The absolute value of 8|Cosθ| is 8√(x² - 8²)/|x|.
The value of the angle θ is Sin−1 (8/x). We need to find the absolute value of 8|Cosθ|.
θ = Sin−1 (8/x)
Sinθ = 8/x
We know the trigonometric identity that Sin²θ + Cos²θ = 1.
Trigonometry is a field of mathematics that explores the connections between triangle side lengths and angles.
(8/x)² + Cos²θ = 1.
Cos²θ = 1 - (8/x)²
Cos²θ = (x² - 8²)/x²
Cosθ = √[(x² - 8²)/x²]
Cosθ = √(x² - 8²)/x
Multiply both the sides with 8.
8Cosθ = 8√(x² - 8²)/x
Apply modulus on both the sides.
A modulus function is one that returns the absolute value of a number or variable.
8|Cosθ| = 8√(x² - 8²)/|x|
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4. Jacob bought some tickets to see his favorite group, and it cost $76. The relationship between the adult tickets, a, and the student's tickets, s, can be expressed by the equation 10a + 8C = 76. If he bought 4 adult ticket, then how student's tickets did he buy? If he bought 2 student ticket, then how adult's tickets did he buy? Which equation shows the number of student tickets as a function of the number of adult tickets? A. C= 68 – 10a B.C=76 – 10a C. C= -4/5a +38/5 D. C=-5/4a+19/2
Given the equation:
[tex]10a+8c=76[/tex]If Jacob bought 4 adult tickets, then a = 4, so we can solve for c:
[tex]\begin{gathered} a=4 \\ \Rightarrow10(4)+8c=76 \\ \Rightarrow8c=76-40=36 \\ \Rightarrow c=\frac{36}{8}=\frac{9}{2}=4.5 \\ c=4.5 \end{gathered}[/tex]therefore, Jacob bought 4 or 5 students tickets.
Now, if Jacob bought 2 student tickets, then c=2 and for 'a' we have the following:
[tex]\begin{gathered} c=2 \\ \Rightarrow10a+8(2)=76 \\ \Rightarrow10a=76-16=60 \\ \Rightarrow a=\frac{60}{10}=6 \\ a=6 \end{gathered}[/tex]therefore, Jacob bought 6 adult tickets.
Finally, to find the equation that shows the number of student tickets as a function of adult tickets, we have to solve for 'c' to get the following:
[tex]\begin{gathered} 10a+8c=76 \\ \Rightarrow8c=76-10a \\ \Rightarrow c=-\frac{10}{8}a+\frac{76}{8}=-\frac{5}{4}a+\frac{19}{2} \\ c=-\frac{5}{4}a+\frac{19}{2} \end{gathered}[/tex]therefore, the function would be c = -5/4a +19/2
a square base pyramid is shown below. find its surgace area. Round to the nearest tenth
Given data
Height = 16.8 ft
Slant height = 19.3 ft
First, you find the base of the right angle triangle in the daigram.
Opposite = 16.8 ft
Hypotenuse = 19.3 ft
Adjacent = b
[tex]\begin{gathered} \text{Appy pythagorus theorem} \\ \text{Opp}^2+Adj^2=Hypotenuse^2 \\ 16.8^2+b^2=19.3^2 \\ 282.24+b^2\text{ = 372.49} \\ b^2=372.49\text{ - 282.24} \\ b^2\text{ = 90.25} \\ b\text{ = }\sqrt[\square]{90.25} \\ b\text{ = 9.5} \end{gathered}[/tex]Next,
The side of the base of the pyramid = 2 x b
= 2 x 9.5
= 19
The square measure 19 ft
To find the surface area of the pyramid, sum the areas of the square base and the area of the four triangles.
Area of the square = 19 x 19 = 361
[tex]\begin{gathered} \text{Area of the four triangles = }\frac{1}{2}\text{ base x height} \\ \text{ = 0.5 x 19 x 19.3} \\ \text{ = 183.35} \\ \text{Area of the four triangle = 4 x 183.35 = 733.4} \end{gathered}[/tex]Toal surface area of the figure = 733.4 + 361
= 1094.4
Use f(x) = 5x − 4 and g(x) = 3 − x2 to evaluate the expression. (a) (f ∘ g)(−2) (b) (g ∘ f)(−2)
The composite functions are evaluated as:
a. (f ∘ g)(−2) = -9
b. (g ∘ f)(−2) = - 193
How to Solve Composite Functions?Given the functions,
f(x) = 5x − 4
g(x) = 3 − x²
a. To find the composite function, (f ∘ g)(−2), we will replace g(-2) instead of x in the function f(x).
