Answer:
the answer is -2 and would be plotted on -2 on a number line
t + 3/4t - 7/2 how do I simplify the 3/4t fraction with t?
Answer:
1 3/4 t -7/2
Step-by-step explanation:
t + 3/4t - 7/2
Get a common denominator for the t terms, which is 4
4/4t + 3/4t - 7/2
7/4 t -7/2
This is an improper fraction so change it to a mixed number
1 3/4 t -7/2
a house increased in value by 36% since it was purchased. The current value is $306,000. What was the value when purchased?
Answer:
$225,000
Step-by-step explanation:
To calculate the percentage change we will apply the formula:
p= N-O/O *100
p is the increased percentage
N is the current value
O is the old value.
Substitute the values in the formula:
36 = 306,000 - O/O *100
Divide both the sides by 100
36/100 = 306,000 - O/O *100/100
36/100 = 306,000 - O/O
Now multiply O at both sides
36/100 * O = 306,000-O/O * O
At R.H.S O will be cancelled by O
At L.H.S 36/ 100 = 0.36
0.36 O= 306,000-O
Combine the like terms:
0.36 O+O =306,000
1.36 O = 306,000
Divide both the terms by 1.36
1.36 O/ 1.36 = 306,000/1.36
O= $225,000
Therefore when the house was purchased its value was $225,000....
Decide whether each of the following statements is true. If false, demonstrate why.
a. 6!= 6.5!
b. 4! + 2! = 6!
C. 6!/3!=2!
Answer:
a is the only true one if you meant 6 times 5!
Step-by-step explanation:
Before we being
n!=n*(n-1)*(n-2)*...(3)(2)(1)
Example: 5!=5(4)(3)(2)(1) and 10!=10(9)(8)(7)(6)(5)(4)(3)(2)(1)
Yes that operation is multiplication.
a) Does 6!=6*5!
Let's see
6!=6*5*4*3*2*1
5!=5*4*3*2*1
So 6*5!=6(5*4*3*2*1)=6*5*4*3*2*1=6!
So true!
b) Does 4!+2!=6! ?
4!=4(3)(2)(1)
2!=2(1)
6!=6(5)(4)(3)(2)(1)
Does
4(3)(2)(1)+2(1)=6(5)(4)(3)(2)(1)
24 +2 =720
26=720 (this is not true)
So 4!+2! is not 6!
c) Does 6!/3!=2! ?
6!=6(5)(4)(3)(2)(1)
3!=3(2)(1)
If you divide 6! by 3!, then the factors 3 and 2 and 1 cancel and you are left with 6(5)(4).
So the question becomes is 6(5)(4)=2!
2!=2(1)=2
6(5)(4)=2?
No way! That is saying 120=2 which is not true.
The evaluations of the statements are: (a) false because non-integer factorials are not defined, (b) false because the sum of 4! and 2! does not equal 6!, and (c) false because 6! divided by 3! is 120, not 2!.
Explanation:Let's evaluate each statement one by one.
a. 6!= 6.5!This statement is false. The factorial function is defined for non-negative integers. Since there is no definition for non-integer factorial such as 6.5!, this comparison is invalid. A correct statement may involve only integer factorials.
b. 4! + 2! = 6!This statement is also false. To show this, let's calculate each factorial:
4! = 4 x 3 x 2 x 1 = 242! = 2 x 1 = 26! = 6 x 5 x 4 x 3 x 2 x 1 = 720Adding 4! and 2! gives 24 + 2 = 26, which is not equal to 6! (720). This statement could be corrected by finding two factorials that add up to another factorial, if such a pair exists.
c. 6!/3!=2!This statement is false. By calculating the factorials, we have:
6! = 7203! = 6Therefore, 6!/3! is equal to 720/6, which simplifies to 120, not 2 (which is the value of 2!). The correct statement is 6!/3! = 120.
