4. At which point does the function y = -x² + 6x - 5 reach its maximum value?

Answer:

See below ~

Step-by-step explanation:

Q1

⇒ Remember that sides opposing larger angles are greater in size

⇒ 75° > 54° > 51°

⇒ AC > BC > AB

Q2

⇒ The exterior angles lie outside the triangle

⇒ ∠1 + ∠2 = ∠6 (Exterior Angle Property)

⇒ ∠1 + ∠2 = ∠P (Exterior Angle Property)

⇒ ∠3 = ∠5 (Vertical Angles)

Answer:

78

Step-by-step explanation:

= 12 x^2 - 30         put in ' - 3 ' for  'x'

= 12 ( -3 )^2 - 30

 = 12 (9) - 30 = 78

Answer:

78

Step-by-step explanation:

Expression:

Evaluate x = 3 according to the question:

[tex]6 \{2 (- 3) {}^{2} - 5) \}[/tex]

Solve this problem, applying PEMDAS.

Hence,the answer to the given expression is 78.

-Regards,Hannah :)

Answer:

13.2 units

Step-by-step explanation:

12 is to 7.2 as   (12+10) is to x

12/7.2   =  (12+10)/x

x = 22 * 7.2/12 = 13.2 units

Answer:

25 degrees

Step-by-step explanation:

arc divided by 2 = angle

50/2=25

Answer:

25

Step-by-step explanation:

Since triangle DBC is isosceles, angles DBC and DCB must be congruent. Angle BDC is 40 so the sum of the measures of the aforementioned angles must be 180 - 40 = 140; divide that by two and you get that the measure of angle DBC is 70. Angles DBC and ABD are supplementary, as they lie on a straight line, so we can deduce the measure of angle DBA is 180 - 70 = 110. The measure of angle DAB is 180 minus the measures of angle DBA and ADB, we figured out angle DBA is 110 degrees and the problem tells us angle ADB is 45 degrees, so we can subtract to get the measure of angle DAB to be 180 - (110 + 45) = 25.

Answer:

25

Step-by-step explanation:

i dont know how to explain i just know thats the answer hahaha

Answer:

122.5 squared

Step-by-step explanation:

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Answer:

x = -75

Step-by-step explanation:

[tex]\frac{3}{5}[/tex] x = - 45 ( multiply both sides by 5 to clear the fraction )

3x = - 225 ( divide both sides by 3 )

x = - 75

Answer:

A

Step-by-step explanation:

Answer:

11,000

Step-by-step explanation:

10% of 10,000 is 1,000 so 5% is 500 and add 2 of 5% you get 1,000 and add it to the old price thus you get 11,000.

The area of this hub cap is about  510.44625 cm².

The area of circle is pi times the square of the radius.

Area of circle =π r²

Circumference (C) = 2π r

80.07 = 2 (3.14) r

76.87/ (2x 3.14) =r

r = 12.75 cm

now, Area be

=π r²

= 3.14*12.5*12.75

=510.44625 cm²

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The percentage of the original block cookie that is packaged and ready to be distributed to stores is: 12.6%.

To calculate the percentage of the original 100lb cookie that is packaged and ready to be distributed, we must perform the following operations:

We must calculate how much each package of 5 cookies weighs, for this we multiply the weight of each cookie (3 ounces) 0.18 pounds by the number of cookies in each package (5).

Next, we need to calculate how much the box containing 14 packages of cookies weighs by multiplying the weight of each package (0.9 lb) by the number of packages in each box (14).

Lastly, we need to calculate how much percentage the weight of each box is equal to the weight of the original 100 lb cookie that Latonya made. For that we divide 100 lbs. by 100 and multiply the result by the final weight of the box (12.6lbs).

Based on the above, each box contains 12.6% of the first 100-lb cookie Latonya made.

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The given inequality 5x - 5y > 70 when written in Slope intercept form is gotten as; y < x + (-14)

The formula for equation of a line in slope intercept form is given by;

y = mx + c

where;

m is slope

c is y-intercept

We are given the inequality as;

5x - 5y > 70

Thus;

Subtract  5x from both sides to get;

-5y > 70 - 5x

divide both sides by -5 to get

y < x + (-14)

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The surface area will be equal to option B which is 1008 square centimeters.

The space occupied by any two-dimensional figure in a plane is called the area. The area of the outer surface of any body is called the surface area.