Therefore, we would have:
(f ∘ g)(−2) = f(g(-2))
f(g(-2)) = 5(3 − (-2²)) − 4
f(g(-2)) = 5(3 − 4) − 4
f(g(-2)) = 5(-1) − 4
f(g(-2)) = -5 − 4
f(g(-2)) = -9
Therefore, (f ∘ g)(−2) = -9.
b. Also, the composite function (g ∘ f)(−2) would be evaluated by replacing f(-2) instead of x in g(x).
Therefore:
(g ∘ f)(−2) = g(f(-2))
g(f(-2)) = 3 − (5(-2) − 4)²
g(f(-2)) = 3 − (-10 − 4)²
g(f(-2)) = 3 − (-14)²
g(f(-2)) = 3 − 196
g(f(-2)) = -193
Therefore, (g ∘ f)(−2) = - 193
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Stephanie was making chocolate chip cookies the recipe called for 9 chocolate chip cookie if Stephanie had a total of 108 chocolate chips how many cookies could she make
Given :
the recipe called for 9 chocolate chip cookie
The total chocolate chips = 108
So, the number of cookies = 108/9 = 12
The approximate areas of Wisconsin and South Carolina are listed below:
Wisconsin: 1.7 x 105 square kilometers
South Carolina: 8.29 × 104 square kilometers
How much larger is Wisconsin? Express your answer using scientific notation.
Step-by-step explanation:
you mean
1.7 × 10⁵ square kilometers (km²) and
8.29 × 10⁴ km²
1.7 × 10⁵ = 17 × 10⁴
how much larger is this than
8.29 + 10⁴ ?
(17 - 8.29) × 10⁴ = 8.71 × 10⁴ km²
so, Wisconsin is 8.71 × 10⁴ km² larger than South Carolina.
Which equation has the solution x = 5?
2x 8 = -2
52 – 7 = 12
-
7x - 4 = 101
9x - 2 = 47
Answer:
I think your missing some signs
write the letter of the table that corresponds with the graph.Explain your answer.
for the table X :
for the table R :
For tabel V :
For tabel Q :
The telephone cable in the illustration currently runs from A to B to C to D.How much cable ( in yards) is required to run from A to D directly? yd
Given
[tex]\begin{gathered} A\text{ to B =106 yd} \\ B\text{ to C= 72yd} \\ C\text{ to D=48 yd} \end{gathered}[/tex]Solution
[tex]\begin{gathered} P\text{ to D = 106+48} \\ P\text{ to D =154} \end{gathered}[/tex]So to find A to D directly, We use pythagoras
[tex]\begin{gathered} AD^2=154^2+72^2 \\ AD^2=23716+5184 \\ AD^2=28900 \\ Take\text{ the square root of both sides} \\ AD=\sqrt[]{28900} \\ AD\text{ =170 } \end{gathered}[/tex]The final answer
170 yd is required to run from A to D directly
Find the absolute maximum and minimum for the given graph. Give your answer as an ordered pair. 5 3 2. 1 2 3 4 5 Absolute maximum: Absolute minimum:
The highest point as well as coordinates on the graph is the absolute maximum and it's coordinates. From the graph, the highest point is where = 0 and y = 4
The coordinate is (0, 4)
The lowest point as well as coordinates on the graph is the absolute minimum and it's coordinates. From the graph, the highest point is where = - 3 and y = - 5
The coordinate is (- 3, - 5)
Find the slope of the line that passesthrough these two points.Point 1Point 2(-4,6) (-1,3)YıX2 Y2y2-yimX2-X1m = [?]X1
The slope m of a line passing through two points A (x₁, y₁) and B (x₂, y₂) is expressed as
[tex]\begin{gathered} m\text{ = }\frac{y_2-y_1}{x_2-x_1}\text{ ----- equation 1} \\ \text{where} \\ (x_1,y_1)\Rightarrow coordinate\text{ of point A} \\ (x_2,y_2)\Rightarrow coordinate\text{ of point B} \end{gathered}[/tex]Given the points: (-4, 6), (-1, 3).
