Let y - x = height of sign
tan 31 = x/24
tan 31 • 24 = x
14.4206548567 = x
tan 42 = y/24
tan 42 • 24 = y
21.6096970631 = y
Now subtract x from y.
y - x = 21.6096970631 14.4206548567
y - x = 7.1890422064
Rounding off to the nearest tenth of a foot, we get 7.2 feet.
The sign for the roof is 7.2 feet.
The height of the sign is approximately 7.2 feet, calculated from the differences in elevation angles and distance.
To determine the height of the sign, we'll start by calculating the height of the roof and the height of the top of the sign from point P.
First, let's define the variables:
[tex]- \( h_1 \):[/tex] height of the roof
[tex]- \( h_2 \)[/tex]: height of the top of the sign
[tex]- \( h_s \):[/tex] height of the sign itself
From point P, the angle of elevation to the roof is [tex]\( 31^\circ \)[/tex] and the angle of elevation to the top of the sign is [tex]\( 42^\circ \).[/tex] The horizontal distance from point P to the base of the building is 24 feet.
Using the tangent of the angles of elevation, we have the following relationships:
[tex]\[\tan 31^\circ = \frac{h_1}{24}\]\[\tan 42^\circ = \frac{h_2}{24}\][/tex]
First, let's calculate [tex]\( h_1 \):[/tex]
[tex]\[h_1 = 24 \times \tan 31^\circ\]Using a calculator to find \( \tan 31^\circ \):\[\tan 31^\circ \approx 0.6009\]\[h_1 = 24 \times 0.6009 \approx 14.422\][/tex]
Next, let's calculate [tex]\( h_2 \):[/tex]
[tex]\[h_2 = 24 \times \tan 42^\circ\][/tex]
Using a calculator to find [tex]\( \tan 42^\circ \):[/tex]
[tex]\[\tan 42^\circ \approx 0.9004\]\[h_2 = 24 \times 0.9004 \approx 21.610\][/tex]
The height of the sign [tex]\( h_s \)[/tex] is the difference between [tex]\( h_2 \) a[/tex]nd [tex]\( h_1 \):[/tex]
[tex]\[h_s = h_2 - h_1\]\[h_s = 21.610 - 14.422 \approx 7.188\][/tex]
To the nearest tenth of a foot, the height of the sign is:
[tex]\[h_s \approx 7.2 \text{ feet}\][/tex]
Thus, the height of the sign is ( 7.2 ) feet.
Which of these is not a possible r-value?
–0.90, –0.67, 0.20, 1.75
a. 1.75
b. -0.90
c. -0.67
d. 0.20
Answer:
a. 1.75
Step-by-step explanation:
r values, or the correlation coefficient must be between -1 and 1, inclusive
-1 is a perfect negative correlation
0 is no correlation
+1 is a perfect positive correlation
1.75 is not between -1 and 1
Write an equation in slope-intercept form for the line that passes through (8,1) and (4,3).
it would be y = −1/2x + 5
What is the volume?
Please help I am confusion
Why is this one Kansas but this one isn’t Arkansas AMERICA EXPLAIN WHAT DO YOU MEAN ARKANSAS
That is because the English language is three child languages standing on each other's shoulders in long trenchcoat pretending to be an adult language.
Also, your answer is 32,000in^3
What is the solution to this equation?
4x + 16 - x = 22 + 6
Answer:
x=4
Step-by-step explanation:
Simplifying
4x + 16 + -1x = 22 + 6
Reorder the terms:
16 + 4x + -1x = 22 + 6
Combine like terms: 4x + -1x = 3x
16 + 3x = 22 + 6
Combine like terms: 22 + 6 = 28
16 + 3x = 28
Solving
16 + 3x = 28
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-16' to each side of the equation.
16 + -16 + 3x = 28 + -16
Combine like terms: 16 + -16 = 0
0 + 3x = 28 + -16
3x = 28 + -16
Combine like terms: 28 + -16 = 12
3x = 12
Divide each side by '3'.
x = 4
Simplifying
x = 4
Hope this helps! And please correct me if I'm wrong so others can have the correct answer.
