Susan has a rectangle and a right triangle.
• The length of the rectangle is 4 more than its width, w.
.
• The length of the shorter leg of the triangle is equal to the rectangle's
width.
• The length of the longer leg of the triangle is twice the length of the
rectangle.

Answer: Municipal Bank will charge him 8% simple interest

Step-by-step explanation:

Answer:

Magnitude: 3√10

Direction angle: 71.56°

Step-by-step explanation:

The magnitude ||v|| of a vector <a,b>, would be:

[tex]||v||=\sqrt{a^{2}+b^{2}[/tex]

[tex]||v||=\sqrt{3^{2}+9^{2}[/tex]

[tex]||v||=\sqrt{9+81}[/tex]

[tex]||v||=\sqrt{90}[/tex]

[tex]||v||=3\sqrt{10}[/tex]

The vector's reference angle would be:

[tex]tan\alpha =|\frac{b}{a}|[/tex]

[tex]tan\alpha =|\frac{9}{3}|[/tex]

[tex]tan\alpha =|3|[/tex]

[tex]tan\alpha =3[/tex]

[tex]\alpha = 71.56[/tex]

If [tex]\alpha[/tex] is your reference angle, then your direction angle ∅ depends on what quadrant the vector is located in. Since <3,9> is located in Quadrant I, then ∅= [tex]\alpha[/tex], which means your direction angle is also 71.56°

Answer:

9.5; 72°

Step-by-step explanation:

A figure made by two intersecting lines or two rays extending from the same point is called an angle.

What is an angle?

Two lines intersect at a location, creating an angle. An "angle" is the term used to describe the width of the "opening" between these two rays.  Angles are used in the design of buildings, roadways, and sports venues by engineers and architects.

A figure made by two intersecting lines or two rays extending from the same point is called an angle.The character ∠ is used to represent it. Angles are frequently expressed in degrees and radians, a unit of circularity or rotation. We encounter angles frequently in life.

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The square of the given numbers 3, 4, and 5 are 9, 16, and 25 respectively.

The square of a number is the product of the number with itself. Therefore, if there is a number x then its square will be the product of x and x. It is denoted by 2 in superscript form over the number whose square is needed to be calculated.

The squares of the given numbers are,

3² = 3 × 3 = 9

4² = 4 × 4 = 16

5² = 5 × 5 = 25

Hence, the square of the given numbers 3, 4, and 5 are 9, 16, and 25 respectively.

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According to the following graph, the reflection point of (-3,4) across the line y = 2 is (-3,0).

The term reflection point in math is defined as

Here we need to find the reflection point of (-3, 4) across the line y = 2.

Here first we have t plot the point on the graph, and then we have to plot the line equation y = 2 on the graph,

Here in order to find the reflection of a point along the x-axis, then we have to keep the abscissa constant and see the reflection of ordinate along the x-axis.

Based on these rule, the resulting graph is obtained as follows.

Through the graph we have identified that the resulting reflection point is (-3,0).

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Answer:

D. Angles 4 and 7

Step-by-step explanation:

Answer 1 and 4 are supplementary angles.

Step-by-step explanation:

Supplementary angles are angles adding up to 180, the only angles listed that are supplementary angles is 1 and 4.

Have a good day!

The Graph solution to this inequality on the number line is lies between -4 > 8.4 and their numbers are -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3.

Draw a circle around the number to indicate an inequality, such as x>3, on a number line (e.g., 3). In case the sign also states equal to, complete the circle (or ). If the sign doesn't include equal to (> or), leave the circle empty.

When plotting an inequality, use the,, >, or sign as a = sign. If the inequality is either or, graph the equation as a dotted line. If the inequality is either or, graph the equation as a solid line.

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Answer:

130°

Step-by-step explanation:

All the interior angles should add up to 540 degrees because it's a pentagon

∠T ≅∠S, so ∠T is also 115°

∠P and ∠R are both 90°

Add everything up and solve for ∠Q:

115 + 115 + 90 + 90 + m∠Q = 540

410 + m∠Q = 540

m∠Q = 130°

The longer ladder can reach 3 8/7 feet higher than the shorter one.

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Answer: [tex]\$5500, \$14,500[/tex]

Step-by-step explanation:

Given

[tex]\$20,000[/tex]  is invested in two accounts with a 12% and 11% rate of interest.

Total interest after a year is  [tex]\$2255[/tex]

Suppose x amount is invested in first, so the remaining amount is invested in other

Simple interest and Compound interest is the same for a year

[tex]\therefore \text{Interest}=\dfrac{P\times R\times T}{100}[/tex]

For first investment

[tex]I=\dfrac{x\times 12\times 1}{100}\\\\I=0.12x[/tex]

For second investment

[tex]II=\dfrac{\left(20,000-x\right)\times 11\times 1}{100}\\\\II=0.11\left(20,000-x\right)[/tex]

The sum of the two must be [tex]\$2255[/tex]

[tex]\Rightarrow 0.12x+0.11\left (20,000-x\right)=2255\\\Rightarrow 0.01x=2255-2200\\\\\Rightarrow x=\dfrac{55}{0.01}\\\\\Rightarrow x=\$5500[/tex]

Remaining amount is

[tex]\Rightarrow 20,000-5500\\\Rightarrow \$14,500[/tex]

Answer:

168 - 147 = 21

21/168 = 12.5

Answer:

Step-by-step explanation:

After simplification the correct matching is

1) 9i - A)[tex]\sqrt{-81}[/tex]

2) 5i[tex]\sqrt{2}[/tex] - C) [tex]\sqrt{-50}[/tex]

3) 12[tex]\sqrt{6}[/tex] - B) 4[tex]\sqrt{54}[/tex]

4) 6i[tex]\sqrt{7}[/tex] - D) [tex]\sqrt{-252}[/tex]

What is simplification?

To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue.

Here to convert radical to simplified form we need to simplify them then

A)=> [tex]\sqrt{-81}[/tex] = [tex](\sqrt{i*9*9} })[/tex] =  9i

B) =>  [tex]4\sqrt{54} = 4\sqrt{9*6}= 4\sqrt{3^2*6}= 4*3\sqrt{6} = 12\sqrt{6}[/tex]

C) => [tex]\sqrt{-50} = \sqrt{i^2*25*2}=\sqrt{i^2*5^2*2}=5i\sqrt{2}[/tex]

D) => [tex]\sqrt{-252} = \sqrt{i^2*36*7}=6i\sqrt{7}[/tex]

Hence the correct matching is

1) 9i - A)[tex]\sqrt{-81}[/tex]

2) 5i[tex]\sqrt{2}[/tex] - C) [tex]\sqrt{-50}[/tex]

3) 12[tex]\sqrt{6}[/tex] - B) 4[tex]\sqrt{54}[/tex]

4) 6i[tex]\sqrt{7}[/tex] - D) [tex]\sqrt{-252}[/tex]

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To simplify a square root, simply factor the number and extract the roots of any perfect squares found from the radical sign.

Simplify a radical expression that use the Product Property.

To convert radicals to simplified forms, we must first simplify them.

A) = [tex]\sqrt{-81}[/tex]

   = ([tex]\sqrt{i*9*9}[/tex] )

   =  9i

B) = 4[tex]\sqrt{54}[/tex]

    = 4[tex]\sqrt{9*6}[/tex]

    = 4[tex]\sqrt{3^{2}*6 }[/tex]

    = 4*3√6

    = 12√6

C) = [tex]\sqrt{-50}[/tex]

    = [tex]\sqrt{i^{2}*25*2 }[/tex]

    = [tex]\sqrt{i^{2}*5^{2}*2 }[/tex]

    = 5i√2

D) = [tex]\sqrt{-252}[/tex]

    = [tex]\sqrt{i^{2}*36*7 }[/tex]

    = 6i√7

As a result, the correct match is

1) 9i - A) [tex]\sqrt{-81}[/tex]

2) 5i - C) [tex]\sqrt{-50}[/tex]

3) 12 - B) 4[tex]\sqrt{54}[/tex]

4) 6i - D)[tex]\sqrt{-252}[/tex]

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Answer:1

Step-by-step explanation:

because 1 devided by 3 is 3 and 1 devided by 25 is 5

'x' is the only variable in the provided polynomial. As a result, the polynomial  4x² - 3x + 7  has one variable.

A polynomial is an expression in mathematics made up of variables (sometimes referred to as indeterminates) and coefficients that only employs the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. A polynomial is an equation that combines variables, constants, and exponents utilizing addition, subtraction, multiplication, and division of numbers (No division operation by a variable).

given

'x' is the only variable in the provided polynomial. As a result, the polynomial  4x² - 3x + 7  has one variable.

The following list includes a few examples of polynomials with one variable: x+2. x2+3x+2.

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Answer:

5x-7-5+X=5-x-5+X

or,6x-12=0

or,6x=12

or,X=12/6

:.X=2

Answer:

B is the answer

Step-by-step explanation:

When you add AOB and NOM its 90 degrees. AOB is 29 + NOM that is 61. 61 + 29 = 90 degrees. Since complementry angles are 90 degrees, it is correct! Pls tell me if its correct or not!

Answer:

B is the answer

Step-by-step explanation:

ADD-

AOB and NOM

=90 degrees

AOB =29

add "NOM"

NOM= 32

=61.

61 + 29 = 90 degrees.

Complementary angles are 90 degrees

value of x = 8 as per logarithm laws.

In mathematics, logarithm is an exponent or power for which a particular number is raised to achieve a required number. In other words, logarithm is a mathematical expression that states about how many times a number can be multiplied by the same number to get some required numbers.

The method of expressing any exponential relationship in the inverse form is called log notation.

In this question, we are given a log base 2 or binary logarithm.

given, ㏒₂ x = 3

     as per the logarithm laws ㏒a y = m

                                          y = a∧m

                               we write. ㏒₂ x = 3

                                                  x = 2³

                            hence, x = 8

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Answer:

P=3000$

T=2 years

R=1.6% per annum

Now,

interest=(3000×2×1.6)/100=96$

Amount=P+interest=3096$

Hence,Conan needs to pay back 3096$ and the interest is 96$

The regular price of a ticket to the game was $204.00.

We can use algebra to solve the problem. Let x be the regular price of a ticket to the game.

We know that the group rate saved Mason $5.75 per ticket, so the regular price of a ticket is x + $5.75.

We know that Mason bought 16 tickets and paid a total of $296.00, so we can set up the following equation:

x + $5.75 = (x + $5.75) * 16 = 16x + $92

So the regular price of a ticket is x = $296.00 - $92 = $204.00

Therefore, the regular price of a ticket to the game was $204.00.

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Answer:

Step-by-step explanation:

Answer:Min:2

Q1:5

Med:7

Q3:13

Max:15

gogle said:

The line about which a three-dimensional figure is rotated to obtain an object identical to the original is a(n) horizontal plane.

The line about which a three-dimensional figure is rotated to obtain an object identical to the original is a horizontal line.

The correct option is A.

Each point in a figure is transformed into a rotation by rotating it a certain amount of degrees around another point.

From the given choices:

The horizontal line is an appropriate line to obtain an object identical to the original.

The line about which a three-dimensional figure is rotated to obtain an object identical to the original is a horizontal line.

Therefore, the required line is a horizontal line.

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The shape of a decagon will remain the same when it is rotated through

its angle of rotational symmetry.

The rotation about the center will carry a regular decagon back to itself is 36°.

Note the following

The angle of rotational symmetry of a decagon is the smallest angle that a decagon can be rotated by such that the image formed by the rotation coincide with the preimage;

A decagon has 10 sides, the interior angle of a regular decagon is given as follows;

Each interior angle =  (n-2)*180/10 = 144⁰

A decagon has a reflective symmetry, therefore, the lines of symmetry joining opposite vertices are straight lines.

The number of diagonals in a decagon = 5

Rotating through the vertex and opposite vertex of the diagonals gives the number of image of the rotation that is similar to the preimage of a decagon as ten.

Therefore, a rotation of  (360/10) = 36⁰, about the center will carry a regular decagon back to itself.

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Therefore , the solution of the given problem of slope comes out to be

y = (-1/2)x + 8.

The slope-intercept formulation of an equation is used to represent each time the formula of a line is stated as y = mx + b. The line's slope is represented by the m. Additionally, b is the b in the y-intercepting point (0, b). For instance, the y-intercept is at (0, 7) and the slope is 3 in the formula y = 3x - 7.

Here,

Locate the slope first.

These two positions (0, 8) and are in the line, therefore we know that (6,5)

Slope: (y2-y1)/(x2 - x1)

Slope = 8-5 / 0-6

Slope = 3/-6 => Slope = -1/2

The gradient is -1/2. When x = 0, you can find the y-intercept. We also know that the line passes through the point (0,8), and since x = 0, the y-intercept is equal to 8.

using the slope-intercept form, which is

Using the equation y = mx + b, where m denotes the slope and b the y-intercept, we get:

y = (-1/2)x + 8

Therefore , the solution of the given problem of slope comes out to be

y = (-1/2)x + 8.

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Answer:

137 cm. are the volume each con... because of 2 serinemital factors...

Step-by-step explanation:

HOPE IT HELPS!!

a=12,d=17-12=5

nth term =a+(n-1)d

36th term=12+(36-1)5

=12+(35×5)

12+175

36th term=187

Answer: 187

Step-by-step explanation: 17 - 12 = 5 and 22 - 17 = 5

aₙ = a₁ + (n - 1) d

where a₁ = 12, n = 36, d = 5

a₃₆ = 12 + (36 - 1) 5

a₃₆ = 12 + 35 × 5

a₃₆ = 12 + 175

a₃₆ = 187

187 is the 36th term

5 * root(x ^ 2, 3) is the equivalent expression.

Simply multiplying the radicands and placing the result behind the radical sign is all that is required to multiply two square roots. The square root of the product of the radicands, in other words, is equal to the product of two square roots.

Only if the numbers under the radical sign are equal can you add or subtract square roots themselves. The original number will still be in the radical sign after adding or subtracting the coefficients (numbers in front of the radical sign). Implement the suggested action.

5 * root(x ^ 2, 3) is the equivalent expression.

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