Determine which equation has the same solutions as the equation below.

4x^2 + 32x − 28 = 0

A.) (x + 4)^2 = 23
B.) 4(x + 4)^2 = 36
C.) 4(x + 8)^2 = 28
D.) (x + 8)^2 = 57

Answer:

Numbers are 6 and 17.

Step-by-step explanation:

Let the two numbers are 'a' and 'b'.

"Sum of these numbers = 23"

a + b = 23 --------(1)

"One number is 7 less than 4 times the other"

a = 4b - 7 ---------(2)

Substitute the value of 'a' in equation (1) from equation (2)

(4b - 7) + b = 23

5b - 7 = 23

5b = 23 + 7

5b = 30

b = 6

From equation (2),

a = 4b - 7

a = 4×6 - 7

a = 24 - 7

a = 17

Therefore, the numbers are 6 and 17.

Answer: 7 and 16

Step-by-step explanation:

Let x be the smaller of the two numbers. We are told that the larger number is five less than three times the smaller number x. Therefore, our two numbers are x and 3x−5. Given that the sum is 23, we find that

x+(3x−5)=23

Solving for x, we find that x=7. So the two numbers are 7,16.

Answer:

1) You know that the addition of all interior angles of a triangle always should add up to 180°

Then, for example, we can construct a triangle with angles

100°, 40°, 40° such that

100° + 40° + 40° = 180°

So we have an example of a triangle that has one angle greater than 90°.

2) Suppose that we have the positive numbers 0.5 and 1.

The product is: P = 0.5*1 = 0.5

the sum is: S = 0.5 + 1 = 1.5

The sum is greater than the product.

Answer:

$535.78

Step-by-step explanation:

First find out the annual earnings. So multiply 3.4% by 445

0.034 x 445 = 15.13

That's what the account earns every year. Now multiply it by 6 to know what it'll get in 6 years.

15.13 x 6 = 90.78

Now add that to the initial value.

90.78 + 445 = 535.78

That's the balance in the account after 6 years...

$535.78

Answer:  y = 0x+3 or y = 3

The slope is 0 and the y intercept is 3. So m = 0 and b = 3.

Plug those into y = mx+b to get y = 0x+3, and that simplifies to y = 3.

This graphs out a horizontal line that passes through the two points (0,3) and (1,3).

Answer:

The answer is 108.

Step-by-step explanation:

This can be solved with a simple proportion. 5/12 = 45/1. For 5 to become 45, you need to multiply by 9. You do the same to the denominator. 12 times 9 is 108.

-3x-4= +12

X negative 3 and 4 then add +12 to it.

Answer:

10 ft^3

Step-by-step explanation:

if a cube is 1/3ft then 3 cubes = 1ft

then 30 cubes = 10ft^3

Answer:

7/8 < 15/16

Step-by-step explanation:

Get a common denominator of 16

7/8 *2/2

14/16

14/16 < 15/16

so 7/8 < 15/16

Your answer would be approximately 30.93

Volume of a sphere is V=4 /3πr^3

Answer:

5x⁵4x³+2x²+5x+3

Polynomials will be closed under an operation if the operation produces another polynomial. (2x2 + 3x + 4) + (x2 - 5x - 3) = 3x2 - 2x + 1

Step-by-step explanation:

Answer: 2/8, 4/8, 4/4, 8,8

Step-by-step explanation:

They all have the denominator of 8.

Answer:

x = 27

Step-by-step explanation:

4(x−9)=4(9+1/3x).

Divide each side by 4

(x−9)=(9+1/3x)

Subtract 1/3 x from each side

x - 1/3x -9 = 9+1/3x -1/3x

2/3x -9 = 9

Add 9 to each side

2/3x -9+9 = 9+9

2/3x = 18

Multiply each side by 3/2

3/2 * 2/3x = 18*3/2

x = 27

Answer:

27

Step-by-step explanation:

4(x−9)=4(9+1/3x)

4x-36=36+(4/3)*x

(12/3)*x-36=36+(4/3)*x

(8/3)*x=72

8x=216

x=27

Answer:

Since the first number after the decimal is lower than 5, you would need to round down.  So the answer would be 17(not 18).

Step-by-step explanation:

Answer: $2227.41

Step-by-step explanation:

A = P(1 + r/n)^nt

Answer:

see below

Step-by-step explanation:

Since the initial value is 5 and it increases by 3 every time x goes up the equation is y = 5 * 3^x.

