Answer:
h = 7.5 cm
Step-by-step explanation:
Firstly, we find the area of the triangular base
Mathematically, we have the area of a triangle as;
A = 1/2 * b * h
A = 1/2 * 5 * 8 = 20 cm^2
Mathematically, we have the formula as;
V= 1/3 * A * h
A is base area and h is height
50 = 1/3 * 20 * h
20h = 3 * 50
20h = 150
h = 150/20
h = 7.5 cm
Which has a larger area, a 4:3 aspect ratio 32 inch TV or a 16:9 aspect ratio 32 inch
TV? Find the side lengths of each of the TV's and the area of each TV to compare.
Explain your reasoning and show all mathematical calculations.
Answers:
The 4:3 tv has the larger areaThe 4:3 tv has width = 25.6 inches and height = 19.2 inches. The area is exactly 491.52 square inchesThe 16:9 tv has width = 27.8904 inches (approximate) and height = 15.68835 inches (approximate). The area is approximately 437.55 square inches.================================================
Explanation:
Let x be some positive real number
The 4:3 aspect ratio means the width (horizontal) portion of the tv is 4x inches while the height (vertical) portion is 3x inches
The ratio 4x:3x reduces to 4:3 after dividing both parts by x.
The 4x by 3x rectangle has the diagonal 32 inches as the instructions state. The tv size is always measured along the diagonal.
So effectively, we have two identical right triangles with legs 4x and 3x, and hypotenuse 32.
Apply the pythagorean theorem to find x
a^2+b^2 = c^2
(4x)^2+(3x)^2 = 32^2
16x^2+9x^2 = 1024
25x^2 = 1024
x^2 = 1024/25
x = sqrt(1024/25)
x = 32/5
x = 6.4
Recall that x is positive, so we ignore the negative square root here.
This 4x by 3x tv then has dimensions of
horizontal width = 4x = 4*6.4 = 25.6 inchesvertical height = 3x = 3*6.4 = 19.2 inchesThese values are exact.
The area is therefore base*height = 25.6*19.2 = 491.52 square inches
This of course only applies to the 4:3 tv that's 32 inches in diagonal.
-------------------------------
Now onto the 16:9 tv.
We'll follow the same steps as the last section. We'll use y this time
The 16:9 ratio becomes 16y:9y
a^2+b^2 = c^2
(16y)^2 + (9y)^2 = 32^2
256y^2 + 81y^2 = 1024
337y^2 = 1024
y^2 = 1024/337
y = sqrt(1024/337)
y = 1.7431510742491 which is approximate
y = 1.74315
So,
horizontal width = 16y = 16*1.74315 = 27.8904vertical height = 9y = 9*1.74315 = 15.68835area = base*height = 27.8904*15.68835 = 437.55435684the area is approximate since the width and height are approximate. It rounds to about 437.55 square inches
-------------------------------
To recap, we found the following:
The 4:3 tv has width and height of 25.6 inches and 19.2 inches respectively. Those values are exact. The area is exactly 491.52 square inches.The 16:9 tv has width and height of approximately 27.8904 inches and 15.68835 inches respectively. The area is approximately 437.55 square inches.The 4:3 tv has larger area.
Help NOW RIGHT NOW
convert 4 years to months
Answer:
48 months
Step-by-step explanation:
12 times 4 48
Answer:
48 months
There's 12 months in 1 year.
So we would multiply 12 months by 4 years to get 48 months
help pls help pls help
Answer:
18.6
Step-by-step explanation:
We know a side and a angle opposite of that side
(AC and Angle B respectively).
We know another side(AB). and are trying to find a angle opposite of it.
Let use Law of Sines rules.
[tex] \frac{ac}{ \sin(angle \: b)} = \frac{ab}{ \sin(angle \: c)} [/tex]
Substitute the values in.
[tex] \frac{22}{ \sin(90) } = \frac{7}{ \sin(x) } [/tex]
Solve for sin x by taking the reciprocal of both sides.
[tex] \frac{ \sin(90) }{22} = \frac{ \sin(x) }{7} [/tex]
Remeber sin 90 =1 and multiply 7 by both sides.
[tex] \frac{1}{22} \times 7 = \sin(x) [/tex]
Take the inverse of sin to find the angle measure.
[tex] \sin {}^{ - 1} (x) = \frac{7}{22} [/tex]
The answer is
18.6
Pls help me with this equation
Answer:
x = 20 degree
Step-by-step explanation:
Hope this helps u !!
