$1862 is Devi red from his biweekly paycheck for medical insurance
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
The annual cost of Randall coverage is 4900.
The college pays 62% of the cost.
We need to find How much is Devi red from his biweekly paycheck for medical insurance
Let us convert 62% to decimal value by dividing with 100
62/100=0.62
Now multiply 0.62 with 4900
0.62×4900
3038
Now subtract 3038 from 4900
4900-3038
1862
Hence, $1862 is Devi red from his biweekly paycheck for medical insurance
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In the figure where 3x20 and 4x-36, which value of x will make aob, a traight line
The value of x that will make aob a straight line equation is x = -6.
To make aob a straight line, we need to make the gradients of both lines equal.
The gradient of the first line is 3x20 = 60.
The gradient of the second line is 4x-36 = 4x-36.
To make the gradients equal, we need to solve the equation 4x - 36 = 60.
Subtracting 36 from both sides gives us: 4x = 96.
Dividing both sides by 4 gives us x = -6.
Therefore, the value of x that will make aob a straight line is x = -6
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Y=-1/2X+6 in standard form
The standard form of linear function y = - (1 / 2) · x + 6 is (1 / 12) · x + (1 / 6) · y = 1.
How to find the definition of a linear function in standard form
In this question we find a linear function in slope-intercept form:
y = m · x + b
Where:
m - Slopeb - InterceptFrom which we must obtain the linear function in standard form:
a · x + b · y = c
Where:
a, b - Depedent coefficients.c - Independent coefficient.We can derive the standard form of the linear equation by algebra properties:
y = m · x + b
(1 / b) · y = (m / b) · x + 1
- (m / b) · x + (1 / b) · y = 1
If we know that m = - 1 / 2 and b = 6, then the equation of the line in standard form is:
- [(- 1 / 2) / 6] · x + (1 / 6) · y = 1
(1 / 12) · x + (1 / 6) · y = 1
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A rectangular con lot of land is 0.4 kilometer long and 0.07 kilometer wide. What is its area in square kilometers?
Answer: 0.28 Km^2
Step-by-step explanation:
A= L x W
=0.4x0.7
=0.28
In the circle below, suppose m WXU= 102° and mLXWV=68°. Find the following.
In the circle below the suppose m WXU=102° and mL XWV=68° then the following is m ZXUV = 88°.
What is cyclic quadrilateral and explain the above answer?Four-sided shapes with all four corners on the same circle are known as cyclic quadrilaterals. A cyclic quadrilateral's internal angles are always added up to 360 degrees.
(a) m / WXU = 102° (Given)
(b) To find m ZXUV, we can use the property that the angles in a cyclic quadrilateral add up to 360°. Since WXU, XWV, and XLV are all inscribed angles that intercept the same arc, they are congruent. Therefore, m WXU = m XWV = m XLV = 102°. Adding these angles together, we have:
102° + 102° + 68° + m ZXUV = 360°
Solving for m ZXUV, we get:
m ZXUV = 360° - (102° + 102° + 68°)
m ZXUV = 88°
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Which of the options below are the terms of the expression 5x² + 9x + 6? Choose all of the correct answers. 5x 9x 6 X x² 5 5x² 9
The terms of the expression are 5x², 9x and 6
What are algebraic expressions?Algebraic expressions are described as expressions that are composed of variables, factors, constants, coefficients and terms.
They are also known to be made up of arithmetic operation, such as;
DivisionAdditionParenthesesMultiplicationSubtractionBracket, etcIt is also important to note that terms in algebraic expressions are seen as summands in a sum that may be different only by a actor.
They can be regrouped by the addition of their coefficients. Like terms are those that has the same variables to the same powers or coefficients.
The types are;
5x², 9x and 6
Thus, they are 5x², 9x and 6
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After a long morning of sledding, Mrs. Fieldhouse made a batch of hot cocoa for her daughter and nighborhood friends. She divided it among 8 mugs. Each mug had more than 9 fluid ounces of hot cocoa. Write an inequality to describe the situation.
x>9 perfectly describes the situation.
In mathematics, inequalities characterise the connection between two non-equal numbers. Inequality implies being unequal. If two values are not equal, we use the "not equal symbol ()". However, various inequalities are employed to compare the numbers, whether they are less than or higher than.
