Given b(x) = |x+41, what is b(-10)?
O-10
0-6
06
O 14

Answer:

question 2

a) rectangle

b) all of the angles are 90 degrees

c) 3+3+4+4=14 units

d) 12 units squared

question 3

if their slopes are the same, they are parallel.

if the lines do not intersect graphically, they are parallel.

if the slopes multiply to -1, they are perpendicular.

if the degree made by the intersection is 90 degrees, the lines are perpendicular.

As per the given data, the number of integers in R ∩ S is 2, and the correct answer is (B) Two.

In mathematics, the intersection of two sets is a set containing all elements that are members of both sets.

In symbols, the intersection of two sets A and B is denoted by A ∩ B, and it contains all elements that belong to both A and B.

The intersection of two sets contains only the elements that are present in both sets. In this case,

R ∩ S = {x | x > 0 and x < 3}

The integers that are present in this set are 1 and 2.

Therefore, the number of integers in R ∩ S is 2, and the correct answer is (B) Two.

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Answer:

a = 1/25

Step-by-step explanation:

The vertex form of the parabola is

y = a(x-h)^2 +k

where (h,k) is the vertex

y = a(x-2)^2 -4

We have a point on the parabola (-3,-3) so substitute this into the equation

-3 = a(-3-2)^2 -4

-3 = a(-5)^2 -4

Add 4 to each side

-3+4 = a(25) +4-4

1 = 25a

Divide each side by 25

1/25 = a

y = 1/25(x-2)^2 -4

By integrating,  the function is f(θ) = -sin(θ) - cos(θ) + θ + 6

What is relationship between integrals and derivatives?

The derivative and the integral are related to each other through the fundamental theorem of calculus:

If f(x) is a continuous function on an interval [a, b], then the function F(x) defined by F(x) = ∫[a, x] f(t) dt is continuous on [a, b] and differentiable on (a, b), and F'(x) = f(x). This means that the derivative of the integral of a function is equal to the original function.

To find f(θ), we need to integrate f''(θ) twice.

f''(θ) = sin(θ) + cos(θ)

Integrating once gives:

f'(θ) = -cos(θ) + sin(θ) + C₁

Using the initial condition f'(0) = 2, we have:

f'(0) = -cos(0) + sin(0) + C₁ = 1 + C₁ = 2

Therefore, C₁ = 1, and we have:

f'(θ) = -cos(θ) + sin(θ) + 1

Integrating again gives:

f(θ) = -sin(θ) - cos(θ) + θ + C₂

Using the initial condition f(0) = 5, we have:

f(0) = -sin(0) - cos(0) + 0 + C₂ = -1 + C₂ = 5

Therefore, C₂ = 6, and we have:

f(θ) = -sin(θ) - cos(θ) + θ + 6

So, the function f(θ) is:

f(θ) = -sin(θ) - cos(θ) + θ + 6

And f''(0) is:

f''(0) = sin(0) + cos(0) = 1

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Answer:

25%

Step-by-step explanation:

125:500

               divide by 5 to make 500 into 100

25:100

             convert to percent

25%

Answer:

320 g

Step-by-step explanation:

To find the recommended daily amount of protein, we can set up a proportion using the given information:

30% of the recommended daily amount = 96 grams

Let "x" represent the recommended daily amount of protein. We can set up the proportion as:

30/100 = 96/x

To solve for x, we can cross-multiply and solve the equation:

30x = 100 * 96

30x = 9600

Dividing both sides by 30:

x = 9600 / 30

x ≈ 320

The constant of proportionality in the box to match the table will be 2/3. Then the last option is correct.

A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.

The table is given below.

x      y

0     0

3      2

6      4

9      6

The variable 'y' is directly proportional to the variable 'x'. Then we have

y ∝ x

y = k x

At (9, 6), the value of the constant 'k' is given as,

6 = 9k

k = 6 / 9

k = 2/3

The proportionality is given as,

y = (2/3) x

The constant of proportionality in the box to match the table will be 2/3. Then the last option is correct.

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1. It is false that when non-Standard unit used is small few unit's are

needed .

