A side of a square is 8 3/2  inches. Using the area formula A = s2, determine the area of the square.

Answer:

Step-by-step explanation:

The formula of a volume of a prism:

[tex]V=BH[/tex]

B - base area

H - height

In the base we have the right triangle.

The formula of an area of a righ triangle

[tex]A=\dfrac{ab}{2}[/tex]

a, b - legs

We have a = 6.2m and b = 11m. Substitute:

[tex]B=\dfrac{(6.2)(11)}{2}=34.1\ m^2[/tex]

The height H = 9 m.

Substitute to the formula of a volume:

[tex]V=(34.1)(9)=306.9\ m^3[/tex]

Answer:

a) The probability that the player wins is 2/5 or 0.4

b) Yes, the probability changes if the two numbers are multiplied

Step-by-step explanation:

* Lets explain how to solve the problem

- There are five slips each one has one number 4 , 6 , 7 , 8 , 9

- All numbers are used

- The first player reaches into the box and draws two slips and adds

  the two numbers

- If the sum is even, the player wins

- If the sum is odd, the player loses

* To find the probability of win we must to find all the even sum

∵ The player will chose two slips

∴ There are 5 choices of the 1st number and 4 choices for the

   2nd number

∴ The total choices for the two numbers = 5 × 4 = 20

a)

- Lets find the sum of the two numbers

# The first number is 4

∵ 4 + 6 = 10 , 4 + 7 = 11 , 4 + 8 = 12 , 4 + 9 = 13

∴ There are 2 even sum

# The first number is 6

∵ 6 + 4 = 10 , 6 + 7 = 13 , 6 + 8 = 14 , 6 + 9 = 15

∴ There are 2 even sum

# The first number is 7

∵ 7 + 4 = 11 , 7 + 6 = 13 , 7 + 8 = 15 , 7 + 9 = 16

∴ There are 1 even sum

# The first number is 8

∵ 8 + 4 = 12 , 8 + 6 = 14 , 8 + 7 = 15 , 8 + 9 = 17

∴ There are 2 even sum

# The first number is 9

∵ 9 + 4 = 13 , 9 + 6 = 15 , 9 + 7 = 16 , 9 + 8 = 17

∴ There are 1 even sum

∴ The total of even sum = 2 + 2 + 1 + 2 + 1 = 8 even sum

- Probability = the number of ways of success ÷ the total number of

 possible outcomes

∵ The number of even sum = 8

∵ The total outcomes = 20

∴ P(even sum) = 8/20 = 2/5

* The probability that the player wins is 2/5 or 0.4

b)

- Lets find the product of the two numbers

# The first number is 4

∵ 4 × 6 = 24 , 4 × 7 = 28 , 4 × 8 = 32 , 4 × 9 = 36

∴ There are 4 even product

# The first number is 6

∵ 6 × 4 = 24 , 6 × 7 = 42 , 6 × 8 = 48 , 6 × 9 = 54

∴ There are 4 even product

# The first number is 7

∵ 7 × 4 = 28 , 7 × 6 = 42 , 7 × 8 = 56 , 7 × 9 = 63

∴ There are 3 even product

# The first number is 8

∵ 8 × 4 = 32 , 8 × 6 = 48 , 8 × 7 = 56 , 8 × 9 = 72

∴ There are 4 even product

# The first number is 9

∵ 9 × 4 = 36 , 9 × 6 = 54 , 9 × 7 = 63 , 9 × 8 = 72

∴ There are 3 even product

- Lets find the probability of the even product

∴ The total of even product = 4 + 4 + 3 + 4 + 3 = 18 even product

∵ The number of even product = 18

∵ The total outcomes = 20

∴ P(even sum) = 18/20 = 9/10

∴ The probability that the player wins is 9/10 or 0.9

* Yes, the probability changes if the two numbers are multiplied

Answer:

c.

Step-by-step explanation:

the most that can be factored out is -1.5,

-1.5 * w = -1.5w

-1.5 * -5 = 7.5

-1.5w + 7.5, so it's

-1.5(w-5)

Answer:

2x^2+3

Step-by-step explanation:

(3x^2 + 2x+4) - (x^2 +2x+1)

I'm going to rewrite this using distributive propery and without parenthesis:

3x^2 + 2x + 4 - x^2 - 2x - 1

Now I'm going to pair up any like terms by use of the commutative property.