Let x be the amount of hot cocoa in fluid ounces that each mug contains.
Since each mug has more than 9 fluid ounces of hot cocoa, we can write the inequality as:
x > 9
We also know that the total amount of hot cocoa made is 8 mugs * the amount of hot cocoa in each mug = 8x.
So the inequality can be written as:
8x > 9*8 = 72
or
x>9
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write a paragraph defending, refuting, or qualifying William Wordsworth's claim about the value of nature. Use a quote from one of his poems to support your claim OR present one of the quotes as a counterargument, if you are refuting his claim.
Answer: William Wordsworth, a prominent figure in the Romantic movement, believed that nature had an immense value and could have a profound impact on the human spirit. In his poem "I Wandered Lonely as a Cloud," he wrote, "Nature never did betray the heart that loved her," which is a claim that nature is a constant source of comfort and inspiration. In this poem he praises nature and its ability to be a source of beauty and joy.
One could argue that Wordsworth's claim is true based on the evidence that nature can have a positive impact on mental and physical health. Studies have shown that spending time in nature can reduce stress, improve mood, and boost overall well-being. Additionally, nature can be a source of inspiration for many artists and poets, including Wordsworth himself, who drew inspiration from the natural world for his poetry.
On the other hand, one could argue that Wordsworth's claim is idealistic and may not apply to everyone or every situation. Some people may not find nature as comforting or inspiring, especially those who live in urban areas with limited access to natural spaces. Additionally, there are negative impacts of human activities on nature, such as pollution and deforestation, which can make it harder for some people to find value in nature.
Overall, while Wordsworth's claim that "Nature never did betray the heart that loved her" is a strong statement, and it holds true for many people, but it's a personal perspective that may not apply to everyone. Each individual has their own relationship with nature and it's not always a constant source of comfort, however, it's a treasure that we should take care of, respect and appreciate in order to achieve a better quality of life.
Step-by-step explanation:
How do you know if a triangle is right acute or obtuse?
if a²+b²>c², the triangle is acute, if a²+b2²=c², the triangle is a right triangle, and if a²+b²<c², the triangle is obtuse.
where a and b are the lengths of the two shorter sides of the triangle and c is the length of the longest side.
A right-angled triangle is a triangle with one of the angles at 90 degrees. A 90-degree angle is called a right angle, and hence the triangle with a right angle is called a right triangle.
An acute triangle has three angles that each measure less than 90°. In an acute-angled triangle, all three internal angles of the triangle are acute, that is, they measure less than 90°.
An obtuse triangle is a triangle with one angle that is greater than 90° degrees, it is not possible for a triangle to have more than one obtuse angle.
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Write each trigonometric ratio as a fraction and as a decimal rounded to
the nearest hundredth.
3. sin C
6. cos C
4. tanA
7. tan C
5. cos A
8. sin A
The trigonometric ratio as a fraction for sinC is , and the decimal is 0.80.
What are trigonometric functions?The trigonometric functions are actual functions that connect the right-angled triangle's angle to the ratios of its two side lengths.
What are the most widely used trigonometric functions?The widely used trigonometric functions are sine, cosine and tangent. The trigonometric functions also operate the inverse of the functions.
For the given triangle the trigonometric values are as follows:
For angle A the opposite side is CB, the adjacent side is AB and the hypotenuse is AC.
For angle C the opposite side is AB, the adjacent side is CB and the hypotenuse is AC.
[tex]sinC = \frac{\text{Opposite side }}{Hypotenuse} = \frac{4}{5} =0.80\\ \\ cosC = \frac{\text{Adjacent side }}{Hypotenuse} =\frac{3}{5} = 0.60\\\\tanA =\frac{\text{Opposite side }}{Adjacent side} = \frac{3}{4} = 0.75\\\\tanC= \frac{\text{Opposite side }}{Adjacent side} =\frac{4}{3} = 1.33\\\\cosA = \frac{\text{Adjacent side }}{Hypotenuse} =\frac{4}{5} = 0.80\\\\sinA= \frac{\text{Opposite side }}{Hypotenuse}=\frac{3}{5} =0.60[/tex]
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The amount of eroded rock is measured in cubic kilometers (km3). A cubic kilometer is a cube that measures 1 km on each side. How many km3 of rock were eroded
The amount of eroded rock in cubic kilometres is 1 km3.
