The line segment AB is divided at point P, which has coordinates P(0,-7.5)
A line segment is a section of a line that connects two locations to create a straight line or we can say that is connects two distinct points together to form a single line. It is extendable to either side.
Given are,
A line segment AB with coordinates of A(0,0 ) and B(-15,0) respectively
Two minor line segments, AP and PB, are created from the line segment AB by the provided point P
We must determine the dividing point's coordinates, or P.
We'll apply the formula provided,
The coordinates of the point P are given by = ([tex]\frac{x1+x2}{2}[/tex],[tex]\frac{y1+y2}{2}[/tex] )
Now, x1 = 0, x2 = 0, y1 = -15, y2 = 0
Putting values in the formula, we get
([tex]\frac{0+0}{2}[/tex], [tex]\frac{0-15}{2}[/tex])
(0,-7.5)
Hence, the point P which partitions the line segment AB have coordinates as P(0,-7.5)
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Rotation 90° counterclockwise around the
origin of the point (-8, 3)
(8,3)
(3,8)
(-8,-3)
(-3,-8)
The answer is (-3.-8)
When we rotate a point 90° counterclockwise around the origin, it's the same as rotating it 270° clockwise around the origin.
When we rotate something 270° clockwise around the origin, the original coordinates (x, y) becomes (-y, x).
Clockwise Rotations (CW) follow the path of the hands of a clock. These rotations are denoted by negative numbers. Counterclockwise Rotations (CCW) follow the path in the opposite direction of the hands of a clock. These rotations are denoted by positive numbers.
The angle of rotation between the two points or vertices is the number of central angles times the measure of a single central angle: angle of rotation =m×α = m × α .
y is 3, and -(3) is just -3, since multiplying negatives make a negative.
x just remains x, but it's in a different position.
This makes the new coordinate (-3, -8)
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Shauna drove 75 miles in 3 hours at a constant speed. How many miles did she drive in 2 hours?
f. 2.5 miles
g. 50 miles
h. 75 miles
i. 100 miles
The total distance traveled in 2-hour time is 50 miles. (option g)
Shauna drove 75 miles in 3 hours at a constant speed, so the total distance covered in 3 hours is 75 miles to find the distance covered in 2 hours, we first need to find the distance or miles covered in 1 hour
To find the distance Shauna traveled in 2 hours, use the following formula: –
Speed = distance/time
Total distance traveled = 75 miles
Total time = 3 hours = 3 hours
Speed = 75/3
Speed = 25 miles per hour
Distance traveled in 2-hour time is 50 miles.
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A certain days plant grows 1 1/6 inches every week.how long will it take the plant to grow 6 1/6 inches
Answer: The amount of long will it take the plant to grow is [tex]5\frac{2}{7}[/tex] weeks.
Step-by-step explanation:
Given data,
A certain days plant grows 1 1/6 inches
It take the plant to grow 6 1/6 inches
Let us assume,
A certain days plant grows = x
It take the plant to grow = y
So ,
we can write,
x = 1 and 1/6
x = 1*1/6
L.C.M is '6',
Then,
x = (6+1) / 6
x = 7/6
Then,
y = 6 and 1/6
y = 6*1/6
y =(1+36) / 6
y = 37/6
So, divide y/x = (37/6) / (7/6)
= 37/6 * 6/7
L.C.M is 42
= 222/42
= 5 12/42
= 5 2/7 weeks
Therefore,
The amount of long will it take the plant to grow is [tex]5\frac{2}{7}[/tex] weeks.
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Let f(x)=2x-1, g(x)=3x, and h(x) = x² + 1. Compute the following:
f(g(-3)) =
Answer:
Step-by-step explanation:g(-3) = 3(-3) = -9
f(g(-3)) = f(-9) = 2(-9) -1 = -18 -1 = -19
b. Is there a pattern in the table? Explain.
Answer:
no photo
Step-by-step explanation:
we need a photo to decide if answer is correct or not
Mike sold 5,640 chickens and 5,732 ducks from his farm. He
made $79,696. If he sold 5,640 chickens and 5,640 ducks, he
would get $78,960. How much money did he make from
selling the 5,732 ducks?
