By finding the side length of the square, we will see that the area is 20 square units.
How to get the area of a square?
For a square of side length S, the area is:
A = S^2
In this case, the side length of the square will be the distance between two consecutive vertices, so we can say that S is the distance between points G and O.
Remember that the distance between two points (x₁, y₁) and (x₂. y₂) is:
[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
So the distance between the points G(1, 0) and O(5, 2) is:
[tex]S = \sqrt{(5 - 1)^2 + (2 - 0)^2} = \sqrt{20}[/tex]
Then the area of this square is:
[tex]A = S^2 = (\sqrt{20})^2 = 20[/tex]
The area is 20 square units.
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A bag contains 12 balls which are numbered from 1 to 12. If two ball are selected at random, what is the probability that the total sum of the balls will be an even number
Answer:
5/11.
Step-by-step explanation:
The number of ways 2 balls can be selected = 12P2
= 12!/10!
= 12*11
= 132.
There are 6 even numbers and 6 odd numbers in the bag.
If both numbers drawn are even there are 6P2 = 30 ways that sum is even.
If the 2 numbers are odd there are also 30 ways that sum is even.
Any other combination wil be odd.
So the required probabilit = 2(3) / 132
= 60/132
= 5/11.
A shoe factory produces 1. 81 × 104 pairs of shoes each month. Estimate how many pairs of shoes the factory will produce if it maintains that rate for 10 years. (There are 1. 2 × 102 months in 10 years. ) 1. Estimate each coefficient: 1. 81 ≈ 2 1. 2 ≈ 1 2. Write the product: (2 × 104)(1 × 102) The shoe factory would make approximately ×106 pairs of shoes in 10 years.
Answer:
w
Step-by-step explanation:
The number of pairs of shoes in the factory is approximately 2 × 10⁶ in 10 years.
What is multiplication?It is also known as the product. If the object n is given to m times then we just simply multiply them.
A shoe factory produces 1.81 × 10⁴ pairs of shoes each month.
Estimate the number of pairs of shoes the factory will produce if it maintains that rate for 10 years.
There are 1.2 × 10² months in 10 years.
1.81 ≈ 2 and 1.2 ≈ 1
The number of shoes in 10 years will be
→ (2 × 10⁴)(1 × 10²)
→ 2 × 10⁶
The number of pairs of shoes in the factory is approximately 2 × 10⁶ in 10 years.
More about the multiplication link is given below.
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PERSEVERE The Flatiron Building in New York City is one of America's oldest skyscrapers, completed in 1902. Its floor plan is approximately a
right triangle. As shown in the figure, 5th Avenue is perpendicular to East 22nd Street, and m 2B is 10 less than 3 times mLC.
a. find the angle measures in the floor plan ( measure of A, B, and C )
b. find measure of BCD in two ways. explain each method in simple terms.
Answer:
a. (A, B, C) = (90°, 65°, 25°)
b. BCD = 155°
Step-by-step explanation:
The interior acute angles of the right triangle can be found by writing an equation representing the relation between them. The exterior angle can be found using the relations between exterior angles and interior angles.
__
a.Angle A is given as a right angle, so measures 90°. Let C represent the measure of angle C in degrees. Then angle B has measure 3C-10. Those two angles are complementary, so ...
C +(3C-10) = 90
4C = 100
C = 25
B = 3(25) -10 = 65
The angle measures are ...
A = 90°B = 65°C = 25°__
b.Angle BCD is the exterior angle adjacent to interior angle C. As such, it is supplementary to angle C:
BCD = 180° -C = 180° -25° = 155°
An exterior angle is equal to the sum of the remote interior angles. That means ...
BCD = A +B = 90° +65° = 155°
_____
Additional comment
An exterior angle is equal to the sum of the remote interior angles, because both the exterior angle and the sum of the remote interior angles are supplementary to the adjacent interior angle. Angles supplementary to the same angle have the same measure.
Answer:
part b is 155
Step-by-step explanation:
Twenty-six cards with the letters from A to Z are face down. What is the probability that a vowel will be chosen?
Answer:
5/26
Step-by-step explanation:
There are 26 letters in the english alphabet then out of that 26 there are 5 vowels so the probability is 5/26
Order their calculations from greatest to least
Leon-------Mika-------Jason------Ashley
√17 - 2-----1 + π/2 -----12/5---------2.5
Answer:
Leon (2.12), Jacon (2.40), Ashley (2.50), Mika (2.57)
Step-by-step explanation:
Putting a mix of rational and irrational numbers into numerical order can be done by using approximations to them of sufficient precision to be able to tell them apart.
