If BE CD, which pair of triangles is similar ?

Answer:34

Step-by-step explanation:

To write a quadratic function f whose zeros are -2 and 9 , we have to factor the function by (x+2) and (x-9).

A quadratic function is a second-degree mathematical function whose graph is a parabola. The general form of a quadratic function is given by f(x) = ax² + bx + c, where a, b and c are constants and a cannot be equal to zero. The variable x represents the input of the function and f(x) represents the output or result of the function. To find the quadratic function of f we first need to multiply these factors, like this:

So the quadratic function whose zeros are -2 and 9 is:

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Answer:

[tex] \frac{ {a}^{x} }{ {a}^{y} } = {a}^{x - y} [/tex]

Using the unitary method, we found that Zach's plants grew  60cm in 7 weeks.

The unitary method is a strategy for problem-solving that involves first determining the value of a single unit and then multiplying that value to determine the required value. Therefore, the goal of this method is to establish values in relation to a single unit. Always write the things that need to be calculated on the right side and the things that are known on the left side to simplify things. The unitary approach must be applied whenever we need to determine the ratio of one quantity to another.

Given that the height the plant grew in 2 weeks  = 2 feet

We are asked to convert it into centimetres.

This can be done using the unitary method.

Now, the unitary method can be used to find the value of multiple units when the value of the single unit is known.

Here we are given,

1 ft = 0.3 m

But we need feet and centimetre relation.

So we use the metre and centimetres relation.

1m = 100cm

Using the unitary method,

0.3m = 0.3* 100 = 30 cm

So,

1 feet = 0.3m = 30 cm

Then,

2 feet = 30 * 2 = 60 cm

Therefore using the unitary method, we found that Zach's plants grew 60 cm in 7 weeks.

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Answer:

9

Step-by-step explanation:

The median is the number in the middle of a set of numbers.

Our set of numbers:  1, 1, 2, 3, 7, 9, 10, 10, 15, 17, 19​

In this case the median is 9

Step-by-step explanation:

[tex]4k + 12 = - 36 \\ 4k = - 36 - 12 \\ 4k = - 48 \\ k = - \frac{48}{4} \\ k = - 12[/tex]

#hope it's helpful to you

$a = -8$ and $b = \frac{-520}{49}$

The matrix equation you provided is:

$$\left[\begin{array}{rr} 5 & a \\ 4 & -5 \end{array}\right]\left[\begin{array}{rr} b & -4 \\ -1 & 5 \end{array}\right]=\left[\begin{array}{rr} 6 \\ -7 \end{array}\right]$$

We can solve for the missing values by using the matrix equation $A \cdot B = C$. In this case, we have $A \cdot B = C$, where $A$ is the matrix on the left, $B$ is the matrix on the right, and $C$ is the matrix on the far right.

We can solve for $a$ and $b$ by using the inverse of $A$. To calculate the inverse of $A$, we use the formula: $$A^{-1} = \frac{1}{\det(A)}\left[\begin{array}{cc} -5 & a \\ 4 & 5 \end{array}\right]$$

The determinant of $A$ is $5 \cdot -5 - 4 \cdot a = -25 - 4a$, so $$A^{-1} = \frac{1}{-25 - 4a}\left[\begin{array}{cc} -5 & a \\ 4 & 5 \end{array}\right]$$

We can then calculate $b$ by multiplying the inverse of $A$ by the matrix $C$. $$\begin{align*}
A^{-1} \cdot C &= \frac{1}{-25 - 4a}\left[\begin{array}{cc} -5 & a \\ 4 & 5 \end{array}\right]\left[\begin{array}{rr} 6 \\ -7 \end{array}\right]\\
&= \frac{1}{-25 - 4a}\left[\begin{array}{rr} -5\cdot 6 + a\cdot (-7) \\ 4 \cdot 6 + 5 \cdot (-7) \end{array}\right]\\
&= \frac{1}{-25 - 4a}\left[\begin{array}{rr} -30 - 7a \\ 24 - 35 \end{array}\right]
\end{align*}$$

Solving for $b$, we have $$\begin{align*}
b &= \frac{-30 - 7a}{-25 - 4a}\\
&= \frac{-30 - 7a}{-25 - 4a}\cdot \frac{25 + 4a}{25 + 4a}\\
&= \frac{25\cdot(-30 - 7a) + 4a\cdot(-25 - 4a)}{25^2 + 4a^2}\\
&= \frac{-750 - 175a - 100a - 16a^2}{625 + 16a^2}
\end{align*}$$

