Answer:
x = 16
Step-by-step explanation:
sqrt x + 3 = 2 sqrt x - 1 subtract sqrt x from both sides
3 = sqrt x -1 add 1 to both sides
4 = sqrt x square both sides
16 = x
help me with this question please
Part a
the given polygon has 8 sides
so
Is a octagon
Part b
The given polygon is not a regular polygon, because all their sides don't have equal lengths and their interior angles are not equals
Every month Pablo earns $40 for walking his neighbors dog after school how much does he earn from his job in one year?
We know that Pablo earns $40 every month.
Then, to calculate how much he makes in a year, we use the fact that a year has 12 months.
Then, we can write:
[tex]40\frac{\$}{\text{month}}\cdot12\text{ }\frac{months}{year}=480\frac{\$}{\text{year}}[/tex]Answer: he earns $480 per year.
A garden that is 10/3 of an acre is to be divided into 5 equal-size areas. What is the size of each area?
Answer:
2/3 of an acre
Explanation:
To find the size of each area, we divide the area of the garden by 5. This gives
[tex]\frac{10}{3}\div5[/tex]Now at this point we remind ourselves that if we are dividing a fraction by a number, then we can turn the division into multiplication by taking the reciprocal of the number.
The number we are dividing our fraction by in this case is 5. Now, the reciprocal of 5 is 1/5 and so we can write the above as
[tex]\frac{10}{3}\div5\Rightarrow\frac{10}{3}\times\frac{1}{5}[/tex]Multiplying the denominators together gives
[tex]\frac{10}{3}\times\frac{1}{5}=\frac{10}{3\times5}=\frac{10}{15}[/tex]Now dividing both the numerator and the denominator by 5 gives
[tex]\frac{10\div5}{15\div5}=\frac{2}{3}[/tex]Hence,
[tex]\frac{10}{3}\div5=\frac{2}{3}[/tex]Therefore, the size of each area is 2/3 of an acre.
#13 how many seconds will it take for a ball dropped from a window 144 feet high to hit the ground below?
Question 13.
Given:
Height = 144 feet.
Let's determine how many seconds it will take for a ball dropped from a window of the given height to hit the ground.
Here, we have the equation:
[tex]y=-16x^2+144[/tex]Where:
y represents the height of the ball after x seconds.
Now, when the ball hits the ground, the height will be 0 ft.
Thus, to find the time at 0 ft, substitute 0 for y and solve for x:
[tex]\begin{gathered} 0=-16x^2+144 \\ \\ 16x^2=144 \end{gathered}[/tex]Divide both sides by 16:
[tex]\begin{gathered} \frac{16x^2}{16}=\frac{144}{16} \\ \\ x^2=9 \end{gathered}[/tex]Take the square root of both sides:
[tex]\begin{gathered} \sqrt{x^2}=\sqrt{9} \\ \\ x=3 \end{gathered}[/tex]Therefore, it will take the ball 3 seconds to hit the ground.
ANSWER:
• (a). y = -16t² + 144
• (b). 3 seconds
x = Round to the nearest hundredth or keep as a s
x=6.67
1) Examining that figure, we can state that we have two similar triangles with proportional sides and congruent angles.
2) So let's write a proportion so that we can find the measure of x
[tex]\begin{gathered} \frac{hipotenuse}{hipotenuse\text{ 2}}=\frac{\text{Leg}}{\text{leg 2}} \\ \frac{18}{10}=\frac{12}{x} \\ 18x=120 \\ x=\frac{120}{18} \\ x=\frac{20}{3}\text{ }\cong6.66667 \end{gathered}[/tex]3) Since the answer must be rounded to the nearest hundredth we have
the answer as x=6.67
Hello, how do I factorize this expression 1-36x^ { 2 } +y ^ { 2 } . Thanks :3
Solution:
Given the expression:
[tex]1-36x^2+y^2[/tex]To obtain the result of the factoring of the above expression, we factor out the common factor.\
In the above expression, there is no common factor.
Hence, the expression cannot be factored.
Perform the following division and write the quotient in trigonometric form. Write the magnitude inround it to two decimal places if necessary.- 8i4 + 5i
Solution
Given
[tex]\begin{gathered} \frac{-8i}{4+5i} \\ \\ \Rightarrow\frac{-8\imaginaryI}{4+5\imaginaryI}\times\frac{4-5i}{4-5i}=\frac{-32i-40}{16+25}=-\frac{40}{41}-\frac{32}{41}i \end{gathered}[/tex][tex]\begin{gathered} \text{ Let }Z=\frac{-40}{41}-\frac{32}{41}i \\ \\ \text{ Magnitude of }Z=|Z|=\sqrt{(-\frac{40}{41})^2+(-\frac{32}{41})^2} \\ \\ \Rightarrow|Z|=\frac{8\sqrt{41}}{41} \end{gathered}[/tex]3.5% of 300 is what number
To find 3.5% of 300, we have to multiply 0.035 by 300.
[tex]0.035\times300=10.5[/tex]Hence, the answer is 10.5.Answer:10.5
Step-by-step
Calculate the average (mean) of the data shown, to two decimal placesx8.325.313.423.9129.312.31.4
Given the set of of data:
x
8.3
25.3
13.4
23.9
12
9.3
12.3
1.4
We are to find the average (mean).
To find the means of a set of data, we first add up the data and divide by the total number of data.
The Formular for mean (m)
Mean (m) = sum of the terms
number of terms
number of terms = 8
Mean (m) = 8.3 + 25.3 + 13.4 + 23.9 + 12 + 9.3 + 12.3 + 1.4
8
Mean (m) = 105.9
8
Mean (m) = 13.2375
Mean (m) = 13.24 ( two decimal places).
Mrs worthy estimate the weight of her puppy to be 20 pounds. The actual weight of the puppy is 25.4 pounds. what is the percent error of Mrs worthy estimation?round to the nearest tenth
Given data:
The estimate weight of the puppy is E=20 pound.
The actual weight is A=25.4 pounds.
The expression for the percentage error is,
[tex]e=\frac{A-E}{A}\times100[/tex]Substitute the given values in the above expression.
[tex]\begin{gathered} e=\frac{25.4-20}{25.4}\times100 \\ =\frac{5.4}{25.4}\times100 \\ =21.26 \end{gathered}[/tex]Thus, the percentage error is 21.26%.
Which of the following mathematical properties is described by the statement, “whatever is done on one side of the equation must also be done on the other side of the equation”? Identity Property of AdditionAssociative PropertyCommunitive PropertyProperty of Equalitytoday guys please
Given the statement 'whatever is done on one side of the equation must also be done on the other side of the equation”, the mathematical properties that described this statement is Property of equality.
For any equality operation, whatever is done on one sides must be carried out on the other side. For example, given the equation;
3x + 3 = 5
We can subtract 3 from both sides to have;
3x+3 - 3 = 5-3
3x = 2
Then we can divide both sides by 3;
3x/3 = 2/3
From the illustration above, you can see that what we did to the left hand side of the equation, we also did for the right. Hence the correct answer is Property of Equality
Write 11/80 as decimal Round to four decimal places as needed
The fraction is given
[tex]\frac{11}{80}[/tex]ExplanationTo determine the decimal form .
[tex]\frac{11}{80}=0.1375[/tex]AnswerHence the answer in decimal form is 0.1375.
The table gives the temperature in degrees Fahrenheit in five cities at 6 AM on the same day used to table to answer the questions.
Looking at the table, the temperature in Boston at 6 AM is -8°F.
(a)
If the temperature had risen by 17°F at noon, then the new temperature is:
[tex]-8\degree F+17\degree F=9\degree F[/tex](b)
The 6 AM temperature in Toronto was -16°F, and -25°F in Fairbanks. The difference is:
[tex]-16\degree F-(-25\degree F)=-16\degree F+25\degree F=9\degree F[/tex]In a box there a total of four prizes: Two of them are worth $4, a single prize worth $26, and a single prize worth $241. A player will reach into the box and draw one of the prizes at random. What is the fair price for this game?
So,
First of all, the player has a 1/4 chance of drawing any of the 4 prizes.
This means that the probability of drawing a prize of $4 is 1/2 because there are 2 prizes worth of $4. The probability of drawing a prize of $26 is 1/4 and the probability of drawing a prize of $241 is also 1/4.
To find the fair price, we need to find the expected value of this problem:
This can be obtained by multiplying any possible value of a price for the probability of drawing a prize of that value and adding all these Hvalues together.
This is:
[tex]\begin{gathered} 4\cdot\frac{1}{2}+26\cdot\frac{1}{4}+241\cdot\frac{1}{4} \\ \\ =\frac{275}{4}=68.75 \end{gathered}[/tex]Therefore, the fair price of this game is $68.75.
If Charlie’s Chocolate Fudge costs $1.95 perpound, how many pounds can you buy for $10.00?Set up a proportion.Make sure that the units match going across.Cross multiply to solve,X =_____ pounds for $10.
Let's use a rule of three:
This way,
[tex]x=\frac{10\cdot1}{1.95}\Rightarrow x=5.13lbs[/tex]We could buy 5.13 pounds
solving the formula for the indicated variable-s = lw + wh + lh, for whow do i start this problem?
The first step we need to take in order to solve the formula for w is changing the side of all the terms that have a w in it to the left side.
[tex]\begin{gathered} s=lw+wh+lh \\ s-lw-wh=lh \end{gathered}[/tex]Then we change switch all the terms that don't have w from the left to the right.
[tex]-lw-wh=lh-s[/tex]Since we have two terms on the left with a "w" we can factor then using the common term:
[tex]w(-l-h)=lh-s[/tex]Now we divide both sides by (-l-h).
[tex]\begin{gathered} w=\frac{lh-s}{-l-h} \\ w=\frac{-lh+s}{l+h} \end{gathered}[/tex]f(x) = -4x – 7 find the equation for the inverse function
Answer:
[tex]f^{-1}(x)=-\frac{1}{4}(x+7)[/tex]
Step-by-step explanation:
[tex]f(x)=-4x-7 \implies x=-4f^{-1}(x)-7 \\ \\ x+7=-4f^{-1}(x) \\ \\ f^{-1}(x)=-\frac{1}{4}(x+7)[/tex]
A dairy farmer wants to mix a 75% protein supplement and a standard 25% protein ration to make 1500 pounds of a high grade 45%protein ration. How manypounds of each should be use!
Okay, here we have this:
Protein Supplement=75%--------->x pounds
Standard Protein= 25% ---------->(1500-x) pounds
Mixture 45% ----------------> 1500
75%x+25%(1500-x)=45%*1500
75x+25(1500-x)=67500
75x+37500-25x=67500
50x=30000
x=30000/50
x=600 pounds Protein Supplement
900 pounds standar Protein
Then he drove home at a speed of 5 blocks every 4 minutes. How do I graph that?
We have to graph the position versus time.
We start by identifying the segments.
1) The initial position (x=0, y=0) is his house.
2) He drove for 4 minutes at a speed of 1 block/min. This means that we have a line with slope m=1 from x=0 to x=4. The value of y when x=4 is also 4.
Then, the final point of this segment is (4,4).
3) He spent 3 minutes in the store. This means that y=4 between x=4 and x=4+3=7.
The final point of this segment is (7,4).
4) He drove at a speed of 2 blocks/minute (slope m=2) for 6 blocks until he got to the bank. Then, the new position is y=7+6=13. If the slope is m=2, then he will spent 6/2=3 minutes to reach the bank. As he already spent 7 minutes, he arrived to the bank at x=7+3=10.
Then, the final position of this segment will be (10,13).
5) Then, he returns at a speed of 5 blocks every 4 minutes. This correspond to a slope m=-5/4. This slope is negative as he is now returning to his house and, then, y is decreasing.
1. The price p (in dollars) and the quantity x sold of a certain product obey the demand equation p = -8x + 600. What quantity x maximizes revenue (R= xp)? What is the maximum revenue? What price should the company charge to maximize revenue?2. Jeff invested some money at 7% simple interest and $5000 more than that amount at 15% simple interest. After 1 year, his total interest from the two accounts was $1300. How much did he invest at each rate?
1.The quantity x maximizes revenue is 80 , the price should be company charge to maximize revenue is 9 or 11.
2. $11875 he invest at each rate.
Given that,
In the question there are 2 question.
1.The market equation p = -8x + 600.
We have to determines how much a specific product costs in dollars and how many units are sold. What value of x optimizes profit (R=xp)?
We know,
R = px
R = p(-8p+160)
R= -8p² +160p
R(16) = -8(16)² +160(16)
R(16) = -2048 + 2560
R(16) = 512
R'= -16p + 160 = 0
Revenue maximizing price p= 160/16 = 20/2 = 10
Maximum revenue R(10) = -8(10)² + 160(10) = -800 + 1600 = 800
x=-8p+160
x =-8(10)+160
x = -80 + 160
x = 80
We get,
792 = -8p² +160p
8p² -160p + 792 = 0
2p² - 40p + 198 = 0
p² -20p + 99 = 0
(p-9)(p-11) = 0
p = 9 or 11 as the prices that give at least 792 in revenue
Therefore, The quantity x maximizes revenue is 80 , the price should be company charge to maximize revenue is 9 or 11.
