we perform the same operation on each side to place the x's on the same side
[tex]\begin{gathered} 17x-17x-10=12x-17x \\ 0x-10=(12-17)x \\ -10=-5x \end{gathered}[/tex][tex]\begin{gathered} \frac{-10}{-5}=\frac{-5x}{-5} \\ 2=x \end{gathered}[/tex]the value of x is 2
Find the image of X (S, 2) rotated 90° about (0, 0).
Solution:
The rule for a rotation by 90° about the origin is;
[tex](x,y)\rightarrow(-y,x)[/tex]Thus;
[tex]X(5,2)\rightarrow X^{\prime}(-2,5)[/tex]CORRECT OPTION: D
The seniors and juniors at sweet valley high school are going on a trip to Busch gardens. The seniors filled 12 Van's and 13 buses with 564 total students. The juniors filled 6 Van's and 13 buses with 492 students. How many students were in each van? in each bus?
The seniors and juniors at sweet valley high school are going on a trip to Busch gardens. The seniors filled 12 Van's and 13 buses with 564 total students. The juniors filled 6 Van's and 13 buses with 492 students. How many students were in each van? in each bus?
step 1
Seniors
Let
x -----> number of students in vans
y -----> number of students in bus
we have
12x+13y=564
Juniors
6x+13y=492
solve the system of equations
Solve by graphing
the solution is the intersection point both graphs
see the attached figure
the solution is the point (12,32)
therefore
In each Vans there are 12 students and in each bus there are 32 studentsPlease solve the problem step by step, to check my final answers.
We are asked to determine the future value and the time for a quarterly compounded interest. To do that we will use the following formula:
[tex]A=P(1+\frac{r}{400})^{4t}[/tex]Where:
[tex]\begin{gathered} A=\text{ future value} \\ P=\text{ initial value} \\ r=\text{ interest rate} \\ t=\text{ time} \end{gathered}[/tex]Part A. We are asked to determine the time in 7 years. To do that we will substitute the value of "t = 7" and "r = 2", we get:
[tex]A=4000(1+\frac{2}{400})^{(4)(7)}[/tex]Solving the operations:
[tex]A=4599.49[/tex]Therefore, in 7 years there will be the amount of $4599.49
Part B. We are asked to determine the time to get the amount of $5000. To do that we will substitute the value of "A = 5000", and we get:
[tex]5000=4000(1+\frac{2}{400})^{4t}[/tex]Now, we solve for "t". First, we divide both sides by 4000:
[tex]\frac{5000}{4000}=(1+\frac{2}{400})^{4t}[/tex]Now, we take the natural logarithm to both sides:
[tex]\ln(\frac{5000}{4000})=\ln(1+\frac{2}{400})^{4t}[/tex]Now, we use the following property of logarithms:
[tex]\ln x^y=y\ln x[/tex]Applying the property we get:
[tex]\operatorname{\ln}(\frac{5,000}{4,000})=4t\operatorname{\ln}(1+\frac{2}{400})[/tex]Now, we divide both sides by the natural logarithm and by 4:
[tex]\frac{1}{4}\frac{\ln(\frac{5000}{4000})}{\ln(1+\frac{2}{400})}=t[/tex]Solving the operations:
[tex]11.19=t[/tex]Therefore, the amount of 5000 will be obtained after 11.19 years.
how do you write 2,360 in scientific notation
Since we have a 4 digits number, we need to move the point three times therefore we need to multiply by ten to the third power, that is:
[tex]2360=2.36\times10^3[/tex]That is the scientific notation of 2360
Complete this table of values to show the relationship between the numbers of cups of orange juice that are made by squeezing the juice from different numbers of oranges.Number of Oranges45?Number of Cups of Juice1?65 oranges = _ cups of juice_ oranges = 6 cups of juice
Hello I need help with This , I am studying but I just don’t understand this
Explanation:
Concept:
The product of two matrices is undefined whenever the rows of the first matrix (reading right to left) do not match the column of the second matrix. However, say that I would need (for some reason) to multiply a 3x3 matrix by a 2x3 one.
Hence,
The final answer is OPTION C
Help me with thisPlease explain in a non-complicated way with as little steps as possible. Thank you.
