Answer
Option C is correct.
AB = 6.3 units
Explanation
In a right angle triangle, the side opposite the right angle is the Hypotenuse, the side opposite the given angle that is non-right angle is the Opposite and the remaining side is the Adjacent.
Using trignometric relations, we can see that TOA wil work for this
Tan θ = (Opp/Adj)
θ = 40°
Opp = AB = ?
Adj = AC = 7.5 units
Tan 40° = (Opp/7.5)
Opp = AB = 7.5 (Tan 40°) = 6.3 units
Hope this Helps!!!
A jar of marbles contains the following: two red marbles, three white marbles, five blue marbles, and seven green marbles.What is the probability of selecting a red marble from a jar of marbles?
ANSWER
[tex]\frac{2}{17}[/tex]EXPLANATION
Given;
[tex]\begin{gathered} n(Red)=2 \\ n(white)=3 \\ n(blue)=5 \\ n(green)=7 \end{gathered}[/tex]The total number of marble is;
[tex]n(Total)=2+3+5+7=17[/tex]Recall, the probability of an event can be calculated by simply dividing the favorable number of outcomes by the total number of the possible outcome
Hence, the probability of selecting a red marble is;
[tex]\begin{gathered} Prob(Red)=\frac{n(Red)}{n(Total)} \\ =\frac{2}{17} \end{gathered}[/tex]which of these is closest to the unit distance between points M and M' ?
the coordinate of M is (-3, -5)
it is given that M is translated 6 unit right , and 5 unit up.
so the coordinate of M' is (-3+6 , -5 + 5) = (3, 0)
so, the distance between M and M' is,
[tex]d=\sqrt[]{(3-(-3))^2+(0-(-5))^2}[/tex][tex]\begin{gathered} d=\sqrt[]{6^2+5^2} \\ d=\sqrt[]{36+25} \\ d=\sqrt[]{61} \end{gathered}[/tex]d = 7.81
so, the closest to the unit distance is 8
thus, the answer is option D
A sample of 7 students was taken to see how many pencils they were carrying.2, 3, 2, 5, 7, 1, 41. Calculate the sample mean.2. Calculate the standard deviation.
Sample mean = 3.43
sample standard deviation = 2.07
Explanation:
Given: 2, 3, 2, 5, 7, 1, 4
Total numbers = 7
1) Sample mean is calculated by finding the average of the data set
[tex]\begin{gathered} \text{Sample mean = }\frac{su\text{ m of data set}}{number\text{ of data set}} \\ \text{sample mean = }\frac{2+3+2+5+7+1+4}{7} \\ \text{sample mean = 24/7 } \\ \text{sample mean = }3.43 \end{gathered}[/tex]2) We have sample standard deviation and population standard deviation.
SInce the question asked for sample mean, we will be calculating sample standard deviation.
Standard deviation is calculated as:
[tex]\begin{gathered} s\tan dard\text{ deviation = }\sqrt[]{\frac{\sum^{}_{}(x_1-mean)^2}{N-1}} \\ \\ s\tan dard\text{ deviation = }\sqrt[]{\frac{\sum ^{}_{}(2-3.43)^2+(3-3.43)^2+(2-3.43)^2+(5-3.43)^2+(7-3.43)^2+(1-3.43)^2+\mleft(4-3.43\mright)^2}{7-1}} \\ s\tan dard\text{ deviation = }\sqrt[]{\frac{25.7143}{6}}\text{ = }\sqrt[]{4.2857} \\ s\tan dard\text{ deviation = }2.07 \end{gathered}[/tex]
What is the value of the expression shown? 5 – a(3² + (ab + 2)² – 7) when a = 2 and b = –3
The expression has a value of -31 when a = 2 and b = –3
How to evaluate the expression?From the question, the expression is given as
5 – a(3² + (ab + 2)² – 7)
Also, we have the values of the variables to be
a = 2 and b = –3
Substitute a = 2 and b = –3 in the expression 5 – a(3² + (ab + 2)² – 7)
So, we have the following equation
5 – a(3² + (ab + 2)² – 7) = 5 – 2 * (3² + (2 * -3 + 2)² – 7)
Evaluate the expressions in the bracket
5 – a(3² + (ab + 2)² – 7) = 5 – 2 * (3² + (-4)² – 7)
Evaluate the exponents
5 – a(3² + (ab + 2)² – 7) = 5 – 2 * (9 + 16 – 7)
So, we have
5 – a(3² + (ab + 2)² – 7) = 5 – 2 * 18
This gives
5 – a(3² + (ab + 2)² – 7) = 5 – 36
Evaluate the difference
5 – a(3² + (ab + 2)² – 7) = -31
Hence, the value of the expression is -31
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It’s supposed to answer in simplest formIf I die is rolled one time find the probability of
A die can have 6 possible outcomes.
