Write an equation for the parabola that has the
given vertex and passes through the given point.
Vertex
(0,-1)
Point
(1,-2)
f(x)= [?](x+ [ ]) ^2 + [ ]

La edad actual de José es de 30 años.

Para resolver este problema, primero debemos establecer ecuaciones basadas en la información proporcionada. Llamemos "x" a la edad actual de José y "y" a la edad actual de Ana. Según la primera condición, la edad de Ana es la mitad de la edad de José, por lo que podemos escribir la ecuación: y = (1/2)x.

La segunda condición nos dice que dentro de 10 años, sus edades serán dos tercios de sus edades actuales. Esto se puede expresar como: (x + 10) * (2/3) = y + 10.

Reemplazando el valor de y en la segunda ecuación con la primera ecuación, obtenemos: (x + 10) * (2/3) = (1/2)x + 10.

Resolviendo esta ecuación, podemos simplificarla y llegar a: 2(x + 10) = 3[(1/2)x + 10].

Al resolver la ecuación resultante, encontramos que x = 30.

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Answer:

\({ \tt{yes \: it \: describes \: a \: functional \: equation \: of \: a \: line}}\)

The graph of the function \(f(x) = (9/4)x^2\) is a symmetric upward-opening parabola.

Overall, the graph represents a quadratic function with a positive leading coefficient, resulting in an upward-opening parabolic curve. The graph has been attached.

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Answer:

16/25

Step-by-step explanation:

Answer:

24,429 cubic inches

YWW:)

Each function on the left should be matched to all points on the right that would be located on the graph of the function as follows;

f(x) = 2x + 2         ⇒   (0, 2).

f(x) = 2x² - 2        ⇒   (-1, 0).

\(f(x) = 2\sqrt{x+1}\)   ⇒   (0, 2).

In Mathematics and Geometry, a function is a mathematical equation which defines and represents the relationship that exists between two or more variables such as an ordered pair in tables or relations.

Next, we would determine the point or ordered pair that represent a solution on the graph of each of the function as follows;

For the ordered pair (0, 2), we have:

f(x) = 2x + 2

2 = 2(0) + 2

2 = 2 (True).

For the ordered pair (-1, 0), we have:

f(x) = 2x² - 2

0 = 2(-1)² - 2

0 = 2 - 2

0 = 0 (True).

For the ordered pair (0, 2), we have:

\(f(x) = 2\sqrt{x+1}\\\\2= 2\sqrt{0+1}\\\\2 = 2\sqrt{1}\)

2 = 2 (True).

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Answer:

1 5/8

Step-by-step explanation:

Answer:

1 and 5/8

Step-by-step explanation:

hdhdbfhfhfvvfvfvfhd

Answer:

n =1/2

Step-by-step explanation:

24n + 60 = 72

24n = 72 - 60

24n = 12 /24

n = 1/2

Answer:

n=1/2

Step-by-step explanation:

24n+60=72

24n=72-60

24n=12

n=12/24

n=1/2

Its option C

Verification

\(\\ \sf\longmapsto x-5y\lt 7\)

\(\\ \sf\longmapsto -3-5(2)\lt 7\)

\(\\ \sf\longmapsto -3-10\lt 7\)

\(\\ \sf\longmapsto -13\lt 7\)

Answer:

The solar panel produce 6.48 × 10⁶ J of energy each day.

Step-by-step explanation:

If the solar cells were 100% efficient and generate 1000 watts of power per square meter

The power generated per square meter will be

\(\frac{100}{100} \times 1000 watts/m^{2}\)

= 1000 watts/m²

This is the power that would be generated per square meter if the solar cells were 100% efficient.

