Answer:
The values of [tex]a[/tex] and [tex]b[/tex] are [tex]5[/tex] and [tex]-\frac{15}{7}[/tex], respectively.
Step-by-step explanation:
There are mistakes in the statement, correct form is presented below:
[tex]5+\frac{\sqrt{3}}{7} + 2\sqrt{3} = a - b\cdot \sqrt{3}[/tex].
By direct comparison we have the following system of equations:
[tex]a = 5[/tex] (1)
[tex]\frac{\sqrt{3}}{7}+2\sqrt{3} = -b\cdot \sqrt{3}[/tex] (2)
In (2) we solve for [tex]b[/tex]:
[tex]\left(\frac{1}{7}+2 \right)\cdot \sqrt{3} = -b\cdot \sqrt{3}[/tex]
[tex]b = -\frac{15}{7}[/tex]
The values of [tex]a[/tex] and [tex]b[/tex] are [tex]5[/tex] and [tex]-\frac{15}{7}[/tex], respectively.
Emir is standing in a treehouse and looking down at a swingset in the yard next door. The angle of depression from Emir's eyeline to the swingset is 30.26° and Emir is 14 feet from the ground How many feet is the base of the treehouse from swingset? Round your answer to the nearest foot
ANSWERS:
15 feet
20 feet
18 feet
24 feet
=============================================
Explanation:
Refer to the diagram below. The goal is to find x, which is the horizontal distance from the base of the tree to the swing set.
Focus on triangle BCD.
The angle B is roughly 30.26 degrees, and this is the angle of depression. This is the amount of degrees Emir must look down (when starting at the horizontal) to spot the swing set.
We know that he's 14 ft off the ground, which explains why AB = CD = 14.
The goal is to find BC = AD = x.
---------------------------
Again, keep your focus on triangle BCD.
We'll use the tangent ratio to say
tan(angle) = opposite/adjacent
tan(B) = CD/BC
tan(30.26) = 14/x
x*tan(30.26) = 14
x = 14/tan(30.26)
x = 23.9965714046732
That value is approximate. Make sure your calculator is in degree mode.
That value rounds to 24 feet when rounding to the nearest whole foot.
Using the slope concept, it is found that the base of the treehouse is 24 feet from swingset.
What is a slope? The slope is given by the vertical change divided by the horizontal change. It's also the tangent of the angle of depression.
In this problem:
The vertical distance is of 14 feet.The horizontal distance is of x feet.The angle of depression is of 30.26º.Hence:
[tex]\tan{30.26^{\circ}} = \frac{14}{x}[/tex]
[tex]0.5834 = \frac{14}{x}[/tex]
[tex]x = \frac{14}{0.5834}[/tex]
[tex]x = 24[/tex]
The base of the treehouse is 24 feet from swingset.
You can learn more about the slope concept at brainly.com/question/18090623
Isabel and Sophia share a bag of 42 sweets. Isabel has 16 sweets. Find the ratio of Sophia's sweets to Isabel's sweets.
Answer:
ratio of Sophia's sweets to Isabel's sweets is
13:8
Answer:
you first have to find the number of sweets that sophia got.by subtracting the total number of sweets minus the number of sweets that isabel got which will be
42-16=26
therefore the ratio will be
16:26
8:13
I hope this helps
The cost,c(x), for a taxi ride is given by c(x)=3x+2.00, where x is the number of minutes. What does the slope mean for this situation
Answer:
for every minute it will cost 3 dollars
Step-by-step explanation:
c(x)=3x+2.00
The cost to get in the taxi is 2 dollars
The slope is 3
3x means that for every minute it will cost 3 dollars
How much is the bill for a person who uses 560 kwh in a month?
Answer:
An electric company calculates a person's monthly bill from the number of kilowatt-hours (kWh), x, used, x 200 The function b(ar) = { 0.102, 0.15(x - 200) +20, 200 determines the bill How much is the bill for a person who uses 800 kWh in a month?
During one week, David worked 16 hours at his normal hourly rate and
7 hours at his time and a half rate. His total pay for the week was
$848.
What is David’s normal hourly rate?
Answer:
43.49
Step-by-step explanation:
let his normal hourly rate be x
16x+7x/2=848
39x/2=848
x=848 ÷ 39/2
=43.48717
A science teacher wrote the table of values below.