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Did do this right using PEMDAS
8/2(2+2)
Solve:
8/2(4)
8/2*4
8/8
=1
Answer:
nope its not. You should count it like this (8 / 2) * (2 + 2)
Step-by-step explanation:
(8 / 2) * (2 + 2)
4 * 4
16
[tex]\text{Hey there!}[/tex]
[tex]\text{PEMDAS means: Parentheses, Exponents, Multiplication, Division, Addition}\\\text{, \& Subtraction}[/tex]
[tex]\text{\underline{No}, it is \underline{NOT} correct because you had to work with the parentheses first}[/tex]
[tex]\dfrac{8}{2}(2 + 2) = \ ? \\ \\ (2 + 2) = 4 \\ \\ \dfrac{8}{2}(4) = \ ? \\ \\ \dfrac{8}{2}= 4 \\ \\ \text{4(4)\ = 16} \\ \\ \boxed{\boxed{\huge\text{Answer should be: 16 }}}[/tex]
[tex]\text{You had to do what was inside the parentheses first, then}\text{ divsion}[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
In a graph, x represents the number of months since a
business opened, and y represents the total amount of
money the business has earned. The following three
points are from the graph:
(2, 1990) (5, 4225) (9, 7205)
Find the slope and y-intercept. Explain what each
represents.
Answer:
The slope is 745 and the y-intercept is 500
The slope means The amount of money increases by $745 per month
The y-intercept means the business opened with initial amount $500
Step-by-step explanation:
* Lets explain how to solve the question
- The graph represents the relation between the number of months
since the business opened and the total amount of money the
business has earned
- The x-axis represents the number of month
- The y-axis represents the amount of money
- In the line the slopes from any two points on the line are equal
- The slope of the line whose end-points are (x1 , y1) and (x2 , y2)
is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
- The equation of the line is y = mx + c ,where m is the slope of the line
and c is the y-intercept
* Lets check is the relation between x and y is linear by calculating the
slopes between each to points
∵ (2 , 1990) , (5 , 4225) , (9 , 7205) are points from the graph
- m1 is the slope of the points (2 , 1990) and (5 , 4225) , m2 is the slope
of the points (5 , 42250) and (9 , 7205) , m3 is the slope of the points
(2 , 1990) and (9 , 7205)
∵ [tex]m_{1}=\frac{4225-1990}{5-2}=745[/tex]
∵ [tex]m_{2}=\frac{7205-4225}{9-5}=745[/tex]
∵ [tex]m_{3=\frac{7205-1990}{9-2}}=745[/tex]
∴ m1 = m2 = m3 = 745
∴ The relation between the number of months and the amount of
money is linear
* The slope is 745
∵ The form of the linear equation is y = mx + c
∵ m = 745
∴ y = 745 x + c
- The y-intercept means the line intersect the y-axis at point (0 , c),
then to find c substitute x and y of the equation by the coordinates
of any point on the line
∵ x = 2 , y = 1990
∴ 1990 = 745(2) + c
∴ 1990 = 1490 + c ⇒ subtract 1490 from both sides
∴ c = 500
∵ c is the y-intercept
* The y-intercept is 500
* The slope represents the rate of increasing of money per month
∴ The amount of money increases by $745 per month
* The y-intercept represents the initial amount of money when the
business opened
∴ The business opened with initial amount $500
Answer:
The slope is 745 and the y-intercept is 500
The slope means The amount of money increases by $745 per month
The y-intercept means the business opened with initial amount $500
Step-by-step explanation:
Will mark brainliest, please answer:)
Find the value of PQ . Round the answer to the nearest tenth. Explain
( Use Pythagorean Theorem 3D rule and Question is above)
Answer:
√135
Step-by-step explanation:
3^2+b^2=12^2
9+b^2=144
9-9+b^2=144-9
b^2=135
√135=b
Simplify (6^-4)^6
Please help me
Answer:
6^ -24
Step-by-step explanation:
We know that a^b^c = a^ (b*c)
(6^-4)^6 = 6^ (-4*6) = 6^ -24
what is the following qoutient? 3√8/4√6
Answer:
3 sqrt(3)
----------- or -----------
2 sqrt(3) 2
Step-by-step explanation:
3 sqrt(8)
-----------------
4 sqrt(6)
3 sqrt(4*2)
-----------------
4 sqrt(3*2)
We know that sqrt(ab) = sqrt(a) sqrt(b)
3 sqrt(4) sqrt(2)
------------------------
4 sqrt(3) sqrt(2)
Canceling the sqrt(2) and sqrt(4) is 2
3*2
----------
4 sqrt(3)
3
-----------
2 sqrt(3)
We can simplify the answer be multiplying by sqrt(3)/sqrt(3)
3 sqrt(3)
----------- * ----------
2 sqrt(3) sqrt(3)
3 sqrt(3)
-----------
2 *3
sqrt(3)
-----------
2
What is the solution to the system of equations?