$
The number of money farmers made by selling 5732 ducks will be $45856.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that Mike sold 5,640 chickens and 5,732 ducks from his farm. He made $79,696. If he sold 5,640 chickens and 5,640 ducks, he would get $78,960.
Form two equations to get the amount:-
5640c + 5732d = 79696
5640c + 5640d = 78960
Solve both the equations by elimination method:-
5640c -5640c + 5732d - 5640d = 79696 - 78960
92d = 736
d = 736 / 92
d = $8
Total amount = $8 x 5732 = $45856
Therefore, the money farmers made by selling 5732 ducks will be $45856.
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What is the length of AB with endpoints A (-1,0) and B (4,-3)
Answer:
√34
Step-by-step explanation:
it would be radical 34.
Evaluate each expression 14^3
At the gift shop, they sell small greeting cards and large greeting cards. The cost of a small greeting card is $1.65 and the cost of a large greeting card is $5.40. How much would it cost to get 3 small greeting cards and 2 large greeting cards? How much would it cost to get xx small greeting cards and yy large greeting cards?
The cost to get 3 small greeting cards and 2 large greeting cards is $15.75 and the it cost to get xx small greeting cards and yy large greeting cards is equals to $1.65(xx) + $5.40(yy)
To find out the cost of three small greeting card we need to multiply the cost of one small greeting card with 3 which equals to $4.95
To find out the cost of two large greeting card we need to multiply the cost of large greeting card with two which equals to $10.80
To find out the cost to get 3 small greeting cards and 2 large greeting cards we need to add $4.95 and $10.80 which equals to $15.75
As explained above to find the cost to get xx small greeting cards and yy large greeting cards we need to multiply with their respective unit price which equals to $1.65(xx) + $5.40(yy)
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Solve |2x - 3| ≤7.
OA.
2-2 and x ≤ 4
OB.
2-3 or x ≤ 2
OC. 2-2 and x ≤ 6
OD. 2-2 and x < 5
The solution of the inequality expression is -2 ≤ x ≤ 5
How to solve the inequality expression?The inequality expression is given as
|2x - 3| ≤7
Remove the absolute bracket
So, we have
2x - 3 ≤ 7 and 2x - 3 ≥ -7
Add 3 to both sides of the inequalities
2x ≤ 10 and 2x ≥ -4
Divide to both sides of the inequalities by 2
x ≤ 5 and x ≥ -2
Rewrite as
-2 ≤ x ≤ 5
Hence, the solution of the inequality expression is -2 ≤ x ≤ 5
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please help it’s urgent thank you!
this is a proportional relationship that can be written as:
P = 5,184*S
Could there be a realtionship?Top see this, just take the quotient between the number of pixels and the number of square inches of each screen, and let's see if we get the same value for the given rows.
31,104/6 = 5,184
For the next row we have:
373,248/72 = 5,184
And so on, you will get the same quotient for the 3 rows, then we can conclude that yes, this is a proportional relationship that can be written as:
P = 5,184*S
Where P is the number of pixels and S is the number of square inches.
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The sum of four consecutive is 490. What are the four consecutive integers
The four consecutive integers are 121, 122, 123, 124.
We have the sum of four consecutive integers equals to 490
We have to determine those integers.
What are Integers?An integer is a number with no decimal or fractional part. It includes negative and positive numbers, including zero.
Assume the first integer is x. Then, the other integers will be -
x + 1 , x + 2 , x + 3.
Therefore -
x + (x + 1) + (x + 2) + (x + 3) = 490
4x + 6 = 490
4x = 484
x = 121
So -
x = 121
x + 1 = 122
x + 2 = 123
x + 3 = 124
Hence, the four consecutive integers are 121, 122, 123, 124.
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1/2(12x+10)+2×
simplify
Function his a transformation of the parent exponential function, f(2)= 2º.
h(z)=-3-2²
Which statement is true?
A. Function h is a horizontal translation of function f
OB.
