According to the given linear equation depth of the dive is 17.59 feet.
What is linear equation?
A linear equation is also known as a one degree equation. The linear equation's highest power is 1. Linear equations are equations with variables on both sides that are multiplied by a constant.
Here the given linear equation is ,
=> y = 0.25+5.78t
Here t is time in seconds which is t=3 seconds.
Put t=3 sec into linear equation then,
=>y=0.25+5.78*3
=>y= 0.25+17.34
=>y=17.59.
Hence depth of the dive is 17.59 feet.
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the ratio of the areas of two different squares is 5:7. if the perimeter of the smaller square is 2cm, what is the area of the other square?
Area of the other square is 7/20 cm²
Let side of the larger square be 'b' and side of the smaller square be 'a'.
Given the perimeter of the smaller square = 2 cm
⇒ 4a = 2
⇒ a = 2/4 = 1/2 cm
Given, ratio of the areas of squares = 5 : 7
⇒ area of smaller square/ area of larger square = 5 : 7
⇒ a²/b² = 5/7
⇒ (1/4)/b² = 5/7
⇒ b² = 7/(5×4) = 7/20
Therefore, area of the larger square = 7/20 cm²
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a company making tires for bikes is concerned about the exact width of its cyclocross tires. the company has a lower specification limit of 22.6 mm and an upper specification limit of 23.0 mm. the standard deviation is 0.14 mm and the mean is 22.8 mm. what is the process capability for the index?
0.5852 is the process capability for the index when standard deviation. is 0.14 mm .
What is standard deviation in math?
Your dataset's average level of variability is represented by the standard deviation. It reveals the average deviation of each statistic from the mean. A low standard deviation denotes that values are grouped close to the mean, whereas a large standard deviation shows that values are often far from the mean.Cpk = minimum of [(23.0 - 22.8)/(3 *0.15),(22.8 - 22.6)/(3 * 0.15)]
= (0.2/0.45) , ( 0.6/0.45)
= (0.44 )( 1.33)
= 0.5852
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Gaton paint a pole uing three different colour a hown. What i the ratio for the length of grey to red to blue? Give your anwer in it implet form uing whole number only. Grey 0. 8 m Red 1. 8 m Blue 0. 6 m Not to cale
The ratio for the length of grey to red to bule is 4:9:3.
What is ratio?Ratio is the relation between two numbers which shows how much bigger one quantity than another. Ratio show how many times one contain show the other one.
According to the question
The given data are -
Grey = 0.8m
Red = 1.8 m
Bule = 0.6 m
By solving these we can get -
=0.8:1.8:0.6
=0.8×10:1.8×10: 0.6×10
=8:18:6
By simplifying it we can get
4:9:3.
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Write the answers in lowest terms leave improper fractions when applicable.Ron not convert to mixed numbers
please help me solve this simultaneous eqn
x+y=7
2x² + y² = 35-3xy
Answer:
x = -2, y = 9
Step-by-step explanation:
x + y = 7 --1
2x² + y² = 35 - 3xy --2
For 1, make y the subject.
y = 7 - x
Substitute y = 7 - x into 2.
2x² + (7 - x)² = 35 - 3x(7 - x)
Simplify and solve for x.
2x² + (49 - 14x + x²) = 35 - 21x + 3x²
3x² - 14x + 49 = 3x² - 21x + 35
7x = -14
x = -2
Substitute x = -2 into y = 7 - x.
y = 7 - (-2)
= 9
Thus, x = -2, y = 9
The figure to the right is comprised of a rectangle and two half circles. The rectangle is 100 ft wide and 10 ft long. Find the total area of the figure. Show your work and/or explain your reasoning.
A-1,000ft^2
B-1,314ft^2
C-120ft^2
D-1,078.5ft^2
Pls help
Answer:
D 1,078.5 ft^2
Step-by-step explanation:
You want the area of a figure composed of a rectangle 100 ft long and 10 ft wide with semicircles of diameter 10 ft at each end.
Rectangle AreaThe area of the rectangle is ...
