Type the correct answer in the box.
✔
b
b
In the figure, a square is inside another bigger square.
If a=4 units and b=3 units, the length of the diagonal of the outside square rounded to the nearest tenth is
Inside square rounded to the nearest tenth is
units.
units and the length of the diagonal of the

I'm going to assume you start with

[tex]\dfrac{6^2 - 4 (3 - \sqrt{25})^2}{|4 - 8|}[/tex]

Let's simplify some pieces of this:

[tex]6^2 = 6\times6 = 36[/tex]

[tex]\sqrt{25} = \sqrt{5^2} = 5[/tex]

[tex](3 - \sqrt{25})^2 = (3 - 5)^2 = (-2)^2 = (-2)\times(-2) = 4[/tex]

[tex]|4 - 8| = |-4| = 4[/tex]

So as a first step we can reduce this to

[tex]\dfrac{6^2 - 4 (3 - \sqrt{25})^2}{|4 - 8|} = \dfrac{36-4\times4}4[/tex]

Now,

[tex]36 = 9\times4[/tex]

so every term contains a factor of 4 that we can cancel:

[tex]\dfrac{36-4\times4}4 = \dfrac{9\times4-4\times4}4 = \dfrac{9-4}1 = 9-4 = \boxed{5}[/tex]

as expected.

The probability that a divisor of 2 or 9 is chosen when the spinner is spun once is 2/3.

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

P(2 or divisor of 9) = section that has a divisor of 2/ total number of sections + section that has a divisor of 2/ total number of sections

1/3 + 1/ 3 = 2/3

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Using trigonometric identities, it is found that the exact value of the secant of the angle is given by:

c. [tex]\sec{\theta} = - \sqrt{5}[/tex]

According to the following identity:

[tex]\sec^2{\theta} = 1 + \tan^2{\theta}[/tex]

The tangent is the inverse of the cotangent, hence in this problem, we have that:

[tex]\tan{\theta} = -2[/tex]

Then, the secant is given as follows:

[tex]\sec^2{\theta} = 1 + (-2)^2[/tex]

[tex]\sec^2{\theta} = 5[/tex]

[tex]\sec{\theta} = \pm \sqrt{5}[/tex]

The angle is in the second quadrant, where the cosine is negative, hence the secant also is and option c is correct, that is:

c. [tex]\sec{\theta} = - \sqrt{5}[/tex]

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Questions:- perimeter

Explanation:- one side is 10 cm another opposite to it

6+x= 10

x= 4 units

so now perimeter

[tex]8 + 8 + 10 + 8 + 4 + 10 \\ 16 + 8 + 4 + 20 \\ 20 + 8 + 20 \\ 40 + 8 = 48 \: units[/tex]

(50, 22.5) is the solution of the system of equations, therefore, the true statement would be: Both plans cost the same when 50 texts are sent.

A solution to the system of linear equations is the point of intersection where both line of each equation meet.

The solution to the system of linear equations given in the graph attached below is (50, 22.5).

(50, 22.5) implies that both plans will cost the total amount when 50 text are sent.

The true statement using the graph would be: Both plans cost the same when 50 texts are sent.

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Answer:

Both plans cost the same when 22 texts are sent

Step-by-step explanation:

on edge

The correct answer is option C.Which is the inequalities that show the graphs are y < x and y > 2.

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

The inequality which is shown in the figure is y < x and y > 2.We can see in the graph when you plot y > 2 then it will cover all the values greater than 2 in the graph.

Similarly, if we plot the inequality y < x on the graph it will cover all the values of y which are less than x and intersect at the point ( 2, 2).

Therefore the correct answer is option C.Which is the inequalities that show the graphs are y < x and y > 2. The graph is attached with the answer below.

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Answer:

4

Step-by-step explanation:

The mode is most common, so it is 4.

The transformation of A is A' = (8, -3)

From the graph, we have:

A = (3,1)

The scale factor and the center of dilation are given as:

k = 2

(a,b) = (-2,1)

The rule of reflection across the axis is:

(x,y) ⇒ (x,-y)

So, we have:

A' = (3,-1)

The rule of dilation is represented as:

(x,y) ⇒ (k(x - a) + a, k(y - b) + b)

So, we have:

A' = (2(3 + 2) - 2, 2(-1 - 1) + 1)

Evaluate

A' = (8, -3)

Hence, the transformation of A is A' = (8, -3)

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Answer:

No

Step-by-step explanation:

You should only use t procedures when the sample sizes are less than 30, as that is when the Central Limit Theorem kicks in.

Essentially, t procedures are good for small samples while z procedures are better for larger samples.

The true statements for this graph are:

B. The domain is the set of all real numbers.

D. The range is the set of all real numbers greater than or equal to zero.

A domain can be defined as the set of all real numbers for which a particular function is defined. For this graph, the vertex of the parabola is (1, 0) and as such, the equation will be given by:

y = (x - h)² + k

y = (x - 2)² + 0

y = x² -4x + 4

Therefore, the graph's domain include a set of all real numbers.