Amount of Hydrogen vs. pH
Amount of Hydrogen, x
(in moles per liter)
pH, f(x)
One-tenth
1
StartFraction 1 Over 100 EndFraction
2
StartFraction 1 Over 1000 EndFraction
3
StartFraction 1 Over 10,000 EndFraction
4
StartFraction 1 Over 100,000 EndFraction
5
Which function models the data in the table?
f (x) = StartFraction 1 Over x EndFraction, x not-equals 0
f (x) = log StartFraction 1 Over x squared EndFraction, x not-equals 0
f (x) = log StartFraction 1 Over x EndFraction, x not-equals 0
f (x) = StartFraction 1 Over x squared EndFraction, x not-equals 0
The best function that models the data is f(x) = log StartFraction 1 Over x EndFraction, x not-equals 0
Find the table attached below
From the table shown, we can see that when x = 1/10, f(x) = 1
Similarly when x = 1/100, f(x) = 2
According to the law of logarithm, we can say that:
Log 10 = 1
Log 100 = 2 etc..
Recall that f(x) = 1 when x = 1/10, this means that;
F(x) = log 10
F(x) = log(1/1/10))
F(x) = log(1/x) since x = 1/10
Similarly if f(x) = 2 when x = 1/100
F(x) = log 100
F(x) = log(1/1/100))
F(x) = log(1/x) since x = 1/100 in this case
On a general note, we can conclude that f(x) = 1/x where x is not equal to zero.
Learn more function models at https://brainly.com/question/11989600
Answer:
A
Step-by-step explanation:
The person above said so
f (x) = StartFraction 1 Over x EndFraction, x not-equals 0
It takes 5 minutes for 10 people to drink 25 pints of water. At this rate, how long would it take 15 people to drink 155 pints of water
Answer:
the time taken for the 15 people to drink 155 pints is 20.67 min.
Step-by-step explanation:
Given;
10 people took 5 mins to drink 25 pints of water
[tex]The \ rate\ for \ 10 \ people = \frac{25 \ pints }{5 \ mins} = 5 \ \frac{pints}{\min} \\\\The \ rate \ for \ 1 \ person = \frac{5}{10} \ \frac{pints}{\min} = 0.5 \ \frac{pints}{\min} \\\\The \ rate \ for \ 15 \ people = 15( 0.5 \ \frac{pints}{\min} )= 7.5 \ \frac{pints}{\min} \\\\Time \ taken \ for \ the \ 15 \ people \ to \ drink \ 155 \ pints = \frac{155 \ pints}{7.5 \ pints/ \min} \\\\= 20.67 \min[/tex]
Therefore, the time taken for the 15 people to drink 155 pints is 20.67 min.
find the exact value of the indicated trigonometric functions for the acute angle a:
Given: cot a= 3 3/7, find: cos a and tan a?
Answer:
cot a = 3 3/7
or, cot a = 24/7
or, tan a = 7/24
So,
cos a = 24/25
tan a = 7/24
Answered by GAUTHMATH
24 cars pass through an intersection each minute while the traffic light is green. In addition, 6 cars pass through the intersection
while the light is yellow. If 84 cars pass through
the intersection during one light cycle (one green light and one yellow light), how long was the green light?
Answer:
3.25 minutes
Step-by-step explanation:
3.25 minutes per green light x 24 = 78
the yellow light is a given, hence 6 cars pass through
78 + 6 = 84 cars
A rectangle with an area of 3990 cm2 is x centimeters wide and (x+4) centimeters long. To the nearest tenth of a centimeter, the width and length are
Answer: width:60.2 cm
Length: 64.2 cm
Step-by-step explanation:
Given
The area of the rectangle is [tex]3990\ cm^2[/tex]
Width of the rectangle is [tex]x\ cm[/tex]
Length of the rectangle is [tex]x+4\ cm[/tex]
Area of the rectangle is the product of length and width
[tex]\therefore 3990=(x+4)x\\\Rightarrow 3990=x^2+4x\\\Rightarrow x^2+4x-3990=0\\\Rightarrow x=60.198\ or\ -65.198\ cm\\\text{Neglecting negative term}\\\Rightarrow x=60.198\approx 60.2\ cm[/tex]
Width of the rectangle is [tex]60.2\ cm[/tex]
Length of the rectangle is [tex]60.2+4=64.2\ cm[/tex]
a) 2(5x – 3) = 24
b)
5(2x + 1) = 50
Answer:
a) x=3
b) x=4.5
Step-by-step explanation:
2(5x – 3) = 24
10x-6=24
10x=30
x=3
5(2x + 1) = 50
10x+5=50
10x=45
x=4.5
One of the factors of x² + y² + 2xy - z² is ?
Answer:
x + y + z.
Step-by-step explanation:
x² + y² + 2xy - z²
= (x + y)^2 - z^2
This is the difference between 2 squares so the factors are:
(x + y + z) and (a + y - z).
Answer: The factors are (x+y+z) and (x+y-z)
In other words, it factors to (x+y+z)*(x+y-z)
=====================================================
Work Shown:
[tex]x^2 + y^2 + 2xy - z^2\\\\(x^2 + 2xy + y^2) - z^2\\\\(x+y)^2 - z^2\\\\(x+y+z)(x+y-z)\\\\[/tex]
Notes:
In the third step, I used the rule (A+B)^2 = A^2+2AB+B^2. For this, A = x and B = y.In the last step, I used the difference of squares factoring rule A^2-B^2 = (A+B)(A-B). In this case, A = x+y and B = z.Full working out for this question please.
Answer:
d 28.8cm2
Step-by-step explanation:
1/2BH
1/2() 12.8() 4.5
28.8
help please tries 2 times
Answer:
(2,1)
Step-by-step explanation:
2x - 2y = 2
5x + 2y = 12
again just add them in this case
7x = 14
x = 2
4 - 2y = 2
-2y = -2
y = 1
Vera uploaded a hilarious video of a squirrel to a funny video website. It was viewed 320 times on the first day. Each day since then, the number of views was 25% more than the day before.
Let f(n) be the number of views Vera's video for on the nth day side she uploaded it.
What kind of sequence is it?
A. Arithmetic sequence
B. Geometric Sequence
Write an explicit formula for the sequence.
f(n)=
Answer:
Step-by-step explanation:
On first day , the video was viewed = 320 times .
We are given that Each day since then, the number of views was 25% more than the day before. This means the likes are increasing 1.25 per day .
So, this situation forms G.P.
Where common ratio r = 1.25
First term = f(1) = 320
Formula of nth term in G.P. =
So, nth term of the given situation :
Where f(n) denotes the number of views on nth day .
So, the number of views Vera's video got on the nth day =
Step-by-step explanation:
What is the measure of JK?
What are factorials? And how do you do them in fractions like
4!5!
——- How do you do that question? And why do you leave
6! The 5! without anything, like why does it not go like
(5)(4)(3)(2)(1)? Why is it like that?
Anyone knowwwww last one
Answer:
26 sqrt(5) + 2 sqrt(10)
Step-by-step explanation:
2 sqrt(5) *(13+sqrt(2))
Distribute
26 sqrt(5) + 2 sqrt(10)
Answer:
[tex]26\sqrt5 +2 \sqrt10[/tex]
Step-by-step explanation:
Evaluate 1/243 ( base must be 1/9)
PLEASE I NEED THIS FAST!
Answer:
(1/9)^2 x 1/3
Step-by-step explanation:
1/243
=> 1 / 3 x 3 x 3 x 3 x 3
=> 1 / 9 x 9 x 3
=> (1/9)^2 x 1/3
Find the value of ‘m’ in 3m+12=15
[tex] \sf3m + 12 = 15 \\ \sf3m = 15 - 12 \\ \sf3m = 3 \\ \sf \: m = \frac{3}{3} \\ \sf \: m \: = \underline{ \bf \: 1}[/tex]
-> Just move all the numbers from the left side to the right side until only the variable is left. Then you can solve the equation & find the required value.
3 m+ 12 = 15
⇔3 m= 3
⇔m= 1
HELP PLEASE
A tuning fork with a period of 1.95 x 10-3 is struck at the same time as a guitar
string. If 24 beats are heard in 6.0 s, find the possible frequency or frequencies of the guitar string.
Answer:
The possible approximate frequencies of the guitar string are 516.82 Hz and 508.82 Hz
Step-by-step explanation:
The given period of the tuning fork, T₁ = 1.95 × 10⁻³ s
The number of beats in 6.0 s = 24 beats
Therefore, the beat frequency, [tex]f_{beat}[/tex] = 4 beats per second = 4 Hz
Let f₁ represent the frequency of the tuning fork, and let f₂ represent the frequency of the guitar string, we have;
f₁ = 1/T₁ = 1/(1.95 × 10⁻³) ≈ 512.82 Hz
We have;
[tex]f_{beat} = \left | f_2 - f_1 \right |[/tex]
[tex]\pm f_{beat} = f_2 - f_1[/tex]
Therefore, we get;
[tex]4 \, Hz= \left | f_2 - 512.82 \, Hz \right |[/tex]
f₂ - 512.82 = ± 4
∴ f₂ = 512.82 ± 4
The possible frequencies of the guitar string, f₂ ≈ 516.82 Hz or f₂ ≈ 508.82 Hz
Can someone help thanks.
Answer:
1/144
Step-by-step explanation: I presume..
And recall something from Algebra...
I hope it helps...
Square it
And reverse it because of the negative
It is a fraction
Answer:
[tex] = { \sf{ \frac{1}{ 144 } }}[/tex]
Step-by-step explanation:
[tex] = { \tt{ \frac{1}{ {12}^{2} } }} = \frac{1}{144} [/tex]
I'LL GIVE BRAINLIEST !!! FASTER
please explain how do you get the answer !
Answer:
70
Step-by-step explanation:
we have the angle of vertex in the isosceles triangle = 180-2*bottom coner= 180-65/2=50
3 angles in the equilateral triangle are equal to 60
we have 50 + 60 +h =the angle of PQR =180
h=70
Answer: h = 70°
In the triangle with Angle R = 65
It is a isoceles triangle as two sides are equal
So base angles will be equall too
Then the third angle will which is the q one will be
65+65+q = 180
q = 180 - 130
q = 50
In the other triangle with all sides equal will be equilateral triangle which means all angles equal = 60
So
Now ATQ
60 + 50 + h = 180
h = 180 - 110 (Angles on a straight line adds upto 180)
h = 70
Must click thanks and mark brainliest
Find the slope of the line that passes through (23, -30) and (-7, 18).
Answer:
slope = - [tex]\frac{8}{5}[/tex]
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (23, - 30) and (x₂, y₂ ) = (- 7, 18)
m = [tex]\frac{18-(-30)}{-7-23}[/tex] = [tex]\frac{18+30}{-30}[/tex] = [tex]\frac{48}{-30}[/tex] = - [tex]\frac{8}{5}[/tex]
The volume of a one is 80 cubic cm what is the volume of the cylinder with the same base and height of the cone
Answer:
240 cubic cm
Step-by-step explanation:
Volume of a cone = 1/3(nr^2h)
volume of a cylinder = nr^2h
n = 22/7
r = radius
The volume of a cone is 1/3 that of a cylinder
to determine the volume of the cylinder with the same parameters as a cylinder, multiply the volume of the cone by 3
80 x 3 = 240 cubic cm
Find the real or imaginary solutions by factoring.
X^4 -3x^2 = -2x^2
Look in the images it is solved.
A textbook store sold a combined total of 240 chemistry and history textbooks in a week. The number of chemistry textbooks sold
was two times the number of history textbooks sold. How many textbooks of each type were sold?
Answer:
160 chemistry books and 80 history books
Step-by-step explanation:
C=chemistry books sold, H=history books sold
C=2H
C+H=240, 3H=240, H=80, C=160
The graph below shows the total cost for lunch, c, when Will and his friends buy a large salad to share and several slices of pizza, p.
A graph titled Lunch Cost. The x-axis shows the number of slices purchased, numbered 1 to 8, and the y-axis shows the cost in dollars, numbered 5 to 40. Blue diamonds appear at points (0, 7.5), (1, 10), (2, 12.5), (3, 15), (4, 17.5), (5, 20), (6, 22.5), (7, 25), (8, 27.5).
For each additional slice of pizza that is purchased, by how much does the total cost of lunch increase?
Answer:
The answer is $2.50
Answer:
the answer would be c because c= $2.50
Step-by-step explanation:
Solve for 2. Round to the nearest tenth, if necessary.
59
K
58°
M
圆
Submit Answer
Answer: 0
PLSSSS HELP
Answer:
x ≈ 94.4
Step-by-step explanation:
Using the tangent ratio in the right triangle
tan58° = [tex]\frac{LM}{KL}[/tex] = [tex]\frac{x}{59}[/tex] ( multiply both sides by 59 )
59 × tan58° = x , then
x ≈ 94.4 ( to the nearest tenth )
Which of the following is equal to the rational expression when x ≠ -4 or 16?
Answer:
C
Step-by-step explanation:
Given
[tex]\frac{x^2-16}{(x-16)(x+4)}[/tex]
The numerator is a difference of squares
x² - 16 = (x - 4)(x + 4)
= [tex]\frac{(x-4)(x+4)}{(x-16)(x+4) }[/tex] ← cancel the common factor (x + 4) on numerator/ denominator
= [tex]\frac{x-4}{x-16}[/tex] → C
