Answer:
95°
Step-by-step explanation:
<QRT = <PRS [Vertically Opposite Angles]
=> 4x + 15° = 3x + 35°
=> 4x - 3x = 35 - 15
=> x = 20
Hence, as value of x is 20 so <QRT is,
<QRT = 4x + 15° = 4 × 20 + 15
= 80 + 15 = 95° (Ans)
16) F(x) = (x + 1)exponetn (2) Identify the function family to which this belongs. A Absolute Value B Constant CLinear D Quadratic
D quadratic
Explanation
\(f(x)=(x+1)^2\)
you can easily identify a function with this :
if the exponent of the variable (x) is 1 , then it is a linear function:example
\(\begin{gathered} y=x,\text{ linear function} \\ y=3x+8 \end{gathered}\)if the exponent of the variable (x) is 2 , then it is a quadratic function
\(\begin{gathered} y=x^2 \\ y=(x+1)^2 \end{gathered}\)the absolute value has this symbol
\(y=\left|x\right|\)a constant function is a number, with no variable, example
\(\begin{gathered} y=4 \\ Y=-7 \end{gathered}\)so, the answer is D quadratic
please fast if could
Answer:9/41
SOH = opposite over hypotenuse
Step-by-step explanation:
Dimitri has let out 40m of his kite string, which makes an angle of 72° with the horizontal ground. If the kite flies directly over Sarah's head, what is the distance between Dimitri and Sarah?
Using the cosine ratio, the distance between Dimitri and Sarah is calculated as approximately 12.4 m.
How to Apply the Cosine Ratio?The cosine ratio is a trigonometric ratio that represents the ratio of the length of the adjacent side to the length of the hypotenuse in a right triangle. It is calculated by dividing the length of the adjacent side by the length of the hypotenuse.
Using the cosine ratio, we have:
Reference angle (∅) = 72 degrees
Hypotenuse length = 40 m
Adjacent length = distance between Dimitri and Sarah = x
Plug in the values:
cos 72 = x/40
x = cos 72 * 40
x ≈ 12.4 [to one decimal place]
Learn more about Cosine Ratio on:
https://brainly.com/question/15793827
#SPJ1
Reflect on the concept of function. What concepts (only the names) did you need to accommodate the concept of function in your mind? What is the simplest function you can imagine? In your day to day, is there any occurring fact that can be interpreted as a function? Is it possible to view a function? What strategy are you using to get the graph of a function?
Answer:
Step-by-step explanation:
For this kind of question you'd be better off if you'd write down and share your own answers to these conceptual questions and then ask for Brainly feedback on what you have written. You'll need to understand the concept of "function" often in algebra and beyond.
What concepts (only the names) did you need to accommodate the concept of function in your mind? input, output, rule, domain, range, mapping, variation (direct and inverse)
Simplest function: y = c (there's only one x-value and y equals that value)
In your day to day, is there any occurring fact that can be interpreted as a function? An electronic parking meter: the amount of time you can park at the meter without risking getting a ticket is dependent upon the number of quarters you insert into the meter, e. g, 15 minutes for 25 centers, 30 minutes for 50 cents, and so on.
Is it possible to view a function? Sure. Graph the function.
What strategy are you using to get the graph of a function? Set up a coordinate plane. Label the horizontal axis "x" and the vertical axis "y". Choose x (input) values that are included in the domain of the function. If the domain includes '0' you will be finding the 'y-intercept' of the function. Write the input and output as a point: (x, y). Plot that point. Choose other x values within the domain and calculate the corresponding y value for each. Plot several more points and draw a line or a curve through them. Of course there are more sophisticated strategies for graphing functions. Remember: If you're working with a function, there is never more than one output or y value for any particular input value.
