Answer:
The simplified expression is d = (5√2) L
Step-by-step explanation:
* Lets explain the problem
- A walking path is shaped like a rectangle
- The width of the rectangle is 7 times its length L
∵ The length of the rectangle is L
∵ The width is 7 times the length
∴ The width of the rectangle is 7L
- The distance between the opposite corners represented by the
diagonal of the rectangle
- The length , the width and the diagonal formed a right triangle
- Its hypotenuse is the diagonal of the rectangle
- Its two legs are the length and the width of the rectangle
* Now we have right triangle use the Pythagoras Theorem to find
the hypotenuse
∵ The length , the width and the diagonal of the rectangle are the
sides of a right triangle
∵ The diagonal is the hypotenuse (h) of the triangle
∵ hypotenuse = √[L² + W²]
∵ The length = L and the width = 7L
∴ h = √[(L)² + (7L)²] = √[L² + 49L²] = √[50L²]
∵ √50 = 5√2
∵ √(L²) = L
∴ h = 5√2 L
∵ The diagonal of the rectangle is the distance between the
opposite corners
∴ The distance between the opposite corners is (5√2) L
* The simplified expression is d = (5√2) L, where L is the length
of the rectangle
To find the distance between opposite corners of the walking path, which is shaped like a rectangle, we need to determine the length of the diagonal.
Given that the width is 7 times the length (l), we can represent the width of the rectangle as \(7l\).
Let's denote the length of the rectangle by \(l\) and the width by \(w\). According to the information, \(w = 7l\).
Now, to find the length of the diagonal, we use the Pythagorean theorem, which states that for a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
For our rectangle, the diagonal forms the hypotenuse, and the length and width are the other two sides of the right-angled triangle. Thus, if we denote the diagonal by \(d\), the Pythagorean theorem gives us:
\(d^2 = l^2 + w^2\)
Substituting the expression for the width:
\(d^2 = l^2 + (7l)^2\)
\(d^2 = l^2 + 49l^2\)
\(d^2 = 50l^2\)
To find \(d\), we take the square root of both sides:
\(d = \sqrt{50l^2}\)
Since \(50\) can be broken down into \(25 \times 2\) and \(25\) is a perfect square, we can simplify the square root as follows:
\(d = \sqrt{25 \times 2 \times l^2}\)
\(d = \sqrt{25} \times \sqrt{2} \times \sqrt{l^2}\)
\(d = 5l \times \sqrt{2}\)
So the simplified expression for the distance between opposite corners of the walking path is:
\(d = 5l\sqrt{2}\)
40 POINTS PLEASE HURRY
Pete grabbed 18 mixed nuts, 2/9 of which were almonds. Which equation shows how to determine the number of almonds Pete grabbed?
A.18 divided by 2/9 =81
B. 18 x 2/9 = 4
C. 2/9 divided by 18=1/81
D. 9/2 divided by 18=1/4
Answer:
B 18*2/9 =4
Step-by-step explanation:
To determine the number of mixed nuts that were almonds, take the number of nuts and multiply by the fraction that were almonds
nuts * 2/9= almonds
18 * 2/9
36/9
4
If sin θ = 3 over 7 and tan θ < 0, what is the value of cos θ? negative square root of 10 negative 2 square root of 10 2 square root of 10 over 7 negative 2 square root of 10 over 7
Answer:
negative 2 square root of 10 over 7
Step-by-step explanation:
The function[tex]f(x)=-3x^{3} +x^{2} +2x[/tex] rises as x grows very small.
A. True
B. False
Answer:
True
Step-by-step explanation:
True.
Like the cubic term -3x^3 is negative, for small values of "x", the dependent variable "y" will rise. All this can be verified by looking at the graph.
Find one positive angle and one negative angle that are coterminal with the given angle. Explain.
10. 255°
12. -800°
Answer: 10) 615° & -105°
12) -440° & 280°
Step-by-step explanation:
Coterminal means it is in the exact same spot on the Unit Circle but one or more rotations clockwise or counterclockwise.
Since one rotation = 360°, add or subtract that from the given angle until you get a positive or negative number.
10) 255° + 360° = 615° (this is a POSITIVE coterminal angle to 255°)
255° - 360° = -105° (this is a Negative coterminal angle to 255°)
12) -800° + 360° = -440° (this is a Negative coterminal angle to -800°)
-440° + 360° = -80° (this is a Negative coterminal angle to -800°)
-80° + 360° = 280° (this is a POSITIVE coterminal angle to -800°)
Final answer:
Coterminal angles for 255° are 615° (positive) and -105° (negative) by adding or subtracting 360° respectively. For -800°, the coterminal angles are -80° (positive) and -1160° (negative).
Explanation:
To find a positive and a negative angle coterminal with the given angle of 255°, we can add or subtract multiples of 360° (the total degrees in a circle). For a positive coterminal angle, we can add 360° to 255°:
255° + 360° = 615°
For a negative coterminal angle, we subtract 360° from 255° until we get a negative result:
255° - 360° = -105°
Similarly, for -800°, to find a positive coterminal angle, we keep adding 360° until we get a positive result:
-800° + 360° = -440°
-440° + 360° = -80°
For a negative coterminal angle, we can subtract 360° from -800°:
-800° - 360° = -1160°
what value is needed to complete the square?
1. x^2-2x+___
2. x^2-6x+___
Answer:
1 and 9
Step-by-step explanation:
To complete the square
add ( half the coefficient of the x- term)²
1
x² + 2(- 1)x + (- 1)² = x² - 2x + 1 = (x - 1)²
2
x² + 2(- 3)x + (- 3)² = x² - 6x + 9 = (x - 3)²
To complete the square for the expressions x² - 2x + ___ and x² - 6x + ___, the required values are 1 and 9, respectively, because these are the squares of half the coefficients of the x terms.
To complete the square for a quadratic expression, we need to add a term that will turn the expression into a perfect square trinomial. For the general form x² + bx + c, the value needed to complete the square is (b/2)².
In the case of x² - 2x + ___, the value of b is -2. Therefore, you need to add (-2/2)² = (1)² = 1.
For the second expression, x² - 6x + ___, the value of b is -6. Here, you add (-6/2)² = (3)² = 9.
So, the values needed to complete the square are:
For x² - 2x + ___, the value is 1.
For x² - 6x + ___, the value is 9.
Convert 135 degrees to radians.
Question 2 options:
2π/3radians
π radians
π/2radians
3π/4radians
ANSWER
[tex] \frac{3\pi}{4} \: radians[/tex]
EXPLANATION
To convert an angle from degrees measure to radians, we multiply by:
[tex] \frac{\pi}{180 \degree} [/tex]
We want to convert 135° to radians.
This implies that,
[tex]135 \degree = 135\degree \times \frac{\pi}{180 \degree} = \frac{3\pi}{4} \: radians[/tex]
The last option is correct.
When Mario has to leave the house for a while, he tethers his mischievous puppy to the corner of a 12 ft-by-8 ft shed in the middle of his large backyard. The tether is 18 feet long. Which description fits the boundary of the locus of points in the yard that the puppy can reach?
A a three-quarter circle of radius 18 ft, quarter circles of radii 10 ft and 6 ft
B a three-quarter circle of radius 18 ft, quarter circles of radii 12 ft and 8 ft
C semicircles of radii 18 ft, 10 ft, and 6 ft
D semicircles of radii 18 ft, 12 ft, and 8 ft
Answer:
a three-quarter circle of radius 18 ft, quarter circles of radii 10 ft and 6 ft
Step-by-step explanation:
i took the test and i got this as the right answer
Answer:
A a three-quarter circle of radius 18 ft, quarter circles of radii 10 ft and 6 ft
Step-by-step explanation:
In order to calculate this, you have to remember that you have a tether that is 18 ft long, thetered to a point, this would make a circle with a radius of 18 ft, but as the center of the circle would be where the theter is knotted, the shed forbids to make a full circle, it rather creates a 3/4 circle, and the dog can acces the other points of the shed, with le length of the theter, that is 8 ft after the long side, and 12 feet after the short side, creating another quarter circle with a radius of 8 and 12 ft.
