Answer:
The flag pole is 38.96 feet tall.
Step-by-step explanation:
The angle of depression from the top of the flagpole to an object on the ground is 33°.
The object is 60 feet from the base of the cliff.
We need to find the height of the flag pole.
Here, base, B = 60 feet
We know that,
[tex]\tan\theta=\dfrac{P}{B}[/tex]
Put all the values to find P.
[tex]P=B\times \tan\theta\\\\P=60\times \tan(33)\\\\P=38.96\ ft[/tex]
So, the flag pole is 38.96 feet tall.
Solve the quadratic equation by using a graphic approach. Round your answer to the hundredths place.
x² - 2x - 4= 0
a. x= 3.24 or x = -1.24
c. x = 4.24 or x = -0.24
b. x = 2.73 or x = -0.73
d. x= 5.24or x = -1.24
Pls explain I’m having a hard time understanding the lesson
Answer:
x = 3.24, x = -1.24
Step-by-step explanation:
The standard form for a quadratic equation is [tex]ax^2+bx+c=0[/tex]. For your equation a = 1, b = -2, c = -4. The quadratic formula you will be using is [tex]x=\frac{-b\pm \sqrt{b^{2} -4ac} }{2a}[/tex].
Plug in a = 1, b = -2, and c = -4 into the formula.
[tex]=\frac{-\left(-2\right)\pm \sqrt{\left(-2\right)^2-4\cdot \:1\cdot \left(-4\right)}}{2\cdot \:1}[/tex]
We'll do the top part first:
[tex]\sqrt{\left(-2\right)^2-4\cdot \:1\cdot \left(-4\right)}[/tex]
Apply rule [tex]- (-a) = a[/tex]
[tex]=\sqrt{\left(-2\right)^2+4\cdot \:1\cdot \:4}[/tex]
Apply exponent rule [tex](-a)^{n} =a^n[/tex] if [tex]n[/tex] is even
[tex](-2)^2=2^2[/tex]
[tex]=\sqrt{2^2+4\cdot \:1\cdot \:4}[/tex]
Multiply the numbers
[tex]=\sqrt{2^2+16}[/tex]
[tex]2^2=4[/tex]
[tex]=\sqrt{4+16}[/tex]
Add
[tex]=\sqrt{20}[/tex]
The prime factorization of 20 is [tex]2^2*5[/tex]
20 divides by 2. 20 = 10 * 2
[tex]=2*10[/tex]
10 divides by 2. 10 = 5 * 2
[tex]=2* \:2*5[/tex]
2 & 5 are prime numbers so you don't need to factor them anymore
[tex]=2*2*5[/tex]
[tex]=2^2*5[/tex]
[tex]=\sqrt{2^2\cdot \:5}[/tex]
Apply radical rule [tex]\sqrt[n]{ab} =\sqrt[n]{a} \sqrt[n]{b}[/tex]
[tex]=\sqrt{5}\sqrt{2^2}[/tex]
Apply radical rule [tex]\sqrt[n]{a^{n} } =a[/tex]; [tex]\sqrt{2^2} =2[/tex]
[tex]=2\sqrt{5}[/tex]
[tex]=\frac{-\left(-2\right)\pm \:2\sqrt{5}}{2\cdot \:1}[/tex]
Because of the [tex]\pm[/tex] you have to separate the solutions so that one is positive and the other is negative.
[tex]x=\frac{-\left(-2\right)+2\sqrt{5}}{2\cdot \:1},\:x=\frac{-\left(-2\right)-2\sqrt{5}}{2\cdot \:1}[/tex]
Positive x:
[tex]\frac{-\left(-2\right)+2\sqrt{5}}{2\cdot \:1}[/tex]
Apply rule [tex]-(-a)=a[/tex]
[tex]=\frac{2+2\sqrt{5}}{2\cdot \:1}[/tex]
Multiply
[tex]=\frac{2+2\sqrt{5}}{2}[/tex]
Factor [tex]2+2\sqrt{5}[/tex] and rewrite it as [tex]=2\cdot \:1+2\sqrt{5}[/tex]. Factor out 2 because it is the common term. [tex]=2\left(1+\sqrt{5}\right)[/tex].