PLS HELPPP!!!!!
its due soon, and mainly its asking for verbal
5 exponent -2 over 3
Given:
\(5^{-\frac{2}{3}}\)On simplification we get,
\(\begin{gathered} 5^{-\frac{2}{3}}=\frac{1}{5^{\frac{2}{3}}} \\ =\frac{1}{(5^2)^{\frac{1}{3}}} \\ =\frac{1}{25^{\frac{1}{3}}} \\ =\frac{1}{\sqrt[3]{25}} \end{gathered}\)Hence, the answer is,
\(\frac{1}{\sqrt[3]{25}}\)a fair die is rolled 100 times.the results are shown below
number:. 1. 2. 3. 4. 5. 6
no of times:. 12. 16. 25. 18. 15. 14
what is the probability of getting
1?
2?
3?
4?
5?
6?
1.) Probability of getting 1: 0.12 or 12%.
2.) Probability of getting 2: 0.16 or 16%.
3.) Probability of getting 3: 0.25 or 25%.
4.) Probability of getting 4: 0.18 or 18%.
5.) Probability of getting 5: 0.15 or 15%.
6.) Probability of getting 6: 0.14 or 14%.
To calculate the probability of getting a specific number on a fair die, we divide the number of times that number appears by the total number of rolls. In this case, the die was rolled 100 times, and the results are given as follows:
Number: 1 2 3 4 5 6
Times: 12 16 25 18 15 14
To find the probability of getting each number, we divide the corresponding number of times by the total number of rolls (100):
Probability of getting 1 = 12 / 100 = 0.12.
Probability of getting 2 = 16 / 100 = 0.16.
Probability of getting 3 = 25 / 100 = 0.25.
Probability of getting 4 = 18 / 100 = 0.18.
Probability of getting 5 = 15 / 100 = 0.15.
Probability of getting 6 = 14 / 100 = 0.14.
Therefore, the probabilities of getting each number on a fair die, based on the given results of 100 rolls, are approximately:
1: 0.12 or 12%,
2: 0.16 or 16%,
3: 0.25 or 25%,
4: 0.18 or 18%,
5: 0.15 or 15%,
6: 0.14 or 14%.
For more question on Probability visit:
https://brainly.com/question/25839839
#SPJ8
can someone help me with this
Answer:
2nd answer option : 6^(13/4)
Step-by-step explanation:
what are we doing, when 2 equal base terms with exponents are multiplied ? we add the exponents !
this is like 3⁴×3³ = 3⁷
because
3×3×3×3 × 3×3×3 = 3×3×3×3×3×3×3 = 3⁷
it is that simple.
and that concept is also valid for any kind of number as exponent. even for fractions and so on.
so,
6^3 × 6^(1/4) = 6^(3 + 1/4) = 6^(12/4 + 1/4) = 6^(13/4)
Sketch a graph of f(x)={- 5 if x < -2 2x-1 if-2 < x≤ 2 0 if x>2. (piecewise)
A graph of the given piecewise-defined function is shown in the image below.
What is a piecewise-defined function?In Mathematics and Geometry, a piecewise-defined function simply refers to a type of function that is defined by two (2) or more mathematical expressions over a specific domain.
Generally speaking, the domain of any piecewise-defined function simply refers to the union of all of its sub-domains. By critically observing the graph of this piecewise-defined function, we can reasonably infer and logically deduce that it is constant over several intervals or domains such as x > 2 and x < -2.
In conclusion, this piecewise-defined function has a removable discontinuity.
Read more on piecewise function here: brainly.com/question/18670055
#SPJ1
Suppose there is a 20.3% probability that a randomly selected person aged 40 years or older is a jogger. In addition, there is a 13.8% probability that a randomly selected
person aged 40 years or older is male, given that he or she jogs. What is the probability that a randomly selected person aged 40 years or older is male and jogs? Would it be
unusual to randomly select a person aged 40 years or older who is male and jogs?
The probability that a randomly selected person aged 40 years or older is male and jogs is (Round to three decimal places as needed.).
There is a 2.17% probability that a randomly selected person aged 40 years or older is male and jogs.
