Can someone help me please ?

Answer:

  (f+g)(x) = 5x +3

Step-by-step explanation:

(f+g)(x) = f(x) +g(x)

  = (2x -6) +(3x +9)

  = 2x +3x -6 +9

(f+g)(x) = 5x +3

Answer:

15 girls.

Step-by-step explanation:

Hope this helps!

Answer:

15 girls

Step-by-step explanation:

2:3 ratio

If you know the amount of boys, then 2x=10, x=5

Now you know that the scale factor is 5

So, multiply 5*3 to get the amount of girls

The surface area of the triangular prism is B. 1,008 \(cm^{2}\)

Triangular Prism is a polyhedron made up of two triangular bases and three rectangular sides. It is a three-dimensional shape that has three side faces and two base faces, connected to each other through the edges.

How to determine this

The surface area of the triangular prism =  Area of the front Triangle + Area of the triangle + Each sides of the triangle by the length of the triangular prism.

Area of the front and back triangle will be the the same given the same base and height

To find the area of the triangle = 1/2 * Base * Height

Where base = 12 cm

Height = 9 cm

Area = 1/2 * 12 cm * 9 cm

Area = 6 * 9 \(cm^{2}\)

Area of the one triangle = 54 \(cm^{2}\)

So, by multiplying each sides of the triangle by the length

= Base * Length

= 12 cm * 25 cm

= 300\(cm^{2}\)

Height * Length

= 9 cm * 25 cm

= 225 \(cm^{2}\)

Then, Hypotenuse * Length

= 15 cm * 25 cm

= 375 \(cm^{2}\)

Surface area = 54\(cm^{2}\) + 54\(cm^{2}\) * 300\(cm^{2}\) + 225\(cm^{2}\) + 375\(cm^{2}\)

Surface Area = 1,008\(cm^{2}\)

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Given that g(x) =f(kx). The graph of function g is graph Z Because the graph a function g is the result of a horizontal compression applied to the graph of function F.

A graph can be described  as a pictorial representation or a diagram that represents data or values in an organized manner.

The graph of the function g(x) = f(kx) is obtained from the graph of f(x) by a horizontal compression or stretching, depending on the value of k.

In conclusion, If k is greater than 1, then the graph of g(x) is obtained from the graph of f(x) by a horizontal compression.

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Answer

The answer is C

Explanation:

1.2 divided by 4 = 0.3

2.4 divided by 8 = 0.3

3.9 divided by 13 = 0.3

**hope this helps.... brainly please if possible

Answer:

bottom left

Step-by-step explanation:

Answer:

450 miles per hour

Step-by-step explanation:

Kelly flies at a distance of 2,100 miles

The time taken for the trip is 4 2/3 hours

Therefore the rate of speed can be calculated as follows

= 2,100 ÷ 4 2/3

= 2,100 ÷ 14/3

= 2100 × 3/14

= 150 × 3

= 450 miles per hour

Answer:

450

Step-by-step explanation:

The value of given quadratic equation at -7 is 247.

What is quadratic equation?

The polynomial equation whose highest degree is two is called a quadratic equation or sometimes just quadratics. It is expressed in the form of:

ax² + bx + c = 0

where x is the unknown variable and a, b and c are the constant terms.

given ,f(x) = \(4x^{2} -8x-5\) to find f(-7)

f(-7)= 4(49)-8(-7)-5

=196+56-5

=247

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Answer:

A.

Step-by-step explanation:

Diameter = 6 cm

SO,

Radius = 3 cm

Now

Slant Height = 5 cm

for Finding the height , We'll use Pythagorean Theorem

c² = a²+b²

5² = 3² + b²

b² = 5²-3²

b² = 25-9

b² = 16

Taking sqrt on both sides

b = 4

So

Height = 4

Now Finding the volume of cone

V = 1/3(πr²h)

V = 1/3(π)(3)²(4)

V = 12π cm³

Answer:

The sum will be close to 1/4

Step-by-step explanation:

1/8+1/6 is 7/24, and 1/4th of that is 6/24, so it is very close.

