The longest possible altitude of the third altitude (if it is a positive integer) is 83.
According to statement
Let h is the length of third altitude
Let a, b, and c be the sides corresponding to the altitudes of length 12, 14, and h.
From Area of triangle
A = 1/2*B*H
Substitute the values in it
A = 1/2*a*12
a = 2A / 12 -(1)
Then
A = 1/2*b*14
b = 2A / 14 -(2)
Then
A = 1/2*c*h
c = 2A / h -(3)
Now, we will use the triangle inequalities:
a < b+c2A/12 < 2A/14 + 2A/h
Solve it and get
h<84
b < a+c2A/14 < 2A/12 + 2A/h
Solve it and get
h > -84
c < a+b2A/h < 2A/12 + 2A/14
Solve it and get
h > 6.46
From all the three inequalities we get:
6.46<h<84
So, the longest possible altitude of the third altitude (if it is a positive integer) is 83.
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What numbers go in the sqaures?
On the first two pairs you need to write 3 and 4, and 6 and 2.
On the second page we have:
1) 4
2) 2 and 7
3) 1
4) 1 and 3
5) 3.
What numbers go in the squares?
a) Here we just need to use scientific notation.
For the first case, the numbers that go in the exponent boxes are the same ones that go in the example, which are 4 in the first one and 2 on the second one.
Then, if we want the difference to be 29,400, then we can use 3 on the first box and 6 on the second. OR, because this is an absolute value, we can just invert those.
This is:
6 and 2 on the first two squares, and 3 and 4 on the second two squares.
b) Here we want to make perfect squares.
For example, on the first case we have:
x*2*2
We need to find the value of x such that this is a perfect square. Notice that we can rewrite this as:
x*2*2 = x*4
Then it only is a perfect square if x = 4.
For the second case:
14*x*y
This is only a perfect square if x*y = 14
Then we can use x = 2 and y = 7.
With similar reasoning, on the next box we have:
2*8*x
2*8 = 16, is already a perfect square, so x = 1.
The next one is:
x*3*y
Here we can define x = 3 and y = 1, so we get a perfect square.
Finally:
3*x
Here the only possible value of x is 3.
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The ratio of Jessica’s stickers to Rod’s stickers is 7:4. Jessica has 21 stickers. How many
stickers does Rod have?
Answer:
12stickers
Step-by-step explanation:
that's all I could do.have a nice day.hope it helps.
Triangles A B C and N M L are shown. Angles B A C and L N M are right angles.
What additional information could be used to prove that △ABC ~ △NML? Check all that apply.
∠B ≅ ∠M
△ABC is a right triangle.
△ABC was rotated and dilated by a scale factor between 0 and 1.
△ABC was translated right and down.
∠C ≅ ∠L
The additional information needed to prove both triangles are similar are:
A. ∠B ≅ ∠M
C. △ABC was rotated and dilated by a scale factor between 0 and 1
E. ∠C ≅ ∠L
What are Similar Triangles?When a triangle is rotated and dilated by a scale factor, the new triangle formed has the same shape but different size of the original triangle. However, all its corresponding angles remains congruent.
Thus, for triangles ABC and NML to be similar to each other, since we already known each have one congruent right angles, the additional information needed are:
A. ∠B ≅ ∠M
C. △ABC was rotated and dilated by a scale factor between 0 and 1
E. ∠C ≅ ∠L
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The mean GPA for 127 residents of the local apartment complex is 1.6. What is the best point estimate for the mean GPA for all residents of the local apartment complex
By the Central Limit Theorem, the best point estimate for the mean GPA for all residents of the local apartment complex is 1.7.
The Central Limit Theorem established that, for a normally distributed random variable X, with mean and standard deviation, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean and standard deviation ;
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this problem, we have that:
The sample of 112 residents has a mean GPA of 1.7.
By the Central Limit Theorem, the best point estimate for the mean GPA for all residents of the local apartment complex is 1.7.
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So please answer this please for 50 points so you can do what im doing.
Answer:
I think it's C
Step-by-step explanation:
Hope it helps
]Triangles H J K and L M N are congruent. Triangle H J K is rotated about point H to form triangle L N M. Triangle L M N is higher than triangle H J K.
Two rigid transformations are used to map ΔHJK to ΔLMN. The first is a translation of vertex H to vertex L. What is the second transformation?
a reflection across the line containing HK
a rotation about point H
a reflection across the line containing HJ
a rotation about point K
The second transformation is a rotation about point H.
What is a congruent triangle?It should be noted that a congruent triangle simply means when two triangles have the same sides and the same angles.
As two rigid transformations, to map ΔHJK to ΔLMN.
The first is a translation of vertex H to vertex L, and the second transformation is a rotation about point H.
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Answer:
B. a rotation about point H
Step-by-step explanation:
got it correct on my quiz
evalute the following integral.
Help me...step by step
Answer:
= ax + b ln x - c/x + C
Step-by-step explanation:
Recall:
integral a dx = ax + C
integral 1/x dx = ln x + C
integral x^(n) = [x^(n +1)]/(n + 1) + C
Also:
c = variable in this problem
C = constant you add when you integrate
Separate each term of the numerator and set it over the denominator.
integral (ax^2 + bx + c)/x^2 dx =
integral [(ax^2)/x^2 + (bx)/x^2 + c/x^2] dx
Simplify each term and separate into the sum of 3 integrals.
= integral (a dx) + integral (b/x dx) + integral (c/x^-2) dx
= ax + b ln x + (cx^-1)/(-1) + C
= ax + b ln x - c/x + C
The process of evaluating a decision in the face of uncertainty by quantifying the likelihood and magnitude of an undesirable outcome is known as _____. Group of answer choices risk analysis regression analysis data mining decision tree analysis
The process of evaluating a decision in the face of uncertainty by quantifying the likelihood and magnitude of an undesirable outcome is known as risk analysis
Risk analysis is define as the the process of identifying and analyzing potential issues that could negatively impact key business initiatives or projects. This process is done in order to help organizations avoid or mitigate those risks.
So, The process of evaluating a decision in the face of uncertainty by quantifying the likelihood and magnitude of an undesirable outcome is known as risk analysis
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Help please!
What’s the answer for graphing the piece wise function to get the right answer?
Answer:
-b
Step-by-step explanation:
The monthly income of Ram is Rs 40,000. If he paid Rs 8,000 as income tax. Find the rate of income tax.
Hello!
Rate of income tax = Tax paid / Monthly income
⇒ Rate = 8,000 / 40,000
⇒ Rate = 0.2
⇒ Rate = 20%
∴ The rate of income tax is 20%.
what is the first quartile of the set of data 14,28,33,42,53,81,97
The first quartile of the data set is 28.
Determining the first quartileFrom the question, we are to determine the first quartile of the given data set
The first quartile or lower quartile, (Q1), is the value under which 25% of data points are found when they are arranged in increasing order.
The given data set is
14,28,33,42,53,81,97
In the given data set, the first quartile is 28.
Hence, the first quartile of the data set is 28
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To prove that ΔAED ˜ ΔACB by SAS, Jose shows that StartFraction A E Over A C EndFraction = StartFraction A D Over A B EndFraction.
Triangle A E D is shown. Line segment B C is drawn from side A D to A E to form triangle A C B.
Jose also has to state that
The other equality which must be stated by Jose is that angles BAC and BAE are congruent and their measures are equal.
What other congruence statements must Jose state?It follows from the task content that Jose is trying to prove the congruence of both triangles by means of the Side-Angle-Side congruence theorem.
It therefore follows that since, Jose has identified that the ratio of corresponding sides are equal as indicated in the task content, the equality which Jose has to state is the angle congruence equality.
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Which congruence criteria cab be used directly from the information about triangles jhk ghl to prove hk and ghl
Triangle JHK and GHL are congruent based on the angle-angle-angle congruency theorem.
What are congruent triangles?Two triangles are said to be congruent if they have the same shape and angles. The ratio of their corresponding sides are also to be proportional.
Given triangle JHK and GHL are congruent based on the angle-angle-angle congruency theorem.
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-2x+9x^6+1-9x^2 how do you answer this question in descending order
Answer:
9x ^ 6 -9x ^ 2-2x + 1
Step-by-step explanation:
When dividing the polynomial using synthetic division, which of the following setup boxes would be used?
The setup boxes in the synthetic division are (b)
How to determine the setup boxes?The dividend is given as:
x^3 + 4x^2 + x - 6
The divisor is given as:
x - 2
Set the divisor to 0
x - 2 = 0
Solve for x
x = 2
Remove the variables in the dividend
1 + 4 + 1 - 6
Remove the arithmetic signs
1 4 1 - 6
So, the setup is:
2 | 1 4 1 - 6
Hence, the setup boxes are (b)
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Solving 8 problems per Minute, Fast Funn can finish his test in time. He was, however, working fast, solving 10 problems per minute. That is why he finished 6 minutes early. How many problems were on the text
The number of problems that were on the text was 240 problems.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Let x represent the total number of problems that were on the text, y represent the time to be spent, hence:
y = x/8
Also:
y - 6 = x/10
x/8 - 6 = x/10
x = 240
The number of problems that were on the text was 240 problems.
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If 3x + 2y = 1 and
2x + 7y = 3
How do you find x and y step by step?
Step-by-step explanation:
there are 2 main approaches (in their core they are the same, of course, but they look different) :
1. use one equation to express one variable by the second, and then use this in the second equation to solve for the remaining variable. with that you go back into the first equation and solve for the first variable.
2. multiply both equations by certain factors as needed, then add both results, so that there is one summary equation with only one variable, and then solve for it. then use that in one of the original equations and solve for the second variable.
using 1.
3x + 2y = 1
3x = 1 - 2y
x = (1 - 2y)/3
2x + 7y = 3
2(1 - 2y)/3 + 7y = 3
2(1 - 2y) + 21y = 9
2 - 4y + 21y = 9
17y = 7
y = 7/17
x = (1 - 2y)/3 = (1 - 2×7/17)/3 = (1 - 14/17)/3 =
= (17/17 - 14/17)/3 = 3/17 / 3 = 1/17
using 2.
multiply first equation by 2, the second by -3
6x + 4y = 2
-6x - 21y = -9
----------------------
0 -17y = -7
-17y = -7
17y = 7
y = 7/17
and so on (as under 1.).
Step-by-step explanation:
First, you can multiply the both equation by one of the coefficient of either X or Y as shown above.
Secondly, after doing that you can multiply one of the equations by the negative sign in order for one of the coefficient to cancel out.
From there you can find X
After getting X , you can put the answer you get into any equation of your choice. collect like terms and then you'll find Y.
Hope this helps. If you don't understand use the picture if the solving above for better explanation. Thanks
Please help ill give whoever answers the best the brainliest answer :)))
Answer:
Distance on the graph is representing the distance from Michelle's home. On her morning jog, Michelle ran to the end of her street, turned around and jogged at a slower pace back home.
A local electronics store offers a rewards card to each of its customers. The number of rewards points a customer earns varies directly with the amount of money, in dollars, that the customer spends at the store. After spending $60 at the electronics store, Jay earned 15 points. If Jay spends 40 at the store, how many points will he earn?
If Jay spends 40 at the store, the number of points he will earn is; 10 points
How to solve direct variation?Let the number of rewards points a customer earns be y
Let the amount of money, in dollars, that the customer spends at the store be x.
Since the number of rewards points a customer earns varies directly with the amount of money, in dollars, that the customer spends at the store, then we can say that;
y ∝ x
Thus;
y = kx
where k is the constant of proportionality.
We are given x = 15 when y = $60. Thus;
60 = 15k
k = 60/15
k = 4
If Jay spends $40, it means the number of points will be;
40 = 4x
40/4 = x
x = 10 points.
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Solve each triangle - find any missing side and angle measures. Round answers to the nearest tenth.
The sides of the right-angle triangle will be 16 units and 20.30 units. And the missing angle will be 52°.
What is a right-angle triangle?It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.
The side AC will be
tan 38° = 12.5 / AC
AC = 15.999
AC ≈ 16 units
Then the side AB will be
AB² = 12.5² + 16²
AB = 20.30 units
We know that the angle sum is 180 degrees. Then we have
∠A + ∠B + ∠C = 180°
38° + ∠B + 90° = 180°
∠B = 52°
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use the distrubutive property to simply -9(n-4)
Answer:
The distrubutive property
-9(n-4)
=-9n+36
30 men can complete a job in 12 days if each man works 8 hours a day. if the job is to be completed with 24 men working at the same rate, how many hours must they work in a day
Answer:
15
Step-by-step explanation:
→ Write the ratio of men to days to hours
30 : 12 : 8
→ Write the new proportion
24 : x : 8
→ Find the multiple between 30 and 24
1.25
→ Multiply by 12
12 × 1.25 = 15
What is the solution to the system of equations {−2x+4y=1−4x+3y=12
The solution to the system of equation is ( -4.5 , -2)
What is a system of Equation ?A system of equation is a set of equations that have a common solution.
The set of equation given are
-2x +4y = 1
-4x +3y = 12
To find the solution , Elimination Method will be used
Multiplying equation 1 by 2 and then
Subtracting equation 1 by 2
-4x +8y = 2
-4x +3y = 12
+ - -
5y = -10
y = -2
Substituting this value to determine the value of x
-2x -8 = 1
-2x = 9
x = -4.5
Therefore the solution to the system of equation is ( -4.5 , -2)
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Point Q is the center of dilation. Rectangle L M N P is dilated to form rectangle L prime M prime N prime P prime. Side L M is 4 inches and side M N is 6 inches. The length of Q L is 12 and the length of L L prime is 42.
Sissy wants to enlarge a picture of a constellation so that she can put it on the wall in her daughter’s room. What will be the area of the enlarged picture on the wall?
24 in.2
108 in.2
224 in.2
486 in.2
The area of the enlarged picture on the wall is gotten as; D: 486 in²
How to use center of Dilation?The formula for Linear scale factor is;
L.S = Image distance/object distance
Thus, from the attached image, we can find the Linear scale factor as;
L.S = OL'/OL
L.S = 54/ 12
L.S = 9/2
Area scale factor is equal to the square of linear scale factor. Thus;
Area scale factor = (9/2)²
Area scale factor = 81/4
Now,
81/4 = Area of larger rectangle/Area of smaller rectangle
Area of the smaller rectangle = 4 ×6 = 24 in²
Thus;
Area of enlarged picture on wall = (81/4) × 24
Area of enlarged picture on wall = 486 in²
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Answer:
Step-by-step explanation:
its D
A student wrote the expression: 2(5x + 3) what are two expressions that are equivalent to the student's expression
Answer:
[tex]\frac{(20x+12)}{2}[/tex] and [tex]\sqrt{100x^2+36}[/tex]
Step-by-step explanation:
The expression 2(5x + 3) equals 10x + 6
One other way to get 10x + 6
[tex]\frac{(20x+12)}{2}[/tex]
finally, you could do:
[tex]\sqrt{100x^2+36}[/tex]
the question is on the image
by the way the 20cm is meant to be 15cm
Answer:
2.36 liters
Step-by-step explanation:
The volume Janet wants is 1/3 of 1/2 of the volume of a sphere with radius 15 cm. The formula for the volume of a sphere is given.
ApplicationThe water volume is ...
V = (1/3)(1/2)(4/3π)(15 cm)³ = 750π cm³ ≈ 2356 cm³
There are 1000 cm³ in 1 liter, so Janet needs about ...
2356 cm³/(1000 cm³/L) = 2.356 L
Janet should put about 2.36 liters of water in the fish tank.
Answer:
it is all I could.
Hope it helps
A 15 foot ladder is placed on the top of a wall. The distance from the bottom of the wall to the bottom of the ladder is 7 feet. Calculate the height of the wall.
The height of the wall from the question is 13.27ft
Pythagoras theoremThe theorem states that the square of the longest side is equal to the sum of square of other two sides.
From the given question
Hypotenuse (ladder length) = 15ft
Adjacent = 7feet
Required
Height of the wall H
According to the theorem
15² = 7² + H²
H² = 225 - 49
H² = 176
H = 13.27feet
Hence the height of the wall from the question is 13.27ft
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The point-slope form of the equation of the line that passes through (–4, –3) and (12, 1) is y – 1 = y minus 1 equals 1/4 left-parenthesis x minus 12 right-parenthesis.(x – 12). What is the standard form of the equation for this line?
The equation in point slope form is y-1 = 1/4(x - 12)
Equation of a lineThe formula for calculating the equation of a line is expressed as;
y = mx + b
m is the slope
b is the intercept
Slope = 1+3/12+4
Slope = 4/16
Slope = 1/4
For the intercept
1 = 1/4(12) + b
b = 1 - 3
b = -2
Hence the equation in point slope form is y-1 = 1/4(x - 12)
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The standard form is:
4y - x = -8
How to get the standard form of the line?We know that the point-slope equation of the line is:
y - 1 = (1/4)*(x - 12)
Expanding the right side, we get:
y - 1 = (1/4)*x - 3
Now we can move the term with x to the left side:
y - (1/4)*x = +1 - 3
y - (1/4)*x = -2
Now we can multiply both sides by 4:
4y - x = -8
This is the standard form of the linear equation.
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HELP PLS! I need this FAST!
30 points and BRAINLIEST!
Answer:
36
Step-by-step explanation:
MC : BC : MB = 1 : √3 : 2
MC : BC = 1 : √3
12 : BC = 1 : √3
BC = 12 : 1/√3
BC = 12 × √3/1
BC = 12 × √3
BC = 12√3
MC : MB = 1 : 2
12 : MB = 1/2
MB = 12 : 1/2
MB = 12 × 2/1
MB = 12 × 2
MB = 24
AB = 2BD
AB = 2CD√3
AB = 2(½BC)√3
AB = 2(½ × 12√3) √3
AB = 2 × 6√3 × √3
AB = 12 × √9
AB = 12 × 3
AB = 36
equation with a slope of -4 and goes through the point (-1,1)
[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]
What's the equation with a slope of -4 that goes through (-1,1)? find it
[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]
The equation used, here is [tex]\bf{y-y1=m(x-x1)}[/tex].
[tex]\bf{y-1=-4(x-(-1)}[/tex] | simplify after putting in the information given
[tex]\bf{y-1=-4(x+1)}[/tex]
[tex]\rule{300}{1.7}[/tex]
[tex]\bf{Result:}[/tex]
[tex]\bf{=y-1=-4(x+1)}[/tex]
[tex]\boxed{\bf{aesthetic\not101}}[/tex]