For this case we must solve the following equation:
[tex]4x + 16-x = 22 +6[/tex]
We add similar terms on both sides of equality:
[tex]3x + 16 = 28[/tex]
We subtract 16 from both sides of the equation:
[tex]3x = 28-16\\3x = 12[/tex]
We divide between 3 on both sides of the equation:
[tex]x = \frac {12} {3}\\x = 4[/tex]
ANswer:
[tex]x = 4[/tex]
What is the smallest integer greater than √148 ?
13
15
14
12
11
Answer 13;
because sqrt148~12.16
Answer:
The smallest integer greater than √148 is 13
Step-by-step explanation:
√169 = 13
√144 = 12
so √148 is between 12 and 13
12 < √148 < 13
On those option choices
11 and 12 are smaller than √148
13, 14 and 15 are greater than √148
The smallest integer greater than √148 is 13
A spinner has 10 equally sized sections, 6 of which are gray and 4 of which are blue. The spinner
is spun twice. What is the probability that the first spin lands on blue and the second spin lands
en gray
Write your answer as a fraction in simplest form.
Answer:
6/25
Step-by-step explanation:
6/10 chance for grey.
4/10 chance for blue.
And = Multiplication
Or = Addition
6/10 times 4/10 = 24/100
24% chance or 6/25 chance it will land on grey and blue.
(Theoretical Probability)
The probability that the first spin lands on blue and the second spin lands on gray is 6/25.
The probability of the first spin landing on blue and the second spin landing on gray can be calculated as follows:
Probability of landing on blue on the first spin = 4/10 = 2/5
Probability of landing on gray on the second spin = 6/10 = 3/5
Multiply the probabilities of each spin: (2/5) * (3/5) = 6/25
Therefore, the probability that the first spin lands on blue and the second spin lands on gray is 6/25.
The utility company made a mistake on Ian’s electric bill. The company has agreed to credit Ian’s account for five transactions, each worth $4.50. What will the net change to Ian’s account be after the utility company lives up to the agreement?
Answer:
the net change would be 22.50!
Step-by-step explanation:
add 4.50 5 times!
Answer:
The net change to Ian’s account after the utility company lives up to the agreement will be $22.50.
Step-by-step explanation:
The utility company made a mistake on Ian’s electric bill.
The company has agreed to credit Ian’s account for five transactions, each worth $4.50
This gives [tex]4.50\times5=22.50[/tex] dollars
So, the net change to Ian’s account after the utility company lives up to the agreement will be $22.50.
50 POINTS! Minimum Value help. Photo attached.
For the function y=-2+5sin((pi/12)(x-2)) what is the minimum value?
- 1 <= sin (a) <= 1
-2+5*(-1)<= -2+5sin(pi/12)(x-2)<= -2 +5*(1)
so
the minimum value of y is
y = - 2 + 5 * ( - 1 ) = - 7
hope this would help you
Answer:
[tex]\Large \boxed{-7}[/tex]
Step-by-step explanation:
We can find the minimum of the function by plotting the function on the graph.
[tex]\displaystyle \mathrm{y=-2+5 \cdot sin(\frac{\pi }{12}(x-2) )}[/tex]
The minimum value is the y value of the lowest point on the graph.
The graph of g(x), shown below, is a vertical shift of the graph of f(x) = 2x.
Write the equation for g(x).
A. g(x) = 2x^ – 1
B. g(x) = 2x^+ 1
C. g(x) = 2x – 1
D. g(x) = 2x + 1
Answer:
c is the answer
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
Identify the measure of arc RPS. PLEASE HELP!!
Angles TOS and ROQ are congruent, so [tex]m\angle ROQ=m\widehat{RQ}=28^\circ[/tex].
RT is a diameter of the circle, so [tex]m\widehat{RT}=180^\circ[/tex], and in particular
[tex]m\angle ROQ+m\angle QOP+m\angle POT=180^\circ\implies m\angle QOP=62^\circ[/tex]
Then
[tex]m\widehat{RPS}=28^\circ+62^\circ+90^\circ+28^\circ=\boxed{208^\circ}[/tex]
The measure of arc RPS = [tex]208^{\circ}$$[/tex].
Measure of arcThe measure of an inscribed angle is half the measure of the intercepted arc.
(The measure of the arc is twice the measure of the angle)
Arc length is a measurement of distance, so it cannot be in radians.