[tex]=\frac{2\left(1+\sqrt{5}\right)}{2}[/tex]
Divide 2 by 2
[tex]x=1+\sqrt{5}[/tex] or [tex]x=3.24[/tex] (You'll probably have to use a calculator for the square root of 5)
^Repeating the process of positive x for negative x in order to get [tex]x=1-\sqrt{5}[/tex] or [tex]x=-1.24[/tex]
HELP ASAP NEED HELP. WILL GIVE BRAINIEST AND 100 POINTS.
Algebra 1
Use the function f(x) = 4x^2 - 7x - 15 to answer the questions.
Part a: completely factor f(x).
Part b: what are the x-intercepts of the graph of f(x)? Show your work.
Part C: describe the end behavior of the graph of f(x). Explain.
Part D: what are the steps you would use to graph f(x)? Justify that you can use the answers obtained in part B and part C to draw the graph.
Answer:
A: [tex]f(x)=(4x+5)(x-3)[/tex]
B: [tex](-\frac{5}{4} , 0)[/tex] and [tex](3, 0)[/tex]
C: They are parallel, which means they have no endpoint.
slope:1/6 point: (24 ,4)
Answer:
y -4 = 1/6(x-24)
y = 1/6x -2
Step-by-step explanation:
We can point slope form
y-y1 = m(x-x1) where m is the slope and (x1,y1) is a point on the line
y -4 = 1/6(x-24)
Or we can write slope intercept form
y = mx+b where m is the slope and b is the y intercept
Substituting the points
4 = 1/6(24)+b
4 = 6+b
4-6 = b
-2 =b
y = 1/6x -2
Answer:
[tex]y = mx + c \\ 4 = (\frac{1}{6} \times 24) + c \\ 4 = 4 + c \\ c = 0 \\ y = \frac{1}{6} x[/tex]
When should a heart rate monitor be used?
Answer:
There are two simple, compelling reasons to use a heart-rate monitor: to train and race at the best pace for you. The table below shows you how to find your perfect paces for: (1) the three most important workouts in any training program; and (2) the four most popular road-race distances.
Step-by-step explanation:
Hope this helps :)
If two lines are intersected by a third line, is the third line necessarily a transversal?
No, The third line does not necessarily be a transversal.
What is Equation of line?
The equation of line with slope 'm' and y intercept at point 'b' is given as;
⇒ y = mx + b
Given that;
Two lines intersected by a third line.
Since, When two lines are parallel to each other and two lines intersected by a third line then, third lines are transversal.
So, Here it is not given two lines are parallel.
Thus, Third line is not necessarily a transversal.
Hence, The third line does not necessarily be a transversal.
Learn more about the transversal visit:
https://brainly.com/question/2141319
#SPJ2
Which statements about the factors of the terms in the expression 12 x + 18 x y minus 24 y are true? Select three options.
The factors common to 12x and 18xy are 1, 2, 3, 6, x, and y.
The factors common to 12x and 18xy are 1, 2, 3, 6, and x.
The factors common to 12x and 24y are 1, 2, 3, 4, 6, and 12.
The GCF of the expression is 6xy.
The GCF of the expression is 6.
Answer:
i think the answer is Options B, C and E holds.
Step-by-step explanation:
this makes options B and C a choice:
Given the expression: 12x+18xy-24y
Factors of 12x=1,2,3,4,6,12 and x
Factors of 18xy=1,2,3,6,9,18,x and y.
Factors of 24y=1,2,3,4,6,8,12,24 and y.
next for E this is why its a choice:
12x+18xy-24y=6(2x+3xy-4y)
Answer:
bce
Step-by-step explanation:
The actual amount in a 12-ounce container of a certain brand of orange juice is normally distributed with mean μ = 12.34 ounces and standard deviation σ = 0.04 ounce. What percentage of the juice bottles contain between 12.24 and 12.30 ounces of orange juice?
