Answer:
first building: 479.2 ftsecond building: 704.2 ftStep-by-step explanation:
Label the mailbox viewpoint, the top of the first building, and the top of the second building points M, A, and B, respectively.
Consider the triangle MAB. You are told length MA is 600 ft, and length AB is 800 ft. Side AB is opposite the 67° angle at M, so we can use the Law of Sines to find other measures of that triangle. Specifically, we want to know the distance MB.
sin(B)/MA = sin(M)/AB
sin(B) = (MA/AB)sin(M) = 600/800·sin(67°) ≈ 0.690379
B ≈ 43.66°
Then the angle at A is ...
180° -67° -43.66° = 69.34°
and the side MB can be found from ...
MB/sin(A) = AB/sin(M)
MB = (sin(A)/sin(M))AB = sin(69.34°)/sin(67°)·800 ≈ 813.2 . . . feet
__
Now, label points on the ground below A and B as A' and B'. This problem is asking for the heights AA' and BB'. Each of these is opposite the angle of elevation to points A and B, respectively, so can be found using the sine relation:
sin(elevation to A) = AA'/MA
AA' = MA·sin(elevation to A) = 600·sin(53°) ≈ 479.2 . . . ft
Similarly, ...
BB' = MB·sin(elevation to B) = 813.2·sin(60°) ≈ 704.2 . . . feet
The first building is 479.2 ft tall; the second is 704.2 ft tall.
The sum of three consecutive odd numbers is 123 what is the smallest of the three numbers
Answer:
39
Step-by-step explanation:
Let the three consecutive odd numbers be:
x+2, x+4, x+6.
The sum of the consecutive numbers is 123 i.e
x+2 + (x+4) + (x+6) = 123
x + 2 + x + 4 + x + 6 = 123
3x + 12 = 123
Collect like terms
3x = 123 — 12
3x = 111
Divide both side by the coefficient of x i.e 3
x = 111/3
x = 37
Now let us find the value of the three odd numbers. This is illustrated:
1st : x + 2 = 37 + 2 = 39
2nd : x + 4 = 37 + 4 = 41
3rd : x + 6 = 37 + 6 = 43
The smallest of the three consecutive odd numbers is 39
lily can travel 60 miles in 1.5 hours. If her speed is reduced by 5 mph,how har can she travel in 3 hours
Answer:
110
Step-by-step explanation:
Answer:
105 miles
Step-by-step explanation:
first we have to find her speed before it is reduced
so
60/1.5
thats equal to 40
she can travel 40 mph
reduce that by 5 so her speed is now 35mph
35*3=105
I need help with this question please?
ANSWER ASAP!!!!!!!!!
The fish is 2.25 ft above the water surface.
Step-by-step explanation:
Step 1: Given expression for height of the fish above the water surface, y = -16x² + 12x where x is time in seconds. Find height after 0.375 seconds⇒ y = -16(0.375)² + 12 × 0.375
= -2.25 + 4.5
= 2.25 ft
Fill in the blank to make a true equation. (-9)(___) = 36 A. - 4 B. 4 C. 6 D. - 6
Answer:
Option A, -4
Step-by-step explanation:
Step 1: Make an equation to represent the problem
(-9)(x) = 36
Step 2: Solve for x by dividing both sides by -9
-9x / -9 = 36 / -9
x = -4
Answer: Option A, -4
An art supply store typically sells bottles of green paint for every 9 bottles of aqua paint. How many bottles of aqua paint does it sell when it sells 30 bottles of green paint?
Final answer:
The store sells 270 bottles of aqua paint when it sells 30 bottles of green paint.
Explanation:
To find out how many bottles of aqua paint the store sells when it sells 30 bottles of green paint, we can set up a proportion. Since the store sells 9 bottles of aqua paint for every 1 bottle of green paint, we have the ratio 9/1. We can set this equal to the unknown quantity, x, over 30 (the number of green paint bottles).
9/1 = x/30
Next, cross multiply to solve for x. Cross multiplying gives us:
9 * 30 = 1 * x
Simplifying this equation gives us:
270 = x
Therefore, the store sells 270 bottles of aqua paint when it sells 30 bottles of green paint.
HELP. Y=-3x + 6
Y=2x - 4
How many solutions can be found for the system of linear equations represented on the graph?
A) no solution
B) one solution
C) two solutions
D)infinitely many solutions
Answer:
one solutions
Step-by-step explanation:
graph both points on a graph if they cross you have one solution, if they never meet you have no solution and if it's one line you have infinite solutions
Final answer:
The two given linear equations y = -3x + 6 and y = 2x - 4 have different slopes, which means they will intersect at exactly one point, indicating that there is one solution to the system.
Explanation:
To find out how many solutions can be found for the system of linear equations represented on the graph, we can observe the slopes and y-intercepts of the given equations. The two equations are:
y = -3x + 6
y = 2x - 4
These are both linear equations in the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. The first equation has a slope of -3 and the second has a slope of 2. Because the slopes are not equal, these lines are not parallel and will, therefore, intersect at one point. When two lines intersect at exactly one point, the system of equations has one solution.
Moreover, since they intersect, they do not have the same line, so they do not have infinitely many solutions. Therefore, the correct answer is one solution (B).
0.1 percent as fraction in simplest form ?
Answer:
1/10
Step-by-step explanation:
Answer:
1/10
Step-by-step explanation:
In its simplest form, expressing the decimal as a fraction to its simplest form will give one over ten.
Therefore if you divide 1/10, the answer will be 0.1. it is also called one-tenth.
Although there are other expressions or fractions that give 0.1, but 1/10 is the simplest of them all, and the question specified to use it in its simplest form.
Which helps to establish a negative credit history?
O Make payments on or before the due date.
O Never miss a payment.
O Pay Sif the full amount with the first monthly statement.
O Pay less than the minimum amount due.
Answer:
D: Pay less than the minimum amount due.
Step-by-step explanation:
•
If AB = 4x + 9, BC = 5x + 2, and AC = 56, find the measure of AB and BC.
Answer:
Step-by-step explanation:
Given that
AB=4x+9
BC=5x+2
Then, AC=56
From vector
AC=AB+BC
Then,
56=4x+9+5x+2
56=9x+11
Subtract 11 from both sides
56-11=9x+11-11
45=9x
Divide both sides by 9
45/9=9x/9
5=x
Then, x=5
Now,
1. AB=4x+9, x=5
AB=4(5)+9
AB=20+9
AB=29
2. Also
BC=5x+2
BC=5(5)+2
BC=25+2
BC=27
i need help finding the area of a figure where the rectnagles area is 5 x 14 and the half circles diameter is 6
Answer:
84.14 square units, total
Step-by-step explanation:
Use the formulas for area of the figures you're interested in.
Rectangle Area
A = LW
Circle Area
A = πr^2
__
Your rectangle area will be ...
A = 5 × 14 = 70 . . . . square units
The area of a full circle with diameter 6 (radius = 6/2 = 3) will be ...
A = π × 3^2 = 9π
The area of a semicircle of that size is half that:
semicircle area = 9π/2 = 4.5π
Then the total area of the two figures is ...
70 + 4.5π ≈ 70 +14.14 = 84.14 . . . square units
2. A boy who is 5 feet 6 inches tall casts a shadow that is 8 feet and 3 inches long. What is the measure of the
angle of elevation of the sun, A, as shown in the picture. Round to the nearest degree. Be careful with your
units in this problem.
Answer:
34°
Step-by-step explanation:
The boy is 5 feet 6 inches tall.
The boy casts a shadow that is 8 feet and 3 inches long.
We know 12 inches equal 1 foot.
Therefore the boy's height is 5.5ft and the shadow is 8.25ft.
