What is the vertex of the parabola? y+1=−14(x−2)2 Enter your answer in the boxes.

Answer:

The values of [tex]a[/tex] and [tex]b[/tex] so that the two linear equations have infinite solutions are [tex]3[/tex] and [tex]\frac{3}{2}[/tex], respectively.

Step-by-step explanation:

Two linear equations with two variables have infinite solution if and only if they are linearly dependent. That is, one linear equation is a multiple of the other one. Let be the following system of linear equations:

[tex]2\cdot x + y = 6[/tex] (1)

[tex]a\cdot x + b\cdot y = 9[/tex] (2)

The following condition must be observed:

[tex]r = \frac{a}{2} = \frac{b}{1} = \frac{9}{6}[/tex] (3)

After some quick operations, we find the following information:

[tex]r = \frac{3}{2}[/tex], [tex]a = 3[/tex], [tex]b = \frac{3}{2}[/tex]

The values of [tex]a[/tex] and [tex]b[/tex] so that the two linear equations have infinite solutions are [tex]3[/tex] and [tex]\frac{3}{2}[/tex], respectively.

Answer:

x = 25.

Step-by-step explanation:

Original cost per person:: 2000/x

Changed cost per person:: 2000/(x-5)

---------------------------

Equation:: changed - original = 20

2000/(x-5) - 2000/x = 20

2000x - 2000x + 2000*5 = 20x(x-5)

10000 = 20x^2-100

----

500 = x^2 - 5x

------------------

x^2 - 5x - 500 = 0

(x+20)*(x-25) = 0

-----

Only positive root makes sense ====> x = 25.

Answer:

c

Step-by-step explanation:

Answer:

Step-by-step explanation:

7x + 3= 24

7x= 24-3

7x= 21

x= 21/7

x= 3

Then we have that

5-4x

5-4(3)

5-12

Answer= -7

Answer:

336 ft ²

Step-by-step explanation:

Find the area of the two triangles

In this case, both triangles are the same, so we can modify the formula for area of triangle

In the formula, we divide by two, but because we multiply the area by two for the two triangles, we can just use base x height

Triangles = 6 x 8 = 48 ft²

top rectangle = 10x12 = 120 ft²

bottom rectangle = 8x12 = 96 ft²

back rectangle = 6x12 = 72 ft²

Total = 48 ft² + 120 ft² + 96 ft² + 72 ft² = 336 ft²

If my answer is incorrect, pls correct me!

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-Chetan K

Answer:

We can’t solve for x and y

Step-by-step explanation:

Answer:

Uhmm We can't do that

Step-by-step explanation:

Answer:

Can you add if you can add you have to add up every thing and the answer will be

Answer:

990.56

Step-by-step explanation:

because, Distance=velocity× time

Answer:

25 in^2

Step-by-step explanation:

So the area of a triangle is (Base * Height) / 2. The base, which is where the triangle "sits" is 10 in. The height is 5 in.

With this, these numbers can both be plugged in to get the answer:

(10 * 5) / 2

50/2

25 in^2

It is squared after the units since it is the area.

Answer:

I think it might have been D, becoming a monarch, because he wanted to rule the world I guess.

Step-by-step explanation:

I recommend you put this under history instead of mathematics.

Step-by-step explanation:

hope it is helpful to you

Answer:

Entire perimeter = 169in

Step-by-step explanation:

add all the inches up

The perimeter of the polygon drawn is the sum of its entire sides , which is 169 inches.

Given the polygon with the measure of its exterior :

The perimeter of the polygon is the sum of the exterior sides of the figure given :

Therefore, the perimeter of the polygon is 169 inches .

Learn more on perimeter : https://brainly.com/question/19819849

#SPJ2

Answer:

6 cm

Step-by-step explanation:

1 cm : 9 meters -->  1cm/9m

? cm : 54 meters -->  ?cm/54m

[tex]\frac{1}{9}=\frac{?}{54}; 54*\frac{1}{9}=?;6=?[/tex]

Answer:is 6cm

Step-by-step explanation:

Given:

In triangle GHI, h = 300 inches, G=30° and H=29º.

To find:

The length of i.

Solution:

We have, G=30° and H=29º.

Using angle sum property, we get

[tex]m\angle G+m\angle H+m\angle I=180^\circ[/tex]

[tex]30^\circ+29^\circ+m\angle I=180^\circ[/tex]

[tex]59^\circ+m\angle I=180^\circ[/tex]

[tex]m\angle I=180^\circ-59^\circ[/tex]

[tex]m\angle I=121^\circ[/tex]

According to Law of sines,

[tex]\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]

Using Law of sines, we get

[tex]\dfrac{h}{\sin H}=\dfrac{i}{\sin I}[/tex]

[tex]\dfrac{300}{\sin 29^\circ}=\dfrac{i}{\sin 121^\circ}[/tex]

[tex]\dfrac{300}{0.4848}=\dfrac{i}{0.8572}[/tex]

Multiply both sides by 0.8572.

[tex]\dfrac{300}{0.4848}\times 0.8572=i[/tex]

[tex]530.44554=i[/tex]

[tex]i\approx 530[/tex]

Therefore, the length of i is about 530 inches.

Answer:

62

Step-by-step explanation:

Khan Academy. I got this correct, so trust me :)

The measurement of the angle A for the considered triangle is found being of 62° approximately.