Answer:
15.25%
Step-by-step explanation:
The actual amount in a 12-ounce container of a certain brand of orange juice is normally distributed with mean μ = 12.34 ounces and standard deviation σ = 0.04 ounce. What percentage of the juice bottles contain between 12.24 and 12.30 ounces of orange juice?
We solve using the z score formula
z-score is is z = (x-μ)/σ,
where x is the raw score
μ is the population mean = μ = 12.34 ounces
σ is the population standard deviation = σ = 0.04 ounce
For x = 12.24
z = 12.24 - 12.34/0.04
z = -2.5
Probability value from Z-Table:
P(x = 12.24) = 0.0062097
For x = 12.30
z= 12.30 - 12.34/0.04
z = -1
Probability value from Z-Table:
P(x = 12.30) = 0.15866
Hence, the probability of the juice bottles contain between 12.24 and 12.30 ounces of orange juice
P(x = 12.30) - P(x = 12.24)
= 0.15866 - 0.0062097
= 0.1524503
Therefore, the percentage of the juice bottles contain between 12.24 and 12.30 ounces of orange juice is calculated as:
= 0.1524503 × 100
= 15.24503%
= 15.25%
8 + (9 · 2 – 3) : 25 – 4 2 : 2
Answer:
14 : -17 : 2
Step-by-step explanation:
8 + (9 · 2 – 3) : 25 – 4 2 : 2
= 14 : -17 : 2
Answer:
- 12.4
Step-by-step explanation:
[tex]8 + \frac{9 * 2 - 3}{25} - \frac{42}{2}[/tex]
[tex]8 + \frac{18 - 3}{25} - 21[/tex]
[tex]8 + \frac{15}{25} - 21[/tex]
[tex]8 + \frac{3}{5} - 21[/tex]
[tex]8 \frac{3}{5} - 21[/tex]
[tex]-12 \frac{2}{5}[/tex]
Please help!!!!!!
Which of these are examples of mutually beneficial interactions? Choose all that apply.
A. Ants living in special hollow thoms in a tree rush out and sting plant-eaters.
B. An orchid grows high in a tree to get more sunlight, but it does not affect the tree.
c. Wolves eat the deer that cannot run as fast as the other deer.
D. A bee gets nectar and pollen from the clover flowers in a meadow.
E. A tick bites a dog and drinks the dog's blood.
Answer:
A. The tree provides shelter for the ants, and the ants help the tree to stay alive
How do you perform constructions related to circles? What theorems and explanations can be used to justify these constructions? How do you perform constructions related to circles? What theorems and explanations can be used to justify these constructions?
Answer and explanation:
To construct a circle, draw a line that represents the diameter of the circle. Bisect the line so that it is a perpendicular bisector of the diameter of the circle. Place your compass at the bisection point/midpoint and draw an arc or better still the whole circle.
Theorem: the perpendicular bisector of a chord passes through the center of a circle.
Note: a diameter of a circle is a chord that passes through the center of a circle.
Help please !!!!!!!!’
Step-by-step explanation:
everything can be found in the picture
A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find the time that the rocket will hit the ground, to the nearest 100th of second.
y=-16x^2+232x+134
Answer:
Step-by-step explanation:
when it touch the ground,y=0
-16x²+232x+134=0
-16(x²-29/2 x+(-29/4)²-(-29/4)²)=-134
-16(x-29/4)²-16(-861/16)=-134
-16(x-29/4)²+861=-134
-16(x-29/4)²=-134-861
(x-29/4)²=-995/-16=995/16
x-29/4=±√995/4
rejecting negative sign
x=29/4+√995/4=(29+√995)/4≈15.14 second
Find the Value of X in this Triangle
Answer:
x = -6
Step-by-step explanation:
All three angles are equal, so all three sides are equal, making this an equilateral triangle
5x+10 = 2x-8
Subtract 2x from each side
5x-2x +10 = 2x-8-2x
3x+10 = -8
Subtract 10 from each side
3x+10-10 = -8-10
3x = -18
Divide by 3
3x/3 = -18/-3
x = -6
The surface of an air hockey table has a perimeter of 32 feet its area is 60 ft.what are the dimensions of the air hockey table
The number -2 is a solution to which of the following inequalities?
