7 grade go math lesson 1.1 adding integers with a common sign

To evaluate `641000√3`, we just need to multiply `641000` by `√3` to get the exact value. Then we can simplify the result if necessary.Using a calculator, we can find: `641000√3 ≈ 1110791.54794`

Rounding to the nearest whole number, we get:`641000√3 ≈ 1110792`Therefore, the closest answer choice to `1110792` is `1125`. Thus, `Evaluate 641000√3` is `1125`. Given that the zeros of the polynomial function are -5 and -3i, we can deduce that the polynomial must also have the zero 3i. This is because complex zeros always come in conjugate pairs, so the conjugate of -3i is 3i.

Therefore, the polynomial function can be expressed as follows:x = -5, x = -3i and x = 3iFor x = -5, we have (x + 5) as one of the factors.For x = -3i, we have (x + 3i) as one of the factors.For x = 3i, we have (x - 3i) as one of the factors.Now, we can find the polynomial of least degree with integral coefficients by multiplying these factors:(x + 5)(x + 3i)(x - 3i) = (x + 5)(x² - (3i)²) = (x + 5)(x² + 9)Expanding this, we get:x³ + 5x² + 9x + 45Therefore, the polynomial function of least degree with integral coefficients that has zeros -5 and -3i is x³ + 5x² + 9x + 45.

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To find the point on the curve r(t)=(2cost, 2sint, e^t) we need to evaluate the x, y, and z coordinates at a specific value of t. Let's choose t=0 for simplicity.

So, plugging in t=0 we have:

r(0) = (2cos(0), 2sin(0), e^0)
r(0) = (2, 0, 1)

Therefore, the point on the curve at t=0 is (2, 0, 1).

To find the point on the curve r(t) = (2cos(t), 2sin(t), e^t) for a specific value of t, you can plug in the value of t into the parameterized equation:

1. Replace t with the specific value you're interested in (e.g., t = a).
2. Compute 2cos(a) for the x-coordinate.
3. Compute 2sin(a) for the y-coordinate.
4. Compute e^a for the z-coordinate.

The point on the curve will be (2cos(a), 2sin(a), e^a).

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Answer:

So I'm assuming Abby is six yrs and she is the same age as bill I'm thinking their both 12 yrs old. pls correct me if I'm wrong.

A ranked frequency distribution of data can be created by sorting the data in ascending or descending order and then counting the frequency of each value.

The given data set is 245, 261, 289, 222, 291, 289, 240, 233, 249, and 200. To create a ranked frequency distribution of this data set, we first need to sort it in ascending or descending order. Let's sort it in ascending order:200, 222, 233, 240, 245, 249, 261, 289, 289, 291 Next, we need to count the frequency of each value. We can do this by going through the data set and counting how many times each value occurs. Here is the frequency distribution table:Value Frequency 200 1222 1233 1240 1245 1249 1261 1289 2291 1 From this table, we can see that the most frequent value is 289, which occurs twice. We can also see that the least frequent values are 200, 222, 233, and 240, which each occur only once.

In conclusion, a ranked frequency distribution of data can be created by sorting the data in ascending or descending order and then counting the frequency of each value. This allows us to see which values are most and least frequent in the data set.

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Answer: D, these Triangles are not similar.

Step-by-step explanation:

Given the line integral, we are to evaluate the integral by definition. Here is the integral given

The line segment from (0, 0, 0) to (0, 1, 2) is given by z = 2y and

x = 0.

Therefore, the parameterization of the line segment is given by r(t) = ti + tj + 2t k. (0 ≤ t ≤ 1)

Substituting this into the integral, we have:∫CF (x, y, z).dr=∫CF (2xy + z) ds

Here s is the length of the curve from (0, 0, 0) to (0, 1, 2).

Therefore, we have to evaluate the integral as follows:

∫CF (2xy + z) ds = ∫10 (2t · 0 · 0 + 2t) dt

= 2

∫10 t dt= [t²]10 = 1

Therefore, evaluating the given line integral we have  = 2

Hence option B is the correct option.

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Explanation:

Comparing y = x^2+bx+c to y = ax^2+bx+c, we see that a = 1.

The vertex given is (-2,3). In general, the vertex is (h,k). So h = -2 and k = 3.

Plug those three values into the vertex form below

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

y = 1(x-(-2))^2 + 3

y = (x+2)^2 + 3

Then expand everything out and simplify

y = x^2+4x+4 + 3

y = x^2+4x+7

We see that b = 4 and c = 7.

The number of 6th graders who made A is 104.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

In this case, about 25% of 6th graders made A in math and there are 416 6th graders,

Those that made A will be:

= Percentage × Total students

= 25% × 416

= 104

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Let \(\vec K,\vec L,\vec M,\vec N\) be vectors pointing the vertices K, L, M, and N, respectively.

The side KL is parallel to and has the same length as the vector

\(\vec L - \vec K = (2\,\vec\imath + 3\,\vec\jmath + 3\,\vec k) - (2\,\vec\imath+2\,\vec\jmath+\vec k) = \vec\jmath + 2\,\vec k\)

Similarly, the side KN is parallel and as long as

\(\vec N - \vec K = (6\,\vec\imath+8\,\vec\jmath+\vec k) - (2\,\vec\imath+2\,\vec\jmath+\vec k) = 4\,\vec\imath+6\,\vec\jmath\)

These vectors have magnitudes

\(\|\vec L - \vec K\| = \sqrt{0^2 + 1^2 + 2^2} = \sqrt5\)

\(\|\vec N - \vec K\| = \sqrt{4^2 + 6^2 + 0^2} = 2\sqrt{13}\)

and their dot product is

\((\vec L - \vec K) \cdot (\vec N - \vec K) = 0\cdot4 + 1\cdot6+1\cdot0 = 6\)

The parallelogram spanned by the vectors \(\vec L-\vec K\) and \(\vec N-\vec K\) has area equal to the magnitude of their cross product, for which we have the identity

\(\bigg\|(\vec L - \vec K) \times (\vec N - \vec K)\bigg\| = \|\vec L - \vec K\| \|\vec N - \vec K\| \sin(\theta) \\\\ \implies \text{area} = 2\sqrt{65} \, \sin(\theta)\)

where \(\theta\) is the angle between the sides KL and KN.

From the dot product identity, we have

\((\vec L - \vec K) \cdot (\vec N - \vec K) = \|\vec L - \vec K\| \|\vec N - \vec K\| \cos(\theta) \\\\ \implies 6 = 2\sqrt{65} \cos(\theta)\)

Then

\(\cos(\theta) = \dfrac3{\sqrt{65}} \implies \sin(\theta) = \sqrt{1-\cos^2(\theta)} = 2\sqrt{\dfrac{14}{65}} \\\\ \implies \text{area} = 2\sqrt{65} \cdot 2\sqrt{\dfrac{14}{65}} = \boxed{4\sqrt{14}}\)

The lengths of the diagonals are 13 and 26 millimeters.

Let the length of the shorter diagonal be x.

Then, the length of the longer diagonal is 2x.

The area of a rhombus is given by (1/2) * d1 * d2, where d1 and d2 are the diagonals.

So we have:

(1/2) * x * 2x = 169

Simplifying this equation, we get:

\(x^2\) = 169

Taking the square root of both sides, we get:

x = 13

Therefore, the length of the shorter diagonal is 13.

And the length of the longer diagonal is 2x = 26.

Hence, the lengths of the diagonals are 13 and 26 millimeters.

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The answer is -2 -1

Answer:

9.5

Step-by-step explanation:

The correct answer is 9.5 because 9.49 is closer to 9.5 than 9.4

Answer:

9.5

Step-by-step explanation:

9.492 to the nearest tenth

First you would round 0.092, which would just be 0.09 because 2 is less than 5. You would then have 9.49. You would then round the 0.49, and since 9 is greater than 5, it would be 9.5 because 9 would round to 10.

Answer:

Line 2 ║ Line 3

Step-by-step explanation:

y = mx + b

~~~~~~~~~~

Line 1: y = - 7x + 6

Line 2: x + (1/3)y = - 6 ⇔ y = - 3x - 18

Line 3: y = - 3x - 8

Line 4: y + 7 = (-1/7)(x + 4) ⇔ y = \(- \frac{1}{7}\) x - \(\frac{43}{7}\)

\(m_{line2}\) = \(m_{line3}\)  ⇒  Line 2 ║ Line 3

Answer:

95

Step-by-step explanation:

9+5=14

95÷19=5

this is the answer (I'm just typing so brainly let's me post)

\(~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$16000\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ t=years\dotfill &10 \end{cases} \\\\\\ A=16000[1+(0.03)(10)] \implies A=16000(1.3)\implies A = 20800\)

Answer:

x < 6.5

y < -1.5

Step-by-step explanation:

y > x - 8

Therefore x < y + 8

y < 5 - x

Therefore x < 5 - y

2x < 13

x < 6.5

6.5 < 5 - y

y < -1.5

Answer:

stylo fabric customer care 9903160322##8944928267

Answer:

the degree is the largest exponent on the variable

answer - 6

Answer:

53°

Step-by-step explanation:

As we can see that ∠3 and ∠7 are corresponding angles. Therefore,

Now calculate the angles of ∠3 and ∠7.

Now we can see that ∠3 and ∠1 are alternate angles and ∠7 and ∠1 are alternate exterior angles. Thus, we can say that

Hence the measure of ∠1 is 53°.

♦♦♦♦♦Hope it helps♦♦♦♦♦

Answer:

The answer is A

Explanation:

I just took this quiz.

The outside area of surface that can be painted is 6075π =19075.5 square feet.

a)The equation of the curve of dome  can be written as

\(x^2+y^2=45^2\\\\x=\sqrt{45^2-y^2}....i\)

The dome is revolving around the y-axis,

the surface area of dome about y-axis can be written as

\(S=\int\limits^a_b 2\pix\sqrt{1+(\frac{dx}{dy})^2} \, dy\)

The surface area of the dome shown in the figure is the sum of the area of the hemisphere 45 ft and the surface area of the band of radius 45 ft and height 22.5 ft.

Differentiating eq. i with respect to x

\(\frac{dx}{dy}=\frac{1}{2}(45^2-y^2)^{\frac{1}{2}-1}(-2y)\\\\\frac{dx}{dy}=-\frac{y}{\sqrt{45^2-y^2}}\\\\\)

substituting  \(\frac{dx}{dy}\) in S,

and also substituting a=45 and b=-22.5

\(S=\int\limits^{45}_{-22.5} \ 2\pi (\sqrt{45^2-y^2})\sqrt{1+(-\frac{y}{\sqrt{45^2-y^2}})^2} \, dy\\\\S=2\pi\int\limits^{45}_{-22.5} \sqrt{45^2-y^2} \sqrt{\frac{45^2-y^2+y^2}{45^2-y^2}}dy\\\\S=2\pi\int\limits^{45}_{-22.5}\sqrt{45^2}dy\\\\S=2\pi\ (45)(45-(-22.5))\\\\S=6075 \pi\ square\ feet\)

Thus, the outside area of surface that can be painted is 6075π square feet

b)The  outside surface area is 6075π =19075.5 square feet

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The area of the surface obtained by the curve rotated along the x-axis is \(S_1=\int\limits_0^{\pi/3}2\pi (\tan x)\sqrt{1+\sec^4x}\;dx\). The area of the surface obtained by the curve rotated along the y-axis is \(S_2=\int\limits_0^{\sqrt{3}}2\pi (\tan^{-1}y)\sqrt{1+\left(\frac{1}{1+y^2}\right)^2}\;dy\).

A surface type that results from rotating a curve around a specific axis is the area of the surface of revolution. The formula for the area around the x-axis is given by, \(S_1=\int\limits_a^b2\pi f(x)\sqrt{1+(f'(x))^2}\;dx\) and around the y-axis is \(S_2=\int\limits_a^b2\pi g(y)\sqrt{1+(g'(y))^2}\;dy\).

a) Given the expression is rotated about the x-axis. Let,

\(\begin{aligned}f(x)&=y\\&=\tan x \in \left[0,\frac{\pi}{3}\right] \end{aligned}\)

Then,

\(f'(x)=\sec^2x.\)

Substitute f(x) and f'(x) value in the S₁ formula, we get,

\(S_1=\int\limits_0^{\pi/3}2\pi (\tan x)\sqrt{1+\sec^4x}\;dx\)

b) Given the expression is rotated about the y-axis. Let,

\(\begin{aligned}x&=g(y)\\&=\tan^{-1}y \in \left[0, \sqrt{3}\right] \end{aligned}\)

Then,

\(g'(y)=\frac{1}{(1+y^2)}\)

Substitute g(y) and g'(y) value in the S₂ formula,

\(S_2=\int\limits_0^{\sqrt{3}}2\pi (\tan^{-1}y)\sqrt{1+\left(\frac{1}{1+y^2}\right)^2}\;dy\)

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The complete question is -

a) Set up an integral for the area of the surface obtained by rotating the curve y=tanx,0≤x≤π/3 about the x-axis.

b) Set up an integral for the area of the surface obtained by rotating the curve y=tanx,0≤x≤π/3 about the y-axis.

The true population mean is (222.52, 227.48) with a 95% confidence interval.

The critical factor for a 90% confidence interval for the true population mean is given by;

Critical factor = (x-μ)/(s/√n)

where, x = sample mean repair cost

s =  standard deviation of a sample

n = sample of stereos

μ  = critical value

⇒ P(-1.96< (x-μ)/(s/√n) < 1.96) = 0.95

⇒ P(-1.96×(s/√n) < (x-μ) < 1.96×(s/√n)) = 0.95

⇒ P(x - 1.96×(s/√n) < μ < x + 1.96×(s/√n)) = 0.95

95% confidence interval for

⇒ μ = (x - 1.96×(s/√n) , x + 1.96×(s/√n))

Here, x = 225, s  = 8.5, and n = 45

⇒ μ = (225- 1.96×(10.81/√13) , 225+ 1.96×(10.81/√13))

⇒ μ = (222.52, 227.48)

Hence, the true population mean is (222.52, 227.48) with a 95% confidence interval.

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The question seems to be incomplete the correct question would be

Calculate the 95% confidence interval for the true population mean based on a sample with x=225, s=8.5, and n=45.

Answer:

Step-by-step explanation:

from cosines theorem:

t² = 11² + 14² - 2•11•14•cos87°

t² = 121 + 196 + 308•0.05236

t² = 333.12688

t = √333.12688

t = 18.2517... ≈ 18.3

Step-by-step explanation:

Interior angles of a 5-gon    sum to   ( 5-2)(180 = 540 degrees

smallest angle =x

largest angle = x + 4d    

          where d is the arithmetic sequence common difference

x + 4d     -x     =  44    shows d = 11

then    x    + x+d    + x+2d   + x+3d   + x + 4d = 540

      5x + 10d = 540      we know d = 11

       5x + 10(11) = 540

         5x = 430

           x = smallest angle = 86 degrees

The smallest interior angle of the pentagon is 86 degrees. This was found by setting up an equation involving the common difference "d" in the arithmetic sequence of angles and solving for "x."

Let's denote the five interior angles of the pentagon as follows:

Let the smallest angle be "x" degrees.

The other four angles form an arithmetic sequence, so we can represent them as x + d, x + 2d, x + 3d, and x + 4d, where "d" is the common difference between the angles.

Now, we know that the difference between the largest angle and the smallest angle is $44^\circ$. Therefore, we can write the equation:

(x + 4d) - x = $44^\circ$

Simplify and solve for "d":

4d = $44^\circ$

Now, divide both sides by 4 to find the value of "d":

d = $44^\circ / 4 = $11^\circ

Now that we know the common difference "d" is $11^\circ", we can find the smallest angle "x" by using the equation for the sum of angles in a pentagon, which is 540 degrees:

x + (x + d) + (x + 2d) + (x + 3d) + (x + 4d) = 540

Simplify and solve for "x":

5x + 10d = 540

5x + 10($11^\circ) = 540

5x + $110 = 540

Now, subtract $110 from both sides:

5x = 540 - $110

5x = $430

Finally, divide by 5 to find the smallest angle "x":

x = $430 / 5 = $86

So, the smallest angle of the pentagon is $86 degrees.

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the solution to the first system of equations is x = 2 and y = 1.

Simultaneous equations, a system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.

There are four methods for solving systems of equations: graphing, substitution, elimination, and matrices.

Given, a system of equations,

y=6x-11,

- 2x - 3y = - 7

To solve this system of equations, we can substitute the expression for y in the second equation with the expression given in the first equation.

y = 6x - 11

-2x - 3(6x - 11) = -7 (substituting y with 6x - 11)

-2x - 18x + 33 = -7

-20x = -40

x = 2

Now we can use this value of x to find y by substituting it in one of the equations. Let's use the first equation.

y = 6x - 11

y = 6(2) - 11

y = 1

Therefore, the solution to the system of equations is x = 2 and y = 1.

You can solve every equation by using this method just change the variables.

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Answer: 64a^8b^2

Step-by-step explanation:

1...  (-8a^4b)^2 .... distribute the exponent which becomes:
(-8)^2(a^4)^2b^2
2...Evaluate the exponent:
64(a^4)^2b^2
3... Power of power:
64a^(4*2)b^2
4... Multiply numbers:
64a^8b^2

Marketing entrepreneurs choose a marketing niche first to prepare to launch their business. Thus, option B is correct.

The portion of a market that a particular product is targeted toward is called a niche market. The product's market niche determines its price range, level of production, target demographics, and feature set that is intended to address a particular market need. Additionally, it is a small market sector. A product or service may occasionally be created specifically to meet the needs of a niche market.

Not all products can be classified by their market niche. The highly specialised niche market competes against numerous super companies and strives to remain viable. Even well-known companies develop products for specific markets; Hewlett-Packard produces separate machines in addition to all-in-one printing, scanning, and faxing units that are aimed at the home office market.

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Answer: Choose a marketing Niche

Step-by-step explanation: Just took the quiz