Simplify the expression inside the [ ] symbols using the law of signs:
[tex]\lbrack-2-(+3)\rbrack=\lbrack-2-3\rbrack=\lbrack-5\rbrack[/tex]Therefore:
[tex]25-\lbrack-2-(+3)\rbrack^2=25-\lbrack-5\rbrack^2[/tex]Notice that (-5)^2=+25. Then:
[tex]25-\lbrack-5\rbrack^2=25-(+25)[/tex]Then, there are two expression which are equivalent to the given expression:
Option a)
[tex]25-(+25)[/tex]Option d)
[tex]25-\lbrack-5\rbrack^2[/tex]Rick has $21 in his wallet. He will pay a $1.75 for each box of tissues he decides to buy at the store. the corporation video shows how much money (Y). In dollars, Rick will have in his wallet after buying X boxes of tissues Which solutions are the equivalent indicate that Rick would be spending more than the $21 he has in his wallet?
We will have the following:
Since we are given:
[tex]y=-1.75x+21[/tex]Then the solution that would indicate he is spending more than he has would be:
[tex](16,-7)[/tex]That is:
[tex]y=-1.75(16)+21\Rightarrow y=-28+21\Rightarrow y=-7[/tex]What is the image of the point (4,0) after a rotation of 90° counterclockwise aboutthe origin?
To rotate a point 90º counterclockwise you have to invert the place fo the coordinates, for example:
(x,y) → (y,x)
Then you have to change the sign of the
use the graph to find when f(x)
x > -7
Explanations:For the graph g(x), select two points on the line
(-7, 4) and (-2, 8)
That is, x₁ = -7, y₁ = 4, x₂ = -2, y₂ = 8
The slope of the line is given as:
[tex]\begin{gathered} m\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ m\text{ = }\frac{8-4}{-2-(-7)} \\ m\text{ = }\frac{4}{5} \end{gathered}[/tex]The equation of a line is given as:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y\text{ - 4 = }\frac{4}{5}(x-(-7)) \\ y\text{ - 4 = }\frac{4}{5}(x+7) \\ y-4=\frac{4}{5}x+\frac{28}{5} \\ y\text{ = }\frac{4}{5}x+\frac{28}{5}+4 \\ y\text{ = }\frac{4}{5}x\text{ + }\frac{48}{5} \\ y\text{ = }0.8x+9.6 \\ g(x)\text{ = 0.8x+9.6} \end{gathered}[/tex]For the graph f(x):
Select the points (-7, 4) and (-3, 2)
[tex]\begin{gathered} m\text{ = }\frac{2-4}{-3-(-7)} \\ m\text{ = }\frac{-2}{4} \\ m\text{ = -0.5} \end{gathered}[/tex]The equation of the line is:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y\text{ - 4 = -0.5(x - (-7)} \\ y\text{ - 4 = -0.5(x + 7)} \\ y\text{ - 4 = -0.5x - }3.5 \\ y\text{ = -0.5x - 3.5 + 4} \\ y\text{ = -0.5x + 0.5} \\ f(x)\text{ = -0.5x + 0.5} \end{gathered}[/tex]f(x) < g(x)
-0.5x + 0.5 < 0.8x + 9.6
-0.5x - 0.8x < 9.6 - 0.5
-1.3x < 9.1
-x < 9.1 / 1.3
-x < 7
x > -7
T+a/N=F I need to solve for a.
Two tugboats are towing a loaded barge and the magnitude of the resultant is 8000 pounds directed along the axis of the barge (see figure). Find the tension (in pounds) in the tow lines when they each make an 18° angle with the axis of the barge. (Round your answers to one decimal place.)tension in tow line from tugboat A lbtension in tow line from tugboat B lb
we have that
Let
A -----> total tension in tugboat A
B -----> total tension in tugboat B
we have
Ax+Bx=8,000 ------> equation 1
Ax=Acos(18)
Bx=Bcos(18)
substitute
Acos(18)+Bcos(18)=8,000 -----> equation 2
and
Ay=By
Asin(18)=Bsin(18)
A=B
therefore
Acos(18)+Bcos(18)=8,000 ------> Acos(18)+Acos(18)=8,000
2Acos(18)=8,000
A=8,000/(2cos(18))
A=4,205.8 pounds
answer is
total tension in tugboat A is 4,205.8 poundstotal tension in tugboat B is 4,205.8 poundsWhich of the following is a continuous random variable?A. P = number of points scored by Stephen Curry in a gaB. T = winning time in the men's 100-meter dash at the 2016 Olympicsc. H = the number of hats sold on Tuesdayd. X = number of incoming flights at the local airport
A continuous random variable is a random variable where the data can take infinitely many values. For example, a random variable measuring the time taken for something to be done is continuous since there is an infinite number of possible times that can be taken.
