The width of a rectangle measures (10u + 3) centimeters, and its length measures (7u - 8) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle? The width of a rectangle measures ( 10u + 3 ) centimeters , and its length measures ( 7u - 8 ) centimeters . Which expression represents the perimeter , in centimeters , of the rectangle ? ​

Answer:

The answer options seem to be missing their exponents for the 10 unit.

Answer is:  5.435778 x [tex]10^{6}[/tex]

Step-by-step explanation:

5,435,778

Move the decimal point to the left until it is between the 5 and 4.  Scientific notation means rewriting the number with only one digit to the left of the decimal point and adding the "x [tex]10^{x}[/tex] after to account for the number of positions the decimal point was moved.  

Count the number of places required for the move.

5,435,778     0

543577.8      1

54357.78      2

5435.778      3

543.5778      4

54.35778      5

5.435778      6

Each move reduces the number by a factor of 10.  This means that the final move to make the number 5.435778 required dividing the original number by 10 a total of 6 times.  By multiplying this last number by 10 a total of 6 times, we obtain the original number.  

We could write this as:    (5.435778)*(10)*(10)*(10)*(10)*(10)*(10)

but that defeats the purpose of scientific notation, which is to simplify the number so that it is 1) easier to read, 2) saves printers paper and ink, and 3) reduces transcription errors.

So scientific notation is the process of writing this as:

5.435778 x [tex]10^{6}[/tex]

The given expression can be simplified as [tex]96x^{9}+3x^{36} +3[/tex].

The given expression is [tex]6x^{9} (7-3).4+3x^{36} +3[/tex].

We need to simplify the given expression.

In mathematics, an algebraic expression is an expression built up from integer constants, variables, and algebraic operations.

First, multiply the numbers 6×4=24.

That is, [tex]24x^{9} (7-3)+3x^{36} +3[/tex].

Next, subtract the numbers 7-3=4.

[tex]24x^{9}.4+3x^{36} +3[/tex]

Finally, multiply the numbers 24×4=96.

[tex]96x^{9}+3x^{36} +3[/tex].

Hence, the given expression can be simplified as [tex]96x^{9}+3x^{36} +3[/tex].

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Answer:

monomial and degree is 2

Answer:

$.46 or 46 cents per foot

Step-by-step explanation:

3 yards = 4.14

1 yard is 3 feet

3 yards is 9 feet

4.14 ÷ 9 = .46

The first and foremost rule for determining if 2 triangles are similar is checking if their angles are the same. Obviously, in this example, the angles are completely different, so the triangles are not similar.

Have a nice day!

And good luck on the assignment!

Answer:

16

Step-by-step explanation:

x^2+16x+16

(x+4)(x+4)

x^2+ 4x+4x+16

Answer:

The answer is C.) 64 on edge.

Answer:

Step-by-step explanation:

Calculate 50% of 684 m.

Give your answer in metres (m).

50% = 1/2

so

684 : 2 = 342 m

Step-by-step explanation:

50% of 684

50/100 × 684

342m ans

The reasoning that may be used for finding the measure of m∠12, is the

same side interior angles theorem.

The correct options using the drop-down menu are;

The sum of ∠1, ∠7, and ∠8 is 180°

∠8 and ∠12 are the same side interior angles

The measure of ∠12 must be = 120°

Stuart is not correct

The complete question is given below:-

In the diagram, line x is parallel to line y,m21= 65°, and m27 = 55°. Stuart says that m212 = 60°. His reasoning is shown. Step 1: mZ8 = 60°, because m21+ m27 +m28 = 180º. Step 2:28 212, because 28 and 212 are corresponding angles. Step 3: So, mZ12 = 60° Use the drop-down menus to explain whether or not Stuart is correct.​

The angle is defined as the span between two intersecting lines or surfaces at or close to the point where they meet.

Given parameters;

Line x ║ line y

m∠1 = 65°, m∠7 = 55°

m∠12 = 60°

Stuart states ∠12 = 60°

The reasoning is presented as follows;

Step 1: m∠8 = 60°, because m∠1 + m∠7 + m∠8 = 180°

Step 2: ∠8 ≅ ∠12, because ∠8 and ∠12 are corresponding angles

Step 3: So, m∠12 = 60°

Using the drop-down menu, we have;

The sum of ∠1, ∠7, and ∠8 is 180° (Sum of angles in the triangle)

∠8 and ∠12 are same side interior angles (by definition)

Same side interior angles are supplementary, therefore;

∠8 +∠12 = 180°

∠12 = 180°  - ∠8

Which gives;

The measure of ∠12 must be 180° - ∠8 = 180° - 60° = 120°

The measure of ∠12 must be = 120°

Stuart is not correct

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The dimensions of the school yard is 58 m and 89 m.