x + 7 > 5
-3 x < 1
x - 7 < -4
Answer:
The answer is the third one, x - 7 < 4
Step-by-step explanation:
factor the following
(a²+b²)²-18(a²+b²)-88
Answer:
[tex] \rm\displaystyle( {a}^{2} + {b}^{2} - 22)( {a}^{2} + {b}^{2} + 4)[/tex]
Step-by-step explanation:
we would like to factor the following:
[tex] \rm\displaystyle ( {a}^{2} + {b}^{2} {)}^{2} - 18( {a}^{2} + {b}^{2} ) - 88[/tex]
let a²+b²=x
thus substitute:
[tex] \rm\displaystyle x {}^{2} - 18x- 88[/tex]
rewrite the middle term as 4x-22x:
[tex] \rm\displaystyle x^{2} + 4x - 22x - 88[/tex]
factor out x:
[tex] \rm\displaystyle x( x^{} + 4)- 22x - 88[/tex]
factor out -22:
[tex] \rm\displaystyle x( x^{} + 4)- 22(x + 4)[/tex]
group:
[tex] \rm\displaystyle( x- 22)(x + 4)[/tex]
substitute back:
[tex] \rm\displaystyle( {a}^{2} + {b}^{2} - 22)( {a}^{2} + {b}^{2} + 4)[/tex]
and we are done!
Sam built a ramp to a loading dock. The ramp has a vertical support 2 m from the base of the loading dock and 3m from the base of the ramp. If the vertical support is 1.2 m in height, what is the height of the loading dock?
Answer:
tan angle = x/5.
Step-by-step explanation:
If I understand your description,
tan angle at bottom of ramp = 1.2/3.
Then tan angle = x/5.
Check my thinking.
Given that a*b = 2a - 3b, then 2*(-3) =
Answer:
2*(-3)= -6
Step-by-step explanation:
I do not see how "a*b=2a-3b" would change the fact 2 times negative 3 is -6
Plse help my grades go in tomorrow and I am currently struggling!!
C⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
I need help with this quickly, I only have a couple hours left before homework is gone.
last day of school is tomorrow....
please answer quickly..
It only has one x intercept
Step-by-step explanation: when you graph it there is only one point where the line meets the x intercept
ILL BRAINLIEST YOU IF YOU HELP ME PLEASE
Answer:
B
Step-by-step explanation:
They are alternate interior angles so that means they are equal
4x - 30 = 2x
2x = 30
x = 15
20 POINTS
The function f(x)=45x represents the number of jumping jacks j(x) you can do in x minutes. How many jumpibg jacks can you do in 10 minutes
Answer:
450 jumping jacks
Step-by-step explanation:
f(10) = 45 (10)
45 * 10 is just 450 :)
Answer:
450.
Step-by-step explanation:
f(10) = 45 * 10 = 450 jumping jacks.
The manufacturer id number for proctor and gamble is (037000) and the item number for a box of bounce fabric softener is (80049). What is the valid upc? A- 0-37000-80049-9 B-0-37000-80049-1 C-1-37000-80049-1 D-1-80049-37000-0
Answer:
A. [tex]UPC = 0-03700-80049-9[/tex]
Step-by-step explanation:
Given
[tex]ID = 037000[/tex]
[tex]Item\ Number = 80049[/tex]
Required
The valid UPC
First, the UPC is represented as:
UPC = ID followed by item number followed by the checksum
So, we have:
[tex]upc = 0-03700-80049-X[/tex]
To calculate X (the checksum)
Add up digits at odd positions
[tex]Odd = (0 + 7 + 0) + (8 + 0 + 9)[/tex]
[tex]Odd = 24\\[/tex]
Multiply by 3
[tex]Product = Odd * 3[/tex]
[tex]Product = 24 * 3[/tex]
[tex]Product = 72[/tex]
Add up digits at even positions
[tex]Even = (3 + 0 + 0) + (0 + 4)[/tex]
[tex]Even = 7[/tex]
Add the product and the sum of even
[tex]Result = Product + Even[/tex]
[tex]Result = 72+7[/tex]
[tex]Result = 79\\[/tex]
The last digit of the UPC is 9.
