Given, sides of the triangle are 7 cm, 24 cm, and 25 cm. Squaring the lengths of the sides of the, we will get 49, 576, and 625. Therefore, the above equation satisfies, Pythagoras theorem. Hence, it is right angled triangle.
Which are side of a right triangle 7 24 and 25?Yes, 7, 24, 25 is a Pythagorean Triple and sides of a right triangle. Yes, 9, 40, 41 is a Pythagorean Triple and sides of a right triangle. No, 11, 56, 57 do not represent the sides of a right triangle.The triangle is therefore not acute. Thirteen plus seven equals twenty, and twenty is more than nine. The Triangle Inequality Theorem is satisfied by this set of side lengths. A triangle is formed by these lengths. No, not in the traditional sense of the word (Euclidean geometry). A "degenerate triangle" is possible, but it isn't exactly a triangle in the sense that we often think of triangle 8 + 7 = 15 the length of any two sides added together.To learn more about side of a right triangle refer to:
https://brainly.com/question/29107389
#SPJ4
A sample of bacteria is growing at an hourly rate of 15% according to the continuous exponential growth function. The sample began with 11 bacteria. How many bacteria will be in the sample after 21 hours
If the sample of bacteria is growing at an hourly rate of 15% continuously and the bacteria began with 11 bacteria then there will be 244.178 samples bacteria after 21 hours.
Given growth of bacteria 15% ,bacteria at beginning 11.
We have to find the number of sample of bacteria after 21 hours.
We have to first form exponential function which shows the growth of bacteria in variable t.
Exponential function which shows the sum is y=P[tex]e^{rt}[/tex]
where P is initial amount ,
r is rate and
y is the sum
So in our problem P=11 and r=0.15
y=11*[tex]e^{0.15t}[/tex]
To find the samples after 21 hours we have to put t=21.
y=11[tex]e^{0.15*21}[/tex]
y=11*[tex]e^{3.1}[/tex]
y=11*22.198 ([tex]e^{3.1}[/tex]=22.198 from e table)
y=244.178
Hence the samples after 21 hours will be 244 approximately.
Learn more about function at https://brainly.com/question/10439235
#SPJ4
Find the cube of (x-1/3x)
Answer:
2/3x
Step-by-step explanation
Answer:
(x³-3x²-3x-1) / (27x³)
Step-by-step explanation:
((x-1) / (3x))³
= (x-1)³ / /3x)³
(x-1)³ = (x-1)(x-1)(x-1) = x³ - 3x² - 3x - 1
then:
(x-1)³ / (3x³) = (x³-3x²-3x-1) / (27x³)
Leticia was driving 45 miles per hour. after traveling for four hours she found that she was to 250 miles east of albertville
Answer:
can you give the question?
Step-by-step explanation:
didnt ask a question
Ali and Baba discovered an underground palace and set out to map all the treasure in it. After carefully mapping the interior, they found that the palace had a vault filled with treasure chests. In each chest, they found either 7 gold bars or 11 silver bars. There were 90 bars in total. How many of them were gold bars?
Answer:
396 gold bars
Step-by-step explanation:
first of all we will find numbers of gold bar 7*99
which is 693 and
we will find number of silver bars 11*99
which is 1089
then 1089-693=
396
Are the ratios 2:1 and 14:6 equivalent?
yes
no
Answer:
Step-by-step explanation:
To check this, we need to know whether
2
1
=
3
2
We have,
2
1
=
2×3
1×3
=
6
3
and
3
2
=
3×2
2×2
=
6
4
We find that
6
3
<
6
4
, which means that
2
1
<
3
2
.
Therefore, The ratio 1:2 is not equivalent to the ratio 2:3
Answer:
No, they aren't equal.
Step-by-step explanation:
Using the order of operations, what should be done first to evaluate 12 divided by (negative 6) (3) + (negative 2)?
According to the order of operations, brackets are solved first which contains the division operation. Hence, 12 is divided by -6 first.
