Answer:
50x.2 is the correct expression. :)
Step-by-step explanation:
50x.2 =10
So you would get a $10 discount off of a $50 video game.
Hope this helps! If you don't mind, please mark as brainliest! Thx :)
Answer:
0.80($50)
Step-by-step explanation:
1.00 times the $50 cost is the initial price of the video.
(1.00 - 0.20) times $50 is the discounted price.
0.80($50) is the desired expression.
Next time, please be sure to share the answer choices. Thanks.
The standard form of the equation of a circle is (x?4)2+(y?2)2=9. What is the general form of the equation? X2+y2+8x+4y+11=0 x2+y2+8x+4y?29=0 x2+y2?8x?4y?29=0 x2+y2?8x?4y+11=0
Answer:
[tex]x^2+y^2-8x-4y+11=0[/tex]
Step-by-step explanation:
We want to find the equation of the circle: [tex](x-4)^2+(y-2)^2=9[/tex] in general form.
We need to expand the parenthesis to obtain: [tex]x^2-8x+16+y^2-4y+4=9[/tex]
This implies that:
[tex]x^2+y^2-8x-4y+20=9[/tex]
We add -9 to both sides of the equattion to get:
[tex]x^2+y^2-8x-4y+20-9=0[/tex]
Simplify the constant terms to get:
[tex]x^2+y^2-8x-4y+11=0[/tex]
The general form of the equation is x^2 + y^2 - 8x -4y - 11 = 0
How to determine the general form?The equation is given as:
(x-4)^2+(y-2)^2=9
Evaluate the exponents
x^2 - 8x + 16 + y^2 -4y + 4 = 9
Collect like terms
x^2 - 8x + y^2 -4y - 9 + 16 + 4 = 0
Evaluate the like terms
x^2 - 8x + y^2 -4y - 11 = 0
Rewrite as:
x^2 + y^2 - 8x -4y - 11 = 0
Hence, the general form of the equation is x^2 + y^2 - 8x -4y - 11 = 0
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The population of a local species of beetle can be found using an infinite geometric series where a1 = 880 and the common ratio is one fourth. Write the sum in sigma notation, and calculate the sum (if possible) that will be the upper limit of this population.
the summation of 880 times one fourth to the i minus 1 power, from i equals 1 to infinity. ; the sum is divergent
the summation of 880 times one fourth to the i minus 1 power, from i equals 1 to infinity. ; the sum is 1,173
the summation of 880 times one fourth to the i power, from i equals 1 to infinity. ; the series is divergent
the summation of 880 times one fourth to the i power, from i equals 1 to infinity. ; the sum is 1,173
Answer: Second Option
"the summation of 880 times one fourth to the i minus 1 power, from i equals 1 to infinity. ; the sum is 1,173"
Step-by-step explanation:
We know that infinite geometrical series have the following form:
[tex]\sum_{i=1}^{\infty}a_1(r)^{n-1}[/tex]
Where [tex]a_1[/tex] is the first term of the sequence and "r" is common ratio
In this case
[tex]a_1 = 880\\\\r=\frac{1}{4}[/tex]
So the series is:
[tex]\sum_{i=1}^{\infty}880(\frac{1}{4})^{n-1}[/tex]
By definition if we have a geometric series of the form
[tex]\sum_{i=1}^{\infty}a_1(r)^{n-1}[/tex]
Then the series converges to [tex]\frac{a_1}{1-r}[/tex] if [tex]0<|r|<1[/tex]
In this case [tex]r = \frac{1}{4}[/tex] and [tex]a_1=880[/tex] then the series converges to [tex]\frac{880}{1-\frac{1}{4}} = 1,173.3[/tex]
Finally the answer is the second option
You're baking a cake with a ratio of 3:4. If you use 2 cups of flour,how many cups of sugar will you use?