Hence, the UPC is:
[tex]UPC = 0-03700-80049-9[/tex]
Factor this polynomial expression. 2X2 + 12x + 18
A. 2(x+3)(x+3)
B. 2(x - 3)(x-3)
c. 2(x+3)(x - 3)
D. (2x + 9)(x+2)
[tex]\longrightarrow{\green{A.\:2 \: ( x + 3)(x + 3) }}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
[tex]2 {x}^{2} + 12x + 18[/tex]
Taking 2 as common factor, we have
[tex] = 2 \: ( {x}^{2} + 6x + 9) \\ = 2 \: ( {x}^{2} + 3x + 3x + 9)[/tex]
Next, we take [tex]x[/tex] as common from first two terms and 3 from last two terms,
[tex] = 2 \: [x(x + 3) + 3(x + 3)][/tex]
Taking the factor [tex](x+3)[/tex] as common,
[tex] = 2 \: ( x + 3)(x + 3)[/tex]
[tex]\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35}}}}}[/tex]
Alex’s paycheck for the last two weeks totaled $239.64. He owes the cell phone company $44.87. How much money does he have left
Answer:
the answer would be 193.77
Step-by-step explanation:
literally, subtract 45.87 from 239.64.
you get 193.77.
(you put 44 instead of 45, so the sum with 44 would be 194, that is incorrect.)
Simplify √49 + [√81 - x(9x = 14)]
[tex]\longrightarrow{\green{- 9 {x}^{2} + 14x + 16}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
[tex] \sqrt{49} + [ \sqrt{81} - x \: (9x - 14) ] \\ \\ = \sqrt{7 \times 7} + [ \sqrt{9 \times 9} - 9 {x}^{2} + 14x] \\ \\ = \sqrt{( {7})^{2} } + [ \sqrt{ ({9})^{2} } - 9 {x}^{2} + 14x ] \\ \\ (∵ \sqrt{ ({x})^{2} } = x ) \\ \\ = 7 + (9 - 9 {x}^{2} + 14x) \\ \\ = 7 + 9 - 9 {x}^{2} + 14x \\ \\ = - 9 {x}^{2} + 14x + 16[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{♡}}}}}[/tex]
Please HELP WITH THIS !!!
The private school enrolled 1050 new students last year and the number of students enrolled this year decreased to 798.What was the percentage decrease in the number of students enrolled?
Answer:
Step-by-step explanation:
Decreased students = 1050 - 798 = 252
Decreased percentage = (decreased students ÷ number of last year students) * 100
= [tex]\frac{252}{1050}*100[/tex]
= 24%
Answer:
24%
Step-by-step explanation:
% change = [tex]\frac{difference}{original amount}[/tex] x 100
; 1050 - 798 = 252
% change = [tex]\frac{252}{1050}[/tex] x 100
% change = 0.24 x 100
% change = 24
the percentage decrease in the number of students enrolled is 24%
I need help please and thank you!!
Answer:
Option 4
Step-by-step explanation:
2x² + 32 = 0
2x² = -32
x² = -16
sqrt(-16) got no real solution. (no real number multiplied by itself will be negative)
a regular polygon has a perimeter of 40 cm and a apothem of 6 cm. find the polygons area
Answer:
a = 120 cm²
Step-by-step explanation:
n = number of sides
edge length
40/n
divide the polygon into n congruent triangles
a = (1/2)(edge * apothem) * number of triangles
a = (1/2)(40/n)(6) * n
n cancels out
a = (1/2)(40)(6)
a = 120 cm²