Answer: The sum will be close to 1/4

Step-by-step explanation:

You can start by making the fractions have the same denominator, (8*6) which gets you 48

You then want to use the butterfly method, so 1/8 becomes 6/48 and 1/6 becomes 8/48. You then add these up to 14/48.

12/48 is 1/4, and 14/48 is close to 12/48, thus making the answer the first option.

Answer:

BOYS = 30.

GIRLS = 12.

Step-by-step explanation:

Boys: B

Girls: G

B = (2/5)G

B + G = 42.

(2/5)G + G = 42

2G + 5G = 210

7G = 210

G = 210/7

G = 30.

B = (2/5)G

B = (2/5)(30)

B = 60/5

B = 12.

Answer:

\(\Huge \boxed{\bold{\text{12 Boys}}}\)

\(\Huge \boxed{\bold{\text{30 Girls}}}\)

Step-by-step explanation:

Let the number of girls be \(g\) and the number of boys be \(b\).

According to the problem: \(b = \frac{2}{5} \times g\)

We also know that the total number of students is 42, so \(b + g = 42\).

Now, we have two equations with two variables:

We can solve these equations to find the values of \(b\) and \(g\).

Step 1: Solve for \(\bold{b}\) in terms of \(\bold{g}\)

From the first equation, we have\(b = \frac{2}{5} \times g\)

Step 2: Substitute the expression for \(\bold{b}\) into the second equation

Replace \(b\) in the second equation with the expression we found in step 1.

\(\frac{2}{5} \times g + g = 42\)

Step 3: Solve for \(\bold{g}\)

Now, we have an equation with only one variable, \(g\):

\(\frac{2}{5} \times g + g = 42\)

To solve for \(g\), first find a common denominator for the fractions:

\(\frac{2}{5} \times g + \frac{5}{5} \times g = 42\)

Combine the fractions:

\(\frac{7}{5} \times g = 42\)

Now, multiply both sides of the equation by \(\frac{5}{7}\) to isolate \(g\):

Step 4: Find the value of \(\bold{b}\)

Now that we have the value of \(g\), we can find the value of \(b\) using the first equation:

So, there are 12 boys and 30 girls in the class.

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

Step-by-step explanation:

\( \frac{30}{wz} = \frac{40}{32 + 40 } \\ wz = 54\)

\( \frac{40}{40 + 32} = \frac{28}{xz} \\ xz = 50.4\)

So the Perimeter is

\(54 + 50.4 + (40 + 32) = 176.4\)

Answer:

Below

Step-by-step explanation:

To find the volume of a cone, you can use the equation V=π r^2 (h/3)

Because the diameter is 7, the radius is 3.5 inch ( r=1/2 d)

V = π (3.5^2)(37/3)

   = 474.64 in^3

I hope that is correct good luck!

Answer:

474.642

Step-by-step explanation:

To find out the volume of the cone is using V= 1/3 TTR^2 * H

We know TT is pie, pie is 3.19 and the radius of the cone is 3.5 inches because half of seven is 3.5.

V=1/3 3.14 * 3.5 * 3.5 * 37 = 474.642

The Greatest Common Divisor (GCD) of 85 and 51 is 17.

The greatest common factor that divides two or more numbers is known as the greatest common divisor (GCD). The highest common factor is another name for it (HCF).

Explanation

Step 1: Divide 85 by 51. The quotient is 1 and the remainder is 34.

Step 2: Divide 51 by 34. The quotient is 1 and the remainder is 17.

Step 3: Divide 34 by 17. The quotient is 2 and the remainder is 0.

Step 4: Since the remainder is 0, the Greatest Common Divisor (GCD) of 85 and 51 is 17.

The GCD of 85 and 51 is 17.

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No, it is not a regular polygon.

A hexagon is a six sided polygon. And a convex hexagon means, the hexagon's vertices are pointed outwards.

And no interior angle has an angle measure more than 180°.

Given:

A polygon.

To be a regular polygon:

Given Hexagon,

should have equal sides and equal angles.

We have no information about the angles and sides.

Therefore, it is not a regular polygon.

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The function has a relative minimum at (-1.278, -0.509) and a relative maximum at (1.278, 2.509).

How to find  x-intercepts?

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

(x⁴/4) - x² + 1 = 0

This is a fourth-degree polynomial equation, which is difficult to solve analytically. However, we can use a graphing calculator or software to find the approximate x-intercepts, which are approximately -1.278 and 1.278.

To find the y-intercept, we set x = 0:

y = (0/4) - 0² + 1 = 1

So the y-intercept is (0, 1).

To find the vertical asymptotes, we set the denominator of any fraction in the function equal to zero. There are no denominators in this function, so there are no vertical asymptotes.

To find the horizontal asymptote, we look at the end behavior of the function as x approaches positive or negative infinity. The term x^4 grows faster than x^2, so as x approaches positive or negative infinity, the function grows without bound. Therefore, there is no horizontal asymptote.

To find the critical points, we take the derivative of the function and set it equal to zero:

y' = x³- 2x

x(x² - 2) = 0

x = 0 or x = sqrt(2) or x = -sqrt(2)

These are the critical points.

To determine the intervals where the function is increasing and decreasing, we can use a sign chart or the first derivative test. The first derivative test states that if the derivative of a function is positive on an interval, then the function is increasing on that interval. If the derivative is negative on an interval, then the function is decreasing on that interval. If the derivative is zero at a point, then that point is a critical point, and the function may have a relative maximum or minimum there.

Using the critical points, we can divide the real number line into four intervals: (-infinity, -sqrt(2)), (-sqrt(2), 0), (0, sqrt(2)), and (sqrt(2), infinity).

We can evaluate the sign of the derivative on each interval to determine whether the function is increasing or decreasing:

Interval (-infinity, -sqrt(2)):

Choose a test point in this interval, say x = -3. Substituting into y', we get y'(-3) = (-3)³ - 2(-3) = -15, which is negative. Therefore, the function is decreasing on this interval.

Interval (-sqrt(2), 0):

Choose a test point in this interval, say x = -1. Substituting into y', we get y'(-1) = (-1)³ - 2(-1) = 3, which is positive. Therefore, the function is increasing on this interval.

Interval (0, sqrt(2)):

Choose a test point in this interval, say x = 1. Substituting into y', we get y'(1) = (1)³ - 2(1) = -1, which is negative. Therefore, the function is decreasing on this interval.

Interval (sqrt(2), infinity):

Choose a test point in this interval, say x = 3. Substituting into y', we get y'(3) = (3)³ - 2(3) = 25, which is positive. Therefore, the function is increasing on this interval.

Therefore, the function is decreasing on the intervals (-infinity, -sqrt(2)) and (0, sqrt(2)), and increasing on the intervals (-sqrt(2), 0) and (sqrt(2), infinity).

To find the inflection points, we take the second derivative of the function and set it equal to zero:

y'' = 3x² - 2

3x² - 2 = 0

x² = 2/3

x = sqrt(2/3) or x = -sqrt(2/3)

These are the inflection points.

To determine the intervals where the function is concave up and concave down, we can use a sign chart or the second derivative test.

Using the inflection points, we can divide the real number line into three intervals: (-infinity, -sqrt(2/3)), (-sqrt(2/3), sqrt(2/3)), and (sqrt(2/3), infinity).

We can evaluate the sign of the second derivative on each interval to determine whether the function is concave up or concave down:

Interval (-infinity, -sqrt(2/3)):

Choose a test point in this interval, say x = -1. Substituting into y'', we get y''(-1) = 3(-1)² - 2 = 1, which is positive. Therefore, the function is concave up on this interval.

Interval (-sqrt(2/3), sqrt(2/3)):

Choose a test point in this interval, say x = 0. Substituting into y'', we get y''(0) = 3(0)² - 2 = -2, which is negative. Therefore, the function is concave down on this interval.

Interval (sqrt(2/3), infinity):

Choose a test point in this interval, say x = 1. Substituting into y'', we get y''(1) = 3(1)²- 2 = 1, which is positive. Therefore, the function is concave up on this interval.

Therefore, the function is concave up on the interval (-infinity, -sqrt(2/3)) and (sqrt(2/3), infinity), and concave down on the interval (-sqrt(2/3), sqrt(2/3)).

To find the relative extrema, we can evaluate the function at the critical points and the endpoints of the intervals:

y(-sqrt(2)) ≈ 2.828, y(0) = 1, y(sqrt(2)) ≈ 2.828, y(-1.278) ≈ -0.509, y(1.278) ≈ 2.509

Therefore, the function has a relative minimum at (-1.278, -0.509) and a relative maximum at (1.278, 2.509).

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Answer:

The number of ways these books can be arranged is 17,280 ways

Step-by-step explanation:

number of ways 4 distinct math books can be arranged = 4! = 4 x 3 x 2 x 1 = 24 ways

number of ways of 5 distinct history book can be arranged = 5! = 5 x 4 x 3 x 2 x 1 = 120 ways

if all of the math books have to be together, but the history books do not have to be together,

↑ H₁ ↑ H₂ ↑ H₃ ↑ H₄ ↑ H₅ ↑ = 6 ways

The upward arrows represent, the number of ways all the maths books can be arranged with the 5 history books.

Total number of ways these books can be arranged = 24 x 120 x 6

                                                                                        = 17,280 ways

Therefore, the number of ways these books can be arranged is 17,280 ways

Answer:

$221,990.70

Step-by-step explanation:

here we need to apply the formula for future value ,,,,

Future Value = Present value (1+r/m)^mt

we insert the values we have in their respective positions. 4 29% = 0.0429 when we convert it by dividing by 100%

340, 000 = PV (1+0.0429/4)^4×10

340, 000/1.5322 = PV

PV = $221,990.70

Answer:

NOT CONGRUENT

Step-by-step explanation:

Given:

AB ≅ CD

∠DCB ≅ ∠DAB

To prove:

ΔABD ≅ ΔDCB

        Statements                                      Reasons

1). AB ≅ CD                                                1). Given

2). ∠DCB ≅ ∠DAB                                    2). Given

3). DB ≅ DB                                              3). Reflexive property

4). ΔABD ≅ ΔDCB                                    4). SSA property of congruence.

But in the given options SSA property is not given.

So the answer is NOT CONGRUENT.

Answer:

$1.50

Step-by-step explanation:

Answer:

\(\huge\boxed{18 + 0i}\)

Step-by-step explanation:

= (3 + 3i)(3 - 3i)

= 3(3 - 3i) + 3i(3 - 3i)

= 9 - 9i + 9i - 9i²

= 9 - 9(-1)

= 9 + 9

In the form a + bi:

\(\rule[225]{225}{2}\)

Answer:

B, C

Step-by-step explanation:

A: √4 = 2, so the side lengths form an equilateral triangle, not a right triangle.

__

B: √(9²+40²) = 41 . . . . these form a right triangle

__

C: √(5² +10²) = √125 . . . . these form a right triangle

Answers:

\(\displaystyle \lim_{x \to 2^{+}} f(x) = 1\\\\\displaystyle \lim_{x \to 2^{-}} f(x) = 1\\\)

Both result in the same limit value. This allows us to say \(\displaystyle \lim_{x \to 2} f(x) = 1\) without the plus or minus over the 2.

The left and right hand limits may not always match like this.

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

Explanation:

The notation \(\displaystyle \lim_{x \to 2^{+}} f(x)\) means that we are approaching x = 2 from the right hand side. This is from the positive direction. So we start at say x = 3 and move to x = 2.5 then to x = 2.1 then to x = 2.01 and so on.