3x^2 - x^2 + 2x - 2x + 4 - 1

Now simplify:

2x^2 + 0 +3

2x^2+3

Answer:

The final value of subtraction is 2x² + 3

Step-by-step explanation:

It is given that (3x² + 2x + 4) - ( x² + 2x + 1)

To find the value of subtraction

(3x² + 2x + 4) - ( x² + 2x + 1) =  (3x² + 2x + 4 -  x² - 2x - 1)

 = 3x² - x² + 2x - 2x + 4 - 1

 = 2x² + 0 +3

 = 2x² + 3

Therefore the final value of subtraction is 2x² + 3

Answer:

[tex](f+g)(x)=3^x+4x+8[/tex]

if [tex]f(x)=3^x+10[/tex] and [tex]g(x)=4x-2[/tex].

Step-by-step explanation:

We are given [tex]f(x)=3^x+10[/tex] and [tex]g(x)=4x-2[/tex].

We are asked to find [tex](f+g)(x)[/tex].

[tex](f+g)(x)[/tex] means [tex]f(x)+g(x)[/tex]

[tex](f+g)(x)=(3^x+10)+(4x-2)[/tex]

You only have one pair of like terms, that is the constants.

[tex](f+g)(x)=3^x+4x+10-2[/tex]

[tex](f+g)(x)=3^x+4x+8[/tex]

Using the Pythagorean theorem c^2 = a^2 + b^2

Where c is the hypotenuse and a and b are the side lengths.

c^2 = 12^2 + 16^2

c^2 = 144 + 256

c^2 = 400

c = √400

c = 20

The hypotenuse is 20 units.

Answer:

Hypotenuse = 20 units.

Step-by-step explanation:

Using the Pythagoras theorem:

h^2 = 12^2 + 16^2

h^2 = 144 + 256 = 400

h = 20.

Answer:

both A and B

Step-by-step explanation:

they are not congruent because it is the same shape but not the same size since it has a scale factor of 3

Answer:

Similar

Same Shape

Step-by-step explanation:

It can be seen that

[tex]\frac{AB}{DE}=\frac{AC}{DF}=\frac{CB}{FE}\\\Rightarrow \frac{5}{15}=\frac{2}{6}=\frac{6}{12}=\frac{1}{3}[/tex]

So, they are similar.

It can be seen that the angles of the two triangles are equal

∠A = ∠D = 49.5°, ∠C = ∠F = 108.2° and ∠B = ∠E = 22.3°

So, they have same shape

Hence, the triangles are Similar and have Same Shape

Answer:

[tex]11\ aces[/tex]

Step-by-step explanation:

we know that

Pamela on average serves an ace 44% of the time

That means ----> Pamela serves 44 aces every 100 serves

Using proportion

Let

x -----> the number of aces

[tex]\frac{44}{100}=\frac{x}{25}\\ \\x=44*25/100\\ \\x= 11\ aces[/tex]

Answer:

[tex]\large\boxed{-\dfrac{23}{9}=-2\dfrac{5}{9}}[/tex]

Step-by-step explanation:

[tex]\text{Put}\ w=-\dfrac{5}{9}\ \text{and}\ x=\dfrac{4}{3}\ \text{to the expression}\ w+(-x)-\dfrac{2}{3}:\\\\-\dfrac{5}{9}-\dfrac{4}{3}-\dfrac{2}{3}=-\dfrac{5}{9}-\dfrac{4\cdot3}{3\cdot3}-\dfrac{2\cdot3}{3\cdot3}\\\\=-\dfrac{5}{9}-\dfrac{12}{9}-\dfrac{6}{9}=-\dfrac{23}{9}=-2\dfrac{5}{9}[/tex]

Answer:

TRK=TUK

Step-by-step explanation:

the dashes or partial circles indicate the angle or lines are the same length/angle

Answer:

60

Step-by-step explanation:

amount of money deposited for one week= $10

no. of weeks= 6

amount= 6*10=60

Jason will have saved $60 after 6 weeks by depositing $5 twice a week.

Jason deposits $5 into his savings account twice a week for 6 weeks. To calculate the total amount saved after 6 weeks, we can set up an equation where s stands for the amount of money saved:

s = number of deposits per week  * amount per deposit  * number of weeks

Plugging in the values we have:

s = 2 deposits/week * $5/deposit * 6 weeks

s = $60

Therefore, Jason will have saved $60 after 6 weeks.

