Answer: The slope of BC is -2.
Step-by-step explanation:
We know that a rectangle has all opposite sides equal and parallel.
Each interior angle is a right angle.
Therefore , if rectangle ABCD is a rectangle then , AB should perpendicular to BC. [ ∵ Angle between AB and BC is 90° .] (1)
Also , slope of line passing through (a,b) and (c,d) : [tex]\dfrac{d-b}{c-a}[/tex]
If A is located at (3, 4) and B is located at (7,6) .
Then , The slope of AB = [tex]\dfrac{6-4}{7-3}=\dfrac{2}{4}=\dfrac{1}{2}[/tex]
Also, the product of slopes of two perpendicular lines is -1.
Then , (Slope of AB) x (Slope of BC) = -1 [From (1)]
[tex]\Rightarrow\ \dfrac{1}{2}\times (\text{Slope of BC})= -1\\\\\Rightarrow\ \text{Slope of BC}=-2[/tex]
Hence, the slope of BC is -2.
1 2/5 hours in minutes
Answer:
84 minutes
HOPE THIS HELPS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Step-by-step explanation:
An hour is 60 minutes
60 x 2/5 = 24
24 minutes plus an hour (60 minutes)
= 84
expanded form for 208,000,478
Answer:
200,000,000
+ 0
+ 8,000,000
+ 0
+ 0
+ 0
+ 400
+ 70
+ 8
Step-by-step explanation:
Answer:
200,000,000
8,000,000
400
70
8
Add up those values straight down to end up with 208,000,478
You can also write the number as
2*10^8 + 8*10^6 + 4*10^2 + 7*10^1 + 8*10^0
what is 5/8 doubled as a fraction
Answer:
5/4
Step-by-step explanation:
doubled is basically multiplied by 2
so 5/8 *2
this would equal 5/8 *2/1
so we multiply the tops together and the bottoms together
so that would mean
10/8
we can divide both the top and bottom by 2 to simplify
this would be
5/4
This can be rewritten as
1 1/4 too.
The fraction 5/8 when doubled gives the fraction 5/4.
Given a fraction 5/8.
We have to find the fraction formed by doubling the fraction 5/8.
Doubling means multiplying by 2.
That is, some number is doubles or make it two times.
Here given fraction is 5/8.
Doubling this frcation, we get,
2 multiplied by 5/8
= 2 × 5/8
2 and 8 in the denominator gets cancelled and we get,
2 × 5/8 = 5/4
Hence the required fraction value is 5/4.
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Roshanda bought pound of ham and pound of roast
beef. How much more roast beef than ham did she buy?
Write in simplest form
Final answer:
Roshanda bought the same amount of roast beef as ham, 0 pounds.
Explanation:
To find out how much more roast beef Roshanda bought compared to ham, we need to subtract the weight of the ham from the weight of the roast beef. Roshanda bought 1 pound of ham and 1 pound of roast beef, so the difference is 1 pound minus 1 pound, which equals 0 pounds. Therefore, Roshanda did not buy more roast beef than ham, they bought the same amount.
Roshanda bought 1/4 pound more roast beef than ham.
To find out how much more roast beef Roshanda bought compared to ham, we need to subtract the amount of ham from the amount of roast beef.
Given:
Ham = 5/8 pound
Roast beef = 7/8 pound
To find the difference:
Roast beef - Ham
= (7/8) - (5/8)
To subtract fractions, we need a common denominator, which is 8 in this case.
= (7/8) - (5/8)
= (7 - 5)/8
= 2/8
Now, simplify the fraction:
2/8 = 1/4
So, Roshanda bought 1/4 pound more roast beef than ham.
Question
Roshanda bought 5/8 pound of ham and 7/8 pol 11 d of roast beef. How much more roast beef than ham did she buy? Write in simplest form.
x/10 =13/7 rounded to the nearest tenth
Answer:
x≈18.6
Step-by-step explanation:
Lets make the fractions have common denominators:
7x/70=130/70
Multiply by 70
7x=130
Divide by 7
x=18.5714285714
Round
x≈18.6
Which of these expressions can be used to calculate the monthly payment for
a 30-year loan for $195,000 at 6.6% interest, compounded monthly?
