He ratio of the lengths of the corresponding sides of two rectangles is 8:3. the area of the larger rectangle is 320 ft2. what is the area of the smaller rectangle? 120 ft2 30 ft2 90 ft2 45 ft2
Find the exact value of tan (arcsin (two fifths)). For full credit, explain your reasoning.
[tex]\rm tan\theta = \dfrac{2}{\sqrt{21} }[/tex]
Step-by-step explanation:
Given :
[tex]\rm sin^-^1(\dfrac{2}{5})=\theta[/tex]
Calculation :
[tex]\rm sin\theta = \dfrac{perpendicular}{hypotenuse}[/tex]
According to Pythagorean theorem,
[tex]a^2+b^2=c^2[/tex]
here a = 2, c = 5. Then,
[tex]2^2+b^2=5^2[/tex]
[tex]b^2=25-4=21[/tex]
[tex]b=\pm\sqrt{21}[/tex]
Nothing is given in the question so we take positive
[tex]b = \sqrt{21}[/tex]
Therefore,
[tex]\rm tan\theta=\dfrac{perpendicular}{base}[/tex]
[tex]\rm tan\theta = \dfrac{2}{\sqrt{21} }[/tex]
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If y varies directly with x and y = 15 when x = 5, what is the value of k?
y = kx
15 = k5
k = 15/5
k = 3
A 125-inch pipe is cut into two pieces. one piece is four times the length of the other. find the lengths of the two pieces.
You can calculate the length of the two pieces of pipe by setting up and solving a simple equation: 'x' stands for the length of the shorter piece, '4x' stands for the length of the longer piece, which will add up to the total length, 125 inches. You will find that 'x' equals 25, meaning the shorter pipe is 25 inches long and the longer one is 100 inches long.
Explanation:This question revolves around a simple equation in algebra. If we say that the shorter piece of pipe's length is 'x', we know from the problem that the longer piece's length is four times this length, or '4x'. The total length of the pipe, 125 inches, is made up of these two pieces. Therefore, those two lengths must add up to 125 inches.
This gives us the equation 'x + 4x = 125'. Combining like terms gives us '5x = 125'. To find 'x', we then divide both sides of the equation by 5, giving us 'x = 25'. Therefore, the shorter piece of pipe is 25 inches long, and the longer piece, being four times this length, is 100 inches long.
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a machine fills 150 bottles of water every 8 minutes. How many minutes will it take this machine to fill 675 bottles?
The minimum sustained wind speed of a Category 1 hurricane is 74 miles per hour. The maximum sustained wind speed is 95 miles per hour. Write an absolute value equation that represents the minimum and maximum speeds. Let v
represent the wind speed.
The absolute value equation that represents the minimum and maximum speeds of a Category 1 hurricane is |v - 84.5| ≤ 10.5, where v is the wind speed.
Explanation:To write an absolute value equation that represents the minimum and maximum speeds of a Category 1 hurricane, you will center it around the average of the two, which is (74 + 95) / 2 = 84.5 mph. The difference between the maximum speed and the average speed is 95 - 84.5 = 10.5 mph. Thus, the absolute value equation to represent the wind speeds of this hurricane category is |v - 84.5| ≤ 10.5, where v represents the wind speed.
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An absolute value equation representing the minimum and maximum sustained wind speeds of a Category 1 hurricane can be written as |v - 84.5| = 10.5, where v is the wind speed in miles per hour. This equation indicates that the wind speed can deviate by 10.5 mph above or below 84.5 mph, encompassing the range of 74 to 95 mph.
Explanation:To represent the minimum and maximum sustained wind speeds of a Category 1 hurricane using an absolute value equation, we can use the variable v to stand for the wind speed. The absolute value of a number represents its distance from zero regardless of direction, which in the context of wind speed means how much the speed differs from a certain value.
For instance, if the center value is the average of the minimum and maximum speeds, that would be (74 + 95) / 2 = 84.5 miles per hour. Therefore, the absolute value equation that represents the wind speeds that form the boundaries of Category 1 could be written as |v - 84.5| = 10.5. This equation means that the Category 1 wind speed, v, can be 10.5 miles per hour above or below 84.5 miles per hour, which corresponds to the range between 74 and 95 miles per hour.
However, there usually isn't just one single absolute value equation to represent this range. Another approach could involve setting two absolute value inequalities that represent the minimum and maximum separately, such as |v - 74| ≥ 0 for the minimum speed and |v - 95| ≤ 0 for the maximum speed.
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Geoffrey wrote the following paragraph proof showing that rectangles are parallelograms with congruent diagonals.
According to the given information, quadrilateral RECT is a rectangle. By the definition of a rectangle, all four angles measure 90°. Segment ER is parallel to segment CT and segment EC is parallel to segment RT by the Converse of the Same-Side Interior Angles Theorem. Quadrilateral RECT is then a parallelogram by definition of a parallelogram. Now, construct diagonals ET and CR. Because RECT is a parallelogram, opposite sides are congruent. Therefore, one can say that segment ER is congruent to segment CT. Segment TR is congruent to itself by the Reflexive Property of Equality. The _______________ says triangle ERT is congruent to triangle CTR. And because corresponding parts of congruent triangles are congruent (CPCTC), diagonals ET and CR are congruent.
Which of the following completes the proof?
A (ASA) Theorem
B (HL) Theorem
C (SAS) Theorem
D (SSS) Theorem
The answer is (SAS) Theorem. Because we know triangle ERT is congruent to triangle CTR, it has the sides ( C& E and R&T, and the angle T&R).
Hope its correct.
Solve for t: 35t + 70 (7-t) = 385
HELP PLEASE THANKS (;
Which number sentence below matches this word problem?
Jen and Marcus got 15 miles up river before they ran out of gas. They floated 9 miles back down river before they reached the shore. How far did they get? A.15 - 6 = 9
B. 9 + 15 = 24 C.15 - 9 = 6
D. 135 9 = 15
Answer: Option 'C' is correct.
Step-by-step explanation:
Since we have given that
Jen and Marcus got 15 miles up river before they ran out of gas. They floated 9 miles back down river before they reached the shore
so, distance they travel before they ran out of gas = 15 miles
distance they floated back down river = 9 miles
So, they are at
[tex]15-9\\\\=6\ miles[/tex]
Hence, They are 6 miles far.
Therefore, Option 'C' is correct.
If two cylinders are similar and the ratio between the lengths of their edges is 4:3 what is the ratio of their volumes
Answer:
64:27
Step-by-step explanation:
Find the midpoint of segment below
Line PQ has endpoints at P (-2,3) and Q (4,1). The center of dilation is (-1,4) and the scale factor is 2. What are the coordinates of the endpoints of P'Q'?
How many revolutions will a car wheel of diameter 26 in. make as the car travels a distance of one mile? (round your answer to the nearest whole number.)?
Answer:
776 revolutions per mile
Step-by-step explanation:
First we need to find the Circumference of the wheel.
Formula for circumference = πD
Where D = Diameter of the car wheel = 26 inches
Circumference of the car wheel = π × 26
= 81.68 inches
We have to find, how many inches make 1 mile.
1 mile = 63360 inches.
To determine the number of revolutions a car wheel of diameter 26 inches will travel,
= 63360 inches ÷ circumference of the car wheel
= 63360 inches ÷ 81.68inches
= 775.71 revolutions per mile
To the nearest whole number = 776 revolutions per mile.
(05.06)Which interval on the graph could be described as linear constant?
A
B
C
D
since A is a horizontal line it is constant
so A would be linear constant
By defining a constant line, we will see that the correct option is interval A.
What is a constant line?
A general linear equation is given by:
y = a*x + b
Where a is the slope and b is the y-intercept.
We say that a line is a constant line if the slope is equal to zero, so we get:
y = b
This would be graphed as a horizontal line.
So we only need to see which interval on the graph has a horizontal line. We will see that the interval is the A interval.
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Which expression is equivalent to (4g^3h^2k^4)^3/8g^3h^2 - (h^5k^3)^5
Given expression:[tex]\frac{\left(4g^3h^2k^4\right)^3}{8g^3h^2}-\left(h^5k^3\right)^5[/tex]
[tex]\left(4g^3h^2k^4\right)^3:\quad 2^6g^9h^6k^{12}[/tex]
[tex]8:\quad 2^3[/tex]
[tex]\frac{\left(4g^3h^2k^4\right)^3}{8g^3h^2}=\frac{2^6g^9h^6k^{12}}{2^3g^3h^2}[/tex]
[tex]=2^3g^6h^4k^{12}[/tex]
[tex]\left(h^5k^3\right)^5=h^{25}k^{15}[/tex]
[tex]\frac{\left(4g^3h^2k^4\right)^3}{8g^3h^2}-\left(h^5k^3\right)^5=2^3g^6h^4k^{12}-h^{25}k^{15}[/tex]
[tex]=8g^6h^4k^{12}-h^{25}k^{15}[/tex]
Therefore, correct option is 4th option [tex]8g^6h^4k^{12}-h^{25}k^{15}[/tex].
Answer:
ANSWER IS D
Step-by-step explanation:
The size of a television is usually indicated by the length of the screens diagonal if a person buys a 20 inch television set that is 12 inches tall how wide is the television
diagonal = sqrt(a^2 +b^2)
20 = sqrt(12^2 +b^2)
20= sqrt(144+b^2)
20^2 = 144 + b^2
400 = 144 + b^2
256 = b^2
b = sqrt(256) = 16
it is 16 inches wide
Find the area of the circle. Leave your answer in terms of pi diameter is 4.1 m
Answer:
Area of the circle will be (4.20 [tex]\pi[/tex])
Step-by-step explanation:
We have to find the area of the circle with diameter given is 4.10 m.
Since radius of a circle is represented by [tex](\frac{diameter}{2})[/tex]
Therefore, radius of the circle = [tex](\frac{4.1}{2})[/tex] = 2.05 m
Formula of the area of a circle is A = [tex]\pi r^{2}[/tex]
So area of the circle with radius 2.05 m will be
A = [tex]\pi (2.5)^{2}[/tex]
= 4.20 [tex]\pi[/tex]
Area of the circle will be (4.20 [tex]\pi[/tex])
The given measurements may or may not determine a triangle. If not, then state that no triangle is formed. If a triangle is formed, then use the Law of Sines to solve the triangle, if it is possible, or state that the Law of Sines cannot be used. B = 137°, c = 9, b = 14
Final answer:
Explanation of units for trigonometric functions and how to apply the Law of Sines in triangle problems.
Explanation:
The units for sine, cosine, and tangent must be dimensionless. These trigonometric functions relate angles to side lengths in a triangle.
The Law of Sines can be used to solve triangles when you have a known angle and the opposite side length. It states that the ratio of the length of a side to the sine of its opposite angle is constant.
When given measurements may or may not form a triangle, you can apply the Law of Sines to determine if a triangle can be solved. If not, it means no triangle can be formed.
Identify an equation in standard form for an ellipse with its center at the origin, a vertex at (9, 0), and a co-vertex at (0, 1).
Help identify measure of arc UV
The measure of arc UV is 24° .
What is arc?An “arc” is a smooth curve joining two endpoints. In general, an arc is one of the portions of a circle. It is basically a part of the circumference of a circle. Arc is a part of a curve.
According to the question
The Triangle formed inside the triangle
with angles 90° , 36° , ∠W
As sum of angle of triangle
99° + 36° + ∠W = 180°
∠W = 180° - 99° - 36°
∠W = 45°
Now,
According to the relation
∠W = [tex]\frac{1}{2}[/tex](arc SP - arc UV)
As
Arc SP = 94° + 20°
= 114°
so ,
45° = [tex]\frac{1}{2}[/tex]( 114° - arc UV)
90° = 114° - arc UV
arc UV = 114° - 90°
= 24°
Hence, the measure of arc UV is 24° .
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Maria needs $2.35 to buy a magazine. The only money she has is a jar of nickels and dimes. Write an equation in standard form for the different amounts of nickels x and dimes y she could use. Show your work :)
can anyone help me calculate AC, AD, and EC?
AC = sqrt(56^2 + 33^2) = 65cm
EC = sqrt(65^2 - 16^2) = 63 cm
to find AD 33-25 = 8
8^2 + 56^2 = AD^2
64 + 3136=3200^2
square root (3200) = 56.5685 round off to 56.6cm
Evaluate 5 | x^3 - 2| + 7 when x = -2.
What changes could you make to values assigned to outcomes to make the game fair? Prove that the game would be fair using expected values. Thank you!
Answer with explanation:
⇒A game will be fair , if there is equal chance of winning and losing.
→The game would be fair , if
Landing on Blue sector gives 3.5 points.
Then the, Expected value will be
[tex]E(x_{i})=x_{i} \times P(x_{i})\\\\E(x)=x_{1} \times P(x_{1})+x_{2} \times P(x_{2})+x_{3} \times P(x_{3})+x_{4} \times P(x_{4})\\\\E(x)=-1 *\frac{2}{7}+(0) *\frac{2}{7}+(1) *\frac{2}{7}+(3.5) *\frac{1}{7}\\\\E(x)=(3.5) *\frac{1}{7}\\\\E(x)=0.50[/tex]
→→By Assigning, Blue sector =3.5 points, the game will become fair, Gives, E(x)=0.50.
A game is considered fair if the expected value for all players is zero, balancing the potential wins and losses over the long run. By adjusting winnings and losses so that the sum of the expected values of all outcomes is zero, and recalculating these expected values, we can prove the fairness of the game.
Explanation:To make a game fair using expected values, one must ensure that the expected value for all players is zero, meaning that there's no advantage or disadvantage to playing the game in the long run. The expected value is calculated by multiplying the value of each possible outcome by its probability and summing these products.
Let's consider the card and coin flipping game and determine its fairness. The expected value (EV) for this game can be expressed as:
EV(face card and heads) = P(face card) * P(heads) * winnings from face card and headsEV(face card and tails) = P(face card) * P(tails) * winnings from face card and tailsEV(non-face card) = P(non-face card) * (P(heads) + P(tails)) * loss from non-face cardTo avoir long-term loss, the sum of the expected values for all outcomes should be zero. If the current values do not result in a fair game, we can adjust the winnings and losses such that the expected value is balanced. By recalculating these probabilities with new values, we can verify if the game is fair or not.
One of the acute angles of a right triangle is 50° and its hypotenuse is 7 inches. find the lengths of its legs to the nearest tenth of an inch.
Final answer:
To determine the lengths of the legs of a right triangle with a hypotenuse of 7 inches and an acute angle of 50°, we use the trigonometric functions cosine and sine. The adjacent leg (A) is approximately 4.5 inches and the opposite leg (B) is approximately 5.4 inches, both to the nearest tenth.
Explanation:
The student asked: "What are the lengths of the legs of a right triangle if one of the acute angles is 50° and the hypotenuse is 7 inches?"
To find the lengths of the legs of a right triangle, we can use trigonometry. The cosine of an angle in a right triangle is equal to the adjacent leg divided by the hypotenuse, and the sine of an angle is equal the opposite leg divided by the hypotenuse.
Since we know the hypotenuse (7 inches) and one acute angle (50°), we can find:
the length of the opposite leg (leg B) using sine (sin(50°) = leg B / 7 inches).
By solving these equations:
leg A = cos(50°) × 7 inches
leg B = sin(50°) × 7 inches
After calculating, we find:
leg A ≈ 4.5 inches (to the nearest tenth)
leg B ≈ 5.4 inches (to the nearest tenth)
what is 475.53 minus 67.37
In parallelogram ABCD, if angle C=110 and angle D=70, what is the sum of the measures of angle A and angle B?
To solve this problem, we must remember that the sum of interior angle of a polygon is:
Sum of interior angles = (n – 2) * 180˚
So, we can say that:
Sum of interior angles = angle A + angle B + angle C + angle D = (4 – 2) * 180˚
Where,
angle C + angle D = 110 + 70 = 180˚
Therefore substituting this value:
angle A + angle B + 180˚ = 2 * 108˚
angle A + angle B = 360˚ - 180˚
angle A + angle B = 180˚ (answer)
Hence we can also conclude that,
angle A + angle B = angle C + angle D
The answer is 180 degrees because...
angle A + angle B + 180˚ = 2 * 108˚
angle A + angle B = 3
angle A + angle B = 180˚ 60˚ - 180˚
Hope this helps, have a BLESSED and wonderful day! As well as as a safe one! :-)
-Cutiepatutie ☺❀❤
which of the diagram below represents the statement. if it is an insect then it has wings
*WILL GIVE BRAINLIEST*(08.03)Consider the following set of equations:
Equation A: y = 2x + 4
Equation B: y = 3x + 1
Which of the following is a step that can be used to find the solution to the set of equations?
2x + 4 = 3x + 1
2x = 3x + 4
2x + 4 = 3x
2x + 1 = 3x + 4