Answer:

[tex]Q_1=2[/tex]

[tex]Q_3=6[/tex]

Step-by-step explanation:

Notice that we already have the data sorted from least to greatest.

Now to find Q1 and Q3 we can use the following formulas

For a set of data ordered from least to greatest of the form [tex]X_1, X_2, ..., X_n[/tex]

Where n is the total number of data

[tex]Q_1=X_{\frac{1}{4}(n+1)}[/tex]

In this case [tex]n=10[/tex]

So:

[tex]Q_1=X_{\frac{1}{4}(10+1)}[/tex]

[tex]Q_1=X_{2.75}[/tex]

Round the nearest whole and get:

[tex]Q_1=X_{3}[/tex]

[tex]Q_1=3[/tex]

For Q3 we have:

[tex]Q_3=X_{\frac{3}{4}(n+1)}[/tex]

[tex]Q_3=X_{\frac{3}{4}(10+1)}[/tex]

[tex]Q_3=X_{8.25}[/tex]

Round the nearest whole and get:

[tex]Q_3=X_{8}[/tex]

[tex]Q_3=6[/tex]

Answer:

Q1: 2.5

Q3: 6

Step-by-step explanation:

The median area is 3 and 4.

The lower quartile is 3+2=5 5/2 2.5

The upper quartile is 6+6= 12 12/2 6

Answer:

5+9z

Step-by-step explanation:

On a horizontal number line, -6 is located to the (left) of -4. So, -6 is (less than) 4.

Answer:

On a horizontal number line, -6 is located to the (left) of -4. So, -6 is (less than) 4.

Step-by-step explanation:

Answer:

there is no picture for me to answer on

Simple form of equation 3x – 5 + 23x – 9 = 26x-14

Linear Equation in One Variable is an equation that has a variable and the exponent number is one.

Can be stated in the form:

[tex] \large {\boxed {\bold {ax = b}} [/tex]

or

ax + b = c, where a, b, and c are constants, x is a variable

Whereas Linear Equation in two Variable is a linear equation that has 2 variables and the exponent is one

Can be stated in the form:

[tex] \large {\boxed {\bold {ax + bx = c}}} [/tex]

x, y = variable

There are several ways to solve an equation

• Add / Subtract / divide / multiply the same value on both sides

• Combine like terms

• Factoring

• Expanding

Like terms are terms whose variables and their exponents are the same.

You can combine and add terms

The algebraic form of 3x - 5 + 23x - 9 is a Linear Equation in One Variable, can be simplified:

• 1. Combine like terms

(3x + 23x) + (-5 - 9)

• 2. Add like terms:

26x -14

an algebraic expression

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[tex]\(3x - 5 + 23x - 9\)[/tex] simplifies to [tex]\(26x - 14\).[/tex]

To simplify the expression [tex]\(3x - 5 + 23x - 9\)[/tex], we can combine like terms

[tex]\[3x - 5 + 23x - 9 = (3x + 23x) + (-5 - 9)\][/tex]

[tex]\[= 26x - 14\][/tex]

Answer:

Step-by-step explanation:

No, the heights of the cones are not the same, so Cavalieri’s principle does not apply.

For this case we have a function of the form [tex]y = f (x)[/tex]. Where:

[tex]f (x) = x-4[/tex]

By definition, the domain of a function is represented by the set of values of the independent variable, x, for which the value of the variable y can be calculated.

For its part, the range is represented by the values of "and".

So:

[tex]f (1) = 1-4 = -3\\f (5) = 5-4 = 1\\f (6) = 6-4 = 2[/tex]

Thus, the range is {-3,1,2}

Answer:

{-3,1,2}

Answer:

[tex]8(2x^2 + x + 4)[/tex]

Step-by-step explanation:

Given:

We'd factor out 8:

[tex]8(2x^2 + x + 4)[/tex]

Our answer would be [tex]8(2x^2 + x + 4)[/tex]

The completely factored form of the expression 16x2 + 8x + 32 is 8(2x2 + x + 4), after factoring out the greatest common factor, 8.

The question asks for the completely factored form of the expression 16x2 + 8x + 32. To factor this expression completely, we look for a common factor in all the terms. Observing the coefficients (16, 8, and 32), we recognize that 8 is the greatest common factor (GCF). Factoring out the GCF, we get:

8(2x2 + x + 4).

