In the diagram below, is an altitude of DEF. What is the length of ? If necessary, round your answer to two decimal places.
Answers
Right triangles EGD and FGE are similar:
(∠G =90, ∠F=∠EDG - having their sides respectively perpendicular)
Then we can write:
EG/FG = GD/GE
7/4 = GD/7 , by cross multiplication→ 7² = 4.GD→ 49 = 4.GD and GD=12.5
2nd Method:
The altitude drawn from the vertex of the right angle of a right triangle to its hypotenuse is the geometric mean between the measures of the two segments of the hypotenuse:
Then EG² = DG x GF
7² = 4 x GD and GD = 49/4 = 12.5
Related Questions
Solve the equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located. x2 + 4x + 3 = 0
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How do I do this someone please explain I need help
Answers
now, she pays in advertising 145 bucks... and for cleaning products, she spends 3 bucks for each washed car... ok.. .so if she washes say "a" automobiles, then she spends 3*a or 3a, ok.... so, her costs for the washing cars business is 145 for ads plus 3a, or 145 + 3a is her Cost.
now, Profit is the surplus amount after you remove the cost expenses, and can only happen if the Revenue is higher or greater than the Cost.
Revenue > Cost
15a > 145 + 3a
when will she turn a profit?
[tex]\bf 15a \ \textgreater \ 145 + 3a\implies 15a - 3a\ \textgreater \ 145\implies 12a \ \textgreater \ 145 \\\\\\ a\ \textgreater \ \cfrac{145}{12}\implies a\ \textgreater \ 12\frac{1}{12}[/tex]
she will turn a profit after washing 12 cars and 1/12 of a car, maybe just the windshield =).... anyhow..... namely, the revenue then is greater than the cost after that, or one can say, after the 13th car washed.
In which of the following quadrilaterals are consecutive angles always congruent? Check all that apply.
Answers
Consecutive angles are next to each other. squares and rectangles are the only to that has angles with the same values that are next to each other
Answer:
Rectangle and Square.
Step-by-step explanation:
To know if the angles of a quadrilateral is congruent you must overlap these angles one over the other, if all elements of the angles coincide, the angles are congruent; if the elements do not match, the angles are not congruent. In quadrilateral rectangle and square consecutive angles are always congruent.
In other words, two or more angles are said congruent if and only if they have the same measurement.
Need help with math problem
Multiply
(3x – 7)(3x – 5)
A.
9x 2 + 6x + 35
B.
9x 2 + 36x + 35
C.
9x 2 – 36x – 35
D.
9x 2 – 36x + 35
Answers
1 step: 3x term
3x*3x - 3x*5 the minus comes as you multiply by -2
2 step: -7 term
-7*3x + 7*5 the second plus comes from -*-=+
add these together
3x*3x-3x*5-7*3x+7*5 and do the multiplications:
9x^2 -15x-21x+35=9x^2-36x+35
Explain how you would use trig ratios to find the height of the tree if you know you are standing 30 feet from the base of the tree when you measure the 37-degree angle.
Answers
make sure your calculator is in Degree mode.
From use of trigonometric ratios, it is seen that the height of the tree is; 22.61 feet
How to work with trigonometric ratios?We are told that you are standing 30 ft from the base of a tree.
Now, the distance from where you are standing to the top of the tree will be the hypotenuse of the triangle formed by you and the tree.
Thus, if the height of the tree is h and the angle the hypotenuse makes with the 30 ft base is 37°, then we have;
h/30 = tan 37
h = = 30 * tan 37
h = 22.61 ft
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in how many ways can a judge award first, second, and third place in a contest with 10 entries
Answers
n!/(n-k)!, where n=total choices available, k=number of choices made.
10!/(10-3)!
10!/7!
720
720. just multiply 10 9 and 8 because first, second, and third, that is means three and that's how many numbers you multiply from 10,so it equals 720.
hope this helps
cheers!
How much dirt is there in a hole 3 feet deep, 6 ft long and 4 ft wide?
Answers
the volume of the hole would be 3 * 6 * 4 =72 cubic feet.
However, since it is a hole, there would be no dirt in it.
Factor the expression.
4r^2 – 64
1)(4r + 5)(r – 16)
2)4(r – 4)(r – 4)
3)(4r – 5)(r + 16)
4)4(r + 4)(r – 4)
Answers
4(r^2-16)
4(r+4)(r-4)
First factor out the gcf. Because (r^2-16) has perfect squares, you can factor it out one more time.