This implies that
[tex]\begin{gathered} x_1=-4, \\ y_1=6, \\ x_2=-1, \\ y_2=3 \end{gathered}[/tex]Thus, substitute the above values into equation 1.
[tex]\begin{gathered} m\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ \text{thus,} \\ m=\frac{3-6}{-1-(-4)} \\ =\frac{-3}{-3} \\ \Rightarrow m=-1 \end{gathered}[/tex]Hence, the
A brand of frozen green beans lists a weight of 32 ounces on its bag. Because of variability in the manufacturing process, the bags often contain slightly more, or less, than 32 ounces of green beans. An inspector takes a random sample of 25 bags of green beans and records their weights. The weights and their relative frequencies are summarized in the histogram below.
A histogram titled Green Beans has actual weight (ounces) on the x-axis, and relative frequency on the y-axis. 31.8 to 31.9, 0.04; 31.9 to 32.0, 0.04; 32 to 32.1, 0.12; 32.1 to 32.2, 0.2; 32.2 to 32.3, 0.36; 32.3 to 32.4, 0.23.
Which interval contains the median bag weight?
31.9–32.0 ounces
32.0–32.1 ounces
32.1–32.2 ounces
32.2–32.3 ounces
The mode of the data lies at the end of the histogram, one can find that more values are concentrated at the ending of histogram, so the data is skewed data. Hence option 2: 32.0–32.1 ounces is the more appropriate.
As per the question statement, a brand of frozen green beans lists a weight of 32 ounces on its bag but because of variability in the manufacturing process, the bags often contain slightly more, or less, than 32 ounces of green beans then an inspector takes a random sample of 25 bags of green beans and records their weights and weights and their relative frequencies are summarized and an histogram was plotted.
A histogram titled Green Beans has been defined by actual weight (ounces) on the x-axis, and the relative frequency on the y-axis.
31.8 to 31.9, 0.04; 31.9 to 32.0, 0.04; 32 to 32.1, 0.12; 32.1 to 32.2, 0.2; 32.2 to 32.3, 0.36; 32.3 to 32.4, 0.23.
So, the mode of the data lies at the end of the histogram, one can find that more values are concentrated at the ending of histogram, so the data is skewed data. Hence option 2: 32.0–32.1 ounces is the more appropriate.
Histogram: A diagram with rectangles whose width is equal to the class interval and whose size is related to the frequency of a variable.Skewed data: When a collection of data deviates from the symmetrical bell curve, or normal distribution, it is said to have skew.To learn more about Histogram, click on the link given below:
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This figure has two intersecting lines and a ray. What is the value of x? What is the measure of the angles? I NEED FULL DETAIL
The value of x in the intersecting lines is 7 and the measure of the angles are 38 and 52 degrees respectively.
How to solve angles?The sum of angles on a straight line is 180 degrees.
Complementary angles are angles that sum up to 90 degrees.
Therefore,
3x + 17 + 6x + 10 = 90 (complementary angle)
combine like terms
3x + 17 + 6x + 10 = 90
3x + 6x + 17 + 10 = 90
9x + 27 = 90
subtract 27 from both sides of the equation
9x + 27 = 90
9x + 27 - 27 = 90 - 27
9x = 63
divide both sides by 9
9x / 9 = 63 / 9
x = 7
3(7) + 17 = 21 + 17 = 38°
6(7) + 10 = 52°
Therefore, the two angles are 38 degrees and 52 degrees respectively.
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(4, -13) and (8,-8) slope formula
Point A (4, -13)
Point B (8, -8)
Slope formula
[tex]\begin{gathered} m=\frac{-8-(-13)}{8-4} \\ m=\frac{-8+13}{4} \\ m=\frac{5}{4} \\ \end{gathered}[/tex]The slope would be 5/4
For the equation, 2x+y=6, complete the following ordered pairs: (0,_), (_,0), (_,-6)
Answers in bold
(0, 6)
(3, 0)
(6, -6)
==============================================
Explanation:
The first point given is (0, _) where we don't know what goes in the blank just yet. Let's call this unknown y. The point is (0, y)
Plug in x = 0 to solve for y.
