The special right triangle is the right triangle that have acute angle values
that simplify the process of finding its dimensions.
The correct values are;
1. The angle the ladder makes with the ground, is approximately 66.93°
2. The length of YZ is approximately 19.18 ft.
3. CB = 7 ft. and AB = 7·√3 ft.
Reasons:
1. The length of the ladder = 15 ft.
Height of the ladder above the ground, h = 13.8 ft.
Required:
The angle the ladder makes with the ground.
Solution:
The angle the ladder makes with the ground is given by the equation;
[tex]sin(\theta) = \dfrac{Length \ of \ the \ ladder}{Height\ of \ the \ ladder \ above the \ ground} = \dfrac{13.8}{15} = 0.92[/tex]
[tex]\theta = arcsin\left(0.92 \right) \approx 66.93^{\circ}[/tex]
2. The given parameters are;
XY = 11
∠Z = 35°
YZ = Required
In a right triangle, the side facing the acute angle is a leg of the triangle.
Therefore;
XY is the opposite side to ∠Z
[tex]sin(\angle Z) = \dfrac{XY}{YZ}[/tex]
Which gives;
[tex]sin(35^{\circ}) = \dfrac{11}{YZ}[/tex]
[tex]YZ= \dfrac{11}{sin(35^{\circ}) } \approx 19.18[/tex]
YZ ≈ 19.18 ft.
3. AC = 14 ft.
∠A = 30
Required:
The length of the other two sides
Solution:
Where by AC is the hypotenuse side, we have;
CB = AC × sin(∠A)
Therefore;
CB = 14 × sin(30°) = 7
CB = 7 ft.
AB = AC × cos(∠A) = 14 × cos(30°) = 7·√3
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1. The angle the ladder makes with the ground, is approximately 66.93°
2. The length of YZ is approximately 19.18 ft.
3. CB = 7 ft. and AB = 7·√3 ft.
Will give brainly if correct
Complete the recursive formula of the arithmetic sequence 8, -5, -18, -31,..
d(1)=
d(n)=d(n-1)+
Answer:
d(1) = 8
d(n) = d(n-1) + (-13)
Explain how to find the greatest number of identical arrangements that can be made with 54 roses and 42 tulips with no flowers left over.
Answer:
GCF(54, 42) = 6 arrangements
Step-by-step explanation:
The number of such arrangements will be the greatest common factor (GCF) of the two numbers. You recall from your times tables that ...
54 = 6×9
42 = 6×7
The factors 9 and 7 have no factors in common, so 6 is the greatest common factor of 54 and 42.
6 identical arrangements of 9 roses and 7 tulips can be made.
_____
Additional comment
When the numbers are small and found in your memorized times tables, finding the GCF is done by consulting your memory. Otherwise, it can be done by factoring, or by using Euclid's algorithm.
When the numbers are factored to primes, the GCF is the product of the prime factors the numbers have in common.
54 = 2×3×3×3
42 = 2×3×7
These factorizations have 2×3 = 6 in common.
__
Euclid's algorithm has you find the remainder from the division of the larger number by the smaller. When that remainder is not zero, it replaces the larger number, and the process repeats. When that remainder is zero, the divisor is the GCF.
54/42 = 1 r 12
42/12 = 3 r 6
12/6 = 2 r 0 . . . . GCF = 6
This algorithm works on numbers of any size (including fractions and mixed numbers), so is especially useful when the factorization is not obvious.
A small bowl of candy holds 75% as much as a large bowl of candy.
If the small holds 36 candy bars how much does the large hold?
Answer:
_____
Step-by-step explanation:
Im pretty sure it would be 45 ____
Figure A
Figure B
Which of the triangles in the two figures above is a right triangle? Explain your choice using
the Pythagorean Theorem to prove it. Note: the figures are not drawn to seale.
Figure B
Step-by-step explanation:The Pythagorean Theorem is [tex]a^2 + b^2 = c^2[/tex], where c is the longest side of the triangle (the hypotenuse).
To find the side length of each square, you have to square root the area of each square. This means that Figure A has side lengths of 3, 6 and 8 units. Figure B has side lengths of 5, 12 and 13 units.
In Figure A, if the triangle is right-angled, the equation [tex]3^2 + 6^2 = 8^2[/tex] must be correct. 9 + 36 = 45. 45 is not equal to 64, so the triangle is not right-angled.
In Figure B, if the triangle is right-angled, the equation [tex]5^2 + 12 ^2 = 13^2[/tex] must be correct. 25 + 144 = 169. 169 is 13 squared, so the triangle is right-angled.
Alternatively, as you are already given the square values for each side length, there is no need to square root and square again. You can just test if the two smaller areas equal the larger area, but the explanation above uses a more detailed example of the Pythagorean Theorem.
How many decimals in multiplication.
Answer:
In multiplication of a decimal by a decimal number we will learn how to find the product of a decimal by another decimal.
