Answer:
the new height of the triangle = 2.449
Step-by-step explanation:
Given that:
the sides of the triangle are 4m in length i.e they are equal. It shows that the triangle is known to be an equilateral triangle.
Let say the triangle is a triangle IJK
Let the length of the side to be i = 4
Definitely
IJ = JK = IK = i = 4
If a midline is drawn and cuts the equilateral triangle in two equal halves of a right-angle triangle. Then, suppose the midline is L
Then ;
[tex]JL = \dfrac{1}{2} JK[/tex]
[tex]JL = \dfrac{1}{2} i[/tex]
Let consider triangle IJL
(IL)² = (IJ)² - (JL)²
[tex](IL)^2 = i^2 - \dfrac{i^2}{4}[/tex]
[tex](IL)^2 = \dfrac{3i^2}{4}[/tex]
[tex](IL) =\sqrt{ \dfrac{3i^2}{4}}[/tex]
[tex]IL =\sqrt{3} \dfrac{i}{2}[/tex]
Area of triangle IJK can be expressed as:
[tex]Area = \dfrac{1}{2}\times Base \times Height[/tex]
[tex]Area = \dfrac{1}{2}\times i \times \sqrt{3}\dfrac{i}{2}[/tex]
[tex]Area = \sqrt{3}\dfrac{i^2}{4}[/tex]
where, i = 4
Then:
[tex]Area = \sqrt{3}\dfrac{4^2}{4}[/tex]
[tex]Area = \sqrt{3} \dfrac{16}{4}[/tex]
[tex]Area =4 \sqrt{3}[/tex]
when the area is exactly half of the original triangle's area, the new height is :
[tex]A = \dfrac{1}{2} \times Area[/tex]
[tex]\sqrt{3} \dfrac{i^2}{4} = \dfrac{1}{2} \times 4\sqrt{3}[/tex]
[tex]\dfrac{i^2}{4} = \dfrac{1}{2} \times 4[/tex]
[tex]\dfrac{i^2}{4} =2[/tex]
[tex]i^2 = 8[/tex]
[tex]i= \sqrt{8}[/tex]
[tex]i= \sqrt{4 \times 2}[/tex]
[tex]i= 2 \sqrt{2}[/tex]
Finally, the new height of the new triangle is:
[tex]IL =\sqrt{3} \dfrac{i}{2}[/tex]
[tex]IL =\sqrt{3} \dfrac{2 \sqrt{2}}{2}[/tex]
[tex]IL =\sqrt{3 \times 2}[/tex]
[tex]IL =\sqrt{6}[/tex]
IL = 2.449 m
is a 2 prime number or a composite number?
Answer:
prime
Step-by-step explanation:
Need help please. In the number 4,001,982.57........ .. .What digit in the hundredths place.
Answer:
it would be what ever number is to the right of 7 but its just a . for me
Step-by-step explanation:
I need help thank you
Answer: C
Step-by-step explanation:
For this problem, we need to translate each point by 4 units left and 3 units down.
Point A
When we move 4 units to the left, x=1. When we move 3 units down, we get y=-2. Therefore, A' is (1,-2).
----------------------------------------------------------------------------------------------------------------
Point B
When we move 4 units to the left, x=3. When we move 3 units down, we get y=2. Therefore, B' is (3,2).
----------------------------------------------------------------------------------------------------------------
Point C
When we move 4 units to the left, x=0. When we move 3 units down, we get y=2. Therefore, C' is (0,2).
----------------------------------------------------------------------------------------------------------------
Point D
When we move 4 units to the left, x=-2. When we move 3 units down, we get y=0. Therefore, D' is (-2,0).