La expresión algebraica que indica: «Si al cuadrado de la suma de dos números a y b le restamos la mitad de c y la diferencia resultante la multiplicamos por 5» es:
The sum of two number a and b is [tex]a+b[/tex]
Its square is [tex](a+b)^2[/tex]
Half of c is [tex]\frac{c}{2}[/tex]
And we have to subtract this from what we got before:
[tex](a+b)^2-\dfrac{c}{2}[/tex]
Finally, we multiply everything by 5:
[tex]5\left[(a+b)^2-\dfrac{c}{2}\right][/tex]
Queremos, a partir de una frase, escribir la correspondiente expresión algebraica.
Obtendremos:
[tex][(a + b)^2 - c/2]*5[/tex]
-----------------------------------
Lo que nos dan es:
"Si al cuadrado de la suma de dos números a y b le restamos la mitad de c y la diferencia resultante la multiplicamos por 5"
Veamos esto en partes, la primera dice:
"Si al cuadrado de la suma de dos números a y b..."
El cuadrado de la suma de dos números a y b se escribe como:
[tex](a + b)^2[/tex]
Ahora tenemos:
"Si al cuadrado de la suma de dos números a y b le restamos la mitad de c ..."
Ahora le restamos la mitad de c a lo que encontramos antes:
[tex](a + b)^2 - c/2[/tex]
Finalmente:
"Si al cuadrado de la suma de dos números a y b le restamos la mitad de c y la diferencia resultante la multiplicamos por 5"
Es decir, debemos multiplicar por 5 a la diferencia (la resta) de arriba:
[tex][(a + b)^2 - c/2]*5[/tex]
Está es la expresión que queriamos encontrar.
Si quieres aprender más, puedes leer:
https://brainly.com/question/24758907
Solve the problem by writing an inequality. A club decides to sell T-shirts for $12 as a fund-raiser. It costs $20 plus $8 per T-shirt to make the T-shirts. Write and solve an equation to find how many T-shirts the club needs to make and sell in order to profit at least $100. Show your work.
Matrix X is shown below.
If matrices X and Y are equal, what is the value of y12+y13+y32+y33?
7.5
27
40
49.5
Answer:
option C
40
Step-by-step explanation:
[tex]x_{nm}[/tex]
here n = number of row
m = number of column
so the labelled 3x3 matrix would be like this
[tex]y=\left[\begin{array}{ccc}y11&y12&y13\\y21&y22&y23\\y31&y32&y33\end{array}\right][/tex]
Given in the question matrixX since matrixY is eaxctly same as matrixX so,
[tex]y=\left[\begin{array}{ccc}1&6&-7\\-5&0&8.5\\-1&14&27\end{array}\right][/tex]
so
y12 = 6
+
y13 = -7
+
y32 = 14
+
y33 = 27
=
40
Answer:
The answer C, is right!
Step-by-step explanation:
polynomials what is the product of
1/2x - 1/4 and 5x^2-2x+6
Answer:
[tex]\frac{5}{2}x^3-\frac{9}{4}x^2+\frac{7}{2}x-\frac{3}{2}[/tex]
Step-by-step explanation:
Given polynomials are [tex]\frac{1}{2}x-\frac{1}{4}[/tex] and [tex]5x^2-2x+6[/tex].
Now we need to find their product which can be done as follows:
[tex]\left(\frac{1}{2}x-\frac{1}{4}\right)\left(5x^2-2x+6\right)[/tex]
[tex]=5x^2\left(\frac{1}{2}x-\frac{1}{4}\right)-2x\left(\frac{1}{2}x-\frac{1}{4}\right)+6\left(\frac{1}{2}x-\frac{1}{4}\right)[/tex]
[tex]=\frac{5}{2}x^3-\frac{5}{4}x^2-x^2+\frac{1}{2}x+3x-\frac{3}{2}[/tex]
[tex]=\frac{5}{2}x^3-\frac{9}{4}x^2+\frac{7}{2}x-\frac{3}{2}[/tex]
Hence final answer is [tex]\frac{5}{2}x^3-\frac{9}{4}x^2+\frac{7}{2}x-\frac{3}{2}[/tex].
(I've been trying to figure this out for 3 days and I really need help)
1. You are opening a snow cone stand. Your cups, which are shaped like a cone, are 4" tall and have a 6" diameter. How much room is there in the cone without a top on the snow cone? (filled to the brim only)
2. The top of your snow cone is a perfect semicircle. It goes all the way across the cone. How many cubic inches of ice in the top of the snow cone?
3. How many cubic inches of snow cone will you be serving?
4.You want to start selling 2 different sizes of cones. You want your new cone to be twice as big as your current cone (top included). You found a cone that has a 6" diameter and is 8" tall. How many cubic inches of snow cone will you have with the new cone?
Check the picture below.
since the diameter of the cone is 6", then its radius is half that or 3", so getting the volume of only the cone, not the top.
1)
[tex]\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=3\\ h=4 \end{cases}\implies V=\cfrac{\pi (3)^2(4)}{3}\implies V=12\pi \implies V\approx 37.7[/tex]
2)
now, the top of it, as you notice in the picture, is a semicircle, whose radius is the same as the cone's, 3.
[tex]\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=3 \end{cases}\implies V=\cfrac{4\pi (3)^3}{3}\implies V=36\pi \\\\\\ \stackrel{\textit{half of that for a semisphere}}{V=18\pi }\implies V\approx 56.55[/tex]
3)
well, you'll be serving the cone and top combined, 12π + 18π = 30π or about 94.25 in³.
4)
pretty much the same thing, we get the volume of the cone and its top, add them up.
[tex]\bf \stackrel{\textit{cone's volume}}{\cfrac{\pi (3)^2(8)}{3}}~~~~+~~~~\stackrel{\stackrel{\textit{half a sphere}}{\textit{top's volume}}}{\cfrac{4\pi 3^3}{3}\div 2}\implies 24\pi +18\pi \implies 42\pi ~~\approx~~131.95~in^[/tex]
Which expression has a negative value?
Answer:
im pretty sure its d
Step-by-step explanation:
-35/5 is the answer
What is the area of a circle with a diameter of 12.6 in.?
Use 3.14 for pi and round your final answer to the nearest hundredth.
Enter your answer in the box.
Hey there! I'm happy to help!
To find the area of a circle, you square the radius and then multiply by pi (3.14 in our case).
The radius is half of the diameter.
12.6/2=6.3
We square this.
6.3²=39.69
We multiply by 3.14
39.69×3.14=124.6266
We round to the nearest hundredth, giving us an area of 124.63 in².
Now you can find the area of a circle! Have a wonderful day! :D
You can use formula for area of circle which simply is pi times square of radius. The radius is half of diameter.
The area of the given circle is 124.63 sq inches
Given that:A circle has diameter of 12.6 inches.To find:Area of circle using pi = 3.14 and approximated to nearest hundredth.
Formula for Area of circle with radius r units:[tex]\text{Area} = \pi \times r^2[/tex]
Finding radius:[tex]\text{Radius} = \dfrac{\text{diameter}}{2}\\ r = \dfrac{12.6}{2} = 6.3 \: \rm inch[/tex]
Finding the area:[tex]Area = \pi \times r^2 \approx 3.14 \times 6.3^2 \approx 124.626 \approx 124.63 \: \rm inch^2[/tex]
Thus, the area of the given circle is 124.63 sq inches
Learn more about area of circle here:
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What is the quotient (x3 – 3x2 + 5x – 3) ÷ (x – 1)?
What is the quotient (x3 + 3x2 + 5x + 3) ÷ (x + 1)?
Answer:
x^2 -2x +3x^2 +2x +3Step-by-step explanation:
The quotient in each case can be found by any of several means, including synthetic division (possibly the easiest), polynomial long division, or graphing.
1. The graph shows you the quotient is (x-1)^2 +2 = x^2 -2x +3.
2. The graph shows you the quotient is (x+1)^2 +2 = x^2 +2x +3.
Graph each function. Label x-axis.
Answer:
Here's what I get.
Step-by-step explanation:
Question 4
The general equation for a sine function is
y = a sin[b(x - h)] + k
where a, b, h, and k are the parameters.
Your sine wave is
y = 3sin[4(x + π/4)] - 2
Let's examine each of these parameters.
Case 1. a = 1; b = 1; h = 0; k = 0
y = sin x
This is a normal sine curve (the red line in Fig. 1).
(Sorry. I forgot to label the x-axis, but it's always the horizontal axes)
Case 2. a = 3; b = 1; h = 0; k = 0
y = 3sin x
The amplitude changes from 1 to 3.