Answer:
$195P00*0.0055(1+0.0055)^360
____________________________
(1+0.0055)^360-1
An opaque bag contains 3 green marbles, 3 red marbles. If two consecutive marbles are drawn without replacement what is the probability that they will both be green?
Final answer:
The probability of drawing two green marbles consecutively without replacement from a bag containing 3 green and 3 red marbles is 1/5 or 20%.
Explanation:
The probability that both marbles drawn consecutively from an opaque bag without replacement will be green is calculated by multiplying the probability of the first event by the probability of the second event. Here, we have 3 green marbles out of a total of 6 marbles. So, the probability of drawing the first green marble is 3/6 or 1/2. After drawing one green marble, there are now 2 green marbles left out of 5 total marbles. Therefore, the probability of drawing a second green marble is now 2/5. To find the combined probability, we multiply these two probabilities together: (1/2) × (2/5) which equals 1/5 or 0.2. Hence, there is a 20% chance that both marbles drawn will be green.
Write a similarity statement relating the three triangles in the diagram
Answer:
b. ∆DEF ~ ∆HDF ~ ∆HED
Step-by-step explanation:
When you name similar triangles, the order of the letters of corresponding angles must be in matching order.
For example, in ∆DEF, ∠D is the right angle, ∠E is the larger acute angle, and ∠F is the smallest angle.
The corresponding parts in ∆HDF are ∠H, ∠D, and ∠F.
In ∆HED, they are ∠H, ∠E, and ∠D.
The similarity statement is
∆DEF ~ ∆HDF ~ ∆HED
The similarity statement relating to the given triangles in the diagram is: B. ∆DEF ~ ∆HDF ~ ∆HED
What is the Right Triangle Similarity Theorem?The right triangle similarity theorem states that when an altitude of a right triangle will divide the triangle to form two similar triangles, which are also similar to the original triangles.The three triangles are similar to each other.When writing similarity statement, the letters of the corresponding angles of the triangles should follow the same order of naming that matches together.Therefore, the similarity statement relating to the given triangles in the diagram is: B. ∆DEF ~ ∆HDF ~ ∆HED
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The figure show a cuboid ABCDEFGH, BC is8 cm and EH is 3 cm. Find the angle ACF, correct to 3 significant figures
Answer:
19.3 degrees
Step-by-step explanation:
The diagonal AC of the rectangle can be found using the Pythagorean Theorem.
8^2 + 3^2 = 73
The square root of 73 = 8.544...
Using this length and the length of FA (which is 3 cm), we can use the inverse of tangent to find the angle.
tangent of the angle = 3 cm/8.544 cm
inverse tangent of (3/8.544) = 19.347...
Hope this helps!
15,35,40 will it make a right triangle
Answer:
NO.
Step-by-step explanation:
If it is a right triangle then by the Inverse of the Pythagoras Theorem:
40^2 = 35^2 + 15^2
Testing:
40^2 = 1600
35^2 + 15^2 = 1225 + 225 = 1450
So the answer is NO>
Answer:
NO.15, 35, 40 it will make an obtuse triangle.Step-by-step explanation:
If a ≤ b ≤ c are sides of a triangle, then a + b > c.
We have a = 15, b = 35, c = 40.
Check:
15 + 35 = 50 > 40 CORRECT
These sides can be the sides of a triangle.
If a ≤ b ≤ c are sides of a triangle, then
if a² + b² = c², then it's a right triangle
if a² + b² < c², then it's an obtuse triangle
if a² + b² > c², then it's an acute triangle
Check:
15² + 35² = 225 + 1225 = 1450
40² = 1600
1450 < 1600 ⇒ 15² + 35² < 40²
Therefore it's an obtuse triangle
A circle with circumference 6 has an arc with a 60° central angle.
What is the length of the arc?