Final answer: D
First, let's write the problem,
[tex]4r^2-64[/tex]
Factor out the common term, which is 4,
[tex]=4\left(r^2-16\right)[/tex]
Then, let's factor this part: [tex]r^2-16[/tex]
We are going to factor it using the difference of squares rule.
[tex]=\left(r+4\right)\left(r-4\right)[/tex]
Our final factored answer would be,
[tex]=4\left(r+4\right)\left(r-4\right)[/tex]
Thanks!
-TetraFish
Harry Hoodeen made $24,567.00 net pay last year. His monthly expenses averaged $1,980.00. How much was left over for savings for the year?
Answers
24,567 - 23760
807
His left over savings was $807.
The average wind speeds for one year at 44 climatic data centers around the United States are as follows:
9.0, 6.9, 9.1, 9.2, 10.2, 12.5, 12.0, 11.2, 12.9, 10.3, 10.6, 10.9, 8.7, 10.3, 10.6, 10.9, 8.7, 10.3, 11.0, 7.7, 11.4, 7.9, 9.6, 8.0, 10.7, 9.3, 7.9, 6.2, 8.3, 8.9, 9.3, 11.6, 10.6, 9.0, 8.2, 9.4, 10.6, 9.5, 6.3, 9.1, 7.9, 9.7, 8.8, 6.9, 8.7, 9.0, 8.9, 9.3
a) Make a stem plot of the average wind speeds data. The frequency in the stem for 9 to 9.9 is?
b) The first quartile for the wind speed data set is?
Answers
There are a total of 48 data
Question a:
The frequency in the stem for 9 to 9.9 is 13 data
Question b:
The location of the first quartile is given by [tex] \frac{n+1}{4} [/tex], where 'n' is the number of data
We have n = 48
Location of the first quartile is at [tex] \frac{48+1}{4}= \frac{49}{4}= 12.25[/tex] rounded down to 12
The value of the lower quartile is on the [tex] 12^{th} [/tex] on the diagram which is 8.7
What is the inverse of f(x)=70x^3/4 ?
Answers
x=(y/70)^(4/3)
The inverse of the function [tex]f(x) = 70x^{(3/4)[/tex] is [tex]f^{(-1)}(x) = (x/70)^{(4/3)[/tex].
Explanation:The inverse of the function [tex]f(x) = 70x^{(3/4)}[/tex] can be found by interchanging the roles of x and y and solving for y. The goal is to isolate y on one side of the equation.
Step 1: Replace f(x) with y: [tex]y = 70x^{(3/4)}[/tex]
Step 2: Swap x and y: [tex]x = 70y^{(3/4)}[/tex]
Step 3: Solve for y: Divide both sides of the equation by 70 and raise both sides to the power of 4/3 to undo the exponent: [tex]y = (x/70)^{(4/3)}[/tex]
Therefore, the inverse of [tex]f(x) = 70x^{(3/4)}[/tex] is [tex]f^{(-1)}(x) = (x/70)^{(4/3)}[/tex].
WILL GIVE A BRAINLIEST PLEASE HELP!!!
Use the formula below to find the 6th term in the geometric sequence.
a(n)=(5)x(3/2)n-1
A.
5
B.
15/2
C.
1,215/32
D.
3,645/64
Answers
In the formula given a₁ = 5, r = 3/2 and n = 6 (we have to find the 6th term value).
a₆ = 5.(3/2)⁶⁻¹ = 5.(3/2)⁵ = 1215/32 (answer C)
1. Given f(x)=3x+8f(x)=3x+8 and g(x)=6x+6g(x)=6x+6 then what is (f+g)(−1))(f+g)(−1)) ?
2. Given f(x)=6x+4f(x)=6x+4 and g(x)=3x+7g(x)=3x+7 then what is (f−g)(1)) ?
Answers
In a survey, the planning value for the population proportion is p*=.35. how large a sample should be taken to provide a 95% confidence interval with a margin of error of .05 (to the nearest whole number)?
Answers
p* = 0.35, the populatin proportion.
Sp = 0.05, the margin of error
Let n = the size of the sample.
Because the standard error is 0.05, therefore
[tex] \sqrt{ \frac{p(1-p)}{n} } =0.05[/tex]
[tex] \sqrt{ \frac{0.35(1-0.35)}{n} } =0.05[/tex]
[tex] \frac{0.2275}{n} =0.05^{2} =0.0025[/tex]
n = 0.2275/0.0025 = 91
Answer: The sample size is 91.
the sum of 3 numbers is 26. the second number is twice the first and the third number is 6 more than the second. find the number
Answers
Answer:
the numbers are 4, 8, 14
Step-by-step explanation:
If we subtract 6 from the third number and from the total, we find that we now have 5 times the first number for a total of 20.
The first number is 4.
The second number is 2×4 = 8.
The third number is 8 + 6 = 14.
Quadrilateral ABCD is a parallelogram with diagonals that intersect at point E. If /,/, /, and /, solve for x.
A.
x = 2
B.
x = 4
C.
x = 6
D.
x = 8
Answers
What is the slope of the line below
Answers
The formula for slope can be found by finding the difference in y between two values divided by the difference in x between the same two values. In this case, you would subtract 4 from 8 and 2 from 4, to get 4/2, or 2. The slope is represented by the variable m, so m = 2.
List all your possibility of outcomes (there are 36 outcomes) if you roll a dice containing numbers 1-6 two times. Determine the probability of each outcome.
Answers
The first coordinates of each pair represent the 1.roll, and the second coordinates the 2nd, roll.
All the possible outcomes are {(1, 1), (1, 2).... (6, 5), (6, 6)}, a total of 36, as can be seen in the table.
Each outcome has a chance of 1 out 36 total possible outcomes of occurring.
So the probability is 1/36=0.02778
1. What is 3/8x < -6 or 5x>2 solved and graphed?
2. What is 2<10 -4d< 6 solved and graphed?
I appreciate your help!
Answers
[tex]3x\ \textless \ -48[/tex] and divide to get x<-16. Now the second one, just divide both sides by 5 to get
[tex]x\ \textgreater \ \frac{2}{5} [/tex]
On a single number line, make 0 your center, put -16 where it belongs in reference to the 0 and put 2/5 where it belongs in reference to the 0. The numbers to the left of -16 are those that are less than -16, and the circle above the -16 is an open one, not including the -16. The numbers to the right of 2/5 are those numbers that are greater than 2/5, so put an open circle above the 2/5 and go to the right with that line. And you can see that you have a big open space between the -16 and the 2/5 where the solution set is not the same at all. For b, solve this one simultaneously. It is a conjunction, an "and", where there will be a solution set that is shared by both values for x. Solve it like this...start by subtracting 10 from both sides:
-8< -4d < -4 Now, when you divide by the negative 4, you have to change the signs to greater than: 2 > d > 1. That means, in words, that "d is less than 2 and greater than 1". On a single number line you will have open circles above the 1 and the 2 and the numbers in between 1 and 2 are shared solutions.
HELP might fail class
Answers
The password pattern is <letter><letter><digit><digit><digit><digit>. Use the Multiplication Principle:
25 x 25 x 9 x 9 x 9 x 9 = 4,100,625
Directions: Describe the transformation. (x,y) -> (5x,5y)
Answers
The transformation (x, y) -> (5x, 5y) is a scaling transformation that dilates a point by a factor of 5 in both the x and y directions, making the entire figure five times larger while preserving its shape.
Explanation:The transformation described by (x, y) -> (5x, 5y) is a scaling transformation or dilation in both the x and y directions by a factor of 5. What this means is that any point on the plane, when subjected to this transformation, will move five times further away from the origin along both axes. For example, if you begin with the point (1, 1), applying this transformation will result in the point (5, 5). This dilation affects all points equally, meaning that the relative distances between points are preserved, but the entire figure is made larger by a factor of 5. Therefore, if you have a figure with dimensions of length and width, after the transformation, both dimensions will be increased by five times their original measure.
Final answer:
The transformation (x, y) -> (5x, 5y) represents a dilation, enlarging a figure by a factor of 5 along both the x-axis and y-axis, which alters size but not shape.
Explanation:
The transformation described by the rule (x, y) -> (5x, 5y) is a geometric transformation known as a dilation or scaling. This type of transformation alters the size of a figure without changing its shape. Specifically, the coordinates of each point in the figure are multiplied by 5, which means that the figure is enlarged by a factor of 5 in both the x-axis (east-west direction) and the y-axis (north-south direction). If, for example, we apply this transformation to a point (1, 2), the resulting coordinates will be (5, 10), and similarly, applying it to (3, 7) would yield (15, 35). This illustrates the dependence of y on x as each x-coordinate and y-coordinate are scaled by the same factor, maintaining the shape but increasing the size.
Need help geometry ^^^
Answers
How can you tell whether a rational expression is in simplest form? Include an example with your explanation.
Answers
for example 4/6 is not simplest form because 2 is a factor of 4 and 6
In its simplest form 4/6 is 2/3.
Rational numbers are numbers that are written as a ratio of two integers.
Let a and b be integers, hence a rational expression can be expressed as a/bIn order to tell whether a rational expression is in its simplest form, we need to ensure no integer can go in both the numerator and the denominator.
For instance, given the rational number 10/15, the simplest form of the rational number will be expressed as (5*2)/(5*3) = 2/3
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What is i^16 simplified
Answers
and fairly sure you know how much that is.
Simplify.
Square root of 121m^8n^4
A. 11mn
B. 11m^2n^2
C. 11m^4n^2
Answers
Answer:
B
Step-by-step explanation:
no
Sandy can assemble a particular type of light fixture in 3/8 hour. it takes her 2/3 hour to hang the fixture and another 1/6 hour to wire the fixture once it is hung. how many fixtures could sandy install in 29 hours?
Answers
Sandy can install a maximum of 24 fixtures in 29 hours.
Explanation:To calculate the number of fixtures Sandy can install in 29 hours, we need to determine the amount of time it takes for Sandy to complete one installation process (excluding assembly time).
Sandy takes 2/3 hour to hang the fixture and another 1/6 hour to wire it, totaling
2/3 + 1/6 = 7/6 hour.
Therefore, Sandy takes 7/6 hour per fixture.
Next, we can calculate the number of fixtures by dividing the total time available (29 hours) by the time it takes for one installation process.
Number of fixtures = Total time available / Time per fixture
Number of fixtures = 29 / (7/6) = 29 * (6/7) = 174/7 = 24.86
Since we can't have a fraction of a fixture, Sandy can install a maximum of 24 fixtures in 29 hours.
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In 1980, the United States' national debt exceeded $9 billion dollars. Express the exact dollar amount in scientific notation.
Answers
Helpppppppppp me!!!!!!!!!
Answers
A) w/9=6
w=9*6
w=54
B) 5q=15
q=15/5
q=3
C)2s-3s=20
-1s=20
s=20/-1 = -20
s=-20
D)4-a=-12
a= 4+12 = 16
a=16
One side of triangle is half the longest side. the third side is 7 feet less than the longest side. the perimeter is 43. find all three sides.
Answers
2y = x
If z is 7 less than x then that equation would look like
X = z +7
The perimeter is the sum of all the sides
P = x + y + z = 43
Now by using all three equations, we can find the value of each variable by plugging into the equations.
First, let's start by changing the first two equations to compare the values of z and y to x.
Y = x/2
Z = x - 7
Now we can use these new equations to plug into the perimeter equation and find the value of x.
43 = x + y + z Plug in your variables
43 = x + x/2 + x-7 Add 7 to both sides
50 = x + x/2 + x Multiply both sides by 2 to get rid of the fraction
100 = 2x + x + 2x Add all your x's together
100 = 5x Divide both sides by 5
X = 20
No we can use the value of x to find the values of y and z by plugging into the two equations before.
2y = 20
Y = 10
Z = 20 - 7
Z = 13
Therefore, the lengths of the sides are 20, 10, and 13
HELP ME PLEASE!
Peter walks 30 feet away from his house and places a mirror on the ground. He backs 6 feet away from the mirror so that he can see the tip of the roof. Peter's eyes are 5 feet above the ground. Peter and the house are both perpendicular to the ground. The angles between the top of the house, the mirror, and the ground and between Peter's eyes, the mirror, and the ground are congruent as shown in the image below:
Image depicts a mirror on the ground between a person and a house. The mirror is 6 feet away from the person and 30 feet away from the house.
What is the height of the house?
Answers
By setting up a proportion based on the similar triangles formed by Peter's line of sight and the analogous line from the top of the house to the mirror, we find that the house is 25 feet tall.
According to the Law of Reflection and the information provided, we have two similar triangles: one formed by Peter's eyes, the mirror, and the point on the ground directly below his eyes, and the other formed by the top of the house, the mirror, and the point on the ground directly below the top of the house.
The first triangle has a height of 5 feet (Peter's eye level) and a base of 6 feet (the distance from Peter to the mirror). The second triangle's height is what we are trying to find (height of the house), and its base is 30 feet (distance from the house to the mirror).
Because the triangles are similar, the ratios of their corresponding sides are equal. So, we can set up the following proportion:
Height of Peter's eyes / Distance to mirror = Height of the house / Distance to mirror from house
5 feet / 6 feet = Height of the house / 30 feet
Now, cross-multiply to solve for the height of the house:
5 feet * 30 feet = Height of the house * 6 feet
Height of the house = (5 * 30) / 6
Height of the house = 150 / 6
Height of the house = 25 feet
Therefore, the height of the house is 25 feet.