Supposing that the two points are (2,4) and (10,10), the distance between them is given by:
A. 10.
What is the distance between two points?Suppose that we have two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
This formula is derived from the Pythagorean Theorem, as the points form a right triangle in the xy-plane, with the hypotenuse being the distance between them.
For this problem, the two points are (2,4) and (10,10), hence the distance between them is given as follows:
[tex]D = \sqrt{(10 - 2)^2+(10 - 4)^2} = \sqrt{100} = 10[/tex]
Hence the distance is of 10 units and option A is correct.
What is the missing information?This problem is incomplete, and I could not find it on any search engine, hence we are going to suppose that the two points are (2,4) and (10,10).
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One week a student exercise 2 hours at school in another 1/4 of an hour at home if 16 of the students total exercise came from plain soccer how much time did the students spend plane soccer that week enter your answer in hours do not include units in your answer
In a week, a student exercise 2 hours at school and another 1/4 of an hour at home.
The total exercise of the students came plain soccer
The total hour a student exercise both home and school is
2 + 1/4
Our LCM is 4
4x2/1 + 4*1/4 /4
8 + 1 / 4
9/4 hours
A student exercise a total of 9/4 hours in a week
If one student exercise a total of 9/4 hours in a week then how many hours will 16 students exercise in a week
Mthematically,
1 student ========= 9/4 hours
16 students ======= x hours
Introduce cross multiplication
1 * x = 16 x 9/4
x = 16 x 9/4
x = 144/4
x = 36 hours
Therefore, 16 students exercise a total of 36 hours in a week
The answer is 36 hours
x = 144 / 4 hours
Find the polynomial function f with real coefficients that has the given degree, zeros, and solution point.
Degree
Solution Point
f(0) = -8
4
Zeros
-4, 1, 1
Polynomial function f with real coefficients that has the given degree, zeros, and solution point is f(x) =2(x⁴ +3x³ -3x²+3x-4).
As given,
Polynomial function f with real coefficients for the given degree, zeros, and solution point is:
Degree 4
Solution Point f(0) = -8
Zeros -4, 1, i
f(x)=k(x +4)(x -1)(x -i)(x +i)
=k (x² + 3x -4) (x² -i²)
=k(x² + 3x -4) (x² +1) ___(1)
Solution point f(0) =-8
-8 =k(0² +3(0) -4)(0² +1)
⇒ k=2
Substitute k=2 in (1)
f(x) =2(x² + 3x -4) (x² +1)
=2(x⁴ +3x³ -3x²+3x-4)
Therefore, polynomial function f with real coefficients that has the given degree, zeros, and solution point is f(x) =2(x⁴ +3x³ -3x²+3x-4).
The complete question is:
Find the polynomial function f with real coefficients that has the given degree, zeros, and solution point.
Degree 4
Solution Point f(0) = -8
Zeros -4, 1, i
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The wholesale price for a shirt is 6.50. A certain department store marks up the wholesale price by 80%. Find the price of the shirt in the department store.
Round your answer to the nearest cent, as necessary.
The new price of the shirt is $11.70
How to determine the price of the shirt in the store?The given parameters are
Price = 6.50
Make up percentage = 80%
The price of the shirt in the store is calculated as
New price = Old price + Old price * Make up percentage
Substitute the known values in the above equation
So, we have the following equation
New price = 6.50 + 6.50 * 80%
Evaluate the product
So, we have the following equation
New price = 6.50 + 5.20
Evaluate the sum
So, we have the following equation
New price = 11.70
Hence, the price of the shirt in the store is $11.70
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mrs green wants to use wood to make a fence around her circular garden. Her garden has a radius of 16 feet How much wood will she need to enclose her garden?.
ANSWER
100.5 feet
EXPLANATION
The radius of the circular garden is 16 feet.
To find how much wood she would need to make a fence around the garden, we need to find the circumference of the garden.
