Instructions: Given the vertex of a quadratic function, find the axis
of symmetry.
Vertex: (5,7)

Answer:

a: 1/12

b: 1/6

c: 1/2

d: 1/2

e: 1/12

f: 1/3

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

Shape = Isosceles Trapezoid

Area = 1/2 (a+b) h

= 1/2 (9+3) x 3

= 18

Answered by Gauthmath

Answer:

Step-by-step explanation:

X = (18/5)/(3/2)

= 18/5 x 2/3

=(18 x 2) / (5x3)

= 90/15

If you don’t want it as a fraction it’s 6!

Hope this helps!

Answer:

tk 30

Step-by-step explanation:

5 dozen = 5 * 12 = 60 oranges

12/4 = 3

total cost = 60 * 3 = tk.180

total sell = 50 * 3 = tk 150

total lose = 180 - 150 = tk 30

Answer:

x=71

Step-by-step explanation:

Since this is an isosceles triangle as indicated by the lines on the sides, the sides lengths are equal.

When the sides are equal, the base angles are equal

x=71

Answer:

50?

Step-by-step explanation:

Because its 50 miles per gallon, so gallon time 50 will be the miles? I'm not sure but i think it is

work and answers below

Answer:

[tex]\text{Part A.}\\(-\frac{1}{8},0),\\(\frac{3}{2},0)\\\\\text{Part B.}\\(\frac{11}{16},\frac{169}{16})\\\\\text{Part C.}[/tex]

Draw a parabola concave down with vertex at [tex](\frac{11}{16},\frac{169}{16})[/tex]. Since the leading coefficient of the equation is -16, the parabola should appear thinner than its parent function [tex]y=x^2[/tex]. Ensure that the parabola passes through the points [tex](\(-\frac{1}{8},0)[/tex] and [tex](\frac{3}{2},0)[/tex].

Step-by-step explanation:

Part A:

The x-intercepts of a function occur at [tex]y=0[/tex]. Therefore, let [tex]y=0[/tex] and solve for all values of [tex]x[/tex]:

[tex]0=-16x^2+22x+3[/tex]

The quadratic formula states that the real and nonreal solutions to a quadratic in standard form [tex]ax^2+bx+c[/tex] is equal to [tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex].

In [tex]-16x^2+22x+3[/tex], assign:

Therefore, the solutions to this quadratic are:

[tex]x=\frac{-22\pm\sqrt{22^2-4(-16)(3)}}{2(-16)},\\x=\frac{-22\pm 26}{-32},\\\begin{cases}x=\frac{-22+26}{-32}=\frac{4}{-32}=\boxed{-\frac{1}{8}},\\x=\frac{-22-26}{-32}=\frac{-48}{-32}=\boxed{\frac{3}{2}}\end{cases}[/tex]

The x-intercepts are then [tex]\boxed{(-\frac{1}{8},0)}[/tex] and [tex]\boxed{(\frac{3}{2},0)}[/tex].

Part B:

The a-term is negative and therefore the parabola is concave down. Thus, the vertex will be the maximum of the graph. The x-coordinate of the vertex of a quadratic in standard form [tex]ax^2+bx+c[/tex] is equal to [tex]x=\frac{-b}{2a}[/tex]. Using the same variables we assigned earlier, we get:

[tex]x=\frac{-22}{2(-16)}=\frac{-22}{-32}=\frac{11}{16}[/tex]

Substitute this into the equation of the parabola to get the y-value:

[tex]f(11/16)=-16(11/16)^2+22(11/16)+3,\\f(11/16)=\frac{169}{16}[/tex]

Therefore, the vertex of the parabola is located at [tex]\boxed{(\frac{11}{16},\frac{169}{16})}[/tex]

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Answer:

  3 ⇒ 12

Step-by-step explanation:

Apparently "a = b" in this case is used to mean f(a) = b. It appears as though the function is ...

  f(x) = x(x+1)

Then f(3) = 3(3+1) = 3·4 = 12

_____

Additional comment

IMO this is a poor use of the equal sign, which should be reserved for situations where the left side expression has the same value as the right side expression.