2. Objects with different shapes can have the same volume. True

3. Length, width and height and multiplied to find volume of a rectangular prism. True

4. It is false that volume is measured in square unit.

5. It is true that Volume is a measure of the amount of space inside an object.

6. The formula for volume of a rectangular prism is V = l × w × h. True

7. It is true that Standard units give a consistent and accurate measure of a container.

8. It is false that Non-Standard units cannot be used to measure volume.

9. Volume is measured in cubic units. True

Volume can be defined as the amount of space inside and object. the object can be in different form such as cone, rectangular prism, cylinder and many other shapes. Even though shapes are different, It is possible for different shapes or objects to have the same volume when measure.

Measurement of volume can be through standard measurement and non standard measurements such as a cup of rice. However, for consistency and the sake of accuracy, it is advisable to always use standard measurements of volume where possible to avoid error that may occur in non standard measurement. The acceptable and recognized unit of volume is cubic meter (\(m^3\)).

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Answer:

3. D 4. B

Step-by-step explanation:

3.  e^2 = g^2 + f^2, answer is d

4. Let a = 3, b = 4, c = 5

2c = 10

2b = 8

2a = 6

10^2 = 8^2 + 6^2

answer is b

3. The Pythagorean theorem states the hypotenuse squared is equal to each side squared added to each other.

The answer is D. E^2 = f^2 + g^2

4.

To keep the proportion you could multiply the sides by the same numbers . The answer would be 2A, 2b, 2c

A rectangular floor with a length of 14 ft and a width of 6 ft, square tiles with an edge length of 3/4 ft, a total of 144 tiles can fit.

To determine how many square tiles can fit in a rectangular floor, we need to calculate the total number of tiles that can fit both horizontally and vertically.

Given:

Length of the rectangular floor = 14 ft

Width of the rectangular floor = 6 ft

Edge length of square tile = 3/4 ft

First, let's calculate the number of tiles that can fit horizontally:

Length of the rectangular floor / Edge length of square tile = 14 ft / (3/4 ft) = 14 ft × (4/3 ft) = 56/3 ft

Since we want a whole number of tiles, we need to round down or take the floor value:

Number of tiles horizontally = floor(56/3) = 18 tiles

Next, let's calculate the number of tiles that can fit vertically:

Width of the rectangular floor / Edge length of square tile = 6 ft / (3/4 ft) = 6 ft × (4/3 ft) = 24/3 ft

Again, we round down or take the floor value:

Number of tiles vertically = floor(24/3) = 8 tiles

To find the total number of tiles, we multiply the number of tiles horizontally by the number of tiles vertically:

Total number of tiles = Number of tiles horizontally × Number of tiles vertically = 18 tiles × 8 tiles = 144 tiles

Therefore, in a rectangular floor with a length of 14 ft and a width of 6 ft, square tiles with an edge length of 3/4 ft, a total of 144 tiles can fit.

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Answer:

\(r ^{2} = (x-4)^2 + (y+1)^{2}\)

Given:

endpoints at (-1, 6) and (9, -8)

Solve for:

the standard equation of a circle having endpoints of a diameter at (-1, 6) and (9,-8).

Step-by-step explanation:

\(d=\sqrt{(x_{2} -x_{1})^2+(y_{2} -y_{1})^2}\)

\(d=\sqrt{(9-(-1))^2+(-8-6)^2}\)

\(d=\sqrt{10^2+-14^2}\)

\(d=\sqrt{100+196}\)

\(d=\sqrt{296}\)

\(d=2\sqrt{74}\)

\(r=\frac{d}{2}\)

\(r=\frac{2\sqrt{74} }{2}\)

\(r=\sqrt{74}\)

\(Center = (\frac{x_{1}+x_{2} }{2} ,\frac{y_{1}+y_{2} }{2})\)

\(= (\frac{-1+9}{2}, \frac{6+(-8)}{2} )\)

\(=(4, -1)\)

\(Center = (4,-1) \\and\\r = \sqrt{74}\)

Equation:

\((\sqrt{74}) ^{2} = (x-4)^2 + (y+1)^{2}\)

\(r ^{2} = (x-4)^2 + (y+1)^{2}\)

*This took forever so I hoped it helped lol*

The equation given in slope-intercept form does not represent the graph because the y-intercept of the graph is equal to 4 while the y-intercept of the equation is equal to 5.

In Mathematics, the slope-intercept form of a line can be calculated by using this linear equation:

y = mx + c

Where:

In Mathematics, the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).

Based on the information provided regarding the equations and graphs, the y-intercept are as follows:

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f(x)=27500(1.073)ˣ is the equation for the function.

