Using a transit, a surveyor measures the angle between two trees to be 111 degrees. If the first tree is 62 feet from the transit and the second tree is 58 feet from the transit, what is the distance between the two trees?
Answers
Answer:
The distance between the two trees is [tex]98.92\ ft[/tex]
Step-by-step explanation:
we know that
Applying the law of cosines
[tex]c^{2}=a^{2} +b^{2} -2(a)(b)cos (C)[/tex]
where
c -----> is the distance between the two trees
a ----> is the distance between the transit and the first tree
b ----> is the distance between the transit and the second tree
we have
[tex]a=62\ ft[/tex]
[tex]b=58\ ft[/tex]
[tex]C=111\°[/tex]
substitute and solve for c
[tex]c^{2}=62^{2} +58^{2} -2(62)(58)cos (111\°)[/tex]
[tex]c^{2}=9,785.38[/tex]
[tex]c=98.92\ ft[/tex]
Related Questions
45 POINTS FOR WHOLE PAGE!!!!!!!!!!!!!
Answers
1. simply: h+245
2. your answer is right
3. 2+1/3n (i believe)
4. 29+5m
5. I’m pretty sure the answer is 29
What are the numbers???
Answers
Answer:
In: 5, 4, 2, 3, 1, and 10.
Out: 40, 32, 16, 24, 8, and 80
Step-by-step explanation:
The first step you should do is to take notice of the pairs that have their "in" and "out" both answered.
The second step is to find out what you must multiply the "in" by to get the "out". In this answer, you must multiply the "in" by 8 to get the "out".
The third step is to do the same thing for all of the values until the chart is completely filled with values.
The fourth step is to check your work!
If you have any questions, please let me know!
The rule is 8
Bc 5 times 8 is 40
32/8 is 4
Either divide or multiply when needed
What is the surface area of a sphere with a diameter of 12 centimeters ?
Answers
Answer:
[tex]A=452.39\ cm^2[/tex]
Step-by-step explanation:
The formula to calculate the surface area of a sphere is the following:
[tex]A=4\pi r^2[/tex]
Where A is the area of the sphere and r is the radius of the sphere.
In this case we know that the diameter d of the sphere is:
[tex]d = 12\ cm[/tex]
The diameter is:
[tex]d = 2r[/tex].
Thus
[tex]r = \frac{d}{2}\\\\r = \frac{12}{2}\\\\r=6\ cm[/tex]
Then the surface area of the sphere is:
[tex]A=4\pi (6)^2\\\\A = 144\pi\ cm^2\\\\A=452.39\ cm^2[/tex]
Answer is provided in the image attached.
The cylinders are similar. The volume of the larger cylinder is 40,635 cubic centimeters. What is the volume of the smaller cylinder?
Answers
Answer:
1505 cubic centimeters
Step-by-step explanation:
Lengths are related by scale factor "k"
Volumes are related by scale factor "k^3"
From large to small:
What multiplied by 18, gives us 6? We can write:
18(k)=6
k = 6/18 = 1/3
So scale factor is 1/3
Now in terms of volume, the larger is given as 40, 635, so we can set up:
40,635 * k^3 = smaller volume
we know k = 1/3, so
40,635 * (1/3)^3 = smaller volume
Thus, smaller volume = 40,635 * (1/3)^3 = 1505
Which value of a would make the following expression completely factored
x^2-a
A)12
B)36
C)49
D)81
Answers
Answer:
A)
Step-by-step explanation:
We know that the expression (x^2 - a^2) can be written as (x-a)(x+a). So an expression of this type: (x^2 - a^2) wouldn't be completely factored because it could be factorized even more.
So we know that 36 = 6^2, 49= 7^2 and 81 = 9^2. So if we choose any of these options (Option B, C and D) it wouldn't be completely factored.
The correct is the option A, given that if a=12, it wouldn't be a perfect square, so it would be completely factored.
So I just did the problem and im pretty sure the answer is A
ABCDEF and EHG are regular polygons. If mHGJ=220* on the exterior of the polygon, mEGJ is congruent to mGED, and mCDJ=136* on the exterior of the polygon, what is the measure of GJD?
Answers
Answer:
96 deg
Step-by-step explanation:
Polygon ABCDE is a regular hexagon. The sum of the measures of the interior angles is (n - 2)180 = (6 - 2)180 = 4(180) = 720. Since it's a regular hexagon, each interior angle measures 720/6 = 120 deg.
