Answer:
21
Step-by-step explanation:
[tex]6*7-7*3[/tex]
Utilizing PEMDAS, we know that all multiplication comes before subtraction.
P - Parenthesis
E - Exponents
M - Multiplication
D - Division
A - Addition
S - Subtraction
Knowing this, multiply the four terms:
[tex]42-21[/tex]
Now subtract:
[tex]21[/tex]
-4 - (x - 2) = 5x + 6
Given the equation:
[tex]-4-(x-2)=5x+6[/tex]We will find the value of x as follows:
[tex]-4-x+2=5x+6[/tex]combine the like terms:
[tex]\begin{gathered} -5x-x=6-2+4 \\ -6x=8 \end{gathered}[/tex]divide both sides by (-6)
[tex]\begin{gathered} \frac{-6x}{-6}=\frac{8}{-6} \\ \\ x=-\frac{4}{3} \end{gathered}[/tex]So, the answer will be x = -4/3
If the eccentricity is a maximum value of 1, is it a circle or a straight line?
Step 1
if the eccentricity is a minimum value of 0 it is a circle because you have only one point and there is no focal distance.
However, if the eccentricity is a maximum value of 1, it would be a line.
Hence, the answer is a straight line.
What is the domain of the function shown in the table? X Y 0 1 1 0 1 3 A. (-2, 0), (-1, 1), (0, 2), (1,3) B. {0, 1,2,3} C. {-2,-1,0,1,2,3) PI D. 1-2. -1,0,1)
The domain of a function is the set of values that the x variable can take.
In this case, those values are:
[tex]\lbrace-2,-1,0,1\rbrace[/tex]how can I draw a horizontal bar chart to represent the recorded data shown above using the approximate lengths in kilometres?
In order to create a horizontal bar chart, let's create horizontal bars, with lengths proportional to each km in the table and the corresponding labels.
So we have:
Factor 3x^2y^2 - 6xy^2
From the binomial:
[tex]3x^2y^2-6xy^2[/tex]We can factor out the GCF by factoring out the GCF of the coefficients, and the lowest power of each variable.
The GCF of 3 and 6 is 3.
The lowest power of x is 1.
The lowest power of y is 2.
Then, we can factor out:
[tex]3xy^2[/tex]Multiply each term by:
[tex]\frac{3xy^2}{3xy^2}[/tex]Which does not change the meaning of the expression, since that fraction is equal to 1:
[tex]\begin{gathered} 3x^2y^2-6xy^2=3x^2y^2\times^{}\frac{3xy^2}{3xy^2}-6xy^2\times^{}\frac{3xy^2}{3xy^2} \\ =3xy^2(\frac{3x^2y^2^{}}{3xy^2}-\frac{6xy^2}{3xy^2}) \\ =3xy^2(x-2) \end{gathered}[/tex]Therefore:
[tex]3x^2y^2-6xy^2=3xy^2(x-2)[/tex]supposed eat tube in the right rectangular prism is 1/2 in unit cube
Given that each cube is ½ unit.
a) The dimension of the prism is:
For the dimensions of a prism, we have:
Length; width; height
[tex]\text{length = 5}\ast\frac{1}{2}=\text{ }\frac{5}{2}\text{ units}[/tex][tex]\text{Width = 4 }\ast\text{ }\frac{1}{2}=\text{ }\frac{4}{2}=\text{ 2 units}[/tex][tex]\text{Height = 3 }\ast\text{ }\frac{1}{2}=\frac{3}{2}\text{ units}[/tex]b) To find the volume of the prism, use the formula below:
[tex]\text{Volume = length }\ast\text{ width }\ast\text{ height}[/tex]Thus, we have:
[tex]\text{Volume = }\frac{5}{2}\ast\frac{2}{1}\ast\frac{3}{2}=\frac{30}{4}=\frac{15}{2}\text{ units cube}[/tex]ANSWER:
[tex]\begin{gathered} a)\text{ length = }\frac{5}{2}\text{ units} \\ \text{ width = 2 units} \\ \text{ height = }\frac{3}{2}units \end{gathered}[/tex][tex]b)\text{ Volume = }\frac{15}{2}\text{ units cube}[/tex]you buy tomatoes in 25 lb cases one batch of Cobb salad requires 5 oz of tomatoes how many portion can be made with one shipment
ANSWER:
80 portion
STEP-BY-STEP EXPLANATION:
What we must do in this case is to convert the number of pounds to ounces, knowing that 1 pound is equal to 16 ounces.
