Answer:
28.9 m
Step-by-step explanation:
First, we can draw a picture. The statue is on the right, with the top of the statue representing the top right corner of the triangle. The angle of elevation to the sun is 78 degrees, so the angle between the shadow and the top of the statue must be 78 degrees as well. Assuming there is no angle of elevation between the shadow and the statue, we can say that the shadow and statue form a 90 degree angle because the shadow is perfectly horizontal and the statue is perfectly vertical.
We are trying to find the hypotenuse of the triangle, or the length from the top of the statue to the end of the shadow. To do this, we can utilize the fact that
cos(x) = adjacent / hypotenuse
cos(78°) = 6 / hypotenuse
divide both sides by cos(78°) and multiply both sides by hypotenuse to solve for the hypotenuse
hypotenuse = 6/cos(78°) ≈ 28.9 m
PLEASE HELP ME
Solve 2x^2-x>15
Show your work
Answer:
x < -5/2 or 3 < x
Step-by-step explanation:
Subtracting 15 puts the relation into a more standard form:
2x^2 -x -15 > 0
(2x +5)(x -3) > 0 . . . . . factor
The zeros of these factors are x = -5/2 and x = 3.
For values of x between those values (-5/2 ≤ x ≤ 3), the product of these factors will be negative or zero. In order for the product to be positive, x must not be in that range.
The solution is ...
x < -5/2 or 3 < x
_____
Additional comment
Several methods are taught for factoring a quadratic expression. One of my favorite is using a graphing calculator to find the zeros. If p is a zero, then (x-p) is a factor.
Another way to approach the factoring of ax^2 +bx +c is to find factor pairs of the product (ac) that have a total of b. Here, that means finding factors of 2(-15) = -30 that have a sum of -1. Consider ...
-30 = (1)(-30) = 2(-15) = 3(-10) = 5(-6)
The sums of these pairs are -29, -13, -7, -1. With the values 5 and -6, you can rewrite the quadratic expression as 2x^2 +5x -6x -15. This can be factored by grouping pairs of terms:
x(2x +5) -3(2x +5)
(2x +5)(x -3) . . . . . . . the factorization we show above.
__
You can see on the graph that the quadratic is greater than 0 when x < -2.5 or x > 3.
If 60% of a KNOWN NUMBER is 180, what is the 40% of that UNKNOWN NUMBER?
Step-by-step explanation:
I think you mean you want to find out 40% of a number,, when 60% of it is 180, so I'll answer that:
60% = 180
÷6
10% = 30
x4
40% = 120
(if you want to find 100%, multiply 30 by 10)
Hopefully this helps :)
An account earns 8.4% interest compounded monthly. If 12,000 is invested in the account initially, how much
interest is earned in this account over a 25 year period?
Answer:
$30,2400
Step-by-step explanation:
First, we need to find how much interest he earns in a month
8.4% of $12,000 = $1,008
Next, we multiply the amount of interest per month by the number of months in 25 years
25 years = 300 months
Now we can multiply the two values to get our final answer
1,008 x 300 = $30,2400
benny uses 2/5 grams (G) of toothpaste each time he brushes his teeth. If benny buys 30-g tube, how many times will be able to brush his teeth?
Answer:
75
Step-by-step explanation:
First divide 2/5 to get 0.4. Then divide 30 by 0.4 to get the answer. A simple way to think about it is how many 0.4 grams are in 30 gram tube.
Please help :)
Chloe is an acrobat in a local circus. Her job is to move across a tightrope from point A to point B while blindfolded! She can only move using the distances that you tell her to move in your instructions. Chloe may go past the ladder. However, if she does, make sure she turns around and goes back toward the ladder.
Use the link: Link
Your Task: Work with your partner to find different combinations of the lengths given in parts (a) through (d) below that will allow Chloe to move from point A and end at point B (the end of the tightrope). You may use each length as many times as you like. .
1. For each crossing, look for at least three different ways to get the acrobat across. *Draw a diagram on your paper that shows the solution with the least amount of steps. *For the neither 2 write a number sentence/equation.
Explanation:
We'll let you draw the diagram. Here are some possible equations. We have listed the shortest sequence first.
(a) 24 = (10 + 10 + 4) = (8 + 8 + 8) = (10 + 8 + 4 + 2)
(b) 17 = (10 + 3 + 2 + 2) = (10 + 3 + 3 + 3 - 2) = (3 + 3 + 3 + 3 + 3 + 2)
(c) 15 = (11 + 4) = (6 + 6 + 3) = (4 + 4 + 4 + 3)
(d) 27 = (19 + 8) = (19 + 12 - 4) = (19 + 12 + 4 - 8)
what is the sum of 4 and -5
Answer:
-1
Step-by-step explanation:
its like subtracting 5 and 4
What is the range of the given function?
