[tex] x_{ 1} = - 7 , x_{ 2} = 4 \\ y_{ 1} = 5 , y_{ 2} = 5[/tex]
Using the distance formula
[tex] \sqrt{(x_{2 } - x_{ 1} {)}^{2} + (y_{ 2} -y_{ 1} {)}^{2} } [/tex]
Substitute with the given values
[tex] \sqrt{(4 - ( - 7 {)}^{2} + (5 - 5 {)}^{2} } [/tex]
[tex] \sqrt{(11 {)}^{2} + (0 {)}^{2} } [/tex]
[tex] \sqrt{121 + 0} = \sqrt{121} [/tex]
[tex] \sqrt{121} = 11[/tex]
Therefore:
Distance [tex] = 11[/tex]
suppose that 10% of people are left handed. if you pick two people at random, what is the probability that they are both left handed? express your answer as a decimal rounded to three decimal places.
The probability that they are both left-handed is 0.01
Probability is the number of ways of achieving success.
the total number of possible outcomes.
Probability takes values between 0 (no chance) and 1 (certain) inclusive.
Complement Rule (probability that an event doesn't occur): P(A') = 1 - P(A) .
Addition rule: P(A ∪ B) = P(A) + P(B) – P(A ∩ B) .
Multiplication rule: P(A ∩ B) = P(A) × P(B) for independent events. P(A ∩ B)
For both, the persons selected at random are left-handed
10 % out of 100 % are left-handed.
Hence the probability that the person is left-handed
P(L) = 10 /100 = 1 / 10 = 0.1
where P(L) is the probability that the person is left-handed.
Therefore both the persons selected are left-handed
= 0.1 * 0.1
= (0.1)^2
= 0.01
Hence the probability that they are both left-handed is 0.01.
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HELP- pleaseeee I’m beggginnngg
The ending number is related to the starting number by n + 9.
To start with this magic number puzzle, let us take a positive number and a negative number. After that we have to perform some simple mathematical operations,
Taking positive number as 10 and negative number as -8.
Now, performing the mathematical operations as described in the next steps.
First starting with positive number which is 10.
Step-1. Add 10
So, 10+10 = 20
Step-2. Multiply by 2
So, 20×2 = 40
Step-3. Subtract 2,
So, 40 - 2 = 38
Step-4. Divide by 2,
So, 38/2= 19
Number chosen in the starting was 10 and at the end it became 19. The number 9 got added to 10.
Now, performing the steps on our negative number which is -8,
Step-1. Add 10
So, 10-8=2
Step-2. Multiply by 2
So, 2×2 = 4
Step-3. Subtract 2
So, 4-2 = 2
Step-4. Divide by 2
So, 2/2 = 1.
Number chosen in the starting was -8 and after performing the steps it became 1.
Now, for any number 'n',
Step-1. Adding 10
So, n+10
Step-2. Multiply by 2
So, 2(n-10) = 2n+20
Step-3. Subtract 2
So, 2n+20-2 = 2n+18
Step-4. Divide by 2.
So, (2n+18)/2 = n+9
The number taken in the starting was n and now it became n+9.
So the ending number becomes 9 times more in the end then the starting number.
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Determine the inverse function of f(x)=1/7x-1/7
The inverse of the function → y= f(x) = 1/7x - 1/7 is -
f⁻¹(x) = 7x + 1.
We have -
y = f(x) = x/7 - 1/7
We have to find its inverse function.
What is the procedure to find inverse of function ?Inverse of a function can be calculated by following the steps mentioned below -
Step 1 - Replace 'y' with 'x' and vice - versa.
Step 2 - Rewrite the equation by solving for 'y'.
Step 3 - Replace 'y' with f⁻¹(x).
According to the question, the equation given is as follows
y = f(x) = x/7 - 1/7
Replace 'y' with 'x', we get -
x = y/7 - 1/7
Now, solve for y -
y/7 = x + 1/7
y = 7(x + 1/7)
y = 7x + 1
Replace 'y' with f⁻¹(x) -
f⁻¹(x) = 7x + 1
Hence, the inverse of the function → f(x) = 1/7x - 1/7 is -
f⁻¹(x) = 7x + 1.