[tex]25\text{ lb}\cdot\frac{16\text{ oz}}{1\text{ lb}}=400\text{ oz}[/tex]Now to calculate the number of portion, we must calculate the quotient between the total in ounces tomatoes and the amount per portion:
[tex]\frac{400}{5}=80[/tex]Choose which of the following demonstrate a dilation centered at the origin: (x,y)→(1.5x,1.5y)
To answer this question, we need to remember that for a dilation centered a the origin, we need to multiply each of the given coordinates by the factor of dilation. In this case, we have that this factor is k = 1.5. This implies that the image is 1.5 greater than the original figure.
We have four graphs, in which:
1. Graph A implies that image A'B'C' is smaller than the original figure. Then, this is not the graph.
2. Graph B implies another kind of transformation. It is not a dilation.
3. We have that graphs C and D are the potential graphs to solve the question.
We need to identify the coordinates of the original figure:
[tex]A(4,5),B(0,2),C(1,-1)[/tex]These are the coordinates for the original figure in both graphs.
Now, to have the corresponding dilation centered at the origin, we need to multiply each of the coordinates by the factor of dilation, k = 1.5. Then, we have:
[tex]A(4,5)\rightarrow A^{\prime}(4\cdot1.5,5\cdot1.5)=A^{\prime}(6,7.5)[/tex][tex]B(0,2)\rightarrow B^{\prime}(0\cdot1.5,2\cdot1.5)=B^{\prime}(0,3)[/tex][tex]C(1,-1)\rightarrow C^{\prime}(1\cdot1.5,-1\cdot1.5)=C^{\prime}(1.5,-1.5)[/tex]Now, we need to check these results for each graph.
We can see that:
Graph C fits the dilation centered at the origin indicated above.
Therefore, the answer to this question is C (graph represented by letter C).
For a given geometric sequence, the 9th term, ag. is equal to -43/64and the 13th term, Q13, is equal to - 172. Find the value of the 17th term, a17. If applicable,write your answer as a fraction.A17=
Hello
To solve this question, we can simply use the formula of finding the nth term of a geometric progression.
[tex]\begin{gathered} T_n=ar^{n-1} \\ a=\text{first term} \\ r=\text{common ratio} \end{gathered}[/tex][tex]\begin{gathered} a_9=ar^8 \\ ar^8=-\frac{49}{64} \\ a_{13}=ar^{12}=-172 \end{gathered}[/tex][tex]\begin{gathered} ar^8=-\frac{49}{64}\ldots\text{equ 1} \\ ar^{12}=-172\ldots equ(ii) \\ \\ \text{divide equation (ii) by equation (}i) \\ \frac{ar^{12}}{ar^8}=-\frac{172}{-\frac{49}{64}} \\ \text{divde both a} \\ \frac{r^{12}}{r^8}=-\frac{172}{-\frac{49}{64}} \\ u\sin g\text{ division law of indicies} \\ r^{12-8}=-172\times-\frac{64}{49} \\ r^4=\frac{-172\times-64}{49} \\ r^4=224.65 \\ \text{take the quartic root of both side} \\ \sqrt[4]{r^4}=\sqrt[4]{224.65} \\ r=3.9 \end{gathered}[/tex]Now that we have the value of the common ratio, we can proceed to solve for the first term which would help us find the 17th term.
we can use either of 9th term or 13th term.
Using the 13th term
[tex]\begin{gathered} a_{13}=ar^{12}=-172_{} \\ ar^{12}=-172 \\ r=3.87 \\ a(3.9)^{12}=-172 \\ a=-\frac{172}{3.87^{12}} \\ a=-0.00001389 \end{gathered}[/tex]Now, let's use this to find the 17th term.
Our first term is -0.0000152 and the common ratio is 3.9
Note: Some of these values was approximated and may differ from person to person.
[tex]\begin{gathered} a_{17}=ar^{16} \\ a_{17}=-(0.00001389)\times(3.9)^{16} \\ a_{17}=-39791.185\approx-39791 \end{gathered}[/tex]From the calculations above, the 17th term of the geometric sequence is approximately -39791
if the point x,y is on the y-axis which off the following is truex=0y=0
1) Given such conditions, the x-coordinate is 0, so we can write
2) x=0, as the true option.
Since there's no rise on this point. We can call
26+(-18) what is the answer
The given expression is
[tex]26+(-18)[/tex]To solve this, we multiply signs,
[tex]26+(-18)=26-18[/tex]Then, we subtract
[tex]26-18=8[/tex]Therefore, the an
simplest answer possible.
8, your answer is 8.
a paintball court charges an initial entrance fee plus a fixed price per ball
Question:
Solution:
According to the given equation, the entrance fee is 5.50 and the fixed price per ball is 0.80n. Thus, the price for 10 balls, NOT INCLUDING the entrance fee (5.50), would be:
[tex]0.80\text{ n = 0.80 (10) = 8}[/tex]we can conclude that the correct answer is:
8.
Find the value of x. *1 point66(3x + 21)5715Ο ΟΟ Ο10
Given that the total sum of interior angles of a triangle = 180 degrees.
Thus, we have:
(3x + 21) + 66 + 57 = 180
Let's find the value of x.
3x + 21 + 66 + 57 = 180
3x + 144 = 180
Subtract 144 from both sides:
3x + 144 - 144 = 180 - 144
3x = 36
Divide both sides by 3:
[tex]\begin{gathered} \frac{3x}{3}=\frac{36}{3} \\ \\ x\text{ = 12} \end{gathered}[/tex]ANSWER:
12
Sing Wu's annual gross pay is $51,400. He takes a married exemption of $4,000. Hisstate income tax rate is 3.5 percent. How much will he pay annually in state tax?
total income is = 51400 $
exemption is = 4000$
so net amount for tax is = 51400 - 4000 = 47,400 $
now 3.5 % of 47,400 as tax is
[tex]47400\times\frac{3.5}{100}=1659[/tex]so he will pay 1659 $ as annual tax.
input 0,1,2,3,4 output 2,1,0,-1,0 what is the rate of change
The rate of change can be thought of as the slope of the line that passes through all the points, when plotted on a the x-y plant.
Alternatively, the rate of change can be thought of as the rate at which the output is changing as compared to the change in input.
According to the second explanation, the rate of change can be written as:
[tex]\text{rate of change=}\frac{change\text{ in output}}{\text{change in input}}[/tex]Now, let us select to inputs and their corresponding outputs.