Angles TOS and ROQ are congruent,
so [tex]$m \angle R O Q=m \widehat{R Q}=28^{\circ}$[/tex].
RT is the diameter of the circle,
so [tex]$m \widehat{R T}=180^{\circ}$[/tex], and in particular [tex]$m \angle R O Q+m \angle Q O P+m \angle P O T=180^{\circ}[/tex]
[tex]\Longrightarrow m \angle Q O P=62^{\circ}$[/tex]
Then
[tex]$$m \widehat{R P S}=28^{\circ}+62^{\circ}+90^{\circ}+28^{\circ}=208^{\circ}$$[/tex]
[tex]$$m \widehat{R P S}=208^{\circ}$$[/tex]
The measure of arc RPS = [tex]208^{\circ}$$[/tex].
Therefore, the correct answer is option (b) [tex]208^{\circ}$$[/tex].
To learn more about the measure of arc
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Please help, Thanks.
Answer:
C
Step-by-step explanation:
49x² + 28xy + 4y² ← is a perfect square of the form
(ax + by)² = a²x² + 2abxy + b²y²
49 = 7² ⇒ a = 7 and 4 = 2² ⇒ b = 2
2ab = 2 × 7 × 2 = 28
Hence
49x² + 28xy + 4y² = (7x + 2y)²
with factor 7x + 2y ⇒ C
The exchange rate of U.S. Dollars to British pounds (?) is .63. You have $4000 to convert to British pounds. How many British pounds will you receive?
Answer:
2,520 pounds
Step-by-step explanation:
Step 1: For this question, all you have to do is multiply 4,000 * 0.63. In other words, you are multiplying the amount you have by the conversion rate. 4,000 * 0.63 is 2,520. That's our answer.
please help! John-Mark recorded the stats for several baseball pitchers. He made a scatterplot showing the
number of games they played and the percentage they lost. Which line is the best fit for this
data?
y = 10x - 70
y = 10x + 70
y = -10x + 110
y = -10x - 110
Answer: Third Option
[tex]y = -10x + 110[/tex]
Step-by-step explanation:
The equation of a line in the pending intersection form has the following form:
[tex]y=mx +b[/tex]
Where m is the slope of the line and b is the intersection with the y axis.
Observe in the graph that the data form a decreasing line. Then the adjustment line must have a negative slope [tex]m <0[/tex].
The first and the second option have positive slopes, therefore we discard them.
Notice in the scatter diagram that the intersection of the line with the y-axis (x = 0) is above 90.
The line of the fourth option has a value of [tex]b = -110 <90[/tex].
Therefore the line that best fits the data is the third option
[tex]y = -10x + 110[/tex]
Note that the line has a slope [tex]m = -10[/tex] and a value of [tex]b> 90[/tex]
What is the cube root of 216x9y18
I’m not sure but I think it might be the second one, 6x^3y^6
the answer is b the second choice
Please please help me out
Answer:
The slant height of the pyramid is 3√2 ft, or to the nearest tenth ft,
4.2 ft
Step-by-step explanation:
The equation for the volume of a pyramid of base area B and height h is
V = (1/3)·B·h. Here, V = 432 ft³, B = (12 ft)² and h (height of the pyramid) is unknown. First we find the height of this pyramid, and then the slant height.
V = 432 ft³ = (144 ft²)·h, so h = (432 ft³) / (144 ft²) = 3 ft.
Now to find the slant height of this pyramid: That height is the length of the hypotenuse of a right triangle whose base length is half of 12 ft, that is, the base length is 6 ft, and the height is 3 ft (as found above).
Then hyp² = (3 ft)(6 ft) = 18 ft², and the hyp (which is also the desired slant height) is hyp = √18, or √9√2, or 3√2 ft.
The slant height of the pyramid is 3√2 ft, or to the nearest tenth ft,
4.2 ft
NEED HELP ASAP!! 20 POINTS!!!! A cylindrical container has a radius of 0.75 meter and a height of 2 meters. The container is filled with gasoline. The density of gasoline is 750 kg/m³.
What is the mass of the gasoline in the container?
Enter your answer in the box. Use 3.14 for π . Round your final answer to the nearest whole number.
The mass of the gasoline in the container is 2657.81grams
Density of an objectThe ratio of the mass of an object to its volume is its density. Mathematically;
Density = Mass/Volume
Mass = density * volume
Given the following
Density = 750 kg/m³.