The surface area of the prism will be calculated as:-

SA = area of the three rectangular faces + area of the triangular faces

Area of the rectangular faces = ( 15 X 25 ) + ( 25 X 12 ) + ( 25 X 9 )

                                                 = 375 + 300 + 225

                                                 = 900 square cm

Area of the triangular  [tex]=\sqrt{(s(s-a)(s-b)(s-c)[/tex]

                                     = [tex]\sqrt{(18(18-15)(18-12)(18-9)}[/tex]

                                     = √2916

                                     = 64

Total area of the rectangular face = 2 x 54 = 108

So the total SA area of the prism will be = 900 + 108= 1008 square cm.

Therefore surface area will be equal to option B which is 1008 square centimeters.

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Answer:

Exact Area =

16pi - 32 square meters

Decimal Approx:

A = 18.3 sq m

Step-by-step explanation:

In degrees, it's 360° all the way around a circle. The 270° in the image is to show you that the small piece (the triangle and yellow segment) are in a 90° part of the circle. That is 1/4 of the circle, this helps with area two ways. We'll find 1/4 of the circle area and also, that makes the triangle base 8 and height 8. This helps us find triangle area. See image.

Answer:

c and a

Step-by-step explanation:

Answer:

it's both A and C

Step-by-step explanation:

2 x 3/8 is the same as 3/8 + 3/8

A percentage is a way to describe a part of a whole. The percentage decrease is 20%.

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

One year, the population of a city was 358,000. Several years later it was 286,400. Therefore, the percentage decrease is,

Percentage decrease = (358,000-286,400)/(358,000) × 100% = 20%

Hence, the percentage decrease is 20%.

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Answer + Step By Step Explanation:

There is no single value for y as the input could differ (x)

y = -3/4x

if x = 0, y = -3/4(0) than y = 0

if x = 1, y = -3/4(1) than y = -3/4

...

if x = 5, y = -3/4(5) than y = -15/4

Answer:

0.1

Step-by-step explanation:

You are adding on 0.1 for each line and since G is the first line after 0, it is 0.1.

Answer:

[tex]5.6 \times 10^{-8}~ m[/tex]

Step-by-step explanation:

[tex]0.000000056\\\\=\dfrac{56}{1000000000}\\\\\\=\dfrac{56}{10^9}\\\\\\=56 \times 10^{-9}\\\\\\=56 \times 10^{-1} \times 10^{-8}\\\\\\=5.6 \times 10^{-8}~[/tex]

Answer:  [tex]\frac{n!}{(n-r)!}[/tex]

The exclamation marks indicate factorial.

For instance, 4! = 4*3*2*1 = 24. You start with the given number and multiply your way down to 1.

For more information, check out the nPr permutation formula.

Using it's concept, it is found that the probability of being a girl and choosing lemonade is given by:

b. 0.2.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, out of 130 people, 26 are girls who choose lemonade, hence the probability is given by:

p = 26/130 = 0.2, which means that option b is correct.

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Answer:

[tex]slo pe \: = \frac{2}{7} [/tex]

Step-by-step explanation:

[tex]y1 = 3\\ x1 = - 8 \\ y2 = 7 \\ x2 = 6[/tex]

[tex]slope = \frac{y2 - y1}{x2 - x1} [/tex]

[tex]sope = \frac{7 - 3}{6 - ( - 8)} [/tex]

[tex]slope = \frac{4}{6 + 8} [/tex]

[tex]slope = \frac{4}{14} [/tex]

[tex] = \frac{2}{7} [/tex]

Answer:

[tex]\textsf{slope}=\dfrac{2}{7}[/tex]

Step-by-step explanation:

[tex]\textsf{let}\:(x_1,y_1)=(-8,3)[/tex]

[tex]\textsf{let}\:(x_2,y_2)=(6,7)[/tex]

Using the slope formula:

[tex]\textsf{slope}=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{7-3}{6-(-8)}=\dfrac{4}{14}=\dfrac{2}{7}[/tex]

Therefore, the slope between the two points (-8, 3) and (6, 7) is 2/7

Answer:

13.) 314.2 in²

15.) 181.5 ft²

Step-by-step explanation:

The area of a circle is found using the equation:

A = πr²

In this equation, "π" represents the number pi (3.14....) and "r" represents the radius (half the diameter).

For 13.), you have been given the radius. Thus, you can substitute it into the equation and solve for "A".

