Answer: The identity is verified. See the explanation.
Step-by-step explanation:
You must keep on mind the following identities:
[tex]csc\theta=\frac{cos\theta}{sin\theta}\\\\csc\theta=\frac{1}{sin\theta}\\\\sin^2\theta+cos^2\theta=1[/tex]
Therefore, by substitution, you can rewrite the identity as shown below:
[tex]1+cot^2\theta=csc^2\theta\\\\1+\frac{cos^2\theta}{sin^2\theta}=csc^2\theta[/tex]
Simpliying, you obtain:
[tex]\frac{sin^2\theta+cos^2\theta}{sin^2\theta}=csc^2\theta\\\\\frac{1}{sin^2\theta}=csc^2\theta\\\\csc^2\theta=csc^2\theta[/tex]
The identity is verified.
Write an expression that, when simplified is equivalent to 15x +7
Answer:
2(7.5x+3.5)
Step-by-step explanation:
I can't remember what these equations are actually called, however in order to solve this you simply multiply 7.5 by 2, and then 3.5 by 2.
A rhombus has one diagonal that is 14 centimeters long and one diagonal that is 12. What is the area of the rhombus?
Answer:
168
14 times 12
Solve -9.4 > 1.7x + 4.2. I need this ASAP
Hello.
We are solving -9.4 > 1.7x + 4.2.
First we need to swap sides:
[tex]1.7x + 4.2 = -9.4[/tex]
Now we need to subtract 4.2 from both sides.
1.7x + 4.2 = -9.4
-4.2 . -4.2
Now let's combine -4.2 + 4.2 which is 0.
We get 1.7x < -9.4 - 4.2
Now let's divide both sides by 1.7
1.7x | -13.6
1.7 1.7
x < -13.6
1.7
So we just divided to get x < -8.
Answer:
[tex]\boxed{\bold{x<-8}}[/tex]
Step By Step Explanation:
Switch Sides[tex]\bold{1.7x+4.2<-9.4}[/tex]
Multiply Both Sides by 10[tex]\bold{1.7x\cdot \:10+4.2\cdot \:10<-9.4\cdot \:10}[/tex]
Refine[tex]\bold{17x+42<-94}[/tex]
Subtract 42 From Both Sides[tex]\bold{17x+42-42<-94-42}[/tex]
Simplify[tex]\bold{17x<-136}[/tex]
Divide Both Sides By 17[tex]\bold{\frac{17x}{17}<\frac{-136}{17}}[/tex]
Simplify[tex]\bold{x<-8}[/tex]
What is 10 minutes before 9
➷ To figure this out, you need to understand that there are 60 minutes in an hour
Subtract 10 from this value:
60 - 50
As it isn't 60 minutes, it wouldn't be 9 anymore
9-1 = 8
The correct answer would be: 8:50
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Emma has 5 3/8 punds of potato salad and 2 7/8 pounds of egg salad for a picnic. How many more pounds of potato salad than egg salad does Emma have? A - 3 pounds B- 2 3/4 pounds C - 2 1/2 pounds D - 2 1/4 pounds
Answer:
The correct answer option is C. [tex]2\frac{1}{2}[/tex] pounds
Step-by-step explanation:
We are given that Emma has [tex]5\frac{3}{8}[/tex] pounds of potato salad and [tex]5\frac{3}{8}[/tex] pounds of egg salad for a picnic.
We are to find out how much more pounds Emma has of potato salad than the egg salad.
To find this, we simple need to subtract the pounds of egg salad from the pounds of potato salad.
[tex]5\frac{3}{8} - 5\frac{3}{8}[/tex] [tex]=\frac{43}{8} -\frac{23}{8} =\frac{43-23}{8} = 2\frac{1}{2}[/tex] pounds
Min's hose can pump 21 gallons of water every hour. How many gallons of water will he fill up if he runs the hose for 2/3 of an hour?
Answer:
14
Step-by-step explanation:
21 divided by 3 =7 7 per 1/3
7x2=14
Final answer:
Min will fill up 14 gallons of water if he runs his hose, which pumps 21 gallons per hour, for 2/3 of an hour.
Explanation:
If Min's hose can pump 21 gallons of water every hour, and he runs the hose for 2/3 of an hour, you would calculate the total gallons of water filled by multiplying the rate (21 gallons/hour) by the time (2/3 hour).