2. Jeff put some money into investments at 7% simple interest and another $5,000 at 15% simple interest. His combined interest from the two accounts after a year was $1300.
We have to find at which rate did he invest how much.
Let C represent the sum Bryan invested in the CD. Then he made a savings account deposit of $5,000 C. Add the interest amounts to reach $1300.00: 15% of the amount in the certificate of deposit is 0.15C, and 7% of the amount in the savings account is 0.07(5,000-C). As a result, we can construct and settle the equation:
0.15C+0.07(5000-C)=1300
0.15C+350-0.07C=1300
0.08C+350=1300
0.08C=1300-350
0.08C=950
C=950/0.08
C=11875.
Therefore, $11875 he invest at each rate.
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( pleassee help asap ! ) what is the solution (11.4 - 10) ÷2 ?
what is the solution (11.4 - 10) ÷2 ?
[tex]\begin{gathered} \frac{11.4-10}{2} \\ \frac{1.4}{2} \\ 0.7 \end{gathered}[/tex]The answer would be 0.7
Refer to the line for Exercises 17-22.SU17. If RS 19 and RV = 71, find SV.18. If UV = 17 and SU17 and SUI = 38, find SV.13 and SX 30, find SV.19. If VX =20. If TW81 and VW = 35, find TV.21. If SW = 44.5 and SV44.5 and SV 37.1, find VW.22. If TU 15.9 and UW = 28.3, find TW.R====TVWX
Given:
RS=19 and RV=71
Find: SV
Explanation: SV= RV-RS
=71-19
=52
Final answer: the required value of SV is 52.
Math Literacy measurements G11 only do 5 and 6 both question are similar
Question 5:
If we divide the total length of the trip by the rate of consumption of the vehicle, we're going to find the amount of liters needed for the trip.
[tex]\frac{250}{9.4}=26.5957447...[/tex]This is the amount of liters needed.
Question 6:
Just as we did in the previous question, first we need to find the amount of liters needed for the trip.
[tex]\frac{2500}{33}=75.7575758...[/tex]Then, using the cost per liter, we can find the total cost of the trip:
[tex]\frac{2500}{33}\times20.20=1530.30303...[/tex]The trip is going to cost R1530.30.
Question 22 ptsYou pay $5 to play a game. To play the game you spin a spinner with 3 colors. If the spinnerlands on blue you earn $20. If the spinner lands on green, you get your $5 back. If the spinnerlands on red, you loose your money. The probabilities of the spinner landing on each color isgiven in the chart below.What is the expected value of this game, given to the nearest penny?Spinner ColorProbabilityBlue0.19Green0.14Red?
GIVEN:
You pay $5 to play a game. To play the game you spin a spinner with 3 colors.
If the spinner lands on blue you earn $20. If the spinner lands on green, you get your $5 back. If the spinner lands on red, you loose your money.
The probabilities of the spinner landing on each color is given in the chart below.
[tex]\begin{gathered} Color----------Probabilities \\ \\ Blue-----------0.19 \\ \\ Green-----------0.14 \\ \\ Red------------0.67 \end{gathered}[/tex]Required;
What is the expected value of this game, given to the nearest penny?
Step-by-step solution;
To solve the question, note that the probability distribution has a blank space. We have the probabilities of landing on a blue color and on a green color. The probability of an event is usually between 0 and 1.00. Therefore, for an experiment with 3 outcomes, the probabilities would all be equal to 1 (regardless of the value given to each outcome). Hence, we are able to calculate the probability of landing on a red color as;
[tex]\begin{gathered} Red=1-(0.19+0.14) \\ \\ Red=0.67 \end{gathered}[/tex]To solve for the expected value of this event, we now have to multiply each probability distribution by the reward attached to each outcome/probability.
For landing on a blue;
[tex]\begin{gathered} Expected\text{ }value=P(x)\times x \\ \\ Expected\text{ }value=0.19\times(\text{\$}20-\text{\$}5) \\ \\ Expected\text{ }value=0.19\times15 \\ \\ EV=2.85 \end{gathered}[/tex]For landing on a green;
[tex]\begin{gathered} EV=0.14\times(\text{\$5}-\text{\$5\rparen} \\ \\ EV=0.14\times0 \\ \\ EV=0 \end{gathered}[/tex]For landing red;
[tex]\begin{gathered} EV=0.67\times(\text{\$0}-\text{\$}5) \\ \\ EV=0.67\times(-5) \\ \\ EV=−3.35 \end{gathered}[/tex]Now we can calculate the expected earnings from playing this game.
We sum up the individual expected earnings as follows;
[tex]\begin{gathered} Expected\text{ }earnings=\Sigma[xP(x)] \\ \\ Expected\text{ }earnings=2.85+0+(-3.35) \\ \\ Expected\text{ }earnings=−0.5 \end{gathered}[/tex]We now have a negative value which means based on the conditions given, the expected earnings from playing this game is a loss of $0.50
ANSWER:
Expected value
[tex]Expecetd\text{ }value=\text{\$}-0.50[/tex]The function of a circle is ysquared +x?=r? where r is the radius (any number). Make a circle with a radius of 16. Where does the circle intersect the X and Y axis? What is the relationship between where the circle intersects the axes and the radius (16)? IThe function of a circle is y?+x?=r? where r is the radius (any number). Make a circle with a radius of 16. Where does the circle intersect the X and Y axis? What is the relationship between where the circle intersects the axes and the radius (16)?
112 the circle of the radius
Step-by-step explanation:
3122
Does the coordinate (-2,5) land on the linear equation y = 2x + 9 ?yesnomaybe
Answer:
Yes
Explanation:
The coordinate (-2,5) corresponds to the point (x, y).
This means that:
x= -2 and y=5
To check if the coordinate land on the equation y=2x+9, calculate the value of y when x= -2
[tex]\begin{gathered} \text{When x=-2} \\ y=2(-2)+9 \\ =-4+9 \\ =5 \end{gathered}[/tex]Therefore, the coordinate (-2,5) land on the linear equation y = 2x + 9.
-15-3r=6r+3c Solve for r.
Answer:
[tex]r=\frac{-c-5}{3}[/tex]Explanation:
We want to solve for r in the equation below;
[tex]-15-3r=6r+3c[/tex]We need to move all terms of r to one side and divide both sides by the coefficient of r.
firstly subtract 6r from both sides;
[tex]\begin{gathered} -15-3r-6r=6r-6r+3c \\ -15-9r=3c \end{gathered}[/tex]then add 15 to both sides;
[tex]\begin{gathered} -15+15-9r=3c+15 \\ -9r=3(c+5) \end{gathered}[/tex]divide both sides by -9;
[tex]\begin{gathered} \frac{-9r}{-9}=\frac{3(c+5)}{-9} \\ r=\frac{-(c+5)}{3} \\ r=\frac{-c-5}{3} \end{gathered}[/tex]Therefore;
[tex]r=\frac{-c-5}{3}[/tex]Is 2/9 equal to a terminating decimal or a repeating decimal?
Since the denominator of 2/9 is 9, 2/9 is equal to a repeating decimal.
[tex]\frac{2}{9}=0.222222\ldots=0.\bar{2}[/tex]Answer: repeating decimal
For an arch length s, area of sector A, and central angle θ of a circle of radius r, find the indicated quantity for the given value. r=4.28 ft, θ= 2.79, s=?
The area of a sector S follows the equation:
[tex]S=\frac{1}{2}r^2\theta[/tex]Where θ is the angle and r the radius.
In this case, we have:
• r = 4.28ft
,• θ = 2.79
We write:
[tex]\begin{gathered} S=\frac{1}{2}(4.28)^2\cdot2.79 \\ S\approx25.554168 \end{gathered}[/tex]Then, the answer, rounded up to two decimal places is
[tex]S=25.55[/tex]Joanie believes that you cannot use cross products to solve the proportion 50 / 3 equals 75 over x 4x she says that if you multiply both sides of the equation by X you get 50 x / 3 equals 75 then if you multiply both sides of the equation by 3 you get 50 x equals 75 which is a different equation then you would get if you cross multiply what mistake did Yuri make in her reasoning?
The proportion is shown below and we cross multiply, do algebra, to solve it.
[tex]\begin{gathered} \frac{50}{3}=\frac{75}{x} \\ 50x=3\cdot75 \\ 50x=225 \\ x=\frac{225}{50} \\ x=\frac{9}{2} \end{gathered}[/tex]If you read the question, so will see this part:
if you multiply both sides of the equation by 3 you get 50 x equals 75
This is the part where there is a problem. You did say to multiply by 3 (both sides). But don't multiply the right hand side of "75" mistakenly.
The last part of this line should be "equals 75 times 3"
This is the mistake.