y = 5x + 2
3x = -y + 10
(4, -18)
(-18, -4)
(7,1)
(1,7)
Answer:
(1, 7)Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}y=5x+2&(1)\\3x=-y+10&(2)\end{array}\right\\\\\text{substitute (1) to (2):}\\\\3x=-(5x+2)+10\\3x=-5x-2+10\qquad\text{add 5x to both sides}\\8x=8\qquad\text{divide both sides by 8}\\x=1\\\\\text{put the value of x to (1):}\\\\y=5(1)+2\\y=5+2\\y=7[/tex]
We just found that a = -0.1 in this system of equations: 3 = 10a + b 2= 20a + b. Find the value of b.
Answer:
b = 4Step-by-step explanation:
Put a = -0.1 to the first an second equation and find velue of b:
3 = 10a + b
3 = 10(-0.1) + b
3 = -1 + b add 1 to both sides
4 = b → b = 4
2 = 20a + b
2 = 20(-0.1) + b
2 = -2 + b add 2 to both sides
4 = b → b = 4
CORRECT
Which set of ordered pairs could be generated by an exponential function?
(0,0), (1, 1), (2, 8), (3, 27)
(0, 1), (1, 2), (2, 5), (3, 10)
(0,0), (1, 3), (2, 6), (3, 9)
(0, 1), (1, 3), (2, 9), (3, 27)
ANSWER
(0, 1), (1, 3), (2, 9), (3, 27)
EXPLANATION
The first and third options are completely out because the y-value of an exponential function is never zero.
For the second option the y-values has no geometric pattern or common ratio.
For the last option, we can observe the following pattern
[tex]1 = {3}^{0} [/tex]
[tex] {3}^{1} = 3[/tex]
[tex] {3}^{2} = 9[/tex]
[tex] {3}^{3} = 27[/tex]
:
:
[tex] {3}^{x} = y [/tex]
The correct choice is the last option
Answer:
D
Step-by-step explanation:
Pleaseeeeeeee help .......ASAP
Answer:
Option A
Step-by-step explanation:
Given:
Center of circle = (h,k)= (3,8)
Radius = r = 5
The standard form of equation of circle with center and radius is:
[tex](x-h)^2+(y-k)^2=r^2\\Putting\ the\ values\\(x-3)^2+(y-8)^2=(5)^2\\Simplifying\\x^2+9-6x+y^2+64-16y=25\\x^2+y^2-6x-16y+9+64=25\\x^2+y^2-6x-16y+73=25\\x^2+y^2-6x-16y+73-25=0\\x^2+y^2-6x-16y+48=0[/tex]
Therefore, the general form of the equation of circle given is:
[tex]x^2+y^2-6x-16y+48=0[/tex]
Hence, option A is correct ..
Ben sold his small online business for $100,000. The purchaser will pay him $20,000 today, then $20,000 every year for the next four years. Assume
that Ben could invest a lump-sum payment today in an account yielding an interest rate of 4% annually. Find the total present value of all five
payments
A.
$87,096
B
$88,384
c. $92,598
D. $93,964
The answer is c $92,598
Answer:
$92,598
Step-by-step explanation:
The purchaser pays Ben $20,000 today and then $20,000 every year for the next 4 years.
The interest rate is 4% per annum.
So the net present value of all the payments is :
20000 + 20000/1.04 + 20000/(1.04^2) + 20000/(1.04^3) + 20000/(1.04^4)
= 20000 + 19230.77 + 18491.12 + 17779.73 + 17096.08
= 92597.7
= 92,598 (approx)
So the net present value of all the payments made to Ben is $92,598.
Find the distance between these points.
R(-1,0), S(8,6)
V(26)
V(85)
3V(13)
Answer:
The distance is equal to [tex]3\sqrt{13}\ units[/tex]
Step-by-step explanation:
we know that
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
we have
[tex]R(-1,0)\\S(8,6)[/tex]
substitute the values
[tex]d=\sqrt{(6-0)^{2}+(8+1)^{2}}[/tex]
[tex]d=\sqrt{(6)^{2}+(9)^{2}}[/tex]
[tex]d=\sqrt{36+81}[/tex]
[tex]d=\sqrt{117}\ units[/tex]
Simplify
[tex]d=3\sqrt{13}\ units[/tex]
Suppose Q and R are independent events. Find P (Q and R) if P(Q) = 4/7
and P(R) = 1/2
Answer:
2/7
Step-by-step explanation:
If two events A and B are independent, then P(A and B)=P(A)P(B).
So since Q and R are independent, then P(Q and R)=P(Q)P(R).
Let's substitute and evaluate:
[tex]P(Q\text{ and }R)=P(Q)\cdot P(R)=\frac{4}{7} \cdot \frac{1}{2}=\frac{4}{14}[/tex].
Both 2 and 14 are divisible by 2, so to reduce 4/14 we could divide top and bottom by 2:
4/14=(4/2)/(14/2)=2/7
6x-2y=-6 find the slope and the y intercept of the line
Answer:
y-int:3
slope:-3
Step-by-step explanation:
6x-2y=-6
change to y=mx+b: -2y=-6x-6
divide by -2
y=3x+3
Solve x^2 - 8x = 3 by completing the square. Which is the solution set of the equation?
1st one
Step-by-step explanation:
I have answered ur question
Answer:
A
Step-by-step explanation:
Given
x² - 8x = 3
To complete the square
add (half the coefficient of the x- term)² to both sides
x² + 2(- 4)x + 16 = 3 + 16
(x - 4)² = 19 ( take the square root of both sides )
x - 4 = ± [tex]\sqrt{19}[/tex] ( add 4 to both sides )
x = 4 ± [tex]\sqrt{19}[/tex]
Solution set is (4 - [tex]\sqrt{19}[/tex], 4 + [tex]\sqrt{19}[/tex] )
why can 0.825 be written as a fraction explain
Answer:
It can be written as 825/1000. You can simplify this to get the simplest form which would be 33/40. All decimals are out of one, they are a part. When you first get a decimal, put the numbers such as 825 on top. The last number is in the thousandths place, so it is out of 1000. 1000 is your denominator. Your fraction is then 825/1000. From here you can simplify if possible.
Hope this helps ^-^
Oliver has 0.5 of a gallon of water. He pours all of the water into 6 containers. If he pours the same amount of water into each container, how many gallons of water does Oliver pour into each container?
PLEASE SHOW WORK
Answer:
1/12 of a gallon of water in each container
Step-by-step explanation:
Answer = [tex]\frac{Water}{Containers}[/tex] = 1/12
Answer:
Oliver poured [tex]\frac{1}{12}[/tex] gallons of water in each container.
Step-by-step explanation:
Oliver has the amount of water = 0.5 gallons.
He pours all of the water into 6 containers.
So amount of water in each container will be = [tex]\frac{\text{Total amount of water}}{\text{Number of containers}}[/tex]
= [tex]\frac{0.5}{6}[/tex]
= [tex]\frac{\frac{1}{2} }{6}[/tex]
= [tex]\frac{1}{12}[/tex] gallons of water.
Therefore, in each container amount of water poured will be [tex]\frac{1}{12}[/tex] gallons.
2 Points
Which shows the equation below written in standard form?
