Two forces of 7 newtons and 11 newtons act on a body at an angle of 60° to each other. Find the magnitude of the resultant force to the nearest whole number.

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.

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:

5+9z

Step-by-step explanation:

Answer:

ALL REAL NUMBERS

Step-by-step explanation:

Any cubic function is ALWAYS R.

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:

[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:

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:

x = 8

Step-by-step explanation:

log₅ (10x − 1) = log₅ (9x + 7)

10x − 1 = 9x + 7

x = 8

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].

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:

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]

The definition of absolute value is the magnitude of a number without the sign.

Hope this helps!

Final answer:

The absolute value of a number indicates its distance from zero on the number line without regard to direction, resulting in a non-negative value. In vectors, the absolute value denotes the magnitude, which is also always positive, even when multiplied by a negative scalar.

Explanation:

Absolute Value Definition

The absolute value of a number is its distance from zero on the number line, regardless of direction. The absolute value of a number is always non-negative, and it is represented by two vertical bars on either side of the number. For instance, the absolute value of -4 is 4, and the absolute value of 4 is also 4. In mathematical notation, this is written as |−4| = 4 and |4| = 4.

In the context of vectors, the absolute value can refer to the magnitude of the vector. When we multiply a vector by a scalar c, the magnitude of the resulting vector becomes the absolute value of cA. If c is positive, the direction of the vector remains the same. If c is negative, the direction is reversed. The magnitude of a vector is always positive, and when calculating the magnitude, we are essentially taking the absolute value of its length.

Significance of the absolute value concept extends to other areas of science as well, such as physics, where it can denote the magnitude of displacement or frequency. For example, the beat frequency between two sounds is defined as the absolute value of the difference between their frequencies because a negative frequency would not make sense.

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.

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:

TRK=TUK

Step-by-step explanation:

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

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:

[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:

(-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)

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:

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:

(-5,-1)

Step-by-step explanation:

First, draw a parallel line to the blue one that has a slope of over 1 to the right and up 1.

Second, look at the new line and see if any of the points are on the line.

All of the other point do not fall on the new line.

Answer:

Option 2nd , 3rd and 5th are correct.

Step-by-step explanation:

Given:

Given line passes through points ( -2 , -4 ) and ( 4 , 2 )

Coordinate of the Point P( 0 , 4 )

To find: Point which lie on the line parallel to given line and passes through point P.

Slope of the given line = [tex]\frac{y_2-y_1}{x_2-x_1}\:=\:\frac{-4-2}{-2-4}\:=\:\frac{-6}{-6}\:=\:1[/tex]

We know that slope of parallel lines ara equal.

So, Using Slope-Point form we get equation of line,

[tex]y-y_1=m(x-x_1)[/tex]

y - 4 = 1 ( x - 0 )

y - 4 = x

x - y = -4

Option 1:

x = -4 , y = 2

LHS = -4 - 2 = -6 ≠ RHS

Thus, This is not required point.

Option 2:

x = -1 , y = 3

LHS = -1 - 3 = -4 = RHS

Thus, This is required point.

Option 3:

x = -2 , y = 2

LHS = -2 - 2 = -4 = RHS

Thus, This is required point.

Option 4:

x = 4 , y = 2

LHS = 4 - 2 = 2 ≠ RHS

Thus, This is not required point.

Option 5:

x = -5 , y = -1

LHS = -5 - (-1) = -4 = RHS

Thus, This is required point.

Therefore, Option 2nd , 3rd and 5th are correct.

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]

Answer:

Step-by-step explanation:

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

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}.

Learn more about domain of a function on:

https://brainly.com/question/10891721

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)

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:

[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:

there is no picture for me to answer on

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