The probability of an event is calculated using the formula:
[tex]P=\frac{number\text{ }of\text{ }required\text{ }outcomes}{number\text{ }of\text{ }total\text{ }outcomes}[/tex]Therefore, the probability of rolling a 1 is gotten to be:
[tex]P=\frac{1}{6}[/tex]The probability is 1/6.
give the coordinates of the image of each point under a reflection across to given line.(0,8); y=x
Answer:
(8, 0)
Explanation:
Whenever a point (x,y) is reflected across the line y=x, the transformation rule is given below:
[tex](x,y)\to(y,x)[/tex]That is, the x-coordinate and y-coordinate change places.
Therefore, the image of the point (0,8) when reflected across the line y=x is:
[tex](8,0)[/tex]The correct answer is (8,0).
The ratio of the lengths of corresponding sides of two similar triangles is 5:8. The smaller triangle has an area of 87.5cm^2. What is the area of the larger triangle
Question:
Solution:
Remember the following theorem: the ratio of the areas of two
similar triangles is equal to the ratio of the squares of their corresponding sides. Then, here A1 and A2 are areas of two similar triangles, and S1 and S2 are their corresponding sides respectively :
S1 : S2 = 5 : 8
then
[tex]\frac{S1}{S2}=\frac{5}{8}[/tex]now, A1 = 87.5. Thus, according to the theorem, we get the following equation:
[tex](\frac{5}{8})^2=\frac{87.5}{A2}[/tex]this is equivalent to:
[tex]\frac{25}{64}=\text{ }\frac{87.5}{A2}[/tex]by cross-multiplication, this is equivalent to:
[tex](A2)(25)\text{ = (64)(87.5)}[/tex]solving for A2, we get:
[tex]A2\text{ =}\frac{(64)(87.5)}{25}=224[/tex]so that, we can conclude that the correct answer is:
The area of the larger triangle is
[tex]224cm^2[/tex]
find the measure of each of the other six angles
The measure of angle 1 is 71º, we can find this, because angle 1 and angle x form a straight line of 180º, so 180º - 109º = 71º
The measure of angle 2 is also 71º, we can use the vertical angles propierty, then m∠1 = m∠2
The measure of angle 3 is 109º, we can use again the vertical angles theorem to find that m∠x = m∠3
Themeasure of angle 7 is 109º. We need to use the alternating exterior angles theorem. Since angle x and angle 7 are not between the parallel lines they're exterior angles; and since they're on opposite sides of the transversal line, they're alternates. Then the theorem says that m∠x = m∠7
The measure of angle 6 is 71º, again we're using the fact that angle 7 and angle 6 forms a straight line, then m∠6 = 180º - 109º = 71º
Now we can find the lasts two measures using the vertical angles theorem.