----------------------------------------------------------------------------------------------------------------
After translating each point, we know that C is the correct answer.
last question. what does a equal
Answer:
x = 25
∠A = 125
Step-by-step explanation:
∠A = ∠B
where
∠A = 6x + 5°
∠B = 4x + 45°
6x + 5° = 4x + 45°
6x - 4x = 45 - 5
2x = 40
x = 40/2
x = 20
plugin x into ∠A = 6x - 5°
∠A = 6x + 5°
∠A = 6(20) + 5°
∠A = 125
Answer:
x = 25
A = 145
Step-by-step explanation:
Write the quadratic function in standard form. f(x) = 3x2 − x + 1
Answer:
It is already in standard form.
Step-by-step explanation:
Vertex Form: f(x) = a(bx - h)² + k
Standard Form: f(x) = ax² + bx + c
If f(x) = 9+ x 2
Find f(9)
Helpppp
Answer:
f(9) = 90
Step-by-step explanation:
f(x) = 9+ x^2
Let x = 9
f(9) = 9+ 9^2
= 9 + 81
= 90
Answer:
f(9) =90
Step-by-step explanation:
[tex]f(x) =9+x^2\\\\f(9)=?[/tex]
Substitute ; x = 9 into the given function
[tex]f(9) = 9+(9)^2\\\\f(9) = 9+81\\\\f(9) = 90[/tex]
On a number line, between which two consecutive whole numbers would the square root of 80 be located? A 7 and 8 B 10 and 11 C 9 and 10 D 8 and 9
Answer:
D. between 8 and 9
Step-by-step explanation:
8*8= 64 9*9=81
80 is between 64 and 81.
Students who have completed a speed reading course have reading speeds that are normally distributed with a mean of 950 words per minute and a standard deviation equal to 220 words per minute. Based on this information, what is the probability of a student reading at more than 1400 words per minute after finishing the course
Answer:
0.020405
Step-by-step explanation:
We solve this question, using z score formula.
z-score formula =
z = (x-μ)/σ,
where x is the raw score
μ is the population mean
σ is the population standard deviation.
From the above question:
x = 1400, μ = 950, σ = 220
z = 1400 - 950/220
z = 2.04545
Determining the probability from Z-Table:
P(z = 2.04545) = P(x<1400) = 0.97959
P(x>1400) = 1 - P(x<1400)
= 1 - 0.97959
= 0.020405
Therefore, the probability of a student reading at more than 1400 words per minute after finishing the course is 0.020405
At Al's Pizza, 57% of the orders included pepperoni pizza. At World's Best Pizza, 11 out of 19 orders included pepperoni pizza. Convert 11/19 to a percent and state at which restaurant did pepperoni pizzas make up a greater percentage of the pizzas sold?
100-57=47% at Als pizza
11/19*100=57.9% at wold best
Therefore world best make greater %
Pepperoni pizzas make up a greater percentage of the pizzas sold 57.9 %.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
The usage of percentages is widespread and diverse. For instance, numerous data in the media, bank interest rates, retail discounts, and inflation rates are all reported as percentages. For comprehending the financial elements of daily life, percentages are crucial.
It is given that 57% of the orders included pepperoni pizza. The percentage of other pizzas is,
100-57 %=47%
If 11 out of 19 orders included pepperoni pizza the percentage of the pepperoni pizza is,
= (11/19) × 100
= 57.9 %
Thus, pepperoni pizzas make up a greater percentage of the pizzas sold 57.9 %.
Learn more about the percentage here:
brainly.com/question/8011401
#SPJ2
Evaluate 4 + 6(a) when a = 2.
Answer:
16
Step-by-step explanation:
Since a = 2, we can plug in 2 for a.
4 + 6(2)
4 + 12
16
7.064 and expanded form
Answer:
seven and sixty-four thousandths
Step-by-step explanation:
in factors it would be
7 x 1
+ 0 x 0.1
+ 6 x 0.01
+ 4 x 0.001
Solve the equation |-2y+5|=2|3y-1|
J.D. power and Associates calculates and publishes various statistics concerning car quality. The dependability score measures problems experienced during the past 12 months by original owners of three-year-old vehicles (those that were introduced for the 2017 model year). For these models of cars, Ford had 1.27 problems per car and Toyota had 1.12 problems per car. Let X be equal to the number of problems with a three-year-old Ford, and Y be equal to the number of problems with a three-year-old Toyota. If you purchased a Ford in the 2017 model year, what is the probability that in the past 12 months the car had a) Can X be distributed as a Poisson random variable? Justify your answer. b) zero problems? c) two or fewer problems? If you purchased a Toyota in the 2017 model year, what is the probability that in the past 12 months the car had d) zero problems? e) two or fewer problems? f) Compare your answers in (d) and (e) to those for the Ford in (b) and (c).
Answer:
Follows are the solution to this question:
Step-by-step explanation:
The Ford car has an issue rate of 1.27.
That means that [tex]\lambda = 1.27[/tex]
Here, [tex]X \sim poisson (\lambda = 1.27)[/tex]
In option (A) :
To make a random variable X a Poisson variable, Parameter:
[tex]\to \lambda \leq 0 .[/tex]
The likelihood of success decreases with increased test numbers.
Mathematics, as [tex]n \longrightarrow \infty, \ \ \ and \ \ \p \longrightarrow 0[/tex].
In option (B) :
You must find it: [tex]P(X =0)[/tex]
[tex]\to P(X=0) = \frac{e^{-\lambda}\cdot \lambda^{0} }{0!} \\\\\to \lambda= 1.27 \\\\=e^{-1.27} \\\\= 0.280832[/tex]
In Option (C):
You must find it: [tex]P( X \leq 2) \\[/tex]
[tex]\to P( X \leq 2) = P(X=0) +P(X=1)+P(X=2) \\\\= \sum_{x= 0}^{2} P(X=x) \\\\= \sum_{x= 0}^{2} \frac{e^{- \lambda} \lambda^{x} }{x!} \\\\= e^{-1.27}\sum_{x= 0}^{2} \frac{ 1.27^{x} }{x!} \\\\ = 0.863964[/tex]
In Option (d):
Its first rating is essential because failures in production could be detected but before the total product becomes defective, this can be reduced.
In Option (e) :
The Toyata car has an issue rate of 1.12
That means that [tex]\lambda = 1.12[/tex]
Here, [tex]Y \sim poisson ( \lambda= 1.12)[/tex]
In Option (f):
You must find it: [tex]P(Y=0)[/tex]
[tex]\to P(Y=0)= \frac{e^{- \lambda } \lambda^{0}}{0!} \\\\\to \lambda = 1.12 \\\\=e^{-1.12}\\\\= 0.32628 \\[/tex]
You must find it: [tex]P(X \leq 2)[/tex]
[tex]\to P( X \leq 2) = P(Y=0) +P(Y=1)+P(Y=2) \\\\= \sum_{x= 0}^{2} P(Y=y) \\\\= \sum_{x= 0}^{2} \frac{e^{- \lambda} \lambda^{y} }{y!} \\\\= e^{-1.12}\sum_{x= 0}^{2} \frac{ 1.27^{y} }{y!} \\\\= 0.896356[/tex]
Comparing [a], [b], for the ford car and [b] and [c] for Toyot effectiveness
Car, its probability that less faults with Toyota car are strong, that's why it's better
Name the intersection of lines p and r.
H
M
L
M
A local company makes cement posts in the shape of the following three-dimensional
composite
The cone and cylinder both have the same radius, while the height of the cylinder is 3 times the height of the cone.
Which equation can be used to find the total volume of the cement post?