For the interior angle, m<CDE = 120
On the exterior of the polygon, m<CDJ = 136
m<CDE + m<CDJ + m<EDJ = 360
120 + 136 + m<EDJ = 360
m<EDJ + 256 = 360
m<EDJ = 104 deg
Triangle EHG is regular. The sum of the measures of the angles of a triangle is 180. For a regular triangle, each angle measures 60 deg.
m<EGH = 60
For exterior angle m<HGJ = 220
m<HGJ(exterior) + m<EGH + m<EGJ = 360
220 + 60 + m<EGJ = 360
m<EGJ + 280 = 360
m<EGJ = 80
m<EGJ = m<GED, so
m<GED = 80
Polygon DEGJ is a quadrilateral. The sum of the measures of its interior angles is 360 deg.
m<EGJ + m<GED + m<EDJ + m<GJD = 360
80 + 80 + 104 + m<GJD = 360
m<GJD + 264 = 360
m<GJD = 96 deg
Answer:
The measure of angle GJD is 96°.
Step-by-step explanation:
It is given that HGJ=220° on the exterior of the polygon, EGJ is congruent to GED, and CDJ=136° on the exterior of the polygon.
Each side and each interior angle of a regular polygon are same.
It is given that ABCDEF and EHG are regular polygons. It means each interior angle of regular hexagon ABCDEF is 120° and each interior angle of regular triangle EHG is 60°.
[tex]\angle EGH+\angle EGJ+\angle HGJ(exterior)=360^{\circ}[/tex]
[tex]60^{\circ}+\angle EGJ+220^{\circ}=360^{\circ}[/tex]
[tex]\angle EGJ+280^{\circ}=360^{\circ}[/tex]
[tex]\angle EGJ=360^{\circ}-280^{\circ}[/tex]
[tex]\angle EGJ=80^{\circ}[/tex]
[tex]\angle GED=\angle EGJ=80^{\circ}[/tex]
[tex]\angle CDE+\angle EDJ+\angle CDJ(exterior)=360^{\circ}[/tex]
[tex]120^{\circ}+\angle EDJ+136^{\circ}=360^{\circ}[/tex]
[tex]\angle EDJ+256^{\circ}=360^{\circ}[/tex]
[tex]\angle EDJ=360^{\circ}-256^{\circ}[/tex]
[tex]\angle EDJ=104^{\circ}[/tex]
The sum of all interior angles of a quadrilateral is 360°.
[tex]\angle GED=\angle EGJ+\angle EDJ+\angle GJD=360^{\circ}[/tex]
[tex]80^{\circ}+80^{\circ}+104^{\circ}+\angle GJD=360^{\circ}[/tex]
[tex]264^{\circ}+\angle GJD=360^{\circ}[/tex]
[tex]\angle GJD=360^{\circ}-264^{\circ}[/tex]
[tex]\angle GJD=96^{\circ}[/tex]
Therefore the measure of angle GJD is 96°.
Given that -5 < -3, which statement is not true?
-5 is to the left of -3 on the number line.
-3 is less than -5,
-3 > -5
-3 is to the right of -5 on the number line.
Answers
Answer:
- 3 is less than - 5 is not true
Step-by-step explanation:
Numbers to the right of numbers on the number line are greater.
Numbers to the left of numbers on the number line are less
- 3 is to the right of -5 on the number line and is greater than - 5
The population of mice in a vacant building is 200. The population of mice grows according to the model: M(t)=200(1.2)^t where t is the time in days. Assuming none of the mice die, how many mice will be in the building at the end of 30 days
Answers
7200. Because 1.2 *30 *200=7200
To estimate the mouse population after 30 days using the given model, M(t)=200(1.2)^t, evaluate the expression with t=30, which results in approximately 47,475 mice.
The student is asking how many mice will be in the building after 30 days according to the exponential growth model M(t) = 200(1.2)^t, where t is the time in days and M(t) is the population of mice at time t. To find the answer, we simply plug the value of 30 days into the model to get M(30) = 200(1.2)^30.
Calculating the expression:
First, calculate 1.2 raised to the power of 30, which gives us approximately 237.3769.
Then, multiply that by the initial population of 200 mice, yielding a result of approximately 47,475.38.
Therefore, after 30 days, assuming no mice die, there will be approximately 47,475 mice in the building.
Vicki gives her children dessert 30% of the time. If her children want to know the probability that they will eat dessert 3 of the 7 days this week, which simulation design has an appropriate device and a correct trial?
A) Roll a die letting 1 represent eating dessert and 2-6 represent not eating dessert. Roll the die three times.
