Answer:
Area of triangle = 1/2 of base × height
Area of triangle = 1/12 of 12×17
Area of triangle = 102m²
A rectangle is shown with the area of 14/32 square in. Label two sides of the rectangle with appropriate fractions that would come up with the area of 14/32 square inches when multiplied together.
The dimensions of the rectangle that would have a value of 14/32 inches square are a length of 2/16 and a width of 31/2 inches.
What are the dimensions of the rectangle?
A rectangle is a 2-dimensional quadrilateral with four right angles that has a value of 360 degrees. It has two diagonals that bisect each other.
Area of a rectangle = length x width
2/16 x 7/2 = 14/32
To learn more about how to calculate the area of a rectangle, please check: https://brainly.com/question/16595449
Fastest answer gets brainliest (must provide an explanation and steps for proof)
Answer:
[tex]\sf g(x+5) = \dfrac{x+6}{4x+17}[/tex]
explanation:
g(x + 5) || this function refers to x = x + 5
solving steps:
[tex]\sf g(x) = \dfrac{1+x}{-3+4x}[/tex]
[tex]\rightarrow \sf g(x+5) = \dfrac{1+(x+5)}{-3+4(x+5)}[/tex]
[tex]\rightarrow \sf g(x+5) = \dfrac{6+x}{-3+4x+20}[/tex]
[tex]\rightarrow \sf g(x+5) = \dfrac{x+6}{4x+17}[/tex]
Answer:
Given function:
[tex]g(x)=\dfrac{1+x}{-3+4x}[/tex]
To find [tex]g(x+5)[/tex], substitute [tex]x+5[/tex] into the function in place of [tex]x[/tex]:
[tex]\implies g(x+5)=\dfrac{1+(x+5)}{-3+4(x+5)}[/tex]
[tex]=\dfrac{1+x+5}{-3+4x+20}[/tex]
[tex]=\dfrac{x+6}{4x+17}[/tex]
Q. If A is a square matrix such that A² = A, then write the value of 7 A −(I + A)³, where I is an identity matrix.
Since [tex]A^2=A[/tex], we have
[tex](I + A)^2 = I^2 + IA + AI + A^2 = I + A + A + A = I + 3A[/tex]
[tex](I + A)^3 = (I + A) (I + 3A) = I^2 + 3IA + AI + 3A^2 = I + 3A + A + 3A = I + 7A[/tex]
Then the target expression is
[tex]7A - (I + A)^3 = 7A - (I + 7A) = \boxed{-I}[/tex]
The diameter of a circle is 12 ft. Find its area to the nearest whole number. Answer: A =
Answer:
113 ft²
Step-by-step explanation:
π = 3.14
r = 6
Use the formula for the area of a circle:
A = πr²
A = 3.14*6²
A = 3.14*36
A = 113.04
A = 113
Hope this helps :)
Answer:
Area = 113 ft²
Step-by-step explanation:
The formula to find the area of a circle is:
Area = π × r²
r is the radius that can be found by taking half of the diameter.
r = [tex]\frac{12}{2}[/tex] = 6
Area = π × 6²
Area = π × 36
Area = 113.09 = 113 [ to the nearest whole number ]
Write an equation in standard form of an ellipse that is 10 units high and 8 units wide. The center of the ellipse is (0, 0).
Answer:
[tex]\frac{x^2}{25} + \frac{y^2}{16} = 1[/tex]
Step-by-step explanation:
Great, so the question already tells you that you're using the standard form of an ellipse. All you gotta do is apply your knowledge of the characteristics of an ellipse graph.
The standard form of an ellipse is:
[tex]1 = \frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2}[/tex]
[tex]h[/tex] and [tex]k[/tex] are the offset, or the coordinates of the center of the ellipse. The center of the ellipse will always be on (h,k). Now because the question says the center is (0,0), we can make h and k equal to 0 in the equation giving:
[tex]1 = \frac{x^2}{a^2} + \frac{y^2}{b^2}[/tex].
Now, the height of the ellipse will always be equal to 2a. The width will be equal to 2b.
Since we are told what the height and width should be, we can find the a and b values quite easily using algebra.
So first, height:
[tex]10 = 2a\\5 = a[/tex]
Now width:
[tex]8 = 2b\\4 = b[/tex]
Subbing for a and b in the equation give you:
[tex]1 = \frac{x^2}{5^2} + \frac{y^2}{4^2}\\=\\1 = \frac{x^2}{25} + \frac{y^2}{16}[/tex]
Liz flips a coin 60 times. The coin lands head up 24 times and tails up 36 times. The EXPERIMENTAL probability of the coin landing headS up is ___%.
Answer:
60%
Step-by-step explanation:
36= heads
36/60= 60%
Answer:
60x24x36=51,840%
Step-by-step explanation:
Simplify.
1/3 ≠ 18n^2 * 2n
Answer:
n³ ≠ 108
Step-by-step explanation:
1/3 ≠ 18n² * 2n
1/3 ≠ 18 * n² * 2 * n
1/3 ≠ 18 * 2 * n² * n
1/3 ≠ 36n³
Cross multiply,
1 * n³ ≠ 3 * 36
n³ ≠ 108
Hence simplified.
Find the area of the shaded polygons.
Answer: 372 sq. un
Step-by-step explanation:
7+24=31
Divided by 2 = 15.5
15.5x24 = 372
A dairy farmer plans to enclose a rectangular pasture adjacent to a river. To provide enough grass for the herd, the pasture must contain 18 square meters. No fencing is required along the river. What dimensions will use the least amount of fencing?
Answer:
390 m (perpendicular to river) x 780 m (parallel to river)
Step-by-step explanation:
Let y be the length of the side parallel to the river, and let x be the length of the sides perpendicular to the river.
The total area and length of fence required are given by:
Rewriting the length of fence as a function of only x:
The value of x for which the derivate of L(x) is zero is the length of x that uses the least amount of fencing:
If x = 390 m, then:
The dimensions that will use the least amount of fencing are 390 m x 780 m
sketch the graph of y=2x^2-3x-4
The response to a question has three alternatives: A, B, and C. A sample of 120 responses provides 60% A, 23% B, and 37% C. Show the frequency and relative frequency distributions
Answer:
0.5,0.2,0.3
Step-by-step explanation:
divide 60,23,37 by 120
Am I right??? Please help me
Function: y = 2x²-5
Find y-intercept:
y = 2(0)²-5
y = -5
Find x-intercept:
2x²-5 = 0
2x² = 5
x² = 2.5
x = ±√2.5
x = -1.5811 , 1.5811
Graph plotted:
Answer:
Vertex and y-intercept (0, -5)
x-intercepts (-1.58, 0) (1.58, 0)
opens upwards
other plot points: (-2, 3) (-1, -3) (1, -3) (2, 3)
Step-by-step explanation:
The graph is not quite correct - it's a little too narrow and doesn't go through the points on the graph.
The y-intercept is when x = 0:
f(0) = 2(0)² - 5
= - 5
Therefore, the y-intercept is at (0, -5)
We also know that the y-intercept is the vertex since the equation is in the form [tex]f(x)=ax^2+c[/tex]
The x-intercepts are when f(x) = 0:
[tex]\implies 2x^2 - 5 = 0[/tex]
[tex]\implies x^2 =\dfrac52[/tex]
[tex]\implies x=\pm1.58113883...[/tex]
As the leading coefficient is positive, the parabola opens upwards.
Finally, input values -2 ≤ x ≤ 2 to find plot points:
(-2, 3)
(-1, -3)
(0, -5)
(1, -3)
(2, 3)
In a circle, a 270° sector has area 300s in? What is the radius of the circle?
.
[tex]\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360}~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ A=300\pi \\ \theta =270 \end{cases}\implies 300\pi =\cfrac{(270)\pi r^2}{360}\implies 300\pi =\cfrac{3\pi r^2}{4} \\\\\\ 1200\pi =3\pi r^2\implies \cfrac{1200\pi }{3\pi }=r^2\implies 400=r^2\implies \sqrt{400}=r\implies 20=r[/tex]
Please answer this relatively quickly, I'm not in very much of a rush but would like to get this done.
Answer: 6
Step-by-step explanation:
Because you have to multiply then remove the fraction and set equal to 0 and solve for x which I’m pretty sure gives u 6
the legnth of a rectangle is three times its width. if the perimeter of the rectangle is 64 in, find the length and width
Step-by-step explanation:
According to the question,
Let the width of rectangle be x and length of rectangle be 3x
Perimeter of Rectangle :- 2(L+B) = 64 in
Putting the values we get ,
2(3x+x) = 64 in
8x = 64 in
x = 8 in
Putting the value of x ,
Width :- 8 Inch
Length :- 24 inch
[tex]\rightarrow[/tex] Length(l) of the rectangle is three times it's width(w) = 3w.
[tex]\rightarrow[/tex] Width(w) of the rectangle = w.
[tex]\rightarrow[/tex] Perimeter of the rectangle = 64in.
To Find:-[tex]\rightarrow[/tex]Length and width of the rectangle.
Solution:-[tex]\rightarrow[/tex] Perimeter of rectangle = [tex]\sf{2(l+w)}[/tex] putting the value of perimeter, l and w from the above given)
[tex]\rightarrow[/tex] 64 = [tex]\sf{2(3w+w)}[/tex]
[tex]\rightarrow[/tex] 64 = [tex]\sf{2(4w)}[/tex]
[tex]\rightarrow[/tex] 64 = [tex]\sf{8w}[/tex]
[tex]\rightarrow[/tex] [tex]\sf{\frac{64}{8}}[/tex]= [tex]\sf{w}[/tex]
[tex]\rightarrow[/tex] [tex]\sf{8}[/tex]= [tex]\sf{w}[/tex]
Therefore, width of the rectangle = 8in.
And Length = 3(8)in. = 24in.
To check whether the answer is correct or not, we can put the value of length and width in the formula = [tex]\sf{2(l+w)}[/tex]
[tex]\rightarrow[/tex] [tex]\sf{=\: 2(24+8)}[/tex]
[tex]\rightarrow[/tex] [tex]\sf{=\: 2(32)}[/tex]
[tex]\rightarrow[/tex] [tex]\sf{=\: 64in.}[/tex]
Since, the perimeter of the rectangle is same as given in the question, therefore the value of length and width are correct.
_______________________________
Hope it helps you:)
super easy algebra 4 x (15- ?) =48
Find the area of the 2.5 m circle using 3.14 or 2/7 four pi
Answer:
Formula for area of circle;
A = π[tex]r^{2}[/tex]
Where 'π' represents pi (22/7 or 3.14), and 'r' is the radius which is being squared.
Plug in your values:-
A = π[tex]r^{2}[/tex]
A = 3.14(2.5^2)
A = 3.14(6.25)
A = 19.625 meters is your answer.
Write the number in standard form
and word form.
7 x 10 + 5 x 1 + 6 x (1/100) + 2 x
(1/1,000)
Answer:
75.062
Step-by-step explanation:
just add and multiply then remember that 1/100 or 1/1000 is just 0.001 or 0.01
Determine the type of symmetry of r =5-sin11ø from the equation, if any. Make sure to confirm graphically. Symmetric with respect to the:
A) pole
B) line /2
C) polar axis
D) none of these
well, let me not bore you to death on how we test it and test it.
[tex]\underline{\textit{testing for symmetry to the }\frac{\pi }{2}~line\qquad \qquad r=-r~~,~~\theta =-\theta } \\\\\\ r=5-sin(11\theta )\implies (-r)=5-sin[11(-\theta )]\implies -r=5-sin(-11\theta ) \\\\\\ \stackrel{symmetry~identity}{-r=5-\stackrel{\downarrow }{[-sin(11\theta )]}}\implies\implies r=-5-sin(11\theta )\impliedby \textit{no dice} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\underline{\textit{testing for symmetry to the polar axis}\qquad \qquad \theta =-\theta} \\\\\\ r=5-sin(11\theta )\implies r=5-sin[11(-\theta )]\implies r=5-sin(-11\theta ) \\\\\\ r=5-[-sin(11\theta )]\implies r=5+sin(11\theta )\impliedby \textit{no dice} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\underline{\textit{testing for symmetry to the pole}\qquad \qquad r=-r} \\\\\\ r=5-sin(11\theta )\implies -r=5-sin(11\theta )\implies r=-5+sin(11\theta )\qquad \textit{no dice}[/tex]
so the symmetry tests didn't pass, notice the picture below though, looks a bit deceiving, it looks as if it'd have π/2 symmery, but it doesn't show in the test.
Please help me with these. God bless you
Answer:
The lines of symmetry in the wheel is infinite.
Explanation:
Since there are an infinite number of lines through the center, a circle has an infinite number of lines of symmetry.
Given the function
[tex]f(x) = (x + 4){(x - 2)}^{2} [/tex]
Determine the end behavior of the graph of the function. Show all/any work
[tex]lim \: f(x) = ( \infty + 4)( \infty - 2) {}^{2} \\ x - > \infty [/tex]
[tex]lim \: f(x) = \infty \times \infty \\ x - > \infty [/tex]
[tex]lim \: f(x)= \infty \\ x - > \infty [/tex]
[tex]lim \: \frac{f(x)}{x} = \frac{x(1 - \frac{4}{x})(x - 2) {}^{2} }{x} \\ x - > \infty [/tex]
[tex]lim \: \frac{f(x)}{x} = (1)( \infty - 2) {}^{2} \\ x - > \infty [/tex]
[tex]lim \: \frac{f(x)}{x} = \infty \\ x - > \infty [/tex]
We can then say that the function f(x)=(x-4)(x-2)² admits an asymptotic direction parallel to the y-axis at +∞ and -∞ as well since we have to follow the same steps.
Put the following investment options in order of least to greatest risk:
starting a business
B-rated bond
speculative stock
property
The order of investment options from least to greatest risk is:
B rated bond.Property.Speculative stock. Starting a business. How risky are some investment options?A B rated bond is considered safer than the rest because there is a high chance that the owners of the bond will redeem it. Property is not very risky but can be susceptible to market shocks.
Speculative stock is the third riskiest because its prices are prone to fluctuation. Starting a business is by far the riskiest because a lot of new businesses fail.
Find out more on risky investments at https://brainly.com/question/25219850.
Answer:
B-rated bond
property
starting a business
speculative stock
Step-by-step explanation:
A laptop computer is purchased for $2350. After each year, the resale value decreases by 35% . What will the resale value be after 4 years?
[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &2350\\ r=rate\to 35\%\to \frac{35}{100}\dotfill &0.35\\ t=years\dotfill &4\\ \end{cases} \\\\\\ A=2350(1 - 0.035)^{4}\implies A=2350(0.965)^4\implies A\approx 2037.87[/tex]
PLEASE HELP!
The scatter plot shows the number of years of experience, x, and the
amount charged per hour, y, for each of 25 dog sitters in Texas.
(a) Write an approximate equation of the line of best fit for the data. It doesn't have to be the exact line of best fit.
(b) Using your equation from part (a), predict the amount charged per hour by a dog sitter with 18 years of experience.
Answer:
(a) [tex]\sf y=\dfrac{11}{20}x+7[/tex]
(b) $16.90
Step-by-step explanation:
Part (a)
Add a line of best fit (see attached).
Find two points on the line: (7, 0) and (20, 18)
Use these points to find the slope of the line:
[tex]\sf slope\:(m)=\dfrac{change\:in\:y}{change\:in\:x}=\dfrac{18-7}{20-0}=\dfrac{11}{20}[/tex]
Use the found slope and one of the points in the point-slope form of the linear equation to find an equation for the line of best fit:
[tex]\sf\implies y-y_1=m(x-x_1)[/tex]
[tex]\sf\implies y-7=\dfrac{11}{20}(x-0)[/tex]
[tex]\sf\implies y=\dfrac{11}{20}x+7[/tex]
Part (b)
Substitute x = 18 into the equation and solve for y:
[tex]\sf\implies y=\dfrac{11}{20}(18)+7=\$16.90[/tex]
Help help help help math math
Answer:
the answer in the question mark that was in the green box ???
Carlos is saving for a new bike. he is paid $6.60 an hour and works 10 hours per week at his after-school job. If he saves 75% of the money he earns, how much does he save each week?
Answer:
16.50 per week
Step-by-step explanation:
6.60 times 10 equals 66 minus 75% equals 16.50
What percent of 1/4 is 1/5
5%
16%
24%
80%
[tex]\text{Let it be x percent}\\ \\\dfrac 14 \times x\% = \dfrac 15\\\\\\\implies\dfrac 14 \times \dfrac x{100} = \dfrac 15\\ \\\\\implies x = \dfrac{400}{5} = 80\\\\\\\text{Hence the answer is}~ 80\%[/tex]
3+(-7)×2-10÷(-5)
please step by step0
[tex]\left[3+(-7)\times 2\right] - \left[10 \div(-5)\right]\\\\=(3-14) +\left(10\times \dfrac 15\right)\\\\=-11+2\\\\=-9[/tex]
Solve for c
Can you pls help me??
Answer:
5(c+3)=85
divide both sides by 5
c+3=17
taking 3 to the other side gives us -3
c=17-3
c=14
Triangle A′B′C′ is a dilation of triangle ABC .
What is the scale factor?
Enter your answer in the box.
Answer:
1/2
Step-by-step explanation:
The scale factor is 1/2 because each side length of [tex]\triangle{A'B'C'}[/tex] is 1/2 of the length of the side lengths of [tex]\triangle{ABC}[/tex].
Hope this helps :)
Answer:
1/2
Step-by-step explanation:
took the test