Select the correct answer from each drop-down menu.
AABC has vertices at A(11,6), B(5, 6), and C15, 17).
AXYZ has vertices at X(-10,5), Y-12, -2), and 2-4,
15).
AMNO has vertices at M-9,-4), M(-3,-4), and 0-3, -15).
A/KL has vertices at (17, -2), K112,-2), and L(12,7).
APQR has vertices at A12, 3), 0112,-2), and R(3,-2).
can be shown to be

_______congruent by a sequence of reflections and translations.
________can be shown to be congruent by a single rotation.

Answer:

x = - 7, x = 0

Step-by-step explanation:

Given

x² + 7x = 0 ← factor out x from each term on the left side

x(x + 7) = 0

Equate each factor to zero and solve for x

x = 0

x + 7 = 0 ⇒ x = - 7

Hi there!

I understand your struggles. Don't worry!

First, factor out x from the equation.

x  times (x+7)=0 (Factor is a number that can be multiplied together to get another number)

When the product of factors equals 0, this means one factor is 0.

Therefore:

x=0

x+7=0

Solve the equation for x.

x=0

x=-7

This equation also has two solutions.

x1 = -7 x2= 0

Answer 1: -7

Answer 2: 0

These are our answers.

You mentioned you were confused about factoring.

Let me give you an example of factoring:

Equation: 2y+6

#1: Both 2y and 6 have a common factor of 2.

2y is 2 x y

6 is 2 x 3

Therefore: The expression can be factored to

2y+6=2(y+3)

Thanks for using Brainly.

- Tutor John

(a) To have exactly one solution, the discriminant of the quadratic equation must be equal to zero.b² - 4ac = 1 - 4(1)(_) = 0

⇒ 1 - 4_ = 0

⇒ _ = 1/4

Substituting the value of _ in the original equation, we get:

x² + x + 1/4 = (x + 1/2)² = 0

⇒ x = -1/2 (as square of a number is always non-negative)

(b) Following the same approach as in part (a), we get:

(-_)² - 4(1)(1) = _² - 4 = 0

⇒ _ = ± 2

Substituting the values of _ in the original equation, we get:

For _ = 2: x² + 2x + 1 = (x + 1)² = 0

⇒ x = -1

For _ = -2: x² - 2x + 1 = (x - 1)² = 0

⇒ x = 1

(c) Following the same approach as in part (a), we get:

1 - 4(_) = 0

⇒ _ = 1/4

Substituting the value of _ in the original equation, we get:

x² + x + 1/4 = (x + 1/2)² = 0

⇒ x = -1/2

(d) Following the same approach as in part (a), we get:

(-_)² - 4(1)(4_) = _² - 16_ - 4 = 0

⇒ _ = 2 ± √5

Substituting the values of _ in the original equation, we get:

For _ = 2 + √5: x² + (2 + √5)x + 5 + 2√5 = (x + (1 + √5))² = 0

⇒ x = -1 - √5

For _ = 2 - √5: x² + (2 - √5)x + 5 - 2√5 = (x + (1 - √5))² = 0

⇒ x = -1 + √5

Hence, we have found the values of the constant _ for each of the given quadratic equations to have exactly one solution and determined the solution for each value.

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The value of ∫ f(x) dx over the interval [3, 5] is 7. none of the option is correct.

To find the value of ∫ f(x) dx, we need to evaluate the integral of the function f(x) over a given interval. In this case, the function f(x) is defined piecewise:

f(x) = 2 for x < 3

f(x) = x - 1 for x ≥ 3

Let's find the integral of f(x) over a specific interval. We'll consider the interval [3, 5] for this example.

∫ f(x) dx = ∫ [2 for x < 3] + ∫ [x - 1 for x ≥ 3]

Since the lower limit of integration is 3, we'll consider the second part of the piecewise function for the interval [3, 5]:

∫ [x - 1 for x ≥ 3] = ∫ (x - 1) dx from 3 to 5

Now, let's evaluate this integral:

∫ (x - 1) dx = ([tex]1/2)x^2 - x[/tex] evaluated from 3 to 5

= [[tex](1/2)(5)^2 - 5] - [(1/2)(3)^2 - 3[/tex]]

= (1/2)(25 - 5) - (1/2)(9 - 3)

= (1/2)(20) - (1/2)(6)

= 10 - 3

= 7

Therefore, the value of ∫ f(x) dx over the interval [3, 5] is 7.

Since the given options for the answer are not specific to any interval, we cannot determine the exact value of the integral without knowing the interval. If there is a specific interval provided, we can evaluate the integral accordingly.

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Answer:

y=2/3x-2

Step-by-step explanation:

Slope intercept is y=m(x)+b

m is the slope, so substitute

b is the y intercept so also substitute

Hope this helps :-)

We have proved that (p - 1)! is congruent to 1 modulo p for an odd prime number p.

To prove that (p - 1)! is congruent to 1 modulo p, where p is an odd prime number, we can pair the numbers from 1 to (p - 1) with their multiplicative inverses modulo p. Since p is an odd prime, all the numbers from 1 to (p - 1) have distinct inverses modulo p.

Let's pair each number with its multiplicative inverse:

1 is paired with (p - 1)

2 is paired with (p - 2)

3 is paired with (p - 3)

...

(p - 2) is paired with 2

(p - 1) is paired with 1

Notice that every pair multiplies to give p modulo p, which is congruent to 0. So, we can ignore the product of each pair.

Now, let's consider the remaining numbers when p is odd. In this case, we have (p - 1)/2 pairs, and the number (p - 1)/2 is not paired with any other number.

Therefore, the product (p - 1)! can be expressed as:

(p - 1)! ≡ (1 * 1 * 1 * ... * (p - 1)/2) modulo p

Since (p - 1)/2 is an integer, we can rewrite the expression as:

(p - 1)! ≡ [(1 * 1 * 1 * ... * (p - 1)/2) * (1)] modulo p

Now, notice that (p - 1)! is congruent to the product of all the numbers from 1 to (p - 1)/2 modulo p. Since each pair of numbers multiplied to give 0 modulo p, we can remove those pairs from the product:

(p - 1)! ≡ [(1 * 1 * 1 * ... * (p - 1)/2) * (1)] modulo p

≡ [(1 * 1 * 1 * ... * (p - 1)/2)] modulo p

≡ 1 modulo p

Therefore, we have proved that (p - 1)! is congruent to 1 modulo p for an odd prime number p.

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Answer:

< 6 cm to > 26 cm i believe

Step-by-step explanation:

Since we have the equation that models the movement of the ball, we simply need to replace the corresponding values in the equation.

Althought there seems to be an X missing, so it should be

y=-0.03*x^2+1.6x  

like this, the graph should be as the picture shows.

We can immediately see in the picture that the football does go over the goal post, let's see how much, by replacing the values:

y=-0.03*40^2+1.6*40=-0.03*1600+64=16

since the pole is 10 ft high, the ball is 6 above the post

In question 8, we have defined a checkerboard matrix, and we need to answer three parts. In 8.1, we will write out the 4x4 checkerboard matrix. In 8.2, we will find the basis for the null space of the matrix and determine the nullity and rank of the matrix. In 8.3, we will discuss the rank and nullity of a 17x17 checkerboard matrix.

8.1) The 4x4 checkerboard matrix will have alternating 1s and 0s based on the pattern defined by the sum of the row and column indices. The matrix will look as follows:

A =   [1, 0, 1, 0],

       [0, 1, 0, 1],

       [1, 0, 1, 0],

       [0, 1, 0, 1]]

8.2) To find the basis for the null space of matrix A, we need to find the vectors that satisfy the equation Ax = 0, where x is a vector. The nullspace is the set of all solutions to this equation. In this case, we can observe that any vector of the form [x, -x, x, -x] will be in the null space. Therefore, the basis for the null space will be a single vector, such as [1, -1, 1, -1]. The nullity of A, which is the dimension of the null space, will be 1. The rank of A can be determined by subtracting the nullity from the number of columns, so the rank will be 4 - 1 = 3.

8.3) The rank and nullity of the 17x17 checkerboard matrix will follow a similar pattern. The matrix will have alternating 1s and 0s based on the pattern defined by the sum of the row and column indices. Since the matrix is square, we can expect that the rank and nullity will have the same value. In this case, the rank and nullity of the 17x17 checkerboard matrix will both be 17/2 = 8.5. However, since rank and nullity must be integers, the rank, and nullity will be 8, with an equal number of linearly independent rows and zero rows.

