ABCD is a rhombus.
y
The coordinates of A are (5, 11)
The equation of the diagonal DB is y = x + 5
The equation of the diagonal AC can be written
in the form y = mx + c where m and c are integers.
Work out the value of m and the value of c.
Answers
From the information given, it is correct to state that M = - 3; while c = 26. This problem relates to a Rhombus. See the definition of a Rhombus below.
What is a Rhombus?A Rhombus is a 2-dimensional quadrilateral whose sides have equal length.
What are the steps for finding M and C?It is given that ABCD is a Rhombus. This means that
AC ⊥ BD; andLine DB is y = (1/3)x + 5Hence, the slope of AC = -3.
This is arrived at as follows:
Given that the diagonals of Rhombus' are perpendicular, hence
I/3 x m = -1 ⇒ -3
⇒ Line y-11 = -3 (x-5)
⇒ Line AC thus ⇒ y = -3x + 26
How do we solve for c?
Recall that the coordinates are (5, 11). Thus let y = -3x + b
Hence, -3 x 5 + b = 11
b = 11 + 15
b = 26.
Therefore the equation is given as:
y = -3X + 26 were:
m = -3; and
c = 26
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Related Questions
Question 8 of 25
A new auditorium is being built for a college. The balcony has 400 seats. The
floor has 50 rows with x seats in each row. The number of people in the
auditorium must be under 1300 to meet safety regulations.
What is the solution of this inequality, and what is its, meaning?
O A. 50x< 1300; The new auditorium must have fewer than 26 seats in
each row on the floor to meet fire safety regulations.
20
21
22
23
24
25
26
27
28
29
30
Answers
Inequalities help us to compare two unequal expressions. The number of seats in each row on the floor must be less than 18.
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.
Given the balcony has 400 seats, and the floor has 50 rows with each row having x number of seats. Therefore, the number of seats on the floor will be,
Number of seats on floor = 50 × x = 50x
Since the total number of seats in the auditorium should be less than 1300, therefore, the inequality can be written as,
Number of seats in balcony + Number of seats on floor < 1300
400 + 50x < 1300
50x < 1300-400
50x < 900
x < 18
Hence, the number of seats in each row on the floor must be less than 18.
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Find if line M is a tangent line to circle B.
Answers
Answer:
No
Step-by-step explanation:
The tangent line must form a right angle with the radius
No, 4 5 6 isn't a right triangle
Answer:
Line m is not a tangent line to circle B.
Step-by-step explanation:
The tangent line to a circle is always perpendicular to the radius.
The line segment measuring 4 units is the radius of Circle B, therefore if line m is a tangent line to the circle, the angle between this segment and the segment measuring 5 units will be a right angle (90°).
We can use Pythagoras' Theorem to check if the triangle is a right triangle.
Pythagoras’ Theorem: [tex]a^2+b^2=c^2[/tex]
(where a and b are the legs, and c is the hypotenuse, of a right triangle)
Therefore, the legs are the line segments measuring 4 and 5, and the hypotenuse is the line segment measuring 6 units.
Substituting the values for the legs into the formula:
[tex]\implies 4^2+5^2=c^2[/tex]
[tex]\implies 16+25=c^2[/tex]
[tex]\implies 41=c^2[/tex]
[tex]\implies c=\sqrt{41}[/tex]
Therefore, as the hypotenuse of the triangle is not √41, the triangle is not a right triangle, and therefore line m is not a tangent line to circle B.
The perimeter of a rectangular corn field is 440 meters. The ratio
of its length to its width is 7:4. What is the length and width of
the field?
Answers
Answer:
Length: 140 meters
width: 80 meters
Step-by-step explanation:
perimeter of a rectangle is 2*(lw)
440/(14+8)=20
Length: 20*7=140 meters
width: 20*4=80 meters
Andy is 6.25 miles north of the center of town. william is at the center of town. at noon they both start walking north.
andy walks at a constant rate of 7.5 miles in 3 hours. william walks at a constant rate of 15 miles in 4 hours.
how many hours does it take william to catch up with andy?
Answers
Answer: 5 hours
Step-by-step explanation:
[tex]speed=\frac{distance}{time}[/tex]
Andy speed = 7.5/3 = 2.5 mph
William speed = 15/4 = 3.75 mph
1. Write an equation that represents the question
let h = # of hours it takes William to catch up with andy
2.5h + 6.25 = 3.75h
2. subtract 2.5h from both sides
6.25 = 1.25h
3. Divide 1.25 from both sides
[tex]\frac{1.25h}{1.25} =\frac{6.25}{1.25}[/tex]
h = 5
Therefore, we know it will take 5 hours for William to catch up with andy.
A pet store has three fish tanks, each holding a different volume of water and a different number of fish.
Tank A holds 40 L and 5 fish. Tank B holds 100 L and 12 fish. Tank C holds 180 L and 23 fish.
Order the tanks by volume per fish from least to greatest.
B A C
Answers
Answer:
Step-by-step explanation:
Remark
The general formula is
Volume per fish = volume of water / number of fish
Givens
40 L and 5 fish
100 L and 12 fish
180 L and 23 fish
Solution
Tank A = 40 L / 5 fish = 8 L / fish
Tank B = 100 L /12 fish = 8.3 L / fish
Tank C = 180 L / 23 fish = 7.83L / fish
Answer
From Least to greatest = C A B
A circular railroad-crossing sign has a diameter of 30 inches.
Which measurement is closest to the area of the sign in square inches?
Answers
Diameter = 30
30/2 = 15 15 is the radius
To find area:
3.14 x 15 x 15 = 706.5
706.5 is the answer
In the parallelogram shown, ae = p − 8, ce = 2p − 58, and de = p 15. parallelogram a b c d is shown. diagonals are drawn from point a to point c and from point d to point b and intersect at point e. what is the length of line segment eb? 42 units 50 units 65 units 73 units
Answers
If diagonals are drawn from point a to point c . The length of line segment eb is 65 units.
Length of line segmentSince the diagonal of parallelogram bisect one another, hence:
AE=CE
EB=DE=P+15
P-8=2P-58
P=50
Hence:
EB=P+15
EB=50+15
EB=65 units
Therefore the length of line segment eb is 65 units.
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Good afternoon, the
correct answer is 65 units
Maisy got a score of 80% correct on an quiz. There were 30 questions on the quiz. How many questions did Maisy get correct?
Answers
Answer:
24 Questions answered correctly
Step-by-step explanation:
So as we know, 30/x = 100/80
100/80 = 1.25
Now we have 30/x = 1.25
Multiply both sides of the equation by x - (30/x)x = (1.25)x
Now we have 30 = 1.25x
Divide both sides by 1.25 - 30/1.25 = 1.25x/1.25
24 = xThe tire's diameter is 1 meter, and it made 8000 rotations during the trip. How far did the bus travel?
Answers
The circumference of the tire = pi x diameter = 3.14 x 1 = 3.14 meters
every rotation the tire travels 3.14 meters
3.14 x 8000 = 25120 meters
1 kilometer = 1000 meters
25,120 meters /100 = 25.12 kilometers
answer: 25.12 kilometers
If the area of a round cricket oval is 27500 square meters, Find the distance from the centre of the ground to the boundary.
Answers
The distance from the centre of the ground to the boundary based on the area given is 93.58 meters.
How to calculate the distance?From the information given, the area of a round cricket oval is 27500 square meters. The information simply wants us to calculate the radius which will be calculated thus:
Area of a circle = πr²
πr² = 27500
(3.14) × r² = 27500
r² = 27500/3.14
r² = 8757.96
r = ✓8757.96
r = 93.58
Therefore, the distance from the centre of the ground to the boundary is 93.58 meters.
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1) How do we find surface area? (What is it?)
2) What is the surface area of this pyramid?
Answers
Answer:
1) First find the base, then one triangle face and multiply it by four
2) 360 units squared
Step-by-step explanation:
10*10 = 100
10*13 = 130
130*2 = 260
260 + 100 = 360
Answer:
Surface Area=360
Step-by-step explanation:
All the triangles of a square pyramid are congruent meaning you can find the area of 1 and multiply by to find the total surface area of all 4 triangles.
Area of a triangle formula= bh/2
Area of 1 triangle= 13*10/2=65
Multiply by 4 to find the total surface area of the triangles: 65*4=260
Then add the area of the square base.
Area of Square base=10*10=100
Add the total area of the triangles and square base: 260+100=360
[(-3)+9] × [(-10)-(-9)]
please solve this
Answers
6 × (-10 + 9)
6 × (-1)
= -6
Feng is starting a running plan to train for a race. In the first week of his running plan, Feng will run 15 miles. The plan calls for Feng to increase his weekly milage by 1.5 miles every week. If Feng sticks to the plan, how many miles would he be expected to run during his 15th week of the training plan?
