Answer:
(f º f)(3) = 30, when f(x) = x² - x
Step-by-step explanation:
This is a great example of composite functions and how to multiply one function by another. (f º f) really means f(f(x)), or replacing every x in the original function f(x) with the function f(x).
Step 1: State the original function.
[tex]f(x) = x^{2} -x[/tex]
Step 2: Insert the function f(x) wherever there is an x.
[tex]f(f(x))=(x^{2} -x)^{2} -(x^2-x)[/tex]
Step 3: Expand anything that has an exponent. Remember: [tex](x+y)^2 = (x+y)(x+y)[/tex]
[tex]f(f(x))=(x^{2} -x)(x^{2} -x) -(x^2-x)[/tex]
Step 4: Foil the parts of the equations in brackets by multiplying the first terms, outside terms, inside terms and last terms in each bracket.
[tex]f(f(x))=(x^{4}-x^3-x^3+x^{2}) -(x^2-x)[/tex]
Step 5: Now you can remove the brackets (don'f forget to switch the symbols for the second brackets because you are subtracting) and sum the like terms.
[tex]f(f(x))=x^{4}-x^3-x^3+x^{2} -x^2+x[/tex]
[tex]f(f(x))=x^{4}-2x^3+x[/tex]
Step 6: Finally, substitute the given x value, which is 3, into the new equation.
[tex]f(f(x))=(3)^{4}-2(3)^3+(3)[/tex]
[tex]f(f(x))=81-54+3[/tex]
[tex]f(f(x))=30[/tex]
Therefore the answer is (f º f)(3) = 30.
Answer:
30
Step-by-step explanation:
Method 1:
ƒ(x) = x² - x
(f∘f)(x) = f(f(x)) = f(x²-x) = (x² - x)² - (x² - x) = x⁴ - 2x³ + x² - x² + x = x⁴ - 2x³ + x
(f∘f)(3) = 3⁴ - 2(3)³ + 3 = 81 - 54 + 3 = 30
Method 2:
f(3) = 3² - 3 = 9 - 3 = 6
(f∘f)(3) = f(f(3)) = f(6) = 6² - 6 = 36 - 6 = 30
One of the legs a right triangle is twice as long as the other and the perimeter of the triangle is 28. Find the lengths of all three sides, to three decimal places
So x 2x are the sides using Pythagorean theorem x^2 + (2x)^2= 5x^2
So the side is the square root of 5x^2 so now we have the third side
The sum of the sides should add to 28 so:
X+2x+√5x=28 factor the x
X(3+√5)=28 and we know √5=2.236
So x= 28/5.236= 5.347
To find the lengths of all three sides of the right triangle, set up two equations using the given information and the Pythagorean theorem. Solve these equations to find the values of x and the lengths of the other two sides.
Explanation:Let x be the length of the shorter side of the right triangle. According to the problem, the longer side is twice as long as the shorter side, so its length is 2x. The perimeter of the triangle is given as 28, so we can set up the equation x + 2x + hypotenuse = 28. Using the Pythagorean theorem, we know that the sum of the squares of the two legs is equal to the square of the hypotenuse, so we can write another equation x^2 + (2x)^2 = hypotenuse^2. Solving these two equations will give us the lengths of all three sides of the triangle.
From the perimeter equation, we have x + 2x + hypotenuse = 28. Simplifying, we get 3x + hypotenuse = 28. Rearranging, we get hypotenuse = 28 - 3x.
Substituting this into the Pythagorean theorem equation, we have x^2 + (2x)^2 = (28 - 3x)^2. Simplifying and solving this equation will give us the value of x, which we can then use to find the lengths of the other two sides of the triangle.
Determine the intercepts of the line.
Y-intercept (0,___)
X-intercept (___,0)
Look at the picture.
The x-intercepts are where the graph crosses the x-axis, and the y-intercepts are where the graph crosses the y-axis.
x-intercept: (-1.2, 0)y-intercept: (0, -0.7)Final answer:
To find the y-intercept of a line, set x to zero in the equation y = mx + b, and the y-intercept is the value of b. To find the x-intercept, set y to zero and solve for x. The intercepts are the coordinates where the line crosses respective axes.
