The length of x in the isosceles right triangle is 15.6 units.
How to find the side of an isosceles triangle?An isosceles triangle is a triangle that has two sides equal to each other and two angles congruent to each other.
The triangle above is an isosceles triangle. The triangle is also a right angle triangle. A right angle triangle is a triangle that has one of it's angles as 90 degrees.
Using Pythagoras's theorem, let's find the side x
c² = a² + b²
where
c = hypotenusea and b are the legsTherefore,
11² + 11² = x²
121 + 121 = x²
x = √242
x = 15.5563491861
Therefore,
x = 15.6 units
learn more on isosceles triangle here:https://brainly.com/question/27022193
#SPJ1
2 1/3 - 4/7
what is the answer to this question
The solution for the algebraic expression 2 1/3 - 4/7 is 37/21
Given,
The algebraic expression ; 2 1/3 - 4/7
We have to solve this expression;
First lets solve the mixed fraction 2 1/3
2 1/3 = (2 x 3) + 1 / 3 = 6 + 1 / 3 = 7/3
Mixed fraction;
A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder. An amalgam of a whole number and a legal fraction is a mixed fraction.
Now,
7/3 - 4/7 = (7 x 7) / (3 x 7) - (4 x 3) / (7 x 3) = 49/21 - 12/21
That is,
49/21 - 12/21 = (49 - 12) / 21 = 37/21
That is,
The solution for the algebraic expression 2 1/3 - 4/7 is 37/21
Learn more about mixed fraction here;
https://brainly.com/question/2753661
#SPJ1
Adi is 5 inches short than Sunee. Sunee is n inches tall. What is an expression that represents Adi's height in inches?
The expression that represents the Adi's height in inches is n - 5.
Expression:
An expression is the mathematical statement which consists of numbers, variables and an arithmetic operation like addition, subtraction and division etc. between them.
Given,
Adi is 5 inches short than Sunee. Sunee is n inches tall.
Here we need to find the expression for Adi's height in inches.
Through the given question we know that,
Sunee is n inches tall.
And Adi is 5 inches lesser than Sunee.
Here we have the word short or less, that represents that we have to reduce that amount from the total.
Therefore, the expression for Adi's height in inches is,
=> n - 5.
To know more about Expression here.
https://brainly.com/question/14083225
#SPJ1
3potniIn a right triangle, the altitude drawn to the hypotenuse divides the hypotenuse into two segments of equal lengths 8 cm and 2 cm. What is the length of the altitude?O 10 cm
Answer:
[tex]\text{The altitude is 4cm.}[/tex]Step-by-step explanation:
Let's illustrate the situation in a diagram to understand.
In a right triangle if the altitude drawn divides the hypotenuse into two segments, then the length of the altitude is the geometric mean of the lengths of the two segments.
Therefore,
[tex]\begin{gathered} \frac{8}{a}=\frac{a}{2} \\ 2\cdot8=a^2 \\ 16=a^2 \\ a=\sqrt[]{16} \\ a=4\text{ cm} \end{gathered}[/tex]What does it mean to say that a number is a perfect square? Give one example of a number that is a perfect square and one that is not. Explain your examples.
A perfect square is a number that is gotten by multiplying it by itself.
An example of a perfect square is 25 and one that is not is 7.
What is a perfect square?A square number, sometimes known as a perfect square, is an integer that is the square of another integer; in other words, it is the product of another integer and itself. For instance, 9 is a square number since it equals 3² and may be expressed as 3 × 3.
A perfect square is a number that can be written as the product of two integers or as an integer's second exponent. 25 is a perfect square because it is the product of the integer 5 and itself, 5 × 5 = 25. A perfect square is a positive integer formed by multiplying an integer by itself.
Learn more about square on:
https://brainly.com/question/27307830
#SPJ1
6 kg of bananas cost $42. How much
would 35 kg cost?
