Answer:
Distributive Property
Step-by-step explanation:
Use the distributive property to multiply each term in each parenthesis.
Example:
To simplify the expression (x-3)(x^2-4x-7), apply the distributive property. The distributive property states to multiply each term in each parenthesis.
x*x^2=x^3
x*-4x=-4x^2
x*-7=-7x
-3*x^2=-3x^2
-3*-4x=12x
-3*-7=21
This gives the expression x^3-4x^2-7x-3x^2+12x+21. Combine like terms and get x^3-7x^2+5x+21.
How many solutions does the equation have?
7x+3−x=3(1+2x)7x+3−x=3(1+2x)
0
1
infinitely many
Answer:
0
if you were confused to the one on top
Need quick help please?! Using the Angle Bisector Theorem solve for x.
Show all work.
Using the Angle Bisector Theorem solve for x.
The "Angle Bisector" Theorem says that an angle bisector of a triangle will divide the opposite side into two segments that are proportional to the other two sides of the triangle.
As, we see the figure, AD bisects angle A
So, Applying Angle Bisector theorem, we get,
[tex] \frac{AC}{CD} =\frac{AB}{BD} [/tex]
[tex] \frac{AC=15}{CD=3} =\frac{AB=(4x+1)}{BD=5} [/tex]
[tex] \frac{15}{3} =\frac{4x+1}{5} [/tex]
15 divide by 3 gives 5
So, we have
5=[tex] \frac{4x+1}{5} [/tex]
To get rid of fractions let us multiply by 5 on both sides
5*5=[tex] \frac{5*(4x+1)}{5} [/tex]
25=[tex] \frac{1*(4x+1)}{1} [/tex]
25=4x+1
To solve for x, let us subtract 1 from both sides
25-1=4x+1-1
24=4x+0
Or, 4x=24
To solve for x, let us divide by 4 on both sides
[tex] \frac{4}{4}x=\frac{24}{4} [/tex]
x=6
Answer: x=6
In how many ways can you choose 3 kinds of ice cream and 2 kinds of toppings from a dessert buffet with 10 differnt kinds of ice cream and 6 kinds of toppings
To choose 3 kinds of ice cream and 2 kinds of toppings from the dessert buffet with 10 different kinds of ice cream and 6 kinds of toppings, you can use the concept of combinations. The total number of ways to choose is 1800.
Explanation:To determine the number of ways to choose 3 kinds of ice cream and 2 kinds of toppings from the dessert buffet, we can use the concept of combinations. We have 10 different kinds of ice cream to choose from, and we want to choose 3 of them. The number of combinations can be calculated using the formula:
C(n, r) = n! / (r!(n-r)!)
where n is the total number of objects (10 ice cream flavors) and r is the number of objects to be chosen (3 ice cream flavors), and ! denotes factorial.
In this case, the number of combinations of ice cream flavors is:
C(10, 3) = 10! / (3!(10-3)!) = 120
Similarly, we have 6 different kinds of toppings to choose from, and we want to choose 2 of them. The number of combinations of toppings is:
C(6, 2) = 6! / (2!(6-2)!) = 15
Therefore, the total number of ways to choose 3 kinds of ice cream and 2 kinds of toppings is the product of the number of combinations of ice cream flavors and toppings:
Total number of ways = 120 * 15 = 1800
A wire 320 in. long is cut into two pieces. one piece is formed into a square and the other into a circle. if the two figures have the same area, what are the lengths of the two pieces of wire (to the nearest tenth of an inch)? circle in square in
The lengths of the two pieces of wire, when one is formed into a square and the other into a circle with equal areas, are approximately 186.3 inches and 133.7 inches respectively.
Explanation:To solve this problem, we first need to understand that the total perimeter of both the square and the circle made from the wire lengths equal to the original wire length, which is 320 inches. Suppose the length of the wire used for the square is 'a' and the length for the circle is 'b'. So, 'a + b = 320' inches.