It would be unusual to randomly select a person aged 40 years or older who is male and jogs.
Step-by-step explanation:
We have these following probabilities.
A 13.9% probability that a randomly selected person aged 40 years or older is a jogger, so .
In addition, there is a 15.6% probability that a randomly selected person aged 40 years or older is male comma given that he or she jogs. I am going to say that P(B) is the probability that is a male. is the probability that the person is a male, given that he/she jogs. So
The Bayes theorem states that:
In which is the probability that the person does both thigs, so, in this problem, the probability that a randomly selected person aged 40 years or older is male and jogs.
So
There is a 2.17% probability that a randomly selected person aged 40 years or older is male and jogs.
A probability is unusual when it is smaller than 5%.
So it would be unusual to randomly select a person aged 40 years or older who is male and jogs.Step-by-step explanation:
(q1) Find the length of the curve described by the function
The value of the Integral at the lower limit from the value of the integral at the upper limit to get the length of the curve.
The length of the curve described by the function f(x) = 1 + 3x^2 + 2x^3 is to be found. The formula used to find the length of a curve is:
L = ∫(sqrt(1 + [f'(x)]^2))dx where f'(x) is the derivative of f(x)We have to first find f'(x):f(x) = 1 + 3x^2 + 2x^3f'(x) = 6x + 6x^2
The integral becomes:L = ∫(sqrt(1 + [6x + 6x^2]^2))dx = ∫(sqrt(1 + 36x^2 + 72x^3 + 36x^4))dx The integral appears to be difficult to evaluate by hand.
Therefore, we use software like Mathematica or Wolfram Alpha to solve the problem. Integrating the expression using Wolfram Alpha gives:
L = 1/54(9sqrt(10)arcsinh(3xsqrt(2/5)) + 2sqrt(5)(2x^2 + 3x)sqrt(9x^2 + 4))The limits of integration are not given. Therefore, the definite integral be solved.
We can, however, find a general solution. We use the above formula and substitute the limits of integration.
Then, we subtract the value of the integral at the lower limit from the value of the integral at the upper limit to get the length of the curve.
To know more about Integral.
https://brainly.com/question/27419605
#SPJ8
Is 604,892 divisible by 4?
Answer:
yes it is 604892÷4=151,223
Find the dimensions of a rectangle with area 512 m2 whose perimeter is as small as possible. (If both values are the same number, enter it into both blanks.)
Answer:
√512 by √512Step-by-step explanation:
Length the length and breadth of the rectangle be x and y.
Area of the rectangle A = Length * breadth
Perimeter P = 2(Length + Breadth)
A = xy and P = 2(x+y)
If the area of the rectangle is 512m², then 512 = xy
x = 512/y
Substituting x = 512/y into the formula for calculating the perimeter;
P = 2(512/y + y)
P = 1024/y + 2y
To get the value of y, we will set dP/dy to zero and solve.
dP/dy = -1024y⁻² + 2
-1024y⁻² + 2 = 0
-1024y⁻² = -2
512y⁻² = 1
y⁻² = 1/512
1/y² = 1/512
y² = 512
y = √512 m
On testing for minimum, we must know that the perimeter is at the minimum when y = √512
From xy = 512
x(√512) = 512
x = 512/√512
On rationalizing, x = 512/√512 * √512 /√512
x = 512√512 /512
x = √512 m
Hence, the dimensions of a rectangle is √512 m by √512 m
From the top of a building 30 meters high, the angle of elevation to the top of a monument is found to be equal to the angle of depression to the foot of the monument. Find the height of the monument.
The height of the monument is 30 meters.
We have,
Let's assume the height of the monument is "h" meters.
From the top of the building, the angle of elevation to the top of the monument is equal to the angle of depression to the foot of the monument. This forms a right triangle with the building, the monument, and the ground.
In this triangle, the opposite side of the angle of elevation is the height of the building, which is given as 30 meters.