Circumference can be found using the formula:
[tex]C\text{ = 2}\pi r[/tex]where r = radius
Therefore:
[tex]\begin{gathered} C\text{ = 2 }\cdot\text{ }\pi\cdot\text{ 16} \\ C\text{ = 100.5 ft} \end{gathered}[/tex]She would need 100.5 ft length of wood to enclose the garden.
Find the value of x so that f ll g. 18x-44 8x-10
Answer:
x = 3.4
Step-by-step explanation:
18x - 44 = 8x - 10
+10
18x - 34 = 8x
-18x
-34 = -10x
/ 10
x = 3.4
Proof:
18 x 3.4 = 61.2 - ( 44 ) = 17.2
8 x 3.4 = 27.2 - ( 10 ) = 17.2
First person to answer this will get brainilest
Find the area of each figure.
Jeff found that one third bag of popcorn weighed 1/4 lb how many pounds will one full bag of popcorn weigh
Based on the weight of one third bag of popcorn, one bag of popcorn weighs 3/4 lb
How to determine the weight of one bag?The statement is given as
One third bag of popcorn weighed 1/4 lb
This means that
1/3 bag = 1/4 lb
Multiply both sides of the equation by 3
So, we have the following equation
3 * 1/3 bag = 1/4 lb * 3
Evaluate the products
So, we have
3/3 bag = 3/4 lb
Evaluate the quotient
So, we have
1 bag = 3/4 lb
Hence, the conclusion is that the weight of one bag is 3/4 lb
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PLEASE HELP I WILL GIVE BRAINLYEST! ALGEBRA 1 HW
The average rate of change of helicopters height when it starts descending is : - 630.01 ft/min
Solution:Rate of change between two points,
We calculate the average rate of change by dividing the change in y (output) by the change in x. (input). And all we're doing visually is calculating the slope of the secant line that connects two points.Follow these steps to calculate the rate of change on a graph when given two points on the graph:
Determine the coordinates of the given points.Determine the difference in the output values.Determine the difference in the input values.Determine the ratio of the change in y to the change in x: ΔyΔx.Here in the question ,
Given two points (0 , 8400) and (13.333 , 0)
to find the average rate of change ,
Average rate of change = y2 - y1/ x2 - x1
by substituting values,
Average rate of change = 0 - 8400/ 13.333 - 0
= - 8400 / 13.333
= - 630.01 ft/min
since the helicopter is descending the rate of change will be negative
so the rate of change of helicopters height is - 630.015 ft/min
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Help please…..?
Number 3 and 4 only
Answer:
3. You determine the sign of a number when you add a negative number and a positive number by taking the signn of the bigger number. For example -4+3 is -1 because the negative number is bigger than the positive so it takes its sign
4. you can make the number possible by making the number negative
What’s the correct answer answer asap for brainlist
The skeletal muscle can fatigue with too much movement or exercise.
what is skeletal muscles?Skeletal muscle, in contrast to smooth muscle and cardiac muscle, is controlled voluntarily. Skeletal muscle is striated, similar to cardiac muscle; it has long, thin, multinucleated fibers that are crossed in a regular manner by fine red and white lines that give the muscle its unique look. Myofibrils, which are made up of sarcomeres joined in series, make up muscle fibers. The arrangement of actin and myosin filaments, which results in the banding pattern of myofibrils, produces the striations of skeletal muscle. The ability of muscular tissue to contract is special. Only the skeletal muscle can be controlled voluntarily out of the three types of muscles (skeletal, smooth, and cardiac).To more learn about skeletal muscle refers to:
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Help with this question
When solving for the lengths of the sides of a right triangle, we can make use of the acronym SOH-CAH-TOA. In this problem, because x is adjacent to the 52-degree angle and we are also given the length of the hypotenuse, we can use the "CAH" part, which stands for cosine x = adjacent/hypotenuse.
[tex]\begin{gathered} \cos\theta=\frac{adjacent}{hypotenuse} \\ \\ \cos52=\frac{x}{18} \\ \\ 18\cos52=x \\ \\ 11.08=x \end{gathered}[/tex]So the answer is x = 11.08.
