The function y = x^2 - 4x + 5 approximates the height, y, of a bird, and its
horizontal distance, x, as it flies from one fence post to another. All distances
are in feet. Complete the square to find and interpret the extreme value
(vertex).
Select two answers: one extreme value and one interpretation.
Height (feet)
Distance (feet)

Answer:

B and D

Step-by-step explanation:

The polynomial x² + 6x - 8 ( from values in first row )

is being evaluated at x = - 5 thus the factor is (x + 5)

If (x + 5) is a factor the remainder = 0

Hence (x + 5) is not a factor since remainder = 12 ≠ 0

When the polynomial is evaluated at x = 5  it's value is 12

The remainder theorem states that f(h) = remainder, hence

f(- 5) = 12 ← remainder

Expand -2(5x+8), simplify, isolate x by moving terms, and solve to get x = -15/8.

To solve the equation -2(5x + 8) = 14 + 6x step by step, here's what was done:

Step 1: Expand the left side of the equation by distributing -2 across the terms inside the parentheses:

-2(5x + 8) = -2 * 5x - 2 * 8 = -10x - 16

So, the equation becomes: -10x - 16 = 14 + 6x

Step 2: Group like terms together. Subtract 6x from both sides to get all the x terms on one side of the equation:

-10x - 6x = 14 + 16

This simplifies to: -16x = 30

Step 3: Now, isolate the variable by dividing both sides by -16:

(-16x)/(-16) = 30/(-16)

This simplifies to: x = -30/16 or x = -15/8

So, the solution for x is x = -15/8.

The complete question is here:

-2(5x+8)=14+6x The equation was solved using the following steps Step 1: -10z-16=14+6z Step 2: -16x-16=14 Step 3: -16x=30 Step 4: z= 21/-16 Step 5: z=- 15/8 Complete the statements below with the process used to achieve steps 1-4 Stop 12 to 5x and 8. Step 26x Step 3 : 16. Step 4: 16.

[tex]

\dfrac{1}{x-1}-\dfrac{3}{x^2+2x-3} \\

\dfrac{1}{x-1}-\dfrac{3}{(x+3)(x-1)} \\

\dfrac{1\cdot(x+3)-3}{(x+3)(x-1)} \\

\dfrac{x+3-3}{(x+3)(x-1)} \\

\dfrac{x}{(x+3)(x-1)}

[/tex]

Hope this helps.

r3t40

Answer:

2log5(x) - 2log5(4)

Step-by-step explanation:

An expression is defined as a set of numbers, variables, and mathematical operations. The expression that is equivalent to log₅(x/4)² is 5log(x) - 5log(4).

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The given expression log₅(x/4)² can be expressed as,

log₅(x/4)²

= 5log(x/4)  {∵ log(aᵇ) = b log(a) }

=5[log(x) - log(4)]

= 5log(x) - 5log(4)

Hence, the expression that is equivalent to log₅(x/4)² is 5log(x) - 5log(4).

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Answer:

B.0.75x + 1.5= 10

Step-by-step explanation:

Answer:

B. 0.75(x)+1.50 = 10

and 11.333333333....

Step-by-step explanation:

Answer:  2x³(x² + 5x - 11)

Step-by-step explanation:

2x⁵ + 10x⁴ - 22x³

Factor out the GCF (2x³)

2x³(x² + 5x - 11)

Since there are no values whose product is -11 and sum is +5, this cannot be factored further.

Answer:

2x^2-4x=14

x^2-2x=7

x^2-2x+1=8

(x-1)^2=8

Answer: $5,591

Step-by-step explanation:

4% = .04

5824 x .04 = 232.96

5824 - 232.96 = 5591

Before sales tax, the car cost $5591

For this case we have the following expression:

[tex]e ^ {\frac {1} {2}}[/tex]

We must evaluate the expression, then:

[tex]e ^ {0.5} =[/tex]

If we enter the expression in a calculator we have that the decimal form is given by:

[tex]1.64872127[/tex]

If we round the expression we have to:

[tex]e ^ {\frac {1} {2}} = 1.7[/tex]

The option that is closest is option A.

Answer:

Option A

Answer:

-6ab+a+1

Step-by-step explanation:

add or subtract like terms.

The difference between (-5ab+a+3) and (ab+2) is calculated by combining like terms and performing the subtraction, resulting in -6ab + a + 1.

To find the difference between the two expressions (-5ab+a+3) and (ab+2), we need to subtract the second expression from the first. Applying the distributive property of subtraction over addition (i.e., a - (b + c) = a - b - c), we get:

Putting it all together, the difference of the two expressions is -6ab + a + 1.

Answer:

Approximately 24 feet.

Step-by-step explanation:

Refer to the two diagrams attached (created with Geogebra.)

The wire between the speaker and the amplifier shall be routed along the wall. The length of the connection depends on the height of the point P at which the wire turns. Point P is shown in green in both diagrams.

To find the optimal position of that turning point, imagine that the two adjacent walls of the room are unfolded into two rectangles in the same plane (diagram 2.) Consider the claim: the shortest connection shall be a straight line that links the two devices when the two walls are unfolded. This explanation will show why this claim is true using the triangle inequality theorem.

Assume this claim is false: the connection will be even shorter if the wire turns at P', which is a point other than P. The length of the connection is now the sum of the two segments:

In contrast, if the wire is routed through point P, the length of the connection will simply be

Point P is on the line that connects the amplifier and the speaker in diagram 2. However, P' is a point other than P, meaning that P' is off the line between the speaker and the amplifier. It is thus possible for the following three points to form a triangle:

By the triangle inequality theorem, the sum of any two sides of a triangle is greater than the length of the third side. To make full use of this theorem, consider the length of the three sides in this triangle:

[tex]\left\{\begin{array}{ll}\left.\begin{aligned}&\text{distance between amplifier and P}'\text{.}\\&\text{distance between P}' \text{ and speaker.}\end{aligned}\right\}&\text{Length of the second connection}\\\text{distance between amplifier and speaker}\end{array}\right.[/tex].

The sum of the first two distances shall be greater than the third. In other words, the length of the connection through P' will be greater than the length of the connection through P. This fact contradicts the assumption that the original claim is false. In other words, the claim that P gives the shortest connection is true.

Find the length of the shortest connection using the Pythagorean Theorem. Refer to the second diagram, the connection is the hypotenuse of a right triangle with

The length of the connection (the hypotenuse) will be:

[tex]\sqrt{23^{2} + 7^{2}}\approx 24[/tex] feet.

An expression is defined as a set of numbers, variables, and mathematical operations. The order of magnitude for the total weight of 5 cars that weigh 3,000 pounds each is 4.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The total weight of the five cars each weighing 3,000 pounds is,

Total weight = Number of cars × Weight of each car

= 5 × 3,000 pounds

= 15,000 pounds.

= 1.5 × 10⁴ pounds

Hence, the order of magnitude for the total weight of 5 cars that weigh 3,000 pounds each is 4.

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Answer:

8640 in ^2

Step-by-step explanation:

1 ft = 12 in

60ft^2 * 12 inches  * 12 inches

             --------------     --------------   = 8640 in ^2

              1  ft                1   ft

Answer:8640

Step-by-step explanation:

Answer:

a. -29

Step-by-step explanation:

The expression is:

24÷(-2)(3)+7

We can see that there is division, multiplication and addition involved. We will use the mathematical DMAS rule to solve the problem. So, division will be done first,

Division will give us:

24÷(-2)*(3)+7

= -12 * 3 + 7

After division, multiplication will be done:

Multiplication will give us:

= -36 +7

which equals to -29

So, option a is the correct answer ..

Answer:

The correct option is B.

Step-by-step explanation:

The correct option is net.

A geometric net is a 2-dimensional shape that can be folded to form a 3-dimensional shape or a solid. Or you can say that  a net is a pattern made when the surface of a three-dimensional figure is laid out flat showing each face of the figure. A solid may have different nets.

The basic steps to determine whether a net forms a solid: are:

1. Make sure that the solid and the net have the same number of faces and that the shapes of the faces of the solid match the shapes of the corresponding faces in the net.  

2. Visualize how the net is to be folded to form the solid and make sure that all the sides are properly fit together.

Nets are helpful when we need to find the surface area of the solids....