To calculate the amount of eroded rock in cubic kilometres, we need to find the volume of the area that has been eroded. The volume of a rectangular shape is found by multiplying the length, width, and height (or depth) together.
In this case, the area that has been eroded is 10 km long, 5 km wide, and 20 m deep. However, we need to convert the depth from meters to kilometres to match the units of the other measurements. Since 1 km = 1000 m, we can convert the depth by dividing by 1000:
20 m / 1000 = 0.02 km
Now that all of the measurements are in kilometres, we can find the volume by multiplying them together:
10 km * 5 km * 0.02 km = 1 km3
So the amount of eroded rock in cubic kilometres is 1 km3.
Complete Question:
The amount of eroded rock is measured in cubic kilometres (km3). A cubic kilometre is a cube that measures 1 km on each side. How many km3 of rock were eroded in an area that is 10 km long, 5 km wide, and 20 m deep?
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Alpha can produce either 18 oranges or 9 apples an hour, while Beta can produce either 16 oranges or 4 apples an hour. Which of the following terms of trade between apples and oranges would allow both Alpha and Beta to gain by specialization and exchange?
A. 1 orange for 0.2 apples
B. 2 apples for 3 oranges
C. 3 apples for 3 oranges
D. 1 apple for 3 orange
A nation cannot have a comparative advantage in the production of every good. Alpha can produce either 18 oranges or 9 apples an hour, while Beta can produce either 16 oranges or 4 apples an hour. The opportunity cost of producing 1 orange for Alpha and Beta, respectively, are: 0.5 apples; 0.25 apples.
What is proportion?A percentage is a component, piece, or amount that is compared to a total. It might be 0 or 1, or any number between 0 and 1. It can be stated numerically or as a percentage. In official statistics, one example would be the proportion of the Canadian population residing in a certain province.
Here,
A country cannot have a competitive advantage in producing every good. Alpha can generate 18 oranges or 9 apples per hour, whilst Beta can produce 16 oranges or 4 apples per hour. The opportunity cost of producing one orange for Alpha and Beta is 0.5 apples and 0.25 apples, respectively.
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Can the sine ratio of an acute angle be greater than 1?
No, the sine ratio of an acute angle cannot be greater than 1. The sine of an acute angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right triangle. Since the side opposite the angle is shorter than the hypotenuse, the ratio will always be less than one.
To what does sin equate?
In contrast to the cosine of an angle, which corresponds to the ratio of the nearby side to the hypotenuse, the sine of an angle is the ratio of the opposite side to the hypotenuse.
It's important to note that if you were to give an angle value greater than 90 degrees, the sine of the angle will be a negative value, but the ratio will still be less than one.
The sine ratio is a value between -1 and 1, and it is impossible for the sine of an acute angle to be greater than 1.
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A student writes an incorrect step while checking if the sum of the measures of the two remote interior angles of triangle ABC below is equal to the measure of the exterior angle.
A triangle ABC is shown. The base of the triangle extends into a straight line. The angle formed between this straight line and the edge of the triangle is marked as p. The angle adjacent to p is marked as o, and the other two angles inside the triangle are marked as m and n.
Step 1: m∠m + m∠n + m∠o = 180 degrees (sum of angles of a triangle)
Step 2: m∠p − m∠o = 90 degrees (alternate interior angles)
Step 3: Therefore, m∠m + m∠n + m∠o = m∠o + m∠p
Step 4: So, m∠m + m∠n = m∠p
In which step did the student first make a mistake and how can it be corrected? (4 points)
a
Step 1; it should be m∠m + m∠n + m∠o = 90 degrees (corresponding angles)
b
Step 1; it should be m∠m + m∠n + m∠o = 90 degrees (adjacent angles)
c
Step 2; it should be m∠o + m∠p = 180 degrees (alternate exterior angles)
d
Step 2; it should be m∠o + m∠p = 180 degrees (supplementary angles)
Answer:
C. Step 2; it should be m∠o + m∠p = 180 degrees (alternate exterior angles)
Step-by-step explanation:
The student first made a mistake in step 2. In order to check if the sum of the measures of the two remote interior angles of a triangle is equal to the measure of the exterior angle, it is necessary to use the property of alternate exterior angles. Alternate exterior angles are angles that are on opposite sides of the transversal and between the same parallel lines, so they are congruent. The measure of alternate exterior angles is always equal to 180 degree. Therefore, the correct statement in step 2 is that m∠o + m∠p = 180 degrees (alternate exterior angles)
Hope this helps
50PTS 50PTS 50PTS [D•O•N•T E•X•P•L•A•I•N]
Answer:x=20
Step-by-step explanation:5x+9 and 3x+11 must add to 180, so you can set these equal to 180 and get 8x+20 = 180, this can be simplified to 8x=160 or x = 20
Answer:
x = 20°
Step-by-step explanation:
Given angles,
→ 5x + 9
→ 3x + 11
Forming the equation,
→ (5x + 9) + (3x + 11) = 180°
{Because, sum of two angles in a straight line leads to 180°}
Now the value of x will be,
→ (5x + 9) + (3x + 11) = 180°
→ 5x + 3x + 9 + 11 = 180°
→ 8x + 20 = 180°
→ 8x = 180° - 20
→ x = 160/8
→ [ x = 20° ]
Hence, the value of x is 20°.
15. A pool can hold 850 gallons. It now has 598 gallons of
water and is being filled at the rate shown. How many
more minutes, m, can water continue to flow into the
pool before it overflows? Write and solve an inequality.
Then graph the solutions.
Jason practiced making soccer goals and kept track of the results. he missed 3 goals but made 9 in one practice session. what can jason predict regarding goals made if his next practice session has 24 tries? jason will make 8 goals. jason will make 16 goals. jason will make 18 goals. jason will make 21 goals.
If Jason missed 3 goals and made 9 goals in one practice session the prediction we can make if the number of tries is 24 , then (c) Jason will make 18 goals .
Jason is practicing for making soccer goals and keeping a track of the results ;
the number of goals missed by Jason is = 3 goals ;
the number of goals that Jason made is = 9 goals ;
So , the total number of goals is = 12 goals ;
the ratio of making a goal to the total goals is = [tex]\frac{9}{12}[/tex] ;
So , the number of goals that Jason will make in 24 tries can be calculated as = [tex]\frac{9}{12} \times 24[/tex]
= [tex]9 \times 2[/tex]
= 18 .
Therefore , the Jason will make 18 goals in 24 tries .
The given question is incomplete , the complete question is
Jason practiced making soccer goals and kept track of the results. he missed 3 goals but made 9 in one practice session. What can Jason predict regarding goals made if his next practice session has 24 tries?
(a) Jason will make 8 goals.
(b) Jason will make 16 goals.
(c) Jason will make 18 goals.
(d) Jason will make 21 goals.
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What is a polynomial class 7?
The polynomial which has a degree of 7 can be known as a polynomial of class 7.
Polynomials are expressions containing of variables and constants. The variable having the highest power forms the degree of the polynomial.
The degree of a polynomial with one variable is known as the highest exponent power of that variable in the mentioned polynomial.
Finding the degree of a polynomial with more than one variable is a simple task , as adding the exponents of each variable in the supplied terms and then determining which term has the highest degree. That is the polynomial's degree.
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Tom got a Mr. Potato Head for his birthday. It came with $3$ hairstyles, $2$ sets of eyebrows, $1$ pair of googly eyes, $2$ sets of ears, and $2$ sets of lips, a pair of regular shoes, and a bonus pair of clown shoes. If a complete Mr. Potato Head personality includes eyebrows, eyes, ears, lips, shoes and optionally hair, how many different wacky personalities can Tom come up with? Note that Mr. Potato Head can be bald. Note: You cannot "mix and match". For example, you cannot take the left eyebrow from one pair and the right eyebrow from the other pair.
Answer: Tom can come up with 13 different wacky personalities for Mr Potato Head.
Step-by-step explanation:
Tom can come up with 3 different hairstyles for Mr Potato Head, 2 sets of eyebrows, 1 pair of googly eyes, 2 sets of ears, and 2 sets of lips. He also has 2 pairs of shoes to choose from. If Mr Potato Head can be bald, Tom can also choose to not include a hairstyle.
In total, Tom can come up with 3+2+1+2+2+2+1=13 different combinations of features for Mr Potato Head. Since each combination represents a different personality, Tom can come up with 13 different wacky personalities for Mr Potato Head.
