how can i get equation b from equation a

Answer:

x1 = -2;

x2 = 3

Step-by-step explanation:

[tex]5 {x}^{2} - 5x - 30 = 0[/tex]

Solve this quadratic equation (a = 5; b = -5; c = -30)

[tex]d = {b}^{2} - 4ac = ( { - 5})^{2} - 4 \times 5 \times ( - 30) = 25 + 600 = 625 > 0[/tex]

x1 = (-b - √d) / 2a = (5 - 25) / 2 × 5 = -20 / 10 = -2

[tex]x2 = \frac{ - b + \sqrt{d} }{2a} = \frac{5 + 25}{2 \times 5} = \frac{30}{10} = 3[/tex]

Answer:

Step-by-step explanation:

15 divided by 15 is 1

3.45 divided by 15 is 0.23

The cost per ounce is 23 cents, or $0.23

The graph that closely matches the function is graph C.

The volume of a regular snowcone is 56.52 in³.

The price per cubic inch of a regular snowcone is $0.05.

In Mathematics and Geometry, the volume of a cone can be determined by using this formula:

V = 1/3 × πr²h

Where:

By substituting the given parameters into the formula for the volume of a cone, we have the following;

Volume of cone, V = 1/3 × πr²h

Volume of regular snowcone, V = 1/3 × 3.14 × 3² × 6

Volume of regular snowcone, V = 56.52 in³.

For the price per cubic inch, we have:

Price per cubic inch = Cost/Volume

Price per cubic inch = 2.85/56.52

Price per cubic inch = $0.05

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El cubo tiene cuatro caras numeradas del 1 al 6, lo que significa que hay un total de 4 posibles resultados en los que se puede obtener un 3 o un 5.

La moneda tiene dos caras, y dado que es imparcial, hay una probabilidad del 50% de que caiga en cara.

Entonces, la probabilidad de que se lance el cubo y la moneda al mismo tiempo y se obtenga un 3 o un 5 y una cara es igual a la probabilidad de obtener un 3 o un 5 multiplicada por la probabilidad de obtener una cara en la moneda.

La probabilidad de obtener un 3 o un 5 es de 2/6, o 1/3. La probabilidad de obtener una cara en la moneda es de 1/2.

Por lo tanto, la probabilidad total es:

1/3 x 1/2 = 1/6

La probabilidad de que caiga en cara y sacar un 3 o un 5 es de 1/6 o aproximadamente 0.1667.

Answer: 5,250

Step-by-step explanation:

250x3=750

750x7

Amelia was at camp for 6 days. The equation used to determine how many days(D) she was at camp is C x D = 6D and S - (C x D) = E

Given data:

S = initial amount = $54

D = the number of days

C = the cost per day = $6

E: the ending amount = $18

Amelia started with S=$54 and spent C=$6 each day at camp.

Therefore, the total amount she spent at camp is given in an algebraic expression that states the product of two variables:

C x D = 6D

Next, she ended with E=$18. So, the equation can be written in algebraic expression that states the difference between the variable:

S - (C x D) = E

Substituting the values in the equation we get:

54 - 6D = 18

54 - 18 = 6D

36 = 6D

D = 6

Therefore, Amelia was at camp for 6 days.

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Answer: 23 meter

Step-by-step explanation:

meters "above"

elevation means the distance above sea level

Yes, the ball reach a height of 25 meters from the ground , got the answer by solving equation given .

what is height ?

Height refers to the vertical distance between a point or an object and a reference level, usually the ground or a specific reference point. In the given context, height refers to the vertical distance of the ball from the ground at any given time, as modeled by the function h(t) = -5t² +7t+24.

In the given question,

h(t) = -5t² +7t+24

To find the time it takes for the ball to reach a height of 25 meters, we set h(t) equal to 25 and solve for t:

-5t² + 7t + 24 = 25

Simplifying, we get:

-5t² + 7t - 1 = 0

Using the quadratic formula, we get:

t = (-(7) ± √((7)² - 4(-5)(-1))) / (2(-5))

t = 1.4 seconds or t = 0.143 seconds (rounded to three decimal places)

Therefore, the ball will reach a height of 25 meters after 1.4 seconds or 0.143 seconds.

