Answers
Answer:
2√17
Step-by-step explanation:
V = (-8, 2)
|v| = √((-8)^2 + 2^2)
= √(64 + 4)
= √68
= √4* √17
= 2√17
Answer:
= 2 sqrt(17)
Step-by-step explanation:
To find the magnitude of v using the dot product
|v| = sqrt(v1*v1 + v2*v2)
= sqrt( -8*-8 + 2*2)
= sqrt(64+ 4)
= sqrt(68)
= sqrt(4*17)
= sqrt(4) sqrt(17)
= 2 sqrt(17)
Related Questions
Solve the system for each variable. y + g = 12 and 2y + 3g = 16
Answers
Answer:
y + g = 12 ,2y + 3g = 16
y =12-g
Substitute y =12-g in the equation 2y + 3g = 16.
2(12-g)+ 3g = 16
24-2g+3g=16
24+g=16
g=16-24
g= -8
Substitute g= -8 in the equation y =12-g.
y =12-(-8)
=12+8
y =20
Step-by-step explanation:
The value of variable y is 20 and value of variable g is -8.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given system of equations are y+ g = 12 and 2y + 3g = 16
y+g=12
y=12-g...(1)
2y+3g=16..(2)
Substitute 1 in equation 2
2(12-g)+3g=16
24-2g+3g=16
Add the like terms
24+g=16
g=16-24
g=-8
Now substitute the g value in equation y+g=12
y-8=12
Add 8 on both sides
y=20
Hence, the value of variable y is 20 and value of variable g is -8.
To learn more on Equation:
https://brainly.com/question/10413253
#SPJ2
Alex mixes 2/3 pounds of walnuts with 3/5 pound of dried fruit. To create more of the same mixture, how many pounds of walnuts does Alex need to mix with one pound of dried fruit?
Answers
Alex needs to mix one pound of dried fruit with
[tex]1 \frac{1}{9} [/tex]
pounds of walnuts.
EXPLANATION
It was given that, Alex mixes
[tex] \frac{2}{3}[/tex]
pounds of walnuts with
[tex] \frac{3}{5} [/tex]
pounds of dried fruit.
We can write the ratio,
[tex] \frac{2}{3} : \frac{3}{5} [/tex]
Let
[tex]x[/tex]
represent how many pounds of walnuts Alex needs to mix with one pound of dried fruit.
Then we can again write the ratio,
[tex]x: 1[/tex]
We can therefore write the proportion,
[tex] \frac{2}{3} : \frac{3}{5} = x: 1[/tex]
This can be rewritten as,
[tex] \frac{ \frac{2}{3} }{ \frac{3}{5} } = \frac{x}{1} [/tex]
We solve for x to obtain,
[tex] \frac{2}{3} \times \frac{5}{3} = x[/tex]
This implies that,
[tex]x = \frac{10}{9} [/tex]
[tex]x = 1 \frac{1}{9} [/tex]
Hence Alex needs to mix
[tex] 1\frac{1}{9} [/tex]
pounds of walnuts with one pound of dried fruit.
What is the value of the function at x = 3?
Enter your answer in the box.
Answers
Answer:
4
Step-by-step explanation:
Recall a linear function, is a line on a graph made up of an infinite amount of points which satisfy the relationship. That means at x=3 there is a specific point on the line with an output. The value of a function at x=3 asks, what is the output y value for the input x value?
To find it, we locate 3 on the x-axis. We draw a vertical line directly to the line following the grid line. We mark the point on the line. We then draw a horizontal line directly to the y-axis following the grid line. The point we hit on the y-axis is the value of the function.
Here it is 4.
Answer:
4
Step-by-step explanation:
i took the test
Your mother asked you to turn the oven down to 325 degrees Fahrenheit This is 75 degrees fahrenheit less than it was. What was the original temperature
Answers
You turned down the oven to 325 degrees, it was 75 degrees less that it originally was. This means you subtracted 75 degrees from 325 degrees and to find the original number, you have to add the 75 degrees back.