Answer:
2 2/3 cups of sugar
Step-by-step explanation:
If your ratio is 3 flour to 4 sugar, and you use 2 cups of flour, set up your proportion as follows:
[tex]\frac{3}{4}=\frac{2}{x}[/tex]
Cross multiply to get 3x = 8 and x = 8/3 which is 2 and 2/3 cups of sugar.
The cups of sugar used is 3/2 corresponding to 2 cups of flour.
What is proportion in ratio?If we are using the ratio of 3 flour to 4 sugar.
We have 2 cups of flour.
Let us consider the amount of sugar be 'y'.
By writing the proportion /as follows:
[tex]\frac{3}{4} = \;\frac{2}{y}[/tex]
4y =6
y =3/2
Thus, the amount of sugar used is 3/2.
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What is the area of the trapezoid? Leave the answer in simplest radical form.
For this case we must find the area of the figure composed of a triangle and a rectangle.
Triangle area:
[tex]A_ {t} = \frac {b * h} {2}[/tex]
Where b is the base and h is the height.
Area of the rectangle:
[tex]A_ {r} = a * b[/tex]
Where a and b are the sides.
The base of the triangle measures:
[tex]13-5 = 8[/tex]
We find the height by trigonometry:
[tex]tg (45) = \frac {h} {b}\\1 = \frac {h} {b}\\b = h[/tex]
So:
[tex]A_ {t} = \frac {8 * 8} {2}\\A_ {t} = 32 \ ft ^ 2[/tex]
On the other hand:
[tex]A_ {r} = 5 * 8\\A_ {r} = 40 \ ft ^ 2[/tex]
Thus, the total are the sum:
[tex](32 + 40) ft ^ 2 = 72 \ ft ^ 2[/tex]
Answer:
Option A
Option is A~ the answer is A
Which of the following expressions is a polynomial?
Answer:
d is the answer i believe
Step-by-step explanation:
Consider the functions below. f(x, y, z) = x i − z j + y k r(t) = 4t i + 6t j − t2 k (a) evaluate the line integral c f · dr, where c is given by r(t), −1 ≤ t ≤ 1.
With
[tex]\vec r(t)=4t\,\vec\imath+6t\,\vec\jmath-t^2\,\vec k[/tex]
we have
[tex]\mathrm d\vec r=(4\,\vec\imath+6\,\vec\jmath-2t\,\vec k)\,\mathrm dt[/tex]
The vector field evaluated over this parameterization is
[tex]\vec f(x,y,z)=\vec f(x(t),y(t),z(t))=4t\,\vec\imath+t^2\,\vec\jmath+6t\,\vec k[/tex]
so the line integral is
[tex]\displaystyle\int_{-1}^1(4t\,\vec\imath+t^2\,\vec\jmath+6t\,\vec k)\cdot(4\,\vec\imath+6\,\vec\jmath-2t\,\vec k)\,\mathrm dt[/tex]
[tex]=\displaystyle\int_{-1}^1(16t+6t^2-12t^2)\,\mathrm dt=-4[/tex]
To evaluate the line integral c f · dr, substitute the values of r(t) into f(x, y, z) to get a new vector function f(t). Find the derivative of r(t) using the chain rule. Take the dot product of f(t) and r'(t) and integrate the result with respect to t over the given bounds.
Explanation:To evaluate the line integral c f · dr, we need to find the dot product of the vector function f and the derivative of r(t). Since c is given by r(t) and the bounds are -1 ≤ t ≤ 1, we can substitute the values of r(t) into f(x, y, z) and compute the dot product.
First, substitute the values of x(t), y(t), and z(t) into f(x, y, z) to get a new vector function f(t).Next, find the derivative of r(t) with respect to t using the chain rule.Take the dot product of f(t) and r'(t) and integrate the result with respect to t over the given bounds (-1 to 1).Compute the integral to find the final answer.
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What is the product of -5 and -8?
Answer:
40
Step-by-step explanation:
-5 x -8 = 40
40, because both numbers are negative, the answer is positive. So you would just multiply like normal.