The opposite side of the angle of depression is the height of the monument, which is "h" meters.
Since the angles of elevation and depression are equal, the triangle is an isosceles triangle.
Therefore, the opposite sides are equal in length.
By setting up the equation:
h = 30
Thus,
The height of the monument is 30 meters.
Learn more about triangles here:
https://brainly.com/question/25950519
#SPJ1
find the missing angle
Answer:
? = 77°
Step-by-step explanation:
the 3 angles in a triangle sum to 180° , that is
? + 35° + 68° = 180°
? + 103° = 180° ( subtract 103° from both sides )
? = 77°
Answer:77
Step-by-step explanation:
180-103=77
Select the correct answer.
Evaluate the following expression when x = -4 and y = 4.
x
6
−
x
4
y
A.
1
,
025
4
B.
1
,
023
4
C.
16
,
385
4
D.
−
1
,
023
4
Answer:
1023/4
Step-by-step explanation:
shown in the picture
1. 320 miles to 500 miles
Answer:
What is your question?? Are you asking which is greater or less than??
Get me right twinnnn
Answer:
\( \frac{9x { }^{2 } - 63x}{ 3x} \\ = \frac{3x(3x - 21)}{3x} \\ = 3x - 21 \)
hope it helps:)
Answer:3x-21
Step-by-step explanation:
\(\frac{9x^{2} - 63x }{3x}\) ⇒ \(\frac{3x * (3x - 21) }{3x}\) ⇒ cancel out 3x ⇒ 3x - 21
please please help last text then finals l give brainliest
1. The x - intercepts of the parabola are
x = 2.5 s and x = 7.5 s2. The meaning of the x-intercepts are the plane takes of at x = 2.5 s and lands at x = 7.5 s
3. The vertex of the parabola is at (5, 80).
What is a parabola?A parabola is a curved shape
1. Given the parabola above, to find the x - intercepts, we proceed as follows.
The x-intercepts are the points at which the graph cuts the x-axis.
They are
x = 2.5 s and x = 7.5 s2. The meaning of the x-intercepts in this problem are the points where the plane takes off and lands on the ground.
The plane takes of at x = 2.5 s and lands at x = 7.5 s
3. The vertex is the maximum point on the graph.
So, we see that the vertex is at x = 5 s and y = 80 ft
So, the vertex is at (5, 80).
Learn more about parabola here:
https://brainly.com/question/28094027
#SPJ1
What is the opposite reciprocal of 2/3?
Answer:The reciprocal of 2/3 is 3/2. The product of 2/3 and its reciprocal 3/2 is 1.
Step-by-step explanation:
s equivalent to the expression (3 x 100) + (5 × 1) + (9×) + (1x)²
100
What is a decimal that is
?
The decimal number that represents the expression (3 * 100) + (7 * 10) + (5 * 1) + (9 * 0.01) + (2 * 0.001) is; 375.092
How to convert numbers to decimal?
We want to find the decimal that is equivalent to the expression (3 * 100) + (7 * 10) + (5 * 1) + (9 * 0.01) + (2 * 0.001).
Thus, we have;
(3 * 100) = 300
(7 * 10) = 70
(5 * 1) = 5
(9 * 0.01) = 0.09
(2 * 0.001) = 0.002
Thus, the given initial expression can now be written as;
300 + 70 + 5 + 0.09 + 0.002 = 375.092
Thus, the decimal number that represents the expression
(3 * 100) + (7 ** 10) + (5 * 1) + (9 * 0.01) + (2 * 0.001) is; 375.092
The complete question is;
What is a decimal that is equivalent to the expression (3 * 100) + (7 ** 10) + (5 * 1) + (9 * 0.01) + (2 * 0.001)?
Read more about decimals at; https://brainly.com/question/7978210
#SPJ1
Which figure has a greater perimeter?
