Distance between (1,4) and (-2,8) is 5 units.
How to find distance between two points?The separation between two points. The coordinates of two points in space are used in the formula.
In coordinate geometry, a two-dimensional or three-dimensional space can be used to calculate the distance between two points using the distance formula.
Let distance between two points ([tex]x_{1}[/tex],[tex]y_{1}[/tex]) and ([tex]x_{2}[/tex],[tex]y_{2}[/tex]) be 'd' then,
d = [tex]\sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2} }[/tex]
We are given two points (1,4) and (-2,8)
So, using formula for distance we get,
d= [tex]\sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2} }[/tex]
=[tex]\sqrt{(-2-1)^{2} + (8-4)^{2} }[/tex]
d [tex]\sqrt{(-3)^{2} + 4^{2} } \\=\sqrt{25} \\=5[/tex]
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If X is less than 0Y is greater than zero and X plus Y equals V which statement about Z is true
I need so much help please save me
Answer:
Step-by-step explanation:
One of the Answers is C
A gardener drew this diagram to find the area of land inside a right-triangular-shaped fence. The length of fence b is 130 feet. The measure of angle A is 42°. What is the area of land inside the fence rounded to the nearest square foot?
The area of land inside the fence is 7600 square feet.
What is the area of the triangle?
If the height of the triangle is 'h' and the base is 'b', then the area of the triangle can be computed by using the formula,
Area = 1/2 * base * height
To find the area of the land inside the fence, we can use the formula for the area of a right triangle:
Area = (1/2) * a * b
where a is the length of one of the legs of the triangle and b is the length of the hypotenuse.
We are given that the length of fence b is 130 feet and that the measure of angle A is 42°. Since the triangle is right, angle A is complementary to angle 90°, so the measure of angle A is 90° - 42° = 48°. Since the measure of angle A is 48°, the other leg of the triangle (which we will call "a") is the side opposite angle A.
We can use the sine function to find the length of side a:
a = b * sin A
= 130 * sin 48°
= approximately 117.3 feet
Substituting these values into the formula for the area of a right triangle gives:
Area = (1/2) * 117.3 feet * 130 feet
= approximately 7600.5 square feet
Rounded to the nearest square foot, the area of land inside the fence is 7600 square feet.
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function rule to find f(10)
Answer:
19
Step-by-step explanation:
replace x with 10
f(10)=9+10
f(10)=19
hopes this helps please mark brainliest
15[tex]\frac{15}{3} =\\[/tex]
The quotient that represents the fraction 15/3 is given as follows:
5.
How to obtain the quotient from the fraction?A fraction has the standard notation given as follows:
Fraction = x/y.
In which the terms have the technical names given as follows:
The top term of the fraction x is called the numerator of the fraction.The bottom term of the fraction x is called the denominator of the fraction.Then the quotient is obtained as the division of the numerator by the denominator.
In this problem, the fraction is given as follows:
15/3.
Then the numerator and the denominator are given as follows:
Numerator: 15.Denominator: 3.Then the quotient is given as follows:
15/3 = 5.
As the division of 15 by 3 has a result of 5.
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HELP NOW A dugout needs to reach at least 54 feet below ground level. This means it needs to be more than 2 1/4 times its current depth. This depth is represented by the inequality 2 1/4d<−54, where d is the current depth of the dugout.
Select from the drop-down to correctly interpret the solution of this inequality.
The current depth of the dugout is *Choose..* feet below ground level.
a. at most 24
b. deeper than 24
c. less than 24
The depth of the dugout is less than 24.
What is inequality?
In mathematics, inequalities describe the relationship between two values that are not equal. Equal means to be equal, not. The "not equal symbol (≠)" is typically used to indicate that two values are not equal. But different inequalities are used to compare the values to determine whether they are less than or greater than.
Consider, the given inequality
[tex]2\frac{1}{4}d < -54[/tex]
Where d is the depth of the dugout.
We have to find the depth of the dugout.
Now to simplify the inequality.
[tex]2\frac{1}{4}d < -54[/tex]
convert improper fraction into a fraction.