PLEASE HELP!!:) need help with this question thanks
Answer:
30%
Step-by-step explanation:
24 of (40 +24 +16) = 3/10 of the turkey sandwiches were made with wheat bread. As a percentage, that is ...
3/10 = 30/100 = 30%
Use △DEF, shown below, to answer the question that follows:
Triangle DEF where angle E is a right angle. DE measures 55. EF measures x. Angle D measures 49 degrees.
What is the value of x rounded to the nearest hundredth? Type the numeric answer only in the box below.
Answer:
63.2702623...
Step-by-step explanation:
The ratio between FE and DE is the tangent of the angle EDF.[tex]tan 49 = \frac x {55}[/tex] or [tex]x= 55*tan 49[/tex]. With a calculator, you get 63.2702623... Cut where needed
55x tan49 =63.270
63.270.
All the students in the sixth grade either purchased their lunch or brought their lunch from home on Monday 24% of the students purchased their lunch 190 students brought their lunch from home how many students ante in the sixth grade?
I believe it is 60 but I’m not sure
Which statement best describes the domain and range of p(x) = 6–x and q(x) = 6x? p(x) and q(x) have the same domain and the same range. p(x) and q(x) have the same domain but different ranges. p(x) and q(x) have different domains but the same range. p(x) and q(x) have different domains and different ranges.
The statement that best describes the domain and range of p(x) and q(x) is:
p(x) and q(x) have the same domain and the same range.
Step-by-step explanation:We are given a function p(x) as:
[tex]p(x)=6-x[/tex]
AS the function is a polynomial function.
Hence it is defined everywhere for all the real values.
Hence, the domain of the function p(x) is: All Real numbers.
and the range of the function p(x) is: All the real numbers.
and the function q(x) is given by:
[tex]q(x)=6x[/tex]
which is also a polynomial function.
Hence, it also has the same domain and range.
Domain and range are specific sets for each function. For given case, p(x) and q(x) have the same domain and range.
What is domain and range of a function?Domain is the set of values for which the given function is defined.
Range is the set of all values which the given function can output.
The domain and range of given functions are:
p(x) = 6-xFor any real number value of x, p(x) just takes 6-x(negates the input and add 6 to it), thus, its always defined, and thus, its domain is all real numbers.
Since p = 6-x is possible to go negatively infinite and positively infinite and always continuous, thus, its range is all real numbers(all numbers are possible as its output)
We can prove the above statement. Let some real number T is not in the range of p(x). But we have T = 6-x => x = 6-T which is a real number, thus, for input 6-T, there is output T. Thus, its a contradiction, and thus, all real numbers are in range of p(x).
Thus,
Range of p(x): [tex]x \in \mathbb R[/tex] (R is all real numbers' set)Domain of p(x): [tex]x \in \mathbb R[/tex]q(x) = 6xIts scaling all numbers. All numbers can be multiplied by 6 and produce a valid result. Thus, its domain is all real numbers.
Suppose that we've T as a real number. Then we can get this as output if we put input as x = T/6 (since then 6x = 6(T/6) = T)
Thus, all real numbers are in its output set, thus, its range is all real numbers.
The Range of q(x): [tex]x \in \mathbb R[/tex] and Domain of q(x): [tex]x \in \mathbb R[/tex]
Hence, for given case, p(x) and q(x) have the same domain and range.
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What is the surface area of the cube below?
A. 486 units^2
B. 729 units^2
C. 405 units^2
D. 508 units^2
The formula of the surface area of a cube is 6 x s²
→ s = 9
→ s² = 9²
→ s² = 81
→ 6 x 81 = 486
So, the surface area of the cube is 486 units².
A .Dog and a cat are 200 meters apart when they see each other. The dog can run at a speed of 30 m/sec, while the cat can run at a speed of 24 m/sec. How soon will the dog catch the cat if the dog starts running after the cat?
Given the speeds of the dog and cat, the dog will catch the cat in approximately 33.33 seconds by covering the 200-meter distance at a relative speed of 6 m/s.
Problem: A dog and a cat are 200 meters apart. The dog runs at 30 m/s, and the cat runs at 24 m/s. How soon will the dog catch the cat?
Calculate the relative speed at which the dog is gaining on the cat: 30 m/s - 24 m/s = 6 m/s.
Divide the initial distance (200 meters) by the relative speed (6 m/s) to find the time it takes for the dog to catch the cat: 200 m / 6 m/s = 33.33 seconds.
y varies directly as x. y = 44 when x = 4. Find y when x = 16.
hope it helps you!!!!!!!!!!!!!!
A plywood template for a kitchen breakfast bar is cut from a circle.
Answer:
25
Step-by-step explanation:
The radius of the circle, which is the perpendicular bisector of a 48-inch diameter kitchen breakfast bar template, is 30 inches. The correct option is C).
Let's break down the information given in the problem:
PQ is the perpendicular bisector of VW, and Q is the midpoint of VW. This means that PQ passes through the center of the circle.
The length of PQ (perpendicular bisector) is 18 inches.
VW is 48 inches in diameter, which means its radius is half of that, i.e., 48 inches / 2 = 24 inches.
Since PQ is the radius of the circle, and it is also the perpendicular bisector of VW, it divides VW into two equal parts, each measuring 24 inches (as VW has a diameter of 48 inches, and Q is the midpoint).
Now, we have a right-angled triangle, with PQ as the hypotenuse and two legs measuring 18 inches and 24 inches. We can use the Pythagorean theorem to find the length of PQ (the radius of the circle):
PQ² = 18² + 24²
PQ² = 324 + 576
PQ² = 900
PQ = √900
PQ = 30 inches
So, the radius of the circle is 30 inches.
The correct answer is option c) 30 inches.
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The total cost of 5 boxes of pasta is $13. There are 12 ounces of pasta in each box. Each box of pasta costas the same amount. What is the cost in dollars, of the min number of boxes needed to total 48 ounces of pasta?
Answer:
The minimum number of boxes needed is [tex]4[/tex] and the cost is [tex]\$10.40[/tex]
Step-by-step explanation:
step 1
Find the cost of one box
by proportion
[tex]\frac{5}{13}=\frac{1}{x}\\ \\x=13/5\\ \\x=\$2.60[/tex]
step 2
Find the number of boxes for 48 ounces of pasta
by proportion
[tex]\frac{1}{12}=\frac{x}{48}\\ \\x=48/12\\ \\x=4\ boxes[/tex]
step 3
Find the cost of 4 boxes
we know that
The cost of one box is [tex]\$2.60[/tex]
so
The cost of 4 boxes is
[tex]\$2.60(4)=\$10.40[/tex]
Final answer:
To determine the cost for 48 ounces of pasta, one must calculate the cost per box and multiply by the number of boxes required to reach 48 ounces. The cost for the needed 4 boxes is $10.40.
Explanation:
The cost of one box of pasta is calculated by dividing the total cost of the pasta by the number of boxes. Since the total cost of 5 boxes of pasta is $13, to find the cost per box, we divide $13 by 5, which is $2.60 per box. To find the cost of the minimum number of boxes needed to total 48 ounces of pasta, we then determine how many boxes are needed. Since each box contains 12 ounces of pasta, we need 48 ounces / 12 ounces per box = 4 boxes of pasta. Finally, we multiply the number of boxes by the cost per box, which is 4 boxes × $2.60 per box = $10.40.
Write 7x^5/11 in radical form. (Show steps please)
Answer:
[tex]7\sqrt[11]{x^{5}}[/tex]
Step-by-step explanation:
we know that
[tex]a^{\frac{n}{m}}=\sqrt[m]{a^{n}}[/tex]
In this problem we have
[tex]7x^{\frac{5}{11}}[/tex]
therefore
[tex]7x^{\frac{5}{11}}=7\sqrt[11]{x^{5}}[/tex]
Explore Three Dimensional Shapes: Investigation 4
I need help with the worksheet
1. Volume is Length x width x height.
Volume = 6 x 4 x 8 = 192 ft^2
Answer is D.