Now, for a 1 square meter panel of solar cells with an efficiency of 30%, the power generated will be

\(\frac{30}{100} \times 1000 watts/m^{2} \times 1m^{2}\)

= 300 watts

This is the power that would be generated by a 1 square meter panel of solar cells with an efficiency of 30%

Now, to determine the energy in joules (J) that the solar panel produce each day

We can determine the energy from the formula

Energy = Power × time

From the question, the solar cells receives the equivalent of 6 hours of direct sunlight per day, that is

Time = (6 × 60 × 60) secs = 21600 secs

Hence,

Energy = 300 watts × 21600 secs

Energy = 6480000 Joules

Energy = 6.48 × 10⁶ J

Answer:

The value is \(E = 6480000 J/day \)

Step-by-step explanation:

The power produced per square meter is \(P = 1000 \ W\)

The efficiency of a solar cell is \(\eta = 100\%\)

The efficiency of 1 square meter panel of solar cells is \(\eta_b = 30\%\)

The duration of sunlight received by a one square meter panel of solar cells is t = 6 * 60 *60 = 21600 seconds

Generally the power generated by 1 square meter panel of solar cells is mathematically represented

\(P_a = \eta_b * P\)

\(P_a = 0.3 * 1000\)

\(P_a = 300\)

Generally the Energy produced by 1 square meter panel of solar cells per day is mathematically represented as

\(E = P_a * t\)

=>     \(E =  300 * 21600 \)

=>    \(E =  6480000 J/day \)

Answer:

C. 5

D. 5√3*

*Check the last one - choice D - make sure it is 5√3 not 53–√ before marking it correct.

Otherwise only choice C is the correct answer

Step-by-step explanation:

The sides of a 30-60-90 triangle are always in the ratio of 1 : √3 : 2.

If the side opposite the 90° angle(the hypotenuse)  = a

If the side opposite the 30° angle: PQ = a

Then the side opposite the 90° angle = 2a

The side opposite the 60° angle = √3a

Since here we are given the hypotenuse = 10

Side opposite the 30° angle = 2a/2 = 10/2 = 5

Side opposite the 60° angle = √3a = √3 · 5 = 5√3

I believe in your choice for D it should be 5√3 but not sure about that so check if it is before marking it correct

Answer:

Options C) and D) are correct

Step-by-step explanation:

Given:  The hypotenuse of a 30°-60°-90° triangle measures 10 inches.

To choose: the correct option

Solution:

ΔKBO is a right-angled triangle.

\(sinO=\frac{side opposite to angle}{sideadjacent to angle}\)

\(= \frac{BK}{KO} \\= \frac{BK}{10}\)

⇒ sin 60°= \(\frac{BK}{10}\)

\(\frac{\sqrt{3} }{2} = \frac{BK}{10}\)

BK = \(\frac{\sqrt{3} }{2} (10) = 5\sqrt{3}\)

CosO = \(\frac{side adjacent to angle}{side opposite to angle}\)

          \(= \frac{BK}{KO} \\= \frac{BO}{10}\)

          ⇒ cos 60° = \(\frac{BO}{10}\)

            \(\frac{1}{2}= \frac{BO}{10} \\BO = \frac{10}{2} = 5\)

By definition of f(x),

f(k) = 1 - 2k + k = 1 - k

Then

f(f(k)) = f(1 - k) = 1 - 2 (1 - k) + k = 3k - 1 = 13

Solve for k :

3k - 1 = 13

3k = 14

k = 14/3

Find f(-1) :

f(-1) = 1 - 2 (-1) + 14/3 = 1 + 2 + 14/3 = 23/3

Answer:

2,4 3,5

Step-by-step explanation:

The buying power of a currency is indeed the number of goods and services that can be purchased with a unit of currency. Real earnings, often known as real pay, is the amount of money an individual or institution earns after accounting for inflation, and the further calculation can be defined as follows:

For point a:

\(\bold{CPI=131.9}\)

Using formula:

\(\text{Purchasing Power of dollar}=\frac{\$1}{CPI} \times 100\)

                                            \(\bold{=\frac{\$1}{131.9} \times 100} \\\\\bold{= \$\ 0.00758 \times 100 }\\\\\bold{= \$\ 0.758}\)

Therefore Purchasing Power of the dollar in 2019 compared to 2002 is $0.758

For point b:

\(\bold{2019-Income = 62,900}\\\\\bold{CPI=131.9}\\\\\)

Using formula:

\(\text{Real Income}=\frac{ \text{Income in 2019}}{CPI} \times 100 \\\\\)

                    \(\bold{=\frac{62900}{131.9}\times 100}\\\\\bold{=476.876421 \times 100}\\\\\bold{= 47687.64}\)

   Therefore Real income, relative to 2002 is 47687.64

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The function is an exponential growth function

The function is given as

y=2(1.06)^9

We can begin by rewriting the given equation as:

y = 2 * 1.06t

So, we have

y = 2 * (1 + 0.06)^t

Now we can see that the equation is in the form y = a*b^t,

where a = 2 and b = 1.06^9

This equation represents exponential growth because the base of the exponent, b = 1.06, is greater than 1.