A relation is a function if it has only One y-value for each x-value.

Since the car's value is expected to appreciate 7.3% each year, the value of the car x years from now can be modeled with an exponential function.

Let's call the current value of the car a, and let's call the annual growth rate r.

Then the function for the value of the car x years from now is:

f(x) = a (1 + r)ˣ

7.3%=0.073

f(x)=27500(1.073)ˣ

Hence, f(x)=27500(1.073)ˣ is the equation for the function.

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Answer:

Step-by-step explanation:

Therefore, the solutions to the equation 0 = |3x + 3| + 3 are x = -2 and x = 0.

To solve the equation 0 = |3x + 3| + 3, we need to eliminate the absolute value. Remember that the absolute value of a number is always non-negative.

First, let's isolate the absolute value term on one side of the equation:

|3x + 3| = -3

Since the absolute value cannot be negative, there are no solutions to the equation as it stands. However, if we modify the equation to make the right side positive, we can find a solution.

To eliminate the absolute value, we can rewrite the equation as two separate equations, considering both the positive and negative cases:

   3x + 3 = -3

   -(3x + 3) = -3

Solving equation 1:

3x + 3 = -3

3x = -6

x = -2

Solving equation 2:

-(3x + 3) = -3

-3x - 3 = -3

-3x = 0

x = 0

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Answer: It will be A that is the best answers

Answer:

208.6 gal/min

Step-by-step explanation:

For 2" pipe,

Given Volume = 463.2 gal, time = 12 min

flow rate for 2" pipe

= Volume ÷ time

= 463.2÷12

= 38.6 gal/min

For 4" pipe,

Given Volume = 1730.4 gal, time = 7 min

flow rate for 4" pipe

= Volume ÷ time

= 1730.4÷7

= 247.2 gal/min

Difference in flow rate = 247.2 - 38.6 = 208.6 gal/min

The rent for The new monthly lease amount is $858.

To find out the new monthly lease amount, we need to take into account that there is one month free, which we need to apply to all the months of the lease period.

A one-year lease is for 12 months.

The total rent amount for 12 months = Regular rent for 12 months - One-month free rent= $936 × 12 - $936 = $11232 - $936= $10296

The free rent is distributed equally across the 12 months:$936 ÷ 12 = $78

The new monthly rent amount is the total rent amount for 12 months divided by the number of months:

Total rent amount for 12 months = $10296

New monthly lease amount = Total rent amount for 12 months ÷ 12

New monthly lease amount = $10296 ÷ 12

New monthly lease amount = $858

Therefore, the new monthly lease amount is $858.

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The probability of rolling a sum that is at most 7 = 1/6

What is probability and example?

sample space (S) = 36

The probability of rolling a sum that is at most 7

No of sample space = { (1,6) ,(2,5) ,(3,4), (4,3),(5,2),(6,1)}

n(s)/ total sample space = 6/36

                                        = 1/6

Therefore, he probability of rolling a sum that is at most 7 = 1/6

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Answer:

(2,1)

Step-by-step explanation:

The line 4y - 2x = 0 can be written in slope-intercept form as y = 1/2x.

So any point that satisfies this equation will lie on the line. For example, the point (2,1) satisfies the equation:

4(1) - 2(2) = 0

So the point (2,1) is on the line.

\(\begin{cases} f(x)=-3x+5\\[1em] f(rx)=-3(rx)+5 \end{cases}\qquad \qquad \begin{cases} g(x)=-1x+5\\[1em] g(x)=f(rx)\\ \qquad -3(rx)+5 \end{cases} \\\\\\ \stackrel{g(x)}{-1x+5}~~=~~\stackrel{g(x)}{-3(rx)+5}\implies -x+5=-3rx+5\implies -x=-3rx \\\\\\ \cfrac{-x}{-x}=3r\implies 1=3r\implies \boxed{\cfrac{1}{3}=r}\)

Answer:

0.667

Step-by-step explanation:

Given that :

Head is twice more likely to occur than a tail.

