Determine the value of "a" for which g(h(a)) = 13

The value of a is 1/4 and the value of h and k is (2,-7/4)

A parabola is a u shaped curve. It is a plane curve whose all points are at a fixed distance form a point called focus.

(x-h)² = 4a(y-k)

It is given that the parabola goes through the point (3, -1), and the vertex is at (2, -2).

Therefore
(x -2)² = 4a(y +2)

The parabola passes through the point (3,-1)

(3-2)² = 4*a(-1+2)

1 = 4 a

a = 1/4

Now to determine the value of focus point , (h,k)

(h = 2)

k = - 2 +1/4 = -7/4

Therefore The value of a is 1/4 and the value of h and k is (2,-7/4)

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Answer:

The slope is 0.98 and the y-intercept is 1.44.

Step-by-step explanation:

The equation is a linear equation in the Slope-Intercept form y=mx+b. It’s called this because it identifies the slope m and the point on the y-axis at which the line intersects.

Answer:

$ 375 / month

Step-by-step explanation:

$ 18 000 / 48 months = 375 /month

The minimum amount he should save per month to achieve his goal is $375.00. Thus, option 2 is correct.

Given that:

Number of months = 48

Monthly savings = $18,000

The minimum amount to save per month can be calculated by dividing the total amount by the number of months:

Minimum monthly savings goal = Total amount to save / Number of months

Minimum monthly savings goal = $18,000 / 48

Minimum monthly savings goal ≈ $375.00

Therefore, the minimum amount he should save per month to achieve his goal is $375.00. Thus, option 2 is correct.

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Answer:

tan A = 5/12

Step-by-step explanation:

The tangent ratio is equal to the length of the side opposite of the angle over the length of the side adjacent to the angle. If we are finding tangent in respect to angle A, the opposite side would be line CB with a length of 5. The adjacent side is line AC with a length of 12. Therefore, the tan A ratio is 5/12.

The t-coordinate of the solution to this system represents C. the time at which the ball and the dog's mouth are at the same height.

A coordinate time scale is a time standard designed for use as the time coordinate in the calculation.

When Laurie throws a tennis ball toward her dog from a height, the t-coordinate of the solution to this system represents the time at which the ball and the dog's mouth are at the same height

The complete question is:

Laurie throws a tennis ball toward her dog from a height of 4.5 ft. The initial vertical velocity of the ball is 18 ft/s. At the same time as Laurie throws the ball, her dog jumps with an initial vertical velocity of 21 ft/s. When the dog jumps, its mouth is 1.5 ft above the ground. What does the t-coordinate of the solution to this system represent?

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Answer:

C

Step-by-step explanation:

I got it right

The x-intercepts of f(x) are common to those of g(x) .

The x-intercept is the point on the coordinate at which a line, curve or plane intersect with the x-axis. The value of y is equal to zero at x-intercept.

For me, it helps to graph everything on the same xy coordinate system. Start with the given graph and plot the points shown in the table. You'll get what you see in the diagram below.

The blue point C in that diagram is on the red parabola. This point is the x intercept as this is where both graphs cross the x axis. Therefore, they have a common x intercept.

Choice 1 is not true due to choice 4 being true. We have f(x) = g(x) when x = 2, which is why f(x) > g(x) is not true for all x.

Choice 2 is not true. Point B is not on the parabola.

Choice 3 is not true. There is only one known intersection point between f(x) and g(x), and that is at the x intercept mentioned above. Of course there may be more intersections, but we don't have enough info to determine this.

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Based on the calculations, the area of this regular polygon (hexagon) is equal to 24 m².

Mathematically, the area of a regular polygon can be calculated by using this formula:

Area = (n × s × a)/2

Where:

Note: The apothem of a regular polygon is half the length of one side.

Therefore, Length = 2 × 2 = 4 meter.

Substituting the parameters into the formula, we have;

Area = (6 × 4 × 2)/2

Area = 48/2

Area = 24 m².

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Answer:

152.3 approximately

Step-by-step explanation:

A polygon with 13 sides (and angles too) would be called tridecagon

Now, the sum of interior angles in a polygon is calculated by dividing the number of angles minus 2 by 180 [(n-2)*180]

(13-2)/180 = 1.980 and to find what is the measure of one angle, we divide the sum by the number of angles the polygon has

1.980/13 = 152.3 approximately

Answer:

x=−2

Step-by-step explanation:

hope it helps yaa

[tex]\sqrt{-1} + 2 = i+2 = 2+i[/tex]

Answer:

L=10y

Step-by-step explanation:

1cm=10mm

Hence, the length in millimeters will be 10 times the value in cm.

Answer:

A, C, and D

Step-by-step explanation:

Hope this helps!

If not, I am sorry.

Answer:

D is the correct option.

All the best!

when receiving this kind of questions, you just need to find a figure that you can calculate the area of or split the figure in multiple figures that you can calculate.

Step-by-step explanation:

The value of x from the given right triangle in rational form is 14√

This is a way of determining the sides and angles of a right triangles

From the given triangle

Opposite = 7√4 = 14

Hypotenuse = x

acute angle = 45 degrees

Using the theorem

sin 45 = 14/x

x = 14/sin45

x = 14√2

Hence the value of x from the given right triangle in rational form is 14√2

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Answer:

Group B

Step-by-step explanation:

You can see even with the same total group b likes the most topppings

Answer: 9/13

Step-by-step explanation:

plato classes

Answer: B. 28.26 ft2

Step-by-step explanation: I did this in school and got it right.

Answer:

B. 28.26 ft²

Explanation:

Here given:

Area of the fountain:

The supplies travelled 45ft and it took 0.6min to get to the next floor.

Trigonometry is the branch of mathematics dealing with the relationship between the sides of a triangle and the angles.

Analysis:

The supplies distance travelled, distance of first floor from second floor and the ground form a right angled triangle.

so that sin 60 = 39/distance travelled by supplies

distance travelled by supplies = 39/sin 60 = 39/0.866 = 45 feet.

speed = distance / time

time = distance / speed = 45/70 = 0.6 min

In conclusion, the distance and time time taken for the supplies to get to the next floor is 45feet and 0.6 min respectively.

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Answer:

Step-by-step explanation

Two angles of a triangle are in the ratio of 2:3 if the third angle is 50 degree find the other two angles

the sum of the interior angles in a triangle is 180°

so

180 - 50 = 130°

130 : 5 = 26° (unit)

26 * 2 = 52°

26 * 3 = 78°

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check

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The answer is good

Work Shown:

x³ + x² + x + 1

(x³ + x²) + (x + 1)

x²(x+1) + 1(x + 1)

(x² + 1)(x + 1)

The basic outline is to pair up the terms into two groups. We factor each group separately, and then factor out the overall GCF (x+1). You can use the FOIL rule to verify the answer.

The factored form of x³ + x² + x + 1 is (x²+1)(x+1).

A number or other mathematical item is factored (or factorised; see English spelling changes) or factored by a number of factors, usually smaller or simpler things of the same kind.

We have,

x³ + x² + x + 1

Now, making groups as

(x³ + x²) + (x + 1)

= x² (x + 1) + (x+1)

= (x²+1)(x+1)

So, resulting expression is  (x²+1)(x+1).

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#1

Scale ratio

#2

Unknown is actual length

So the ratio is

#3

The proportion is

#4

Must be multiplied with 0.75

#5

Actual length is 7.5ft

Answer:

Question 1

Given scale:  1 in = 10 ft

[tex]\textsf{Therefore, the scale as a ratio}=\sf \dfrac{\boxed{10}\:ft}{\boxed{1}\:in}[/tex]

Question 2

The ratio of the garden's actual length to its length in the drawing:

[tex]\sf \dfrac{x\:ft}{0.75\:in}[/tex]

Question 3

Therefore, the proportion is:

[tex]\sf \dfrac{10\:ft}{1\:in}=\dfrac{x\:ft}{0.75\:in}[/tex]

Question 4

Multiply both sides of the proportion by 0.75 to find x

Question 5

[tex]\begin{aligned}\textsf{Proportion}: \quad \quad \;\sf \dfrac{10\:ft}{1\:in} & = \sf \dfrac{x\:ft}{0.75\:in}\\\\\textsf{Mulitply both sides by 0.75}: \quad \sf 0.75\cdot \dfrac{10}{1} & = \sf 0.75 \cdot \dfrac{x}{0.75}\\\\\textsf{Simplify}: \quad \quad \quad \sf 7.5 & = \sf x\end{aligned}[/tex]

Therefore, the actual length of the garden is 7.5 ft

Answer:

A   x+2 would move the coordinate 2 units to the right while (x)+2 would move the coordinate 2 up and 2 to the right

Step-by-step explanation:

sorry i couldnt do the second part i ran out of time

Answer:

.................................................

Step-by-step explanation:

edge 2022

The number of months when the gyms cost the same is 5 months.

Total cost of joining the gym = registration fee + (cost per month x number of months)

When the gyms costs are the same, the two above equations would be equal to each other:

50 + 20m = 70 + 10m

20m - 10m = 70 - 20

10m = 50

m = 50 / 10

m = 5

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Answer:

The value of sin 30 degrees is 0.5. Sin 30 is also written as sin π/6, in radians. The trigonometric function also called as an angle function relates the angles of a triangle to the length of its sides.

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Inverse Cosine Law of Sines Formula

The surface area of the triangular prism is 153 cm².

Area = A + B + C

       =(9 × 15) + (0.5×6×3) + (0.5×6×3)

       = 135 + 9 + 9

       = 153 cm²

Hence, the surface area of the triangular prism is 153 cm².

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