Answers
Answer:
37.5 miles
Step-by-step explanation:
y = 1.5x + 15
1.5 * 15 = 22.5
22.5 + 15 = 37.5
PLEASEEE HELPPPPP
Triangle A and Triangle B are similar triangles that have corresponding angle measures of 98 degrees and 43 degrees . What is the angle measure of the third angle in Triangle A and Triangle B?
Answers
Answer:
47 degrees
Step-by-step explanation:
Similar just means they may be different sizes but have the same angle measure. That means the angles will be identical in both triangles A and B.
All angles must add up to 180 degrees. We already have two angles, so we just need to find the last one. 90+43= 133.
180-133=47.
In order to select new board members, the French club held an election. 20% of the 40 members of the club voted. How many members voted?
Answers
The number of members is an illustration of proportions, and there are 200 members in the club
How to determine the members that vote?The given parameters are:
French = 20%
French = 40
Let the number of members be x.
So, we have:
20% * x= 40
Divide both sides by 20%
x = 200
Hence, there are 200 members in the club
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Find the surface area of a square pyramid with side length 5 Fr and slant height 5 ft.
Answers
Answer:
75 ft²
Step-by-step explanation:
Surface Area :
Area (4 triangles) + Area (base)4 x 1/2 x 5 x 5 + 5 x 550 + 2575 ft²Given:
All sides are 5 feet in length.
To find:
The surface area of:
Square (base)4 Triangle SidesStep-By-Step-Solution:
Step 1
Find the surface area of the square (base)
Formula:
[tex]SA=L*W[/tex]
Find:
[tex]SA=5*5\\=25[/tex]
The surface area of the square (base) is 25ft²
Step 2
Find the surface area of the 4 triangles
We know that to find the surface area of 1 triangle, we do this:
[tex]SA=\frac{1}2} *B*H[/tex]
But to find the surface area of 4 triangle, we will have to do this:
[tex]SA=2*B*H[/tex]
Find:
[tex]SA=2*5*5\\=2*25\\=50[/tex]
The surface area of the 4 triangles in the sides are 50ft²
Step 3
Find the total surface area (by adding all SA's found before)
Just add! EASY!!!
25+50=75ft²
The total Surface Area of the Square Pyramid is 75ft²Here are pairs of equivalent expressions, one in standard form and the other in factored form. Find
the missing numbers.
1. x2 +
+
and (x – 9) (x - 3)
2. 22 – 9x + 20 and (x – 4) (x +
Answers
The first equation will be x²-12x+27=(x-9)(x-3). The second equation will be x²-9x+20=(x-5)(x-4).
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
1. For the first equation to be complete, we need to expand the factors, therefore, we can write,
(x-9)(x-3)
= x² - 9x - 3x + 27
=x²-12x+27
Hence, the first equation will be x²-12x+27=(x-9)(x-3).
2. For the second equation to be complete, we need to factorise the left side of the equation, therefore, we can write,
x²-9x+2
= x²-5x-4x+20
= x(x-5)-4(x-5)
=(x-5)(x-4)
Hence, the second equation will be x²-9x+20=(x-5)(x-4).
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Answer:
Step-by-step explanation:
lern it yourself
The radius of a circle is 7 millimeters. What is the circle's circumference?
Answers
Answer:
The circumference of a circle with a radius of 7 millimeters is 44.0 (rounded to the nearest tenth).
Step-by-step explanation:
The circumference of a circle is the distance around the outside of the circle. The circumference along with the diameter and radius are the 3 major aspects of a circle.
The circumference of a circle is found using this formula:
[tex]c=2\pi *r[/tex] - or - [tex]c=\pi *d[/tex]For this problem, the radius has been given, so to solve, let's use the formula: [tex]c=2\pi *r[/tex].
It has been given that the radius is equal to 7 and the unit of measure is millimeters.
So to start, let's plug the radius in the formula.
It should look like this: [tex]C=2\pi *7[/tex]
After plugging the radius into the formula, we now have to multiply [tex]2\pi[/tex] by [tex]7[/tex]; resulting in: ≈ [tex]43.9823[/tex] (estimate)
Now rounding to the nearest tenth:
≈ [tex]44.0[/tex]
a×b=2a+16 two positive consecutive even integers
Answers
The solution of the given two positive consecutive even integers will be a = 20 and b = 21
What is an integer?An integer is a number whose values are ranges from 0 to infinite positive and zero to infinite negative.
Given that :
2a-3b = -23
a and b are consecutive
Find:
a and b
Computation:
a = b - 1
So,
2a-3b = -23
2(b-1)-3b = -23
2b - 2 - 3b = -23
-b = -21
b = 21
So
a = b - 1
a = 21-1
a = 20
Hence the solution of the given two positive consecutive even integers will be a = 20 and b = 21
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13. How are squares and triangles the same? How are they different?
Answers
Answer:
Squares and triangles are both polygons and right triangles and squares both have at least one right angle. They are different because squares have 4 sides and triangles have 3. Also, triangle have a total of 180 degrees while squares have a total of 360 degrees.
Hope this helped you! I would appreciate a Brainliest if this helped! Have a good day!
The volume of the rectangular pyramid below is 3240 units^3
3
. Find the value of xx.
Answers
The pyramid with a volume of 3240 unit³, base of 20 by 18 unit has a height of 27 unit
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Volume of pyramid = (1/3) * area of base * height
Hence:
3240 = (1/3) * (20 * 18) * x
x = 27 units
The pyramid with a volume of 3240 unit³, base of 20 by 18 unit has a height of 27 unit
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PLS HELP WILL GIVE BRAINLYEST!!! WHOEVER ANSWERS IN THE NEXT 2 HRS WILL GET 100 PTS.
(08.05;08.06 HC)
The box plot below shows the total amount of time, in minutes, the students of a class surf the Internet every day:
A box plot is shown. The left-most point on the plot is 20 and the right-most point is 95. The box is labeled 37.5 on the left edge and 60 on the right edge. A vertical line is drawn inside the rectangle at the point 50.
Part A: List two pieces of information that are provided by the graph and one piece of information that is not provided by the graph. (4 points)
Part B: Calculate the interquartile range of the data, and explain in a sentence or two what it represents. (4 points)
Part C: Explain what affect, if any, there will be if an outlier is present. (2 points)
Answers
Answer:
it shows that the least amount is 37.5 minutes it shows the most amount of time is 60 minutes one thing it does not show is how many students where in the class
Step-by-step explanation:
Answer:
this is for A Part A: it shows that the least amount is 37.5 minutes
it shows the most amount of time is 60 minutes
one thing it does not show is how many students where in the class
Step-by-step explanation:
Well, you need to know the aton mic weight of Platinum (Pt) and the number of atoms per mole. The answer to the former is 195.084 g/mole and the latter is 6.023 * 10^23 atoms/mole. Then, multiply everything as shown below:
Number of atoms = (1 g) * (1/195.084 g/mole) * 6.023 * 10^23 atoms/mole
Number of atoms = 3.087 * 10^21 atoms
Note, I’ve included units on everything and you can see that they all cancel except for atoms. Dragging the units along can be a pain but it is a great way to check that they way the numbers are being combined is
Which multiplication expression does the model show?
Answers
Explanation is that the bar is not fully full so it should be reasonable
What is the length of the equal sides of an isosceles right-angle triangle, with a hypotenuse of 15cm?
Answers
Answer:
8.66
Step-by-step explanation:
15/sqrt(3) = 8.66 (to nearest hundreth)
3/4(x+2)=x-2 . solve for x
Answers
the answer is
x=2
Find the slope and the y-intercept of the linear function shown below
Answers
Answer:
You give no Problem or answers to choose from
Step-by-step explanation:
Sorry
A professional painter knows that it takes 0.29 ounces of the paint he prefers to cover 1 square foot of wall. If he calculates that he will need 92.8 ounces of paint to cover an 8-foot wall, then how wide is the wall he is planning to paint?
Answers
Answer:
The wall is 40 feet wide.
Step-by-step explanation:
92.8 / 0.29 = 320 square feet
320 / 8 = 40 feet
I can give brainliest to the best answer, please help
Answers
Answer:
KPJ= 40 degrees
Step-by-step explanation:
EPG=35
EPG=FPK because they are symmetrical
135+105=140
180-140=40
DPE=40
DPE=KPJ because they are symmetrical
KPJ=40
Someone please help I’m literally so close to finishing this assignment and schools almost over so I need to bring up my grade quick
Answers
Step-by-step explanation:
if that is a problem for the end of the school year, what problems did you solve during the year ?
this question needs one of the basic principles of angles :
the sum of all angles around one point on one side of a line is always 180°, because that line can be seen as the diameter of a circle, and the point is the center of that circle. so, all angles in one side of the line are representing a half-circle.
this special point here is clearly T.
and 85 + x = 180
x = 180 - 85 = 95°
(06.04)
Determine the solution to the system of equations graphed below and explain
your reasoning in complete sentences.
WILL MARK BRAINLIEST