Using the slope concept, it is found that the angle between the ladder and the floor will be of 33.69º.
What is a slope?The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.
In this problem, we have that:
The angle is of 45º.The vertical distance is the height of h.The horizontal distance is of 3m.Hence:
tan(45º) = h/3.
1 = h/3.
h = 3 m.
If the ladder slides 1 m down, the height will be of 2m, hence the angle will be given as follows:
[tex]\tan{\theta} = \frac{2}{3}[/tex]
[tex]\theta = \arctan{\left(\frac{2}{3}\right)}[/tex]
[tex]\theta = 33.69^\circ[/tex]
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sally sweeps 20 floors in 4 hours , at the same rate , how many floors can sally sweep in 6 hours ?
Answer:
35 Floors in 6 Hours
Step-by-step explanation:
20 / 4 = X Floors Per Hour
floors per hour = 5
6*5 = 35 Floors
If 343* = 494-x, what is the value of x?
5/8
8/5
2
8
Answer: [tex]\frac{8}{5}[/tex]
Step-by-step explanation:
343 is equal to 7 to the power of 3.
49 is equal to 7 to the power of 2.
You can then make the equation:
[tex](7^{3})^x = (7^2)^{4-x}[/tex]
The powers law means if something is to the power of something, it is multiplied.
So, we can remove the 7 and make the equation:
3x = 2(4-x)
3x = 8 - 2x
5x = 8
x = [tex]\frac{8}{5}[/tex]
You can verify this by plugging it in,
[tex]343^{8/5} = 11388.6066[/tex]
[tex]49^{4-(8/5)} = 11388.6066[/tex]
Which expression is equivalent to
i need help asap
The probabilities that Sani, Kolo and Tato will hit a target are 3/4, 2/3 and 7/3 respectively If all three men shot once what is the probability that target will be hit only once
Step-by-step explanation:
get the lcm of the numerals and the denominators then simplify
hope it is correct
The graph represents a function.
2
Which ordered pair can be plotted together with these four points, so that the resulting graph still represents a function?
O (2, -1) O (-5,2) O (2,-5) (-2,5)
(-5, 2) is the only point which we plot in given graph then it still represent a function.
What is Function?A function is a special type of relation in which each and every element of set A have a unique image in its codomain set B.
Here, Given points on graph
{(-4, 2), (-2, -3), (2, 3), (3, -1)}
2 and -2 are already available in given ordered pair.
so only (-5, 2) is the only option which satisfies the definition of function.
Thus, (-5, 2) is the only point which we plot in given graph then it still represent a function.
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The standard form of an absolute value function is f(x)= alx-h+k. Which of the following represents the vertex?
O (-k,h)
O (-h,k)
O (k,h)
O (h,k)
Answer:
vertex = (h, k )
Step-by-step explanation:
the standard form of an absolute value function is
f(x) = a | x - h | + k
where (h, k ) are the coordinates of the vertex
How many dogs were in the sample?
each number under the leaves section would be a dog
answer: 11
Answer:
11
Step-by-step explanation:
I think of a number and divide it by 3. The result is 2 less than the number I first thought of. Find the number I first thought of.
Answer:
Let the number be x
so, x/4 = x-3
x = 4(x-3)
x= 4x-12
x-4x = -12
-3x = -12
x= 12/3
x = 4
Step-by-step explanation:
Hope this helps! (:
Please mark me Brainliest!can u give the direct answer of 1 and 2
[tex] {a}^{3} . \\ \\ {a}^{5}. \\ \\ {a}^{9} . \\ \\ {a}^{m + n}. \\ \\ {x}^{1} = x.\\ \\ {x}^{3}. \\ \\ {x}^{3}. \\ \\ {x}^{m - n} . \\ \\ {y}^{6} . \\ \\ {y}^{12} . \\ \\ {y}^{18} . \\ \\ {y}^{ab}. \\ \\ 1. \\ \\ 1. \\ \\ {px}^{1} = px.[/tex]
••••••••••••••••••••••••••••••••••••••[tex]343 .\\ \\ 16 .\\ \\ 3125 .\\ \\ \frac{ - 8}{27} .[/tex]
PLEASE PLEASE HELP WILL MARK BRAINLIEST!!
