Answer: 125
Step-by-step explanation:
4/25 = 20/Y
Cross multiply to get the equation
4Y = 500
Divide both sides by 4
Y=125
y=5 when x=20.
Given that, y is inversely proportional to x. When y = 25 , x = 4.
We need to find the y value when x=20.
What is inversely proportional?Inversely proportional variables or quantities are those in which if one variable increases the other will decrease, and if one variable decreases the other increases.
Now, y∝1/x
⇒y=k/x
⇒25=k/4
⇒k=100
Thus, the y value when x=20.
y=100/20=5
Therefore, y=5 when x=20.
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Line A has an x-intercept of -4 and a y-intercept of 8. What is its slope?
Answer:
Step-by-step explanation:
We can use the intercept form of the equation of a line, then solve for y.
Intercept form
x/(x-intercept) +y/(y-intercept) = 1
x/-4 +y/8 = 1
__
Solving for y, we have ...
-2x +y = 8 . . . . multiply by 8
y = 2x +8 . . . . add 2x
The coefficient of x is 2, so the slope is 2.
__
The graph shows you the rise is 8 for a run of 4, so ...
slope = rise/run = 8/4
slope = 2
how many millimeters are in a meter
Answer:
There are 1000 millimeters in a meter.
Step-by-step explanation:
I really hope this helps in any way.
Answer:
1,000
Step-by-step explanation:
The word millimeter has the prefix of 'milli-'.
'Milli-' means a thousand.
Applying the prefix meaning to the word, a millimeter would be a thousandth of a meter.
There are 1,000 millimeters in a meter.
Brainilest Appreciated.
How many distinct triangles can be formed for which mzA
= 75°, a = 2, and b = 3?
O No triangles can be formed.
One triangle can be formed where angle B is about 15°.
One triangle can be formed where angle B is about 40°.
Two triangles can be formed where angle B is 40° or
140°
We are given
m∠A = 75 deg
a = 2
b = 3
Apply the Law of Sines.
sin(B)/b = sin(A)/a
sin(B)/3 = sin(75)/2
sin(B) = (3*sin(75))/2 = 1.45
The value of the sin function cannot exceed 1.
This means that the triangle cannot exist.
Answer: No distinct triangles
Answer: A no triangles can be formed
Step-by-step explanation:
two angles of a triangle measure 32 degrees and 62 degrees what is the measure of the third angle? A) 76 degrees B) 86 degrees C) 94 degrees D) 96 degrees
Answer:
86 B
Step-by-step explanation:
32+62=94
180-94=86
The sum of the interior angles of a triangle always add up to 180 degrees.
Answer:
The third angle is 86
Step-by-step explanation:
The sum of the angles of a triangle add to 180
32+62+x = 180
94+x = 180
Subtract 94 from each side
x = 180-94
x =86
Please Help...Anyone? I am revising for a test tomorrow, so please explain how you get the answer, too.. The ratios of the ages of Sunil and his Wife is 4:3. After 4 years, the ratio will be 9:7. What is the present age of Sunil
Answer:
32 years old
Step-by-step explanation:
Please see attached picture for full solution.
Let Sunil's present age be 4x and his wife's present age be 3x.
please solve it 90 POINTS please help- PLEASE HELP its Identify the following for the quadratic relations please slove it all please if you can save the picture and do it on the page -
i Will give brainliest
Answer:
[tex]\boxed{\mathrm{view \: explanation}}[/tex]
Step-by-step explanation:
2)
a) elimination method
b) substitution method
c) substitution method
For the first part we can elimate the y variable by subtracting the equations. We can then find the value of x.
For the second part we can substitute y as 2x+5 in the second equation and solve for x.
For the third part we can substitute y as 4x+3 in the first equation and solve for x.
3)
[tex]\boxed{\mathrm{view \: attachment}}[/tex]
a set of five numbers has a mode of 24 a median of 21 a mean of 20 . work out what the numbers could be
Answer:
Step-by-step explanation:
The mode is 24 so we know that at least 2 of the 5 numbers are 24.
The mean is 20 so we know that the 5 numbers add up to 100.