A = LW
A = (100 ft)(10 ft) = 1000 ft²
Circle AreaThe two half-circles have the area of a whole circle with radius 5 ft.
A = πr²
A = π(5 ft)² = 25π ft² ≈ 78.5 ft²
Total AreaThe area of the figure is the sum of the areas of its parts:
total area = rectangle area + circle area
total area = 1000 ft² +78.5 ft² = 1078.5 ft²
The total area of the figure is about 1078.5 ft².
The sum of 8 and a certain number is equal
to the product of the number and 3. Find
the number.
Answer:
4
Step-by-step explanation:
1.) Create an equation. If we let the number be x, we get x+8=3x
2.) Solve. If you move x to the other side, we get 2x=8. Finally, by dividing by 2 on each side, we get x=4. Therefore, the number is 4.
Answer:
4
Step-by-step explanation:
create an equation thus 8+x =3x
8+X=3x
collect like terms
8=3x-x
8=2x
divide both sides by 2
8/2=2x/2
X=4
A recipe for a single sheet of brownies asks for ¼ cup of flour. You want to make 5 sheets of brownies. How much flour do you need?
Answer:
1 1/4 cup of flour
Step-by-step explanation:
1/4 × 5 = 1 1/4
Which if the following represents the location of any unit rate, m, as graphed on a coordinate plane?
(1) (1, m) (3) (0, m)
(2) (m, 1) (4) (m, 0)
The answer choice which represents the location of any unit rate, m as graphed on a coordinating plane is; Choice 1; (1, m).
Unit rate on a coordinate planeIt follows from the task content that the answer choice which represents the location of any unit rate, m on a coordinate plane.
Hence, since the slope is defined as the rate of change on a graph such that slope = ∆y/∆x.
In this case, when the change in y with respect to x is to be equal to m.
Therefore, the location as required is the point defined by; (1, m).
Such that; Unit rate = (m - 0)/(1 - 0)
Ultimately, the required location of the unit rate is; Choice 1; (1, m).
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Work out the equation of the straight line that passes through (2, 3) and
(5, 18).
Give your answer in the form y = mx + c, where m and c are integers or
fractions in their simplest forms.
Answer:
Y=5X-7
Step-by-step explanation:
(2,3)
Y-Yo=m(X-Xo)
Y-3=m(X-2)
Y-3=mX-2m
Y=mX-2m+3
(5,18)
18=m(5)-2m+3
18=5m-2m+3
18=3m+3
18-3=3m
15=3m
15/3=m
5=m
Y=5X-2(5)+3
Y=5X-10+3
Y=5X-7
an unbiased coin is tossed four times. what is the probability that coin lands heads up at least once? (round your answer to three decimal places.)
The probability of getting at least one head is 15/16.
What is probability?
The ratio of positive outcomes to all possible outcomes of an event is known as the probability.
Formula for probability = favourable outcomes/ total outcomes
Main body:
if 4 coins are tossed , total no. of outcomes = 2⁴ = 16
In a toss there are 2 outcomes T or H
so, Probability of getting Head = 1/2
The probability of getting at least 1 head = 1- probability of getting no heads
⇒1 - Probability of getting tail in 4 tosses
⇒ 1 - (1/2)⁴
⇒ 1 - 1/16
⇒ 15/16
So the probability of getting at least one head is 15/16.
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Please help me out with this
Answer:
6\sqrt3
Step-by-step explanation:
Since 30-60-90 tri, small side is 6.
This means x=[tex]6\sqrt3[/tex]
Answer:
[tex]x = 6\sqrt{3}[/tex]
Step-by-step explanation:
Utilize the trigonometric ratio cosine.
[tex]\cos(30\textdegree ) = \dfrac{x}{12}[/tex]
Solve for x by multiplying both sides by 12.
[tex]12\cos(30\textdegree ) = x[/tex]
[tex]12\left(\dfrac{\sqrt{3}}{2} \right) = x[/tex]
[tex]x = 6\sqrt{3}[/tex]
Can somebody please help me appreciate it
Area of semicircle is 76.93 [tex]units^{2}[/tex].
