Find the value of x. Then the measure of each angle

Answer: The diver's new depth is 11.8 feet below the water's surface.

Step-by-step explanation:

Since we have given that

Depth below the water's surface = 15 feet

The diver swims up slowly at 0.5 feet per second for 4 seconds.

Number of miles he swims up is given by

[tex]0.5\times 4\\\\=2\ feet[/tex]

Number of miles he swims up for 3 more seconds at 0.4 feet per second.

So, Number of miles he swims up is given by

[tex]0.4\times 3\\\\=1.2\ feet[/tex]

So, the diver's new depth would be

[tex]-15+2+1.2\\\\=-15+3.2\\\\=-11.8\ feet[/tex]

Hence, the diver's new depth is 11.8 feet below the water's surface.

It will take 36 minutes for an object to travel 5 1/5 miles at a steady speed of 8 2/3 mph.

To find out how long it will take an object traveling at a steady speed of 8 2/3 mph to travel 5 1/5 miles, you can use the formula

time = distance / speed.

First, convert the mixed numbers to improper fractions:

Speed: 8 2/3 mph = (8 × 3 + 2) / 3 = 26/3 mph

Distance: 5 1/5 miles = (5 × 5 + 1) / 5 = 26/5 miles

Next, calculate the time:

Time = Distance / Speed

= (26/5) miles / (26/3) mph

= (26/5) × (3/26) hours

= 3/5 hours

To convert hours into minutes, multiply by 60:

= 3/5 hours × 60 minutes/hour

= 36 minutes

Solve for b, i.e separate b in one side and the other terms in the other side

A = ah + bh

A - ah = bh

(A - ah) / h = b

[tex]b= \frac{A-ah}{h} [/tex]

I hope that helps!

Answer: Each dimension would be 21.1875 inches and 2.375 inches respectively.

Step-by-step explanation:

Since we have given that

Width of a surfboard = [tex]21\dfrac{3}{16}\ inches[/tex]

Thickness of a surfboard = [tex]2\dfrac{3}{8}\ inches[/tex]

We need to rewrite each dimension as a decimal.

We first write it in improper fraction:

Width becomes

[tex]21\dfrac{3}{16}\\\\=\dfrac{339}{16}\ inches[/tex]

Thickness becomes

[tex]2\dfrac{3}{8}\\\\=\dfrac{19}{8}\ inches[/tex]

Now, we change it into decimal form:

[tex]\dfrac{339}{16}=21.1875\ inches\\\\and\\\\\dfrac{19}{8}=2.375\ inches[/tex]

Hence, each dimension would be 21.1875 inches and 2.375 inches respectively.

Final answer:

The rule for the function with the given points is f(x) = x^2 + 2/19, as derived from observing the relationship between x-values and their corresponding y-values where the y-values increase by the square of the x-value with a constant fractional part of 2/19.

Explanation:

To find the rule for the function represented by the set of points given, we need to look for a pattern in the y-values relating to the x-values. The provided points are (0,2/19), (1,1 2/19), (2,4 2/19), (3, 9 2/19), (4, 16 2/19), and (5, 25 2/19). Observing the differences between the y-values, it appears that the fractional part remains constant at 2/19, whereas the whole number part increases by the square of the x-value. Therefore, we can express the function rule as f(x) = x2 + 2/19.

Let's verify this by substituting the x-values from the points into our proposed rule:

As we can see, the values match perfectly, confirming that the rule of the function is indeed f(x) = x2 + 2/19.

Suppose that you have a stack of pennies. If you want to know without counting whether there is an odd or even number of pennies, then you have to split them into two parts, for example,  placing one coin left and one coin  right.

If the number of pennies is even, then no coins will left, if the number is odd, then one coin will be extra.

Answer:  there are 20 orange skittles and 10 red skittles in the bag.

Explanation:

Since we have given that

Let the number of red skittles be x

Let the number of orange skittles be 2x

According to question,

[tex]2x-x=10\\x=10[/tex]

So, there are 10 red skittles in the bag and

The number of orange skittles in the bag is given by

[tex]2x=2\times 10=20[/tex]

Hence, there are 20 orange skittles and 10 red skittles in the bag.

The number of red and orange Skittles in the bag are;

I. Red skittles, R = 10

II. Orange skittles, S = 20

To find the number of red and orange Skittles in the bag;

Translating the word problem into a mathematical (algebraic) expression, we would have;

[tex]R = S - 10[/tex]  ....equation 1.

[tex]S = 2R[/tex]  ....equation 2.

Substituting eqn 2 into eqn 1, we have;

[tex]R = 2R - 10\\\\2R - R = 10[/tex]

Red skittles, R = 10

To find the number of orange skittles;

[tex]S = 2[/tex] × [tex]10[/tex]

Orange skittles, S = 20

Read more: https://brainly.com/question/20758742

area of a square - S^2, where S is the length of a side

 to find S when you know the area, take the square root

 so S = sqrt(8)

S = 2.828

rounded to nearest hundredth = 2.83 inches

Answer:

2300

Step-by-step explanation:

List A. –5, –2.1, 0.3, 3.1, is ordered from least to greatest.

To determine which list is ordered from least to greatest, we need to compare the numerical values in each list and arrange them in ascending order. Here's a step-by-step explanation:

List A is properly ordered from least to greatest:

Therefore, the correct answer is: A

The number square root of 220 is greater than that of 14 3/4.

Given are two numbers.

The square root of 220 and 14 3/4.

We have to find which number is greater.

We know that :

14 3/4 = 14 + 3/4 = 14.75

Now,

14² = 196

15² = 225

So the number 220 lies between 196 and 225.

So √220 lies between 14 and 15.

Since 220 is closest to 225 which is the square of 15, the square root os 220 is more close to 15.

√220 ≈ 14.8

Hence √220 is greater.

Learn more about Square Roots here :

https://brainly.com/question/29286039

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we have

[tex]y\leq 2x+1[/tex] ------> inequality A

The solution of the inequality A is the shaded area below the solid red line

see the attached figure N [tex]1[/tex]    

[tex]y>-2x-3[/tex] ------> inequality B

The solution of the inequality B is the shaded area above the dotted blue line

see the attached figure N [tex]2[/tex]

therefore

The solution of the system of inequalities is the shaded area between the solid red line and the dotted blue line

see the attached figure N [tex]3[/tex]

therefore

the answer in the attached figure N [tex]3[/tex]

The horse weighs 615 pounds.

Let's assume the rider's weight is x.

The horse's weight is 6 times the rider's weight plus 45 pounds: 6x + 45.

The total weight of the horse and rider is 710 pounds: 6x + 45 + x = 710.

Combining like terms: 7x + 45 = 710.

Subtract 45 from both sides: 7x = 665.

Divide both sides by 7: x = 95.

So, the rider weighs 95 pounds.

Substitute x = 95 back into the equation to find the horse's weight: 6(95) + 45 = 570 + 45 =

The horse weighs 615 pounds.

To solve this problem, we will set up an equation where [tex]\( h \)[/tex] represents the horse's weight and [tex]\( r \)[/tex] represents the rider's weight. According to the problem:

1. The horse's weight is 45 pounds more than six times the rider's weight, so we can express this as:

[tex]\[ h = 6r + 45 \][/tex]

2. The total weight of the horse and the rider is 710 pounds, so we have:

[tex]\[ h + r = 710 \][/tex]

Now we have a system of equations:

[tex]\[ h = 6r + 45 \][/tex]

[tex]\[ h + r = 710 \][/tex]

We can substitute the first equation into the second to solve for \( r \):

[tex]\[ (6r + 45) + r = 710 \][/tex]

[tex]\[ 7r + 45 = 710 \][/tex]

Now, we solve for[tex]\( r \)[/tex]:

[tex]\[ 7r = 710 - 45 \][/tex]

[tex]\[ 7r = 665 \][/tex]

[tex]\[ r = \frac{665}{7} \][/tex]

[tex]\[ r = 95 \][/tex]

Now that we have the rider's weight, we can find the horse's weight:

[tex]\[ h = 6r + 45 \][/tex]

[tex]\[ h = 6 \times 95 + 45 \][/tex]

[tex]\[ h = 570 + 45 \][/tex]

[tex]\[ h = 615 \][/tex]