Now, we can solve for $a$ by substituting $b$ into the equation $A \cdot B = C$. $$\begin{align*}
A\cdot B &= \left[\begin{array}{rr} 5 & a \\ 4 & -5 \end{array}\right]\left[\begin{array}{rr} b & -4 \\ -1 & 5 \end{array}\right]\\
&= \left[\begin{array}{rr} 5b + a(-4) & 5(-4) + a(5) \\ 4b - 5(-1) & -5(-1) - 5(5) \end{array}\right]\\
&= \left[\begin{array}{rr} -20 - 4a & 25 + 5a \\ 4b - 5 & 25 - 25 \end{array}\right]
\end{align*}$$

Comparing this to the equation $A\cdot B = C$, we can solve for $a$: $$\begin{align*}
6 &= -20 - 4a\\
-7 &= 4b - 5\\
&= 4\left(\frac{-750 - 175a - 100a - 16a^2}{625 + 16a^2}\right) - 5\\
&= \frac{-3000 - 700a - 400a - 64a^2}{625 + 16a^2} - 5\\
&= \frac{-3500 - 700a - 400a - 64a^2}{625 + 16a^2}\\
\end{align*}$$

By comparing this to the equation $6 = -20 - 4a$, we can solve for $a$: $$\begin{align*}
-3500 - 700a - 400a - 64a^2 &= -20 - 4a\\
64a^2 + 400a + 700a + 3520 &= 0\\
a^2 + 5a + 56 &= 0\\
(a + 8)(a + 7) &= 0\\
a &= -8 \;\text{or}\; -7
\end{align*}$$

Thus, the missing values are $a = -8$ and $b = \frac{-520}{49}$.

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According to the information, the expressions that would match the descriptions would be both expressions have the same result, so it doesn't matter which description they are associated with. both are the largest and the smallest value.

To find the correct descriptions that match the expressions we must look at the graph. In this case q and n represent two numbers on the number line. In this case, to relate them to a description we must find the number to which they refer:

In accordance with the above, we could say that the descriptions would look like this:

In this case, both expressions have the same result, so it doesn't matter which description they are associated with. both are the largest and the smallest value.

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The match of the terms and correct locations are:

1. A - Amplitude

2. B is compression

3. C is rarefaction

A longitudinal wave is a form of wave in which its direction of propagation is similar to the direction of vibration of the particles of the medium through which the wave is travelling. The waves generated by a stretched or compressed spiral spring produces longitudinal waves.

When a spiral spring is streched or compressed, on removal of the force a series of compression and rarefactions of the sections of the spring are produced. This sections vibrates in the direction of propagation of the waves produced.

Thus the match of the terms and correct locations are:

i. A - Amplitude

ii. B is compression

iii. C is rarefaction

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Answer:

The argument of the logarithmic function should be greater than zero.

Thus, for y = log(-x + 3) - 1 to be real-valued, we need:

-x + 3 > 0

or

x < 3

So, the domain of the function is all real numbers less than 3.

To find the range, let's consider the behavior of the logarithmic function.

As x approaches 3 from the left, the argument of the logarithm approaches zero from the negative side, which means the logarithm approaches negative infinity.

As x approaches negative infinity, the argument of the logarithm becomes very large and negative, which means the logarithm approaches negative infinity.

Therefore, the range of the function y = log(-x + 3) - 1 is all real numbers.

Step-by-step explanation:

Answer:

I think the answer is C. 65 m

Step-by-step explanation:

Answer:

L=22

Step-by-step explanation:

For the area of a rectangle you have to multiply the width by the length.

This problem would look like L*W=A. Being that you already have the area and the width, you would just have to fill in for these.

L*6.5=143

Then just follow the rules of PEMDAS to sole for L. In this case this would be dividing 6.5 by both sides.

L=22

14 : 25 best represents the number of unshaded squares to total squares. The solution has been obtained by using arithmetic operations.

The four mathematical operations that result from dividing, multiplying, adding, and subtracting are quotient, product, sum, and difference.

We are given a figure in which some squares are shaded and rest are unshaded.

Number of total squares = 10 × 10 = 100

Number of shaded squares = 44

So, Number of unshaded squares = 100 - 44 = 56

Ratio of unshaded squares to total squares is as follows

56 : 100

Reducing to the lowest, we get

14 : 25

Hence, 14 : 25 best represents the number of unshaded squares to total squares.

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Answer:

The given rectangle is not fully defined, as it is missing some measurements such as the length and width. Without this information, it is not possible to accurately calculate the perimeter of the rectangle.

However, assuming that the missing measurement is the width of the rectangle, then the expressions given by the five students would be:

2(3x + 4x + 3) = 14x + 6

2(6x + 6) + 2(4x + 6) = 20x + 24

2(3x + 3) + 2(4x + 3) = 14x + 12

2(6x + 3) + 2(4x + 3) = 20x + 12

2(6x + 3x) + 2(3 + 4x) = 18x + 10

Note that all expressions follow the formula for the perimeter of a rectangle, which is P = 2l + 2w, where l is the length and w is the width of the rectangle.

Therefore, the correct answer is C. Log 65/177 y = x.

The correct answer is C. Log 65/177 y = x.

To solve the equation in exponential form, we need to use the properties of logarithms. The equation Y^x = 65 / 177 can be rewritten in logarithmic form as Log Y (65/177) = x. Using the property of logarithms, Log a^b = b Log a, we can rewrite the equation as Log (65/177) Y = x. This is the same as option C, Log 65/177 y = x.

Therefore, the correct answer is C. Log 65/177 y = x.

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Answer:$880

Step-by-step explanation:

1/3 1/3 1/3 1/3 1/3 1/3 1/3 1/3 1/3 1/3 1/3 1/3 1/3 1/3 1/3 1/3
4    8   12  16  20 24 28 32 36 40 44 48 52 56 60 64

55 55 55 55 55 55 55 55 55 55 55 55 55 55 55 55
so to explain 1 cheese pizza to 3 pepperonis(1/3) that is 4 pizzas together, and we do that until 64. If pepperoni pizza is 15 each, we time that by 3 which is 45, plus the 10 for cheese pizza which makes it 55. we do 55 dollars until we equal the 64 pizzas, which is 16 together. so 55 x 16=880 dollars selling pizza

Sure, here are the answers to Exercises 4.4 1 for Propositions 1.5 through 1.8:

Proposition 1.5: If two triangles have two sides and the included angle of one equal to two sides and the included angle of the other, then the triangles are congruent.

Does the proposition hold on a sphere?

No, the proposition does not hold on a sphere. A counterexample is two triangles on a sphere with the same side lengths and angles but with different shapes.

If it does not, give a counterexample and briefly explain what goes wrong.

The problem is that the definition of congruence for plane triangles does not apply to triangles on a sphere since the side lengths and angles are not independent. Two triangles with the same side lengths and angles can have different shapes on a sphere.

If it does hold, does Euclid's proof work? If it does not, briefly explain what goes wrong.

Euclid's proof assumes that the side lengths and angles of the triangles are independent, which is not the case on a sphere. Therefore, his proof does not work for triangles on a sphere.

Proposition 1.6: If two triangles have two angles and a side of one equal to two angles and a side of the other, then the triangles are congruent.

Does the proposition hold on a sphere?

No, the proposition does not hold on a sphere. A counterexample is two triangles on a sphere with the same angle measures and side lengths but with different shapes.

If it does not, give a counterexample and briefly explain what goes wrong.

The problem is that the definition of congruence for plane triangles does not apply to triangles on a sphere since the side lengths and angles are not independent. Two triangles with the same angle measures and side lengths can have different shapes on a sphere.

If it does hold, does Euclid's proof work? If it does not, briefly explain what goes wrong.

Euclid's proof assumes that the angle measures and side lengths of the triangles are independent, which is not the case on a sphere. Therefore, his proof does not work for triangles on a sphere.

Proposition 1.7: If two triangles have two sides and an angle of one equal to two sides and an angle of the other, then the triangles are congruent.

Does the proposition hold on a sphere?

No, the proposition does not hold on a sphere. A counterexample is two triangles on a sphere with the same side lengths and angle measures but with different shapes.

If it does not, give a counterexample and briefly explain what goes wrong.

The problem is that the definition of congruence for plane triangles does not apply to triangles on a sphere since the side lengths and angles are not independent. Two triangles with the same side lengths and angle measures can have different shapes on a sphere.

If it does hold, does Euclid's proof work? If it does not, briefly explain what goes wrong.

Euclid's proof assumes that the side lengths and angles of the triangles are independent, which is not the case on a sphere. Therefore, his proof does not work for triangles on a sphere.

Proposition 1.8: If two triangles have three sides of one equal to three sides of the other, then the triangles are congruent.

Does the proposition hold on a sphere?

No, the proposition does not hold on a sphere. A counterexample is two triangles on a sphere with the same side lengths but with different shapes.

If it does not, give a counterexample and briefly explain what goes wrong.

The problem is that the definition of congruence for plane triangles does not apply to triangles on a sphere

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-17.

According to the remainder theorem, the remainder when dividing a polynomial f(x) by a linear factor x-a is equal to f(a). In this case, we want to find the remainder when dividing f(x) = -4x^3 + 2x^3 -3x+5 by x - 2, so we need to find f(2).

f(2) = -4(2)^3 + 2(2)^3 -3(2) + 5
f(2) = -4(8) + 2(8) -6 + 5
f(2) = -32 + 16 -6 + 5
f(2) = -17

Therefore, the remainder when dividing f(x) = -4x^3 + 2x^3 -3x+5 by x - 2 is -17.

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The perimeter of Raina's pigpen is 1020 feet.

Perimeter is the total distance around the edge of a two-dimensional shape. It is the sum of the lengths of all sides of the shape. Perimeter is typically measured in units such as inches, feet, meters, or centimeters, depending on the system of measurement being used.

To find the perimeter of the rectangular pigpen, we need to add up the lengths of all four sides. The formula for the perimeter of a rectangle is:

perimeter = 2 * length + 2 * width

Plugging in the values we know, we get:

perimeter = 2 * 325 + 2 * 185

perimeter = 650 + 370

perimeter = 1020

Therefore, the perimeter of Raina's pigpen is 1020 feet.

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Answer:

-x + 6.5 > 1 Is true.

Step-by-step explanation:

The explaination is given in the Picture.

The values of F(x), h(x), and g(x) when x=3 are 42, -230, and 6, respectively.

The given functions are F(x)=−529, F(x)=x^2+33, h(x)=∣x∣−233, and g(x)=2x.

To find the value of F(x) when x=3, we can substitute x=3 into the equation F(x)=x^2+33 and solve for F(x):
F(x)=x^2+33
F(3)=3^2+33
F(3)=9+33
F(3)=42

Similarly, to find the value of h(x) when x=3, we can substitute x=3 into the equation h(x)=∣x∣−233 and solve for h(x):
h(x)=∣x∣−233
h(3)=∣3∣−233
h(3)=3−233
h(3)=-230

And to find the value of g(x) when x=3, we can substitute x=3 into the equation g(x)=2x and solve for g(x):
g(x)=2x
g(3)=2(3)
g(3)=6

Therefore, the values of F(x), h(x), and g(x) when x=3 are 42, -230, and 6, respectively.

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The product between f(x) and g(x) is equal to -6x² + 37x - 35.

The product of two functions, (fg)(x), is defined as f(x)*g(x). Therefore, to find the product of the given functions, we simply need to multiply them together:

(fg)(x) = (6x -7)(5 - x)

Using the distributive property, we can simplify this expression:

(fg)(x) = (6x)(5) - (6x)(x) - (7)(5) + 7(x)

(fg)(x) = 30x - 6x² - 35 + 7x

Combining like terms, we get:

(fg)(x) = -6x² + (30x + 7x) - 35

(fg)(x) = -6x² + 37x - 35

So the product of the two functions is (fg)(x) = -6x² + 37x - 35.

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Since PNDM got dilated about the origin and formed P' N' D' M', the dilation rule is (x, y)    →    (2x, 2y).

In Geometry, the scale factor of a geometric figure can be calculated by dividing the dimension of the image (new figure) by the dimension of the pre-image (original figure):

Scale factor = Dimension of image (new figure)/Dimension of pre-image(original figure)

Substituting the given parameters into the scale factor formula, we have the following;

Scale factor = Dimension of image/Dimension of pre-image

Scale factor = 4/2

Scale factor, k = 2.

Therefore, the dilation rule is given by:

(x, y)      →    (kx, ky)

(x, y)      →    (2x, 2y)

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Answer:

Step-by-step explanation:

Answer:

[tex]f^{-1}[/tex] = [tex]\frac{x-3}{2}[/tex]

The inverse of a function is just the opposite of the function.

Answer:

1,254 - whole number; 0.13 - terminating; 0.123456789... - non-terminating/non-repetitive; 0.143143143... - repeating decimal

Step-by-step explanation:

A whole number is a number without any decimals or fractions. A terminating number is one that has an end. A non-terminating number is one that continues on forever. A repeating number is one that has the same pattern and continues on forever.

Answer:

[tex]x^2+5x+4+\dfrac{3x-8}{x^2+5x-4}[/tex]

Step-by-step explanation:

The dividend is the polynomial which has to be divided.

The divisor is the expression by which the dividend is divided.

Given:

Following the steps of long division, divide the given dividend by the divisor:

[tex]\large \begin{array}{r}x^2+5x+4\phantom{)}\\x^2+5x-4{\overline{\smash{\big)}\,x^4+10x^3+25x^2+3x-24\phantom{)}}}\\{-~\phantom{(}\underline{(x^4+\phantom{(}5x^3-\phantom{(}4x^2)\phantom{-b)))))))))}}\\5x^3+29x^2+3x-24\phantom{)}\\-~\phantom{()}\underline{(5x^3+25x^2-20x)\phantom{)))..}}\\4x^2+23x-24\phantom{)}\\-~\phantom{()}\underline{(4x^2+20x-16)\phantom{}}\\3x-8\phantom{)}\end{array}[/tex]

The quotient q(x) is the result of the division.

The remainder r(x) is the part left over:

The solution is the quotient plus the remainder divided by the divisor:

[tex]\implies q(x)+\dfrac{r(x)}{b(x)}=\boxed{x^2+5x+4+\dfrac{3x-8}{x^2+5x-4}}[/tex]

The mean of the list  is 7

The standard deviation of the list is 4/69

The linear regression equation is y = 227.5 + 0.65*x
The percentile rank on the Math portion for a student with a Verbal percentile rank of 80% is approximately 73.5%.

2a) The mean of the list can be computed by adding all of the numbers in the list together and dividing by the number of items in the list.

Mean = (9+2+5+4+12+10)/6 = 42/6 = 7

2b) The standard deviation of the list can be computed by finding the difference between each number in the list and the mean, squaring these differences, finding the average of these squared differences, and then taking the square root of this average.

Standard deviation = sqrt(((9-7)^2 + (2-7)^2 + (5-7)^2 + (4-7)^2 + (12-7)^2 + (10-7)^2)/6) = sqrt(22) = 4.69

3a) The linear regression equation can be found using the formula:

y = b0 + b1*x

Where b0 is the y-intercept and b1 is the slope. The slope can be found using the formula:

b1 = r*(SDy/SDx)

Plugging in the given values:

b1 = 0.80*(85/105) = 0.65

The y-intercept can be found using the formula:

b0 = meany - b1*meanx

Plugging in the given values:

b0 = 570 - 0.65*525 = 227.5

So the linear regression equation is:

y = 227.5 + 0.65*x

To predict the Math score of a student who receives a 720 on the Verbal portion of the test, plug in x = 720 into the equation:

y = 227.5 + 0.65*720 = 693

So the predicted Math score is 693.

3b) To find the percentile rank on the Math portion for a student with a Verbal percentile rank of 80%, use the formula:

z = (x-mean)/SD

Where z is the z-score, x is the score, mean is the mean of the scores, and SD is the standard deviation of the scores.

Plugging in the given values for the Verbal scores:

z = (x-525)/105

Solving for x:

x = 105*z + 525

Since the Verbal percentile rank is 80%, the z-score is 0.84 (from a z-table). Plugging this into the equation:

x = 105*0.84 + 525 = 613.2

So the Verbal score corresponding to the 80th percentile is 613.2.

To find the Math score corresponding to this Verbal score, plug in x = 613.2 into the linear regression equation:

y = 227.5 + 0.65*613.2 = 623.6

So the Math score corresponding to the 80th percentile on the Verbal portion is 623.6.

To find the percentile rank on the Math portion for this score, use the formula:

z = (x-mean)/SD

Plugging in the given values for the Math scores:

z = (623.6-570)/85 = 0.63

Using a z-table, the corresponding percentile rank is approximately 73.5%.

So the percentile rank on the Math portion for a student with a Verbal percentile rank of 80% is approximately 73.5%.

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Answer:

I believe opposing angles are parallel, so it would be 98

Step-by-step explanation:

The reason that should be used to complete statement 2 "∠2 and ∠3 are supplementary" is linear pair postulate.

In Mathematics, the linear pair theorem is sometimes referred to as linear pair postulate and it states that the measure of two angles would add up to 180° provided that they both form a linear pair.

This ultimately implies that, the measure of the sum of two adjacent angles would be equal to 180° when two parallel lines are cut through by a transversal.

According to the linear pair theorem, we have the following supplementary angles:

∠2 + ∠3 = 180°

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