The median is 21 so the third number is 21.
100-(24+24+21)= 31
Now, I am pretty certain that the last 2 numbers can be anything as long as they add up to 31 AND they are not also 21 because 24 then would no longer be the mode.
E.g. 24, 24, 21, 11 & 20
Find the solution of this system of equations
- 2x + 10y = -22
-2x - 4y = 6
Answer:
x = 1, y = -2
Step-by-step explanation:
- 2x + 10y = -22 _______(1)
-2x - 4y = 6 _______(2)
From (1),
10y + 22 = 2x
x = (10y + 22) / 2
x = 5y + 11 .______(3)
Substitute (3) into (2),
-2 ( 5y + 11) -4y = 6
-10y - 22 - 4y = 6
-14y = 6 + 22
-14y = 28
y = 28/ -14
y =-2
Substitute y = -2 into (3).
x = 5y + 11
x = 5(-2) + 11
x = -10 + 11
x = 1
Therefore, the solution is x = 1, y = -2.
A restaurant offers 6 choices of appetizer, 8 choices of main meal, and 5 choices of dessert. A customer can choose to eat just one course, or two different courses, or all three courses. Assuming all choices are available, how many different possible meals does the restaurant offer?
Step-by-step explanation:
For one course:
6+8+5=
Two courses with appetizers and main meals (* means times)
6*8
Two courses with appetizers and dessert
6*5
Two courses with main meals and dessert
8*5
A large stand of fir trees occupies 24 hectares. The trees have an average density of 1 tree per 20m squared. A forester estimates that each tree will yield 300 board-feet. Estimate the yield of the stand if one-tenth of the trees are cut.
Answer:
The yield of the stand if one-tenth of the trees are cut is 360000 board-feet.
Step-by-step explanation:
First, let is find the total amount of fir trees that occupies the area of 24 hectares. (1 hectare = 10000 square meters)
[tex]n = \sigma \cdot A[/tex]
Where:
[tex]\sigma[/tex] - Surface density, measured in trees per square meter.
[tex]A[/tex] - Total area, measured in square meters.
Given that [tex]\sigma = \frac{1}{20}\,\frac{tree}{m^{2}}[/tex] and [tex]A = 24\,h[/tex], the total amount of fir trees is:
[tex]n = \left(\frac{1}{20}\,\frac{trees}{m^{2}} \right)\cdot (24\,h)\cdot \left(10000\,\frac{m^{2}}{h} \right)[/tex]
[tex]n = 12000\,trees[/tex]
It is known that one-tenth of the tress are cut, whose amount is:
[tex]n_{c} = 0.1 \cdot n[/tex]
[tex]n_{c} = 0.1 \cdot (12000\,trees)[/tex]
[tex]n_{c} = 1200\,trees[/tex]
If each tree will yield 300 board-feet, then the yield related to the trees that are cut is:
[tex]y = S\cdot n_{c}[/tex]
Where:
[tex]S[/tex] - Yield of the tress, measured in board-feet per tree.
[tex]n_{c}[/tex] - Amount of trees that will be cut, measured in trees.
If [tex]n_{c} = 1200\,trees[/tex] and [tex]S = 300\,\frac{b-ft}{tree}[/tex], then:
[tex]y = \left(300\,\frac{b-ft}{tree} \right)\cdot (1200\,trees)[/tex]
[tex]y = 360000\,b-ft[/tex]
The yield of the stand if one-tenth of the trees are cut is 360000 board-feet.
What do the Nineteenth Amendment and the Indian Citizenship Act of 1924
have in common?
O A. They both affected American Indians directly.
O B. They both allowed certain Americans to own property.
O C. They both permitted free expression with some restrictions.
O D. They both provided suffrage to a group of Americans.
Answer:
D
Step-by-step explanation:
Suffrage is the right to vote, and the nineteenth amendment gave women the right to vote, and the indian citizenship act of 1924 gave native americans the right to vote
There is a bag filled with 5 blue, 6 red and 2 green marbles. A marble is taken at random from the bag, the colour is noted and then it is not replaced. Another marble is taken at random. What is the probability of getting 2 blues?
Answer:
Step-by-step explanation:
Total marbles = 5 + 6 + 2 = 13
P( getting blue ball from first draw) = 5/13
The marble is not replaced. So, Now total marbles will be 12 & number blue marbles will be 4
P( getting blue ball from second draw) = 4/12 = 1/3
P(getting two blues) = [tex]\frac{5}{13}*\frac{1}{3}\\[/tex]
= 5/39
When constructing parallel lines with a compass and straightedge, how should you start the construction? Measure the length of the original line and make an arc. Create a line that intersects the given line with your straightedge. Open the compass to the width of the line and draw two arcs. Use a straightedge to create two arcs above and below the line.
Answer:
The second choice.
Step-by-step explanation:
Open the compass to the width of the line and draw two arcs.
These arcs should be on the same side of the original line.
You can then draw the parallel line with the straight edge just touching the top of each arc.
Parallel lines can be drawn using compass and straightedge using the concept of corresponding angle.
What are the parallel lines?Two lines are called parallel when they never meet each other if they are increased on the either side of them.
When constructing parallel lines with a compass and straightedge we can follow the below mentioned steps.
1. At first we need to draw a straight line. Then take a random point on it.
2. After that, we need to take a random point above the line that is drawn. Then, we need to connect two points.
3. After that, draw two arcs using the compass. First arc is on the angle formed by two lines drawn. The next arc is on the line that connects two points.
4. Now using the compass, we can copy the angle formed on the first line on the point above the first line.
5. Now, complete the angle on the point above the first line. These two lines are parallel lines.
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convert the decimal to a simplified fraction 0.8=
Answer:
4/5
Step-by-step explanation:
You know 0.8 x 10 = 8, so 8/10 is the fraction.
Now, simplify 8/10.
8/10 = 4/5
Answer:
4/5
Step-by-step explanation:
Step 1: Convert decimal to fraction
0.8= 8/10
Step 2:Simplify
8/10=4/5
Which of the following is the correct factored form of the given equation? 6x^2 -13x - 8 = 0
Answer:
the 2nd
Step-by-step explanation:
Which expression represents a difference of squares ?
Answer:
first and last options
Step-by-step explanation:
Difference of squares are in the form a² - b². The only choices that satisfy this are 25x² - 36 and 1 - 16x².
Answer:
1 and 4
Step-by-step explanation:
The graph below shows the price of different numbers of beach balls at a store: Which equation can be used to determine p, the cost of b beach balls? b = 5.50p p = 5.50b p = 11b b = 11p
Answer:
p = 5.50b
Step-by-step explanation:
2 beach balls cost 11
4 beach balls cost 22
6 beach balls cost 33
So each (1) ball b costs 5.50 ($) p
trig and picture pls help
Answer:
Im pretty sure that the answer is 32.
Step-by-step explanation:
Hope this helps
Write a two-column proof. Given: <2 is congruent to <5; Segment AB is congruent to Segment DE Prove: Segment BC is congruent to Segment EC
Answer:
proof
Step-by-step explanation:
Statements
Reasons
<2 is congruent to <5; Segment AB is congruent to Segment DE
Given
<3≅<4
Vertical angle theorem
ΔCDB≅ΔCAE
AAS
Segment BC is congruent to Segment EC
CPCTC
The segment BC is congruent to segment EC and this can be proven by using the properties of a triangle and the given data.
Given :
Angle 2 is congruent to angle 5.Segment AB is congruent to Segment DE.The following steps can be used in order to prove that segment BC is congruent to segment EC:
Step 1 - Using the triangle properties it can be proven that segment BC is congruent to segment EC.
Step 2 - According to the vertical angle theorem, angle 3 is congruent to angle 4.
Step 3 - Now, according to the AAS (Angle Angle Side) postulate, triangle CDB is similar to triangle CAE.
Step 4 - So, according to the CPCTC, segment BC is congruent to segment EC.
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Which polynomial identity will prove that 35 = 27 + 8?
if AB is 3/4 and CD is 8/-6 are the parallel, perpendicular or niether
Answer:
neither
Step-by-step explanation:
parallel lines have the same slope, perpendicular lines' slopes are the negative inverse of eachother.