Explanation:
To determine the intercepts of a line, you need to find the points where the line crosses the axes. The y-intercept is the point where the line crosses the y-axis, and it is found when the value of x is 0. If we have a linear equation in the form y = mx + b, the y-intercept is the value of b, which is the y-coordinate when x is zero.
To find the x-intercept, we need to find the value of x when y is zero. This can be done by setting the y-value in the equation y = mx + b to zero and solving for x. The resulting x-value will be the x-coordinate of the x-intercept.
For example, if we have a linear equation y = -2x + 3, the y-intercept occurs when x is zero, which means y = 3. So the y-intercept is (0,3). To find the x-intercept, we set y to 0 and solve for x: 0 = -2x + 3, resulting in x = 1.5. Thus, the x-intercept is (1.5,0).
Can somebody help me answer this plz?
the answer would be 47.5
Find the odds for and the odds against the event rolling a fair die and getting a 1 comma a 2 comma or a 5.
Answer:
1/2 for or against
Step-by-step explanation:
There is a six sided die so the chance of getting one side is 1/6.
To get the sum for 3 sides, just do 1/6 + 1/6 + 1/6 = 3/6 or 1/2.
(4x ^2+2x+1) (x^2-3x+5)
Answer:
You need to multiply the polynomials. Please see attached picture for answer.
= 4x ^4 + -10x^3 + 15x^2 + 7x +5
Step-by-step explanation:
You need to multiply each term step by step
(4x ^2+2x+1)*(x^2) + (4x ^2+2x+1)*(-3x) + (4x ^2+2x+1)*5
= (4x ^4 + 2x^3 +x^2) + (-12x ^3 - 6x^2 -3x) + (20x ^2+10x+5)
= 4x ^4 + -10x^3 + 15x^2 + 7x +5
2. Four devices (A, B, C, D) contain a total 225GB of data. - The device A has half as much data as device B. - The device C has five times as much data as device B and device D combined. - The sum of twice the amount of data on device C and four times the amount of data on the device D is equal to the difference between 500GB and the amount of data on device B. Determine the amount of data (in GB) on each device.
To solve the data distribution problem among four devices, we use a system of equations representing the conditions given for the data storage among devices A, B, C, and D. By expressing all variables in terms of the amount on device B and solving, we determine the data distribution to be 35 GB, 70 GB, 105 GB, and 15 GB for devices A, B, C, and D respectively.
Solving the Data Distribution Problem
Let's represent the amount of data on devices A, B, C, and D as a, b, c, and d respectively. Given that the total amount of data is 225 GB, we have:
a + b + c + d = 225 GB (1)a = 0.5b (2)c = 5(b + d) (3)2c + 4d = 500 GB - b (4)From these equations, we can express everything in terms of b and subsequently find the values of a, b, c, and d. To demonstrate, let's substitute (2) and (3) into (1) and solve for b:
0.5b + b + 5(b + d) + d = 2256.5b + 6d = 225 (5)Now, using equation (3), we can express d in terms of b and substitute into (5):
c = 5(b + d)Let d = [tex]\(\frac{c}{5}[/tex]- b\) (6)Substitute c from (3) into (4), and then d from (6) into the result:
2*(5(b + d)) + 4d = 500 - b10b + 10d + 4d = 500 - b (7)Simplify (7) and solve for b:
10b + 14d = 500 - b11b + 14d = 500 (8)By substituting (6) into (8):11b + [tex]14(\(\frac{c}{5} - b\))[/tex] = 500Solve this equation to find b, then use b to find a, c, and d accordingly.We calculate a = 35GB, b = 70GB, c = 105GB, and d = 15GB. These are the amounts of data on devices A, B, C, and D respectively.
Devices A, B, C, and D contain approximately 9.0 GB, 18.1 GB, 157.4 GB, and 13.4 GB, respectively.
Let's denote:
- The amount of data on device A as [tex]\(x\)[/tex] GB.
- The amount of data on device B as [tex]\(y\)[/tex] GB.
- The amount of data on device C as [tex]\(z\)[/tex] GB.
- The amount of data on device D as [tex]\(w\)[/tex] GB.
Given:
1. [tex]\(x = \frac{1}{2}y\)[/tex]
2. [tex]\(z = 5(y + w)\)[/tex]
3. [tex]\(2z + 4w = 500 - y\)[/tex]
We know that the total amount of data on all devices is 225 GB:
[tex]\[x + y + z + w = 225\][/tex]
We'll use these equations to solve for [tex]\(x\), \(y\), \(z\), and \(w\)[/tex].