Which choice is equivalent to the product below when x > 0?
A. x/9
B. 1/3
C. x/3
D. 1/9
The equivalent expression to given expression is 1/3.
What is Equivalent Expression?Equivalent expressions are defined as algebraic expressions which give the same resulting expression. An algebraic expression (or) a variable expression is defined as a combination of terms by the operations such as addition, subtraction, multiplication, division.
Here, given expression
[tex]\sqrt{2/x^2} X \sqrt{x^2/18}[/tex]
= [tex]\sqrt{2 X x^2/18x^2}[/tex]
= [tex]\sqrt{1/9}[/tex]
= 1/3
Thus, the equivalent expression to given expression is 1/3.
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helpppppppppppppppppppppppppppppppppppppppp
Answer:
70
Step-by-step explanation:
Valeria doesnt want any lollipops left over, but identical, so that means you have to add. You can divide the two colors otherwise you get a decimal, which you cant break a lollipop into, or an indefinite letter, a lollipop cant fit in that as well. The only sensible thing is to add them.
can anybody help me?
f(-2) = 2(-2)² - 8(-2) + 6 = 30
f(-1) = 2(-1)² - 8(-1) + 6 = 16
f(0) = 2(0)² - 8(0) + 6 = 6
f(1) = 2(1)² - 8(1) + 6 = 0
f(2) = 2(2)² - 8(2) + 6 = -2
The value of a car decreases as shown in the table below.
A 2-column table with 6 rows. The first column is labeled years after purchase with entries 0, 1, 2, 3, 4, 5. The second column is labeled value (dollar sign) with entries 25,000; 18,000; 14,000; 10,500; 8,000; 6,000.
Which statements are true? Check all that apply.
The statements which are true from the given table are:
The function that best represents the data is f(x) = 24,512(0.755)x.
The function decreases indefinitely.
It is reasonable to interpolate the value of the car at 4.5 years.
What is Depreciation?Depreciation refers to the accounting method where the value of a tangible asset reduces over a period of time.
The value of the car is shown with the purchase with entries that shows its value over time,
The function that best represents the data is f(x) = 24,512(0.755)x and that this function decreases indefinitely.
The statements which are true from the given table are:
The function that best represents the data is f(x) = 24,512(0.755)x.
The function decreases indefinitely.
It is reasonable to interpolate the value of the car at 4.5 years.
The complete question is
"The value of a car decreases as shown in the table below.
A 2-column table with 6 rows.
The first column is labeled years after purchase with entries 0, 1, 2, 3, 4, 5.
The second column is labeled value (dollar sign) with entries 25,000; 18,000; 14,000; 10,500; 8,000; 6,000.
Which statements are true? Check all that apply.
The function that best represents the data is f(x) = 24,512(0.755)x.
The function that best represents the data is f(x) = 554x2 – 5,439x + 24,600.
The function decreases indefinitely.
It is reasonable to interpolate to the value of the car at 4.5 years.
It is reasonable to extrapolate to 40 years"
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Use 8a+16c.
What is the value of the expression when a = –5 and c = –1? Enter your answer in the box.
Is (x + 7) a factor of f(x) = x³ - 3x² + 2x - 8?
Answer:
x=-7
0=(-7)³-3(-7)²+2(-7)-8
=-343-147-14-8
0≠-512
x+7 isn't a factor
Please Help! What is the value of x?
Answer:
4.1968
Explanation:
Given that:
angle: 25°
opposite: x
adjacent: 9
So, use the tan rule:
opposite/adjacent = tan(x)
x/9 = tan(25)
x = 9tan(25)
x = 4.1968
Option A
What subjects together do more than half of the class like?
Math 9 people
Science 3 people
Art 5 people
Writing 3 people
History 1 person
Math and Writing
Science and History
Art and Science
History and Math
Answer:
Math and Writing
Step-by-step explanation:
Well if we add up all the people we get (9 + 3 + 5 + 3 + 1) = 21. Half of that is 10.5 so the sum of the two subjects must be at least 11. The amount of people that like Math and Writing is 11 people so the two subjects that more than half the class like are Math and Writing.