To multiply a decimal number by a decimal number, we first multiply the two numbers ignoring the decimal points and then place the decimal point in the product in such a way that decimal places in the product is equal to the sum of the decimal places in the given numbers.
The amount of sales of single scoop ice-cream cones during the summer s(c0 varies directly with the number of customers c. Ten customers bought a total of $44 worth of ice-cream cones. Which equation can be used to find the ice-cream sales for c customers?
Answer:
s(c)= 4.4c
Step-by-step explanation:
Please someone answer these for me this is confusing this is a major try to find the domain range and end behavior for all of these
Answer:?? I don't understand that sorry, I'm unhelpful
Step-by-step explanation:
help asap pleaseeeee
Answer:
Its the last one!
Step-by-step explanation:
Remember
closed circle is less than or equal to and greater than or equal to
open circles are the less than and greater than!
and because it is the
less than or equal to because its going up.(left)
Please help me with this
Answer:
make me brainliest
Step-by-step explanation:
1: x ≤ 18/5
2: x > 4
3: x ≤ 4
4: x < 12
5: x > 1/4
6: x ≤ 2
7: x ≤ 5
8: x > 10
9: x < 5/2
10:7/3x^2 + 4/3x + 12
11: 2 < x < 15
12:25/2 < x ≤ 45/2
Last summers, students who worked earned an average of $80 a week with a standard deviation of $12. What percentage of students earned more that $104 per week?
Answer:
2.28%Step-by-step explanation:
Given:
μ = 80σ = 12x = 104Find z-score:
z = (x - μ)/σz = (104 - 80)/12 = 2Percent value corresponding to 2 as per z-table is 0.9772. This is corresponding to 97.72%.
Percentage of students earned more than $104:
100 - 97.72 = 2.28Un pilón de riego está lleno en sus cuatro séptimas partes y contiene 1 600 m3 de agua. ¿Cuántos metros cúbicos caben en el pilón?
Veremos que el volumen total que cabe en el pilón es 2,800 m^3
Sabemos que el pilón tiene una capacidad máxima V.
Tambíen sabemos que de momento, el pilón tiene 1,600 m^3 de agua, y esto es equivalente a 4/7 de la capacidad máxima.
Entonces podemos plantear:
(4/7)*V = 1,600m^3
Podemos resolver esta ecuación para V si multiplicamos ambos lados por (7/4), así obtenemos:
V = (7/4)*1,600m^3 = 2,800 m^3
Es decir, el volumen total que cabe en el pilon es 2,800m^3
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In health class, Baldwin is learning about making healthy food choices. For a lesson on
digestive health, his teacher asks everyone to track how much fiber they eat daily. At
breakfast, Baldwin has a banana. He also has raisin bran cereal, which contains 3.7 grams of
fiber. In all, Baldwin eats 6.8 grams of fiber at breakfast.
Use an equation to find the amount of fiber in the banana.
Answer:
There are 3.1 fibers in rhe banana
Step-by-step explanation:
6.8-3.7=3.1
3
Assume that a randomly selected subject is given a one density test those test scores are normally distributed with a mean of 0 and a standard deviation of 1
Answer:
See Image below for answer:)
Step-by-step explanation:
65 - 2x ≥ 150, whats the answer!!!
Answer:
x <= -42.5
Step-by-step explanation:
65 - 2x >= 150
-2x >= 150 - 65
-2x >= 85
2x <= -85
x <= -85/2
x <= -42.5
A graph representing a proportional relationship goes through the origin:
Question 2 options:
Always
Sometimes
Never
When it feels like it
The graph representing a proportional relationship ALWAYS goes through the origin (0, 0).
Recall:
A proportional relationship graph represents a relation between two variables that are directly proportional to each other.In a proportional graph, the constant of proportionality, k, remains the same.The graph attached below shows a proportional graph between time and water used.In the proportional relationship graph, the line goes through the origin (0, 0) as shown in the image attached below.
Therefore, the graph representing a proportional relationship ALWAYS goes through the origin (0, 0).Learn more about proportional relationship on:
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6×6√3 what is the area
Answer:
For which shape ?! You need to know the rule.
We can repeat the derivative operation: the second derivative $f''$ is the derivative of $f'$, the third derivative $f'''$ is the derivative of $f''$, and so on. Find a function $f$ such that $f'$ and $f''$ are not the function 0, but $f'''$ is the constant function 0.
Answer:
f(x) = x^2
Step-by-step explanation:
Any quadratic (2nd-degree) function will have 0 as its third derivative.
f(x) = ax² +bx +c
f'(x) = 2ax +b
f''(x) = 2a
f'''(x) = 0
Perhaps the simplest such function is f(x) = x^2.
can someone please help me solve this!