Answer:
length of an arc = 1unit
Step-by-step explanation:
given that the circumference of a circle = 6
central angle = 60
length of the arc =?
recall that the circumference of a circle = 2πr
6 = 2πr
r = 6/2π
now to calculate the length of an arc
recall,
length of an arc = 2πr(Ф/360)
length of an arc = 2π(6/2π) × 60/360
length of an arc = 6 × 60/360
length of an arc = 360/360
length of an arc = 1unit
therefore the length of the arc whose circumference is 6 and arc angle is 60° is evaluated to be 1unit
Which of the following equations is equivalent to x - y = 5?
x - 2y = 30
4x - 3y = 30
3x - 4y = 30
Answer:
[tex]6x-6y=30[/tex]
Step-by-step explanation:
The complete options are
a) x - 2y = 30
b) 4x - 3y = 30
c) 3x - 4y = 30
d) 6x - 6y = 30
The given equation is
[tex]x-y=5[/tex]
Verify option d
we have
[tex]6x-6y=30[/tex]
Divide by 6 both sides
[tex](6x-6y)/6=30/6[/tex]
[tex]\frac{6x}{6}-\frac{6y}{6}=\frac{30}{6}[/tex]
[tex]x-y=5[/tex]
therefore
[tex]x-y=5[/tex] and [tex]6x-6y=30[/tex] are equivalent
Answer:
3x -4y = 30
Step-by-step explanation:
This table shows how many sophomores and juniors attended two school events. What is the probability that the student attended the jazz concert, given
Answer:
A. 0.60
Step-by-step explanation:
make a proportion so
36 over 60 = x over 100
36*100= 3600
3600/60
60
.60
The probability that the student attended the jazz concert is 0.60. The correct answer is option A.
What is probability?Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Probability = Number of favorable outcomes / Number of sample
It is given from the table that the student who attended the jazz concert is 36 out of 60 students. Then the probability that the student attended the jazz concert is calculated as below:-
Probability = Number of favorable outcomes / Number of sample
Probability = 36 / 60
Probability = 0.60
Therefore, the probability that the student attended the jazz concert is 0.60. The correct answer is option A.
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Leeza is making labels in the shape of parallelograms Each label has an area of 18 square centimeters and a base of 6 centimeters. What is the height of each label
I think it's 3
It should be 3 because if you have a base of 6 then your height must be 3 to get 18.
Identify the value(s) that are not restrictions on the variable for the rational expression
2y^2 + 2/
Y^3– 5y^2+ y - 5
-1
0
-5
1
5
To find the values that are not restrictions on the variable in a rational expression, we need to evaluate the expression for the given values. By substituting the values -1, 0, -5, 1, and 5 into the expression, we can determine if they result in a zero denominator or not. The values 0 and 5 are not restrictions on the variable.
Explanation:The rational expression is given by [tex](2y^2 + 2) / (y^3- 5y^2+ y - 5)[/tex]. To identify the values that are not restrictions on the variable, we need to determine which values of y make the denominator equal to zero. To find these values, we can set the denominator [tex](y^3-5y^2+ y - 5)[/tex] equal to zero and solve for y using synthetic division or factoring. By substituting the given values of -1, 0, -5, 1, and 5 into the expression, we can determine whether they result in a zero denominator or not. If the denominator is not zero for a particular value of y, then that value is not a restriction on the variable.
Let's check:
For [tex]y = -1: (2(-1)^2 + 2) / (-1^3 - 5(-1)^2 + (-1) - 5) = (-2 + 2) / (-1 + 5 - 1 - 5) = 0 / -2 = 0[/tex]
For [tex]y = 0: (2(0)^2 + 2) / (0^3 - 5(0)^2 + (0) - 5) = (2 + 2) / (0 - 0 + 0 - 5) = 4 / -5 ≠ 0[/tex]
For [tex]y = -5: (2(-5)^2 + 2) / (-5^3 - 5(-5)^2 + (-5) - 5) = (2(25) + 2) / (-125 + 125 - 5 - 5) = (50 + 2) / -10 \ne 0[/tex]
[tex]For y = 1: (2(1)^2 + 2) / (1^3 - 5(1)^2 + (1) - 5) = (2 + 2) / (1 - 5 + 1 - 5) = 4 / -8 = -0.5 \ne 0 For y = 5: (2(5)^2 + 2) / (5^3 - 5(5)^2 + (5) - 5) = (2(25) + 2) / (125 - 125 + 5 - 5) = (50 + 2) / 0 \ne 0[/tex]
From the calculations, we can determine that the values 0 and 5 are not restrictions on the variable because they do not result in a zero denominator. Therefore, the correct answer is 0 and 5.
