Answers
Step-by-step explanation:
you have both points : (1, 1) and (5, 5).
so, we don't need to do any triangle calculations to get the height of the main triangle.
all we need to do is calculate the distance between these 2 points.
2 points in a coordinate grid create a right-angled triangle.
the direct distance is the Hypotenuse (the side opposite of the 90° angle). and the legs are the x- and the y-coordinate differences (one up or down the other left or right).
and we can use Pythagoras
c² = a² + b²
c being the Hypotenuse a and b being the legs.
so, how long are these legs here ?
the x-difference is 5 - 1 = 4.
also the y-difference is 5 - 1 = 4
so,
distance² = 4² + 4² = 16 + 16 = 32
distance = sqrt(32) = sqrt(16×2) = 4×sqrt(2) =
= 5.656854249...
the distance of P to the line RQ is 5.656854249...
Related Questions
The standard deviation of the weights of elephants is known to be approximately 15 pounds. We wish to construct a 95% confidence interval for the mean weight of newborn elephant calves. Fifty newborn elephants are weighed. The sample mean is 244 pounds. The sample standard deviation is 11 pounds. Round all answers to the nearest hundredth. Conclusion: We estimate with 95% confidence that the mean weight of all elephants is between?
Answers
Confidence interval is written as
point estimate ± margin of error
In this case, the point estimate is the sample mean
the formula for calculating margin of error is expressed as
[tex]\text{margin of error = z }\times\frac{\sigma}{\sqrt[]{n}}[/tex]where
σ = population standard deviation
n = sample size
z is the z score corresponding to a 95% confidence level. From the standard normal distribution table, z = 1.96
From the information given,
σ = 15
n = 50
sample mean = 244
By substituting these values into the formula,
[tex]\text{margin of error = 1.96 }\times\frac{15}{\sqrt[]{50}}\text{ = 4.16}[/tex]Thus,
confidence interval = 244 ± 4.16
Lower limit of conidence interval = 244 - 4.16 = 239.84
Upper limit of conidence interval = 244 + 4.16 = 248.16
Conclusion: We estimate with 95% confidence that the mean weight of all elephants is between 239.84 pounds and 248.16 pounds
What is the volume of this aquarium??in.in?in5 in.20 in.14 in.12 in.10 in
Answers
ANSWER :
2040 in^3
EXPLANATION :
From the problem, we have an aquarium.
If we divide the solid into two parts, we will have two rectangular prisms :
The big prism is 10 in by 12 in by 14 in.
The small prism is 5 in by 12 in by (20 - 14 = 6) 6 in
The volume formula of a prism is :
[tex]V=lwh[/tex]The volume of the solid is the sum of the volumes of two prisms.
That will be :
[tex]\begin{gathered} V=10(12)(14)+5(12)(6) \\ V=2040in^3 \end{gathered}[/tex]If 1000 pennies are put into rolls of 50 pennies, how many rolls will be made?
Answers
100 divided by 50=20
Answer:
12
Step-by-step explanation:
50x2=100
100x10=1000
2+10=12
Earl Miller, a customer of J. Crew, will pay $400 for a new jacket. J. Crew has a 60% markup on selling price. What is the most that J. Crew can pay for this jacket?
Answers
If Earl Miller, a customer of J. Crew, will pay $400 for a new jacket. J. Crew has a 60% markup on selling price. The most that J. Crew can pay for this jacket is $160.
How to find the total payment?Given parameters:
Cost of new jacket = $400
Markup = 60%
Now let find the amount that was paid for the jacket using this formula
Amount = Cost of new jacket × ( 1- markup)
Let plug in the formula
Amount = $400 × ( 1 - .60 )
Amount = $400 × .40
Amount = $160
Therefore we can conclude that the amount of $160 was paid the most.
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26/w = 5/6 what is w?
Answers
Here, the expression is 26/w=5/6.