Given that, the areas of both the square and the circle are equal. The area of a square is side^2 and the side of our square will be 'a/4' (since a square has four equal sides) and the area of a circle is πr^2, with the circumference being 2πr or 'b' in this case, so the radius is 'b / (2π)'.
Setting these two areas equal gives us the equation '(a/4)^2 = π * (b/ (2π))^2'. Solving this system of equations, we find that 'a' is approximately 186.3 inches and 'b' is approximately 133.7 inches.
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A(n) _ shows you the schedule of payments on a loan and the total interest and payments at the end of the loan.
A. payoff table
B. amortization table
C. payment table
D. interest table
Secured debts must have _.
A. collateral
B. real property
C. low interest rates
D. certified lenders
You are purchasing a car for $12,985.00 with the help of your parents. How much interest is saved in the first month by you using their good credit rating compared to your fair credit rating?
A. $14.61
B. $54.15
C. $15.15
D. $69.25
(Secured APR for good credit is 5.00%, and for the unsecured APR it is 5.90%. Secured APR for fair credit is 6.40%, and for unsecured APR it is 7.25%.)
Answer: 3.A
Step-by-step explanation: At the exallent rating
Find the distance from A to C.
Answer:
√74
Step-by-step explanation:
a^2 + b^2 = c^2
7^2 + 5^2 = c^2
49 + 25 = c^2
74 = c^2
√74 = √c^2
In order to solve the following system of equations by addition, which of the following could you do before adding the equations so that one variable will be eliminated when you add them? 2x-4y=5 6x-3y=10 A.Multiply the top equation by -3 and the bottom equation by 2. B.Multiply the top equation by -2. C.Multiply the top equation by -3. D.Multiply the top equation by 3 and the bottom equation by 4.
Answer:
c is correct
Step-by-step explanation:
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Divide the following polynomial and then place the answer in the proper location on the grid. Write your answer in order of descending powers of y.
(y 3 - y 2 + y + 3) ÷ (y + 1)
THE ANSWER IS:
y^2-2y+3
The reason I included the correct answer is that this question has not been asked yet and I figured that someone might need to know this. Feel free to answer the question and get the points! :)
Answer:
y²-2y+3
Step-by-step explanation:
We write the dividend, y³-y²+y+3, under the box and the divisor, y+1, to the left of the box.
We first divide y³ by y; this is y². We write this above the box, over -y². We multiply the divisor by y²:
y²(y+1) = y³+y²
This goes under the divisor. We then subtract:
(y³-y²)-(y³+y²) = -2y². We then bring down the next term, y; this gives us -2y²+y.
We then divide -2y² by y; this is -2y. This goes above the box beside the y² in the quotient. We then multiply the divisor by -2y:
-2y(y+1) = -2y²-2y
We now subtract:
(-2y²+y)-(-2y²-2y) = 3y. We bring down the last term, 3; this gives us 3y+3. We divide 3y by y; this is 3. This goes beside the -2y in the quotient. We then multiply this by the divisor:
3(y+1) = 3y+3. We then subtract: (3y+3)-(3y+3) = 0
This makes the quotient y²-2y+3.
Estimate the circumference of a circle that has a diameter of 13 yards.
Show the result in yards.
Final answer:
To estimate the circumference of a circle with a diameter of 13 yards, use the formula C = π * d where π is approximated as 3.14. The estimated circumference is 40.82 yards.
Explanation:
To estimate the circumference of a circle that has a diameter of 13 yards, you can use the formula for the circumference of a circle, which is π times the diameter (C = π * d). The value of π (pi) can be rounded to 3.14 for convenience in calculation. Using this rounded value of π:
Circumference = 3.14 * 13 yards= 40.82 yards
Therefore, the estimated circumference of the circle is 40.82 yards.
which completely describes the polygon
Answer:
NONE OF THE ABOVE!!
Step-by-step explanation:
A regular polygon is equilateral and equiangular, and also, can be inscribed into a circle. The polygon shown doesn't meet any of these conditions.
Charise is buying 6 packets of seeds to plant in her garden Each packet of seeds is $2 19, Estimate her total cost by rounding Is the estimate an underestimate or an overestimate?