Substituting [tex]\(x = \frac{1}{2}y\)[/tex] into the equation for the total amount of data:
[tex]\[\frac{1}{2}y + y + z + w = 225\][/tex]
[tex]\[y + 2y + z + w = 225\][/tex]
[tex]\[3y + z + w = 225\][/tex]
[tex]\[y = \frac{225 - z - w}{3}\][/tex]
Now, we'll use this expression for [tex]\(y\)[/tex] to rewrite the other equations:
From equation 2:
[tex]\[z = 5\left(\frac{225 - z - w}{3} + w\right)\][/tex]
[tex]\[z = \frac{5}{3}(225 - z - w) + 5w\][/tex]
[tex]\[z = \frac{5}{3}(225) - \frac{5}{3}z - \frac{5}{3}w + 5w\][/tex]
[tex]\[z + \frac{5}{3}z + \frac{5}{3}w = \frac{5}{3}(225) + 5w\][/tex]
[tex]\[\frac{8}{3}z + \frac{5}{3}w = \frac{1125}{3} + \frac{15}{3}w\][/tex]
[tex]\[8z + 5w = 1125 + 15w\][/tex]
[tex]\[8z = 1125 + 10w\][/tex]
[tex]\[z = \frac{1125 + 10w}{8}\][/tex]
From equation 3:
[tex]\[2z + 4w = 500 - \frac{225 - z - w}{3}\][/tex]
[tex]\[2z + 4w = 500 - \frac{225}{3} + \frac{1}{3}z + \frac{1}{3}w\][/tex]
[tex]\[2z + \frac{1}{3}z + \frac{1}{3}w + 4w = \frac{1500 - 225}{3}\][/tex]
[tex]\[2z + \frac{1}{3}z + \frac{13}{3}w = \frac{1275}{3}\][/tex]
[tex]\[\frac{7}{3}z + \frac{13}{3}w = \frac{1275}{3}\][/tex]
[tex]\[7z + 13w = 1275\][/tex]
[tex]\[7\left(\frac{1125 + 10w}{8}\right) + 13w = 1275\][/tex]
[tex]\[7(1125 + 10w) + 104w = 10200\][/tex]
[tex]\[7875 + 70w + 104w = 10200\][/tex]
[tex]\[174w = 2325\][/tex]
[tex]\[w = \frac{2325}{174}\][/tex]
[tex]\[w = 13.4\][/tex]
Substituting [tex]\(w = 13.4\)[/tex] into the equation for [tex]\(z\)[/tex]:
[tex]\[z = \frac{1125 + 10(13.4)}{8}\][/tex]
[tex]\[z = \frac{1125 + 134}{8}\][/tex]
[tex]\[z = \frac{1259}{8}\][/tex]
[tex]\[z = 157.375\][/tex]
Substituting [tex]\(w = 13.4\)[/tex] into the expression for [tex]\(y\)[/tex]:
[tex]\[y = \frac{225 - z - w}{3}\][/tex]
[tex]\[y = \frac{225 - 157.375 - 13.4}{3}\][/tex]
[tex]\[y = \frac{54.225}{3}\][/tex]
[tex]\[y = 18.075\][/tex]
Substituting [tex]\(y = 18.075\)[/tex] into the equation for [tex]\(x\)[/tex]:
[tex]\[x = \frac{1}{2}y\][/tex]
[tex]\[x = \frac{1}{2}(18.075)\][/tex]
[tex]\[x = 9.0375\][/tex]
So, the amount of data on each device is approximately:
- Device A: [tex]\(9.0\)[/tex] GB
- Device B: [tex]\(18.1\)[/tex] GB
- Device C: [tex]\(157.4\)[/tex] GB
- Device D: [tex]\(13.4\)[/tex] GB
Vector performed an experiment at a local farm to determine if the addition of bananas to his biomass cow manure recipes helps produce more or less energy. He collected random samples of manure and bananas from the farm, prepared 15 bottles of each of both mixtures, and placed a balloon on top of each bottle. After two weeks he measured the circumference of each ballon in centimeters; the bigger the balloon grew, the more energy that was produced. The results of the experiment are displayed in the box plots below.
What can Vector report to his local Biogas Club about the results of his experiments?
(Need the answer as soon as possible, thank you )
Answer:
About 75% of the time, the mixture of cow manure and mashed bananas IS LIKELY to produce MORE biogas than pure cow manure on THIS local farm.
Step-by-step explanation:
(don't worry I guessed and got it correct)
In his experiment, Vector can report that bananas added to cow manure results in more energy production, as indicated by larger balloon growth. However, "he should mention that other factors may also influence the results".
Explanation:Since the exact data from Vector's experiment isn't provided, I would still be able to draw a generalized conclusion based on the given situation. Vector produced bio-gas from cow manure and bananas, and the growth of balloons served as an indication of energy production. If the balloons corresponding to the banana-mixture bottles grew larger than the manure-only ones, it would imply that adding bananas creates more energy. Increased biogas production can be observed with larger circumference balloons because more gas fills up the balloon, causing it to grow larger. Thus, the experimenting student can report in Biogas Club that using a banana-enhanced biomass recipe for cow manure can potentially increase biogas production. It is, however, crucial to note that various other factors can influence gas production, and it might be beneficial to continue research and experimentation.
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he table shows a pattern of exponents.
Answer:
Step-by-step explanation:
each new value is obtained by dividing the previous value by 5. For example, if we have 125, the next value is 125/5, or 25.
Answer:
Divide the previous value by 5
Step-by-step explanation:
5³, 5², 5¹, 5⁰, 5⁻¹, 5⁻²
The pattern of the exponents is evident that to get the next term, we divide the previous value by 5.
5³, to get 5², we divide 5³ by 5
To get 5¹, we divide 5² by 5 and so on.
Describe the relationships among the four terms.
Answer:
An angle bisector intersects the middle of an angle and basically cuts it in half equally, leaving 2 parts. The relationship includes an angle having to exist in order to have a bisector. A ray starts at a one point, represented usually by a dot and goes off for ever in a direction whereas a line extends infinitely in both directions.
Step-by-step explanation:
future value = P × (1+ i)t `"present value" = "P" / (1 + i)^"t"` What would be the value of $100 after 10 years if you earn 11 percent interest per year?
Answer: $283.94
Step-by-step explanation:
[tex]A=P(1+r)^t\\\\\bullet P=100\\\bullet r=11\% \implies 0.11\\\bullet t=10\\\\\\A=100(1.11)^{10}\\.\ =283.94[/tex]
6(2x-1)-12=3(7x+6
Please help ALGEBRA
Answer:
x=-4
Step-by-step explanation:
6(2x-1)-12=3(7x+6)
Distribute
12x -6 -12 = 21x +18
Combine like terms
12x-18 = 21x+18
Subtract 12x from each side
12x-12x-18 = 21x-12x+18
-18 = 9x+18
Subtract 18 from each side
-18-18 = 9x+18-18
-36 = 9x
Divide by 9
-36/9 = 9x/9
-4 =x
Yolanda tossed a coin 15 times. The results were 9 heads and 6 tails. Determine the experimental probability of tossing tails.
The experimental probability of tossing tails in the given scenario is 0.4 or 40%, which is determined by dividing the number of tails (6) by the total number of tosses (15).
Explanation:The student is asking to determine the experimental probability of tossing tails when a coin was tossed 15 times and resulted in 9 heads and 6 tails. Experimental probability is calculated by dividing the number of times an event occurs by the total number of trials. In this case, the coin landed as tails 6 times out of 15 tosses.
To find the experimental probability of tossing tails, use the formula:
Experimental Probability of Tails = Number of Tails / Total Number of Tosses
So, it would be:
Experimental Probability of Tails = 6 / 15
Experimental Probability of Tails = 0.4 or 40%
Based on the sample results about what proportion of the population has a favor social network
Answer: 0.8
Step-by-step explanation:
i guessed and got it correct
The sample results about 0.8% proportion of the population has a favor social network.
What is social network ?A social network is a website that enables users to connect and exchange information, pictures, and videos. People who participate in social networking activities may do so for personal or professional reasons.Type of social network? social media sites.Networks for sharing mediaDiscussion boardsNetworks for bookmarking and content curation.Networks of user reviews.Learn more about social network https://brainly.com/question/2083119
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Select the two values of x that are roots of this equation
The answers are:
B. [tex]\frac{-3-\sqrt{29}}{2}[/tex]
C. [tex]\frac{-3+\sqrt{29}}{2}[/tex]
Why?We can use the quadratic equation to find the two values of x that are roots of the given equation. We must remember that most of the quadratic equations have two roots, however, we could find quadratic equations with just one root or even with no roots, at least in the real numbers.
Quadratic equation:
[tex]\frac{-b+-\sqrt{b^{2}-4ac} }{2a}[/tex]
So,
From the given equation we have:
[tex]a=1\\b=3\\c=-5[/tex]
Substituting it into the quadratic equation to find the roots, we have:
[tex]\frac{-b+-\sqrt{b^{2}-4ac} }{2a}=\frac{-3+-\sqrt{3^{2}-4*1*-5} }{2*1}\\\\\frac{-3+-\sqrt{3^{2}-4*1*-5} }{2*1}=\frac{-3+-\sqrt{9+20} }{2}\\\\\frac{-3+-\sqrt{29}}{2}[/tex]
So,
[tex]x_{1}=\frac{-3-\sqrt{29}}{2}\\\\x_{2}=\frac{-3+\sqrt{29}}{2}[/tex]
Hence, the correct options are B and C.
multiply and simplify (x+3) squared
Answer:
[tex]\large\boxed{(x+3)^2=x^2+6x+9}[/tex]
Step-by-step explanation:
Use the FOIL: (a + b)(c + d) = ac + ad + bc + bd
[tex](x+3)^2=(x+3)(x+3)\\\\=(x)(x)+(x)(3)+(3)(x)+(3)(3)\\\\=x^2+3x+3x+9\qquad\text{combine like terms}\\\\=x^2+(3x+3x)+9\\\\=x^2+6x+9[/tex]
You can use
[tex](a+b)^2=a^2+2ab+b^2[/tex]
[tex](x+3)^2=x^2+2(x)(3)+3^2=x^2+6x+9[/tex]
Choose the solution set represented by the following graph.
{x | x R, x < -2}
{x | x R, x > -2}
{x | x R, x ≤ -2}
{x | x R, x ≥ -2}
Answer:
The solution set represented by the following graph is:
{x | x∈ R, x < -2}
Step-by-step explanation:
Clearly from the figure we could see that the solution set is to the left of ' -2' and excluding the point '-2' since there is a open circle at -2.
This means that -2 is not included in the set.
Also in interval; form the set of points that belong to the solution set are:
(-∞,-2)
in set-builder form it is written as:
{x | x∈ R, x < -2}
Answer:
Option A.
Step-by-step explanation:
We need to find the solution set represented by the given graph.
From the given figure it is clear that there is an open circle around -2 and shaded region lie left side of -2.
Open circle around -2 represents that -2 is not included in the solution set.
Shaded area towards left of -2 represents that the solution must be less than -2. It means the sign of inequality is "<".
From the given graph it is clear that value of x lie in the interval (-∞,-2). So, the solution set is
[tex]\text{Solution set}=\{x|x\in R,x<2\}[/tex]
Therefore, the correct option is A.
Kary created the table below to graph the equation r=1+2sin theta. Kary thinks she made a mistake.
the answer is D. (4.24,pi/4)
The mistake in the table is located at point [tex](r, \theta) = \left(4.24, \frac{\pi}{4} \right)[/tex].
How to evaluate a function with respect to a given table
In this question we must evaluate the function [tex]r(\theta) = 1 + 2\cdot \sin \theta[/tex], where [tex]\theta[/tex] in radians, for all [tex]\theta[/tex] set in the table and looks that all values of [tex]r[/tex] match with all corresponding values in the table.
According to the table, [tex]r\left(\frac{\pi}{4} \right) = 4.24[/tex] but the evaluation of the function brings out a different result:
[tex]r\left(\frac{\pi}{4} \right) = 1 + 2\cdot \sin \frac{\pi}{4}[/tex]
[tex]r\left(\frac{\pi}{4} \right) = 1 + 2\cdot \left(\frac{\sqrt{2}}{2} \right)[/tex]
[tex]r\left(\frac{\pi}{4} \right) = 1 + \sqrt{2}[/tex]
[tex]r\left(\frac{\pi}{4} \right) \approx 2.414[/tex]
The mistake in the table is located at point [tex](r, \theta) = \left(4.24, \frac{\pi}{4} \right)[/tex]. [tex]\blacksquare[/tex]
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Represent the following expressions as the power of a number a.
1/a^2 · 1/a^3
Answer:
a⁻⁵
Step-by-step explanation:
1/a²·1/a³
Multiply numerators and denominators
= (1 × 1)/(a² × a³)
= 1/a⁵
= a⁻⁵
What is the name of this angle?
Answer:
1. is an acute angle
2. is an acute angle
Step-by-step explanation:
Both the angles are less than 90° so the angles are both acute.
Write an equation in slope-intercept form of the line that passes through the given point and is parallel to the graph of the given equation. (-5,-8); y=-3x+5
a parallel line to that equation will have the same exact slope, so
[tex]\bf y=\stackrel{\stackrel{m}{\downarrow }}{-3}x+5\impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
then we're really looking for the equation of a line whose slope is -3, and runs through (-5,-8)
[tex]\bf (\stackrel{x_1}{-5}~,~\stackrel{y_1}{-8})~\hspace{10em} slope = m\implies -3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-8)=-3[x-(-5)] \\\\\\ y+8=-3(x+5)\implies y+8=-3x-15\implies y=-3x-23[/tex]
у₁=kx+b; y₂= -3x+5
y₁||y₂⇒ k= -3; y₁= -3x+b
-8 =-3*(-5)+b
-8=15+b
-23=b
y₁= -3x-23
Which inequality is equivalent to -x < 8?x < 8 x > 8 x < -8 x > -8
The inequality equivalent to -x < 8 is x > -8.
Option D is the correct answer.
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
We have,
-x < 8
Interchange < with > and divide both sides by a negative sign.
x > -8
Thus,
x > -8 is equivalent to -x < 8.
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Tracis Bank charges $2 for withdrawals at nonbank ATMs and a fee of $2.50 per month for debit card. last month she paid $10.50 in ATM and debit card fees how many numbers ATM withdrawals did she make
Answer:
5 withdrawals
Step-by-step explanation:
Since $10.50 ends in $0.50, you know that she must have made at least one $2.50 transaction.
10.50 - 2.50 = 8
8/2 = 4 (she made four $2 transactions)
She made 4 $2 transactions and 1 $2.50 transaction.
4 + 1 = 5
She made 5 transactions total.
Which of these systems of linear equations has an infinite number of solutions?
A. 3x-8y=21
6x-16y=46
B. 3x+6y=22
6x+12y=44
C. 5x+9y=2-
10x-14y=48
D. 5x-9y=20
10x+18y=40
Answer: 3x+6y=22
6x+12y=44
Step-by-step explanation: my math teacher told me
3x+6y=22 and 6x+12y=44 system of linear equations have an infinite number of solutions.
When will a system of equations have an infinite number of solutions?A system of linear equations will have an infinite number of solutions when the equations are the same. That is, when the equations coincide.
We can find which system of equations have infinite number of solutions as shown below:Let's take the system,
3x-8y=21
6x-16y=46
Divide the second equation throughout by 2:
We get 3x-8y=23, This is not the same as the first equation. This system does not have infinitely many solutions.
Let's take the system,
3x+6y=22
6x+12y=44
Divide the second equation throughout by 2:
We get 3x+6y=22, This is the same as the first equation. This system has infinitely many solutions.
Let's take the system,
5x+9y=2
10x-14y=48
Divide the second equation throughout by 2:
We get 5x-7y=24, This is not the same as the first equation. This system does not have infinitely many solutions.
Let's take the system,
5x-9y=20
10x+18y=40
Divide the second equation throughout by 2:
We get 5x+9y=20, This is not the same as the first equation. This system does not have infinitely many solutions.
Therefore, we have found the system of equations contained in option B has infinitely many solutions.
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If f(x)=3/x-3, what is (f•f)(x)?
answer is B and it is the answer no questions asked hands down im the smartest person in the world
Answer:
B.
NEXT SLIDE:
A.
then
A, D.
then
A.
that's all i have time for. (im doing the assignment rn, but i have to log out and eat dinner! byeeee!)