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2(6×7) + 2(3×7) + 2(3×6)

= 162

The complete table is:

x       f(x)

-8       -8

-1        -8

1          -8

And the graph can be seen in the image at the end.

Here we have the function:

f(x)  = -8

This is a constant function, for every input that we use, the output will be the same one, then:

f(-8) = -8

f(-1) = -8

f(1) = -8

Then the complete table is:

x       f(x)

-8       -8

-1        -8

1          -8

And the graph of these 3 points can be seen in the image at the end.

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The volume of container M can be calculated using the formula for the volume of a cylinder:

V = πr^2h

where V is the volume, r is the radius, and h is the height.

Substituting the given values, we have:

V = π(3 in)^2(9.5 in)

V ≈ 254.47 cubic inches

Let x be the volume of one box of sugar. According to the problem, the cook emptied one box of sugar into the container, and then added some fraction of another box to completely fill it. This means that the total volume of sugar added is equal to 1 + some fraction of x.

We can set up an equation to solve for x:

1 + (1/n)x = 254.47

where n is the fraction of the second box of sugar added.

Solving for x, we get:

x = (254.47 - 1) n

x = 253.47n

To find the value of n, we can subtract 1 box of sugar from the total volume added, and then divide by the volume of one box:

n = (254.47 - 1) / x

n = 253.47 / x

Substituting the expression for x from above, we get:

n = 253.47 / (253.47n)

n^2 = 253.47 / 1

n ≈ 15.93

Therefore, the volume of one box of sugar is approximately:

x ≈ 253.47 / 15.93

x ≈ 15.91 cubic inches

The finance charge is $3,723.20, which is closest to option A, $3,719.20.

The total amount of financing that your friend needed for the new sports car was:

$32,000 purchase price - $6,000 trade-in value = $26,000

Your friend financed $26,000 at 6.76% APR over 48 months, with a monthly payment of $619.15.

We can use the monthly payment and the APR to calculate the finance charge over the 48-month period. The finance charge is the difference between the total amount paid (48 months x $619.15 = $29,723.20) and the original amount financed ($26,000).

Finance charge = Total amount paid - Original amount financed

= $29,723.20 - $26,000

= $3,723.20

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Answer:

4x^2 + 24x.

Step-by-step explanation:

To find the product of 4x(x+6), we can use the distributive property of multiplication.

4x(x+6) = 4x * x + 4x * 6

= 4x^2 + 24x

Answer: 16x

Explanation:

4x(x+6)

4x+12x

16x

The Probability that the randomly selected car has either air-conditioning or automatic transmission or both is 0.9252.

The total number of cars sold in April is = 147,

⇒ n(S) = 147,

Let the cars which has Air Conditioning is denoted by "A", and

the number of cars which has automatic transmission be denoted by "B",

the number of cars which has AC = n(A) = 81,

the number of cars which are automatic be = n(B) = 82,

the number of cars which has only AC = n(A∩B') = 54,

the number of cars which are only automatic is = n(A'∩B') = 11,

the number of cars which has neither = n(A'∩B') = 11,

So, the probability that car has neither of these is = 11/147,

We know that, P(A'∩B') = P((A∪B)'),

So, P(A∪B) = 1 - P((A∪B)') = 1 - 11/147 = (147 - 11)/147 = 136/147 = 0.9252,

Therefore, the required probability is 0.9252.

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[tex]sin(40) = BC/10[/tex][tex]sin(40) = BC/10[/tex]Distance from Centroid to Midpoint of AB ≈ 2.5 cm. Therefore, the measurements of the centroid and the medians of the triangle have been calculated and confirmed using a ruler. The diagram of the triangle with the measurements.

To find the centroid of a right triangle ABC with angle A = 40 degrees and AB = 10 cm, we first need to find the lengths of the other sides of the triangle. Let's call the length of BC as x and the length of AC as y.