We can re-write it in the form y = a(1+r)t,

we can find the value of r by subtracting 1 from 1.06 which is 0.06 and the value of a is 2.

so we have y = 2(1+0.06)^t

So, the equation represents exponential growth with a = 2 and r = 0.06

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The time needed until there is one person for square yard of land is given as follows:

240 years.

An exponential function has the definition presented according to the equation as follows:

\(y = ab^x\)

In which the parameters are given as follows:

The parameter values for this problem are given as follows:

a = 5374000, b = 1.037.

Hence the exponential function for the population after t years is given as follows:

\(P(t) = 5374000(1.037)^t\)

The time needed for the population of 33,000,000,000 is obtained as follows:

\(5374000(1.037)^t = 33000000000\)

\((1.037)^t = \frac{33000000000}{5374000}\)

\((1.037)^t = 6140.677\)

\(t = \frac{\log{6140.677}}{\log{1.037}}\)

t = 240 years.

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Answer:

(x) ∠CAB

Step-by-step explanation:

In ΔCOD and ΔBOA

\(\frac{OA}{OB} = \frac{OD}{OC} \\\\\implies \frac{OC}{OB} = \frac{OD}{OA}\)

Also,

∠COD = ∠BOA (vertically opposite angles)

⇒ ΔCOD and ΔBOA are similar

⇒ ∠CDO = ∠BAO

⇒ ∠CDB = ∠BAC

⇒ ∠CDB = ∠CAB

A cut parallel to the vertical axis, directly through the vertical axis. Option C is correct.

Axes for the figure are defined as the imaginary lines that toward which measurement of the figures are taken.

Here,
When cutting the pyramid through axis perpendicular axis to the vertical axis, the shape produced would be a quadrilateral. But when we cut the pyramid through the vertical axis it produces the triangle.

Thus, a cut parallels the vertical axis, directly through the vertical axis. Option C is correct.

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Answer:

1/8", 1/4", 3/8", 5/8", 3/4", 12"

Step-by-step explanation:

First, make all of the fractions have similar denominators. We'll use eighths.

1/4 = 2/8

3/4 = 6/8

The rest are either whole numbers or already have a denominator of 8.

2/8, 6/8, 12, 1/8, 3/8, 5/8.

Rearrange.

1/8, 2/8, 3/8, 5/8, 6/8, 12.

Now we take the fractions we converted, and change them back to their original form. Then we'll have the answer.

1/8, 1/4, 3/8, 5/8, 3/4, 12.

---

hope it helps

The measure of the angle A as required to be determined in the task content is; 16.7°.

It follows from the task content that the measure of the angle A is to be determined.

By using the trigonometric ratio;

tan (A) = BC / AC

Hence, by substitution; it follows that;

tan (A) = 6 / 20

Hence, by simplification; we have that;

tan A = 3/10

tan A = 0.3

Therefore, to determine A;

A = tan-¹ (0.3)

A = 16.7°.

Ultimately the measure of angle A as required to be determined is; 16.7°.

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Answer:

A

Step-by-step explanation:

since she wants to keep 300 in her account first you would subtract 300 from 600 to get 300. Then you would divide it by 20 to get 15 so your answer would be a because she want's to keep at least 300 in her account.

Answer:

12 books

Step-by-step explanation:

if she can read 3 books in 2 weeks

then she can read 12 books in eight weeks because you multiply both numbers by 4.

2 times 4 = 8

3 times 4 = 12

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√(a² + b²)²  - 4a²b²cos²θ is the product of the lengths of the two diagonals is given by the expression.

What is a mathematical expression?

A mathematical expression is a phrase that includes at least two numbers or variables, at least one arithmetic operation, and the expression itself. This mathematical operation may be addition, subtraction, multiplication, or division.

                                An expression's structure is as follows: Number/variable, Math Operator, Number/Variable is an expression.

we have AB as a, AD as b and the angle between them is theta.

So using the cosine rule, we have

  BD = √a² + b² - 2abcosθ

So now consider the triangle ABC

Here AB is a, BC is b and the angle is 180-theta

So using cosine rule, we get AC as

   AC = √a² + b² - 2abcosθ( 180 - θ )

    AC = √a² + b² - 2ab(-cosθ )

    AC = √a² + b² - 2abcosθ

Now we have the two diagonals AC and BD. So multiplying, we get

 AC × BD = √a² + b² + 2abcosθ × √a² + b² - 2abcosθ

Simplifying, we get

AC × BD = √(a² + b² + 2abcosθ) × (√a² + b² - 2abcosθ)

AC × BD = √(a² + b²)² - (2abcosθ)²

AC × BD = √(a² + b²)²  - 4a²b²cos²θ

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The direction and angle of rotation include the following: C. 180° counterclockwise rotation.

In Mathematics and Geometry, the rotation of a point 180° about the origin in a clockwise or counterclockwise direction would produce a point that has these coordinates (-x, -y).

Furthermore, the mapping rule for the rotation of a geometric figure about the origin is given by this mathematical expression:

(x, y)                                            →            (-x, -y)

Coordinates of point A (-6, 5)  →  Coordinates of point A' = (6, -5)

In conclusion, this transformation rule (x, y) → (-x, -y) is used for the 180° rotation of a geometric figure about the origin in a clockwise or counterclockwise (anticlockwise) direction.

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Answer:9 is g and b

Step-by-step explanation:

because they all involved the answer

The set of factors used to factor the given trinomial are -4 and -4. Therefore, option C is the correct answer.

The given trinomial is x²-8x+16.

Factors of 16           Sum of factors

-1 and -16               -1+(-16)=-17

-2 and -8                  -2+(-8)=-10

-4 and -4                  -4+(-4)=-8

The set of factors would used to factor the trinomial are -4 and -4.

Therefore, option C is the correct answer.

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Based on the definition of  parallelogram, the conclusion about the quadrilateral is that: D. The quadrilateral is a parallelogram, because there are two pairs of equal slopes, and thus two pairs of parallel opposite sides.

If a quadrilateral is a parallelogram, the two pairs of opposite sides will be parallel to each other.

If two sides of a shape have the same slopes, it then means the shape is a parallelogram.

The quadrilateral that is given is said to have the following:

Two equal slopes of 5/4 and 5/4; and 2/5 and 2/5, this means the sides that have the same slope values are opposite to each other.

Since they are opposite to each other and they have the same slope, therefore, the conclusion about the described shape is: D. The quadrilateral is a parallelogram, because there are two pairs of equal slopes, and thus two pairs of parallel opposite sides.

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Answer:

x = (z - y)/(a - b)

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

Step 1: Define

ax - bx + y = z

Step 2: Solve for x

Answer:

The solution for x will be:

\(x=\frac{z-y}{a-b}\)

Step-by-step explanation:

Given the expression

\(ax-bx+y=z\)

subtract y from both sides

\(ax-bx+y-y=z-y\)

simplify

\(ax-bx=z-y\)

Factor ax-bx = x(a-b)

\(x\left(a-b\right)=z-y\)

Divide both sides by a-b;  a≠b

\(\frac{x\left(a-b\right)}{a-b}=\frac{z}{a-b}-\frac{y}{a-b};\quad \:a\ne \:b\)

simplify

\(x=\frac{z-y}{a-b};\quad \:a\ne \:b\)

Therefore, the solution for x will be:

\(x=\frac{z-y}{a-b}\)

The value of the permutation P(5,0) is 1.

To find the value of the permutation P(5,0), we can use the formula:

P(n, r) = n! / (n - r)!

In this case, we have n = 5 and r = 0.

Substituting these values into the formula, we get:

P(5,0) = 5! / (5 - 0)!

Since any number factorial is equal to 1, we have:

P(5,0) = 5! / 5!

Simplifying further:

P(5,0) = 1

Therefore, the value of the permutation P(5,0) is 1.

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