Hello!
We have the following expression:
[tex]2a\cdot a\cdot3a+b\cdot4b[/tex]Let's multiply and simplify it, look:
[tex]6a^3+4b^2[/tex]We multiply a*a*a, so we can rewrite it as a³. The same with b*b as b².
So, the answer in the simplified form is:
6a³ + 4b²
Find the distance between the two points: (8, 3) and (-2, 6). Round your answer to 2 decimal places.
To find the distance between two points we have to use the following formula:
[tex]d=\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]Where d is the distance, x2 and x1 are the x coordinates of the points and y2 and y1 are the y coordinates of the points:
[tex]\begin{gathered} d=\sqrt{(8-(-2))^2+(3-6)^2} \\ d=\sqrt{(10)^2+(-6)^2\frac{}{}} \\ d=\sqrt{100+36} \\ d=\sqrt{136} \\ d=11.66 \end{gathered}[/tex]It means that the distance between these two points is 11.66.
Find -48a divided by 8 when a=1 write your answer in simplest form
-48a÷ 8 can be written as,
[tex]\frac{-48a}{8}[/tex]Put a=1 in the above exprression and solve.
[tex]\frac{-48\times1}{8}=-6[/tex]Therefore, the solution is -6.
= help please!!
ODECIMALS
Ordering decimals
Order these numbers from least to greatest.
1.85, 1.7, 1.805, 1.7051
Answer:
1.7, 1.7051, 1.805, 1.85
Step-by-step explanation:
Solve on the interval [0, 2pi):3 sec x - 2 = 13 sec x =3secx= 1cos = -1Is it 0?
3 sec x - 2 = 1
Add 2 to both sides
3 sec x = 1+ 2
3 sec x = 3
divide both sides by 3
sec x = 3/3
sec x = 1
[tex]\begin{gathered} \text{ sec x = 1} \\ x=sec^{-1}1 \\ x\text{ = 0 } \\ \text{and also, the interval is \lbrack{}0, 2}\pi\rbrack \\ x\text{ = 2}\pi \\ \text{The answer is x = 0 and x = 2}\pi \end{gathered}[/tex]Find the sum and enter it in the box below. Enter your answer as a polynomialin descending order, and use the caret() for exponents. For example, youwould write 4x as 4x^2.(x8 - x) + (3x + 2)
(x^8-x)+(3x^8+2) = (opperating like terms:)
x^8+3x^8-x+2 =
4x^8-x+2
The answer will be 4x^8-x+2
Please show me how to solve/graph this Algebra 2 problem step by step, thank you!
Explanation:
Step 1. We have a piecewise function defined for certain x value intervals.
for x values between -4 and -1, the definition is:
[tex]f(x)=x+6,\text{ for }-4And for the x values between -1 and 5, the definition is:[tex]f(x)=-2x+7,\text{ for }-1Step 2. We need to graph the function, for that, we start with the definition for x values between -4 and -1[tex]\begin{equation*} f(x)=x+6 \end{equation*}[/tex]To graph this, we compare it with the general line function
[tex]f(x)=mx+b[/tex]where m is the slope (the rate of change of the line) and b is the y-intercept. In this case, for f(x)=x+6, the slope is m=1, and the y-intercept is 6, if we were to graph this line in the whole plane, it would look as follows:
But since this is just the definition of the function for the values between -4 and -1, the result is:
Step 3. Now we consider the second definition of the function:
[tex]\begin{equation*} f(x)=-2x+7 \end{equation*}[/tex]Comparing it with the general line function
[tex]f(x)=mx+b[/tex]where m is the slope (the rate of change of the line) and b is the y-intercept.
Here in f(x)=-2x+7, the slope is m=-2, and the y-intercept is b=7, which means that the line is decreasing at a rate of -2, and that it crosses the y-axis at 7.