Using trigonometry, we can find that:

[tex]sin(40) = BC/10[/tex]

[tex]BC = 10*sin(40)[/tex]

BC ≈ 6.427 cm

[tex]cos(40) = AC/10[/tex]

[tex]AC = 10*cos(40)[/tex]

AC ≈ 7.664 cm

Now that we have the lengths of all three sides of the triangle, we can find the coordinates of the centroid. The centroid is the point where the three medians of the triangle intersect, and each median passes through a vertex of the triangle and the midpoint of the opposite side.

To find the centroid, we first find the midpoint of each side of the triangle:

[tex]Midpoint of AB = (0, 5)[/tex]

[tex]Midpoint of AC = (3.832, -1.864)[/tex]

[tex]Midpoint of BC = (-3.832, -1.864)[/tex]

Next, we find the coordinates of the centroid by averaging the coordinates of the three vertices:

[tex]Centroid = ((0+3.832-3.832)/3, (5-1.864-1.864)/3)[/tex]

[tex]Centroid = (0, 0.424)[/tex]

To confirm that the measurements of the centroid are correct, we can measure the distances from the centroid to the vertex and to the midpoint of the opposite side for all three medians. These distances are known as the medians of the triangle.

The median from vertex A passes through the centroid and the midpoint of BC. The distance from the centroid to vertex A is one-third the length of this median. Using the distance formula, we can find that:

[tex]Distance from Centroid to A = \sqrt((0-0)^2 + (0.424-0)^2)[/tex]

Distance from Centroid to A ≈ 0.424 cm

The distance from the centroid to the midpoint of BC is also one-third the length of the median from vertex A. The midpoint of BC is (-3.832/2, -1.864/2) = (-1.916, -0.932). Using the distance formula, we can find that:

[tex]Distance from Centroid to Midpoint of BC = \sqrt((0-(-1.916))^2 + (0.424-(-0.932))^2)[/tex]

Distance from Centroid to Midpoint of BC ≈ 2.532 cm

We can use similar methods to find the distances from the centroid to the vertices and midpoints of the other sides of the triangle. The final measurements and diagram are shown below:

Distance from Centroid to A ≈ 0.424 cm

Distance from Centroid to Midpoint of BC ≈ 2.532 cm

Distance from Centroid to B ≈ 2.532 cm

Distance from Centroid to Midpoint of AC ≈ 3.508 cm

Distance from Centroid to C ≈ 3.608 cm

Distance from Centroid to Midpoint of AB ≈ 2.5 cm

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To determine the type of vertex created by this quadratic function, we need to find the vertex of the parabola. The vertex of a parabola is the point where the parabola reaches its minimum or maximum value.

The given equation [tex]h(t) = -0.25t^2 + 2t + 4[/tex] represents the height of the basketball as a function of time.

The vertex of a quadratic function in the form of   [tex]f(x) = ax^2 + bx + c[/tex] can be found by using the formula:

[tex]x = -b/2a[/tex]

[tex]y = f(x) = a(x^2) + bx + c[/tex]

where (x,y) is the vertex of the parabola.

Comparing this with the given equation  [tex]h(t) = -0.25t^2 + 2t + 4[/tex] , we see that a = -0.25, b = 2, and c = 4.

Substituting these values in the formula, we get:

[tex]t = -2/(2\times(-0.25)) = 4[/tex]

[tex]h(4) = -0.25(4)^2 + 2(4) + 4 = 6[/tex]

Therefore, the vertex of the parabola is [tex](4, 6)[/tex] . Since the coefficient of the t^2 term is negative, the parabola opens downwards, and the vertex represents the maximum point of the parabola. The quadratic function   [tex]h(t) = -0.25t^2 + 2t + 4[/tex] would create a maximum vertex.

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The probability that a randomly selected household has a savings account is  57.16%. therefore, correct option is (C) 57.16%.

Given,

A survey revealed that 21.5% of the households had no checking account.

