a) -36 b) 36
1) To simplify those expressions let's expand them to better grasp the result:
[tex]\begin{gathered} -6^2=-1\times6^2=-1\cdot36=-36 \\ \end{gathered}[/tex]When the minus sign is accompanying the number without parentheses, we can read it as -1 times the power. That's why -6²=-1 * 36 = -36
b) For the second power we can write out the following:
[tex](-6)^2=(-6)\cdot(-6)=36[/tex]2) Hence, we can state that the answers are -36 and 36
Aubrey spends a winter day recording the temperature once every three hours for science class. At 9 am, the temperature was -4.6°F. Between 9am and noon, the temperature increased by 4.2°F. Between noon and 3pm, the temperature went down 8.3°F. Between 3pm and 6pm, the temperature decreased by 6.9°F. What was the temperature at 6pm?
The temperature at 6pm is 15. degrees F if Aubrey spends a winter day recording the temperature once every three hours for science class.
What is a sequence?It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
It is given that:
Aubrey spends a winter day recording the temperature once every three hours for science class.
The temperature between 9 am and noon:
= -4.6 + 4.2
= -0.4 degree F
Between noon and 3pm, the temperature went down 8.3°F.
= -0.4 - 8.3
= -8.7 degrees F
Between 3pm and 6pm, the temperature decreased by 6.9°F.
= -8.7 - 6.9
= 15. degrees F
Thus, the temperature at 6pm is 15. degrees F if Aubrey spends a winter day recording the temperature once every three hours for science class.
Learn more about the sequence here:
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Due 05/05/200:00Tickets to a school play cost $3 for students and $8 for adults. On opening night, $1,000 was collected and 150 tickets sold Use substitution to solvea system of equations to find how many of each kind of ticket were sold? Enter your answers in the boxesstudent ticketsadult tickets
We will use the next variables
x is the number of tickets sold for students
y is the number of tickets sold for adults
First equation
x+y=150
Second equation
3x+8y=1000
we isolate the x of the first equation
x=150-y
we substitute the equation above in the second equation
3(150-y)+8y=1000
450-3y+8y=1000
we sum like terms
5y=1000-450
5y=550
y=550/5
y=110
Then we substitute the value of y in the equation with x isolate
x=150-y=150-110=40
x=40 and y=110
The students sold
40 tickets for students
110 tickets for adults
what is the minimum amount of shrink wrap she will need?
we know that
To find out the minimum amount of shrink, you need to calculate the surface area
The surface area of the figure is equal to the area of its two triangular faces and its three rectangular faces
so
SA=2[(1/2)(4)(2.2)]+(3)(4)+(2.2)(3)+(3)(4.6)
SA=8.8+12+6.6+13.8
SA=41.2 in^2
answer is option CI was out for quarantine and teacher won’t help, I need help!
A linear equation can be written as:
[tex]y=mx+b[/tex]Let:
y = c = Cost
x = h = Hours
Using the data, we can create a 2x2 system of equations. So:
[tex]\begin{gathered} x=2,y=20 \\ 20=2m+b_{\text{ }}(1) \\ ---------- \\ x=8,y=50 \\ 50=8m+b_{\text{ }}(2) \end{gathered}[/tex]Using elimination method:
[tex]\begin{gathered} (2)-(1) \\ 50-20=8m-2m+b-b \\ 30=6m \\ m=\frac{30}{6} \\ m=5 \\ so\colon \\ 20=2(5)+b \\ b=10 \end{gathered}[/tex]Therefore,the linear equation is given by:
[tex]y=5x+10[/tex]For a equation of the form y = mx + b
m = Slope (rate)
b = y-intercept (Initial value)
Therefore the hourly rate for renting a bicycle is $5 and the deposit is $10
Use the information from the previous question to answer this question now that you know the length of the missing side of the triangle, find the actual distance. Since each unit on the grid is zero. 5 mile, the ferry will travel about blank miles
Solution
find the actual distance. Since each unit on the grid is 0.5 mile, the ferry will travel about
Length of the missing side of the triagle = 10.2
Unit on the grid = 0.5mile
[tex]\begin{gathered} 1\text{unit -}\longrightarrow\text{ 0.5 mile} \\ 10.2\text{unit}--\longrightarrow x \\ x=\frac{10.2\times0.5}{1} \\ x=5.1 \end{gathered}[/tex]Hence the correct answer is Option C
what is 20/5*(3.8)=?
Given:
[tex]\frac{20}{5}\cdot3.8=\text{?}[/tex]first, we will find the result of dividing 20 by 5, then multiply the result by 3.8
so, the answer will be as follows:
[tex]\begin{gathered} \frac{20}{5}\cdot3.8 \\ \\ =4\cdot3.8=15.2 \end{gathered}[/tex]So, the answer will be 15.2
Please help!Which equation best represents the relationship between x and y in the graph?A. y = -3/4x - 3B. y = -4/3x - 3C. y = -3/4x - 4D. y = -4/3x - 4
Recall that the equation of a line in slope-intercept form is given by
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept of the line.
The y-intercept is the point where the line intersects the y-axis.
From the graph, we can see that the line intersects the y-axis at y = -3
So, the y-intercept is -3
The slope of the line is given by
[tex]m=\frac{\text{rise}}{\text{run}}=\frac{-3}{4}[/tex]The rise is the vertical distance between the two points on the line.
The run is the horizontal distance between the two points on the line.
So, the equation of the line is
[tex]y=-\frac{3}{4}x-3[/tex]Therefore, option A is the correct answer.
Type the correct answer in each box.In this figure, sin ZQOP=cos ZRand cosZROQ sin 2
From the given figure, we have:
[tex]\begin{gathered} \sinSimilarly,[tex]\begin{gathered} \cosMauricio is buying his wife flowers for their anniversary. The florist has 5 red roses, 4 yellow roses, and 3 pink roses. What is the probability he will select 1 yellow rose the 2 red rose. Independent or Dependent
We will have the following:
The probability will be given by:
[tex]p=(\frac{1}{12})(\frac{5}{11})(\frac{4}{10})\Rightarrow p=\frac{1}{66}[/tex][tex]\Rightarrow p=0.01515151515\ldots\Rightarrow p\approx0.015[/tex]So, the probability of that happening is approximately 15%.
It is dependent.
bill:$42,tax 9%,tip,18%
We have the next information
Bill $42
tax 9%
tip 18%
if the total is 42
the tax will be
42*.09=$3.78
the tip will be
42*.18=$7.56
An archaeologist finds dinosaur bones 100 miles East and 200 miles North of his office. He finds whale bones 100 miles East and 300 miles South of his office. Graph and label these two points. How far apart are they?
Let's draw a picture of our problem:
where the red point (100 East, 200 Norh) represents the place where Archaeologist found the dinosaur. The blue point (100 East, 300 South) represents the place where Arcaeologist found the whale bones. Additionally, the green point (0,0) represents Arcaeologist's offfice.
The sum of two numbers is 26. The larger number is one less than twice the smaller number. Find the numbers.
Answer:7,9
Step-by-step explanation: The smallest number is 7 and the biggest number is 9
fresh flowers charges $1.50 per flower and a $10 delivery fee. beautiful bouquets does not change a delivery fee but charges $4.00 per flower. which equation would allow you to find the number of flowers that would make the cost the same.1.50+ 10x=41.50x+10=41.50x + 10=4x1.50+ 10x=4
Step 1 : Let's review the information provided to us to answer the question correctly:
Fresh flower price = $ 1.50
Delivery = $ 10
Bouquets per flower = $ 4.00
Step 2:
Let x to represent the number of flowers, either fresh or in bouquet
Point M is located at (-4,-6)What is located 4units from point M?
We have a point M located at (-4,-6).
We have to identify what is located 4 units from point M.
We can draw a circle with center at M with a radius of 4 units.
The circumference will include all the points that are 4 units away from M.
We can draw them as:
We can see that none of the points listed is 4 units from M.
The y-axis is located 4 units away from M.
Other point that is 4 units from M is for example (-4,-2).
-14x +P = Qx + 18find the values of P and Q the equation has infinite solutions
To have infinite solutions, both sides of the equation must be equal, we have to end with a statement that is true no matter what:
-14x+P = Qx+18
-14x = Qx
So, Q must be -14
-14x = -14x
For the next term
P = 18
So:
-14x+18 =-14x+18
Values:
P =18
Q=-14
A motivational speaker charges $5 for an adult's ticket and $2 for a child's ticket. For one event, he sold 785 tickets for $3280. How many adult tickets were sold? a) 785 b) 570 c) 215 d) 58
Answer:
the number of adult ticket sold is 570
[tex]x=570[/tex]Explanation:
Let x represent the number of adult ticket and y represent the number of child's ticket.
Given that he charges $5 for an adult's ticket and $2 for a child's ticket.
For one event, he sold 785 tickets.
So, we have;
[tex]x+y=785\text{ -----1}[/tex]he sold 785 tickets for $3280.
Then;
[tex]5x+2y=3280\text{ ------2}[/tex]let us solve by substitution.
make y the subject of formula in equation 1 and substitute to equation 2;
[tex]y=785-x[/tex]substituting to equation 2;
[tex]\begin{gathered} 5x+2y=3280 \\ 5x+2(785-x)=3280 \\ 5x+1570-2x=3280 \\ 5x-2x=3280-1570 \\ 3x=1710 \\ x=\frac{1710}{3} \\ x=570 \end{gathered}[/tex]Therefore, since x represent the number of adult tickets sold, then the number of adult ticket sold is 570
[tex]x=570[/tex]Which point is a solution to the system of inequalities below?A. (1,2)B. (4,7)C. (0,3)D. (-1,1)
For this problem we have the following two inequalities given:
[tex]x+2y\ge4\text{, y}-2x<0[/tex]And we want to find the point of solution to the system of inequalities and for this case we can work with equations
[tex]x+2y=\text{4 (1) }[/tex][tex]y-2x=\text{ 0 (2)}[/tex]If we solve for x from equation (1) we got:
[tex]x=\text{ 4}-2y\text{ (3)}[/tex]And replacing equation (3) into equation (2) we got:
[tex]y-2(4-2y)=\text{ 5y}-8=\text{ 0}\rightarrow y=\text{ }\frac{8}{5}=\text{ 1.6}[/tex]And solving for x we got:
[tex]x=\text{ 4}-(2\cdot1.6)\text{ = 0.8}[/tex]So then the intersection point between the two lines is (0.8,1.6). If we analyze all the possible options we have this:
(1,2)
Fill in the missing number to complete the pattern.18, 12, _ , 0
The given pattern starts with an 18, then we have a 12, we can go from 18 to 12 by subtracting 6 from the initial number. By subtracting 6 from 12, we get the number that goes on the right side of 12, that is:
12 - 6 = 6
Then, fill the missing number with a 6.
18, 12, 6, 0
Marco wants to take a taxi cab ride if the cost to ride is 7.00 with the cost per m is 0.25 per mile and mr. o can only spend 30 write linear inequality that model
Each ride has a fixed cost of 7 and a cost that increases proportionally to the distance travelled of 0.25 per mile. Therefore the total cost of the ride is:
[tex]\text{ cost(x)}=0.25\cdot x+7[/tex]Where "x" is the distance in miles. Marco can only spend 30 on his ride, therefore the cost must be less or equal to that value.
[tex]\begin{gathered} \text{ cost(x)}\leq30 \\ 0.25\cdot x+7\leq30 \end{gathered}[/tex]We can solve the linear equation by isolating the "x" variable on the left side.
[tex]\begin{gathered} 0.25\cdot x\leq30-7 \\ 0.25\cdot x\leq23 \\ x\leq\frac{23}{0.25} \\ x\leq92 \end{gathered}[/tex]Marco's travel must be shorter or equal to 92 miles.
Find WX.Write your answer as an integer or as a decimal rounded to the nearest tenth.WX = ____
The give figure is of a triangle WXY right angled at X.
From the figure, WY=10 and
Using trigonometric property in the triangle,
[tex]\cos \theta=\frac{\text{adjacent side}}{\text{hypotenuse}}[/tex][tex]\begin{gathered} \cos Find WX by solving the above equation.[tex]\begin{gathered} WX=10\times\cos 44^{\circ} \\ =7.2 \end{gathered}[/tex]Therefore, WX=7.2.
using your place value vocabulary, describe the place value pattern you see occur in these four problems.10 × $8 = $8010 × $0.80 = 8.00$5.40 ÷ 10 = $0.54$0.60 ÷ 10 = $0.60
The place value of 8 on multiply by 10 becomes tens
The place value of the 8 in 0.80 by multiply with 10 becomes ones
Teh place of 5 on dividing with 10 becomes tenths
The place of 6 from 0.60 on divide by 10 becomes tenths
Linda Davis agreed to lend money to Alex Luciano at a special interest rate of 7% per year, on the condition that he borrow enough that would pay her $500 in interest over a four-year period. What was the minimum amount Alex could borrow?
It is given that,
[tex]\begin{gathered} Rate(R)\text{ = 7\%} \\ I\text{ = \% 500} \\ T\text{ =3 years} \end{gathered}[/tex]Interest is given by the formula,
[tex]I\text{ = }\frac{PRT}{100}[/tex]Substituting the value in the formula,
[tex]\begin{gathered} 500\text{ = }\frac{P\times7\times4}{100} \\ 50000\text{ = 28P} \\ P\text{ = }\frac{50000}{28} \\ P\text{ = 1785.71 } \end{gathered}[/tex]Thus the minimum amount to be borrowed is $ 1785.71.
Leila drove to the mountains last weekend. There was heavy traffic on the way there and the trip took 7 hours. When Leila drove home, there was no traffic and the trip only took 4 hours. If her average rate was 27 miles per hour faster on the trip home, how far does Leila live from the mountains
We have the next formula
[tex]d=r\cdot t[/tex]where d is the distance, r is the rate and t is the time.
For the trip going
d=r*7
For the trip returning
d=(r+27)*4
Then we solve
7r=4r+108
We solve for r
7r-4r=108
3r=108
r=36
Then for d
d=36*7
d=252 miles
ANSWER
she lives 252 miles far from the mountains
Determine if the two triangles are congruent.• If they are, complete the congruence statement; and identify how they are congruent.• Otherwise, select "Not Congruent" for BOTH drop downs.Be sure to identify any corresponding angles or sides that you know are congruent!AniBby[ Select ]AACB ZA [Select ]
Triangle ACB is congruent with triangle DCB by SAS
Because they have two sides of equal lenght (AC - DC and common side CB) and an agle of equal measure (A - D)
HELP PLEASE and please give out a good answer. Which ones are right? Or wrong?
You have the following equation for model the amount of money raised by selling concessions related to the number of fans:
y = 5.2x - 20
The previous equation has the form of a line y =mx + b, where m is the unit rate of change and b a constant value.
The first sentence is true because in the given situation m = 5.2 and it is the unit rate of change.
The second sentence is false because the constant -20 is independent of the number of fans.
The third sentence is true because if no fans are attended, then x=0 and
y = 5.2*0 - 20
y = -20
that is, there is a loss of money.
in art class, Rafi made 5 clay bowls to send to family members. the bowls are fragile, so Rafi bought a roll of bubble wrap to protect them. he used a total of 11 feet of bubble wrap to wrap the bowls. how much bubble wrap did Rafi use for each bowl?
Number of bowls: 5
Bubble wrap = 11 feet
To find how many bubble wrap he used for each bowl, divide the bubble graph length by the number of bowls.
11 / 5 = 2.2
2.2 feet for each bowl
Hi so sorry i need help in geometry i think its asking if the two given angles are coterminal or not
Given these two angles:
[tex]\frac{5\pi}{4}[/tex][tex]-\frac{3\pi}{4}[/tex]You need to remember that, by definition, two angles are coterminal if the Difference (the result obtained by subtracting them) is:
[tex]360\text{\degree or }2\pi[/tex]Then, you need to set up:
[tex]\frac{5\pi}{4}-(-\frac{3\pi}{4})[/tex]Solving the Subtraction, you get:
[tex]=\frac{5\pi}{4}+\frac{3\pi}{4}[/tex][tex]=\frac{8\pi}{4}[/tex][tex]=2\pi[/tex]Hence, the answer is: They are Coterminal Angles.
in a class, 2/3 of the pupils are boys. If there are 15 more boys than girls, how many pupils are there in the class (use equation method)
Solution
Step 1:
Let the number of pupils = n
[tex]\begin{gathered} Number\text{ of boys = }\frac{2}{3}n \\ Number\text{ of girls = }\frac{2}{3}n\text{ - 15} \end{gathered}[/tex]Step 2:
Write an equation to find the value of n
[tex]\begin{gathered} \frac{2}{3}n\text{ + }\frac{2}{3}n\text{ - 15 = n} \\ \frac{4n}{3}\text{ - n = 15} \\ \frac{4n\text{ - 3n}}{3}\text{ = 15} \\ \frac{n}{3}\text{ = 15} \\ \text{n = 15 }\times\text{ 3} \\ \text{n = 45} \end{gathered}[/tex]Final answer
There are 45 pupils in the class.
A sample of 34 customers was taken at a local computer store. The customers were asked the prices of the computers they had bought. The data are summarized in the following table. Find the mean price for the sample. Round your answer to the nearest dollar
To find the mean we will sum the prices (total price, including repeated values) and divide by the total number of computers, then
[tex]m=\frac{14\cdot1400+11\cdot800+3\cdot2600+6\cdot1500}{34}[/tex]Using a calculator
[tex]\begin{gathered} m=\frac{45200}{34} \\ \end{gathered}[/tex]Do the division (use a calculator)
[tex]\begin{gathered} m=\frac{45200}{34} \\ \\ m=1329.41 \end{gathered}[/tex]The mean price is 1329.41
The recycling center processed 36,000 pounds of recyclable materials. How many tons of recyclable materials are processed? A 18 TonC 72,000 TonB 38,000 TonD 180 Ton
We were told that the recycling center processed 36,000 pounds of recyclable materials. We would convert from pounds to tonnes. Recall,
1 tonne = 2000 pounds
Thus, x tonnes = 36000 pounds
By cross multiplying, we have
2000x = 36000
x = 36000/2000
x = 18
18 tons of recyclable materials were processed