Line AB is a straight
line.
9
1. m∠AOB = ____
Statement
1. ________
Reason
2. m∠AOE+m∠EOF+m∠FOB=m∠____ 2. ________
3. x + ____ +20° = ____ 3. Substitution
4. x = ____ 4. Algebra

Our function is a parabola, therefore, it has only one critical point which is its vertex. Since the coefficient of the squared term is negative, the vertex is the maximum point.The critical points of a function are given by the zeros of the first derivative. The first derivative of our function is:

The solutions for the following equation are the critical points of the original function:

The maximum point happens at x = - 3.

To find the corresponding value, we just have to evaluate x = - 3 into our function:

The maximum value of the function is 1, and it occurs at x = - 3.

Answer: The function has a maximum value

               The function's maximum value is 1

               The function's maximum value occurs at x=-3

Step-by-step explanation:

Given equation: [tex]g(x) = -3x^ - 18x - 26[/tex]

We shall use the differentiation method to find the answer.

Differentiating the equation, we get   [tex]g'(x) = - 6x - 18[/tex]

equating g'(x) = 0,

[tex]-6x - 18 = 0\\-6x = 18 \\x = -3[/tex]

Hence the minimum/ maximum value of the function lies in x = -3

on equating x>-3, g'(x) is negative

on equating x<-3, g'(x) is positive

this proves that first, the function was increasing and after x = -3, the function started to decrease hence at x=-3, the function g(x) was at its maximum value

The function's maximum value at x=-3 is

[tex]g(x) = -3x^2 - 18x - 26\\g(-3) = -3(-3)^2 - 18(-3) - 26\\g(-3) = -3(9) +54 -26\\g(-3) = 54 - 27 -26\\g(-3) = 1[/tex]

The correct transformation for  f(x) = 3x+1 to g(x) = −3x−5 is a reflection over the y-axis, and a translation 4 units down. Option D

This is further explained below.

A point, line, or geometric figure may be transformed in one of four ways, each of which affects the shape and/or location of the object.

Pre-Image refers to the object's initial shape, while Image, after transformation, refers to the object's ultimate shape and location.

Generally, the equation for the function is mathematically given as

f(x) = 3x+1

The transformed function

g(x) = −3x−5

In conclusion, The transformations consist of Reflection along the y-axis.

The translation of down four units

Hence, a reflection over the y-axis, and a translation 4 units down. Option D

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Answer:

-10x - 29 = -18x + 91

x = 15

Step-by-step explanation:

29 less than -10 times a number is equal to -18 times the number plus 91:

-10x - 29 = -18x + 91

add 21 to both sides:

-10x - 29 + 29 = -18x + 91 + 29

-10x  = -18x + 120

add 18x to both sides:

-10x + 18x  = -18x + 120 + 18x

8x = 120

divide both sides by 8:

8x/8 = 120/8

x = 15

The cost c of these t-shirts in her currency of Krona is; C: 608.313 Krona

We are told that;

A foreign exchange student wants to buy gifts for her family.

She gets a deal at;

7 shirts = $97.93

Now, she wants to buy 5 shirts for her family at that given deal. Thus;

Cost of 5 shirts in dollars = (97.93 * 5)/7 = $69.95

Now, the exchange rate of dollar to krona is given as;

1 U.S. Dollar = 8.6964 Krona

Thus; $69.95 = (69.95 * 8.6964)/1 = 608.313 Krona

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Since the situation can be since as an  arithmetic sequence, her salary after 3 years is $73,000. After t years, her salary is a function of t, that is a(t) = 64000 + 3000 t

The given situation can be seen as an arithmetic sequence. The nth term of an arithmetic sequence is given by the formula:

a(n) = a(1) + (n - 1) . d

Where:

a(1) = the first term

d = the common difference.

The problem can be translated into an  arithmetic sequence with:

a(1) = $67000

d = $3000

Kylie's salary after 3 years is a(3),

a(3) = a(1) + (3 - 1) . d

a(3) = Kylie's salary  + 2 . 3000 = 73000

Hence, after 3 years, Kylie's salary is $73,000

Her salary after t years, means n = t. Therefore,

a(t) = a(1) + (t - 1) . d

a(t) = 67000 + (t -1) . 3000

a(t) = 64000 + 3000 t

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Answer:

I think the answers are the last two.

Step-by-step explanation:

A rational number is any faction with a denominator not being 0. For example, 1/2, 1/5, 3/6, etc. Also, the number 0 is also a rational number.

If you think any other ones are also the answer, just use my explanation to help it clear stuff up. :)

The slope of AB = 2

The slope of CD = 2

Both lines are parallel lines.

The lines that are perpendicular to each other have slope values that are negative reciprocal of each other.

For example, if the a line's slope is a, the line that is perpendicular to it will have a slope of -1/a. This is because the negative reciprocal of a is -1/a, and (a)(-1/a) = -1.

On the other hand, the lines that are parallel to each other will have the same slope value.

