How many unit segments are there from 3 to 7?

The dimensions of the rectangle are 7 feet by 9 feet.

Let's use algebra to solve this problem.

Let x be the width of the rectangle in feet. Then, according to the problem, the length of the rectangle is 2 feet longer than the width, or x + 2 feet.

The area of a rectangle is given by the formula\(A = length x width.\) So, we can write:

A = (x + 2) x x

Simplifying this expression, we get:

A = x^2 + 2x

We know from the problem that the area of the rectangle is 63 square feet. So, we can substitute this value for A and solve for x:

63 = x^2 + 2x

Rewriting this equation in standard form:

x^2 + 2x - 63 = 0

Now, we can use the quadratic formula to solve for x:

x = (-2 ± sqrt(2^2 - 4(1)(-63))) / (2(1))

x = (-2 ± sqrt(4 + 252)) / 2

x = (-2 ± sqrt(256)) / 2

x = (-2 ± 16) / 2

x = -9 or x = 7

Since the width of the rectangle cannot be negative, we reject the solution x = -9. Therefore, the width of the rectangle is 7 feet.

The length of the rectangle is 2 feet longer than the width, or x + 2 = 7 + 2 = 9 feet.

So, the dimensions of the rectangle are 7 feet by 9 feet.

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Answer:  \(2\sqrt{2}+\sqrt{3}\\\\\)

a = 2 and b = 1

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

Explanation:

Set the expression equal to the given form we want. Then square both sides so we get rid of the outer-most square root

\(\sqrt{11+4\sqrt{6}} = a\sqrt{2}+b\sqrt{3}\\\\\left(\sqrt{11+4\sqrt{6}}\right)^2 = \left(a\sqrt{2}+b\sqrt{3}\right)^2\\\\11+4\sqrt{6} = \left(a\sqrt{2}\right)^2+2*a\sqrt{2}*b\sqrt{3}+\left(b\sqrt{3}\right)^2\\\\11+4\sqrt{6} = 2a^2+2ab\sqrt{2*3}+3b^2\\\\11+4\sqrt{6} = 2a^2+3b^2+2ab\sqrt{6}\\\\\)

In the third line, I used the rule that (x+y)^2 = x^2+2xy+y^2

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

At this point, we equate the non-radical and radical terms to get this system of equations

\(\begin{cases}11 = 2a^2+3b^2\\ 4\sqrt{6} = 2ab\sqrt{6}\end{cases}\)

The second equation turns into 4 = 2ab when we divide both sides by sqrt(6)

Then 4 = 2ab turns into ab = 2 after dividing both sides by 2.

We're told that a,b are rational numbers. Let's assume that they are integers (which is a subset of the rational numbers).

If so, then we have these four possibilities

If a,b are negative, then you'll find that \(a\sqrt{2}+b\sqrt{3}\) overall is negative. But this contradicts that \(\sqrt{11+4\sqrt{6}}\) is positive. So a,b must be positive.

Let's assume that a = 1 and b = 2. If so, then,

2a^2+3b^2 = 2(1)^2+3(2)^2 = 14

but we want that result to be 11 instead.

Let's try a = 2 and b = 1

2a^2+3b^2 = 2(2)^2+3(1)^2 = 11

which works out perfectly.

Therefore,

\(\sqrt{11+4\sqrt{6}} = 2\sqrt{2}+\sqrt{3}\\\\\)

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

Checking the answer:

Use a calculator to find that

\(\sqrt{11+4\sqrt{6}} \approx 4.5604779\\\\2\sqrt{2}+\sqrt{3} \approx 4.5604779\\\\\)

both have the same decimal approximation, so this is a fairly informal way to confirm the answer.

Another thing you can do is to take advantage of the idea that if x = y, then x-y = 0

So if you want to see if two things are equal, you subtract them. You should get exactly 0 or something very small (pretty much equal to 0).

One exponential function with the given features is y = 2^x - 3, and is graphed at the end of the answer.

An exponential function is defined as follows:

y = a(b)^x + c.

In which:

The graph of the function has a horizontal asymptote at y = -3, hence:

c = -3.

For a and b, they can assume any non-negative values, hence we attribute these following values:

a = 1, b = 2.

The graph is given at the end of the answer.

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Answer:

-48.19

Step-by-step explanation:

Given the data:

City Price ($) Sales

River Falls 1.30 100

Hudson 1.60 90

Ellsworth 1.80 90

Prescott 2.00 40

Rock Elm 2.40 38

Stillwater 2.90 32

We could obtain a simple regression model of the data above using a linear regression calculator :

The regression model obtained is :

ŷ = -48.19277X + 161.38554

The change in sales per unit change in price is the value of the slope or gradient :

From the general linear regression equation :

y = mx + c

m = slope ;

Slope = - 48.19 ; hence, there is a drop in sales by about 48 units as the change in sales as the price of candy bar goes up by about $1.00

Answer:

i think 64?

Step-by-step explanation:

its supposed to be the same on the bottom, right?

Answer: The letter "x" is often used in algebra to mean a value that is not yet known. It is called a "variable" or sometimes an "unknown". In x + 2 = 7, x is a variable,

Step-by-step explanation:

Answer:

A. 8

Step-by-step explanation:

The angle shown is a 90 degree right angle (shown by the box where the vertex is)

We see that the first angle inside the right angle is 50 degrees, so the other angle must be 40 because the degrees must add up. We can set up an equation here.

\(5x=40\)

After dividing both sides by 5, we get x = 8

A set is simply the group of related item.

Let:

\(C \to\) Those who eat corn

\(M \to\)Those who eat millet

\(x \to\) Those who eat both

So, we have:

\(C = 400\)

\(M= 290\)

\(None = 60\)

\(Total = 730\)

(a) The number of those who eat both

To do this, we make use of the following equation

\(Total =C + M - x + None\)

The above equation represents the sum of all possible subsets

So, we have:

\(730 =400 + 290 - x+ 60\)

Collect like terms

\(x =400 + 290 + 60 -730\)

\(x =20\)

Hence, 20 villagers eat both

(b) Number of those that eat only one

We have:

\(C = 400\)

\(M= 290\)

The number (n) of those that eat only one is:

\(n =C -x+ M - x\)

\(n = 400 - 20 + 290 - 20\)

\(n =650\)

Hence, 650 villagers eat only one

See attachment for the Venn diagram that illustrates the set

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Answer:  The answer to the question is $59.05

Step-by-step explanation:

Good Luck

Answer:

the answer is 3 1/2 hours

Explanation: Just add all the fractions and numbers and subtract that by 9 1/4

Answer: C

Step-by-step explanation:

For our unknown value x, the opposite side = 10 and the adjacent side = 18, using this information you can use SOH CAH TOA.

TOA refers to opposite over adjacent, which would be

tan x = 10/18.

Hope this helps!

Answer:

12.5 cents per box

Step-by-step explanation:

First, find the price difference of the cases.

11.99 - 10.49 = $1.50

We want to find the money saved per box so divide $1.50 by 12.

1.50/12 = 12.5 cents

When a scientific team uses special equipment to measures the pressure under water and finds it to be 159 pounds per square foot, the depth is around 70 feet.

It's important to note that pressure increases as depth increases under water. The pressure in pounds per square foot, P, at a depth of d feet is given by the equation:

P = 0.433d + 14.7 where 0.433 is a constant for water, and 14.7 is the pressure at the surface.

In order to find the depth at which the pressure is 159 pounds per square foot, we need to solve the equation for

d.P = 0.433d + 14.7

Substitute P = 159 and solve for

d.159 = 0.433d + 14.7

Subtract 14.7 from both sides.

144.3 = 0.433d

Divide both sides by 0.433 to isolate d.

d ≈ 333.06

Hence, when a scientific team uses special equipment to measures the pressure under water and finds it to be 159 pounds per square foot, the depth is around 70 feet.

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TRUNCATED to one decimal place, it's 50.2

ROUNDED to one decimal place, it's 50.3

The round-off of 50.272 to 1 decimal place using rules of rounding

numbers are 50.3.

Rounding off numbers means making a number simpler by adjusting it to its nearest place according to certain rules.

Rounding a number to one decimal place means keeping only the first digit after the decimal point and neglecting the rest. In this case, the digit in the second decimal place is 7, which is greater than or equal to 5. As per the rounding rules, if the digit is greater than 5, the preceding digit is increased by 1.

So, 50.272 becomes 50.3 when rounded to one decimal place.

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Answer:

.48

Step-by-step explanation:

16 cups in a gallon so 8.64 divided by 16 is .48

Answer:

$0.27 a cup

Step-by-step explanation:

16 cups in a gallon so 32 cups in 2 gallons, so 8.64 divided by 32 = .27

Answer: 72 cm

Step-by-step explanation:

78 is the hypotenuse, so that it will be the c

30^2 + b^2 = 78^2

900 + b^2 = 6084

b^2 = 5184

b= 72cm

The required value of x is 22 degrees for the given figure.

Adjacent angles are a sort of additional angle. Adjacent angles share a common side and vertex, such as a corner point. Their points do not overlap in any manner.

As we know that supplementary angles are defined as when pairing of angles addition to 180° then they are called supplementary angles.:

According to the given figure, it can be written as follows:

2x + 24 + 6x - 20 = 180

8x + 4 = 180

8x = 180 - 4

8x = 176

x = 176/8

x = 22

Therefore, the required value of x is 22 degrees for the given figure.

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The complete question is as follows:

Find the value of x for the below figure.

To eliminate the roots in 1.1 and 1.2, we can use trigonometric substitution. In 1.1, we can substitute x = 4 sin(theta) to eliminate the root of 4. In 1.2, we can substitute z = 7 sin(theta) to eliminate the root of 7.

1.1. V64+2 + 1 We can substitute x = 4 sin(theta) to eliminate the root of 4. This gives us:

V64+2 + 1 = V(16 sin^2(theta) + 2 + 1) = V16 sin^2(theta) + V3 = 4 sin(theta) V3 1.2. V4z2 – 49

We can substitute z = 7 sin(theta) to eliminate the root of 7. This gives us:

V4z2 – 49 = V4(7 sin^2(theta)) – 49 = V28 sin^2(theta) – 49 = 7 sin(theta) V4 – 7 = 7 sin(theta) (2 – 1) = 7 sin(theta)

Here is a more detailed explanation of the substitution:

In 1.1, we know that the root of 4 is 2. We can substitute x = 4 sin(theta) to eliminate this root. This is because sin(theta) can take on any value between -1 and 1, including 2.

When we substitute x = 4 sin(theta), the expression becomes V64+2 + 1 = V(16 sin^2(theta) + 2 + 1) = V16 sin^2(theta) + V3 = 4 sin(theta) V3

In 1.2, we know that the root of 7 is 7/4. We can substitute z = 7 sin(theta) to eliminate this root. This is because sin(theta) can take on any value between -1 and 1, including 7/4.

When we substitute z = 7 sin(theta), the expression becomes: V4z2 – 49 = V4(7 sin^2(theta)) – 49 = V28 sin^2(theta) – 49 = 7 sin(theta) V4 – 7 = 7 sin(theta)

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7×(15+7-4+(x+y×38))^3 when x = 4 and y = 9

7×(15+7-4+(4+9×38))^3

=> 7×(15+7-4+(4+342))^3

=> 7×(15+7-4+346)^3

=> 7×364^3

=> 7×48228544

=> 337599808

The height of the wall where the ladder reaches will be 23.6 feet.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.

Avery leans a 24-foot ladder against a wall so that it forms an angle of 80° with the ground.

The height of the wall where the ladder reaches is given as,

\(\text{sin 80}^\circ \sf =\dfrac{h}{24}\)

\(\sf h = 24 \times \text{sin 80}^\circ\)

\(\sf = 24 \times \text{0.9848}\)

\(\sf h = 23.63\thickapprox\bold{23.6 \ feet}\)

The height of the wall where the ladder reaches will be 23.6 feet.

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The area of of the circle is approximately 286 square meters (rounded to the nearest whole number).

A circle is simply a closed 2-dimensional curved shape with no corners or edges.

The area of a circle is expressed mathematically as;

A = πr²

The circumference of a circle is expressed as:

C = 2πr

Where r is radius and π is constant pi ( π = 3.14 )

First, we determine the radius r of the circle:

Given that the circumference is 60m.

60 = 2 × 3.14 × r

r = 60 / 6.28

r = 9.55 m

Now, plug r = 9.55 m into A = πr² and find the area:

A = πr²

A = 3.14 × ( 9.55 m )²

A = 286 m²

Therefore, the area is 286 square meters.

The complete question is:

The circumference of a circle is 60m. What is the area of the circle to the nearest whole number?

A. 60m

B. 30m

C. 286m

D. 900m

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Answer:

a+k ≤ 35

8a+4k ≤ 190

Some possible combinations are 10 adults and 20 kids

5 adults and 29 kids

Step-by-step explanation:

Let k= number of kids

a = number of adults

a+k ≤ 35  since you can have at most 35

8a + 4k ≤ 190 since the most you can spend is 190

Some possible combinations are 10 adults and 20 kids

(10+30 < 35 and 8*10+4*20 = 80+80 =160< 190)

Another possible combination

5 adults and 29 kids

(5+29 < 35  and 5*10 + 4*29 =50+116=166)

Answer:

a. 1

b. 2.

Step-by-step explanation:

a) There are a total of 10 numbers so we have:

4 * 10 = 3+5+6+8+9+2+1+0+5+x

40 = 39 + x

x = 1.

b) 5*6 = 28 + x

x = 2.

Answer:

150° and 210°

Step-by-step explanation:

1) to drow a circle with radius=1 in the system of coordinates like in the attached picture;

2) to mark point (-√3/2)≈-0.866 on X-axis (in the picture it is the point M);

3) to graph line AB through point M, the line AB || Y-axis and the points A and B are on the circle with radius=1;

4) to measure the angles ∠ROA and ∠ROB (the points are marked with red colour);

5) finally, m(∠ROA)=150°; m(∠ROB)=210°.

To calculate the cash balance at the end of the period, we need to consider the cash inflows and outflows.

Starting cash balance: $4,520

Cash inflows: $1,654 (receivables collected)

Cash outflows: $1,961 (payments to suppliers) + $500 (cash expenses)

Total cash inflows: $1,654

Total cash outflows: $1,961 + $500 = $2,461

To calculate the cash balance at the end of the period, we subtract the total cash outflows from the starting cash balance and add the total cash inflows:

Cash balance at the end of the period = Starting cash balance + Total cash inflows - Total cash outflows

Cash balance at the end of the period = $4,520 + $1,654 - $2,461

Cash balance at the end of the period = $4,520 - $807

Cash balance at the end of the period = $3,713

Therefore, the cash balance at the end of the period is $3,713.

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The percentage of items that will weigh at least 11.7 ounces is 3.22%.

The weight of items produced by a machine is normally distributed with a mean (μ) of 8 ounces and a standard deviation (σ) of 2 ounces. We need to determine the percentage of items that will weigh at least 11.7 ounces using this information. The given information is as follows:

Mean (μ) = 8 ounces

Standard deviation (σ) = 2 ounces

Let X be the weight of the item produced by the machine.

Then the random variable X ~ N(8, 2²) = N(8, 4)

We need to find the percentage of items that will weigh at least 11.7 ounces. That isP(X ≥ 11.7)

We can calculate it as follows:

z = (11.7 - μ) / σ = (11.7 - 8) / 2 = 1.85

P(X ≥ 11.7) = P(Z ≥ 1.85)

We can look up this probability in the standard normal distribution table or use a calculator.

Using the standard normal distribution table, we can find that the probability of a Z-value being greater than or equal to 1.85 is approximately 0.0322.

Therefore, the percentage of items that will weigh at least 11.7 ounces is:

P(X ≥ 11.7) = P(Z ≥ 1.85) ≈ 0.0322 ≈ 3.22%

Therefore, the answer is 3.22%.

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(−6,−4)

M at h way is great help for future questions

This matrix has a pivot in every column, so the set of polynomials {p1, p2, p3} is linearly independent.

There are no scalars c1, c2, c3 (not all zero) that satisfy the equation c1p1(x) + c2p2(x) + c3p3(x) = 0 for all x.

To test the linear independence of the set of polynomials, we can make each coordinate vector a column of the matrix and perform row operations to transform the matrix to row-echelon form.

If the resulting matrix has a pivot in every column, then the set of polynomials is linearly independent.

If there is a column without a pivot, then the set of polynomials is linearly dependent.

To demonstrate, let's consider the set of polynomials {p1, p2, p3}.

where:

p1(x) = x2 - 3x + 2p2(x)

= -x2 + 2xp3(x)

= 3x2 - 4x - 1

We will create a matrix with the coordinate vectors of each polynomial as columns:

\($$\begin{pmatrix}1 & -1 & 3\\-3 & 2 & -4\\2 & 0 & -1\end{pmatrix}$$\)

Now, we will perform row operations to transform the matrix to row-echelon form:

\($$\begin{pmatrix}1 & -1 & 3\\0 & -1 & 5\\0 & 0 & 1\end{pmatrix}$$\).

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Answer:

X=-33

Step-by-step explanation:

Answer:

x= -33

Step-by-step explanation:

Subtract 9 from both sides:

2/3x+9-9=-13-9

Simplify the arithmetic:

2/3 · x =-13-9

Simplify the arithmetic:

2/3 · x = -22

Multiply both sides by inverse fraction 3/2:

2/3x ·3/2= -22 ·3/2

Group like terms:

 2/3 ·3/2x= -22 ·3/2

Simplify the fraction:

x=-22 · 2/3

Multiply the fractions:

x= -22·2/3 ÷2

Simplify the arithmetic:

x = -33

The correct choice is within your skills and abilities.

Once you get to determine things you are capable of and things you are not capable of, you will be able to concentrate on your strengths more. This will in turn produce big results as compared to if you opted to concentrate on your weaknesses.

It will also result in no or less time wasted in doing what you are less capable of.

Its almost close to impossible to be able to do everything. Each person is gifted in a certain area or skill or capability. We are all different and that's okay.

Its so important to concentrate in the areas you are more comfortable with. This will help you much with improving your skills and abilities.

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Answer:

Step-by-step explanation:

a you just had to say a

Answer:

the answer is 5/6

Step-by-step explanation:

the company is not the first BFF to come to mr as default

the answer is 5/6. have a good day