A = πr²

A = π(10)²

A = π x (100)

A = 314.2 in²

For 15.), you have been given the diameter. To find the radius, you need to divide this value by 2. Once you find the radius, you can plug it into the equation and simplify like above.

diameter = 15.2 ft
radius = 7.6 ft

A = πr²

A = π(7.6)²

A = π x (57.76)

A = 181.5 ft²

Answer: decrease the resources invested

Step-by-step explanation:

The box-and-whisker plot that illustrates the given data set is shown in the image below (see attachment).

A box-and-whisker plot consists of the following values of a data set: min, max, lower quartile, median, and upper quartile.

Here, Given the data set,

30, 22, 22, 27, 28, 23, 24, 25, 26, 23

the five-number summary for the box-and-whisker plot would be:

Minimum: 22

Quartile Q1: 22.75

Median: 24.5

Quartile Q3: 27.25

Maximum: 30

Thus, the box-and-whisker plot that illustrates the given data set is shown in the image below (see attachment).

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Answer:

90π in²

Step-by-step explanation:

  r = 3 in

  h = 10 in

     [tex]\sf \boxed{\text{\bf Surface area of cylinder =$\pi r^2h$}}[/tex]

                                                   [tex]= \pi 3*3*10\\\\= 90 \pi \ in^2[/tex]

In this question it is given that the radius of a cylinder is 3 inches. The height of the cylinder is 10 inches. We are asked to calculate the surface area of the cylinder in terms of π .

Radius = 3 inches

Height = 10 inches

We know,

[tex] \star \: \small \boxed{\rm{ Surface \: area \: of \: a \: cylinder = πr²h}}[/tex]

Substituting the values we get

[tex] \small\sf{ Surface \: area \: of \: a \: cylinder = π × 3² × 10}[/tex]

[tex] \small\rm{ Surface \: area \: of \: a \: cylinder = π × 3 \times 3 × 10}[/tex]

[tex] \small\rm Surface \: area \: of \: a \: cylinder = π × 90[/tex]

[tex] \small\sf{ Surface \: area \: of \: a \: cylinder = \bf{90 π \: inches²}}[/tex]

Answer:

≈0.71 or [tex]\frac{\sqrt{2}}{2}[/tex].

sin(45°) =  approximately 0.71. The value is also equal to [tex]\frac{\sqrt{2}}{2}[/tex].

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Answer:

Step-by-step explanation:

The median is defined as the middle value of a data set when all the data is arranged in numerical order.

If there is an even number of values, and therefore no middle value, then the median is calculated as the mean value of the two middle values.

Answer:

[tex] {x}^{ - 2} = \frac{1}{ {x}^{2} } \: \: –> {7}^{ - 2} = \frac{1}{ {7}^{2} } = \frac{ 1}{49} \\ \\ {x}^{ - 1} = \frac{1}{ {x}^{1} } \: –> {7}^{ - 1} = \frac{1}{ {7}^{1} } = \frac{1}{7} \\ \\ {x}^{0} –> {7}^{0} = 1 \\ \\ {x}^{1} –> {7}^{1} = 7 \\ \\ {x}^{2} –> {7}^{2} = 49[/tex]

If the  -8 is under the square root, then...

[tex]\displaystyle L = \lim_{x\to -3} \sqrt{x^2-8}\\\\L = \sqrt{(-3)^2-8}\\\\L = \sqrt{9-8}\\\\L = \sqrt{1}\\\\L = 1\\\\[/tex]

OR

If the -8 is not under the square root, then...

[tex]\displaystyle L = \lim_{x\to -3} \sqrt{x^2}-8\\\\L = \sqrt{(-3)^2}-8\\\\L = \sqrt{9}-8\\\\L = 3-8\\\\L = -5[/tex]

Either way, we replace x with -3 and simplify.

For more information, refer to the direct substitution rule for limits.

The limit of   [tex]\lim_{x \to \-(-3)} \sqrt{x^{2} -8}[/tex] is one.

A limit is the value that a function approaches as the input approaches some value. Limits are essential to calculus and mathematical analysis, and are used to define continuity.

The given limit is [tex]\lim_{x \to \-(-3)} \sqrt{x^{2} -8}[/tex]

Now replace x with -3 as limit value is -3

√(-3)²-8

Square root over minus three square minus eight

The three square is nine

√9-8

When eight is subtracted from nine we get one.

√1

The square root of one is always one

[tex]\lim_{x \to \-(-3)} \sqrt{x^{2} -8}[/tex]=1

Hence, [tex]\lim_{x \to \-(-3)} \sqrt{x^{2} -8}[/tex] is one.

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