B) Roll a die letting 1 represent eating dessert and 2-6 represent not eating dessert. Roll the die seven times.
C) Using a table of random digits select a digit between 0 and 9. Let 0-2 represent eating dessert and 3-9 represent not eating dessert. Select three digits.
D) Using a table of random digits select a digit between 0 and 9. Let 0-2 represent eating dessert and 3-9 represent not eating dessert. Select seven digits.
Answers
The simulation design that has an appropriate device and a correct trial for this scenario is:
Using a table of random digits select a digit between 0 and 9. Let 0-2 represent eating dessert and 3-9 represent not eating dessert. Select three digits.The correct option is C.
Which simulation design has an appropriate device and a correct trial?The simulation which involves using a table of random digits to select a digit between 0 and 9, letting 0 - 2 represent eating dessert and 3 - 9 represent not eating dessert, and then selecting three digits has an appropriate device and a correct trial.
This simulation design is given below:
To simulate the probability of eating dessert in 3 of the 7 days this week, we would select three digits from the table of random digits and count the number of 0s, 1s, and 2s. The number of 0s, 1s, and 2s would correspond to the number of days the children eat dessert, and the number of 3s, 4s, 5s, 6s, 7s, 8s, and 9s would correspond to the number of days the children do not eat dessert.
We would repeat this process many times (e.g., 1000 times) to obtain an estimate of the probability of eating dessert 3 of the 7 days this week.
Learn more about simulation and probabilities at: https://brainly.com/question/1231005
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What property is shown in the equation? a(b × c) = (a × b)c
Answers
Answer:
Commutative Property
Step-by-step explanation:
"Changing the order but not the result"
A rectangular pyramid is sliced so the cross section is perpendicular to its base and passes through its vertex. What is the shape of the cross section? trapezoid rectangle triangle square
Answers
Answer:
rectangle. trapezoid. triangle. A sphere is sliced so that the cross section does not intersect the center of the sphere
Answer:
sorry im late to this but it is a triangle
Step-by-step explanation:
because when you cut it horizontally and look at the top it is a rectangle so that is wrong trapezoid is when you look at it from the side when cut horizontally so that is wrong there is no square so that instantly becomes wrong because it is a rectangular pyramid when perpendicular it will provide you with a triangle
Which of the following are right triangles? A) Triangle ABC: AB=76 BC=357 AC=365
B) Triangle ABC: AB=123 BC=836 AC=845
Answers
ANSWER
AB=76 BC=357 AC=365 This triangle is a right triangle.
EXPLANATION
We use the Pythagoras Theorem to determine whether the triangles are right triangles.
According to this theorem, the square of the hypotebuse is equal to the sum of the squares of the two shorter legs.
We have:
AB=76 BC=357 AC=365
[tex] {365}^{2} = {76}^{2} + {357}^{2} [/tex]
133225=5776+127449
133225=133225
For the second triangle, we have;
B) Triangle ABC: AB=123 BC=836 AC=845
845²=123²+826²
714025=15129+682276
714025≠697405
The first triangle is a right triangle
Answer:
the firsst one
Step-by-step explanation:
Evaluate the sum
A. 306
B. 240
C. 360
D. 272
Answers
Answer:
Option D. [tex]272[/tex]
Step-by-step explanation:
we know that
To evaluate the sum , use the formula
[tex]S=\frac{1}{2}(a1+an)n[/tex]
where
a1 is the first term
an is the last term
n is the number of terms
In this problem
For n=1 ------> a1=2(1)=2
For n=16 ------> an=2(16)=32
n=16 terms
substitute in the formula
[tex]S=\frac{1}{2}(2+32)16[/tex]
[tex]S=272[/tex]
the difference between a number and 2
Answers
Answer:
n-2
Step-by-step explanation:
Difference means subtraction
n-2
If f(x)=|x| + 9 and g(x) =-6 , which describes the value of (f+g)(x)
Answers
Answer:
Step-by-step explanation:
This has a very brief answer when you know what it means.
f(x) + g(x) = abs(x) + 9 - 6
f(x) + g(x) = abs(x) + 3
Answer:
f + g)(x) = |x| + 3
Step-by-step explanation:
Add the two functions together:
f(x) = |x| + 9
+g(x) = - 6
------------------------
f(x) + g(x) = |x| + 9 - 6
= |x| + 3
The label f(x) + g(x) can be rewritten as (f + g)(x).