Answer:

i) The maximum height  of the ball 'x' = 1.5 seconds

ii)   The maximum height  = 42

 Step-by-step explanation:

Step(i):-

Given h(x) = - 16 x² + 48 x +6   ...(i)

Differentiating equation (i) with respective to 'x'

[tex]h ^{l} (x) = - 16 (2 x) +48 (1)[/tex]   ...(ii)

Equating Zero

- 3 2 x + 4 8 = 0

- 32 x = - 48

    x = 1.5

step(ii):-

The maximum height of the ball 'x' = 1.5

Again Differentiating equation (ii) with respective to 'x'

[tex]h ^{ll} (x) = - 16 (2 x) < 0[/tex]

The maximum height 'x' = 1.5

h(x) = - 16 x² + 48 x +6  

h(1.5) = - 16 (1.5)² +4 8 (1.5) +6

         =   42

The maximum height at x = 1.5 is  = 42

Final answer:-

i) The maximum height  of the ball 'x' = 1.5 seconds

ii)   The maximum height  = 42

Answer:

a and b are similarity i think that's what your looking 4 idk

Step-by-step explanation:

Answer:

The equation for this function in point slope form: y = -3x+47

Step-by-step explanation:

We are given that a swimming pool is being drained at a constant rate of 3 inches (depth of the water) per hour.

Slope is the rate of change per unit represented by m

So, m = -3

General equation : y = mx+c ----1

y represents the depth of water

t represents the time

The depth of the water after 5 hours is 32 inches.

So, y =32 and x =5

Substitute the values in the equation

So,32=-3(5)+c

32=-15+c

32+15=c

47=c

Substitute the value of c and m in 1

So, The equation for this function in point slope form: y = -3x+47

Answer:

x = 18

Step-by-step explanation:

This problem can be solved using concept of Pythagoras theorem.

Pythagoras theorem states that in a right angled triangle, if "a" and "b" are sides containing the right angle and h is hypotenuse then the relation between them is [tex]a^2 + b^2 = h^2[/tex]

_________________________________________

Given in the problem

a = 24

b = x

h = x+12

applying Pythagoras theorem

[tex]24^2 + x^2 = (x+12)^2\\=> 576 + x^2 = x^2 + 24x + 144\\=>576 = x^2 + 24x + 144 - x^2\\=> 576 = 24x + 144 \\=> 576 - 144= 24x\\=> 432 = 24x\\=> x = 432/24 = 18[/tex]

for (x+12)^2 we have used formula [tex](a+b)^2 = a^2 + 2ab + b^2[/tex]

Thus, value of x is 18.

Answer: z = 28 degrees

Step-by-step explanation:

Since this is an isosceles triangle, two of the angles are congruent.

180 - 124 = 56

56/2 = 28

Answer:

70%

Step-by-step explanation:

42/60= 0.7 = 7/10 = 70%

Answer:

Look at the attachment

Answer:

The Pythagorean theorem states that, for all 90-degree triangles, the relationship between the lengths of the sides is given by the formula a^2 + b^2 = c^2.

DISTANCE FORMULA

The study of geometry in a graphical environment is called co-ordinate geometry.

In co-ordinate geometry, the standard formula for calculating the distance between 2 points is called the distance formula.

Step-by-step explanation:

Answer:

Short answer: They are essentially the same thing.

The distance formula is derived from the Pythagorean Theorem

We have distance formula:

[tex]D = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]

Pythagorean Theorem:

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

The shortest distance between two points if a line. If you draw a line in the cartesian plane both points will have an x-coordinate and y-coordinate. Note that it forms a right triangle! Therefore, the distance between those points is the hypotenuse.

We can have a point [tex]a=(x_{1}, y_{1})[/tex] and point [tex]b=(x_{2}, y_{2})[/tex]

But once [tex]a[/tex] and [tex]b[/tex] can be positive or negative:

[tex]c = \sqrt{a^2+b^2}= D = \sqrt{(\pm a)^2+(\pm b)^2}[/tex]

Answer:

C

Step-by-step explanation:

x-intercept occurs when y=0.

2x -3y= 8

When y=0,

2x -3(0)= 8

2x= 8

x= 8 ÷2

x= 4

Thus the coordinates is (4,0).

To list out the range, you list the y coordinate values of each point of the function. Each point is of the form (x,y). Any duplicate values are tossed out when we talk about a set. All we care about are the unique values. It's common practice to sort the values of the set from smallest to largest.

Side note: Choice A is listing the x values of each point, which is the domain.

Answer:

y=(x+2)²-3

Step-by-step explanation:

when y=x² shifted 3 units down

its eq. is y=x²-3

when it is also shifted 2 units left then its eq. is

y=(x+2)²-3

Answer:

[tex]x=-3[/tex]

Step-by-step explanation:

[tex]-3x-8+6=7[/tex]

[tex]-3x-2=7[/tex]

[tex]-3x-2+2=7+2[/tex]

[tex]-3x=9[/tex]

[tex]$\frac{-3x}{3} =\frac{9}{3} $[/tex]

[tex]-x=3[/tex]

[tex]x=-3[/tex]

Answer:

Wrote it in the explanation :)

Step-by-step explanation:

Expression One: c + 25% = price of gas in august

Expression Two: c + 0.25 = price of gas in august

Expression Two would be easier to use if we knew "c" because the numbers are already in decimal form. If it were in percentage form, it would cause us an extra step to  convert it into a decimal.

Please tell me if you have any further questions...

Hope this helped!!

The answer is f(x)=1/2x+25