Given y= -5x^2 +30x -9, find the axis of symmetry.

x= -30
x= 6
x= 3
x= -3

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Explanation:

Both legs are the same length, as indicated by the tickmark.

Use the pythagorean theorem to solve for x

[tex]a^2+b^2 = c^2\\\\( \sqrt{10} )^2 + ( \sqrt{10} )^2 = x^2\\\\10 + 10 = x^2\\\\x^2 = 20\\\\x = \sqrt{20}\\\\x = \sqrt{4*5}\\\\x = \sqrt{4}*\sqrt{5}\\\\x = 2\sqrt{5}\\\\[/tex]

We know that :

⊕  Sum of the interior angles in a Pentagon should be equal to 540°

⇒  x° + (2x)° + (2x)° + 90° + 90° = 540°

⇒  (5x)° = 540° - 180°

⇒  (5x)° = 360°

[tex]\sf{\implies x^{\circ} = \dfrac{360^{\circ}}{5}}[/tex]

⇒ x° = 72°

Answer:

[tex]y = \frac{1}{2}x + 6[/tex]

Step-by-step explanation:

[tex]Let \ (x _1 y _ 1 ) = ( 6 , 9 ) \ and \ (x _ 2 , y _ 2 ) \ = ( 0 , 6 )\\\\[/tex]

Step 1 : Find slope, m

              [tex]slope, m = \frac{y _ 2 - y _ 1}{x_ 2 - x_ 1 } = \frac{6 - 9}{0 - 6 } = \frac{-3}{-6} = \frac{1}{2}[/tex]

Step 2 : Find the equation

                [tex](y - y _ 1 ) = m ( x - x_ 1) \\\\( y - 9 ) = \frac{1}{2} (x - 6 ) \\\\y = \frac{1}{2}x - 3 + 9 \\\\y = \frac{1}{2}x + 6[/tex]

Answer:

y = 1/2x + 6

Step-by-step explanation:

y = mx + b is the formula. m is the slope and to calculate that you use the slope formula y2 - y1/ x2 - x1.

(6, 9)  is the first coordinate so 6 is x1 and 9 is y1. Similarly in (0, 6), x2 is 0 and y2 is 6. Now if we put that into the slope formula it would look something like this: 6-9/0-6. that comes to -3/-6. simplify and cancel out the negatives and you get 1/2 which is the m ( slope).

The b is the y-intercept, which is the y value for where the x is 0. In this question, they already give you the coordinate where x is 0. (0, 6). x is 0 and y is 6. therefore the b (y-intercept) is 6.

Put all of this into y =mx +b, and you get y= 1/2x + 6.

If you want to make sure you did it right, just plug in one of the coordinates into this equation. Let's use  (6, 9).

9 = 1/2 (6) + 6

9 = 3 + 6

9 = 9. It works out, therefore the equation right.

Hope this helps

Answer:

The current temperature = 34.2°C

Step-by-step explanation:

Initial temperature = 46.8°C

After 20 minutes temperature reduced by 12.6°C

Therefore, the current temperature is = 46.8°C - 12.6°C = 34.2°C

Step-by-step explanation:

i dont know i guess we'll never know

Answer:

44.8 cm

Step-by-step explanation:

Given

See attachment for shapes

[tex]P_A= 56cm[/tex]

Required

The perimeter of B

Let the length of a side of the square that makes up A be, l.

So, we have:

[tex]P_A = 10 * l[/tex] --- because A is formed by 10 sides of l

[tex]56 = 10 * l[/tex]

[tex]l =\frac{56}{10}[/tex]

[tex]l =5.6[/tex]

The perimeter of B is:

[tex]p_B = 8*l[/tex] --- because B is formed by 8 sides of l

[tex]p_B = 8*5.6[/tex]

[tex]p_B = 44.8[/tex]

The question given is incomplete, find the possible version in the comment below.

Answer:

9765625 ways

Step-by-step explanation:

To solve questions of this kind, we can apply the product rule ;

We have 10 different questions, each with 5 alternative options, even though there is only one correct answer, the number of answers that can be chosen (either correct or incorrect) is 5 ;

Therefore, we have 5 possible choices for each question :

Question 1 = 5 ; question 2 = 5,....