To find out how much water Min fills up:
Multiply the amount of water his hose pumps per hour by the fraction of the hour he runs it.21 gallons/hour × 2/3 hour = 14 gallons.Therefore, Min will fill up 14 gallons of water if he runs the hose for 2/3 of an hour.
Evaluate the exponential function f(x)=8^x+1 Which value completes the table?
A.0
B.3
C.9
D.25
The value of exponential function, which completes the table for variable x at 1/3 is 3. The option B is correct.
Exponential function is the function in which the function growth or decay with the power of the independent variable.
The curve of the exponential function depends on the value of its variable.
The exponential function with dependent variable y and independent variable x can be written as,
[tex]y=a^x[/tex]
Here, [tex]x[/tex] is the variable in the power of a number.
Given information-
The given exponential function in the problem is,
[tex]f(x)=8^x+1[/tex]
The value of function at the value of variable x as 1/3 has to be find to complete the table. Put 1/3 in the above equation on the place of x as,
[tex]f(x)=8^{\frac{1}{3}}+1[/tex]
The number 8 can be written as the [tex]2^3[/tex]. Thus,
[tex]f(x)=(2^3)^{\frac{1}{3}}+1\\f(x)=(2)^{\dfrac{3\times1}{3}}+1\\f(x)=(2)^1+1\\f(x)=2+1\\f(x)=3[/tex]
Thus the value of exponential function, which completes the table for variable x at 1/3 is 3. The option B is correct.
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sharon is 3 years old less than twice her younger brother's age. Let (s) repressent sharons age and (b) repressent her brother's age. which equation could be used to show sharons age?
A: s = 3-2b
B: b = 2x-3
C: s = 2b-3
D: b = 3 -2x
E: s = 3b-2
If Sharon is 3 years younger, then it's s = 3-b. However, it's twice her brothers age, which makes the formula our final answer, A, or [tex]s = 3 - 2b[/tex]
The correct option is A
Which statement BEST describes how the graph of g(x)=-3x^2 compares to the graph of f(x)=x^2?
Reminder:(Number 12 for the picture has the answers for the question)
Answers are attached in the 2 pics below. Please check!
Help, please!
Show how the GCF of the numbers 10 and 15 can be used to reduce the fractions [tex]\frac{10}{15}[/tex]
Answer: [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
The greatest GCF is 5 because 5 goes into 15, and 10. Therefor, the answer would be 2/3.
* Hopefully this helps:) Mark me the brainliest:)!!!
Answer:
⅔
Step-by-step explanation:
Find all the factors of 10 and 15.
Factors of 10: 1, 2, 5, 10
Factors of 15: 1, 2, 3, 5, 15
The highest factor that is in both 10 and 15 is 5.
To reduce the fraction 10/15, divide both the numerator and denominator
by 5.
10/15 = (10 ÷ 5)/(15 ÷ 5) = ⅔
Is 976-522 more or less than 400? Explain how you can tell without finding the exact difference
[tex]\bold{Hey\ there!} \\ \bold{976-522=454}\\ \boxed{\boxed{\bold{Thus, 400\ is\ \underline{LESS\ THAN}\ 976-522}}} \\ \bold{Just\ solve\ your\ particular\ equation} \\ \\ \bold{Good\ luck\ on\ your\ assignment\ \& \ enjoy\ your\ day!} \\ \\ \\ \\ \frak{LoveYourselfFirst:)}[/tex]
Louis found two bakeries to provide bagels for his sub shop. The first bakery offers 350 bagels for $168.00 and the second bakery offers 475 bagels for $209. How much will Louis pay for 800 bagels if he buys from the bakery with the lower price?
Answer:
$352Step-by-step explanation:
Find out the price of one bagel by dividing the price by the number of bagels:
350 Bagels = $168
1 Bagel = $0.48
475 Bagels = $209
1 Bagel = $0.44
0.48 > 0.44
This means the second bakery has the lower price.
Louis wants 800 bagels, so multiply the price by 800.
0.44 * 800 = $352
You can check it's lower by comparing it with the first bakery.
0.48 * 800 = $384
384 > 352
The graph of an equation representing a direct variation passes through the point (6, 10). Give another point with integral coordinates that is also on the graph of this equation.
[tex]\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ (\stackrel{x}{6},\stackrel{y}{10})\qquad \textit{we know that } \begin{cases} x=6\\ y=10 \end{cases}\implies 10=k6\implies \cfrac{10}{6}=k\implies \cfrac{5}{3}=k \\\\\\ therefore\qquad \boxed{y=\cfrac{5}{3}x}[/tex]
to get another point, we simply can pick a random independent variable, namely "x", say hmmmm x = 9, thus
[tex]\bf y=\cfrac{5}{3}(\stackrel{\stackrel{x}{\downarrow }}{9})\implies y=5\cdot \cfrac{9}{3}\implies y=10~\hspace{7em}\boxed{(9, 10)}[/tex]
To find another point with integral coordinates on the graph of the equation representing a direct variation, we can use the given point (6, 10) and the fact that the equation represents a direct variation. By finding the value of the constant of variation, we can substitute an integral x-value to find the corresponding y-value for another point on the graph.
Explanation:To find another point with integral coordinates on the graph of the equation representing a direct variation, we need to use the given point (6, 10) and the fact that the equation represents a direct variation. A direct variation equation has the form y = kx, where k is the constant of variation. In this case, we can use the given point to find the value of k. When x = 6 and y = 10 in the equation y = kx, we can substitute these values to solve for k: 10 = k * 6. Solving for k, we get k = 10/6 = 5/3.
Now that we know the value of k, we can find another point with integral coordinates. Let's try x = 3. Using the equation y = kx, we can substitute x = 3 and k = 5/3 to find y: y = (5/3) * 3 = 5.
So, another point with integral coordinates on the graph of the equation representing a direct variation is (3, 5).
What is the answer to 8x^3+125 by factoring the perfect cube?
Answer:
[tex]\large\boxed{8x^3+125=(2x+5)(4x^2-10x+25)}[/tex]
Step-by-step explanation:
[tex]8x^3+125=2^3x^3+5^3=(2x)^3+5^3\\\\\text{use}\ a^3+b^3=(a+b)(a^2-ab+b^2)\\\\=(2x+5)((2x)^2-(2x)(5)+5^2)\\\\=(2x+5)(4x^2-10x+25)[/tex]
How did the absent minded professor burn his ear?
He was ironing when the phone rang.
The absent-minded professor burned his ear due to the lens effect caused by sunlight reflecting off a concave mirror. The mirror focused the sunlight onto his ear, causing it to burn.
Explanation:The absent-minded professor burned his ear due to the lens effect caused by sunlight reflecting off a concave mirror. When the professor held the mirror close to his ear and exposed it to sunlight, the mirror focused the sunlight onto his ear, causing it to burn.
The concave mirror has a curve that causes the light rays to converge at a specific point called the focal point. This concentrated light energy resulted in the burning sensation on the professor's ear.
This phenomenon is similar to using a magnifying glass to focus sunlight onto an object and create heat. The concave mirror acted as a magnifying glass, amplifying the intensity of the sunlight and leading to the ear burn.
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What is the value of x?
Answer options: 15, 35, 25, 30
➷ Angles subtended by the same arc are equal
Therefore, x = 30 degrees.
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➶ Good Luck (:
➶ Have A Great Day ^-^
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The answer is 30 Degrees
..............................................
Which of the following could be the equation for a parabola that opens to the left with vertex (-17,2)?
Answer:
C
Step-by-step explanation:
Just plugging in the given x or y values, you can rule out both A and B, only C and D work out logically.
-17=-3(2-2)²-17
-17=0-17
-17=-17✓
2=3(x+17)1+2
2=0+2
2=2✓
With parabolas, if you're talking in terms of y=x², it will be vertical. If talking in terms of x=y², it will be horizontal. As we're looking for something horizontal (open to the left), we need a x=y² formula. Of C and D, only C is an x=y² formula, and thus the answer.
When making a telephone call using a calling card, a call lasting 5 minutes cost $0.95. A call lasting 13 minutes cost $1.75. Let y be the cost of making a call lasting x minutes using a calling card. Write a linear equation that models the cost of making a call lasting x minutes.
A. y = 10x - 981/20
B. y = -0.1x + 1.45
C. y = 0.1x + 0.45
The linear equation that models the cost of making a call lasting x minutes using a calling card is y = -0.1x + 1.45.
Explanation:To write a linear equation that models the cost of making a call lasting x minutes using a calling card, we can use the given information about two calls. If a 5-minute call costs $0.95 and a 13-minute call costs $1.75, we can set up two equations:
0.95 = 5m + b
1.75 = 13m + b
Solving these equations, we find that m = -0.1 and b = 1.45. Therefore, the linear equation that models the cost of making a call lasting x minutes is y = -0.1x + 1.45.
What is the product? (7x2y3)(3x5y8)
i don't know if this is the correct answer 3360y^2
Answer:
Product [tex](21) ( x^{7})(y^{11})[/tex].
Step-by-step explanation:
Given : [tex](7x^{2} y^{3})(3x^{5} y^{8})[/tex].
To find : product .
Solution : We have given that
[tex](7x^{2} y^{3})(3x^{5} y^{8})[/tex].
Combine like terms
[tex](7 * 3) ( x^{2}*x^{5})(y^{3}*y^{8})[/tex].
By the exponential rule : if the base of two exponent is same then power must be added . [tex]x^{a} *x^{b} = x^{a+b}[/tex].
Then
[tex](21) ( x^{2+5})(y^{3+8})[/tex].
[tex](21) ( x^{7})(y^{11})[/tex].
Therefore, Product [tex](21) ( x^{7})(y^{11})[/tex].
Simplify -3 over 5 divided by 7 over 6.
A = -7 over 10
B = -18 over 35
C = 18 over 35
D = 7 over 10
Answer:
Simplify:
-3/5 ÷ 7/6
Step-by-step explanation:
1. To solve you have to switch the ÷ to x, but once you do that 7/6 would be switched too:
-3/5 x 6/7
2. Simplify,
-18/35
So, the answer to this is B.
Hope this Helped!!!!!
~Shane
harold deposits $30 a week into a savings account. hid balance in his savings account grows by a constant rate. true or false
Point O is the center of the circle. What is the value of X?
Answer options: 24, 15, 27, 20
Answer: FIRST OPTION
Step-by-step explanation:
To solve this problem you must apply the Intersecting Secant-Tangent Theorem. By definition, when a secant line and a tangent lline and a secant segment are drawn to a circle from an exterior point:
[tex](Tangent\ line)^2=(Secant\ line)(External\ Secant\ line)[/tex]
The total measure of the secant shown is:
[tex]18+Diameter[/tex]
If the radius is 7, then the diameter is:
[tex]D=7*2=14[/tex]
Therefore:
[tex]Secant\ line=18+14=32[/tex]
You also know that:
[tex]External\ Secant\ line=18\\Tangent\ line=x[/tex]
Keeping the above on mind, you can substitute values and solve for x:
[tex]x^{2}=32*18[/tex]
[tex]x=\sqrt{576}\\x=24[/tex]
The measure of the side length of the tangent line PQ to the circle O is 25 units
What is the measure of side length x?From the image, Line segment PQ is a tangent line because it touches the curve at point Q.
Therefore, triangle PQO forms a right triangle.
Leg 1 of the right triangle = OQ = 7
Leg 2 of the right triangle = PQ = x
Hypotenuse = PO = 18 + 7 = 25
Now, to solve for the measure of side length x, we use the Pythagoras theorem:
PQ = √( PO² - OQ² )
Plug in the values:
x = √( 25² - 7² )
x = √( 625 - 49 )
x = √576
x = 24
Therefore, the value of x is 24.
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help and show work for #7
Answer:
If you give the diameter and the radius, as well as the circumference, I will be of more help :)
Step-by-step explanation:
I hope this helps, if it doesn't then just message me and ill be more than happy to help :)
Write the ratio 14:56
In its simplest form
Answer:
14/14 = 1 and 56/14 = 4
Thus, 14:56 ratio simplified is 1:4
hope this helps:)sorry if it doesnt
brainliest plz
in a bag if marbles there are 7 blue, 6 red, pick one marble out. without replacing the first marble pick another marble out. how many ways can u pick two red marbles?
Answer:
1
Step-by-step explanation:
If you only take out 2 marbles, you have to take out red marbles both times to have 2 red marbles. There is no other option.
Start with the standard formula for the area of a triangle, and rewrite it to solve for the base, b.
Answer:
2A/h = b
Step-by-step explanation:
The formula for area of a triangle is
A = 1/2 bh
Multiply each side by 2
2A = 2*1/2 bh
2A = bh
Divide each side by h
2A/h = bh/h
2A/h = b
Answer:
b=2A/h
Step-by-step explanation:
The formula for area of a triangle is
A = 1/2 bh
Multiply each side by 2
2*1/2 bh = 2A
bh = 2A
Divide each side by h
bh/h = 2A/h
b = 2A/h
an online retailer sells cans of tennis balls look at the first rule to find the unit rate then use the unit rate to complete the table to show the cost of ordering 100 and 250 cans.
please help as soon as possible.
To find the unit rate, divide total cost by number of cans bought.
$30 / 12 cans = $2.50 per can.
Now multiply the unit cost by the number of cans you want to buy:
2.50 x 100 = $250.00
2.50 x 250 = $625
Which of the following is the graph of f(x) = x2 − 4x − 5?
A. graph of a quadratic function with a minimum at 2, negative 9 and x intercepts at negative 1 and 5
B. graph of a quadratic function with a minimum at 3, negative 4 and x intercepts at 1 and 5
C. graph of a quadratic function with a minimum at 2.5, negative 2.4 and x intercepts at 1 and 4
D. graph of a quadratic function with a minimum at negative 1.5, negative 6.2 and x intercepts at 1 and negative 4
The answer is A because completing the square gives a minimum of 2,-9 and factorising gives roots of 5 and -1 :)
Answer:
Minimum at (2,-9) and intercepts are (-1,5)
Step-by-step explanation:
f(x) = [tex]x^2 -4x-5[/tex]
completing square method adding and subtracting the square of half of coefficient of 4 ,we get
f(x) = [tex]x^2 -4x+4 -4 -5[/tex]
f(x) =[tex](x-2)^2 -9[/tex]
on comparing it with standard vertex form [tex](x-h)^{2} +k[/tex]
where k is suppose to be the minimum value
on comparing it we get k = -9
which is minimum value of f(x)
at x =2
and if we find the zeros of
[tex]x^2 -4x-5[/tex] ,we get
[tex]x^2 -5x+x -5[/tex]
[tex]x^2 -4x-5[/tex]
x(x-5)+1(x-5)
(x+1)(x-5)
on setting it equals zero ,we get
x+1 =0 and x=5
x =-1 and x=5
therefore option A is answer
Minimum at (2,-9) and intercepts are (-1,5)
HELP PLX 46 POINTS!
The diameter of the semicircle with center O, shown below, is 4 units. What is the area of the shaded region?
Answer:
Area = 2
Step-by-step explanation:
Givens
The leg and the height of the right angle triangle are both radii of the semi circle.
The diameter of the semicircle is 4
Solution
radius = diameter /2
radius = 4/2
radius = 2
Area = 1/2 * b * h
b = 2
h = 2
Area = 1/2 * 2 * 2
Area = 2
Answer:
2 units²
Step-by-step explanation:
The diameter is 4 units.
The radius is 4/2 = 2 units.
The two legs of the triangle are a measure of 2 units or just the radius length.
Area of triangle = bh × 1/2
2 × 2 × 1/2
4/2 = 2
Which of the following equations will make a V-shaped graph?
y = |x|
y = 2x
x 2 + 5 = y
y = 1/3x
Y=|x|. An absolute value has a V shape.
Final answer:
The equation that will make a V-shaped graph is y = |x|, as it plots the absolute value of x, creating a V shape by reflecting points on the positive side of the y-axis for both positive and negative values of x.
Explanation:
The student asked which of the following equations will make a V-shaped graph. The answer is y = |x|. This is because the absolute value function produces a graph that is V-shaped, reflecting the positive distance from zero for both positive and negative values of x. The other options presented, such as y = 2x, would produce a straight line; x² + 5 = y (correctly read as y = x² + 5) would produce a parabola; and y = 1/3x would also result in a straight line, just with a different slope. Only the graph of y = |x| has the distinct V shape as it plots the absolute value of x, meaning it reflects the points on the positive side of the y-axis for both positive and negative values of x.