Order of Operations
Given expression is,
(12 ÷ (-6))(3) + (-2)
According to the BODMAS rule of operations, the precedence order of operations is as follows,
Brackets > Of > Division > Multiplication > Addition > Subtraction
Hence, we will start by solving the brackets first, then solve the division and then the addition.
Evaluation
Solving the given expression as per the order of operations,
Brackets are solved first, then division followed by multiplication and then addition. Division is always of the highest precedence among all operations after brackets and of.
12 ÷ (-6)(3) + (-2)
= 12 ÷ (-6)(3) - 2 [∵ +(-n) = -n]
= (-2)(3) -2
= -6 - 2
= -8
Thus, solving the +(-2) and then division of 12 by (-6) are the first operations to be performed in order to evaluate the given expression.
Learn more about operations here:
https://brainly.com/question/9559872
#SPJ4
The number of bacteria in a certain population increases according to a continuous exponential growth model with a growth rate parameter of 4.9% per hour how many hours does it take for the size of the sample to double
Answer:
14.5 hours to the nearest tenth.
Step-by-step explanation:
4.9% = 0.049.
If the original number is 50 it will double to 100 so
100 = 50(1.049)^t
1.049^t = 2
t * log 1.049 = log 2
t = log 2 / log 1.049
= 14.49 hours,
Geometric Series
It has 6 terms, increases by a factor of 4, and has a sum of 1365. Find the value of the first term.
Since the geometric series has 6 terms, increases by a factor of 4, and has a sum of 1365, the value of the first term is 1.
What is the sum of a geometric series?The sum of a geometric series is given by
Sₙ = a(rⁿ - 1)/(r - 1) with r > 1 where
n = number of terms, a = first term and r = common ratioNow, since our Geometric Series has 6 terms, n = 6. Also, it increases by a factor of 4, so, r = 4 and has a sum of 1365, so Sₙ = 1356. So,we have that
n = 6, Sₙ = S₆ = 1365 andr = 4The value of the first termSince we require the first term, a , making a subject of the formula, we have
a = Sₙ(r - 1)/(rⁿ - 1)
Substituting the values of the variables into the equation, we have
a = Sₙ(r - 1)/(rⁿ - 1)
a = S₆(r - 1)/(r⁶ - 1)
a = 1365(4 - 1)/(4⁶ - 1)
a = 1365(3)/(4096 - 1)
a = 4095/4095
a = 1
So, the value of the first term is 1.
Learn more about geometric series here:
https://brainly.com/question/2899779
#SPJ1
Consider the graph of rational function f
f(x)
-4
I
T
1
-2
6-
4-
2+
-2-
-4-
-6.
0
4+12
O
N.
2
Which equation represents function ?
OA f(2)= =+
OB. f(2)=426
Oc f(2)==
OD. f(2)=342-6
TY
6
X
Answer: B
Step-by-step explanation:
There is a hole at x=2, so the numerator and denominator should both have a factor of x-2.
This eliminates everything except for B.
N=
Help me please!!! Asap thanks so much :)
Answer:
n = 100
Step-by-step explanation:
the area (A) of the sector is calculated as
A = area of circle × fraction of circle
given A = 40π , then
πr² × [tex]\frac{n}{360}[/tex] = 40π
π × 12² × [tex]\frac{n}{360}[/tex] = 40π
144π × [tex]\frac{n}{360}[/tex] = 40π ( divide both sides by π )
144 × [tex]\frac{n}{360}[/tex] = 40 ( multiply both sides by 360 to clear the fraction )
144n = 14400 ( divide both sides by 144 )
n = 100
3. Assume that the likelihood of a child under the age of ten watching PBS is 0.76. Three children are
chosen at random. Use the binomial formula to calculate the following probabilities: (You must show
your work and round the solution to the nearest thousandths place.)
a. exactly two children will watch PBS
b. at most two children will watch PBS
C. at least 2 children will watch PBS
Using the binomial distribution, the probabilities are given as follows:
a) 0.4159 = 41.59%.
b) 0.5610 = 56.10%.
c) 0.8549 = 85.49%.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.For this problem, the values of the parameters are:
n = 3, p = 0.76.
