My sister is 16 years old. My brother says that his age minus fifteen is equal to my sister's age. How old is my brother?

Enter an equation, using b as your variable, to find how old my brother is.

The equation is

My brother is
years old.

Answer:

44 ft

Step-by-step explanation:

To find the height of the tree, h, model the given scenario as a two right triangles and solve using the tan trigonometric ratio.

[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]

See attached for a diagram modelling the given information.

Create two tan ratios using the given information, and rearrange each equation to isolate x.

Equation 1

Given:

Therefore:

[tex]\begin{aligned}\implies \tan 42^{\circ}&=\dfrac{h}{x+12}\\\\ x+12&=\dfrac{h}{\tan 42^{\circ}}\\\\ x&=\dfrac{h}{\tan 42^{\circ}}-12\end{aligned}[/tex]

Equation 2

Given:

[tex]\begin{aligned}\implies \tan 50^{\circ}&=\dfrac{h}{x}\\\\ x&=\dfrac{h}{\tan 50^{\circ}}\end{aligned}[/tex]

To find the value of h, substitute equation 2 into equation 1 to eliminate x and solve for h:

[tex]\implies \dfrac{h}{\tan 50^{\circ}}=\dfrac{h}{\tan 42^{\circ}}-12[/tex]

[tex]\implies \dfrac{h}{\tan 50^{\circ}}-\dfrac{h}{\tan 42^{\circ}}=-12[/tex]

[tex]\implies \dfrac{h\tan 42^{\circ}-h\tan 50^{\circ}}{\tan 50^{\circ}\tan 42^{\circ}}=-12[/tex]

[tex]\implies \left(\dfrac{\tan 42^{\circ}-\tan 50^{\circ}}{\tan 50^{\circ}\tan 42^{\circ}}\right)h=-12[/tex]

[tex]\implies h=\dfrac{-12\tan 50^{\circ}\tan 42^{\circ}}{\tan 42^{\circ}-\tan 50^{\circ}}[/tex]

[tex]\implies h=44.1967977...[/tex]

Therefore, the approximate height of the tree to the nearest foot is 44 ft.

The required probability of the randomly selected households either having internet access or cable television is equal to 0.85.

Let us consider 'A' represents the number of house hold has internet access.

And 'B' represents the number of house hold has cable television.

P(A) = 75%

      = 0.75

P(B) = 80%

       = 0.80

Number of household has both internet access and cable television

= P( A∩B)

= 70%

= 0.70

Probability of randomly selected household either with internet access or cable are P( A∪B) :

P( A∪B) = P(A) + P(B) - P( A∩B)

Substitute the value we get,

⇒  P( A∪B) = 0.75 + 0.80 - 0.70

⇒  P( A∪B) =  0.85

Therefore, the probability of household having either internet access or cable television is equal to 0.85.

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Measures of angles, x = 93° and y = 97°

A cyclic quadrilateral is a quadrilateral with all four vertices on a circle. Also called an inscribed quadrilateral. A circle consisting of all vertices around a polygon is known as the circumcircle.

Given,

Interior angles of quadrilateral

= x° , y° , 83°

Arc angles on the center of circumcircle are 64° and 122°.

angle made by chord on the center is twice to the angle made on the circumference of the circle

64° + 122° = 2x

186° = 2x

x = 186°/2

x = 93°

In cyclic quadrilateral,

Sum of opposite interior angles is 180°

y + 83° = 180°

y = 180° - 83°

y = 97°

Hence, measure of angles x and y are 93° and 97° respectively.

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Answer:

y=0.5x+30?

Step-by-step explanation:

Answer:

Step-by-step explanation:6

The equation and value of x , the distance of 1 lap around the path at the park is 4.8x + 1.2 = 3.6.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

Florian ran 1.2 miles and walked 4.8 laps around the path at the park for a total distance of 3.6 miles.

As, we know the number of them (4.8) would be multiplied by the variable (x). We also know that 1.2 is the constant.

So, the equation can be framed as

4.8x + 1.2 = 3.6

4.8x = 2.4

x = 0.5

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The question attached here seems to be incomplete the remaining portion is given below:

3.6 x + 1.2 = 4.8; x = 1 mile

4.8 x + 1.2 = 3.6; x = 1 mile

3.6 x + 1.2 = 4.8; x = 0.5 mile

4.8 x + 1.2 = 3.6; x = 0.5 mile

5 x = negative 58

The angle 'b' measure 120 degrees from the diagram.

The given diagram is a circle geometry. Given the following parameters

x= 44° and;

a = 32°

In order to determine the measure of angles 'b'. we will use the expression below;

x = 1/2(b + a)

44 = 1/2 (b- 32)
88 = b - 32

b = 88 + 32

b = 120 degrees

Hence the measure of the angle 'b' from the diagram is 120 degrees.

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The number of more cups that she needs to put in will be 28 cups.

An answer to a formula is any variable value that fulfills the equal outcomes, that is, it tends to make the Left Hand Side (LHS) and Right Hand Side (RHS) of the formula equal. To solve an equation, you must locate the feasible solution) to that formula.

A recipe for cookies calls for 3 Cups of sugar. And t has already put in 31 Cups. Then the equation is given as,

t + 3 = 31

t = 31 - 3

t = 28 cups

The number of more cups that she needs to put in will be 28 cups.

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The points where the curve intersect the paraboloid is (2, 0, 4).

To find the points of intersection, we set the two equations equal to each other and solve for x, y, and z.

Now, to find the point where the curve r(t) intersects the paraboloid z = x² + y², we can substitute the given value of t into the parametric equations of the curve.

The curve is defined as:

r(t) = t i + (2t - t²) k

where i and k are unit vectors in the x and y directions, respectively.

value of t is given.

Setting t = 2, we have:

x = 2

y = 2(2) - (2)² = 0

z = x² + y² = 4 + 0 = 4

So, the point of intersection is (2, 0, 4).

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_____The given question is incorrect, the correct question is given below:

At what point does the curve r(t)=ti+(2t−t2)k, where t= 2

intersect the paraboloid z=x²+y².

The transformation that did not take place is a dilation, as the side lengths for both triangles are constant.

For this problem, the side lengths remain constant, hence a dilation did not take place.

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The measure of angle ∠2 is 50° for the given lines.

Lines are straight with little depth or width. Perpendicular lines, intersecting lines, transversal lines, and other types of lines will be covered. An angle is a shape formed by two rays emerging from a common point. In this field, you may also come across alternate and corresponding angles.

Given that the angle is 50°. The vertically opposite angles for the lines are equal. The vertically opposite angle of 50° is ∠2.

The value of angle ∠2 is,

∠2 = 50°

Therefore, the value of angle ∠2 will be 50°.

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The circumference of the circle is 6.55π

The circumference of a circle is given by the formula:

C = πd

Where d is the diameter of the circle.

We are given that the diameter is 6.55, so we can substitute this value into the formula to find the circumference:

C = π(6.55)

Evaluate

C = 6.55π

Hence, the circumference of the circle, in terms of pi, is approximately 6.55π

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Complete question

Find the circumference of the circle in terms of pi

Diameter = 6.55

Answer:

s = 9

Step-by-step explanation:

A = s^2

81 = s^2

√81 = s

s = 9

Answer:

3x+4=6

Step-by-step explanation:

The missing length of the geometric system of right triangles is equal to 15.833 centimeters.

Herein we find the case of a geometric system formed by ten right triangles, whose missing length can be found by means Pythagorean theorem and trigonometric functions, whose definitions are shown below:

Pythagorean theorem

r = √(x² + y²)

Trigonometric function

cos θ = x / r

Where:

Now we proceed to determine the missing length:

First triangle:

x = 8 / cos 28°

x = 9.061

x' = 9.061 - 2.5

x' = 6.561

Second triangle

x = (6.561 + 3.6) · cos 11°

x = 9.974

x' = 9.974 - 2

x' = 7.974

Third triangle

x = √[(7.974 + 2.9)² - 3.8²]

x = 10.188

x' = 10.188 - 1

x' = 9.188

Fourth triangle

x = (9.188 + 3.2) · cos 43°

x = 9.060

x' = 9.060 - 1

x' = 8.060

Fifth triangle

x = (8.060 + 1) / cos 30°

x = 10.462

Sixth triangle

x = (10.462 + 3.2 + 1.9) · cos 19°

x = 14.714

Seventh triangle

x = (14.714 - 4.8 - 1.1) / cos 46°

x = 12.688

Eighth triangle

x = √[(12.688 + 1.7)² + 3.2²]

x = 14.740

Ninth triangle

x = (14.740 - 2.73) · cos 22°

x = 11.135

x' = 11.135 - 2.24

x' = 8.895

Tenth triangle

x = (8.895 + 6.9) / cos 4°

x = 15.833

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The total number of miles Ahmad drove the truck is given by the equation A = 238.988 miles ≈ 240 miles

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

The base fee of the truck = $ 20.95

The cost for each mile driven = $ 0.84

The total amount Ahmad paid = $ 221.7

Let the total number of miles be A

Now , the equation will be

The total amount Ahmad paid = base fee of the truck + cost for each mile driven x total number of miles

Substituting the values in the equation , we get

221.7 = 20.95 + ( 0.84 )A

Subtracting 20.95 on both sides of the equation , we get

0.84A = 200.75

Divide by 0.84 on both sides of the equation , we get

A = 238.988 miles

Hence , the equation is A = 238.988 miles

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Answer: look at the image for the answer

Step-by-step explanation:

Answer:

Step-by-step explanation:

The equation h = -0.0159d² + 290 models the curve of the natural stone bridge, where h is the height of the curve in feet and d is the width of the curve in feet.

To find the vertex of the curve, we need to use the formula x = -b / 2a, where x represents the x-coordinate of the vertex and a and b are coefficients of the quadratic equation. In this case, the quadratic equation is h = -0.0159d² + 290, so a = -0.0159 and b = 0. To find the vertex, we plug these values into the formula:

x = -b / 2a = 0 / (2 * (-0.0159)) = 0

So the x-coordinate of the vertex is 0, which means the vertex is at the point (0, 290).

The vertex tells us that the highest point of the bridge (the vertex) is at a width of 0 feet. This means that the bridge is tallest at its center, and the height decreases as the width increases in either direction. Additionally, since the coefficient of the squared term is negative, the parabolic curve is downward-facing, which indicates that the bridge curves downward as it extends outward.

To find the span of the rainbow bridge, we need to find the width of the bridge where the height is 0. This represents the point where the bridge intersects with the river. To do this, we set h = 0 and solve for d:

0 = -0.0159d² + 290

0.0159d² = 290

d² = 290 / 0.0159

d ≈ 77.36

So the width of the bridge where the height is 0 is approximately 77.36 feet. Therefore, the span of the rainbow bridge is approximately 154.72 feet (twice the width at the point where the height is 0).

The wavelength of the wave is 0.125 m.

A periodic wave's wavelength is its spatial period, or the length over which its shape repeats. It is a property of both traveling waves and standing waves as well as other spatial wave patterns. It is the distance between two successive corresponding locations of the same phase on the wave, such as two nearby crests, troughs, or zero crossings.

A sinusoidal waveform's wavelength (λ) is determined by the equation

λ= ν/f,

where ν denotes the wave's phase speed (or magnitude of the phase velocity) and f denotes its frequency.

According to the given information,

Speed of transverse wave, ν = 25 m/s

Frequency, f = 200 Hz

We know the formula, λ= ν/f

By substituting the values, we get

λ = 25/200

λ = 0.125m

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This question is related to Physics.

After multiplying and adding given equations, new equations are
3x² + 2xy - 8y² = -273 and 4x - 2y = -32 respectively.

Solutions of the equations are x = -5 and y = 6.

A linear equation is an equation in which the greatest power of a variable is always 1. Also called the 1 degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. where x is a variable, A is a coefficient, and B is a constant.  

Given equations,

a) x + 2y = 7

b) 3x - 4y = -39

Multiplying both equations

(x + 2y)(3x - 4y) = (7)(-39)

Using Foil method (a+b)(c+d) = ac + ad + bc + bd

3x² - 4xy + 6xy - 8y² = -273

3x² + 2xy - 8y² = -273

Which is a new equation.

Adding both equations

(x + 2y)+(3x - 4y) = (7)+(-39)

Adding like terms, we get

4x - 2y = -32

Solving the equations (a) and (b)

a) x + 2y = 7

x = 7 - 2y

Substituting x in terms of y in equation (b)

b) 3x - 4y = -39

3(7 - 2y) - 4y = -39

21 - 6y - 4y = -39

-10y = -60

y = 6

then x = 7 - 2(6)

⇒ x = - 5

Hence, x = -5 and y = 6 are solutions of given equations.

3x² + 2xy - 8y² = -273 is the equation, after multiplying both equations.

4x - 2y = -32 is equation after both equations are added.

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Using a standard normal distribution table, we can find the closest value to 0.99, which is 2.33. Therefore, the z-score for a 98% confidence interval is 2.33.

To calculate the z-score for a 98% confidence interval, we can use a standard normal distribution table or a calculator with a built-in z-score calculator. To calculate the z-score for a 98% confidence interval, we can use the following formula:

z = invNorm(1 - (1 - confidence level) / 2)

Where "invNorm" is the inverse normal distribution function, and "confidence level" is the level of confidence expressed as a decimal. For a 98% confidence level, we have:

z = invNorm(1 - (1 - 0.98) / 2)

z = invNorm(0.99)

Using the table, we can find the z-score corresponding to a cumulative area of 0.98 by looking up the closest value to 0.98 in the table.

invNorm(0.98) = 2.33.

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Answer:

65 m²

Step-by-step explanation:

area of parallelogram = base × height

base = AB = 3 m + 10 m = 13 m

height = 5m

area = 13 m × 5 m

area = 65 m²

Monica's age is 20 years and her father's age is 52

Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time. For example, below are some simultaneous equations: 2x + 4y = 14 4x − 4y = 4.

Represent Monica's age by x and her father's age by y

y -x = 32 equation 1

y-16= 9(x-16)

= y-16 = 9x -144

y-9x = -144+16

y - 9x = -128 equation 2

subtract equation 2 from 1

-x-( -9x )= 32-(-128)

8x = 160

x = 160/8

x = 20

substitute 20 for x in equation 1

y = 32+x

y = 32+20

y = 52

Therefore Monica's age is 20 and her father's age is 52

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There are 168 hours in a week. Therefore, there are approximately 0.536 weeks in 90 hours.

Time conversion is the process of converting a given amount of time from one unit of measurement to another. It involves using conversion factors to change the numerical value of the time while keeping the duration constant.

For example, converting a duration from hours to minutes involves using a conversion factor of 60 minutes per hour. To convert, you multiply the number of hours by 60 to get the equivalent duration in minutes.

To get this answer, you can divide the number of hours (90) by the total number of hours in a week (168):

90 hours ÷ 168 hours/week = 0.536 weeks (rounded to three decimal places)

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The Domain is 0 ≤ x ≤ 4 and Range is 0 ≤ y ≤ 80.

The range of values that we are permitted to enter into our function is known as the domain of a function.  A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

Given:

We know that the domain of a function is the set of values that we are allowed to plug into our function.

From the Graph the x values ranges from 0 to 4.

So, domain is 0 ≤ x ≤ 4.

and, the range is the corresponding output for the input

From the Graph the y values ranges from 0 to 80.

So, Range is 0 ≤ y ≤ 80.

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Clark earns $6 in interest when t = 10 years, and with principle balance of $120.

When someone borrows a particular amount of money, they must pay interest. This phrase is frequently used in relation to banks, loans, payments, and investments. It is connected to the percentage, rate, and duration for which the borrowed amount of money is owed.

Using the formula I = prt, we can calculate the amount of interest earned by Clark over a period of 10 years:

I = prt

I = (0.005)(120)(10)

I = 6

Therefore, when t = 10 years, Clark earns $6 in interest.

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Answer:

Quadrant III

Step-by-step explanation:

hope it helps :-)

Using the cosine ratio, the value of x, to the nearest tenth, is: 39.3°.

The cosine ratio is part of the trigonometric ratios, which is given as:

cos ∅ = length of adjacent side / length of hypotenuse.

Given the following:

Length of adjacent side = 6.5

Length of hypotenuse = 8.4

Reference angle (∅) = x

Plug in the values:

cos x = 6.5/8.4

x = cos^(-1)(6.5/8.4)

x = 39.3°

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The simplified form of the given expression 4.03x + 10x⁶, is [tex]x(4.03x + 10x^5)[/tex]

An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation.

Given that an expression 4.03x + 10x⁶

We need to simplify it,

4.03x + 10x⁶

Applying the exponent rule: [tex]a^{b+c}=a^ba^c[/tex]

[tex]x^6=x^5x[/tex]

[tex]=4.03x+10x^5x[/tex]

Factor out common term x,

[tex]=x\left(4.03+10x^5\right)[/tex]

Hence, the simplified form of the given expression 4.03x + 10x⁶, is [tex]x(4.03x + 10x^5)[/tex]

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The number of students that have veggies as a snack is equal to 51 students according to the circle graph.

A circle graph is also called a pie chart, and it can be defined as a type of graph that is used for the graphical representation of the proportional relationship between each part to a whole, especially by dividing a circle into various sectors or sections.

Given that, there are 300 students at a school, the number of students that have veggies as a snack can be calculated as follows;

Number of students that had veggies = 17/100 × 300

Number of students that had veggies = 0.17 × 300

Number of students that had veggies = 51 students.

Hence, the number of students that have veggies as a snack is equal to 51 students according to the circle graph.

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The complete question is :-

Refer to the circle graph below. Suppose there are 300 students at York Middle School. Determine the number of students that have veggies as a snack. No Snack 12% Fruit. 23% Chips · 18% Cheese 15% Veggies 17% L Cookies 15%​