Given,
Diameter = 14 units
Radius = r = 14/2
= 7 units
Area of semicircle = [tex]\frac{1}{2}\pi r^{2}[/tex]
= (3.14*7*7)/2
= 153.86/2
= 76.93
Hence, Area of semicircle is 76.93 [tex]units^{2}[/tex].
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.suppose that every hour there are two new bacteria in a colony for each bacterium that was present the previous hour, and that all bacteria 2 hours old die. the colony starts with 100 new bacteria. a) set up a recurrence relation for the number of bacteria present after n hours. b) what is the solution of this recurrence relation? c) when will the colony contain more than 1 million bacteria?
a) Relation of recurrence for the number of bacteria remaining after n hours is [tex]a_{n} = a_{n-1} + 2a_{n-1} - a_{n-2} = 3a_{n-1}-a_{n-2}[/tex]
b) the solution to this recurrence relationship is [tex]a_{n} = (50 + 30\sqrt{5}) [(3 + \sqrt{5}) / 2]^{n} - (30\sqrt{5} - 50) [(3 - \sqrt{5}) / 2]^{n}[/tex]
c) There will be more than a million microorganisms after 7 hours.
A recurrence relation is an equation that states that some combination of the previous terms and the nth term in a series of numbers equals 1.
a) a₀ = 100, a₁ = 300 Every hour the bacteria - bacteria before two hours, and every hour the bacteria + 2(existing bacteria). Consequently, the corresponding recurrence relationship is [tex]a_{n} = a_{n-1} + 2a_{n-1} - a_{n-2} = 3a_{n-1}-a_{n-2}[/tex] where n is an hour reference.
(b) The associated difference equation is
r² - 3r + 1 = 0
⇒ r = [3 ± (√9 - 4)] / 2 = (3 ± √5) / 2
hence, the answer is [tex]a_{n} = a[(3 + \sqrt{5}) / 2] ^{n} + b [(3 - \sqrt{5}) / 2] ^{n}[/tex]
Using n = 0 as the initial condition, we have a₀ = 100 = a + b → (1)
putting n = 1,
⇒ √5 (a - b) = 300 → (2)
(1) ⇒ √5 (a + b) = 100√5
By combining these relationships, we have
a = [(300 + 100√5) / 2√5] = 50 + 30√5
therefore, b = 50 - 30√5
Consequently, the answer to the equation is [tex]a_{n} = (50 + 30\sqrt{5}) [(3 + \sqrt{5}) / 2]^{n} - (30\sqrt{5} - 50) [(3 - \sqrt{5}) / 2]^{n}[/tex]
c) if there are more than one million bacteria, i.e.
[tex]a_{n} = (50 + 30\sqrt{5}) [(3 + \sqrt{5}) / 2]^{n} - (30\sqrt{5} - 50) [(3 - \sqrt{5}) / 2]^{n} > 1,000,000[/tex]
⇒ log (50 + 30√5) + n {log (3 + √5)} - log2} - log {30√5 - 50} - n {log (3 - √5) - log2} > log 1,000,000
⇒ 2.06849 + n {0.719 - 0.3010} - 1.2325 - n {-0.41797} > 6
⇒ 0.835975n > 5.16401
⇒ n > (5.16401 / 0.83975)
Therefore, n > 6.177, or after 7 hours, there will be more than 1 million bacteria.
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ignoring twins and other multiple births, assume that babies born at a hospital are independent random events with the probability that a baby is a boy and the probability that a baby is a girl both equal to 0.5. what is the probability that at least one of the next three babies is a boy?
The probability that at least one of the next three babies is a boy is 0.875.
What is probability ?Probability turned into added into arithmetic to are expecting the possibility of an occasion occurring. Probability essentially approach how in all likelihood it's miles that some thing will happen. This is the fundamental principle of possibility and is likewise utilized in possibility distributions to examine feasible consequences of random experiments.
