Evaluate angles d and e, giving reason for your answer​

Answer:

See below

Step-by-step explanation:

The vertex form of a parabola is  y = a(x - h)^2 + k

If the leading coefficient is positive, the parabola opens upward, and (h, k) represents the vertex, or turning point.

1a. The leading coefficient is 4, which is positive, meaning the parabola opens upwards. From the vertex form, we can say the vertex(turning point) is (2, 7).

1b. The leading coefficient is -3, which is negative, meaning the parabola opens downwards. From the vertex form, we can say the vertex(turning point) is (-6, 4).

1c. The leading coefficient is -1, which is negative, meaning the parabola opens downwards. From the vertex form, we can say the vertex(turning point) is (-4, -3).

To write the vertex form of a parabola, we need to complete the square. A perfect square trinomial is in the form a^2 + 2ab + b^2. In these cases we are already given a^2 and 2ab.

2a. We can say x^2 corresponds to a^2 because it is a square and 2ab corresponds to 6x. From this, we can say a = x. Now, we can plug that in:

2ab = 6x

2(x)b = 6x

b = 3

Therefore, the last term b^2, is 3^2 or 9. We can add 9 and subtract nine to keep the equation equivalent:

y = x^2 + 6x + 9 - 9 - 2

Now, we can factor the square into (a + b)^2 and simplify:

y = (x + 3)^2 - 11

From this form, the vertex(turning point) will be (-3, -11). Since the leading coefficient is 1, which is positive, the parabola opens upwards, meaning the turning point is a minimum.

2b. We can say x^2 corresponds to a^2 because it is a square and 2ab corresponds to -2x. From this, we can say a = x. Now, we can plug that in:

2ab = -2x

2(x)b = -2x

b = -1

Therefore, the last term b^2, is (-1)^2 or 1. We can add 1 and subtract nine to keep the equation equivalent:

y = x^2 - 2x + 1 - 1 + 11

Now, we can factor the square into (a + b)^2 and simplify:

y = (x - 1)^2 + 10

From this form, the vertex(turning point) will be (1, 10). Since the leading coefficient is 1, which is positive, the parabola opens upwards, meaning the turning point is a minimum.

Answer:

51.33

Step-by-step explanation:

Step-by-step explanation

From the boat's standpoint, which is what we want anyway, there is a right triangle, with the distance from the lighthouse the adjacent side, the opposite is 200,' and the boat the point desired. The tangent is needed.

From the boat's standpoint, which is what we want anyway, there is a right triangle, with the distance from the lighthouse the adjacent side, the opposite is 200,' and the boat the point desired. The tangent is needed.tangent 18.33 degrees (33 minutes is 33/60 of a degree)=200x

Answer:

x = 82

Step-by-step explanation:

1/3(12/7 + 9/7) + 3⁴ =

1/3(21/7) + 3⁴ =

1/3(3) + 3⁴ =

1 + 81 = 82

Answer:

[tex]13x+4y+12[/tex]

Step-by-step explanation:

Combine all the like terms & then solve:

[tex](4x+2x+7x)+(-5y+9y)+(4+6+2)[/tex]

[tex]13x+4y+12[/tex]

[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { \: 13x + 4y + 12}}}}}}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

[tex]4x - 5y + 2x + 4 + 6 + 9y +7 x + 2[/tex]

Combining like terms, we have

= [tex] \:( 4x + 2x + 7x ) + (9y- 5y )+ (4 + 6 + 2)[/tex]

= [tex] \: 13x + 4y + 12[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}[/tex]

Answer:

In picture

Step-by-step explanation:

Brainliest please

Answer:

width?

8-W-52

2(w-8) +2w=52

(W-8)+W=52

2(8-W) +2w=52

Answer:

Suman 37 km/hr

Narayan 43 km/hr

(extremely sorry if this is wrong!!)

Step-by-step explanation:

We can use the formula distance divided by time is speed.

480/6 = 80.

Their speeds must add up to 80 km/hour

Lets set suman as a variable, lets say s.

Narayan has a speed 6 more than suman so we say 6+s

6+s+s = 80

subtract 6 from both sides

s+s = 74

add like terms

s+s = 2s

2s = 74

divide both sides by 2.

74/2=37

s=37

Suman's speed is 37 km/hr.

Narayan's speed would be 6 more than Suman's so we do 6+37

which makes 43 km/hr

Answer:

The volume of each cube is one cubic centimetre so the volume of the rectangular prism above is 60 cubic centimetres, or 60 cm3.The volume of each cube is one cubic centimetre so the volume of the rectangular prism above is 60 cubic centimetres, or 60 cm3.

Answer: is b

Step-by-step explanation:

Answer:

if f(n) = 4n + 7 and g(n) = 2n + 3, find (g-f)(n)

-2n - 4

f(x) = 2x - 3 and g(x) = 5 - 2x, find f/g (x)

2x - 3 / 5 - 2x

Step-by-step explanation:

Answer:

7 in

Step-by-step explanation:

Answer:

a = 7 in

Step-by-step explanation:

[tex]Area = \frac{a+b}{2} \times h\\\\26.25 = \frac{a + 10.5}{2} \times 3\\\\26.25 \times 2 = (a+ 10.5) \times 3\\\\52.5 = (A + 10.5) \times 3\\\\\frac{52.5}{3} = a + 10.5\\\\17.5 = a + 10.5\\\\a = 17.5 - 10.5 = 7[/tex]

Answer:

38.92 dollars

Step-by-step explanation:

Given:

AD is diameter of the circle, AB is the tangent, and measure of arc ADC is 228 degrees.

To find:

The [tex]m\angle CAB[/tex] and [tex]m\angle CAD[/tex].

Solution:

AD is diameter of the circle. So, the measure of arc AD is 180 degrees.

[tex]m(arcADC)=m(arcAD)+m(arcDC)[/tex]

[tex]228^\circ=180^\circ+m(arcDC)[/tex]

[tex]228^\circ-180^\circ+=m(arcDC)[/tex]

[tex]48^\circ+=m(arcDC)[/tex]

The measure inscribed angle is half of the corresponding subtended arc.

[tex]m\angle CAD=\dfrac{1}{2}\times m(arcDC)[/tex]

[tex]m\angle CAD=\dfrac{1}{2}\times 48^\circ[/tex]

[tex]m\angle CAD=24^\circ[/tex]

AB is the tangent. So, [tex]m\angle BAD=90^\circ[/tex] because radius is perpendicular on the tangent and the point of tangency.

[tex]m\angle BAD=m\angle CAB+m\angle CAD[/tex]

[tex]90^\circ=m\angle CAB+24^\circ[/tex]

[tex]90^\circ -24^\circ=m\angle CAB[/tex]

[tex]66^\circ=m\angle CAB[/tex]

Therefore, [tex]m\angle CAB=66^\circ[/tex] and [tex]m\angle CAD=24^\circ[/tex].

Answer:

(b) 360 degrees

Step-by-step explanation:

Required

The central angle

The central [tex]angle[/tex] of a circle is [tex]360^o[/tex]. This implies that the central [tex]angle[/tex]of the pie chart is also [tex]360^o[/tex], because a pie chart is always in [tex]form[/tex] of a [tex]circle.[/tex]

Answer:

Using the slope-intercept form, the slope is 2 .

Answer:

H0 : μ = 6.2

H1 : μ ≠ 6.2

Step-by-step explanation:

Population mean, μ = 6.2 ppm

The hypothesis :

Null, H0 : = The mean level of Ozone is normally 6.2 ppm ;

The alternative hypothesis is the researcher's claim that the current ozone level is not normal, that is it may be higher or lower than the normal value in ppm

Hence, the hypothesis could be written as :

H0 : μ = 6.2

H1 : μ ≠ 6.2

Answer:

2400

2640

360

Step-by-step explanation:

the retailer has to sell it for the same price as the dealer.

so, both mark it for 2400 sale price.

if a customer buys it at the retailer, the retailer makes the 15% discount he got from the dealer as profit.

2400 = 100%

1% = 2400/100 = 24

15% = 24×15 = 360

the retailer makes this profit no matter what other fees or taxes are added.

the final price is then including 10% VAT

2400 = 100%

10% = 24×10 = 240

final price = SP + VAT = 2400 + 240 = 2640

Answer:

The answer is D. 1. You can form only 1 perpendicular line.

Answer:

16.36 the proof is in the picture

Step-by-step explanation:

Answer:

Music club last box

Reason: There are equal number if members

Physics club first box

Reason: There are more older than young people

Sports Club third box

Reason: There are more younger people than older people

History Club takes the second box

Step-by-step explanation:

Hope this helps please like and mark as brainliest

Answer:

Mean= 12.2

Median= 14

Step-by-step explanation:

The mean of the data can be calculated as follows

= 2+5+13+15+18+20/6

= 73/6

= 12.2

Mean= 12.2

The median can be calculated as follows

Arrange the numbers in an orderly way

2, 5, 13, 15, 18, 20

= 13+15/2

= 14

Median= 14

Answer:

Mass = 1.3 Kilograms.

Step-by-step explanation:

Given the following data;

Force = 55.1 N

Acceleration = 41.6 m/s²

To find the mass of the stone in kg;

Newton's Second Law of Motion states that the acceleration of a physical object is directly proportional to the net force acting on the physical object and inversely proportional to its mass.

Mathematically, it is given by the formula;

Force = mass * acceleration

Substituting into the formula, we have;

55.1 = mass * 41.6

[tex] Mass = \frac {55.1}{41.6} [/tex]

Mass = 1.3 Kilograms

Answer:

18.84 feet.

Step-by-step explanation:

The formula for the circumference of a circle is:

2Pi*radius

The radius would be half the diameter so 3.

2*3.14*3

Given:

[tex]m=0.56x-0.25[/tex]

[tex]n=0.20x-0.03[/tex]

To find:

The sum of m and n.

Solution:

We have,

[tex]m=0.56x-0.25[/tex]

[tex]n=0.20x-0.03[/tex]

The sum of m and n is:

[tex]m+n=(0.56x-0.25)+(0.20x-0.03)[/tex]

Combining the like terms, we get

[tex]m+n=(0.56x+0.20x)+(-0.25-0.03)[/tex]

[tex]m+n=(0.76x)+(-0.28)[/tex]

[tex]m+n=0.76x-0.28[/tex]

Therefore, the sum of m and n is [tex]m+n=0.76x-0.28[/tex].

Answer:

The percentages are as follows: 1) 16.6%, 2) 12.5%, 3) 200%, 4) 225%, and 5) 1.5%.

Step-by-step explanation:

To find the rate, or percent, for each of the following items, the following calculations must be performed:

1) Base 72; percentage 12 = 12/72 = 0.1666 x 100 = 16.6

2) Percentage 28; base 224 = 28/224 = 0.125 x 100 = 12.5

3) Base 20; percentage 40 = 40/20 = 2 x 100 = 200

4) Base 44; percentage 99 = 99/44 = 2.25 x 100 = 225

5) Percentage 126; base 8400 = 126/8400 = 0.015 x 100 = 1.5

Therefore, the percentages are as follows: 1) 16.6%, 2) 12.5%, 3) 200%, 4) 225%, and 5) 1.5%.

Answer:

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

The factors of 5 are: 1, 5

The factors of 11 are: 1, 11

The factors of 13 are: 1, 13

Therefore the greatest/highest common factor is 1.

Answer:

(6x²+13x+6) ÷ (2x+3) sq in

Step-by-step explanation:

Volume = base × height

6x³+13x²+6x = (2x²+3x)h

Divide both sides by (2x²+3x)

(6x³+13x²+6x) ÷ (2x²+3x) = (2x²+3x)h ÷(2x²+3x)

By Factorization

x(6x²+13x+6) ÷ x(2x+3) = h

h= (6x²+13x+6) ÷ (2x+3)

Therefore the height of the prism is (6x²+13x+6) ÷ (2x+3) sq in

Answer: yuh Step-by-step explanation: yuh

Answer:

11/8, 7/4, 8/2

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