Because we started with values x > 2, we will use the third definition of the piecewise function

if x > 2, then f(x) = 3x-5

Plug in x = 2 to get

f(x) = 3x-5

f(2) = 3(2)-5

f(2) = 6-5

f(2) = 1

This shows \(\displaystyle \lim_{x \to 2^{+}} f(x) = 1\)

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

For the other limit, we're approaching x = 2 from the negative side. So we could start at say x = 0, then move to x = 1, then to x = 1.5 then to x = 1.9 then to x = 1.99, and so on.

We're using x values such that x < 2 now.

So we'll be using the first definition of the piecewise function

If x < 2, then f(x) = x^2 - 3

f(x) = x^2-3

f(2) = 2^2-3

f(2) = 4-3

f(2) = 1

We end up with \(\displaystyle \lim_{x \to 2^{-}} f(x) = 1\)

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

Both right hand limit and left hand limit result in the same value

Because \(\displaystyle \lim_{x \to 2^{+}} f(x) = \displaystyle \lim_{x \to 2^{-}} f(x) = 1\)

We can shorten that to \(\displaystyle \lim_{x \to 2^{}} f(x) = 1\) meaning we can approach x = 2 from either direction to arrive at the same limiting value.

A thing to notice is that f(2) is not equal to 1. Instead the second line of the piecewise function says f(2) = 3.

The fact that the limit as x approaches 2 and f(2) don't agree means this function is not continuous at x = 2.

The graph shows this. We have a removable discontinuity where we effectively picked the point off the graph and move it upward.

See the diagram below.

The transformation of f(x) to p(x) is that (a) the graph is reflected and shifted down

From the question, we have the following parameters that can be used in our computation:

The functions f(x) and g(x)

In the function equations, we can see that

f(x) = x²

p(x) = -f(x) - 3

So, we have

Vertical Difference = 0 - 3

Evaluate

Vertical Difference = - 3

This means that the transformation of f(x) to p(x) is that f(x) is reflected and shifted down 3 units to p(x).

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Answer:

Step-by-step explanation:

Determine the two consecutive multiples of 10 that bracket 551

551 is between 550 and 560

555 is the midpoint between 550 and 560

As illustrated on the number line, 551 is less than the midpoint (555)

Therefore, 551 rounded to the nearest ten = 550

551 rounded to the nearest ten with a number line

Answer: 551.36

Step-by-step explanation:

“Of” means you have to multiply so multiply 133.5 and 413 and you will get 55,135.5 then you move the decimal point to the right 2 times and that will be 551.355, then since there is a five you change the other five to a 6 (5 or more raise the score 4 or less let it rest) and that will be 551.36.

Answer: 25

Step-by-step explanation: The absolute value is the distance between a number and zero. The distance between  − 25  and  0  is  25

Answer:

\(\Huge \boxed{25}\)

Step-by-step explanation:

\(|-25|\)

The absolute value of a number is the distance of that number from zero.

Applying absolute value rule : \(|-a|=a\)

\(|-25|=25\)

The solution set of this inequality is {x| x > -6.1}

Here we have the inequality:

2x + 8 > -4.2

To find the solution set, we need to isolate the variable x in one of the sides of the inequality. Doing that we will get:

2x + 8 > -4.2

2x > -4.2 - 8

2x > -12.2

x > -12.2/2

x > -6.1

So the set of all numbers larger than -6.1, this in number form is:

{x| x > -6.1}

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Step-by-step explanation:

h(x) =-x-4

h(x)=9

=>9=-x-4

=>x=-13

Answer:

We place 9 in the first expression instead of h (x)

Then we solve the equation

9=-x-4

x=-13

Step-by-step explanation:

The y-intercept is the value where the line crosses the y-axis.

y-intercept of Line 1 (blue) = 4.

y-intercept of Line 2 (red) = 1.