Of those households with no checking account, 40% had savings accounts.= 21.5% × 40%= 0.086%66.9%

had regular checking accounts. Of the households with regular checking accounts,

71.6% had a savings account.= 66.9% × 71.6%= 47.8916%11.6% had now accounts.

Of the households with now accounts,

79.3% had savings accounts.= 11.6% × 79.3%= 9.1828%

Therefore, the probability that a randomly selected household has a savings account is:

0.086 + 47.8916 + 9.1828 = 57.16%

So, the correct option is (C) 57.16%.

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The first term of the polynomial in standard form must be 4y⁴

If Julian wrote the last term as -3x⁴, the terms with the highest degree must have a coefficient of 3.

To get the standard form, we need to combine like terms and arrange the terms in descending order of degree.

The polynomial can be simplified as follows:

4x²y²-2y⁴-8xy³+9x³y+6y⁴-2xy³-3x⁴+x²y²

= -3x⁴ + (4x²y² + x²y²) + (-2y⁴ + 6y⁴) + (-8xy³ - 2xy³) + 9x³y

= -3x⁴ + 5x²y² + 4y⁴ - 10xy³ + 9x³y

Therefore, the standard form of the polynomial is

-3x⁴ + 5x²y² + 4y⁴ - 10xy³ + 9x³y

= 4y⁴ + 5x²y² + -3x⁴ - 10xy³ + 9x³y

The term with the highest degree is -3x⁴, and the terms are arranged in descending order of degree. The answer is not one of the options given.

Therefore, the first term of the polynomial in standard form must be 4y⁴.

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Answer:

y = 10 x = 8

Step-by-step explanation:

the triangles are exactly the same meaning that each right triangle would have the same measurements and side lengths

A triangle always equals 180 degrees

Answer:

lbozo

Step-by-step explanation:

Step-by-step explanation:

16 is tangent and the radial (12) is perpendicular

so this is a right triangle

   Use Pythagorean theorem

      ?^2  = 12^2 + 16^2

?^2 = 400

? = 20 units

A shape is moved to the right by 5 units. Transformation: Translation

A shape is flipped over a line. Transformation: Reflection

A shape is rotated 90 degrees clockwise. Transformation: Rotation

A shape is moved diagonally to the left and up by 3 units. Transformation: Translation

A shape is reflected over the line y = x. Transformation: Reflection

In geometry, a translation is a type of transformation that moves every point of a figure or an object in a straight line without changing its size, shape, or orientation. It is also referred to as a slide.

To perform a translation, you select a vector (which determines the distance and direction of the movement) and apply it to every point of the figure or object. For example, if you want to translate a shape 4 units to the right and 2 units up, you would add 4 to the x-coordinates of all the points and add 2 to the y-coordinates of all the points.

Situation 1: A shape is moved to the right by 5 units.

Transformation: Translation

Situation 2: A shape is flipped over a line.

Transformation: Reflection

Situation 3 : A shape is rotated 90 degrees clockwise.

Transformation: Rotation

Situation 4 : A shape is moved diagonally to the left and up by 3 units.

Transformation: Translation

Situation 5: A shape is reflected over the line y = x.

Transformation: Reflection

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Complete question:

Determine if each situation is a rotation, a translation, or a reflection.

Answer:

The length of the hypotenuse is 39. In the step by step explanation I included the Pythagorean Theorem formula and how it converted to the equation here to solve the problem.

Step-by-step explanation:

a² + b² = c²

15² + 36² = 1,521

√1,521 = 39

39 = c

Answer:

156

Step-by-step explanation:

The value of the expression 2x^2 - 5xy when x = -3 and y = 8 is 138.

To find the value of the expression, 2x^2 - 5xy, when x = -3 and y = 8, we just need to substitute the given values into the expression.

So, 2x^2 - 5xy becomes 2*(-3)^2 - 5*(-3)*8 = 2*9 + 15*8 = 18 + 120 = 138

Therefore, the value of the expression 2x^2 - 5xy when x = -3 and y = 8 is 138.

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