The angle of elevation of the sun is given by the tangent of the angle A.
[tex] \tan(A) = \frac{5.5}{8.25} [/tex]
[tex]\tan(A) = 0.6667[/tex]
[tex]A= {\tan}^{ - 1} (0.6667)[/tex]
[tex]A=33.69 \degree[/tex]
To nearest degree is 34°
Answer: 34 degrees
Step-by-step explanation:
the boy is 5’6
5x12=60+6=66
The shadow is 8’3
8x12=96+3=99
You would use tan(X)= 5.5/8.25
calculate to get 33.69 round to 34.
Consider the given statement. At least one gift in the bag is wrapped.
For each statement below, determine whether it is a negation of the given statement is True or False.
At least one gift in the bag is not wrapped.
Not every gift in the bag is wrapped.
Every gift in the bag is wrapped.
None of the gifts in the bag are wrapped.
Answer:
The negation to the given statement "At least one gift in the bag is wrapped - true" is " At least one gift in the bag is not wrapped" - False
At least one gift in the bag is not wrapped - False Not every gift in the bag is wrapped-True Every gift in the bag is wrapped-False None of the gifts in the bag are wrapped-FalseStep-by-step explanation:
Given statement is At least one gift in the bag is wrapped is true
The negation to the given statement is " At least one gift in the bag is not wrapped" - False
To determine whether the statement is a negation of the given statement is True or False :
At least one gift in the bag is not wrapped - False Not every gift in the bag is wrapped-True Every gift in the bag is wrapped-False None of the gifts in the bag are wrapped-FalseOrder the side lengths of the triangle from shortest to longest.
59°
56°
1659
The storm dropped 1 3/12 feet of snow during the first hour and 9/12 foot more during the second hour. how much snow fell during those to hours?
i need help
Answer:
your answer would be 2
Step-by-step explanation:
Convert 1 3/12 into an improper fraction which is 5/4
Then add it with 9/12
5
/4 + 9
/12
(5 × 12) + (9 × 4)
---------------------------
4 × 12
= 96/48
= 96 ÷ 48
-------------------
48 ÷ 48
= 2
2 is your answer hope this helps :)
Answer:
2 feet
Step-by-step explanation:
To find the total amount of snow that fell, we add
1 3/12 + 9/12
add the fractions
3/12+9/12 = 12/12 =1
Add the whole numbers
1 plus the whole number from the fraction
1+1 =2
what is 2 and 1 4th times 1 and 1 half
Answer:
3 3/8
Step-by-step explanation:
PICTURE SHOWN
Write the equation of the given line in
slope- intercept form
Answer:
y=2x+3
Step-by-step explanation:
Answer:
y = -3x - 1
Step-by-step explanation:
Point Slope Form: (y - y1) = m(x - x1)
Step 1: Find the slope using [tex]\frac{y2 - y1}{x2 - x1}[/tex]
(x1, y1) = (-1, 2)
(x2, y2) = (1, -4)
m = [tex]\frac{-4 - 2}{1 -(-1)}[/tex]
m = [tex]\frac{-6}{1+1}[/tex]
m = [tex]\frac{-6}{2}[/tex]
m = -3
Step 2: Plug into point slope form and solve for y
(y - y1) = m(x - x1)
(y - 2) = -3(x - (-1))
y - 2 = -3(x + 1)
y - 2 + 2 = -3x - 3 + 2
y = -3x - 1
Answer: y = -3x - 1
Name the property shown by each statement and which is associative or commutation or simply
Answer:
The associative property states that you can add or multiply regardless of how the numbers are grouped. By 'grouped' we mean 'how you use parenthesis'. In other words, if you are adding or multiplying it does not matter where you put the parenthesis. Add some parenthesis any where you like!.
The Commutative property states that order does not matter. Multiplication and addition are commutative.
hope this helps please mark brainliest!
The relationship between the weight y gram and the edge x cm for a cube of gold is y = 19.3x3 A cube of gold weighs 652 grams. Calculate the length of the edge of the cube in centimeters. Answer with two decimal places.
The length of the edge of the cube is 3.23 cm .
Step-by-step explanation:
We have , The relationship between the weight y gram and the edge x cm for a cube of gold is y = 19.3x3 or [tex]y = 19.3x^3[/tex] . A cube of gold weighs 652 grams i.e. y = 652 . Let's calculate value of x from above data:
[tex]y = 19.3x^3[/tex]
⇒ [tex]y = 19.3x^3[/tex]
⇒ [tex]652= 19.3x^3[/tex]
⇒ [tex]19.3x^3=652[/tex]
⇒ [tex]\frac{19.3}{19.3}x^3=\frac{652}{19.3}[/tex]
⇒ [tex]x^3=\frac{652}{19.3}[/tex]
⇒ [tex]\sqrt[\frac{1}{3} ]{x^3} = \sqrt[\frac{1}{3} ]{\frac{652}{19.3}}[/tex]
⇒ [tex]({x^3})^\frac{1}{3} =({\frac{652}{19.3}})^\frac{1}{3}[/tex]
⇒ [tex]x =(33.78)^\frac{1}{3}[/tex]
⇒ [tex]x =3.23[/tex]
Therefore, the length of the edge of the cube is 3.23cm.
Suppose the diameter of a circle is \color{green}{6}6start color green, 6, end color green units. What is its circumference?
Answer:
C = 6pi units
or
C is approximately 18.84 units
Step-by-step explanation:
The circumference of a circle is given by
C = pi *d
The diameter is 6 units
C = 6*pi units
If we approximate pi by 3.14
C = 6*3.14
C = 18.84 units
make b the subject of the formula a = *square root* b+6
The required formula with b subject is [tex]b = a^{2} - 6[/tex].
Given that ,
a is the subject of the formula,
[tex]a = \sqrt{ b + 6}[/tex]
We have to make b is the subject for the formula,
[tex]a = \sqrt{ b + 6}[/tex]
Squaring both the sides,
[tex]a^{2} = b + 6[/tex]
[tex]b = a^{2} - 6[/tex]
Hence , The required formula with b subject is [tex]b = a^{2} - 6[/tex]
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To make b the subject of the formula a = √(b+6), you need to isolate b on one side of the equation. The solution is b = a² - 6.
Explanation:To make b the subject of the formula a = √(b+6), we need to isolate b on one side of the equation. Here are the steps:
Square both sides of the equation to remove the square root: a² = b + 6Subtract 6 from both sides: a² - 6 = bTherefore, b = a² - 6.
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Use the quadratic formula to solve the equation
Answer:
=3
=2
Step-by-step explanation:
12−5+6=0
using the Quadratic Formula where
a = 1, b = -5, and c = 6
=−±2−4‾‾‾‾‾‾‾‾√2
=−(−5)±(−5)2−4(1)(6)‾‾‾‾‾‾‾‾‾‾‾‾‾‾√2(1)
=5±25−24‾‾‾‾‾‾‾√2
=5±1‾√2
The discriminant 2−4>0
so, there are two real roots.
Simplify the Radical:
=5±12
=62=42
which becomes
=3
=2
hope this helps :)
What is it I really need to know please
Answer:
12
Step-by-step explanation:
Just take 35 and subtract 23.
What is the 10th term 1,
1/2,1/4
Answer:
The 10th term will be:
[tex]a_{10}=\frac{1}{512}[/tex]
Step-by-step explanation:
Considering the sequence
[tex]1,\:\frac{1}{2},\:\frac{1}{4}...[/tex]
A geometric sequence has a constant ratio r and is defined by
[tex]a_n=a_0\cdot r^{n-1}[/tex]
[tex]\mathrm{Compute\:the\:ratios\:of\:all\:the\:adjacent\:terms}:\quad \:r=\frac{a_{n+1}}{a_n}[/tex]
[tex]\frac{\frac{1}{2}}{1}=\frac{1}{2},\:\quad \frac{\frac{1}{4}}{\frac{1}{2}}=\frac{1}{2}[/tex]
[tex]\mathrm{The\:ratio\:of\:all\:the\:adjacent\:terms\:is\:the\:same\:and\:equal\:to}[/tex]
[tex]r=\frac{1}{2}[/tex]
[tex]\mathrm{The\:first\:element\:of\:the\:sequence\:is}[/tex]
[tex]a_1=1[/tex]
[tex]\mathrm{Therefore,\:the\:}n\mathrm{th\:term\:is\:computed\:by}\:[/tex]
[tex]a_n=\left(\frac{1}{2}\right)^{n-1}[/tex]
Putting n = 10 to determine in the nth term to determine the 10th term
[tex]a_{10}=\left(\frac{1}{2}\right)^{10-1}[/tex]
[tex]a_{10}=\left(\frac{1}{2}\right)^9[/tex]
[tex]\mathrm{Apply\:exponent\:rule}:\quad \left(\frac{a}{b}\right)^c=\frac{a^c}{b^c}[/tex]
[tex]a_{10}=\frac{1^9}{2^9}[/tex]
[tex]a_{10}=\frac{1}{2^9}[/tex] ∵ [tex]1^9=1[/tex]
[tex]a_{10}=\frac{1}{512}[/tex] ∵ [tex]2^9=512[/tex]
Therefore, the 10th term will be:
[tex]a_{10}=\frac{1}{512}[/tex]
A Pentagon is transformed according to the rule R0, 180°. Which is another way to state the transformation?
(x,y)>(-x,-y)
(x,y)>(-y,-x)
(x,y)>(x,-y)
(x,y)>(-x,y)
The another way to state the transformation would be [tex](x,y)>(-x,-y)[/tex]
Solution:
Rotation about the origin at [tex]180^\circ[/tex]: [tex]R_{180^\circ}A \rightarrow O = R_{180^\circ} (x, y) \rightarrow (-x,-y)[/tex]
The term R0 means that the rotation is about the origin point. Therefore, (R0,180) means that we are rotating the figure to [tex]180^\circ[/tex] about the origin.
So, the transformation of the general point (x,y) would be (-x,-y) when it is rotated about the origin by an angle of [tex]180^\circ[/tex].
Hence according to the representation, the expression would be [tex](x, y) \rightarrow (-x, -y)[/tex].
The transformation R0, 180° is equivalent to reflecting each point (x, y) in a Pentagon across the origin, resulting in the new coordinates (-x, -y).
The transformation rule R0, 180° involves rotating a point (x, y) within a Pentagon by 180 degrees around the origin. In this transformation, each point is mirrored or reflected across the origin. To express this transformation differently, we can say that (x, y) is mapped to its mirror image in both the x-axis and y-axis. In other words, the x-coordinate is reversed (negated), and the y-coordinate is also reversed (negated).
So, the alternative way to state this transformation is: (x, y) > (-x, -y). This means that any point (x, y) in the original Pentagon will become (-x, -y) after the transformation.
For example, if we have a point (2, 3) within the Pentagon, applying the transformation yields (-2, -3). This means the point's x-coordinate is changed from 2 to -2, and the y-coordinate is changed from 3 to -3. This transformation is essentially a 180° rotation or a reflection through the origin.
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Find, to the nearest degree, the angle of elevation of the sun when a person 170 cm tall casts of shadow 220 cm long.
Trigonometry
Answer:
Θ = 52°
Step-by-step explanation:
Once you've set up the triangle, you can see that the adjacent side is 170 cm and the opposite side is 220 cm.
tanΘ = [tex]\frac{220}{170}[/tex]
Θ = tan-1 (220/170)
Θ = 52°
The angle of elevation of the sun when a person 170 cm tall casts of shadow 220 cm long is 37.694°.
