A parabola opens to the left. Which could be the equation of the parabola?
(x – 4)2 = 4(y + 3)
(x – 4)2 = –4(y + 3)
(y – 4)2 = 4(x + 3)
(y – 4)2 = –4(x + 3)

To solve this question:

Doing this, we get that the system is, with the 3 equations:

[tex]9a^2 + 3b + c = 8[/tex]

[tex]75a + 15b + 3c = 20[/tex]

[tex]36a + 6b + c = 5[/tex]

Equation of a parabola:

A parabola is a second degree polynomial, having an standard equation of:

[tex]y = ax^2 + bx + c, a \neq 0[/tex]

Point (3,8)

This means that when [tex]x = 3, y = 8[/tex]. So

[tex]y = ax^2 + bx + c, a \neq 0[/tex]

[tex]8 = a\times3^2 + 3b + c[/tex]

[tex]9a^2 + 3b + c = 8[/tex]

Thus, [tex]9a^2 + 3b + c = 8[/tex] is the first equation.

(5,20/3)

This means that when [tex]x = 5, y = \frac{20}{3}[/tex]. Thus

[tex]y = ax^2 + bx + c, a \neq 0[/tex]

[tex]\frac{20}{3} = a\times5^2 + 5b + c[/tex]

[tex]25a + 5b + c = \frac{20}{3}[/tex]

[tex]75a + 15b + 3c = 20[/tex]

Thus, [tex]75a + 15b + 3c = 20[/tex] is the second equation.

(6,5)

This means that when [tex]x = 6, y = 5[/tex]. Thus

[tex]y = ax^2 + bx + c, a \neq 0[/tex]

[tex]5 = a\times6^2 + 6b + c[/tex]

[tex]36a + 6b + c = 5[/tex]

Thus, [tex]36a + 6b + c = 5[/tex] is the third equation.

After all, the system of equations is:

[tex]9a^2 + 3b + c = 8[/tex]

[tex]75a + 15b + 3c = 20[/tex]

[tex]36a + 6b + c = 5[/tex]

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Answer:

a, b, c

Step-by-step explanation:

f(x) = 3(1/4)^x

a. (-2, 48)

f(-2) = 3(1/4)^(-2) = 3(4)^2 = 3 * 16 = 48

(-2, 48) is on the graph.

b. (0, 3)

f(0) = 3(1/4)^(0) = 3(1) = 3

(0, 3) is on the graph.

c. (2, 3/16)

f(2) = 3(1/4)^(2) = 3(1/16) = 3/16

(2, 3/16) is on the graph.

d. (12, 0)

f(12) = 3(1/4)^(12) = 3(0.000000596)

f(12) does not equal zero.

(12, 0) is not correct

Answer: [tex]\frac{d}{r} = t[/tex]

Step-by-step explanation: To solve for t in the equation d = rt, all we have to do is get t by itself on the right side of the equation.

Since t is being multiplied by r, we simply divide both sides of the equation by  r. On the right, the r's cancel and we are left with r.

On the left side of the equation we have [tex]\frac{d}{r}[/tex].

Therefore, our answer is [tex]\frac{d}{r} = t[/tex].

Answer: Third option is correct.

Step-by-step explanation:

Since we have given that

[tex]2x>-10---------------------------(1)[/tex]

and

[tex]3x<24------------------------------(2)[/tex]

From eq(1), we have

[tex]\dfrac{2x}{2}>\dfrac{-10}{2}\\\\x>-5[/tex]

From eq(2), we have

[tex]3x<24\\\\\dfrac{3x}{3}<\dfrac{24}{3}\\\\x<8[/tex]

So, compound inequality becomes

[tex]-5<x<8[/tex]

Hence, Third option is correct.

Answer:

square root of 8

Step-by-step explanation:

because it is 8 squared

The length of the hypotenuse of a right triangle with legs of 2 units each is the square root of 8 units.

In a right triangle, the length of the hypotenuse can be found using the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. If each of the two legs is 2 units, then the length of the hypotenuse can be found as follows:

hypotenuse2 = leg12 + leg22

hypotenuse2 = 22 + 22

hypotenuse2 = 4 + 4

hypotenuse2 = 8

Therefore, the length of the hypotenuse is the square root of 8 units.

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Answer: -5

Step-by-step explanation:

The slope of a line passing through (a,b) and (c,d) is given by :-

[tex]\text{Slope}=\dfrac{d-b}{c-a}[/tex]

Then the slope of the line AB contains points A (3, −2) and B (1, 8) will be :-

[tex]\text{Slope}=\dfrac{8-(-2)}{1-(3)}\\\\\Rightarrow\text{Slope}=\dfrac{10}{-2}-5[/tex]

Hence, the slope of the line AB contains points A (3, −2) and B (1, 8) = -5

Since the gold is worth $1566.80 per ounce, then the nugget is worth $1284.776.

