i have to use interval notation to answer the question ( attachment )

The value of the trigonometric ratios  are;

sin A = 2/5

cos A = 3/5

tan A = 2/3

It is important to note that there are six different trigonometric identities and their ratios.

We have;

From the diagram shown, we have;

sin θ = opposite/hypotenuse

cos θ = adjacant/hypotenuse

tan θ = opposite/adjacent

Then,

sin A = 6/15 = 2/5

cos A = 9/15 = 3/5

tan A = 6/9 = 2/3

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The value of the trigonometric ratios  are;

sin A = 2/5

cos A = 3/5

tan A = 2/3

It is important to note that there are six different trigonometric identities and their ratios.

We have;

From the diagram shown, we have;

sin θ = opposite/hypotenuse

cos θ = adjacant/hypotenuse

tan θ = opposite/adjacent

Then,

sin A = 6/15 = 2/5

cos A = 9/15 = 3/5

tan A = 6/9 = 2/3

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Answer:

Step-by-step explanation:

Answer:

your answer is correct. a trapezoid can be defined by it's set of parallel sides

Step-by-step explanation:

If the shape you're looking at doesn't have at least one set of parallel sides, it's not a trapezoid;

Given that Line a is parallel to Line b (Line a ║ Line b), the triangle that is similar to ΔJKH is 1. ΔMKN

Similar triangles are triangles that have congruent corresponding angles, and in which all three corresponding sides are proportional.

The given parameter is Line a is parallel to Line b, which gives: a║b

Two triangles are similar if they satisfy the following conditions:

According to alternate angles theorem, the angles ∠JHK in ΔJKH is congruent to the ∠KNM in triangle ΔMKN

Similarly, the angle ∠HJK in ΔJKH is congruent to the ∠KMN in ΔMKN

Therefore, ΔJKH is similar to ΔMKN by Angle-Angle, AA similarity postulate.

The correct option for the triangle similar to ΔJKH is option 1. ΔMKN

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It takes 10 minutes for the number of bacteria in the population to double.

To determine the time it takes for the number of bacteria in a population to double, we need to find the value of t when the function f(t) equals twice the initial number of bacteria.

The given function is f(t) = 60,000 * 2^(t/10).

To find the time it takes for the number of bacteria to double, we set f(t) equal to twice the initial number of bacteria, which is 2 * 60,000 = 120,000:

120,000 = 60,000 * 2^(t/10).

Next, we can simplify the equation by dividing both sides by 60,000:

2 = 2^(t/10).

Since both sides of the equation have the same base (2), we can equate the exponents:

t/10 = 1.

To solve for t, we multiply both sides by 10:

t = 10.

Therefore, it takes 10 minutes for the number of bacteria in the population to double.

This result is obtained by setting the growth rate of the bacteria population in the given function. The exponent t/10 determines the rate of growth, and when t is equal to 10, the exponent becomes 1, resulting in a doubling of the initial number of bacteria.

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The graph of the y+2x=6 is given in the attachment.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The standard equation of a line is expressed as y = mx + b, m is the slope

and b is the y-intercept.

Given the equation y = 2x - 2

If x = -2

y = 2(-2) - 2

y = -4-2

y = -6

If x  = 4

y = 2(4) - 2

y = 8-2

y = 6

The point (-2, -6) and (4, 6 )must be on the line graph.

Hence, the graph of the y+2x=6 is given in the attachment.

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The inequality 3/7 x 7 ≤ 7 is true.

The left-hand side, which simplifies to 3, is less than or equal to the right-hand side, which is 7.

To evaluate the inequality 3/7 x 7 ≤ 7, we can simplify the expression on the left-hand side and compare it to the value on the right-hand side.

First, let's calculate 3/7 x 7:

(3/7) x 7 = 3

So, the expression simplifies to 3 ≤ 7.

Now, let's compare 3 to 7. Since 3 is less than 7, we can conclude that 3 ≤ 7 is true. In other words, 3 is less than or equal to 7.

To understand this visually, imagine a number line. Placing a point at 3 and another point at 7, we can see that 3 is to the left of 7. The "less than or equal to" symbol (≤) indicates that the left-hand side can be equal to or less than the right-hand side. In this case, 3 is indeed less than 7, satisfying the inequality.

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Answer:

x+4=36

Step-by-step explanation:

you would subtract 4 on each side

x+4=36

  -4   -4

x=32

The probability that the Yankees will lose when they score fewer than 5 runs is 0.821 (nearest to the thousandth).

For two events A and B:

The chain rule states that the probability that A and B both occur is given by:

\(P(A \cap B) = P(A)P(B|A) = P(B)P( A|B)\)

Lets suppose here that:

Suppose A' and B' are their complementary events, then we have:

Then, by the given data, we have:

\(P(A) = 0.56\\P(B) = 0.61\\P(A' \cap B') = 0.32\)

We've to find \(P(A' | B')\)

Using chain rule, we have:

\(P(A'|B') = \dfrac{P(A' \cap B')}{P(B')}\)

Since P(B') = 1-P(B) = 100.61 = 0.39, therefore, we get:

\(P(A'|B') = \dfrac{P(A' \cap B')}{P(B')} = \dfrac{0.32}{0.39} \\\\P(A'|B') \approx 0.821\)

Thus, the probability that the Yankees will lose when they score fewer than 5 runs is 0.821

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Part A: distance travelled by athlete when she reaches her maximum is 1.3 m.

Part B: her maximum height: 5 m.

Th equation is-

y = -1.2x² + 3.12x +3.

horizontal distance - x

Part A: distance travelled by athlete when she reaches her maximum:

Comparing given equation with standard form of quadratic equation:

x = -b/a

x = -3.12/2(-1.2) = 1.3

Thus, distance travelled by athlete when she traveled horizontally and reaches her maximum of 1.3 m.

Part B: her maximum height:

y = -1.2x² + 3.12x +3.

Put x = 1.3

y = -1.2(1.3)² + 3.12(1.3) +3.

On solving:

y = 5.028

y = 5 m

Thus, her maximum height, round to the nearest tenth of a meter is 5 m.

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The measure of the angle of the trapezoid is:

∠W = 110°

∠X =  110°

∠Y = 70°

∠Z = 70°

For an isosceles trapezoid, the base angles are equal. That is:

∠Z = ∠Y

∠W = ∠X

Since ∠X = (13x -7)° and ∠Y = (8x -2)°. Thus:

∠Z = (8x -2)°

∠W = (13x -7)°

Also, the sum of opposite angles an isosceles trapezoid is 180°. That is:

∠W + ∠Y = 180° and ∠Z + ∠X = 180°

Thus, we can say:

(13x -7)° + (8x -2)° =  180°

21x - 9 = 180

21x = 180 + 9

21x = 189

x = 189/21

x = 9

Substitute x = 9:

∠W = (13x -7)°

∠W = 13(9) - 7

∠W = 110°

∠X =  110° (∠X = ∠W)

∠Y = (8x -2)°

∠Y = 8(9) -2

∠Y = 70°

∠Z = 70°  (∠Z = ∠Y)

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The solution to the equation sqrt 2-3x / sqrt 4x = 2 is x = -2/3.

To solve the equation, we must first clear the denominators and simplify the equation. We can do this by multiplying both sides by sqrt(4x) and then squaring both sides. This gives us:
sqrt 2-3x = 4sqrt x
2 - 6x + 9x² = 16x
9x² - 22x + 2 = 0
Using the quadratic formula, we can find that x = (-b ± sqrt(b² - 4ac)) / 2a. Plugging in a = 9, b = -22, and c = 2, we get:
x = (-(-22) ± sqrt((-22)² - 4(9)(2))) / 2(9)
x = (22 ± sqrt(352)) / 18
x = (22 ± 4sqrt22) / 18
Simplifying this expression, we get:
x = (11 ± 2sqrt22) / 9
Therefore, the solution to the equation is x = -2/3.
To solve the equation sqrt 2-3x / sqrt 4x = 2, we must clear the denominators and simplify the equation. This involves multiplying both sides by sqrt(4x) and then squaring both sides.

After simplifying, we end up with a quadratic equation. Using the quadratic formula, we can find that the solutions are x = (11 ± 2sqrt22) / 9.

However, we must check that these solutions do not result in a division by zero, as the original equation involves square roots. It turns out that the only valid solution is x = -2/3.

Therefore, this is the solution to the equation.

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The difference between Walter and Denise's gas usage is 0.83 - 0.75 = 0.08 gallons. Therefore, Walter uses 0.08 gallons more gas than Denise.

Number is a mathematical object used to count, measure, and label. It is an abstract concept that describes a quantity or amount. Numbers can be represented in various forms, including words, symbols, and numerals. Numbers are also used to measure distance, time, and weight, as well as to express amounts of money. Numbers play a vital role in many areas of life, from science and engineering to economics and finance.

To calculate how much more gas Walter uses than Denise, we need to find the difference between the amount of gas each person uses.

Denise uses 3/4 of a gallon of gas, so 3/4 of a gallon is equal to 0.75 gallons. Walter uses 5/6 of a gallon of gas, so 5/6 of a gallon is equal to 0.83 gallons.

The difference between Walter and Denise's gas usage is 0.83 - 0.75 = 0.08 gallons. Therefore, Walter uses 0.08 gallons more gas than Denise.

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Answer:

23552

Step-by-step explanation:

23, 92, 368...   is a geometric sequence.

first term = a = 23

common ratio = r = 2 term ÷ first term = 92 ÷ 23 = 4

nth term = \(ar^n^-^1\)

6th term = \(23*(4)^6^-^1\)

\(=23*4^5\)

\(=23*1024\)

\(=23552\)

Hope this helps :)

Pls brainliest...

The limits lim x→ −4 f(x) is 5

The method is substitution method

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

−5x − 15 ≤ f(x) ≤ x² + 3x + 1

The limits is given as

lim x→ −4 f(x)

By direct substitution, we have

−5(-4) − 15 ≤ f(x) ≤ (-4)² + 3(-4) + 1

Evaluate the exponents and the products

20 − 15 ≤ f(x) ≤ 16 - 12 + 1

Evaluate the difference

5 ≤ f(x) ≤ 5

This means that

f(x) = 5

So, we have

lim x→ −4 f(x) = 5

The method used is the direct substitution method

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Answer:

Sure, here are the answers to your questions:

**A) The value of $f(-5)$ is $-2$.**

To find the value of $f(-5)$, we can simply substitute $x=-5$ into the equation $f(x)=-2x^2-8x+14$. This gives us:

$$f(-5)=-2(-5)^2-8(-5)+14=-2(25)+40+14=-50+54=4$$

**B) The vertex of the parabola is $(2,6)$.**

To find the vertex of the parabola, we can complete the square. This involves adding and subtracting $\left(\dfrac{{b}}{2}\right)^2$ to both sides of the equation, where $b$ is the coefficient of the $x$ term. In this case, $b=-8$, so we have:

$$\begin{aligned}f(x)&=-2x^2-8x+14\\\\ f(x)+20&=-2x^2-8x+14+20\\\\ f(x)+20&=-2(x^2+4x)\\\\ f(x)+20&=-2(x^2+4x+4)\\\\ f(x)+20&=-2(x+2)^2\end{aligned}$$

Now, if we subtract 20 from both sides, we get the equation of the parabola in vertex form:

$$f(x)=-2(x+2)^2-20$$

The vertex of a parabola in vertex form is always the point $(h,k)$, where $h$ is the coefficient of the $x$ term and $k$ is the constant term. In this case, $h=-2$ and $k=-20$, so the vertex of the parabola is $(-2,-20)$. We can also see this by graphing the parabola.

[Image of a parabola with vertex at (-2, -20)]

**C) The $y$-intercept is the point $(0,14)$.**

The $y$-intercept of a parabola is the point where the parabola crosses the $y$-axis. This happens when $x=0$, so we can simply substitute $x=0$ into the equation $f(x)=-2x^2-8x+14$ to find the $y$-intercept:

$$f(0)=-2(0)^2-8(0)+14=14$$

Therefore, the $y$-intercept is the point $(0,14)$.

**D) The two values of $x$ that make $f(x)=0$ are $2.5$ and $-3.5$.**

To find the values of $x$ that make $f(x)=0$, we can set the equation $f(x)=-2x^2-8x+14$ equal to zero and solve for $x$. This gives us:

$$-2x^2-8x+14=0$$

We can factor the left-hand side of the equation as follows:

$$-2(x-2)(x-3)=0$$

This means that either $x-2=0$ or $x-3=0$. Solving for $x$ in each case gives us the following values:

$$x=2\text{ or }x=3$$

However, we need to round our answers to two decimal places. To do this, we can use the calculator. Rounding $x=2$ and $x=3$ to two decimal places gives us the following values:

$$x=2.5\text{ and }x=-3.5$$

Therefore, the two values of $x$ that make $f(x)=0$ are $2.5$ and $-3.5$.

Answer:

Step-by-step explanation:

(x - 7)/2= -4

x - 7 = -8

x = -1

(y - 6)/2= -7

y - 6 = -14

y = -8

(-1, -8)

The midpoint of AB is M(-4, -7). If the coordinates of A are (-7, -6), then the coordinates of B is; (-1, -8)

Midpoint, as the word suggests, means the point which lies in the middle of something. Midpoint of a line segment means a point which lies in the mid of the given line segment. Suppose we've two endpoints of a line segment as: Then, its coordinates are:

\(x = \dfrac{p+m}{2}\)

and

\(y = \dfrac{q+n}{2}\)

Given that midpoint of AB is M(-4, -7). If the coordinates of A are (-7, -6),then the midpoint be M(x,y) on that line segment.

Then, its coordinates are;

(x - 7)/2= -4

x - 7 = -8

x = -1

(y - 6)/2= -7

y - 6 = -14

y = -8

Therefore, the coordinates of B is; (-1, -8)

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This function is a piece-wise function, that means it has different expressions for each interval of x.

In order to find f(8), we need to identify which expression should we use for x = 8.

Looking at the intervals, we can see that x = 8 is not defined in any interval.

Therefore f(8) is undefined.

Answer:20

Step-by-step explanation: so first take out the amount of salary increased so it will be- 48-40=-8

After take out the percentage of the increased amount which was $-8 and the original amount which was $40 so 8/40 × 100

Percentage increase would be 16.67% or if thats not right try 20%

i hope this helps!!!!

Answer:

The answer is "\(x_k= -\frac{9}{16} (-2)^k + \frac{9}{16} 2^k +\frac{3}{8} k\times 2^k\\\\\)"

Step-by-step explanation:

\(\to F(Z)=\frac{3z(z-1)}{z^3-2z^2-4z+8}\\\\\to \frac{F(Z)}{z}=\frac{3z(z-1)}{z(z^3-2z^2-4z+8)}\\\\\to \frac{F(Z)}{z}=\frac{3(z-1)}{(z^3-2z^2-4z+8)}\\\\\to \frac{F(Z)}{z}=-\frac{9}{16} \frac{1}{z+2} + \frac{9}{16} \frac{1}{z-2} +\frac{3}{4} \frac{1}{(z-2)^2}\\\\\to F(Z)=-\frac{9}{16} \frac{z}{z+2} + \frac{9}{16} \frac{z}{z-2} +\frac{3}{4} \frac{z}{(z-2)^2}\\\\\to x_k= -\frac{9}{16} (-2)^k + \frac{9}{16} 2^k +\frac{3}{8} k\times 2^k\\\\\)

Answer:  The product will always be a positive number.

Step-by-step explanation:

You can find the solution by using  any numbers and following the same procedure.

Let's say the six negative numbers are all -1      and  the three positive numbers are all positive  1's.

-1 * -1* -1 * -1 * -1 * -1  *  1 * 1 * 1  = 1  

Since the solution is  positive one, then it means  that the product will always be positive.

This statement essentially establishes a relationship between the sets X, Y, and z, stating that there exists a subset Y for each element x in X such that the elements in Y are present in some subset z of X.

The given statement is a symbolic representation of a logical proposition involving quantifiers and logical connectives. Let's break down its meaning:

∀ X ∃ Y ∀u(u ∈ Y ↔ ∃z(z ∈ X ∧ u ∈ z))

The symbol ∀ (universal quantifier) indicates that the statement applies to all elements in the set X.

The symbol ∃ (existential quantifier) indicates that there exists at least one element in the set Y.

The statement can be interpreted as follows:

"For all elements x in the set X, there exists a set Y such that for every element u in Y, u is an element of Y if and only if there exists a set z in X such that u is an element of z."

In simpler terms, the statement asserts that for every element x in the set X, there is a set Y that contains elements u if and only if there exists a set z in X that also contains u.

It is important to note that the precise meaning and implications of this statement may depend on the context and interpretation of the sets X, Y, and their elements.

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The Figure above represents the given triangle OPQ with sides o, p, and q

Using Law of Cosines

Note that o=700cm; p=840cm; q=620cm

Substituting the given values in the expression will give

To get angle P, we have

Hence∠P to the nearest degree is 79°

Answer:

79

Step-by-step explanation:

The function represented by the graph with the given transformations is |–x| + 2.

The function represented by the given transformations is |–x| + 2.

Let's analyze the transformations step by step:

Reflection across the x-axis:

Reflecting the parent absolute value function across the x-axis changes the sign of the function. The positive slopes become negative, and the negative slopes become positive. This transformation is denoted by a negative sign in front of the function.

Translation right 2 units:

Translating the function right 2 units shifts the entire graph horizontally to the right. This transformation is denoted by subtracting the value being translated from the input of the function.

Combining these transformations, the function |–x| + 2 results. The negative sign reflects the function across the x-axis, and the subtraction of 2 units translates it right. The absolute value is applied to the negated x, ensuring that the function always returns a positive value.

Thus, the function represented by the graph with the given transformations is |–x| + 2.

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Answer: -lx-2l

Step-by-step explanation:

Answer:

37

Step-by-step explanation:

To find the fifth term , we have to take the value of n as 5

So, F(5)= 6.5 (5) +4.5

= 32.5 + 4.5

= 37

Answer:

2 packages of buns, 3 packages of hotdogs

Step-by-step explanation:

Answer: 3 hotdogs and 2 hotdog buns

Step-by-step explanation: 8x3 = 24

12x2 = 24

Answer:

hjgkulihjoj;l

Step-by-step explanation:

Answer:

0.0003125%

Step-by-step explanation:

the answer to your question might be (B).