Let f(x) = x + 7 and g(x) = x − 4. Find f(x) ⋅ g(x). (1 point)

It will take about 9.5 months (or 10 months rounded up) for the rabbit population to reach 5,800.

Let's use the formula for exponential growth to solve this problem:

N = N0 * 2^(t/k)

Where:

N0 = initial population (8 rabbits)

N = final population (5,800 rabbits)

k = doubling time (1 month)

t = time in months (what we're trying to find)

Substituting the values we have:

5,800 = 8 * 2^(t/1)

Dividing both sides by 8:

725 = 2^(t/1)

Taking the logarithm of both sides (base 2):

log2(725) = t/1

t = log2(725) ≈ 9.515

So it will take about 9.5 months (or 10 months rounded up) for the rabbit population to reach 5,800.

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The value of the house last year was approximately $164,000.

To calculate the value of the house last year, we need to find 80% of the current value. Since the value decreased by 20%, it means the current value represents 80% of the original value.

Let's denote the original value of the house as X. We can set up the following equation:

0.8X = $205,000

To find X, we divide both sides of the equation by 0.8:

X = $205,000 / 0.8 = $256,250

Therefore, the value of the house last year was approximately $256,250. However, we need to round the answer to the nearest cent as per the given instructions.

Rounding $256,250 to the nearest cent gives us $256,249.99, which can be approximated as $256,250.

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The equation of the parabola with focus (2,5) and directrix x=18 is (x - 18)² + (y - 5)² = (y - (5 + (18 - 2) / 2))².

A parabola is a conic section, the intersection of a right circular conical surface and a plane parallel to a generating

straight line of that surface.

The focus of a parabola is a fixed point on the interior of a parabola used in the formal definition of the curve.

The directrix is a straight line perpendicular to the axis of symmetry and placed symmetrically with respect to the focus.

The axis of symmetry is the line through the focus and perpendicular to the directrix.

The vertex of a parabola is the point where its axis of symmetry intersects the curve. It is the point where the parabola changes direction or "opens

up" or "opens down.

The directrix is a fixed straight line used in the definition of a

parabola. It is placed such that it is perpendicular to the axis of symmetry and at a distance from the vertex equal to the

distance between the vertex and focus. It is the line that is equidistant to the focus and every point on the curve.Here's

the solution to the given problem:

The distance between the directrix and the focus is equal to p = 16 (since the directrix is x = 18, the parabola opens to the left, so the distance is measured horizontally)

The vertex is (h,k) = ((18+2)/2,5) = (10,5)

Then we can use the following formula: (x - h)² = 4p(y - k)

Substitute the vertex and the value of p. (x - 10)² = 64(y - 5)

Expand and simplify. (x - 10)² + (y - 5)² = 64(y - 5)

The equation of the parabola is (x - 10)² + (y - 5)² = 64(y - 5).

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Using compatible numbers and adjusting them helps us to perform mental math and make calculations faster. This method also helps us to estimate answers and check if the actual answer is reasonable or not.

To find sums, I would prefer to use the method of using compatible numbers and adjusting. The reason behind this is that it can help me to perform mental calculations and solve mathematical problems faster.What are compatible numbers?Compatible numbers are numbers that are close to the actual numbers, but are easier to work with mathematically. They are rounded numbers that make it easier to perform mental math. Once we have the answer, we can adjust it to get the correct answer.To solve an addition problem using compatible numbers, we choose numbers close to the actual numbers in the problem. For example, if we are adding 45 and 32, we can round the numbers to 50 and 30. Then we add 50 and 30 to get 80, which is the compatible number sum. But this is not the actual answer because we rounded the numbers, so we need to adjust. We subtract 5 from 50 and add 3 to 30 to get 45 and 33, respectively. Then we add the adjusted numbers (45 and 33) to get the correct answer, which is 78.Using compatible numbers and adjusting them helps us to perform mental math and make calculations faster. This method also helps us to estimate answers and check if the actual answer is reasonable or not.

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Answer:

I don`t see the attachment

Step-by-step explanation:

We can see here that the volume of the solid is = 3 861cm³

Volume is the amount of space that an object occupies. It is measured in cubic units, such as cubic centimeters, cubic meters, or cubic feet. The volume of an object can be calculated by multiplying its length, width, and height.

In order to find the volume of the solid, we can find the volumes of the trapezoid and cuboid separately and then add them up.

Thus, volume of trapezoid

= 1/2 (a + b) × h × l

where:

a = 6cm

b = 17cm

h = 22 - 8 = 14cm

l = 13 cm

V = 1/2 (6 + 17) × 14 × 13 = 2 093cm³

Volume of cuboid will be:

=  l × b × h

Where

l = 17cm

b = 13cm

h = 8cm

17 × 13 × 8 = 1 768cm³

Thus, volume of solid = Volume of trapezoid + Volume of cuboid

V = 2 093cm³ + 1 768cm³ = 3 861cm³.

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Answer:

c

Step-by-step explanation:

(3.14)(15*15)(315)=222548

Answer:

35$

Step-by-step explanation:

It will take 10 years and 11 months to payoff the balance. The total interest is $2,574.43

Answer: L=46in

Step-by-step explanation:

Using the formulaP=2(l+w)Solving forll=P2﹣w=1362﹣22=46in

The price we have to pay for the disc after 10% discount is 1467 dollars.

Percentage is the value per hundredth.

According to the given question we bought a disc which costs 1630 dollars there's a 10% discount we have to find how much i have to pay.

10% of 1630 dollars will be

= (10/100) × 1630 dollars.

= 16300/100 dollars.

= 163 dollars.

So, the price we have to pay for the disc after 10% discount is

= (Total amount - Discount amount)

= ( 1630 - 163 ) dollars.

= 1467 dollars.

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Answer:

30

Step-by-step explanation:

500 g = 1/2 kg => 2 weeks he loses 1 kg

105 - 90 = 15 kg

So he needs to take 30 weeks in total. ( 15 * 2)

Let weeks be x

So

Main Answer: Only one triangle can be drawn with side lengths of 3 units, 4 units, and 5 units and no matter how they are oriented,it will always have the same shape and size.

Supporting Question and Answer:

What is the condition for determining if a triangle can be formed with a given set of side lengths?

The condition for determining if a triangle can be formed with a given set of side lengths is to check whether the sum of the lengths of any two sides is greater than the length of the third side, as stated by the Triangle Inequality Theorem. If this condition is not satisfied, then the three sides cannot form a triangle.

Body of the Solution:

The correct answer is:(A) triangles, because triangles with the same three side lengths are the same shape and size no matter how they are positioned.

This is because, according to  the Side-Side-Side congruence criterion, if the three sides of one triangle are equal in length to the three sides of another triangle, then the two triangles are congruent,which means they have the same angles and size. Since a triangle is determined by its three side lengths, and the side lengths of the given triangle are fixed at 3, 4, and 5 units, there is only one unique triangle that can be formed with these side lengths. It is important to note that the position or orientation of the triangle does not affect its shape or size, hence any other triangles that may appear to have the same side lengths would be congruent to the original triangle, and thus be considered the same triangle.

Option (B) is incorrect because reflection changes the orientation of the triangle, but does not change its shape or size.

Option (C) is incorrect because the order in which the sides are written does not affect the shape or size of the triangle.

Option (D) is incorrect because, as explained earlier, a triangle can be formed with side lengths of 3, 4, and 5 units.

Final Answer:  Therefore, Only one triangle can be drawn with side lengths of 3 units, 4 units, and 5 units and the correct option is:

(A) triangles, because triangles with the same three side lengths are the same shape and size no matter how they are positioned.

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The correct answer is A) triangles, because triangles with the same three side lengths are the same shape and size no matter how they are positioned.

Triangles with side lengths of 3 units, 4 units, and 5 units can be drawn in many different ways, but they will have the same shape and size. This is because the side lengths are relatively small compared to the overall size of the triangle, so the shape of the triangle is not significantly affected by the orientation of the sides.

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Answer:

u said youll mark me brainliest

Step-by-step explanation:

Answer:

speed of boat is 35 mph

speed of river is 5mph.

Step-by-step explanation:

Let the speed of boat be u mph

let the speed of river be v mph

When boat travel downstream

in that case flow  of river will support the speed of boat hence

speed of river will be added to speed of boat

Thus,

speed of boat in downstream = speed of boat + speed of river = u + v

Given

the boat travels at 40 mph downstream

thus,

u + v = 40           -----1

When boat travel upstream

in that case flow  of river will oppose the speed of boat hence

speed of river will be subtracted from  speed of boat

Thus,

speed of boat in downstream = speed of boat -speed of river = u - v

Given

the boat travels at 30 mph upstream

thus,

u - v = 30  ----2

adding 1 + 2

we have

u + v = 40  

+ u - v = 30

2u = 70

u = 70/2 = 35

Thus,

speed of boat is 35 mph

using u = 35 in u + v = 40  

we have

35 + v = 40

v = 40 - 35 = 5

Thus, speed of river is 5mph.

Answer:

y = 2/3

Step-by-step explanation:

14 = 6(2) + 3y

14 = 12 + 3y

2 = 3y

y = 2/3

The missing length of the triangle can be found using the Pythagorean Theorem which states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

We can use the formula c² = a² + b² where c is the hypotenuse, a is the opposite side and b is the adjacent side.

To find the missing length, we can rearrange the formula to solve for b: b² = c² - a². Substituting the given values,

we have: b² = (0.5)² - (0.3)².

Simplifying the equation, we get: b² = 0.16.

Taking the square root of both sides, we get: b = 0.4 cm.

Therefore, the missing length of the triangle is 0.4 centimeters.

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Answer:

The Answer is Y = 0 or Option 2.

Answer:

its b

Step-by-step explanation:

Answer:

(-5, 7)

Step-by-step explanation:

Translate A left 6, and up 4

The following column A and B can be matched as:

1 - b, 2 - c, 3 - d, 4 - a

Its equivalent expressions are:

x² = 1/\(x^{-2}\)

\(x^{4}\) ÷ \(x^{3}\) = \(x^{4}\) / x³ = x

(x²)² = \(x^{2+2}\) =  \(x^{4}\)

x³. x³. x³ = \(x^{3+3+3}\) = \(x^{9}\)

The symbol written above and to the right of a mathematical expression indicating the operation of raising power is called exponents.