A right triangle has side lengths d, e and f as shown below use the lengths to find sin x cos x and tan x
BRAINLIEST
Answer:
sin is d/f
cos is e/f
tan is d/e
Step-by-step explanation:
sin is opposite over hypotenuse
cos is adjacent over hypotenuse
tan is opposite over adjacent
Some old hippie, caught another hippie, tripping on acid
Does anyone know the answer ?!?
Answer:
40/100 = .4 = 40%
Step-by-step explanation:
Need Help ASAP. Will give Brainliest.
Answer:
-6
Step-by-step explanation:
The y-intercept is where the line crosses the y-axis which in this case is -6
Hope this helps
[tex]\text{Solve for x:}\\\\3x + 9 = 12\\\\\text{Thank you.}[/tex]
Hi there!
»»————- ★ ————-««
I believe your answer is:
[tex]x = 1[/tex]
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]\boxed{\text{Calculating the Answer...}}\\\\3x+9=12\\--------\\\rightarrow 3x + 9 -9 = 12 - 9\\\\\rightarrow 3x = 3\\\\\rightarrow \frac{3x=3}{3}\\\\\rightarrow \boxed{x=1}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Answer:
x = 1
Step-by-step explanation:
(x + a = b
x = b - a)
or
(x + a = b
x + a - a = b - a [subtract both sides by a ]
x + 0 = b - a [ - a + a = 0 ]
x = b - a )
[tex]3x + 9 = 12\\3x + 9 - 9 = 12 - 9\\3x + 0 = 3\\3x = 3\\\\\frac{3x}{3} = \frac{3}{3}\\\\x = 1[/tex]
What is the following quotient?
V6+ V11
√5 + √3
Answer:
The second one, my order is different, but they are equivalent answers
Step-by-step explanation: 6 22 22 18
(√6 + √11) / (√5 +√3) multiple top and by (√5 - √3) note the minus
(√6 + √11) × (√5 - √3) / (√5 +√3) x (√5 - √3)
(√30 + √55 - √18 - √33) / (5 - 3)
(√30 + √55 - 3√2 - √33) / 2
Enter three letters (ASA, SAS, or SSS) to identify the criterion that shows the pair of
triangles to be congruent.
Answer: ASA
Step-by-step explanation:
If QR = 8 and PR = 14, what is PQ? Write your answer as a decimal or integer.
Drag the number of solutions to match the equation. Each tile may be used only once. 4(3x+2)=4(2x+3)+4x vacío 10(x+4)–3=14x+1 vacío 12(10x+15)–32=2x+6+3x
Step-by-step explanation:
The given equation is :
4(3x+2)=4(2x+3)+4x
Solving LHS, = 12x+8
Solving RHS, = 8x+12+4x
So,
12x+8 = 8x+12+4x
12x + 8 = 12x +12
12x cancel out from both sides, the given equation becomes not defined.
8f(x)=x
2
+6x+8f, left parenthesis, x, right parenthesis, equals, x, squared, plus, 6, x, plus, 8
1) What are the zeros of the function?
Write the smaller xxx first, and the larger xxx second.
\text{smaller }x=smaller x=start text, s, m, a, l, l, e, r, space, end text, x, equals
\text{larger }x=larger x=start text, l, a, r, g, e, r, space, end text, x, equals
2) What is the vertex of the parabola?
Answer:
-2 and -4
Step-by-step explanation:
Given the function f(x) = x² + 6x + 8
If f(x) = 0
x² + 6x + 8 = 0
Factorize
x² + 4x + 2x+ 8 = 0
x(x+4)+2(x+4) = 0
(x+2)(x+4) = 0
x+2 = 0 and x+4 = 0
x = -2 and -4
Hence the zero of the function is -2 and -4
if the circumfrence of a circl is 18π inches, what is the radius of the circle
Answer:
r≈2.86
Step-by-step explanation:
Using the formula
C=2πr
Solving forr
r=C
2π=18
2·π≈2.86479
determine the equation of the circle graphed below.
( help me please )
Answer:
The circle's center is at (5, -2)
The radius is 4
Equation is
(x -5)^2 + (y - - 2)^2 = 4^2
(x -5)^2 + (y +2)^2 = 16
http://www.1728.org/circle.htm
Step-by-step explanation:
what is the scale factor from figure a to figure b
Answer:
times 2 ( x 2 )
Step-by-step explanation:
These two quadrilaterals are similar because figure A's sides are 20 times less than figure B's sides. Figure A's top base is 22 while figure B's top base is 44. To find the value of figure B's side, we multiply by 2. All the sides of figure A will be similar to the figure B if multiplied by 2.