2. Divide the volume by the height to get the area of the base.
Area of base = 312 / 12 = 26 in^2
Answer is D.
3. A 1/2 x 8 x 6 = 24 x 12 = 288 cm^3
B. (12 +6)/2 x 5 = 45 x 14 = 630 m^3
4. See attached picture.
For quadrilateral abcd, determine the most precise name for it. A(-2,3),B(9,3),C(5,6)D(2,6). Show your work and explain.
Answer:
ABCD is an isosceles trapezoid.
Step-by-step explanation:
The line AB will be horizontal (parallel to the x axis), because the y values are both 3. It is 9--2 = 11 units long.
CD is also parallel to the x axis because the y values of C and D are both 6. Itis 5 - 2 = 3 units long.
The x values of the four points are all different so ABCD is a trapezoid.
Let's check the lengths of the line segments AC and BD:
AC = √((5--2)^2 + (6-3)^2 = √58.
BD = √((9-2)^2 + (3-6)^2 = √58.
They are equal in length so:
ABCD is an isosceles trapezoid.
(-9,-35) and (2,9) are two anchor points on the trend line, then find the equation of the line
Answer:
the desired equation is y = 4x + 1
Step-by-step explanation:
As we move to the right from (-9, -35) to (2, 9), x increases by 11 and y increases by 44. Thus, the slope of the line in question is
m = rise / run = 44/11 = 4.
Using the slope-intercept form of the equation of a straight line, we substitute 4 for m, 2 for x and 9 for y, obtaining:
y = mx + b → 9 = 4(2) + b. Thus, b = 1, and the desired equation is
y = 4x + 1
By using the slope-intercept form of a line and the given anchor points, we find that the equation of the line is y= 4x - 1.
Explanation:The subject of this question is to find the equation of a trend line using two anchor points (-9,-35) and (2,9). We can calculate the equation of a line using the slope-intercept form y = mx + b, where m represents the slope and b represents the y-intercept.
First, calculate the slope (m) which is (y2-y1)/(x2-x1) = (9 - (-35))/(2 - (-9)) = 44/11 = 4.
Then, with the slope (m = 4) and one point (2,9), plug in these values into the slope-intercept form to solve for the y-intercept (b). 9 = 4*2 + b. Solving for b gives -1.
So, the equation of the trend line is y= 4x - 1.
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Find the maximum value of the function for the polygonal convex set determined by the given system of inequalities
Answer:
A. at (8,7) the maximum value is 98
Step-by-step explanation:
First draw the region, that is bounded by all inequalities. This is the triangle with vertices (6,1), (2,5) and (8,7).
Now you can see where the line f(x,y)=7x+6y intersect this region. The maximum value will be at endpoints of this region:
at (6,1), f(6,1)=7·6+6·1=42+6=48;at (2,5), f(2,5)=7·2+6·5=14+30=44;at (8,7), f(8,7)=7·8+6·7=56+42=98.Thus, the maximum value of the function is 98 at the point (8,7).
Consider the following equation
0=x^2-10x-27
Complete each statement about the solutions to the equation.
The negative solution is between ..(A)...and ..(B)...
(A ) -2,-13,-3,12
(B)-1,-11,-2,-12
The positive solution is between...(B)...and..(C)...
(B)11,2,12,1
(C)3,12,13,2
Answer:
The negative solution is between -3 and -2
The positive solution is between 11 and 13
Step-by-step explanation:
we have
[tex]0=x^{2} -10x-27[/tex]
The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to
[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]
in this problem we have
[tex]x^{2} -10x-27=0[/tex]
so
[tex]a=1\\b=-10\\c=-27[/tex]
substitute in the formula
[tex]x=\frac{10(+/-)\sqrt{-10^{2}-4(1)(-27)}} {2(1)}[/tex]
[tex]x=\frac{10(+/-)\sqrt{208}} {2}[/tex]
[tex]x=\frac{10(+)\sqrt{208}} {2}=12.21[/tex]
[tex]x=\frac{10(-)\sqrt{208}} {2}=-2.21[/tex]
therefore
The negative solution is between -3 and -2
The positive solution is between 11 and 13
Answer:
Negative solution is between -3 and -2
Positive solution is between 12 and 13
Step-by-step explanation:
The first section of a newspaper has 16 pages. Advertisements take up 3 3/8 of the pages. How many pages are not advertisements?
Answer:
12.62
Step-by-step explanation:
you divide 3 by 8, then add the quotient of that to 3, then subtract that from 16
Answer:
Givens
The first section has 16 pages.Advertisements take up 3 3/8 of the pages.First, we need to the number of pages dedicated to advertisements.
Let's transform the mixed number into a fraction
[tex]3\frac{3}{8}=\frac{27}{8}[/tex]
Now, let's multiply this fraction with the number of pages
[tex]\frac{27}{8} \times 16= 54[/tex]
That is, there are 54 pages dedicated to advertisements.
Pages without advertisements are 5/8, which is
[tex]\frac{5}{8} \times 16=5(2)=10[/tex]
Find the Area of the circle... PLEASE HELP
Answer: Is it 169? i think that wright maybe.
Answer: 530.92916
Step-by-step explanation:
A=πr2=π·132≈530.92916
Forty slips of paper are numbered 1 through 40 and are distributed among a group of people. A random number generator is used to select a single number between 1 and 40, inclusively. A fair decision is made using this process. How many people could be in this group?
6
8
12
15
Answer:
The number of people in the group must divide 40. 8 is the only selection that divides 40.
Considering the factors of 40 for even distribution of the slips of paper, 8 people can be fairly included in the group as 8 is a factor of 40. The correct answer is option b) 8.
To determine how many people could be in the group when forty slips of paper numbered 1 through 40 are distributed, and a random number generator selects a single number from this range, we need to consider the factors of 40. Each person must get at least one slip of paper, and the distribution needs to be equal to maintain fairness. The factors of 40 are 1, 2, 4, 5, 8, 10, 20, and 40. However, the only possible numbers of people in the group, given by the options, are 6, 8, 12, and 15. Out of these, 8 is a factor of 40, meaning the slips of paper can be distributed evenly among 8 people.
Thus, the correct answer to the student's question is option b) 8.
Please help fast.
A number cube is rolled and a coin is tossed. The number cube and the coin are fair. What is the probability that the number rolled is greater than 4 and the coin toss is tails? Write your answer as a fraction in simplest form.
Answer:
[tex]\frac{1}{6}[/tex]
Step-by-step explanation:
In probability theory, "AND" means multiplication and "OR" means "addition".
We can find the 2 probabilities separately and multiply them (as there is "AND")
So,
Probability number rolled greater than 4 = number of numbers that are greater than 4/total number of numbers
There are 2 numbers greater than 4 in a die (5 & 6) and total 6 numbers, so
P(number greater than 4) = 2/6
Now,
Probability that tails come up in coin toss = 1/2 (there are 1 tail and 1 head in a coin)
Hence,
P(number greater than 4 and tails in coin) = 2/6 * 1/2 = 1/6
To find the probability of rolling a number greater than 4 on a die and getting tails on a coin toss, you multiply the individual probabilities: (1/3) for the die roll and (1/2) for the coin toss, resulting in a combined probability of 1/6.
Explanation:The question is asking to find the probability of a specific combined event involving the roll of a number cube (a six-sided die) and the flip of a coin. To solve this problem, we need to calculate the probability that the number cube shows a number greater than 4 (which can be either a 5 or 6) and that the coin toss results in tails.