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Choose one value that is in the domain of both y(x) = x² and y² = x and that is greater than
0. Substitute that value into y(x) = x² and y² = x and then simplify. Explain how your answers
help to show that the graph on the left represents a function while the graph on the right
represents a relation. Show your work and use function notation where possible
I
We take the value 2 for which y(2)=4 and [tex]y^{2}[/tex]=2 and see that y(x)=[tex]x^{2}[/tex] is a function and [tex]y^{2}[/tex]=x is a relation.
Domain is the set of values that a variable can take in an algebraic expression.For the equation y(x)=[tex]x^{2}[/tex], x can take any value from negative infinity to positive infinity so we can say that the domain for x is (-∞,∞). For the equation [tex]y^{2}[/tex]=x, x can take any value greater than or equal to zero. Since x=[tex]y^{2}[/tex] we can't take a negative value for x because squared numbers are always positive, so the domain of x will be [0,∞). The common domain for both the equations is [0,∞). Let us choose a value from this common domain,let's say 2. Then for
y(x)=[tex]x^{2}[/tex]⇒y(2)=4 ...(i)
[tex]y^{2} =x[/tex]=2 then y=±[tex]\sqrt{2}[/tex]...(ii)
A function always has an output variable and one or more input variables.For first equation, y is the output variable and x is the input variable. A relation states that two expressions are equal and one is not dependant on another. For equation (i) y is dependant on x but in equation (ii) both the variables are independant.
Thus we can conclude that y(x)=[tex]x^{2}[/tex] is a function and [tex]y^{2}[/tex]=x is a realtion.
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the density of a certain material is such that it weighs 3 grams per fluid ounce of volume. express this density in ounces per liter.
The density of the material in ounce per liter is 0.1059 ounce per liter.
How to express the density in ounce per liter?The ounce per liter conversion selector on this page selects the density measurement unit to convert to starting from ounces per liter (oz/L).
Given that,
Density = 3 grams per fluid ounce
Convert grams to ounce.
1 grams = 0.0353 ounce
Then
Density = 3 * 0.0353 ounce per fluid grams
= 0.1059 ounce per fluid grams
Convert fluid gram to liter
Density = 0.1059 ounce per 1000 liter
= 0.0001059 ounce per liter
Hence, the density in ounce per liter is 0.0001059 ounce per liter.
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Show graphically that the system of linear equations 5x – y = 14 ; x – 2y =1 has a unique solution. Write the coordinates where line x – 2y =1 intersects the X-axis. Write the solution.
The graph of the system of linear equations is shown in the image below, where the solution is: (3, 1)
The coordinates where x - 2y = 1 intersects the x-axis (horizontal axis) is: (-14, 0)
How to Determine the Solution to the System of Equations?Given the linear equations:
5x – y = 14 ---> equation 1
x – 2y = 1 ---> equation 2
Rewrite both equations in slope-intercept form as y = mx + b, where b represents the y-intercept of the line and m represents the slope.
5x - y = 14
-y = -5x + 14
y = 5x - 14 (slope is 5 and y-intercept is -14)
x - 2y = 1
-2y = -x + 1
y = 1/2x - 1/2 (slope is 1/2, and the y-intercept is -1/2).
Therefore, the graph of the system of linear equations is shown in the image below, where the solution is: (3, 1)
The coordinates where x - 2y = 1 intersects the x-axis (horizontal axis) is: (-14, 0)
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•The total surface Areas of a cone of base radius r and perpendicular height h, his given by s=πr ² +πr√(r²+h²). iF r and h are each increasing at the rate of 0.5m/s and 0.2m/s respectively, find the rate at which s is increasing at the instant when r=3m and h =4m
The rate of change of the surface area of the cylinder is approximately to 18.473 square meters per second.
What is the rate of change of the surface area of a cone?