2x+y = 6
2*0+y = 6
0+y = 6
y = 6
Therefore, the point is (0,6) which is the y intercept. This is where the graph crosses the y axis.
------------------------
Next we move onto (_,0)
Plug in y = 0 to find x
2x+y = 6
2x+0 = 6
2x = 6
x = 6/2
x = 3
The point (_, 0) updates to (3,0) which is the x intercept. This is where the graph crosses the x axis.
------------------------
Lastly, we'll use y = -6 to find x.
2x+y = 6
2x-6 = 6
2x = 6+6
2x = 12
x = 12/2
x = 6
We go from (_, -6) to (6, -6)
------------------------
We can use a graphing tool like Desmos to visually confirm the answers. See below.
what is the answer to 2 3/5 if converted to a fraction greater than 1
Convert the mixed number into a simple fraction:
2 3/5 = (2x5+3) /5 = 13/5
13/5 > 1
what is 10-6+8/2x3 please help
Answer:
16
Step-by-step explanation:
I’m having trouble I need this answered, it is apart of my ACT prep guide
Question:
Solution:
According to the data of the problem, the series is given by the following expression:
[tex]\sum ^{\infty}_{n\mathop=1}\frac{n}{3^n}=\frac{1}{3^1}+\frac{2}{3^2}+\frac{3}{3^3}+\cdots[/tex]now, remember the ratio test:
Suppose we have the series
[tex]\sum ^{}_{}a_n[/tex]Define,
[tex]L\text{ =}\lim _{n\to\infty}|\frac{a_{n+1}}{a_n}|[/tex]Then,
if L<1, the series is absolutely convergent (and hence convergent).
if
L>1, the series is divergent.
if
L=1 the series may be divergent, conditionally convergent, or absolutely convergent.
Applying this definition to the given series, we obtain:
[tex]L\text{ =}\lim _{n\to\infty}|\frac{(n+1)3^n_{}}{n3^{n+1}_{}}|=\frac{1}{3}<1[/tex]then, the given series is absolutely convergent (and hence convergent). So that, we can conclude that the correct answer is:
In a battle, Iceman beings to freeze iron man's suit. By the end of the battle, Iron Man's suit dropped to -4.5 deF. If Iceman was able to decrease Iron Man's suit by 73.2. What temperature did Iron Man's suit start at?
By solving a linear equation, we can see that the initial temperature of the suit is 68.7F
What temperature did Iron Man's suit start at?
We know that at the end of the battle, Iron Man's suit was at a temperature of -4.5 degrees Fahrenheit.
We know that Iceman decreased Iron Man's temperature by 73.2 F, so, if the initial temperature of the suit is T, then we can write the linear equation:
T - 73.2F = -4.5F
We can solve this equation for T.
T = -4.5F + 73.2F = 68.7F
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ABC-DEF. what is the scale factor of triangle ABC to triangle DEF
in the given triangles the scale factor will be the ratio of the hypotenuse of DEF and the hypotenuse of ABC
so ratio = 30/10 = 3
thus the scale factor is 3
so the value of the sides of ABC is,
x = 27/3
x = 9
y = 18/3
y = 6
Understanding of Multiplying by a Fraction Name: Draw a number line model to represent each multiplication problem. Then solve the problem.2/3×1/2=how do you do this
We have following:
1.
[tex]\frac{2}{3}\cdot\frac{1}{2}=\frac{2\cdot1}{3\cdot2}=\frac{2}{6}=\frac{1}{3}[/tex]2.
[tex]\frac{5}{6}\cdot\frac{3}{4}=\frac{5\cdot3}{6\cdot4}=\frac{15}{24}=\frac{5}{8}[/tex]The earliest known unit of length to be used in a major construction project is the “megalithic yard” used by. Builders of stone-henge in southwestern Britiian about 2600 b.c. If 1 megalithic yard= 2.72 plus minus 0.05 ft, convert this length to inches. (Round to the nearest tenth of an inch.)
1 megalthic yard = 2.722 feet ( this means they multiplied with 2.722 to get to feet)
now we need to convert feet to inches :
1 ft = 12 inches
2.722 ft = x
cross multiply
2.722 x 12 = 1 X
therefore x = 32,664
rounding off to the nearest tenth of an inch is equivalent to 32.6 inches
Urgent!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!A bicycle company produces y blcycles at a cost represented by the polynomial y ^ 2 + 10y + 400, 000 . The revenue for y represented by 3y^ 2 +10y+700. Find a polynomial that represents their profit. If the company only has enough materials to make 400 bicycles , should it make the bicycles ?
In order to calculate the profit, let's subtract the revenue and the cost:
[tex]\begin{gathered} \text{profit}=\text{revenue-cost} \\ \text{profit}=3y^2+10y+700-(y^2+10y+400000) \\ \text{profit}=2y^2-399300 \end{gathered}[/tex]Now, for 400 bicycles, let's calculate the profit:
[tex]\begin{gathered} \text{profit}=2\cdot400^2-399300 \\ \text{profit}=320000-399300 \\ \text{profit}=-79300 \end{gathered}[/tex]Since the profit is negative, the company should not make the bicycles.
What is the solution to -3/7m<21?
m < 49
m > 49
m > -49
m < -49
Answer:
[tex]m>-49[/tex]
Step-by-step explanation:
[tex]m>21(-7/3)=-49[/tex]
7. Brian is packing boxes that can contain two types of items, board games and remote control cars. Board games weigh 3 pounds and remote controlled cars weigh 1.5 pounds, and the box can hold no more than 24 pounds. Also, in each box, the amount of remote control cars must be at least 4 times the amount of board games. Let x represent the number of board games. Let y represent the number of remote controlled cars.A. Write the system of inequalities that represents this situation. You should have 2 different inequalities that you wrote. B. Graph the system of inequalities on the coordinate plane below.
A)
[tex]\begin{gathered} 3x+1.5y\leq24\Rightarrow inequality(1) \\ y\ge4x\rightarrow inequality(2) \end{gathered}[/tex]Explanation
Step 1
Let x represents the number of board games
Let y represent the number of remote controlled cars
i)
a)Board games weigh 3 pounds
b) remote-controlled cars weigh 1.5 pounds
The box can hold no more than 24 pounds( in other words it must be equal or less thant 24),so
[tex]3x+1.5y\leq24\Rightarrow inequality(1)[/tex]ii) in each box, the amount of remote control cars must be at least 4 times the amount of board games( in other words, the number of remote control cars must be equal or greater than 4 times the amount of board games, so,
hence
[tex]y\ge4x\rightarrow inequality(2)[/tex]so,
A)
[tex]\begin{gathered} 3x+1.5y\leq24\Rightarrow inequality(1) \\ y\ge4x\rightarrow inequality(2) \end{gathered}[/tex]Step 2
graph the inequalities
a) set the sign = to convert the inequality in a funcion, isolate for y
b) fnd 2 coordinates of the line
C) draw the line
[tex]\begin{gathered} \leq\rightarrow\text{ continuous line} \\ \ge\rightarrow\text{ cointinuous line} \end{gathered}[/tex]i)
[tex]\begin{gathered} 3x+1.5y=24 \\ 1.5y=24-3x \\ y\leq\frac{24-3x}{1.5} \\ y=16-2x \\ \text{when x= 0} \\ y=16-0 \\ so,P1(0,16) \\ \text{when =3} \\ y=16-2(3) \\ y=16-6=10 \\ so\text{, P2(3,10)} \end{gathered}[/tex]draw a line(continuosus) that passes trougth P1 and P2
ii)
[tex]\begin{gathered} y\ge4x\rightarrow y=4x \\ \text{when x=0} \\ y=4\cdot0=0 \\ so\text{ , P3(}0,0) \\ \text{and when x= 2} \\ y=4(2)=8 \\ so,\text{ P4}(2,8) \end{gathered}[/tex]draw a line(continuosus) that passes trougth P3 and P4
I hope this helps you
A point is plotted on a coordinate grid at (-3, 4). How far is the point from point (0, 0)?