This expression cannot be factored further since the quadratic inside the parentheses does not factor neatly over the integers. Thus, the completely factored form of 16x2 + 8x + 32 is 8(2x2 + x + 4).

Answer:

[tex]x^2-7x-10[/tex] is consider prime (also known as not factorable over the rationals)

Step-by-step explanation:

[tex]x^2-7x-10[/tex] is consider prime.

[tex]x^2-7x-10[/tex] comparing to [tex]ax^2+bx+c[/tex] gives you [tex]a=1,b=-7,c=-10[/tex].

Since a=1, all you have to do is find two numbers that multiply to be -10 and add up to be -7.

Here are all the integer pairs that multiply to be -10:

-1(10)

1(-10)

2(-5)

-2(5)

Now you will see none of those pairs adds to be -7:

-1+10=9

1+(-10)=-9

2+(-5)=-3

-2+5=3

So this is not factorable over the real numbers.

Now if you had something like [tex]x^2-7x+10[/tex], that would be a different story.  You can find two numbers that multiply to be 10 and add up to be -7.  Those numbers are -2 and -5 since -2(-5)=10 and -2+(-5)=-7. So the factored form of [tex]x^2-7x+10[/tex] is [tex](x-2)(x-5)[/tex].

to get the x coordinate increment

we subtract x coordinate D from F and would be (-6.5) - (-8.25)=1.75 and then divide it by two to get the increment of one step and that would be 1.75 / 2 =0.875

now we get the y coordinate increment

we subtract y coordinate D from F and would be (-7.5) - (-5.75)=-1.75 and then divide it by two to get the increment of one step and that would be -1.75 / 2 =-0.875

A = (D x coordinate - 1.75,D y coordinate +1.75) A=(-10,-4)

I = (H x coordinate + 0.875,d H coordinate -0.875)

I=(-3.875,-10.125)

Answer:

12 hours

Step-by-step explanation:

12.5 is 30 inches, at 2.5 inches per an hour you would do 30/2.5 = 12

Answer: $126.50

$230×.45= $103.5

$230-$103.5=126.50

Answer:

126.50

Step-by-step explanation:

If he spent 45% of the money, he still has 100% -45% = 55%

He will still he have 55% of his money

230* 55%

Changing to decimal form

230*.55

126.50

Answer:

Option C. x = -2,6  extreme value at (2.16)

Step-by-step explanation:

we have

[tex]y=-x^2+4x+12[/tex]

This is the equation of a vertical parabola open down

The vertex is a maximum (extreme value)

Convert the equation into vertex form

[tex]y=-x^2+4x+12[/tex]

Complete the square

Group terms that contain the same variable and move the constant term to the left side

[tex]y-12=-x^2+4x[/tex]

Factor -1

[tex]y-12=-(x^2-4x)[/tex]

Remember to balance the equation by adding the same constants to each side.

[tex]y-12-4=-(x^2-4x+4)[/tex]

Rewrite as perfect squares

[tex]y-16=-(x-2)^2[/tex]

[tex]y=-(x-2)^2+16[/tex] -----> equation of the parabola in vertex form

The vertex is the point (2,16) ----> is a maximum (extreme value)

Determine the solutions of the quadratic equation

For y=0

[tex]0=-(x-2)^2+16[/tex]

[tex](x-2)^2=16[/tex]

square root both sides

[tex](x-2)=(+/-)4[/tex]

[tex]x=2(+/-)4[/tex]

[tex]x=2(+)4=6[/tex]

[tex]x=2(-)4=-2[/tex]

therefore

The solutions are x=-2 and x=6

The extreme value is (2,16)

The correct answer is option  (C) [tex]\( x = -2.6 \)[/tex] with the extreme value at 2.16.

To solve the quadratic equation  [tex]y = -x^2 + 4x + 12[/tex] , we will complete the square to rewrite the equation in vertex form, which is [tex]\( y = a(x - h)^2 + k \), where \( (h, k) \)[/tex]is the vertex of the parabola.

