The length of one part of BC is approximately x = 4 units.
What is the median of the triangle?
In a triangle, a median is a line segment that joins a vertex to the midpoint of the opposite side. Each triangle has three medians, and they all intersect at a single point called the centroid.
Let ABC be the given triangle with AB = 5, AC = 7, and BC = 8. Let D be the midpoint of BC so that AD is a median of triangle ABC.
Since AD is a median, it divides BC into two equal parts. Let x be the length of one part of BC, so the other part has a length 8 - x.
Then, we have:
x + 8 - x = 8
Simplifying, we get:
8 = 8
This equation is true, so our assumption that x is one part of BC is correct.
Now, we can use the Pythagorean theorem to find x. Let E be the foot of the altitude from A to BC, so that AE is perpendicular to BC. Then, we have:
BE² + AE² = AB² (by the Pythagorean theorem)
CE² + AE² = AC² (by the Pythagorean theorem)
Since D is the midpoint of BC, we have:
BE = CE = BC/2 = 8/2 = 4
Therefore, the length of one part of BC is approximately x = 4 units.
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A vending machine randomly dispenses gumballs of three flavors: orange, grape, and cherry. If the machine currently contains 20 orange, 12 grape, and 7 cherry gumballs, what is the least number of gumballs the machine must dispense in order to ensure that three orange gumballs have been dispensed
Answer:
22
Step-by-step explanation:
Find the worst case scenario.
Worst case:
12 grape gumballs, 7 cherry gumballs, and 3 orange gumballs.
12 + 7 + 3 = 22
The answer is 22 gumballs.
Hope this helps :)
Have a great day!
How do you find the volume of cubes and rectangular prisms?
To find the volume of a cube or rectangular prism, multiply the length, width, and height of the shape. The formula is V = l × w × h, where V represents volume, l represents length, w represents width, and h represents height.
Cubes and rectangular prisms are both three-dimensional shapes, which means they have volume. Volume is the amount of space an object occupies. To find the volume of a cube or rectangular prism, you need to know its dimensions. The dimensions of a cube or rectangular prism are its length, width, and height.
Volume of a Cube
A cube is a three-dimensional shape that has six equal square faces. To find the volume of a cube, you need to know the length of one of its sides. The formula for finding the volume of a cube is:
Volume = side x side x side
Or
V = s³
Where V is the volume and s is the length of one of its sides.
Volume of a Rectangular Prism
A rectangular prism is a three-dimensional shape that has six faces. The faces of a rectangular prism are rectangles. To find the volume of a rectangular prism, you need to know the length, width, and height of the shape. The formula for finding the volume of a rectangular prism is:
Volume = length x width x height
Or
V = lwh
Where V is the volume, l is the length, w is the width, and h is the height of the rectangular prism.
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I’m not getting any answer for my problems
PLEASE HELP MEEEEEEEEEEEEEEEEEEEEEEE easdyfhrdfghfchdfchfch
HELP PLEASE WILL GIVE BRAINLIST DUE TONIGHT
Answer:
-2
Step-by-step explanation:
The common difference is
8-10
-2
Find the equation of the axis of symmetry of the graph of the function. y=x^2-2x-9
solve it in the picture
The equation of the axis of symmetry is x = 1 ⇒ 3rd answer
Here, we have,
* Lets revise the general form of the quadratic function
- The general form of the quadratic function is f(x) = ax² + bx + c,
where a, b , c are constant
# a is the coefficient of x²
# b is the coefficient of x
# c is the y-intercept
- The meaning of y-intercept is the graph of the function intersects
the y-axis at point (0 , c)
- The axis of symmetry of the function is a vertical line
(parallel to the y-axis) and passing through the vertex of the curve
- We can find the vertex (h , k) of the curve from a and b, where
h is the x-coordinate of the vertex and k is the y-coordinate of it
# h = -b/a and k = f(h)
- The equation of any vertical line is x = constant
- The axis of symmetry of the quadratic function passing through
the vertex then its equation is x = h
* Now lets solve the problem
∵ f(x) = x² -2x-9
∴ a = 1 , b = -2 , c = -9
∵ The y-intercept is c
∴ The y-intercept is -9
∵ h = -b/2a
∴ h = 2/2(1) = 2/2 = 1
∴ The equation of the axis of symmetry is x = 1.