Answer:
Math and Writing
Step-by-step explanation:
Number of students who like each subject:
Math = 9Science = 3Art = 5Writing = 3History = 1Total number of students = 9 + 3 + 5 + 3 + 1 = 21
Half of 21 = 21 ÷ 2 = 10.5
Therefore, more than half the class would be > 10.5 students
Total number of students who like:
Math and Writing = 9 + 3 = 12Science and History = 3 + 1 = 4Art and Science = 5 + 3 = 8History and Math = 1 + 9 = 10Therefore, the only combination of subjects that more than 10.5 students like is Math and Writing as 12 > 10.5
The function h(x) is given below.
h(x) = {(3, –5), (5, –7), (6, –9), (10, –12), (12, –16)}
Which of the following gives h–1(x)?
{(3, 5), (5, 7), (6, 9), (10, 12), (12, 16)}
{(–5, 3), (–7, 5), (–9, 6), (–12, 10), (–16, 12)}
{(3, –5), (5, –7), (6, –9), (10, –12), (12, –16)}
{(5, 3), (7, 5), (9, 6), (12, 10), (16, 12)}
The inverse function will be h⁻¹(x) = {(–5, 3), (–7, 5), (–9, 6), (–12, 10), (–16, 12)}. Then the correct option is B.
What is inverse of a function?Suppose that the given function is
f:X → Y
Then the inverse of the considered function will be
f⁻¹: Y → X
The function h(x) is given below.
h(x) = {(3, –5), (5, –7), (6, –9), (10, –12), (12, –16)}
Then the coordinate of the inverse function gets swapped.
h⁻¹(x) = {(–5, 3), (–7, 5), (–9, 6), (–12, 10), (–16, 12)}
Then the correct option is B.
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36 students for 3 teachers =
1.0
5
12 students for 1 teacher.
Answer:
12
Step-by-step explanation:
36 divided by 3 =12 for 1 teacher
please help me
I'll mark you brainlist
Answer:
There are 16 notes of 20 paise's and 12 notes of 5 paise's.
Explanation:
The amount of notes for of 20 paise and 5 paise coins are not given.
So let there be x 20 paise's coins and y 5 paise's coins.
Equation buildup:
20x + 5y = 380 ___eq 1
20y + 5x = 380 - 60
20y + 5x= 320 ___ eq 2
Make x the subject for both:
1st
[tex]\rightarrow \sf 20x + 5y = 380[/tex]
[tex]\rightarrow \sf 20x = 380-5y[/tex]
[tex]\rightarrow \sf x = 19-0.25y[/tex]
2nd
[tex]\sf \rightarrow 20y + 5x = 320[/tex]
[tex]\sf \rightarrow 5x = 320-20y[/tex]
[tex]\sf \rightarrow x= 64-4y[/tex]
Solve them simultaneously:
[tex]\sf \rightarrow 64-4y =19 - 0.25y[/tex]
[tex]\sf \rightarrow -4y+0.25y =19 -64[/tex]
[tex]\sf \rightarrow -3.75y =-45[/tex]
[tex]\sf \rightarrow y =12[/tex]
Find x:
[tex]\sf \rightarrow x = 64-4y[/tex]
[tex]\sf \rightarrow x = 64-4(12)[/tex]
[tex]\sf \rightarrow x = 16[/tex]
In a word processing document or on a separate piece of paper, use the guide to construct a two column proof proving that triangle RST is congruent to triangle RSQ given that RS ⊥ ST, RS ⊥ SQ, and ∠STR ≅ ∠SQR.