Round the answer to the 2 decimal digit
Answer:
245
Step-by-step explanation:
6 - 42
35 - x
cross multiply
6x = 35 × 42
6x = 1470
x = 1470 ÷ 6
x = 245
Question 2
help pls its hard i forgt how to do it
Answer: 52
Step-by-step explanation:
a^2+b^2=c^2
x is the hypotenuse (c). You can find the hypotenuse by finding the opposite of the right angle
48^2+20^2=2304+400=2704
√2704=52
x=52
535(-8) ??? What is the answer
Answer: the answer is -4280
Step-by-step explanation:
A balcony at an apartment can hold up to 1,816 kilograms. How many 160-pound people can the balcony hold?
The balcony can hold 25 people of 160-pound weight.
According to the question,
We have the following information:
The maximum weight balcony can hold = 1816 kg
Weight of 1 person = 160 pound
Now, we will convert this weight into kilogram so that both the measurements have same units.
1 pound = 0.454 kg
160 pound = 160*0.454 kg
160 pound = 72.64 kg
Now, let's take the number of people balcony can hold to be x.
So, we have:
72.64x = 1816
x = 1816/72.64
x = 25
Hence, the number of people the given balcony can hold is 25.
To know more about pound here
https://brainly.com/question/27994061
#SPJ1
what’s the answer to this?
The correct option is B: They both are correct. The function g is the function f translated 4 units and it is also the function f translated 4 units to the left.
What is referred as the translation?In geometry, translation refers to a function that shifts an object a specified distance. The component is not otherwise altered. It has not been rotated, mirrored, or resized.When performing a translation, this same initial object is referred to as the pre-image, as well as the object after translation is referred to as the image.for the given question.
The parent function is f(x) = x + 1.
The translated function is g(x).
As, it is shown in the graph that there is a shift of 4 units up as well as 4 units to the left of the original line.
It mean both Veronica and Drawn are correct.
Thus, The function g is the function f translated 4 units and it is also the function f translated 4 units to the left.
To know more about the translation, here
https://brainly.com/question/1574635
#SPJ13
Please answer quickly
Answer:
[tex]y+2=\frac{5}{2} (x-6)[/tex]
Step-by-step explanation:
point-slope form: y-y1=m(x-x1)
x1=6
y1=-2
m=5/2
[tex]y+2=\frac{5}{2} (x-6)[/tex]
the half-life of carbon 14 is 5715 years. an artifact has been located such that only 10% of the original amount of carbon 14 remains in the item. Rounded to the nearest year, how old is the artifact?
The age of the radioactive artifact is approximately 19029.6 years old
RadioactivityRadioactivity is the phenomenon of the spontaneous disintegration of unstable atomic nuclei to atomic nuclei to form more energetically stable atomic nuclei. Radioactive decay is a highly exoergic, statistically random, first-order process that occurs with a small amount of mass being converted to energy.
To solve this problem, we have to find the disintegration constant and we can use the formula of half-life of the sample to do that.
The half-life of a sample is given as;
[tex]T_\frac{1}{2}=\frac{ln}{\lambda}\\T_\frac{1}{2} =\frac{ln}{5715} \\ T_\frac{1}{2} = 0.000121\\[/tex]
The formula of radioactivity is given as
[tex]N = N_oe^(^-^\lambda ^t)[/tex]
Substituting the values into the equation
[tex]N = N_oe^(^-^\lambda ^t)\\\frac{N}{N_o} = e^-^(^\lambda ^t)\\0.1 = e^-^(^0^.^0^0^0^1^2^1^*^t^)\\t = 19029.6 years[/tex]
The artifact is approximately 19029.6 years.
Learn more on radioactivity here;
https://brainly.com/question/26626062
#SPJ1
Given the slope of a line is -2 and it passes through the point (4,-5), write the equationof the line in standard form.
Answer:
The equation of the line is;
[tex]y=-2x+3[/tex]Explanation:
Given that
the slope of a line is -2 and it passes through the point (4,-5).