First, we find the probability of rolling a number greater than 4 on a six-sided die. There are 2 favorable outcomes (5 or 6) out of 6 possible outcomes, so the probability of this event is 2/6, which simplifies to 1/3.
Next, we calculate the probability of getting tails on a coin flip. Since a coin has two sides, and only one side is tails, the probability is 1/2.
To find the combined probability of both events happening together, we multiply the probabilities of the individual events:
Combined Probability = Probability (Number > 4) × Probability (Tails) = (1/3) × (1/2)
Therefore, the combined probability is:
(1/3) × (1/2) = 1/6
The math club has 16 members, 2 girls and 14 boys. What is the ratio of girls to boys in the math club
How would i rewrite this equation so it is not in fraction form
-5/(1-cos(-x))
[tex]\bf -\cfrac{5}{1-cos(-x)}\implies -\cfrac{5}{\underset{\textit{symmetry identity}}{1-cos(x)}}\impliedby \begin{array}{llll} \textit{let's multiply top/bottom}\\ \textit{by the conjugate 1+cos(x)} \end{array} \\\\\\ \cfrac{-5}{1-cos(x)}\cdot \cfrac{1+cos(x)}{1+cos(x)}\implies \cfrac{-5(1+cos(x))}{\underset{\textit{difference of squares}}{[1-cos(x)][1+cos(x)]}} \\\\\\[/tex]
[tex]\bf \cfrac{-5[1+cos(x)]}{1^2-cos^2(x)}\implies \cfrac{-5-5cos(x)}{\underset{\textit{pythagorean identity}}{1-cos^2(x)}}\implies \cfrac{-5-5cos(x)}{sin^2(x)} \\\\\\ \cfrac{-5}{sin^2(x)}-\cfrac{5cos(x)}{sin^2(x)}\implies -5\cdot \cfrac{1}{sin^2(x)}-5\cdot \cfrac{1}{sin(x)}\cdot \cfrac{cos(x)}{sin(x)} \\\\\\ -5\cdot csc^2(x)-5\cdot csc(x)\cdot cot(x)\implies \boxed{-5csc^2(x)-5csc(x)cot(x)}[/tex]
-4(x - 2) - 3x = 2(5x - 7) + 6
After distributing and combining like terms, this problem should read:
7 - 8x = -10 + 8x
-15x = 10x - 8
8x - 6 = 7x - 3
-11x + 8 = 10x - 8
-7x + 8 = 10x - 8
Answer: last option.
Step-by-step explanation:
To apply the Distributive property, remember that:
[tex]c(a-b)=ca-cb[/tex]
Then, applying this, you get:
[tex]-4(x - 2) - 3x = 2(5x - 7) + 6\\\\(-4)(x)+(-4)(-2)-3x=(2)(5x)+(2)(-7)+6\\\\-4x+8-3x=10x-14+6[/tex]
Combine like terms means that you need to add the like terms.
Therefore, you get:
[tex]-7x+8=10x-8[/tex]
You can observe that the expression obtained matches with the expression provided in the last option.
Find the area of the circle with a circumference of 30π . Write your solution in terms of π and round to the nearest hundredth.
Area in terms of π:____
Answer Choices:
Hi again.
Answer
= option d, 225π mm^2
Circumference = 2πr
30π = 2πr
30 = 2r
30 / 2 = r
15 = r
Area = π[tex]r^{2}[/tex]
[tex]15^{2}[/tex]π
225π
The area of the circle in terms of the π will be 225π mm²
What is an area of the circle?The area of the circle is defined as the space occupied by the circle in the three-dimensional plane. The circle is the locus of the point equidistant from its centre.
It is given in the question that:-
Circumference = 2πr
30π = 2πr
30 = 2r
30 / 2 = r
15 = r
Area = πr²
Area =π(15)²
Area = 225π mm²
Hence the area of the circle will be 225π mm²
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