An angle measures 64.2° more than the measure of its complementary angle. What is the measure of each angle?

The value of x found using the assumption, ΔABC is an isosceles triangle and the measure using the fact that ∠ABC > ∠ACB are;

a) x = 4.5

The assumption made is that the triangle is an isosceles triangle

b) {x ∈ Z| -6 ≤ x ≤ 8}

An isosceles triangle is a triangle that has a pair of congruent sides.

Let ΔABC be an isosceles triangle, we get;

∠ABC is congruent to ∠ACB, (∠ABC ≅ ∠ACB), therefore, by the definition of congruence triangles, we get;

m∠ABC = m∠ACB

The question indicates that the measure of the angles are;

∠ABC  = 100 - 12·x

∠ACB = 8·x + 10

Which indicates, by the substitution property, that we get;

100 - 12·x = 8·x + 10

100 - 10 = 8·x + 12·x = 20·x

100 - 10 = 90 = 20·x

20·x = 90

x = 90/20 = 4.5

The assumption made is that the triangle ΔABC is an isosceles triangle

b) ∠ABC > ∠ACB, therefore;

100 - 12·x > 8·x + 10

100 - 10 > 8·x + 12·x = 20·x

100 - 10 = 90 > 20·x

20·x < 90

x <  90/20 = 4.5

x < 4.5

The possible integer values of x can be found as follows;

100 - 12·x ≥ 0

100 ≥ 12·x

x ≤ 100/12 = 8.[tex]\overline{3}[/tex]

x ≤ 8.[tex]\overline{3}[/tex]

100 - 12·x ≤ 180

100 - 180 ≤ 12·x

12·x ≥ -80

x ≥ -80/12 = -6.[tex]\overline{6}[/tex]

x ≥ -6.[tex]\overline{6}[/tex]

Similarly, we get;

8·x + 10 ≥ 0

x ≥ -10/8 = -1.25x

x ≥ -1.25

8·x + 10 ≤ 180

x ≤ (180 - 10)/8 = 21.25

x ≤ 21.25

The possible integer value of x, using the interval, x ≥ -6.[tex]\overline{6}[/tex], x ≤ 8.[tex]\overline{3}[/tex] are therefore; -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, which can be expressed as; {x ∈ Z| -6 ≤ x ≤ 8}

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Answer:

The solution to the equation is **x = 3.24**. Here is how I solved it:

First, I isolated the square root term by subtracting 7 from both sides of the equation:

5 square root x = -9

Then, I divided both sides by 5 to get the square root of x alone:

square root x = -9/5

Next, I squared both sides to eliminate the square root:

x = (-9/5)^2

Finally, I simplified the right side by multiplying the fractions:

x = 81/25

x = 3.24

I checked my answer by plugging it back into the original equation and verifying that both sides are equal:

5 square root 3.24 + 7 = -2

-2.01 + 7 = -2

4.99 = -2

Since the difference is very small, I concluded that x = 3.24 is a valid solution.

Step-by-step explanation:

Using the unitary method we found that the amount that Bill should receive is $500 and the amount that his boss owes him is $26.

What is meant by the unitary method?

The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. Once we have determined the value of a single unit, we may multiply that value by the number of units needed to determine the value of the other units. The concept of ratio and proportion is mostly applied using this way. Recognizing the units and values is crucial when using the unitary technique to a problem.

Given,

    Money received for each document = 25 cents

  Number of documents prepared by Bill = 2000

  The amount he received = $474

a) The correct total pay that Bill should receive = 2000*25 = 50,000cents

   Using the unitary method,

                   1 dollar = 100 cents

                  50,000 cents = 50000/100 = $500

b) The amount that his boss owes him = 500 - 474 = $26

Therefore using the unitary method we found that the amount that Bill should receive is $500 and the amount that his boss owes him is $26.

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Answer:a

Step-by-step explanation:

The area of the given composite shape with two rectangles is 68 m²

What is a rectangle?

There are four right angles on the quadrilateral that forms the rectangle. Every corner or vertex has a right angle where the two sides meet. It differs from a square, which has all of its sides of equal length, in that the opposite sides of the rectangle are equal in length. Two dimensions and flatness combine to make a rectangle.

The figure can be divided into a rectangle with a length of 8m and breadth of 6m and another rectangle of length 5m and breadth = (10-6) = 4m.

