Answer:
36 meters
Step-by-step explanation:
A=1/2b×h
108sq. m=1/2.6m×h
both side canceling meter
h=2×108m/6
h=36m. answer
The height of the triangle is 12 meters, and the base of the triangle is 18 meters.
Let's denote the height of the triangle as "h" meters. According to the given information, the base of the triangle is 6 meters longer than the height, so the base can be represented as "(h + 6)" meters.
The area of a triangle is given by the formula: Area = (1/2) * base * height
We are given that the area of the triangle is 108 square meters, so we can write the equation as:
108 = (1/2) * (h + 6) * h
Now, let's solve for "h":
108 = (1/2) * (h² + 6h)
Multiply both sides by 2 to eliminate the fraction:
216 = h² + 6h
Rearrange the equation in standard quadratic form:
h² + 6h - 216 = 0
Now, let's solve this quadratic equation for "h." We can factor it or use the quadratic formula. Factoring, we get:
(h + 18)(h - 12) = 0
Setting each factor to zero:
h + 18 = 0 or h - 12 = 0
Solving for "h" in each case:
h = -18 (discard this negative value as height cannot be negative) or h = 12
Since height cannot be negative, we take the positive value of "h," which is 12 meters.
Now, we can find the base by using the given relationship: base = height + 6
base = 12 + 6 = 18 meters
So, the height of the triangle is 12 meters, and the base of the triangle is 18 meters.
Learn more about triangles here:
https://brainly.com/question/29083884?
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Assuming p: she is beautiful,q :she is clever,the verbal form of ~p^ (~q) is she is beautiful but not clever. she is beautiful and clever she is not beautiful and not clever.she is beautiful or not clever.
Answer:
C. she is not beautiful and not clever.
Step-by-step explanation:
A. she is beautiful but not clever. B. she is beautiful and clever
C. she is not beautiful and not clever.
D. she is beautiful or not clever.
p: she is beautiful
q :she is clever
~p^ (~q) in verbal form
~p = she is not beautiful
~q = she is not clever
~p^ (~q) = she is not beautiful and not clever.
C. she is not beautiful and not clever.
si franco comió 8/3 de pizza y Fabián comió 5/6 de la misma pizza. ¿quien comió más ? si quedó 4/9 de pizza.
Answer:
Franco comió 8/3 de pizza.
Fabián comió 5/6 de pizza.
Queremos saber quien comió más.
Entonces básicamente queremos ver cuál número es más grande, 8/3 o 5/6,
Podemos reescribir el primero como:
8/3 = (2 + 3 + 3)/3 = 2/3 + 3/3 + 3/3 = 2/3 + 1 + 1
= 2 + 2/3
En cambio, para el número 5/6, el numerador es menor que el denominador, entonces sabemos que:
5/6 < 1
Claramente podemos ver que 8/3 > 5/6
Entonces podemos concluir que Franco comió más.
Use the exact values of the ratios and find the value of tan 45° + sin 30°
Answer:
1.5
tan45=1
sin30=1/2
so 1+1/2=1.5 or 3/2
Taking 0.5 cm as 1 unit, plot the following points on the graph paper: A(1,3), B (-3,-1), C (1,- 4), D (- 2,3), E (0-8), F (1.0)
Answer:
It's letter c
Step-by-step explanation:
you have to × the 0.5 and 1
Answer fast please and thanks!
Answer:
tan 30 = x / 15
General Formulas and Concepts:
Trigonometry
[Right Triangles Only] SOHCAHTOA[Right Triangles Only] tanθ = opposite over adjacentStep-by-step explanation:
Step 1: Define
Identify variables
Angle θ = 30°
Opposite Leg = x
Adjacent Leg = 15
Step 2: Solve for x
Substitute in variables [tangent]: tan 30 = x / 15Answer:
3rd one
Step-by-step explanation:
Recall that
Sin = opposite over hypotenuse
Cos = adjacent over hypotenuse
Tan = opposite over adjacent
For the angle with a measure of 30 degrees we are given it's adjacent side length and need to find it's opposite side length
When dealing with opposite and adjacent we use tangent
If tan = opposite over adjacent
Then tan30 = x / 15 and the correct answer choice is the third one
If someone can pls give the answer with steps that would be greatly appreciated :)
[tex]\sf \bf {\boxed {\mathbb {TO\:FIND:}}}[/tex]
The measures of [tex]x[/tex] and [tex]y[/tex].
[tex]\sf \bf {\boxed {\mathbb {SOLUTION:}}}[/tex]
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf {x\:=\: 210°\:and\:\:y\:=\: -30°}}}}}}[/tex]
[tex]\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:EXPLANATION:}}}[/tex]
An exterior angle of a triangle is equal to sum of two opposite interior angles.
And so we have,
[tex] 40° = 70° + y[/tex]
[tex]➪ \: y= 40° - 70°[/tex]
[tex]➪ \: y = - 30°[/tex]
Also,
[tex]\sf\pink{Sum\:of\:angles\:on\:a\:straight\:line\:=\:180°}[/tex]
[tex]y[/tex] + [tex]x[/tex] = [tex]180°[/tex]
[tex]➪ \: -30° + x= 180°[/tex]
[tex]➪ \:x = 180° + 30°[/tex]
[tex]➪ \:x = 210°[/tex]
[tex]\sf\purple{Therefore,\:the\:measures \:of\:the\:unknown\:angles\:are\:"x=210°"\:and\:"y=-30°.}[/tex]
[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{ヅ}}}}}[/tex]
A cylindrical water tower has a volume of
10007 ft.
If the tower is 10 ft tall, what is the radius of the tower?
Answer:
r≈17.85
Step-by-step explanation:
I believe this is correct, if not feel free to let me know and I will fix it. I'm sorry in advance if it is incorrect.
Answer:
r=17.85
Step-by-step explanation:
i just got it and did the math
Please help so urgent
Answer:
Option E. None of the above.
Step-by-step explanation:
From the question given above, the following data were obtained:
f(x) = (x – 5)/(2x + 3)
Inverse of f(x) => f¯¹(x) =?
Recall:
When a function f(x) is multiplied by it's inverse f¯¹(x), the result is equal to 1 i.e
f(x) × f¯¹(x) = 1
With the above information, we can determine the inverse of function given above as follow:
f(x) = (x – 5)/(2x + 3)
Inverse of f(x) => f¯¹(x) =?
f(x) × f¯¹(x) = 1
(x – 5)/(2x + 3) × f¯¹(x) = 1
f¯¹(x)(x – 5) / (2x + 3) = 1
Cross multiply
f¯¹(x)(x – 5) = (2x + 3)
Divide both side by (x – 5)
f¯¹(x) = (2x + 3) / (x – 5)
Thus, the inverse of the function is (2x + 3) / (x – 5).
Option E gives the correct answer to the question.
Bill notes that his apple tree is 45 the size of his pear tree. His apple tree is 4 meters tall. How tall is the pear tree?
Answer:
11.25 m
Step-by-step explanation:
45 divide by 4
because the Apple tree is 45 the size of pear tree
Answer: 5
Step-by-step explanation:
A geneticist conducts an experiment with peas, one sample of offspring consisted of 450 green peas and 157 yellow peas. Based on these results, estimate the probability of getting an offspring pea that is green.
Answer: 0.738
Step-by-step explanation:
11. Mendelian Genetics. When Mendel conducted his famous genetics experiments with peas, one sample of offspring consisted of 428 green peas and 152 yellow peas. Based on those results, estimate the probability of getting an offspring pea that is green. Is the result reasonably close to the value that was expected?
p0 = 428/(428 + 152) = 0.737931
If you round your answer of 0.737931 to three decimals you will
get 0.738.
A rock group plans three concert tours over a period of 30 weeks. The tour in Britain will be twice as long as the tour in France and the tour in Germany will be 2 weeks shorter than the tour in France. How many weeks will they be in France?
Answer:
8 weeks
Step-by-step explanation:
Let x represent how many weeks they will be in France.
The tour in Britain can be represented by 2x, since it is twice as long as the one in France.
The tour in Germany can be represented by x - 2, since it is 2 weeks shorter.
Create an equation and solve for x:
(x) + (2x) + (x - 2) = 30
4x - 2 = 30
4x = 32
x = 8
So, they will be in France for 8 weeks
Which expression is equivalent to a^7
Answer:
here is your answer
Step-by-step explanation:
here is your answer
Here is a table of values for y = f(x).
Х
-2 -1 0 1 2 3
4.
5
6
f(x) 5
6 7 8 9 10 11 12 13
Mark the statements that are true.