A rectangle is a polygon with four sides , It has opposite sides parallel and equal.

It is given that

A rectangular school yard has a perimeter of 294 meters

Perimeter of a rectangle is given by

P = 2(Length +Breadth)

294 = 2( L+B)

147 = L+B

Area of a rectangle is given by

L*B = 5162

B = 5162/L

L + 5162/L =147

L² -147L +5162 = 0

L² -58L - 89L+5162 = 0

L(L-58) -89(L-58)

L = 58 , 89

The dimensions of the school yard is 58 m and 89 m.

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Answer:

C

Step-by-step explanation:

7 × ln(x) = 2.4

ln(x) = 2.4/7 = 0.342857143...

x = e^0.342857143... = 1.408967466... ≈ 1.41

Answer:

y = -0.5x - 3.5

Explanation:

Take two points: (1, -4), (3, -5)

Find slope:

[tex]\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]

[tex]\rightarrow \sf slope \ (m) : \dfrac{-5-(-4)}{3-1} = -\dfrac{1}{2}[/tex]

Equation:

[tex]\sf y- y_1 = m (x - x_1)[/tex]

[tex]\rightarrow \sf y- (-4) = -\dfrac{1}{2} (x -1)[/tex]

[tex]\rightarrow \sf y+ 4 = -\dfrac{1}{2} x + \dfrac{1}{2}[/tex]

[tex]\rightarrow \sf y = -\dfrac{1}{2} x + \dfrac{1}{2} - 4[/tex]

[tex]\rightarrow \sf y = -0.5 x -3.5[/tex]

The formula of a line is:

[tex]f(x) = kx + b[/tex]

k — stands for tg of line angle
b — stands for the y value of a point where the line crosses y axis.

We can see 2 points:
A (1, -4)
B (3, -5)

We can make a system of equations:

[tex]k*1+b=-4\\k*3+b=-5\\[/tex]

From second equation:

[tex]b = -5 - 3k[/tex]

Let's put b in first equation:

[tex]k-5-3k=-4\\-2k=1\\k=- \frac{1}{2}[/tex]

Now we can find b:

[tex]b = -5 -3*- \frac{1}{2}\\b = -5 + 1.5\\b = -3.5[/tex]

The answer is:
-0.5x -3.5

The Standard form of the equation of circle is (x+21)² + (y+19)² = 849

To transform general form to a standard form, you can use completing the square method or you can convert this equation

x² + y² + Dx + Ey + F = 0 to x² + y² + (-2h)x + (-2k)y + (h²+k²-r²) = 0

Here, Given: x² + y² + 42x + 38y − 47 = 0

Required: Find the values of h, k, and r using this formula

x² + y² + (-2h)x + (-2k)y + (h²+k²-r²) = 0

On comparing we get,

-2h = 42

  h = 21

-2k = 38

 k = 19

-47 = h² + k² - r²

-47 = 21² + 19² - r²

   r² = 849

  r = √849

Thus, the Standard form of the equation of circle is (x+21)² + (y+19)² = 849

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hello hello hello

Step-by-step explanation:

hi hi hi

Addition is one of the four fundamental mathematical operations. The correct option is E, None of these choices are correct.

Addition is one of the four fundamental mathematical operations, the others being subtraction, multiplication, and division. When two whole numbers are added together, the total quantity or sum of those values is obtained.

1. The annual premium cost for Michael's family is $5,260. The company pays 70% of the cost. Therefore, the cost he needs to may is,

30% of $5,260

= 0.30 × $5260

= $1578

Since the premium is needed to be paid in 52 week, therefore, the premium cost per week will be,

Premium cost = $1578/52 = $30.35

Hence, the correct option is C, $30.35.

2. Brenda annual premium is $3,500. Also, her medical bills is totaling to $12,000. Therefore, the total amount that is paid by the Brenda in purchasing Insurance and paying the bill is,

Amount Brenda spend = $3,500 + $12,000 = $15,500

The policy has a $500 deductible and pays 80% of all medical costs with a stop-loss provision of a limit of $4,000 for out-of-pocket expenses, after the deductible is paid. Therefore, the amount that she can get is,

Amount she can get = $500 + $4,000 = $4,500

Now, the amount that she needs to pay from her pocket is,

Amount = $15,500 - $4, 500  = $11,000

Hence, the correct option is E, None of these choices are correct.

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Solving the exponential function, the resulting logarithmic expression is:

x = ln(4).

Considering an exponential equation involving Euler number e, the expression is solved applying the natural logarithm ln, which is the inverse function to the exponential function, to both sides of the equation.

Hence:

[tex]e^{x} = 4[/tex]

Applying ln to both sides:

[tex]\ln{e^x} = \ln{4}[/tex]

Since ln and e are inverse, we can isolate x, hence:

[tex]x = \ln{4}[/tex]

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The value of CD is 10.7 cm , Option C is the right answer.

A line segment is a line of fixed measure.

From the figure , as Triangle ABC is a right angled triangle

sin 30 degree = (Perpendicular / Hypotenuse)

∠ B = 30° , AB= 10 cm

sin 30 = AC/10

AC = 5 cm.

To determine CD ,

In Triangle ADC ,

tan 25 = Perpendicular / Base

tan 25 = AC / CD

tan 25 = 5 / CD

CD = 5 / 0.4663

CD = 10.7 cm

Therefore the value of CD is 10.7 cm , Option C is the right answer.

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Answer: C

Step-by-step explanation: 10.7 cm

Answer:     [tex]\boldsymbol{2(x-2)(5x+7)}[/tex]

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

Work Shown:

[tex](4x^2-16)+3(2x-4)(x+1)\\\\4(x^2-4)+3*2(x-2)(x+1)\\\\4(x-2)(x+2)+3*2(x-2)(x+1) \ \text{ ... difference of squares rule}\\\\2*2(x-2)(x+2)+3*2(x-2)(x+1)\\\\2(x-2)(2(x+2)+3(x+1))\\\\2(x-2)(2x+4+3x+3)\\\\\boldsymbol{2(x-2)(5x+7)}\\\\[/tex]

The answer has been confirmed with WolframAlpha which is basically a calculator app, but does a ton more than any average calculator.

The CAS (computer algebra system) in the app GeoGebra is another tool I use all the time.

Yet another way to confirm the answer is to graph the original expression and the answer as separate functions. You should find they produce the exact same curve. One curve perfectly overlaps the other. This visually verifies the two expressions are the same thing, just written a different way of course.

Let me know if you have any questions about any step. The basic idea I did was to pull out the GCF and then combine like terms.

Answer: $329.8

[tex]3298-(\frac{90}{100} *3298)\\= 3298 - 2968.2\\= 329.8[/tex]

The amount Keiko pays annually is $329.8

To answer the question, we need to know the amount Keiko pays annually

Since Keiko health insurance premium annually is $3298 and if his employer pays 90% of the premium, we want to know how much Keiko pays.

Since the employer pays 90% of the premium, the employer pays x = 90% of $3298

= 0.9 × 3298

= $2968.2

So, the amount Keiko pays annually is y = premium - amount employer pays, x

= $3298 - $2968.2

= $329.8

So, the amount Keiko pays annually is $329.8

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Answer:

Step-by-step explanation:

Exponent law:

    [tex]\sf \bf a^m * a^n = a^{m+n}\\\\ (a^m)^n = a^{m*n}[/tex]

    [tex]\sf a^{-m}=\dfrac{1}{a^m}[/tex]

       First convert radical form to exponent form and then apply exponent law.

 [tex]\sf \sqrt{3}=3^{\frac{1}{2}}\\\\\sqrt{5}=5^{\frac{1}{2}}[/tex]

[tex]\sf \left(\dfrac{(\sqrt{3}*3^{-2}}{(\sqrt{5})^2}\right)^{\frac{1}{2}}= \left(\dfrac{3^{\frac{1}{2}}*3^{-2}}{(5^{\frac{1}{2}})^2} \right )^{\frac{1}{2}}[/tex]

                      [tex]= \left(\dfrac{3^{\frac{1}{2}-2}}{5^{\frac{1}{2}*2}}\right)^{\frac{1}{2}}\\\\=\left(\dfrac{3^{\frac{1-4}{2}}}{5}\right)^{\frac{1}{2}}\\\\=\left(\dfrac{3^{\frac{-3}{2}}}{5}\right)^{\frac{1}{2}}\\\\=\dfrac{3^{\frac{-3}{2}*{\frac{1}{2}}}}{5^{\frac{1}{2}}}\\\\ =\dfrac{3^{{\frac{-3}{4}}}}{5^{\frac{1}{2}}}[/tex]

Step-by-step explanation:

I think 1 is true.

3 is false. it's $10 per hour

Answer:

nr.3 300x0.12=36rolls
nr.4 300x0.21=63 rolls

total number on rolls on nr.3 and nr.4= 99

Step-by-step explanation:

Calculate the probability for nr.3

Always try to get 100%

1=13%

2=5%

3=?

4=21%

5=19%

6=30%

Add all the percentage

1+2+4+5+6= 88%

now calculate the percentage for nr.3

100%-88%=12%

give a estimated total number of times the dice will land on nr.3 or nr.4 after 300 rolls

nr.3 300x0.12=36rolls
nr.4 300x0.21=63 rolls

total number on rolls on nr.3 and nr.4= 99

Step-by-step explanation:

please mark me as brainlest

Answer:

The measure of each interior angle of a regular decagon is 144 degrees.

Step-by-step explanation:

The measure of the interior angles of a decagon is 1440, due to the formula being (n-2)(180). Since a decagon is a ten sided shape, it would be (10-2)(180).

8 x 180= 1440.

Next, we divide the total by the number of the sides the polygon has—ten. 1440 divided by 10 is 144, so the measure of each interior angle is 144 degrees.

Answer:

Vertex

Vertex are the end points of parabola where it opens up

locus are the group of points

latus rectum is the line parallel to it .

Answer:

the answer is just 6

Step-by-step explanation:

Answer:

Step-by-step explanation:

An absolute value of a number is written like this | x |, where x could be any number that you want.

The absolute value is a math function that counts from your given number to 0.

Example: If you put the number 3, the function will count from 3 to 0, and the number will be 3.

| 3 | = 3

If you input the number 8, from 8 to 0 are 8 numbers. So, the output's function will be 8.

| 8 | = 8

If you input a negative number, for example, -6, the function will do the same thing. It will count from -6 to 0. From -6 to 0, are 6 numbers.

| -6 | = 6

Any number that you input in this function, will always output the same number, but positive

| -10 | = 10

| -46348 | = 46348

Hope I helped !

Answer:

See Below

Step-by-step explanation:

The equation for this scenario would be  ( compounded annually)

6600 ( 1 + .006)^6         = £ 6841.19

Answer:

Brian will have £6841.19 after 6 years.

Step-by-step explanation:

The compound interest formula is:

[tex]A = P( 1 +\frac{r}{100} )^{n}[/tex] ,

where A is the final amount, P is the initial (principal) amount invested (£6600), r is the interest rate (0.6%) and n is the number of years the money is kept for (6 years).

Using the formula:

[tex]A = 6600(1 + \frac{0.6}{100} )^{6}\\\\A = 6841.19[/tex]

Answer:

x² + 4x - 21 = 0

x² + 7x - 3x - 21 = 0

x ( x + 7 ) -3 ( x + 7 ) = 0

( x - 3 ) ( x + 7 ) = 0

∴ x - 3 = 0              or              x + 7 = 0

  x = 0 + 3                               x = 0 - 7

  x = 3                                      x = -7

Answer:

-4

+3

12

-0.5, 12.25

x = -0.5

Step-by-step explanation:

The x intercepts are the values of x when y = 0 ie the roots of the equation
[tex]-x^2 -x +12 = 0[/tex]

or

[tex]x^2 + x - 12 = 0[/tex]

We can re-write the above as:
(x+4) (x-3) = 0
This gives the two roots as x = -4 and x = +3. Leftmost (smallest) root is -4 and rightmost(largest) root is +3

y intercept is when x = 0. Plugging into the original equation, y value at x = 0 is 12

Vertex x value is given by the formula -b/2a where a is the coefficient of x^2 and b the coefficient of x

Here a = -1, b= -1 so vertex x value = - (-1)/(-1).2 = - 1/2 = -0.5

Plugging this value of x into the original function gives the vertex y value
[tex]y = - (0.5^{2}) - (-0.5) + 12\\= -0.25 + 0.5 + 12 = 12.25[/tex]

The line of symmetry is the vertical line corresponding to the vertex x value so line of symmetry is at x = -0.5

The graph of the quadratic function shows these values