Using the formula of midpoint of a line, the coordinate of the endpoint k is (-6, 31)
What is Midpoint of a LineThe midpoint of a line is the point that is halfway between the two end points of the line. It can be found by taking the average (mean) of the x-values and the average (mean) of the y-values of the two endpoints.
The formula of midpoint of a line is given as;
M(x, y) = (x₂ + x₁) / 2, (y₂ + y₁) / 2
Since we have the midpoint and one endpoint, we can use the coordinate to find the missing coordinate.
The x - coordinate is calculated as;
-1 = (4 + x₁) / 2
-2 = 4 + x₁
x₁ = -2 - 4
x₁ = -6
The y - coordinates is calculated as;
8 = (-15 + y₁) / 2
16 = -15 + y₁
y₁ = 16 + 15
y₁ = 31
The coordinates of k is (-6, 31)
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prime numbers of the form p and p+2, where p is a prime number, are known as ______ prime numbers
Prime numbers of the form p and p+2, where p is a prime number, are known as twin prime numbers.
What is the Prime numbers about?
A twin prime is a prime number that is either 2 less or 2 more than another prime number. For example, the number 3 and 5 are twin primes, because they are both prime and the number 5 is 2 more than 3. Similarly, the number 5 and 7 are also twin primes, because they are both prime and the number 7 is 2 more than 5.
Therefore, Twin primes are considered as interesting numbers in number theory because of their relative rarity, rare in nature and because they are the building blocks for certain types of primes such as Sophie Germain primes and safe primes.
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Please answer question 10 and 11 please
Answer:
d7-dx=(20x|x-3|+40)x x-3 (|x-3+2)x| x-3|
Step-by-step explanation:
Hope this helps :D
In the construction of bridges, engineers use a formula to help
determine the allowable stress on a bridge rocker, a component of the
bridge that handles the stress and weight placed on the pavement of the
bridge. The engineers use the formula F =11/300d (F − 13), where F is the
strength of the steel in kilopound per square inch and d is the diameter
of the rocker in millimeters.
Solve the formula F =11/300d (F − 13) for d.
From the engineers formula given, making d the subject of the formula gives us; d = 300F/(11(F - 13))
How to change the subject of the formula?
We are given the engineers formula as;
F = (¹¹/₃₀₀)d(F - 13)
Where;
F is the strength of the steel in kilopound per square inch.
d is the diameter of the rocker in millimeters.
From the given formula, we can start by;
Multiply both sides by 300 to get;
300F = 11d(F - 13)
Divide both sides by 11(F - 13) to get;
d = 300F/(11(F - 13))
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X 1 3 5 7
у -9 -17 -25 -33
find the equation of the linear function represented by the table in slope intercept form
The equation of the linear function represented by the table in slope intercept form is y = -4x - 5.
What is slope-intercept form?
The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation.
Given two points (x,y), the slope is the change in y divided by the change in x.
The points are (1,-9) and (3,-17) -
m = (y2-y1)/(x2-x1)
m = [-17-(-9)]/(3-1)
m = -8/2
m = -4
Then the slope equation will be -
y = -4x + b
Taking points (1,-9) and substituting in the equation to get the value of b -
-9 = -4(1) + b
-9 = -4 + b
-9 + 4 = b
b = -5
Therefore, the slope intercept form of equation is y = -4x - 5.
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draw the graph of y=_3x_4
Answer:
I can’t tell if both number are positive, ones negative ect but here’s the answer if both are negativ, let me know if the numbers are negative or positive and I can come back and give ya the right answer! Xoxo
Step-by-step explanation:
How many rectangular faces are in a right triangular prism?
Answer: A right triangular prism is a 3-dimensional geometric shape that has a triangular base and three rectangular faces that connect the base to the top. A rectangular prism has three pairs of rectangular faces that are congruent, these faces are perpendicular to each other and connected by edges.
So, in a right triangular prism there are 3 rectangular faces which are the lateral faces (the one that connects the base and the top)
A triangular prism also has 3 triangular faces which are the base faces
So in total, a right triangular prism has 3 rectangular faces and 3 triangular faces.
Step-by-step explanation:
what is m=5 n=3 mn+9
Answer: 24
Step-by-step explanation:
Given that m=5 and n=3, we can plug our values into the given expression to evaluate.
(5)(3)+9 [multiply]
15+9 [add]
24
The reason we multiplied before we added was due to the order of operations. Order of operations tells us to always multiply or divide first before we add or subtract. In this case, the multiplication happens to come first so we multiply, then add.
a ball is thrown from the top row of seats in a stadium the function h(t)=-16t^2+80t+96 gives the height, in feet, of the ball t seconds after it is thrown. how long will it be before the ball hits the ground?
The number of seconds it takes ball to before hit the ground is 6 seconds.
What is the solution of a quadratic equation?The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.
Given that, a ball is thrown from the top row of seats in a stadium the function h(t)=-16t²+80t+96 gives the height, in feet, of the ball t seconds after it is thrown.
When ball hits the ground h=0
So, -16t²+80t+96=0
-16(t²-5t-6)=0
t²-5t-6=0
By using splitting middle term method, we get
t²-6t+1t-6=0
t(t-6)+1(t-6)=0
t-6=0 or t+1=0
t=6 or t=-1
Time can not be negative integer.
Therefore, the number of seconds it takes ball to before hit the ground is 6 seconds.
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Given that a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6, select the statement that could be true for g. A. g(0) = 2 B. g(-4) = -11 C. g(7) = -1 D. g(-13) = 20
A function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6 then g(-13) = 20
What is a function?A relation is a function if it has only One y-value for each x-value.
Given a a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45
and that g(0) = -2 and g(-9) = 6,
x=-20 then g(-20)=-5
x=-19 then g(-19)=-4
x=-18 then g(-18)=-3
x=-17 then g(-17)=-2
x=-16 then g(-16)=-1
x=-15 then g(-15)=0
x=0 then g(0)=-2
x=-9 then g(-9)=6
By observing this we can say that as x values are decreasing the function values are increasing and vice versa
So option D is correct
Hence, a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6 then g(-13) = 20
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I need help, I know it gave me the answer but I don’t understand how it got (-3) someone explain please
Answer: h=14
Step-by-step explanation:
If x=-18, then
h=17+(-18)/6
h=17+(-3)
h=17-3
h=14
Answer:
Step-by-step explanation:
so, the calculation was : h = 17 + [tex]\frac{-18}{6\\}[/tex]
To subtract "[tex]\frac{-18}{6}[/tex] " we need to make it the same denominator as "17"
(it's not written but technically 17 = [tex]\frac{17}{1}[/tex] )
Yet, we see that [tex]\frac{-18}{6} =\frac{-3* 6}{1*6}[/tex]
We just need to remove both the 6 that are not useful here and :
[tex]\frac{-3*6}{1*6} =\frac{-3}{1}= -3[/tex]
We obtain h = 17 - 3 = 14
hope it helped :)
Which of the following sets of numbers could not represent the three sides of a triangles?
9,23,34
10,24,31
8,14,21
5,14,16
Answer:
pretty sure it's B. Let me know if im wrong
Step-by-step explanation:
please help asap
will give brainliest
Answer: 109 it says 109 in the corner of b and d
pls help with this question find the slope from 1-6
Answer:
Step-by-step explanation:
1. ( -2, 2), (-1, 5)
(5 - 2)/(-1 + 2)= 3/1= 3
2. (-4, 2), (2, 0)
(0 - 2)/(2 + 4) = -2/6 = -1/3
3. (0, 3), (5, 1)
(1 - 3)/(5 - 0)= -2/5
4. (0, 0), (1, 1)
(1 - 0)/(1 - 0)= 1/1= 1
5. (3, 0), (3, 1)
(1 - 0)/(3 - 3) = 1/0 = undefined
6. (0, -1) (1, -1)
(-1 + 1)/(1 - 0)= 0/1 = 0
Find the mean, median, and mode for 0, 4, 6, 11, 9, 8, 9, 1, 5, 9, 7. Round to the nearest tenth if needed.
Answer:
Mean - 6.2 Median - 7 Mode - 9
Step-by-step explanation:
You can find the mean by adding all the given numbers and dividing them by how many numbers you added.
The median is the middle value of the set of numbers, order them from least to greatest and find the middle value.
Mode is the number that occurs the most.