Example:

a² and b³

2 and 3 are exponents.

We have,

x²                      \(x^{9}\)

\(x^{4}\) ÷ \(x^{3}\)               1/\(x^{-2}\)

(x²)²                   x

x³. x³. x³           \(x^{4}\)

We need to find its equivalent expressions

x² = 1/\(x^{-2}\)

\(x^{4}\) ÷ \(x^{3}\) = \(x^{4}\) / x³ = x

(x²)² = \(x^{2+2}\) =  \(x^{4}\)

x³ . x³ . x³ = \(x^{3+3+3}\) = \(x^{9}\)

Thus the following column A and B can be matched:

1 - b

2 - c

3 - d

4 - a

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Answer:

7(32)=7(30+2)=7*2=210+14=224

Step-by-step explanation:

nd the star is the multiplacations sign bcz i dont have the dot mk.

Answer:

mcd(28,48) = 4

Para encontrar el mcd de 28 y 48:

Los factores de 28 son 28, 14, 7, 4, 2, 1.

Los factores de 48 son 48, 24, 16, 12, 8, 6, 4, 3, 2, 1.

Los factores en común de 28 y 48 son 4, 2, 1, los cuales intersectan los dos conjuntos arriba.

En la intersección de los factores de 28 ∩ factores de 48 el elemento mayor es 4.

Por lo tanto, el máximo común divisor de 28 y 48 es 4.

The equation of the perpendicular bisector is of the form \($y = mx + b$\), where \($m = -\frac{1}{2}$\)  and \($b = 4$\).

The equation of the perpendicular bisector of the line segment connecting the points \($(-3,8)$\) and \($(-5,4)$\)has the form \($y = mx + b$\).

To find the equation of the perpendicular bisector, we first need to find the midpoint of the line segment connecting the two points. The midpoint formula is given by:

Midpoint \(= $ \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) $\)

Using the given points $(-3,8)$ and $(-5,4)$, we can calculate the midpoint as follows:

Midpoint\(= $ \left( \frac{-3 + (-5)}{2}, \frac{8 + 4}{2} \right) = (-4, 6) $\)

Now that we have the midpoint, we need to determine the slope of the line segment connecting the two points. The slope formula is given by:

Slope \(= $ \frac{y_2 - y_1}{x_2 - x_1} $\)

Using the coordinates $(-3,8)$ and $(-5,4)$, the slope can be calculated as follows:

Slope \(= $ \frac{4 - 8}{-5 - (-3)} = \frac{-4}{-2} = 2 $\)

The slope of the perpendicular bisector is the negative reciprocal of the slope of the line segment. Therefore, the slope of the perpendicular bisector is $-\frac{1}{2}$.

Now, using the midpoint $(-4, 6)$ and the slope $-\frac{1}{2}$, we can find the equation of the perpendicular bisector by substituting these values into the slope-intercept form equation $y = mx + b$:

$6 = -\frac{1}{2} \cdot (-4) + b$

Simplifying the equation:

$6 = 2 + b$

$b = 6 - 2 = 4$

Therefore, the equation of the perpendicular bisector of the line segment connecting the points $(-3,8)$ and $(-5,4)$ is:

$y = -\frac{1}{2}x + 4$

Hence, the equation of the perpendicular bisector is of the form $y = mx + b$, where $m = -\frac{1}{2}$ and $b = 4$.

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Answer:

Step-by-step explanation:

2x + 8 = 8

Subtract 8 from both sides.

2x = 0

Divide both sides by 2.

x = 0

The required number, eight more than twice a number is eight, is 0.

Given that,
To find the number which is eight more than twice a number is eight.

The technique in computation to use and analyze the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

In mathematics, it vends on a number of procedures according to the declarations. There are four primary arithmetic operators, addition, subtraction, multiplication, and division,

Let the number be x,
The eight more than twice a number is eight. So,
8 = 2x + 8
2x = 0
x = 0

Thus, the required number, eight more than twice a number is eight, is 0.

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The probability that the customer is a good risk is 0.70 and the probability that the customer is not a poor risk is 0.957.

To calculate the probability of the customer being a good risk, we need to divide the total number of good risk customers (7732) by the total number of customers (11,102). This gives us 7732/11102 = 0.7000. To calculate the probability of the customer not being a poor risk, we can subtract the total number of poor risk customers (949) from the total number of customers (11,102). This gives us 11102-949 = 10,153. We then divide this number by the total number of customers, giving us 10,153/11,102 = 0.9571. Therefore, the probability that the customer is a good risk is 0.70 and the probability that the customer is not a poor risk is 0.9571.

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Answer:

3.59

Step-by-step explanation:

Answer:

-∞ < x < 4

Step-by-step explanation:

→ The graph touches the y axis at 4, therefore 4 part of the range. As h ( x  ) has a vertical asymptote it will never touch the line x = 1, therefore -∞.