Therefore,
[tex]\begin{gathered} \frac{26}{w}=\frac{5}{6} \\ w=\frac{26\times6}{5} \\ w=\frac{156}{5} \\ w=31.2 \end{gathered}[/tex]So, the value of w is 31.2
Hey I need help on this question so today I want you help me solve it please
Answers
Definitions in Algebra
A variable is a letter or symbol that represent numbers in a general way.
A coefficient is a number that multiplies a variable
A term is a combination of numbers and variables, all of them multiplied.
An exponent represents multiple products, like 2*2*2= 2^3
The answer is shown in the image below:
Lines that are perpendicular have slopes that arethe same or opposite and reciprocal.
Answers
When lines are perpendicular the slopes of both are opposite and reciprocal, that is:
[tex]m\text{ and - }\frac{1}{m}[/tex]In words, if we have a line with slope = m, the perpendicular line to that line will have a slope = - 1/m ( opposite and reciprocal).
I inserted a picture of the question, please give a VERY SHORT explanation
Answers
To multiply two polynomials we have to multiply each term in one polynomial by each term in the other polynomial, and then add the similar terms, as follows:
The average adult heart pumps about 84. mL/s of blood at 72 beats per minute. Suppose you need to calculate how long it would take the average heart tocirculate 6300. mL of blood.Set the math up. But don't do any of it. Just leave your answer as a math expressionAlso, be sure your answer includes all the correct unit symbols.
Answers
There are two ways to interpret the problem.
1) One is that a heart circulates 84ml of blood per second, although this makes the information of the beats per minute unnecessary.
In that case, an average heart would circulate 6300 ml of blood as shown in the next expression:
[tex]\begin{gathered} 6300=84t \\ \Rightarrow t=\frac{6300}{84} \end{gathered}[/tex]Where t is the time expressed in seconds
2) A second approach, and the one that makes better sense, is that each beat of the heart pumps 84ml per beat. Then, the expression that gives us the time needed to reach 6300ml of blood is:
[tex]\begin{gathered} \frac{84ml}{\text{beat}},\frac{72beats}{\min } \\ \Rightarrow84\cdot\frac{72ml}{\min}=\frac{6048ml}{\min } \end{gathered}[/tex]In that case, the equation that expresses the time needed by the heart to bump 6300ml of blood is:
[tex]\begin{gathered} 6300=6048\cdot t \\ \Rightarrow t=\frac{6300}{6048} \end{gathered}[/tex]With t being the time given in minutes
Fill in the blanks to find other expressions for 8%a. __ for every 100, b. __for every 50, c. 1 for every __, d. 0.5 for every __. 150
Answers
Using ratios, the sentences regarding a percentage of 8% are given as follows:
a. 8 for every 100.
b. 4 for every 50.
c. 1 for every 12.5.
d. 0.5 for every 6.25.
Ratio between two amountsThe ratio between two amounts a and b is given by the division of a by b, as follows:
r = a/b.
One example of ratio is a percentage, as a percentage of x% is equivalent to the ratio of x to 100, that is:
r = x/100.
Hence a percentage of 8% is equivalent to the following ratio:
r = 8/100.
That is, 8 for every 8.
Ratios are fractions, and they can be simplified, dividing both the numerator and the denominator by the same amount, as is the case in this problem:
r = 4/50 (simplifying by 2, four for every 50).r = 1/12.5 (simplifying by 4, one for every 12.5).r = 0.5/6.25 (simplifying by 2, 0.5 for every 6.25).More can be learned about ratios at https://brainly.com/question/2328454
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Factor the expression using the GCF. 11. 24 - 9 12. 14x + 63
Answers
Recall that the GCF of two ( or more numbers) is the highest number that divides exactly the two numbers.
11.- Notice that:
[tex]\begin{gathered} 24=3\cdot8, \\ 9=3\cdot3. \end{gathered}[/tex]Therefore:
[tex]9-24=3(8-3)\text{.}[/tex]12.- Notice that.
