation. Then, we get:
[tex]\frac{7}{5}-x+\frac{3}{2}=\frac{6}{5}[/tex]this is equivalent to:
[tex]\frac{7}{5}+\frac{3}{2}-x=\frac{6}{5}[/tex]this is equivalent to:
[tex]\frac{14+15}{10}-x=\frac{6}{5}[/tex]that is:
[tex]\frac{29}{10}-x=\frac{6}{5}[/tex]solving for x, we obtain:
[tex]\frac{29}{10}-\frac{6}{5}=x[/tex]that is:
[tex]x=\frac{29}{10}-\frac{6}{5}=\frac{29-12}{10}=\frac{17}{10}[/tex]so that, the blank space would be:
[tex]\frac{17}{10}[/tex]and the complete expression would be:
[tex]\frac{7}{5}-\frac{17}{10}+\frac{3}{2}=\frac{6}{5}[/tex]I need help with finding the area and perimeter of the letter o
Answers
Check below, please.
1) In this question, we're going to remember two concepts: The perimeter is the sum of the lengths of each segment of each letter.
2) So let's start counting each tiny square so that we can get to know the length.
The letter "L" is actually, with this typography, two rectangles:
So, the perimeter (2P) is equal to:
2P =15 +15 +7+3+3+10+3
2P= 56 units
As for the area:
Using the Rectangle formula, then we can write down the area as:
Area:
[tex]\begin{gathered} A=l\cdot w \\ A_1=3\cdot15=45u^2 \\ A_2=10\cdot3=30u^2 \\ A_L=30+45=75u^2 \end{gathered}[/tex]3) In this letter "O" we can divide it into two trapezoids, and two parallel rectangles:
Note that we need to find the length of those corners shaped like triangles, we can use the Pythagorean Theorem, considering the "rise over run" and write:
[tex]\begin{gathered} a^2=3^2+2^2 \\ a^2=9+4 \\ a^2=13 \\ \sqrt[]{a^2}=\sqrt[]{13} \\ a=3.6 \end{gathered}[/tex]So the Perimeter can be written:
[tex]\begin{gathered} 2P=3.6+3.6+3.6+3.6+5+5+12+12+12+12+3+3 \\ 2P_O=78.4 \end{gathered}[/tex]And for the area, we can find the area of those two trapezoids and two rectangles writing this:
[tex]\begin{gathered} A_O=2(\frac{(B+b)h}{2})+2(w\times l) \\ A_O=2(\frac{(9+3)3}{2})+2(12\times3)_{} \\ A_O=108u^2 \end{gathered}[/tex]4) And now, finally the letter "u":
For the corners let's assume they are triangles, and then we can write the following since those corners are like hypotenuses:
[tex]\begin{gathered} a^2=5^2+2^2 \\ a^2=25+4 \\ a=\sqrt[]{29}\approx5.4 \end{gathered}[/tex]And for the inclined lower part of the letter "u", we can write:
[tex]\begin{gathered} a^2=1^2+2^2 \\ a=\sqrt[]{5}\approx2.2 \end{gathered}[/tex]Therefore, we can write the Perimeter as:
[tex]\begin{gathered} 2P=2(5.4)+2(2.2)+4+3(2)+4(13) \\ 2P_U=77.2 \end{gathered}[/tex]And for the area, we can see from bottom to top: One trapezoid, a par of parallelograms, and two rectangles. Hence, we can write:
[tex]\begin{gathered} A_U=\frac{(B+b)h}{2}+2(l\cdot w)+2(l\cdot w) \\ A_U=\frac{(6+4)3}{2}+2(2\cdot2)+2(2\cdot13) \\ A_U=75u^2 \end{gathered}[/tex]5) So, each letter by area and perimeter:
[tex]\begin{gathered} A_L=75u^2 \\ 2P_L=56u \\ -- \\ A_O=108u^2 \\ A_O=78.4u \\ -- \\ A_U=75 \\ 2P_U=77.2 \end{gathered}[/tex]See attached pic of problem. I have to show cancelling of units and answer has to show proper number of significant figures.
Answers
We have that 1 cubic meter is equivalent to 1.308 cubic yards. Then, we can use a rule of three to find the value in yards of 1.37 cubic meters:
[tex]\begin{gathered} 1m^3\rightarrow1.308yd^3 \\ 1.37m^3\rightarrow x \\ \Rightarrow x=\frac{(1.37m^2)(1.308yd^3)}{1m^3}=1.37(1.308yd^3)=1.792yd^3 \\ \Rightarrow x=1.792yd^3 \end{gathered}[/tex]therefore, 1.37m³ is equivalent to 1.792yd³
Find the equation of the line containing the points (42.3,82) and (42.8,94) more
Answers
Let's remember that the equation of a line always has the form:
[tex]y=m\cdot x+b[/tex]where "m" and "b" are constant numbers that we must find. Now, let's find "m" first. "m" is called the slope of the line, and it represents the relationship between the changes in y (second component) and the changes in x (first component). So it isn't surprising that we can compute it by:
[tex]m=\frac{94-82}{42.8-42.3}=\frac{12}{0.5}=24[/tex]Having calculated "m", we know that, (for the point (42.3,82) must lie in the line)
[tex]82=24\cdot(42.3)+b[/tex]Then,
[tex]b=82-24\cdot(42.3)=933.2[/tex]This implies that the equation of our line is
[tex]y=24\cdot x-933.2[/tex]Here is a graph of the line:
Comment: Our line is represented with a red color.
Julia has been measuring the length of her baby's hair. The first time it was 6 cm long and after one month it was 2 cm longer. If the hair continues to grow at this rate, determine the function that represents the hair growth and graph it.
Answers
Given that,
The length of baby's hair at first time = 6cm
After a month, the length was 2 cm longer = 6 + 2 = 8 cm
As mentioned in the question, the hair continues to grow at this rate. Therefore, after two months, the length would be = 8 + 2 = 10 cm
It results in a sequence with a common difference of 2,
6, 8, 10, 12, ............
If a sequence has a common difference, it is called an arithmetic sequence. In such sequences, the nth term is calculated as:
an = a1 + (n-1)*d
Here,
a1 = first term = 6
d = common difference = 2. (8-6 or 10 - 8 = 2)
Now, put all the values in the equation,
an = a1 + (n-1)*d
an = 6 + (n-1)*2
an = 6 + 2n - 2
an = 2n + 4
an = 2(n+2)
Hence, the function that represents growth is an = 2(n+2).
By varying the value of 'n', you can get the values of 'an'. Both will generate ordered pairs that will help you in plotting. For example:
n = 1
an = 2(n+2) = 2(1+2) = 2 (3) = 6
=> ordered pair (1, 6)
n = 2
an = 2(n+2) = 2(2+2) = 2 (4) = 8
=> ordered pair (2, 8)
n = 3
an = 2(n+2) = 2(3+2) = 2 (5) = 10
=> ordered pair (3, 10)
n = 4
an = 2(n+2) = 2(4+2) = 2 (6) = 12
=> ordered pair (4, 12)
With the ordered pairs, you can plot the graph.
Use the Distributive Property to rewrite each expression without parentheses.1. 6(x+3)2. 5(y-4)3. - 7(m-1)4. 9(3x + 2)5. -3(7 +3p)6. 1 (8x-10)
Answers
The distributive property states:
[tex]a(b+c)=a\cdot b+a\cdot c[/tex]so:
[tex]\begin{gathered} 6(x+3)=6\cdot x+6\cdot3=6x+18 \\ 5(y-4)=5\cdot y-5\cdot4=5y-20 \\ -7(m-1)=-7\cdot m-7\cdot(-1)=-7m+7 \\ 9(3x+2)=9\cdot3x+9\cdot2=27x+18 \\ -3(7+3p)=-3\cdot7-3\cdot3p=-21-9p \\ 1(8x-10)=1\cdot8x+1\cdot10=8x-10 \end{gathered}[/tex]what is the driving distance from the hospital to City Hall
Answers
Coordinate of the Hospital = (-6, -4)
Coordinate of City Hall = (0,0)
[tex]\begin{gathered} \text{Distance betw}en\text{ two points = }\sqrt[]{(x_2-x_{1)^2+}(y_2-y_1)^2} \\ \\ =\sqrt[]{(0-(-6))^2+(0-(-4))^2} \\ =\sqrt[]{(0+6)^2+(0+4)^2} \\ =\sqrt[]{6^2+4}^2 \\ =\sqrt[]{36\text{ +16}} \\ =\sqrt[]{52} \\ =2\sqrt[]{13}\text{ or 7.21} \end{gathered}[/tex]The Hill family and the Stewart family each used their sprinklers last summer. The water output rate for the Hill family's sprinkler was 15 L per hour. Thewater output rate for the Stewart family's sprinkler was 25 L per hour. The families used their sprinklers for a combined total of 55 hours, resulting in atotal water output of 1025 L. How long was each sprinkler used?Note that the ALEKS graphing calculator can be used to make computations easier.Х5?Hill family's sprinkler: hoursStewart family's sprinkler: [hoursM
Answers
The Hill family and the Stewart family each used their sprinklers last summer. The water output rate for the Hill family's sprinkler was 15 L per hour. The
water output rate for the Stewart family's sprinkler was 25 L per hour. The families used their sprinklers for a combined total of 55 hours, resulting in a
total water output of 1025 L. How long was each sprinkler used?
Let
x ------> the number of hours of Hill family's sprinkler
y ------> the number of hours of Stewart family sprinkler
so
we have that
x+y=55 -------> x=55-y ------> equation 1
15x+25y=1025 ------> equation 2
Solve the system
Substitute equation 1 in equation 2
15(55-y)+25y=1025
solve for y
825-15y+25y=1025
10y=1025-825
10y=200
y=20
Find the value of x
x=55-20) -----> x=35
therefore
Hill family's sprinkler: 35 hoursStewart family's sprinkler:20 hoursThe US consumes an average of 5.25 million metric tons of bananas per year. There are 317 million people in the US and there are 1000 kg in 1 metric ton. How many kilogram of bananas are consumed per person in a year? Round answer (except last one) to three significant digits. 365 days in a year.
Answers
The US consume 5.25 million metric tons of banana per year.
This is equivalent to 5.25 million x 1000kg = 5250 000 000 kg
US population = 317 million = 317 000 000
The number of kilogram of bananas consumed per person per year
= 5250 000 000 kg / 317 000 000
=16.6 kg
Therefore, the number of kilogram of bananas that are consumed per person per year is 16.6kg
15x²y/(x+1)^3* (x+1)/24x^5y
Answers
The simplified value of the given expression in the form of a fraction is [tex]\frac{5}{8\cdot(x+1)^2\cdot x^3}[/tex] .
The given expression is: [tex]\frac{15x^2y}{(x+1)^3}\cdot\frac{(x+1)}{24x^5y}[/tex]
we will use the properties of exponents to simplify the expression.
Taking the powers of the like terms and combining we get :
[tex]\implies \frac{15x^2y}{(x+1)^3}\cdot\frac{(x+1)}{24x^5y}[/tex]
[tex]\implies \frac{15}{24} \times \frac{x^{2-5}y^{(1-1)}}{(x+1)^{3-2}}[/tex]
[tex]\implies \frac{5}{8\cdot(x+1)^2\cdot x^3}\\[/tex]
Therefore we get the simplified equation for the expression.
Expressions are mathematical statements that comprise either numbers, variables, or both and at least two terms associated by an operator. Mathematical operations include addition, subtraction, multiplication, and division.
In mathematics, there are two different types of expressions: algebraic expressions, which also include variables, and numerical expressions, which solely comprise numbers. A set sum of money appears to be a constant.
A variable is a symbol that has no predetermined value. A term may consist of one constant, one variable, or a combination of variables and constants multiplied or divided. A number that is additionally multiplied by a variable is referred to as the coefficient in an expression.
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i don’t understand this very well, i think growth and decay but not sure
Answers
She bought the bike by 3,000 six years ago, we are assuming the value of her mountain bike depreciated 20% each year
1 year
3,000*20% = 600
2year
3,000-600 = 2,400*20% = 480
3year
2,400-480 = 1920*20% = 384
4 year
1920-384= 1,536*20% = 307.2
5 year
1,536-307.2= 1,228.8*20% = 245.76
6year
1,228.8 - 245.76 = 1,043.04*20% = 208.608
1,043.04 - 208.608 =834.432
Rounded to the nearest dollar
= 834
In AOPQ, OQ is extended through point Q to point R, m PQR = (7x – 19)º, mZOPQ = (2x – 3)°, and mZQOP = (x + 16). Find mZPQR.
Answers
Solution
For this case we can do the following:
m < PQR = 7x -19
m < OPQ= 2x-3
m < QOP= x+16
We need to satisfy that:
(180- m Replacing we got:
(180- 7x +19) + 2x -3 + x+16= 180
-7x +2x +x = -19+3 -16
-4x = -32
x= 8
Then m
Which choice best represents the sum of (5 + 8x -3) and (9x -6)1: 17x + -42: 17x + 43: x + 144: x + - 14
Answers
We can solve the expression as:
[tex]\begin{gathered} (5+8x-3)+(9x-6) \\ 2+8x+9x-6 \\ 17x-4 \end{gathered}[/tex]The answer is 1. 17x-4.
Match these equation balancing steps with the description of what was done in each step.Step 1:12x - 6 = 10 6x - 3 = 5 -Add 3 to both sides -Divide both sides by 6 -Divide both sides by 2 Step 2: 6x - 3 = 5 6x = 8 -Add 3 to both sides -Divide both sides by 6 -Divide both sides by 2 Step 36x = 8 x= 4/3 -Add 3 to both sides -Divide both sides by 6 -Divide both sides by 2
Answers
Step 1:
6x - 3 = 5
[tex]\begin{gathered} \text{add 3 to both sides} \\ 6x-3+3=5+3 \\ 6x=8 \end{gathered}[/tex]step 2:
6x = 8
[tex]\begin{gathered} \text{Divide both sides by 6} \\ \frac{6x}{6}=\frac{8}{6} \\ x=\frac{4}{3} \end{gathered}[/tex]Step 3:
x = 4/3
[tex]\begin{gathered} \text{divide both sides by 2} \\ x=\frac{8}{6}=\frac{4}{3} \end{gathered}[/tex]
Daryl loaned his friend $2,500 to help him with his business. If his friend pays Daryl back in one year with 15% simple interest how much will he owe Daryl all together?
Answers
Answer:
$2875
Explanation
Given
Principal P = $2,500
Rate R = 15%
Time T = 1year
Get the interest on $2500
Simple Interest = PRT/100
Simple Interest = 2500 * 15 * 1/100
Simple Interest = 25*15
Simple Interest = $375
Amount owed altogether = Pricipal + Interest
Amount owed altogether = $2500 + $375
Amount owed altogether = $2875
Patricia keeps apples in 3 bins and 2 crates in her store. Each bin can hold no more than 200 pounds. Each crate can hold no more than 50 pounds. Which number line represents all of the possible weights, in pounds, of apples Patricia can keep in her store?
Answers
Given:
The bins can hold no more than w(b) < 200 pounds.
The crate can hold no more than w(c) < 50 pounds.
The number of bins is n(b) = 3.
The number of crates is n(c) = 2.
The objective is to find the correct number line for the graph.
Explanation:
The maximum quantity of bins can be calculated as,
[tex]\begin{gathered} Q(b)The maximum quantity of crate can be calculated as,[tex]\begin{gathered} Q(c)To find the maximum store capacity:The maximum store capacity can be calculated as,
[tex]undefined[/tex]Translate this sentence into an equation.The product of 5 and Julie's height is 80.Use the variablej to represent Julie's height.
Answers
ANSWER:
5 x j = 80
STEP-BY-STEP EXPLANATION:
The sentence as an equation would be the multiplication of j and 5 equal to 80, just like this:
[tex]5\times j=80[/tex]Jennie has $300 and spends $15.What percent of her money is spent?
Answers
ok
Total money = $300
money spend = $15
300 ---------------------- 100
15 ---------------------- x
x = (15 x 100)/300
x = 1500/300
x = 5
Jennie spent 5% of her money
To solve it, use a rule of three. $300 is 100%, so we need to calculate which percent is $15 of the total amount.
In a rule of three, it's necessary to use cross multiplication and then division.
That's why I multiplied 15 by 100 and then I divided by 300.
15 is 5% of $300
in the function y=-2(x-1)+4 what effect does the number 4 have onthe graph, as compared to the graph of the function 7OA. t shifts the graph down 4 unitsO B. t shifts the graph 4 units to the leftOcHshifts the graph up 4 unitsOD.t shifts the graph 4 units to the right
Answers
Given:
y = -2(x - 1) + 4
The effect the number 4 has on the graph of the function is that there will be a vertical shift of 4 units up.
+4 here indicates a vertical shift of 4 upwards
ANSWER:
C) It shifts the graph up 4 units