Given the following:

A(−6 , −9)

B(8, 19)

C(0, −4)

D(2, 0)

Find the slope (m) of AB:

Slope of AB = (19 -(-9))/(8 -(-6))

Slope of AB = 28/14

Slope of AB = 2

Find the slope (m) of CD:

Slope of CD = (0 -(-4))/(2 - 0)

Slope of CD = 4/2

Slope of CD = 2

The graph of both lines are shown below.

Thus, the slope of AB and CD are the same, therefore, we can conclude that lines AB and CD are parallel to each other.

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There is a 0.0003 chance that the sample mean was 18.2 ounces or more if the actual mean is 18 ounces.

So, let Y be a random variable with box weights.

These are the sample size and mean:

N's standard deviation is then roughly followed by Y ( μ = 18, SD = 0.32).

Z score is displayed as:

Where z has a mean of 0 and a standard deviation of 1 and is a normal standard variable.

Given that the standard deviation is given and that sample size n is 30. y roughly follows the Normal distribution.

If the sample mean was 18.2 ounces or more and the actual mean was 18 ounces, the probability that this was the case is given as:

[tex]\begin{aligned}&P[Y \geq 18.2]=P\left[\frac{\sqrt{n(y-u)}}{S D} \geq \frac{\sqrt{30}(18.2-18)}{0.32}\right. \\&=P\left[z \geq \frac{\sqrt{30}+0.2}{0.32}\right] \\&=P\left[z \geq \frac{1.0954}{0.32}\right] \\&=P[z \geq 3.4233] \\&=0.0003\end{aligned}[/tex]

Therefore, there is a 0.0003 chance that the sample mean was 18.2 ounces or more if the actual mean is 18 ounces.

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Answer:

£75 > £70 Therefore Sally is wrong.

Step-by-step explanation:

1. First we need to find the volume of the sand pit  

     60x40x100= 24,000[tex]cm^{3\\[/tex]

 Volume= 24,000[tex]cm^{3\\[/tex]

2. We need to convert 8 liters to [tex]cm^{3\\[/tex] so, all the units are the same

     1 liter= 1,000[tex]cm^{3\\[/tex]

     8 liters= 8,000[tex]cm^{3\\[/tex]

3. We then do 24,000[tex]cm^{3\\[/tex] divide by 8,000[tex]cm^{3\\[/tex] to see how many bags, we need

    24,000[tex]cm^{3\\[/tex]/ 8,000[tex]cm^{3\\[/tex] = 30

so, Sally needs 30 bags

4. We know one bag cost £2.50 to know how much 30 bags cost we do

   £2.50 x 30 = £75

so, we know 30 bags cost £75

5. Sally statement was said that it would cost less than £70 which is false as it costs £75

6. Therefore the final answer is £75>£70 so Sally is wrong.

Answer:

a) No equation/Contradiction

b) One Solution/Conditional

c) Infinite Solutions/Neither

Step-by-step explanation:

a) you combine like terms: 7x+9=7x-8

    then subtract 7x from both sides, since 9 isn't equal to -8 there is no solution that would make it a contradiction

b) Combine likes: 13x-7=12x+21

    subtract 12 x: x-7=21

    add 7: x=14

c)  Combine like terms: -3x+24=-3x+24

     24=24

The percentile rank of a value with a z-score of 1.33 as given in the task content is; 9.18% (10th percentile).

It follows from the task content that the percentage rank of.the value whose z-score is; 1.33 as in the task content is to be determined.

As evident in the image attached (z-score table) , it can be inferred that a z-score of 1.33 corresponds to 40.82% on the table.

Also, since the z-score is positive, the percentage of data values which are above the z score 1.33 is 50% - 40.82%.

And ultimately, the percentile rank of a value which has a z-score of 1.33 as given in the task content is therefore; 9.18%.

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The probability of getting heads on both occasions will be 0.25.

It should be noted that probability simply means the likelihood that a particular event will happen.

In this case, if I flip a coin, i have a 50 percent chance that it will land on heads and after the first coin flip, we still have a 50 percent chance that the next flip will result in a head.

The probability will be:

= P(head) × P(head)

= 50% × 50%

= 1/2 × 1/2

= 1/4

= 0.25

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The table of values for the given equation, y = 1/x, is

x            y

-3         -1/3

-2         -1/2

-1           -1

0           ∞

1            1

2          1/2

3          1/3

From the question, we are to determine the table of values for the given function

The given equation is y = 1/x

We will determine the values of y for certain values of x

When x = -3

y = 1/x

y = 1/-3

y = -1/3

When x = -2

y = 1/x

y = 1/-2

y = -1/2

When x = -1

y = 1/x

y = 1/-1

y = -1

When x = 0

y = 1/x

y = 1/0

y = ∞

When x = 1

y = 1/x

y = 1/1

y = 1

When x = 2

y = 1/x

y = 1/2

When x = 3

y = 1/x

y = 1/3

Thus,

The table of values is

x            y

-3         -1/3

-2         -1/2

-1           -1

0           ∞

1            1

2          1/2

3          1/3

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Answer:

18

Step-by-step explanation:167-5=162

95-5=90

18is hcf of 162 and 90 then answer is 18

Answer:

0

Step-by-step explanation:

because the rule says have u understand

Step-by-step explanation:

Momentum = Mass (kg) × ∆Velocity (m/s)

Momentum = 0.142kg × (45.1 -- 0)m/s

Momentum = 0.142 × 45.1

Momentum = +6.4042kgm/s

The magnitude is positive because only the pitcher can give the baseball its final velocity which appeared to be 45.1m/s

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From the given options,√75 and 5π are the irrational numbers with a value greater than 5.