This can be written as :

5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 = 5^10 = 9765625 ways

Answer:

Step-by-step explanation:

x=[tex]\sqrt{100+16}[/tex]

x=[tex]\sqrt{116}[/tex]

x=2[tex]\sqrt{29[/tex]

Answer:

[tex] x = \blue{2\sqrt{29}} [/tex]

Step-by-step explanation:

[tex] a^2 + b^2 = x^2 [/tex]

[tex] 4^2 + 10^2 = x^2 [/tex]

[tex] 16 + 100 = x^2 [/tex]

[tex] x^2 = 116 [/tex]

[tex] x = \sqrt{116} [/tex]

[tex] x = \sqrt{4 \times 29} [/tex]

[tex] x = \blue{2\sqrt{29}} [/tex]

Answer: 28 hours

Step-by-step explanation:

1. Write original equation: 7.15x=3.40x+105

2. Combine like terms to isolate x: 3.75x=105

3. Divide both sides by same amount to find x: x=28

They would have to work 28 hours to earn the same amount of money.

Answer:

TU ≈ 12.96

Step-by-step explanation:

Using the Altitude on Hypotenuse theorem

(leg of outer triangle)² = (part of hypotenuse below it) × (whole hypotenuse)

TU² = UV × SU = 6 × 28 = 168 ( take square root of both sides )

TU = [tex]\sqrt{168}[/tex] ≈ 12.96 ( to the nearest hundredth )

Answer:

Step-by-step explanation:

Use the slope formula here along with the fact that the slope is equal to 1:

[tex]1=\frac{-6-1}{x-4}[/tex] and

[tex]1=\frac{-7}{x-4}[/tex]  and cross multiply to get x - 4 = -7 so

x = -3

Answer:

x = 2, BD = 13

Step-by-step explanation:

Given 2 intersecting chords , then

The product of the parts of one chord is equal to the product of the parts of the other chord, that is

4(5x - 1) = 6 × 6 = 36 ( divide both sides by 4 )

5x - 1 = 9 ( add 1 to both sides )

5x = 10 ( divide both sides by 5 )

x = 2

Then

BD = 5x - 1 + 4 = 5(2) + 3 = 10 + 3 = 13

Answer: AOB

This is because angle AOB on top adds with BOC down below to get the largest angle AOC. See the diagram below.

Answer:

a = 2

b = 0

c = 3

Step-by-step explanation:

if I understand correctly the problem should look like

2x⁴ + 2x³ + 5x² + 3x + 3 = (x² + x + 1)(ax² + bx + c)

let's calculate the right side

ax⁴ + ax³ + ax² + bx³ + bx² + bx + cx² + cx + c

as there is only one term of x⁴, we know a = 2

as there is only one term without any x, we know c = 3

now we get

2x⁴ + 2x³ + 2x² + bx³ + bx² + bx + 3x² + 3x + 3

remember, that is equal to

2x⁴ + 2x³ + 5x² + 3x + 3

after subtracting 2x⁴ and 3 from both sides we get

2x³ + 5x² + 3x = 2x³ + 2x² + bx³ + bx² + bx + 3x² + 3x

we subtract 2x³ and 3x from both sides and get

5x² = 2x² + bx³ + bx² + bx + 3x² = 5x² + bx³ + bx² + bx

we subtract 5x² from both sides and get

0 = bx³ + bx² + bx

=> b must be 0 to make this true for all values of x

Answer:

120

Step-by-step explanation:

i dont know the exact reason but the formula to problems like this is the actual number which is 5 in this sitaution and then multiply the numbers below it. For the equation i did 5x4x3x2x1 and i got 120

Answer:

2703

explanation:

12×189=2268

2268+435=2703

Darrel earned 1503 dollars that week.

Suppose we are given how many no. are there from 224 to 358.

To find do the following (358 - 224 + 1) = 135 numbers.

According to the question Darrel receives a weekly salary of 435 dollars. In addition, 12 dollars is paid for every item sold in excess of 100 items.