Here, we can make the following approximations:
√17 -2 ≈ 2.12
1 +π/2 ≈ 2.57
Of course, the decimal value of 12/5 is 2.40, so the numbers will be arranged in order if Mika moves to the right end:
Leon (2.12), Jacon (2.40), Ashley (2.50), Mika (2.57)
__
Your calculator can help with this.
A software store has put some of its inventory on sale. games are marked down by 15%, and security programs are marked down by 18%. if you pay $35.70 each for two games and $22.96 for a security program, how much have you saved? a. $17.64 b. $14.84 c. $12.24 d. $11.34
The amount we saved after paying $35.70 each for two games and $22.96 for a security program is $11.34.
What is the discount?A discount refers to an amount deducted from the normal selling price of an object.
Let x be the original price of one game and y be the original price of one security program.
Given pay $35.70 each for two games and $22.96 for a security program.
The total pay with discount
$35.70 + $22.96 = $58.66
Also, 100% - 15% = 85%
100% - 18% = 82%
here, we have
0.85 (2x) = 35.70
1.70x = 35.70
x = $21
0.82 y = 22.96
y = $28
the total pay without discount
2x + y = 2 (21) + 28
= $70
The amount saved is 70 - 58.66 = 11.34
Therefore, the amount we saved after paying $35.70 each for two games and $22.96 for a security program is $11.34.
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Answer:
d. $11.34
Step-by-step explanation:
what is an easy method to workout 35% of 70
Step-by-step explanation:
[tex]70 \times \frac{35}{100} = 24 .5 [/tex]
Answer:
24.5
Step-by-step explanation:
35% can be broken down into 10% + 10% + 10% + 5%
To find 10% of 70, divide 70 by 10.
To divide a number by 10, move the decimal point 1 place to the left.
⇒ 70 ÷ 10 = 7
So 10% = 7
5% is half of 10%
⇒ 5% = 7 ÷ 2 = 3.5
Therefore,
10% + 10% + 10% + 5% = 7 + 7 + 7 + 3.5
= 21 + 3.5
= 24.5
Kate has five sandwiches to share with three of her friends. If each person gets the same amount of sandwich, how much will each person get?
Answer: Each person gets 1 1/4 of a sandwich.
Step-by-step explanation: Kate is sharing five sandwiches, and there are three friends with her too. Each person gets a sandwich, but you have to cut the last one three times to make fourths for everyone. So, each person gets 1 and 1/4 of a sandwich.
Hope this helps! :)
If each person gets the same amount of sandwich then each person get
is 5/3.
What is Fraction?
The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.
The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.How many sections of the fraction are displayed or chosen is shown in the numerator. It is positioned above the fractional bar in the upper portion of the fraction.
We have,
Total sandwiches = 5
Total number of people = 3
Now, we have to equally divide 5 sandwiches among 3 Friends.
So, Each person get
= 1 full sandwich and 2/3 part
= 1 2/3 parts
= 5/3
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M is the midpoint of AB. If the coordinates of A are (-1,5), and the coordinates of M are (3,3), what are the coordinates of B?
I need the answer asap!
Answer:
B = (5, 1).
Step-by-step explanation:
From the formula for the midpoint of a line :-
(-1 + x)/2 , (5 + y)/2 = (6/2, 6/2) where x and y are the coordinates of B.
so (-1 + x)/2 = 6/2
-1 + x = 6
x = 5.
and (5 + y)/2 = 6/2
5 + y = 6
y = 1.
Finn, Michael, and Chris are going to have a movie night this weekend. Together, they have 31
movies. If they decide to randomly choose three movies, what is the probability that the three they choose will consist of each of their favorite movies? Assume they have different favorites. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth
The probability that the three they choose will consist of each of their favorite movies is 1/29791.
What is probability?It 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.
It is given that:
Finn, Michael, and Chris are going to have a movie night this weekend. Together, they have 31 movies.
Total number of outcomes = 31
They choose three movies out of 31
Let us assume that Finn, Michael, and Chris have 1 favorite movie out of 31.
The probability that the three they choose will consist of each of their favorite movies:
= (1/31)(1/31)(1/31)
= 1/29791
Thus, the probability that the three they choose will consist of each of their favorite movies is 1/29791.
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PLSSSSSS HELPPP Assemble the proof by dragging the tiles to the Statements and Reasons columns.