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Answer:
x = 1
Step-by-step explanation:
The axis of symmetry of a quadratic function in the form y = ax² + bx + c can be found using the following formula:
\(x=\dfrac{-b}{2a}\)
For the given equation y = x² - 2x - 9:
a = 1b = -2c = -9Substitute the values of a and b into the formula to find the equation for the axis of symmetry:
\(\begin{aligned}x&=\dfrac{-b}{2a}\\\\\implies x&=\dfrac{-(-2)}{2(1)}\\\\&=\dfrac{2}{2}\\\\&=1\end{aligned}\)
Therefore, the axis of symmetry is:
\(\boxed{x=1}\)
help me out please i think it's correct but
Answer:
Step-by-step explanation:
your answer along with the work is down below please go and check it out also sorry I'm wrong have nice day:)
A Friday the 13th study provides data on traffic accident related emergency room admissions. The distributions of these counts from Friday the 6th and Friday the 13th are shown below for six such 6th 13th diff Mean 7.5 10.83 -3.33 SD 3.33 3.6 3.01 6 6 6 n paired dates along with summary statistics. You may assume that conditions for inference are met. (a) Conduct a hypothesis test to evaluate if there is a difference between the average numbers of traffic accident related emergency room admissions between Friday the 6th and Friday the 13th.
There is a significant difference between the average numbers of traffic accident related emergency room admissions between Friday the 6th and Friday the 13th.
To conduct a hypothesis test to evaluate if there is a difference between the average numbers of traffic accident related emergency room admissions between Friday the 6th and Friday the 13th, we can use a paired t-test. The null hypothesis would be that there is no difference between the means of the two populations, while the alternative hypothesis would be that there is a difference.
We can calculate the paired differences by subtracting the number of admissions on Friday the 6th from the number of admissions on Friday the 13th. Then we can calculate the mean and standard deviation of these differences. Using the given data, the mean of the differences is 10.83 - 7.5 = 3.33 and the standard deviation of the differences is 3.6.
Next, we can calculate the t-statistic by dividing the mean difference by the standard deviation of the differences and multiplying by the square root of the sample size. Using the given data, the t-statistic is (3.33 - 0) / (3.6 / sqrt(6)) = 3.07.
We can look up the critical value for a two-tailed test with 5 degrees of freedom (n-1) at a significance level of 0.05. The critical value is 2.571.
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Write a function A that models the amount to which the account grows after T years
item (a):
Using the formula given in the question, we have
\(A=P(1+\frac{r}{n})^{nt}\)Our principal investment P is equal to $4000, our interest r is 3 1/4 %, writting this in decimal form we have
\(3\frac{1}{4}=3+\frac{1}{4}=3.25\)Since it is a percentage, to write in decimal we divide by 100
\(\frac{3.25}{100}=0.0325\)And finally, our n value is 365 since it is compounded daily, and we have 365 days in a year.
Then, our function is
\(A(t)=4000(1+\frac{0.0325}{365})^{365t}_{}\)item (b):
To find A(30), we just need to evaluate this value in the function we created before
\(A(30)=4000(1+\frac{0.0325}{365})^{365\cdot30}_{}=10604.2085587\ldots\approx10604.21\)This means that with an investment of $4000, with this rate Joe is going to have a return of $10604.21.
question 19 the list 76, 56, 93, 24, 45, 88, 13, 7 , 37 is sorted using bucket sort with 4 buckets. which buck will contain 45?
Bucket number 2 will contain 45 after sorting the data.
According to the statement, we are given that a data list is sorted using bucket sort with 4 buckets and we have to find which bucket will contain the number 45.
So, the given data list is:
76, 56, 93, 24, 45, 88, 13, 7, 37
The list of data is sorted into buckets and the data contains numbers from 0 to 100.
We know that the 100 numbers are being sorted with 4 buckets which means each bucket contains 25 numbers.
So, let us consider
BUCKET 1: 0 to 25
It contains data numbers 7, 13, and 24.
Now,
BUCKET 2: 25 to 50
It contains data numbers 37 and 45.
Now,
BUCKET 3: 50 to 75
It contains data number 56.
Now,
BUCKET 4: 75 to 100
It contains data numbers 76, 88, and 93.
From sorting, the 45 number sort in bucket 2.
So, bucket number 2 will contain 45 after the list is sorted.
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In each part, determine whether the given 3-tuple is a solution of the linear system 2xı – 4x2 – x3 =1 X1 - 3x2 + x3 = 1 3x1 - 5x2 – 3x3 = 1 (a) (3,1,1) (b) (3, -1,1) (c) (13,5, 2) (d) (13,5,2) (e) (17,7,5)
is option A
(a) (3,1,1) is not a solution of the linear system 2xı – 4x2 – x3 =1 X1 - 3x2 + x3 = 1 3x1 - 5x2 – 3x3 = 1The linear system is given as follows:2x1 – 4x2 – x3 =1X1 - 3x2 + x3 = 13x1 - 5x2 – 3x3 = 1For (a) (3,1,1) (x1, x2, x3) = (3,1,1)Substitute x1 = 3, x2 = 1, and x3 = 1 into the linear system.2xı – 4x2 – x3 = 12(3) – 4(1) – 1 = 4X1 - 3x2 + x3 = 13 – 3(1) + 1 = 13x1 - 5x2 – 3x3 = 13(3) – 5(1) – 3(1) = 7Therefore, (a) (3,1,1) is not a solution of the linear system.The answer is option A.
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Can someone plz help me find the area for this composite figure plzzzz I beg u
\(S_1 = \frac{a+b}{2}h = \frac{7+9}{2}*5=\frac{18*5}{2}= 9 * 5 = 45~m^2\)
\(S_\triangle = \frac{ab}{2} = \frac{5*9}{2} = \frac{45}{2} = 22,5~m^2\)
\(S = S_1 + S_\triangle = 45 + 22,5 = 67,5~m^2\)
Answer: 67,5 m².
Answer:
Rat rat rat rat:)
Step-by-step explanation:
Suppose you know that ∠S and ∠Y are complementary, and that m∠S = 2(m∠Y) − 60°. Find m∠Y.
The value of m∠Y is
I NEED HELP!!! PLS
Answer:
m∠Y=50°
Step-by-step explanation:
So, we know that ∠S+∠Y=90 and that m∠S=2(m∠Y)-60.
If you plug those things into the equation, you get (2[m∠Y]-60)+m∠Y=90.
Then you multiply 2 and m∠Y: 2m∠Y-60+m∠Y=90.
Combine like terms: 3m∠Y-60=90.
Then you add 60 to both sides: 3m∠Y=150
Divide 3 on both sides: 3∠Y=50
HELP IF U WANNA BE BRAINLIEST
Step-by-step explanation:
\( \because \sqrt{18} = 4.24264069 \\ \\ \therefore \: 4 < 4.24264069 < 5 \\ \\ \therefore \: 4 < \sqrt{18} < 5 \\ \\ \sqrt{18} \: fall \: between \: 4 \: and \: 5 \\ \\ \because \sqrt{18} = 4.24264069 \approx \: 4 \\ \\ \therefore \: 4 \: is \: closer \: to \: \sqrt{18} \)
Solve for y: 3x - y^2 = 25
Answer:
Square root ( 3x - 25)
Step-by-step explanation:
3x - y^2 = 25
- y^2 = 25 - 3x
y ^2 = 3x - 25
y = Square root ( 3x - 25)
Which geometric solids would model the tent?
cone and sphere
cylinder and cone
pyramid and rectangular prism
triangular prism and rectangular prism
Please help 100 points! MATHAMATICS
Congratulations dear user, All the answers given by you are absolutely correct!!
How do I make m the subject by rewriting the formula I=mv-mu
Answer:
m = \(\frac{l}{v-u}\)
Step-by-step explanation:
l = mv-mu (factor out m from mv and mu)
l = m(v-u) - (divide both sides by (v-u))
l/v-u =m
PLEASE HELP WILL MARK AS BRAINLIEST
Your savings account has a balance of $125. You add $22 a month to this balance. Which equation shows your balance, b, in m months?
A. b( m) = $125 m + $22
B.m( b) = $125 b + $22
C. m( b) = $125 + $22 b
D.b( m) = $125 + $22 m
Answer:
d
Step-by-step explanation:
you are adding 22 dollars each month and 125 is your starting balance
The equation shows your balance, b, in m months will be b( m) = $125 + $22 m.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that,
Savings account balance = $125
Money added per month = $22
The obtained equation is,
b( m) = $125 + $22 m.
Thus, the equation shows your balance, b, in m months will be b( m) = $125 + $22 m.
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The density of zinc is 7130 kg/m3
.
(b) Work out the mass of 5 m3
of zinc.
Answer:
Uhdhdb
Step-by-step explanation:
Jsjddj hdhdhhdb
what is the density of the rock???!!!!!!!!!!
Answer:
he actual densities of pure, dry, geologic materials vary from 880 kg/m3 for ice (and almost 0 kg/m3 for air) to over 8000 kg/m3 for some rare minerals. Rocks are generally between 1600 kg/m3 (sediments) and 3500 kg/m3 (gabbro).
Step-by-step explanation:
How do I solve for this?
Answer:
use a midpoint formulae (X2+X1 /2 ; Y2 + Y1 /2 )
(-2+3/2 ; -2+4/2 )
X = 1/2 ; Y = 1
If Ahmad ran 3/4 miles in 20 minutes, how far could he run in 1 hour?
Answer:
2 1/4 miles
Step-by-step explanation:
20+20+20 = 60/ 1hour
3/4+3/4= 1 1/2+ 3/4 =2 1/4
Answer:
2 1/4
Step-by-step explanation:
20min * 3 = 60 min
3/4 * 3 = 2 1/4
Hope this helps, have a great day:)
HEYOOO 60 POINTS
just answer this very complicated math question to get some easy points
*brailiest for most pizzazz* :
1 + 1 = ?
Answer:
1 + 1 = 2
Step-by-step explanation:
you add one and add another one and together thetr is two. so you would have two left.
Solve the following equation for A. Be sure to take into account whether a letter is
capitalized or not.
4 = gA
Answer:
4/a
Step-by-step explanation:
Odell and Tamra paint two walls with the same dimensions . Odell paints of a wall . Tamra paints of the other wall . Conjecture : Odell and paint the same amount . 2/6; 1/3
According to simplification of fractions, the conjecture "Odell and paint the same amount" is proven to be true.
What is a conjecture?
A mathematical assertion that hasn't been thoroughly proven is referred to as a conjecture. When one observes a pattern that holds true in numerous instances, hypotheses start to form. A pattern may be true in many instances, but that does not guarantee that it will be true in all instances.
To determine if Odell and Tamra painted the same amount, we need to compare the amounts they painted.
Odell painted 2/6 of a wall, which can be simplified to 1/3 of a wall.
Tamra painted 1/3 of a wall, which is also equivalent to 1/3 of a wall.
Since both Odell and Tamra painted 1/3 of a wall, it appears that the conjecture is true, and they painted the same amount.
We can also see this by comparing the fractions they painted directly.
1/3 = 1/3
Therefore, it is likely that Odell and Tamra painted the same amount, and the conjecture is true.
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Which is greater, 4 or 126?
Answer:
126
Step-by-step explanation:
4 is less than 126 so 126 > 4
I
Table for a linear equation
Fill in the table using this function rule.
y = 5x-2
X
y
Х
?
- 1
0
1
2
can you make two triangles that are not congruent that have three pairs of congruent angles?
if two triangles have three pairs of congruent angles, then they must be congruent to each other by the Angle-Angle-Angle (AAA) congruence theorem, and thus cannot be non-congruent.
No, it is not possible to make two triangles that are not congruent and have three pairs of congruent angles. This is because if two angles of a triangle are congruent, then the third angle must also be congruent by the Angle Sum Theorem, which states that the sum of the angles in a triangle is always 180 degrees. If two triangles have three pairs of congruent angles, then all three angles in each triangle are congruent, meaning they have the same measure. However, this does not guarantee that the sides of the triangles are congruent. In order for two triangles to be congruent, they must have the same angle measures as well as the same side lengths. Therefore, if two triangles have three pairs of congruent angles, then they must be congruent to each other by the Angle-Angle-Angle (AAA) congruence theorem, and thus cannot be non-congruent.
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If x=3 and y=7, evaluate the following expression: 20+2(3y−4x)
Given
x = 3, y = 7
To find out:
The value of 20 + 2(3y - 4x)
Solution:
20 + 2(3y - 4x)Let us put the value of x and y as given.
= 20 + 2 (3 × 7 - 4 × 3)Now, solve the bracket portion. First do the multiplication.
= 20 + 2 (21 - 12)Now, subtract.
= 20 + 2 (9)Multiply 9 with 2.
= 20 + 18Finally, add the two.
= 38Answer:
38
Hope you could understand.
If you have any query, feel free to ask.