V= 4pi(r^2)h
V= 4pi(r^4)h
V= 10/3pi(r^2)h
V= 8/3pi(^2)h
Answer:
[tex] V = \frac{10}{3} \pi r^2h [/tex]
Step-by-step explanation:
The cone has the following given dimensions:
Radius = r
Height = h
Volume of a cone = ⅓πr²h
The Cylinder has:
Radius = r
Height = 3h
Volume of the cylinder = πr²h = πr²*3h = 3πr²h
Volume of the cement post = volume of Cone + volume of Cylinder
Equation to find total volume of cement post:
V = ⅓πr²h + 3πr²h
[tex] V = \frac{\pi r^2h}{3} + \frac{3 \pi r^2h}{1} [/tex]
[tex] V = \frac{1(\pi r^2h) + 3(3 \pi r^2h)}{3} [/tex]
[tex] V = \frac{\pi r^2h + 9 \pi r^2h}{3} [/tex]
[tex] V = \frac{10 \pi r^2h}{3} [/tex]
[tex] V = \frac{10}{3} \pi r^2h [/tex]
A local company makes cement posts in the shape of the following three-dimensional composite. The cone and cylinder both have the same radius, while the height of the cylinder is 3 times the height of the cone. Which equation can be used to find the total volume of the cement post?
Answer:
Hi, the answer is B. V=10/3pir^2h.
Step-by-step explanation:
Answer:
The answer you selected is right! The answer is indeed 10/3 pi r^2 h :)
Step-by-step explanation:
Bright Thinker approved
In the equation, y = mx + b, the letter b is the
Answer:
The letter by is the y-intercept
Step-by-step explanation:
60:48 in its simplest form
Solution :-
Given ratio to us is 60 : 48 and we are required to convert it into simplest form .
For this first find the HCF of 60 and 48 .
= 48 ) 60 ( 1
- 48
__________
12 ) 48 ( 4
- 48
__________
0
Hence the HCF ( 60,48 ) is 12 .
Now divide the given ratio by 12 .
= [tex]\sf \dfrac{60\div 12}{48\div 12}[/tex]
= [tex]\sf \dfrac{5}{4}[/tex]
=[tex]\sf 5:4[/tex]
[tex]\boxed{\green{\bf{\dag Hence\: the\:simplest\:form\:is\:5:4.}}}[/tex]
The width of a rectangle is 3 feet less than it’s length. The perimeter of the rectangle is 98 feet. Find the dimensions of the rectangle
Answer:
The length is 26 feet and the width is 23 feet
Step-by-step explanation:
Let l represent the length of the rectangle.
The width can be represented by l - 3, since it is 3 feet less than the length
Set up an equation:
l + l + (l - 3) + (l - 3) = 98
Add like terms and solve for l:
l + l + (l - 3) + (l - 3) = 98
4l - 6 = 98
4l = 104
l = 26
So, the length is 26 feet.
Since the width is l - 3, we can plug this in for l to find the width:
l - 3
26 - 3
= 23
So, the length is 26 feet and the width is 23 feet
The angle measures of a figure Response area stay the same after a translation, reflection, or rotation.
Factor completely:
6z2 + 18z
Answer:
6z(z+3)
Step-by-step explanation:
6z square + 18z
take common..
6z(z+3)
Divide: 3 8 ÷ 5 12 The quotient is
Hey there!
ANSWER: [tex]\frac{9}{10}[/tex]
EXPLANATION:
[tex]3/8[/tex] ÷ [tex]5/12[/tex]
Make the numerator 12 and denominator 5.
[tex](\frac{3}{8})(\frac{12}{5})[/tex]
Now put both numerators together and the denominators together.
[tex]\frac{(3)(12)}{(8)(5)}[/tex]
Now multiply numerator by numerator and denominator by denominator.
Numerator:
[tex]3*12=36[/tex]
Denominator:
[tex]8*5=40[/tex]
[tex]\frac{36}{40}=\frac{9}{10}(ANSWER)[/tex]
Hope this helps!
[tex]-TestedHyperr[/tex]
Answer:
the answer is 9/10
HELP!! ASAP!!!!!!!!!!!!!!!!!!!1
Answer:
No, No, Yes, Yes
Step-by-step explanation:
Answer:
No. What is wrong with you? I'm getting my points back this way.
1 2 3 4 5 6 7 8 9 0
Find the Range of the function.
y = 2x + 4 Domain: 0, 1, 2,
Answer:
y= 2x + 4
x = 4 + 2
x = 6
Step-by-step explanation:
is it helpful please tell in comments
Suppose g(x) = x- 2/x + 1. Evaluate g(4)
a
- 8
b
2/5
c
6/5
d
- 2
Answer:
B. 2/5
Step-by-step explanation:
g(x)=x-2/x+1
g(4)=4-2/4+1
g(4)=2/5
tammy purchased a prepaid phone card for $20. long distance calls cost 24 cents a minute using this card. tammy used her card only once to make a long distance call. if the remaining credit on her card is $12.32. how many minutes did her call last?
Answer:
About 14 - 15 Minutes!
Step-by-step explanation:
24 cents x $12.32 = 295.68 (Multiplication)
295.68/20.00 (Division.)
14.784 (Answer and Estimated.)
BRAINLIEST +15 POINTS UP FOR GRABS!!!
Pick all line pairs that intersect each other.
1. Line AB and Line CD
2. Line CD and Line BE
3. Line BE and Line AB
4. No two lines shown intersect each other.
WILL GIVE BRAINLIEST TO FIRST CORRECT ANSWER (STEP-BY-STEP APPRECIATED)!
Answer:
Line BE and Line AB
Step-by-step explanation:
On the graph you can see that these two lines cross each other.
HURRY AND ANSWER AS FAST AS YOU CAN!!! PLEASE I NEED THESE BY TODAY The length of a rectangle is (2x - 7)inches and the width is (x2 - 5) inches. Find an expression for the perimeter of the rectangle. A) 2x3 + 35B) x2 - 2x + 2X) x2 + 2x - 12 D) 2 x 2 + 4x -24 The sum of −15x2 −5x + 11 and another polynomial expression is −9x2 + 3x −10. What is the other polynomial expression? A) 24x2 + 8x − 8 B) 6x2 + 8x − 21 C) − 24x2 + 8x + 8 D) − 24x2 + 8x − 8
Answer:
Q1.
Perimeter = 2(Length + Width)
Perimeter = [tex]2((2x-7)+(x^2-5))[/tex]
[tex]2\left(2x-7\right)+2\left(x^2-5\right)[/tex]
[tex]4x-14+2x^2-10[/tex]
[tex]2x^2+4x-24[/tex]
Q2.
[tex](-9x^2+3x-10)-(-15x^2-5x+11)[/tex]
[tex]-9x^2+3x-10+15x^2+5x-11[/tex]
[tex]6x^2+8x-21[/tex]
Lisa is standing on a dock beside a lake. She drops a rock from her hand into the lake. After the rock hits
the surface of the lake, the rock's distance from the lake's surface changes at a rate of -3 inches per
second. If Lisa holds her hand 6 feet above the lake's surface, how far from Lisa's hand is the rock 4
seconds after it hits the surface?
A
Answer:
5 feet
Step-by-step explanation:
1 second =-3 inches what of
4 seconds=?
-3×4÷1=-12 inches
-12 inches =-1 foot
6 feet + (-1) foot= 5 feet
greatest common factor of 27 & 45
Answer:
isnt 9?
Step-by-step explanation:
i asked google lololol
Answer:
9.
Step-by-step explanation:
Factors of 27: 1, 3, 9, 27
Factors of 45: 1, 3, 5, 9, 15, 45.
The GCF (Greatest Common Factor) of 27 and 45 is NOT 1, 3, or 27 because 27 is not a factor of 45, and since we are trying to figure out the GREATEST common factor, one and three do not work either. If you need more help, feel free to ask! I am on Brainly from 1 - 2 pm. EST, so if you have any further questions about this subject or my answer, feel free to ask me!