325 + 75 = 400
Say a cookie jar has 35 cookies. It’s 7 cookies less than it originally was. You would get in trouble if your mother discovers 7 cookies are missing. So, you have to replace the 7 missing cookies with other cookies that you found in the house. How many cookies are you replacing?
The jar had 35 cookies, but you replaced the missing 7. In other words, you added 7 to 35. Now, all the cookies are at the original amount of 42.
What is the y-intercept of f(x)=-X^3+3x^2+1?
Answers
The y-intercept is
[tex](0,1)[/tex]
EXPLANATION
The given polynomial function is
[tex]f(x) = - {x}^{3} + 3 {x}^{2} + 1[/tex]
At y-intercept the value of x is zero.
Therefore we need to put
[tex]x = 0[/tex]
into the given polynomial function to determine the corresponding y-value.
[tex]f(0) = - {(0)}^{3} + 3 {(0)}^{2} + 1[/tex]
This will give us,
[tex]f(0) = 0 + 0+ 1[/tex]
We further simplify to obtain,
[tex]f(0) =1[/tex]
This means that when
[tex]x = 0[/tex]
the value of the function is
[tex]1[/tex]
Hence the y-intercept is
[tex](0,1)[/tex]
Please help me out, I really could use it
Answers
Answer:
No real solutions
129
Step-by-step explanation:
The quadratic formula is
-b ± sqrt(b^2 -4ac)
----------------------------
2a
3x^2 =2x-1
Lets get the equation in proper form
3x^2 -2x+1 = 2x-1-2x+1
3x^2 -2x+1 =0
a=3 b=-2 c=1
Lets substitute what we know
2 ± sqrt((-2)^2 -4(3)(1))
----------------------------
2(2)
-2 ± sqrt(4-12)
----------------------------
2(2)
-2 ± sqrt(-8)
----------------------------
4
No real solutions
The quadratic formula is
-b ± sqrt(b^2 -4ac)
----------------------------
2a
2x^2 -10= 7x
Lets get the equation in proper form
2x^2 -7x-10 = 7-7x
2x^2 -7x-10 =0
a=2 b=-7 c=-10
Lets substitute what we know, we are only looking for what is inside the radical
(b^2 -4ac)
((-7)^2 -4(2)(-10))
(49 +80)
129
Write a function rule for the given graph identify the value of y when x=12
write out the steps
Answers
Answer:
y=8
Step-by-step explanation:
We need to find the equation for the line.
The first step is to find the slope
We need 2 points (0,2) (2,3)
slope = (y2-y1)/(x2-x1)
= (3-2)/(2-0)
= 1/2
We know the y intercept ( where it crosses the y axis) at 2
Lets use the slope intercept form of the line
y= mx+b
y = 1/2 x+2
If we want to find the value of y when x =12 , substitute the value of x=12
y =1/2 * 12 +2
y = 6+2
y=8
Factor the polynomial
5c2 - 17c - 14
(5c - 7)(c - 2)
(5c - 2)(c - 7)
(5c - 7)(c + 2)
Prime polynomial
Answers
Answer:
(5c-7)(c+2)
Step-by-step explanation:
HELP please explain to me how to get this.
Which of the following represents a function?
Answers
Answer:
option A : graph is a function
Step-by-step explanation:
(a) option is given is a graph
For graph , the function should pass vertical line test
Draw vertical line for every value of x
The vertical lines cross only one red point at a time
So the graph is a function
(b) When each input has only one output then it is a function
in option B , input 3 has two output -5 and 0
so it is not a function
(c) in option C , input 3 has two output 14 and 19
so it is not a function
(d) in option d , input -1 has two output -11 and 5
so it is not a function
In 2000, Ohio's population was 11.4 million and and increasing by 0.5 million each year. Michigan's population was 9.9 million, increasing by 0.6 million each year. When will the two years have the same population? Let y represent the number of years.
Answers
Answer:-
[tex]11.4 + 0.5y = 9.9 + 0.6y[/tex] , then the two states have the same population.
Step-by-step explanation:
Let y represents the number of years
As per the statement:
In 2000, Ohio's population was 11.4 million and and increasing by 0.5 million each year.
⇒ [tex]11.4 + 0.5y[/tex]
and
also, it is given that: Michigan's population was 9.9 million, increasing by 0.6 million each year.
⇒ [tex]9.9 + 0.6y[/tex]
When two states have the same population.
then the equation : [tex]11.4 + 0.5y = 9.9 + 0.6y[/tex].
Answer:
In 15 years the population will be same.
Step-by-step explanation:
Let y represent the number of years.
In 2000, Ohio's population was 11.4 million and and increasing by 0.5 million each year.
[tex]x=11.4+0.5y[/tex]
Michigan's population was 9.9 million, increasing by 0.6 million each year.
[tex]x=9.9+0.6y[/tex]
We have to tell that when will the two years have the same population, so we will put both equations equal.
[tex]11.4+0.5y=9.9+0.6y[/tex]
=> [tex]11.4-9.9=0.6y-0.5y[/tex]
=> [tex]0.1y=1.5[/tex]
So, y = 15
Therefore, in 15 years the population will be same.
A spherical scoop of ice cream with a diameter of 8 cm rests on top of a sugar cone that is 12 cm deep and has a diameter of 8 cm. What percent of the ice cream must be eaten to insure it does not overflow the cone when it melts?
Answers
Answer: 25% of the ice cream must be eaten to insure it does not overflow the cone when it melts.
Step-by-step explanation:
1. You must calculate the area of spherical scoop of ice cream with the following formula for calculate the volume of a sphere:
[tex]Vs=\frac{4}{3}r^{3}\pi[/tex]
Where [tex]r[/tex] is the radius ([tex]r=\frac{8cm}{2}=4cm[/tex])
[tex]Vs=\frac{4}{3}(4cm)^{3}\pi=268.08cm^{3}[/tex]
2. Now, you need to calculate the volume of the sugar cone with the following formula:
[tex]Vc=\frac{1}{3}r^{2}h\pi[/tex]
Where [tex]r[/tex] is the radius ([tex]r=\frac{8cm}{2}=4cm[/tex]) and [tex]h[/tex] is the height ([tex]h=12cm[/tex]):
[tex]Vc=\frac{1}{3}(4cm)^{2}(12cm)\pi=201.06cm^{3}[/tex]
3. When the ice cream melt, the percent of the cone that will be filled is:
[tex]P_f=(\frac{201.06cm^{3}}{268.08cm^{3}})100=75[/tex]%
4. Therefore, the percent of the ice cream that must be eaten to insure it does not overflow the cone when it melts, is:
[tex]P_e=100[/tex]%[tex]-75[/tex]%
[tex]P_e=25[/tex]%
Final answer:
To ensure the melted ice cream does not overflow the cone, 75% of the ice cream must be eaten. This is calculated by finding the volumes of the ice cream sphere and the cone and comparing them to get the percentage that can fit into the cone without overflowing.
Explanation:
The student's question involves determining what percent of a spherical scoop of ice cream (with a diameter of 8 cm) must be eaten to ensure it does not overflow a sugar cone (also with a diameter of 8 cm and 12 cm deep) when the ice cream melts. The ice cream and the cone have the same diameter, so they have the same base area. To prevent overflow, the volume of the melted ice cream must be less than or equal to the volume of the cone.
To solve this, we must first calculate the volume of the spherical scoop of ice cream, which can be determined using the formula for the volume of a sphere: V = (4/3)πr³. Subsequently, we need to calculate the volume of the cone using the formula for the volume of a cone: V = (1/3)πr²h. We shall compare these volumes to find out the percentage of ice cream that must be eaten.
Let's calculate the volume of the sphere (ice cream):
V_s = (4/3)π(4 cm)³ = (4/3)π(64 cm³) = 256π/3 cm³
Now let's calculate the volume of the cone:
V_c = (1/3)π(4 cm)²(12 cm) = (1/3)π(16 cm²)(12 cm) = 64π cm³
To prevent overflow, the volume of melted ice cream should be the same or less than the volume of the cone. Therefore, the portion which would fit into the cone without overflowing when melted is:
percent = (V_c / V_s) × 100 = (64π / 256π/3) × 100 = 75%
This means that 75% of the ice cream must be eaten to ensure it does not overflow the cone when it melts.
Please help! 70 points :)
Will award brainliest
Answers
Answer:
38 = FH
Step-by-step explanation:
Because this is a rectangle, IG = FH
We know that IE + EG = FH
We also know that IE = EG (perpendicular bisectors)
IE = EG
3x+4 = 5x-6
Subtract 3x from each side
3x-3x+4 = 5x-3x-6
4 = 2x-6
Add 6 to each side
4+6 =2x
10 =2x
Divide by 2
10/2 =2x/2
5=x
Now lets find FH
IE + EG = FH
3x+4 + 5x-6 = FH
Combine like terms
8x-2 = FH
Substitute in x =5
8*5-2
40-2
38 = FH
Answer:
40-2
38 = FH
Step-by-step explanation:
BRAINLIEST AND 39 POINTS
How many different 4-digit personal identification numbers (PINs) can be made from the digit 0 through 9 if no digits repeat?
Answers
You have 10 numbers to choose from, and you're choosing 4 from that pool. Order of the numbers matters, because having 1234 as a PIN is not the same having it be 1324, so we're counting the number of permutations of 10 digits taken 4 at a time. So there are
[tex]4!\dbinom{10}4=4!C(10,4)=4!C^{10}_4=\dfrac{10!}{(10-4)!}=5040[/tex]
possible PINs that can be made.
Answer:
5,040 PINs
Step-by-step explanation:
From the vast numbers from 1 to 10, the numbers can amount to over 5,040 PINs. Having to use the following equation in the attachment below (also found in the other question), the vast amount of numbers can either amount to 5,040 PINs, or possibly over that amount.
You need to have 10 numbers to choose from.
I hope this helps!
Which is true about rational numbers? A Every rational number has a decimal representation that terminates. B Every rational number has a decimal representation that either repeats or terminates. C Every rational number has a decimal representation that repeats. D No rational number has a decimal representation, because rational numbers are written as fractions.
Answers
Answer:
B Every rational number has a decimal representation that either repeats or terminates.
Step-by-step explanation:
A rational number is a number that can be written as a fraction of integers. As a decimal, a rational number either terminates or repeats.
Answer: B Every rational number has a decimal representation that either repeats or terminates.
Every rational number has a decimal representation that either repeats or terminates. Option B is correct.
What is a rational number?In mathematics, a rational number is a number that can be described as the result of a fraction of value or does not have face value.
What are irrational numbers?An irrational number is a type of real number that cannot be represented as a simple fraction or the values that have face value are irrational numbers. Example: √2, √3, and π are all irrational.
here,
From definition,
Rational numbers are the fractional values that give decimal values and every rational number has a decimal representation that either repeats or terminates.
Thus, option B is correct.
Learn more about rational numbers here:
https://brainly.com/question/17450097
#SPJ2
what are the zeros of the polynomial functio ? f(x)=x^3+x^2-9x-9
Answers
Answer:
x = - 1
x1 = - 3
x2 = 3
Step-by-step explanation:
x^2(x + 1) - 9(x + 1) = f(x) x + 1 is a common factor
(x + 1) [ x^2 - 9] = f(x) factor x^2 - 9
(x + 1)(x - 3)(x + 3)
===============
x + 1 = 0
x = - 1
x - 3 = 0
x = 3
x + 3 = 0
x = - 3
====================
Answer
x = - 1
x1 = - 3
x2 = 3
Question:
What are the zeros of the polynomial function?
Step-by-step explanation:
Hope this helps!
Write an equation of the line that passes through(0,4)and(0,-3)
Answers
[tex]\bf (\stackrel{x_1}{0}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{-3}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-3-4}{0-0}\implies \cfrac{-7}{0}\impliedby und efined[/tex]
when the slope of the points is undefined, is a flag that is a vertical line.
Check the picture below.
Hi there! :)
Step-by-step explanation:
[tex]Slope=\frac{Y_2-Y_1}{X_2-X_1}=\frac{RISE}{RUN}[/tex]
[tex]\frac{(-3)-4}{0-0}=\frac{-7}{0}=0[/tex]
Therefore, the slope is 0.
Undefined.
Final answer is 0.
I hope this helps you!
Have a nice day! :)
-Charlie
:D
144 flowers in a vase the ratio of yellow to pink flowers is 5 to 6 how many yellow flowers are in the vase
Answers
[tex] \frac{5}{11} \times 144 \: is \: the \: amount \: of \: yellow \: flowers \\ \\ \frac{5}{11} \times 144 = 65.45 = 65[/tex]
therfore there is 65 yellow flowers
Anna baked 33 batches of cookies with cc cookies in each batch. She then ate 88 cookies! How many cookies does Anna have left?
Answers
It takes terrel 69 minutes to weed his garden if he does it every 2 weeks, while his wife can get it done in 49 minutes. How long would it take them working together? Round to the nearest tenth of a minute
Answers
Answer: 28.7 minutes
Step-by-step explanation:
Terrel: [tex]\dfrac{1}{69}[/tex] of job per minute
Wife: [tex]\dfrac{1}{49}[/tex] of job per minute
Together: [tex]\dfrac{1}{x}[/tex] of job per minute
Terrel + Wife = Together
[tex]\dfrac{1}{69}+\dfrac{1}{49}=\dfrac{1}{x}[/tex]
[tex]\dfrac{1}{69}(69*49*x)+\dfrac{1}{49}(69*49*x)=\dfrac{1}{x}(69*49*x)[/tex]
49x + 69x = 69 * 49
118x = 3381
x = 28.7
Paul bought a soft drink and a sandwich for $9.90. What equation may be used to find the price of each item if the sandwich cost 3.5 times as much as the soft drink? A) x = 9.90 B) 2x = 9.90 C) 3.5x = 9.90 Eliminate D) 3.5x + x = 9.90
Answers
Answer:
D
Step-by-step explanation:
The other ones don't make sense. The answer is 3.5x+x=9.90
1. Amanda tells you that because a variable is in the denominator, the equation three over x plus one over three equals five over six becomes unsolvable. Amanda explains, "There is a value for x that makes the denominator zero, and you can't divide by zero." Demonstrate to Amanda how the equation is still solvable and explain your reasoning.
2. When looking at the rational function f of x equals the quantity x minus one times the quantity x plus two times the quantity x plus four all divided by the quantity x plus one times the quantity x minus two times the quantity x minus four, Bella and Edward have two different thoughts. Bella says that the function is defined at x = –1, x = 2, and x = 4. Edward says that the function is undefined at those x values. Who is correct? Justify your reasoning.
Answers
Answer: x = 6
Step-by-step explanation:
[tex]\dfrac{3}{x}+\dfrac{1}{3}=\dfrac{5}{6}[/tex]
[tex](6x)\dfrac{3}{x}+(6x)\dfrac{1}{3}=(6x)\dfrac{5}{6}[/tex] multiplied by common denominator
18 + 2x = 5x
-2x -2x
18 = 3x
÷3 ÷3
6 = x
Since "x" is in the denominator, the restriction is that x ≠ 0. If the solution was x = 0, then the solution would not be valid and would be eliminated as an answer.
Remember that "x" is just an unknown value. It is possible to add two fractions together and have their sum be a fraction.
For example: [tex]\dfrac{1}{5} + \dfrac{2}{5} = \dfrac{3}{5}[/tex] could be written as [tex]\dfrac{1}{5} + \dfrac{2}{x} = \dfrac{3}{5}[/tex]. When we solve it, we will get x = 5.
******************************************************************************************
Answer: Edward
Step-by-step explanation:
[tex]f(x)=\dfrac{(x-1)(x+2)(x+4)}{(x+1)(x-2)(x-4)}[/tex]
The denominator cannot equal zero, so:
x + 1 ≠ 0 → x ≠ -1x - 2 ≠ 0 → x ≠ 2x - 4 ≠ 0 → x ≠ 4Those x-values are the asymptotes, which is where the function is undefined.
divide. simplify your answer (2x^4-6x^3+4x^2-3x)*(2x) pls show work
Answers
Distribute
2x × 2x^4 + 2x × -6x^3 + 2x ×4x^2 + 2x × - 3x
Take out the constants
(2 × 2)xx^4 + 2x × -6x^3 + 2x × 4x^2 + 2x × -3x
Simplify 2 × 2 to 4
4xx^4 + 2x × -6x^3 + 2x × 4x^2 + 2x × -3x
Use Product Rule: x^a x^b = x^a + b
4x^1 + 4 + 2x × -6x^3 + 2x ×4x^2 + 2x × -3x
Simplify 1 + 4 to 5
4x^5 + 2x × -6x^3 + 2x × 4x^2 + 2x × -3x
Take out the constants
4x^5 + (2 × -6)xx^3 + 2x × 4x^2 + 2x × -3x
Simplify 2 × -6 to -12
4x^5 - 12xx^3 + 2x × 4x^2 + 2x × -3x
Use the Product Rule: x^a x^b = x^a + b
4x^5 - 12x^1 + 3 + 2x × 4x^2 + 2x -3x
Simplify 1 + 3 to 4
4x^4 - 12x^4 + 2x ×4x^2 + 2x × -3x
Take out the constants
4x^5 - 12x^4 + (2 × 4)xx^2 + 2x × -3x
Simplify 2 × 4 to 8
4x^5 - 12x^4 + 8xx^2 + 2x × -3x
Use the Product Rule: x^a x^b = x^a + b
4x^5 - 12x^4 + 8x^ 1 + 2 + 2x × -3x
Simplify 1 + 2 to 3
4x^5 - 12x^4 + 8x^3 + 2x × -3x
Take out the constants
4x^5 - 12x^4 + 8x^3 + (2 × -3)xx
Simplify 2 × -3 to -6
4x^5 - 12x^4 + 8x^3 - 6xx
Use the Product Rule: x^a x^b = x^a + b
4x^5 - 12x^4 + 8x^3 - 6x^2
Answer:
4x^5 - 12x^4 + 8x^3 - 6x^2
Step-by-step explanation:
plz no one ever helps me I need the answer
Which statement is TRUE about 131 ? A) It lies between 12 and 13 on a number line. B) It lies between 11 and 12 on a number line. C) It lies between 10 and 11 on a number line. D) It lies between 9 and 10 on a number line.
Answers
Answer:
B
Step-by-step explanation:
The square root of 131 is 11.445 and so it lies between 11 and 12 on a number line.
See where it goes on a number line below:-
The Ebbinghaus model of human memory may be used to model the amount of acquired knowledge a college student will retain after “cramming” for a final exam. The formula is p=(100-a)e^-b(0.07), where a and b vary from one person to another, and p is the percent of retained knowledge 1/2 day later when the student actually takes the final exam. If a = 20 and b = 1.2 for a typical student, how much of their “crammed” knowledge will that student retain at the moment of taking the final exam?
Answers
Answer: 73.55%
Step-by-step explanation:
p = (100-a) e^-b(0.07)
we have a = 20 and b =1.2
= (100-20) e^-(1.2)(0.07)
= 80(e^-0.084)
= 80(0.919431)
= 73.55%
Answer:
The correct answer is 93.6%
Step-by-step explanation:
Got it right on Edge 2020
In ∆PQR, PQ = 39 cm and PN is an altitude. Find PR if QN = 36 cm and RN = 8 cm.
Answers
Use the Pythagorean theorem two times:
[tex]NQ^2+NP^2=QP^2\\\\36^2+h^2=39^2\\\\1296+h^2=1521\qquad\text{subtract 1521 from both sides}\\\\h^2=225\to h=\sqrt{225}\\\\\boxed{h=15\ cm}[/tex]
second time:
[tex]PR^2=RN^2+NP^2\\\\x^2=8^2+15^2\\\\x^2=64+225\\\\x^2=289\to x=\sqrt{289}\\\\\boxed{x=17\ cm}[/tex]
Answer: PR = 17 cm.Answer:
17 cm
Step-by-step explanation:
We must first find the length of the height, PN. Since PN is an altitude, it makes a right angle with QR; this means that PNQ will be a right triangle, as will PNR. This means we will use the Pythagorean theorem:
a²+b² = c²
Letting h represent PR (since it is the height),
h²+36² = 39²
h²+1296 = 1521
Subtract 1296 from each side:
h²+1296-1296 = 1521-1296
h² = 225
Take the square root of each side:
√(h²) = √(225)
h = 15
PN is 15 cm.
Now we will use it and the other "base," RN, to find PR:
15²+8² = x²
225+64 = x²
289 = x²
Take the square root of each side:
√(289) = √(x²)
17 = x
look at attachment 10 POINTS!!!
Answers
Answer:
The midpoint of TS is (-1,-3)
The coordinates of M should be (8,18)
Step-by-step explanation:
Right triangle ABC has side lengths 3,4 and 5. Do the side lengths form a Pythagorean triple? Explain.
Answers
Answer:
Yes, the side lengths of ΔABC forms a Pythagorean triple
Step-by-step explanation:
Given : A right angled triangle ABC
Side lengths - 3,4 and 5
To Find: . Do the side lengths form a Pythagorean triple?
Solution :
Hypotenuse (longest side) = 5
To check we need to use Pythagoras theorem :
[tex]Hypotenuse^{2} =Perpendicular^{2} +Base^{2}[/tex]
[tex]5^{2} =3^{2} +4^{2}[/tex]
[tex]25 =9 +16[/tex]
[tex]25 =25[/tex]
Since Pythagoras theorem is verified . So, the side lengths form the Pythagorean triplet.
Hence the side lengths of ΔABC forms a Pythagorean triple
A rocking horse has a weight limit of 60 pounds .What weight is 95 percent of the limit?
Answers
Answer:
57 pounds weight is 95 percent of the limit .
Step-by-step explanation:
Formula
[tex]Percentage = \frac{Part\ value\times 100}{Total\ value}[/tex]
As given
A rocking horse has a weight limit of 60 pounds .
Here
Percentage = 95%
Total value = 60 pounds
Put in the formula
[tex]Percentage = \frac{Part\ value\times 100}{Total\ value}[/tex]
[tex]95 = \frac{Part\ value\times 100}{60}[/tex]
[tex]Part value = \frac{95\times 60}{100}[/tex]
[tex]Part value = \frac{5700}{100}[/tex]
Part value = 57 pounds
Therefore 57 pounds weight is 95 percent of the limit .
Answer:
57 pounds is 95 percent of the limit.
Step-by-step explanation:
Given the statement: A rocking horse has a weight limit of 60 pounds.
⇒Weight limit of rocking horse = 60 pounds.
To find what weight is 95 percent of the limit.
Let x be the weight.
then;
x = 95% of 60
[tex]x = \frac{95}{100} \times 60[/tex]
or
x = [tex]\frac{95 \times 60}{100} = \frac{5700}{100} = 57[/tex]
therefore, 57 pounds is 95 percent of the limit.
math help please!!!!!!!!!!! will mark brainly
Answers
Answer:
B)3/8
Step-by-step explanation:
So there are 3 yellow or blue in total. So 3/8.
Answer:
3/8
Step-by-step explanation:
There are 8 pieces of equal size (and thus equal probability). 3 of them qualify as "success" (yellow or blue), so 3 out of 8 is the probability.
In a recent election the new mayor received three votes for every vote received by her opponent. The new mayor received 2058 votes. How many votes did her opponent receive?
Answers
As per the given values, the opponent received 686 votes.
Explanation:Total votes received by Mayor = 2058.
To find out how many votes the opponent received, we need to determine the ratio of votes received between the new mayor and her opponent. Given that the new mayor received three votes for every vote received by her opponent, we can set up the equation:
3x = 2058
where x represents the number of votes received by the opponent. To solve for x, we divide both sides of the equation by 3:
x = 2058 ÷ 3
= 686
Therefore, the opponent received a total of 686 votes.
Learn more about Vote count here:https://brainly.com/question/30701353
#SPJ2