Here excess of 100 items means after 100 which is 101.

He sold 189 items so his addition earning is for (189 - 101 + 1) = 89 items.

Given for each item he is paid 12 dollars.

∴ For 89 items he is paid (89 × 12) dollars which is

= 1068 dollars.

So in that week Darrel earns total of (435 + 1068) dollars.

= 1503 dollars.

Learn more about these types of problems here :

https://brainly.com/question/16093003

#SPJ2

Answer:

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

Answer:

Wouldn't it be B?

Step-by-step explanation:

When you have a radical like -[tex]\sqrt{25}[/tex], it would be -5 because the negative is added after the radical is simplified. When the negative is in the inside like your [tex]\sqrt{-25}[/tex], then you can ignore the negative temporarily and simplify to get 5. Then you add an imaginary number.

So it would be 5i?

5si = good

Answer:

they are congruent im pretty sure

Step-by-step explanation:

looks like they are congruent by SAS

Answer:

the function is decreasing on the interval (-∞,-2) and increasing on the interval (-2,∞)

B

Step-by-step explanation:

first we take the first derivative

x²+4x-1 = 2x+4

set this equal to 0 and solve

2x+4= 0

2x= -4

x= -2

we then have two intervals

(-∞,-2) u (-2,∞)

to find out whether something is decreasing on increasing on these intervals just plug in any number in the interval

if the result is positive it's increasing

if it's negative it's decreasing

Let's plug in x= -4 for the interval (-∞, -2)

2(-4)+4= -4

it's negative so it's decreasing on this interval

let's then plug in x=0 for the interval (-2,∞)

2(0)+4= 4

this is positive so it's increasing on this interval

So the function is decreasing on the interval (-∞,-2) and increasing on the interval (-2,∞)

which is equal to to B

Answer:

y=-5x+4

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(-16-(-6))/(4-2)

m=(-16+6)/2

m=-10/2

m=-5

y-y1=m(x-x1)

y-(-6)=-5(x-2)

y+6=-5(x-2)

y+6=-5x+10

y=-5x+10-6

y=-5x+4

Answer: [tex]\dfrac{35}{6}\ \text{days},\ 35\ \text{days}[/tex]

Step-by-step explanation:

Given

Andrew can paint  times faster than the other

Suppose the other person take 6x days

So, andrew takes only x days to paint alone

When they work together, it took them 5 days i.e.

[tex]\Rightarrow \dfrac{1}{x}+\dfrac{1}{6x}=\dfrac{1}{5}\\\\\Rightarrow \dfrac{6+1}{6x}=\dfrac{1}{5}\\\\\Rightarrow x=\dfrac{35}{6}\ \text{days}[/tex]

So, time taken by the to finish individually is given by

[tex]\Rightarrow \text{Andrew= }\dfrac{35}{6}\ \text{days}\\\\\Rightarrow \text{Other Person}=6\times \dfrac{35}{6}\\\\\Rightarrow \text{Other Person}=35\ \text{days}[/tex]

Answer:

The function represents the height of the water in the bucket

Step-by-step explanation:

Given

[tex]f(t) = -t^2 + 4t[/tex]

Required

State what the function represents

From the question, we understand that t represents the time spent while the function illustrates the water level in the bucket.

This implies that f(t) calculates the height of the water in the bucket, given the value of time (t)

Answer:

[tex]{ \tt{ - \frac{3}{8} + \frac{1}{6} }} \\ { \bf{l.c.m \: of \: 8 \: and \: 6 = 24}} \\ { \tt{formular = \frac{(l.c.m \times denominator \div numerator)}{l.c.m} }} \ \\ \\ = \frac{(24 \times 8 \div - 3) + (24 \times6 \div 1)}{24} \\ = - \frac{5}{24} [/tex]

Answer:

$3100

Step-by-step explanation:

Just do 0.025*14000=350. Then add it to $2750

Answer:

Decreasing linear

Step-by-step explanation:

An arithmetic sequence decreases by a set amount every time through subtraction, so that means it's linear