Determine the volume
Volume = πr²h
Volume =3.14(0.75)² * 2
Volume = 3.54375 m³
Determine the mass
Mass = 750 * 3.54375
Mass = 2657.81grams
Hence the mass of the gasoline in the container is 2657.81grams
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Answer:
2649 kg
Step-by-step explanation:
I just took the test
A rectangle has length (3x-8) and width (2x-7) cm .Write down and simplify an expression for the perimeter of the rectangle. So show me the answer and its working out.
The expression for the perimeter of a rectangle with length (3x-8) cm and width (2x-7) cm is P = 2 * ((3x - 8) + (2x - 7)). After simplification, the final expression for the perimeter is P = 10x - 30 cm.
Explanation:The perimeter of a rectangle is given by the formula 2 * (length + width). Here, the length of the rectangle is given as (3x - 8) cm and the width is given as (2x -7) cm. Therefore, substituting these into the formula the expression for the perimeter (P) is P = 2 * ((3x - 8) + (2x - 7)).
To simplify this, we first add up the like terms within the parentheses giving us P = 2 * (5x - 15). Then, apply the distributive property of multiplication over addition to simplify further and we get P = 10x - 30 cm. This is the simplified expression for the perimeter of the rectangle.
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Identify the value of y and the length of each chord. HELP ASAP!!
Answer:
y = 57, PQ = 60, RS = 28
Last option is the answer
Step-by-step explanation:
3 * y = 9 * 19
3y = 171
y = 57
PQ = 3 + 57 = 60
RS = 9 + 19 = 28
Answer:
y = 57; PQ = 60; RS = 28
Step-by-step explanation:
The product of lengths of parts of a chord is a constant, so ...
PT·TQ = RT·TS
TQ = y = RT·TS/PT = 9·19/3 = 57
Of course the total chord length is the sum of its parts, so ...
PQ = PT +TQ = 3 +57 = 60
RS = RT +TS = 9 +19 = 28
Then your answer choice is ...
y = 57; PQ = 60; RS = 28.
The diameter of the circlular garden is 16 feet what is the approximate area of the garden? Please hurry
Find the exact solution of the following quadratic equation by using the Quadratic Formula. x^2-7x= 60
a.
{–12, 5}
c.
{–10, 24}
b.
{–5, 12}
d.
{60, 67}
Answer:
B. {-5, 12}
Step-by-step explanation:
the quadratic equation is given by the formula
x = -b± √b² - 4ac
2a
where a is the coefficient of x², b is the coefficient of x, and c is the constant
in the equation; x² - 7x -60 = 0
a = 1, b = -7, c = -60
x = -(-7)± √(-7)² - 4*1*-60 (negative sign multiplied by negative sign will
2*1 a positive sign)
x = 7 ± √49 + 240
2
x = 7 ± √289
2
x = 7 ± 17
2
x= 7 + 17 or 7 - 17
2 2
x = 24/2 or -10/2
x = 12 or -5
Write the following integers in order from greatest to least. +4, -2, +1, -5, +3
4, 3, 1, -2, -5
Hope this helps.
The following integers from the greatest to least are as follows:
+4, +3, +1, -2, -5
The given series has 6terms. What is the sum of the terms of the series 10+25+40+...+85
A.) 285
B.) 365
C.) 350
D.) 325
Answer:
A.) 285
Step-by-step explanation:
The sum of an arithmetic series is the sum of the first and last terms multiplied by half the number of terms.
(10 +85)·6/2 = 285 . . . sum of 6 terms
When Richard works out, he spends 12 minutes doing cardio and 18 minutes doing resistance training. Cooper's workout consists of 10 minutes of cardio and 16 minutes of resistance training. Who does a higher ratio of cardio to resistance training?
Answer:
Richard, at 2/3, versus Cooper, at 5/8
Step-by-step explanation: 12 min
Richard's ratio of cardio to resistance is R = ------------ = 2/3
18 min
10 min
Cooper's is C = ------------ = 5/8
16 min
The LCD here is 24. Rewrite 2/3 and 5/8 with denominator 24 for greater ease in comparing the two fractions/ratios:
R = 16/24 and C = 15/24
So it becomes obvious that Richard does a higher ratio of carido to resistance.
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers. Perform the operation indicated, then place the answer in the proper location on the grid. Write your answer in descending powers of m. (5m3 + 3mn2) + (-7m2n + mn2 - n3) - (mn2 + 2m3)
Answer:
[tex]3m^3-7m^2n+3mn^2-n^3[/tex]
Step-by-step explanation:
[tex](5m^3 + 3mn^2) + (-7m^2n + mn^2 - n^3) - (mn^2 + 2m^3)\\Solving:\\5m^3 + 3mn^2 -7m^2n + mn^2 - n^3 - mn^2 - 2m^3\\Adding\,\,like\,\,terms\,\,\\5m^3 -2m^3+ 3mn^2 -mn^2+mn^2-7m^2n-n^3\\3m^3 +3mn^2-7m^2n-n^3\\Arranging\,\,in\,\,desecnding\,\,order\,\,in\,\,power\,\,of\,\,m\\3m^3-7m^2n+3mn^2-n^3[/tex]
If 2x−3y=11 and 3x+15=0, what is the value of y? These are the choices given:
a) -7 b)-5 c)-1/3 d)3 e)10
Answer:
A.-7
Step-by-step explanation:
If [tex]2x-3y=11[/tex] and [tex]3x+15=0[/tex]
To know the value of y we need to clear x in the equation [tex]3x+15=0[/tex] and the result replace it in [tex]2x-3y=11[/tex].
Then, let's clear x in the equation [tex]3x+15=0[/tex]
[tex]3x=-15\\x=-\frac{15}{3} =-5[/tex]
Substituting the value of x in the equation [tex]2x-3y=11[/tex]
[tex]2(-5)-3y=11\\-10-3y=11\\-3y=11+10\\y=\frac{11+10}{-3} \\y=\frac{21}{-3}\\ y=-7[/tex]
Answer:
a) y = -7.
Step-by-step explanation:
2x − 3y = 11
3x + 15 = 0
From the second equation:
3x = -15
x = -5.
Substitute this value in the first equation:
2(-5) - 3y = 11
-10 - 11 = 3y
3y = -21
y = -7.
Moon Sporting Goods received a shipment of tennis rackets and marked them up 45%. The cost of the tennis rackets to Moon was $85. What is the minimum selling price for the tennis racket?
Answer:
$123.25
Step-by-step explanation:
A selling price reflecting a 45% markup can be found by multiplying the wholesale price ($85) by (1 + 0.45), or 1.45:
1.45($85) = $123.25
Based on the data table provided below, how many people would we expect to pick a snake as their favorite animal if 440 people were asked their preferences? Favorite Animal Number Panda 13 Snake 10 Tiger 17 Dolphin 15 104 80 136 120
Answer:
80 just did it in a lesson
Step-by-step explanation:
Answer:
Yeah the other dude is right it is 80
Step-by-step explanation:
15 pts awarded and brainliest will be chosen!!!
Which of the following is the solution to | x+11 |< 17?
Answer:
A. x < 6 and x > - 28
Step-by-step explanation:
We have been given the following inequality;
| x+11 | < 17
We can replace the absolute value function by re-writing the inequality as;
-17< x+11<17
subtract 11 from both sides;
-17-11<x+11-11<17-11
-28<x<6
splitting this we have;
x<6
x>-28
Answer:
A. x < 6 and x > - 28
Step-by-step explanation:
| x+11 |< 17
x + 11 < 17
x < 6
-(x + 11) < 17
-x - 11 < 17
-x < 28
x > - 28
Answer
6 > x > -28 (x < 6 and x > - 28)
Write the following integers in order from greatest to least. -3, 0, -2, -8, +3
The following integers from the greatest to least are as follows:
+3, 0, -3, -2, -8
The answer is +3,0,-2,-3,-8
help please thanks!!!!!
Answer:
B
Step-by-step explanation:
The interquartile range is the difference between the upper quartile ( the right side of the box plot ) and the lower quartile ( the left side of the box plot )
For cars this is 29 - 22 = 7 and
For minivans is 21 - 18 = 3
Answer:
The second one, cars 7mpg, minivans 3mpg
Step-by-step explanation:
This is because if you subtrect the upper quartile from the lower quartile you get a range this range is the answer to the queestion.