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Answer:

b=la/rx

Step-by-step explanation:

The given tableau represents a linear program being solved using the M-Method. It depicts the current solution and the values of the decision variables x1 and x2, along with their respective costs.

The tableau provided is a representation of the simplex method in solving a linear program. The decision variables x1 and x2 are shown along with their respective costs in the "Solution" row. The "Basic" row indicates which variables are currently in the basis.

To find the optimal solution, we need to ensure that all the coefficients in the bottom row (excluding the last column) are non-negative. If any negative values exist, we would perform row operations to pivot and select a different basic variable.

In this specific case, the coefficients in the bottom row are 1, -¹/4, -¹/4, and 0. Since the coefficient of -¹/4 is negative, we can select that column to perform the pivot operation. This would involve dividing the corresponding row (a3) by -¹/4, resulting in 3 + 4M in the pivot position.

The tableau will be adjusted accordingly, and the process would continue iteratively until an optimal solution is obtained. The objective is to maximize the solution value in the "Solution" row while ensuring non-negativity in the bottom row coefficients.

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K: (-4,4)

L: (-1,-3)

M: (1.5,0.5)

N: (4,3.5)

pls brainliest

Answer:

Rotation of 90 degrees counterclockwise about the origin

Step-by-step explanation:

well counterclockwise means you rotate the figure to the left and this figure is rotated to the left

Answer:

  56 cm

Step-by-step explanation:

Here's what the question is asking for.

  150 ≤ 1.25h ≤ 220

  120 ≤ h ≤ 176 . . . . the range of heights that can use the skis

  176 -120 = 56 cm . . . . the difference in heights

__

Here's an easier way to calculate it.

  220/1.25 -150/1.25 = (220 -150)/1.25 = 70/1.25 = 56

  The height difference is 56 cm.

_____

We judge one subtraction and one division to be easier and less error-prone than two divisions and a subtraction.

Answer:

1) 5√5

= 5^1 * 5^(1/2)

= 5^(1 + 1/2)  

= 5^(3/2)

Value of n = 3/2

2) Create equivalent expressions in the equation that all have equal bases, then solve for  n.

n = 5/2

The required simplified value ox n in both expressions is given as 1) n = 3/2 and 2) n = 5/2.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
(1)
5√5 can be written in form 5ⁿ.
5√5= 5ⁿ
[tex](5)^{1 + 1/2} = 5^n\\n = 3/2[/tex]

Similarly,
(2)

2√8 = 2ⁿ
n = 5/2

Thus, the required simplified value ox n in both expressions is given as 1) n = 3/2 and 2) n = 5/2.

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Answer:

It's a, 4

Step-by-step explanation:

Answer:

=42+115x

10x

Step-by-step explanation:

3(7/5x+ 4) – 2( 3/2- 5/4)

=21/5x+12-2(6/4-5/4)

=21/5x+12-2×1/4

=21/5x+12-1/2

=21/5x+24/2-1/2

=21/5x+23/2

=42/10x+115x/10x

=42+115x

10x

We have to find the time required for an object to cool from 300°F to 260°F by evaluating the following where t is time in minutes:t = 10/ln 2 ∫260300 (1/T - 100) dT.

To find the time t, let's first evaluate the integral using integration by substitution: Let u = T, then du/dT = 1 dT= du

Now we have,[tex]t = 10/ln 2 ∫260300 (1/T - 100) dT= 10/ln 2 ∫260300 (1/u - 100) du= 10/ln 2 ln|u| - 100u |_260^300= 10/ln 2 [ ln|300| - ln|260| - 100(300) + 100(260) ]= 10/ln 2 [ 5.7038 -  3000 + 2600 ]= 10/ln 2 ( - 94.6913 ) ≈ 133.4775[/tex]

minutes.

Therefore, the time required for the object to cool from 300°F to 260°F is approximately 133.4775 minutes.

