Add like terms on the left hand side:
[tex]x^2y((1)-5)+xy^2(-4+(2))[/tex]equating both sides:
[tex]\begin{gathered} (1)-5=11 \\ so\colon \\ (1)=16 \\ ----- \\ -4+(2)=6 \\ so\colon \\ (2)=10 \end{gathered}[/tex]Answer:
(1) = 16
(2) = 10
Which step could she have used instead to simplify the expression (3t)4?
Instead of doing what she did, she could have use power properties. Remember you can distribute powers if you have a multiplication, as following:
[tex]\mleft(3t\mright)^4=3^4t^4[/tex]Thus,
[tex]\mleft(3t\mright)^4=3^4t^4\rightarrow(3t)^4=81t^4[/tex]Simplify theExpression 194,000×0.00020 using scientific notation and express your answer in scientific notation.
Hello
To solve this question, we can either use a scientific calculator or the traditional method.
For the purpose of this session, i'll use a scientific calculator because it is fast and efficient.
[tex]undefined[/tex]What is the relationship between a conditional statement and its converse?
For Conditional Statement:
For the conditional of a statement x and y, this means x depends on y. If y occurs, x must also occur.
This conditional statement is represented by:
y -----> x
For its Converse:
A converse of the statement above is just like an opposite or reverse of its conditional statement.
Given the conditional statement above:
y -----> x
The converse will be the opposite as written below :
x----->y
Bottles of water sell for $1.50 eachGraph the relationship between the number of bottles of water sold and the total cost Proportional relationships
The function that we have to draw is:
[tex]y\text{ = 1.5x}[/tex]y is the total cost. x is the number of bottles of water sold. I attach a picture of the graph. But before that, let's find some points to put in the graph. I will get two points, when x = 0 and when x = 1:
[tex]y\text{ = 1.5}\times0=0[/tex][tex]y\text{ = 1.5}\times2=3[/tex]Thus the points will be A = (0,0) and B = (2,3). Then the graph will be:
How many gallons of a 50% antifreeze solution must be mixed with 90 gallons of 15% antifreeze? Use the six-step method.
Let
x -----> number of gallons of a 50% antifreeze
we have that
0.50(x)+0.15(90)=0.40(x+90)
Solve for x
0.50x+13.5=0.40x+36
0.50x-0.40x=36-13.5
0.10x=22.5
x=225
therefore
The answer is 225 gallons of a 50% antifreezeQuestion 15x+2y=-715x+6y=21No solution, One solution, or infinite solution?Question 3.6x+4y=103x+2y=5No solution, one solution, or infinite solution?
Question 1
No solution
Question 3
No solution
Explanation:Given the pair of equations:
5x + 2y = -7
15x + 6y = 21
Notice that the second equation can be obtained by mulitiplying the first equation by 3, this makes the pair have no solution.
A pair of equations where one is a multiple of the other has no soution.
Similarly for
6x + 4y = 10
3x + 2y = 5
No solution
PLEASE NEED HELP ASAP DUE IN 1hrThe volume of the quarter sphere sized tank is 226,195 and tank 1 and 2 volume is 81640.
Answer:
Explanation:
Given:
The volume of the quarter sphere sized tank = 226,195
The volume of tank 1 and 2 volume = 81640
Maximum density of killer whales = 0.000011142 whales per cubic ft
To find:
the maximum number of killer waves allowed in the main show tank
The formula for density:
[tex]density\text{ = }\frac{mass}{volume}[/tex][tex]undefined[/tex]the author selected 90 subjects from the california health survey and 52 were female construct and interpret a 99% confidence interval for the percentage of adult Californians that are female. round to the nearest hundredth place
The answer is this:
[tex](0.44389,0.71211)[/tex]But we have to round those numbers to the nearest hundredth (two decimal places), so:
[tex]\begin{gathered} 0.44389\approx0.44 \\ 0.71211\approx0.71 \end{gathered}[/tex]Therefore, the answer is :
[tex](0.44,0.71)[/tex]a confidence interval for a population proportion is given by:
[tex]\begin{gathered} p\pm Zc\sqrt[]{\frac{p\cdot(1-p)}{n}} \\ \end{gathered}[/tex]Some common confidence levels are:
[tex]\begin{gathered} 90\colon Zc\approx1.645_{} \\ 95\colon Zc\approx1.960 \\ 99\colon Zc\approx2.576 \end{gathered}[/tex]In this case:
[tex]\begin{gathered} n=\text{ Sample size=90} \\ p=\text{proportion of females}=\frac{52}{90}\approx0.578 \end{gathered}[/tex]You replace those values into the equation, and you can find the confidence interval
Tia is working to get enough money to buy a new cell phone she had already saved $220 but needs to have atleast $595 to buy the phone each week at her job she saves $50 for the cost of the phone
Let
x ------> the number of weeks
Remember that
" at least" -----> means greater than or equal to
so
The inequality that represent this situation is
[tex]\begin{gathered} 220+50x\ge595 \\ 50x\ge595-220 \\ 50x\ge375 \\ x\ge7.5\text{ weeks} \end{gathered}[/tex]therefore
The minumum number of weeks is 7.5
Juan is driving on a highway. he uses one gallon of gas every 25 miles he drives. the distance d (in miles) he drives on g gallons of gas. how far does Juan drive if he uses 4 gallons?