What is trigonometry?Trigonometry deals with the relationship between the sides and angles of a right-angle triangle.
A person 170 cm tall casts of shadow 220 cm long.
Then the angle will be
[tex]\rm tan \theta = \dfrac{Perpendicular }{Base}[/tex]
We have
Perpendicular = 170 cm
Base = 220 cm
Then
[tex]\rm tan \theta = \dfrac{170}{220}\\\\\\ \theta \ \ \ \ = tan^{-1} \dfrac{170}{220}\\\\\\\theta \ \ \ \ = 37.694^o[/tex]
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Helppppppppppppppppppp
What does the value of y have to be so that
(3, y) and (-5,6) have a slope of -1 between them?
Answer:
y= -2
Step-by-step explanation:
Please see attached picture for full solution.
(From the 4th to 5th line, I multiplied both sides by 8)
Which of the following expressions are equivalent to 4+(14-2)4+(14−2)4, plus, left parenthesis, 14, minus, 2, right parenthesis?
Choose 3 answers:
Choose 3 answers:
(Choice A)
A
4-(-14-2)4−(−14−2)4, minus, left parenthesis, minus, 14, minus, 2, right parenthesis
(Choice B)
B
(4-14)-2(4−14)−2left parenthesis, 4, minus, 14, right parenthesis, minus, 2
(Choice C)
C
4-(-14)-(2)4−(−14)−(2)4, minus, left parenthesis, minus, 14, right parenthesis, minus, left parenthesis, 2, right parenthesis
(Choice D)
D
4+14+(-2)4+14+(−2)4, plus, 14, plus, left parenthesis, minus, 2, right parenthesis
(Choice E)
E
-(-4-14)-2−(−4−14)−2
To simplify the expression 4 + (14 - 2), subtract 2 from 14, then add 4 to get the equivalent expression. The three equivalent expressions are: 20, -12, and 16.
To simplify the expression 4 + (14 - 2), we need to perform the operations inside the parentheses first. This means subtracting 2 from 14, which gives us 12. Then, we add 4 to 12, resulting in 16. Therefore, the expression 4 + (14 - 2) is equivalent to 16.
The three expressions that are equivalent to 4 + (14 - 2) are:
A. 4 - (-14 - 2) = 4 - (-16) = 4 + 16 = 20
B. (4 - 14) - 2 = -10 - 2 = -12
C. 4 - (-14) - (2) = 4 + 14 - 2 = 16
PLEASE ANSWER ASAP!
Dylan solved an inequality to determine the amount of lemonade, in cups, that fit in a cooler already containing ice and lemon wedges. His solution is graphed on the number line below.
How should the graph be interpreted? Select two options.
1. at most 19 cups
2. 19 cups or less
3. more than 19 cups
4. a minimum of 19 cups
5. no fewer than 19 cups
Answer:
1 + 2
Step-by-step explanation:
When we look at the number line, we can see that the inequality is:
x ≤ 19
This means that all values of "x", must be equal to or less than 19.
To find the correct answer choices, we must keep that equation in mind.
1. at most 19 cups - this answer choice does work, because it shows that 19 is the limit (which is what our inequality represents)
2. 19 cups or less - this answer choice works as well because it shows that 19 is the maximum and all other values of "x" must be below that.
3. more than 19 cups - this goes against our inequality, since "x" can't exceed 19. This means that this answer choice must be incorrect.
4. a minimum of 19 cups - this answer choice also cannot be correct since it shows that "x" can go over 19 (which we know is false).
5. no fewer than 19 cups - this is also wrong because it wants "x" to go over the value of 19, which it can't do.
Answer:
Step-by-step explanation:
A and b
Divide using Long division (6x^3-26x-21+x^2) by (-7+3x)
Step-by-step explanation:
Hope it helps you in your learning process.