Determine if the side lengths 2.1in,4in,7.9in form a triangle

Answer:

After 1.25 seconds the twig land on the bush.

Step-by-step explanation:

Given function that shows the height of twig from the ground after t seconds,

[tex]h(t)=-16t^2+30[/tex]

When twig is on the bush,

h(t) = 5 feet   ( ∵ the distance from bush to ground = 30 - 25 = 5 feet )

[tex]\implies -16t^2+30=5[/tex]

[tex]-16t^2=-25[/tex]

[tex]t^2=\frac{25}{16}[/tex]

[tex]\implies t=\pm \frac{5}{4}[/tex]  

Since, time can not be negative,

Hence, t = [tex]\frac{5}{4}[/tex] ≈ 1.25

Therefore, after 1.25 seconds the twig land on the bush.

Answer:

64

Step-by-step explanation:

took the test

The correct answer is £166, £581.

To share £747 in the ratio of 2:7 between Tom and Ben.

Let's define the total parts: 2 + 7 = 9

Tom's share: [tex]\frac{2}{9} \times 747 = \frac{1494}{9} = £166[/tex]

Ben's share: [tex]\frac{7}{9} \times 747 = \frac{5229}{9} = £581[/tex]

Therefore, the calculation to share £747 in the ratio of 2:7 between Tom and Ben is:

[tex]\text{Tom's share} &= \frac{2}{9} \times 747 = \frac{1494}{9} = £166[/tex]..

[tex]\text{Ben's share} &= \frac{7}{9} \times 747 = \frac{5229}{9} = £581\end{aligned}[/tex]

Where Tom receives £166, and Ben receives £581.

This question falls under the combinatorial mathematics branch. Due to the complex nature of the problem which involves permutations and combinations, it's necessary to use a systematic approach or a computer algorithm to find the total number of scoring sequences that keeps the game 'relatively close'. Hence, the actual numerical answer would require a stronger background in combinatorics.

This question belongs to the subject of combinatorial mathematics, particularly involving permutations and combinations. In this scenario, 'relatively close' is defined as the number of goals scored by the two teams never differing by more than two. The total number of goals scored in the game is twelve.

Let's denote the two teams as Team A and Team B. The game can start in three ways: either Team A scores twice, Team B scores twice, or each team scores once. After that, at any point, the next goal can either maintain the score within the 'relatively close' range of two goals or equalize the score.

Determining the total number of scoring sequences under these conditions requires generating a tree diagram and counting all the possible paths, subject to the condition that the absolute difference between the number of goals for the two teams does not exceed two at any stage. Due to the combinatorial complexity, this task could be difficult without using a systematic approach or computer algorithm.

Therefore, to actually answer this question, one would require a stronger background in combinatorics, and most likely the assistance of programming or mathematics software to execute a brute force count or implement a more advanced mathematical solution.

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Final answer:

The arc length of a circle with a radius of 10 units and a central angle of 97° is calculated using the formula for arc length, yielding an arc length of approximately 16.975 units.

Explanation:

The question asks us to find the arc length of a circle with a certain radius when a central angle is given. To find the arc length, we use the formula:

Arc length (s) = (θ/360) × 2πr

Where θ is the central angle in degrees, r is the radius of the circle, and π is approximately 3.14159. Since we know the central angle is 97° and the radius is 10, we can plug these values into the formula:

s = (97/360) × 2×π×10

s ≈ (97/360) × 2× 3.14159 × 10

s ≈ 16.975

Therefore, the arc length is approximately 16.975 units.

Answer:x+2<1x<1-2x<-1-1 does not satisfy the inequality because though-1 is lesser than 0 but not lesser than

Given is the Rate of each hamburger = 2.10 dollars each.

The number of hamburgers that we sell = 3 hamburgers.

Charges for all 3 hamburgers = 3 x 2.10 = 6.30 dollars.

Tax charged on these 3 hamburgers = 0.38 dollars.

Total Bill = Charges for 3 hamburgers + Tax

Total Bill = 6.30 + 0.38 = 6.68 dollars.

Customer paid = 10 dollars.

The amount to be returned to customer = Bill paid by customer - Total Bill charged = 10 - 6.68 = 3.32 dollars.

Hence, the customer would get a change of 3.32 dollars.

Answer:

70 is the answer choise I picked it and got it correct

Step-by-step explanation:

Answer:the volume of cylinder is 785

volume of the sphere is 523.33

the volume of the water that can remain is 261.8

Step-by-step explanation: algebra nation answer

It says that the recipe for 9 servings would require 3/4 cup milk.

He wants to prepare recipe for 6 servings. Let's assume it requires X cups milk.

Now we can use concept of proportions to solve this problem.

The proportion of X cups for 6 servings would be same as 3/4 cup milk for 9 servings. Mathematically, we can write it as follows :-

[tex] \frac{X \;cups \;milk}{6 \;servings} = \frac{\frac{3}{4} \;cups \;milk}{9 \;servings} \\\\
Or\; \frac{X \;cups \;milk}{\frac{3}{4} \;cups \;milk} = \frac{6 \;servings}{9 \;servings} \\\\
\frac{X }{\frac{3}{4} } = \frac{6 }{9 } \\\\
X = \frac{6}{9}*\frac{3}{4} \\\\
X = \frac{6*3}{9*4} \\\\
X = \frac{18}{36} \\\\
X = \frac{1}{2} \;cup \;milk [/tex]

Hence, we require [tex] \frac{1}{2} [/tex] cup milk for 6 servings.