Answer:
Hope this helps
Step-by-step explanation:
Similar Triangles... Yes
QR similar to SR
ang. QRP = ang. SRT
ang. p = ang. t
=> similar
An isosceles triangle has area of 140 ft2. If the base is 18 ft, what is the length of each leg? Round your answer to the nearest tenth
Answer: 18.0 feet
Step-by-step explanation:
Shelly rolls a dice 36 times. How many of those times should she expect it to land on a 1?
Answer:
it will land on "1" exactly 12 times
I need help 1 through 13 please and thank you
Answer
Let's get to it!
Step-by-step explanation:
1) There are 15 pounds of chees on that platter. (3+5+3+4=15)
2) The total weight is 32 ounces and 6 pounds.
3) 35 gallons of coffee are brewed per day. (5+5+5+5+5+5+5=35)
4) The cook peeled 50 pounds of potatoes per hour (200 divided by 4)
5) There is a total of 4/8 or 1/2 of an ounce
6) 2/8 ounces of oregano is left.
7) This recipe requires 1 and 1/2 pounds of meat.
(This is all I could do without paper) sorry, hope this helps.
I need help.ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
use a kittykat proportion
Step-by-step explanation:
Please i need help !!!
Answer:
Jenna is correct.
Step-by-step explanation:
See attached image.
!!40 points and Brainliest if it’s correct!!ANSWER IT ONLY IF YOU KNOW THE ANSWER. IF YOU DONT KNOW DONT ANSWER IT. Make sure you explain please!
Which of the following shows the correct first step to solve x^2 - 16x = -21 by completing the square?
A)x^2 - 16x + 64 = -21
B) x^2 - 16x + 64 = -21 + 64
C) x^2 - 16x + 16 = -21 + 16
D) x^2 - 16x + 8 = -21 + 8
For using completing the square, first make sure that the coefficient of x² is 1, if it's not 1, then you need to make it 1, by dividing both sides of the equation by the coefficient whatever it is. So, jere the coefficient of x² is 1, so now we need to develop a whole square on both sides, for which,we will add the square of half of coefficient of x on both sides, so adding (-16/2)² = (-8)² = 64 on both sides, we will be having :
[tex]{:\implies \quad \sf x^{2}-16x+64=-21+64}[/tex]
Which suits the B) option
Hence, Option B) is correct
A sector with arc measure 72º has an
area of 80 square feet. Determine
the radius of the circle.
A 18 ft
C 12 ft
B 20 ft
D 16ft
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Let's find the Radius ~
[tex]\qquad \sf \dashrightarrow \: area = \frac{ \theta}{360} \times \pi {r}^{2} [/tex]
[tex]\qquad \sf \dashrightarrow \: 80= \frac{ 72}{360} \times \pi {r}^{2} [/tex]
[tex]\qquad \sf \dashrightarrow \: {r}^{2} = \frac{80 \times 360}{72 \times \pi} [/tex]
[tex]\qquad \sf \dashrightarrow \: {r}^{2} = \frac{80 \times 5}{ \pi} [/tex]
[tex]\qquad \sf \dashrightarrow \: {r}^{} = \sqrt\frac{400}{ \pi} [/tex]
[tex]\qquad \sf \dashrightarrow \:r = \frac{20}{ \sqrt{\pi} } [/tex]
or
[tex]\qquad \sf \dashrightarrow \:r \approx 11.28 \: ft[/tex]
I hope you understood the whole procedure, let me know if you have doubts ~
➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖
Help me with this question!!
50 points + Brainliest
No spammers allowed
Thanks in advance.
No. 7.a
Answer:
∠BAC = 35°
AC = 5 cm
BD = 2.4 cm
Step-by-step explanation:
As ΔABC ~ ΔBDC then ∠CBD ≅ ∠BAC
As ∠CBD = 35° then ∠BAC = 35°
Using Pythagoras' Theorem
CB² + AB² = AC²
⇒ 3² + 4² = AC²
⇒ 25 = AC²
⇒ AC = 5 cm
As ΔABC ~ ΔBDC then
AB : AC = BD : BC
⇒ 4 : 5 = BD : 3
[tex]\sf \implies \dfrac45=\dfrac{BD}{3}[/tex]
[tex]\sf \implies BD=\dfrac{12}{5}=2.4\:cm[/tex]
**A right triangle with legs of 3cm and 4cm, and a perpendicular line from the hypotenuse to the right angle vertex, does not have an internal angle CBD of 35°. It should be 36.87°. So if you use SOHCAHTOA to find the length of BD, it will be incorrect. See attached diagram**
Answer:
35°, 5 units, 2.4 unitsStep-by-step explanation:
Given
ΔABC ~ ΔBDCCorresponding angles are congruent
∠BAC ≅ ∠DBC m∠BAC = m∠DBC = 35°Use Pythagorean to find the length of AC
[tex]AC = \sqrt{AB^2+BC^2} =\sqrt{3^2+4^2} =\sqrt{25} =5[/tex]The ratio of corresponding sides is equal
BD/AB = BC/ACBD/4 = 3/5BD = 4*3/5BD = 2.4please help!!!!! i will give brainliest!