The point at (-3, 4) is at a distance of 5 units from the point (0, 0).
How far is the point from (0, 0)?For two points (x₁, y₁) and (x₂, y₂), the distance between them is given by the formula:
distance = √( (x₁ - x₂)² + (y₁ - y₂)²)
In this case, we want to get the distance between (-3, 4) and (0, 0), using the above formula we will see that the distance is:
distance = √( (-3 - 0)² + (4 - 0)²) = √25 = 5
The distance is 5 units.
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rrange the equations in increasing order of the value of their solutions.-2=4–1793+4 = -1.11-163.20 +5.7 = -2.50110.10-1.60+44 = -7!ResetNea
-6, -2, 1, 2
Explanation:
We need to solve each expression individually:
1) 1/4 x + 5/2 x - 2 = 4 - 1/4 x
Collecting like terms:
1/4 x + 5/2 x + 1/4 x = 4 + 2
[tex]\begin{gathered} \frac{x\text{ + 5x(2) + x}}{4}=\text{ 6} \\ \frac{12x}{4}=\text{ 6} \\ 3x\text{ = 6} \\ x\text{ =2} \end{gathered}[/tex]2) 7.9x + x + 4 = -1.1x - 16
Collecting like terms:
7.9x + x + 1.1x = -16 -4
10x = -20
x = -20/10
x = -2
3) 3.2x + 5.7 = -2.5x
Collecting like terms:
3.2x + 2.5x = 5.7
5.7x = 5.7
x = 5.7/5.7
x = 1
4) 10.1x - 1.6x + 44 = -7
Collecting like terms:
8.5x = -7-44
8.5x = -51
x = -51/8.5
x = -6
The solutions: 2, -2, 1, -6
Arranging in increasing order of their solution (smallest to the highest):
-6, -2, 1, 2
a. What is KL? __. b. What is the coordinate of the midpoint of KL? __?c. Point C lies between points K and L. The distance between points K and C is __ of KL. What is the coordinate of point C? __.
Given the graph of the line segment KL on the number line
As shown:
The coordinates of k = -9
The coordinates of L = 15
a. What is KL?
[tex]\begin{gathered} KL=15-(-9)=15+9=24 \\ KL=24 \end{gathered}[/tex]b. What is the coordinate of the midpoint of KL?
Let the midpoint = M
[tex]M=\frac{K+L}{2}=\frac{-9+15}{2}=\frac{6}{2}=3[/tex]So, the coordinates of the midpoint = 3
35Todd forgot the first two numbers of his locker combination. The numbers can be any number 1 through 6. What istprobability that he will guess the first number correctly and the second number incorrectly?OAOB.olaroc.OD.ResetSubmit
Answer:
A. 5/36
Explanation:
The total number of possible number choice = 6
Only 1 out of 6 can be correct, thus:
[tex]P(\text{he will guess the first number correctly)}=\frac{1}{6}[/tex]There are 5 incorrect numbers, therefore:
[tex]P(\text{he will guess the }\sec ond\text{ number incorrectly)}=\frac{5}{6}[/tex]Therefore, the probability that he will guess the first number correctly and the second number incorrectly:
[tex]\begin{gathered} =\frac{1}{6}\times\frac{5}{6} \\ =\frac{5}{36} \end{gathered}[/tex]The correct choice is A.
QUESTION 1
The ingredients for Apple Crumble cost you $1.45 per serving. If your bakery menu lists a price of $4.95 for your Apple Crumble, then what percent
of the sale goes to the food cost?
The percentage of sale that goes to the food cost is 341.3%.
The ingredients for Apple crumble cost = $1.45 per serving.
The selling price of the Apple crumble = $4.95
percentage of the sale that goes to the food cost = ?
according to the question, we formulate:
% sale that goes to the food cost = cost of ingredients/selling price of the apple crumble×100
% sale = 4.95/1.45 × 100
% sale = 3.41 × 100
% sale = 341.3%
Hence the percentage of sale that goes to the food cost is 341.3%.
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Just need a simple explanation.