1) [tex]\overline{RS} \perp \overline{ST}, \overline{RS} \perp \overline{SQ}, \angle STR \cong \angle SQR[/tex] (given)
2) [tex]\overline{RS} \cong \overline{RS}[/tex] (reflexive property)
3) [tex]\angle RST[/tex] and [tex]\angle RSQ[/tex] are right angles (perpendicular lines form right angles)
4) [tex]\triangle RST \cong \triangle RSQ[/tex] (AAS)
what is the cos? trigonometry
Answer:
Cos, a abreviation of cosine is used in trigonometry, and it represents the ratio of the hyptenuse and the adjacent side of a right triangle (a triangle with a right/90 degree angle). The formula for evaluating cosine/cos is the length of the adjacent side of the triangle divided by length of the hypotenuse of the triangle. To be clear, the hypotenuse is the side of the triangle the 90 degrees is facing, and the adjacent side is the side across the hypotenuse.
Step-by-step explanation:
Answer:
A trigonometric function that for an acute angle is the ratio between the leg adjacent to the angle when it is considered part of a right triangle and the hypotenuse.
What is cos law?
The cos law or cosine law defines the relationship between the sides and the angles of the triangle. This law is also known as the law of cosine or cosine rule. According to this law,
c2 = a2 + b2 − 2ab cos α
Where a, b and c are the sides of the triangle.
Calcular la altura, h de un arbol sabiendo que, si nos situamos 8 metros de la base del tronco, vemos la parte superior de su copa en un angulo de 36.87*
Utilizando trigonometría, veremos que la altura del arbol es 6m.
¿Como obtener la altura del arbol?
Podemos visualizar la situación como un triangulo rectangulo.
La altura del arbol será el cateto opuesto al angulo de 36.87°.
La distancia a la base del tronco, que es 8 metros, será el cateto adjacente a dicho angulo.
Entonces, podemos usar la relacion:
tan(θ) = (cateto opuesto)/(cateto adjacente).
Reemplazando lo que conocemos, y definiendo:
altura = cateto opuesto = H.
tendremos:
tan(36.87°) = H/8m
Resolviendo para H:
H = tan(36.87°)*8m = 6m
Así, concluimos que la altura del arbol es 6m.
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Will a stand that can hold up to 40 pounds support a21-kilograms television? Explain. Use 2.2 lb=1kg.
Answer: No
Step-by-step explanation:
Weight limit = 40 Lb
Weight given = 21 kg
Conversion factor
2.2 Lb = 1 kg
2.2 x 21 = 46.2
46.2 Lb = 21 kg
46.2 > 40, the stand cannot support the TV
TV > stand
Picture shown PLEASE HELP
Answer:
m= –4
So, you only need to of the points to find the slope, why not choosing the first two:
[tex]m = \frac{y2 - y1}{x2 - x1} = = = > \\ m = \frac{12 - 8}{ - 3 - ( - 2)} = = = > \\ m = \frac{4}{ - 1} = - 4[/tex]
so basically, this is the slope your looking for
4sin2xcosx+sin3x=sin<3,14+x>
The solution to 4sin2xcosx+sin3x=sin<3,14+x> is x = nπ, where n = ±{0, 0.5, 1, 1.5....}
How to solve the equation?The equation is given as:
4sin2xcosx+sin3x=sin<3,14+x>
Rewrite properly as:
4sin(2x)cos(x)+sin(3x)=sin(3.14+x)
Next, we split the equation as follows:
y = 4sin(2x)cos(x)+sin(3x)
y = sin(3.14+x)
Next, we plot the graph of both equations (see attachment)
From the attached graph, we have:
x = nπ, where n = ±{0, 0.5, 1, 1.5....}
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help please!!!!!!!!!
Find the value of x. Round the length to the nearest tenth.
Answer:
5.1 yd
Step-by-step explanation:
tan(25°) = x/11
x = 11tan(25°)=5.1 yd
Pls help ill give brainiest
I am lazy to type so here look at the picture and there is your answer
A rotation R takes A(1,-3) to A'(3,5) and B(0,0) to B'(4,-6). find the centre of rotation?
The center of rotation will be (0,4). The points are plotted and the center is found with the help of a graph.
What exactly is a circle?It is a point locus drawn equidistant from the center. The radius of the circle is the distance from the center to the circumference.
Given points;
A(1,-3)
A'(3,5)
B(0,0)
B'(4,-6)
C is the center point of rotation.
The given points are plotted on the graph and obtained as the center of rotation will be (0,4).
Hence the center of rotation will be (0,4).
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