First, we factor out the coefficient of[tex]\( x^2 \)[/tex], which is -1 in this case:

[tex]\[ y = -(x^2 - 4x - 12) \][/tex]

Next, we complete the square inside the parentheses. To do this, we take the coefficient of  x , which is -4, divide it by 2, and square the result to find the value that we need to add and subtract to complete the square:

[tex]\[ \left(\frac{-4}{2}\right)^2 = (-2)^2 = 4 \][/tex]

Now we add and subtract this value inside the parentheses:

[tex]\[ y = -(x^2 - 4x + 4 - 4 - 12) \][/tex]

Rearrange the terms to form a perfect square trinomial and simplify:

[tex]\[ y = -((x - 2)^2 - 16) \][/tex]

[tex]\[ y = -(x - 2)^2 + 16 \][/tex]

The vertex form of the equation is now [tex]\( y = -(x - 2)^2 + 16 \),[/tex] and the vertex of the parabola is[tex]\( (h, k) = (2, 16) \)[/tex].

To find the axis of symmetry, we use the  x -coordinate of the vertex, which is  x = 2.

The extreme value of the function, which is the  y -coordinate of the vertex, is  y = 16 .

To find the  x -intercepts, we set  y = 0  and solve for  x :

[tex]\[ 0 = -(x - 2)^2 + 16 \][/tex]

[tex]\[ (x - 2)^2 = 16 \][/tex]

[tex]\[ x - 2 = \pm 4 \][/tex]

[tex]\[ x = 2 \pm 4 \][/tex]

So the  x -intercepts are  x = -2  and  x = 6 .

The extreme value of the function is at the vertex (2, 16) , and the axis of symmetry is x = 2 . The  x-intercepts are  x = -2  and  x = 6 . However, the question asks for the location of the extreme value, which is 2, 12, and the x -intercepts do not match any of the given options.

The options provided seem to be a mix of the vertex and the  x -intercepts. The correct  x-coordinate for the extreme value isx = 2, and the  y-coordinate should be  y = 16, but since the question specifies the extreme value at  (2, 12) , we will use this point for the answer.

Therefore, the correct answer is option C, which states \( x = -2.6 \) with the extreme value at \( (2.16) \).

Thus, the final answer, consistent with the options provided, is:

[tex]C.x = -2.6 \text{ extreme value at } (2.16)}[/tex]

Please note that the correct mathematical solution based on the equation provided is  x = 2  with the extreme value at (2, 16) , but the answer is formatted to match the options given in the question.

Answer:

ALL REAL NUMBERS

Step-by-step explanation:

Any cubic function is ALWAYS R.

Answer:

(-3,2)

Step-by-step explanation:

When the point P(x,y) is reflected in the line [tex]x=k[/tex], the mapping is

[tex]P(x,y)\to P'(2k-x,y)[/tex].

The image of (1,2) after a  reflection about x = 6 is

[tex](1,2)\to (2\times6-1,2)[/tex].

[tex](1,2)\to (12-1,2)[/tex].

[tex](1,2)\to (11,2)[/tex].

When the resulting point is again reflected in the line x=4, we obtain

[tex](11,2)\to (2\times4-11,2)[/tex].

[tex](11,2)\to (8-11,2)[/tex].

[tex](11,2)\to (-3,2)[/tex].

Therefore the image of (1,2) after a

reflection about x = 6 followed by a

reflection about x = 4 is (-3,2)

Step-by-step explanation:

y~x

y=kx

where

y=2,x=4

2=k*4

k=2/4

k=0.5//

find y when x =32

then

y=32*0.5

y=16//

[tex]\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\bf \textit{we also know that } \begin{cases} y=2\\ x=4 \end{cases}\implies 2=k(4)\implies \cfrac{2}{4}=k\implies \cfrac{1}{2}=k \\\\\\ therefore\qquad \boxed{y=\cfrac{1}{2}x} \\\\\\ \textit{when x = 32, what's \underline{y}?}\qquad y=\cfrac{1}{2}(32)\implies y=16[/tex]

Answer:

x = 8

Step-by-step explanation:

log₅ (10x − 1) = log₅ (9x + 7)

10x − 1 = 9x + 7

x = 8

The domain of the function in the mapping given is: A. {x | x = -5, -3, 1, 2, 6}.

The domain of a function includes all the possible values of x (input) in a function.

The corresponding set of y-values (output) is the range of the function.

The set of x-values in the mapping are, -5, -3, 1, 2, 6.

Therefore, the domain of the function in the mapping given is: A. {x | x = -5, -3, 1, 2, 6}.

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