Express 2x² - 12x + 7 in the form a (x + b)² + c, where a, b and c are constants.

Answer:

[tex]\displaystyle y=\frac{30x}{6(x-4)}[/tex]

Step-by-step explanation:

Keep in mind that a rational function with a vertical asymptote at [tex]x=4[/tex] means the denominator must be 0 when [tex]x=4[/tex] is plugged in.

This means we have [tex]\displaystyle y=\frac{6}{x-4}[/tex] so far.

To account for the horizontal asymptote at [tex]y=5[/tex], we need to adjust the numerator and denominator so that they are the same degree and that the leading coefficients have a ratio of 5. We can do this by multiplying the numerator by 5x and the denominator by 6.

This leaves us with [tex]\displaystyle y=\frac{30x}{6(x-4)}[/tex] as the translated equation since the end behavior of the function is [tex]\displaystyle y=\frac{30x}{6x}=5[/tex]. See attached graph.

Answer:

[tex] d = sin(39) \times 30[/tex]

In simplifying the given expression, the error made was in Step 4. 7c - 41 is wrong. The correct answer should be -c - 59.

In simplifying expressions, like the one given, first apply the distributive property to clear out the bracket.

Next is to combine like terms. In step 4, there was an error in the calculation while combining like terms.

-6c - 3c + 10c should give us -c NOT 7c.

Also, 3 - 12 - 50 should give us -59 not -41.

Therefore, the correct answer should be:

-c - 59.

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Answer:

Yes

Step-by-step explanation:

When there are 2 rows

When there are 3 rows

Therefore, there will be more erasers per row in 2 equal rows than in 3 equal rows.

Answer:

A.8.8 units

Step-by-step explanation:

Answer:

The correct answer is 8.8 units

Step-by-step explanation:

I just got it correct.

Answer:

15.24 millimeters

Step-by-step explanation:

6 * 2.54 = 15.24 mm.

Answer: should be 15.24

Step-by-step explanation: quick maths

Answer:

80%

Step-by-step explanation:

You multiple .8 by 100 to find percentage, giving you 80%.

Answer:

i don’t know

Step-by-step explanation:

I don’t know

Answer:

t + 11 = 29

Step-by-step explanation:

Since you are combining your total and your friend's total marbles together, this will be an addition equation.

t + 11 = 29

Answer:

33 degrees

Step-by-step explanation:

(4x+1) and (2x-19) add up to 180 degrees

[tex](4x+1)+(2x-19)=180\\6x-18=180\\6x=198\\x=33[/tex]

Answer:

volume = 14,137

Step-by-step explanation:

radius is the diameter divided by 2

30÷2=15

radius = 15 then square

15^2 = 225

formula of volume of a cone is 1/3*pi*raduis^2*the height

1/3(3.14)(225)(60)= 14,137

The volume of a cone with a diameter of 30 feet and a height of 60 feet is 14130.

The volume of the cone is given by;

[tex]\rm Volume \ of \ cone=\dfrac{1}{3}\pi r^2h\\\\Where;\ r = radius \ and \ h = height[/tex]

The volume of a cone with a diameter of 30 feet and a height of 60 feet.

The radius of the cone is;

[tex]\rm Radius =\dfrac{Diameter}{2}\\\\Radius=\dfrac{30}{2}\\\\Radius=15[/tex]

Substitute all the values in the formula

[tex]\rm Volume \ of \ cone=\dfrac{1}{3}\pi r^2h\\\\ Volume \ of \ cone=\dfrac{1}{3}\times 3.14 \times 15^2 \times 60\\\\Volume \ of \ cone=14130[/tex]

Hence, the volume of a cone with a diameter of 30 feet and height of 60 feet is 14130.

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Answer:

9

Step-by-step explanation:

18%of 50

18/100×50

0.18×50= 9

Answer:

9

Step-by-step explanation:

18% of 50

We can rewrite it as,

> 18/100 * 50

Solving,

Hence,18% of 50 = 9

Answer:

[tex]5x - 2y = - 10 \\ 5x = - 10 + 2y \\ x = \frac{ - 10 + 2y}{5} \\ \\ [/tex]

when y=0,-5,5,-10,10

then x=-2,-4,0,-6,2

Answer:

[tex] \implies \boxed{\rm t = \frac{ - 5}{8} }[/tex]

Step-by-step explanation:

8t-15=32t

Group the terms then subtract:

=>8t-32t=15

=>-24t=15

Divide both sides by -24:

[tex] \implies \rm \cfrac{ - 24t}{ - 24} = \cfrac{15}{ - 24} [/tex]

[tex] \rm \implies \: t = \cfrac{ - 5}{8} [/tex]

Answer: Check the step by step

Step-by-step explanation:

Measure of <2 = 37.3 because opposite sides of a line are congruent. To find < 1, you have to add that plus <2 ( 37.3 ) to equal 180. 180 -37.3 = 142.7

For <3, it is also gonna be 142.7 ( as said before, opposite sides are congruent. ) and for <4, it is gonna be 79.4.  Hope this helps! If you have any other questions,  let me know! :D

If the volume of the cube is 1/27 cubic inches. Then the volume of the prism will be 10 cubic inches.

A closed solid with two parallel rectangular bases joined by a rectangle surface is known as a rectangular prism.

A prism is completely filled with 270 cubes that have an edge length of 1/3in.

Then the volume of the prism will be given as

Volume of prism = 270 (volume of the cube)

Then the volume of the cube will be

Volume of cube = (edge)³

Volume of cube = (1/3)³

Volume of cube = 1/27 cubic inches

Then the volume of the prism will be

Volume of prism = 270 × (1/27)

Volume of prism = 10 cubic inches

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The ranges values of the function f(x) are: {-89,-9,7} - Option D.

The domain of a function is the set of input values for which the function is real and defined. In the other words, when you define the domain, you are indicating for which values x the function is real and defined.

While the domain is related to the values ​​of x, the range is related to the possible values ​​of y that the function can have.

Here, you need to replace the domain values in the given equation.

f(x)=-2x²+9

       f(x)=-2*(-3)²+9

        f(x)=-2*9+9

       f(x)=-18+9=-9

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Answer:

60

Step-by-step explanation:

lets say the number is X so:

X-3/4X=15

then multiple both sides by 4 then you will get

4X-3X=60

SO:X=60

Answer:

Step-by-step explanation:

let x be the number that we are trying to figure out.

the statement “The difference between a number and three fourths of itself is 15”  means  x + (3/4)x = 15

then

(1/4)x = 15

Then

x = 4 × 15

Then

x = 60

The slant height of the right circular cone will be  [tex]l=2\sqrt5}[/tex]

The formula for the slant height of the cone is given as:

[tex]l^2=r^2+h^2[/tex]

Here we have

r=2 units

h=4 units

By putting the values we will get

[tex]l=\sqrt{4^2+2^2[/tex]

[tex]l=\sqrt{16+4[/tex]

[tex]l=\sqrt{20}[/tex]

[tex]l=2\sqrt{5}[/tex]

Hence the slant height of the right circular cone will be  [tex]l=2\sqrt5}[/tex]

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Answer:

625 eggs are sold in a restaurant

2500-100%

x- 25%

62500=100x

x=625 eggs

Answer:

21875

Step-by-step explanation:

25% x 35 x 2500

= 0.25 x 35 x 2500

=21875

Using it's concept, it is found that the probability that a person who is above 35 years old has a hemoglobin level of 9 or above is of 0.247.

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

Researching the problem on the internet, we find a table, which says that there are 162 participants above 35 years old, and 40 have hemoglobin levels of 9 and above, hence the probability is given by:

p = 40/162 = 0.247.

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Answer:

Actually, its option C when the hemoglobin level is of 9 or above

Step-by-step explanation:

C. 0.531

a) The range of the given data set is 25.

b) The standard deviation of the given data set is 10.1.

The given data set is 141, 116, 117, 135, 126, 121.

a) The range is the difference between the highest and lowest values within a set of numbers.

Range = Highest value - Lowest value

= 141-116

= 25

So, the range is 25.

b) Set up the formula for sample standard deviation. The standard deviation of a set of values is a measure of the spread of its values.

[tex]s=\sqrt{\frac{(x_i-\bar x)^2}{n-1} }[/tex]

Here, mean ([tex]\bar x[/tex]) = [tex]\frac{141+116+117+135+126+121}{6}[/tex]

= 126

[tex]s=\sqrt{\frac{(141-126)^2+(116-126)^2+(117-126)^2+(135-126)^2+(126-126)^2+(121-126)^2}{6-1}}[/tex]

[tex]s=\sqrt{\frac{(15^2+(-10)^2+(-9)^2+(9)^2+(0)^2+(-5)^2}{5}}[/tex]

[tex]s=\sqrt{\frac{(225+100+81+81+25)}{5}}[/tex]

[tex]s=\sqrt{\frac{512}{5}}[/tex]

s=10.1

So, the standard deviation is 10.1.

Therefore,

a) The range of the given data set is 25.

b) The standard deviation of the given data set is 10.1.

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Answer:

10.2956

Step-by-step explanation:

formula:

d = √((x2-x1)2 + (y2-y1)2)

(x1, y2) and (x2, y2)

 (-5,2) and (4,-3).

Find the difference between coordinates:

(x2-x1) = (4 - -5) = 9

(y2-y1) = (-3 - 2) = -5

Square the results and sum them up:

(9)2 + (-5)2 = 81 + 25 = 106

Now Find the square root and that's your result:

Exact solution: √106 = √106

Approximate solution: 10.2956

Answer:

y=14; x=72

Step-by-step explanation:

y=(21×2)/3; x=(48×21)/14

Answer:

u drag the green dot thing over to the coordinate (6,8)

Step-by-step explanation:

i put a black dot where i think ur supposed to drag the green dot to

Answer:

Step-by-step explanation:

the discount percentage :

[tex]\frac{472-118}{472} \times100 = 75 \%[/tex]

The percentage decrease ( discount percentage ).

[tex]\large\boxed{\sf{formula = 100 \times \frac{(final - initial)}{initial} }}[/tex]

We'll have to subtract 472 ( initial value ) from 118 ( final value).

[tex]472 - 118[/tex]

[tex] = 354[/tex]

Now, we'll have to divide 354 ( difference ) by 118 ( initial value ) and multiply by 100.

[tex] 100 \times \frac{354}{118} [/tex]

[tex]\large\boxed{\sf{ = 75\% }}[/tex]

Hence, the discount percentage is 75.

Answer:

The A graph applies to the first and fourth statement

The B graph applies to the second and third statement

The number of ducks in a pond increasing is a 100% bar with an extra 40% added to it (looks like graph A from the previous question)

The number of mosquitos decreasing by 80% is a bar within the already existing 100% (looks like graph B from the previous question)

Step-by-step explanation:

none further needed

Answer:

A

Step-by-step explanation:

the area (A) of a kite is calculated as

A = [tex]\frac{1}{2}[/tex] × d₁ × d₂ ( d₁ and d₂ are the diagonals )

here d₁ = 2 + 2 = 4 and d₂ = 3 + 7 = 10 , then

A = [tex]\frac{1}{2}[/tex] × 4 × 10 = 2 × 10 = 20 cm²

Answer:

A) 20 cm^2

Step-by-step explanation:

Area of a kite is the product of the 2 diagonals divided by 2.

= (4*10)/2

= 20