Answer:
See below.
Step-by-step explanation:
The volume of the box is given by the expression.
V(x) = x^3 - 2x^2 - 15x
To find the possible dimensions of the box, we need to solve for the values of x that make the volume positive. A box with negative volume is not physically meaningful.
Setting V(x) > 0, we get.
x^3 - 2x^2 - 15x > 0
Factorizing the left-hand side, we get.
x(x^2 - 2x - 15) > 0
Now, we can find the values of x that make each factor positive.
For x > 0, both factors are positive.
For x^2 - 2x - 15 > 0, we can factor it as (x - 5)(x + 3) > 0. This inequality is true when x < -3 or x > 5.
Therefore, the possible dimensions of the box are.
x > 0 and x < -3, or
x > 0 and x > 5.
However, we need to remember that the dimensions of a physical box must be positive. Therefore, the only valid solution is,
x > 0 and x > 5.
So the possible dimensions of the box are.
Length, width, and height > 5 units.
Answer:
Factor the polynomial.
x
(
x
−
5
)
(
x
+
3
Step-by-step explanation:
You are offered a job that pays $34,000 during the first year, with an annual increase of 6% per year beginning in the second year. That is, beginning in year 2, your salary will be 1.06 times what it was in the previous year. What can you expect to earn in your fourth year on the job? Round your answer to the nearest dollar.
9 N = 480 ´ 109
(a) Write N as a number in standard form.
(1)
(b) Write N as a product of powers of its prime factors.
Show your working clearly.
(3)
(c) Find the largest factor of N that is an odd number.
Answer:
(a) To write 9 N as a number in standard form, we need to express it as a number between 1 and 10 multiplied by a power of 10. To do this, we can divide 9 N by 10 until we get a number between 1 and 10:
9 N = 480 × 10^9
9 N ÷ 10 = 48 × 10^9
9 N ÷ 10^2 = 4.8 × 10^9
9 N ÷ 10^3 = 0.48 × 10^9
9 N ÷ 10^4 = 0.048 × 10^9
9 N ÷ 10^5 = 0.0048 × 10^9
Therefore, 9 N = 4.8 × 10^10.
(b) To write N as a product of powers of its prime factors, we can first factorize N:
480 × 10^9 = 2^5 × 3 × 5 × 10^9
Then, we can express 10^9 as 2^9 × 5^9 and substitute it in the factorization:
2^5 × 3 × 5 × 2^9 × 5^9 = 2^14 × 3 × 5^10
Therefore, N = 2^14 × 3 × 5^10.
(c) To find the largest factor of N that is an odd number, we need to remove all factors of 2 from the factorization of N. We can do this by dividing N by 2 as many times as possible:
N = 2^14 × 3 × 5^10
N ÷ 2 = 2^13 × 3 × 5^10
N ÷ 2^2 = 2^12 × 3 × 5^10
N ÷ 2^3 = 2^11 × 3 × 5^10
N ÷ 2^4 = 2^10 × 3 × 5^10
N ÷ 2^5 = 2^9 × 3 × 5^10
N ÷ 2^6 = 2^8 × 3 × 5^10
N ÷ 2^7 = 2^7 × 3 × 5^10
N ÷ 2^8 = 2^6 × 3 × 5^10
N ÷ 2^9 = 2^5 × 3 × 5^10
N ÷ 2^10 = 2^4 × 3 × 5^10
N ÷ 2^11 = 2^3 × 3 × 5^10
N ÷ 2^12 = 2^2 × 3 × 5^10
N ÷ 2^13 = 2 × 3 × 5^10
N ÷ 2^14 = 3 × 5^10
Therefore, the largest factor of N that is an odd number is 3 × 5^10.
If h = 13 units and r = 6 units, then what is the volume of the cone shown above?
The vοlume οf the cοne is 156π cubic units
What is cοne?A cοne is a three-dimensiοnal geοmetric fοrm with a flat base and a smοοth tapering tip οr end. A cοne is made up οf a cοllectiοn οf line segments, half-lines, οr lines that link the apex—the cοmmοn pοint—tο every pοint οn a base that is in a plane οther than the apex.
Given,
h = 13 units and r = 6 units
We knοw the fοrmula tο determine vοlume οf cοne; that is
(1/3)πr²h
Where r= radius οf the cοne
h= height οf the cοne
We put the value οf h and r in the fοrmula
(1/3)πr²h
= (1/3)π6² *13
=156π cubic units
The vοlume οf the cοne is 156π cubic units
Hence the cοrrect answer is 156π cubic units
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< Back to task
In the quadrilateral below, angles DAB and BCD are the same size.
What is the size of angle DAB?
D
228
34° -B
Answer >
The size of angle DAB in the quadrilateral is 49°.
How to find the size of angle DAB?The sum of the interior angles of a quadrilateral is 360°. We can say:
∠A + ∠B + ∠C + ∠D = 360°
∠A + 34° + ∠C + 228° = 360°
∠A + ∠C + 262° = 360°
∠A + ∠C = 360 - 262
∠A + ∠C = 98
Since angles DAB and BCD are the same size. This implies ∠A = ∠C. Thus:
∠A + ∠A = 98
2∠A = 98
∠A = 98/2
∠A = 49°
Therefore, the size of angle DAB is 49°.
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Complete Question
Check the attached image
plot four different points whose -coordinates are half their -coordinates. do these points lie on a line?
The four points with y-coordinates half their x-coordinates are (0,0), (2,1), (4,2), and (6,3). These points do lie on a line, as they all satisfy the linear equation y = x/2.
To plot four points whose y-coordinates are half their x-coordinates, we can choose any four values of x and then compute the corresponding values of y using the equation y = x/2. For example
If x = 0, then y = 0/2 = 0, so the first point is (0,0).
If x = 2, then y = 2/2 = 1, so the second point is (2,1).
If x = 4, then y = 4/2 = 2, so the third point is (4,2).
If x = 6, then y = 6/2 = 3, so the fourth point is (6,3).
We can plot these points on a coordinate plane
As we can see from the plot, the four points do lie on a straight line. This is because the equation y = x/2 is the equation of a linear function with slope 1/2 and y-intercept 0. Therefore, any two points on this line will have a constant slope between them, and thus the four points will be collinear.
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Write an equation for line t. Show or explain how you determined your equation.
Enter your equation and your work or explanation in the box provided.
Answer:
[tex]y - 3 = \frac{2}{3} (x - 3)[/tex]
[tex]y = \frac{2}{3} x + 1[/tex]
[tex]2x - 3y = - 3[/tex]
Step-by-step explanation:
[tex]m = \frac{ - 5 - 3}{ - 9 - 3} = \frac{ - 8}{ - 12} = \frac{2}{3} [/tex]
[tex]y - 3 = \frac{2}{3} (x - 3)[/tex]
[tex]y - 3 = \frac{2}{3} x - 2[/tex]
[tex]y = \frac{2}{3} x + 1[/tex]
[tex]3y = 2x + 3[/tex]
[tex] - 2x + 3y = 3[/tex]
[tex]2x - 3y = - 3[/tex]
PLEASE HELP ME!!
A beach ball has a volume of approximately 10,332 in³. Find the approximate radius of the beachball. Use 3.14 for π. Round your answer to the nearest tenth
Answer:
Step-by-step explanation:
Given diameter of a beach ball is d=10 inches.Let us find the radius of the beach ball:d=2 r10=2×rr=102∴r=5Therefore, the radius of a beach is 5 inches.Let us find the volume of air contained inside the beach ball:V=43 π×r3=43 π×53=43 π×125=500π3∴V=523.59877Therefore, the volume of air contained inside the beach ball is approximately 523.6 in3.
Answer:
The formula for the volume of a sphere is:
V = (4/3)πr³
We can rearrange this formula to solve for the radius (r):
r = [(3V) / (4π)]^(1/3)
where V is the volume of the sphere.
Substituting the given volume of the beach ball, we get:
r = [(3 × 10,332 in³) / (4 × 3.14)]^(1/3)
r = 10.27 in
Rounding to the nearest tenth, the approximate radius of the beach ball is 10.3 inches.
a. For which angle measures, 0, between 0 and
2π radians is cos(0) = 0? Label the
corresponding points on the unit circle.
b. What are the values of sin(x) for these angle
measures?
for the angle measures where cos(0) = 0, sin(x) equals 1 for π/2 radians and -1 for 3π/2 radians.
cos(0) = 0 when the angle is π/2 or 3π/2 radians.
To label the corresponding points on the unit circle, we can use the following conventions:
The angle 0 radians (or 0 degrees) starts at the positive x-axis and goes counterclockwise.
The angle π/2 radians (or 90 degrees) is at the positive y-axis.
The angle π radians (or 180 degrees) is at the negative x-axis.
The angle 3π/2 radians (or 270 degrees) is at the negative y-axis.
So, for cos(0) = 0, the corresponding angle measures are π/2 and 3π/2 radians. On the unit circle, these correspond to the points (0, 1) and (0, -1), respectively.
the values of sin(x) for these angle measures:
sin(π/2) = 1
sin(3π/2) = -1
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Duri wants their backpack to weigh less than 45 pounds.
Use w to represent weights where Duri can carry their backpack.
This inequality represents that the weight of Duri's backpack is w < 45
How to represent the backpack as an expressionGiven that
Weight = Less than 45 pounds
We can use the inequality symbol to represent Duri's weight limit as follows:
w < 45
This inequality states that the weight of Duri's backpack, represented by w, must be less than 45 pounds.
Any weight value for w that satisfies this inequality is within Duri's weight limit and can be carried in their backpack.
For example, if Duri's backpack weighs 30 pounds, then w = 30 satisfies the inequality w < 45, so Duri can carry this weight.
However, if the backpack weighs 50 pounds, then w = 50 does not satisfy the inequality w < 45, so Duri cannot carry this weight.
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Complete the table
Original Price
Percent of Discount
15%
Sale Price
$146.54
The final result for the money is [tex]172.40[/tex] after you multiply it by a percent.
What does a maths percent mean?In essence, percentages are fractions with a 100 as the denominator. We place the percent sign (%) next to the number to indicate that the number is a percentage.
What does the word "percentage" actually mean?Rather than being stated as a fraction, a percent is a piece of an entire thing expressed as just a number between zero and 100. Nothing is zero percent; everything is 100 percent; half of something is 50 percent; and nothing is zero percent. You divide the part of the total by its entirety and multiply the result by 100 to get the percentage.
[tex]w-[0.15]=146.54[/tex]
so [tex]w-85p=146.54[/tex]
[tex]146.54[/tex] divided by [tex]80=1.724[/tex] so when you make it a percent it turns it into [tex]172.40[/tex] which is the final answer for the money.
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The table shows the ratios of black and white keys on pianos of various size
The ratio of black and white keys of piano give correct values of A, B, C as 9, 52, 130.
The ratio of black to white keys of Piano of different sizes are as follow,
Black A 36 63 90
White 13 B 91 C
From the table of black and white keys relation of proportionality is equal to,
( A / 13 ) = ( 36 / B ) = ( 63 / 91 ) = ( 90 / C )
This implies ,
( A / 13 ) = ( 63 / 91 )
⇒ A = ( 63 / 91 ) × 13
⇒ A = ( 9 / 13 ) × 13
⇒ A = 9
Similarly,
( 36 / B ) = ( 63 / 91 )
⇒ B = 36 × ( 91 / 63 )
⇒ B = 36 × ( 13 / 9 )
⇒ B = 52
And
( 63 / 91 ) = ( 90 / C )
⇒ C = 90 × ( 91 / 63 )
⇒ B = 90 × ( 13 / 9 )
⇒ B = 130
Therefore, the correct values of A , B, C using the ratio of black and white keys of the piano is equal to 9, 52, 130.
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The above question is incomplete, the complete question is:
The table below shows the ratios of black to white keys on pianos of various sizes.
Black A 36 63 90
White 13 B 91 C
Determine which table has the correct values for A, B, and C.
Unit 1 is m feet, unit 2 is n feet unit 3 is k dollars per square feet, write an expression that could result in a final unit measure of dollars
The expression that could result in a final unit measure of dollars is given by (mnk²) dollars.
To write an expression that could result in a final unit measure of dollars, we need to consider the units given.
We have three units, i.e., m feet, n feet, and k dollars per square foot.
To convert these units to dollars, we need to multiply the given units with appropriate conversion factors.
The conversion factor for the given units is as follows:
Unit 1: 1 foot = k dollars (Conversion factor)
Unit 2: 1 foot = k dollars (Conversion factor)
Unit 3: 1 square foot = 1 x k dollars = k dollars (Conversion factor)
Now, let us write the expression that results in a final unit measure of dollars.
The expression should be written in HTML format.
Let us begin: Final Unit Measure = (Unit 1) x (Unit 2) x (Unit 3)
Final Unit Measure = (m feet) x (n feet) x (k dollars per square foot)
Final Unit Measure = m x k dollars x n x k dollars per square foot
Final Unit Measure = (m x k x n x k) dollars
Final Unit Measure = (mnk²) dollars.
Thus, the expression that could result in a final unit measure of dollars is given by (mnk²) dollars.
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a newsletter publisher believes that under 69% 69 % of their readers own a rolls royce. is there sufficient evidence at the 0.10 0.10 level to substantiate the publisher's claim? state the null and alternative hypotheses for the above scenario.
No, there is not sufficient evidence to substantiate the claim at the 0.10 level. Null Hypothesis (H0): p ≤ 0.69; Alternative Hypothesis (H1): p > 0.69
A newsletter publisher believes that under 69% of their readers own a Rolls Royce.
No, there is not sufficient evidence to substantiate the claim at the 0.10 level. In order to substantiate the claim at the 0.10 level, the publisher would need to collect data from their readers and perform a hypothesis test to compare the observed percentage of readers with the claimed percentage.
Null Hypothesis: The proportion of the newsletter readers that own a Rolls Royce is less than or equal to 69%.
Null Hypothesis (H0): p ≤ 0.69
Alternative Hypothesis: The proportion of the newsletter readers that own a Rolls Royce is greater than 69%.
Alternative Hypothesis (H1): p > 0.69
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PLEASEEEEE HELPPPPPPP!!!!!!!
A line segment contains endpoints A(-1, 2) and B(2, 5).
Determine the point that partitions line segment AB into a 3: 6 ratio.
A 4,5/3
B 0,3
C 1/3,3
D -2,1
Answer:
We can find the point that partitions line segment AB into a 3:6 ratio by using the formula for finding a point that divides a line segment into two parts in a given ratio.
Let's call the point we're looking for "P". According to the formula, the coordinates of point P can be found using the following equations:
x-coordinate of P = [(6 * x-coordinate of A) + (3 * x-coordinate of B)] / 9
y-coordinate of P = [(6 * y-coordinate of A) + (3 * y-coordinate of B)] / 9
Using the coordinates of points A and B given in the problem, we can plug them into these equations and simplify to find the coordinates of point P:
x-coordinate of P = [(6 * -1) + (3 * 2)] / 9 = 0
y-coordinate of P = [(6 * 2) + (3 * 5)] / 9 = 3.33 (rounded to two decimal places)
Therefore, the point that partitions line segment AB into a 3:6 ratio is approximately (0, 3.33), which is closest to option A: 4,5/3.
Aileen has 40 colored marbles inside a bag. There are blue, red, and white marbles. All the marbles are the same size. Aileen randomly selects 10 marbles, one at a time, out of the bag and records the color of each marble. Each marble is replaced before the next marble is selected. The table shows her results. Aileen's Bag of Marbles Color of Frequency Marble Blue Red White 3 1 6 Click on the bar graph to show how many blue marbles, red marbles, and white marbles are MOST LIKELY inside Aileen's bag of marbles. Number of Marbles + 28 26 24 22 20 18 16 14 12 10 ∞ CO 8 6 4 2 0
The most likely number of marbles in Aileen's bag is given as follows:
Blue marbles: 12.Red marbles: 4.White marbles: 24.How to obtain the most likely number of marbles?The most likely number of marbles is obtained applying the proportions in the context of the problem.
Out of 10 marbles, from the sample, the results are given as follows:
3 blue marbles.1 red marbles.6 white marbles.Aileen has 40 colored marbles inside a bag, which is four times the size of the sample, hence the most likely number of marbles in Aileen's bag is obtained as follows:
Blue marbles: 12, as 4 x 3 = 12.Red marbles: 4, as 4 x 1 = 4.White marbles: 24, as 4 x 6 = 24.More can be learned about proportions at https://brainly.com/question/24372153
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Compare the amount of sand in the top cone of the hourglass to the amount there will be when the height of the sand in the top cone is only 1 inch.
HINT: The cones are similar
the amount of sand in the top cone when the height of the sand is only 1 inch is (h-1)/h times the amount of sand in the top cone originally.
the cones are similar, their volumes are proportional to the cube of their heights. Let's denote the height of the top cone as h, and the radius of the top and bottom bases as r. Then, the volume of the top cone can be expressed as:
V₁ = (1/3)π[tex]r^2[/tex]h
If the height of the sand in the top cone is reduced to 1 inch, then the height of the remaining sand in the top cone is (h-1) inches. The volume of the remaining sand in the top cone can be expressed as:
V₂ = (1/3)π[tex]r^2[/tex](h-1)
To compare the amount of sand in the top cone in these two scenarios, we can take the ratio of their volumes:
V₂/V₁ = [(1/3)π[tex]r^2[/tex](h-1)] / [(1/3)π[tex]r^2[/tex]h] = (h-1)/h
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PLEASE HELP - WORTH 30 POINTS
Answer: 1,023 combinations & 4/5 chance
Step-by-step explanation: A bunch of weird math with the first answer, but the 2nd answer is just every clothing article that isn't red over the total amount of articles simplified (8/10 = 4/5).
Hope this helped!
Which expression is equivalent to (1/2[cos(Pi/5) + sin(Pi/5)])5 ?
A) 1/32 [cos(Pi/5)+i sin(Pi/5)]
B) 1/32[cos(Pi) + i sin(Pi)]
C) 1/10[cos(Pi/5) + i sin(Pi/5)]
D) 1/10[cos(Pi)+ i sin(Pi)]
the answer of given function is equivalent to option (C) 1/10[cos(Pi/5) + i sin(Pi/5)]
Define trigonometric functionTrigonometric functions are mathematical functions that relate angles and sides of triangles. There are six primary trigonometric functions: sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc).
We can simplify the expression (1/2[cos(π/5) + sin(π/5)])5 as follows:
([tex]\frac{1}{2}[/tex][cos(π/5) + sin(π/5)])5
= [tex]\frac{5}{2}[/tex][cos(π/5) + sin(π/5)]
Now, we can use Euler's formula:
e^ix = cos(x) + i sin(x)
to rewrite this expression in the form a + bi:
[tex]\frac{5}{2}[/tex][cos(π/5) + sin(π/5)]
= [tex]\frac{5}{2}[/tex][[e^(i(π/5) + (-π/2))]
=[tex]\frac{5}{2}[/tex][[e^(-iπ/2) e^(iπ/5)]
= [tex]\frac{5}{2}[/tex][[-i(cos(π/5) + i sin(π/5))]
=[tex]\frac{5}{2}[/tex][[-i cos(π/5) + 5/2 sin(π/5)]
Therefore, the equivalent expression in the form a + bi is:
-[tex]\frac{5}{2}[/tex][ cos(π/5) + (5/4) i sin(π/5)
And simplifying this expression, we get:
-[tex]\frac{5}{2}[/tex][ cos(π/5) + (5/4) i sin(π/5) = (1/10) [cos(π/5) + i sin(π/5)]
Therefore, the answer is option (C) 1/10[cos(π/5) + i sin(π/5)].
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in 2005 the population of a district was 35,700 with a continuous annual growth rate of approximately 4%, what will the population be in 2030 according to the exponential growth function?
The population of a district in 2005 was 35,700 with a continuous annual growth rate of approximately 4%. the population in 2030 will be approximately 97,209 according to the exponential growth function.
The formula for the continuous exponential growth is given by the formula:
P = Pe^(rt)
where,P is the population in the future.
P0 is the initial population.
t is the time.
r is the continuous interest rate expressed as a decimal.
e is a constant equal to approximately 2.71828.In this problem, the initial population P0 is 35,700. The rate r is 4% or 0.04 expressed as a decimal. We want to find the population in 2030, which is 25 years after 2005.
Therefore, t = 25.We will now use the formula:
P = Pe^(rt)P = 35,700e^(0.04 × 25)P = 35,700e^(1)P = 35,700 × 2.71828P = 97,209.09.
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Answer: I got 97,042.7
Step-by-step explanation:
Which inequality statement describes the two numbers on a number line? "2 and a number 9 units to the left of 2"
Answer:
Step-by-step explanation:
The inequality statement that describes the two numbers on a number line "2 and a number 9 units to the left of 2" would be:
x < 2
where x represents the number that is 9 units to the left of 2.
Tyler has run 10. 4 miles,which is 65 percent of the total distance he plans to run this week. What is the total distance that Tyler plans to run this week
Tyler has run 10.4 miles, which is 65% of the total distance he plans to run this week. Tyler plans to run a total of 16 miles this week.
Let's use "x" to represent the total distance that Tyler plans to run this week. According to the problem, Tyler has already run 10.4 miles, which is 65% of the total distance he plans to run. We can set up an equation to represent this information:
10.4 = 0.65x
To solve for x, we can divide both sides of the equation by 0.65:
x = 10.4 ÷ 0.65
x = 16
Therefore, the total distance that Tyler plans to run this week is 16 miles.
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A scientist put 14.7 grams of a substance on a scale. She then put another 7.12 grams of the substance on the scale.
How many grams of the substance are on the scale?
What is 4.8 x 0.1 ?
Question :
4.8 x 0.1 =
Answer: 0.48
Step-by-step explanation:
× 0.1 = ÷10
÷ 0.1 = ×10
× 0.01 = ÷100
÷ 0.01 = ×100
So, we do=
4.8 x 0.1 = 4.8 ÷ 10
= 0.48
So our answer is 0.48
the perimeter of an isosceles triangle is 56 in. the ratio of the sides is 5:4. find the lengths of the sides and the base of the triangle
The perimeter of an isosceles triangle is the sum of the length of the sides. In this case, the perimeter is 56 inches. The ratio of the sides is [tex]5:4.[/tex]
To calculate the lengths of the sides and base, we need to first calculate the lengths of the two equal sides. To do this, divide the perimeter (56 inches) by the sum of the ratio (5 + 4) which is 9. This gives us a result of 6.2 inches for the two equal sides.
To calculate the length of the base, multiply the two equal sides by the ratio of 5:4, which gives us a result of 7.5 inches for the base.
Therefore, the lengths of the sides and the base of the triangle are: two equal sides of 6.2 inches, and a base of 7.5 inches.
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each time a hurricane arrives, a new home has a 0.4 probability of experiencing damage. the occurrences of damage in different hurricanes are mutually independent. calculate the mode of the number of hurricanes it takes for the home to experience damage from two hurricanes.
As per the given probability, the mode of the number of hurricanes it takes for the home to experience damage from two hurricanes is either one or two hurricanes, depending on which sequence is more likely to occur.
The probability of the DD sequence is 0.4 x 0.4 = 0.16. This means that there is a 16% chance that the home will experience damage in both the first and second hurricanes.
The probability of the DN sequence is 0.4 x 0.6 = 0.24. This means that there is a 24% chance that the home will experience damage in the first hurricane but not in the second hurricane.
The probability of the ND sequence is 0.6 x 0.4 = 0.24. This means that there is a 24% chance that the home will not experience damage in the first hurricane but will experience damage in the second hurricane.
To determine the mode of the number of hurricanes it takes for the home to experience damage from two hurricanes, we need to consider which sequence is most likely to occur.
In this case, the DN and ND sequences have the same probability, which means that there are two possible modes: one and two hurricanes.
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Jhoney ate 3 apples and have 2 left how much did he eat?
By probability , 3 Apples are left .
What does a probability simple definition entail?
A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.
The probability is a metric for determining how likely an event is to occur. It gauges how likely an event is. The probability equation is stated by the following notation: P(E) = Number of Favorable Outcomes/Number of Total Outcomes.
Jhoney ate = 3 apples
= 2 left
he eat = ³C₂
= 3!/(3-2)! 2!
= 3
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a ship travels 70 km on a bearing of 27 0 , and then travels on a bearing of 147 0for 180 km. find the distance of the end of the trip from the starting point.
The distance of the end of the trip from the starting point is 193.1321 km.
The ship goes 180 kilometers on bearing after 70 km of subsequent journey.
The starting point in this case is A, and the ending point is C.
We now discover distance AC:
As we can see, a right-angled triangle results.
The Pythagorean Theorem states that in a right triangle, the sum of the squares of the two sides that make up the right angle is equal to the square of the hypotenuse. This can be expressed mathematically as a^2 + b^2 = c^2, where a and b are the two sides that make up the right angle, and c is the hypotenuse.
Use Pythagoras's principle.
c = √a² + b²
The distance in the Hypotenuse in our case is now.
c = √(70)² + (180)²
c = √4900 + 32400
c = √37,300
c = 193.1321 km
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The complete question is:
A ship travels 70 km on a bearing of 27 degrees, and then travels on a bearing of 147 degrees for 180 km. Find the distance of the end of the trip from the starting point.
9. The linear regression equation is = 34.38x - 91.75. Use the equation to predict how far this
4.38x-91-75 Use
person will travel after 10 hours of driving.
The answer of the given question based on the linear regression is , the predicted distance the person will travel after 10 hours of driving is approximately 252.05 miles.
What is Distance?Distance is measurement of length between the two points or objects. It is a scalar quantity that only has a magnitude and no direction. In mathematics, distance can be measured in various units such as meters, kilometers, miles, or feet, depending on the context.
Distance can be calculated using the distance formula, which is based on the Pythagorean theorem in two or three dimensions.
Assuming the equation you meant to write is y = 34.38x - 91.75, where y is the predicted distance traveled in miles and x is the number of hours driven, we can use this equation to predict how far the person will travel after 10 hours of driving:
y = 34.38x - 91.75
y = 34.38(10) - 91.75
y = 343.8 - 91.75
y = 252.05
Therefore, the predicted distance the person will travel after 10 hours of driving is approximately 252.05 miles.
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During 10 hours of driving, the projected distance according to linear regression is roughly 252.05 miles.
What is Distance?The term "distance" refers to the length between two points or objects. Having merely a magnitude and no direction, it is a scalar quantity. Depending on the situation, distance in mathematics can be expressed in a variety of ways, including meters, kilometers, miles, or feet.
The distance formula, which depends on the Pythagorean theorem in either two or three dimensions, can be used to compute distance.We may use this equation to forecast how far the individual would go after 10 hours of driving, assuming the equation you meant to write is
y = 34.38x - 91.75, where y is the expected distance travelled in miles and x is the number of hours driven:
y = 34.38x - 91.75
y = 34.38(10) - 91.75
y = 343.8 - 91.75
y = 252.05
The estimated distance that the driver will cover after 10 hours on the road is 252.05 miles.
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The complete question is,
The equation for linear regression is = 34.38x - 91.75. Calculate this person's estimated distance after 10 hours of driving using the equation: 4.38x-91-75.
A farmer wants to fence in a rectangular portion of land along one side of her barn. She uses the side of the barn for one side of the rectangle, and makes the other three sides from a total of 60 feet of fencing. Find the side lengths that give the maximum area she can fence in, as well as the maximum area. Show all of your work.
the answer is 62x IAM take a guess so
please help me solve this i’ll mark brainliest
Answer:
Step-by-step explanation:
From the parallel lines, we know that corresponding angles are congruent, so:
(2y+78) = X
We also know that vertically opposite angles are equal:
X=5y
Substitute for X:
2y+78=5y
Solve:
2x-5x=-78
-3x=-78
x=26
Therefore, the measure of angle WXZ is 26.