[tex]2\frac{1}{4} = \frac{9}{4}[/tex]
⇒ 9/4d < -54
Multiply both sides by 4/9
⇒ d < -54 x 4/9
d < -6 x 4
d < -24
Hence, the depth of the dugout is less than 24.
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A zookeeper ha a 28 gallon of water. He divide the water equally amoung 13 animal. How many gallon of water doe each animal get?
If zookeeper have to divide the 28 gallon of water equally among 13 animal then each animal will get 2.15 gallon of water.
How much means 1 gallon?8 pints, 4 quarts, or 16 cups make up a gallon. Depending on whether you use Imperial or Metric measurements, there are 128 fluid ounces in a gallon.
Is 3 liters the same as 1 gallon?The volume of a gallon is about equal to 3.78541 liters. Consequently, a gallon is larger than three liters.
According to given to given condition
total amount of water:
=28 gallon
no. of animals:
=13 animal
then each animal get water:
=28/13
=2.15 gallon of water
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Kayla is working two summer jobs, making $10 per hour lifeguarding and $21 per
hour tutoring. Last week Kayla worked 4 times as many hours tutoring as she worked
lifeguarding and earned a total of $188. Write a system of equations that could be
used to determine the number of hours Kayla worked lifeguarding last week and the
number of hours she worked tutoring last week. Define the variables that you use to
write the system.
Answer:
10L + 21t = 188
t = 4L
Step-by-step explanation:
Let L be the number of hours spent lifeguarding and t be the number of hours spent tutoring. Kayla earned $188 total, so 10L+ 21t = 188(the number of hours spent lifeguarding/tutoring times how much she gets paid every hour). We also know that she spent 4 times longer tutoring than lifeguarding, so t = 4L. These are our systems of equations.
Find the roots of the factored polynomial.
(x–3)2
Write your answer as a list of values separated by commas.
Answer:
×=3
......................
a particular bank has two loan modification programs for distressed borrowers: home affordable modification program (hamp) modifications, where the federal government pays the bank $1,000 for each successful modification, and non-hamp modifications, where the bank does not receive a bonus from the federal government. in order to qualify for a hamp modification, borrowers must meet a set of financial suitability criteria. what type of hypothesis test should we use to test whether borrowers from this particular bank who receive hamp modifications are more likely to re-default than those who receive non-hamp modifications?
Hypothesis test for µ1 – µ2 can be used to test whether borrowers from this particular bank who receive hamp modifications are more likely to re-default than those who receive non-hamp modifications.
The Independent Samples t Test analyses the means of two separate groups to see if there is statistical support that the population mean values are statistically substantially different. Independent Samples t Test is known as parametric test.
The population means are deemed to be different if the two-sample means are sufficiently dissimilar from one another.
The null and alternative hypothesis for the programs is
H0: μ1 - μ2=0
H1: μ1 - μ2 ≠0
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Determine the slope of the line.
A. 2/1
B. -2/1
C. 1/2
D -1/2
Someone please help me!!!!
Answer: A 2/1
Step-by-step explanation:
Determine the slope of the line by finding 2 points
(2,-1),(4,3)
use slope formula
y2-y1/x2-x1
plug in and solve
3+1/4-2
4/2
2
the slope is 2 or 2/1
8th grade math help pls
Carrie Mae is designing a brace for a large rectangular painting. The painting measures 60 inches by 35 inches. What is the measure of the diagonal brace? Round you answer to the nearest tenth of an inch.
The measure of the diagonal brace of the rectangular painting is 69.5 inches.
What is a diagonal?A diagonal is a line segment that joins one corner (vertex) of a polygon to another but is not an edge (side). In other words, it joins any two non-adjacent vertices of a polygon. So, we form a diagonal in a polygon when we directly join any two vertices which are not joined by any side.
