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1. Write an equation in standard form of a line that has a slope of 4 and passes through the point (-4,-4).

The value of t is 8 and the value of r is 8√2. The solution has been obtained by using trigonometry.

What is trigonometry?

The study of triangle sides, angles, and relationships is the focus of the mathematical field of trigonometry.

We are given a right angled triangle with an angle 45° and the perpendicular measuring 8.

Using trigonometry,

We know that tan theta = opposite side/ adjacent side

So,

⇒tan 45° = 8/t

⇒1 = 8/t (tan 45° = 1)

⇒t = 8

Similarly,

We know that cos theta = adjacent side/hypotenuse

So,

⇒cos 45° = 8/r

⇒1/√2 = 8/r (cos 45° = 1/√2)

⇒r = 8√2

Hence, the value of t is 8 and the value of r is 8√2.

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Since, there are multiple questions so, the question answered above is attached below.

Answer:

C

Step-by-step explanation:

You are able to simplify both of the 2/8ths and it comes to be 2/8 + 2/8 = 4/8

Then you have 6 different combination to choose from.

"Information available from the question"

For dessert you can choose

Apple, cherry, blueberry, or peach pie to eat, and milk or juice to drink.

To find the how many different combinations of one pie and one beverage are possible?

Now, According to the question:

To eat: Apple pie, Cherry pie, or peach pie = 3 desserts

To drink: milk or juice = 2

Then you can choose one from each:

Then your choices are:

(apple, milk) (apple, juice) (cherry, milk)(cherry, juice) (peach, milk) and (peach, juice)= 6

Then you have 6 different combination to choose from.

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The surface area and volume of the figure is 108 cm² and 96 cm³ respectively

An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either  be linear, quadratic, cubic, depending of the degree of the variable.

The surface area of the figure = 2(1/2 * 4 cm * 3 cm) + (8 cm * 3 cm) + (8 cm * 4 cm) + (8 cm * 5 cm) = 108 cm²

The volume of figure = area of base * height = (1/2 * 4 cm * 3 cm) * 8 cm = 96 cm³

The surface area and volume of the figure is 108 cm² and 96 cm³ respectively

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The standard form of the given exponent is 0.00000094359.

What are Exponents?

A number's exponent demonstrates how many times we are multiplying a given number by itself. 3⁴, for instance, indicates that we are multiplying 3 by four. 3 × 3 × 3 × 3 is its expanded form. The power of a number is another name for an exponent. A whole number, fraction, negative number, or decimal are all acceptable.

[tex]9.4359 \times 10^{-7}[/tex]

Use  [tex]10^{-7} = 1/10^7[/tex]  Because a⁻ᵇ = 1/aᵇ

= 9.4359  ×1/10⁷

= ( 9.4359)/10⁷

= ( 9.4359)/10000000

= 0.00000094359

The standard form of the given exponent is 0.00000094359

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Answer:

[tex]slope = - \frac{8}{5} [/tex]

Step-by-step explanation:

So it looks like on the line, we have two dots.

Let's find those points, starting from the left one.

The left point is: (-1, 4) --- (x1, y1)

The right point is: (4, -4) --- (x2, y2)

**These are in (X, Y) form**

Now to find the slope, you use this equation

[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]

Now let's plug our numbers into this equation

[tex]m = \frac{ - 4 - 4}{4 - ( - 1)} = \frac{ - 8}{5} = - \frac{8}{5} [/tex]

Two negatives make a positive, so 4-(-1) is the same as 4+1.

(8k+k26) after matching, (10k+72k2) because a trinomial cannot be factored 3k2 + 18k - 13

In maths, a coefficient is a cubic, a sequence, or the exponential coefficient of a descriptive word in an expression. Any phrase is acceptable, though digits are frequently used. If the equations are variables, and so the word "parameter" also could refer to the variables themselves. A coefficients is the product of either a number and then a variable. Some occurrences of correlations are: The coefficient as in sentence . The variable is multiplied by it amount when word g has a coefficient of 1. example Since "z" is a factor and the term's interpretation is 6z, the multiplier is 6. The square root of x has a score of one.

given

((8k +  (k2)) -  6) -  ((7 - 10k) -  2k2)

The first term is 3k2 and it has a 3 coefficient.

The coefficient of the middle word, +18k, is 18.

"The constant," the final term, is -13.

Step 1: Add the constant 3 • -13 to the coefficient of the first term to get -39.

Step 2 is to identify two -39 factors whose combined value is equal to the middle term's coefficient of 18, which is 18.

      -39    +    1    =    -38

     -13    +    3    =    -10

     -3    +    13    =    10

     -1    +    39    =    38

(8k+k26) after matching, (10k+72k2) because a trinomial cannot be factored 3k2 + 18k - 13 .

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Answer:

y = -3(x + 0.5)² - 45.25

Step-by-step explanation:

a = -3

b = -3

c = -47

h = -b/2a = -(-3)/2(-3) = -1/2

k = c - b²/(4(-3)) = -46 - (-3)²/(-12) = -45.25

f(x) = -3(x - (-1/2))² - 45.25

y = -3(x + 0.5)² - 45.25

Answer:

2700

Step-by-step explanation:

turn 2% into a decimal and multiply by 135,000.

Answer:

$ 56.34

Step-by-step explanation:

    height = h = 2. 1m

    diameter = 0.7m

            radius = diameter ÷2

                    r  = 0.7 ÷ 2 = 0.35 m

Substitute the values of r and h in the below mentioned formula and find the surface area of the tank.

[tex]\boxed{Area \ of \ cylindrical \ tank = 2\pi r((r + h)}[/tex]

                                            = 2 * 3.14 * 0.35 (0.35 + 2.1)

                                            = 2 * 3.14 * 0.35 * 2.45

                                            = 5.39 square meter

To find the cost of painting the surface area of tank, multiply the cost of painting per square meter by the total surface area of tank.

Cost of painting = 5.93 * 9.50

                           = $ 56.34

The sum of the interior angles of polygon A is 1260°.

The sum of angles of the exterior angles of a polygon A is 360°

Polygon A

A polygon with 9 sides is called a nonagon. The sum of interior angles of a Nonagon is 1260°. This can be calculated using the formula (n -2) * 180, where n is the number of sides.

Thus, the sum of the interior angles of polygon A is 1260°.

The sum of the exterior angles of a polygon is 360°.Thus, the sum of angles of the exterior angles of a polygon A is 360°.

Polygon B

Polygon B has 7 sides i.e. n = 7

sum of angles of the interior angles of polygon B = (7-4) * 180 = 900°

Thus, y = 900- 135 - 140 - 150 - 120 - 135 - 120 = 100°

x = 180 - 100 = 80°  (sum of angles on a straight line is 180°)

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Answer:

The height of the lamp posts is 20.49 m and the distance between them is 70.98 m.

Step-by-step explanation:

Draw a diagram using the given information (see attachment).

[tex]\boxed{\begin{minipage}{7 cm}\underline{Tan trigonometric ratio} \\\\$\sf \tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\end{minipage}}[/tex]

Use the tan trigonometric ratio to create two equations for h.

Triangle ACD:

[tex]\implies \tan 30^{\circ}=\dfrac{h}{x}[/tex]

[tex]\implies h=x\tan 30^{\circ}[/tex]

[tex]\implies h=\dfrac{\sqrt{3}}{3}x[/tex]

Triangle BCD:

[tex]\implies \tan 45^{\circ}=\dfrac{h}{x-15}[/tex]

[tex]\implies h=(x-15)\tan 45^{\circ}[/tex]

[tex]\implies h=(x-15)\cdot 1[/tex]

[tex]\implies h=x-15[/tex]

Substitute the second equation into the first equation and solve for x:

[tex]\implies x-15=\dfrac{\sqrt{3}}{3}x[/tex]

[tex]\implies x-\dfrac{\sqrt{3}}{3}x=15[/tex]

[tex]\implies \dfrac{3-\sqrt{3}}{3}x=15[/tex]

[tex]\implies (3-\sqrt{3})x=45[/tex]

[tex]\implies x=\dfrac{45}{3-\sqrt{3}}[/tex]

[tex]\implies x=35.4903810...[/tex]

To find h, substitute the found value of x into the second equation and solve for h:

[tex]\implies h=x-15[/tex]

[tex]\implies h=35.4903810...-15[/tex]

[tex]\implies h=20.4903810...[/tex]

[tex]\implies h=20.49\; \sf m\;\;(2\;d.p.)[/tex]

As the distance between the two lamp posts is 2x:

[tex]\implies 2x=2 \cdot 35.4903810...[/tex]

[tex]\implies 2x=70.9807621...[/tex]

[tex]\implies 2x=70.98\; \sf m\;\;(2\;d.p.)[/tex]

Therefore:

Answer:

Step-by-step explanation:

The rate of change is just the slope of the equation and/or graph.

for the linear function A, y = 2/3x + 5, the slope (therefore rate of change) is 2/3. For B (I can't make it out that clear), 3/2. That gives the answer for C: 3/2 is greater than 2/3.

Answer:

[tex] \frac{ - 17}{2} [/tex]

Step-by-step explanation:

[tex]3(x - 4) = 5(x + 1)[/tex]

[tex]3x - 12 = 5x + 5[/tex]

[tex]3 - 12 - 5x = 5x + 5 - 5x [/tex]

[tex]3x - 12 - 5x = 5[/tex]

[tex]3x - 12 - 5x + 12 = 5 + 12[/tex]

[tex]3x - 5x = 5 + 12[/tex]

[tex]3x - 5x = - 2x[/tex]

[tex]5 + 12 = 17[/tex]

[tex] - 2x = 17[/tex]

[tex] \frac{ - 2x}{2} = \frac{17}{ - 2} [/tex]

[tex]x = \frac{17}{ - 2} [/tex]

[tex]x = \frac{ - 17}{2} [/tex]

The values of x in the triangles are x = 17 and x = 52

Triangle 1

From the question, we have the following parameters that can be used in our computation:

The triangle

Using the law of cosines to solve for x, we have

x^2 = 7^2 + (8√2)^2 - 2 * 7 * (8√2) * cos(135 degrees)

Evaluate the like terms and multiply

x^2 = 289

Take the square roots

x = 17

Triangle 2

Here, we have"

Using the law of cosines to solve for x, we have

x^2 = 28^2 + 32^2 - 2 * 28 * 32 * cos(120 degrees)

Evaluate the like terms and multiply

x^2 = 2704

Take the square roots

x = 52

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The ratio of the number of astronauts on Earth to the total number of astronauts is 7 : 30.

A ratio is a mathematical expression that compares two or more values by dividing the size of one value by the size of another.

Ratios can be expressed in several different forms, including fractions, decimals, or percentages, and can be used to compare quantities, measurements, or other values in a meaningful way.

Ratios provide a way to express the relationship between two or more values in a compact and concise format, and can be used in a variety of fields, including mathematics, science, finance, and engineering.

If the space program has 23 astronauts in outer space and 7 astronauts on Earth, then the ratio of the number of astronauts on Earth to the total number of astronauts is:

7 : (23 + 7) = 7 : 30

You can simplify the ratio to 7/30 or approximately 0.23 or 23%.

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Answer:

224.7

Step-by-step explanation:

sin 57 = 98/ ?

? = 98/sin57° = 224.7

Answer:

Rise over run for the first one is x=300 and y=600

The number of mice in the category is 38

From the question, we have the following parameters that can be used in our computation:

The histogram

The total number of mice with birth weights below 12 g is the sum of the frequency of bars less than 12 g

Using the above as a guide, we have the following:

Total = 4 * 4 + 4 + 4 + 7 + 7

Evaluate

Total = 38

Hence, the number of mice is 38

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The Adding and Subtracting Rational Expression Calculator is a free online tool that displays the results of rational number arithmetic operations.

A rational expression is nothing more than the product of two polynomials. In other words, it is a fraction with polynomial numerator and denominator. Rational expressions resemble fractions with variable denominators (and often numerators too).

Adding or subtracting rational expressions involves four steps: All fractions must be written as equivalent fractions with a common denominator. Combine the fractions to form a single fraction with a common denominator. Reduce the complexity of the expression at the top of the fraction. Reduce the fraction to its simplest terms.

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Answer:

1 and 10

Step-by-step explanation:

Account #1: one year (because it doubles each year)

Account #2: ten years (100 * 10 = 1000)

The BEST estimate for the x-coordinate of the solution to this system is -4

From the question, we have the following parameters that can be used in our computation:

The graph

On the graph, we can see that the lines intersect at

Approximately (-4, 3)

This means that the x-cooridnate of the solution is

x = -4

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Answer:

Step-by-step explanation:

The area of the brick walkway in the front yard is 122 square feet.

An open, flat object with four straight sides and one pair of parallel sides is referred to as a trapezoid or trapezium.

A trapezium's non-parallel sides are referred to as the legs, while its parallel sides are referred to as the bases. The legs of a trapezium can also be parallel. The parallel sides may be vertical, horizontal, or angled.

The altitude is the measurement of the angle perpendicular to the parallel sides.

We know, The area of a trapezoid is,

(1/2)×(sum of the two parallel sides)×height, And The area of a rectangle is (length×width).

From the given, Diagram the total area would be the sum of the area of a rectangle and a trapezoid which is,

= [(15×6) + (1/2)(10 + 6)×4] square feet.

= [90 + 32] square feet.

= 122 square feet.

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Answer:

7.8 cm

Step-by-step explanation:

One tenth of a centimeter = [tex]\frac{1}{10} (1 cm)[/tex] = 0.1 cm . This means the answer has to be rounded to 1 decimal place.

Length of BE = Length of ED = [tex]\frac{6}{2}[/tex] = 3 cm

Focus on the triangles AED and CED. These two are right-angled triangles.

In both triangles, sides AE and CE are perpendicular sides, whose lengths will be calculated using Pythagorean Theorem:

Triangle AED:

[tex]AD^{2} = AE^{2} + ED^{2}[/tex]

[tex]AD^{2} - ED^{2} = AE^{2}[/tex]

[tex]AE^{2} = 6^{2} - 3^{2}[/tex]

Taking square root on both sides of the equation to get rid of the square:

[tex]AE = \sqrt{6^{2} -3^{2} }[/tex]

[tex]AE = \sqrt{36 - 9}[/tex]

[tex]AE = \sqrt{27}[/tex] cm

Triangle CED:

[tex]CD^{2} = CE^{2} + ED^{2}[/tex]

[tex]CE^{2} = CD^{2} - ED^{2}[/tex]

[tex]CE^{2} = 4^{2} - 3^{2}[/tex]

Taking square root on both sides of the equation to get rid of the square:

[tex]CE = \sqrt{4^{2} -3^{2} }[/tex]

[tex]CE = \sqrt{16 - 9}[/tex]

[tex]CE = \sqrt{7}[/tex] cm

Length of AC = Length of AE + Length of EC

∴ Length of AC = [tex](\sqrt{27} + \sqrt{7})[/tex] cm

                          = 7.841 cm

  Length of AC = 7.8 cm (Rounded to the nearest tenth of a centimeter)

The way that increasing the amount of charge on an object affects the electric force it exerts on another charged object is; The electric force increases because the amount of charge has a direct relationship to the force

The amount of charge on an object due to the effect of the force that is exerted on it can be calculated by using the formula :

F = E × q

Where;

F is the electric force.

E is the energy.

q is the charge.

The electric force between charged particles at rest is known as electrostatic force.

The magnitude of the electric force between point charges is directly proportional to the multiplication of the charges and inversely proportional to the distance between them.

Therefore, we conclude that increasing the amount of charge on an object would increase the electric force because the amount of charge has a direct relationship with the force.

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The values of the expressions when evaluated are 10000 and 1000

From the question, we have the following parameters that can be used in our computation:

This means that

Species = 10^4 = 10000

Threatened = 10^3 = 1000

Hence, the values are 10000 and 1000

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60<5x+40

60-40<5x

20<5x

x>4

The coordinate of the point R of the line segment QS will be (-3.8, -0.4). Then the correct option is A.

Let A (x₁, y₁) and B (x₂, y₂) be a line segment. Then the point P (x, y) divides the line segment in the ratio of m:n. Then we have

x = (mx₂ + nx₁) / (m + n)

y = (my₂ + ny₁) / (m + n)

The endpoints are Q(-6, -2) and S(5, 6). And m:n is 1:4. Then the coordinate of the point R is given as,

x = (5 · 1 + (-6) · 4) / (1 + 4)

x = -3.8

y = (6 · 1 + (-2) · 4) / (1 + 4)

y = -0.4

The coordinate of the point R of the line segment QS will be (-3.8, -0.4). Then the correct option is A.

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Answer:

Let x be the number of red M&Ms.

Then the number of blue M&Ms is x + 5, the number of yellow M&Ms is x - 9, and the number of brown M&Ms is (1/2)x + 13.

The total number of M&Ms is 135, so we can write an equation:

x + (x + 5) + (x - 9) + (1/2)x + 13 = 135

Simplifying this equation, we get:

3.5x + 9 = 135

Subtracting 9 from both sides, we get:

3.5x = 126

Dividing both sides by 3.5, we get:

x = 36

So there are 36 red M&Ms, 41 blue M&Ms (36 + 5), 27 yellow M&Ms (36 - 9), and 31 brown M&Ms (1/2 * 36 + 13).

Answer:

Step-by-step explanation:

r: the number of red M&Ms

b: the number of blue M&Ms

y: the number of yellow M&Ms

br: the number of brown M&Ms

We can translate the given information into equations:

r + b + y + br = 135 (the total number of M&Ms is 135)

b = r + 5 (there are five more blue M&Ms than red ones)

y = r - 9 (there are nine less yellow M&Ms than red ones)

br = 13 + (1/2)r (there are thirteen more brown M&Ms than half the number of red ones)

We can use equations 2, 3, and 4 to substitute for b, y, and br in equation 1:

r + (r + 5) + (r - 9) + (13 + (1/2)r) = 135

Simplifying this equation, we get:

3.5r + 9 = 135

Subtracting 9 from both sides, we get:

3.5r = 126

Dividing both sides by 3.5, we get:

r = 36

Now that we know the value of r, we can use equations 2, 3, and 4 to find the values of b, y, and br:

b = r + 5 = 36 + 5 = 41

y = r - 9 = 36 - 9 = 27

br = 13 + (1/2)r = 13 + (1/2)(36) = 31

Therefore, the number of red, blue, yellow, and brown M&Ms in the mixture are 36, 41, 27, and 31, respectively.