Applying the slope-intercept form of equation;
[tex]y-y_1=m(x-x_1)[/tex]Substituting the values of the slope and coordinates;
[tex]\begin{gathered} y-(-5)=-2(x-4) \\ y+5=-2x+8 \\ y=-2x+8-5 \\ y=-2x+3 \end{gathered}[/tex]Therefore, the equation of the line is;
[tex]y=-2x+3[/tex]Answer:
2x + y = 3
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = - 2 , then
y = - 2x + c ← is the partial equation
to find c substitute (4, - 5 ) into the partial equation
- 5 = - 8 + c ⇒ c = - 5 + 8 = 3
y = - 2x + 3 ← in slope- intercept form
add 2x to both sides
2x + y = 3 ← equation in standard form
Two similar pyramids have slant height of 4 and 6.1. Find the scale factor.2. If the volume of the smaller pyramid is 48 meters cubed, what is the volume of the larger pyramid?
1) Considering that the slant height of those pyramids is 4 and 6, we can find the scale factor by dividing their slant heights:
[tex]\frac{6}{4}=\frac{3}{2}\text{ or 1.5}[/tex]So we can state that the bigger pyramid is larger than the 1st pyramid by a scale factor of 1.5.
2) For the Volume of the Pyramid, we can write out the formula below:
[tex]V=\frac{1}{3}\cdot Ab\cdot h[/tex]Since the scale factor is 1.5 Then we can state that
[tex]\begin{gathered} V=\frac{48}{\frac{3}{2}} \\ V=32 \end{gathered}[/tex]the Volume of the smaller one is by similarity 1.5 or 3/2 times smaller than the larger one.
3) Hence, the answers are:
1.k=1.5
2. 32 m³
Part A
Andy is scuba diving. he starts at sea level and then descends 10.5 feet in 2 1/2 minutes what was Andy’s average change in elevation in feet per minute?
Part B
If he continues at this rate, Andy will be … in relation to sea level
A. -20.25
B. -25.5
C. -27.3
D. 30.6
Marking brainliest for answereing both
a. The change in elevation in feet per minute is 4.2 per feet.
b. If he continues at this rate,then Andy will be -25.2 feet below sea level.
Given Andy starts scuba diving at sea level and then descends 10.5 feet in 2 1/2 minutes.
we need to determine Andy's average change in elevation in feet per minute =?
therefore rate of descent = total descent/total time
time = 2 1/2 minutes = 5/2 minutes.
= -10.5/5/2
= -4.2 feet per minute.
Part B.
If he continues at this rate,the relation to sea level after 6 minutes will be:
= -4.2 × 6
= -25.2
Hence we get the required answers.
Learn more about Distance and time here:
https://brainly.com/question/17146782
#SPJ1
Your question is incomplete. Please find the missing content below.
Andy is scuba diving. He starts at sea level and then descends 10.5 feet in 2 1/2 minutes.
Part A How would you represent Andy's change in elevation? Express your answer as an integer. Enter your answer in the box. feet per minute.