[tex]\begin{gathered} 14x=7\cdot2x, \\ 63=7\cdot9. \end{gathered}[/tex]Therefore:
[tex]14x+63=7(2x+9)\text{.}[/tex]Answer:
11.-
[tex]3(8-3)\text{.}[/tex]
12.-
[tex]7(2x+9)\text{.}[/tex]
Fifth grade > Y.5 Compare and convert Which is more, 1/2 of a pound or 6 ounces? of a pound 2. 6 ounces neither; they are equal Submit
Answers
We should know that :
1 pound = 16 ounces
The question is :
Which is more, 1/2 of a pound or 6 ounces?
so,
1/2 of a pound = 1/2 x 16 = 8 ounces
So,
8 ounces > 6 ounces
so, the answer is option 1
The more is 1/2 of a pound
Mr. Edmonds is packing school lunches for a field trip for the 6th graders of Apollo Middle school. He has 50 apples and 40 bananas chips. Each group of students will be given one bag containing all of their lunches for the day. Mr. Edmonds wants to put the same number of apples and the same number of bananas in each bag of lunches. What is the greatest number of bags of lunches Mr.Edmonds can make? How many apples and bananas will be in each bag?
Answers
Simplify the expression leave expression in exact form with coefficient a and b so we have a✔️b.
Answers
coefficient of a = 2x
Explanation:[tex]\text{The expression: 2}\sqrt[]{x^2y}[/tex]Simplifying:
[tex]\begin{gathered} \sqrt[]{x^2}\text{ = x} \\ 2\sqrt[]{x^2\times y}\text{ = 2x}\sqrt[]{y} \end{gathered}[/tex]Since we are told the coefficient of a can be the product of a number and variable:
[tex]\begin{gathered} 2x\sqrt[]{y}\text{ is in the form a}\sqrt[]{b} \\ a\text{ = 2x},\text{ b = y} \\ 2\text{ = number, x = variable} \\ 2x\text{ = product of number and variable} \\ \text{coefficient of }a\text{ = 2x} \end{gathered}[/tex]Identify the property of real numbers illustrated in the following equation.(+6) + [y? • (-4)] = [y2 • (-4)] + (-6)
Answers
Given
[tex]\mleft(+6\mright)+\mleft[y^2•(-4)\mright]=\mleft[y^2•(-4)\mright]+(-6)[/tex]Answer
Commutative property of addition
B. Are the graphs of y = a|x| and y = |ax| the same when a is negative? Why?
Answers
The absolute value gives always a positive number.
If a is negative, then a|x| is negative and |ax| is positive.
Therefore, the graph of y=a|x| won't be the same as the graph of y=|ax|.
Another way to see it, is by using the property:
[tex]\mleft|ax\mright|=\mleft|a\mright|\cdot\mleft|x\mright|[/tex]Since a is negative, then |a| = -a. So, |ax| = -a|x|, which is clearly different from a|x|.
Convert do you need to the specified equivalent unit round your answer to the nearest 1 decimal place, if necessary
Answers
Answer:
There are 59251.5 decigrams in 209 ounces.
Step-by-step explanation:
We'll solve this using the rule of three.
We know that there are 28.35 grams in an ounce. This way,
This way,
[tex]\begin{gathered} x=\frac{209\times28.35}{1} \\ \\ \Rightarrow x=5925.15 \end{gathered}[/tex]And since we know there are 10 decigrams in a gram, we'll have that:
This way,
[tex]\begin{gathered} y=\frac{5925.15\times10}{1} \\ \\ \Rightarrow y=59251.5 \end{gathered}[/tex]This way, we can conclude that there are 59251.5 decigrams in 209 ounces.
Hello good night everyone I need help with number 6 I’m so lost I’m abt to cry
Answers
We have to add and substract this complex numbers.
In this type of problems, where we have to add or substract complex numbers, we need to have the real and imaginary terms separated.
In this case, we already have all the terms as real or imaginary.