Answer:

BF = 16

Step-by-step explanation:

18/12 = 1.5 * 6 = 9

Since DE and BF are parallel and DB and EF are parallel, they comprise a parallelogram. This means that DB = EF

DB = EF = 9

24/1.5 = 16

DE = 16

BF = 16

The statement which can be proven true using the given theorem (congruence) is Segment BF = 16.

By the congruence theorem;

Hence, AE/EC = BF/FC.

Therefore; 12/18 = BF/24

Hence, BF = 24× 12/18

Read more on congruent triangles;

https://brainly.com/question/1675117

Answer:

y  ≥ 5x+ (-3)

Step-by-step explanation:

greater than or equal to ≥

The sum means add

y  ≥ 5x+ (-3)

Answer:

Option D, y ≥ 5x + (-3)

Step-by-step explanation:

Step 1:  Make an expression

The value of y is greater than or equal to the sum of five times the value of x  and negative three.

The value of y is greater than or equal to ← y ≥

The sum of five times the value of x  and negative three ← 5x + (-3)

y ≥ 5x + (-3)

Answer:  Option D, y ≥ 5x + (-3)

Answer:

n+3

Step-by-step explanation:

1/2 × 2(n+3)=n +3

I hope this helps

Answer:

6x+y

Step-by-step explanation:

Answer:

33.00 355.2

5.0m x 6.7m 33.50 360.6

5.0m x 6.8m 34.00 366.0

5.0m x 6.9m 34.50 371.4

5.1m x 6.0m 30.60 329.4

5.1m x 6.1m 31.11 334.9

5.1m x 6.2m 31.62 340.4

5.1m x 6.3m 32.13 345.8

5.1m x 6.4m 32.64 351.3

5.1m x 6.5m 33.15 356.8

5.1m x 6.6m 33.66 362.3

5.1m x 6.7m 34.17 367.8

5.1m x 6.8m 34.68 373.3

5.1m x 6.9m 35.19 378.8

Answer: A=πr²      

A=3.14(1.6inch)²                     r=d/2⇒3.2/2⇒1.6

A=3.14×2.56in²

A=8.0384in²

A≈8.04

now circumference,

C=2πr

C=2×3.14×1.6in

C=10.048in

C≈10.05

Answer:

1/6

Step-by-step explanation:

We want to find how long it takes for the bacteria to lose half its size. We can do this by taking one point of the bacteria and finding how long it takes to go to half its size. When t=0, 9300 * (1/64)^t = 9300 * 1 = 9300 as anything to the power of 0 is 1. Therefore, we can solve for t when the end result of the bacteria is 9300/2= 4650, making our equation

4650 = 9300 * (1/64)^t

divide both sides by 9300

1/2 = (1/64)^t

First, we can tell that 2^6 = 64*. Because of this, we can say that (1/2)^6 = 1^6/2^6 = 1/64, so (1/64)^(1/6) = 1/2. We know this because

(1/2)^6 = 64

take the 6th root of both sides

(1/2) = (64)^(1/6)

. This means that t=1/6, so the bacterial culture loses 1/2 of its size every 1/6 seconds

* if this is harder to figure out, e.g. 3 and 729, we can plug (log₃729) into a calculator

Answer:

0.17 seconds

Step-by-step explanation:

i got this correct on Khan   :)

i hope it helps

Answer: Number 1 is 150

Step-by-step explanation: If you put 72 / 48% in your calculator, you will get your answer.

Answer:

6

Step-by-step explanation:

The given function to us is ,

[tex]\rm\implies f(x)= log_a(x) [/tex]

And its value at 7 is 2 , that is ,

[tex]\rm\implies f(x)= log_a(7) =2[/tex]

Taking this ,

[tex]\rm\implies 2= log_a(7) [/tex]

In general we know that ,

[tex]\bf\to log_a b = c ,\ then \ a^c = b [/tex]

Using this , we have ,

[tex]\rm\implies a^2 = 7 [/tex]

Squarerooting both sides ,

[tex]\rm\implies a =\sqrt{ 7 }[/tex]

Therefore , when x is 343 ,

[tex]\rm\implies f(343)= log_{\sqrt7} ( 343) [/tex]

We can write , 343 as 7³ ,

[tex]\rm\implies f(343)= log_{\sqrt7}7^3 [/tex]

[tex]\rm\implies f(343)= log_{7^{\frac{1}{2}}} 7^3 [/tex]

This can be written as ,

[tex]\rm\implies f(343)= \dfrac{ 3}{\frac{1}{2}} [/tex]

[tex]\rm\implies \boxed{\blue{\rm f(343)= 6 }}[/tex]

Hence the required answer is 6.

Answer:

Step-by-step explanation:

First, I would find the point on the curve. By substituting t=1, I get (x, y). Next, I will try to eliminate the t and make a xy equation. In this case, the t's will cancel out in 'x=t-t-1" which wouldnt make this a curve. To find the equation of the tangent line, find the deretitave of the xy equation, and subsitute x in to find the slope at that point. Next, use point slope form to find the equation at the point.

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Answer:

  B.  x^2/3^2 + y^2/4^2 = 1

Step-by-step explanation:

The graph looks like a circle, but is not. It is a unit circle scaled by a factor of 3 in the x-direction and a factor of 4 in the y-direction. Thus, its equation is ...

  (x/3)^2 +(y/4)^2 = 1

  x^2/3^2 +y^2/4^2 = 1

Answer:

3 =f

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp/ adj

tan 60 = f/ sqrt(3)

sqrt(3) tan 60 = f

sqrt(3) * sqrt(3) = f

3 =f

Answer:

yeah, teachers kinda suck

Answer:

170 students total

Step-by-step explanation:

43x2=86

86+43+31+10=170

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Answer:

  (b)  AB overbar congruent to CD overbar

Step-by-step explanation:

AB with an overbar is the way that line segment AB is designated, where appropriate typesetting is possible. Thus the statement the line segments are congruent is fully equivalent to ...

  AB overbar congruent to CD overbar

Answer:

1. 16%

2. The middle 95% of newborn babies weigh between 6.2 and 9 pounds.

3. 2.5%

4. Approximately 50% of newborn babies weigh more than 7.6 pounds.

5. 83.85%

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean of 7.6 pounds, standard deviation of 0.7 pounds

1. What percent of newborn babies weigh more than 8.3 pounds?

7.6 + 0.7 = 8.3.

So more than 1 standard deviation above the mean.

The normal distribution is symmetric, which means that 50% of the measures are below the mean and 50% are above.

Of those above the mean, 100 - 68 = 32% are more than one standard deviation above the mean. So

[tex]0.32*0.5 = 0.16[/tex]

16% of newborn babies weigh more than 8.3 pounds.

2. The middle 95% of newborn babies weigh between and pounds.

Within 2 standard deviations of the mean, so:

7.6 - 2*0.7 = 6.2 pounds

7.6 + 2*0.7 = 9 pounds.

The middle 95% of newborn babies weigh between 6.2 and 9 pounds.

3. What percent of newborn babies weigh less than 6.2 pounds?

More than 2 standard deviations below the mean, which is 5% of the 50% below the mean, so:

[tex]p = 0.05*0.5 = 0.025[/tex]

2.5% of newborn babies weigh less than 6.2 pounds.

4. Approximately 50% of newborn babies weigh more than pounds.

Due to the symmetry of the normal distribution, the mean, so 7.6 pounds.

Approximately 50% of newborn babies weigh more than 7.6 pounds.

5. What percent of newborn babies weigh between 6.9 and 9.7 pounds?

6.9 = 7.6 - 0.7

9.7 = 7.6 + 3*0.7

Within 1 standard deviation below the mean(68% of the 50% below) and 3 standard deviations above the mean(99.7% of the 50% above). So

[tex]p = 0.68*0.5 + 0.997*0.5 = 0.8385[/tex]

83.85% of newborn babies weigh between 6.9 and 9.7 pounds.

Answer:

6) 6[tex]\sqrt{2}[/tex]

9) 40

10) [tex]\frac{5\sqrt{2} }{2}[/tex]

11) 13

Step-by-step explanation:

6)A right triangle rule: if 2 legs are equal, the hypotenuse is the length of that leg*[tex]\sqrt{2}[/tex]

9) Pythagorean Theorem

[tex]a^{2} +b^{2} =c^{2}[/tex]

We know the hypotenuse (41) so we substitute that for c and 9 for b now we need to find a

[tex]\sqrt{41^{2}-9^{2} }[/tex] which gives us 40

10) same with #6 but we do the opposite. SInce we have the hypotenuse, we can divide that by [tex]\sqrt{2}[/tex] because we know that if 2 legs are equal, the hypotenuse is multiplied by [tex]\sqrt{2}[/tex]. Multiply the numerator and denominator by [tex]\sqrt{2}[/tex] because we can't have a square root in the denominator.

11) like #9 we have the a and b but we need to find c

a=5 b=12 c=r

so [tex]\sqrt{5^{2}+12^{2} }[/tex] which gives us 13

[tex] {h}^{2} = {p}^{2} + {b}^{2} [/tex]

[tex] {c}^{2} = {6}^{2} + {6}^{2} \\ {c}^{2} = 36 + 36 \\ c = \sqrt{2( {6}^{2} )} \\ c = \sqrt{2}{\sqrt{ {6}^{{2}} } } \\ c = 6 \sqrt{2} \: \: \: ans[/tex]

SOLUTION->

[tex] {h}^{2} = {p}^{2} + {b}^{2} [/tex]

[tex] {41}^{2} = {x}^{2} + {9}^{2} \\ 1681 = {x}^{2} + 81 \\ 1681 - 81 = {x}^{2} \\ 1600 = {x}^{2} \\ x = \sqrt{40 \times 40} \\ x = 40 \: \: \: ans[/tex]

GIVEN

[tex]{h}^{2} = {p}^{2} + {b}^{2} [/tex]

[tex] {5}^{2} = {s}^{2} + {s}^{2} \\ 25 = 2 {s}^{2} \\ 12.5 = {s}^{2} \\ \sqrt{12.5} = s \\ 3.5 = s \: \: \: ans[/tex]

[tex] {h}^{2} = {p}^{2} + {b}^{2} [/tex]

[tex] {r}^{2} = {12}^{2} + {5}^{2} \\ {r}^{2} \\ 144 + 25 \\ {r}^{2} = 169 \\ r = \sqrt{13 \times 13} \\ r = 13 \: \: \: \: ans[/tex]

HOPE IT HELPED

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \star \: DEVIL005 \: \star[/tex]

here's the answer to your question

Answer:

The equation will be "[tex]y=x-3[/tex]".

Step-by-step explanation:

Given:

Points (12, 9) = (x, y)

⇒ [tex]x=9t^2+3[/tex]

then,

 [tex]\frac{dy}{dt}=18t[/tex]

or,

⇒ [tex]y=6t^3+3[/tex]

then,

 [tex]\frac{dy}{dt}=18t^2[/tex]

⇒ [tex]\frac{dy}{dx}=\frac{18t^2}{18t}[/tex]

        [tex]=t[/tex]

By using the point slope form.

The equation of tangent will be:

⇒ [tex]y-9=1(x-12)[/tex]

   [tex]y-9=x-12[/tex]

          [tex]y=x-12+9[/tex]

          [tex]y=x-3[/tex]

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Answer:

  162 mi²

Step-by-step explanation:

The area on the map is ...

  18(1 in)²

Then the area on the ground will be ...

  18(3 mi)² = 18·9 mi² = 162 mi²

Answer:  D) The base is e^(-1)

We use the rule that x^(-k) = 1/(x^k). That allows us to say e^(-1) = 1/(e^1) = 1/e

The 1/e is the base of the exponential (1/e)^x

In general, the exponential b^x has base b.