9 - 7x = (4x-3)2 + 5
O A. 16x2 - 17x- 5 = 0
O B. 16x2-31x+ 5 = 0
O C. 16x2 - 31x- 5 = 0
O D. 16x2 - 17x+ 5 = 0
Answer:
D
Step-by-step explanation:
Given
9 - 7x = (4x - 3)² + 5 ← expand the squared factor
9 - 7x = 16x² - 24x + 9 + 5, that is
9 - 7x = 16x² - 24x + 14 ( subtract 9 - 7x from both sides )
0 = 16x² - 17x + 5, that is
16x² - 17x + 5 = 0 ← in standard form → D
Find the second, fifth, and ninth terms of the sequence.
an = -7 + (n - 1) 4
Answer:
- 3, 9, 25
Step-by-step explanation:
To find the required terms of the sequence substitute n = 2, 5, 9 into the given rule, that is
[tex]a_{2}[/tex] = - 7 + (2 - 1)4 = - 7 + (1 × 4) = - 7 + 4 = - 3
[tex]a_{5}[/tex] = - 7 + (5 - 1)4 = - 7 + (4 × 4) = - 7 + 16 = 9
[tex]a_{9}[/tex] = - 7 + (9 - 1)4 = - 7 + (8 × 4) = - 7 + 32 = 25
The second, fifth, and ninth terms of the sequence are -3, 9, and 25, respectively.
The second, fifth, and ninth terms of the sequence defined by the formula an = -7 + (n - 1) * 4 are -3, 9, and 25, respectively.
To find the second, fifth, and ninth terms of the sequence given by the formula an = -7 + (n - 1) * 4, we can simply plug the corresponding values of n into the formula.
For the second term (a2), where n=2:
a2 = -7 + (2 - 1) * 4
a2 = -7 + 1 * 4
a2 = -7 + 4
a2 = -3
For the fifth term (a5), where n=5:
a5 = -7 + (5 - 1) * 4
a5 = -7 + 4 * 4
a5 = -7 + 16
a5 = 9
For the ninth term (a9), where n=9:
a9 = -7 + (9 - 1) * 4
a9 = -7 + 8 * 4
a9 = -7 + 32
a9 = 25
Therefore, the second, fifth, and ninth terms of the sequence are -3, 9, and 25, respectively.
I need help please.
Answer:
Step-by-step explanation:
1/5 + 1/5^-2
1/5 + 1/25
1/5 = 5*1 / 5*5
5/25 + 1/25
6/25 which cannot be reduced or changed.
Find the exact value of tan ^-1 (-root of 3)
Write your answer in radians in terms of n.
To find the exact value of tan^-1(-sqrt(3)), we first rewrite the equation using the definition of the arctangent function. Next, we use the trigonometric identity sin^2(x) + cos^2(x) = 1 to simplify the equation and solve for sin(x). We find that sin(x) = sqrt(3)/2. By looking at the unit circle, we determine that the angle whose sine is sqrt(3)/2 is pi/3 radians. Therefore, the exact value of tan^-1(-sqrt(3)) in radians is -pi/3 + 2*pi*n, where n is an integer.
To find the exact value of tan^-1(-sqrt(3)), we need to recall the definition of the arctangent function. The arctangent function returns an angle whose tangent is equal to a given number. In this case, we are looking for an angle whose tangent is -sqrt(3). Since tan(x) = sin(x)/cos(x), we can rewrite the equation as -sqrt(3) = sin(x)/cos(x).
Next, we can use the fact that sin^2(x) + cos^2(x) = 1 to rewrite the equation as -sqrt(3) = sin(x)/sqrt(1 - sin^2(x)). Cross-multiplying and rearranging, we get -sqrt(3)*sqrt(1 - sin^2(x)) = sin(x).
Now, we can square both sides and simplify the equation to get -3*(1 - sin^2(x)) = sin^2(x). Expanding and rearranging, we have -3 + 3sin^2(x) = sin^2(x). Combining like terms and isolating sin^2(x), we get sin^2(x) = 3/4. Taking the square root of both sides, we find sin(x) = sqrt(3)/2.
Finally, we can find the angle whose sine is sqrt(3)/2 by looking at the unit circle. The angle is pi/3 in radians. Therefore, the exact value of tan^-1(-sqrt(3)) in radians is -pi/3 + 2*pi*n, where n is an integer.