ANSWER:
100 miles
STEP-BY-STEP EXPLANATION:
The situation is defined by the following function:
[tex]D=25g[/tex]In this case, the value of g is 4, we substitute and calculate the distance77
[tex]\begin{gathered} D=25\cdot4 \\ D=100\text{ mi} \end{gathered}[/tex]Which means that with 4 gal of gas, Juan can drive 100 miles.
Find the measure of angle Aa=26.61 km, b= 21.46 km, c= 19.62 km
ANSWER:
The value of angle A is 80.61°
STEP-BY-STEP EXPLANATION:
Given:
a=26.61 km,
b= 21.46 km
c= 19.62 km
We can calculate the value of angle A by means of the law of cosines, which is as follows:
[tex]a^2=b^2+c^2-2\cdot b\cdot c\cdot\cos(A)[/tex]We solve for A and then substitute to calculate it, like this:
[tex]\begin{gathered} 2\cdot b\cdot c\cdot\cos(A)=b^2+c^2-a^2 \\ \\ \cos(A)=\frac{b^2+c^2-a^2}{2\cdot b\cdot c} \\ \\ A=\cos^{-1}\left(\:\frac{b^2+c^2-a^2}{2\cdot\:b\cdot\:c}\:\right) \\ \\ \text{ We repalcing} \\ \\ A=\cos^{-1}\left(\:\frac{21.46^2+19.62^2-26.61^2}{2\cdot\:21.46\cdot\:19.62}\:\right) \\ \\ A=\cos^{-1}(0.1631) \\ \\ A=80.61\degree \end{gathered}[/tex]The value of angle A is 80.61°
You Tube SS Student and par What are the coordinates of point G? 5 D E 4 3 2 1 -5 -4 3 -2 -1 0 2 3 4. 5 -1 N -3 F -4.
In the graph, you can see that the x coordinate of point G is -1 and that the y coordinate of the point is 0.
[tex](x,y)\rightarrow G(-1,0)[/tex]Then, the coordinates of the point G are (-1,0).
A classroom board is 36 inches wide and 24 inches tall. Cheryl is putting ribbon along the outside edge of the board. How many inches of ribbon will she need?
Data:
Wide: 36in
Tall: 24in
The total inches of ribbon Cheryl needs is equal to the perieter of the classroom board.
As a classroom board is rectangular you get the perimeter whit th next formula:
[tex]P=2W+2T[/tex]Then, for the given board:
[tex]\begin{gathered} P=2(36in)+2(24in) \\ P=72in+48in \\ P=120in \end{gathered}[/tex]Then, Cheryl
Mindy buys ribbon at a cost of $1 per 18 inches. At this rate, how many yards of ribbon can she buy for $20?
$1 ---> 18 inches
$20 ---> x inches of ribbon
[tex]\begin{gathered} x\times1=18\times20 \\ x=360 \end{gathered}[/tex]answer:
360 inches of ribben for $20
Name the property that is illustrated by each statement in the picture a), b), and c)
Given:
(a)
[tex]\frac{1}{2}(2x+2)[/tex]Use distributive property is:
[tex]a(x+y)=ax+ay\ldots\ldots\ldots\ldots.(distributive\text{ property)}[/tex][tex]\begin{gathered} =\frac{1}{2}(2x+2) \\ =\frac{1}{2}(2x)+\frac{1}{2}(2) \\ =x+1 \end{gathered}[/tex](b)
[tex]2a+(3b+c)[/tex]Use aasociative property of addition:
[tex]\begin{gathered} =a+(x+y) \\ =(a+x)+y \end{gathered}[/tex][tex]\begin{gathered} =2a+(3b+c) \\ =(3b+c)+2a\ldots\ldots\ldots\ldots(\text{associative property of addition)} \end{gathered}[/tex](c)
[tex]\frac{1}{4}\lbrack(-a+a)+4\rbrack[/tex][tex]\begin{gathered} \frac{1}{4}\lbrack(-a+a)+4\rbrack=\frac{1}{4}\lbrack0+4\rbrack \\ \text{Use substraction property} \end{gathered}[/tex]Graph the solution set on the number line and write the solution in interval notation. Six more than b exceeds 2.