Part B If he continues at this rate, where will Andy be in relation to sea level after 6 minutes? feet
A. -20.25
B. -25.5
C. -27.3
D. 30.6
Please someone help me figure out this scientific notation question
Scientific notation: 10¹
Integer: 10
The average radius of the sun is 10 times greater than the average
Explanation:The average radius of Jupiter:
[tex]R_J=4.34\times10^4miles_{}_{}[/tex]The average radius of the sun:
[tex]R_s=4.32\times10^5miles[/tex]The ratio of the two Radii
[tex]\frac{R_s}{R_J}=\frac{4.32\times10^5}{4.34\times10^4}[/tex][tex]\begin{gathered} \frac{R_s}{R_J}=0.995\times10 \\ \frac{R_s}{R_J}=9.95 \\ \frac{R_s}{R_J}=10\text{ (to the nearest integer)} \end{gathered}[/tex]The average radius of the sun is 10 times greater than the average
Five pulse rates are randomly selected from a set of measurements. The five pulso rates have a mean of 74 4 boats per minute. Four of the pulse rates are 84, 66, 79, and 57a. Find the missing valueb. Suppose that you need to create a list of n values that have a specific known mean. Some of thon values can be freely selected. How many of the n values can be froely assigned before the remaining valuesare determined? (The result is referred to as the number of degrees of freedom.)a. The missing value isbeats per minute
(a)
We have five pulse rates randomly selected with a mean of 74.4 beats per minute. We have four pulse rates given. We let x be the value of the fifth pulse rate. We have n equals 5 here since we have sample space of 5. We illustrate the mean of the pulse rates as
[tex]\begin{gathered} \operatorname{mean}=\frac{\sum x}{n} \\ \\ 74.4=\frac{84+66+79+57+x}{5} \end{gathered}[/tex]Let's solve for the value of x. We have
[tex]\begin{gathered} 74.4=\frac{286+x}{5} \\ 286+x=(74.4)\cdot5 \\ 286+x=372 \\ x=372-286 \\ x=86 \end{gathered}[/tex]Hence, the missing value is equal to 86.
Answer: 86
(b) The number of degrees of freedom is calculated using the equation
[tex]\text{Degrees of freedom}=n-1[/tex]We already identified that the sample space n is equal to 5. Hence, the degrees of freedom is equal to
[tex]\text{Degrees of freedom}=5-1=4[/tex]Answer: 4
1.64285714286
Round up the number
Answer: 1.6 or 2
Step-by-step explanation:
If you are rounding it to the nearest tenths then the answer is 1.6 but if you are rounding to the nearest whole number then its 2.
Jaclyn has $120 saved and earns $40 each month in allowance. Pedro has $180 saved and earns $20 a month in allowance.
If they both save their entire allowances, how long will it take before Jaclyn and Pedro have saved the same amount of money?
Enter your answer in the box
Answer:
3 months
Step-by-step explanation:
120 + 40m = 180 + 20m
Collect like terms
40m - 20m = 180 - 120
20m = 60
Divide
m = 60/20
m = 3
It will take them 3 months before Jaclyn and Pedro have saved the same amount of money.
combine the like terms to create an equivalent expression -4r - 2r + 5
Answer:8r+7-6r-5Combine the like terms=8r-6r+7-5Thenafter, simplify=2r+2
good luck
Step-by-step explanation:
A bouncy ball is dropped such that the height of its first bounce is 3.75 feet and each successive bounce is 79% of the previous bounce's height. What would be the height of the 7th bounce of the ball? Round to the nearest tenth (if necessary).
The ball would bounce to a height of 0.92 feet at the 7th bounce
How to determine the height of the 7th bounce of the ballThe given parameters are
Initial height = 3.75 feet
Rate of bounce = 79%
The height of the ball after n-th bounce is represented as
H(n) = A * rⁿ⁻¹
Where
A = Initial height = 3.75 feetr = Rate of bounce = 79%n = Number of bounceIn this case, we have
n = 7
So, we have
H(7) = 3.75 * (79%)⁷⁻¹
Evaluate the difference
H(7) = 3.75 * (79%)⁶
Evaluate the product
H(7) = 0.92
Hence, the height of the 7th bounce of the ball is 0.92 feet
Read more about exponential functions at
https://brainly.com/question/11464095
#SPJ1
please help!!!!
Submit a picture of your work :
Prove: All right angles are congruent. Use the definition of a right angle and the definition of congruent angles to prove
All right angles are congruent which is determined by the definitions of a right angle and congruent angles.
What are congruent angles?Congruent angles are two or more angles that are identical to each other. As a result, the measurements of these angles are equivalent.
Given that ∠1 and ∠2 are right angles.
By the definition of right angles i.e. right angle is one that is exactly 90 degrees. It is precisely one-quarter of a circle. When a pie is divided into four equal pieces, the tip of each slice forms a straight angle.