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Which is the equation of a line perpendicular to the line y
This is a linear equation in standard form [tex]\( Ax + By = C \).[/tex] None of the options provided in the multiple-choice question exactly match this equation in standard form
To find the equation of a line perpendicular to the given line and passing through a specific point, follow these steps:
1. Identify the slope of the original line.
The line given is [tex]\( y = -10x + 1 \)[/tex]. The slope (m) of this line is -10.
2. Find the perpendicular slope:
The slope of a line perpendicular to another line is the negative reciprocal of the original line's slope. Therefore, the perpendicular slope [tex]\( m_{\perp} \) is \( \frac{1}{10} \)[/tex] because [tex]\( m_{\perp} = -\frac{1}{m} \).[/tex]
3. Use the point-slope form to find the equation:
The point-slope form is [tex]\( y - y_1 = m_{\perp}(x - x_1) \)[/tex], where [tex]\( (x_1, y_1) \)[/tex] is the point the line passes through, which is (5,7) in this case.
4. Plug in the point and the perpendicular slope:
[tex]\( y - 7 = \frac{1}{10}(x - 5) \)[/tex].
5. Simplify the equation to get it into slope-intercept form [tex](\( y = mx + b \))[/tex]:
[tex]\( y = \frac{1}{10}x - \frac{1}{10}(5) + 7 \)[/tex].
[tex]\( y = \frac{1}{10}x - \frac{1}{2} + 7 \)[/tex].
[tex]\( y = \frac{1}{10}x + \frac{13}{2} \)[/tex] after combining like terms.
The equation in slope-intercept form is [tex]\( y = \frac{1}{10}x + \frac{13}{2} \),[/tex]which corresponds to one of the choices given in the multiple-choice question. Let's identify which one it is.
The equation that represents a line which is perpendicular to the line [tex]\( y = -10x + 1 \)[/tex] , passing through the point (5,7), is:
[tex]\[ y = \frac{1}{10}x + \frac{13}{2} \][/tex]
This can be simplified to:
[tex]\[ 10y = x + 65 \][/tex]
Or:
[tex]\[ x - 10y = -65 \][/tex]
This is a linear equation in standard form \( Ax + By = C \). None of the options provided in the multiple-choice question exactly match this equation in standard form
The graph shows the relationship between the total cost and the number of erasers bought at the student store. Which of the statements is true?
Answer:
the answer is D
Step-by-step explanation:
if you look on the graph and compare the statements you'll see none of them correlate except for the last one. 7 erasers cost 3.50, since the point on the graph is (7, 3.50)
Answer:
The correct option is D) Seven eraser cost $3.50
Step-by-step explanation:
Consider the provided graph.
The graph shows the relationship between the total cost and the number of erasers bought at the student store.
Here the x-axis represents the number of erasers bought and the y-axis represents the total cost.
Now consider the provided options.
Options (A) Each eraser cost $1.00
This option is incorrect because when x = 1 the value of y = 0.5, that means the cost of each eraser is $0.5
Options (B) Each eraser cost $1.50
This option is incorrect as the cost of each eraser is $0.5
Options (C) Three eraser cost $6
This option is incorrect because when x = 3 the value of y = 1.5, that means the cost of 3 eraser is $1.5
Options (D) Seven eraser cost $3.50
This option is correct because when x = 7 the value of y = 3.5, that means the cost of 7 eraser is $3.5
There are 40 students in a class. Girl:
make up 60% of the class. 25% of the
girls wear glasses. How many girls in
the class wear glasses?
Answer:
6
Step-by-step explanation:
60% of 40 = 24
25% of 24 = 6
Therefore, 6 girls in the class wear glasses.
need help asap. Consider the diagram.
Given that r||s and q is a transversal, we know that by the [________].
ANSWER
alternate interior angles theorem
EXPLANATION
According to the alternate interior angles theorem, when two parallel lines are are intercepted by a straight line (transversal) the angles in the interior corners of a Z-shape pattern are congruent.
From the above diagram line r is parallel to line s, therefore
[tex] \angle \: 3 \cong \angle6[/tex]
and
[tex] \angle \: 4\cong \angle5[/tex]
because they are alternate interior angles.
See attachment for how to spot alternate interior angles.
Question:
Given that r||s and q is a transversal, we know that by the [________].
Answer:
alternate interior angles theorem
If a triangle has sides of lengths 5, 8 and 12, it is a right triangle. true or false
Answer:
False.
Step-by-step explanation:
To see if these sides can form a right triangle, all we need to do is see if the following equation holds [tex]a^2+b^2=c^2[/tex] where [tex]c[/tex] is the larger measurement. [tex]a \text{ and } b[/tex] it doesn't really matter which you assign as 5 or 8.
So I'm choosing the following [tex]a=5,b=8,c=12[/tex].
[tex]c[/tex] has to be 12 because 12 is the largest.
Now we got to see if [tex]a^2+b^2=c^2[/tex] holds.
That is, we need to see if [tex]5^2+8^2=12^2[/tex] holds.
[tex]5^2+8^2=12^2[/tex]
[tex]25+64=144[/tex]
[tex]89=144[/tex]
That's totally false. 89 is definitely not 144 so 5,8, and 12 cannot be put together to form a right triangle.
Which double angle or half angle identity would you use to verify the following: csc x sec x = 2 csc 2x
Answer:
b
Step-by-step explanation:
I would use b.
Why?
[tex]2 \csc(2x)[/tex]
[tex]2 \frac{1}{\sin(2x)}[/tex]
[tex]\frac{2}{\sin(2x)}[/tex]
[tex]\frac{2}{2\sin(x)\cos(x)}[/tex]
[tex]\frac{1}{\sin(x)\cos(x)}{/tex]
[tex]\frac{1}{\sin(x)\frac{1}{\cos(x)}[/tex]
[tex]\csc(x) \sec(x)[/tex]
I applied the identity sin(2x)=2sin(x)cos(x) in line 3 to 4.
Answer: OPTION B.
Step-by-step explanation:
It is important to remember these identities:
[tex]csc(x)=\frac{1}{sin(x)}\\\\sec(x)=\frac{1}{cos(x)}[/tex]
Knowing this, we can say that:
[tex]csc(x) sec(x)=\frac{1}{sin(x)}*\frac{1}{cos(x)}=\frac{1}{sin(x)*cos(x)}[/tex]
Now we need to use the following Double angle identity :
[tex]sin(2x)=2sin(x)cos(x)[/tex]
And solve for [tex]sin(x)cos(x)[/tex]:
[tex]\frac{sin(2x)}{2}=sin(x)cos(x)[/tex]
The next step is to make the substitution into [tex]\frac{1}{sin(x)*cos(x)}[/tex] and finally simplify:
[tex]\frac{1}{\frac{sin(2x)}{2}}=\frac{\frac{1}{1}}{\frac{sin(2x)}{2}}=\frac{2}{sin(2x)}=2csc(2x)[/tex]
Jenson has a basket containing oranges, apples, and pears. He picks a piece of fruit from the basket 40 times, replacing the fruit before each draw. From these 40 trials Jenson estimates that the probability of picking an orange is 0.25, the probability of picking an apple is 0.3, and the probability of picking a pear is 0.45. How many times did Jenson pick an apple during the 40 trials?
[tex]\large\boxed{12\,\text{apples}}[/tex]
Step-by-step explanation:In this question, we're trying to find how many apples Jenson picked from the basket.
Lets gather information that can help us.
Important information:
Picked a fruit from a basket 40 timesProbability of picking an apple is 0.3With the information above, we can solve the question.
We know that he picked up a fruit 40 times, but we need to find how many apples he picked up during the 40 times.
The probability of picking an apple is 0.3, which is equivalent to 30%
This means that 30% of the 40 times he picked an apple.
We would multiply 40 by 0.3 to get our answer.
[tex]40*0.3=12[/tex]
This means that Jenson picked 12 apples.
I hope this helped you out.Good luck on your academics.Have a fantastic day!Answer: B.12
Step-by-step explanation: