The height of the mountain is 2936.39 feet.
Given,
In the question:
The angle of elevation to the top of the mountain is 25°.
To find the height of the mountain, we can draw triangles as in the image attached.
Now, According to the question:
Let's call the height of the mountain 'h', and the distance from the first point (25degrees) to the mountain 'x'.
Then, we can use the tangent relation of the angles:
tan(29) = h/x
tan(25) = h/(x+1000)
tan(25) is equal to 0.4663, and tan(29) is equal to 0.5543, so:
h/x = 0.5543 -> x = h/0.5543
using this value of x in the second equation:
h/(x+1000) = 0.6009
h/(h/0.5543 + 1000) = 0.4663
h = 0.4663 * (h/0.5543 + 1000)
h = 0.8412h + 466.3
0.1588h = 466.3
h = 466.3 / 0.1588 = 2936.39 feet
Hence, the height of the mountain is 2936.39 feet.
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Hello, a little confused on this section. Thanks for your help!
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
graph
Step 02:
notation for domain and range:
we must analyze the graph to find the solution.
graph:
The domain is reflected on the x-axis and the range is reflected on the y-axis.
Inequality / Agebraic:
D:
R:
Interval:
D:
R:
Set-Builder:
D:
R:
you raise pigs when you purchase the pig it weigh 46 pounds with in 5-6 months you pig will gain 380% in weight how much should it weigh by then round to the nearest whole number
The weight of the pigs is 220.8 pounds.
How to calculate the value?From the information, when you raise pigs when you purchase the pig it weigh 46 pounds with in 5-6 months you pig will gain 380% in weight.
Therefore, the weight by then will be:
= Normal weight + ( Percentage × Previous weight)
= 46 + (380% × 46)
= 46 + 174.8
= 220.8
The weight is 220.8 pounds.
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The mass of a typical comet is about 1 x 10¹3 kg, while the mass of a typical asteroid is about 3 x 10¹⁹ kg.
Approximately how many times the mass of a typical comet is the mass of a typical asteroid?
100,000 times
300,000 times
1,000,000 times
O 3,000,000 times
The mass of the typical comet is 3,000,000 times the mass of a typical asteroid which is the fourth option among the given options.
It is given in the question that:-
Mass of a typical comet = [tex]1*10^{13}kg[/tex]
Mass of a typical asteroid = [tex]3*10^{19}kg[/tex]
We have to find the how many times the mass of a typical comet is the mass of a typical asteroid.
Mass of a typical asteroid/ Mass of a typical comet is given by:-
[tex]\frac{3*10^{19}}{1*10^{13}}=3*10^6[/tex]
We can write [tex]3*10^6[/tex] as 3,000,000.
Hence, the mass of the typical comet is 3,000,000 times the mass of a typical asteroid which is the fourth option among the given options.
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hi I'm 9 years old my name is Emma can
Given:
Perimeter = 40 feet,
The measure of the four sides is 11 feet, g, 11 feet, and g.
We know that the perimeter = the sum of the four sides.
[tex]\text{perimeter =11+g+11+g}[/tex]Replace perimeter =40, we get
[tex]\text{40=11+g+11+g}[/tex]Adding 11 and 11, we get
[tex]\text{40=11+11+g+g}[/tex][tex]\text{40=22+g+g}[/tex]Andre and Lin are discussing whether it is possible to define latitude and temperature in a way that makes sense to talk about temperature as a function of latitude. They are considering different options. Here are the options: a. Finding the temperature right now in cities with different latitudes b. Finding the daily high temperature at cities that have different latitudes c. Finding the average high temperature in a specific month, e.g., September, at cities that have different latitudes d. Finding the average yearly temperature at cities that have different latitudes None of these options are perfect. All have flaws. Choose one option and give the advantages and disadvantages of the option for talking about temperature as a function of latitude. Answer in the space below
All answers are kind of similar and none of these options are perfect.
We are going to chose the opcion b, the advantage is that the daily high temperature at cities give us a statistical sample about how latitude impact the temperature and how is the clime in those days.
Disadvantages is that we dont know the lower temperature and how the latitude impact in this case.
number one name three collinear points number to name four coplanar Point number three name two sets of lines intersect number for name two points not contained in the plane
The points lying on a single line are called colinear points. So here,
KJD are colinear points as they are lying on a same line.
Points lying on the same plane are called coplanar points. So here, IJFE are coplanar points.
The two sets of line intesects are KD and CF, IG and FH.
The two points that are not in the plane are A and B.
how many liters of 10% salt water do you need to add to 5 liters of 25% salt to make 15% salt?
Answer:
You will need 10 liters of 10% salt water
Step-by-step explanation:
Josh wants to use Rockaway Hall, the Groove Guru Band, and PJ's Party Supplies. Josh has a total of
650 dollars and wants to invite 25 people. His friend told him he would be able to afford the band for 4 hours. Is that true?
1) Assume that x is the number of hours and that y is the total cost. To model, write an equation. 2) Tutoring his friend in geometry is the second way he can get money.
One of the first areas of mathematics is geometry, along with arithmetic.
What is the Bernoulli inequality?A mathematical inequality that closely resembles the exponentiations of 1 + x is known as Bernoulli's inequality, named after Jacob Bernoulli. In actual analysis, it is frequently used. It contains a few helpful variations, including those for any integer r 0 and real number x > 1. If x 0 and r 2, the inequality is strictly true.A statement about raising a number to a natural power is made by the binomial inequality: and. It can be easily demonstrated by induction and is essentially a condensed version of the binomial theorem.A mathematical inequality that closely resembles the exponentiations of 1 + x is known as Bernoulli's inequality, named after Jacob Bernoulli. In actual analysis, it is frequently used.To learn more about Bernoulli inequality refer to:
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The roots of unity (1) may be calculated from the equation x3-1=0. What are they?
we find the root of x² + x + 1 has it can't be factorized
Using quadratic formula:
[tex]x\text{ = }\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]for a² + bx + c = 0
comparing: x² + x + 1
where a = 1, b = 1, c = 1
[tex]\begin{gathered} x\text{ = }\frac{-1\pm\sqrt[]{(1)^2^{}-4(1)(1)}}{2(1)} \\ x\text{ = }\frac{-1\pm\sqrt[]{1^{}-4}}{2} \end{gathered}[/tex][tex]\begin{gathered} x\text{ = }\frac{-1\pm\sqrt[]{-3}}{2}\text{= }\frac{-1\pm\sqrt[]{-1(3)}}{2} \\ Since\text{ we can't find the square root of a negative number, we apply complex root} \\ \text{let i}^2\text{ = -1} \\ x\text{ = }\frac{-1\pm\sqrt[]{3i^2}}{2} \end{gathered}[/tex][tex]\begin{gathered} x\text{ = }\frac{-1\pm\sqrt[]{3i^2}}{2}\text{ = }\frac{-1\pm i\sqrt[]{3^{}}}{2} \\ x\text{ = }\frac{-1+i\sqrt[]{3^{}}}{2}or\text{ }\frac{-1-i\sqrt[]{3^{}}}{2} \\ \end{gathered}[/tex][tex]\begin{gathered} \text{The roots of x}^3\text{ - 1 = 0 are:} \\ 1\text{ and }\frac{-1\pm i\sqrt[]{3^{}}}{2} \\ 1\text{ and }\frac{\text{-1 }}{2}\pm\text{ }\frac{i\sqrt[]{3^{}}}{2}\text{ (option C)} \end{gathered}[/tex]Please assist me in understanding how to solve number 4
Solution:
Given that;
y varies directly with the square of x
[tex]y\propto x^2[/tex]This expression above becomes
[tex]\begin{gathered} y=kx^2 \\ Where\text{ k is the constant} \end{gathered}[/tex]When
[tex]y=10\text{ and x}=5[/tex]Substitute the values for x and y into the expression above to find k
[tex]\begin{gathered} y=kx^2 \\ 10=k(5)^2 \\ 10=k(25) \\ 10=25k \\ Divide\text{ both sides 25} \\ \frac{25k}{25}=\frac{10}{25} \\ k=\frac{2}{5} \end{gathered}[/tex]The expression becomes
[tex]\begin{gathered} y=kx^2 \\ y=\frac{2}{5}x^2 \end{gathered}[/tex]a) The value of y when x = 20
[tex]\begin{gathered} y=\frac{2}{5}x^2 \\ y=\frac{2}{5}(20)^2 \\ y=\frac{2}{5}(400) \\ y=160 \end{gathered}[/tex]Hence, the value of y is 160
b) The value of x when y = 40
[tex]\begin{gathered} y=\frac{2}{5}x^2 \\ 40=\frac{2}{5}x^2 \\ Crossmultiply \\ 40(5)=2x^2 \\ 200=2x^2 \\ Divide\text{ both sides by 2} \\ \frac{200}{2}=\frac{2x^2}{2} \\ 100=x^2 \\ x^2=100 \\ Square\text{ root of both sides} \\ \sqrt{x^2}=\sqrt{100} \\ x=10 \end{gathered}[/tex]Hence, the value of x is 10
Rectangle WXYZ has vertices located at W(−6, 4), X(−6,−1), Y(2,−1), and Z(2, 4) on a coordinate plane. It is translated 4 units right and 2 units down to produce rectangle W'X'Y'Z'. What is the location of the vertices of the transformed rectangle?
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
Rectangle WXYZ
W(−6, 4)
X(−6,−1)
Y(2,−1)
Z(2, 4)
Step 02:
Translated
4 units right ===> x + 4
2 units down ===> y - 2
W' (−6+4, 4 -2) = W' (-2, 2)
X' (−6+4,−1 - 2) = X' (-2,-3)
Y' (2+4,−1-2) = Y' (6,-3)
Z' (2+4, 4-2) = Z' (6, 2)
The answer is:
W' (-2, 2)
X' (-2,-3)
Y' (6,-3)
Z' (6, 2)
(3,-8),(-2,5) write an equation for the line in point slope form .Then rewrite the equation in slope intercept form
The equation for the line in point-slope form is:
[tex]y-y_1=m(x-x_1)[/tex]Where m is the slope and (x1, y1) is a point of the line. If we have two points (x1,y1) and (x2, y2), the slope is equal to:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]So, replacing (3, -8) and (-2, 5), we get that the slope and the equation of the line are:
[tex]m=\frac{5-(-8)}{-2-3}=\frac{5+8}{-5}=\frac{-13}{5}[/tex][tex]\begin{gathered} y-(-8)=\frac{-13}{5}(x-3) \\ y+8=-\frac{13}{5}(x-3) \end{gathered}[/tex]Therefore, the equation in slope-intercept form is calculated as:
[tex]\begin{gathered} y+8=-\frac{13}{5}x-\frac{13}{5}\cdot(-3) \\ y+8=-\frac{13}{5}x+\frac{39}{5} \\ y=-\frac{13}{5}x+\frac{39}{5}-8 \\ y=-\frac{13}{5}x-\frac{1}{5} \end{gathered}[/tex]Answer: Point-slope form:
[tex]y+8=-\frac{13}{5}(x-3)[/tex]slope-intercept form:
[tex]y=-\frac{13}{5}x-\frac{1}{5}[/tex]Hi I need help with question 3 :) . Directions: For each real world situation, write and solve a system of equations . Give the solution as either an ordered pair or list what each variable is worth . Then explain what the solution means in terms of the situation
3.
We know that Hobby Land sells art supplies two different ways.
We can represent the situation with a system of equations
[tex]\begin{cases}x+y=139\ldots(1) \\ 4x+7y=781\ldots(2)\end{cases}[/tex]Where x is the cost of one easel and y represents the cost of one paint set.
Now, we must solve the system of equations.
We can multiply equation (1) by -4
[tex]\begin{gathered} -4(x+y)=-4(139) \\ -4x-4y=-556\ldots(3) \end{gathered}[/tex]Then, we can add (3) + (2)
[tex]\begin{gathered} -4x-4y=-556 \\ 4x+7y=781 \\ -------------- \\ 3y=225 \end{gathered}[/tex]Now, we can solve the equation for y
[tex]\begin{gathered} 3y=225 \\ y=\frac{225}{3}=75 \end{gathered}[/tex]Finally, to find x we can replace the value of y in the equation (1)
[tex]\begin{gathered} x+75=139 \\ x=139-75=64 \end{gathered}[/tex]So, the cost of one easel is $64.
Solution as either an ordered pair:
- (64, 75).
what is the mean of 36,38,39,28,34
We are to find the mean of
[tex]36,\text{ 38, 39, 28, 34}[/tex]Finding mean
[tex]\begin{gathered} M\text{ean = }\frac{36\text{ + 38 + 39 + 28 + 34 }}{5} \\ Mean\text{ = }\frac{175}{5} \\ M\text{ean = 35} \end{gathered}[/tex]Therefore,
mean = 35
The drama club is selling tickets to their play to raise money foe the show's expenses. They are selling both adult tickets and student tickets. The auditorium can hold no more than 109 people. Write an inequality that could represent the possible values for the number of student tickets sold,s, and the number of adult tickets sold,a, that would satisfy the constraint
Adult (A)
student (S)
Total people= 109
the maximum number of tickets is 109, in this case is possible 109.
than means
A + S ≤ 109
or
109 ≥ A + S
1.In hockey, a player gets credited with a "point" in their statistics when they get an assist or goal.The table shows the number of assists and number of points for 15 hockey players after a season.assistspoints222816184672292691322allo San818131750712173427581834Make a scatter plot of this data. Make sure to scale and label the axes
From the information given, the number of points gotten depends on the number of assists. this means that the independent variable, x which would be on the horizontal axis is the number of assists and the dependent variable, y which would be on the vertical axis is the number of points. We would plot these values on the scatter plot. the plot is shown below
The number of points is on the vertical axis.
The number of assists is on the horizontal axis
A rectangle is graphed on a coordinate plane and then reflected across the y-axis. If a vertex of the rectangle was at (x, y), which ordered pair represents the corresponding vertex of the new rectangle after the transformation? F (y, x) G (-x, -y) H (-x, y) J (x, y)
Let's say that the vertex is the following red point:
Then, its reflection across y-axis would be the blue point:
If we observe the coordinates, we will have that:
(5, 3) is transformed into (-5, 3). This is going to happen no matter the coordinate:
help meeeeeeeeee pleaseee !!!!!
If the average daily sales price of the toy is $6.50, then 2750 toys will have been sold overall.
Variables and functionsIn the case of a function from one set to the other, each element of X receives exactly one element of Y. The function's domain and codomain are respectively referred to as the sets X and Y as a whole.
While the dependent values are the codomain, the independent values are known as the domain.
Given that y = 6000 - 500x is the function that depicts the price-sales relationship for the quantity of toys
The total number of toys sold if the toy sells for $6.50 per day is: y = 6000 - 500 (6.50) y = 6000 - 3250 y = 2750 toys
The total quantity of toys sold is provided above.
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There are 6000 students at Mountain High School, and 1/4 of these students are seniors. If 2/3 of the seniors are in favor of the school forming a debate team and 1/5 of the remaining students (not seniors) are also in favor of forming a debate team how many students do not favor this idea?
hello
tp solve this question, let's get the data out
we have a total of 6000 students. 1/4 of the students are seniors, let's find the numbers of seniors in the school
the number of senior students are
[tex]\frac{1}{4}\times6000=1500[/tex]we have 1500 seniors in the school.
we can find the seniors in support of a debate team by multiplying 2/3 by 1500
[tex]\frac{2}{3}\times1500=1000[/tex]now we know that 1000 students are in support of the debate team. let's subtract the numbers of students in support of debate team from numbers of seniors in the schoolto giveus the numbers of seniors that are not in support of debate team.
[tex]1500-1000=500[/tex]500 seniors from the school are not in support of a debate team.
Also note that 1/5 of the remaining students are not in support of the debate team.
which would be
[tex]\begin{gathered} 6000-1500=4500 \\ \frac{1}{5}\times4500=900 \end{gathered}[/tex]now, we can add the numbers of seniors that are not in support of a debate team plus number of remaining students not in support of a debate team
[tex]500+900=1400[/tex]from the calculationabove, a total of 1400 students are not in support of the idea
Consider the following equation find the X- and y- Intercepts, if possible
Answer:
x-intercept: (-1/2, 0)
y-intercept: (0, 1)
Explanation:
The x-intercept is the point where the graph crosses the x-axis, so to find the x-intercept, we need to replace y = 0 on the given equation and solve for x
y - 2x = 1
0 - 2x = 1
-2x = 1
-2x/(-2) = 1/(-2)
x = -1/2
Then, the x-intercept is (-1/2, 0)
The y-intercept can be calculated replacing x = 0 and solving for y, so
y - 2x = 1
y - 2(0) = 1
y - 0 = 1
y = 1
Then, the y-intercept is (0, 1)
Therefore, the answers are
x-intercept: (-1/2, 0)
y-intercept: (0, 1)
Determine the perimeter of this shape. Use 3.14 for pi. the numbers are 12m and 15 m
We are asked to find the perimeter of the figure. To do that we will add the perimeters of the semi-circle and the rectangle.
To determine the perimeter of the semi-circle we will use the following formula:
[tex]P_{c\text{ }}=\frac{\pi D}{2}[/tex]The diameter is 12 m. Replacing in the formula we get:
[tex]P_c=\frac{\pi(12m)}{2}[/tex]Solving the operations:
[tex]P_c=\frac{3.14(12)}{2}=6.28m[/tex]Now we will find the perimeter of the rectangle by adding the length of all of its sides:
[tex]P_R=15m+12m+15m=42m[/tex]Now, the perimeter of the figure is the sum of the perimeters we found:
[tex]\begin{gathered} P=P_c+P_R \\ \end{gathered}[/tex]Replacing:
[tex]P=6.28m+42m=48.28m[/tex]Therefore, the perimeter of the figure is 48.28m
if the author sells x Books per day his profit will be : J(X)= (-0.001x^2)+3x-1800Find the max profit per dayFind the amount of books the author must sell for the most profit
The given function in a quadratic function in standard form where
a = -0.001, b = 3, and c = -1800
It is a parabola that is facing downwards, therefore, the vertex of this parabola, (x,y) is the maximum of the function where
x is the amount of books that the author must sell for the most profit, and
y is the max profit per day.
We can find the vertex using
[tex]x=\frac{-b}{2a}[/tex]Substitute the following values, and we get
[tex]\begin{gathered} x=\frac{-b}{2a} \\ x=\frac{-3}{2(-0.001)} \\ x=\frac{-3}{-0.002} \\ x=1500 \end{gathered}[/tex]Now that we have x, plug it in the original function to solve for y
[tex]\begin{gathered} J(x)=\mleft(-0.001x^2\mright)+3x-1800 \\ J(1500)=-0.001(1500)^2_{}+3(1500)-1800 \\ J(1500)=-2250+4500-1800 \\ J(1500)=450 \end{gathered}[/tex]We have determine that the vertex of the function is at (1500,450). We can now conclude that
The max profit per day is $450.
The amount of of books the author must sell for the most profit is 1500 books.
Bert opened a savings account 4 years ago the account earns 13%interest compounded monthly if the current balance is 1,000.00 how much did he deposit initially
To answer this question we need to remember the formula:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where r is the interest rate, n is the number of times it is compounded in a given time t.
In this case we know that A=1,000, r=0.13, n=12 and t=13. Plugging this values in the formula and solving for P we have:
[tex]\begin{gathered} 1000=P(1+\frac{0.13}{12})^{12\cdot4} \\ P=\frac{1000}{(1+\frac{0.13}{12})^{12\cdot4}} \\ P=596.19 \end{gathered}[/tex]Therefore, the initial deposit was $596.19
What makes a function a function?
In a relationship between two variables x and y, the data set is a function, if every element of the domain corresponds to exactly one element of the range
that means
one element of x corresponds to exactly one element of y
In any function, there is an input value (independent variable or x variable) and there is an output value (dependent variable or y variable)
What makes a function a function? ------> one element of the input (variable x) corresponds to exactly one element of the output (variable y)
What is 7050.387 rounded to the nearest ten
Hello!
When we round something to the nearest tenth, it means that the number must have just one decimal place.
Let's analyze this number and round it:
7050.387
How can we write 387 as one number?
Well, it's very close to 400, and we can "hide" these zeros.
Let's try it:
[tex]7050.387\cong7050.400\cong7050.4\cancel{00}[/tex]Answer:7050.4.
Lines from Point/Slope (Diagonal Only) Nov 23, 9:40:49 AM What is the equation of the line that passes through the point (-4, -2) and has a slope of - Answer: Submit Answer attempt 2 out of 2
The point-slope form of a line is:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line, and m is the slope
Replacing with point (-4, -2), we get:
y - (-2) = m(x - (-4))
y + 2 = m(x + 4)
If the slope is, for example, 3, the equation would be:
y + 2 = 3(x + 4)
If the slope is -2/5, the equation would be:
y + 2 = -2/5(x + 4)
Brainliest and 20 points please solve
Answer:
part a: x = 5
part b: no
Step-by-step explanation:
part a : 8x + 3 = 9x - 2, subtract 8x from both sides which leaves you with 1x or just x. add 2 to both sides which gives you 5. 5 is equal to 1x.
part b: a complementary angle is 2 angles whos sum equals 90 degrees. m<ABC = 43 & m<DBE = 43 & they both equal 86 not 90.
Answer/Step-by-step explanation:
A C
\ (8x + 3) /
\ /
\ /
\ /
B
/ \
/ \
/ \
/ (9x - 2) \
D E
A. Solve for x.
m∠ABC = m∠DBE
(8x + 3) = (9x - 2)
8x + 3 = 9x - 2
-9x -9x
------------------------
-x + 3 = -2
-3 -3
--------------------
-x = -5
÷-1 ÷-1
----------------
x = 5
B. Are vertical angles also complementary angles?
No, vertical angles are angles that are congruent to each other or in other words, equal. In the equation above (8x + 3) = (9x - 2). If I were to plug 5 into the equation I would get
(8(5) + 3) = (9(5) - 2)
(40 + 3) = (45 - 2)
43 = 43
Complementary angles equal to 90°. It wouldn't make sense to add these numbers together because I would end up with a fraction if I set the equation equal to 90°
I hope this helps!
Ashley pounds 98 pounds one year ago .If she weight 112 pounds what is the percent increase in her weight ?
Answer:
The increase to the nearest percent is 14%
Step-by-step explanation:
[tex]\frac{112 - 98}{98}[/tex] The percent of increase is the weight change over the original amount
.14285714285 To change a decimal to a percent, move the decimal two places to the right.
Rounded to the nearest percent is
14%
The length of the longest slide is what inches the other two sides will each be what inches in length?
We know that the rod from which we made the triangle is 13 in long, this means that the perimeter of the triangle. from the diagram given we notice that the perimeter is:
[tex]x+(x-1)+(x-1)[/tex]equating this to 13 and solving for x we have:
[tex]\begin{gathered} x+(x-1)+(x-1)=13 \\ 3x-2=13 \\ 3x=13+2 \\ 3x=15 \\ x=\frac{15}{3} \\ x=5 \end{gathered}[/tex]Hence, the value of x=5 which means that the longest side measure 5 inches. To determine the length of the other sides we notice that they are given by x-1, which means that their length is 5-1=4 inches,
Therefore, the length of the longest side is 5 inches. The other two sides will each be 4 inches in length.
Identify the algebraic expression for the given word phrase.
6 times the sum of r and 9
A. 6 + r + 9
B. 6 (r + 9)
C. r (6 + 9)
D. 6r + 9
b because 6 times the sum of r and 9 means 6(r+9)