If we were to graph this line in the whole plane, it will look as follows (in blue):
But since that is the definition of the function only for the interval from -1 to 5, we only consider the line for that specific x-interval, we represent the point at -1 with an open circle and at 5 with a filled circle to represent that 5 is included in the segment:
Answer:
20 over 25 equals 60 over 75 true or false
20 over 25 equals 60 over 75 true or false
we have
20/25=60/75
Multiply the left side by 3/3
(3/3)(20/25)=60/75
so
60/75=60/75
therefore
answer is trueWendy is a waitress and has $15,000 toinvest, and wishes to gain $4,200 in interestover the next eight years. Approximatelywhat is the minimum simple interest rateWendy needs to reach her goal?
The formula for determining simple interest is expressed as
I = PRT/100
where
I = interest earned
R = interest rate
T = number of years
P = principal or amount invested
From the information given,
P = 15000
I = 4200
T = 8
Thus, we have
4200 = (15000 x R x 8)/100
4200 = 1200R
R = 4200/1200
R = 3.5
The required interest rate is 3.5%
Question 8 of 40The cost of renting a bicycle is $9 for the first hour plus another $4 for eachadditional hour. Which of the following represents this situation, where Cisthe total cost of renting a bicycle for h hours?O A. C= 9h+4O C. C = 13hOD. C= 4h+9SUBMITB. C= 4(h-1) +9°
Based on the given information, for 1 hour the cost is $9, for additional hours each hour cost $4. For example, for 2 hours, the cost is $4 + $9 = $13 and for 3 hours is $4 + $4 + $9 = $17.
Based on the previous calculation, you can conclude that following expression represent the given situation.
C = 4(h - 1) + 9
Hence, the answer is option B.
8.) Order the following numbers Smallest to dargest on a number explain. your reason soning. 7, √53,1 34, 6, √ 25
Given the numbers:
[tex]7,\sqrt[]{53},\sqrt[]{34},6,\sqrt[]{25}[/tex]We will arrange the numbers from the least to the greatest
there are two methods:
First, square all the numbers then arrange them then get the original numbers
so, the square of the numbers will be:
[tex]49,53,34,36,25[/tex]the order from the least to the greatest will be:
[tex]25,34,36,49,53[/tex]So, the order of the given numbers will be:
[tex]\sqrt[]{25},\sqrt[]{34},6,7,\sqrt[]{53}[/tex]the second method is by using the calculator to find the square roots of the radicals, it will give the same answer
Which situation can be modeled by the equation y= 3x + 25? Select one: A rental car costs $25 per day plus a $3 charge for cleaning. A rental car costs a one-time fee of $25 plus $3 for each hour. A rental car costs a one-time fee of $25 plus an additional $3 charge for processing. A rental car costs $25 per day plus $3 per gallon of fuel needed upon return to fill the tank.
Here, given the linear equation, we want to select which of the options can correctly be modeled by the given equation
As we can see from the equation, the cost $25 represents a fixed cost, while 3 multiplied by x is based on a certain recurring amount
Thus, we can have our answer here as;
A rental car costs a one-time fee of $25 plus $3 for each hour
The $25 is the fixed cost, while the other amount that adds to it is dependent on the number of hours for which the car was driven
a business has $5000 in cash, but then it pays $500 cash to make a purchase. after the transaction is posted, what is the balance in the Cash T-account a. $500 credit balanceb. $500 debit balancec.$4500 credit balanced. $4500 debit balance
The initial amount of cash, P=$5000.
The amount paid for purchase, C=$500.
The balance amount after paying for a purchase is,
[tex]\begin{gathered} B=P-C \\ =5000-500 \\ =4500 \end{gathered}[/tex]Therefore, the credit balance is $4500.
Hence, option c is correct.
Can some help me answer this
I need an answer and explanation about how it corrects the misconceptions the artist had
The artist thought a decrease of 14% over the original tile 50 x 50, that's why she thought 49 x 49 was wrong.
But when she calculated she correctly calculated a decrease by 14% over the 57 x 57 tile that's how she had the same results.