Answer:
The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain. .The range is the resulting y-values we get after substituting all the possible x-values.
Step-by-step explanation:
What is the largest power of 2 that is a divisor of 13^4 - 11^4?
Answer:
[tex]2^5[/tex]
Step-by-step explanation:
Given:
[tex](13^4 - 11^4)(13^2+11^2)[/tex]
add all together with exponents
=48*290
= Then turn into a smaller exponent
= [tex]2^4 * 3 * 2*145[/tex]
combine like terms
[tex]2^4 *2[/tex]
=[tex]2^5[/tex]
Answer:
5
Step by step explanation :
13^4-11/4=13920
2^5=32
13920÷32=435
Therefore largest power = 5
Please mark me as the brainliest answer
Thank you ☺
can anyone help me pls ??
Answer:
A
Step-by-step explanation:
Volume of a cylinder= πr² *height.height=volume÷πr²height=250÷π(which in this case we are using 3.14)3²height=8.85=AThe exchange rate at the post office is £1 = €1.17. How many euros do I get for £280?
Answer:
327.21 euros.
Step-by-step explanation:
The solution set of inqulity 4>-2x in R is …
[tex]4>-2x\\\\\implies -\dfrac{4}2 <\dfrac{-2x}{-2}\\\\\implies -2<x\\\\\implies x >-2\\\\\text{Interval, }~ (-2, \infty)[/tex]
What is an equivalent expression to 7x - 3y + 8x ?
Answer:
15x-3y
Step-by-step explanation:
Ok, this question might seem hard but its not! theres only 2 varibles here, x and y. In this problem we add the 2 numbers that are x which gives us 15x and then the -3y gets added to the rephrasment.
Jenna has 38 coins. She uses 19 coins to buy a notebook. How many coins does she have left?
Explain how you can solve and check this problem.
Answer: 19 coins
Step-by-step explanation:
38-19=19
To check, take any one of the nubers and replace it with x, and when you solve for x. you'll get that number back. For example:
Let x represent the amount used to buy a notebook
19+x=38
x=38-19
x=19
A plant food company recommends mixing a teaspoon of food with every gallon of water and only adding a
teaspoon when the water level goes above the next whole gallon
Which graph models the number of teaspoons of food depending on the amount of water?
Answer:
The answer is A. Edge 2022. Hope this helps
Step-by-step explanation:
The next closest one would've been C. But they asked for the teaspoons based on the amount of water not over a constant period of time. So A is right.
Answer:
A
Step-by-step explanation:
A plane travels 460 miles per hour. how many miles does the plane travel in feet per second?
Answer:
674.667 feet per second
Plz, Help Me Quickly!!!
What is the equation of a horizontal ellipse with a major axis = 12 and a minor axis = 10?
The equation of the horizontal ellipse is [tex]\frac{x^2}{144}+\frac{y^2}{100}=1[/tex]
Ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant.
The standard form of an ellipse with horizontal major axis is:
[tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1[/tex]
Where a > b
since a = 12, b = 10, hence:
[tex]\frac{x^2}{12^2}+\frac{y^2}{10^2}=1\\\\\frac{x^2}{144}+\frac{y^2}{100}=1[/tex]
The equation of the horizontal ellipse is [tex]\frac{x^2}{144}+\frac{y^2}{100}=1[/tex]
Find out more on ellipse at: https://brainly.com/question/19507943
In two or more complete sentences, describe the transformation(s) that take place on the parent function, f(x) = log(x), to achieve the graph of g(x) = log(-2x-4) + 1.
Using translation concepts, it is found that the parent function was:
Reflected over the x-axis.Horizontally compressed by a factor of 2.Shifted right 4 units.Shifted up 1 unit.The parent function is:
[tex]f(x) = \log{x}[/tex]
The first transformation is:
[tex]\log{x} \rightarrow \log{-x}[/tex]
Which means that it was reflected over the x-axis.Then, [tex]\log{-x} \rightarrow \log{-2x}[/tex], which means that it was horizontally compressed by a factor of 2.
Then, [tex]\log{-2x} \rightarrow \log{-2x - 4}[/tex], which means that it was shifted right 4 units.
Finally, 1 was added to the function, which means that it was shifted up 1 unit.
To learn more about translation concepts, you can take a look at https://brainly.com/question/4521517
which inequality is a true statement select each correct answer
Answer:
A. False
B. True
C. False
D. False
E. True
Hope This Helps!!!
sooooooooooooooooooooooooooooo easy
Answer:
11/12..................