Step-by-step explanation:
Good Luck Catching up fellow Edge people!!!
(8c+5)(-2c-3) simplify
(8c+5)(-2c-3)
Multiply each term together, then combine like terms:
8c * -2c = -16c^2
8c *-3 = -24c
5 * -2c = -10c
5 *-3 = -15
Now combine:
-16c^2 - 24c -10c -15
Simplify:
-16c^2 -34c -15
Answer:
-16c^2 - 24c -10c -15
Step-by-step explanation:
Find the volume of the composite figure shown. Use 3.14 to approximate pi. Round your answer to the tenths.
Answer:
21499.4 in³
Step-by-step explanation:
1. Find the area of the face:
a. Triangle: 1/2*b*h = 1/2*30*15 = 225 in²
b. Rectangle: b*h = 22*30 = 660 in²
c. Semi-circle: 1/2*πr² = 1/2*π*(d/2)² = 1/2*3.14*11² = 189.97 in²
d. Total: 225 + 660 + 189.97 = 1074.97 in²
2. Find height: 20 in
3. Find volume: 1074.97*20 = 21499.4 in³
Check the picture below.
so, the composite is really, a triangular prism on top of a rectangular prism with a semi-circle.
now, if we can just get the volume of each individual solid, then we're golden.
for the triangular prism, its volume is simply the triangular face's area times the length, in this case 20.
for the rectangular prism, is the same, the rectangular face's area times the length.
now, for the semicircle is the same, let's recall, the area of a full circle is πr², so the area of half a circle is (πr²)/2. Notice in the picture, the semi-circle has a radius of 11.
[tex]\bf \stackrel{\textit{area of the triangle}}{\left[\cfrac{1}{2}(30)(15) \right]}(\stackrel{\textit{length}}{20})~~+~~ \stackrel{\textit{rectangle's area}}{(22\cdot 11)}(\stackrel{\textit{length}}{20})~~+ \stackrel{\textit{semi-circle's area}}{\left(\cfrac{\pi 11^2}{2} \right)}(\stackrel{\textit{length}}{20}) \\\\\\ 4500+4840+1210\pi \implies \stackrel{\pi =3.14}{13139.4}[/tex]
can someone pls help me and don’t make fun of me bc it’s easy for you☺️
Answer:
7
Step-by-step explanation:
Find the greatest common factor of 28 and 35, which is 7. That means that each group will have seven people.
To go more into detail, there will be 4 groups of 6th graders and 5 groups of 7th graders.
Can anyone help me, please
Answer:
243
Step-by-step explanation:
Step 1:
Find the volume of each square: do 3/4*3/4*3/4.
Each square's volume is 27/64.
Step 2:
Find the volume of the cube.
Multiply 8*6*12.
8*6*12=576.
Step 3:
Do 576*27/64.
576*27/64=243.
is graph shows the number of dogs that were treated everyday over the past year. What can you tell about the average number of dogs treated by each veterinarian in the past year?
Could you show the graph please?
Answer:
On average, A New Leash on Life Animal Clinic treats more dogs per day than No Ruff Stuff Animal Hospital.
I know this cause I just got it right on I-Ready lol
Help Please!!
It takes an Amtrak train about 8 hours to travel from Los Angeles to San Francisco.
If the entire trip is 400 miles, what is the average speed of the Amtrak train?
Show your work in the box below, including the proper units for your answer.
Thank You!
Answer:
50 miles per hour
Step-by-step explanation:
Here,
Time= 8 hours
Distance=400 miles
The speed is calculated by dividing the distance by time.
So,
Average Speed=Distance/Time
= 400/5
=50 miles per hour
The average speed of the Amtrak train traveling from Los Angeles to San Francisco, which is a distance of 400 miles in 8 hours, is 50 miles per hour.
The subject of this question is Mathematics, specifically involving the concept of speed which is a part of physical science and physics. To find the average speed of the Amtrak train, we need to divide the total distance traveled by the time taken for the journey. The total distance from Los Angeles to San Francisco is given as 400 miles, and the time taken is 8 hours.
To calculate the average speed, use the formula:
Average Speed = Total Distance / Total Time
Substituting the given values:
Average Speed = 400 miles / 8 hours = 50 miles/hour
Therefore, the average speed of the Amtrak train is 50 miles per hour.