Thus:
for input 0, we have output 2
for input 3, we have output -1
Therefore:
[tex]\text{change in input = 3-0=3}[/tex]and:
[tex]\text{change in output= -1-2 = -3}[/tex]The rate of change is thus:
[tex]\begin{gathered} \text{rate of change=}\frac{change\text{ in output}}{\text{change in input}} \\ \Rightarrow\text{rate of change=}\frac{-3}{3}=-1 \\ \Rightarrow\text{rate of change=}-1 \end{gathered}[/tex]Therefore, the rate of change is -1
A right rectangular prism has a base area of 24 cm2. Its volume, in cubic centimeters, is not a whole number 1 h 1 1 -- - 1 1 - B w Select the measures that could be two of the dimensions of this prism. To select a measure, click the measure. To deselect a measure, click it again. length = 6 cm width = 4 cm length = 6.1 cm height = 2 cm width = 3.9 cm height = 8.4 cm length = 7.5 cm width = 3.5 cm length = 12 cm height = 15.1 cm width = 10.5 cm height = 9 cm
ANSWER
EXPLANATION
Of the boxes that say the length and width of the prism, we have to see which ones have 24 as a product - since this is the area of the base. There are two - the two on the left - the first one:
[tex]A=l\times w=6\operatorname{cm}\times4\operatorname{cm}=24\operatorname{cm}^2[/tex]This is correct, because the area is 24cm²
The second one:
[tex]A=l\times w=7.5\times3.5=26.25[/tex]This is not the right base area, so these dimensions are not right.
Then, with the rest of the dimensions we have the height. The volume of a prism is the product of its dimensions or, in other words, the product of the area of the base and its height. Therefore, since we know that the area of the base is 24, we just have to multiply that by the given height and see which ones give not a whole number as a result.
24 is a whole number, so when it is multiplied by a whole number the result is another whole number, so the options where the height is a whole number can't be right.
Then we just have to see if the mentioned product with the heights of the remaining options is a decimal.
For the bottom option in the middle: height = 15.1:
[tex]V=24\times15.1=362.4[/tex]Not a whole number --> correct
For the upper option on the right: height 8.4:
[tex]V=24\times8.4=201.6[/tex]Not a whole number --> correct
The lengths of the two legs in a triangle are 10 and 24. What is the length of the hypotenuse?OSubmitсab
Answer:
The length of the hypotenuse is;
[tex]26\text{ units}[/tex]Explanation:
Given the triangle in the attached image.
The length of the two legs given as;
[tex]\begin{gathered} a=10 \\ b=24 \end{gathered}[/tex]Applying Pythagorean thereom;
[tex]\begin{gathered} a^2+b^2=c^2 \\ c=\sqrt[]{a^2+b^2} \end{gathered}[/tex]substituting the given values;
[tex]\begin{gathered} c=\sqrt[]{10^2+24^2} \\ c=\sqrt[]{100+576} \\ c=\sqrt[]{676} \\ c=26 \end{gathered}[/tex]Therefore, the length of the hypotenuse is;
[tex]26\text{ units}[/tex]
Score on last try: 0 of 25 pts. See Details for more. > Next question You can retry this question below P R Line n bisects line QR. IF PQ = 2x and QR = 8x - 12; Find PR. x 5 Submit Question
When a line bisects another in a certain point it creates two segments, these must be equal in length. So the sum of their lengths is equal to the length of the whole line. In this case the line QR was divided in PQ and PR, so we have:
[tex]QR=PQ+PR[/tex]We want to find the length of PR, so we need to isolate it on the left side:
[tex]PR=QR-PQ[/tex]Applying the expressions for QR and PQ we have:
[tex]\begin{gathered} PR=8x-12-(2x) \\ PR=8x-2x-12 \\ PR=6x-12 \end{gathered}[/tex]The segment PR measures "6x - 12".
I need help on this and I don’t think my answer is correct. Please help.