This is a question relating to multiplication. Therefore, in order to know the worth of the nugget, we've to multiply 0.82 by $1566.80. This will be:

= 0.82 × $1566.80

= $1284.776

Therefore, the value of the nuggets is $1284.776.

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The two trains will be 330 miles apart after 2.5 hours.

To find how long it takes for the two trains to be 330 miles apart, we can apply the formula for relative velocity:

Relative velocity = sum of their speeds

The first train is moving east at 60 mph, and the second train is moving west at 72 mph. So their relative velocity is 60 mph + 72 mph = 132 mph.

To find the time it takes for the trains to be 330 miles apart, we can use the formula:

Distance = speed × time

330 miles = 132 mph × time

Solving for time, we have:

Time = 330 miles / 132 mph = 2.5 hours

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The student must make monthly payments of $1,020.63 to repay the $3,000 loan with $61.88 in interest over 3 months.

The student has borrowed $3,000 for 3 months and the interest incurred on this loan is $61.88. To find the monthly payment, we need to add the total interest to the principal borrowed and then divide it by the number of payments (which is 3 in this case).

The total repayment amount is calculated as $3,000 principal + $61.88 interest = $3,061.88.

Now, we divide the total repayment amount by the number of monthly payments:

Monthly Payment = Total Repayment Amount / Number of Payments

Monthly Payment = $3,061.88 / 3

Monthly Payment = $1,020.63

Therefore, the student will need to make monthly payments of $1,020.63 to repay the $3,000 loan over 3 months.

The pair of triangles that are congruent by ASA is [tex]\boxed{\bf option (d)}[/tex].

Further explanation:

Triangles are congruent when all the corresponding sides and interior angles are equal.

There are four theorems by which we say that the triangles are congruent.

1. Side-Side-Side(SSS)

If all the three sides of a triangle are equal to the corresponding sides of the other triangle, then the two triangles are congruent by SSS theorem.

2. Angle-Side-Angle(ASA)

If any two angles and the included side between the angles of one triangle are equal to the corresponding two angles and the included side between the angles of the second triangle then the two triangles are congruent by ASA theorem.

3. Side-Angle-Side(SAS)

If any two sides and angle between the sides of one triangle are equal to the corresponding two sides and angle between the sides of the second triangle then the two triangles are congruent by SAS theorem.

4. Hypotenuse Leg (HL)

If the hypotenuse and side of a right angled triangle is equal to the hypotenuse and a side of the other right angled triangle then the triangles are congruent by HL theorem.

Option (a)

The first figure shows one side is included between the two angles but the second figure shows two angles and one side as shown in below attachment.

Both the figures don’t have a single property from the above mentioned properties.

Therefore, option (a) is incorrect.

Option (b)

The first figure shows one angle between the two sides and the second figure also shows one angle between the two sides as shown in below attachment.

Both have the same property.

Therefore, the triangles are congruent by SAS rule not by ASA.

Thus, option (b) is incorrect.

Option (c)

The first figure shows one angle between the two sides and the second figure also shows one angle between the two sides as shown in below attachment.

Both have the same property.

Therefore, the triangles are congruent by SAS rule not by ASA rule.

Thus, option (c) is incorrect.

Option (d)

The first figure shows two angles and one side is included between them and the second figure shows two angles and one side is included between them as shown in below attachment.

Both have the same property.

Therefore, the triangles are congruent by ASA rule.

Thus, option (d) is correct.

Hence, the [tex]\boxed{\bf option (d)}[/tex] is correct as the triangles are congruent by ASA rule.

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Answer details:

Grade: Middle school

Subject: Mathematics

Chapter: Angles and Triangles

Keywords: Triangles, angles, sides, congruent triangles, similar triangles, SAS theorem, ASA theorem, SSS theorem, HL theorem, geometry, translation, rotation, reflection, mirror image.

The pair of triangles that are congruent by the Angle-Side-Angle Congruent Theorem (ASA) are the pairs that have two corresponding angles and an included side that are congruent to each other which is: Option D.

Recall:

The Angle-Side-Angle Congruent Theorem (ASA) states that two triangles are considered congruent if they have two corresponding angles that are congruent and an included side that are congruent to each other.

The included side is the side that is lie between the two congruent angles in each of the triangles.

Thus, form the pairs of angles given, the pair in option d has two corresponding angles and an included side that are congruent to each other in each triangle.

Therefore, the pair of triangles that are congruent by the Angle-Side-Angle Congruent Theorem (ASA) are the pairs that have two corresponding angles and an included side that are congruent to each other which is: Option D.

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Answer:

A. [tex]f(x) = (x-12)^2[/tex]

Step-by-step explanation:

The parent function [tex]f(x) = x^2[/tex] can be shifted 12 units to the right by moving its vertex 12 units to the right. The parent function has a vertex at (0,0) since [tex]f(0) = 0^2=0[/tex]. It will shift to (12,0) so [tex]f(12) =(12-a)^2=0[/tex]. The only value of a which will make it 0 is 12. So the equation is [tex]f(x) = (x-12)^2[/tex]