Answer:
48 sq. units
Step-by-step explanation:
The area of a trapezoid is given by half sum of the bases multiplied by the height
[tex]=\frac{1}{2} (a+b)h[/tex]
where a and b are the two parallel sides of the trapezoid and h is the height or amplitude of the trapezoid
But you are aware that, the median of a trapezoid is equal to half the sum of the bases, thus the first part of the formulae is covered by the median
[tex]Median=\frac{1}{2} (a+b)[/tex]
Hence area, A, of a trapezoid is simplified to product of median and amplitude
[tex]A=amplitude*median\\\\A=6*8=48sq.units[/tex]
Answer:
=48 sq. units.
Step-by-step explanation:
Area of a trapezoid =h× (a+b)/2
(a+b)/2 is the median ( half of the sum of the two parallel sides also called the bases.
Median=8 inches
Altitude is the distance between the two parallel sides= 6 inches
A=6 inches×8 inches
=48 sq. units.
How do I define slope?
What is slope?
dlqndpQAI:?s
Step-by-step explanation:
Konichiwa~! My name is Zalgo and I am here to help you out on this great day. Hmm, how do you define slope... Well, the slope or "gradient" of a line is a number that describes both the steepness and direction of the line itself. Now, slope is "a surface of which one end or side is at a higher level than another; a rising or falling surface".
I hope that this helps you! :P
"Stay Brainly and stay proud!" - Zalgo
(By the way, can you mark me Brainliest? I'd greatly appreciate it! Arigato~! X3)
Can you help me with this question? I'll reward *30 points
I just need help with this one question so that I could solve the others. Thanks!
* Edit: I originally set up the question to reward 30 points, but for some reason I can only reward 15. If you don't get 30, then I'm sorry. I'm still kind of new to this site
Answer:
you would first have a straight, increasing line with a small slope. (walking slowly and consistently)
then you have a flat, straight line (not moving as you pet the kitten)
then you have a big, increasing slope (running fast)
then it's straight line again(distance doesnt change at friend's house)
and then a decreasing line with pretty big slope all the way to the x axis(running home)
Factor by grouping
[tex]4r {}^{3} + 10r {}^{2} - 10r - 25[/tex]
A.
[tex](2r {}^{2} + 5)(2r - 5)[/tex]
B.
[tex](2r {}^+ 5)(2r {}^{2} - 5)[/tex]
C.
[tex](2r + 5)(2r {}^{2} - 5)[/tex]
D.
[tex](2r - 5)(2r {}^{2} - 5)[/tex]
Answer:
C
Step-by-step explanation:
Nice work using latex. I admire anyone who has skills with it.
It looks like this question can be grouped using to sets of brackets.
(4r^3 + 10r^2) : Pull out the common factor. 2r^2* (2r + 5)
The second set of brackets is a little bit tricker. Minus signs are not to be ignored.
(-10r - 25) : -5(2r + 5)
Now put both together,
2r^2(2r + 5) - 5(2r + 5)
Notice that there is a common factor on either side of that isolated minus sign. The common factor is 2r + 5. Use the distributive property to pull it out.
(2r + 5)(2r^2 - 5)
It looks like C will be the answer.
Please answer this
Two poles, AB and ED, are fixed to the ground with the help of ropes AC and EC, as shown:
Two right triangles ABC and EDC have a common vertex C. Angle ABC and EDC are right angles. AB is labeled 13 feet, AC is labeled 15 feet, EC is labeled 10 feet, and ED is labeled 4 feet.
What is the approximate distance, in feet, between the two poles?
11.14 feet
16.65 feet
14.35 feet
15.59 feet
Check the picture below.
so we can simply use the pythagorean theorem for each triangle and get "w" and "z".
[tex]\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-b^2}=a \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \sqrt{15^2-13^2}=w\implies \sqrt{225-169}=w\implies \sqrt{56}=w\implies 7.48\approx w \\\\\\ \sqrt{10^2-4^2}=z\implies \sqrt{100-16}=z\implies \sqrt{84}=z\implies 9.17\approx z \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \stackrel{w+z}{16.65}~\hfill[/tex]
Applying the Pythagorean Theorem, the approximate distance in feet, between the two poles is: b. 16.65 feet
Recall:
For a right triangle where c is the hypotenuse and a and b are the other legs of the right triangle, the Pythagorean Theorem states that: c² = a² + b².