Function h is a reflection and a translation of function f
OC. Function h is a vertical translation of function f
OD. Function his a reflection and a dilation of function
According to the question, the true statement is the function 'h' is a vertical translation of a function ''f.
What is exponential function?
The exponential function can be defined as the base of two with the integer powers. The base can be represented as common factors as well as common multipliers. The graph representation of the exponential function can be called as "rate of change". It either increases or decreases or constant with respect to another functions.
The transformation of a function can be performed either with translation, reflection, vertical sliding or horizontal sliding. It can be done with the help of the calculated values known as asymptotic. And the end behavior of the function is always consistent.
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In China, the highest elevation is Mount Everest and the lowest elevation is Turpan Pandi. Mount Everest is located at 8850 m above sea level. Turpan Pandi is located at -154 m. What is the distance between the highest and the lowest points of elevation?
PLEASE I NEED HELP GREATLY APPRECIATE IT!
The distance between the highest and the lowest points of elevation is 9904 meters.
What is the distance?In order to determine the distance between the highest and the lowest points of elevation, subtract the heights of both places from each other.
Subtraction is a mathematical operation that is used to determine the difference between two or more numbers. The sign used to denote subtraction is -.
Height of mount Everest - height of Turpan Pandi
8850 - (-154)
8850 + 154 = 9004m
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Solve each equation. 3(2-c)=-(c+4)
The solution of the given equation 3(2-c)=-(c+4) is c = 5.
According to the given question.
We have an equation
3(2 - c ) = -( c + 4)
Since, we have to solve the above equation for c.
Therefore, the solution of the above equation is gievn by
3(2 - c) = -( c + 4)
⇒ 3(2) -3(c) = -c -4 (by distributive law)
⇒ 6 -3c = -c - 4
⇒ 6 + 4 -3c = -c (adding 4 both the sides)
⇒ 10 -3c = -c
⇒ 10 = -c + 3c ( adding 3c both the sides)
⇒ 10 = 2c
⇒ 10/2 = c (multiply both the sides by 2)
⇒ 5 = c or c = 5
Hence, the solution of the given equation 3(2-c)=-(c+4) is c = 5.
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the 4th and 5th terms of a GP are -13.5 and 40.5 find the first term and the sum of the first five terms
Answer:
First term: 0.5
Sum of the first give terms: 30.5
Step-by-step explanation:
General form of a geometric sequence:
[tex]a_n=ar^{n-1}[/tex]
where:
[tex]a_n[/tex] is the nth terma is the first termr is the common ratioGiven terms:
[tex]a_4=-13.5[/tex][tex]a_5=40.5[/tex]To find the common ratio r, divide consecutive terms:
[tex]\implies r=\dfrac{a_5}{a_4}=\dfrac{40.5}{-13.5}=-3[/tex]
To find the first term, substitute the found value of r and one of the terms into the general formula:
[tex]\begin{aligned}\implies a_5 =a(-3)^4 & = 40.5\\81a & = 40.5\\a & = \dfrac{40.5}{81}\\a & = 0.5 \end{aligned}[/tex]
Sum of the first n terms of a geometric series:
[tex]S_n=\dfrac{a(1-r^n)}{1-r}[/tex]
To find the sum of the first 5 terms of the geometric sequence, substitute n = 5 and the found values of a and r into the formula:
[tex]\begin{aligned}\implies S_5 & =\dfrac{0.5(1-(-3)^5)}{1-(-3)}\\\\& =\dfrac{0.5(1+243)}{1+3}\\\\& =\dfrac{0.5(244)}{4}\\\\& =\dfrac{122}{4}\\\\ & = 30.5\end{aligned}[/tex]
Therefore, the sum of the first 5 terms is 30.5.
please help if you can, vv appreciated!!
Answer:
I believe 72
Step-by-step explanation:
Identify the hypothesis and conclusion of conditional statement.
If three points lie on a line, then they are collinear.
The hypothesis is the phrase following the word if = " three points lie on a line"
The conclusion is the phrase following the word then = "they are collinear."
What is hypothesis?A specific, verifiable prediction of what the researcher(s) believe the study's results will be is known as a hypothesis (plural: hypothese). It is stated at the outset of the investigation.
Most often, this entails speculating on a potential correlation between two variables: the independent variable (what the researcher modifies) and the dependent variable (what the research measures).
The null hypothesis and the alternative hypothesis (known as the experimental hypothesis when the technique of examination is an experiment) are traditionally written as two separate forms of the hypothesis in research.
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Which of the following statements describe the steps to copy XY? Select all that apply.
X
OA. Use a ruler to draw line and label point M.
OB. Use a straightedge to draw line and label point M.
OC. Place a compass point at X and open the compass to length XY.
OD. Using the same setting, place the compass point at M, draw an arc through line , and mark point N as t
Find the sum of each infinite geometric series. 0.5+0.05+0.005+ . . . .
The sum of the infinite geometric series 0.5+0.05+0.005+ . . . is S = 0.55556
The given geometric series is:
0.5 + 0.05 + 0.005 + . . .
The common ratio (r) of a geometric series is given by:
r = a(n) / a(n - 1)
Notice that in the given series:
a(1) = 0.5
a(2) = 0.05
a(3) = 0.005
Hence, the common ratio is
r = a(2) / a(1) = 0.05/0.5 = 0.1
Since 0 < r < 1, the series is convergent and the sum exists.
Use the sum formula:
S = a(1) / (1 - r)
Substitute a(1) = 0.5 and r = 0.1 into the formula:
S = 0.5 / (1 - 0.1)
= 0.5 / (0.9)
= 0.55556
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Solve each system.
5x + y = 0 , 5x + 2y = 30
After solving each system, 5x + y = 0, 5x + 2y = 30, the values of x and y are calculated to be -6 and 30 respectively.
The given equations are considered linear equations as the highest power of the variables in these equations is one.
By rearranging the first equation, the value of y can be found to be,
5x + y = 0
y = -5x
Putting the calculated value of y in the second equation,
5x + 2y = 30
5x + 2(-5x) = 30
5x - 10x = 30
-5x = 30
x = 30 / -5
x = -6
To solve for y, put x = -6 in the first equation as follows,
5x + y = 0
5(-6) + y = 0
-30 + y = 0
y = 30
Hence, the values of x and y in these systems are calculated to be -6 and 30 respectively.
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Simplify each expression by rationalizing the denominator.
3√5/√11
The simplified expression after rationalizing the denominator is [tex]3\sqrt{55} / 11[/tex].
The given expression is,
[tex]3\sqrt{5} /\sqrt{11}[/tex] equation 1
Name the given expression as equation 1.
To simplify the given expression first we need to rationalize the denominator that is [tex]\sqrt{11}[/tex] .
To rationalize the denominator we need to multiply and divide the given equation 1 by [tex]\sqrt{11}[/tex] . On multiplying and dividing the given equation 1 by [tex]\sqrt{11}[/tex], we will get
[tex]3\sqrt{5} /\sqrt{11}[/tex] = ( [tex]3\sqrt{5}[/tex] ×[tex]\sqrt{11}[/tex])/([tex]\sqrt{11}[/tex] ×[tex]\sqrt{11}[/tex])
On further simplifying the expression , we will get
= ([tex]3\sqrt{5}[/tex] × [tex]\sqrt{11}[/tex])/11 = [tex]3\sqrt{55} / 11[/tex]
So, we can conclude that the simplified expression after rationalizing the denominator is [tex]3\sqrt{55} / 11[/tex].
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What is the radius of a table with a circumference of 10 feet?
A. 1.6 ft B. 2.5 ft
C. 3.2 ft D. 5 ft
The radius of a table with a circumference of 10 feet is A. 1.6 ft .
What is circumference of circle?A circle's outside boundary is called the circumference and can be measured, or calculated, by using
Circumference = 2πr
where r is the radius of circle.
Now it is given that,
Circumference of table = 10 feet
Since, Circumference = 2πr
⇒ 2πr = 10
⇒ r = 10/2π
⇒ r = 10/6.28
⇒ r = 1.59
⇒ r ≈ 1.6 feet
Thus, the radius of a table with a circumference of 10 feet is A. 1.6 ft
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Can you have a relation that is not, a function? Can you have a function that is not a relation? Explain.
If you consider the relationship between two quantities, an input/output machine can be used to represent this relationship. You have a function if there is only one output for each input. You have a relation if not.
Can a relationship exist that isn't a function?
A relation might translate inputs to numerous outputs. When it converts each input into exactly one output, something is a function. A subset of the set of all relations is the set of all functions. This implies that while all relations are functions, not all functions are relations.What is relation in math?
A collection of ordered pairs having one item from each set makes up a relation between two sets. If the ordered pair (x,y) is present in the relation and the objects x and y come from different sets, then the objects are said to be connected. One kind of relation is a function.Learn more about relation
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10 less than 5 times a number is equal to 15.
05(2-n) = 15
5-10n = 15
10-5n = 15
5n-10 15
Answer:
5n - 10 = 15.
Step-by-step explanation:
If the number is n then 5 times it is 5n.
10 less than this is 5n - 10.
So, the equation is
5n - 10 = 15.
Consider flipping coins until either two heads hh or heads then tails ht first occurs. by conditioning on the first coin toss, find the probability that ht occurs before hh.
The probability that ht occurs before hh IS 1/3
Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.
P(HH)=1/4
P(HT)=1/4
p(HT) = ½×p(TH) + ½×1 = p(TH)/2 + 1/2.
p(HH) = p(HH)/2
p(HT) = p(TH)/2 + 1/2
p(TH) = p(HH)/2 + p(HT)/2
p(TT) = p(TH)/2 + p(TT)/2
p(HH) = 0.
p(TH) = p(HT)/2
p(HT) = p(HT)/4 + 1/2
p(TH) = 1/3
p(TT) = p(TH) implies p(TT) = 1/3
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How do i do this problem
A clearance rack is marked as 35% off the regular price. a shirt on the clearance rack has a regular price of $45.99. if there is 7.25% sales tax, what will the shirt ring up for at the register? a. $17.26 b. $21.67 c. $29.89 d. $32.06 please select the best answer from the choices provided a b c d
According to the question, the given data for the clearance rack is as written below:
Regular price of the clearance rack = $[tex]$ 45.99[/tex]
Sales tax = [tex]7.25[/tex] percent
As per the question, multiply the given marked percentage with the regular price to get the exact value.
Therefore, Marked price(in $) = [tex]45.99X0.35 = 16.10[/tex]
Now, subtract the calculated price from the regular price:(in $)[tex]45.99-16.10 = 29.89[/tex]
Multiply the regular price with the sales tax: [tex]29.89X0.0725 = 2.17[/tex]
Add the tax price with the calculated regular price to know the register price: [tex]29.89+2.17=32.06[/tex]
Therefore, [tex]32.06[/tex] is the amount for the shirt ring up for at the register.
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The midpoint of AB
is M(-3, 0)M(−3,0). If the coordinates of AA are (1, -4)(1,−4), what are the coordinates of BB?
The required coordinate of b is given as (-7, 4 ).
Given that,
To determine the coordinate of b if M is the midpoint of AB. A(1, -4) and M(-3 ,0).
What is the midpoint?The midpoint is that point the line whose distance from both the ends of the line is equal.
Here,
We have given two coordinates one of the endpoints of AB and the other is midpoint M i.e. A(1, -4) and M(-3, 0).
Definition of midpoint says,
x = [x₁ + x₂] / 2 ; y = [y₁ + y₂] / 2
x₁ = 1, x = -3 , y₁ = -4, y = 0
now,
-3 = [1 + x₂] / 2 ; 0 = [-4 + y₂] / 2
x₂ = -6 - 1 ; y₂ = 0 + 4
x₂ = -7 : y₂ = 4
Thus, the required coordinate of b is given as (-7, 4 ).
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