Therefore, scale factor of figure A to figure B is multiply by 2.
hope this helps...
Answer:
Scale factor is 1 to 2
or given the actual question that you asked (a-b vs b-a)
2 to 1
Step-by-step explanation:
b / -7 = 4
solve question correctly
Answer:
b/-7=4
b=4*-7
b= - 28
Step-by-step explanation:
If this helps you mark as brainlist.!
Answer: -28
Variable/unknown - B
Numbers we know: -7 and 4.
How to solve: Use inverse division. The inverse of division is multiplication.
7 has a negative sign. However, 4 is positive.
N + P = N
P + N = N
Rules of integers:
If both the signs of the two numbers are the same, it will be positive.If both the signs of the two numbers are different, it will be negative.-7 is negative.
4 is positive.
Formula: N + P = N
-7 x 4 = -28
Final answer: -28
The table above shows the value of Henry’s car for each o of the first 3 years after it is purchased. The values form a geometric sequence. What will be the approximate value of the car in the 10th year?
A $2,680
B. $5,240
C. $6,550
D. $2,150
Answer:
D.
Step-by-step explanation:
You need to use a graphing calculator to figure it out.
PLS HELP ASAP!! THX
For questions 6-9 refer to the box plots (Assume their positions are on the same number line). Write your responses in complete sentences using content specific vocabulary.
Answer:
Did you find them ?
Step-by-step explanation:
In order for the data in the table to represent a linear function with a rate of change of –8, what must be the value of a?
Given:
Consider the below figure attached with this question.
The rate of change of the linear function is -8.
To find:
The value of a.
Solution:
If a linear function passes through the points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], then the rate of change of the linear function is:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
From the given table, it is clear that the linear function passes through the points (10,27) and (11,a). So, the slope of the linear function is:
[tex]m=\dfrac{a-27}{11-10}[/tex]
[tex]m=\dfrac{a-27}{1}[/tex]
[tex]m=a-27[/tex]
The rate of change of the linear function is -8.
[tex]-8=a-27[/tex]
[tex]-8+27=a[/tex]
[tex]19=a[/tex]
Therefore, the value of a is 19.
Answer:
it is C
Step-by-step explanation:
Here are five number cards. 19 13 10 14 22 Two of the five cards are picked at random. Work out the probability that the total of the two numbers is more than 32 + Total marks: 3
Answer:
Here are five number cards.
19
13
10
14
22
Two of the five cards are picked at random.
Work out the probability that the total of the two numbers is more than 32
+
Total marks: 3
The probability that the total of the two numbers is more than 32 is 2/5.
What is Probability ?Probability is the study of likeliness of an event to happen.
The number cards given are 19 , 13 , 10 , 14 , 22
The Probability when two number cards are drawn then th sum is moire than 32 is ?
Probability = Favourable Outcomes / Total Outcomes
Total outcomes when total cards is 5 and no. of cards drawn is 2
= [tex]\rm ^5C_2[/tex]
= ( 5 * 4 * 3 * 2 * 1)/(( 3 * 2 )(2.1))
= 10 outcomes
Favourable Outcomes
= ( 19 , 14) (19,22) (13,22)(14,22)
= 4
Probability = 4/10 = 2/5
Therefore the probability that the total of the two numbers is more than 32 is 2/5.
To know more about Probability
https://brainly.com/question/11234923
#SPJ2
A hall which is 8m long is represented on a diagram as 4 cm long. What is the scale of the diagram?
Answer:
1cm to 2m
Step-by-step explanation:
self explanatory i think
15 _ { 10 } + X _ { 2 } = 11011 _ { 2 }
11011₂ = 2⁴ + 2³ + 2¹ + 2⁰ = 27
15 + x₂ = 27
x₂ = 12 = 8 + 4 = 2³ + 2² = 1100₂
please help me out real quick.
Answer:
[tex]\text{B. }3x+4=3x+2\sqrt{3x-11}-10[/tex] only for [tex]3x+4\in [0, \infty)[/tex]
Step-by-step explanation:
Key formulas used:
[tex]\sqrt{x}^2=|x|[/tex] [tex](a+b)^2=a^2+2ab+c^2[/tex]Given [tex]\sqrt{3x+4}=1+\sqrt{3x-11}[/tex],
We can use the first formula on the left side of the equation.
In this case, for [tex]\sqrt{x}^2=|x|[/tex], [tex]x=3x+4[/tex], we have:
[tex]\sqrt{3x+4}^2=|3x+4|[/tex]
Similarly, we can use the second formula on the right side of the equation.