Answer:
Option 1 and 4
Step-by-step explanation:
**PLS HELP ILL GIVE BRAINLIEST** Explore
Fill in each blank with a number or expression such that each row and column has the same sum.
The missing expressions to the empty blanks are 2x, 2x - 1, x - 1 and x + 3.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Sum of each row = sum of each column = x + 2 + x + 2 = 2x + 4
Hence:
a + x + 2 + 2 - x = 2x + 4
a = 2x
b + 5 - x + x = 2x + 4
b = 2x - 1
c + 5 - x + 2x = 2x + 4
c = x - 1
d + 2 + x - 1 = 2x + 4
d = x + 3
The missing expressions to the empty blanks are 2x, 2x - 1, x - 1 and x + 3.
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What is the volume of the triangular prism
Answer:
A.
Step-by-step explanation:
hope its help^^
#carry on learningWhat is 2925 divided by 15
Convert 0.595 to a fraction in simplest form
0.595
= 595/1000
= 119/200
Can someone help me with this question
Step-by-step explanation:
y = 4
2x + 3y = 6
1) 2x + (3 x 4) = 6
2) 2x + 12 = 6
3) 2x = -6
4) x = -3
Answer:
1. 2x + 3(4) = 6, 2. 2x + 12 = 6, 3. 2x = -6, 4. x = -3
Step-by-step explanation:
Step 1: 2x + 3(4) = 6
Step 2: 2x + 12 = 6
Step 3: 2x = -6
Step 4: x = -3
Hope this helps :)
classify these polynomials based on the degree and number terms 3x^2
Answer:
3x² is "monomial" according to the number of term(s) and "Quadratic" based on degree
Carlos has a 12300 millimeters long piece of wook. he wants to cut it into 3 equal lengths. how long will each piece be in meters?
Answer:
4.1 meters each
1000 milileters go into 1 meter
Step-by-step explanation:
Answer:
Step-by-step explanation:
12300/3= 4100 1 meter = 1000 millimeters
4100/1000=4.1 meters
Find the measure of angle PRT.
Select one:
A. 45°
B. 90°
C. 120°
D. 180°
Answer:
The measure of angle PRT would be:
B.) 90 degrees
Step-by-step explanation:
Have a great rest of your day
#TheWizzer
The angle letters PRT all will connect at one point which is the angle we will measure.
Angle PRT = 90 degrees
Please help! will give brainlest! locks in 30 min!
Let dnbe the number of n-digit positive integers using only the digits 1, 2, 3, 4, 5, 6, or 7 (with repetition permitted), such that no two consecutive digits are even
The nth term of the sequence whose integers are between 1 -7 such that there is the permission of repetition but no two consecutive digits must be even is 1.254 × 10¹¹
What are consecutive numbers?
Consecutive numbers are those numbers that succeed each other in increasing order from least to greatest. The numbers that are given:
1, 2, 3, 4, 5, 6, or 7 are all consecutive.Now, suppose a (n) denotes the number of n-digit positive integers as stated in the question, thereby using:
1, 2, 3, 4, 5, 6, or 7 with the permission of repetition; no two consecutive digits are even.Then, the number of n can be computed as n!
= (7!) × (6!) × (5!) × (4!) × (3!) × (2!) × (1!)
= 1.254 × 10¹¹
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The nth term of the series of integers is between 1 -7 such that there is the permission of repetition but no two consecutive digits must be even is 1.254 × 10¹¹
What are consecutive numbers?Consecutive numbers are those numbers that succeed by each other in increasing order from lowest to greatest such are 1, 2, 3, 4, 5, 6, or 7.
Now, suppose n represents the number of n-digit positive integers.
1, 2, 3, 4, 5, 6, or 7 with the permission of repetition no two consecutive digits are even.
Then, the number of n can be calculated as n!
= (7!) × (6!) × (5!) × (4!) × (3!) × (2!) × (1!)
= 1.254 × 10¹¹
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