The parameter a controls the amplitude of the wave (the blue line in Fig. 1).
Case 3. a = 3; b = 1; h = 0; k = 2
y = 3sin x - 2
The graph shifts down two units.
The parameter k controls the vertical shift of the wave (the green line
in Fig. 1).
Case 4. a = 3; b = 4; h = 0; k = 2
y = 3sin(4x) - 2
The period decreases by a factor of four, from 2π to π/2.
The parameter b controls the period of the wave (the purple line in Fig. 2).
Case 5. a = 3; b = 4; h = -π/4; k = 2
y = 3sin[4(x + π/4)] - 2
The graph shifts π/4 units to the left.
The parameter h controls the horizontal shift of the wave (the black dotted line in Fig. 2).
[tex]\boxed{a = 3; b = 4; h = \frac{\pi}{2}; k = -2}}[/tex]
[tex]\text{amplitude = 3; period = } \dfrac{\pi}{2}}[/tex]
[tex]\textbf{Transformations:}\\\text{1. Dilate across x-axis by a scale factor of 3}\\\text{2. Translate down two units}\\\text{3. Dilate across y-axis by a scale factor of } \frac{1}{4}\\\text{4. Translate left by } \frac{\pi}{4}[/tex]
Question 6
y = -1cos[1(x – π)] + 3
[tex]\boxed{a = -1, b = 1, h = \pi, k = 3}[/tex]
[tex]\boxed{\text{amplitude = 1; period = } \pi}[/tex]
Effect of parameters
Refer to Fig. 3.
Original cosine: Solid red line
m = -1: Dashed blue line (reflected across x-axis)
k = 3: Dashed green line (shifted up three units)
b = 1: No change
h = π: Orange line (shifted right by π units)
[tex]\textbf{Transformations:}\\\text{1. Reflect across x-axis}\\\text{2. Translate up three units}\\\text{3. Translate right by } \pi[/tex]
MATH HELP
use distance = rate time (d=rt) to find the number of miles per hour Etty must drive to go 45 miles in 35 minutes. ( remember time is written in hours?
Answer:
rate=1.28571428571.. (1.29) miles per minute, or 77.1428571429.. (77.14) mph
Step-by-step explanation:
"use distance = rate time (d=rt) to find the number of miles per hour Etty must drive to go 45 miles in 35 minutes. ( remember time is written in hours?"
distance=rate*time--- we know distance and time
45 mi= rate*35
rate=45/35
rate=1.28571428571 miles per minute, or 77.1428571429 mph
Answer:
Step-by-step explanation:
77/14mph
Determine if the graph is symmetric about the x-axis, the y-axis, or the origin.
r = 4 cos 3θ
Answer:
It is symmetric about the x-axis because cos(3θ) = cos(-3θ).
It is not symmetric about the y-axis because cos(3θ) is not equal to cos(3(pi-θ)).
It is not symmetric about the origin because cos(3θ) is not equal to -cos(3θ).
Answer:
The graph is symmetric about x- axis.
Step-by-step explanation:
We are given that an equation
[tex]r=4 cos 3\theta[/tex]
We have to find the graph is symmetric about x- axis , y-axis or origin.
We taking r along y-axis and [tex\theta [/tex] along x- axis
When the graph is symmetric about x= axis then (x,y)=(-x,y)
[tex] \theta [/tex] is replaced by [tex]-\theta[/tex] and r remain same then we get
[tex] r=4cos (-3\theta)[/tex]
We know that cos (-x)=cos x
Therefore, [tex] r=4cos 3\theta[/tex]
Hence, the graph is symmetric about x- axis.
When the graph is symmetric about y- axis then (x,y)=(x,-y)
Now, r is replaced by -r then we get
[tex]-r=4cos 3\theta [/tex]
[tex] r=-4 cos {3\theta}[/tex]
[tex] r=4 cos {\pi-3\theta}[/tex]
Therefore, the graph is not symmetric about y-axis.