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Answer:

your right it's d

Step-by-step explanation:

it's d it's d it's d it's d

Answer:

the domain is real number

Answer:

Two times one hundred three

2.0 × 103

Answer:

1/2

Step-by-step explanation:

2/4=1/2

Answer:

its 1/2

Step-by-step explanation:

if you divided the denominator and the numerator by 2 you get 1 for the numerator and 2 for the denominator.

which = 1/2

Answer:

ok

Step-by-step explanation:

An increase in the tax rate (T) will result in a lower equilibrium interest rate (i) and a lower equilibrium output level (Y). It's important to note that these effects depend on various assumptions and the specific functional forms of the equations in the IS/LM model.

A. To calculate the effect of the change in government spending (G) on the equilibrium interest rate (i) and output level (Y), we need to analyze the IS/LM model.

In the IS/LM model, the equilibrium is determined by the intersection of the IS curve (goods market equilibrium) and the LM curve (money market equilibrium).

Effect on the equilibrium interest rate (i):

An increase in government spending (G) will shift the IS curve to the right. This is because higher government spending increases aggregate demand, leading to higher output and income. As a result, there is upward pressure on the interest rate.

The shift in the IS curve will cause the equilibrium interest rate (i) to increase.

Effect on the equilibrium output level (Y):

With the increase in government spending (G), the IS curve shifts to the right, indicating higher aggregate demand. This leads to an increase in the equilibrium output level (Y). The increase in government spending directly contributes to the increase in output through the autonomous component of aggregate demand (G).

In summary, an increase in government spending (G) will result in a higher equilibrium interest rate (i) and a higher equilibrium output level (Y).

B. To calculate the effect of the change in the tax rate (T) on the equilibrium interest rate (i) and output level (Y), we again analyze the IS/LM model.

Effect on the equilibrium interest rate (i):

A change in the tax rate (T) affects disposable income (YD) and, consequently, consumption (C). An increase in the tax rate reduces disposable income, leading to a decrease in consumption. This decrease in consumption reduces aggregate demand and shifts the IS curve to the left. The shift in the IS curve will cause the equilibrium interest rate (i) to decrease.

Effect on the equilibrium output level (Y):

The decrease in consumption resulting from the increase in the tax rate (T) reduces aggregate demand, which in turn leads to a decrease in the equilibrium output level (Y). The decrease in consumption directly affects the aggregate demand component related to consumption (C), resulting in a lower equilibrium output level (Y).

In summary, an increase in the tax rate (T) will result in a lower equilibrium interest rate (i) and a lower equilibrium output level (Y).

It's important to note that these effects depend on various assumptions and the specific functional forms of the equations in the IS/LM model.

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======================================================

Explanation:

There are 3 colors of sweaters {red, green, purple} and 2 colors of skirts {tan, black}

So far there are 3*2 = 6 different outfit combinations. Imagine a table with 3 rows representing the sweater colors and 2 columns representing the skirt colors. There would be 6 cells in the table representing each possible combination. One cell would have (red sweater, tan skirt) for instance.

For each of those 6 combinations, we also have 2 shoe colors. So overall we have 6*2 = 12 outfit combinations

The tree diagram is shown below. Note how there are 3*2*2 = 12 different paths to follow.

Answer:

3/8

I just yeeted it into my calculator

Answer:

b = (-c + d) /a

or

b = (d - c) /a

b is equal to d minus c all over a

Step-by-step explanation:

ab + c =d

ab +c -c = d - c

ab = -c + d

b = (-c + d) /a

or

b = (d - c) /a

Answer:

The answer is

Step-by-step explanation:

The midpoint M of two endpoints of a line segment can be found by using the formula

[tex]M = ( \frac{x1 + x2}{2} , \: \frac{y1 + y2}{2} )\\[/tex]

From the question the points are

A(-2, 3), B(5,-1)

The midpoint is

[tex]M = ( \frac{ - 2 + 5}{2} \: , \: \frac{3 - 1}{2} ) \\ = ( \frac{3}{2} \: , \: \frac{2}{2} )[/tex]

We have the final answer as

[tex]( \frac{3}{2} \: , \: 1) \\ [/tex]

Hope this helps you

Answer:

menuu ate 2/5 of the orange

Step-by-step explanation:

the full orange is 5/5

Renu ate 3/5 of the orange.

We can create the following equation

5/5 = 3/5 + x

NB : x is the part of the orange that menuu ate

now make x the subject of formula

x = 5/5 - 3/5

x = 2/5

mennu ate 2/5 of the orange