1) Since the ceramic artist is aware that clay shrinks by 14% then the calculation should be:
[tex]50\cdot(1+0.14)=57[/tex]2) So since the dimensions will shrink it, then this artist correctly calculated the new tile to 57 x 57 (since squares have the same length and width)
2.2) When the clay was in the oven, it shrank following this equation (minus 14%):
[tex]57\times(1-0.14)=57\times(0.86)=49.02[/tex]She thought that there was an error, probably because she calculated
a decrease of 14% of that original tile would yield a 43 x 43 tile, instead
of 57 x 57 Because: 50x ( 1-0.14)= 43.
3) Hence, the answer is:
The artist calculated a decrease of 14% over the original tile 50 x 50, that's
why she thought 49 x 49 was wrong.
34,600 The number between 1 and 10: __The power of 10: __The number in scientific notation: __Can you help me withe the blank spaces
Problem:
34,600
The number between 1 and 10: __
The power of 10: __
The number in scientific notation: __
Solution:
The number between 1 and 10 is 3
The power of 10 is 4
The number in scientific notation is
3.46 × 10^4
Solve using substitution methody= -5x + 2y= -10x + 7
ANSWER
(1, -3)
EXPLANATION
Since we have y in function of x in both equations, we can replace the first equation into the second and solve for x:
[tex]\begin{gathered} -5x+2=-10x+7 \\ -5x+10x=7-2 \\ 5x=5 \\ x=1 \end{gathered}[/tex]And then replace x = 1 into one of the equations to find the value of y:
[tex]\begin{gathered} y=-5x+2 \\ y=-5\cdot1+2 \\ y=-5+2 \\ y=-3 \end{gathered}[/tex]The solution is (1, -3)
i need to know what x equals
Answer:
x = 13
Step-by-step explanation:
The tiny marks on all three sides means this shape is an equilateral triangle (all three sides are the same) This means that all three angles are also the same. 180° degrees in a triangle, so all three angles are 60°.
Use this info to set up an equation.
4x + 8 = 60°
Subtract 8.
4x = 5 2
Divide by 4.
x = 13
what does the point (1,5) represent
The point (1,5) is:
Like it is shown this means that we have to move one unit in the right direction and 5 units up.
You are baking a casserole. The recipe calls for 1/3 of a cup of beans tomake 4 servings. How many cups of beans would you need to make 28servings?
According to the problem, a 1/3 cup of beans is equivalent to 4 servings. To know the number of cups of beans for 28 servings, we just have to use the rule of three.
[tex]x=28\cdot\frac{\frac{1}{3}}{4}=28\cdot\frac{1}{12}=\frac{7}{3}=2\frac{1}{3}[/tex]Hence, we need 2 1/3 cups of beans for 28 servings.Find the area. Leave answer in terms of pi.A) 91 kmC) 647 kmB) 167 kmD) 257 km
The figure we have is a circle and we need to find its area.
To find the area of any circle we use the following formula:
[tex]A=\pi r^2[/tex]Where A is the area, and r is the radius of the circle.
Step 1. Identify the radius of the circle.
The radius is a line that goes from the center of the circle to a point in the circumference. In this case, the radius is shown in red in the following diagram:
Thus:
[tex]r=5kn[/tex]Step 2. Once we know the radius, we can substitute its value into the area formula:
[tex]A=\pi r^2[/tex]substituting r=5km:
[tex]A=\pi(5km)^2[/tex]And we solve the operations since 5^2 is equal to 25:
[tex]A=25\pi km^2[/tex]The indications are to leave the answer in terms of pi, which means that we don't substitute the value of pi in the answer, thus, that is the final answer.
Answer:
[tex]D)\text{ }25\pi km^2[/tex]solve the equation for y7x + 4y = 8
To solve the equation for a variable we need to isolate the variable on the left side of the equation. The expression is:
[tex]7x+4y=8[/tex]To start we need to subtract by "7x" on both sides of the equation.
[tex]\begin{gathered} 7x+4y-7x=8-7x \\ 4y=8-7x \end{gathered}[/tex]We then need to divide both sides by 4.