Item a:
The probability is P(X = 2), hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{3,2}.(0.76)^{2}.(0.24)^{1} = 0.4159[/tex]
Item b:
The probability is P(X < 3), hence:
P(X < 3) = 1 - P(X = 3)
In which:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{3,3}.(0.76)^{3}.(0.24)^{0} = 0.4390[/tex]
Then:
P(X < 3) = 1 - P(X = 3) = 1 - 0.4390 = 0.5610 = 56.10%.
Item c:
The probability is:
[tex]P(X \geq 2) = P(X = 2) + P(X = 3) = 0.4159 + 0.4390 = 0.8549[/tex]
More can be learned about the binomial distribution at https://brainly.com/question/24863377
#SPJ1
what is the
area of
Rectangle with the length 3 XY
and width
14X2y
Answer: [tex]42x^3 y^2[/tex]
Step-by-step explanation:
[tex]A=(3xy)(14x^2 y)=42x^3 y^2[/tex]
WILL VOTE BRAINLIEST FOR THE FIRST RIGHT ANSWER
Answer:
B
Step-by-step explanation:
Let t and d be their ages now.
2 years ago, their ages were t - 2 and d 2.
Now, Tyler is 3 years older than David: t = d + 3
2 years ago, Tyler was 4 times as old as David: t - 2 = 4(d - 2)
The system of equations is:
t = d + 3
t - 2 = 4(d - 2)
Answer: B
Answer:
D
Step-by-step explanation:
Determine if the following lines are parallel (never intersect), perpendicular (intersect at a 90 degree angle), intersecting (intersect at just one point), or coinciding (intersect at all points)?
y = -6x − 8, -x + 6y = 12
Answer:
These lines are perpendicular.
Step-by-step explanation:
Put both equations in the slope intercept form of a line.
y = -6x - 8 This is already in the slope intercept form for a line
-x + 6y = 12 Add x to both sides of the equation
6y = x + 12 Divide through the whole equation by 6
y = 1/6x +2
Now we compare the two slopes of -6 and 1/6. They are negative reciprocals of each other. That means that the line are perpendicular.
If p= the motorcycle's original price in dollars, which algebraic expression
represents the reduced price?
A. 275-p
B. 275p
C. 275+ p
D. p - 275
Answer: D
Step-by-step explanation:
If the original price was p, a price reduction would be p- the amount. Per the given answers, $275 is used for the reduction amount.
Construct the indicated confidence interval for the population mean mu.
Using the z-distribution, the confidence interval is given by: (11.95, 12.65).
What is a z-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.z is the critical value.n is the sample size.[tex]\sigma[/tex] is the standard deviation for the population.In this problem, we have a 90% confidence level, hence[tex]\alpha = 0.9[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so the critical value is z = 1.645.
The other parameters are given as follows:
[tex]\overline{x} = 12.3, \sigma = 1.5, n = 50[/tex]
Hence the bounds of the interval are:
[tex]\overline{x} - z\frac{\sigma}{\sqrt{n}} = 12.3 - 1.645\frac{1.5}{\sqrt{50}} = 11.95[/tex]
[tex]\overline{x} - z\frac{\sigma}{\sqrt{n}} = 12.3 + 1.645\frac{1.5}{\sqrt{50}} = 12.65[/tex]
More can be learned about the z-distribution at https://brainly.com/question/25890103
#SPJ1
7 cm
Intro
5 cm
A
5 cm
D
4 cm
B
E
3 cm
3 cm
C
7 cm
Which face has an area of 28 cm²?
Face
4 of 10
Done
Answer:
Step-by-step explanation:
Solution
The length of all the rectangles is 7
You need the width to be 4
Area rectangle = L*w
Area rectangle = 7*4
Area rectangle = 28
Answer: B
Solve for x and show your steps. Is the solution extraneous? Check your work to show how you determined if the solution is extraneous or not.
The square root of the quantity 3 x plus 12 end quantity equals 9.
The value of x from the given expression is 23
Radical equationsGiven the following equation
√3x+12 = 9
Square both sides
√3x+12)² = 9²
3x + 12. = 81
Subtract 12 from both sides
3x + 12 - 12 = 81- 12
3x = 69
x = 23
Hence the value of x from the given expression is 23
Learn more on equations here: https://brainly.com/question/2972832
#SPJ1
x = 8, y = 11
The variables x and y vary inversely. Use the given values to write an equation relating x and y . Then find y when x=2.
[tex]y = \frac{1}{mx} [/tex]
[tex]11 = \frac{1}{8m} [/tex]
[tex]m = \frac{1}{88} [/tex]
[tex]y = \frac{1}{ \frac{1}{88}x } = \frac{88}{x} [/tex]
[tex]when \: x = 2 \\ y = \frac{88}{2} = 44[/tex]
Can someone do this please?
Answer:
<1 =73
Step-by-step explanation:
The sum of the angles of a triangle add to 180 degrees
72+ 35 + <1 = 180
Add like terms
107 + <1 = 180
Subtract 107 from each side
<1 = 180-107
<1 =73
Which of the following is the graph of f(x) = x2 − 5x + 4? WILL MARK BRAINLIEST
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
C) graph of a quadratic function with a minimum at 2.5, negative 2.25 and x intercepts at 1 and 4
Step-by-step explanation:Standard Form of a Quadratic Function: ax² + bx + c = 0, where a ≠ 0
Given function: x² - 5x + 4
⇒ a = 1, b = -5, c = 4
The minimum of a function is the lowest point of its parabola. We can use the following formula to find the vertex or the minimum of the function: [tex]x=\dfrac{-b}{2a}[/tex] . This will give us the x-value of the vertex, and we will need to solve for the y-value.
The vertex or minimum.
Step 1: Find the x-value of the vertex.
[tex]\\\implies x=\dfrac{-(-5)}{2(1)}\\\\\implies x=\dfrac{5}{2}=2.5[/tex]
Step 2: Find the y-value of the vertex by substituting 2.5 as the value of x in the given function.
[tex]\\\implies x^2 - 5x + 4\\\\\implies 2.5^2-5(2.5)+4\\\\\implies 6.25-12.5+4\\\\\implies -2.25[/tex]
Vertex: (2.5, -2.25)
The x-intercepts (roots).
We can use the Quadratic Formula to find the roots of this function.
Quadratic Formula: [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex] when [tex]ax^2+bx+c=0[/tex]
Equation: x² - 5x + 4 = 0
⇒ a = 1, b = -5, c = 4
Step 1: Substitute the values of a, b, and c into the formula.
[tex]\\\implies x=\dfrac{\bold{-(-5)}\pm\sqrt{\bold{(-5)^2}\bold{-4(1)(4)}}}{\bold{2(1)}}\\\\\implies x=\dfrac{5\pm\sqrt{\bold{25-16}}}{2}\\\\\implies x=\dfrac{5\pm\sqrt{\bold{9}}}{2}\\\\\implies x=\dfrac{5\pm3}{2}[/tex]
Step 2: Separate into two possible cases.
[tex]x_1=\dfrac{5-3}{2}\implies \dfrac{2}{2}\implies \boxed{1}\\\\x_2=\dfrac{5+3}{2}\implies \dfrac{8}{2}\implies \boxed{4}[/tex]
The x-intercepts of the given function are 1 and 4.
Learn more about quadratic equations here:
brainly.com/question/28105589
brainly.com/question/27988150
(‼️‼️I WILL MARK BRAINLIEST PLEASE HELP‼️‼️)Dilate the figure by the scale factor. Then enter
the new coordinates.
K = 5
(-3,-1)
A
(-1,-4) C
B(2,-2)
A' ([?], [ ])
B' ([ ], [ ])
C' ([ ], [ ])
Triangle ABC is dilated by a scale factor of 5 to get A'(-15, -5), B'(10, -10) and C'(-5, -20)
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, translation, rotation and dilation.
Rigid transformation preserves the shape and size of the figure. Reflection, translation, rotation are rigid transformations.
Triangle ABC has vertices at A(-3, -1), B(2, -2) and C(-1, -4). It is then dilated by a scale factor of 5 to get A'(-15, -5), B'(10, -10) and C'(-5, -20)
Find out more on transformation at: https://brainly.com/question/4289712
#SPJ1
Quick algebra 1 question for 25 points!
Only answer if you know the answer, quick shout-out to Dinofish32, tysm for the help!
Yes
It's inverse variationSee
3 contractors took 8hours
4 contractors took 6hours
We observe
No of contracter increases hence time decreasesSo it's inverse variation
Answer:
[tex]\fbox {Yes}[/tex]
Step-by-step explanation:
An inverse variation can be seen when two factors are compared, if one factor is seen to be increasing, then naturally the factor should be decreasing.
Here, as the number of contractors increase, the time taken to complete the work decreases.
∴ Hence, this represents an inverse variation.
What are the two numbers on the upper left and the three on the bottom?
The computation of the equation shows.that x is -4 and y is 0.6.
How to calculate the value?4x + 5y = -1
-5x - 8y = 10
The value of x and y will be calculated thus:
-5 × (4x + 5y = -1)
4 × -(5x - 8y = 10)
-20x - 25y = 5
-20x -32y = 40
Add the equation
57y = 45
y = 45/75 = 0.6
Since 4x + 5y = -1
4x + 5(0.6) = -1
4x + 3 = -1
x = -1 - 3
x = -4
Learn more about equations on:
brainly.com/question/2972832
#SPJ1
At a charity fundraiser, each female attendant donated $1,200 and each male attendant donated $800. If the average donation at the fundraiser was $900, what was the ratio of the number of female attendants to the number of male attendants.
Using the mean concept, the ratio of the number of female attendants to the number of male attendants was of 3.
What is the mean?The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.
In this problem:
There were f + m donations.The sum was of 1200f + 800m.The average was of 900.Hence:
[tex]\frac{1200f + 800m}{f + m} = 900[/tex]
1200f + 800m = 900f + 900m
100m = 300f
[tex]\frac{f}{m} = 3[/tex]
Hence the ratio was of 3.
More can be learned about the mean of a data-set at https://brainly.com/question/20640860
#SPJ1
Subject
mathematics, 06.11.2020 05:30 tonya3498
2. (15 points) sheila needs to hire a babysitter for the evening. the babysitter charges $10 for each
hour and also charges for the time she spends driving to and from the house. she thinks it will take
1.5 hours of total driving time. sheila is willing to spend $80 for the night for babysitting.
a. write an equation to determine for how many hours sheila can afford to hire the babysitter.
b. use the guess-and-check method to determine how many hours of babysitting sheila can
afford.
c. sheila finds another babysitter that lives much closer to her and would only need 1 hour of
driving time. however, she charges $15 per hour. write an equation to determine how many hours
of babysitting sheila could buy from her.
d. can sheila afford the same amount of babysitting from the second sitter as she could from the
first sitter?
a. The equation we get is 10(1.5 + x) = 80, where x is the number of hours Sheila can afford to hire the babysitter.
b. Sheila can afford the babysitter for 6 hours and 30 minutes.
c. The equation we get is 15(1 + x) = 80, where x is the number of hours Sheila can afford to hire the new babysitter.
d. Sheila can afford to hire the new babysitter for 4 hours and 20 minutes, while the first babysitter was hired for 6 hours and 30 minutes.
Thus, Sheila can't afford the same amount of babysitting from the second sitter as she could from the first sitter.
a. We assume the hours affordable to Sheila be x hours.
Per hour charge of the babysitter = $10.
Time taken by the babysitter traveling = 1.5 hours.
Therefore, total chargeable time = 1.5 + x.
Therefore, the total charge by the babysitter = $10(1.5 + x).
This needs to be equal to the amount Sheila is willing to spend, that is, $80.
Thus, the equation we get is: 10(1.5 + x) = 80.
b. We are asked to determine the hours Sheila can afford to hire the babysitter.