7. Let A=(8,9,10,11,12,13).
n=
a. How many subsets does A have?
b. How many proper subsets does A have?
subsets.
a. A has
(Type a whole number.)
b. A has
(Type a whole number.)
proper subsets.
a. A has 64 subsets.
b. A has 63 proper subsets.
What are subsets and proper subsets?If all of the items of Set A are also present in Set B, Set A is said to be a subset of Set B. Set A is, in other words, contained within Set B.
If Set B has at least one element that is not present in Set A, Set A is considered a proper subset of Set B.
If a set has "n" members, the number of subsets of that set is 2ⁿ, and the number of proper subsets of that subset is 2ⁿ-1.
Given:
Set A=(8,9,10,11,12,13)
Number of elements in the given set,n = 6
a. Number of subsets of A = 2ⁿ = 2⁶ = 64
b. Number of proper subsets of A = 2ⁿ-1 = 2⁶-1 =63
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Determine the solution for 45= 3(4b - 1).
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\mathsf{45 = 3(4b - 1)}[/tex]
[tex]\mathsf{3(4b - 1) = 45}[/tex]
[tex]\mathsf{3(4b) + 3(-1) = 45}[/tex]
[tex]\mathsf{12b - 3 = 45}[/tex]
[tex]\large\textsf{ADD 3 to BOTH SIDES}[/tex]
[tex]\mathsf{12b - 3 + 3 = 45 + 3}[/tex]
[tex]\large\textsf{Simplify it}[/tex]
[tex]\mathsf{12b = 45 + 3}[/tex]
[tex]\mathsf{12b = 48}[/tex]
[tex]\large\textsf{DIVIDE 12 to BOTH SIDES}[/tex]
[tex]\mathsf{\dfrac{12b}{12} = \dfrac{48}{12}}[/tex]
[tex]\large\textsf{Simplify it}[/tex]
[tex]\mathsf{b = \dfrac{48}{12}}[/tex]
[tex]\mathsf{b = 4}[/tex]
[tex]\huge\textsf{Therefore, your answer should be: \boxed{\mathsf{b = 4}}}\huge\checkmark[/tex]
[tex]\huge\textsf{Good luck on your assignment \& enjoy your day!}[/tex]
Find the indicated complement.
A certain group of women has a 0.04% rate of red/green color blindness. If a woman is randomly selected, what is the
probability that she does not have red/green color blindness?
Scientists determined that Alaska's average winter was -30.2C. The difference between this temperature and Alaska's highest recorded temperature was 50.33 degrees. What was Alaska’s highest recorded temperature?
*
Answer: -82.2
Step-by-step explanation:
A car rental agency charges $150 per week plus $0.30 per mile to rent a car. Express the weekly cost to rent the car, f, as a function of the number of miles driven during the week, x.
If the number of miles driven is 'x', then the weekly cost to rent a car f(x) is:
[tex]f(x)=0.3x+150[/tex]the cities A B C in respective order lie approximately in a straight line. the distance from city a ti b is 100miles. the distance from city A to city C is 110miles. find the distance from city b to city c
Based on the distance between Cities A and B and also cities A and C, and the fact that the cities are on a straight line, the distance between City B and City C can be found to be 10 miles
How to find the distance?The distance between cities A and B and cities A and C are related because they are on a straight line.
This means that the distance between cities A and B and cities A and C can be used to find the distance between cities B and C and also the distance between cities A and B and cities B and C can be used to find the distance between A and C.
To find the distance between cities B and C, formula is:
= Distance between cities A and C - Distance between cities A and B
= 110 - 100
= 10 miles
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fourteen less than three fourth of a number is negative eight. find the number . translate each sentence into an equation and solve
Answer: n = 8
Step-by-step explanation:
Let the number be n:
The equation is:
[tex]\frac{3}{4}[/tex]n - 14 = -8
Now to solve:
[tex]\frac{3}{4}[/tex]n - 14 + 14 = -8 + 14
[tex]\frac{3}{4}[/tex]n = 6
[tex]\frac{4}{3}[/tex]×[tex]\frac{3}{4}[/tex]n = 6×[tex]\frac{4}{3}[/tex]
n = 8
-4x^2-5x=-9 please show a step by step answer
We can solve the quadratic equation using factorization method.