When the graph is symmetric about y- axis then (x,y)=(x,-y)
Now, r is replaced by -r then we get
[tex]-r=4cos 3\theta [/tex]
[tex] r=-4 cos3\theta[/tex]
[tex] r=4 cos (\pi-3\theta)[/tex]
[tex](\theta,r)\neq (\theta,-r)[/tex]
Therefore, the graph is not symmetric about y-axis.
When the graph is symmetric about origin then (-x,-y)=(x,y)
Replaced r by -r and [tex]\theta [/tex] by-[tex]\theta[/tex]
Then we get [tex] -r=4cos3(-\theta)[/tex]
[tex] -r= 4 cos 3\theta[/tex]
Because cos(-x)=cos x
[tex] r=-4 cos 3\theta [/tex]
[tex](-\theta,-r)\neq(\theta,r)[/tex]
Hence, the graph is not symmetric about origin.
A certain forest covers an area of 2600 km 2 suppose that each year this area decreases by 9% . What will the area be after 5 years ?
Answer:
Final answer is approx 1622.48 square kilometers.
Step-by-step explanation:
Given that a certain forest covers an area of 2600 km 2 suppose that each year this area decreases by 9% . Now we need to find about what will the area be after 5 years.
So we need to plug these values into decay formula which is given by:
[tex]A=P(1-r)^t[/tex]
Where P=2600
r= rate = 9%= 0.09
t=time = 5 years
Plug these values into above formula, we get:
[tex]A=2600(1-0.09)^5[/tex]
[tex]A=2600(0.91)^5[/tex]
[tex]A=2600(0.6240321451)[/tex]
[tex]A=1622.48357726[/tex]
Hence final answer is approx 1622.48 square kilometers.
Final answer:
Using the exponential decay formula, A = A_0 (1-r)^t, the forest area after 5 years with an annual decrease of 9% is approximately 1622.4 km².
Explanation:
To calculate the forest area after 5 years with an annual decrease of 9%, we can use the formula for exponential decay. The original area of the forest is 2600 km2.
Formula for exponential decay: A = A_0 (1-r)^t, where A is the area after time t, A_0 is the original area, r is the rate of decrease, and t is time in years.Convert the percentage to a decimal: r = 9% or r = 0.09.Substitute the values into the formula: A = 2600 (1-0.09)^5.Calculate: A ≈ 2600 (0.91)^5.Compute the final area: A ≈ 2600 * 0.624 ≈ 1622.4 km2.So, if the forest continues to decrease by 9% annually, the area will be approximately 1622.4 km2 after 5 years.
Stefan's family rented a rototiller to prepare an area in their backyard for spring planting. The rental company charged an initial fee of $43 with an additional fee per hour. If they paid $64 after renting the rototiller for 7 hours, what was the hourly fee?
Answer:
The hourly fee is $ 3.
Step-by-step explanation:
Given,
The initial fee = $ 43,
Let x be the additional hourly fee ( in dollars ),
Thus, the total additional fee for 7 hours = 7x dollars,
And, the total fee for 7 hours = Initial fee + Additional fee for 7 hours
= ( 43 + 7x ) dollars,
According to the question,
43 + 7x = 64
7x = 21 ( Subtracting 43 on both sides )
x = 3 ( Divide both sides by 7 )
Hence, the hourly fee is $ 3.
Answer:
7h+43=64
$3
Step-by-step explanation:
did it on edge
Which solid does NOT have the net form? hexagonal prism hexagonal pyramid rectangular prism rectangular pyramid
Answer:
hexagonal pyramid
Step-by-step explanation:
The dairy cows on Mr. Aaron's farm eat 9,315 pounds of grain in 3 months.How many pounds of grain will the cows eat in one month.
Answer:
3,105
Step-by-step explanation:
the answer is 3,105 because you simply take the total number that was eaten in 3 months and divide it by 3 since they only want to know what was eaten in 1 month
is this right? in the triangle below what ration is csc 0?
Answer:
[tex]\frac{13}{5}[/tex]
Step-by-step explanation:
we know that
[tex]csc(\theta)=\frac{1}{sin(\theta)}[/tex]
In this problem
[tex]sin(\theta)=\frac{1.5}{3.9}[/tex]
substitute
[tex]csc(\theta)=\frac{3.9}{1.5}[/tex]
Multiply by 10 both numerator and denominator
[tex]csc(\theta)=\frac{39}{15}[/tex]
Divide by 3 both numerator and denominator
[tex]csc(\theta)=\frac{13}{5}[/tex]
A function is created to represent the amount of money you save or spend each day of the week. What restrictions would be made to the range?
A) The range would only include integers.
B) The range would only include positive integers.
C) The range would only include negative integers.
D) The range would include all real numbers.
The range would only include positive integers.
Answer B
A company mixes pecans, cashews, peanuts, and walnuts to make a batch of mixed nuts. About 15.4% of the mixed nuts in a batch are pecans. If a batch contains 77 pounds of pecans, how many pounds of mixed nuts are in a batch altogether? Enter your answer in the box.
Answer:
500 lb
Step-by-step explanation:
You have to make a proportion:
[tex]\frac{part}{whole} = \frac{percent}{100}[/tex]
77 lb is part of the whole weight ( which we don't know) so 77 will go on top
The problem tells us that 15.4% of the total weight is pecans so 15.4 will go over 100 (since % are out of 100)
[tex]\frac{77}{x} = \frac{15.4}{100}[/tex]
Then you cross multiply giving you: 7700 = 15.4x
then you divide 15.4 to both sides to isolate x which will give you 500
Final answer:
To find the total weight of a batch of mixed nuts where pecans make up 15.4% and weigh 77 pounds, we set up a proportion and solve for the total weight, resulting in 500 pounds for the whole batch.
Explanation:
The question asks how many pounds of mixed nuts are in a batch altogether if 77 pounds are pecans, which represent 15.4% of the mix. To find the total weight, we need to set up a proportion where 15.4% corresponds to 77 pounds, and we want to find 100% (the whole mix).
We can set up the equation like so: 15.4 / 100 = 77 / x, where x stands for the total weight of the mixed nuts. To find x, we solve for x using algebra: x = 77 / (15.4 / 100). When you perform the calculation, the result is x = 500 pounds. So, the batch of mixed nuts weighs 500 pounds in total.
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Pyramid A is a square pyramid with a base side length of 9 inches and a height of 10 inches. what is the volume
Check the picture below.
[tex]\bf \textit{volume of a pyramid}\\\\ V=\cfrac{1}{3}Bh~~ \begin{cases} B=&area~of\\ &its~base\\ h=&height\\ \cline{1-2} B=&\stackrel{9\times 9}{81}\\ h=&10 \end{cases}\implies V=\cfrac{1}{3}(81)(10)\implies V=270[/tex]
Let A = {x | x < 5} and B = {x | x ≤ 7}. Find A B.
Answer:
A B = {x | x < 5}
Step-by-step explanation:
The domain of A B will be given by {x | x < 5}
The domain of A is given as {x | x < 5} while that of B is {x | x ≤ 7}. From this we can infer that the domain of A is a subset of B since A is contained in B. The domain of A B is simply the intersection of these two sets which is A.
A rectangular ower garden is 5.3 yards wide and 9.4 yards long. A uniform path of
width 2 yards is laid around the garden. Find the area of the path.
Answer:
74.8 square yards
Step-by-step explanation:
The centerline of the path is a rectangle 5.3+2 = 7.3 yards wide and 9.4+2 = 11.4 yards long. The perimeter of that rectangle is 2(7.3+11.4) = 37.4 yards long. The area of the path is this length times the width of the path:
path area = (37.4 yd)(2 yd) = 74.8 yd²
The area of the path is 74.8 square yards.
First, we calculate the area of the garden:
[tex]\[ A_{\text{garden}} = \text{length} \times \text{width} = 9.4 \text{ yards} \times 5.3 \text{ yards} \][/tex]
[tex]\[ A_{\text{garden}} = 49.82 \text{ square yards} \][/tex]
Next, we need to find the area of the entire region including the path. The path adds an additional width of 2 yards on all sides of the garden.
The total length and width of the region including the path are:
[tex]\[ \text{Total length} = 9.4 \text{ yards} + 2 \times 2 \text{ yards} = 13.4 \text{ yards} \][/tex]
[tex]\[ \text{Total width} = 5.3 \text{ yards} + 2 \times 2 \text{ yards} = 9.3 \text{ yards} \][/tex]
Now we calculate the area of the entire region including the path:
[tex]\[ A_{\text{total}} = \text{Total length} \times \text{Total width} = 13.4 \text{ yards} \times 9.3 \text{ yards} \][/tex]
[tex]\[ A_{\text{total}} = 124.62 \text{ square yards} \][/tex]
Finally, we subtract the area of the garden from the total area to find the area of the path:
[tex]\[ A_{\text{path}} = A_{\text{total}} - A_{\text{garden}} \][/tex]
[tex]\[ A_{\text{path}} = 124.62 \text{ square yards} - 49.82 \text{ square yards} \][/tex]
[tex]\[ A_{\text{path}} = 74.8 \text{ square yards} \][/tex].
Find the maximum value of the function for the polygonal convex set determined by the given system of inequalities (Picture provided)
Answer:
- The maximum value is 86 occurs at (8 , 7)
Step-by-step explanation:
* Lets remember that a function with 2 variables can written
f(x , y) = ax + by + c
- We can find a maximum or minimum value that a function has for
the points in the polygonal convex set
- Solve the inequalities to find the vertex of the polygon
- Use f(x , y) = ax + by + c to find the maximum value
∵ 3x + 4y = 19 ⇒ (1)
∵ -3x + 7y = 25 ⇒ (2)
- Add (1) and (2)
∴ 11y = 44 ⇒ divide both sides by 11
∴ y = 4 ⇒ substitute this value in (1)
∴ 3x + 4(4) = 19
∴ 3x + 16 = 19 ⇒ subtract 16 from both sides
∴ 3x = 3 ⇒ ÷ 3
∴ x = 1
- One vertex is (1 , 4)
∵ 3x + 4y = 19 ⇒ (1)
∵ -6x + 3y = -27 ⇒ (2)
- Multiply (1) by 2
∴ 6x + 8y = 38 ⇒ (3)
- Add (2) and (3)
∴ 11y = 11 ⇒ ÷ 11
∴ y = 1 ⇒ substitute this value in (1)
∴ 3x + 4(1) = 19
∴ 3x + 4 = 19 ⇒ subtract 4 from both sides
∴ 3x = 15 ⇒ ÷ 3
∴ x = 5
- Another vertex is (5 , 1)
∵ -3x + 7y = 25 ⇒ (1)
∵ -6x + 3y = -27 ⇒ (2)
- Multiply (1) by -2
∴ -6x - 14y = -50 ⇒ (3)
- Add (2) and (3)
∴ -11y = -77 ⇒ ÷ -11
∴ y = 7 ⇒ substitute this value in (1)
∴ -3x + 7(7) = 25
∴ -3x + 49 = 25 ⇒ subtract 49 from both sides
∴ -3x = -24 ⇒ ÷ -3
∴ x = 8
- Another vertex is (8 , 7)
* Now lets substitute them in f(x , y) to find the maximum value
∵ f(x , y) = 2x + 10y
∴ f(1 , 4) = 2(1) + 10(4) = 2 + 40 = 42
∴ f(5 , 1) = 2(5) + 10(1) = 10 + 10 = 20
∴ f(8 , 7) = 2(8) + 10(7) = 16 + 70 = 86
- The maximum value is 86 occurs at (8 , 7)
Answer:
B (5, 1)
Step-by-step explanation:
** WILL GIVE 15 POINTS FOR THIS ONE QUESTION + BRAINLIEST **
The graph below shows the solution to a system of inequalities:
Which of the following any qualities is modeled by the graph?
Answer:
x + 4y ≤ 15; y ≥ 0
Step-by-step explanation:
The graph doesn't do a very good job of modeling any of the given equations. However, the equations listed above seem the best fit.
The slope of the top (left) line is negative, so the equation will be of the form ...
x + 4y = something
When y=0, x=15, so the "something" is expected to be 15.
However, the line appears to go through points (6, 2) and (-2, 4). Both of these points are on the line x + 4y = 14.
The graph is shaded below the line so the values of x and y that are in the shaded area will add to less than 15 (or 14). Hence, the inequality will be ...
x + 4y ≤ something . . . . . part of the 3rd answer choice
The fact that the shading does not go below y=0 means the other limit is ...
y ≥ 0 . . . . . part of every answer choice.