For any triangle ABC, with side measures |BC| = a. |AC| = b. |AB| = c,

we have, by law of sines,

[tex]\dfrac{sin\angle A}{a} = \dfrac{sin\angle B}{b} = \dfrac{sin\angle C}{c}[/tex]

Remember that we took

[tex]\dfrac{\sin(angle)}{\text{length of the side opposite to that angle}}[/tex]

For the considered triangle, we can use sine rule.

In triangle ABC, we're given that:

The side opposite to angle A is BC and the side opposite to angle B is AC. Thus, by sine law, we get:

[tex]\dfrac{\sin(m\angle A)}{|BC|} = \dfrac{sin(m\angle B)}{|AC|}\\\\\dfrac{\sin(m\angle A)}{15} = \dfrac{\sin(28^\circ)}{8}\\\\\sin(m\angle A ) \approx \dfrac{15 \times 0.46947}{8} \approx 0.88026\\\\m\angle A \approx \sin^{-1}(0.88026)\\\\m\angle A \approx 61.67^\circ, 118.32^\circ[/tex]

But since angle A is acute(angle with measure of less than 90 degrees), thus, m∠A ≈ 61.67° ≈ 62°

Thus, the measurement of the angle A for the considered triangle is found being of 62° approximately.

Learn more about law of sines here:
https://brainly.com/question/17289163

Answer:

given:

height[h]=8mm

radius [r]=5mm

Now,

Volume of cone=1/3 πr²h=⅓×3.14×5²×8=209mm³

C) 209 mm³ is a required answer.

Answer:

Total appearances = 9+180+3 = 192. It is obvious that the most frequent digit is 1. Number of digits from 1 to 1000. Total = 2893.

Step-by-step explanation:

2x+y=3

y=3-2x.....eqn (1)

x=3y+5.....eqn(2)

substituting the value of y from eqn 1

x=3(3-2x)+5

x=9-6x+5

x+6x=14

7x=14

x=14/7

x=2

substituting the value of x in eqn 1

y=3-2×2

y=3-4

y=-1

therefore,

x=2

y=-1

Answer:

solution given:

Area of triangle ABC=½b×h=½×18×21=189km²

Area of square DEFG=l²=9²=81km²

Area of rectangle DHIJ=l×b=4×13=52km²

Total area =189+81+52=322 square kilometers.

Answer:

[tex] \rm\displaystyle A _{ \text{total}} = 322 {km}^{2} [/tex]

Step-by-step explanation:

refer the attachment

we have a triangle,a rectangle and a square

in order to figure out the area of the total figure we need to figure out the area the attached figure first

the triangle has a base of 18 km and a height of 13+6+2=21km

thus,

the area of the triangle is

[tex] \displaystyle \frac{1}{2} \times 18 km\times 21km[/tex]

reduce fraction:

[tex] \displaystyle 9 km\times 21km[/tex]

simplify multiplication:

[tex] \displaystyle 189 km ^{2} [/tex]

the rectangle has a length of 13km and a width of 4km

thus,

the area of the rectangle is

[tex] \displaystyle 13km \times 4km[/tex]

simplify multiplication:

[tex] \displaystyle {52km}^{2} [/tex]

the length of every sides of the square is 9km

thus,

the area of the square is

[tex] \displaystyle {(9km)}^{2} [/tex]

simplify square:

[tex] \displaystyle {81km}^{2} [/tex]

[tex] \rm\displaystyle A _{ \text{total}} = A_{ \text{triangle}} + A_{ \text{rectangle}} + A_{ \text{square}}[/tex]

substitute:

[tex] \rm\displaystyle A _{ \text{total}} = 189 {km}^{2} + 52 {km}^{2} + 81 {km}^{2} [/tex]

simplify addition:

[tex] \rm\displaystyle A _{ \text{total}} = 322 {km}^{2} [/tex]

Answer:

16

Step-by-step explanation:

b x h is finding a square or rectangle, but since a triangle is half of a rectangle or square you can divide that by 2. So, 8 (b) x 4 (h) = 32, 32 / 2 = 16. Hope this helps! :D

Answer:

the correct answer is D

Step-by-step explanation:

because the -9 5/8 is in absolute value marks.

Answer:

g(x)=(x+5)^2

Step-by-step explanation:

the account looks like this, because you invert the sign 5 is negative to the left, so for the result to be negative in the account it has to be positive

g(x)=(x+5)^2

(x+5)^2=0

x+5=0

x=0-5

x=-5

Good Studies!!!

Answer: 0.5

Step-by-step explanation:

You need to use

Brackets

Indices

Division

Multiplication

Addition

Subtraction

7 + 5 =12

12 - 16 = -4

-4 / 8 = -0.5

-0.5 + 3 = 2.5

2.5 - 2 = 0.5

Answer: 4

Step-by-step explanation: 7+5=12

12×2=24

24- (4×4)= 24-16=8

8÷8=1

1+3=4

Answer:

[tex]1/2y - 21/4 = -35/4[/tex]

[tex]1/2y = 21/4 -35/4[/tex]

[tex]1/2y = - 7/4[/tex]

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

Answer:

true

Step-by-step explanation:

subject?

Answer: Yes, they are independent because P(Texas) ≈0.45 and P(Texas/Brand A)≈0.45