Time has no specific integer of values and it is continuous, while the other variables like number of points, number of hats, number of incoming flights can have discrete values and as such are called a discrete variable
With this, we can therefore say that the correct option of an example of a continuous random variable will be
T= WINNING TIME IN THE 100-METER DASH AT THE 2016 OLYMPICS
THE CORRECT OPTION WILL BE OPTION B
Study the diagram of circle L, where RS is tangent to circle L at point S.Also, RS = 24, RL = 26, and LS is a radius.What is the length of the radius, r?
From the figure given,
Where RS is perpedicular to the radius LS and L is the centre of the circle,
Given that
[tex]\begin{gathered} RS=24\text{ units} \\ RL=26\text{ units and } \\ LS=r\text{ units} \end{gathered}[/tex]The formula to find the value of r is the Pythagorean theorem, which is given as
[tex](\text{HYP)}^2=(OPP)^2+(\text{ADJ)}^2[/tex]Where
[tex]\begin{gathered} \text{HYP=RL}=26\text{ units} \\ OPP=RS=24\text{ units} \\ \text{ADJ=LS}=r\text{ units} \end{gathered}[/tex]Substitute the values into the formula of the Pythagorean theorem
[tex]\begin{gathered} (RL)^2=(RS)^2+(LS)^2 \\ 26^2=24^2+r^2 \\ 676=576+r^2 \\ \text{Collect like terms} \\ r^2=676-576 \\ r^2=100 \\ \text{Square root of both sides} \\ \sqrt[]{r^2}=\sqrt[]{100} \\ r=10\text{ units} \end{gathered}[/tex]Hence, the length of radius, r is 10 units
Divide (Simplify answers appropriately.) 3 - es) B o 28 63 D 2 35
The given expression is:
[tex]3\frac{1}{2}\div\text{ 7}\frac{4}{5}[/tex]Convert each of the mixed fractions into improper fraction
[tex]3\frac{1}{2}=\frac{7}{2}[/tex][tex]7\frac{4}{5}=\text{ }\frac{39}{5}[/tex]The given expression then becomes:
[tex]\begin{gathered} \frac{7}{2}\div\frac{39}{5} \\ =\text{ }\frac{7}{2}\text{ }\times\frac{5}{39} \\ =\text{ }\frac{35}{78} \end{gathered}[/tex]Orlando eats 5 out of 8 pieces of his pizza. What percent of his pizza does Orlando eat?
In order to find the percent of the pizza Orlando eat, we just need to divide the number of pieces he ate by the total number of pieces, and then put the result in percentage:
[tex]\frac{5}{8}=0.625=62.5\text{\%}[/tex]So Orlando ate 62.5% of the pizza.
Compare the numbers using >,<, or =A -14___-12 B) |-5|____|-3| C) -3.2_____-32
Given:
The value is
[tex]\begin{gathered} (A)-14_{\text{ }---}-12 \\ \\ (B)|-5|_{---}|-3| \\ \\ (C)-3.2_{---}-32 \end{gathered}[/tex]Find-:
The comparison between all number
Explanation-:
The comparison is
(A)
Minus sign change the property of compression
Then,
[tex](A)-14<-12[/tex](B)
The mode sign always gives a positive value, then
[tex]\begin{gathered} |-5|=5 \\ \\ |-3|=3 \end{gathered}[/tex]The value is
[tex]|-5|>|-3|[/tex](C)
Apply similar properties then expression
[tex]-3.2>-32[/tex]Each individual letter of the word Wisconsin is placed on a piece of paper, and all 9 pieces of paper are placed in a hat. If one letter is selected at random from the hat, find the probability that a consonant is selected.P(consonant)-(Type a fraction. Simplify your answer.)
GIVEN:
We are told that all the individual letters of the word WISCONSIN are placed on a piece of paper. Then all nine pieces of paper are placed in a hat.
Required;
Find the probability that a letter chosen at random is a consonant.
Step-by-step solution;
The probability of an event is given by the formula;
[tex]P[event]=\frac{number\text{ }of\text{ }required\text{ }outcomes}{number\text{ }of\text{ }all\text{ }possible\text{ }outcomes}[/tex]The number of all possible outcomes is the total number of letters that stands a chance of being selected, and that is 9. The number of required outcomes for this experiment is 6 (that is, 6 consonants).
Therefore, the probability of selecting a consonant by random is;
[tex]\begin{gathered} P[consonant]=\frac{6}{9} \\ \\ P[consonant]=\frac{2}{3} \end{gathered}[/tex]ANSWER:
The probability of selecting a consonant is;
[tex]P[consonant]=\frac{2}{3}[/tex]An unbiased 4-sided and an unbiased 6-sided dice are rolled. The score on the 6-sided dice is subtracted from the score on the 4-sided dice. Find P(positive)
We have two unbiased dices: one 4-sided and one 6-sided.
The event in this case is the difference between the score from the 4-sided dice and the score from the 6-sided dice.
We have to find the probability that this event is positive.
We can start by stating a result for the 4-sided dice. We start with P4 = 4, meaning that the 4-sided dice gives us a score of 4.
In order to have a positive event, the 6-sided dice has to have a score of 3 or less (NOTE: we consider the result positive if it is strictly greater than 0, meaning the a score of 4 from the 6-sided dice would result in 0 and it is not considered within the probability of the event "positive"). The event of P6 < 3 has a probability of 3/6=0.5.
Then, we can do this for the other 3 possible results of the 4-sided dice:
- If we get P4 = 3, then the 6-sided dice should have a score of 2 or less.
- If we get P4 = 2, then the 6-sided dice should have a score of 1.
- If we get P4=1, then there is no score for the 6-sided dice that makes the result positive.
Then, we can write the probabilities of each combinations of scores as:
[tex]P=P_4(x=4)\cdot P_6(y\le3)+P(x=3)\cdot P_6(y\le2)+P(x=2)\cdot P_6(y<1)+P(x=1)\cdot P(y<0)[/tex]If we replace this with the probabilities, we get:
[tex]\begin{gathered} P=P_4(x=4)\cdot P_6(y\le3)+P(x=3)\cdot P_6(y\le2)+P(x=2)\cdot P_6(y<1)+P(x=1)\cdot P(y<0) \\ P=\frac{1}{4}\cdot\frac{3}{6}+\frac{1}{4}\cdot\frac{2}{6}+\frac{1}{4}\cdot\frac{1}{6}+\frac{1}{4}\cdot0 \\ P=\frac{3}{24}+\frac{2}{24}+\frac{1}{24} \\ P=\frac{6}{24} \\ P=\frac{1}{4} \end{gathered}[/tex]NOTE: each result from the 4-sided dice has a probability of 1/4 of happening, while each score from the 6-sided dice has a probability of 1/6.
Answer: P(positive) = 1/4 = 0.25
determine whether the mean value theroem applies to the function
Given:
[tex]g(x)=\frac{6x}{x+5}[/tex]solution;
the graph of function is not continues in the intervel [-6,3] then mean value theroem is not applicable.
Which of the following shows the graph of y = -(2)* – 1?y10--10-8-6-4-288 10 X10 -Ty108
The graph for the equation
[tex]y=-(2)^x-1[/tex]is given by
The movie critic liked to count the number of actors in each movie he saw. Number of actors Number of movies 5 3 23 2 29 2 31 1 98 2 X is the number of actors that a randomly chosen movie had. What is the expected value of X? Write your answer as a decimal.
xi (number of actors) number of movies probability(p(x)) p(x)xi
5 3 0.3 1.5
23 2 0.2 4.6
29 2 0.2 5.8
31 1 0.1 3.1
98 2 0.2 19.6
Expected value = 1.5+4.6+5.8+3.1+19.6 = 34.6
can the given information be used to prove triangle ABC is congruent to triangle EDC explain your reasoning
SOLUTION:
Case: Congruence
Method:
Compare the triangles
[tex]\frac{15}{10}\equiv\frac{12}{8}\ne\frac{21}{12}[/tex]Final answer:
The scale factor is not consistent
Hence the given information cannot be used to prove triangle ABC is congruent to triangle EDC.
You deposit $735 in an account that earns simple interest at an annual rate of 6.4%. How much money is in the account after 8 years?
Answer:
376.32
Step-by-step explanation:
735×6.4%×8
.................
The amount of money an account with simple interest at an annual rate of 6.4% would be $376.32 after 8 years.
What is simple interest?Simple interest is a method of calculating the interest charge. Simple interest can be calculated as the product of principal amount, rate and time peroid.
Simple Interest = (Principal × Rate × Time) / 100
Given that deposit amount is $735 in an account that earns simple interest at an annual rate of 6.4%.
Amount = $735
Rate = 6.4%
Time = 8 years
Therefore, Simple Interest = (Principal × Rate × Time) / 100
Simple Interest = 735 × 6.4% × 8
Simple Interest = 735 × 6.4/100 × 8
Simple Interest =376.32
Hence, the amount of money an account with simple interest at an annual rate of 6.4% would be $376.32 after 8 years.
Learn more about simple interest here;
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What is 280 decreased by 47.2 %? Round your answer to two decimal places if needed.
Given:
The original number given is 280.
Required:
The number is to be obtained by decreasing the original number by 47.2 %.
Explanation:
47.2% of the original number is calculated as,
[tex]\begin{gathered} 47.2\text{ \% of 280 = }\frac{47.2}{100}\times280 \\ 47.2\text{ \% of 280 = }\frac{47.2\times280}{100} \\ 47.2\text{ \% of 280 = 132.16} \end{gathered}[/tex]The new number obtained is calculated as,
[tex]\begin{gathered} New\text{ number = 280 - 132.16} \\ New\text{ number = 147.84} \end{gathered}[/tex]Answer:
Thus the number obtained by decreasing 280 by 47.2% is 147.84.
In Mr. Siegel's class, 15% of the students are in the Scrapbooking Club and 45% are in the Cooking Club. His remaining students are in the Board Game Club. Drag numbers to the table to express the percent of students in each club as a fraction and a decimal. Club Fraction Decimal Scrapbooking Club Cooking Club Board Game Club
15% = 15/100 = 3/20 = 0.15 of the students are in the scrap booking club.
45% = 45/100 = 9/20 = 0.45 are in the cooking club.
100% - 60% = 40% = 40/100 = 2/5 = 0.4 are in the board game club.
Find the value of s in the interval [0, pi/2] that makes the statement true. Round to four decimal places. sin s= 0.9503
Answer:
71.8603 degrees.
s = 1.2542 (in radians)
Explanation
Given the equation sin s= 0.9503
You are to find the value of s that satisfies the equation
sin s= 0.9503
Take arcsin of both side
arcsin(sin s) = arcsin(0.9503)
s = 71.8603 degrees
Hence the value of s in the interval [0, pi/2] that makes the statement true is 71.8603 degrees.
s = 1.2542 (expressed in radians)
marlo has a photogrph this is 5 inches wide and 7 inches tall.he wants to enlarge the photo to fit in a frame that is 32 inches tall.if the length and width will be scaled proportionally,what is the width of the frame for the enlarged photo?round to one decimal place.
Given: a photograph is 5 inches wide and 7 inches tall.
He wants to enlarge the photo to fit in a frame that is 32 inches tall.
So, the length and the width will be scaled proportionally
So, the scale factor = r= new length over the lod length
[tex]r=\frac{32}{7}[/tex]It must be the same ratio: new width to old width
Let the new wide = x
so,
[tex]\frac{x}{5}=\frac{32}{7}[/tex]solve for x:
[tex]x=\frac{32}{7}\cdot5=\frac{160}{7}=22\frac{6}{7}in[/tex]So, the answer will be: the new width = 22 6/7 inches
A twelve-sised die with sides labeled 1 through 12 will be rolled once. Each number is equally likely to be rolled. What is the probability of rolling a number less than 4?
Explanation:
There are 3 posible outcomes with a number less than 4: 1, 2 & 3. This is the numerator
The total posible outcomes is 12. This is the denominator
Now we have to write and simplify the fraction:
[tex]\frac{3}{12}=\frac{1}{4}=0.25[/tex]Answer:
The probability of rolling a number less than 4 is 1/4
A rectangular swimming pool with a length of 18 meters and a width of 6 meters is surrounded by a concrete patio. The patio is a uniform 3 meters width around the entire pool. What is the area of the patio?
The area of the combined patio and swimming pool is
[tex]\begin{gathered} (18\text{ m}+3\text{ m})(6\text{ m}+3\text{ m}) \\ =(21\text{ m})(9\text{ m}) \\ =189\text{ m}^2 \end{gathered}[/tex]The area of the swimming pool is
[tex](18\text{ m})(6\text{ m})=108\text{ m}^2[/tex]Subtract the combined area to the area of the swimming pool and we get
[tex]189\text{ m}^2-108\text{ m}^2=81\text{ m}^2[/tex]Therefore, the area of the patio is 81 square meters.