⇒ m ∠1 =90° ; m ∠2 = 90°
By the substitution to get
⇒ m ∠1 = m ∠2
Therefore, ∠1 ≅ ∠2
Hence, all right angles are congruent which is determined by the definitions of a right angle and congruent angles.
Learn more about the angles here :
https://brainly.com/question/28835566
#SPJ1
a steel sphere with a 3-inch radius is made by removing metal from the corners of a cube that has the shortest possible side lengths. how many cubic inches are in the volume of the cube?
The volume of the cube with the shortest possible side lengths is 216 cubic inches.
If a steel sphere with a 3-inch radius is made by removing metal from the corners of a cube that has the shortest possible side lengths, then the side lengths of the cube must be equal to the diameter of the sphere.
side length of cube = diameter of sphere
side length of cube = 2 x radius of sphere
side length of cube = 2 x 3 inches
side length of cube = 6 inches
The volume of the cube can be calculated using the formula below.
V = s³
where V = volume and s = side length of cube
V = (6 inches)³
V = 216 cubic inches
Learn more about volume of cube here: https://brainly.com/question/8738162
#SPJ4
6. Which of the following facts, if true, would allow you to prove that lines I and m are parallel? (1 point)
5/6
7 8
m22-m23
m27+m28=180*
Om24-m25
m26+m22=180°
1
3
4
2
m
Answer:
The first 3 answers
Step-by-step explanation:
∠2 and ∠3 are vertical angles which means they are congruent. That would then make ∠1 and ∠4 congruent.
∠7 and ∠8 = 180 means that is a straight line.
∠4 and ∠5 are alternate interior angles which make them congruent.
That would then mean ∠3 and ∠4 = 180 which is a straight line because ∠3 would then be a corresponding angle to ∠7.
A person has lost a card game and is counting the points left in his hand. He announces that he has five fours and five sevens. Write this statement as a number expression.
The statement as number expression is given by the total number of points are 55.
What is Mathematical expression?
An expression is a finite combination of symbol and numbers depending on the context
We are given that A person has lost a card game and he is counting the points left in his hand.
His cards were five fours and five sevens
And we have to write this statement as number expression
Now there are five fours that is [tex]5*4=20 points[/tex]
And five sevens that is [tex]5*7=35 points[/tex]
Hence the total number of points are 20+35=55 points.
To learn more about Expression please refer
https://brainly.com/question/723406
#SPJ13
Solve the multiple-angle equation. (Enter your answers as a comma-separated list. Use n as an arbitrary integer. Enter your response in radians.)2 cos 2x − 1 = 0
Given:
The function is:
[tex]2\cos2x-1=0[/tex]Find-:
The value of "x"
Explanation-:
The value of x is:
[tex]\begin{gathered} 2\cos2x-1=0 \\ \\ 2\cos2x=1 \\ \\ \cos2x=\frac{1}{2} \\ \end{gathered}[/tex]Solve for x is:
[tex]\begin{gathered} \cos2x=\frac{1}{2} \\ \\ 2x=\cos^{-1}(\frac{1}{2}) \\ \\ 2x=\frac{\pi}{3}+2\pi n\text{ and }2x=\frac{5\pi}{3}+2\pi n \end{gathered}[/tex]The value of "x" is:
[tex]\begin{gathered} 2x=\frac{\pi}{3}+2\pi n \\ \\ x=\frac{\pi}{2\times3}+\frac{2\pi n}{2} \\ \\ x=\frac{\pi}{6}+\pi n \end{gathered}[/tex]Another value of "x" is:
[tex]\begin{gathered} 2x=\frac{5\pi}{3}+2\pi n \\ \\ x=\frac{5\pi}{3\times2}+\frac{2\pi n}{2} \\ \\ x=\frac{5\pi}{6}+\pi n \end{gathered}[/tex]So, the answer is:
[tex]x=\frac{\pi}{6}+\pi n,\frac{5\pi}{6}+\pi n[/tex]1) Round the number to the underlined place value.