Thus, f + g)(x) = |x| + 3
Factor this expression 2
Answers
Answer:
Step-by-step explanation:
16x^4+56x^2+49
(4x^2+7)^2
The area of the trapezoid
Answers
The area of that trapeziod is 28 inches.
Answer:
Step-by-step explanation:
The area is a+b/2
so the answer is 28
Assessment 1
4. Use the recipe shown in the table to answer the questions below.
Use pictures, tables or number
sentences to solve the task.
Grandma's Recipe for Su
ecipe for Sugar Cookies
1% cups butter
2 cups sugar.
4 eggs
4 teaspoon baking powder
1 YA cups flour
14 teaspoon salt
a) How many cups of sugar are needed for each egg? How do you know?
Answers
a)Each egg requires 0.5 cups of sugar in Grandma's recipe.
b)The ratio of baking powder to salt is 3:1.
a) The recipe uses 2 cups of sugar and 4 eggs. To find out how many cups of sugar are needed per egg, we divide the total cups of sugar by the number of eggs:
2 cups of sugar / 4 eggs = 0.5 cups of sugar per egg
So, 0.5 cups of sugar are needed for each egg.
b) Ratio of baking powder to salt
The recipe calls for 3/4 teaspoon of baking powder and 1/4 teaspoon of salt. To find the ratio of baking powder to salt, we divide the amount of baking powder by the amount of salt:
(3/4) teaspoon of baking powder / (1/4) teaspoon of salt = 3
Thus, the ratio of baking powder to salt is 3:1. This means there is three times as much baking powder as salt in the recipe, which aligns with your sister's observation.
The complete question is:
Use the recipe shown in the table to answer the questions below. Use pictures, tables or number sentences to solve the task. Grandma's Recipe for Sugar Cookies 1/2 cups butter 2 cups sugar 4 eggs 34 teaspoon baking powder 1 % cups flour 14 teaspoon salt a) How many cups of sugar are needed for each egg? How do you know? Your sister notices that she needs three times as much baking powder as salt in this recipe. b)What is the ratio of baking powder to salt? Explain your reasoning in words.
What is the answer to the question??
Answers
Answer:
[tex]c=15[/tex]
Step-by-step explanation:
Use the Pythagorean Theorem.
[tex]a^2+b^2=c^2 \\ \\ 9^2+12^2=c^2 \\ \\ 81+144=c^2 \\ \\ c^2=225 \\ \\ c=\sqrt{225} \\ \\ c=15[/tex]
Which is the equation of the given line in point- slope form?
y - 0 = 1(x+8)
y - 0 = -1(x-8)
y = - x + 8
y - 8 = -1(x+0)
Answers
Answer:
[tex]y-0=-1(x-8)[/tex]
Step-by-step explanation:
The given line passes through (0,8) and (8,0).
The slope of this line is [tex]m=\frac{8-0}{0-8} =-1[/tex].
The point-slope form is given by:
[tex]y-y_1=m(x-x_1)[/tex]
We substitute the slope and the point (8,0) to get:
[tex]y-8=-1(x-0)[/tex]
We substitute the slope and the point (0,8) to get:
[tex]y-0=-1(x-8)[/tex]
Answer please? Solve math
Answers
Answer:
(a)
Step-by-step explanation:
To rationalise the fraction multiply the numerator/denominator by the conjugate of the denominator.
The conjugate of [tex]\sqrt{3}[/tex] + [tex]\sqrt{x}[/tex] is [tex]\sqrt{3}[/tex] - [tex]\sqrt{x}[/tex]
Hence
[tex]\frac{\sqrt{9}(\sqrt{3}-\sqrt{x} ) }{(\sqrt{3}+\sqrt{x} )(\sqrt{3}-\sqrt{x} ) }[/tex]
= [tex]\frac{3(\sqrt{3}-\sqrt{x} }{3-x}[/tex]
= [tex]\frac{3\sqrt{3}-3\sqrt{x} }{3-x}[/tex] → (a)
Brooke is using shiny rocks to make necklaces. Each necklace has 5 shiny rocks. Make a table that shows the number of shiny rocks used for 10, 15, 20, and 25 necklaces
Answers
Answer:
10 necklaces = 50 rocks
15 necklaces = 75 rocks
20 necklaces = 100 rocks
25 necklaces = 125 rocks
Step-by-step explanation:
A table that shows the number of shiny rocks used for 10, 15, 20, and 25 necklaces:
| Number of necklaces | Number of shiny rocks used |
| 10 | 50 |
| 15 | 75 |
| 20 | 100 |
| 25 | 125 |
To calculate the number of shiny rocks used, we simply multiply the number of necklaces by the number of shiny rocks per necklace. For example, to calculate the number of shiny rocks used for 10 necklaces, we multiply 10 by 5:
10 necklaces * 5 shiny rocks/necklace = 50 shiny rocks
We can do the same calculation for 15, 20, and 25 necklaces to get the following results:
15 necklaces * 5 shiny rocks/necklace = 75 shiny rocks
20 necklaces * 5 shiny rocks/necklace = 100 shiny rocks
25 necklaces * 5 shiny rocks/necklace = 125 shiny rocks
Therefore, the table above shows the number of shiny rocks used for 10, 15, 20, and 25 necklaces.
