if

sin150°=1/2 fiind sin75°​

The statement to prove that the sum of the interior angles of ΔABC is 180° should be completed as follows;

Statements                                                        Reasons

Points A, B, and C form a triangle.        ⇒        Given

Let DE be a line passing through B and parallel to AC. ⇒ definition of parallel lines

∠3 ≅ ∠5 and ∠1 ≅ ∠4             ⇒    alternate interior angle theorem.

m∠1 = m∠4 and m∠3 = m∠5  ⇒    congruent angles have equal measures.

m∠4 + m∠2 + m∠5 = 180°    ⇒    angle addition and definition of a straight line

m∠1 + m∠2 + m∠3 = 180°      ⇒  substitution

In Mathematics, congruence of angles can be defined as a theorem which states that two (2) angles are congruent when the measure of their angles are equal.

This ultimately implies that, two (2) congruent angles would always have equal measures as depicted in triangle ABC with line DE;

m∠1 = m∠4 and m∠3 = m∠5

By applying the Alternate Interior Angles Theorem to triangle ABC and line DE, we have the following:

∠3 ≅ ∠5 and ∠1 ≅ ∠4

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Answer:

a. The scale is 1 inch to 4 feet. This can be written as a ratio: 1:4

b. Using the ratio from part a, the scale proportion is: 1/4 = width of the drawing/50 feet

c. To find the width of the drawing, we will use cross multiplication and solving for the width, we have 1/4 * 50 feet = width of the drawing/50 feet = 1* 50/4 =12.5 inches.

The width of the drawing on the blueprint is 12.5 inches.

Step-by-step explanation:

The answer to each part is mentioned below.

Given is that Juan has a blueprint of a professional basketball court. The scale is 1 inch to 4 feet and the professional basketball court is 50 feet wide.

After the dilation, the relation between final and initial dimensions of the image is -

y = Kx

where -

{K} is a dimensionless quantity called scale factor.

{a} -

the scale as a ratio can be written as -

K = (1 inch/4 feet) = (1/12 feet/4 feet) = (1/48) = 1 : 48

K = 1 : 48

{b} -

We can write the scale proportion as -

(1/48) = (x/50)

{c} -

The width of the professional basketball court in the blueprint is -

x = 50/48

x = 1.05 feet

Therefore, the answer to each part is mentioned above.

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The equations give values of 1/2 and -11/8

you should be aware that two equations are solved simultaneously if they are solved together

The given equations are

-8x+10y=16 .............................1

-4x-5y=13 ..................................2

Multiply equation 2 by 2 to have

-8x -10y=26

Subtract equation 1 from equation 2

-8x+10y=16

-(-8x-10y=26)  To get

The we have 20y = 10

Make y the subject of the relation

y=1/2

Put y = 1/2 in equation 1

-8x +10(1/2) = 16

-8x +5 = 16

-8x = 16-5

-8x = 11

Making x the subject of the formula we have

x=-11/8

In conclusion the values of x and y are -11/8 and 1/2 respectively

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A scale factor of 7 is it an enlargement neither.

Scale factor is a ratio of two corresponding lengths, areas, or volumes of similar shapes. When two shapes are similar, one can be enlarged or reduced to create the other. The scale factor is the number by which a figure is multiplied or divided to form a similar figure. It is used in many areas of mathematics, including geometry, trigonometry, and algebra. It is also used in engineering and architecture to create drawings of scaled-down or scaled-up objects.

A scale factor of 7 does not necessarily indicate an enlargement or reduction; it simply states that the size of an object has been multiplied by a factor of 7. It could either increase or decrease the size of the object, depending on the original size of the object and the direction of the scale factor.

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Exploring Base Ten Blocks : Measure 1 x 1 x 1 cm with units of "ones."

Measure 1 cm by 1 cm by 10 cm for each rod, where tens are the unit of length.

Hundred times flats Count 1 cm by 10 cm by 10 cm.

Cubes are thousands; the dimensions are 10 cm x 10 cm x 10 cm.

Our base ten number system is spatially represented by Base Ten Blocks. The four separate concrete representations known as "Base Ten Blocks" are generally used in middle school arithmetic after being introduced in elementary school.