Answer:
B
Step-by-step explanation:
[tex]4x^{2}-11x-3=0\\4x^{2}-12x+x-3=0\\4x(x-3) + (x-3) = 0\\(4x+1)(x-3)=0[/tex]
B is factorable through this method
Ada is making fresh orange juice for her family. She discovers that for every 3 oranges she squeezes, she gets 5 ounces of juice. Select all the ratios that have the same constant of proportionality as Ada's observation.
The ratios that have the same constant of proportionality as Ada's observation 15/9, 30/18
According to the question:
We are required to select all the ratios that have the same constant of proportionality as Ada's observation.let y and x represent amount of juice and oranges respectively;
y = juices squeezed outx = Oranges squeezed iny = k × x5 = k × 35 = 3kk = 5/3
The ratios equivalent to the constant of proportionality is 15/9, 30/18
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Answer:
Step-by-step explanation:
9:15 15:25 6:10
5) You roll a fair six-sided die twice. The
first roll shows a one and the second roll
shows a three.independent or dependent?
Answer:
Happy Chrismas My friend.
What is the value of the expression x² + y² given x = 10 and y = 2?
A. 104
B. -98
C. 89
D. -89
Answer:
A. 104Step-by-step explanation:
Find a job that uses trigonometry. Include an image depicting the job and a description of how the trigonometric concepts learned in this module are used in the job.
Engineering
In engineering you need to determine the structure of shapes, buildings.The distance from base to building top total length of carpets,the settings of CCTV cameras for perfect view you need trigonometric functions like sin ,cos,tan etcThe points (−4, −3) and (3, y) lie on the same line.
If the slope of the line is 2, what is the value of y?
PLEASE I HELP!!!!!!
Answer:
y= 11
Step-by-step explanation:
[tex]\boxed{slope = \frac{y _{1} - y_2 }{x_1 - x_2} }[/tex]
Substituting the coordinates and value of slope:
[tex] \frac{y - ( - 3)}{3 - ( - 4)} = 2[/tex]
[tex] \frac{y + 3}{3 + 4} = 2[/tex]
[tex] \frac{y + 3}{7} = 2[/tex]
Multiply both sides by 7:
y +3= 2(7)
y +3= 14
Subtract 3 from both sides:
y= 14 -3
y= 11
330,000,000,000,000,000,000,000 mass using a one-digit whole number times a power of 10.
Answer:
Step-by-step explanation:
330,000,000,000,000,000,000,000 has 22 zeros, so we can immediately say
33x10^22
This should be expressed using just a single decimal point, so we can move the decimal point two more spaces to the left, and add 2 to the exponent:
3.33x10^23
The question states a one digit whole number, so make it 3x10^23, although it seems an insult to the 0.33. Go with the one you prefer.
Determine if the table represents a linear function, quadratic function, or exponential function.
Answer:
Quadratic
Step-by-step explanation:
Formula: ax^2+bx+c
PLEASE HELP THIS IS DUE IN THIRTY MINUTES
I FINNA GIVE YOU 30 POINTS, THAS A SCORE
You have $4800 to spend on fencing to enclose a rectangular area. You also want to make TWO pens as shown below. The cost of the vertical sides is $2.00 per foot and the horizontal sides cost $5.00 per foot. You desire to enclose the largest possible area you can.
a) Given x is the dimension of one side of the rectangle, enter an expression for the other dimension of the rectangle. Your answer should have an "x" in it. Also select appropriate units.
b) Find an expression for the area of the rectangle only in terms of x. Check the appropriate units.
c) What are the dimensions of the rectangle with the largest enclosed area? Enter your dimensions as a list of numbers separated by a comma. Start with the value of side labeled x FIRST.
d) What is the largest area you can enclose in a rectangle using feet of fencing?
Answer:
D
Step-by-step explanation:
pls give ans for the following image
Answer:
7 [tex]\frac{1}{8}[/tex]
Step-by-step explanation:
The reciprocal of a number n is [tex]\frac{1}{n}[/tex]
The reciprocal of 8 is [tex]\frac{1}{8}[/tex]
The reciprocal of [tex]\frac{1}{7}[/tex] is [tex]\frac{1}{\frac{1}{7} }[/tex] = 7
sum = 7 + [tex]\frac{1}{8}[/tex] = 7 [tex]\frac{1}{8}[/tex]
Simplify the function f (x) = one-half (27) Superscript StartFraction 2x Over 3 EndFraction. Then determine the key aspects of the function.
The initial value is
.
The simplified base is
.
The domain is
.
The range is
.
Answer:
1/2.....9......all real numbers......y > 0
Step-by-step explanation:
got this right on edge 2021. hope this helps
Answer:
The initial value is
✔ 1/2
.
The simplified base is
✔ 9
.
The domain is
✔ all real numbers
.
The range is
✔ y > 0
.
Step-by-step explanation:
Hello can someone pls help me with this
Answer:
simple y=5x
Step-by-step explanation:
This is because y and x are the same because anything times 0 is 0 and when x becomes 1, 1*5=5 and that continues the chain