we have the function
[tex]f(x)=\frac{1}{2}x+8[/tex]Make a table
For each value of x, substitute in the given function to obtain the value of f(x)
For x=0
[tex]f(x)=\frac{1}{2}(0)+8=8[/tex]For x=1
[tex]f(x)=\frac{1}{2}(1)+8=\frac{17}{2}[/tex]For x=2
[tex]f(x)=\frac{1}{2}(2)+8=9[/tex]For x=3
[tex]f(x)=\frac{1}{2}(3)+8=\frac{19}{2}[/tex]For x=4
[tex]f(x)=\frac{1}{2}(4)+8=10[/tex]For x=5
[tex]f(x)=\frac{1}{2}(5)+8=\frac{21}{2}[/tex]For x=6
[tex]f(x)=\frac{1}{2}(6)+8=11[/tex]What is the complement of a 30 1/2 degree angle
Answer:
[tex]59\frac{1}{2}\text{ degrees}[/tex]Explanation:
Here, we want to get the complement of the given angle
Mathematically, when two angles are complementary, they add up to be 90 degrees
What this means is that the sum of an acute angle and its complement is 90 degrees
Here, let us call the complement angle x
Mathematically:
[tex]\begin{gathered} x\text{ + 30}\frac{1}{2}\text{ = 90} \\ \\ x\text{ = 90- 30}\frac{1}{2} \\ \\ \text{ x= 59}\frac{1}{2} \end{gathered}[/tex]Which system is represented in the graph? y > x2 – 3x + 2y ≥ –x2 + 1 y < x2 – 3x + 2y < –x2 + 1 y ≥ x2 – 3x + 2y ≤ –x2 + 1 y > x2 – 3x + 2y < –x2 + 1
Explanation
To find the answer, we will have to find the equations that define the two functions
For the first graph
[tex]\begin{gathered} let \\ f(x)=a(x+1)(x-1) \\ when\text{ } \\ x=0,\text{ y=1} \\ 1=a(1)(-1) \\ a=-1 \\ Thus \\ y\ge-1(x^2-1) \\ y\ge-x^2+1 \end{gathered}[/tex]For the second graph (The purple)
[tex]\begin{gathered} g(x)=a(x-1)(x-2) \\ when\text{ x=0,y=2} \\ 2=a(0-1)(0-2) \\ a=\frac{2}{-1\times-2}=\frac{2}{2}=1 \\ \\ a=1 \\ Thus,\text{ we have} \\ g(x)>1(x-1)(x-2) \\ g(x)>x^2-3x+2 \\ y>x^2-3x+2 \end{gathered}[/tex]Thus, the answer is
[tex]\begin{gathered} y\ge-x^2+1 \\ y>x^2-3x+2 \end{gathered}[/tex]Find the values of that makes the quadrilateral a parallelogram.4x6x – 8X=
At first we should know that :
Foe any parallelogram, the diagonals bisects each other
so, for the given figure :
[tex]6x-8=4x[/tex]Solve for x :
[tex]\begin{gathered} 6x-4x=8 \\ 2x=8 \\ \\ x=\frac{8}{2}=4 \end{gathered}[/tex]so, the answer is : x = 4
Completely factor the trinomial, if possible. 20x^2+13x-7
The trinomial is given to be:
[tex]20x^2+13x-7[/tex]STEP 1:
Rewrite the middle term such that we can break the expression. Multiply the first and last terms of the expression:
[tex]20x^2\times(-7)=-140x^2[/tex]Find two multipliers of -140x² that will add up to +13x:
[tex]Multipliers=20x,-7x[/tex]Replace 13x in the expression by the multipliers:
[tex]20x^2+20x-7x-7[/tex]STEP 2:
Collect the common terms in each pair of numbers:
[tex]\Rightarrow20x(x+1)-7(x+1)[/tex]STEP 3:
Factor the expression by collecting the like terms:
[tex]\Rightarrow(x+1)(20x-7)[/tex]ANSWER:
The factored expression is:
[tex](x+1)(20x-7)[/tex]I am working through data sets and exponential relations. I currently have to create a data set that contains such exponential relation.I chose f(x) = 2^(x+2) (I believe that is a valid choice.)Thus my data set would be as follows:__x__ __y__ 0 4 1 8 2 16 3 32 4 64 5 128 6 256 7 512 8 1,024Is this correct, or have I made a mistake somewhere? My graph result looks very different than others in the class.