CalculationProbability of the complement of event B:
The probability of the complement of event B is computed as follows:
P(B* )=1-P(B) P(B)=14(1-(0.5x0.5)) = 0.25
The probability of the complement of event B is B) 0.25.
Probability that at least one of the next three babies is a boy:
The probability that at least one of the next three babies is a boy is computed as follows:
at least one of the next three babies is a boy =1-(0.5x0.5x0.5) =1-0.125 = 0.875
The probability that at least one of the next three babies is a boy is D) 0.875.
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Simplify x raised to the negative second power over y raised to the fourth power.
y raised to the fourth power over x raised to the negative second power
y raised to the fourth power over x raised to the second power
1 over the quantity x raised to the second power times y raised to the fourth power end quantity
−x2y4
Answer:
Step-by-step explanation:
(x 2 y) 4 = x2*4 y 1*4 = x 8 y4
An exponent raised to another exponent means to multiply the exponents. If a number does not have a visible exponent, then it is an implied 1.
The required simplified form of the expression is 1 / (x² · y⁴) which is the correct answer would be an option (D).
How to use laws of exponents?When multiplying similar bases, keep the base and add the exponents the same. When comparing one power to another, keep the base constant and multiply the exponents. Keep the base constant when dividing like bases and subtract the denominator exponent from the numerator exponent.
Simplify x raised to the negative second power over y raised to the fourth power.
The expression is given in the question below as:
x⁻² / y⁴
The expression can be simplified as follows:
⇒ x⁻² / y⁴
⇒ (1 / x²) / (y⁴)
⇒ 1 / (x²) · y⁴)
⇒ 1 / (x² · y⁴)
Therefore, the simplified form of the expression is 1 / (x² · y⁴).
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Yvonne is thinking of a number. Fifty decreased by three times the number is the same as seven times the number increased by 80. Set it up in a equation.
After forming the algebraic equation, he equation of the given statement is 7x+80=3x−50.
In the given question,
Yvonne is thinking of a number.
Fifty decreased by three times the number is the same as seven times the number increased by 80.
We have to set it up in a equation.
To set it up in a equation we divide the step in small steps.
Firstly the statement is saying that fifty decreased by three times the number.
Let the number be x.
So three times of a number is 3x and 50 decreased means 3x−50.
Next statement is saying that seven times the number increased by 80.
As the number is x so seven times of a number is 7x and increased by 80 means 7x+80.
The both statement is equal to each other.
So 7x+80=3x−50
So the equation of the given statement is 7x+80=3x−50.
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Solve for the side or angle in the right triangles below. Show all of your work....
1)
X
12
18°
2)
25
10
The side and angle is in the right angle triangle respectively x = 3, 68°.
What is a right angle triangle?
A right triangle, also known as a right-angled triangle, is a triangle with one angle that is a right angle (i.e., a 90-degree angle) and two perpendicular sides.
We have,
[tex]1) Opposite = x, \ Adjustment = 12, \ \theta = 18.\\\\2) Opposite = 25, \ Adjustment = 10, \ \theta = ?.[/tex]
How to determine the angle in a right angled triangle,
[tex]Sin (\theta ) = \frac{Opposite}{Hypotenuse}[/tex][tex]Tan (\theta ) = \frac{opposite}{adjacent}[/tex]
[tex]cos(\theta) = \frac{Adjacent}{Hypotenuse}[/tex]
[tex]1) \ Opposite = x, Adjustment = 12, \ \theta = 18.[/tex]
[tex]cos(\theta) = \frac{Adjacent}{Hypotenuse}[/tex]
[tex]Hypotenuse = \frac{Adjacent}{cos(\theta)}[/tex]
[tex]Hypotenuse = \frac{Adjacent}{cos(18)}[/tex]
[tex]= 12.61755[/tex]
[tex]Opposite = \sqrt{Hypotenuse^{2} - Adjacent^{2} }[/tex]
[tex]= \sqrt{12.6175466908592 - 122}[/tex]
[tex]= \sqrt{15.202484496012}[/tex]
∴ [tex]Opposite(x) = 3.89904[/tex]
[tex]2) \ Opposite = 25, \ Adjustment = 10, \ \theta = ?.[/tex]
[tex]Hypotenuse = \sqrt{{Opposite^{2} - Adjacent^{2} }[/tex]
[tex]= \sqrt{25^{2} + 10^{2} }[/tex]
[tex]= \sqrt{725} \\\\= \ 26.92582 \ = \ 5\sqrt{29}[/tex]
[tex]\theta =\ sin^{-1} {\frac{Opposite }{Hypotenuse} }[/tex]
[tex]\theta = \ sin^{-1} (\frac{25}{26.92} )[/tex]
[tex]\theta = \ sin^{-1} (\frac{25}{26.92} )[/tex]
[tex]= sin^{-1} (0.92847669088526)[/tex]
[tex]\theta = \ 68[/tex]°
Hence, The side and angle is in the right angle triangle respectively x = 3, 68°.