The distance between the two poles = BC + DC
Given:
AB = 13 feetAC = 15 feet EC = 10 feetED = 4 feet.Apply the Pythagorean Theorem to find BC and DC respectively.
Length of BC:
BC = √(AC² - AB²)
SubstituteBC = √(15² - 13²)
BC = 7.48 feet
Length of DC:
DC = √(EC² - ED²)
SubstituteDC = √(10² - 4²)
DC = 9.17 feet
The distance between the two poles = 7.48 + 9.17 = 16.65 feet
Learn more about Pythagorean Theorem on:
https://brainly.com/question/18282315
Do the table and the equation represent the same function ? Y=390+11(x)
Answer:
No
Step-by-step explanation:
We are given the following equation of a function and a table for the corresponding values of this function:
[tex]y=390+11(x)[/tex]
We are to determine if the equation and the table represent the same function.
To check that, we will substitute the value of x in the equation to see if it gives the same values of y as in the table.
[tex]y=390+11(-30)[/tex] ---> (-30, 60)
[tex]y=390+11(-28)[/tex] ---> (-28, 82)
[tex]y=390+11(-26)[/tex] ---> )-26, 104)
Since these paired values differ from the ones given in the table. Therefore, table and equation do not represent the same function.
NOOOO the answer is no now just trust me and get your free answer boom..
what are the domain and range of the function f(x)= 2x+1
Answer:
Domain: All the real numbers
Range: All the real numbers
Step-by-step explanation:
The domain of a function is the complete set of possible values of the independent variable 'x'. That is to say, all the values that 'x' can take:
In this case, f(x)= 2x+1, the independent variable has no restrictions. Meaning that 'x' can take all the Real Values. In set notation: x∈ℝ.
The range of a function is the complete set of all possible resulting values of the dependent variable 'y'. In this case, given that the independent variable has no restrictions, the dependent variable 'y' can take any value. So, the range is: y ∈ ( −∞, ∞ ) - All the real numbers.
Which ordered pair is the best estimate for the solution of the system of equations?
(7,5, 0.5)
(7, 0.5)
(7,0)
(7,0)
Answer:
The best estimate for the solution of the system of equations is the ordered pair (7, 0.5)
Step-by-step explanation:
The way to solve this problem is to take a deep look into the picture, where we can see that the interception between the lines occurs right in x=7. thus, eliminating the first choice.
Next, we can see that the interception is somewhere far from the 'x' axis, hence 'y' variable can not be zero in this point.
Thus, we have our possible solution, without knowing anything else, the ordered pair (7, 0.5).
Remember, a system of equation has a solution when an interception occurs between its equations
Solve 4^x- 3 = 18. Round to the nearest thousandth.
4^(x- 3) = 18
ln[4^(x- 3)] = ln(18)
ln4(x - 3) = ln(18)
ln4x - ln4(3) = ln18
ln4x = ln18 + 3ln4
x = [ln18 + 3ln4]/ln4
x = 5.0849625007
x is approximately 5.085.
To solve the equation 4^x - 3 = 18, isolate the exponential term, take the logarithm of both sides, apply the power rule, and then divide to solve for x. The solution to the nearest thousandth is x ≈ 2.416.
Explanation:To solve the equation 4^x - 3 = 18, first add 3 to both sides of the equation to isolate the exponential term:
4^x = 18 + 3
4^x = 21
Now, take the logarithm of both sides. You can use any logarithm base, but it's most common to use either the natural logarithm (ln) or the common logarithm (log base 10). For this example, we'll use the common logarithm.
log(4^x) = log(21)
Using the power rule for logarithms, which states that log(a^b) = b * log(a), you can write:
x * log(4) = log(21)
Now, divide both sides by log(4) to solve for x:
x = log(21) / log(4)
Use a calculator to find the value of x. Be sure to round your answer to the nearest thousandth, as the problem instructs. The answer comes out to:
x ≈ 2.416
This value of x solves the original equation when rounded to the nearest thousandth.
The average rate of change of g(x) between x=4 and x=7 is 5/6. Which statement must be true?
A) g(7)-g(4)=5/6
B) g(7-4)/7-4=5/6
C) g(7)-g(4)/7-4=5/6
D) g(7)/g(4)=5/6
Answer:
Choice C)
[tex]\displaystyle \frac{g(7) - g(4)}{7 - 4} = \frac{5}{6}[/tex].
Step-by-step explanation:
The average rate of change of a function is:
[tex]\displaystyle \frac{\text{Change in Function Value}}{\text{Change in Independent Variable}}[/tex].
Note that [tex]\text{Change} = \text{Final Value} - \text{Initial Value}[/tex].
For this question,
Initial Independent Variable value: 4;Final Independent Variable value: 7.As a result,
Change in Independent Variable value: [tex]7 - 4[/tex].Initial function value: g(4);Final function value: g(7).As a result,
Change in function value: [tex]g(7) - g(4)[/tex].The average rate of change in the value of [tex]g(x)[/tex] between [tex]x = 4[/tex] and [tex]x = 7[/tex] will be:
[tex]\displaystyle \frac{g(7)-g(4)}{7 - 4}[/tex].
Which equation of the line written in standard form has has a slope of 6 and contains the points (-1,-3)
keeping in mind that standard form for a linear equation means
• all coefficients must be integers, no fractions
• only the constant on the right-hand-side
• all variables on the left-hand-side, sorted
• "x" must not have a negative coefficient
[tex]\bf (\stackrel{x_1}{-1}~,~\stackrel{y_1}{-3})~\hspace{10em} slope = m\implies 6 \\\\\\ \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-(-3)=6[x-(-1)]\implies y+3=6(x+1) \\\\\\ y+3=6x+6\implies y=6x+3\implies -6x+y=3\implies 6x-y=-3[/tex]
PLEASEEEEEEEEEE HELP ASAP PLEASEEEEEEEEEE
Answer:
3rd choice
Step-by-step explanation:
In division for variables with same base, you do subtract top exponent minus bottom exponent. She did that correctly since -3-(-1)=-3+1=-2 and -2-1=-3.
The problem said m=-2 and n=4 and she replace m with (-2) and n with (4). She did this correctly.
You can multiply base numbers unless the exponents are the same 4 doesn't have the exponent -2 on it so you can't do (4(-2))^(-2)
The error is the 3rd option.
We start with
[tex]\dfrac{4m^{-3}n^{-2}}{m^{-1}n}[/tex]
Simplifying the exponents, we have
[tex]\dfrac{4m^{-3}n^{-2}}{m^{-1}n} = 4m^{-3}n^{-2} (mn^{-1}) = 4m^{-3+1}n^{-2-1}=4m^{-2}n^{-3}[/tex]
So, the exponents are ok.
If we plug the values, we have
[tex]4m^{-2}n^{-3} \mapsto 4(-2)^{-2}(4)^{-3} = 4\cdot \dfrac{1}{(-2)^2}\cdot\dfrac{1}{4^3} = 4\cdot \dfrac{1}{4}\cdot \dfrac{1}{64} = \dfrac{1}{64}[/tex]
So, she didn't apply the exponent -2 correctly.
Simplest form to write
(2×6)³/²
Answer: [tex]24\sqrt{3}[/tex]
Step-by-step explanation:
You need to remember that [tex]\sqrt[n]{a}[/tex] can be written in the following for:
[tex]a^{\frac{1}{n}}[/tex]
Knowing this and given the expression [tex](2*6)^{\frac{3}{2}}[/tex], you need to multiply the numbers inside the parentheses:
[tex](12)^{\frac{3}{2}}[/tex]
Rewrite it in this form:
[tex]=\sqrt{12^3}==\sqrt{1,728}[/tex]
Descompose 1,728 into its prime factors:
[tex]1,728=2*2*2*2*2*2*3*3*3=2^6*3^3[/tex]
Applying the Product of power property, which states that:
[tex](a^m)(a^n)=a^{(m+n)}[/tex]
You can say that:
[tex]=\sqrt{1,728}=\sqrt{2^6*3^2*3}[/tex]
Simplifying, you get:
[tex]=2^3*3\sqrt{3}=24\sqrt{3}[/tex]
Yuri buys a ton of straw every year. The first time he bought straw, in Year 0, it cost $150.00. He
notices the price is getting less expensive, at a rate of 1.5% per year.
Yuri sketches a graph of the situation.
Which statement is true?
Helpppp me
Answer: the graph decreases from left to right
Step-by-step explanation:
because the price over time is getting cheaper the graph will decrease from 0 onward
(pls mark me the brainliest)
Answer:
The graph decreases from left to right.
Step-by-step explanation:
Given,
The original cost of the straw, P = $ 150.00,
The rate of decreasing per year, r = 1.5% = 0.015
Thus, the price after x years,
[tex]C(x)=P(1-r)^x[/tex]
[tex]\implies C(x) = 150(1-0.015)^x=150(0.985)^x[/tex]
Which is an exponential function,
∵ An exponential function [tex]f(x) = ab^x[/tex] has,
Decay : if 0 < b < 1, ( decreasing from left to right )
Growth : if b > 1, ( increasing from left to right )
Since, 0.985 < 1
Thus, the graph is decreasing from left to right,
if x = 2,
C(2) = [tex]150(0.985)^2[/tex] = 145.53375 ≠ 147.75,
I.e. (2, 147.75) does not lie on the graph,
If x = 3,
C(3) = [tex]150(0.985)^3[/tex] = 143.35 ≠ 141.20
i.e. (3, 141.20) does not lie on the graph.
Simplify.
7x + 3y - 2 + 6x + 1 + y squared 2
Thank you! ;)
Answer:
Its B. y^2 + 3y + 13x - 1
Step-by-step explanation:
It's easy add or subtract the like terms.
Hope my answer has helped you if not i'm sorry in advance.
Find f(–2) for the function f(x) = 3x2 – 2x + 7. −13 −1 1 23
Answer:
f(-2) = 23Step-by-step explanation:
[tex]f(x)=3x^2-2x+7\\\\f(-2)\to\text{put x = -2 to the equation of a function:}\\\\f(-2)=3(-2)^2-2(-2)+7=3(4)+4+7=12+4+7=23[/tex]
Answer:
The correct option is 4. The value of f(-2) is 23.
Step-by-step explanation:
The given function is
[tex]f(x)=3x^2-2x+7[/tex]
We have to find the value of f(-2). It means we need to find the value of function f(x) at x=-2.
Substitute x=-2 in the given function to find the value of f(-2).
[tex]f(-2)=3(-2)^2-2(-2)+7[/tex]
On simplification we get
[tex]f(-2)=3(4)-(-4)+7[/tex]
[tex]f(-2)=12+4+7[/tex]
[tex]f(-2)=23[/tex]
The value of f(-2) is 23. Therefore the correct option is 4.
Terry sold 30 cans of paint at a total cost of $425. A can of paint holding one quart cost $10 each. A can of paint holding one gallon cost $15 each. The equations and graph below can be used to determine the number of cans of paint Terry sold, where x represents the number of quarts of paint, and y represents the number of gallons of paint.
Number of cans: x + y = 30
Total cost of cans: 10x + 15y = 425
A. 42 quarts, 28 gallons
B. 25 quarts, 5 gallons
C. 5 quarts, 25 gallons
D. 15 quarts, 15 gallons
Step-by-step explanation:
from the graph above, the intersect of both lines would give the answer...
C. 5 quarts, 25 gallons
You can substitute the values in both equations to verify the answer
suppose that g(x)=f(x)+2. which statement best compares the graph of the g(x) with the graph of f(x)?
Answer:
Step-by-step explanation:
The graph of g(x) is the same as that of f(x), EXCEPT that the graph of f(x) has been translated upward by 2 units.
The function is added and with a positive number so the function will shift towards the left , Option D is the correct answer.
What is a function ?A function can be defined as an algebraic expression which states relation between an independent and a dependent variable.
A function always comes with a defined range and domain.