A range refers to a set of all real numbers that connects with the elements of a domain. For this graph, we can observe that only real numbers greater than or equal to zero (0) are connected to the values on the x-axis of the domain.

In conclusion, we can logically deduce that the true statements for this graph are:

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Answer:

9. 20,001

10. 100,001

11. 4,999

12. 999,999

Step-by-step explanation:

64

x=154(vertically opposite angle)

d =p

then mpn =154-90 = 64

angle epm is straight angle

The value of x and y is (5,2)

We have given that,

4x + 2y = 9 ........(1)

x - 2y = 1.......(2)

We have to solve the simultaneous equation

A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

adding equations 1 and 2 so we get,

4x + 2y = 9

x - 2y = 1

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

5x-0y=10

[tex]5x=10\\x=10/2\\x=5[/tex]

Use the value of x in equation 2 so we get,

[tex]5-2y=1[/tex]

[tex]-2y=1-5[/tex]

[tex]-2y=-4[/tex]

[tex]y=-4/-2[/tex]

[tex]y=2[/tex]

Therefore the value of x and y is (5,2)

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Answer:

a

2

​

=9a+b

2

​

Step-by-step explanation:

Answer:

Step-by-step explanation:

(a²+b²)²=(a²-b²)²+4a²b²=(a²-b²)²+4(ab)²=9²+4×3²=9²(1+4)

a²+b²=3√5

(a+b)²=a²+b²=2ab=3√5+2(3)=3(2+√5)

a+b=√3√(2+√5)

The following way is a way which can not be used to represent the solution of 5(x + 2) ≥ 7x + 2(x - 1) is "A number line with a closed circle on 3 and shading to the right".

5(x + 2) ≥ 7x + 2(x - 1)

5x + 10 ≥ 7x + 2x - 2

5x + 10 ≥ 9x - 2

5x - 9x ≥ -2 - 10

-4x ≥ - 12

x ≤ -12/-4

x ≤ 3

Therefore, the correct answer is "A number line with a closed circle on 3 and shading to the right".

The complete question:

Which of the following is not a way to represent the solution of the inequality 5(x + 2) greater than or equal to 7x + 2(x − 1)? . A number line with a closed circle on 3 and shading to the right. . A number line with a closed circle on 3 and shading to the left. . 3 greater than or equal to x . x less than or greater to 3

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The solution to the equation one-third (x + 9) = negative 12 is  x = -45

The equation is given as:

one-third (x + 9) = negative 12

Rewrite properly as:

1/3 (x + 9) = -12

Multiply both sides by 3

x + 9 = -36

Subtract 9 from both sides

x = -45

Hence, the solution to the equation one-third (x + 9) = negative 12 is  x = -45

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Using proportions, it is found that the ordered pair that represents the location of the layover is given by: (2.75, 1.5).

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, the flight distance is partitioned in a ratio of 3:1, hence:

L - Nv = 3/4(Ny - Nv).

This ratio is applied for both coordinates, hence, for the x-coordinate:

[tex]x + 4 = \frac{3}/{4}(5 + 4)[/tex]

[tex]x = \frac{27}{4} - \frac{16}{4}[/tex]

[tex]x = \frac{11}{4}[/tex]

x = 2.75.

For the y-coordinate:

[tex]y = \frac{3}/{4}(2 - 0)[/tex]

[tex]y = \frac{6}{4}[/tex]

x = 1.5.

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Neither of these statements are true.

x/∞ = 0 is a nonsensical statement. It's more accurate to say

[tex]\displaystyle \lim_{y\to\infty} \frac xy = 0[/tex]

for any real number x. The important bit is that y is an arbitrarily large number as it approaches ∞. To convince yourself that this expression approaches 0 as y gets larger and larger, try fixing x and pick any increasing sequence of numbers for y.

For example, let x = 1 and take y from the sequence of increasing powers of 10, {10, 10², 10³, …}, which grows without bound. Then

1/10 = 0.1

1/10² = 0.01

1/10³ = 0.001

and so on. Naturally, the larger the power of 10 and thus the larger y gets, the closer x/y gets to 0.

Similarly, x/0 is nonsense, but the "limit-ized" version of the claim is also incorrect. For any fixed real number x, the limit

[tex]\displaystyle \lim_{y\to0} \frac xy[/tex]

does not exist. Suppose x > 0. If y approaches 0 from above, then y > 0 and x/y > 0 and

[tex]\displaystyle \lim_{y\to0^+} \frac xy = +\infty[/tex]

which you can convince yourself is true by reversing the example from before. Let x = 1 and take y from the sequence of decreasing powers of 10, {1/10, 1/10², 1/10³, …}, which converges to 0. Then

1/(1/10) = 10

1/(1/10²) = 100

1/(1/10³) = 1000

and so on. The smaller y gets (while still being positive), the larger x/y becomes.

But now suppose y < 0 and that y approaches 0 from below. Then x/y < 0, and

[tex]\displaystyle \lim_{y\to0^-} \frac xy = -\infty[/tex]

The limits from either side do not match, so the limit as y approaches 0 does not exist.

You can use the same reasoning for when x < 0.

The case of x = 0 is special, however. Since y is approaching 0, it's never actually the case that y = 0. 1/y is then some non-zero real number, and multiplying it by x = 0 makes x/y = 0. Then

[tex]\displaystyle \lim_{y\to0} \frac 0y = 0[/tex]

So in general,

[tex]\displaystyle \lim_{y\to0} \frac xy = \begin{cases}0 & \text{if }x = 0 \\ \text{does not exist} & \text{otherwise}\end{cases}[/tex]

Answer:

I think it is c

Step-by-step explanation:

I graphed it

Reason:

The friend should have multiplied the exponents.

This is what the steps should look like:

[tex](r^6)^4 = r^{6*4}\\\mbox{ \ \ \ \ \ \ } =r^{24}[/tex]

The reason for the multiplication is because we have four copies of [tex]r^4[/tex] added together. Repeated addition can be shortened to multiplication.

In other words,

[tex](r^6)^4 = (r^6)*(r^6)*(r^6)*(r^6) = r^{6+6+6+6} = r^{6*4} = r^{24}[/tex]

Answer:

229

Step-by-step explanation:

(my work for the problem is in the photo I attached)

(I also wrote this step-by-step in the photo because I can explain things better as I do them)

This will be a little bit confusing without me writing out the numbers, so mainly this is if you can't read my handwriting

  -3       + 8         =      5    ;  5       + 8    =     13

(1st term)                   (2nd term)            (3rd term)

Instead of adding 8 repeatedly (repeated addition), we can use multiplication.

To get the 3rd term in this sequence, we had to add 8 twice, which could also be done by multiplying 8 twice (8 x 2)

13 + 8 = 21

         (4th term)

to get the 4th term, we added 8 three times (or, 8 x 3)

So, if we are looking for the 30th term in a sequence, we will have to add 8, 29 times (8 x 29) to our original term.

8 x 29 = 232

-3 + 232 = 229

This means that the 30th term of the sequence will be 229.

Answer:

a) Prepare a frequency table for the data

Step-by-step explanation:

Answer:

52 weeks are there in a year

Step-by-step explanation:

365/7

The function C(g) that represents the total daily cost, C, of producing x golf clubs is C = 1671 + 60g

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

We have:

A plant can manufacture 50 golf clubs per day at a total daily cost of $4671 and 70 golf clubs per day for a total cost of $5871.

Let's suppose x is the fixed cost and y is the variable cost.

4671 = 50y + x …(1)

5871 = 70y + x …(2)

1200 = 20y

y = 60

x = 1671

Total cost:

C(g) = 1671 + 60g

g is the number of golf per day.

Slope = 60

y- Intercept = 1671 (from the graph)

Thus, the function C(g) that represents the total daily cost, C, of producing x golf clubs is C = 1671 + 60g

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The interval at which the function decrease is (-2,0) and the number of tulip bulb in the garden is 12.8

From the table, we can see that the value of the function decreases from 12 to 3 and finally to 0, when the values of x increase from -2 to 0

Hence, the interval at which the function decrease is (-2,0)

The square garden has a side length x.

So, the area (A) of the garden is:

A = x²

From the question, we understand that 5 tulip bulbs are to be planted per unit area.

This means that the number of bulb in the garden is:

n = 1/5 * x²

Evaluate

n = 0.2x²

When the side length of the garden is 8, we have:

n = 0.2 * 8²

Evaluate

n = 12.8

Hence, the number of tulip bulb in the garden is 12.8

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We simplify the expression -2√15(-8 + 10√15) = 150 + 16√15

To answer the question, we need to know what surds are

Surds are square roots of positive integers.

Since we have  -2√15(-8 + 10√15), we simplify the expression

So, -2√15(-8 + 10√15) = -2√15 × (-8) + 10√15 × √15 (expanding the bracket)

= -2× (-8) × √15 + 10 × √(15 × 15)

=  16 × √15 + 10 × √15²

=  16 × √15 + 10 × 15

=  16√15 + 150

=  150 + 16√15

So, we simplify the expression -2√15(-8 + 10√15) = 150 + 16√15

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The table shows that it is more likely to wait at red during daytime by 2.92%.

Day

Green = 2 min

Red = 3 min

Yellow = 20 sec = 0.333 min

Total day cycle time= 5.33 min

Night

Green = 3 min

Red = 4 min

Yellow = 30 sec = 0.5 min

Total night cycle time= 7.5 min

Pday= 3 min/5.33 min= 0.5625

Pnight= 4 min/7.5 min= 0.5333

Pdifference= 0.02917 = 2.92%

Therefore it is more likely to wait at red during the daytime by 2.92%.

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