Then, we can group the real terms on one side and the imaginary terms on the other side and simplify them. We can do it like this:
[tex]\begin{gathered} (7-2i)-(-1-4i)+3 \\ 7-2i+1+4i+3 \\ (7+1+3)+(-2i+4i) \\ 11+2i \end{gathered}[/tex]Answer: 11 + 2i
Graph a right triangle with the two points forming the hypotenuse. Using the sides,find the distance between the two points in simplest radical form.
Answers
Answer:
Explanation:
Given the points:
[tex](7,-5)\text{ and }(2,-7)[/tex]The graphed right triangle is given below:
Using the sides, we then find the distance between the two points, d.
By the Pythagorean theorem:
[tex]\begin{gathered} d^2=[5-(-7)]^2+[7-2]^2 \\ d^2=[5+7]^2+5^2 \\ d^2=12^2+5^2 \\ d^2=144+25 \\ d^2=169 \\ d^2=13^2 \\ \implies d=13 \end{gathered}[/tex]The distance between the two poi
Write an inequality for the graph shown below. Use x for your variable. + -11-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 X
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according to the graph, inequality is:
[tex]x\ge3[/tex](a) Teresa owns 9 shares of a certain stock. Yesterday the total value of her shares went down by90 dollars. What was the change in value for each share?dollarsHelp ASAP PLEASE
Answers
we have that
Divide $90 by the number of shares
so
90/9=$10
the answer is $10
What tip will Brady get if a customer adds a 15% tip to his $18.52 meal cost?
Answers
Brandy will get a tip of $2.778
Here, we want to get the amount of tip Brandy will get
In the question, the tip is 15% of $18.52
That will mathematically be;
[tex]\begin{gathered} \frac{15}{100}\text{ }\times\text{ \$18.52} \\ \\ =\text{ }\frac{277.8}{100}\text{ = \$2.778} \end{gathered}[/tex]Choose the scenarios that demonstrate a proportional relationship for each person's income.
Millie works at a car wash and earns $17.00 per car she washes.
Bryce has a cleaning service and charges $25.00 plus $12.50 per hour.
Carla makes sandwiches at her job and earns $7.85 per hour.
Tino is a waiter and makes $3.98 per hour plus tips.
Answers
The scenarios that demonstrate a proportional relationship for each person's income are :
Millie works at a car wash and earns $17.00 per car she washes.Carla makes sandwiches at her job and earns $7.85 per hour.Consider the income as y in each scenario
Scenario 1
Millie works at a car wash and earns $17.00 per car she washes.
Consider the number of car she washes as x
y = 17x
y ∝ x
This is a proportional relationship
Scenario 2
Bryce has a cleaning service and charges $25.00 plus $12.50 per hour.
The relationship will be
y = 25 +12.50x
where x is the number of hours
This is not a proportional relationship
Scenario 3
Carla makes sandwiches at her job and earns $7.85 per hour.
The relationship will be
y = 7.85x
y ∝ x
Where x is the number of hours
This is a proportional relationship
Scenario 4
Tino is a waiter and makes $3.98 per hour plus tips.
The relationship will be
y = 3.98x + tips
Where x is the number of hours
This is not a proportional relationship
Hence, the scenarios that demonstrate a proportional relationship for each person's income are
Millie works at a car wash and earns $17.00 per car she washes.Carla makes sandwiches at her job and earns $7.85 per hour.Learn more about proportional relationship here
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Sketch the graph and circle the points that are solutions. (0-0)(2,5)(-3,-5)(-3,2)
Answers
(-3,-5)
1) Let's plot both inequalities to solve that geometrically at first.
y ≤ -1/3x -2
y< 2/3x +1
2) Since the possible solutions to that Linear system of Inequalities are within the darker and common region, after examining those options we can write:
The only (-3,-5) of those is a possible solution to that System.
3) Hence the only possible solution between them is (-3,-5).
