Find the value of x that makes triangle ABC congruent to triangle DEF

The quadratic function passing through the point (1,12) and whose x-intercepts are (−2,0) and (3,0) is f(x) = 6x² - 6x - 36, The quadratic function whose vertex is (3,−9) and which is passing through the point (−1,15) is f(x) = -¼x² + (3/2)x - (9/4).

Formula for the quadratic function passing through the point (1,12) and whose x-intercepts are (−2,0) and (3,0) can be obtained as follows:

Using the x-intercepts to get the factors of the quadratic function: f(x) = a(x + 2)(x - 3).

Since the graph passes through (1, 12), we can substitute these coordinates to get a value for the coefficient a:12 = a(1 + 2)(1 - 3)12 = -6a6 = aTherefore, the formula for the quadratic function is:f(x) = 6(x + 2)(x - 3).

The answer   is  = 6(x + 2)(x - 3)To write this in standard form, we need to multiply out the brackets:f(x) = 6(x² - x - 6)f(x) = 6x² - 6x - 36.

The final answer  in standard form is f(x) = 6x² - 6x - 36.b) The formula for the quadratic function whose vertex is (3,−9) and which is passing through the point (−1,15) can be obtained as follows:

Using the vertex form of a quadratic function:f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola.Substitute the coordinates of the vertex to get:f(x) = a(x - 3)² - 9We still need to find the value of a.

To do this, we can use the point (-1, 15) that the parabola passes through:15 = a(-1 - 3)² - 915 = 16a24a = -6a = -¼Substitute a into the equation:f(x) = -¼(x - 3)² - 9.

The  answer f(x) = -¼(x - 3)² - 9.

To write this in standard form, we need to multiply out the brackets and simplify:f(x) = -¼(x² - 6x + 9) - 9f(x) = -¼x² + (3/2)x - (9/4)The final answer  in standard form is f(x) = -¼x² + (3/2)x - (9/4).

In conclusion, the quadratic function passing through the point (1,12) and whose x-intercepts are (−2,0) and (3,0) is f(x) = 6x² - 6x - 36, whereas, the quadratic function whose vertex is (3,−9) and which is passing through the point (−1,15) is f(x) = -¼x² + (3/2)x - (9/4).

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The value of x is 17

The congruent arcs are (b) PQ and SR

The radius is 12 units

The value of PQ is 4

The length YZ is 19 units

In this question, we make use of the property of congruent sides

So, we have

3x - 24 = x + 10

When evaluated, we have

2x = 34

Divide by 2

x = 17

By the definition of congruent arcs, congruent arcs are arcs that have equal measures

In this figure, the congruent arcs are PQ and SR i.e. (b) PQ and SR

The radius of the circle is calculated as

r² = (25 + r)² - 35²

When expanded, we have

r² = 625 + 50r + r² - 1225

So, we have

50r = 600

Divide both sides by 50

r = 12

In this question, we make use of the property of congruent sides

So, we have

PQ = SR

Where

SR = 4

When evaluated, we have

PQ = 4

The length of YZ in the circle is calculated as

YZ² = (9 + 8)² + 8²

So, we have

YZ² = 17² + 8²

When expanded, we have

YZ² = 289 + 64

So, we have

YZ² = 353

Take the square root of both sides

YZ = 19

Hence, the length YZ is 19 units

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Dominic receives 12 pounds on an item whose usual price is 80 pounds

The given parameters are:

Discount =15%

Price = p

Amount of discount = d

The equation that represents the amount of discount offered (d) on an item whose usual price is p is

d = Discount * p

This gives

d = 15% * p

Evaluate

d = 0.15p

In (a), we have

d = 0.15p

Here, p = 80

So, we have

d = 0.15 * 80

Evaluate

d = 12

Hence, Dominic receives 12 pounds on an item whose usual price is 80 pounds

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Answer:

If the store is offering a discount of 15% off the usual price

the equation is \(D=0.15p\)

Dominic gets a £12

discount on an item whose usual price i

The bacterial culture loses half it's size every 0.167 seconds.

An exponential function has the definition presented as follows:

y = ab^x.