Answer: The purple triangle
Step-by-step explanation:
Perimeter is the distance around the shape. Adding up the sides of the purple triangle gives us 46.8ft while the green one only gives us 32.5ft. Therefore the purple triangle has the greater perimeter.
Simplify -7 1/8 - (-9 1/2)
Answer:
Convert 7 1/8 to an improper fraction.
Simplify 7 * 8 to 56
-56 + 1/8 - (-9 1/2)
Simplify 56 + 1 to 57
-57/8 - (-9 1/2)
Convert 9 1/2 to an improper fraction.
-57/8 - (-9 * 2 + 1/2)
Simplify 9 * 2 to 18
-57/8 - (-18 + 1/2)
Simplify 18 + 1 to 19
-57/8 - (-19/2)
Simplify brackets
-57/8 + 19/2
Find the LCD
LCD = 8
Make the denominators the same as the LCD
-57/8 + 19 * 4/2*4
Simplify. Denominators are now the same
-57/8 + 76/8
Join the denominators
-57 + 76/8
Simplify
19/8
Convert to a mixed fraction.
2 3/8
Your answer is D.
Step-by-step explanation:
Mr. Green has a class of 15 students. He can spend $20 on each student to buy math supplies for the year. He first buys all of his students calculators,
which costs a total of $85.05. After buying the calculators, how much does he have left to spend on each student?
$_
15 times 20 is 300
300 - 85.05 = 214.95
214.95/15 =
14.33
What is the minimum possible value of this decimal? Use words, pictures, or numbers to explain your reasoning.
Answer:
if 2.4 is there it will become -2. 4
There are 210 calories in a 12 ounce drink if Katie drinks 5 ounces how many calories did she drink
Answer:
she drank a total of 87.5 calories
Step-by-step explanation:
you divide 210 by 12, and multiply by 5! :)
Answer:
87.5
Step-by-step explanation:
calories per oz is 210/12=17.5 then 5x17.5=87.5
someone help me with this plz
Answer:
Yes
Step-by-step explanation:
QM is parallel to NR so we can say
angle MQP = angle NRP and
angle QMP = angle PNR
(Alternate angles)
Question also shows that Line QM = Line NR
So the two triangles PMQ and PNR are congruent by Angle Side Angle (ASA)
If a turtle can crawl 1/2 foot in 40 minutes, how many feet can he crawl in an hour and a half?
Answer:
120 minutes or 2 hours
Step-by-step explanation:
1/2 x 3 = 1 1/2
40 x 3 = 120 or 2 hours
Francium is an element with a half-life of 22 minutes. 1000 grams of francium is placed into a bowl determine how much Francium (in grams) will be left after 2 hours
The amount of the element, Francium, that will remain after 2 hours is 31.25 grams.
Half-life problemTo determine how much francium will be left after 2 hours, we need to calculate the number of half-lives that occur within that time period.
Given that the half-life of francium is 22 minutes, we can calculate the number of half-lives in 2 hours (120 minutes):
Number of half-lives = (Total time elapsed) / (Half-life)
Number of half-lives = 120 minutes / 22 minutes ≈ 5.4545
Since we can't have a fraction of a half-life, we take the integer part, which is 5.
Each half-life represents a halving of the amount of francium. So, after 5 half-lives, the remaining amount of francium can be calculated using the formula:
Remaining amount = Initial amount * (1/2)^(Number of half-lives)
Given that the initial amount is 1000 grams, we can calculate the remaining amount after 2 hours:
Remaining amount = 1000 grams * \((1/2)^5\)
Remaining amount ≈ 1000 grams * 0.03125
Remaining amount ≈ 31.25 grams
Therefore, after 2 hours, approximately 31.25 grams of francium will be left.
More on half-life can be found here: https://brainly.com/question/31666695
#SPJ1
What are the outputs of the function below?
-6, -3, 1, 5
-6, -3, 4, 6
-8, 2, 4, 6
-8, 2, 1, 5
Answer:
\(5 { \times 54}^{2} \)