First, let's re-write the equation:
[tex]\begin{gathered} -4x^2\text{ - 5x = -9} \\ \text{divide through by -1 } \\ 4x^2\text{ + 5x = 9} \\ Re-\text{arranging, we have} \\ 4x^2\text{ + 5x - 9 = 0} \end{gathered}[/tex]Next, we try to factorize the expression by the left:
[tex]\begin{gathered} 4x^2\text{ - 4x + 9x - 9 = 0} \\ (4x^2\text{ - 4x) + (9x - 9) = 0} \\ 4x\text{ (x - 1) + 9(x -1)}=0 \\ (4x\text{ + 9)(x - 1)}=0 \end{gathered}[/tex]Next, we equate each factor to zero to find the value of x
[tex]\begin{gathered} 4x\text{ + 9 = 0} \\ 4x\text{ = -9} \\ \text{x = }\frac{-9}{4} \\ x\text{ - 1 = 0} \\ x\text{ = 1} \end{gathered}[/tex]We can conclude that :
[tex]x\text{ = 1 or }\frac{-9}{4}[/tex]We can also do a check by substituting the value of x back into the equation:
[tex]undefined[/tex]What is the length of XY
SolutionSoltuion:
From the question, the given value id
[tex]\begin{gathered} XQ=3 \\ XR=RW \\ XR+RW=XW \\ XQ=QY \\ XQ+QY=XY \end{gathered}[/tex]By applying the theorem above, we will have the value of XY be
[tex]\begin{gathered} XQ+QY=XY \\ XQ=3 \\ QY=3 \\ XY=3+3 \\ XY=6 \end{gathered}[/tex]Hence,
The final answer = 6
find the area of a circle with a radius of 6 centimeters use 3.14 for [tex]\pi[/tex]
Radius = 6 cm
The area of circle is given by:
[tex]\begin{gathered} A=\pi r^2\text{ } \\ \pi\text{ = 3.14} \\ A\text{ = 3.14 }\cdot6^2 \end{gathered}[/tex][tex]A=113.04cm^2[/tex]A = 113.04 cm^2
A triangle has side lengths of,x, x+1, and 11. Find each side length when the perimeter is 30 inches
The sides of the triangle whose perimeter is 30 are given by-
[a] = 9 , [b] = 10 , [c] = 11.
What is the perimeter of triangle?
The perimeter of triangle is the sum of its sides. Mathematically -
Perimeter [P] = a + b + c
Given is a triangle whose side measurements are x, x + 1, and 11. The perimeter of triangle is 30 inches.
From the definition of the perimeter of a triangle -
Perimeter = sum of its sides
x + (x + 1) + 11 = 30
x + x + 1 + 11 = 30
2x + 12 = 30
2x = 18
x = 9
Now -
Length of side 1 = [a] = 9
Length of side 2 = [b] = 10
Length of side 3 = [c] = 11
Therefore, the sides of the triangle whose perimeter is 30 are given by-
[a] = 9 , [b] = 10 , [c] = 11.
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Let f(x)=x^2−12 and g(x)=13−x.
Perform the composition or operation indicated. (fg)(4)
Answer:
69
Step-by-step explanation:
Rule:
[tex](fg)(x) = f(g(x))[/tex]
So,
[tex](fg)(4) = f(g(4))[/tex]
First solve g(4).
[tex]g(4) = 13 - 4[/tex]
[tex]g(4) = 9[/tex]
Plug g(4) into f(x).
[tex]f(g(4)) = (g(4))^2-12[/tex]
[tex]f(g(4)) = (9)^2-12[/tex]
[tex]f(g(4)) = 81-12[/tex]
[tex]f(g(4)) = 69[/tex]
25. To make an enclosure for chickens, a rectangular
area will be fenced next to a house. Only three sides
will need to be fenced. There is 120 ft of fencing
material.
X
a. What quadratic function represents the area of the
rectangular enclosure, where x is the distance from the house?
Answer:
y = x(120 -2x)
Step-by-step explanation:
You want the quadratic function representing the area of a rectangular enclosure such that three sides of it have a total length of 120 feet.
AreaThe dimension perpendicular to the house is given as x. There are two length of fence with that dimension, so the remaining fence is (120 -2x). This is the length that can be used parallel to the house.
The area (y) is the product of the dimensions of the enclosure:
y = x(120 -2x)
__
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A 1nch candle burns in 4hours at what rate does the candle burn in inches per hour
Answer:
4 1x4=4 so 4 is ur answer
Step-by-step explanation:
Drag a statement or reason to each box to complete this proof.
Given: the measure of angle A B D equals 60 degrees. The measure of angle D B C equals 40 degrees. Prove: triangle A B C is an obtuse triangle. Art: triangle A B C with horizontal base B C is drawn. A bisector B D is drawn on A C. The bisector divides A C into two parts A D and D C.
1. m∠ABD = 60°, m∠DBC=40° Given
2. m∠ABD + m∠DBC = m∠ABC ________
3. ______ Substitution Property of Equality
4. ______ Simplifying
5. ∠ABC is an obtuse angle. _________
6. △ABC is an obtuse triangle. Definition of obtuse triangle
Boxes needed to put in _________
100° = m∠ABC
60° + 40° = m∠ABC
Definition of obtuse angle
Angle Addition Postulate
The table to complete the proof is as follows
Equation statement
1. m∠ABD = 60°, m∠DBC=40° Given
2. m∠ABD + m∠DBC = m∠ABC Angle Addition Postulate
3. 60° + 40° = m∠ABC Substitution Property of Equality
4. 100° = m∠ABC Simplifying
5. ∠ABC is an obtuse angle. greater than 90 degrees
6. △ABC is an obtuse triangle. Definition of obtuse triangle
What is obtuse angles?When an angel is greater than 90 degrees the angle is said to be an obtuse angle.
For the question solved here m∠ABC is greater than 90 degrees hence an obtuse angle.
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Brian is driving on a highway. He uses one gallon of gas every 40 miles he drives. The distance, D (in miles), he travels on g gallons of gas is given by the following function.
D (g) = 40g
How far does Brian drive if he uses 4 gallons of gas?
what is the slope of this line?
SOLUTION
From the question,
We have that the equation of the line is 5x + 2y = 9.
2y = - 5 x + 9
Divide both sides by 2, we have :
y = 1/ 2 ( -5x + 9 )
The slope of this line = -5 / 2
What is the scale factor of the dilation?
The scale factor for the square LMNO to L'M'N'O' is k = 1/2.
What is the scale factor of the dilation?Remember that for any length L, a dilation of scale factor k gives a new length L' such that:
L' = k*L
Look at line LM, it has a length:
L = √(6^2 + 2^2) = √40
Now line L'M' has a length:
L' = √(1^2 + 3^2) = √10
Then we can see that:
L' = k*L
√10 = k*√40
√10/√40 = k
√(1/4) = k
1/2 = k
The scale factor is 1/2.
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Please expand (3x+4)(5x-2)(4x-3) and simplify fully.
The complete expansion of the expression would give; 60x^3 - 11x^2 - 74x + 24
How can the expression be expanded?To expand an expression means that we should be able to obtain the original long expression that was factorized in order to get it. In this case, the expression that we have is (3x+4)(5x-2)(4x-3). We would now have to carry out the expansion in stages.
1) (3x+4)(5x-2)
15x^2 - 6x + 20x - 8
2) We can now carry out the next step in the expansion as we multiply the bracket with the last term in the expression;
15x^2 - 6x + 20x - 8(4x-3)
60x^3 - 45x^2 - 24x^2 + 18x + 80x^2 - 60x -32x + 24
We can now collect the like terms;
60x^3 - 45x^2 - 24x^2 + 80x^2 + 18x - 60x - 32x + 24
60x^3 - 11x^2 - 74x + 24
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