Measure 1 x 1 x 1 cm with units of "ones."

Measure 1 cm by 1 cm by 10 cm for each rod, where tens are the unit of length.

Hundred times flats Count 1 cm by 10 cm by 10 cm.

Cubes are thousands; the dimensions are 10 cm x 10 cm x 10 cm.

When names are given based on shape rather than value, it is possible to rename the pieces as needed. For instance, a class learning decimals can use the flat to represent a unit and then determine the value of the other components.

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The vertical line test can be used to determine whether a graph represents a function. A vertical line includes all points with a particular x value.

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From the graph solution of system of equations is (0, -2). Therefore, option D is the correct answer.

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

The given equation is y=2x-2.

Graph the line using the slope and y-intercept, or two points.

Slope: 2

y-intercept: (0, -2)

Now,

A) y=2(x+1)

2x-2=2(x+1)

No solution

B) y=2(x-1)

2x-2=2(x-1)

No solution

C) y=2(x-2)

2x-2=2(x-2)

No solution

D) y=-2(x+1)

2x-2=-2(x+1)

2x-2=-2x-2

4x=0

x=0

Substitute x=0 in y=-2(x+1), we get y=-2

Therefore, option D is the correct answer.

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Answer:

[tex]\textsf{a)\;\;passes\;through\;$(-2, 18.75)$\;and\;$(1, 1.2)$}[/tex]

     [tex]\textsf{$a$-value:\;\;3 \quad $b$-value: \;\;0.4}[/tex]

     [tex]\textsf{Equation: \quad $y=3 (0.4)^x$}[/tex]

[tex]\textsf{b)\;\;passes\;through\;$(0, 6)$\;and\;$(2, 8.64)$}[/tex]

     [tex]\textsf{$a$-value:\;\;6 \quad $b$-value: \;\;1.2}[/tex]

     [tex]\textsf{Equation: \quad $y=6 (1.2)^x$}[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function}\\\\$y=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}[/tex]

Given points:

Substitute both points into the exponential function formula to create two equations:

Divide the equations to eliminate a, then solve for b:

[tex]\implies \dfrac{18.75}{1.2}=\dfrac{ab^{-2}}{ab}[/tex]

[tex]\implies15.625=\dfrac{b^{-2}}{b}[/tex]

[tex]\implies15.625=b^{-2}b^{-1}[/tex]

[tex]\implies15.625=b^{-3}[/tex]

[tex]\implies15.625=\dfrac{1}{b^{3}}[/tex]

[tex]\implies b^{3}=\dfrac{1}{15.625}[/tex]

[tex]\implies b=0.4[/tex]

Substitute the found value of b into the second equation and solve for b:

[tex]\implies 1.2=0.4a[/tex]

[tex]\implies a=3[/tex]

Therefore, the exponential equation is:

[tex]y=3 (0.4)^x[/tex]

-------------------------------------------------------------------------------------------

Given points:

Substitute point (0, 6) into the exponential function formula and solve for a:

[tex]\implies 6=ab^0[/tex]

[tex]\implies 6=a(1)[/tex]

[tex]\implies a=6[/tex]

Substitute the found value of a and point (2, 8.64) into the exponential function formula and solve for b:

[tex]\implies 8.64=6b^2[/tex]

[tex]\implies b^2=\dfrac{8.64}{6}[/tex]

[tex]\implies b^2=1.44[/tex]

[tex]\implies b=\sqrt{1.44}[/tex]

[tex]\implies b=1.2[/tex]

Therefore, the exponential equation is:

[tex]y=6 (1.2)^x[/tex]

Answer:1200

Step-by-step explanation:

Answer:

[tex]\textsf{Function:} \quad y=120\left(1.016\right)^{4t}[/tex]

The balance of the account after 6 years is $175.64 (nearest cent).

Step-by-step explanation:

To write a function that represents the balance y (in dollars) of the investment account after t years, substitute the given values into the compound interest formula.