P(head) = p(H) = 2/3

P(tail) = p(T) = 1/3

If coin is tossed 3 times :

P(H = 0) :

1st toss = tail ;2nd toss = tail ; 3rd toss =. Tail

(1/3) * (1/3) * (1/3) = 1 / 27

P(H= 1)

HTT, THT, TTH

(2/3 * 1/3 * 1/3) + (1/3 * 2/3 * 1/3) + (1/3 * 1/3 *2/3)

= 2/27 + 2 /27 + 2/27

= 6/27 = 2/9

P(H=2)

HHT, HTH, THH

(2/3 * 2/3 * 1/3) + (2/3 * 1/3 * 2/3) + (1/3 * 2/3 * 2/3)

= 4/27 + 4/27 + 4/27

= 12 / 27

= 4 /9

P(H = 3)

HHH

(2/3 * 2/3 * 2/3)

= 8 / 27

X ___ 0 ___ 1 ____ 2 ____ 3

P(x) _ 1/27 _ 2/9 __ 4/9 __ 8/27

E(X) = (0 * (1/27)) + (1 * (2/9)) + (2 * (4/9)) + (3 * (8/27)) = 2

E(X) = 2

Var(X) = Σx²p(x) - E(X)²

= (0^2 * (1/27)) + (1^2 * (2/9)) + (2^2 * (4/9)) + (3^2 * (8/27)) - 2^2

= 4.667 - 4

= 0.667

Hence, Var(x) = 0.667

The maximum volume of the cylinder is approximately 1257 cubic centimeters.

The volume V of a right circular cylinder with radius r and height h is given by:

V = πr²h

Substituting the given expressions for the radius and height of the cylinder, we get:

V = πx²(800/πx - x)

Simplifying the expression, we get:

V = 800x - πx³

To find the maximum value of V, we need to find the value of x that maximizes V. We can do this by taking the derivative of V with respect to x, setting it equal to zero, and solving for x:

dV/dx = 800 - 3πx² = 0

3πx² = 800

x² = 800/3π

x ≈ 6.43

Substituting this value of x back into the expression for V, we get:

V ≈ 1257

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The number of square inches of cardboard that are needed to make one

the container is 18.

We have,

The volume of the triangular prism.

= Area of the triangle x height

Now,

Height = 6 in

And,

To find the area of a triangle, we can use Heron's formula.

A = √(s(s-a)(s-b)(s-c))

where s is the semi-perimeter of the triangle, calculated as:

s = (a + b + c) / 2

In this case, the side lengths of the triangle are 3.2 in, 3.2 in, and 2 in.

Let's calculate the area using Heron's formula:

s = (3.2 + 3.2 + 2) / 2 = 4.2

A = √(4.2(4.2 - 3.2)(4.2 - 3.2)(4.2 - 2))

A = √(4.2 x 1 x 1 x 2.2)

A = √(9.24)

A ≈ 3.04 square inches

Now,

The volume of the triangular prism.

= Area of the triangle x height

= 3.04 x 6

= 18.24 in²

Now,

Area of one cardboard.

= 1² in²

= 1 in²

Now,

The number of square inches of cardboard that are needed to make one

container.

= The volume of the triangular prism / Area of one cardboard

= 18.24 in² / 1 in²

= 18.24

= 18

Therefore,

The number of square inches of cardboard that are needed to make one

the container is 18.

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Answer:

The sales for the store 7 days after the end of the advertising campaign is  

          \(G_7 =\)$3849.74

Step-by-step explanation:

From the question we are told that

    The daily sales on the end of campaign day is  \(G_o\) =  $8,500

     The  daily sales three days after end of campaign day is  \(G_3\) = $ 5,100

     The  usual day sales of the store is \(G_u\)  =  $ 3,500

Generally the Newton's Law of Cooling (Heating). equation is  mathematically represented as

         \(G_t = G_u+ [(G_o -S_u ) * e^{-(k*t)}]\)

Here t is the number of day after the campaign ended

Now substituting values to obtain the constant k

For  t =  3

         \(G_3 = G_u + [(G_o -S_u ) * e^{-(k*3)}]\)

          \(5100 = 3500 [(8500 -3500 ) * e^{-(k*3)}]\)

         \(e^{-(k*3)} = 0.32\)

=>     \(-3k = ln (0.6)\)

=>      \(-3k = -1.1394\)

=>        \(k = 0.380\)

So at  t =  7

     \(G_7 = G_u + [(G_o -S_u )] * e^{-(k*7)}\)

substituting values

    \(G_7 = 3500 + [(8500 -3500 )] * e^{-(0.3780*7)}\)

    \(G_7 =\)$3849.74