I need help with this problem Math relatedsimplify in radical form:^3{120a^4b^5c
Answers
Sara, this is the solution:
∛ 120a^4b^5c
Lets solve factor by factor:
∛ 120 = ∛ 8 * 15 = 2∛ 15
∛a^4 = a^4/3
∛b^5 = b^5/3
∛c (We can't simplify this factor)
In consequence, we have:
2a^(4/3) b^(5/3)∛ 15c
Writing the equation of a circle centered at the origin given it’s radius or appoint on the circle
Answers
The equation of the circle has the following form:
[tex](x-h)^2+(y-k)^2=r^2[/tex]Where
(h,k) are the coordinates of the center of the circle
r is the radius of the circle
If the center of the circle is at the origin, (0,0) and it passes through the point (0,-9), since both x-coordinates are equal, the length of the radius is equal to the difference between the y-coordinates of the center and the given point:
[tex]r=y_{\text{center}}-y_{point=}0-(-9)=0+9=9[/tex]The radius is 9 units long.
Replace the coordinates of the center and the length of the radius in the formula:
[tex]\begin{gathered} (x-0)^2+(y-0)^2=9^2 \\ x^2+y^2=81 \end{gathered}[/tex]So, the equation of the circle that has a center in the origin and passes through the point (0.-9) is:
[tex]x^2+y^2=81[/tex]May I please get help with this I have tried multiple times to get the correct answer but still could not get them right. I am confused on how I should draw the dilation as I have tried many times as well.
Answers
After performing dilation centered at the origin we get
(a) shortest side of original figure=2 units
shortest side of the final figure=6units
(b) shortest side of the final figure=3×shortest side of the original figure
(c) True
(d) False
What is the dilation of the figure centered at origin?A transformation called a dilatation alters a figure's size without altering its shape. A figure might become larger or smaller due to dilation. For instance.
The image is smaller than the preimage when the scaling factor is between 0 and 1. Reductions are referred to as dilations with scale factors between 0 and 1.
The image is larger than the preimage if the scaling factor is greater than 1. Enlargements are defined as a dilation with a scale factor greater than 1.
To get the size of the edge we multiply the size of original lenght by scale factor.
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1. flight 1007 will hold 300 passengers the airline has booked 84% of the plane already. How many seats are open for the last-minute Travelers?2.Carly interviewed students to ask their favorite kind of television programs. 12 students claimed that they preferred comedies, 18 like drama 13 enjoy documentaries, and 7 voted for news programs what percentage of the students selected comedies?
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The total passengers in the flight is P=300.
Determine the passenger who booked the seat in the flight.
[tex]\begin{gathered} Q=\frac{84}{100}\cdot300 \\ =252 \end{gathered}[/tex]The number of seats booked by passenger is 252.
Determine the seats available for last-minutes travelers.
[tex]\begin{gathered} S=300-252 \\ =48 \end{gathered}[/tex]So 48 seats available for the last minute travelers.
Which ordered pair is a solution set for the linear equation, x + 16 = 6y? A (16,4) B (2, 3) C (-4,-2) D (-10,-1)
Answers
Explanation
to figure out if a pair is a solution, just replace x and y values and check if the equation is true,then
Step 1
[tex]\begin{gathered} x+16=6y \\ A)(16,4)\rightarrow when\text{ x=16 and y =4} \\ \text{replace} \\ 16+16=6\cdot4 \\ 32=24\rightarrow False,then\text{ A is not a solution} \end{gathered}[/tex]Step 2
[tex]\begin{gathered} B)(2,3)\rightarrow whenx=\text{ 2 and y=3} \\ x+16=6y \\ \text{replace} \\ 2+16=6\cdot3 \\ 18=18\rightarrow true \\ so\text{ B is a solution} \end{gathered}[/tex]Step 3
[tex]undefined[/tex]13. (08.05 MC)What is the shape of the cross section taken perpendicular to the base of a cylinder? (1 point)CircleRectangleSquareTriangle
Answers
ANSWER
Rectangle
EXPLANATION
If we take a cross-section perpendicular to the base of a cylinder,
We get a rectangle.
The base of the cylinder is circular and the
Answer: Rectangle
Step-by-step explanation:
I got it right on the test