The measure of angle 5 is 71º, because m∠6 = m∠5
The measure of angle 4 is 109º, because m∠7 = m∠4
using first principles to find derivatives grade 12 calculus help image attached much appreciated
Given: The function below
[tex]y=\frac{x^2}{x-1}[/tex]To Determine: If the function as a aximum or a minimum using the first principle
Solution
Let us determine the first derivative of the given function using the first principle
[tex]\begin{gathered} let \\ y=f(x) \end{gathered}[/tex]So,
[tex]f(x)=\frac{x^2}{x-1}[/tex][tex]\lim_{h\to0}f^{\prime}(x)=\frac{f(x+h)-f(x)}{h}[/tex][tex]\begin{gathered} f(x+h)=\frac{(x+h)^2}{x+h-1} \\ f(x+h)=\frac{x^2+2xh+h^2}{x+h-1} \end{gathered}[/tex][tex]\begin{gathered} f(x+h)-f(x)=\frac{x^2+2xh+h^2}{x+h-1}-\frac{x^2}{x-1} \\ Lcm=(x+h-1)(x-1) \\ f(x+h)-f(x)=\frac{(x-1)(x^2+2xh+h^2)-x^2(x+h-1)}{(x+h-1)(x-1)} \end{gathered}[/tex][tex]\begin{gathered} f(x+h)-f(x)=\frac{x^3+2x^2h+xh^2-x^2-2xh-h^2-x^3-x^2h+x^2}{(x+h-1)(x-1)} \\ f(x+h)-f(x)=\frac{x^3-x^3+2x^2h-x^2h-x^2+x^2+xh^2-2xh-h^2}{(x+h-1)(x-1)} \\ f(x+h)-f(x)=\frac{x^2h+xh^2-2xh+h^2}{(x+h-1)(x-1)} \end{gathered}[/tex][tex]\begin{gathered} \frac{f(x+h)-f(x)}{h}=\frac{x^{2}h+xh^{2}-2xh+h^{2}}{(x+h-1)(x-1)}\div h \\ \frac{f(x+h)-f(x)}{h}=\frac{x^2h+xh^2-2xh+h^2}{(x+h-1)(x-1)}\times\frac{1}{h} \\ \frac{f(x+h)-f(x)}{h}=\frac{h(x^2+xh^-2x+h^)}{(x+h-1)(x-1)}\times\frac{1}{h} \\ \frac{f(x+h)-f(x)}{h}=\frac{x^2+xh-2x+h}{(x+h-1)(x-1)} \end{gathered}[/tex]So
[tex]\lim_{h\to0}\frac{f(x+h)-f(x)}{h}=\frac{x^2-2x}{(x-1)(x-1)}=\frac{x(x-2)}{(x-1)^2}[/tex]Therefore,
[tex]f^{\prime}(x)=\frac{x(x-2)}{(x-1)^2}[/tex]Please note that at critical point the first derivative is equal to zero
Therefore
[tex]\begin{gathered} f^{\prime}(x)=0 \\ \frac{x(x-2)}{(x-1)^2}=0 \\ x(x-2)=0 \\ x=0 \\ OR \\ x-2=0 \\ x=2 \end{gathered}[/tex]At critical point the range of value of x is 0 and 2
Let us test the points around critical points
[tex]\begin{gathered} f^{\prime}(x)=\frac{x(x-2)}{(x-1)^2} \\ f^{\prime}(0)=\frac{0(0-2)}{(0-1)^2} \\ f^{\prime}(0)=\frac{0(-2)}{(-1)^2}=\frac{0}{1}=0 \\ f^{\prime}(2)=\frac{2(2-2)}{(2-1)^2}=\frac{2(0)}{1^2}=\frac{0}{1}=0 \end{gathered}[/tex][tex]\begin{gathered} f(0)=\frac{x^2}{x-1}=\frac{0^2}{0-1}=\frac{0}{-1}=0 \\ f(2)=\frac{2^2}{2-1}=\frac{4}{1}=4 \end{gathered}[/tex]The function given has both maximum and minimum point
Hence, the maximum point is (0,0)
And the minimum point is (2, 4)
3. x-intercept 4, y-intercept 2, passes through 5. Center on x = 3, radius 13, passes through Center on the y-axis, radius 5, x-intercept 3 cle having the given center and radius. (b) C (-2,-5), r = 4 (d) C(2, -3), r= 6 ving the given properties. (0,0) (6, 5)
Samantha, this is the solution to problem 5:
With the information given in the statement you can solve for k, where k is the center in y:
(x-h)^2 + (y-k)^2 = r^2
(6-3)^2 + (5-k)^2 = (√(13))^2
(3)^2 + (5-k)^2 = 13
9+(5-k)^2 = 13
(5-k)^2 = 4
√((5-k)^2) = √4
5-k = 2
-k = -3
k = 3
Then the equation of the circle will be
(x-3)^2 + (y-3)^2 = 13
wich choice shows the correct solution to 2544÷8?
ANSWER:
318
STEP-BY-STEP EXPLANATION:
We have the following operation:
[tex]2544÷8[/tex]So the answer is 318
Roberts Company has the following sales budget for the first four months and the year:
January February March April
Budgeted units to sell
200
400
800
950
Total - 2,350
Sales price per unit
$25
$25
$25
$25
Total-$25
Total sales
$5,000
$10,000
$20,000
$23,750
Total - $58,750
What is the new amount of budgeted total sales for March if the budgeted number of units is expected to be 1,100 units instead of 800 units?
A. $27,500
B. $10,000
C. $47,500
D. $66,250
Using some simple mathematical operations we can conclude that the new amount of budgeted total sales is (D) $66,250.
What are mathematical operations?Calculating a value using operands and a math operator is referred to as performing a mathematical "operation." The math operator's symbol has predetermined rules that must be applied to the supplied operands or numbers. A mathematical action is called an operation. Mathematical operations include addition, subtraction, multiplication, division, and finding the root.So, new amount of budgeted total sales for March:
So, we know that:
2350 × 25 = $58,750And 2350 is further:
2350 = 200 + 400 + 800 + 950.Let's replace 800 with 1100.
Now, solve as follows:
200 + 400 + 1100 + 950 = 2,6502,650 × 25 = $66,250Therefore, using some simple mathematical operations we can conclude that the new amount of budgeted total sales is (D) $66,250.
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If f(x)=x squared + 3x - 10 then over which of the following intervals is f(x)<0 ?
Given data:
The given function is f(x)= x^2 +3x-10.
The given inequality is,
[tex]\begin{gathered} f(x)<0 \\ x^2+3x-10<0 \\ x^2+5x-2x-10<0 \\ x(x+5)-2(x+5)<0 \\ (x+5)(x-2)<0 \\ -5Thus, the value of x is -5The length of a new rectangular playing field is 7 yards longer than quadruple the width. If the perimeter of the rectangular playing field is 454 yards, what are its dimensions?
The dimensions of new rectangular playing field are 183 yards and 44 yards, by the concept of perimeter of rectangle.
What is perimeter of rectangle?The whole distance that the sides or limits of a rectangle cover is known as its perimeter. Since a rectangle has four sides, its perimeter will be equal to the sum of those four sides. Given that the perimeter is a linear measurement, the rectangle's perimeter will be expressed in meters, centimeters, inches, feet, etc.
Formula, perimeter of rectangle =2× (length +width)
Given, perimeter of rectangular playing field = 454 yards (equation 1)
Let us assume, width =x
According to question length = 4x+7 (quadruple=4times)
By the above equations,
Perimeter=2×(4x+7+x)
2×(5x+7) =454 (by equation 1)
Dividing the above equation by 2 both the sides
(5x+7) =227
Subtracting the above equation by 7 both the sides
5x=220
Dividing the above equation by 5 both the sides
x=44
Therefore, the required width of new rectangular playing field is 44 yards and length of new rectangular playing field is 183 yards
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Madeline is a salesperson who sells computers at an electronics store. She makes a base pay of $80 each day and then is paid a $20 commission for every computer sale she makes. Make a table of values and then write an equation for P,P, in terms of x,x, representing Madeline's total pay on a day on which she sells xx computers.
I need equation
The equation for 'P', representing Madeline's total pay on a day on which she sells 'x' computers is → P = 80 + 20x.
Given, At an electronics store, Madeline sells computers as a salesperson. She receives a $80-per-day base salary in addition to a $20 commission for each computer she sells.
What is Equation Modelling?
Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We can model the equation for Madeline's total pay as follows -
P = base pay + (number of sold computer) × (cost of 1 computer)
P = 80 + 20x
Therefore, the equation for 'P', representing Madeline's total pay on a day on which she sells 'x' computers is → P = 80 + 20x
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Question 39.Find the inverse of the given function. Graph both functions on the some set of axes and show the line y=x as a dotted line in the graph.
First, to find the inverse of a function, call the original function "x" and call call "x" in the original function as the inverse function:
[tex]\begin{gathered} f(x)=5x+1 \\ x=5f^{-1}(x)+1 \end{gathered}[/tex]Now, we solve for the inverse function:
[tex]\begin{gathered} x=5f^{-1}(x)+1 \\ 5f^{-1}(x)+1=x \\ 5f^{-1}(x)=x-1 \\ f^{-1}(x)=\frac{x}{5}-\frac{1}{5} \end{gathered}[/tex]To graph lines, we can find two points in it and draw a line that passes through both.
Let's pick x = 0 and x = 1 for the first equation:
[tex]\begin{gathered} f(0)=5\cdot0+1=1 \\ f(1)=5\cdot1+1=6 \end{gathered}[/tex]So, we plot the points (0, 1) and (1, 6).
For the inverse, we can simply invet the coordinates, which is the same as picking x = 1 and x = 6:
[tex]\begin{gathered} f^{-1}(1)=\frac{1}{5}-\frac{1}{5}=0 \\ f^{-1}(6)=\frac{6}{5}-\frac{1}{5}=\frac{5}{5}=1 \end{gathered}[/tex]Thus, we have the points (1, 0) and (6, 1).
The line y = x is jus the diagonal that passes though point (0, 0) and (1, 1), for example.
Putting these points and drawing the lines, we get:
An inspector found 18 defective radios during an inspection. If this is 0.024% of the total number of radios inspected, how many radios were inspected?
Total number of defected radios is 18
Let the total number of defective radios be taken as y
If 0.024% of the total number of radios inspected are defective, i.e 0.024% of y
[tex]\frac{0.024}{100}y=18[/tex]Solve for y, by cross multiplying
[tex]\begin{gathered} \frac{0.024}{100}y=18 \\ 0.024y=18\times100 \\ \text{Divide both sides by 0.024} \\ \frac{0.024y}{0.024}=\frac{1800}{0.024} \\ y=75000 \end{gathered}[/tex]Hence, the number of radios inspected, y, is 75000
Boris's cat will be having four kittens. Boris performs asimulation by tossing a coin to model whether thesekittens will be male or female.• Let'heads (H) = female kitten• Let tails (T) = male kittenThe results of the simulation are:
Given:
Boris performs a simulation by tossing a coin to model whether these kittens will be male or female.
The total number of sample space is, N = 10.
Head for female kitten
T for male kitten.
The objective is to find the probability that at least three of the kittens will be male.
Fromthe obtained simulation, the number of sample space with at least thee tail (T) is, n(T)=4
Now, the probability of at least three of the kittens will be male can be calculated by,
[tex]undefined[/tex]convert 7 ounces to grams. Round to the nearest whole number
Answer:
[tex]198\text{ g}[/tex]Explanation:
Here, we want to convert from ounces to grams
Mathematically,we have it that:
[tex]1\text{ ounce = 28.3}495\text{ g}[/tex]7 ounces will be the product of 7 and this
Mathematically,we have this as;
[tex]7\text{ }\times\text{ 28.3495 = }198.4465[/tex]To the nearest whole number, this is 198 g
Consumption and savings if real domestic output is $370 billion and planned investment is $15 billion
The consumption is 355 billion .
Given,
In the question:
Consumption and savings if real domestic output is $370 billion and planned investment is $15 billion.
Now, According to the question:
Based on the given condition,
Formulate;
Aggregate expenditure (consumption)= Output - Savings= Investment
370 - 15
Calculate the sum or difference
= 355billion
Hence, The consumption is 355 billion .