Irrational numbers are real numbers that cannot be represented as simple fractions. It cannot be expressed mathematically.

We need to find an irrational value which is greater than 5 from the options given as follows:

A. √75

B. 5.9

C. 5pi

D. 5

Options B and D are not irrational numbers so both are incorrect options.

For Option A,

[tex]\sqrt{75}[/tex] = 8.66

For Option C,

5π = 15.70

We can see that both options A and C have irrational value greater than 5.

As a result, from the options given,√75 and 5π are irrational numbers with a value greater than 5.

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MATHEMATICALLY

[tex]s - p = 40[/tex]

IT SIMPLY MEANS THAT THE DIFFERENCE BETWEEN s as a large number and p as a small number is 40.

For given triangle, the value of x is 22.

In this question, we have been given three angles of triangle.

We need to find the value of x.

We can observe that (6x - 7)° is an exterior angle.

So, the third angle of the triangle is 180° - (6x - 7)°

We know that the sum of the all angles of the triangle is 180°

2x° + (103 - x)° + [180° - (6x - 7)°] = 180°

2x + 103 - x + 180 - 6x + 7 = 180

2x - x - 6x + 103 + 180 + 7 = 180

-5x + 290 = 180

-5x = 180 - 290

-5x = -110

x = 22

Therefore, for given triangle, the value of x is 22.

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Answer:

arc RPQ = 305°

Step-by-step explanation:

• the angle at the centre is equal to the measure of the arc that subtends it.

arc RP = ∠ ROP = 125°

∠ QOS and ∠ ROP are vertically opposite angles and are congruent, so

∠ QOS = 125° and so arc SQ = 125°

RS is a straight angle , then

∠ POS = 180° - 125° = 55°

arc PS = 55° ( arc subtending the angle at centre

Then

arc RPQ = RP + PS + SQ = 125° + 55° + 125° = 305°

The equation of a line that is parallel to line y=3x+5 and goes through the point (6,-7) is y = 3x + 2

A line's equation is an algebraic way of expressing the collection of points that make up a line in a coordinate system. The many points that collectively make up a line on the coordinate axis are represented as a group of variables (x, y) to create an algebraic equation, also known as an equation of a line. Any line's equation can be used to determine whether a given point is on the line or not.A linear equation with a degree of one is the equation for a line.

Given that : the equation of a line is parallel to line y=3x+5 and goes through the point (6,-7)

y=3x+5 is the equation for the given line.

This type of line is called a slope intercept. The line has a slope of m=3.

The slope of parallel lines is equal. As a result, all lines with slope m=3 will be perpendicular to one another.

y=3x+2 is an example of a line that is parallel to the supplied line.

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Let's use the variable x to represent the price of the television set before taxes.

If the tax rate is 4%, then the original price is multiplied by 1.04, so it is equal 1.04x.

The final price is $520, so we have:

So the price before taxes is $500.00.

Answer:

take x=1

2(1)-y=9

2-y=9

-y=9-2

y= - 7

= (1,-7)

Answer:

-9

Step-by-step explanation:

16-25=-9

Answer: -9

Step-by-step explanation:

In case whereby At a garage sale, Liyah priced her scooter for $15.50. She ended up selling it for $10.75 the percent of decrease in the price of the scooter is 30.65%.

The price that she bought the scooter is given as $15.50

The price that she sold the scooter is given as  $10.75

The the amount that was lost will now be ( $15.50-  $10.75 )= $4.75

Then the percent of decrease will now be calculated as  ($4.75/ $15.50 *100%)

Then the  percent of decrease will now be 30.65%

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The final expression of the simplified version is 28x + 8y + 2.

We know that, to simplify means to obtain the lowest possible form of the of the expression. The expression is written in its simplest form  when there are no more ambiguities left in the way that it is written.

Given the expression;

-2(3x + 12y - 5 - 17x - 16y + 4)

We can now expand the expression to have;

-6x - 24y + 10 + 34x + 32y - 8

This could further simplify to

-6x + 34x  - 24y + 32y + 10 - 8

To obtain the  final simplified expression, we have;

28x + 8y + 2

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Answer:

-1.5,-3,-16,011

Step-by-step explanation:

that is the answer as u know it has negative sign and -3 is smaller

Answer: -6, -3, -1.5, 0, 11

Step-by-step explanation:.