In this case, for [tex](a+b)^2=a^2+2ab+c^2[/tex], [tex]a=1, b=\sqrt{3x-11}[/tex], we have:
[tex](1+\sqrt{3x-11})^2=1^2+2\cdot 1\cdot \sqrt{3x-11}+\sqrt{3x-11}^2,\\=1+2\sqrt{3x-11}+3x-11,\\=3x+2\sqrt{3x-11}-10[/tex]
Therefore, when you square both sides of the equation, you get:
[tex]\boxed{\text{B. }3x+4=3x+2\sqrt{3x-11}-10}[/tex]
*Important:
This answer choice is actually only correct if [tex]3x+4>0[/tex], because of the first formula we used. If [tex]3x+4<0[/tex] (negative), then [tex]3x+4\neq \sqrt{3x+4}^2,\text{ if }3x-4<0[/tex]. Graphically, you can show this since the line [tex]y=\sqrt{x}^2[/tex] is not equal to [tex]y=x[/tex] but instead [tex]y=|x|[/tex]. [tex]y=\sqrt{x^2}[/tex] and [tex]y=x[/tex] only overlap if you restrict the domain to [tex][0, \infty)[/tex] (positive numbers), hence [tex]\text{B. }3x+4=3x+2\sqrt{3x-11}-10[/tex] only for [tex]3x+4\in [0, \infty)[/tex].
PLEASE HELP!!!!!! A linear function has a y-intercept of -12 and a slope of 3/2. What is the equation of the line?
A. Y= 3/2x - 12
B. Y= 3/2x + 12
C. Y= 2/3x - 12
D. Y= -12x - 3/2
Answer:
A, y = 3x/2 - 12
Step-by-step explanation:
Use the equation y = mx + b.
m = 3/2
b = -12
y = 3x/2 - 12
Answer:
Here is your Answer
Step-by-step explanation:
Its A
A. Y = 3/2x - 12
Please Help!!!! Please!!!!!!!!
9514 1404 393
Answer:
see attached
Step-by-step explanation:
I found it easiest to draw arcs of radii AB and AC centered at A, and arcs of radii DB and DC centered at D. The intersection points of those arcs mark the points B' and C'. These are points B and C reflected across line AD.
Joining A, B', C', and D will make a figure symmetrical about AD.
After researchers conditioned a dog to salivate to the sight of a triangle, they presented the triangle alone to the dog every three minutes. Over the course of several trials, the amount of saliva the dog secreted in response to the triangle decreased to zero. At that point, the researchers put the dog back in his cage for three hours. What happened the after the three hours the dog rested and went through the conditioning process again
Answer: Spontaneous recovery likely occurred, and the dog salivated in response to the triangle
Step-by-step explanation:
Spontaneous recovery is the reappearance of the conditioned response when a rest period has taken place or when there's a period of lessened response.
In this case, since the researchers put the dog back in his cage for three hours after which the dog went through the conditioning process again after the three hours, then there'll be a spontaneous recovery.
distributive law to simplify 15x13 + 15x17
Answer:
420 is the answer
hope it helps
Step-by-step explanation:
plz mark me brainleast
WILL GIVE BRAINLIEST AND 20 POINTS!
Find the equation of the line which passes through the point (11,8) and is parallel to the given line. Express your answer in slope-intercept form. Simplify your answer.
6x+8y=15
Step By Step Explanation:
y = - 3/4× + 15/8Step 1Swap sides so that all variable terms are on the left hand side.[tex] - \frac{3}{4} x + \frac{15}{8} = y[/tex]Step 2Subtract [tex]\frac{15}{8}[/tex] from both sides.[tex] - \frac{3}{4} \times = y - \frac{15}{8} [/tex]Step 3Divide both sides of the equation by -[tex]\frac{3}{4}[/tex] which is the same as multiplying both sides by the reciprocal of the fraction.[tex] \frac{ - \frac{3}{4} \times}{- \frac{3}{4} } = \frac{y - \frac{15}{8} }{ - \frac{3}{4} } [/tex]Step 4Dividing by [tex]-\frac{3}{4}[/tex] undoes the multiplication by [tex]-\frac{2}{4}[/tex][tex]x = \frac{y - \frac{15}{8} }{ - \frac{3}{4} } [/tex]Step 5Divide [tex]y-\frac{15}{8}[/tex] by -\frac{3}{4} by multiplying [tex]y-\frac{15}{8}[/tex] by the reciprocal of [tex]-\frac{3}{4}[/tex][tex]\color{Green}x = \frac{ - 4y}{3} + \frac{5}{2} [/tex]