Step-by-step explanation:
the true answers are:
A. f(-1)=6
D. the domain for f(x) is the set
{-2,-1,0,1,2,3,4,5,6}
What are the solutions to x2 -8x =13
Answer:
See image below for answer:)
Step-by-step explanation:
Simplify 3 · 2x. What is the coefficient?
• 2
• 3
• 6
Answer:
6x coefficient is 6. the number next to the letter
Step-by-step explanation:
What the cubic inches…
Step-by-step explanation:
The radius r is 5 in (r = D/2). so the volume V of the beach ball is
[tex]V= \dfrac{4 \pi}{3}r^3 = \dfrac{4 \pi}{3}(5\:\text{in})^3[/tex]
[tex]\:\:\:\:\:= 523.6\:\text{in}^3[/tex]
The lengths of nails produced in a factory are normally distributed with a mean of 5.16 centimeters and a standard deviation of 0.04 centimeters. Find the two lengths that separate the top 8% and the bottom 8%.
Answer:
The length that separates the top 8% is of 5.2162 centimeters, and the length that separates the bottom 8% is of 5.1038 centimeters.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 5.16 centimeters and a standard deviation of 0.04 centimeters.
This means that [tex]\mu = 5.16, \sigma = 0.04[/tex]
Length that separates the top 8%
The 100 - 8 = 92th percentile, which is X when Z has a p-value of 0.92, so X when Z = 1.405.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.405 = \frac{X - 5.16}{0.04}[/tex]
[tex]X - 5.16 = 1.405*0.04[/tex]
[tex]X = 5.2162[/tex]
Length that separates the bottom 8%
This is the 8th percentile, which is X when Z has a p-value of 0.08, so X when Z = -1.405.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.405 = \frac{X - 5.16}{0.04}[/tex]
[tex]X - 5.16 = -1.405*0.04[/tex]
[tex]X = 5.1038[/tex]
The length that separates the top 8% is of 5.2162 centimeters, and the length that separates the bottom 8% is of 5.1038 centimeters.
What is the tens digit in the sum 7! + 8! + 9! + … + 2006!
You can get the tens digit of any number n by computing the quotient
(n (mod 100)) / 10
and ignoring the remainder.
Taking the given sum (mod 100) gives
7! + 8! + … + 2006! ≡ 7! + 8! + 9! (mod 100)
since the last 1997 terms (i.e. 10! up to 2006!) in the sum are multiples of 100. That is,
• every term beyond 100! is obviously a multiple of 100
• every term beyond 25! contains a factor of both 4 and 25
• every term beyond 10! contains two factors each of both 2 and 5 (i.e. every factorial term contains 4, 5, and 10)
The remaining sum is easy to compute by hand:
7! + 8! + 9! = 7! (1 + 8 + 8 × 9) = 5040 × 81 = 408,240
so the tens digit is 4.
Select the correct answer. Using synthetic division, find (2x4 + 4x3 + 2x2 + 8x + 8) ÷ (x + 2). A. B. C. D.
Step-by-step explanation:
If you use synthetic division, you get,
[tex]2x {}^{3} + 2x + 4 + \frac{0}{x + 2} [/tex]
Which is,
[tex]2x {}^{3} + 2x + 4[/tex]
Answered by GAUTHMATH
Answer:
The correct answer is:
2x^3+2x+4
Step-by-step explanation:
I got it right on the Plato test.
No step by step answers or links
Answer:
1. k = 15
2. d = 20
3. n = 3
Having trouble with these questions, please help.
Answer:
(a)=50%(b)=2.1and(c)=16.1
Step-by-step explanation:
Hope this helps
if the ratio of the volume of two cubes is 1 : 8 , then find the ratio of the total surface area of the two cubes
Answer:
V = L^3 where v is volume and L the length of one side
A = 6 * L^2 total area of cube with side L
A = 6 * V^2/3 area of cube expressed in V
A2 / A1 = (V2 / V1)^2/3 6 cancels
A2 / A1 = 8^2/3 = 4 ratio of areas
-5(-3x+1)= 45 solve for x
Answer:
x=[tex]\frac{10}{3}[/tex]
Step-by-step explanation:
Hi there!
We are given the equation -5(-3x+1)=45 and we need to solve for x
we do this by isolating x by itself on one side of the equation; the numbers (the value of x) is on the other side
First, do the distributive property and distribute -5 on -3x and 1 on the left side (multiply both -3x and 1 by -5)
15x-5=45
add 5 to both sides (-5+5=0)
15-5=45
+5 +5
_________
15x=50
divide both sides by 15 (15÷15=1)
15x=50
÷15 ÷15
________
x=[tex]\frac{50}{15}[/tex]
we can simplify this fraction by factoring five out of 50 and 15
x=[tex]\frac{10*5}{3*5}[/tex]
cancel 5 out of the numerator and denominator
x=[tex]\frac{10}{3}[/tex]
The answer can be left as an improper fraction
Hope this helps! :)
The police measured the skid marks made by a car that crashed into a tree. The formula used to approximate the distance in feet that it takes to stop a car after the brakes are applied for a car traveling at a rate of r miles per hour is d= 0.045 r^2 + 1.1 r . If the measurement gave a braking distance of 250 ft, was the driver exceeding the legal speed limit of 55 mi/h? Find the speed of the car before the brakes were applied.
Replace r in the equation with 55 mph and solve for d.
D = 0.045(55)^r + 1.1(55)
Simplify:
D = 0.045(3025) + 60.5
D = 136.125 + 60.5
D = 196.625
At the speed limit of 55 mph the skid mark would be 196.625 feet long.
Because the skid mark was greater than that it was going faster than 55 mph.
To find the speed the car was going replace d with 250 and solve for r:
250 = 0.045r^2 + 1.1r
Multiply both sides by 1000 to remove decimals:
250000 + 45r^2 + 1100r
Subtract 250000 from both sides
45r^2 + 1100 -250000 = 0
Use the quadratic formula to solve:
R = -1100 + sqrt(1100^2 14x45(-250000) /(2 x45)
R = 63.308 miles per hour
The speed of the car was 63.3 miles per hour
Jestina has A apples, she gave 5 to her sister, enter an expression to represent the number of apples jestina has now!! (show work please!)
Answer: A-5
Step-by-step explanation:
Jestina has A apples
she gave 5 away
so she has 5 fewer apples than she had before
so A-5 is the amount of apples she has now
What equation is always true?
Answer: 4)
Step-by-step explanation: angles 2 and 3 equal 7 because they are both missing angle 4 to make it either 180 degrees or 360 degrees respectively.
simplification please
Answer:
5
Step-by-step explanation:
WHen we raise a power to a power, we multiply them, in this case 5 is the base so we can just ignore it for now and replace it with x.
(X^1/3)^3
Multiply 1/3 by 3 and we get 1
So:
X^1
Which does nothing, so we can simplify to just:\
X
Remember x is 5 so the answer is:
5
Suppose that y varies inversely with x. Write a function that models the inverse function x=7 when y=3
9514 1404 393
Answer:
y = 21/x
Step-by-step explanation:
The inverse variation relation means ...
y = k/x
For the given values, we can determine the constant k:
3 = k/7
3×7 = k = 21
Then the function is ...
y = 21/x
Any help? Algebra I
9514 1404 393
Answer:
2p +3d = 18.25; 4p +2d = 27.50popcorn: $5.75; drink: $2.25Step-by-step explanation:
a) Let p and d represent the prices of a bag of popcorn and a drink, respectively.
Mohamed's purchase is ...
2p +3d = 18.25
Miguel's purchase is ...
4p +2d = 27.50
__
b) We can subtract half the second equation from the first to get an equation for the cost of a drink.
(2p +3d) -1/2(4p +2d) = (18.25) -1/2(27.50)
2d = 4.50 . . . . . . simplify
d = 2.25 . . . . . . divide by 2
4p +2(2.25) = 27.50 . . . . substitute for d in the second equation
4p = 23.00 . . . . . . . . . subtract 4.50
p = 5.75 . . . . . . . . . divide by 4
The cost of a bag of popcorn is $5.75; the cost of a drink is $2.25.
Triangle G Y K is shown. Angle G K Y is a right angle. Angle K G Y is 60 degrees and angle G Y K is 30 degrees. The length of G K is 27.
Given right triangle GYK, what is the value of tan(G)?
One-half
StartFraction StartRoot 3 EndRoot Over 2 EndFraction
StartFraction 2 StartRoot 3 EndRoot Over 3 EndFraction
StartRoot 3 EndRoot
Answer:
The answer is A
Step-by-step explanation:
just took it on egde