-17.625
if A=D and C =F which additional statement does not allow you to conclude that ABC=DEF?1. AC=DF2.B=E3.BC=EF4.AB=DE
Given that 2 of the angles are congruent, we can conclude that the others angles are congruent too, because the sum of inner angles of a triangle is equal to 180. So the additional information we need is
[tex]\angle B\cong\angle E[/tex]And having that we could use AAA criteria. Also we could need AC = DF and use ASA criteria.
In places where there are crickets, the outdoor temperature can be predicted by the rate at which crickets chirp. One equation that models the relationship between f = 1/4 * c + 40 , chirps and outdoor temperature is where c is the number of chirps per minute and ƒ is the temperature in degrees Fahrenheit. a. Suppose 110 chirps are heard in a minute. According to this model, what is the outdoor temperature? b. If it is 75 deg * F outside, about how many chirps can we expect to hear in one minute? c. The equation is only a good model of the relationship when the outdoor temperature is at least 55 deg * F (Below that temperature, crickets aren't around or inclined to chirp.) How many chirps can we expect to hear in a minute at that temperature?
HELPPPP ME PLEASEEEEEEE
a. Using the equation of the relationship, the temperature outdoor would be 67.5 °F.
b. 140 chirps in a minute.
c. 60 chirps at that temperature is expected.
d. The graph for the relationship is given below.
e. 1/4 is the unit rate or slope = in 1/4°F per chirp.
f. 40 represents the starting or initial temperature.
What is the Graph of a Linear Equation?The graph of a linear equation, y = mx + b, will have a slope value of m, and an initial value or y-intercept of b, which is the point on the y-axis that the line intercepts.
Given the equation, f = ¼c + 40, where:
f = temperature in degrees Fahrenheit
c = number of chirps
1/4 represents the temperature in °F per chirp
40 represents the initial temperature
a. Substitute c = 110 into the equation, f = ¼c + 40:
f = ¼(110) + 40
f = 67.5
The outdoor temperature is predicted to be 67.5 °F.
b. Substitute f = 75 into the equation, f = ¼c + 40:
75 = ¼c + 40
75 - 40 = ¼c
35 = 1/4c
4(35) = c
c = 140
140 chirps would be heard in a minute.
c. Substitute f = 55 into the equation, f = ¼c + 40:
55 = ¼c + 40
55 - 40 = ¼c
15 = c/4
4(15) = c
c = 60
Expect to hear 60 chirps at that temperature.
d. The graph for f = ¼c + 40 is in the attachment.
e. 1/4 is the unit rate or slope, which is the temperature in °F per chirp.
f. 40 tells us about the equation of the relationship that the initial temperature where we can start expecting the crickets to chirp starts from 40 °F.
Learn more about the linear graph on:
https://brainly.com/question/19040584
#SPJ1
The graph of a figure is shown below.
Which graph represents the reflection of this figure across the x-axis?
the first triangle in the photo
which is reflected on the x-axis
A graph which represents the reflection of this figure across the x-axis is: graph 5.
What is a reflection across the x-axis?In Mathematics, a reflection across the x-axis would maintain the same x-coordinate while the sign of the y-coordinate changes from positive to negative. Therefore, a reflection across the x-axis is given by this transformation rule:
(x, y) → (x, -y) = (3, 1) → (3, -1).
(x, y) → (x, -y) = (4, 0) → (4, 0).
(x, y) → (x, -y) = (3, -1) → (3, 1).
(x, y) → (x, -y) = (4, -2) → (4, 2).
(x, y) → (x, -y) = (2, -4) → (2, 4).
(x, y) → (x, -y) = (0, -2) → (0, 2).
In conclusion, a reflection across the x-axis would transform the geometric figure to that shown in the graph attached in the image below.
Read more on reflection here: brainly.com/question/20602330
#SPJ1
a jury pool has 22 men and 16 women, from which 12 jurors will be selected. assuming that each person is equally likely to be chosen and that the jury is selected at random, find the probability that the jury consists of