The situation can be represented as three inequalities: g + p < 120, g < 45, p > 30, where g is the time spent in the gym and p is the time spent in the pool.
Explanation:The situation you described can be represented as a system of inequalities. Let's denote gym time as g and pool time as p. Then, the system of inequalities would be the following:
g + p < 120 (you want to spend less than 120 minutes in the gym and in the pool total)g < 45 (you want to spend less than 45 minutes in the gym)p > 30 (you want to spend more than 30 minutes in the poolThese inequalities represent the constraints on how you can divide your time between the gym and the pool. Any solution to this system would be a pair of numbers (g, p) that satisfy all three inequalities, meaning it's a valid way for you to divide your time.
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The correct system of inequalities is Option 1: x + y < 120 (representing the total time constraint), x < 45 (reflecting the condition of spending less time in the gym), and y > 30 (representing the condition of spending more time in the pool). This corresponds to Option 1 in the given systems of inequalities.
Explanation:The correct system of inequalities that represents your time allocation between the gym and the pool is Option 1. Let's define x as the time you spend in the gym and y as the time you spend in the pool. According to the given conditions and constraints, the total time, which is the sum of x and y, should be less than 120 minutes (x + y < 120). Furthermore, you want to spend less than 45 minutes in the gym (x < 45) and more than 30 minutes in the pool (y > 30). These three inequalities jointly form a system that accurately represents your situation at the gym and pool.
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The complete question is given below:
You have less than 120 minutes to spend in the gym and in the pool. You want to spend less than 45 minutes in the gym and more than 30 minutes in the pool. Which system represents the situation?
Option 1:
x + y < 120
x < 45
y > 30
Option 2:
x + y = 120
x = 45
y = 30
Option 3:
x + y <= 120
x < 45
y > 30
Option 4:
x + y < 120
x <= 45
y >= 30
Please help!? I'll give you a medal:D
1. a tessellation is a ___________________ pattern of figures.
A. Reflecting
B. Repeating
C. Symmetrical.
2. A tessellation has no _______
A. Gaps and overlays
B. translations
c. repeated figures.
Suppose that G(x) = F(x - 8). Which statement best compares the graph of G(x) with the graph of F(x)? apex
A.The graph of G(x) is the graph of F(x) shifted 8 units to the right.
B.The graph of G(x) is the graph of F(x) shifted 8 units to the left.
C.The graph of G(x) is the graph of F(x) shifted 8 units up.
D.The graph of G(x) is the graph of F(x) shifted 8 units down.
Answer:
B
Step-by-step explanation:
The graph of G(x) = F(x - 8) is the graph of F(x) shifted 8 units to the right, option A.
When comparing the graph of G(x) = F(x - 8) with the graph of F(x), we note that there is a horizontal shift involved. Following the rules for transformations, subtracting a positive constant from the independent variable x results in shifting the graph to the right by that constant. Therefore, the statement that best compares the graph of G(x) with the graph of F(x) is: The graph of G(x) is the graph of F(x) shifted 8 units to the right, option A.
This is similar to the effect observed when comparing the functions f(x) and f(x - 2), where the latter's graph is a rightward shift of the former's graph by 2 units.
please help understand this and get it done.
A animal shelter has 16 puppies. If the puppies are 32% of the total dogs and cats population, how many dogs and cats are in the animal shelter?
The total number of animals in a shelter is 50 and number of cats in the shelter is 34.
Given that, a animal shelter has 16 puppies. If the puppies are 32% of the total dogs and cats population.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Let x be the total number of dogs and cats are in the animal shelter.
So, 32% of x=16
⇒ 32/100 ×x=16
⇒ 0.32x=16
⇒ x=16/0.32
⇒ x=50
So, number of cats =50-16
= 34
Therefore, the total number of animals in a shelter is 50 and number of cats in the shelter is 34.
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Pls, answer!! I will mark the 1st person to answer correctly with work as brainliest for 20 points!
given that (-8,- 7) in on the graph of f(x), find the corresponding point for the fuction f(x -4)
an internet passcode consists of a digit followed by a letter, followed by another digit. Assuming the digits are 0-9, how many different passcode are possible?
Answer:
2600
Step-by-step explanation:
Which of the following is true about the polynomial 4x^3 - 2x? Select all that apply.
A. The polynomial has two terms.
B. The polynomial is a fourth degree polynomial with the appropriate third or fourth terminology replacement.
C. The polynomial has a leading coefficient of 3.
D. The polynomial is written in standard form.
Simplify by using radical. Rationalize denominators.
[tex] 2a^{-1/2} [/tex]
Answer:
[tex]\frac{2\sqrt a}{a}[/tex]
Step-by-step explanation:
The given equation is [tex]2a^{-1/2}[/tex]
The exponent rule: [tex]x^{-a}=\frac{1}{x^a}[/tex]
Using this rule, we get
[tex]2a^{-1/2}\\\\=\frac{2}{a^1/2}[/tex]
We can rewrite this in radical form as
[tex]\frac{2}{\sqrt a}[/tex]
Rationalize the denominator by multiplying numerator and denominator by [tex]\sqrt a[/tex]
[tex]\frac{2}{\sqrt a}\cdot \frac{\sqrt a}{\sqrt a}[/tex]
On simplifying
[tex]\frac{2\sqrt a}{a}[/tex]
The line through (8, 0) with slope -3/4 in slope-intercept form
PLEASE HELP!!!! :(
A person is watching a boat from the top of a lighthouse. The boat is approaching the lighthouse directly. When first noticed, the angle of depression to the boat is 17°31'. When the boat stops, the angle of depression is 46°41'. The lighthouse is 200 feet tall. How far did the boat travel from when it was first noticed until it stopped? Round your answer to the hundredths place.
By using the tangent function and the angles of depression given, we can calculate the distances from the boat to the lighthouse when it was first spotted and when it stopped. Subtracting the second distance from the first gives us the distance the boat traveled.
Explanation:This is a question about Trigonometry, involving the concepts of angles of depression and distances. In the situation presented, we are given the height of the lighthouse (200 feet), and two angles of depression - 17°31' when the boat was first noticed and 46°41' when the boat stopped. We can use the tangent function to calculate the distance from the lighthouse to the boat at these two points, then subtract these distances to find how far the boat traveled.
The tangent of an angle in a right triangle is equal to the opposite side divided by the adjacent side. Therefore, when the angle of depression was 17°31', we can use the equation tan(17°31') = 200/distance1 to solve for the first distance. Similarly, for the angle of depression 46°41', we use the equation tan(46°41') = 200/distance2.
Solving these two equations separately will give us the distances from the boat to the lighthouse at these two moments. Then we subtract distance2 from distance1 to get the distance the boat traveled.
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6.The Polygon Similarity Postulate states that two polygons are similar if and only if there is a correspondence between their angles and their sides so that all corresponding angles are and all sides are proportional. _________
7.Similar figures have the same shape but are not necessarily the same size.
True
False
8.A directed line segment partitioned with a ratio of 4:3 would be divided into how many equal parts.
4
3
7
12
9.The ratio of the length of a side of an image to the length of the corresponding side of its pre-image is called the scale factor.
True
False
10.All properties of Proportions are valid, given that there is no ______________ in the denominator of the fraction representing the ratios.
What is the slope of the line 3x + 4y = -11?
answers:
3\4
-3\4
3
4
Final answer:
To find the slope of the line given by 3x + 4y = -11, the equation is rearranged into the slope-intercept form, yielding a slope (m) of -3/4.
Explanation:
The question asks: What is the slope of the line 3x + 4y = -11?
To find the slope of the line, we first need to rearrange the equation into the slope-intercept form, which is y = mx + b, where m is the slope, and b is the y-intercept. Starting with the given equation
3x + 4y = -11We isolate y on one side by first moving 3x to the right side of the equation, and then dividing everything by 4:
4y = -3x - 11y = (-3/4)x - 11/4Now, in the form of y = mx + b, it's clear that the slope (m) of the line is -3/4.
The yearly profit of a company in thousands of dollars is given by the finction P(x) =3000+1200-6x^2 where x is the amount in thousands the company spneds on advertising. Find the amount ,x, that the company has to spend to maxamize its profit
On a game show, a contestant randomly chooses a chip from a bag that contains numbers and strikes. The theoretical probability of choosing a strike is 15. The bag contains 8 strikes. How many chips are in the bag?
Final answer:
To find the probability of selecting 3 green marbles out of 10, use the combinations formula. The calculation involves 455 * 6435 divided by 1027227812 to determine the probability.
Explanation:
To calculate the probability of choosing exactly 3 green marbles out of 10 selected, we use the concept of combinations. The formula for combinations is nCr = n! / r!(n-r)!. In this case, the calculation would be 15C3 * 35C7 / 50C10, which simplifies to 455 * 6435 / 1027227812, resulting in the probability of choosing exactly 3 green marbles out of 10 selected.
Lucy watched TV for 25 of an hour on Monday. She watched 79 of an hour on Tuesday. What day did she spend more time watching TV?
Find the angle with a tangent ratio of 0.9325
Answer:
B. 43
Step-by-step explanation:
Help me please!!!!!!!
Carla borrowed $1,400 for three months at 9.75% interest. How much
interest did she pay for the loan?
a. $34.13
b. $49
c. $136.50
d. $1,547
HELP ASAP (ANSWER IS NOT D)
Carla paid $34.13 as interest for the $1,400 loan at 9.75% for three months that is option A is the correct answer.
The interest Carla paid for the loan is $34.13.
Calculate the interest using the formula: Interest = Principal x Rate x Time.
Substitute the values for Principal, Rate, and Time into the formula to find the interest amount.
For Carla's loan ($1,400 at 9.75% for three months), the interest is calculated to be $34.13.
Determine whether each triangle with sides of given lengths is a right triangle. Hint: Set a2+b2=c2a2+b2=c2 If One side is equal to the other, then it's a right triangle. It sides are not equal, then it's not a right triangle. a = 6 cm b= 8 cm c = 10 cm
answers yes or no
What is the sum of the first 7 terms of the series −8+16−32+64−
helpppppppppppppppppp
Construction is under way at an airport. This map shows where the construction is taking place. If Road A and Road B are parallel, what is the distance from P to Q on Road C?433 feet
975 feet
1,050 feet
1,477 feet
Answer:
if your asking for plato it will be B
Step-by-step explanation:
got it correct just now
A science test, which is worth 100 points, consists of 24 questions. Each question is worth either 3 points or 5 points. If x is the number of 3-point questions and y is the number of 5-point questions, the system shown represents this situation. x + y = 24 3x + 5y = 100 What does the solution of this system indicate about the questions on the test? The test contains 4 three-point questions and 20 five-point questions. The test contains 10 three-point questions and 14 five-point questions. The test contains 14 three-point questions and 10 five-point questions. The test contains 20 three-point questions and 8 five-point questions.
The answer to your question is B :)
What power do you raise a number to to get the square root of it?
ABCD is a rectangle. Find the length of each diagonal.
Answer: The correct answer is 3
Step-by-step explanation:
C = 3
AC = 3/3 = 1
BD = 4 - 3 = 1
The length of each diagonal is 12/5. This demonstrates that in a rectangle, the diagonals are always equal in length.
In a rectangle, the diagonals are equal in length. Therefore, we can equate [tex]\(AC\) and \(BD\)[/tex].
Given [tex]\(AC = \frac{C}{3}\) and \(BD = 4 - C\)[/tex], we set them equal: [tex]\(\frac{C}{3} = 4 - C\)[/tex]. Solving for \(C\) yields [tex]\(C = \frac{12}{5}\)[/tex].
Substituting this value back into either [tex]\(AC\) or \(BD\)[/tex] gives us the length of the diagonals.
Thus, the length of each diagonal is [tex]\(AC = BD = \frac{12}{5}\)[/tex]. This demonstrates that in a rectangle, the diagonals are always equal in length.
Can someone help me...?
What is the solution to the equation 5x = 40?
Complete the table. Original Price Percent 112 of Discount 32% Sale Price
Answer:
$76.16
Step-by-step explanation:
$76.16
He measure of one angle of an octagon is twice that of the other seven angles. what is the measure of each angle? answer: ,
The measure of one angle in an octagon is 135.625 degrees.
Explanation:Let's denote the measure of one angle as x.
Since there are eight angles in an octagon,
the sum of all the angles in the octagon is 180(x) + 7(2x) = 180x + 14x = 194x.
We know that the sum of the angles in any polygon is equal to (n-2) times 180 degrees, where n is the number of sides of the polygon.
Therefore, 194x = (8-2) × 180. Solving this equation,
we find that x = 135.625. So, the measure of each angle is 135.625 degrees.
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