Determine the missing angle measure.
Answer:
19°
Step-by-step explanation:
In this problem, we have complementary angles, which add up to 90° as indicated by the right angle symbol. So, getting x° is as simple as 90°-71°=19°.
Marla is four years less than twice as old as Darla. If the sum of their ages is 47, how old is Marla?
Marla is 30 years old.
Let marla age be x and Darla age be y
Given : Marla is four years less than twice as old as Darla
What is equation ?
In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
Marla is four years less than twice as old as Darla can be represented as : 2y - x = 4
sum of their ages is 47 can be represented as : x + y = 47
Solving both the equation using addition we got ,
3y = 51
y = 17
Substituting the value of y in x + y =47 , we get
x + 17 = 47
x = 47 -17
x = 30
Hence , Marla is 30 years old.
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1) Alice decides to take a trip from the East Coast of the United States to the West Coast. While planning, she chooses to drive, fly, and ride a train. Her first leg of the trip is traveling by car, from Sacramento, California to Denver, Colorado. Along the way, she fills up her tank using regular unleaded gas, costing $4.65 per gallon, and premium gas, $4.95 per gallon. After driving for many hours, Alice finally makes it to Denver, Colorado spending $874.80 in gas.
a) Let r represent gallons of regular unleaded gas and let p represent gallons of premium gas. Create an equation that models the situation.
Incorrect but attempt was made (1 pt) Partially correct
(2-4 pts) Fully Correct
(5 pts)
b) If Alice purchases 87 gallons for regular unleaded gas, how many gallons of premium gas did she purchase? Show all work to receive full credit.
Provided incorrect answer and no work shown (1 pt) Incorrect answer with work shown or Correct answer with no work shown
(2 pts) Correct with partial work shown (3-4 pts) Fully Correct with all work shown
(5 pts)
a) The equation that models Alice's total cost of filling up her car tank using regular unleaded gas and premium gas is 4.65r + 4.95p = 874.80.
b) Based on the above equation, if Alice purchases 87 gallons of regular unleaded gas, it means that she also purchases 95 gallons of premium gas.
What is an equation?An equation is a mathematical statement equating two or more mathematical expressions using the equation sign (=).
The cost per gallon of regular unleaded gas = $4.65
The cost of premium gas per gallon = $4.95
The total cost for gas = $874.80
Let gallons of regular unleaded gas = r
Let gallons of premium gas = p
Equation:4.65r + 4.95p = 874.8
If r = 87, the value of p is:
4.65(87) + 4.95p = 874.8
404.55 + 4.95p = 874.8
4.95p = 470.25
p = 95 gallons
Thus, during Alice's first leg from the East Coast to the West Coast, she purchases 87 gallons of unleaded and 95 gallons of premium gas for her car.
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Please help I will give Brainiest answer
Answer: b
Step-by-step explanation:
4-3
——-
13.40- 10.05
= 1/3.35
=b
Please help me understand
The transformation is shifted up 2 units.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
The given function is f(x)=-2x+3.
Here, the slope m of a line is -2 and y-intercept is 3
A) If the function g(x)=f(x)+k, where k=2.
Now, g(x)=-2x+3+2
g(x)=-2x+5
Here, the slope m of a line is -2 and y-intercept is 5
B) The slope of both functions are same
To find the transformation, compare the function to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis, and if there is a vertical stretch.
Shifted up 2 units
Therefore, the transformation is shifted up 2 units.
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What kind of triangle has 65 65 50?
Isosceles Triangle has 50°, 65°, 65°
An isosceles triangle is a triangle that has two sides of equal length. The two equal sides are called the legs and the third side is called the base of the triangle.
Properties of Isosceles Triangle:
The two equal sides of an isosceles triangle are known as ‘legs’, and the angle between them is called the vertex angle or apex angle.In an isosceles triangle, if two sides are equal, then the angles opposite to the two sides correspond to each other and are also always equal.The isosceles triangle has three acute angles, meaning that the angles are less than 90°.The sum of three angles of an isosceles triangle is always 180°. The side opposite the vertex angle is called the base and the base angles are equal, and perpendicular to the apex angle bisecting the base and the apex angle.To know more about Isosceles Triangle:
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PLEASE HELPPPP
(image below)
Answer:
b
Step-by-step explanation:
I think number B is the answer. because the square becomes root when it crosses the = . So, the answer is B
Answer:
b. ±√60
Step-by-step explanation:
You want to know the solution to x² = 60.
SolutionIn general, the process of solving for a variable's value requires you to "undo" what is done to the variable. This generally means you use inverse operations. The inverse of the squaring operation is the square root operation.
Taking the square root of both sides, we get ...
√(x²) = √60
|x| = √60 . . . . . . simplify the left side
x = ±√60 . . . . . . . write the equivalent without the absolute value bars
__
Additional comment
As with any operation performed on an equation, it must be done to both sides of the equal sign.
You will get a ±(radical) result whenever you take an even-index root: square root, fourth root, sixth root, and so on. Odd-index roots will have the same sign as the value under the radical.
√64 = ±8
∛64 = 4; ∛-64 = -4
Estimate the amount of the tip by rounding the bill to the nearest ten dollars before calculating. 15% tip on a bill of $706.03 The amount of the tip is approximately
Answer: To estimate the tip, you can first round the bill to the nearest ten dollars. In this case, $706.03 rounded to the nearest ten dollars is $710.
Next, you can calculate the tip by multiplying the rounded bill amount by the tip percentage, 15% in this case.
15% of $710 is 15/100 * 710 = 106.50
So the amount of the tip is approximately 106.50
It's worth mentioning that this method of approximation is not always precise, but it can be a quick and easy way to calculate an estimate when you don't need a very precise answer.
Step-by-step explanation:
1. Length and breadth of a rectangular table-top are 36 cm and 24 cm respectively. Find its perimeter.
Answer:
120 cm.
Step-by-step explanation:
The perimeter of a rectangle is found by adding up the length of all four sides. In this case, the length is 36 cm and the breadth is 24 cm. Therefore, the perimeter of the rectangular table-top is
2 (length + breadth) = 2 (36 + 24) = 2 × 60 = 120 cm.
This probability distribution shows the
typical grade distribution for a Geometry
course with 35 students.
Grade
A
BCDF
Frequency
5
10
15
3
2
Find the probability that a student earns a
grade of A, B, or C.
p=[?]
Enter a decimal rounded to the nearest hundredth.
Answer:
85.71% probability
Step-by-step explanation:
30 of 35 of the students are in abc range so take 35/100% or 0.35 and go 30/0.35 and you get 85.71%
select the correct answer. Solve the quadratic equation. (x + 4)(x + 1) = 0
x = 4 or x = 1
x = -4 or x = 1
x = -4 or x = -1
x = 4 or x = -1
Answer:
x = -4 or x = -1
Step-by-step explanation:
Let's check
x = -4
(-4 + 4)(-4 + 1) = 0
(0)(-3) = 0
0 = 0
Let's check x = -1
(-1 + 4)(-1 + 1) = 0
(-3)(0) = 0
0 = 0
So, x = -4 or x = -1 is correct answer!
Question
A hot-air balloon is 1200 feet off the ground and its altitude is slowly changing at a constant rate of −712 feet per second.
How many seconds, s, will it take for the balloon to drop to below 310 feet?
Drag and drop a symbol and value to correctly complete the solution to this inequality.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
s Response area Response area
The number of seconds, it takes for the balloon to drop below 310 feet is 1.25 seconds
How to calculate the expression?To find out how many seconds it will take for the balloon to drop to below 310 feet, we need to use the information provided and some basic algebra.
Given the starting altitude of the balloon, we know:
h(0) = 1200 feet
The rate of change of the altitude, or the speed at which the altitude is changing, is given as:
dh/dt = −712 feet/second
This tells us that the altitude of the balloon is decreasing at a rate of 712 feet per second. To find out how long it will take for the altitude to drop to 310 feet or less, we can set up the following equation:
h(t) = h(0) + dh/dt * t
We know that h(t) must be less than or equal to 310 feet, so we can substitute this value in for h(t) and solve for t:
310 = 1200 + (−712) * t
This equation can be solved for t by isolating t on one side and then dividing both sides by −712:
t = (1200 - 310) / −712
t = (890) / (−712)
t = 1.25 seconds.
So it will take 1.25 seconds for the balloon to drop below 310 feet.
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