It is given in the question that
There are two functions
g(x), f(x)
and they are related as
g(x)=f(x)+2.
and it has been asked that which statement given in the option describes it the best.
A. The graph of g(x) is the graph of f(x) shifted 2 units to the right.
B.The graph of g(x) is the graph of f(x) shifted 2 units down.
C.The graph of g(x) is the graph of f(x) shifted 2 units up.
D. The graph of g(x) is the graph of f(x) shifted 2 units to the left.
When a function is added , subtracted or multiplied it shifts or translates, and the new function is called the translated function
As the function is added and with a positive number so the function will shift towards the left.
Therefore , D is the answer the graph of G (x) is the graph of f(x) shifted 2 units to the left.
To know more about Function
https://brainly.com/question/12431044
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need help
function inputs and outputs
Answer:
h(9) = 62
Step-by-step explanation:
Equate 8x - 10 = 62 and solve for x
8x - 10 = 62 ( add 10 to both sides )
8x = 72 ( divide both sides by 9 )
x = 9
That is h(9) = 62
ine segment AB has endpoints A(–4, –10) and B(–11, –7). To find the x-coordinate of the point that divides the directed line segment in a 3:4 ratio, the formula x = (x2 – x1) + x1 was used to find that x = (–11 – (–4)) + (–4).
Therefore, the x-coordinate of the point that divides AB into a 3:4 ratio is
Answer:
-7
Step-by-step explanation:
The coordinates of the point wich divide the segment AB, where [tex]A(x_A,y_A),\ B(x_B,y_B)[/tex] in ratio [tex]m:n[/tex] can be calculated using formula
[tex]C\left(\dfrac{nx_A+mx_B}{m+n},\dfrac{ny_A+my_B}{m+n}\right)[/tex]
In your case,
[tex]A(-4,-10)\\ \\B(-11,-7)\\ \\m:n=3:4\Rightarrow m=3,\ n=4[/tex]
Hence,
[tex]C\left(\dfrac{4\cdot (-4)+3\cdot (-11)}{3+4},\dfrac{4\cdot (-10)+3\cdot (-7)}{3+4}\right)\\ \\C\left(-\dfrac{49}{7},-\dfrac{61}{7}\right)\\ \\C\left(-7,-\dfrac{61}{7}\right)[/tex]
Therefore, x-coordinate of the point that divides AB into a 3:4 ratio is -7.
which percent is equal to 2.5?
A. 2.5%
B. 25%
C. 250%
D. 2.500%
Answer:
The answer is C.250%
Step-by-step explanation:
Got it right on the quiz
PLEASE HELP ME PLEASE I NEED HELP AS FAST AS POSSIBLE
What is the expression b10 called?
A) monomial
B) binomial
C) trinomial
D) polynomial
Answer:
monomial
Step-by-step explanation:
because it has one variable which in this case is b and one number in this case is 10
Answer:
MONOMIAL
Step-by-step explanation:
Andrew is riding his bike. He biked a distance of 14 miles at a rate of 7 miles per hour. Using the distance formula, d = rt, solve for Andrew's time in minutes
d = rt ( d = distance, r = rate (speed) and t = time)
14 = 7t
Divide both sides by 7:
t = 14/7
t = 2 hours
1 hour = 60 minutes.
2 hours x 60 = 120 minutes total.
Based on the distance Andrew went and the rate at which he went, Andrew's time in minutes was 120 minutes.
The distance formula is:
Distance = Rate x Time
Andrew's time is therefore:
14 = 7 x Time
Time = 14 / 7
= 2 hours
In minutes this is:
= 2 x 60 minutes per hour
= 120 minutes
In conclusion, Andrew covered that distance in 120 minutes.
Find out more at https://brainly.com/question/18591848.
what is the length of the line segment with endpoints -3, -8 and 10,- 8
let's notice the y-coordinate is the same for both points, thus is a horizontal line.
Check the picture below.
reduce fraction: a^3+a^2b/5a times 25/3b+3a
ANSWER
[tex] \frac{5a}{3} [/tex]
EXPLANATION
The given fractions are:
[tex] \frac{{a}^{3} + {a}^{2} b}{5a} \times \frac{25}{3b + 3a} [/tex]
We factor to obtain:
[tex]\frac{{a}^{2}(a + b)}{5a} \times \frac{25}{3(a + b)} [/tex]
We cancel the common factors to get:
[tex]\frac{{a}(1)}{1} \times \frac{5}{3(1)} [/tex]
We multiply the numerators and also multiply the denominators to get:
[tex] \frac{5a}{3} [/tex]
Therefore the two fractions simplifies to [tex] \frac{5a}{3} [/tex]
if you purchase a hundred items that cost $0.25 each how much would the item cost all together
Cost of items = $0.25 × 100
= $25.00
if Cos 30° equals rad 3/2 then the sin 60° equals
a) 0
b) 1/2
c) rad 3/2
d) 1
Answer:
c) rad 3/2
Step-by-step explanation:
If Cos 30° equals rad 3/2 then the sin 60° equals rad 3/2.
Graph the linear equation. Find three
points that solve the equation, then plot
on the graph.
2x – 3y = -6
Answer:
3,4
6,6
9,8
Step-by-step explanation:
Which of the following is equal to the square root of the cube root of 5 ? (1 point)
5 to the power of 1 over 3
5 to the power of 1 over 6
5 to the power of 2 over 3
5 to the power of 3 over 2
Answer: Second Option
5 to the power of 1 over 6
Step-by-step explanation:
The square root of the cubic root of 5 is written as follows
[tex]\sqrt[2]{\sqrt[3]{5}}[/tex]
Now use the following property of the roots
[tex]\sqrt[m]{\sqrt[n]{x}}=\sqrt[m*n]{x}[/tex]
In this case [tex]m = 2[/tex] and [tex]n=3[/tex] and [tex]x=5[/tex]
So we have that
[tex]\sqrt[2]{\sqrt[3]{5}}=\sqrt[2*3]{5}[/tex]
[tex]\sqrt[2*3]{5}=\sqrt[6]{5}[/tex]
Now use the following property
[tex]\sqrt[n]{x^h}=x^{\frac{h}{n}[/tex]
So we have that:
[tex]\sqrt[6]{5}=5^{\frac{1}{6}}[/tex]
The answer is the second option
5 to the power of 1 over 6
Answer:
5 to the power of 1 over 6
Step-by-step explanation:
What is the vertex of (y+3)^2=12(x-1)
Answer:
The vertex is (1,-3)
Step-by-step explanation:
Just look for the numbers that make the inner parts 0. Here, x - 1 is 0 when x = 1 and y + 3 is 0 when y = -3.
Answer:
Step-by-step explanation:
Compare:
(y+3)^2=12(x-1)
(y - k)^2 = 12(x - h)
Here we see that k = -3 and h = 1. Thus, the vertex of this horiz. parabola is (1, -3). We know that this parabola is horiz. because it's y or y+3 that is squared, not x or x-1.
What is the equation of the line that is parallel to the line 5x + 2y = 12 and passes through the point (-2, 4)?
y=-x-1
y=-x+5
y=x-1
y=x+5
Answer: [tex]y=-\frac{5}{2}x-1[/tex]
Step-by-step explanation:
The equation of the line in Slope-Intercept form is:
[tex]y=mx+b[/tex]
Where "m" is the slope of the line and "b" is the y-intercept.
Write the equation of the given line in Slope-Intercept form by solving for "y":
[tex]5x + 2y = 12\\\\2y=-5x+12\\\\y=-\frac{5}{2}x+6[/tex]
You can observe that the slope of this line is:
[tex]m=-\frac{5}{2}[/tex]
Since the slopes of parallel lines are equal, then the slope of the other line is:
[tex]m=-\frac{5}{2}[/tex]
Now, substitute the slope and the point (-2, 4) into [tex]y=mx+b[/tex] and solve for "b":
[tex]4=-\frac{5}{2}(-2)+b\\\\4=\frac{10}{2}+b\\\\4-5=b\\\\b=-1[/tex]
Then the equation of the line parallel to the given line is:
[tex]y=-\frac{5}{2}x-1[/tex]