For such more question on number
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Which number can each term of the equation be multiplied by to eliminate the decimals before solving? –m + 0.02 + 2.1m = –1.45 – 4.81m
Answers
Answer:
100
Step-by-step explanation:
The given equation is;
–m + 0.02 + 2.1m = –1.45 – 4.81m
The highest decimal places is 2.
This implies that, we must multiply each term of the equation by [tex]10^2=100[/tex] before solving in order to eliminate the decimal.
In that case the equation becomes;
–100m + 2 + 210m = –145 – 481m
Hence the number is 100
Answer:
easy answer 100
Step-by-step explanation:
Does anyone know this
Answers
Answer:
a2+1)-(4+2a2)
Step-by-step explanation:
to solve this, we need to get rid of the brackets as follow:
3a2+1-4-2a2
ading the common terms we have:
a2 - 3
that is all.
Plz mark me brainlist!!!
What would be the dimensions for the poster at 1/4 times it’s current size
Answers
Answer:
D. Length = 9 cm; width = 6 cm
Step-by-step explanation:
Find 1/4 of the length and 1/4 of the width.
1/4 * 36 cm = 9 cm
1/4 * 24 cm = 6 cm
Answer: D. Length = 9 cm; width = 6 cm
The ratio to boys to girls in Ms.chunningham's class is 2 to 3. There are 18 girls in the class.What is the total number of students in ms.chunningham's class?
A. 12
B. 30
C.45
D.27
Answers
Answer:
B.30
Step-by-step explanation:
This was picked because if u divide 18 by 3. You get 6 and if u multiply it by 2. You get 12 plus the 18 equals 30.
Which expresión is equivalent to -3x - (x-1) + 3/2 (3x + 3)?
A. 1/2x + 11/2
B. 1/2x + 7/2
C. 5/2x + 11/2
D. 5/2x + 7/2
Answers
Answer:
[tex]\large\boxed{A.\ \dfrac{1}{2}x+\dfrac{11}{2}}[/tex]
Step-by-step explanation:
[tex]-3x-(x-1)+\dfrac{3}{2}(3x+3)\qquad\text{use the distributive property}\\\\=-3x-x-(-1)+\left(\dfrac{3}{2}\right)(3x)+\left(\dfrac{3}{2}\right)(3)\\\\=-3x-x+1+\dfrac{9}{2}x+\dfrac{9}{2}\qquad\text{combine like terms}\\\\=\bigg(-3x-x+\dfrac{9}{2}x\bigg)+\bigg(1+\dfrac{9}{2}\bigg)\\\\=\bigg(\dfrac{-6}{2}x-\dfrac{2}{2}x+\dfrac{9}{2}x\bigg)+\bigg(\dfrac{2}{2}+\dfrac{9}{2}\bigg)\\\\=\dfrac{-6-2+9}{2}x+\dfrac{2+9}{2}=\dfrac{1}{2}x+\dfrac{11}{2}[/tex]
What is the square root of 36. Please help
Answers
Answer:
±6
Step-by-step explanation:
Whenever you are finding the square root of something, it will ALWAYS result in a negative and positive number, or else depending on the situation of a problem.
Ex: Distance Formula → POSITIVE ANSWER ONLY
I am joyous to assist you anytime.
F(x) = x^2. What is g(x)?
Answers
Answer:
The correct answer is C. g(x) = 1/4x^2
Step-by-step explanation:
In order to determine if the graph fits, take the point that is given on the parabola and see if it fits the equation. To do that we plug it in and see if it gives a true statement.
(2, 1)
g(x) = 1/4x^2
1 = 1/4(2)^2
1 = 1/4(4)
1 = 1 (TRUE)
simplify the expression
(2b/3)^4
Answers
Answer:
2b/3 * 2b/3 * 2b/3 * 2b/3
Good luck!!
Answer:
16b^4/81
Step-by-step explanation: