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, in the presented question, we can conclude that Interval   [tex](0, 1): f(0) 5, f(1) -3[/tex], indicating that the function switches signs and has a zero in the interval  [tex](0, 1).[/tex]

Interval  [tex](4, 3): f(-4) -41, f(-3) 5,[/tex]therefore, the function reverses its sign and has a zero in the interval  [tex](-4, -3).[/tex]

Interval  [tex](3, 2): f(-3) 5, f(-2) -9,[/tex] indicating that the function changes sign and has a zero in the interval  [tex](-3, -2).[/tex]

Interval [tex](2, 1): f(-2) -9, f(-1) 1[/tex], therefore the function reverses its sign and has a zero in the interval  [tex](-€2, -1).[/tex]

Interval [tex](1, 0): f(-1) 1, f(0) 5[/tex], so the function does not change sign and the interval may or may not contain a zero [tex](-1, 0).[/tex]

Interval  [tex](0, 1): f(0) 5, f(1) -3,[/tex] indicating that the function switches signs and has a zero in the interval  [tex](0, 1).[/tex]

Therefore, in the presented question, we can conclude that Interval   [tex](0, 1): f(0) 5, f(1) -3[/tex], indicating that the function switches signs and has a zero in the interval  [tex](0, 1).[/tex]

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The foci of the hyperbola is  (0,2[tex]\sqrt5[/tex]) and ([tex]0,-2\sqrt5)[/tex].

The two fixed points that are located inside each curve of a hyperbola are known as its foci, and they are important for the formal description of the curve.

Here the given equation of the hyperbola is [tex]4y^2-x^2=16[/tex] .

Now writing the given equation into standard form then,

=> [tex]4y^2-x^2=16[/tex]

=> [tex]-x^2+4y^2=16\\[/tex]

=> [tex]\frac{-x^2}{4}+\frac{4y^2}{4}=\frac{16}{4}[/tex]

=> [tex]\frac{-x^2}{4}+y^2=4[/tex]

=> [tex]\frac{-x^2}{4\times4}+\frac{y^2}{4}=1[/tex]

=> [tex]\frac{-x^2}{16}+\frac{y^2}{4}=1[/tex]

Here we know that [tex]\frac{(y-k)^2}{a^2}-\frac{(x-h)^2}{b^2}=1[/tex] then a=2 and b=4 , (h , k)=(0,0)

Then c=[tex]\sqrt{a^2+b^2}=\sqrt{2^2+4^2}=\sqrt{4+16}=\sqrt{20}=2\sqrt{5}[/tex].

Then foci is (0,0+c) and (0,0-c) then,

=> (0,2[tex]\sqrt5[/tex]) and ([tex]0,-2\sqrt5)[/tex]

Hence the foci of the hyperbola is  (0,2[tex]\sqrt5[/tex]) and ([tex]0,-2\sqrt5)[/tex].

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Yes, it is true that Triangle FGH is a right triangle.

We check whether the Pythagorean theorem holds true for these sides to determine if this triangle is a right triangle. According to the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the squares of the right triangle's legs.

a² + b² = c²

If this is a right triangle, the hypotenuse will be the longest side, and the other two sides will be the legs. We have these when we incorporate the Pythagorean theorem.

6²+(√45)² = 9²

36+45 = 81

which implies that  right triangle because the assertion is true.

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Answer:

To find the number of bracelets Alia can make, we need to divide the total length of the silver chain she has by the length of each bracelet.

Total length of silver chain = 36 1/4 inches

Length of each bracelet = 7 1/4 inches

To divide fractions, we need to invert the second fraction and multiply:

(36 1/4) ÷ (7 1/4) = (145/4) ÷ (29/4) = (145/4) x (4/29) = 5

Therefore, Alia can make 5 bracelets with the given amount of silver chain.

Answer:

5 bracelets

Step-by-step explanation:

Given Information:

Clearly, the number of bracelets possible (say x) multiplied by the amount of chain required for 1 bracelet will result in the total chain length (36 1/4).

Now, we can divide 7 1/4 on both sides to find value of x (total bracelets).

Therefore, Alia can make 5 bracelets.

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The area of the felt is (5L - 4W - 5) / 4 (inches)².

What is an area?

To find the area of the felt, we need to know the dimensions of the picture and the frame.

Let's say the length of the frame is L and the width of the frame is W.

Then, according to the problem:

To find the area of the felt, we need to subtract the area of the picture from the area of the frame. The area of the frame is L x W, and the area of the picture is (4L - 5) / 4 x (W - 1). So the area of the felt is:

Felt area = Frame area - Picture area

= L x W - (4L - 5) / 4 x (W - 1)

= (4LW - 4W) / 4 - (4LW - 5L - 4W + 5) / 4

= (5L - 4W - 5) / 4

Therefore, the area of the felt is (5L - 4W - 5) / 4 (inches)². Note that we can't simplify this expression further without knowing the specific values of L and W.

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Complete question is: Greg covered the back of the picture with a piece of felt. The picture is 1 1/4 inches shorter than the fram and 1 inch less in width the area of the felt is (5L - 4W - 5) / 4 (inches)².

Area of triangle= 24 cm²

Area of sector= 72.243 cm²

Total area= 96.243 cm².

A polygon with three sides and three vertices is called a triangle. It is one of the fundamental geometric forms. Triangle ABC is the designation for a triangle with points A, B, and C. In Euclidean mathematics, any three points that are not collinear produce a distinct triangle and a distinct plane.

The portion of a disc enclosed by two radii and an arc is called a circular sector, also known as a circle sector or disc sector. The smaller area is referred to as the minor sector, and the bigger area as the major sector. A sector is referred to as a component of a circle made up of the circular's arc and its two radii.

In this question,

Area of triangle= 1/2 × base × height

                         = 1/2 × 6 ×8

                         = 24 cm²

Area of sector = (θ/360°) × πr²

                        = (82/360) × πr²

Here r=√6²+8²

          = 10 cm

Area of sector = (82/360) × π10²

                        = 0.23 × 314.1

                        = 72.243 cm²

Total= 24 cm²+72.243 cm²= 96.243 cm².

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The angles and lines that match the angles and lines in the diagram consisting of two lines and their common transversal to the correct description  are;

Alternate Interior Angles; 2. ∠4 and ∠8

Consecutive Exterior  Angles; 5. ∠1 and ∠6

Alternate Exterior Angles; 3. ∠1 and ∠5

Transversal; line l

Consecutive Interior Angles; 4. ∠3 and ∠4

Corresponding Angles; 1. ∠1 and ∠7

A transversal is a line that intersects two or more other lines.

The description of the relationship between the angles in the question are;

Alternate Interior Angles

Alternate interior angles are a pair of angles formed when a transversal intersects two lines. They are located between the two lines on opposite side of the transversal.

Consecutive Exterior Angles

Consecutive Exterior Angles are a pair of angles formed when a transversal intersects two lines. They are located outside the two lines on the same side of the transversal

Alternate Exterior Angles

Alternate exterior angles are a pair of angles formed when a transversal intersects two lines. They are located outside the two lines on the opposite sides of the transversal.

Consecutive Interior Angles

Consecutive Interior Angles, also known as Same-Side Interior Angles are a pair of angles formed when a transversal intersects two parallel lines. They are located between the two parallel lines on the same side of the transversal.

Corresponding Angles

Corresponding angles are a pair of angles formed when a transversal intersects two lines. They are located on the same relative positions with respect to the transversal and the two lines.

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Answer:

asdfasdfasdf

Step-by-step explanation:

asdf

Hence, 160 mL of oxygen is contained inside a 200 mL air tank using the same ratio as a 500 mL air tank.

Ratios contrast two figures by ordinarily dividing them. A/B would be your formula if you were trying to compare one piece of data (A) to some other data point (B). We are multiplying information A by data B, as this suggests. In the event that A and B are both 5, for example, your ratio would've been 5/10.

80% of 500 mL of oxygen if indeed the air tank contains 80% oxygen & 20% nitrogen, which is:

0.80 x 500 mL = 400 mL

This means that the air tank contains 400 mL of oxygen and 100 mL of nitrogen.

To find the amount of oxygen in a 200 mL air tank that contains the same ratio, we need to use proportions:

If 500 mL contains 400 mL of oxygen, then 1 mL contains 400/500 = 0.8 mL of oxygen.

Therefore, if 200 mL contains the same ratio of oxygen, it will contain:

0.8 mL x 200 mL = 160 mL

So, the amount of oxygen in a 200 mL air tank with the same ratio as the 500 mL air tank is 160 mL.

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Answer:(-3, -7)

Step-by-step explanation: (7-3,-) look the middle is (3,-6)        and instead on   7 is 6 bec in 7-

Answer10 toooooooooooo the third poewedd

Step-by-step explanation:

The volume of the cone is  2119. 5 cubic centimeters

The formula used for calculating the volume of a cone is expressed as;

V = πr² h/3

Given that the parameters are namely;

Now, substitute the values, we have;

Volume , V = 3.14 × 15² × 9/3

Divide the values, we have;

Volume = 3.14 × 225 × 3

Multiply the values, we get;

Volume, V = 2119. 5 cubic centimeters

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The surface area of an ice cube with 4 cm sides is 96 square centimeters.

It is a measurement of the sum of all the areas of the faces, sides, and any other surfaces of an object. For example, a cube has six square faces, each with the same area.

To find the surface area of an ice cube with 4 cm sides, we need to add up the areas of all six faces. Each face is a square with side length 4 cm, so the area of each face is:

Area of one face = (side length)² = 4 cm × 4 cm = 16 cm²

Since there are six faces on a cube, the total surface area of the ice cube is:

Total surface area = 6 × (area of one face) = 6 × 16 cm² = 96 cm²

Therefore, the surface area of an ice cube with 4 cm sides is 96 square centimeters.

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Answer:37

Step-by-step explanation:

<UYW=<UYV+<VYW=36+2x=110

2x=110-36=74

x=74/2=37

Answer:

∠w = 50°

∠y = 130°

Step-by-step explanation:

Angles ∠w and ∠y are supplementary angles, which means their sum is 180.

4x + 6 + 12x - 2 = 180

16x + 4 = 180

16x = 176

x = 11

To find the angle measures replace x with 11

∠w = 4x + 6

∠w = 4*11 + 6

∠w = 50°

Now, ∠y

∠y = 12x - 2

∠y = 12*11 - 2

∠y = 130°

Step-by-step explanation:

remember the trigonometric triangle inscribed in a circle (the norm circle with radius = 1).

for a larger system the leg lengths are sine and cosine multiplied by the radius (which is the Hypotenuse of the right-angled triangle).

the longer leg is opposite of the larger angle (60°).

the shorter leg is opposite of the smaller angle (30°).

what is the desired solution ? the length of the Hypotenuse ? or what ?

6 = sin(60)×Hypotenuse

Hypotenuse = 6/sin(60) = 6/(sqrt(3)/2) = 12/sqrt(3) =

= 6.92820323... ≈ 6.9

The opposite of the oppsite of 28,or (-28), is equivalent to the option (c) 28

The opposite of a number is the number with the opposite sign.

For example, the opposite of 28 is -28, and the opposite of -28 is 28.

So, the opposite of the opposite of 28, or (-28), is the opposite of -28, which is 28.

This means that the answer is (c) 28.

To explain it further, think of the number line. 28 is a positive number, so its opposite is a negative number, which is -28.

Now, the opposite of -28 is a positive number, which is 28. So, the opposite of the opposite of 28 is 28.

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Answer:  y = -2 - 2 * (x - 1).

Step-by-step explanation: The pattern is a linear function with a slope of -2 and an intercept of -2. The slope of a line is the change in y over the change in x. In this case, the change in y is -2 and the change in x is 1. Therefore, the slope is -2/1 = -2. The intercept is where the line crosses the y-axis, which is at y = -2 when x = 1. Therefore, the equation of the line is y = mx + b where m is the slope and b is the intercept. Substituting m = -2 and b = -2 gives us y = -2 - 2 * (x - 1).

Hope this helps, and have a great day!

Para preparar un pastel, Anita tenía un paquete de harina de 1 1/3 kg:  0.83 kg

Primero, debemos convertir 1 1/3 kg a una fracción común. 1 1/3 kg es igual a 4/3 kg o 1.33 kg. Luego, podemos simplificar 3/6 a 1/2.
Ahora podemos restar 1/2 de 1.33 kg para encontrar la cantidad de harina que sobró.
1.33 kg - 1/2 kg = 1.33 kg - 0.5 kg = 0.83 kg
Entonces, Anita le sobró aproximadamente 0.83 kg de harina después de preparar su pastel.
Es importante recordar que la medición y las cantidades de los ingredientes son cruciales al preparar cualquier receta de cocina. Es importante seguir las instrucciones cuidadosamente para obtener resultados exitosos en la cocina.

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Answer:

To solve the linear programming problem, we need to first graph the feasible region determined by the constraints, and then evaluate the objective function at each corner point of the feasible region to find the maximum value of z.

Plotting the lines corresponding to the inequalities, we get:

Graph of the feasible region:

The feasible region is the shaded polygon in the graph. We can see that the vertices of the feasible region are (2, 9), (2, 12), (4, 7), and (8, 2).

Next, we evaluate the objective function at each of these vertices to find the maximum value of z.

At (2, 9): z = 7x + 2y = 7(2) + 2(9) = 23

At (2, 12): z = 7x + 2y = 7(2) + 2(12) = 31

At (4, 7): z = 7x + 2y = 7(4) + 2(7) = 35

At (8, 2): z = 7x + 2y = 7(8) + 2(2) = 58

Therefore, the maximum value of z is 58, which occurs at the point (8, 2).

Hence, the answer is: the maximum value of z is 58.

Answer: 3

Step-by-step explanation:

Answer:  3

Step-by-step explanation:

16/4=unit rate =4

1 in 4 hour

3 for 12 hours

Answer:

To find the coordinates of A' after the translation, we need to apply the motion rule to the coordinates of A:

(x, y) → (x + 2y - 5, y - 6)

Substituting the coordinates of point A, which is (4, -4), into this motion rule, we get:

A' = (4 + 2(-4) - 5, -4 - 6) = (-3, -10)

Therefore, the coordinates of A' after the translation are (-3, -10).

Answer:The expression −4x−2y−3 can be written as −4/x^2y^3.

Multiplying both numerator and denominator by -1, we get 4/x^2y^3.

Hence, option A, −4x^2y^3, is equivalent to −4x−2y−3.

Step-by-step explanation:

Finding [tex]g(x)[/tex] given that we know [tex]f(x)[/tex] and the graphs for both functions. The correct option is D:

[tex]g(x) = (x/3)^2[/tex]

Looking at the graph on the image, we notice that [tex]f(x)[/tex] and [tex]g(x)[/tex] are two quadratic functions, and [tex]g(x)[/tex] is just a dilation o f[tex]f(x)[/tex].

This means that:

[tex]g(x) = A*f(x)[/tex]

Where A is a real number.

We know that:

[tex]f(x) = x^2[/tex]

By looking at the graph in the image, we know that [tex]g(3) = 1[/tex].

Then we can write:

[tex]g(3) = A*f(3) = A*3^2 = 1[/tex]

We can now solve for A:

[tex]A*3^2 = 1[/tex]

[tex]A*9 = 1[/tex]

[tex]A = 1/9[/tex]

We will have:

[tex]g(x) = (1/9)*f(x) = (1/9)*x^2 = (x/3)^2[/tex]

Therefore, the correct option is D.

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Complete question in image attached.

According to the solving this algebra approximately 1.43 quarts of pure antifreeze to the initial 5 quarts of 10% antifreeze solution to obtain a 30% antifreeze solution.

what is algebra?

Mathematical operations are applied to abstract symbols rather than concrete numbers in the field of algebra, which also includes other formal manipulations. The area of mathematics known as geometry is concerned with the qualities of the space that objects are in as well as the shape of the objects themselves.

According to the given information:

Let Q be the number of quarts of pure antifreeze to be added.

Let 0.10(5) be the amount of antifreeze in the initial 5 quarts of the 10% antifreeze solution, which is 0.5 quarts.

To obtain a 30% antifreeze solution, the amount of antifreeze in the final solution should be 0.3(5+Q) quarts.

Since we are only adding pure antifreeze, the amount of antifreeze in the final solution will be the sum of the antifreeze in the initial solution and the antifreeze we add:

0.5 + Q = 0.3(5+Q)

Now we can solve for Q:

0.5 + Q = 1.5 + 0.3Q

0.7Q = 1

Q = 1/0.7

Q ≈ 1.43

Therefore, we need to add approximately 1.43 quarts of pure antifreeze to the initial 5 quarts of 10% antifreeze solution to obtain a 30% antifreeze solution.

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The statement that is true, given that ΔCBX ≅ ΔSML, would be G. XC ≅ ML.

Given that ΔCBX ≅ ΔSML, we can use the properties of congruent triangles to determine which statement is true. The correspondence between the vertices of the two triangles is as follows:

C ↔ S

B ↔ M

X ↔ L

XC ≅ ML is true because XC corresponds to the side connecting vertices X and C in ΔCBX, and ML corresponds to the side connecting vertices M and L in ΔSML. Since the triangles are congruent, their corresponding sides are congruent.

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Answer:

The area remaining, correct to the nearest square meter, is approximately 436 square meters.

Step-by-step explanation:

To find the area remaining, we need to subtract the area of the flower bed and the area of the pool from the total area of the garden.

The total area of the garden is:

40m x 15m = 600 square meters

The flower bed is 1m wide and runs along two shorter sides and one long side of the garden. So the area of the flower bed is:

(40m + 2 x 1m) x (15m + 2 x 1m) - 40m x 15m

= (42m x 17m) - (40m x 15m)

= 714 - 600

= 114 square meters

Now let's calculate the area of the pool. The diameter of the pool is 8m, so the radius is 4m. The area of the pool is:

π x (4m)^2

= 16π

≈ 50.27 square meters (rounded to two decimal places)

So the area remaining is:

600 square meters - 114 square meters - 50.27 square meters

≈ 435.73 square meters

Therefore, the area remaining, correct to the nearest square meter, is approximately 436 square meters.

Answer:

Both data sets represent multiplicative relationships. In Table A, y is 3.5 times x, and in Table B, y is 9.2 times x.

The correct statement is: Both data sets represent multiplicative relationships. In Table A, y is 3.5 times x, and in Table B, y is 9.2 times x.