Solving right triangles
Find measure of < j.

Answer:

Let's define the variables:

M = mother's age

D = daughter's age.

"a mother is twice as old as her daughter"

This can be written as:

M = 2*D

"5 years from now she will be thrice as old as her daughter"

(M + 5) = 3*D

We want to know how old is the mother five years from now.

First, our equations are:

M = 2*D

(M + 5) = 3*D

First, we need to isolate one of the variables in one of the equations, because for the solution we want the mother's age, we should isolate the daughter's age.

Let's isolate D in the first equation:

M/2 = D

Now we can replace this in the other equation:

Now we can replace this on the other equation:

(M + 5) = 3*(M/2)

M + 5 - (3/2)*M = 0

-(1/2)*M + 5 = 0

5 = (1/2)*M

2*5 = M = 10

So the mother is 10 years old (this hasn't a lot of sense, maybe there is a wrong number on the question)

and 5 years from now, the mother will be:

10 + 5 = 15 years old.

Answer:

[tex]x = 15[/tex]

[tex]y = 25[/tex]

Step-by-step explanation:

Given

See attachment for MNPQ and RSTU

Required

Find x and y

To solve this question, we make use of equivalent ratios of corresponding side lengths.

The ratio of corresponding sides are:

[tex]MN : RS[/tex]

[tex]NP : ST[/tex]

[tex]PQ : TU[/tex]

[tex]MQ : RU[/tex]

From the attachment, we have:

[tex]MN : RS \to 18 : 30[/tex]

[tex]NP : ST \to x : 25[/tex]

[tex]PQ : TU \to 15 : y[/tex]

To solve for x, we equate [tex]MN : RS[/tex] and [tex]NP : ST[/tex]

[tex]18 : 30 = x : 25[/tex]

Express as fraction

[tex]\frac{18 }{ 30 }= \frac{x }{ 25}[/tex]

Make x the subject

[tex]x = 25 * \frac{18 }{ 30 }[/tex]

[tex]x = \frac{25 * 18 }{ 30 }[/tex]

[tex]x = \frac{450}{ 30 }[/tex]

[tex]x = 15[/tex]

To solve for y, we equate [tex]MN : RS[/tex] and [tex]PQ : TU[/tex]

[tex]18 : 30 = 15 : y[/tex]

Express as fraction

[tex]\frac{18 }{ 30 }= \frac{15 }{ y}[/tex]

Make y the subject

[tex]y = 15 * \frac{30 }{ 18 }[/tex]

[tex]y = \frac{15 *30}{ 18 }[/tex]

[tex]y = \frac{450}{ 18 }[/tex]

[tex]y = 25[/tex]

Answer:

22 ft

Step-by-step explanation:

The circumference of a circle with given diameter d is C = (3.14)d.

Here, C = (3.14)(7 ft) = 21.98 ft, or approximately 22 ft

Answer:

Step-by-step explanation:

Here,

It gives the diameter of a [tex]\huge{\bigcirc}[/tex]d=7feet,

Here,

[tex]\pi = 3.14[/tex]

Then the circumference of that circle is

Hence

The circumference of that circle is 23ft 

Answer:

3111.5.

Step-by-step explanation:

3112 - 0.5 = 3111.5.

Answer:

8 A

Step-by-step explanation:

V = 20 volts

R = 2.5 ohms

I=?

By Ohm's Law

[tex] \because \: I \: = \frac{V}{R} \\ \\ \therefore \: I= \frac{20}{2.5} = \frac{200}{25} = 8 \: Ampere[/tex]

Answer:

90

Step-by-step explanation:

If we know that for every cup, we can take 3 of 1/3-ounce cups, we can use an equation that looks like this:

number of cups × 3 = total 1/3-ounce cups

If there are 30 cups, then we can simply insert 30 into the equation.

30 × 3 = 90

Therefore, you can make 90 1/3-ounce cups from the cereal box.

Answer:

Linear

Step-by-step explanation:

Linear means the graph is a straight line. If you plot the points, the line will be straight, therefore it is linear.

The following presumption has to be verified in order to establish whether the collection of ordered pairs fulfills an exponential function: The x-coordinates must have the same increment or a consistent difference.

A mathematical function of form f (x) = aˣ is an exponential function. "x" is a variable, while "a" is a constant that serves as the function's basis and must be bigger than 0. The transcendental number e, or roughly 2.71828, is the foundation for exponential functions that are most frequently utilized.

Characteristics are:

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Answer:

81

Step-by-step explanation:

by corresponding angles from angle ABC

Answer:

240x is=f simplfied.

Step-by-step explanation:

x = 6 does not satisfy the given equation.

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that an equation, 5(x – 3) = x + 13

Checking if x = 6 satisfy the equation or not,

5(x – 3) ? x + 13

5(6-3) ? 6+13

5×3 ? 19

15 ≠ 19

Hence, x = 6 does not satisfy the equation.

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Answer:

it should be x+12

Step-by-step explanation:

if x is bigger than -11, then the answer will always be positive

We have given a function; [tex]|x+12|, if x > -11[/tex] if x is bigger than -11, then the answer will always be positive.

A function is defined as a relation between the set of inputs having exactly one output each.

We have given a function;

[tex]|x+12|, if x > -11[/tex]

The modulus of any number always gives the positive term.

if x is bigger than -11, then the answer will always be positive.

Let x = 2

then we get

[tex]|x+12| = |2+12| \\\\= 14[/tex]

So, we can see that the answer is positive.

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Answer:

C:  (-8, 2)

Step-by-step explanation:

Given parabola:

[tex]y=-\dfrac{1}{8}x^2-2x-4[/tex]

For the quadratic equation in the form y = ax² + bx + c, the x-value of the vertex is -b/2a.  

Therefore, the x-value of the vertex of the given parabola is:

[tex]\implies x=-\dfrac{b}{2a}=-\dfrac{-2}{2\left(-\frac{1}{8}\right)}=-8[/tex]

To find the y-value of the vertex, input x = -8 into the given equation:

[tex]\implies y=-\dfrac{1}{8}(-8)^2-2(-8)-4=4[/tex]

Therefore, the vertex (h, k) of the parabola is (-8, 4).

The focus of the parabola is (h, k+p) where:

Therefore:

[tex]\implies \textsf{Focus}=\left(-8,4+\dfrac{1}{4\left(-\frac{1}{8}\right)}\right)=\left(-8,2)[/tex]

When sin θ = - 3/5 and the terminal side of θ lies in quadrant III, then cos θ is  -4/5

The terminal side of an angle refers to the line that intersects the initial line to make an angle

In the problem the terminal side is said to be in the third quadrant and the in the third quadrant sin θ = - 3/5

sin θ = opposite / hypotenuse

using Pythagoras the adjacent is 4, in third quadrant we have -4

cos θ = - adjacent / hypotenuse = -4/5.

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Answer:

[tex]\small\mathfrak\red{here \: is \: your \: solution..} \\ \\ we \: know \: that \: tangent \\ from \: a \: same point \: are \: equal \\ \\ tr = 9 | an = 7 | eg = 5 \\ \\ tr = ta | an = gn | eg = re \\ \\ ta = 9 | gn =7 | re = 5 \\ \\ hence \: perimeter \: = 2(9 + 7 + 5) \\ \\ perimeter = 42 \: \\ \\ \huge\mathfrak\purple{hope \: it \: helps...}[/tex]

Answer:

It's actually worth 10 points

Answer:

3. 17.2°

Step-by-step explanation:

The angles for the right triangle are 90°, 72.8°, and 17.2°.

Answer:

3) if you were to draw vertical lines through this graph you would have instances where an 'x' value would have more than one unique 'y' value

Step-by-step explanation:

functions must have one unique 'y' value for each 'x' value

The third graph represent a relation that is not a function

A relation is a function if it has only One y-value for each x-value.

The third one doesn't represent a function, because for some values of "x", you get two different values for "y" (which should not happen, if that were a function).

In order to see it better, you can trace a vertical line onto that graph.

If that line and the graph intersects in more than one point, then that graph doesn't represent a function.

In every function, you must have a single "y" value for each "x" in the domain.

Hence, the third graph represent a relation that is not a function

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The largest prime number that divides the quantity is the largest prime number less than 5.5e+22.

A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers. A prime number that divides a quantity is a prime number that is a factor of that quantity.

We can start by computing the values of the factorials, and then use the property of modular arithmetic to find the prime divisors of the quantity.

0! = 1

1! = 1

2! = 2

3! = 6

...

50! = 30414093201713378043612608166064768844377641568960512000000000000

Now we can write the expression as

(0! + 1x1!) + (2x2!) + (3x3!) + ... + (50x50!)

We can notice that the number is very large, and it's impractical to factorize it using traditional methods.

We can use the property that if n is not divisible by a prime number p, then n! is not divisible by p^2. So we can eliminate all the powers of 2 and 5 from the expression, since 2 and 5 are the only prime factors of the factorials.

The next step would be to check if the remaining number is divisible by any prime numbers.

Since it's impractical to check for all the prime numbers, we can use the fact that the largest prime number is less than the square root of the number in question. Therefore, we can check for all primes less than √(50!) = √(30414093201713378043612608166064768844377641568960512000000000000)

Which is approximately 5.5e+22.

Therefore, the largest prime number that divides the quantity is the largest prime number less than 5.5e+22.

It's important to note that this is a very large number and checking for all prime numbers less than it would take a long time. And thus, answer cannot be given.

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The coordinate of the reflection is (-y, -x)

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

Point = (x, y)

Reflection:  Across the line y=−x

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

So, we have

Image = (-y, -x)

Hence, the image is (-y, -x)

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Answer:

2 ≥ p

Step-by-step explanation:

-14 ≤ -7p

Divided both sides by -7. Because divided by a negative number, the < will turn to >

So, the equation is

2 ≥ p

Because there is an equal, the circle will be close and to the left of 2.

Answer:

2 ≥ p

Step-by-step explanation:

Have a great day :) <3

Answer:

Step-by-step explanation:

Plug in 5 for h

6(5)+7(5)

30+35=65

65

Answer:

[tex] \sf \: 6h + 7h = 65[/tex]

Step-by-step explanation:

Given information,

→ 6h + 7h

→ h = 5

Now the final value will be,

→ 6h + 7h

→ 6(5) + 7(5)

→ 30 + 35

→ 65 => final value

Hence, the answer is 65.

Answer:

36 degrees

Step-by-step explanation:

angle 1 and 2 are the same

good luck!

Complementary angles are of 90°.

So, angle 1 + angle 2 = 90°

=> 36° + angle 2 = 90°

=> angle 2 = 90° - 36°

=> angle 2 = 54°

Answer:

Nora needs to work 10 hours to get 70 dollars to be able to have 115 to buy the new phone.

Step-by-step explanation:

45+7x = 115

45+7(10)

45+70

115

(Hope this helped! If you have any questions about this please comment) :D

Answer:

Step-by-step explanation:

x=tan^{-1}(-0.8645) \approx -40.84°,-40.84+180,-40.84+360

x=139.16°,319.16°

The values of x in the interval 0° < x < 360° for which tan(x) = -0.8645 are approximately 139.18° and 299.18°.

To find the values of x in the interval 0° < x < 360° for which tan(x) = -0.8645, you can use the inverse tangent function (also known as arctan or atan). The inverse tangent function will give you the angle whose tangent is equal to the given value.

Using a calculator or a math software that supports trigonometric functions, you can take the inverse tangent (arctan) of -0.8645 to find the angle:

arctan(-0.8645) ≈ -40.82°

Since tangent is a periodic function with a period of 180°, you can find other angles that satisfy the equation by adding or subtracting multiples of 180°:

-40.82° + 180° ≈ 139.18°

-40.82° + 2 * 180° ≈ 299.18°

So, the values of x in the interval 0° < x < 360° for which tan(x) = -0.8645 are approximately 139.18° and 299.18°.

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Step-by-step explanation:

20 workers finish work in 21 days.

the necessary work effort is 20×21 = 420 workdays.

the same effort is needed even if the overall time is shorter.

x workers in 15 days.

x × 15 = 420

x = 420/15 = 28 workers.

so, 28-20 = 8 additional workers are needed to finish the work in 15 days.

The parabola narrows as the quadratic coefficient increases. The parabola's width increases as the quadratic coefficient decreases.

The graphs' width and whether or not they slant upward or downward depend on the quadratic term's coefficient, a for the parent function.

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For the given figure, where m and nare relatively prime positive integers. The value of m+n is 32.

The law of cosines, also known as the law of cosines, relates all three sides of a triangle to one angle of the triangle. Most useful for searching for missing information in triangles. For example, if you know all three sides of a triangle, you can use the law of cosines to find the measure of the angle. Similarly, if you know two sides and the angle between them, you can find the length of the third side by the law of cosines.

Let X be the intersection of the circles with centers B and E, and Y be the intersection of the circles with centers C and E.

Since the radius of B is 3, AX = 4.

Assume AE = p.

Then EX and EY are radii of circle E and have length 4 + p.

AC = 8, and ∠CAE = 60° because we are given that triangle T is equilateral.

Using the Law of Cosines on Δ CAE, we obtain

(6+p)² =p² + 64 - 2(8)(p) cos 60

The 2 and the cos 60 terms cancel out:

p² + 12p + 36 = p² + 64 - 8p

12p+ 36 = 64 - 8p

p = 28/20

= 7/5

The radius of circle E is 4 + (7/5)

= 27/5,

So, the answer is 27 + 5 = 32

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