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ A=P\left(1+\frac{r}{n}\right)^{nt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]

Given values:

Substitute these values into the formula:

[tex]\implies y=120\left(1+\dfrac{0.064}{4}\right)^{4t}[/tex]

[tex]\implies y=120\left(1+0.016\right)^{4t}[/tex]

[tex]\implies y=120\left(1.016\right)^{4t}[/tex]

To calculate the balance of the account after 6 years, substitute t = 6 into the function:

[tex]\implies y=120\left(1.016\right)^{4 \cdot 6}[/tex]

[tex]\implies y=120\left(1.016\right)^{24}[/tex]

[tex]\implies y=120\left(1.46368961...\right)^{24}[/tex]

[tex]\implies y=175.642753...[/tex]

Therefore, the balance of the account after 6 years is $175.64 (nearest cent).

Answer:

x<2 or x>5

Step-by-step explanation:

3x+2<8 4x+4>24

4x>24-4

3x<8-2

4x>20

3x<6

x>5

x<2

Answer: x∈(-∞,2]U(5,∞)

Step-by-step explanation:

[tex]\displaystyle\\\left [ {{3x+2\leq 8} \atop {4x+4 > 24}} \right. \ \ \ \ \left [ {{3x\leq 6\ (1)} \atop {4x > 20}\ (2)} \right.[/tex]

Divide both parts of the equation (1) by 3 and divide both parts of the equation (2) by 4:

[tex]\displaystyle\\\left [ {{x\leq 2} \atop {x > 5}} \right. \\\\Hence,\\\\x\in(-\infty,2]U(5,\infty)[/tex]

The equations equivalent to the given equation are -2y+1/2(3x+7/2) and 1/4(-8y+6x+7). The solution has been obtained by using the simplification method.

What is simplification?

Simplifying in mathematics refers to the process of working with and understanding an equation in a way that makes it more understandable or transparent. The process of grouping similar terms together so that the problem can no longer be solved further is known as simplification.

We are given -2y + 3/2x + 7/4

In order to find which expression is equivalent to the given, we need to simplify the expressions.

a. -1/2xy+7/4

This is not the same expression as given.

b. 3/2x-2(y+7/2)

⇒ 3/2x - 2y - 7

This is not the same expression as given.

c. -1/4y+3/2 (y+x)

⇒ -1/4y + 3y/2 + 3x/2

This is not the same expression as given.

d. -2y+1/2(3x+7/2)

⇒ -2y + 3x/2 + 7/4

This is the same expression as given.

e. 1/4 (-8y+6x+7)

⇒-2y + 3x/2 + 7/4

This is the same expression as given.

Hence, the equations equivalent to the given equation are -2y+1/2(3x+7/2) and 1/4(-8y+6x+7).

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The standard deviation of the difference in means is (-1.96, 1.96).  There is no significant difference between coverage speed at 95%

The speed characteristics are given as_

[tex]$$ \begin{aligned}\bar{x}_1 & =35.5 & \bar{x}_2 & =38.7 \\\sigma_1 & =7.5 & \sigma_2 & =7.4 \\n_1 & =250 & n_2 & =280\end{aligned}$$[/tex]

The standard deviation is a summary measure of the differences of each observation from the mean. If the differences themselves were added up, the positive would exactly balance the negative and so their sum would be zero.

So

[tex]$$\begin{aligned}z=\frac{\overline{x_1}-\bar{x}_2}{\sqrt{\frac{\sigma_1^2}{n_1}+\frac{\sigma_2^2}{n_2}}} & =\frac{35.5-38.7}{\sqrt{\frac{(7.5)^2}{250}+\frac{(7.4)^2}{280}}} \\& =\frac{-3.2}{\sqrt{0.225+0.1956}} \\& =\frac{-3.2}{0.64852} \\\z & =-4.9343\end{aligned}$$[/tex]

at 95% confidence acceptance region is: [tex]$$(-1.96,1.96)[/tex]

But [tex]$z \notin(-1.96,1.96)$[/tex]

So, there is no significant difference between coverage speed at 95%.

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The standard deviation of the difference in means is 0.4696 and acceptance region is (-1.96 , 1.96). So, there was no significant difference between the average speed sample data at the 95% confidence level.