Answer:
the estimate is an over estimate because 2.19 time 6 equals 13.14 and you sya 15 dollors so so it is an over estimate
Step-by-step explanation
i hope this helps i hate math
it took team tool bella 2 1/3 hours to hike 4 2/3 miles. whats their average speed in mph
Table a shows the average low temperatures recorded in a city during the first three months of the year. table b shows the average low temperatures recorded in the city during the next four months of the year. what is the difference in the medians of the two sets of data?
a.1
b.4
c.5
d.13 12)
This is not enough information, sorry
Please help!!
What transformations of the parent function f(x) = |x| should be made to graph, f(x) = - |x| + 5?
What is the solution to the inequality: 10x + 18 < -2?
Answer: x<−2
(just had a test)
hope this helps
What is 1/10 of an income of $97.50?
$9.75
$0.98
$975.00
$9,750.00
The purple shape is a dilation of the black shape. What is the scale factor of the dilation?
Answer:
Scale factor = [tex] \frac{1}{2} [/tex]
Explanation:
The purple shape is a dilation of the black shape.
A dilation is a transformation that produces an image that is the same shape as the original, but is a different size.
Now findd the scale factor.
If given two shapes and need to find the scale factor, We must know which one was the original and which one is the image or the new shape. Then we need to know the length of corresponding sides and set them up in a ratio like so:
Scale Factor = [tex] \frac{purple}{black} [/tex]
Scale factor = [tex] \frac{10}{20} = \frac{1}{2} [/tex]
What is the domain of the square root function graphed below?
Answer:
x ≥ 0
Step-by-step explanation:
The function is graphed starting at 0 and going up the positive x-axis.
These are numbers that are greater than 0; thus the domain is greater than or equal to 0, or
x ≥ 0
The domain of the function is (d) x >= 0
How to determine the domain?From the graph, we have the following highlight:
The x values of the function starts at 0 and extends the right0 is inclusive of the x valuesSince 0 is inclusive, we make use of the greater than or equal to inequality
Hence, the domain of the function is (d) x >= 0
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what is equivalent to (3^6/y^-5)^2
What is the 30th term of the arithmetic series 4, 7, 10, …? 88 89?
What is the value of z in the equation z − 3 = 22? 7.33 19 25 66
Answer:
The answer is 25
Step-by-step explanation:
In a box of 500 colored balls, 75 are black, 150 are green, 175 are red, 70 are white, and 30 are blue. what are the probabilities of selecting a ball of each color.
Please help me. Thank you very much.
ryan invests a sum of money in a saving account with a fixed annual interest rate of 4.31% compounded monthly. After 10 years, the balance reaches $12,835.94. What was the amount of the initial investment?
We calculate P to be approximately $7,759.58, which is the amount Ryan invested initially.
To determine the initial investment that Ryan made, which grew to $12,835.94 after 10 years with an annual interest rate of 4.31% compounded monthly, we will use the formula for compound interest:
[tex]A = P(1 + r/n)^{nt}[/tex]
Where:
A is the amount of money accumulated after n years, including interest.
P is the principal amount (the initial amount of money).
r is the annual interest rate (decimal).
n is the number of times that interest is compounded per year.
t is the time the money is invested for, in years.
We know that:
A = $12,835.94
r = 4.31/100 = 0.0431
n = 12
t = 10
We need to solve for P:
P = A /[tex](1 + r/n)^{nt}[/tex]
Substituting the known values, we get:
P =[tex]$12,835.94 / (1 + 0.0431/12)^{12*10}[/tex]
P = $12,835.94 / [tex](1 + 0.0035925)^{120}[/tex]
P = $12,835.94 / ([tex]1.0035925)^{120}[/tex]
Calculating the value inside the parenthesis first:
[tex](1.0035925)^{120}[/tex] = 1.654297553
Now, we divide the final amount by this compound factor:
P = $12,835.94 / 1.654297553
P ≈ $7,759.58
Therefore, Ryan's initial investment was approximately $7,759.58.