Francis surveyed a random sample of 70 students at Franklin High School about their favorite season. Of the students surveyed, 18 chose fall as their favorite season. There are 1816 students at Franklin High School.
Complete question is;
Francis surveyed a random sample of 70 students at Franklin High School about their favorite season. Of the students surveyed, 18 chose fall as their favorite season. There are 1816 students at Franklin High School. Based on the data, what is the most reasonable estimate for the number of students at Franklin High School whose favorite season is fall?
Answer:
467
Step-by-step explanation:
We are told that 18 out of 70 of the surveyed students' favorite season is fall. This when expressed in fraction, gives; 18/70.
Now we need to multiply this fraction by the total number of Franklin High School students in order to get the estimate for the number of students at Franklin High School whose favorite season is fall. Total number of students = 1816. Thus, estimate is;
1816 × 18/70 = 467
Thus, the most reasonable estimate for the number of students at Franklin High School whose favorite season is fall would be 467.
which of the following angles is coterminal with 5pi/3? pi/3, 2pi/3, 4pi/3, 5pi/3
Answer:
5pi/3
Step-by-step explanation:
For two angles to be co-terminal, one must differ from the other by a multiple of 2pi.
The angle of consideration is 5pi/3
Let us consider the options one by one and see if they differ from the angle of consideration by a multiple of 2pi.
5pi/3 - pi/3 = 4pi/3
5pi/3 - 2pi/3 = 3pi/3 = pi
5pi/3 - 4pi/3 = pi/3
5pi/3 - 5pi/3 = 0 = 0(2pi)
5pi/3 is co-terminal with itself
Juan hiked to the top of a 3,000-foot mountain and back down without taking a break. Which graph best represents Juan's distance from the top of the mountain during the entire hike?
Answer:
Top left graph.
Step-by-step explanation:
If Juan didn't take a break, there is no plateau/flat line. And if he started hiking up and then down, then the graph should be an upside-down V shape.
Answer:
Graph A is the most acuurate
Find the length of the side labeled x. Round intermediate values to the nearest tenth. Use the rounded values to calculate the next value. Round your final answer to the nearest tenth.
Answer:
11.67
Step-by-step explanation:
Data given in the question
∠ADC = 42°
∠BAC = 68°
Let us assume that AC be Y
Now
In ΔACD
tan 42° = AC ÷ CD = Y ÷ x ...............................(i)
In ΔACB
tan 68° = BC ÷ AC = 26 ÷ Y ..........................(ii)
Now take the value of Y from the equation (ii)
Y = 26 ÷ Tan 68° ...................... (iii)
Now place the value of Y in equation (i)
So,
Tan 42° = 26 ÷ tan 68° × X
X = 26 ÷ tan 68° × Tan 42° ......................(iv)
Now placing the values of tan 42° and tan 68° in equation (iv)
So,
X = 26 ÷ 0.900 × 2.475
= 11.67
The tan 42° = 0.900
And, the tan 68° = 2.475
Factor completely [tex]3x^3-3x^2-18x[/tex].
A - 3x(x + 3)(x + 2)
B - 3x(x + 3)(x − 2)
C - 3x(x − 3)(x + 2)
D - 3x(x − 3)(x − 2)
Will give Brainliest!
Answer:
The answer is 3x(x - 3)(x + 2)
Step-by-step explanation:
3x³ - 3x² - 18x
Factor out 3x from the expression
We have
3x ( x² - x - 6)
Solve the terms in the bracket
We have
3x ( x² + 2x - 3x - 6)
Factor out x the expression in the bracket
We have
3x ( x ( x + 2) - 3( x + 2) )
Factor out x + 2 from the expression in the bracket
We have the final answer as
3x ( x - 3) (x + 2)Hope this helps you.
Find w please help me
Answer:
w = 77°
Step-by-step explanation:
From the picture attached,
WXYZ is a quadrilateral having 4 interior angles,
m∠y = 90°
Therefore, (2x - 10) = 90°
2x = 90 + 10
2x = 100
x = 50
Now, m∠z = (x + 15)° = 65°
m∠x = (3x - 22)° = 150 - 22
= 128°
Sum of interior angles of a polygon = (n - 2)×180°
where n = Number of sides of the polygon
If n = 4,
m∠u + m∠x + m∠y + m∠z = (4 - 2) × 180°
w + 128 + 90 + 65 = 360
w = 360 - 283
w = 77°
Therefore, measure of w = 77°
Drag the tiles to the boxes to form correct pairs. Not all tiles will be used. Match the circle equations in general form with their corresponding equations in standard form. x2 + y2 − 4x + 12y − 20 = 0
(x − 6)2 + (y − 4)2 = 56
x2 + y2 + 6x − 8y − 10 = 0
(x − 2)2 + (y + 6)2 = 60
3x2 + 3y2 + 12x + 18y − 15 = 0
(x + 2)2 + (y + 3)2 = 18
5x2 + 5y2 − 10x + 20y − 30 = 0
(x + 1)2 + (y − 6)2 = 46
2x2 + 2y2 − 24x − 16y − 8 = 0
x2 + y2 + 2x − 12y − 9 = 0
Answer:
1) For [tex]x^2 + y^2 - 4x + 12y - 20 = 0[/tex], the standard form is [tex](x-2)^2 + (y+6)^2 = 60\\[/tex]
2) For [tex]x^2 + y^2 + 6x - 8y - 10 = 0[/tex], the standard form is [tex](x + 3)^2 + (y - 4)^2 = 35\\[/tex]
3) For [tex]3x^2 + 3y^2 + 12x + 18y - 15 = 0[/tex], the standard form is [tex](x + 2)^2 + (y+ 3)^2 = 18\\[/tex]
4) For [tex]5x^2 + 5y^2 - 10x + 20y - 30 = 0[/tex], the standard form is [tex](x - 1)^2 + (y+ 2)^2 = 11\\[/tex]
5) For [tex]2x^2 + 2y^2 - 24x - 16y - 8 = 0[/tex], the standard form is [tex](x - 6)^2 + (y+ 4)^2 = 56\\[/tex]
6) For[tex]x^2 + y^2 + 2x - 12y - 9 = 0[/tex], the standard form is [tex](x+1)^2 + (y-6)^2 = 46\\\\[/tex]
Step-by-step explanation:
This can be done using the completing the square method.
The standard equation of a circle is given by [tex](x - a)^2 + (y-b)^2 = r^2[/tex]
1) For [tex]x^2 + y^2 - 4x + 12y - 20 = 0[/tex]
[tex]x^2 - 4x + y^2 + 12y = 20\\x^2 - 4x + 2^2 + y^2 + 12y + 6^2 = 20 + 4 + 36\\(x-2)^2 + (y+6)^2 = 60\\[/tex]
Therefore, for [tex]x^2 + y^2 - 4x + 12y - 20 = 0[/tex], the standard form is [tex](x-2)^2 + (y+6)^2 = 60\\[/tex]
2) For [tex]x^2 + y^2 + 6x - 8y - 10 = 0[/tex]
[tex]x^2 + 6x + y^2 - 8y = 10\\x^2 + 6x + 3^2 + y^2 - 8y + 4^2 = 10 + 9 + 16\\(x + 3)^2 + (y- 4)^2 = 35\\[/tex]
Therefore, for [tex]x^2 + y^2 + 6x - 8y - 10 = 0[/tex], the standard form is [tex](x + 3)^2 + (y - 4)^2 = 35\\[/tex]
3) For [tex]3x^2 + 3y^2 + 12x + 18y - 15 = 0[/tex]
Divide through by 3
[tex]x^2 + y^2 + 4x + 6y = 5[/tex]
[tex]x^2 + y^2 + 4x + 6y = 5\\x^2 + 4x + 2^2 + y^2 + 6y + 3^2 = 5 + 4 + 9\\(x + 2)^2 + (y+ 3)^2 = 18\\[/tex]
Therefore, for [tex]3x^2 + 3y^2 + 12x + 18y - 15 = 0[/tex], the standard form is [tex](x + 2)^2 + (y+ 3)^2 = 18\\[/tex]
4) For [tex]5x^2 + 5y^2 - 10x + 20y - 30 = 0[/tex]
Divide through by 5
[tex]x^2 + y^2 - 2x + 4y = 6[/tex]
[tex]x^2 + y^2 -2x + 4y = 6\\x^2 - 2x + 1^2 + y^2 + 4y + 2^2 = 6 + 1 + 4\\(x - 1)^2 + (y+ 2)^2 = 11\\[/tex]
Therefore, for [tex]5x^2 + 5y^2 - 10x + 20y - 30 = 0[/tex], the standard form is [tex](x - 1)^2 + (y+ 2)^2 = 11\\[/tex]
5) For [tex]2x^2 + 2y^2 - 24x - 16y - 8 = 0[/tex]
Divide through by 2
[tex]x^2 + y^2 - 12x - 8y = 4[/tex]
[tex]x^2 + y^2 - 12x - 8y = 4\\x^2 - 12x + 6^2 + y^2 - 8y + 4^2 = 4 + 36 + 16\\(x - 6)^2 + (y+ 4)^2 = 56\\[/tex]
Therefore, for [tex]2x^2 + 2y^2 - 24x - 16y - 8 = 0[/tex], the standard form is [tex](x - 6)^2 + (y+ 4)^2 = 56\\[/tex]
6) For [tex]x^2 + y^2 + 2x - 12y - 9 = 0[/tex]
[tex]x^2 + 2x + y^2 - 12y = 9\\x^2 + 2x + 1^2 + y^2 - 12y + 6^2 = 9 + 1 + 36\\(x+1)^2 + (y-6)^2 = 46\\[/tex]
Therefore, for[tex]x^2 + y^2 + 2x - 12y - 9 = 0[/tex], the standard form is [tex](x+1)^2 + (y-6)^2 = 46\\\\[/tex]
For Plato / Edmentum
Just to the test and got it right ✅
Soon Yi loves to bake, and she is making flaky pastry. Soon Yi starts with a layer of dough 2 22 millimeters ( mm ) (mm)left parenthesis, start text, m, m, end text, right parenthesis thick. The baking process then involves repeatedly rolling out and folding the dough to make layers. Each time Soon Yi rolls and folds the dough, the thickness increases by 8 % 8%8, percent. What is the smallest number of times Soon Yi will have to roll and fold the dough so that the resulting dough is at least 2.5 mm 2.5mm2, point, 5, start text, m, m, end text thick
Answer:
3times
Step-by-step explanation:
Baking Process: repeatedly rolling out and folding the dough to make layers
Soon Yi starts with a layer of dough = 2millimeters
Each time Soon Yi rolls and folds the dough, the thickness increases by 8 % = 1 + 8 %
When time = 1
Thickness = 2(1 + 8 %) = 2(1+0.08)
= 2(1.08) = 2.16
For time = n
Thickness = 2(1 + 8 %)^n = 2(1.08)^n
When thickness ≥ 2.5mm, n= ?
2.5 = 2(1.08)^n
2.5/2 = (1.08)^n
1.25 = (1.08)^n
Since the numbers are close (1.25 and 1.08), we can compute by multiplying 1.08 by itself till we get 2.5.
1.08 ×1.08× 1.08 = 1.259712
(1.08)³ is a bit above 1.25
2(1.08)³ satisfies the thickness of at least 2.5mm
Let's check our answer using the formula:
When n = 3
2(1.08)³ = 2 × 1.259712 = 2.519424
This satisfies the thickness of at least 2.5mm
Therefore, the smallest number of times Soon Yi will have to roll and fold the dough so that the resulting dough is at least 2.5 mm = 3
Classify the following triangle.Check all that apply
Answer:
B and D
Step-by-step explanation:
=> All of the sides are unequal so it's a scalene triangle.
=> It have a 90 degrees angle, so it is a Right Angled Triangle.
Answer:
B. Scalene
D. Right
Step-by-step explanation:
The triangle is a scalene triangle, because all the three sides have different lengths.
The triangle is a right triangle, because it has an angle of 90 degrees.