Consider the sequence 5, 12, 19, 26, ... Enter numbers in the boxes to represent the fourth term as an ordered pair. ( , )

Answer:

\(\sqrt{2}\)

Step-by-step explanation:

We can use pytho theorem to find X because its a right triangle, so:

a^2 + b^2 = c^2

plug our numbers

1^2 + 1^2 = x^2

simplify

1+1 = x^2

2=x^2

answer = root2

Answer:

Geometric figure: Straight Line

Slope = 120.000/2.000 = 60.000

x-intercept = 346/-60 = 173/-30 = -5.76667

y-intercept = 346/1 = 346.00000

Step-by-step explanation:

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

y-(-4+60*x+350)=0

STEP

1

:

Equation of a Straight Line

1.1 Solve y-60x-346 = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line y-60x-346 = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when x = 0 the value of y is 346/1 so this line "cuts" the y axis at y=346.00000

y-intercept = 346/1 = 346.00000

Calculate the X-Intercept :

When y = 0 the value of x is 173/-30 Our line therefore "cuts" the x axis at x=-5.76667

x-intercept = 346/-60 = 173/-30 = -5.76667

Calculate the Slope :

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 346.000 and for x=2.000, the value of y is 466.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 466.000 - 346.000 = 120.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

Slope = 120.000/2.000 = 60.000

Geometric figure: Straight Line

Slope = 120.000/2.000 = 60.000

x-intercept = 346/-60 = 173/-30 = -5.76667

y-intercept = 346/1 = 346.00000

The temperature at 8:00 A.M. was 15°C.

Using the given information:
1. At 7:00 P.M., the temperature was 16°C.
2. This temperature was 9°C less than the temperature at 2:00 P.M.

We can use this information to find the temperature at 2:00 P.M.:
Temperature at 2:00 P.M. = 16°C (temperature at 7:00 P.M.) + 9°C
Temperature at 2:00 P.M. = 25°C

3. The temperature at 2:00 P.M. was 10°C higher than the temperature at 8:00 A.M.

Now, we can find the temperature at 8:00 A.M.:
Temperature at 8:00 A.M. = 25°C (temperature at 2:00 P.M.) - 10°C
Temperature at 8:00 A.M. = 15°C

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Answer:

2 forms

Step-by-step explanation:

hope this helps <3

\( \sf \longrightarrow \: \frac{8}{5} \div 6 \\ \)

\( \sf \longrightarrow \: \frac{5}{8} \times 6 \\ \)

\( \sf \longrightarrow \: \frac{5 \times 6}{8} \\ \)

\( \sf \longrightarrow \: \frac{30}{8} \\ \)

\( \sf \longrightarrow \: \frac{8}{30} \\ \)

\( \sf \longrightarrow \: 0.26 \\ \)

_____________________________

The ordered pairs (-1, -6), (2, -18), (0, 0), and (-4, -12) do not correspond to the intervals where the graph of f(x) is decreasing. The pairs (1, -2) and (-3, -18) are the correct ones.

To determine where the graph of f(x) is decreasing, we need to examine the intervals where the function's derivative is negative. The derivative of f(x) is given by f'(x) = -3x^2 - 8x + 3.

Now, let's evaluate f'(x) for each of the given x-values:

f'(-1) = -3(-1)^2 - 8(-1) + 3 = -3 + 8 + 3 = 8

f'(2) = -3(2)^2 - 8(2) + 3 = -12 - 16 + 3 = -25

f'(0) = -3(0)^2 - 8(0) + 3 = 3

f'(1) = -3(1)^2 - 8(1) + 3 = -3 - 8 + 3 = -8

f'(-3) = -3(-3)^2 - 8(-3) + 3 = -27 + 24 + 3 = 0

f'(-4) = -3(-4)^2 - 8(-4) + 3 = -48 + 32 + 3 = -13

From the values above, we can determine the intervals where f(x) is decreasing:

f(x) is decreasing for x in the interval (-∞, -3).

f(x) is decreasing for x in the interval (1, 2).

Now let's check the ordered pairs in the table:

(-1, -6): Not in a decreasing interval.

(2, -18): Not in a decreasing interval.

(0, 0): Not in a decreasing interval.

(1, -2): In a decreasing interval.

(-3, -18): In a decreasing interval.

(-4, -12): Not in a decreasing interval.

Therefore, the ordered pairs (-1, -6), (2, -18), (0, 0), and (-4, -12) are not located in the intervals where the graph of f(x) is decreasing. The correct answer is: (1, -2), (-3, -18).

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Note the complete and the correct question is

Q- Consider the function below, which has a relative minimum located at (-3, -18) and a relative maximum located at 1/3, 14/27).

\(f(x) = -x^3 - 4x^2 + 3x\).

Select all ordered pairs in the table which are located where the graph of f(x) is decreasing: Ordered pairs: (-1, -6), (2, -18), (0, 0),(1 , -2), (-3 , -18), (-4. , -12)

Answer: D

Step-by-step explanation:

Since we are given that the x value is -1, we can eliminate A and C because the -1 is in the y coordinate.

To find the proper y value, we plug x into the equation.

y=-2x+5                                                 [plug in x=-1]

y=-2(-1)+5                                              [multiply -2 and -1]

y=2+5                                                    [add 2 and 5]

y=7

Now that we have the y value, we know the coordinate (-1,7) which makes D the correct answer.

Answer:

x = -7

x = 5

Step-by-step explanation:

The standard form of quadratic equations is

Ax^2 + Bx + C = 0

The factors need to multiply together to be C and add together to be B.

The two numbers that will multiply together to be -35 and add together to be 2 are -5 & 7.

The factor pairs are (x+7)(x-5). Zero product property means we set each of those factor pairs = 0 and solve.

x + 7 = 0

-7 -7 Subtract 7 from each side to solve

x = -7

x - 5 = 0

+5 +5 Add 5 to each side to solve

x = 5

To solve the equation, factor x²+2x−35 use the formula x² +(a + b) x + ab = (x + a)(x + b). To find a and b, set up a system to be solved.

a + b = 2

ab = −35

Since ab is negative, a and b have opposite signs. Since a+b is positive, the positive number has a greater absolute value than the negative. Show all pairs of integers whose product is −35.

Calculate the sum of each pair.

The solution is the pair that gives sum 2.

Rewrite the factored expression (x + a)(x + b) with the values obtained.

To find solutions to equations, solve x−5=0 and x+7=0.

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The mean number of movies that the students saw is 13.5 (rounded to the nearest tenth).

To find the mean number of movies the students saw, you need to calculate the average of the given data. Here are the reported numbers of movies seen by the 6 students: 14, 11, 15, 19, 12, 10.

To calculate the mean, you sum up all the reported numbers and divide by the total number of students. In this case, the total number of students is 6.

So, let's calculate the mean:

(14 + 11 + 15 + 19 + 12 + 10) / 6 = 81 / 6 = 13.5

Therefore, the mean number of movies that the students saw is 13.5 (rounded to the nearest tenth).

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Answer:

The graph is NOT a function

Step-by-step explanation:

If I draw a vertical line everywhere on the graph, a vertical line must not touch two points. If You see how the graph curves on top off the bottom? Drawing a vertical line would hit two points

Answer:

divide 88 by the number of x

88/8= 11

X = 11

Answer:

x=11

Step-by-step explanation:

8x=88

You use inverse operation which means you would divide 8 on both sides to isolate x on one side resulting in x=11

Answer:

n>10.2 or n>51/5

Step-by-step explanation:

4n+2(n+1)>n+52 distribute 2 to everything in the parentheses

4n+2n+1>n+52 combine like terms

6n+1>n+52 subtract 1 from both sides

6n>n+51 subtract n from both sides

5n>51 divide both sides by 5

n>10.2

Answer:

n>10.2

Step-by-step explanation:

3. The factored polynomial is p(x) = (x - 1)(x - 5)

4. The factored polynomial is p(x) = (x + 3)²

A polynomial is a mathematical expression in which the power of the unknown is greater than or equal to 2.

3. To factorize the polynomial using the graph, we see that the polynomial cuts the x - axis at x = 1 and x = 5.

This implies that its factors are (x - 1) and (x - 5)

So, the factored polynomial is p(x) = (x - 1)(x - 5)

4. To factorize the polynomial using the graph, we see that the polynomial touches the x - axis at only one point x = -3. So,it has repeated roots

This implies that its factors are (x - (-3)) = (x + 3) twice

So, the factored polynomial is p(x) = (x + 3)²

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Answer: : it is 4 over 8 and *

Step-by-step explanation:

Solution

Step 1

Given data for C(x), the bakery's pricing

Required

Step 1

To find the cost of 8 hot cocoa bombs

Step 2

To find the cost of 18 hot cocoa bombs

To find the C(30)

Step 4

What C(30) represents.

C(30) represents the cost of ordering 30 hot cocoa bombs which is $105

Answer:

\(t = 15.7\)

Step-by-step explanation:

Given

\(Principal = 25000\) --- P

\(Amount = 75000\) --- A

\(Rate = 7\%\) --- R

Required

Determine the time (t)

Using continuous growth formula:

We have

\(A = Pe^{rt}\)

Convert rate to decimal

\(Rate = 7\%\)

\(r = 0.07\)

Substitute values for A, P and r

\(75000 = 25000 * e^{0.07t}\)

Divide both sides by 25000

\(3 = e^{0.07t}\)

Rewrite the exponential function as logarithmic, we have:

\(ln3 = 0.07t\)

Reorder

\(0.07t = ln3\)

Divide both sides by 0.07

\(t = \frac{ln3}{0.07}\)

\(t = \frac{1.09861228867}{0.07}\)

\(t = 15.69\)

\(t = 15.7\)

Hence, the time is approximately 15.7 years

Answer:

Hence, the proportion of workers is younger than \(35\) years old is \(0.3481\)

Step-by-step explanation:

(a)

(b)

Younger workers than \(35\) years

     \(P=\frac{<35}{\text{sum of function}}\)

\(\Rightarrow P=\frac{4794+13273+30789}{140335}\)

\(\Rightarrow P=\frac{48856}{140335}\)

\(\Rightarrow P=0.3481\)

The probability that you win is 6%, and the two choices are dependent events option (B) is correct.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

It is given that:

A standard deck of playing cards contains 52 total cards, 13 of which are "spades".

The probability of the first draw:

Probability = favorable outcomes/total outcomes

First draw: 1/4

For the second draw:

Second draw = 12/51

The probability that you win = (1/4)(12/51) = 3/51

In percent:

= (3/51)x100

= 5.88 = 6%

Thus, the probability that you win is 6%, and the two choices are dependent on events option (B) is correct.

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The total volume of the composite figure is; 381 m³

The formula for volume of a prism is;

V = Bh

where;

B is area of triangular base

h is height of prism

Thus;

V = (¹/₂ * 3 * 5) * 6

V = 45 m³

Volume of bottom cuboid is given by the formula;

V = Length * width * height

Thus;

V = 16 * 7 * 3

V = 336 m³

Total volume of composite figure = 45 m³ + 336 m³

Total volume of composite figure = 381 m³

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Answer:

x = -8

Step-by-step explanation:

When h(x) = 48, you can simply just plug it back into the first equation. Don't let the h(x) confuse you!

Think of it like saying y = -4x + 16, y = 48.

48 = - 4x + 16

32 = - 4x

8 = -x

Divide by -1 both sides.

-8 = x

Answer:

Hello! answer: 90

Step-by-step explanation:

I split the trapezoid into 2 then did base × height ÷ by 2 cause the way I split it it made 2 triangles

10 × 12 = 120 10 × 6 = 60 120 + 60 = 180 180 ÷ 2 = 90 therefore 90 is our area Hope that HELPS!

Answer:

2.200 = 2.2 = 2.20 = 2.2000 = 2.20000...I could go on...

Step-by-step explanation:

The number of different choices of eleven questions that a student can make on an exam with sixteen questions is 4,096.

This number can be calculated by the combination formula. The combination formula is used to calculate the number of combinations of a certain size that can be made from a larger set. In this case, the larger set is sixteen questions and the smaller set is eleven questions. The combination formula, written as C (n,r) is equal to n! / (r! (n-r)!), where n is the size of the larger set and r is the size of the smaller set. Applying this formula to the problem at hand, 16! / (11! (16-11)!), yields 4,096.

There are sixteen cards, and eleven of them must be chosen, so the number of different choices for eleven questions is 4,096.

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Answer:

The margin of error for the 94% confidence interval is 0.6154.

Step-by-step explanation:

The (1 - α)% confidence interval for population mean is:

\(CI=\bar x\pm z_{\alpha/2}\cdot\frac{\sigma}{\sqrt{n}}\)

The margin of error of this interval is:

\(MOE=z_{\alpha/2}\cdot\frac{\sigma}{\sqrt{n}}\)

The critical value of z for 94% confidence level is, z = 1.88.

Compute the margin of error for the 94% confidence interval as follows:

\(MOE=z_{\alpha/2}\cdot\frac{\sigma}{\sqrt{n}}\)

          \(=1.88\times\frac{3}{\sqrt{84}}\\\\=0.6154\)

Thus, the margin of error for the 94% confidence interval is 0.6154.

Answer:

Shoes with discount = $17

Necklace = Price * 0.85

Step-by-step explanation:

-If the tennis shoes store sells other things than shoes-

Shoes = $20.00

Discount = 15%

*Price expressed as a percentage*

Price without discount = 100%

Price after discount = 100% - 15%

Price after discount = 85%

*Normal price*

Price without discount = 20

Price after discount = 20 * 0.85

Price after discount = 17

Answer:

x=2

Step-by-step explanation:

10 - (x + 3) = 5

To solve for x, we can start by simplifying the left side of the equation:

10 - (x + 3) = 5

10 - x - 3 = 5

7 - x = 5

Next, we can isolate x on one side of the equation by subtracting 7 from both sides:

7 - x = 5

7 - x - 7 = 5 - 7

-x = -2

Finally, we can solve for x by dividing both sides of the equation by -1:

-x = -2

x = 2

Therefore, the solution to the equation is x = 2.

The surface areas for each figures are:

1. The surface area of the cuboid is:

Top and bottom: 2(10 ft x 4 ft) = 80 ft²

Front and back: 2(10 ft x 5 ft) = 100 ft²

Sides: 2(4 ft x 5 ft) = 40 ft²

Total surface area = 80 + 100 + 40 = 220 ft²

2. The surface area of the cuboid is:

Top and bottom: 2(18 cm x 5 cm) = 180 cm²

Front and back: 2(18 cm x 5 cm) = 180 cm²

Sides: 2(5 cm x 5 cm) = 50 cm²

Total surface area = 180 + 180 + 50 = 410 cm²

3. The surface area of the prism is:

Top and bottom: 2(5 cm x 14 cm) = 140 cm²

Front and back: 2(5 cm x 12 cm) = 120 cm²

Sides: 2(12 cm x 14 cm) = 336 cm²

Total surface area = 140 + 120 + 336 = 596 cm²

4. The surface area of the stacked cuboids is:

Top and bottom of first cuboid: 2(6 cm x 7 cm) = 84 cm²

Front and back of first cuboid: 2(6 cm x 2 cm) = 12 cm²

Sides of first cuboid: 2(7 cm x 2 cm) = 28 cm²

Front and back of second cuboid: 2(7 cm x 2 cm) = 28 cm²

Sides of second cuboid: 2(2 cm x 4 cm) = 8 cm²

Front and back of third cuboid: 2(2 cm x 10 cm) = 40 cm²

Sides of third cuboid: 2(10 cm x 8 cm) = 160 cm²

Total surface area = 84 + 12 + 28 + 28 + 8 + 40 + 160 = 360 cm²

5. The surface area of the cylinder is:

Top and bottom: 2π(6 mm)² = 72π mm²

Side: 2π(6 mm)(5 mm) = 60π mm²

Total surface area = 72π + 60π = 132π mm²

6. The surface area of the cylinder is:

Top and bottom: 2π(1 ft)² = 2π ft²

Side: 2π(1 ft)(10 ft) = 20π ft²

Total surface area = 2π + 20π = 22π ft²

7. The surface area of the cylinder stacked on a cube is:

Top and bottom of cylinder: 2π(5 m)² = 50π m²

Side of cylinder: 2π(5 m)(8 m) = 80π m²

Surface area of cube: 6(10 m x 13 m) = 780 m²

Total surface area = 50π + 80π + 780 = (130π + 780) m²

8. The surface area of the cylinder is:

Top and bottom: 2π(9 in)² = 162π in²

Side: 2π(9 in)(4 in) = 72π in²

Therefore, the total surface area of the cylinder is:

2(162π in²) + 72π in² = 396π in²

So the surface area of the cylinder is 396π square inches.

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Image transcribed:

Find the surface area of each figure.

10 ft

18 cm

5 cm

4 ft

5 ft

3.

4.

6 cm

7 cm

2 cm

5 cm

12 cm

14 cm

4 cm

10 cm

8 cm

Find the surface area of each cylinder. Leave your answer in terms of π.

5.

6 mm

6.

1 ft

5 mm

10 ft

7.

5 m

8.

4 in.

8 m

10 m

9 in.

13 m

11 m

247

Journal and Practice Workbook

Geometry

Using Pascal's triangle and the difference quotient formula, we expand (x + h)^2 and simplify the expression to (2hx + h^2) / h. As h approaches 0, the term h becomes negligible, and we are left with 2x, which represents the derivative of x^2.

To use Pascal's triangle to find x^2 using the difference quotient formula, we can follow these steps:

1. Write the second row of Pascal's triangle: 1, 1.

2. Use the coefficients in the row as the binomial coefficients for (x + h)^2. In this case, we have (1x + 1h)^2.

3. Expand (x + h)^2 using the binomial theorem: x^2 + 2hx + h^2.

4. Apply the difference quotient formula: f(x + h) - f(x) / h.

5. Substitute the expanded expression into the formula: [(x + h)^2 - x^2] / h.

6. Simplify the numerator: (x^2 + 2hx + h^2 - x^2) / h.

7. Cancel out the x^2 terms in the numerator: (2hx + h^2) / h.

8. Divide both terms in the numerator by h: 2x + h.

9. As h approaches 0, the term h becomes negligible, and we are left with the derivative of x^2, which is 2x.

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Answer:

---------------------------

There are two triangular faces with base of 16 cm and height of 15 cm and three rectangular faces.

Find the sum of areas of all five faces:

The vocabulary term for segment a is an apothem.

The area of this polygon is 41.6 yd².

In Mathematics and Geometry, the area of a regular polygon can be calculated by using this formula:

Area of regular polygon = (n × s × a)/2

Where:

By substituting the given parameters into the formula for the area of a regular polygon, we have the following:

Area of regular polygon = (6 × 4 × 2√3)/2

Area of regular polygon = (24 × 2√3)/2

Area of regular polygon = 83.1/2

Area of regular polygon = 41.6 yd².

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