To find the area of the whole figure, we first find the areas of small and big rectangles and sum their areas.

Area of small rectangle = length * breadth = 5*4 = 20 m²

Area of big rectangle = length * breadth  = 8 * 6 = 48 m²

Therefore the area of the given composite shape with two rectangles is 20+48 = 68 m².

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Here are three statements explaining why each of the objects doesn't belong with the others:

Sphere:

Cylinder:

Pyramid:

Cube:

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Answer:

Step-by-step explanation:

here's a more detailed explanation:

The assistant received a raise of 10%, which means that their salary increased by 10% of the original salary. The new salary after the raise is given as 47,585.

To find the original salary before the raise, we need to reverse the effect of the raise. To do this, we divide the new salary by the factor that represents the increase, which is 1 plus the raise as a decimal.

The raise as a percentage is 10%, which is equivalent to 0.10 as a decimal. Therefore, the factor that represents the increase is 1 + 0.10 = 1.10.

We can now use this factor to find the original salary by dividing the new salary by the factor:

Original salary = New salary / (1 + Raise as a decimal)

Original salary = 47,585 / (1 + 0.10)

Original salary = 47,585 / 1.10

Original salary = 43,259.09

So the salary before the raise was 43,259.09.

Answer:

To solve a right triangle, we can use the Pythagorean theorem, which states that the sum of the squares of the two smaller sides equals the square of the largest side. In this triangle, we have:

a^2 + b^2 = c^2

Plugging in the values we have:

18.7^2 + b^2 = 46.4^2

Solving for b, we have:

b = √(46.4^2 - 18.7^2)

b = √(2159.36 - 349.69)

b = √1809.67

b = 42.6 cm (rounded to the nearest tenth)

Next, we can use the tangent function to find angles A and B:

tan(A) = a/b = 18.7/42.6 = 0.439

A = tan^-1(0.439) = 24° 26' (rounded to the nearest minute)

And, using the Pythagorean theorem:

c^2 = a^2 + b^2 = 18.7^2 + 42.6^2 = 346.69 + 1809.67

B = 90° - A = 90° - 24° 26' = 65° 34' (rounded to the nearest minute)

So the solution is:

a = 18.7 cm

b = 42.6 cm

c = 46.4 cm

A = 24° 26'

B = 65° 34'

C = 90°

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given the information that the polynomial function P(x) has leading coefficient 1, has roots of multiplicity 2 at x = 1 and x = 0, and a root of multiplicity 1 at x = -5, we can use this information to find a possible formula for P(x).

A polynomial function's roots are the values of x that make the function equal to zero. If a root has multiplicity n, it means that (x - root) is a factor of the polynomial function n times.

So, based on the given information, we know that P(x) must be divisible by the factors (x - 1)^2, (x - 0)^2, and (x + 5), and that the leading coefficient must be 1.

Putting it all together, a possible formula for P(x) is:

P(x) = (x - 1)^2 (x - 0)^2 (x + 5) = (x^2 - 2x + 1)(x^2)(x + 5) = x^6 - 7x^5 + 17x^4 - 22x^3 + 17x^2 - 7x + 5

So, the possible formula for P(x) is P(x) = x^6 - 7x^5 + 17x^4 - 22x^3 + 17x^2 - 7x + 5.

Answer:   [tex]P(\text{x}) = \text{x}^2(\text{x}-1)^2(\text{x}+5)[/tex]

Explanation:

If k is a root of P(x), then x-k is a factor. The multiplicity is the exponent for that factor.

For instance, the root x = 1 with multiplicity 2 leads to the factor [tex](\text{x}-1)^2[/tex]

The leading coefficient is the number out front. For example, if the leading coefficient was 8, then we'd have [tex]P(\text{x}) =8\text{x}^2(\text{x}-1)^2(\text{x}+5)[/tex]

However, we change that "8" to a "1" since the leading coefficient is 1 here.

That's how we get to

[tex]P(\text{x}) = 1\text{x}^2(\text{x}-1)^2(\text{x}+5)[/tex] aka [tex]P(\text{x}) = \text{x}^2(\text{x}-1)^2(\text{x}+5)[/tex]

Optionally if you were to expand everything out, combine like terms, and simplify then you'd get

[tex]P(\text{x}) = \text{x}^2(\text{x}-1)^2(\text{x}+5) = \text{x}^5 + 3\text{x}^4- 9\text{x}^3+5\text{x}^2[/tex]

I don't recommend doing this because you lose the information about the roots along with their corresponding multiplicities. It's better to keep things factored.