Speed data was collected on a section of road during and after repair work. Now the significance level for mean rate = 95% = 0.95 The equation for the standard deviation of the mean difference is:

σd = √(σ₁²/n₁ + σ₂²/n₂).

For the first data sample,

Sample mean for average velocity, X₁

= 35.5 mph

sample size, n₁ = 250

standard deviation, σ₁ = 2.5 mph

sample seconds, sample mean for

average velocity, X₂ = 38.7 mph

sample size, n₂ = 280

standard deviation, σ₂ = 7.4 mph.

It is statistically significant to see if there is a difference between the two population means. Using the two sample Z =( X₁-bar - X₂-bar )/√(σ₁²/n₁) + (σ₂²/n₂)}

Substituting all known values,

Z = ( 35.5 - 38.

7 )/(2,5)²/250 + (7,4)²/280

=> Z = - 3,2/√0,025 + 0.1956

=> Z = -3.2/0.4696

=> Z = - 6.8832

95% confidence interval, tolerance range is (-1.96, 1.96). However, Z∉(-1.96 , 1.96)

So, there is no signification difference for means between avaerage speed at 95%.

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Complete question :

Speed data were collected at a section of highway during and after utility maintenance work: The speed characteristics are given as, and as shown below. Determine whether there was any significant difference between the average speed at the 95% confidence level (Z=1.96). The standard deviation of the difference in means is given as σd = √(σ₁²/n₁ + σ₂²/n₂). DATA: uav₁= 35.5 mph, uav₂= 38.7 mph ,σ₁ = 2.5 mph, σ₂= 7.4 mph n₁ = 250, n₂ = 280

Option B : observed frequencies  are the frequencies obtained from the performance of an experiment for a goodness-of-fit test .    

The frequency, or outcomes, that are gathered during an experiment are known as observed frequencies. This is frequently the collection of data that is documented in mathematics. The distinction between an observed frequency and an expected frequency is described on the display poster. Counts derived from experimental data are known as observed frequencies. In other words, you really take measurements when the data is being collected. For instance, you might roll a die ten times and then tally the number of times each number appears. Following the experiment, the count is made. The observed frequencies are these numbers, and the sign for an observed frequency is O. There are k entries in the table. There are n total observed frequencies. Calculating predicted frequencies involves multiplying the probability.

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If z is a standard normal variable then the probability of P(-1.5 < z < 1.09) is 0.79533

Here it is given that Z is a standard normal variable. This imples that the mean of Z is 1 and the standard deviation is 0. Hence we get

μ = 1

σ = 0

Now we need to find the probability P(-1.5 < z < 1.09)

We know that P(a < X < b) = P(X < b) - P(X < a)

= P(z < 1.09) - P(z < -1.5)

We know that P(x < -a) = 1 - P(x < a)

= P(z < 1.09) + P(z < 1.5) - 1

Now looking up the s-score for 1.09 and 1.5 in the z-table we get

0.86214 + 0.93319 - 1

= 0.79533

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A. The range of the sample data is 4 mi/gal.

B. The variance of the sample data is 0.98 mi/gal.

C. The standard deviation of the sample data is 0.99 mi/gal.

D. The decrease of 4 mi/gal is not unusual because it is within two standard deviations of the mean (4 mi/gal is less than 2*0.99 mi/gal).

A. To find the range of the sample data, we need to find the difference between the largest and smallest values in the sample. In this case, the largest value is 4 mi/gal and the smallest value is 1 mi/gal. The range is the difference between these two values, which is 4 mi/gal - 1 mi/gal = 3 mi/gal.

B. To find the variance of the sample data, we first need to find the mean of the sample. The mean is calculated by summing all the values in the sample and dividing by the number of values in the sample. In this case, the mean is [tex]\frac{(2+1+2+1+3+3+4+2+2+2+2+2+2+2+2+3+2+2+2+2+2)}{20} = 2.05[/tex].