Given:
The function is,
[tex]f(x)=2^{x+2}[/tex]Solve the given function for some values of x,
[tex]\begin{gathered} \text{for x=0,} \\ f(x)=2^{0+2}=4 \\ \text{for x=1} \\ f(x)=2^{1+2}=8 \\ \text{for x=2,} \\ f(x)=2^{2+2}=16 \\ \text{for x=3,} \\ f(x)=2^{3+2}=32 \\ \text{for x=4,} \\ f(x)=2^{4+2}=64 \\ \text{for x=5,} \\ f(x)=2^{5+2}=128 \\ \text{for, x=6,} \\ f(x)=2^{6+2}=256 \\ \text{for x=7,} \\ f(x)=2^{7+2}=512 \\ \text{for x=8,} \\ f(x)=2^{8+2}=1024 \end{gathered}[/tex]What is a palindrome number? Select one:a. A decimal number that continues without repeating or ending. b. A sequence that reads the same backwards as forward. c. The 21rst prime number. d. The Chuck Norris of numbers
The palindrome number is the number that remains the same when its digits are reversed
so, the answer will be option b.
A sequence that reads the same backward as forward.
5. If the point (3,-2) is on the graph of y = a[x] + b, what will be the y-coordinate at x = -3?
Thae equation given is;
y= a[x] + b
From the equation, when the absolute value of x is 3, the value of y is -2 as from the point, then
when x = -3, the absolute value of x will be 3 and the y-coordinate will be -2
Answer ; B. -2
One marble is randomly drawn and then replaced from a jarcontaining two white marbles and one black marble. A secondmarble is drawn. What is the probability of drawing a white andthen a black?
Event A: drawing a white marble
Event B: drawing a blck marble
Probability of drawing a white and then a black (with replacement:
[tex]\begin{gathered} P(A,B)=P(A)*P(B) \\ \\ P(A,B)=\frac{#white\text{ }marbles}{#marbles}*\frac{#black\text{ }marbles}{#marbles} \\ \\ P(A,B)=\frac{2}{3}*\frac{1}{3} \\ \\ P(A,B)=\frac{2}{9} \end{gathered}[/tex]Then, the probability of drawing a white and then a black is 2/9The ratio of the side length of Square A to the side length of Square Bin 4:9. The perimeter ofSquare Als 48 yards. What is the perimeter of Square B?
We have the next given information:
The ratio for the side length of square A to the side length of Square B is 4:9
The perimeter of Square A is equal to 48 yards.
A square has all four equal side lengths.
The perimeter is given by the sum of all the side lengths.Therefore, P = 4L.
The perimeter of square A = 48, then each length will be 48/4 =12.
Now, 12 is 4:9 of one side for square B.
Hence, one side of the square B:
12/4 =3
3*9 = 27
The side length of square B=27.
Replace on the perimeter formula P=4L, Where L represents the length.
Then
The perimeter of square B = 4(27)
=108
The perimeter of square B is 108 yards.
,
What is the area in square inches of a piece of legal paper that is 8.5 inches by 14 inches?
Okay, here we have this:
Considering the provided measures, we are going to calculate the requested area, so we obtain the following:
So let's remember that a sheet is rectangular, and the area of a rectangle is equal to height times width, therefore substituting we have:
Area of a piece of legal paper=8.5 inches * 14 inches
Area of a piece of legal paper=119 square inches.
Finally we obtain that the Area of a piece of legal paper is 119 square inches.
If you start with $100, and invest your money and get an annual 10% interest rate, how much money will you have in 2 years?
We have to find the final value FV of an investment.
The initial value is PV = $100.
The annual interest rate is r = 10% = 0.10 (we assume it not compounded).
The number of periods is n = 2 years.
We can express the final value with the following formula using the simple interest:
[tex]\begin{gathered} FV=PV(1+n*r) \\ FV=100(1+2*0.10) \\ FV=100(1.2) \\ FV=120 \end{gathered}[/tex]Answer: you will have $120 in 2 years.