XYZ Company
Balance Sheet
Assets
Cash
$45,000
Inventory $41,000
Property $134,000
Total Assets:
Liabilities
Notes
Wages
Equity
Stock
$55,000
$56,000
$50,000
Investment $59,000
Total Liabilities + Equity:
Using the balance
sheet, calculate XYZ
Company's total
assets - liabilities.
Total Assets - Liabilities = $ [?]
Enter
PH
Skip
On solving the provided question, we can say that - by formula of simple interest we have SI = [tex]2200 X 2 X 4/100 = > 17600/100 = > 176[/tex]
what is interest ?Multiplying the principal by the interest rate, time, and other factors yields simple interest. Simple return equals principle times interest times hours is the marketed formula. It is easiest to compute interest using this formula. A percentage of the principle balance is how interest is most commonly computed. For instance, he will only pay his portion of the 100% interest if he borrows $100 from a buddy and promises to pay it back with 5% interest. $100 (0.05) = $5. When you borrow money, you must pay interest, and when you lend money, you must charge interest. Most of the time, interest is expressed as a yearly percentage of the loan amount. The interest rate on the loan is known as this percentage.
here
principal, p = 2200
rate, r = 2%
time, t = 4 rs,
so SI = P X R X T/100
SI -
[tex]2200 X 2 X 4/100\\17600/100\\176[/tex]
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List the data in the following stem-and-leaf plot. The leaf represents the tenths digit.
Separate the numbers in the list by a comma. The list is:
151,154,154,157,165,166,178,183,186,186
The data represented by the steam-leaf plot is 115, 138, 145, 145, 156, 166, 168, 168, 175, and 187.
What is a stem leaf plot?A stem and leaf plot, also known as a stem and leaf diagram, is a way to arrange data so that it is simple to see how frequently various sorts of values occur. It is a graph that displays ordered numerical data. A stem and a leaf are divided into each piece of data.
A stem and leaf plot is shown as a customized table with the first or final digit of each data value divided into a stem and the remaining digit in a leaf.
9 I 0 ⇒ 9 on the stem and 0 on the leaf read as 90.
Given, A stem leaf plot and the leaf represents the tens digit.
As the leaf represents tens digits the data set can be represented by,
115, 145, 145, 175, 156, 166, 187, 138, 168, 168.
Representing the data set in ascending order we have,
115, 138, 145, 145, 156, 166, 168, 168, 175, 187.
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What is the vertex of the function?
f(x) = 3(r - 2)2 + 4
Answer:
(2,4)
Step-by-step explanation:
The vertex of a parabola in the form of [tex]y=a(x-h)^2+k[/tex] is [tex](h,k)[/tex]. In this function, we have [tex](2,4)[/tex] as our vertex.
-15 POINTS-
Don’t explain.
Y=[?]
Step-by-step explanation:
of course I need to explain it, since you don't know how to get it. that is the purpose of Brainly. not to be a calculator slave to you, but to enable you to solve similar problems on your own in the future.
both shapes are similar.
that means that
1. both have the same angles
2. there is one common scaling factor for all pairs of corresponding sides (and other lengths as heights, ...).
we need 2. here to solve.
AB / EF = f = 3/2
x = AD
x / EH = f = 3/2
x / 2.4 = 3/2
x = 2.4 × 3/2 = 7.2 / 2 = 3.6
100 POINTS PLEASE HELP!!! PICTURE IS ATTACHED.
The simplified expression is [tex]c^2 d^2 e^6 / b^8[/tex]
How simplification of an expression work?The given expression is [tex](a^0 b^-4 cde^3)^2[/tex]
We know that any number raised to the power of 0 is 1.
Therefore,[tex]a^0 = 1[/tex].
Also, any number raised to the power of -1 is its reciprocal.
Therefore, [tex]b^-4 = 1/b^4[/tex]
Simplifying the above expression we get
[tex](1*1/b^4 * cde^3)^2 = (cde^3/b^4)^2[/tex]
Now, we apply the rule that [tex](a^m * a^n) = a^(m+n)[/tex]
So, [tex](cde^3/b^4)^2 = c^2 d^2 e^6 / b^8)[/tex]
Hence the simplified expression is [tex]c^2 d^2 e^6 / b^8[/tex]
Please note, when an exponent is raised to another exponent, we can multiply the exponents, so [tex](a^m)^n = a^(m*n)[/tex]
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on Monday the solar panels on a house produced 37.124 units of energy. On Tuesday, the solar panels produced 2,846 fewer units of energy than on Monday. What is the total number of units of energy in two days.
The total number of units of energy produced in the two days is 71,402.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Monday:
Energy = 37,124
Tuesday:
Energy = 37,124 - 2846 = 34278
The total energy produced.
= 37124 + 34278
= 71402
Thus,
The total number of energy in two days is 71,402.
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Tickets to a basketball game can be ordered online for a set price per ticket plus a $5.50 service fee. The total cost in dollars for ordering 5 tickets is $108.00. Which linear function represents c, the total cost, when x tickets are ordered? (A service fee is a single fee applied to the total, no matter the number of tickets purchased).
Considering the definition of a line, the linear function that represents the total cost when x tickets are ordered is c= 20.5x + 5.50.
What is a linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Total cost in this caseIn this case, you know:
Tickets to a basketball game can be ordered online for a set price per ticket plus a $5.50 service fee. This is, as service fee is a single fee applied to the total, no matter the number of tickets purchased, the value of "b" is 5.50.The total cost in dollars for ordering 5 tickets is $108.00Being Total cost= set price per ticket× amount of tickets + 5.50, then:
108=set price per ticket× 5 + 5.50
108 - 5.50= set price per ticket× 5
102.5= set price per ticket× 5
102.5÷5= set price per ticket
20.5= set price per ticket
Finally, the total cost is Total cost= 20.5× amount of tickets + 5.50.
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Answer:
Its letter A
Step-by-step explanation:
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Write the quotient as a mixed number.
26÷3=8 R2
When we divide 26 by 3 we get 8 as a quotient and 2 as a remainder, the Mixed Fraction is [tex]8\frac{2}{3}[/tex]
What is a mixed Number ?A full number plus a legal fraction are combined to form a mixed number. Mixed numbers, commonly referred to as mixed fractions, make it easier for humans to comprehend numbers.
A full number and a legal fraction make up a mixed number. A mixed number like [tex]2\frac{x}{y}[/tex] is one where 1/4 is the correct fraction and 2 is the whole number portion. It should be emphasized that once mixed numbers are transformed into an incorrect fraction, they are simple to add, subtract, multiply, and divide.
Steps to convert Improper fraction to Mixed Fraction :
Divide the numerator by the denominator to obtain the remainder and quotient as the first step. 43 divided by 9 in this situation yields 4 as the quotient and 7 as the remainder.Step 2: This quotient (4) becomes the mixed number's whole number component. While the denominator stays the same, the remainder (7) becomes the numerator portion.Step 3: As a result, 43/9 becomes a mixed number and is written as , meaning that 43/9 = [tex]4\frac{7}{9}[/tex].So when we divide 26 by 3 we get 8 as a quotient and 2 as a remainder so the Mixed Fraction is : [tex]8\frac{2}{3}[/tex]
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coordinate plane with line g that passes through the points negative 3 comma 6 and 0 comma 5 What is the equation of the line in slope-intercept form that is perpendicular to line g and passes through the point (1, −2)?
An equation of the line in slope-intercept form that is perpendicular to line g and passes through the point (1, −2) is y = 3x - 5.
How to determine an equation of this line?Mathematically, the standard form of the equation of a straight line (slope-intercept form) is given by this mathematical expression;
y = mx + c
Where:
m represents the slope.x and y are the points.c represents the intercept.From the information provided, we have the following points on line g:
Point = (-3, 6)
Point = (0, 5)
Next, we would determine the slope of line g as follows;
Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope, m = (y₂ - y₁)/(x₂ - x₁)
Slope, m = (5 - 6)/(0 - (-3))
Slope, m = -1/3
In Mathematics, a condition that must be met for two lines to be perpendicular is given by:
m₁ × m₂ = -1
-1/3 × m₂ = -1
m₂ = 3
At point (1, -2), an equation of this line can be calculated in slope-intercept form as follows:
y - y₁ = m(x - x₁)
y - (-2) = 3(x - 1)
y + 2 = 3x - 3
y = 3x - 3 - 2
y = 3x - 5
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Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°
Answer:
m∠5+m∠6=180°
m∠2+m∠3=m∠6
m∠2+m∠3+m∠5=180°
Step-by-step explanation:
Verify each option
case A) we have
m∠5+m∠3=m∠4 ----> equation A
we know that
m∠3+m∠4=180° -----> by supplementary angles
m∠4=180°-m∠3 ----> equation B
substitute equation B in equation A
m∠5+m∠3=180°-m∠3
m∠5+m∠3+m∠3=180°
This equation is true when m∠2=m∠3
Therefore Is not always true
case B) we have
m∠3+m∠4+m∠5=180° ----> equation A
we know that
m∠3+m∠4=180° -----> by supplementary angles
m∠4=180°-m∠3 ----> equation B
substitute equation B in equation A
m∠3+(180°-m∠3)+m∠5=180°
m∠5=0°
This option is not true
case C) we have
m∠5+m∠6=180°
we know that
m∠5 and +m∠6 are supplementary angles
so
Their sum is always 180 degrees
Therefore this option is always true
case D) we have
m∠2+m∠3=m∠6 -----> equation A
we know that
m∠5+m∠6=180° ----> by supplementary angles
m∠6=180°-m∠5 ----> equation B
substitute equation B in equation A
m∠2+m∠3=180°-m∠5
m∠2+m∠3+m∠5=180°
Remember that the sum of the interior angles of a triangle must be equal 180 degrees
Therefore this option is always true
case E) we have
m∠2+m∠3+m∠5=180°
Remember that the sum of the interior angles of a triangle must be equal 180 degrees
This option is always true
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A line passes through the origin (−1, 1) and (4, n). Find the value of n.
The line y = - x has a coordinate value of (4, - 4) passing through the origin.
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and equation of a line in slope-intercept form is
y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.
Given, A line passes through the origin, (−1, 1) and (4, n).
So, The slope of the line is,
m = (1 - 0)/(- 1 - 0).
m = - 1.
Now,
1 = -1(-1) + b.
b = 0.
y = - x.
At x = 4,
y = - 4.
So, The point (4, n) is (4, - 4).
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Four student government officers want to go to the state convention. It will cost them $100 for registration, $375 for transportation and food, and $41 per person for the hotel. There is $425 budgeted for the convention in the student government savings account. They can earn the rest of the money they need by having a car wash. If they charge $5 per car, how many cars must they wash in order to have enough money to pay for the trip?
cars___?
Answer:
$100 + $375 + $41(4) = $516
$516 - $425 = $91
$91 / $5 = 18.2 cars
Therefore, the four student government officers must wash 18 cars in order to have enough money to pay for the trip.
3a+14b
I'm not good at math, it's my weakest subject
On solving the question, we can say that y using the given information we can prove that similar angle m ∠ABC = m ∠EDC.
What are similar angles?Polygons' corresponding sides and corresponding angles are compared as part of the geometric tests for congruence and similarity. With care taken to maintain the order of adjacency, each side and each angle in one polygon is paired with a side or angle in the other polygon in these tests.
Given:
m ∠1 = m ∠2
m ∠2 = m ∠4
We have to prove that m ∠ABC = m ∠EDC
∠EDC = ∠3 + ∠4
m ∠ABC = m ∠1 + m ∠2
m ∠EDC = m ∠3 + m ∠4
m ∠1 + m ∠2 = m ∠3 + m ∠4
m ∠ABC = m ∠EDC
Hence, by using the given information we can prove that
m ∠ABC = m ∠EDC.
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Use triangles to find the sum of the interior angle measures of the polygon.
SHOW YOUR WORK.
The sum of the interior angle measures of the polygon is 900 degrees
How to determine the sum of interior angles
From the image shown, we can see that the polygon has 7 sides.
A polygon with seven sides is called a heptagon
It is important to note that the number of triangles in a heptagon is 5.
Also, the sum of angles in a triangle is 180 degrees.
Now, the formula for calculating the sum of interior angles of a polygon is expressed as;
= (n - 2) 180
Where; n is the number of sides of the polygon
Substitute the value
= (7-2)180
Subtract the value
= 5(180)
= 900 degrees
Hence, the sum is 900 degrees
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Which radicals are already in the simplest form?
4 less than three sevenths as an algebraic expression