The diagonal of the brace and the length of one side and width of one side form a right-angled triangle and by Pythagoras we have
diagonal^2 = length(L)^2 + width(W)^2
diagonal^2 = 60^2 + 35^2
diagonal^2 = 3600 + 1225
diagonal^2 = 4825
diagonal = [tex]\sqrt{4825}[/tex]
diagonal = 69.5 inches
In conclusion the diagonal of the brace is 69.5 inches
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Ally got a haircut for $45. She wants to leave a 20% tip. How much money should she give the hair dresser altogether?
Answer:
$9
Step-by-step explanation:
20*45/100=9
So Ally should tip $9
Answer
$9.00
Reason
(45 * 0.20) = 9.
a right triangle's height is 3 times the length of its base. if the area of the triangle is 150, what is its height?
The height of the right triangle if the area of the triangle is 150 square units = 30 units
In this question, we have been given a right triangle's height is 3 times the length of its base.
We need to find the height of the right triangle if the area of the triangle is 150 square units.
Let h be the height and b is the base of the right triangle.
A right triangle's height is 3 times the length of its base.
So we get an equation,
h = 3b ............(1)
Using the formula of area of right triangle,
A = 1/2 * b * h
150 = 1/2 * b * 3b .........(from equation (1))
300 = 3b^2
b^2 = 100
b = 10
Subatitute above value of b in equation (1),
h = 3 * 10
h = 30 units
Therefore, the height of right triangle is 30 units
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How do I find the sum of the measures of the marked angles?
Answer: Total angles on the 4
Step-by-step explanation:
The sum of the marked angles = Total angles on the 4 straight lines – Sum of the interior angles of the quadrilateral. Sum of interior angles of polygon of 4 sides = (4 – 2) *1800 =3600
Hence, sum of the marked angles = 4 * 180° – 360° = 720° – 360° = 360°
function rule to find f(3)
Answer:
30
Step-by-step explanation:
Substitute and multiply :))
f(3)=10(3)
f(3)=30
Write an equation of a line in slope-intercept form for the table
The equation of the line in slope-intercept form is y = -2x+8
How to write the equation of a line in slope-intercept form?The equation of a line is an algebraic form of representing the set of points, which together form a line in a coordinate system
The slope-intercept form of the equation of a line is y = mx+b,
where m is the slope and b is the y-intercept
Given the table, pick any two points in order to find the slope:
point 1: x₁ = 0, y₁ = 8
point 1: x₂ = -2, y₂ = 12
slope (m) = (y₂-y₁) / (x₂-x₁)
slope (m) = (12-8)/(-2-0) = 4/(-2) = -2
Using y = mx+b and x₁ = 0, y₁ = 8:
8 = -2(0) + b
b = 8
y = -2x+8
Thus, the equation of the line is y = -2x+8
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The legs of a right triangle are 3 units and 6 units. What is the length of the hypotenuse? Round your answer to the nearest hundredth. (5 points)
Question 4 options:
1)
5.20 units
2)
6.71 units
3)
9.00 units
4)
18.00 units
The length of the hypotenuse is 6.71
How to calculate the length of the hypotenuse ?The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this rule, the areas of the squares on the other two sides add up to the area of the square whose side is the hypotenuse, or the side across from the right angle. This theorem can be expressed as the Pythagorean equation, which is an equation relating the lengths of the sides a, b, and the hypotenuse c:
[tex]{\displaystyle a^{2}+b^{2}=c^{2},}[/tex]
Given ,
Pythagorean therum
a^2 + b^2 = c^2....a and b are ur legs and c is the hypotenuse
3^2 + 6^2 = c^2
9 + 36 = c^2
45 = c^2...take the sqrt of both sides....this eliminates the ^2
sqrt 45 = c
6.708 rounded = 6.71 = c
Therefore the length of the hypotenuse is 6.71
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how many license plates can be made using either 3 digits followed by 3 letters, or 3 letters followed by 3 digits?
Answer:
infinite
Step-by-step explanation:
the law in most states in the usa states there must be 3 letters and 3 numbers so there could be infinite
-hope this helps-
WILL MAKE BRAINLIEST
Adam records the increase in the height, in centimeters, of a plant each week for 10 weeks. His data are shown.
4.5, 3.2, 8.0, 9.1, 10.2, 6.8, 7.2, 95, 10.0, 8.8
Adam wants to display the data on a box plot.
What are the values of the lower quartile, median, and upper quartile that Adam should use for his box plot?
Lower quartile
Median =
Upper quartile =
The values needed for the box plot that Adams wants to display are:
Lower quartile = 6.8
Median = 8.4
Upper quartile = 9.5
How to Find the Lower Quartile, Median, and Upper Quartile?Given the following data that represents the records of the increase in the height of a plant for 10 weeks, 4.5, 3.2, 8.0, 9.1, 10.2, 6.8, 7.2, 9.5, 10.0, 8.8, in order to draft a box plot, the following steps are what Adams should take to find each of the values needed.
Step 1: Order the data set from least to the greatest.
3.2, 4.5, 6.8, 7.2, 8.0, 8.8, 9.1, 9.5, 10.0, 10.2
Step 2: Find the median.
The median is the middle of the data set = (8.0 + 8.8)/2 = 16.8/2 = 8.4
Step 3: Find the lower quartile which is the center of the first part of the data that is divided by the median.
Lower quartile = 6.8
Step 4: Find the upper quartile which is the center of the second part of the data that is divided by the median.
Upper quartile = 9.5
Therefore, the values that Adam needs for his box plot are:
Lower quartile = 6.8
Median = 8.4
Upper quartile = 9.5
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if l lll m, solve for x (9x+25)° (13x-19)° (17y+5)°
The angles, x = 11 and y = 3,if l ll m,
What are angles?When two rays are linked at their ends, they create an angle in geometry. The sides or arms of the angle are what are known as these rays.
When two lines meet at a point, an angle is created.
An "angle" is the measurement of the "opening" between these two rays. It is symbolized by the character. The circularity or rotation of an angle is often measured in degrees and radians.
Angles are a common occurrence in daily life.
Angles are used by engineers and architects to create highways, structures, and sports venues.
According to our question-
A transversal intersects the parallel lines marked by the letters "l" and "m.
The two suplementary angles have the radii (13x - 19°) and (17y + 5)°, respectively.
Thus, (13x - 19)° plus (17y + 5)° equals 180°.
13x + 17y = 180 + 14
13x + 17y = 194 ————(1) (1)
The comparable angles are (9x + 25) and (13x - 19).
Consequently, (9x + 25) = (13x - 19)
9x - 13x = -19 - 25
-4x = -44
x = 11
By changing equation's value for 'x' (1),
13x + 17y = 194
13(11) + 17y = 194
17y = 194 - 143
17y = 51
y = 3
As a result, the solution will be x = 11 and y = 3.
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4. Express the following in exponential form: 4x 4x4 x5x5x5
Answer: 4^3 * 5^3
Step-by-step explanation: 4 repeats itself 3 times and 5 repeats itself 3 times
4^3 * 5^3
Put the numbers in numerical order
4 comes before 5
Answer:
[tex] { 4}^{3} \times {5}^{3} [/tex]
Step-by-step explanation:
I'd assume your x's stand for multiplication, so using that logic there are three fours and three fives. Each being multiplied by itself, so the simplified/exponential version of the equation is:
[tex] {4}^{3} \times {5}^{3} [/tex]
Make sure you put in numerical order (4 goes before 5).
Evaluate one and seven tenths raised to the sixth power divided by one and seven tenths raised to the fifth power, all raised to the second power.
1
1.7
2.89
3.4
The given exponents simplified as 2.89. Therefore, option C is the correct answer.
What is the exponent?Exponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself.
Given that, one and seven tenths raised to the sixth power divided by one and seven tenths raised to the fifth power, all raised to the second power.
Now, ((1.7)⁶÷(1.7)⁵)²
= (1.7)²
= 2.89
The given exponents simplified as 2.89. Therefore, option C is the correct answer.
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Joseph and Raquel are building a scale model of the Alamo Mission for their Texas history project using a scale in which 2 inches represents 30 feet. The enclosed area of the Alamo Mission was 480 feet long and 160 wide.