In this fulcrum, the weights are perfectly balanced. How far must the fulcrum be located from the 40 lb. weight if the bar is 11 feet long? x (to the nearest tenth) =
Answer:
[tex]x=6.11 feet[/tex]
Step-by-step explanation:
Given that in a fulcrum weights are perfectly balanced.
One side 40 lb weight is there and another side 50 lb weight is given
Let x be the length of 40 lb weight from fulcrum. Then 50 lbs is at a distance of 11-x.
Then we have since weights are perfectly balanced
[tex]40x = 50(11-x)\\90x=550\\x=6.111[/tex]
Thus we get [tex]x=6.11[/tex]feet
Evaluate without the use of a calculator 10^-2
you plan to take $450 U.S on a trip to South Africa. How many rands is this if one U.S dollar equals 3.70 rands ?
822 rands
1,216 rands
1,665 rands
8,222 rands
Given:
one U.S dollar equals 3.70 rands. To find how many rands does 450 U.S dollars equal to, we need to multiply 450 with 3.70
Solution:
[tex] 1 \; U.S \; dollars \; = \; 3.70 \; rands\\ \\ 450\; U.S\; dollars= 450 \times 3.7 \; rands=1665 \; rands [/tex]
Conclusion:
1665 rands equals $450.
Which is a possible expression for the series
–7 + 12 –17 +22 –27
A 60 cm rope is tied to the handle of a bucket which is then whirled in a vertical circle.
The scenario described in the question involves using a rope to whirl a bucket in a vertical circle. This relates to the physics concepts of centripetal force, tension in the rope, and gravity. The tension in the rope provides the centripetal force needed for the curved path of the bucket, and the scenario implies a constant speed and a counterbalance between tension and gravity at the highest point of the circle.
Explanation:The question involves a principle of physics known as centripetal force, which is the force that makes a body follow a curved path. Its direction is always orthogonal to the motion of the body, towards the fixed point of the instantaneous center of curvature of the path.
In this case, the 60 cm rope tied to the bucket and whirled in a vertical circle becomes a system where the bucket, the force of gravity, and the tension in the rope all play a part. When the bucket is whirled, it experiences a centripetal force that keeps it moving in a circle. This force comes from the tension in the rope, which always pulls the bucket towards the center of the circle (the hand holding the rope). Hence, there are two key forces in this scenario - the force of gravity, pulling the bucket downward, and the tension in the rope providing the centripetal force.
Since the question does not state otherwise, we can reasonably assume that the movement is steady, implying the speed of the bucket is constant. In such a case, the swinging bucket will rise to a certain point, where the tension in the rope and the gravity cancel each other, causing the bucket to start falling back to the other side, therefore, forming the vertical circular path.
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The 1997 value of an object was $9500. In 2012, it was worth $5000. The annual percent of decay has been constant. What is the annual percent of decay? A) 1.19% B) 2.19% C) 3.19% D) 4.19%
Answer:
The answer is D.Step-by-step explanation:
If the object starts with a value [tex]V_0[/tex], and a annual percent of decay d, after a year the value will be
[tex]V_1 = V_0 * d[/tex]
after 2 years, taking now [tex]V_1[/tex] as the starting value
[tex]V_2 = V_1 * d = V_0 * d * d [/tex]
[tex]V_2 = V_0 * d^2 [/tex]
and so on, after n years the value will be:
[tex]V_n = V_0 * d^n[/tex]
Now, in 1997 the value was $9500, in 2012 the value was $5000. Between 1997 and 2012 there are 15 years, so, our equation will be:
[tex] \$5000 = \$ 9500 * d^{15}[/tex]
Working it a little
[tex] \frac{\$5000}{\$ 9500} = d^{15}[/tex]
[tex] (\frac{\$5000}{\$ 9500})^{1/15} = d[/tex]
[tex] (0.5263})^{1/15} = d[/tex]
[tex] 0.9581 = d[/tex]
This mean that, after a year, the value will be at 95.81 %, this is, a decay rate of 4.19%.