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how do you do that 52 + 19 = 71
Answer:
1
52
+ 19
____
71
Step-by-step explanation:
add 2+9 and get 11
carry the one
add 1+1+5 and get 7
71
A regular polygon is shown, with the measure of one of its angles labeled 7x − 21. 9 sided regular polygon with one angle labeled 7 times x minus 21 Determine the value of x. x = 17 x = 23 x = 29 x = 140
The correct value of x = 23.
Each interior angle of an n-sided regular polygon is given by 180 (n-2)/n degrees.
Given that:
n = 9
Therefore, each interior angle＝180 x (9-2)/9 degrees
Each interior angle = 180 x 7/9
Each interior angle = 140°
Each internal angle of a regular polygon having 9 sides is 140°.
Also, given that:
A 9-sided regular polygon with one angle equals 7x-21.
For the polygon to be a 9-sided regular polygon, the angles must equal 140°.
Checking the value of x from the given option which one satisfies the value of interior angle = 140°.
Option 1, x= 17
=> 7 x 17 - 21 = 98° which is wrong.
Option 2, x= 23
=> 7 x 23 - 21 = 161-21 = 140° which is correct.
Option 3, x= 29
=> 7 x 29 - 21 = 203-21 = 182° which is wrong.
Option 4, x= 140
=> 7 x 140 - 21 = 980- 21 = 959° which is wrong.
Only, the value of x = 23 satisfies the value of a 9-sided regular polygon with one angle equal to 7x-21.
Hence, the correct value of x = 23
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Answer:
The correct value of x = 23.
Step-by-step explanation:
a company advertises that its training program raises sat scores by an average of at least 30 points. a random sample of test-takers who had completed the training showed a mean increase smaller than 30 points. write the hypotheses for a left-tailed test of the mean
Type - I error states that the training program actually raised the score but statistically, it is not.
Type-II error states that the training program does not actually raise the score but statistically, it raised the scores.
Given statement is
"A random sample of test-takers who had completed the training showed a mean increase smaller than 30 points."
Hypothesis is,
Null hypothesis H0 :μ ≥ 30 (claim)
Alternate hypothesis H1 :μ < 30 (actual result)
in the null hypothesis, we have to consider the claim and the other in the alternate hypothesis.
In the given context of the problem, the Type-1 error will be stated below
" If in reality, the training program raises the SAT score by more than or equal to 30 points and statistically the claim is rejected".
The training program actually raised the score but statistically, it is not.
Type-II error
" If in reality, the training program does not raise the SAT score by more than or equal to 30 points and statistically the claim is failed to reject".
The training program does not actually raise the score but statistically, it raised the scores.
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(03.02 MC)
Elevator 1 in a hotel moved from ground position to a final position of +18 feet. Elevator 2 in the same building moved from ground to a final position of −20 feet. Which statement best describes the final positions of these two elevators?
Group of answer choices
A.) Elevator 1 is 18 feet below ground level, and Elevator 2 is 20 feet above ground level.
B.) Elevator 1 is 18 feet above ground level, and Elevator 2 is 20 feet below ground level.
C.) Elevator 1 is 18 feet below ground level, and Elevator 2 is 20 feet above the position of Elevator 1.
D.) Elevator 1 is 18 feet above ground level, and Elevator 2 is 20 feet below the position of Elevator 1.
Elevator 1 is 18 feet above ground level, and Elevator 2 is 20 feet below ground level.
Option B is the correct answer.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Elevator 1 in a hotel moved from ground position to a final position of +18 feet.
+18 means the elevator is 18 feet above the ground floor.
Elevator 2 in the same building moved from the ground to a final position of −20 feet.
-20 feet means the elevator is 20 below the ground floor.
Thus,
Elevator 1 is 18 feet above ground level, and Elevator 2 is 20 feet below ground level.
Option B is the correct answer.
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The data collected on the number of points scored in a basketball season are represented in the box plot. A box plot uses a number line from 13 to 33 with tick marks every one-half unit. The box extends from 16 to 31 on the number line. A line in the box is at 24. The lines outside the box end at 14 and 32. The graph is titled Number of Points, and the line is labeled Points Scored in Basketball. What value does 25% of the data lie above? Find the value. Lower quartile (Q1) = 14 Lower quartile (Q1) = 16 Upper quartile (Q3) = 24 Upper quartile (Q3) = 31
The value that lie above 25% of the data of the box plot is: 31.
Lower quartile (Q1) = 14
Upper quartile (Q3) = 31
What is a Box Plot?A box plot tells us the following values of a data set as shown in the diagram attached:
Minimum value, which is 14Lower quartile, which is 16 (25% of the data is below this value)Median, which is 24 (50% of the data is below this value)Upper Quartile, which is 31 (75% of the data is below this value)Maximum value, which is 32.Using the box plot that shows the information given about the data collected on the number of points scored, we can conclude that:
Lower quartile (Q1) = 14
Upper quartile (Q3) = 31
25% of the data lie above 31, which is the upper quartile.
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Kyla finished a 100 meter race in one and three-eighths minutes. The winner of the raced finished in one-third of Kyla's time.
How many minutes did it take for the winner of the race to finish?
A eight thirty-thirds
B eleven twenty-fourths
C one and three twenty-fourths
D one and four-elevenths
The winner of the race finished the race in eleven twenty-fourths(11/24) minutes which is option B
What is mixed fraction?A fraction represented with its quotient and remainder is a mixed fraction. For example, 2 1/3 is a mixed fraction, where 2 is the quotient, 1 is the remainder. So, a mixed fraction is a combination of a whole number and a proper fraction.
Kyla finished her race in 1 3/8 minutes.
converting this to improper fraction, we have 11/8 minutes
The winner of the race finished in 1/3 of Kyla's time which is 1/3 x 11/8
= 11/24 minute
The winner of the race finished in 11/24 minute.
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quick! 80 points!! 1. Answer the following questions.
Questions
What is an amount between $2 and $10? (A) _$4_________
What is an amount between $10 and $20? (B) ___$15_______
What is an amount greater than $50? (C) __$62________
What is your name? (D) ____Kareem_____________
What is the name of an item that you will buy only once? (E) ______Bell___________
What is the name of an item that you will buy more than once? (F) ____Toy cats_________
2. Create a word problem that leads to an inequality by filling in the blanks with your corresponding answers.
Word Problem
(D) ___Kareem______________ is going shopping for (E) _____bell____________ and (F) ____toy cats____________.
The cost of (E) ___Bell______________ is (B) ___$15_______ and the cost of each (F) ____toy cats_____________ is (A) _$4_________.
If (D) __Kareem_______________ can spend at most (C) __$62________, how many (F) _______Toy cats__________ can be purchased?
3. Write an inequality of the form Ax + B ≤ C to represent the word problem using your answers for A, B, and C. Solve the inequality and show your work.\
4. Graph the solution to your inequality on a number line or describe, in words, how to graph the inequality on a number line.62
5. Explain what the solution means in the context of the word problem.
5. An action or process of solving a problem
Thats all I can answer for u :D
A company has a target profit of $204,000. The company's fixed costs are $305,000. The contribution margin per unit is $40. What is the break-even point in unit sales?
7,625 units
breakeven point= $305,000/$40=7,625
The break-even point in unit sales of the company is $7,625.
Define the term break-even point?The break-even threshold is reached when overall costs and total revenues are equal, leaving your small firm with no net benefit or loss. In other words, you've achieved the point in production where the revenue from a product equals the cost of manufacture.According to the question,
A corporation aims to make $204,000 in profit.The corporation has $305,000 in fixed expenses.The contribution margin is $40 for each unit.Thus,
Break-even point = fixed costs/margin per unit
Break-even point = $305,000/$40
Break-even point = $7,625
Thus, the break-even point in unit sales of the company is $7,625.
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Question 1 (1 point) Which pair of equations represents lines that are perpendicular Y=2x+8 y = 2x + 2 y = 1/2x +4 y = -2x-3 y 1/2x + 3 y = 2x-4
Only y = - 2x - 3...(iv) and y = (1/2)x...(v) are perpendicular to each other as the negative reciprocal of - 2 is 1/2.
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and the equation of a line in slope-intercept form is
y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.
We know lines that are perpendicular to each other have a slope that is negative reciprocal of each other.
The given lines are,
y = 2x + 8...(i)
y = 2x...(ii)
2y = (1/2)x + 4.
y = (1/4)x + 2...(iii)
y = - 2x - 3...(iv).
y = (1/2)x...(v)
3y = 2x - 4.
y = (2/3)x - 4/3...(vi)
So, only y = - 2x - 3...(iv) and y = (1/2)x...(v) are perpendicular to each other as the negative reciprocal of - 2 is 1/2.
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Calculate height of lighthouse pls :) thx
The height of lighthouse is 72.54
Given,
In the question:
To see the figure:
To find the height of lighthouse.
Now, According to the question:
In Triangle ABD
tan 20° = [tex]\frac{h}{20 + x}[/tex]
0.36 = [tex]\frac{h}{20 + x}[/tex]
=> (20 + x)0.36 = h
=> 0.72 + 0.36x = h
=> x = [tex]\frac{h - 72}{0.36}[/tex] .....(1)
In Triangle ABC
tan 34° = h/x
=> 0.67 = [tex]\frac{h}{\frac{h-72}{0.36} }[/tex]
=> 0.67 = 0.36/h - 72
=> 0.67 (h - 72) = 0.36
=> h - 72 = 0.54
=> h = 0.54 + 72
=> h = 72.54
Hence, The height of lighthouse is 72.54
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there is a total of 85 tiles work out the number of blue tiles
The number of blue tiles is 68.
Given:
Red tiles = 1/5 of the total
Total tiles = 85
Red tiles = 1/5*85
= 17.
Number of blue tiles = total tiles - red tiles
= 85 - 17
= 68.
Therefore the number of blue tiles is 68.
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HI PLS HELP ME ON MY MATH HOMEWORK I WILL ALSO GIVE BRAINLIEST
Considering the parallel and triangle sum properties and the isosceles triangle properties the only correct part option is 2
How to interpret the figuresOption 1
The angle 52 degrees is base angle of isosceles triangle therefore say angle at the third angle is x such that
x + 52 + 52 = 180 (triangle sum property)
x + 104 = 180
x = 76
The figure shows that the base angle of the triangle at the base is equal to 76 too
32 + 2x = 180 (triangle sum property for isosceles triangle)
x = 74
The two angles 74 and 76 are not equal - wrong option
Option 2
x + 2 * 76 = 180 (triangle sum property for isosceles triangle)
x = 28
The figure shows that the base angle of the triangle at the base is equal to 28
124 + 2x = 180 (triangle sum property for isosceles triangle)
x = 28
The two angles 28 and 28 are equal hence a right option
Option 3
wood you believe it, I past plain geometry - wrong
would you believe it, I passed plain geometry - correct
Option 4
The triangle in the parallelogram the isosceles triangle with base angle 27
The alternate interior angle is showing same base angle as 29
and the two angles 27 and 29 are not equal
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