Given the statement:
"Six more than b exceeds 2"
-The first part, six more than b can be expressed as a sum, you have to add 6 to the variable "b".
-The word "exceeds" indicates that the previous part of the sentence is greater than the second part, to express this you have to use the symbol ">"
The inequality can be written as:
[tex]6+b>2[/tex]The next step is to solve the inequality for b, to do so you have to pass "6" to the right side of the inequality by applying the opposite operation to both sides of it:
[tex]\begin{gathered} 6-6+b>2-6 \\ b>-4 \end{gathered}[/tex]This expression indicates that the variable "b" can take values greater than -4. Note that the symbol ">" does not include the equal sign, which means that "-4" is not included in the interval of definition for the possible values of "b".
To draw this in the number line, you have to start from -4 and draw the line towards +∞, and, since the initial value is not included, you have to draw a blank dot at the endpoint of the line:
To express the inequality as an interval you have to use round brackets, this way you will indicate that the values at the endpoints are not included:
[tex](-4,+\infty)[/tex]Alyssa attempted to smplify the four numeric expressions shown here #1 11+3X3 14X3 42 #2 80 divided by 2+4 40 divided by 4 40 #3 4(3 divided by 7) 4(10) 40 #4 5X10-10 50-10 40 which simplification is not correct?
When we have expressions where multiplications, divisions, additions and substractions are made, we have an order to solve them: First, we have to solve multiplications and divisions and then we can solve additions and substractions.
The one that has a mistake is #1, because she has:
[tex]11+3\cdot3[/tex]She should have solved 3*3 first, and then add 11 to the result:
[tex]\begin{gathered} 11+3\cdot3 \\ 11+9 \\ 20 \end{gathered}[/tex]The error is in that she add the 11 to a 3, and then multiplicate the result, what is incorrect.
The other expressions are solved in the right order.
Answer: #1
Here are two figures. A B C o Choose all the correct statements that apply to the two above figures. the rightmost and leftmost points on figure A are further apart than any pair of points on figure B the two figures are congruent the two shapes have points across from each other that are the same distance apart as the same two points on the other figure the leftmost and rightmost points on figure B have points that correspond to points on figure A figure A and figure B have corresponding points the two figures are not congruent
Statements
Figure A is ellipse, Figure B is a circle
1) Is TRUE, furthermore points distance is bigger than in figure B
2) Is FALSE, figures have different curves.
3) Is TRUE. There are points in figure A which distance is equal in fig B
4) Is TRUE. There can be corresponding points
5) Is TRUE . Because they are closed figures, without knots
6) Is TRUE. Both figure have different shape, are not congruent.
A family buys 4 airline tickets online. The family buys travel insurance that costs $16 per ticket. The total cost is $752. Let x represent the price of one ticket. Write an equation for the total cost. Then find the price of one ticket. Which equation represents this situation? O A. 752 = 4x + 16 OB. 752 = 4(x + 16) O C. 16 = 4x + 752 OD. 752 = 16(x + 4)
Travel insurance
$16 per ticket
Total cost
$752
x = price of the ticket
Equation for the total cost
752 = 4(x+16)
The answer is letter B 752 = 4(x+16)
x + 16 = 752/4
x + 16 = 188
x = 188 -16
x = $172
gr 12 calcFind the critical points on the given interval and identify the nature of them
SOLUTION
The critical point is the point where the derivative of the function is equal to zero or undefined.
So, for
[tex]f(x)=2^xcos(x)\text{ }[/tex]the derivative becomes
[tex]\begin{gathered} \frac{d}{dx}(2^xcos(x)) \\ apply\text{ the product rule} \\ \frac{d}{dx}(2^x)cos(x)+\frac{d}{dx}(cos(x))2^x \\ 2^xln(2)cos(x)+(-sin(x))(2^x) \\ =ln(2)2^xcos(x)-2^xsin(x) \end{gathered}[/tex]Setting the derivative to zero, we have
I need to figure out if they are given,proven,multiplication property,division property,additional property,subtraction property distributive property
Given data:
The given expression is 3(x+5)=75.
The given expression can be written as,
[tex]\begin{gathered} 3(x+5)=75\text{ (Given)} \\ 3x+15=75\text{ (Distributiv property)} \\ 3x=60\text{ (Subtraction property)} \\ x=20\text{ (Division property )} \end{gathered}[/tex]Suppose that a loan of $5500 is given at an interest rate of 3% compounded each year.Assume that no payments are made on the loan. Follow the instructions below do not do any rounding. A/ find the amount owed at the end of one year B/ find the amount owed at the end of two years
Answer:
A) $5,665
B) $5,834.95
Explanation:
We were given that:
Loan, P = $5,500
Interest Rate, r = 3% = 3/100 = 0.03
Compounding, n = annually = 1
Time, t = ?
The amount owed is obtained using the formula:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]A) At the end of one year:
[tex]\begin{gathered} Time,t=1year \\ A=5500(1+\frac{0.03}{1})^{1*1} \\ A=5500(1+0.03) \\ A=5500(1.03) \\ A=\text{\$}5,665 \end{gathered}[/tex]B) At the end of two years:
[tex]\begin{gathered} Time,t=2years \\ A=5500(1+\frac{0.03}{1})^{1*2} \\ A=5500(1+0.03)^2 \\ A=5500(1.03)^2 \\ A=\text{\$}5,834.95 \end{gathered}[/tex]The length of a rectangular poster is 5 more inches than three times its width. Thearea of the poster is 42 square inches. Solve for the dimensions (length and width) ofthe poster.
Let l and w be the length and width of the poster, respectively; therefore, according to the question,
[tex]\begin{gathered} l=3w+5 \\ and \\ A=42 \end{gathered}[/tex]What is 7 2/3 % more than 50
What is 7 2/3 % more than 50
we have that
7 2/3%=7+2/3=23/3 %-----> Convert to decimal
(23/3)/100=23/300
Multiply by 50
50*(23/300)=23/6 ------> convert to mixed number
23/6=18/3+5/3=6 5/3
the answer is
50+ 6 5/3
56 5/3What is the range of the function f(x) = -6^2 +5
SOLUTION
[tex]f(x)=-6x^2+5[/tex]Evaluate -7(5 + 3) - 1-61. 0-50 -14 0-84 062 NEXT QUESTION ASK FOR HELP
Given:
[tex]-7(5+3)-|-6|=?[/tex]Note: the absolute value of the negative number is the positive of that number
So, we will simplify it as follows:
[tex]\begin{gathered} -7(5+3)-|-6| \\ =-7\times8-6 \\ =-56-6 \\ =-62 \end{gathered}[/tex]So, the answer will be -62
Find an ordered pair (x, y) that is a solution to the equation. x-6y=6 (x, y) = (6,- 1) 8 X 5 ?
Answer:
The ordered pair (x,y) that is a solution to the equation is;
[tex](x,y)=(0,-1)[/tex]Explanation:
We want to find an ordered pair that is a solution to the given equation;
[tex]x-6y=6[/tex]Let us find the corresponding value of y at x=0;
[tex]\begin{gathered} x-6y=6 \\ 0-6y=6 \\ -6y=6 \\ \frac{-6y}{-6}=\frac{6}{-6} \\ y=-1 \end{gathered}[/tex]So, at x=0, y= -1.
The ordered pair (x,y) that is a solution to the equation is;
[tex](x,y)=(0,-1)[/tex]The diameter of a baseball is 7.5cm. What is the surface area of a baseball? What is the volume?
the surface area of a sphere is
[tex]4\pi r^2[/tex]and r=diameter/2
so r= 3.75
and
[tex]surfacearea=4\cdot\pi\cdot3.75^2=176.71cm^2[/tex]and the volume of a sphere is
[tex]\frac{4}{3}\cdot\pi\cdot r^3[/tex]so:
[tex]\text{volume}=\frac{4}{3}\cdot\pi\cdot3.75^3=220.89cm^3[/tex]There are 17 students in a class, and 4 of them will be chosen to go on a field trip. How many ways can these students be chosen?
• Given number of students (n) = 17
r = 4
• Number of ways = Ncr = 17C4
= 17! /4! (17-4)!
= 17! /4! (13!)
= (17! *16!*15!*14! )/ 4!
= 2380
This means that these students be chosen in 2380 different ways .
I need help on this one (last tutor I had said it was a quiz when it is not!
Looking at the image above, we can see that I replicated the ruler all along the length and width. I made it to make it easier to count how many rulers we used to measure the length and the width.
Look that we use 3.5 rulers to measure the length, but if each measure is 200ft, then the length is 200ft multiplied by 3.5, which is
[tex]\begin{gathered} \text{ length }=3.5\cdot200\text{ ft} \\ \\ \text{length }=700\text{ ft} \end{gathered}[/tex]For the width we used 2 rulers, then the width will be 2 multiplied by 200 ft which is
[tex]\begin{gathered} \text{ width }=2\cdot200 \\ \\ \text{width }=400\text{ ft} \end{gathered}[/tex]Final answer:
[tex]\begin{gathered} \text{length }=700\text{ft} \\ \\ \text{width }=400\text{ft} \\ \end{gathered}[/tex]