In which the parameters are given as follows:

The function in the context of this problem is defined as follows:

B(t) = 9300(1/64)^t.

The time needed for the population to lose half it's size is obtained as follows:

(1/64)^t = (1/2)

Considering the powers of two, in the denominator causing the negative signal, we have that:

2^(-6t) = 2^(-1)

6t = 1

t = 1/6

t = 0.167 seconds.

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Answer:

49th term = 225

Step-by-step explanation:

The following sequence: -15, -10, -5, 0, -5... is an example of an arithmetic progression.

An arithmetic progression or AP for short, is a sequence in which the difference between successive terms is constant. This difference is known as the common difference, and can be found by subtracting a term by its preceding term.

The general formula, for the nth term of an arithmetic progression, is thus:

Tn = a + (n - 1)d, where a = first term, and d = common difference.

In the sequence: -15, -10, -5, 0, 5...,

a = -15, and d = -10--15 = 5

T49 = -15 + (49 - 1)5 = 225

∴ 49th term = 225

The regular polygon with an exterior angle measuring 120 will have 3 equal sides. Thus, an equilateral triangle have three equal sidea and angles is a regular polygon.

Regular polygon: A regular polygon is both "equiangular" and "equilateral," meaning it has all sides that are the same length and interior angles that are the same size.

The following algorithm determines an ordinary polygon's exterior angle:

Exterior Angle = \(360 Degrees / Sides\)

We can therefore make up an equation if the exterior angle measurement is \(120\) degrees:

\(120 = 360/n\) the number of sides being n

\(n (sides) = 360/120 = 3\)

Three sides \(=\) triangles are polygons with three sides.

An equilateral triangle is a regular three-sided polygon.

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Answer:

12 + 24 = 2(6 + 12)

Step-by-step explanation:

hope this helpss :D

much appreciated if this were marked brainliest <3

Answer:

=12

=2(6+12)

=2(6)+2(12)

=12+24

Step-by-step explanation:

Hope that this is helpful .

Have a great day.

Answer:

1.4 m

Step-by-step explanation:

let x = height of the tent

sin20 = x/4        

x = 4(sin20) = 1.368 ≈ 1.4 m

The value of the constant k in the equation m(t) = m(0) * 10^(-kt) can be determined by using the given information that 400 grams of the material decays to 40 grams in 10 years.

We are given the equation m(t) = m(0) * 10^(-kt) to describe the decay of the radioactive sample, where m(t) is the mass at time t, m(0) is the initial mass, and k is the constant we need to find.

Using the given information, we can substitute the values into the equation:

m(t) = 400 grams

m(0) = initial mass (unknown)

t = 10 years

m(t) = m(0) * 10^(-kt)

Substituting the values, we have:

400 = m(0) * 10^(-k * 10)

To find the value of k, we can rearrange the equation and solve for k:

10^(-k * 10) = 400 / m(0)

Taking the logarithm of both sides, we have:

-10k = log(400 / m(0))

Simplifying further:

k = -log(400 / m(0)) / 10

Now we can use the fact that the material decays to 40 grams in 10 years:

40 = m(0) * 10^(-k * 10)

Substituting the value of k we found, we have:

40 = m(0) * 10^(log(400 / m(0)) / 10 * 10)

Simplifying further:

40 = m(0) * 10^(log(400 / m(0)))

Now we need to solve this equation to find the value of m(0). We can use trial and error or numerical methods to find the value that satisfies the equation.

Once we find the value of m(0), we can substitute it back into the equation for k:

k = -log(400 / m(0)) / 10

Therefore, the value of k can be determined by solving the equation using the given information.

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Answer: -2

Step-by-step explanation: The line has a slope of -2/1, which is just -2.

Answer:

Add 1 1/2 each time

Step-by step explanation

-2 add 1 1/2 is -1/2 then add 1 1/2 to that 1/2, etc

can i get brainliest?

Let

x------> the number of multiple choice question

y------> the number of free response question

we know that

-----> equation A

-----> equation B

Substitute equation B in equation A

Find the value of x

therefore

the answer is

the number of multiple choice question are

the number of free response question are

Answer:

Graph D > Graph A > Graph C > Graph B

Step-by-step explanation:

The closer the data points are to each other along the line of best fit, the greater the value of their correlation coefficient, and vice versa.

Therefore, the graphs can be arranged in descending other (from the highest to the lowest) based on the values of their correlation coefficients as follows:

Graph D > Graph A > Graph C > Graph B

Answer:

See image

Step-by-step explanation:

Plato

Answer:

y = − x + 4

Step-by-step explanation:

Use the slope formula and slope-intercept form  y = m x + b  to find the equation.

Answer:

B. f(x) = x^4 -19x^2 +244x -928

Step-by-step explanation:

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form.

4, -8, and 2 + 5i

A.) f(x) = x^4 - 6x^3 - 20x^2 + 122x - 928

B.) f(x) = x^4 - 19x^2 + 244x - 928

C.) f(x) = x^4 - 6x^3 + 20x^2 - 122x + 928

D.) f(x) = f(x) = x^4 - 61x^2 + 244x - 928

A polynomial function with real coefficients has complex roots in both conjugates, hence the minimum polynomial is of the 4th degree with roots

4, -8, 2 + 5i, 2 - 5i

A polynomial can be found by expanding the following factors:

P(x) = (x-4)(x+8)(x-2-5i)(x-2+5i)

= (x-4)(x+8)(x^2-4x+29)

= x^4 -19x^2 +244x -928

Answer:

-27 °C

Step-by-step explanation:

-15 -12 = -27

Jara has 2 alternatives: -2 and -1 A number line is a diagram that depicts numbers,

As we walk along the line from left to right, the numbers rise. Positive numbers are often to the right and negative numbers to the left of zero, which is typically in the middle of the line.

Jara wants to choose a negative number that, in this instance, is closer to zero than -3. This suggests that instead of choosing -3, she should choose a negative integer that is situated nearer to zero on the number line.

-2 and -1 are the two negative numbers that are nearer to zero than -3. On the number line, these values are to the right of -3 and are nearer to zero than -3.

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Answer:

-3 1/2 - 1 5/6 = -16/ 3  = -5 1/ 3

≅ -5.3333333

isosceles triangle so angle Q = angle R

and sum of the angles of a triangle = 180

so

y + y + 84 = 180

2y = 96

y = 48

Answer:

The answer is 7.

Step-by-step explanation:

3*3=9

9-2

= 7 :)

A fair decision is made when outcomes are equally likely, while a biased decision occurs when certain outcomes are favored or more likely than others.

It seems that you are describing two types of decision-making scenarios: "fair decision" and "biased decision."

Fair Decision:

A fair decision is made when the outcomes of an event are considered to be equally likely. In this case, there is no favoritism towards any particular outcome, and the decision is based on an even playing field where each outcome has an equal chance of occurring.

Biased Decision:

A biased decision occurs when certain outcomes of an event are favored or more likely than others. This means that there is a preference or inclination towards specific outcomes, which can influence the decision-making process. Biases can arise due to various factors such as personal beliefs, preferences, or external influences.

It's important to note that biases can affect decision-making in both positive and negative ways. Biased decisions may lead to unfair treatment or inaccurate judgments if they are not based on objective and unbiased evaluation of the available information.

In summary, a fair decision is made when outcomes are equally likely, while a biased decision occurs when certain outcomes are favored or more likely than others.

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Lines 'a' and 'c' are parallel lines.

We have to given that,

There are three lines are shown in image.

We know that,

In a parallel line,

If two angles are alternate angles then both are equal to each other.

And, If two angles are corresponding angles then both are equal to each other.

Now, From the given figure,

In lines a and c,

Corresponding angles are 65 degree.

Hence, We can say that,

Lines a and c are parallel lines.

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To approach this type of problem, you have to make a couple of reasonable assumptions - first, that each worker works at the same pace, and second, that the effort to build each wall is the same.

Next, figure out how much effort is required to build one wall. The effort is measured in “working days”. So, how many days does one worker need to build one wall, or how many workers would be required to build one wall in one day? We can calculate this by dividing the 25 worker days used to build five walls by the number of walls (5). So we need five worker days per wall.

(5 workers) x (5 days) = 25 worker-days;

25 worker days/5 walls = 5 worker days per wall.

With 100 workers, it will take five days to build 100 walls. Each worker will build one wall in 5 days. So it will also take 5 days for all 100 workers to build all 100 walls.

100 x 5 = 500 worker days;

500 worker-days / 100 workers = 5 days (answer)

The radius of the circle is approximately 10.17 units (rounded to two decimal places).

To find the radius of the circle, we need to use the formula that relates the central angle to the length of the arc and the radius of the circle. The formula is given as:

arc length = radius x central angle

In this case, the arc length is given as 24.4 and the central angle is given as 2.4 radians. Substituting these values in the formula, we get:

24.4 = r x 2.4

Solving for r, we get:

r = 24.4 / 2.4

r ≈ 10.17

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The point (-3,-5) is in the third quadrant.

The first quadrant, designated as Quadrant I, is the upper right quadrant. Both the x-axis and the y-axis in this quadrant are positive.

The second quadrant, known as Quadrant II, is the top left quadrant. The x-axis has negative values and the y-axis has positive values in this quadrant.

The third quadrant, often known as Quadrant III, is the bottom left quadrant. Both the x-axis and the y-axis have negative values in this quadrant.

The fourth quadrant, known as Quadrant IV, is the bottom right quadrant. The x-axis in this quadrant is positive, whereas the y-axis is negative.

The point (-3,-5) lies in quadrant 3. A point is said to be in the third quadrant if both of its coordinates are negative.

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Answer:

The value of x = 12

Angle 1 =  78°

Angle 2 =  78°

Angle 3 =  24°

Step-by-step explanation:

The given triangle is isosceles triangle because AB = BC

We know that sum of angles of triangle = 180°

and Isosceles sides have same angles.

We have Angle 1 = (6x+6)°

Angle 2 = (6x+6)°

Angle 3= (2x)°

We can write

\((6x+6)^{\circ}+(6x+6)^{\circ}+2x^{\circ}=180^{\circ}\)

Solving this equation we can find value of x

\((6x+6)^{\circ}+(6x+6)^{\circ}+2x^{\circ}=180^{\circ}\\6x+6+6x+6+2x=180\\14x+12=180\\14x=180-12\\14x=168\\x=\frac{168}{14}\\x=12\)

So, the value of x = 12

Now finding angles

Angle 1 = (6x+6)° = 6(12)+6 = 72+6 = 78°

Angle 2 = (6x+6)°= 6(12)+6 = 72+6 = 78°

Angle 3= (2x)°= 2(12) = 24°

Answer: 55 degrees / Acute angle.

Step-by-step explanation:

The angle is less than a right angle, bent forward so it's less than 90 degrees, meaning it's an acute angle.

Answer: Standard form:

2x − 18 = 0

Factorization:

2(x − 9) = 0

Solutions:

x = 18

2

= 9

Step-by-step explanation:

12. It's solved you are correct.

Step-by-step explanation:

2x6=12 Also Please mark me brainelst btw mate 2x6 is 12 and 6x2=12. Thanks. I do not know if I'm right.

17  is the value of discriminant for quadratic equation.

What in mathematics is a quadratic equation?

A quadratic equation is a second-order polynomial equation in one variable using the formula x = ax2 + bx + c = 0 and a 0.

                               The fundamental theorem of algebra ensures that it has at least one solution because it is a second-order polynomial problem. Real or complex solutions are also possible.

General form of a quadratic equation is

ax² + bx + c = 0

The Discriminant of the quadratic equation is denoted by D and defined as

D = b² - 4ac

The given Quadratic equation is

√2x² - 5x + √2 = 0

Comparing with the general equation of quadratic equation ax² + bx + c = 0 we get

a = √2 , b = - 5 , c = √2

Value of Discriminant

      = b² - 4ac

      = (-5)² - 4 * √2 * √2

       = 25 - 8

       = 17      

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Answer:m

Step-by-step explanation: