Writing Describe another method
for solving the expression in
Exercise 1. Does this method always
work? Explain.

[tex]y = -\frac{1}{9}(x - 1)^2 - 6[/tex]

Step-by-step explanation:

The vertex form of the equation for a parabola is given by

[tex]y = a(x - h)^2 + k[/tex]

where (h, k) are the coordinates of the parabola's vertex. Since the vertex is at (1, -6), we can write the equation as

[tex]y = a(x - 1)^2 - 6[/tex]

Also, since the parabola passes through (4, -7), we can use this to find the value for a:

[tex]-7 = a(4 - 1)^2 - 6 \Rightarrow -7 = 9a - 6[/tex]

or

[tex]a = -\frac{1}{9}[/tex]

Therefore, the equation of the parabola is

[tex]y = -\frac{1}{9}(x - 1)^2 - 6[/tex]

Similar triangles may or may not be congruent

The value of x that makes both triangles similar is 4.5

The equivalent ratio of both triangles is:

[tex]\mathbf{2 : 1 = 9 : x}[/tex]

Express the above equivalent ratio as a fraction

[tex]\mathbf{\frac 12= \frac x9 }[/tex]

Multiply both sides of the fraction by 9

[tex]\mathbf{\frac 12\times 9 = \frac x9 \times 9 }[/tex]

Cancel out common factors

[tex]\mathbf{\frac 12\times 9 = x}[/tex]

Divide 12 by 9

[tex]\mathbf{4.5 = x}[/tex]

Rewrite the above expression as:

[tex]\mathbf{x = 4.5 }[/tex]

Hence, the value of x is 4.5

Read more about similar triangles at:

https://brainly.com/question/14926756

Answer:

c

Step-by-step explanation:

Answer:

Step-by-step explanation:

sin(-430)=-sin(430)=-sin(360+70)=-sin 70

Answer:

0.020

0.0200

Step-by-step explanation:

Because there's always an imaginary 0 at the end, so there are infiite equivalant answers to this.

Hope this helps, and stay safe!! :))))

Answer:The number of nickles is 6  

The number of dims is 12 .

Step-by-step explanation:

Given as :

Sum of total number of dims and nickels coins = 18

The value of total combination = $1.50

Let The total number of dims = d

Let The total number of nickels = n

1 nickles = $0.05

1 dims = $0.1

According to question

Total number of dims and nickels coins = number of dims + number of nickels

Or, d + n = 18            .........1

And

$0.1 ×d + $0.05 ×n = $1.50

Or, 0.1 d + 0.05 n = 1.50            .........2

Now, Solving eq 1 an eq 2

0.1 × (d + n) - (0.1 d + 0.05 n) = 0.1 × 18 - 1.50

Or, (0.1 d - 0.1 d) + (0.1 n - 0.05 n) = 1.8 - 1.50

Or, 0 + 0.05 n = 0.3

Or, 0.05 n = 0.3

∴  n =

i.e n = 6

So, The number of nickles = n = 6

Put the value of n int eq 1

∵ d + n = 18

Or, d = 18 - n

Or, d = 18 - 6

i.e d = 12

So, The number of dims = d = 12

Hence, The number of nickles is 6 and the number of dims is 12 .

Step-by-step explanation:

Lets check if the three conditions hold.

1 : Continuity of g on the interval [0,2]

First, g(x) is a continuous function on R, as the sum of a cubic function wich is continuous on R, and a linear polynomial of the form ax + b which is also continuous on R. Finally g is also continuous on the interval [0,2]

2 : Differentiable on the same interval

Since the cubic function and the linear polynomial one are differentiable on R, g also is differentiable and particularly on the interval [0,2]

Also we have g'(x) = 2*3*x² - 3 = 6x² - 3

3 : Do we have g(0) = g(2) ?

Lets compute g(0) = 2*0^3 - 3*0 + 1 = 1

And g(2) = 2*2^3 - 3*2 + 1 = 2 * 8 - 6 + 1 = 16 - 6 + 1 = 11

Since g(0) ≠ g(2), Rolle's theorem is not applicable. Thus unfortunately, we can not conclude that there exist c ∈ (0,2) such that f'(c) = 0

Step-by-step explanation:

we will add 3+37=40

40/8=5

mark me brainlist plz

Answer:

You have to add a certain amount of a number to 3 7/8 to make five. Or the easy way, 5 - 3 7/8 = 1 1/8

Step-by-step explanation:

If you want can you make me brainlyist?

Also, I hope this helped!

Answer:

For any natural number m, we know that

2m, \mathrm{m}^{2}-1, \mathrm{m}^{2}+1m

2

−1,m

2

+1 is a Pythagorean triplet.

i. 2m = 6

\begin{array}{l} \Rightarrow \mathrm{m}=\frac{6}{2}=3 \\ \mathrm{m}^{2}-1=3^{2}-1=9-1=8 \\ \mathrm{m}^{2}+1=3^{2}+1=9+1=10 \end{array}

⇒m=

2

6

=3

m

2

−1=3

2

−1=9−1=8

m

2

+1=3

2

+1=9+1=10

∴ (6, 8, 10) is a Pythagorean triplet.

ii. 2m = 14

\begin{array}{l} \Rightarrow \mathrm{m}=\frac{14}{2}=7 \\ \mathrm{m}^{2}-1=7^{2}-1=49-1=48 \\ \mathrm{m}^{2}+1=7^{2}+1=49+1=50 \end{array}

⇒m=

2

14

=7

m

2

−1=7

2

−1=49−1=48

m

2

+1=7

2

+1=49+1=50

∴ (14, 48, 50) is not a Pythagorean triplet.

iii. 2m = 16

\begin{array}{l} \Rightarrow \mathrm{m}=\frac{16}{2}=8 \\ \mathrm{m}^{2}-1=8^{2}-1=64-1=63 \\ \mathrm{m}^{2}+1=8^{2}+1=64+1=65 \end{array}

⇒m=

2

16

=8

m

2

−1=8

2

−1=64−1=63

m

2

+1=8

2

+1=64+1=65

∴ (16, 63, 65) is a Pythagorean triplet.

iv. 2m = 18

\begin{array}{l} \Rightarrow \mathrm{m}=\frac{18}{2}=9 \\ \mathrm{m}^{2-1}=9^{2}-1=81-1=80 \\ \mathrm{m}^{2}+1=9^{2}+1=81+1=82 \end{array}

⇒m=

2

18

=9

m

2−1

=9

2

−1=81−1=80

m

2

+1=9

2

+1=81+1=82

∴ (18, 80, 82) is a Pythagorean triplet

Step-by-step explanation:

For any natural number greater than 1,(2m,m

2

−1,m

2

+1) is Pythagorean triplets.

So, if one number is 2m, then another two numbers will be m

2

−1 and m

2

+1.

Given, one number = 4

Then Pythagorean triplets:

2m=4 or m = 2

So,

m

2

−1=(2)

2

−1=4−1=3

m

2

+1=(2)

2

+1=4+1=5

Now, (3)

2

+(4)

2

=(5)

2

Or 9 + 16 = 25.

I hope you all like this answer.

Mark as a brainlist.

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Answer:

proportional

Step-by-step explanation:

hope this helps

Let's try it! If we set these two ratios equal to each other and cross-multiply, the results should be the same if they are, in fact, proportional.

8/20 = 20/80

400 ? 640

400 and 640 are not the same number, so these ratios are not proportional.

Hope this helps!! :)

Answer:

bet but need barinlyist

Step-by-step explanation:

[tex] = > 6a - 2b[/tex]

[tex] = > 6(5) - 2(7)[/tex]

[tex] = > 30 - 14[/tex]

[tex] = > 16[/tex]

10 quarters 6 nickels 18 dimes

Answer:

0.9m²

Step-by-step explanation:

Find the area of the larger circle, the radius is 0.85m because the diameter is double this - 1.7m:

Find the area of the smaller circle, the radius is 0.65 because the diameter is double this - 1.3m:

Subtract the two area:

289/400π - 169/400π = 120/400π = 3/10π or 0.942477.. ≈ 0.9m²

Answer:

1/4 · x⁴

Step-by-step explanation:

Answer:

Step-by-step explanation:

If one of the data points has the form (0,a)

, then a is the initial value. Using a, substitute the second point into the equatio f(x)=a(b)x, and solve for b.If neither of the data points have the form (0,a)

, substitute both points into two equations with the form f(x)=a(b)x Solve the resulting system of two equations in two unknowns to find a and b.Using the a and b found in the steps above, write the exponential function in the form f(x)=a(b)x.

Hey there! Your answer is:

7 inches

Explanation:

If Tyler is 5 inches tall, he needs to grow 7 inches to be a foot tall. This is because 12 inches are in 1 foot. We can do a simple subtraction problem to figure this out.

12 inches - 5 inches = 7 inches

Since Tyler is 5 inches tall, we know that if we subtract 12 inches from 5 inches we will get the number of inches he needs to grow.

I hope this answer helps you out! Let me know if you have any questions and have a wonderful day/night!

Answer:

[tex]y - 5 = - 3(x - 3)[/tex]

Step-by-step explanation:

our original equation

[tex]y = \frac{1}{3} x - 7[/tex]

A perpendicular slope of a line is the negative reciprocal

So our slope would be -3

point slope form is

[tex]y - y1 = m(x - x1)[/tex]

let's substitute our given point (3, 5) and our perpendicular slope, -3

[tex]y - 5 = - 3(x - 3)[/tex]

27.400

Step-by-step explanation:

187X187 = 34.969

87X87=7.569

34.969 - 7569 = 27.400

Use the identity

(a + b)² = a ² + 2ab + b ²

Then rewrite 187² as

187² = (100 + 87)² = 100² + 2•100•87 + 87²

Subtract 87² eliminates the last term from above, so we're left with

(100² + 2•100•87 + 87²) - 87²

= 100² + 2•100•87

= 10000 + 2•8700

= 10000 + 17400

= 27400

Answer:

800

Step-by-step explanation:

Hope this helps

Answer:

800, if it's higher than 50 you can round it to the next hundred

Answer:

I don't know what to do sorry

Answer:

the weight of each marble is 2.55 grams

30/5 is equal to 6

this is your x-intercept

30/3 is equal to 10

this is your y-intercept

I think you know what to do now :)

(0,10) and (6,0)

look at the image of the graph

Answer: 3 is constant term, 6ab is variable term, and C is variable term

Answer:

3: Constant term, 6ab: Variable term, C: Variable term

Step-by-step explanation:

Answer:

27 minutes

Step-by-step explanation: