Which of the following is a rational number?
square root 97square root 98, square root 99, square root 100

square root 97
square root 98
square root 99
square root 100

Part A: Find a rational number that is between 5.2 and 5.5. Explain why it is rational. (2 points)

Part B: Find an irrational number that is between 5.2 and 5.5. Explain why it is irrational. Include the decimal approximation of the irrational number to the nearest hundredth. (3 points)

Answer:

x = 2

Step-by-step explanation:

Given 2 intersecting chords in a circle, then

The product of the parts of one chord is equal to the product of the parts of the other chord , that is

12x = 6(x + 2) = 6x + 12 ( subtract 6x from both sides )

6x = 12 ( divide both sides by 6 )

x = 2

Answer:

[tex]x=2[/tex]

Step-by-step explanation:

The term 'secant' refers to a line segment that intersects a circle in two places. When two secants intersect inside a circle, one can use the product of lengths theory to form ratios between the parts of intersection between the secants. This ratio can be described as the following, let ([tex]secant_A[/tex]) and ([tex]secant_B[/tex]) represent the two secants in the circle. Part (1) and (2) will refer to the two parts formed after the intersection of the secants.

[tex](secant_A_1)(secant_A_2)=(secant_B_1)(secant_B_2)[/tex]

Use this formula in the given situation, substitute the given values in and solve for the unknown,

[tex](secant_A_1)(secant_A_2)=(secant_B_1)(secant_B_2)[/tex]

[tex](6)(x+2)=(12)(x)[/tex]

Simplify,

[tex](6)(x+2)=(12)(x)[/tex]

[tex]6x+12=12x[/tex]

[tex]12=6x[/tex]

[tex]x=2[/tex]

Answer:

CAUTION HERE !!!!!

if you suggested edits are accurate the solution would be...

[tex]\frac{3p^2 - 5p+9}{6p^2}[/tex]

that is not one of your choices, but is is almost identical to choice "D"

which is different by [tex]6px^2[/tex]  vs   [tex]6p^2[/tex]

which i think is your comment ????  

Step-by-step explanation:

Answer:

Step-by-step explanation:

Product means multiplication (×)

Let

The unknown number = m

product of five and a number = 5 × m

= 5m

product of five and a number is divided by 8, the result is 12

5m / 8 = 12

Cross product

5m = 8 * 12

5m = 96

m = 96/5

= 19.2

m = 19.2

Therefore,

The unknown number = m = 19.2

Check:

5m / 8 = 12

5(19.2) / 8 = 12

96/8 = 12

a) (0, 1)

The graph will cross the y-axis at the y-intercept. We can easily find this value by putting the given equation into slope-intercept form (y = mx + b).

y - 4x = 1

y = 4x + 1

The y-intercept is (0,1).

b) k = 6.5

We first need to find c, or the y-intercept. This is given to us on the graph, where the line crosses the y-axis at (0,-3).

Therefore, our line is y = 2x - 3.

Then, we can plug in 10 for y from the point (k,10) and solve for k (which is the same as x).

10 = 2x - 3

13 = 2x

x = 6.5

Hope this helps!

Answer: (3.5,-2)

Step-by-step explanation:

To solve this problem, all we have to do is plug in y=-2 into either equations from step one to find the coordinate. To make sure we have the right x-coordinate, let's plug in y for both equations.

4x-7y=28        [plug in y=-2]

4x-7(-2)=28    [multiply]

4x+14=28       [subtract both sides by 14]

4x=14              [divide both sides by 4]

x=3.5

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

6x-5y=31        [plug in y=-2]

6x-5(-2)=31    [multiply]

6x+10=31       [subtract both sides by 10]

6x=21             [divide both sides by 6]

x=3.5

Now, we know the solution to the system is (3.5,-2).

Answer:

(3.5, -2)

Step-by-step explanation:

Hi there!

We are given a system of equations, and the value for y is already solved (y=-2)

We want to find the value of x

To do that, substitute -2 as y into either one of the equations in the system (the system has the equations 4x-7y=28 and 6x-5y=31) and solve for x

Let's use 4x-7y=28, although picking 6x-5y=31 is completely fine

Substitute -2 as y into the equation

4x-7(-2)=28

Multiply

4x+14=28

Subtract 14 from both sides

4x=14

Divide both sides by 4 and simplify

x=7/2, or 3.5

We found the value of x in the system

Substitute the values of x and y into a point form (x, y)

The solution is (3.5, -2)

Hope this helps!

Answer:

Step-by-step explanation:

Mistake in Line 2 : Was in the determining the values for a ,b,c

Mistake in Line 4 : Not taking the square roots of both sides.

Step-by-step explanation:

[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]

First Mistake : Line 2

[tex]a = x \\ b = 6 \\ c = 10[/tex]

Second Mistake : Line 4

[tex]136 = {x}^{2} \\ not \\ 136 = x[/tex]

Correct Solution :

[tex] {x}^{2} + {6}^{2} = {10}^{2} \\ {x}^{2} = {10}^{2} - {6}^{2} \\ {x}^{2} = 100 - 36 \\ [/tex]

[tex] {x}^{2} = 64 \\ \sqrt{ {x}^{2} } = \sqrt{64} \\ x = 6[/tex]

Answer:

19: 5

Step-by-step explanation:

Total fruit  is 5+10+4 = 19

fruit: pears

19: 5

Answer:

19:5

Step-by-step explanation:

5+10+4= 19

Pears= 5

yes it is possible, although it doesn't always occur.

Your answer is: True

Answer:  Choice B

[tex]\text{As } x \to \infty, \ f(x) \to \infty[/tex]  and [tex]\text{As } x \to -\infty, \ f(x) \to \infty[/tex]

==========================================================

Explanation:

Assuming that the only roots are x = -3 and x = 2, as shown by the table, then notice how f(x) > 0 at the very right hand side of the table. This indicates that f(x) will remain positive for this tail end. If f(x) were to become negative, then there would have to be another root somewhere beyond x = 2 (but that contradicts the assumption made at the top of the paragraph).

This allows us to say [tex]\text{As } x \to \infty, \ f(x) \to \infty[/tex]

In other words, as x gets bigger, so does y. Both head to positive infinity together. We can informally describe this end behavior as "rises to the right".

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

For the left side of the table, we also have positive f(x) values to the left of the root. So we see that f(x) > 0 as x heads off in the negative infinity direction.

We would then say [tex]\text{As } x \to -\infty, \ f(x) \to \infty[/tex]

Regardless of what direction x goes (positive or negative infinity), the y = f(x) values are heading off to positive infinity. Informally, we could say "rises to the left".

Both endpoints rise together to positive infinity. Think of a parabolic curve that opens upward as one example.

All of this points to choice B as our final answer. Choice B can be rephrased as [tex]\text{As } x \to \infty \text{ or } x \to -\infty, \text{ then } \ f(x) \to \infty[/tex]

Answer:rrrrrrrr

rrrrrrrrrr

Step-by-step explanation:

rrrrrrrrrrrrrrr

The equation for the scenario is x + x+1 + x+2 = 117 and largest number is 40.

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.

Let x be the first number:

The other numbers are:

x+1, x+2

The sum of three consecutive numbers is 117:

x + x+1 + x+2 = 117

3x + 3 = 117

3x = 114

x = 38

x+ 1 = 38+1 = 39

x+2 = 38+2 = 40

Thus, the equation for the scenario is x + x+1 + x+2 = 117 and largest number is 40.

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hope it helps✓✓✓✓✓✓✓✓✓

Answer: A for 10

Step-by-step explanation:

Answer:

write question in short form

Step-by-step explanation:

Answer: x=4

Step-by-step explanation:

Concept:

There are three ways to solve the system of equations

Here, we would use substitution because we have two same variables.

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

Solve:

Given

y = -2x + 8

y = x - 4

Substitute

-2x + 8 = x - 4

Add 4 on both sides

-2x + 8 + 4 = x - 4 + 4

-2x + 12 = x

Add 2x on both sides

-2x + 12 + 2x = x + 2x

12 = 3x

Divide 3 on both sides

12 / 3 = 3x / 3

x = 4

Hope this helps!! :)

Please let me know if you have any questions

Answer:

259 ft.

Step-by-step explanation:

A triangle is a polygon with three sides and three angles. Types of triangles are isosceles. scalene, equilateral, acute, obtuse and right angled triangle.

A right angled triangle is a triangle in which one of the angles is 90 degrees. Trigonometric ratios show the relationship between the angles of a right angle triangle and its sides.

Let h represent the height of the house above water, hence using trigonometric ratios:

tan(26) = h / 531

h = 531 * tan(26)

h = 259 ft.

Answer:

Step-by-step explanation:

(y2-y1)/(x2-x1)

Answer:  -6 only (choice B)

This is because the point (0,-6) is on the blue line. This is the y intercept.

Choice C would be true if you wanted to solve f(x) = 0, instead of f(0) itself.

Answer:

-6

Step-by-step explanation:

f(0) means what is the output when the input is 0

x=0 y= -6

Answer:

obtuse angle

Step-by-step explanation:

Answer:

obtuse angle

Step-by-step explanation:

Answer:

Hello

Answer B: 32.58°

Step-by-step explanation:

[tex]sin (\widehat{A})=\dfrac{35}{65} \\\\\widehat{A}=arcsin(\dfrac{7}{13} )=32.5789...^o[/tex]

Answer:

You didn't give me any specifics about what you want me to solve or do.

Answer:

A

Step-by-step explanation:

Subustion works because we already know two things are congruent so we just "substitute the angles into for the variables.

We know Angle A equal Angle B so we can replace angle A into m of Angle B and set it equal to Angle B variables.

We dont do know algebra operation to solve for the variable so we B and C aren't the option.