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Answer:
-1,0,-5,1
Step-by-step explanation:
3. A prop for the theater club’s play is constructed as a cone topped with a half-sphere. What is the volume of the prop? Round your answer to the nearest tenth of a cubic inch. Use 3.14 to approximate pi, and make certain to show your work. Hint: you may need to find the volume of the component shapes.
The volume of the prop is calculated to be 2,712.96 cubic inches.
Step-by-step explanation:
Step 1:
The prop consists of a cone and a half-sphere on top. We will have to calculate the volumes of the cone and the half-sphere separately and then add them to obtain the total volume.
Step 2:
The volume of a cone is determined by multiplying [tex]\frac{1}{3}[/tex] with π, the square of the radius (r²) and height (h). Here we substitute π as 3.14. The radius is 9 inches and the height is 14 inches.
The volume of the cone : [tex]V=\pi r^{2} \frac{h}{3}[/tex] = [tex]3.14 \times 9^{2} \times \frac{14}{3}[/tex] = 1,186.92 cubic inches.
Step 3:
The area of a half-sphere is half of a full sphere. The volume of a sphere is given by multiplying [tex]\frac{4}{3}[/tex] with π and the cube of the radius (r³).
Here the radius is 9 inches. We take π as 3.14.
The volume of a full sphere = [tex]V=\frac{4}{3} \pi r^{3}[/tex] = [tex]\frac{4}{3} \times 3.14 \times 9^{3}[/tex] = 3,052.08 cubic inches.
The volume of the half-sphere = [tex]\frac{3,052.08}{2}[/tex] = 1,526.04 cubic inches.
Step 4:
The total volume = The volume of the cone + The volume of the half sphere,
The total volume = 1,186.92 + 1,526.04 = 2,712.96 cubic inches.
Find the area of the circle (radius = 6)
Answer:
A =36 pi
or approximately
A =113.04
Step-by-step explanation:
To find the area of a circle, we use the formula
A = pi r^2, where r is the radius
A = pi (6)^2
A = 36 pi
We can approximate pi as 3.14
A = 36 (3.14)
A is approximately 113.04
Answer: 113.1 unit^2
Step-by-step explanation:
A=πr^2
=π(6)^2
=113.0973355 unit^2
Samantha Vega's gross weekly salary is $600. Her weekly federal withholding is $35.00. The Social Security
tax is 6.2% of the first $97,500. The Medicare tax is 1.45% of gross pay. The state tax is 1.5% of gross pay.
Each week she pays $12.40 for medical insurance. What are Samantha's total deductions?
Answer:
$102.30
Step-by-step explanation:
Answer:
2600
The gross pay $2,600 if $572 is the tax amount.
Step-by-step explanation:
Which is the most accurate way to estimate 52% of 71?
To estimate 52% of 71, you can use either the proportion method or the multiplication method by setting up a proportion or multiplying 0.52 by 71.
Explanation:To estimate 52% of 71, you can use either proportion or multiplication. Here's how:
Proportion method: Set up the proportion 52/100 = x/71, where x represents the unknown value. Cross-multiply and solve for x. Multiplication method: Multiply 52% (or 0.52) by 71.Using the proportion method:
52/100 = x/71
71 * 52 = 100 * x
x = 36.92 (rounded to 37)
Using the multiplication method:
0.52 * 71 = 36.92 (rounded to 37)
the perimeter of a rectangle is 400 meter. The length is three times the width. Which of the following best describes the length of the rectangle?
Length of the rectangle is 150 m.
Step-by-step explanation:
Step 1:
Let the width of the rectangle be x. Then the length = 3x. Given that perimeter = 400 m, find the length.
Perimeter of the rectangle = 2 (length + breadth)
400 = 2 (3x + x)
400 = 8x
∴ x = 400/8 = 50
⇒ Width is 50 m
∴ Length = 3x = 150 m
Select all that apply. A coin is flipped and a number cube is rolled. Which of the following are true?
The sample space has 12 different outcomes.
The sample space has 8 different outcomes.
Each result is equally likely.
Heads and an even number are very likely.
Answer:
1. True
2. False
3.True
4.False
systems of equation
Answer:?
Step-by-step explanation:
explain why zero is considered its own opposite.
please help, will mark brainiest. 20+ POINTS
Answer:
2.5•2 = 5
Step-by-step explanation:
The resulting two-dimensional cross-section is the area of a square.