We have got the equation 10(1.5 + x) = 80, where x is the hours Sheila can afford to hire the babysitter.
Thus, by solving this equation, we can determine the hours Sheila can afford to hire the babysitter.
10(1.5 + x) = 80,
or, 1.5 + x = 8,
or, x = 8 - 1.5 = 6.5 = 6 hours and 30 minutes.
Thus, Sheila can afford the babysitter for 6 hours and 30 minutes.
c. Per hour charge of the new babysitter = $15.
Time taken by the new babysitter traveling = 1 hour.
Therefore, total chargeable time = 1 + x.
Therefore, the total charge by the new babysitter = $15(1 + x).
This needs to be equal to the amount Sheila is willing to spend, that is, $80.
Thus, the equation we get is: 15(1 + x) = 80.
d. We are asked whether Sheila affords the same amount of babysitting from the second sitter as she could from the first sitter.
To determine this, we need to find the hours she affords from the second babysitter, for which, we solve the equation 15(1 + x) = 80 as follows:
15(1 + x) = 80,
or, 1 + x = 80/15,
or, x = 80/15 - 1 = 65/15 = 13/3 = 4 hours and 20 minutes.
Sheila can afford to hire the new babysitter for 4 hours and 20 minutes, while the first babysitter was hired for 6 hours and 30 minutes.
Thus, Sheila can't afford the same amount of babysitting from the second sitter as she could from the first sitter.
Learn more about writing and solving equations at
https://brainly.com/question/24145091
#SPJ4
Cody Ray's credit card company uses the unpaid-balance method and charges a monthly periodic rate of
1.8%. His finance charge was $17.54, he made $376.90 in new charges and a $250 payment.
Based on Cody Ray's credit card details and the unpaid-balance method, Cody Ray's unpaid balance is $144.44 and his previous balance is $144.44. His new balance is $147.04
What are Cody Ray's balances?His unpaid balance is:
= Purchases + Finance charge - (Payments + Credit)
= 376.90 + 17.54 - 250
= $144.44
Previous balance is the $17.54 finance charges.
New balance:
= Unpaid balance + Finance charge + New Purchases
= 144.44 + (144.44 x 1.8%)
= $147.04
Find out more on credit card balances at https://brainly.com/question/6872962
#SPJ1
Rule 1: Multiply by 2 then add 1 starting from 1.
Rule 2: Divide by 2 then add 4 starting from 40.
I need to make a sequence and I need help :)
PLease dont delete my question :(
Rule 1:
1, 3, 7, 15, 31, 63, 127, 255, 511, 1023 etc
Rule 2:
40, 24, 16, 12, 10, 9, 8.5, 8.25, 8.125, 8.0625 etc
Hope this helps!
verify commutative property of multiplication and addition 5 4
- -
2 5
then what will the answer of this with prof and detaling
The commutative property of multiplication addition is illustrated below.
How to illustrate the information?The commutative property implies that the changing of orders of the numbers doesn't have a effect on the value.
In this case, 5 × 4 = 20. Also, changing them to 4 × 5 is still 20.
Likewise 2 + 5 as 5 + 2 gives 7.
Learn more about multiplication on:
brainly.com/question/10873737
#SPJ1
The volume of a cone is 37x³ cubic units and its height is x units.
Which expression represents the radius of the cone's base, in units?
3x
6x
О Злх2
97X2
The radius of the cone's base in the unit is 9*7x².
Which expression represents the radius of the cone's base, in units?Given:
The volume of a cone is 3*7x³ cubic units Its height is x units.To find:
The expression represents the radius of the cone's base, in units.Solution:
As we know, the volume of the cone formula is
V = πr²h/3
So, lets us compare the above formula with the given expression;
πr²h/3 = 3*7x³
Here, h is represented as x, we get;
πr²x/3 = 3*7x³
πr²/3 = 3*7x²
r²= 9*7x²
Hence, the radius of the cone's base, in units, is 9*7x².
To learn more about volume, refer to:
https://brainly.com/question/3390425
#SPJ9