You can use a graphing tool like Desmos or GeoGebra to verify the answer.

The correct answer is

d) 4:16

Area and Perimeter of Similar Polygons:

Polygons are said to be similar when their corresponding angles are equal and their corresponding sides are in the same proportion. The perimeters and areas of identical polygons have a unique relationship, just as their corresponding sides do.

Perimeters: The scale factor and the perimeters ratios of perimeters are similar. In reality, the scale factor is identical to any ratio between any two similar forms (diagonals, medians, midsegments, altitudes, etc.).

Areas: If the scale factor of the sides of two similar polygons is [tex]\frac{m}{n}[/tex]

, then the ratio of the areas is [tex](\frac{m}{n} )^{2}[/tex].

(Area of Similar Polygons Theorem). Because area is a two-dimensional quantity, you square the ratio.

It is given that ,

the ratio of perimeters of two similar quadrilateral is 2:4.

now,

to find the ratio of area , we can take two quadrilaterals, say square.

Square ABCD of side 2 units and Square PQRS of side 4 units.

now ratio of areas,

[tex]=\frac{area of square ABCD}{area of square PQRS} \\\\=\frac{2*2}{4*4} \\\\=\frac{4}{16}[/tex]

If the given ratio of perimeters can be further solved as 1:2, then we can see that the ratio of areas can also be further solved as 1:4.

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Answer:B

Step-by-step explanation: the graph moves x vertically -1 while y is moved vertically to 4

The ratio of the number of sixth-graders who visited the science museum to the number of sixth-graders who visited the history museum is

10:39.

What is meant by the ratio of two quantities?

A ratio displays the multiplicity of two numbers. Mathematicians use the term "ratio" to compare two or more numbers. It serves as a comparison tool to show how big or tiny an amount is in relation to another. Two quantities are compared using division in a ratio. In this case, the dividend is referred to as the "antecedent" and the divisor as the "consequent." In general, a: b, which can be interpreted as "a is to b," is used to denote a ratio between two quantities, let's say "a" and "b."

Given,

  Number of students who picked the science museum = 10

Number of students who picked the history museum = 39

The ratio of students who visited the science museum to students who visited the history museum = 10:39.

Therefore the ratio of the number of sixth-graders who visited the science museum to the number of sixth-graders who visited the history museum is 10:39.

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The missing side length from the given figure is 6 ft.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

From the figure,

Missing side = x

Now,

The expression we can make from the figure.

= 16 - 10

= 6 ft

Thus,

The missing side length is 6 ft.

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The revenue corresponding to break even condition for selling x units is $4.28.

An evaluation of the model's accuracy in estimating the link between X and y is done using a cost function. In most cases, this is represented as a difference or distance between the projected value and the actual value. The price element (you may also see this referred to as loss or error.)

To break even (R = C) we have:

7.8 √x + 22,000 = 13.82x

Substitute the value of x = u² thus:

7.8u +22000 = 13.8u²

13.8u² - 7.8u - 22000 = 0

The quadratic formula is given as:

u = -b ± √b² - 4ac / 2a

u = -(-7.8) ± √(-7.8)²- (4)(13.82)(22000) / 2(13.82)

u = 7.8 ± 7.8 / 27.64

u = 7.8 + 7.8 / 27.64

u = 0.56

Back substituting the value of u:

x = u²

x = (0.56)²

x = 0.31

Substituting the value of x is R:

R = 13.82 (0.31)

R = 4.28

Hence, the revenue corresponding to break even condition for selling x units is $4.28.

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Answer:

5 seconds

Step-by-step explanation:

d = vt + 16t² , that is

vt + 16t² = d

substitute d = 480, v = 16 into the equation

16t + 16t² = 480 ( divide through by 16 )

t + t² = 30 ( subtract 30 from both sides )

t² + t - 30 = 0 ← in standard form

(t + 6)(t - 5) = 0 ← in factored form

equate each factor to zero and solve for t

t + 6 = 0 ⇒ t = - 6

t - 5 = 0 ⇒ t = 5

t > 0 , then t = 5

the object will hit the ground 5 seconds later

Answer:

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

As per given we have:

Substitute these into given equation and solve for t:

The first value of t is discarded as time can't be negative, so the answer is 5 seconds.

The solution to the equation 4x² = 16 is x = 2.

Given the equation in the question;

4x² = 16

x = ?

To solve for x, first divide both terms by 4.

4x² = 16

4x²/4  = 16/4

x² = 4

Take the square roots of both sides

√x² = ±√4

x = ±2

x = -2 or 2.

Therefore, the value of x is 2.

Option D)2 is the correct answer.

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Answer:

D.2

Step-by-step explanation:

[tex]4 {x}^{2} = 16 \\ \frac{4 {x}^{2} }{4} = \frac{16}{4} \\ {x}^{2} = 4 \\ \sqrt{ {x}^{2} } = \sqrt{4} \\ x = \sqrt{4} \\ x = 2[/tex]

On solving the provided question we can say that equations are = .60x + .85y = .75(180)

A mathematical equatiοn is a formula that joins two statements and uses the equal symbol (=) tο indicate equality. A mathematical statement that establishes the equality of twο mathematical expressiοns is known as an equation in algebra. Fοr instance, in the equatiοn 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart.

The relationship between the twο sentences on either side of a letter is described by a mathematical formula. Often, there is οnly one variable, which also serves as the symbοl. for instance, 2x – 4 = 2.

t x = the number of ounces of Sοlution A

y = the number of ounces of Sοlution B

x + y = 180    

y = 180 - x

Solving equation -

0.60 + 0.85y = 0.75(180)

0.60 + 0.85y = 135

60x + 85y = 13500

60x + 85(180-x) = 13500

60x + 15300 - 85x = 13500

-25x = -1800

x = 72ounces

y = 180 - 72

y = 108 ounces        

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Using matrix inversion, the value of x and y are 1.104 and 39.704 respectively

The system of equations can be written in matrix form as:

|  -650    1 |   | x |   |  175    |

|  120     1 |   | y |   |  25,080 |

To solve for x and y, we can use matrix inversion to get:

| x |   |  -650    1 |^-1   |  175    |

| y | = |  120     1 |     |  25,080 |

Using matrix inversion, we get:

| x |   |  -0.00016  0.00875 |   |  175    |    | 1.104 |

| y | = |  0.00476   0.00004 |   |  25,080 | =  | 39.704 |

Therefore, the solution to the system of equations is x = 1.104 and y = 39.704.

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The local maximums are at x = -4 and x = 4, and the value of the local maximum is f(x) = 1.

For a function f(x), we define a local maximum as a value of x = c such that:

f(c) ≥ f(x)

for any value of x in a given interval.

Here we can see two local maximums on the graph, and we can see that these are at:

x = -4 and x = 4

b) And the local maximum value of f is the value that the function takes in the maximum, we can see that:

f(-4) = f(4) = 1

The value of the local maximum is y = 1.

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The value of a, b, and c are 1, -2, and 6 respectively.

The y-intercept of this quadratic function is 6.

The axis of symmetry of this quadratic function is 1.

The vertex of this quadratic function is (1, 5).

Mathematically, the axis of symmetry of a quadratic function can be calculated by using this mathematical expression:

Axis of symmetry, Xmax = -b/2a

Where:

a and b represents the coefficients of the first and second term in the quadratic function.

For the given quadratic function f(x) = x² - 2x + 6, we have:

Axis of symmetry, Xmax = -b/2a

Axis of symmetry, Xmax = -(-2)/2(1)

Axis of symmetry, Xmax = 2/2 = 1.

Vertex (h, k) = (1, 5).

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

y-intercept = 6.

Lastly, we would create a table and then graph the quadratic function as follows;

x         y

0         6

2         2

5         11

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Answer:

0.0152 is the probability that the first 5 locations are in water and the last 2 locations are on land.

Answer:

[tex]6\pi[/tex]

Step-by-step explanation:

There's two things to note here, we're dealing with a semi-circle and also a semi-circle that has some area taken out of it.

The area of a circle can be calculated using the formula: [tex]A=\pi r^2[/tex] where "r" is the radius, equal to half the diameter.

Since we're dealing with the semi-circles, we can just divide this area by two to get: [tex]A=\frac{\pi r^2}{2}[/tex]

Now as noted, we have some of the area taken out, but fortunately it's just another semi-circle. We can simply calculate the area of the entire semi-circle, and then calculate the area of the semi-circle inside and subtract them.

So the diameter of the entire thing is just 8 ft, so the radius is half of this, equal to 8 ft. That means the area is: [tex]A=\frac{\pi (4)^2}{2}=A = \frac{\pi * 16}{2} = 8\pi[/tex]

One mistake that may be made here, is assuming the radius of the smaller semi-circle is just two, as provided in the image. It's actually the radius of the inner semi-circle plus two which gives us the radius of the outer circle, of 4 feet. Now luckily in this case, it actually still results in 2 ft (since 2 + 2 = 4), but in other examples, that may noe be the case.

So now let's calculate the area of the inner semi-circle: [tex]A=\frac{\pi (2)^2}{2}=2\pi[/tex]

Now let's just subtract the areas: [tex]8\pi - 2\pi = 6\pi[/tex], so the area is 6 pi

Answer:

Step-by-step explanation:

The length of the line segment between two points in a plane can be calculated using the distance formula. Given two points (x1, y1) and (x2, y2), the distance between them is given by the following formula:

d = √((x2 - x1)^2 + (y2 - y1)^2)

In this case, the two points are (3, 5) and (7, 3). Plugging these values into the formula, we get:

d = √((7 - 3)^2 + (3 - 5)^2)

d = √((4^2) + (2^2))

d = √(16 + 4)

d = √20

So, the length of the line segment between the two points (3, 5) and (7, 3) is √20.

Answer:

3 inches is approximately equal to 76.2 millimeters.

Step-by-step explanation:

Answer:

3 inches = 76.2 millimeters

Step-by-step explanation:

Answer:

The original price of the shoes was $53.

The discount percentage was 20%.

The discount amount was 53 * 0.2 = 10.6.

The sale price after the discount was 53 - 10.6 = 42.4.

The processing fee percentage was 20%.

The processing fee amount was 42.4 * 0.2 = 8.48.

The final price after the processing fee was 42.4 + 8.48 = 50.88.

Therefore, the discount was $10.60, and the final price was $50.88.

Step-by-step explanation:

Answer:

After rounding the nearest tenth of a square foot, the surface area of the  circular cylinder is 131.88 feet^2.

Step-by-step explanation:

To find surface area of a right circular cylinder we can use the formula,

A = 2πrh + 2πr^2

Here A is surface area,

π is mathematical constant ,

r is radius, and h is the height of the cylinder.

We have

r = 3 ft

h = 4 ft,

Now we put the values to find the surface area,

A = 2π × 3 × 4 + 2π ×3^2

A = 24π + 18π

A = 42π

A= 42×3.14                             (we know π = 3.14 )

A = 131.88

After rounding the nearest tenth of a square foot, the surface area of the  circular cylinder is 131.88 feet^2.

The most specific name for the quadrilateral is trapezoid, the correct option is C.

A quadrilateral is defined as a two-dimensional shape with four sides, four vertices, and four angles. There are two main types: concave and convex. There are also various subcategories of convex quadrilaterals, such as trapezoids, parallelograms, rectangles, rhombi, and squares.

Given;

The figure with 4 sides and two opposite are equal

Now,

In the figure two opposite sides are equal in length

But they all are not parallel only on pair of opposite sides are parallel.

Also, the figure the adjacent angle are equal.

Therefore, the quadrilateral will be trapezoid.

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Answer:

190°

Step-by-step explanation:

Subtract 360° (this is one complete rotation)

"coterminal" is the exact same angle, but 360° bigger (or smaller)

550° - 360°

= 190°

The required measure of angle p in triangle DBC is given as ∠p = 59.14°.

If you know the lengths of two sides of a right triangle, you can use trigonometric ratios to calculate the measures of one (or both) of the acute angles.

Here,

Consider triangle ABD

Apply the Pythagorean theorem to determine the measure of DB,
DB² = AD² + AB²
DB² = 6² + 5²
DB² = 61
DB = 7.81

Now,
Apply the trig ratio in triangle DCB,
cosp = 4/7.81
p = 59.14°

Thus, the required measure of angle p in triangle DBC is given as ∠p = 59.14°.

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