What should the length of the enclosed area of the scale model be in inches?
Responses
Representative fraction is a form of scale that can be used to change the size of an object to form an image. The required length is 32 inches.
A scale is a fraction of numbers that can be used to either increase or decrease the size of a given object. It is majorly referred to as representative fraction in scale drawing.
Representative fraction = [tex]\frac{length on drawing}{original length}[/tex]
In the given question, we have;
12 inches = 1 feet
x inches = 30 feet
So that:
x = 30 x 12 inches
= 360 inches
representative fraction = [tex]\frac{2 inches}{360 inches}[/tex]
= 5.56 x [tex]10^{-3}[/tex]
Thus, given that the length of the Alamo Mission is 480 feet long. Then:
480 feet = 480 x 12 inches
= 5760 inches
So that,
the required length in inches = 5760 x 5.56 x [tex]10^{-3}[/tex]
= 32 inches
Therefore the expected length of the Alamo Mission is 32 inches.
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The table and scatter plot show the number of ice cream stand customers along with the high temperature for a given day. The line of fit represents the predicted number of customers y, on a day with a high temperature of x°F. Which statement correctly analyzes the residuals?
High Temperature (°F) Customers
82 805
76 612
91 1218
87 1074
85 894
79 675
A)
The smallest residual is 14, and the largest residual is 51. The largest residual corresponds to an outlier in the data.
B)
The smallest residual is 14, and the largest residual is 51. The largest residual does not correspond to an outlier in the data.
C)
The smallest residual is 18, and the largest residual is 45. The largest residual corresponds to an outlier in the data.
D)
The smallest residual is 18, and the largest residual is 45. The largest residual does not correspond to an outlier in the data.
Based on the information provided, the correct statement is: The smallest residual is 14, and the largest residual is 51. The largest residual corresponds to an outlier in the data.
A residual is the difference between the actual value of the dependent variable (in this case, the number of customers) and the predicted value of the dependent variable based on the model (in this case, the line of fit). In other words, it is the error or deviation between the observed data and the model.
In this case, the smallest residual is 14, and the largest residual is 51. This means that the model is most accurate when predicting the number of customers on days with temperatures close to 82°F and least accurate when predicting the number of customers on days with temperatures close to 91°F. The large residual of 51 corresponds to an outlier in the data, which means that the model is not a good fit for this data point and may not accurately predict the number of customers on days with temperatures close to 91°F.
Option A is correct because it correctly describes the range and magnitude of the residuals and identifies the largest residual as corresponding to an outlier in the data. Options B, C, and D are all incorrect because they either do not correctly describe the range or magnitude of the residuals or do not correctly identify the largest residual as corresponding to an outlier in the data.
What do you mean by statistical?
statistics is defined as: the branch of mathematics dealing with data collection, organization, analysis, interpretation and presentation.
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Explain how you would use a number line to find the absolute value of –12.
Answer:
12 notches from both left and right of 0
you want the absolute value of (-12). all that means is how far is the number away from 0. in this case it's just 12
Let point P be (2,4) and Q be (-7, -2). (a) What are the coordinates of the midpoint of segment PQ? Use slope to verify that this point is on the line through P and Q, and use the distance formula to show that this point is just as far from P as it is from Q.
Answer:
Step-by-step explanation:
The midpoint of a line segment with endpoints (x1, y1) and (x2, y2) is:((x1 + x2)/2, (y1 + y2)/2)Substituting the coordinates of points P and Q into the formula, we get:((2 + (-7))/2, (4 + (-2))/2) = (-2.5, 1)The coordinates of the midpoint of segment PQ are (-2.5, 1).To verify that this point is on the line through P and Q, we can find the slope of the line using the coordinates of points P and Q:slope = (y2 - y1)/(x2 - x1) = (-2 - 4)/(-7 - 2) = -6/-9 = 2/3We can then use the point-slope form of a linear equation to write the equation of the line through points P and Q:y - y1 = m(x - x1)
y - 4 = (2/3)(x - 2)We can substitute the coordinates of the midpoint (-2.5, 1) into this equation to see if it is a solution:1 - 4 = (2/3)(-2.5 - 2)
-3 = -10/3The equation is true, so the midpoint (-2.5, 1) is on the line through points P and Q.To show that this point is just as far from P as it is from Q, we can use the distance formula to find the distance from the midpoint to points P and Q:distance = √((x2 - x1)^2 + (y2 - y1)^2)distance from (-2.5, 1) to (2, 4) = √((2 - (-2.5))^2 + (4 - 1)^2) = √(4.5^2 + 3^2) = √(20.25 + 9) = √(29.25) = 5.4distance from (-2.5, 1) to (-7, -2) = √((-7 - (-2.5))^2 + (-2 - 1)^2) = √(4.5^2 + 3^2) = √(20.25 + 9) = √(29.25) = 5.4. Since the distance from the midpoint to points P and Q is the same, the midpoint is just as far from P as it is from Q.
3. Students are taking three busses to go on a field trip. On the first bus there were 14 students, on the second, 18 students, and on the third bus there were 12 students. The total number of students would then be: 14+18+12 To calculate the total students, their chaperone, Ms. Flores decides to add 18 and 12 to get 30 and then adds 14 to get 44. What property is Ms. Flores using to add these numbers in this order?
Ms. Flores using to add these numbers in this order is follow Commutative Property of Addition.
What is Commutative Property of Addition?
No matter what sequence the addends are in when we add two or more integers, the result is always the same. This characteristic may be expressed as A + B Equals B + A. In this case, 2+4=4 + 2 = 6. Due to the fact that the total of both phrases is 6, 2+4 is equivalent to 4+2. The Commutative Property of Addition refers to this.
On the first bus there were 14 students, on the second, 18 students, and on the third bus there were 12 students. The total number of students would then be: 14+18+12=44.
Ms. Flores decides to add 18 and 12 to get 30
18+12= 30
And then adds 14
30+14=44
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if you are sexually active, what are the odds of you contracting an sti by the time you are 25 years old?
The odds of you contracting an sti by the time you are 25 years old is 50%.
Even if a person has only had one physical relationship, that partner could be infected. Of course, the risks of contracting STDs (also known as sexually transmitted illnesses, or STIs) increase if a person has unprotected intercourse with a variety of partners.
Many persons with STDs have no evident indications or symptoms. As a result, individuals may assume they are "clean" and inform partners they don't need to use a protection.
But that's not a good idea. For example, almost six out of ten young people infected with HIV are unaware of their status. As a result, they risk infecting others with the AIDS virus.
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a solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. the total volume of the solid is 12 cubic centimeters. find the radius of the cylinder that produces the minimum surface area of the solid.
11.4 centimeters is the radius of the cylinder .
What does volume mean in plain terms?
The capacity of a solid shape is determined using volume, a three-dimensional quantity.
It implies that a closed figure's volume determines how much three-dimensional space it can fill.
The volume of a cylinder is given by
v = πr²h
The total volume of the two hemispheres is given by
v' = 2× 2/3 πr³
v' = 4/3 πr³
Now, the total volume of the solid is given by:
[tex]V_{T}[/tex] = πr²h + 4/3 πr³
Now, substitute the value of the total volume in the above expression and then solve for h.
12 = πr²h + 4/3 πr³
h = 12/πr² - 4r/3
Now, the surface area of the curved surface is given by:
A = πrh
Now, the surface area of the two hemispheres is given by
A' = 2 × (2πr² )
A' = 4πr²
Now, the total area is given by
[tex]A_{T}[/tex] = 2πr ( 12/πr² - 4r/3) + 4πr²
Simplify the above expression.
[tex]A_{T} =[/tex] 24/r + 4πr²/3
Now, differentiate the total area with respect to 'r'.
[tex]\frac{dA_{T} }{dr}[/tex] = -24/r² + 8πr/3
Now, equate the above expression to zero.
0 = -24/r² + 8πr/3
Simplify the above expression in order to determine the value of 'r'.
8πr³ = 60
r = 11.4
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