We already know two things are equal so we dont need to use transitive.

The reason that best supports statement 5 in the given proof is option A. Substitution.

The process of substituting an algebraic letter for its value is known as substitution.

Take the equation 8 - 4x as an example. Depending on what number x is, this can take a wide range of values. For example, if we are told x = 3 then we can substitute 3 in place of x.

Let's take an example,

x ÷ 2 =  (5x - 54)

x ÷ 2 × 2 = 2 × (5x - 54)

x = 10x - 108

then by multiplication property of equality, we can multiply 2 on both sides and rewrite the equation,

x = 10x - 108

Let's take another example,

x - 2 = 2

then by addition property of equality, we can add 2 on both sides and rewrite the equation,

x - 2 + 2 = 2 + 2

x = 4

In math, if A=B and B=C, then A=C

For example, if A is 5 then by the transitive property we can conclude that B and C are also equal to 5.

Two geometric figures are said to be congruent or to be in a congruence relation if they can be superposed on top of each other and remain the same throughout.

In the given question -

Finally, in the fifth reason, we can conclude that it is substitution because by the second reason m of ∠A is congruent to m of ∠B. So, if we remember the substitution we can assign the value of m∠A to the value of m∠B because both are congruent by the second reason.

Therefore, the reason that best supports statement 5 in the given proof is Substitution.

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Answer:

Radius

Step-by-step explanation:

Radius is multiplied by 2pi

Answer:

Its either 2(A+7=5) or 2(A+7) =5

Step-by-step explanation:

You have 5 digits.Youdonot say if duplication is allowed. I will assume not

For the first digit you have 5 choices. One of the 5 digits is gone.

You now have 4 digits to choose from. You pick one. Now you have but 3 left.

The total answer if 5*4*3*2*1 = 120

Answer:

22.6 feet

SOH - CAH - TOA

you are working with "o" opposite , and "a" adjacent.

O/A is TOA - tan()

tan(37) = x/30

x = 30* tan(37) = 22.6

Step-by-step explanation:

Given:

Radius of circle is 13 cm

Height of triangle is 5 cm

To find:

Value of 'a' and 'b'

Steps:

To find value of 'a', we will use Pythagoras theorem as the triangle is a right angle triangle,

A² + B² = C²

[tex]a^{2} + 5^{2} = 13^{2}[/tex]

[tex]a^{2} + 25 = 169[/tex]

[tex]a^{2} = 169 - 25[/tex]

[tex]a^{2} = 144[/tex]

[tex]\sqrt{a^{2}}=\sqrt{144}[/tex]

[tex]a = 12[/tex]

Now to find the value of 'b', i will use law of cosine,

[tex]c=\sqrt{a^{2}+b^{2}-2ab(cos\beta ) }[/tex]

[tex]12 = \sqrt{13^{2}+5^{2}-2(5)(13)(cos\beta )}\\12=\sqrt{169 + 25-130(cos\beta )}\\12=\sqrt{194-130(cos\beta )}\\144 = 194 - 130(cos\beta )\\50 = 130(cos\beta )\\cos\beta = 0.3846\\\beta = cos^{-1}(0.3846)\\\beta = 67.38[/tex]

Therefore, the values of 'a' and 'b' is 12 and 67.38 respectively

Happy to help :)

If u need any help feel free to ask

The total surface area of the given prism is 336 cm².

Given that, a=3.44 cm, b=5 cm and h=10 cm.

The surface area of a pentagonal prism = 5ab + 5bh square units.

a = apothem length of the pentagonal prism.

b = base length of the pentagonal prism.

h = height of the pentagonal prism.

Now, the surface area of a pentagonal prism

=5×3.44×5+5×5×10= 336 cm²

Therefore, the total surface area of the given prism is 336 cm².

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Answer:

y=x-5

Step-by-step explanation:

Hi there!

We want to write an equation of the line that passes through the points (8,3) and (0,-5) in slope-intercept form

Slope-intercept form is given as y=mx+b, where m is the slope, and b is the y intercept

So let's first find the slope of the line

The formula for the slope calculated from two points is [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points

We have everything needed to find the slope, but let's label the values of the points to avoid any confusion

[tex]x_1=8\\y_1=3\\x_2=0\\y_2=-5[/tex]

Now substitute into the formula

m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

m=[tex]\frac{-5-3}{0-8}[/tex]

Subtract

m=[tex]\frac{-8}{-8}[/tex]

Simplify

m=1

The slope is 1

Here is the equation of the line so far:

y=1x+b (can also be written as y=x+b)

We need to find b

The equation passes through both (8, 3) and (0, -5), so we can substitute the values of either one of them as x and y to solve for b

Let's take (8, 3) for example

Substitute 8 as x and 3 as y

3=1(8)+b

Multiply

3=8+b

Subtract 8 from both sides

-5=b

Substitute -5 as b into the equation

y=x-5

Hope this helps!

Answer:

a(y_2)_b(y_2) =a_b)(y_2(