Next, we need to subtract the mean from each value in the sample, square the result, and divide it by the number of values in the sample. The variance is

[tex][(2-2.05)^2 + (1-2.05)^2 + (2-2.05)^2 + (1-2.05)^2 + (3-2.05)^2 + (3-2.05)^2 + (4-2.05)^2 + (2-2.05)^2 + (2-2.05)^2 + (2-2.05)^2 + (2-2.05)^2 + (2-2.05)^2 + (2-2.05)^2 + (2-2.05)^2 + (3-2.05)^2 + (2-2.05)^2 + (2-2.05)^2 + (2-2.05)^2 + (2-2.05)^2] = 19.6[/tex]

[tex]\frac{19.6}{20} = 0.98 mi/gal.[/tex]

C. To find the standard deviation, we take the square root of the variance. The standard deviation is  [tex]\sqrt{0.98} = 0.99 mi/gal[/tex]

D. The standard deviation measures the amount of variation or dispersion in the data. The standard deviation is used to determine how much the values in a sample differ from the mean. If a value is more than two standard deviations away from the mean, it is considered unusual. In this case, the value of 4 mi/gal is less than 2*0.99 mi/gal = 1.98 mi/gal away from the mean, so it is not considered unusual.

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Answer:

the answer to the question is 9.9 in the nearest tenth

Answer: $8,849

Step-by-step explanation: 17,698 divided by two people is 8,849, therefore each sister paid $8,849.

Answer: $8849

Step-by-step explanation: We are given that the total amount both sisters pay is $17698. They each pay for a fraction though. That fraction is 1/2 since they each pay for half. We multiply this fraction by the total which is 17698 to find our answer.

If there were three sisters and they each paid one-third, we would multiply the total price by 1/3 to find our answer.

To determine how long it will take for a ball to fall from the top of a building 74 ft tall to ground level, we can use the formula:

t = √(2*d/g)

where t is the time in seconds, d is the distance in feet, and g is the acceleration due to gravity (approximately 32.2 ft/s^2 on Earth).

Plugging in the values:

t = √(2*74 / 32.2)

t ≈ 3.63 seconds

So the ball will take approximately 3.63 seconds to fall to the ground level.

It's important to note that this calculation assumes that there's no air resistance and the ball is dropped vertically. In reality, air resistance and the ball's trajectory would affect the time it takes to fall.

A possible equation to represent the total number of roses the florist will need to use in this situation is 36 + 12x= y.

This is a short mathematical expression that relates variables represented by letters by using mathematical symbols such as  +, -, x, and the symbol =.

Based on this, a possible equation is 36 + 12x= y.

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The number of hours Ramiro worked overtime is 5 hours.

Ramiro earns $20 an hour during the week and $30 an hour for overtime on the weekends.

One week, Ramiro earned a total of $650. he worked a total of 30 hours, including both weekday and weekend hours.

The number of hours Ramiro worked on the weekend can be calculated as follows;

using equation,

let

x = number of hours worked during the week

y = number of hours worked during overtime

Hence,

20x + 30y = 650

x + y = 30

multiply equation(ii) by 20

20x + 30y = 650

20x + 20y = 600

subtract the equations

10y = 50

y = 50 / 10

y  =5

Therefore, the number of hours worked overtime is 5 hours.

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Answer:

h(x) =-5x^2 -1

Step-by-step explanation:

same function just move down 3 so y intercept changes only and 2-3= -1.

The rate, in inches per hour, at which rain fell during that time on Friday is 3/10 inches per hour.

Option d is the answer

Rate is the ratio that compares two quantities of different units. It can be used to express how fast something is changing, or how much of one quantity is present for a certain amount of another quantity.

In this case, the rate, in inches per hour, at which rain fell during that time on Friday will be:

rate = (3/4) / (2 1/2)

rate = 3/10 inches per hour

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Complete Question

Rain fell at a constant rate for 2 1/2 hours on Friday. During that time, the total amount of rain that fell was 3/4 inch. What is the rate, in inches per hour, at which rain fell during that time on Friday?

a 3 1/3

b 1 7/8

c 8 1/5

d 3/10

Answer: $32.60

Step-by-step explanation:

(4)(2.30) + (6)(3.90)

= 32.60

Answer:

for him it send 4 small packages it will cost 9.20

For him to send 6 large packages it will cost 23.40

23.40 + 9.20 = 32.60

Step-by-step explanation:

Formula: Quanity x Cost = Total

After Totals + Costs = Exact Total

The area of the warehouse floor is 1000 square yards. This can be calculated using the formula A = lw, where A is the area, l is the length, and w is the width. Therefore, in this case A = 40 x 25 = 1000.

The calculated answer is the result of a mathematical equation or calculation. Calculations can range from simple addition and subtraction to complex integrations and derivatives. By using mathematical formulas, equations, and algorithms, the calculated answer can be used to solve problems and make predictions. Calculated answers can be used in fields such as science, engineering, economics, and finance. Calculated answers can also be used to make decisions about investments, projects, and other business decisions. In addition, calculated answers can be used to analyze data and make decisions based on the results.

The area of the warehouse floor is 1000 square yards. This can be calculated using the formula A = lw, where A is the area, l is the length, and w is the width. Therefore, in this case A = 40 x 25 = 1000.

The total volume of the cartons is 12500 cubic yards. This can be calculated using the formula V = lwh, where V is the volume, l is the length, w is the width, and h is the height. Therefore, in this case V = 40 x 25 x 3 = 12500.

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As a result, the coordinates of the equations y = 2x and 3y = 7x + 3 throughout the range of  -3 ≤ x ≤ 4 are (-3,-6) and (-3,8), respectively.

When it comes to geometry, a coordinate system is a technique that uses one or more integers or coordinates to specify the exact location of points or other geometrical objects on a manifold, such as Euclidean space. Locating a point or item on a two-dimensional plane requires the usage of pairs of integer coordinates. Two numbers known as the x and y coordinates serve as a description of a point's location on a 2D plane. a collection of figures that signify exact locations. Most often, the figure contains two numerals. The first number denotes the distance from front to rear, and the second number denotes the distance from top to bottom. In (12.5), for example, there are 12 units below and 5 above.

given

y = 2^x and 3y = 7x + 3 over the interval -3 ≤ x ≤ 4.

as x = -3

y = 2^x= 2^-3 = -8  

y = 8

3y = 7x+3

3y= 7*-3 +3

3y = -21 + 3

y = -6

As a result, the coordinates of the equations y = 2x and 3y = 7x + 3 throughout the range of  -3 ≤ x ≤ 4 are (-3,-6) and (-3,8), respectively.

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The transformation that maps the quadrilateral into itself is [-1 0] and [ 0 -1] and the vertices of the quadrilateral is (-3,-4),(2,5),(-2,-5),(3,4)

a. A point symmetry about the origin is a transformation that maps a figure onto itself by reflecting it across the origin. This transformation is known as a central reflection or an isometry, and it is represented by the matrix (with respect to the standard basis)

[-1 0]

[ 0 -1]

b. To find the other two vertices of the quadrilateral, we can apply the transformation to the given vertices.

The transformation maps (2,5) to (-2,-5) and (-3,-4) to (3,4).

So, the other two vertices of the quadrilateral are (-2,-5) and (3,4)

So the quadrilateral will be (-3,-4),(2,5),(-2,-5),(3,4)

Note that a quadrilateral with point symmetry about the origin is called a kite.

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Answer:

x=-8

Step-by-step explanation:

Follow the steps in the image.

-Hope this Helped

The numeric value of the function f(x) = 3x² + 4x - 2 at x = x + 1 is obtained as follows:

f(x + 1) = 3x² + 10x + 3.

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

The function for this problem is defined as follows:

f(x) = 3x² + 4x - 2

The numeric value at x = x + 1 is found replacing both instances of x by x + 1, hence:

f(x + 1) = 3(x + 1)² + 4(x + 1) - 2

f(x + 1) = 3(x² + 2x + 1) + 4x + 4 - 4

f(x + 1) = 3x² + 6x + 3 + 4x

f(x + 1) = 3x² + 10x + 3.

Learn more about the numeric values of a function at brainly.com/question/28367050

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