Area of a square is equal to:
[tex]A=bh[/tex]
Having
[tex]b = 2.5\ in\\h = 2\ in[/tex]
substitute
[tex]A=2.5*2=5\ in^{2}[/tex]
The elevation of the surface of the Dead Sea is -424.3 meters. In 2005, the height of Mt. Everest was measured as 8,844.43 meters. How much higher was Mt. Everest?
Answer:
8,420.43 meters higher im pretty sure
Step-by-step explanation:
If you do 8,844.43-424.3, you get 8,420.83
Answer:
9,268.73 meters higher
Step-by-step explanation:
Add the elevation of Mt.Everest to the absolute value of the elevation of the Dead Sea. That equation looks like: 8,844.43 + |-424.3| = 9,268.73
Mt.Everest was 9,268.73 meters higher than the Dead Sea in 2005.
Is (-5,-5) a solution of y>- 2x + 4?
Answer:
No, (-5, -5) is not a solution
Step-by-step explanation:
Step 1: Plug in -5 for y and -5 for x
y > -2x + 4
-5 > -2(-5) + 4
-5 > 10 + 4
-5 > 14
Answer: No, (-5, -5) is not a solution
Noah wants to clean his second story windows and plans to buy a ladder that will reach at least
22
feet high. If he leans the ladder against the house so that the base of the ladder makes a
51.5
∘
angle with the ground, how long of a ladder should he buy? Please round to one decimal place
Answer:
Noah should buy a ladder of length greater than 28.1 ft to reach at least 22 feet height.
Step-by-step explanation:
Given:
Noah has to reach at least 22 ft height.
Angle made by the base of ladder with the ground = 51.5°
To find the length of the ladder.
Solution:
On drawing the situation, we get a right triangle. The hypotenuse of the triangle represents the length of the ladder.
In triangle ABC.
∠C = 51.5°
AB = 22 ft
Applying trigonometric ratio to find AC (length of the ladder).
[tex]\sin\theta = \frac{Opposite\ side}{Hypotenuse}[/tex]
[tex]\sin C=\frac{AB}{AC}[/tex]
Plugging in values.
[tex]\sin 51.5\°=\frac{22}{AC}[/tex]
Multiplying AC both sides.
[tex]AC\sin 51.5\°=\frac{22}{AC}\times AC[/tex]
[tex]AC\sin 51.5\°=22[/tex]
Dividing both sides by [tex]\sin 51.5\°[/tex]
[tex]\frac{AC\sin 51.5\°}{\sin 51.5\°}=\frac{22}{\sin 51.5\°}[/tex]
[tex]AC=\frac{22}{\sin 51.5\°}[/tex]
[tex]AC=28.1\ ft[/tex]
Thus, Noah should buy a ladder of length greater than 28.1 ft to reach at least 22 feet height.
Which point on the graph shows the price of 6 ounces of cheese? Use the formula y=x÷2 to find y when x is 6.
The value of y is 3 when x is 6.
Solution:
The given table is the amount of cheese in ounces and the cost price.
Let x represents the amount of cheese and y represents the cost price.
The formula which derived from the table is y = x ÷ 2.
That is [tex]$y=\frac{x}{2}[/tex].
To find the value of y when x is 6:
[tex]$y=\frac{x}{2}[/tex]
Substitute x = 6 in the formula, we get
[tex]$y=\frac{6}{2}[/tex]
y = 3
Hence the value of y is 3 when x is 6.
Find BC
AC = 7
BD = 7.5
DE = 1.5
AE = 11
5
CE=AE-AC=4
CD=CE-DE=4-1.5=2.5
BC=BD-CD=7.5-2.5=5
question 1: find the volume of a cube whose total surface area is 486cm^2
Solution:
The surface area of cube is given as:
[tex]Surface\ area = 6a^2[/tex]
Where, "a" is the length of side of cube
Given that, surface area = 486 square centimeter
[tex]486 = 6a^2\\\\a^2 = \frac{486}{6}\\\\a^2 = 81\\\\a = 9[/tex]
Find the volume of cube:
[tex]volume\ of\ cube = a^3\\\\volume\ of\ cube = 9^3\\\\volume\ of\ cube = 9 \times 9 \times 9\\\\volume\ of\ cube = 729[/tex]
Thus volume of cube is 729 cubic centimeter