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Sarkis OganesyanCombine Like Terms (Basic, Decimals)May 20, 11:02:29 AMA triangle has side lengths of (1.1p + 9.59) centimeters, (4.5p - 5.2r)centimeters, and (5.3r + 5.4q) centimeters. Which expression represents theperimeter, in centimeters, of the triangle?14.89 + 5.6p + 0.2rO 0.1r + 5.6p + 14.99Submit Answer-0.7pr + 10.7qr + 10.6pq9.7qr + 10.9pr
The sides of the triagle have lengths:
1.1 p + 9.5 q
4.5 p - 5.2 r
5.3 r + 5.4 q
Or:
1.1 p + 0 r + 9.5 q
4.5 p - 5.2 r + 0 q
0 p + 5.3 r + 5.4 q
If we want to calculate the perimeter of the triangle, we just need to sum the three lenghts:
(1.1 + 4.5) p + (-5.2 + 5.3) r + (9.5 + 5.4) q
= 5.6 p + 0.1 r + 14.9 q
A publisher for promising new novel figures fixed costs at $61,000 and variable cost at $1.50 for each book produced if the book is sold to distributors for $15 each how many must be produced and sold for publisher to break even?
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given information
[tex]\begin{gathered} For\text{ the cost price function:} \\ Fixed\text{ cost=\$61,000 = constant} \\ Variable\text{ cost = \$1.50 }\times\text{ number of books} \\ Let\text{ x be the number of books produced} \end{gathered}[/tex]The function for the cost price becomes:
[tex]61000+1.5x[/tex]STEP 2: Get the function for the selling price
The function for the selling price becomes:
[tex]\text{ \$}15x[/tex]STEP 3: Calculate the number of books required to break even
To get the breakeven, the cost price will be equal to selling price. Therefore,
[tex]\begin{gathered} 61000+1.5x=15x \\ Subtract\text{ 1.5x from both sides} \\ 61000+1.5x-1.5x=15x-1.5x \\ 61000=13.5x \\ Divide\text{ both sides by 13.5} \\ \frac{61000}{13.5}=\frac{13.5x}{13.5} \\ 4518.518519=x \\ x\approx4519 \end{gathered}[/tex]Hence, the number of books that must be produced and sold to get a breakeven is approximately 4519
Solve for the remaining angle and sides of the triangle described below. Round to the nearest hundredtheA = 50°. B = 45,a=3
Given:
The angels and sides of the triangle are
A = 50°. B = 45°, and a=3
Aim:
We need to find the angle C and sides c and b.
Explanation:
Use sine law.
[tex]\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}[/tex][tex]\text{ Consider }\frac{\sin A}{a}=\frac{\sin B}{b}\text{ to find side b.}[/tex]Substitute A = 50°. B = 45°, and a=3 in the equation.
[tex]\frac{\sin 50^o}{3}=\frac{\sin 45^o}{b}[/tex][tex]b=\frac{\sin 45^o}{\sin 50^o}\times3[/tex][tex]b=2.77[/tex]Use the triangle sum property to find the angle C.
[tex]A+B+C=180^o[/tex]Substitute A = 50°. and B = 45° in the equation.
[tex]50^o+45^o+C=180^o[/tex][tex]95^o+C=180^o[/tex][tex]C=180^o-95^o[/tex][tex]C=85^o[/tex][tex]\text{ Consider }\frac{\sin A}{a}=\frac{\sin C}{c}\text{ to find side c.}[/tex]Substitute A = 50°. C= 85°, and a=3 in the equation.
[tex]\frac{\sin50^o}{3}=\frac{\sin 85^o}{c}[/tex][tex]c=\frac{\sin 85^o}{\sin 50^o}\times3[/tex][tex]c=3.90[/tex]Final answer:
[tex]C=85^o[/tex][tex]b=2.77[/tex][tex]c=3.90[/tex]Several friends go to a casino and do some gambling. The following are the profits each of these friends make: $120, -$230, $670, -$1020, $250, -$430, and -$60. What is the average profit of this group? A. $100 B. -$100 C. -$1020 D. $397
The average profit of this group is B. -$100.
The average represents the total profits and losses generated by the group of friends, divided by the number in the group.
The average is the data set's mean after performing the mathematical operations of addition and division on the data values.
Friends Profits
A $120
B -$230
C $670
D -$1020
E $250
F -$430
G -$60
Total -$700
Average profit = -$100 (-$700/7)
Thus, we can conclude that the friends generated an average profit of B. -$100 from gambling or a total loss of $700.
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A Snack company can pack 15 granola bars in a box how many boxes are needed for 600 granola bars ?
Answer:40
Step-by-step explanation: 15 bars to a box.
600 bars in total.
600/15= 40
40 boxes of granola bars
Solve for the missing side of the triangle. Round to the hundredths place if needed.
The Pythagoras theorem gives the relation for the right-angle triangle between the perpendicular, base, and hypotenuse thus the perpendicular x will be 14.70.
What is a triangle?A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices.
Triangle is a very common figure to deal with in our daily life.
In a triangle, the sum of all three angles is 180°
As per the given right-angle triangle,
Pythagoras' theorem states that in a right-angle triangle →
Hyp² = Perp² + Base²
In the given triangle Hyp = 21 , Base = 15 and Perp = x
So,
21² = x² + 15²
x² = 21² - 15²
x = √216 = 14.6993 ≈ 14.70
Hence "The value of x for the given right-angle triangle is 14.70 units".
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Could you solve the table
The relation is decreasing by a factor of 2 each time, so:
[tex]\begin{gathered} y-9=-2(x-0) \\ y=-2x+9 \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} y(100)=-2(100)+9 \\ y(100)=-200+9 \\ y(100)=-191 \end{gathered}[/tex]Answer:
-191
hello can you help me with this trigonometry question and this a homework assignment
You have:
sin 2A = -√7/4
In order to determine the value of sin A, first calculate the value of angle A by using sin⁻¹ over the previous equation, just as follow:
sin⁻¹(sin 2A) = sin⁻¹(-√7/4) In this way you cancel out the sin
2A = -41.41° divide by 2 both sides
A = -41.41°/2
A = -20.705°
however, take into account that angle A is in the third quadrant. Then, it is necessary to consider the result A=-20.705° is respect to the negative x-axis.
To obtain the angle respect the positive x-axis (the normal way), you simply sum 180° to 20.705°:
20.705 + 180° = 200.705°
Next, use calculator to calculate sinA:
sin(200.705°) = -0.3535
Please help with the question below (please try to answer in maximum 10/15 minutes).
Solution:
Given the dimensions of the composite figure below
[tex]\begin{gathered} For\text{ the cuboid:} \\ l=12\text{cm} \\ w=4\text{ cm} \\ h=3cm \\ For\text{ the triangular prism:} \\ a=3\text{ cm} \\ b=4\text{ cm} \\ c=13\text{ cm} \\ h=5\text{ cm} \end{gathered}[/tex]To find the surface area, SA, of the composite figure, the formula
[tex]SA=2(lh)+2(wh)+(lw)+2(\frac{1}{2}lh)+(bc)+(ah)[/tex]
Substitute the values of the variables into the formula above
[tex]\begin{gathered} SA=2\left(12\cdot3\right)+2\left(3\cdot4\right)+\left(12\cdot4\right)+2\left(\frac{1}{2}\left(12\cdot5\right)\right)+\left(13\cdot4\right)+\left(4\cdot5\right) \\ SA=2(36)+2(12)+(48)+(60)+(52)+20 \\ SA=72+24+48+60+52+20 \\ SA=276\text{ cm}^2 \end{gathered}[/tex]Hence, the surface area, SA, is
[tex]276\text{ cm}^2[/tex]For what values of b will F(x) = logb x be a decreasing function?A.0 < b < 1B.0 > b > -1C.b > 0D.b < 0
Given:
There is a function given as below
[tex]F(x)=\log_bx[/tex]Required:
For what value of b the given function in decreasing
Explanation:
The given function is logarithm function
also written as
[tex]F(x)=\frac{log\text{ x}}{log\text{ b}}[/tex]The base b is determines that if the function is increasing or decreasing
here
for
[tex]0the given function is decreasingfor
[tex]b>1[/tex]the given function is increasing
Final answer:
[tex]0