Answer:
J) 11/12
Step-by-step explanation:
While shopping at his local home improvement store, Chen noticed that the directions for an extension ladder state, “This ladder is most stable when used at a 60° angle with the ground.” He wants to buy a ladder to paint a two-story house. How long does his ladder need to be in order to reach the top of the house if the house is 27 feet tall?
The length of the ladder needed to reach the top of the house is 31.2 feet.
Trigonometric ratio is used to show the relationship between the sides and the angles of a right angled triangle.
Let d represent the length of the ladder. Using trigonometric ratio:
[tex]sin(60)=\frac{27}{d} \\\\d=\frac{27}{sin(60)} =31.2\ feet[/tex]
The length of the ladder needed to reach the top of the house is 31.2 feet.
Find out more at: https://brainly.com/question/4326804
Please answer these questions.(please include work/explanation)(1)
Answer:
Hi there!
I will help you answering the questions, if you do not understand what I'm working about, you can ask me on comment section.
Number 1First of all, we need to multiple the separated function.
[tex] \sf2(3x + 4)(x - 1)(x - 3) \\ = \sf(6x + 8)(x - 1)(x - 3) \\ \tt multiple \: the \: first \: equation \\ \tt(6x + 8) \: with \: (x - 1) \\ \sf = (6x \times x + 6x \times - 1 + 8 \times x + 8 \times - 1)(x - 3) \\ = \sf({6x}^{2} + 2x - 8)(x - 3) \\ \tt then \: multiple \: the \: last \: one \\ \tt (6 {x}^{2} + 2x - 8) \: with \: (x - 3) \\ \sf = \boxed{ \bold{ \red{ {6x}^{3} - 16x {}^{2} - 14x + 24}}}[/tex]
So the right answer is A
━━━━━━━━━━━━━━━━━
Number 2the graph has four zeros at :
-4-2/309After that we make them equal with 0, here is the thing:
x = -a is equal with x + a = 0
So we can conclude that :
-4 → x + 4 = 0-2/3 → 3x + 2 = 00 → x = 09 → x - 9 = 0Then we substitute them to a function :
x(x + 4)(3x + 2)(x - 9) = 0
3x⁴ - 13x³ - 118x² - 72x = 0
Then we looking on the option which one is equal with the answer above.
The right answer is B
━━━━━━━━━━━━━━━━━
Hope It Helps!
Which three points are collinear?
according to defination of collinear points :Three or more points are said to be collinear if they all lie on the same straight line.
therefore, A,B,C points are collinear.
Scientists say we should sleep 3/8 of a day.How about many hours is this
Answer:
9 hours
Step-by-step explanation:
Answer:
[tex]\huge\color{skyblue}\boxed{\colorbox{black}{Answer ☘}}[/tex]
number of hours in a day = 24
according to scientists ,
we should sleep number of hours = 3/8
therefore ,
[tex] \frac{3}{8} \: of \: 24 \: hours = \frac{3}{8} \times 24 \\ = > 9 \: hours[/tex]
hope helpful~
If one of you guys wouldn’t mind helping me do this question it would really speed up the process I have like 10 minutes now
Answer:
13. 70(two digits 7 times 10 which is a multiple of 5)
Hope This Helps!!!
The art club in Northwestern middle school is selling candy bars as a fundraiser. each art club member....
Which exponential expression is equivalent to the product shown 2/3×2/3×2/3×2/3×2/3×2/3×2/3?
Answer:
B. (2/3) x (2/3) x (2/3)
C. 8/27
D. 2^3 /3^3
hope this helps
HELPPPPPPP PLSSSSS!!!!!! 100 points
Given: Angle T S R and Angle Q R S are right angles; Angle T Is-congruent-to Angle Q
Prove: Triangle T S R Is-congruent-to Triangle Q R S
Triangles T S R and Q R S share side S R. Angles T S R and S R Q are right angles. Angles S T R and S Q R are congruent.
Step 1: We know that Angle T S R Is-congruent-to Angle Q R S because all right angles are congruent.
Step 2: We know that Angle T Is-congruent-to Angle Q because it is given.
Step 3: We know that Line segment S R is-congruent-to line segment R S because of the reflexive property.
Step 4: Triangle T S R Is-congruent-to Triangle Q R S because
of the ASA congruence theorem.
of the AAS congruence theorem.
of the third angle theorem.
all right triangles are congruent.
Answer:
B.of the AAS congruence theorem.
Step-by-step explanation:
hope this helps!
Erin tried to multiply 70 x 30 by decomposing 70 and 30 into multiples of 10. Her work is below.
A-Step 1
B-Step2
C-Step3
D-Step4
E-Erin did not make a mistakes.
Find the domain and range of the function represented by the graph . What’s the domain an range
Can someone plz help Me?
Answer:
D
Step-by-step explanation:
As the y value doesn't change between the points that means that it would be reflected over the y axis