In this question we find a formula for the surface area of a cone, of which we must estimate its rate of change by applying derivative rules and the concept of rate of change. The rate of change is the first derivative of the equation:
ds / dt = 2π · r · (dr / dt) + π · √(r² + h²) · (dr / dt) + π · r · [0.5 / √(r² + h²)] · [2 · r · (dr / dt) + 2 · h · (dh / dt)]
If we know that r = 3 m, h = 4 m, dr / dt = 0.5 m / s and dh / dt = 0.2 m / s, then the rate of change of the surface area of the cone is:
ds / dt = 2π · (3 m) · (0.5 m / s) + π · √[(3 m)² + (4 m)²] · (0.5 m / s) + π · (3 m) · [0.5 / √[(3 m)² + (4 m)²] · [2 · (3 m) · (0.5 m / s) + 2 · (4 m) · (0.2 m / s)]
ds / dt ≈ 18.473 m² /s
The rate of change of the surface area of the cylinder is approximately to 18.473 square meters per second.
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3. Exponential Function:
Bacteria grows on food by doubling every hour.
If the bacteria initially covers 10% of the food, it will
cover the entire food source in 3.3 hours.
Answer:
[tex]y=0.1(2)^x[/tex]
where x is time in hours, and y is the number of bacteria in percent in decimal form.
Step-by-step explanation:
General form of an exponential function:
[tex]y=ab^x[/tex]
where:
a is the initial value (y-intercept).b is the base (growth/decay factor) in decimal form.Define the variables:
Let x = time (in hours)Let y = number of bacteria (in percent in decimal form)If the bacteria grows on food by doubling every hour then the growth rate b = 2.
If the bacteria initially covers 10% of the food then y = 10% when x = 0.
Therefore, a = 10% = 0.1.
Therefore, the equation is:
[tex]y=0.1(2)^x[/tex]
Substitute x = 3.3 into the found equation:
[tex]\begin{aligned}x=3.3 \implies y & =0.1(2)^{3.3}\\& =0.9849155307...\\& =1.0\:\sf (nearest\:tenth)\end{aligned}[/tex]
As 1.0 = 100%, this justifies the claim.
[tex]\begin{array}{|c|c|c|}\cline{1-3} x & y & y \\\cline{1-3} 0 & 10\% & 0.1\\\cline{1-3} 1 & 20\% & 0.2\\\cline{1-3} 2 & 40\% & 0.4\\\cline{1-3} 3 & 80\%\ & 0.8\\\cline{1-3} 4 & 160\% & 1.6\\\cline{1-3}\end{array}[/tex]
circles with centers $(2,1)$ and $(8,9)$ have radii $1$ and $9,$ respectively. the equation of a common external tangent to the circles can be written in the form $y
The value of b in the equation of common external tangent to both the given circles is 3.75.
A circle is a shape formed by all points in a plane that are at a particular distance from the centre. It is the curve sketched out by a point moving in a plane so that its distance from a particular point remains constant.The equation of a circle with a centre at (2,1) and a radius of 1 is : (x - 2)² + (y - 1)² - 1² = 0.The equation of a circle with a center at (8,9) and a radius of 9 is : (x - 8)² + (y - 9)² - 9² = 0.The equation of the common external tangent is :y = mx + b, where m < 0If m < 0, then the circles touch each other.We will get the equation of the common external tangent by equating the equations of both the circles.(x - 2)² + (y - 1)² - 1² = (x - 8)² + (y - 9)² - 9²(y - 1)² - (y - 9)² = (x - 8)² - (x - 2)² + 1² - 9²(2y -10)(8) = (2x - 10)(-6) + 1 - 8116y - 80 = -12x + 60 - 8016y = -12x + 60y = (-3/4)x + (15/4)y = -0.75x + 3.75y = mx + bOn comparison, we get b = 3.75.To learn more about tangent, visit :
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List the numbers in order from least to greatest.
5/8, 1/2, 0.3 , -3/5 , -0.8 , -1/10
Answer:
-3/5, -1/10, -0.8, 0.3, 1/2, 5/8
Step-by-step explanation:
negatives are always less than positive numbers. As you can see the first numbers that are negative count down and then once it turns positive the numbers count up. For example, it goes -3,-1,-0 then 0,1,5
How do you do these problems and solve
These questions are equations of one variable. An equation is an expression which has an equal sign, which is then evaluated isolating the variable in one side if the equation.
1) r + 12 = 36
r = 36 -12
r = 24
2) 22+ m = 24
m = 24 - 22
m = 2
3) -27 = n - 29
n = 2
4) -5 = b -26
b = 21
5) -17 = x -23
x = 5
6) v - 26 = - 4
v = 22
7) x+12 = 38
x = 26
8) 8= -12+ a
a = 20
9) b- 21 = 4
b = 25
10) 2 = x - 23
x = 25
11) x + 25 = 46
x = 21
12) -18 = x - 22
x = - 4
These questions are equations of one variable. An equation is an expression which has an equal sign, which is then evaluated isolating the variable in one side if the equation.
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use the foil method to evaluate the expression: left parenthesis 2 plus square root of 3 right parenthesis left parenthesis square root of 3 minus 7 right parenthesis
-5√3 - 11 is value of expression.
What do math Surds mean?
An expression with a square root, cube root, or other root symbol is called a surd. Since the decimals of irrational numbers do not finish or recur, they cannot be expressed properly in decimal form. Surds are used to write irrational numbers precisely.( 2 + √3) (√3 - 7)
First = 2√3
outer = 2(-7) = -14
inner = √3 √3 = 3
last = √3 (- 7)
= 2√3 + (- 14) + 3 + ( - 7√3)
= -5√3 - 11
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What clockwise angle rotations, if any, between 0 degrees and 360 degrees make the figure rotate onto themselves?
A clockwise 360 degrees angle rotation will make the figure rotate onto themselves.
Any angle rotations other than a 0 degree or a 360 degree will change the figure and so does not rotate onto themselves.
To rotate onto themselves, which means the figure should not be changed after the rotation transformation, we have to rotate it 360 degrees.
We are asked for a clockwise angle rotation, so the require angle rotation is of 360 degrees.
0 degree angle rotation will not make a rotation. So we will go with a 360 degree rotation. Any figure after a 'full circle' clockwise rotation will goes onto themselves.
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Geometry question!!
Please help i’ll give points!
Answer:
63°
Step-by-step explanation:
[tex]m\angle OZQ=m\angle OZP+m\angle PZQ \\ \\ 125^{\circ}=62^{\circ}+m\angle PZQ \\ \\ m\angle PZQ=63^{\circ}[/tex]
Avani is making smoothies. Each smoothie uses cup of yogurt. How many cups of
yogurt does she need to make 17 smoothies? Express your answer in simplest form.
5
16
Answer type: Mixed number
Submit Answer
Avani needs 6 cups of yogurt.
To find the amount of yogurt required for specified number of smoothies, simple multiplication operation needs to be performed.
For 1 smoothie, the required amount of yogurt = 3/8 cups
So, the required amount of yogurt for 17 smoothies = (3/8) × 17
Performing multiplication and division to find the amount of yogurt required
Amount of yogurt required = 51/8 cups
Converting the fraction into fraction into decimal -
Amount of yogurt required = 6.375 cups
Rounding off the number of cups to convert it in simplest form -
Number of cups of yogurt required = 6 cups
Hence, the amount of yogurt for making 17 smoothies is 6 cups.
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The complete question is -
Avani is making smoothies. Each smoothie uses 3/8 cups of yogurt. How many cups of yogurt does she need to make 17 smoothies? Express your answer in simplest form.
The teacher is handing out note cards to her students. She gave 48 note cards to the first student, 54 note cards to the second student, 60 note cards to the third student, 66 note cards to the fourth student, and 72 note cards to the fifth student. If this pattern continues, how many note cards will the teacher give to the sixth student?
Answer:
She will give 78 students to the sixth student.
Step-by-step explanation:
The pattern is adding 6 each time.
Use the point slope form to write the equation of a line that passes through the point (1,-17) with slope 4
The equation of line passing through (1, -17) with slope 4 will be y = 4x - 21 .
What is the slope intercept form of a line ?
The equation of line that can be written as y = mx + c, where m is the slope and c is the line's y-intercept, is known as a slope intercept form.
The equation of a line which is passing through point (1 , -17) with slope m = 4 can be found by using the slope intercept form which is given by :
y = mx + c
Here ; m is the slope and c is the y - intercept of the line.
So ;
The point given is (x , y) = (1, -17) and slope m = 4. Let's use these values to find out the equation of the line. But before that let's find out the value of y-intercept (c).
-17 = (4 × 1) + c
c = - 17 - 4
c = -21
Hence , the equation of line passing through (1, -17) will be :
y = 4 × x + (-21)
or
y = 4x - 21
Therefore , the equation of line passing through (1, -17) with slope 4 will be y = 4x - 21 .
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PLEASE HELP!!!
Solve.
-2x+3y-z=-2
3x + y = 4
-2y+2z=4
Enter your answer, in the form (x, y, z), in the boxes in simplest terms.
Step-by-step explanation:
the second equation gives us right away
y = 4 - 3x
we can use that now in the 3rd equation :
-2(4 - 3x) + 2z = 4
-8 + 6x + 2z = 4
6x + 2z = 12
3x + z = 6
z = 6 - 3x
now we use both in the 1st equation :
-2x + 3(4 - 3x) - (6 - 3x) = -2
-2x + 12 - 9x - 6 + 3x = -2
-8x + 6 = -2
-8x = -8
x = 1
y = 4 - 3x = 4 - 3×1 = 4 - 3 = 1
z = 6 - 3x = 6 - 3×1 = 6 - 3 = 3
so,
(1, 1, 3)
if i drop a watermelon from the top of a water tower, and it takes 3.34 seconds to hit the ground, calculate how tall the tower is in meters.
The height of the water tower is found to be 54.66 meters.
What is acceleration due to gravity?A free-falling object is one that is falling solely due to gravity.
Some key features regarding the acceleration due to gravity are-
A free-falling component has a downward acceleration of 9.8 m/s/s (on Earth). This magnitude for the acceleration of a free-falling object is so significant that it has its own name. The acceleration of gravity is the acceleration of any object moving solely under the influence of gravity. In fact, the acceleration of gravity is so important quantity that scientists have a special symbol to represent it - the symbol g. The most precise numerical value for gravity's acceleration is 9.8 m/s/s.Now, according to the question;
It takes a watermelon 3.34 sec to reach the ground.
Use the equation of motion in straight line.
D = (1/2) x (gravity) x (time)²
D is the height of the water tower.
= (1/2) x (9.8 m/s²) x (3.34 sec)²
= (4.9 m/s²) x (11.16 sec²)
D = 54.66 meters.
Thus, the height of the water tower is estimated as 54.66 meters.
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Gary, the school chef, needs to make 40
tacos for every 15 students. How many tacos
would Gary need to prepare for 3 students?
The number of tacos that is needed for 3 students is 8 tacos.
How many tacos would be needed for 3 students?
The first step is to determine the number of tacos that is needed for one student. To determine this value, divide the total number of tacos by the total number of students.
Division is the mathematical operation that is used to determine the quotient of two or more numbers. Division entails splitting a number into equal groups using another number. The sign used to denote division is ÷
Tacos that should be prepared for one student = total tacos / number of students
= 40 / 15
In order to determine the number of tacos needed for 3 students, multiply the result gotten in the previous step by 3. Multiplication is the process used in determining the product of two or more numbers. The sign used to denote multiplication is x .
Tacos needed for 3 students = (40 / 15) x 3 = 8
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1. 3x-2x² = 7
2. 5-2x² = 6x
3. (x+3)(x + 4) = 0
4. (2x+7)(x-1)=0
5. 2x(x-3) = 15
Answer:
No 3
2x+4x+3x+12=0
9x+12=0
9x=0_12
9x=-12
divide by 9
x=1.333
25. ALGEBRA Angle E and Angle F are supplementary. The measure of angle E is 54 more than the
measure of Angle F. Find the measures of each angle.
The measure of each angle is , ∠E = 117° and ∠F = 63°
What is an angle ?In the geometry, angle is defined as the geometry formed by the multiple rays. Or we can also say that the angle is a figure formed by two rays with having same initial point. The rays are also known as the sides of the angle. A angle can have two rays.
What are supplementary angles?Angles which are on the same line are supplementary angles. The sum of supplementary angles are always equals to 180 degree.
Some common terms related to angles :
Endpoint : It is the point where the rays met to each other.Ray : Ray is the side or line segment on which angle is formed.Curve : It is a line but not straight i.e. a bended line.Tangent : A line which touches the surface of curve.In the given question:
Let measure of ∠E = x
and, measure of ∠F = y
as ∠E and ∠F are supplementary angles therefore their sum is 180
i.e. m∠E + m∠F = 180
=> x + y =180
also, m∠E is 54 more than m∠F
=> y+54 + y = 180
=> 2y + 54 = 180
=> y = 180-54 / 2 = 63
and , x = y + 54 = 63 + 54 = 117
Hence, ∠E = 117 degree and ∠F = 63 degree
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HI, I need help!! I'm so lost on how to solve this.
Answer:
3⁹
Step-by-step explanation:
you can use a calculater and it will give 19683 and 3⁹ gives 19683
Area of Circles Area of Circles Area of Circles
The area of the circle with the radius is 192 square feet
How to calculate the area of the circle?The figure represents the given parameter
On the figure, we have the radius (r) to be
r = 8 ft
The area of a circle is calculated as
A = πr^2
Where π is given as
π = 3
So, we have
A = 3 * 8^2
Evaluate the exponent
A = 3 * 64
Evaluate the product
A = 192
Hence, the area of the circle with the radius is 192 square feet
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the area of the circle is 201.06
Find the value of x and y.
Question 2(Multiple Choice Worth 5 points)
(Irrational Numbers LC)
Describe in words where √60-11 would be plotted on a number line.
O Between -3 and -4, but closer to -3
O Between -3 and -4, but closer to -4
O Between 7 and 8, but closer to 8
O Between 7 and 8, but closer to 7
The number √60 - 11 will be plotted between -3 and -4, but closer to -3 (Option A), as seen by number system.
What is number system?A system of writing numbers is known as a number system. It is the mathematical notation for consistently employing digits or other symbols to represent the numbers in a particular set. It represents the arithmetic and algebraic structure of the numbers and gives each number a distinct representation.Given: √60 - 11
The value of √60 - 11 is given as: √60 - 11 = 7.2 (approx.) - 11 = -3.2
Thus, as seen from the calculation of the value of the given number, √60 - 11 will lie between -3 and -4, but closer to -3 as -3.2 is closer to -3 than to -4.
Hence, The number √60 - 11 will be plotted between -3 and -4, but closer to -3 (Option A), as seen by number system.
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Write 2.5 as a mixed number and as an improper fraction. Write your answers in simplest form.
Answer:5/2 and 2 1/2
Step-by-step explanation:
Answer:
Step-by-step explanation:
2.5 as a mixed number is 2 1/2 since 1/2 = 0.5
2.5 as an improper fraction is 5/2
martin s cat weighs 12.37 pounds. what is this weighs written as a mixed number
Answer:
your mixed fraction would be 12 37/100
Step-by-step explanation:
The number has two parts the whole number part is 12, and the decimal part is .37, 12 would be the whole number part of your mixed fraction and we will convert the .37 to become the fraction part of your mixed fraction.
You have to convert the decimal part into a fraction since there are two decimal places you will have 100 in the denominator .37 becomes 37/100 simplify this fraction if possible.
which of rthe following goups of scores would hav ethe smallest standard deviation 20, 40, 60, 80, 100
In dataset 60 is the data is spread more tightly around the mean than in other datasets. Accordingly, it would have a smaller standard deviation.
n dataset C, the data is spread more tightly around the mean than in other datasets. Accordingly, it would have a smaller standard deviation
Standard deviation is 60
What do you mean by standard deviation?The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed. In contrast, a high or low standard deviation indicates that the data points are, respectively, above or below the mean. A standard deviation that is close to zero implies that the data points are close to the mean. The curve at the top is more dispersed and has a greater standard deviation than the curve at the bottom, which is more concentrated around the mean and has a lower standard deviation.
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HELPPPPPPPPPPPPPPPPPPPPPPPPP! whats 1+1