[tex]\begin{gathered} \frac{4y}{4}=\frac{8-7x}{4} \\ y=\frac{8-7x}{4} \end{gathered}[/tex]In a triangle, the measure of the second angle is half the measure of the first. The third angle is
5 degrees more than twice the measure of the first. Find the measures of the three angles.
Answer:
50; 25; 105
Step-by-step explanation:
Sum of the angles of triange is 180, so we have 2x + x + 2*2x + 5 = 180 (x is number of degrees of second angle), if I understood word 'twice' correctly.
Next, let me solve this:
2x + x + 4x + 5 = 180
7x + 5 = 180
7x = 175
x = 25
So, second angle is 25 degrees, first is 25*2=50 degrees and third is 50*2+5=105 degrees.
Hope that this was helpful.
find the of change of the distance D from the origin of a point moving on the graph off …dx/dt= 9 units per second. Write the exact answer do not round
Given:
D is start origin that mean (0,0) moving with graph :
[tex]f(x)=x^2[/tex]It move x then y is
[tex]\begin{gathered} f(x)=x^2 \\ y=x^2 \end{gathered}[/tex]Point is (2,4)
Distance is:
[tex]D=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2_{}}[/tex]Where,
[tex]\begin{gathered} x_2=x \\ x_1=0 \\ y_2=x^2 \\ y_1=0 \end{gathered}[/tex]So distance is:
[tex]\begin{gathered} D=\sqrt[]{(x-0)^2+(x^2-0)^2} \\ D=\sqrt[]{x^2+x^4} \end{gathered}[/tex][tex]\begin{gathered} \frac{dD}{\differentialDt t}=\frac{d(\sqrt[]{x^2+x^4})}{\differentialDt t} \\ =\frac{1}{2\sqrt[]{x^2+x^4}}(2x+4x^3)\frac{dx}{\differentialDt t} \end{gathered}[/tex][tex]\begin{gathered} \text{when x=2} \\ \frac{dx}{\differentialDt t}=9 \end{gathered}[/tex][tex]\begin{gathered} =\frac{1}{2\sqrt[]{(2^2+2^4)}}((2\times2)+(4\times2^3))\times9 \\ =\frac{324}{6.92820} \\ =46.7653 \end{gathered}[/tex]The slope of the graph shown below is:
A 5/4
B -5/4
C 3/4
D -3
Please help me
We can use the slope equation to help us do this:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are two points that fall on the lineSolving the Question⇒ First, pick two clear points that falls on the given graph:
(0,2), (4,-3)
⇒ Plug these into the equation and solve:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}\\\\m=\dfrac{-3-2}{4-0}\\\\m=\dfrac{-5}{4}[/tex]
AnswerB) -5/4
where would the shape be located after a translation of 5 units to the right
First we determine the coordinates of the points of the shape:
p1 (-2, 4)
p2 (-2, 1)
p3 (-4, 3)
p4 (-4, 4)
After that, we add +5 to the x components, getting the following:
P1' (3, 4)
P2' (3, 1)
P3' (1, 3)
P4' (1, 4)
The shapes below have congruent perimeters. Find the value of x.
Step-by-step explanation:
that is a strange way to express to situation.
what they mean here is that the perimeters are of identical lengths.
other than the total length the perimeters have nothing in common. therefore, I would have never used the word "congruent" for that. if that would have been the answer to a question like "what statement describes the relationship between the 2 perimeters ?", I would have flagged this as wrong.
anyway, so, the perimeters are of equal length. that means
x + 6 + x + 3 + x + 9 = 2(x + 4) + 2(x + 1)
3x + 18 = 2x + 8 + 2x + 2 = 4x + 10
3x + 8 = 4x
8 = x
Please solve this and it also says show work, I really need help!
Explanation
Given that 12 players chose a bottle of water which is 3/4 of the total number of players (p). The equation to determine p can be seen below
We can create the equation below;
[tex]\begin{gathered} \frac{3}{4}\text{ of p =12} \\ \frac{3}{4}\times P=12 \\ Cross\text{ multiply} \\ 3p=12\times4 \\ Divide\text{ both sides by 3} \\ p=\frac{12\times4}{3} \\ p=4\times4 \\ p=16 \end{gathered}[/tex]Answer: The total number of players at the baseball game is 16
Answer the questions below about the quadratic function. g(x) = 3x ^ 2 - 6x + 5
In order to find a critical value (maximum or minimum) we need to compute the first derivative, which is given by
[tex]\frac{d}{dx}g(x)=6x-6[/tex]Then, a critical value ocurrs when
[tex]\frac{d}{dx}g(x)=0[/tex]which implies that
[tex]6x-6=0[/tex]So by adding 6 to both side, we have
[tex]\begin{gathered} 6x=6 \\ then \\ x=\frac{6}{6} \\ x=1 \end{gathered}[/tex]Therefore, there is a maximum or minimum at x=1.
In order to see if the point represents a maximum or minimum, we need to find the second derivative of our function, which is given by
[tex]\frac{d^2}{dx^2}g(x)=6[/tex]We have that if the second derivative is positive, the point represents a minimum and if it is negative, the point represents a maximum. In our case, since the second derivative is greater than zero (positive number) there is a minimum point at x=1. Then, by substituting this values into the function, we get
[tex]\begin{gathered} g(1)=3(1^2)-6(1)+5 \\ g(1)=3-6+5 \\ g(1)=2 \end{gathered}[/tex]so the minimum point is located at (1,2).
Therefore, with the above information, the answers are:
Does the function have a minimum or maximum values? Answer: Minimum
Where does the minimum or maximum value occur? Answer: x=1
Whats is the funtion's minimum or maximum values? Answer: 2
Mrs.Byrne's class went raspberry picking. The data show the weights of the cartons of raspberries thestudents picked.Weight of Cartons of RaspberriesPicked (in pounds)112 1 2 3 1 4 3 3 14 4 4 4 4 4 4 4 4To all public transportHow many pounds of raspberries did Mrs.Byrne's class pick in all?The class pickedpoundscould you explain the problem
8.
The weights of the cartons of raspberries picked by the students are:
[tex]\frac{3}{4},\frac{1}{4},\frac{2}{4},\frac{4}{4},\frac{1}{4},\frac{1}{4},\frac{2}{4},\frac{3}{4},\frac{3}{4}[/tex]To complete the table, on the first column you have to write each observed weight, those are: 1/4, 2/4, 3/4, and 4/4
Then, on the second column, you have to write one tally, for each box that has the said weight.
For example, for the weight 1/4 pounds, there are three boxes that weighed 1/4pounds, so you have to write three tallies.
For "2/4 pounds", there were 2 boxes that had this weight, so you have to write two tallies.
For "3/4" pounds, there were 3 boxes that had this weight, so you have to write three tallies.
For "4/4 pounds", there was only one box that measures this weight, so you have to write one tally.
For the number line, you have to make a "dot plot", below the line you have to write each possible weight: 1/4, 2/4, 3/4, and 4/4. Then you have to draw points above each weight, one for each box that measured the said weight:
9.
The heaviest box of raspberries weighed 4/4 pounds
The lightest box of raspberries weighed 1/4 pounds
To determine the difference between both of them you have to subtract 1/4 from 4/4:
[tex]\frac{4}{4}-\frac{1}{4}=\frac{4-1}{4}=\frac{3}{4}[/tex]The difference between the heaviest and the lightest boxes is 3/4 pounds.
10.
To determine the total pounds that the class picked, you have to add the weights of all cartons:
[tex]\frac{3}{4}+\frac{1}{4}+\frac{2}{4},\frac{4}{4}+\frac{1}{4}+\frac{1}{4}+\frac{2}{4}+\frac{3}{4}+\frac{3}{4}=5[/tex]They picked 5 pounds of raspberries.
Understanding Reciprocals in Division of Fractions 4 1 Complete the steps: g + 2 2 Rewrite the division problem as multiplication: Multiply the numerators and the denominators. The answer is Intro
Given:
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