Answer:

15/9 =1.7

if u divide 3 by both of them you will have 5/3  .5/ 3 with give you 1.666666667 aproximately to 1.7 that is in one decimal plave

Step-by-step explanation:

Answer:

Because of the minus sign

2 becomes - 2

The answer is -2

Multiply a and 7

Multiply a and 1

The a just gets copied along.

The answer is a

a

7*a evaluates to 7a

Multiply b and 4

Multiply b and 1

The b just gets copied along.

The answer is b

b

4*b evaluates to 4b

7*a+4*b evaluates to 7a+4b

Multiply -2 by 7a+4b

we multiply -2 by each term in 7a+4b term by term.

This is the distributive property of multiplication.

Multiply -2 and 7a

Multiply 1 and a

The a just gets copied along.

a

-2 × 7a = -14a

Multiply -2 and 4b

Multiply 1 and b

The b just gets copied along.

b

-2 × 4b = -8b

-2*(7*a+4*b) evaluates to -14a-8b

Multiply c and 6

Multiply c and 1

The c just gets copied along.

The answer is c

c

6*c evaluates to 6c

The answer is -14a-8b-6c

-2*(7*a+4*b)-6*c evaluates to -14a-8b-6c

The final answer is

-14a-8b-6c

Step-by-step explanation:

Please mark brainliest and have a great day!

[tex]\text{Hey there!}[/tex]

[tex]\text{In order for you to solve this equation, you need to DISTRIBUTE!}[/tex]

[tex]\text{The algebraic formula for distribution is: a(b+c) = a(b)+a(c) = ab + ac}[/tex]

[tex]\text{Now, that we have that portion solved, we can answer your question!}[/tex]

[tex]\text{3.5(2h) + 3.5(4.5)}[/tex]

[tex]\text{3.5(2h) = 7h}[/tex]

[tex]\text{3.5(4.5) = 15.75}[/tex]

[tex]\text{= 7h + 15.75}[/tex]

[tex]\boxed{\boxed{\bf{Answer:7h+15.75}}}\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

Step-by-step explanation:

A= 1 * 1 = 2

A2 = 1 * (1 * 1)

A2 = 1 * 1

A2 = 1

a3 = 1 * 1 * (1 * 1)

a3 = 1 *1 * 1

a3 = 1 * (1*1)

a3 = 1* 1

a3 = 1

You keep on going in this manner until you hit 1^65 = 1

The only thing you have to accept is that (1 * 1) = 1

Answer:

A. y - x = -4

Step-by-step explanation:

y=x-4

To get infinite equations, the equation must be equal to y=x-4

We will solve each of these for y to see if they are identical

A. y - x = -4  

 Add x to each side

y-x+x = x-4

y = x-4

This is the same

It will give infinite solutions

B. y - x = -2

y-x+x = x-2

y =x-2

This is not the same.

It is parallel and will give no solutions

C. y - 4 = x

y-4+4 = x+4

y = x+4

This is parallel and will give no solutions

D. y + 4x = 1

y +4x-4x = -4x+1

This will intersect at a point

Answer: The correct answer is c.

Step-by-step explanation:

I just answered the question for school

Answer:

x=7

Step-by-step explanation:

Solve for x:

3 x + x + 5 = 33

x + 3 x = 4 x:

4 x + 5 = 33

Subtract 5 from both sides:

4 x + (5 - 5) = 33 - 5

5 - 5 = 0:

4 x = 33 - 5

33 - 5 = 28:

4 x = 28

Divide both sides of 4 x = 28 by 4:

(4 x)/4 = 28/4

4/4 = 1:

x = 28/4

The gcd of 28 and 4 is 4, so 28/4 = (4×7)/(4×1) = 4/4×7 = 7:

Answer:  x = 7

The larger number is 26 and the smaller number is 7.

To determine the solution, take the following steps:

The given equation is  x + 3x + 5 = 33

Combine similar terms: x + 3x =33 - 5

Add similar terms: 4x = 28

Divide both sides by 4 : 7

The larger number = 33 - 7 = 26

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Answer:

90°

Step-by-step explanation:

a full rotation is 360° but since there are 4 angles, then divide the 360 by 4 and you'll get 90°

Answer:

10y^7

Step-by-step explanation:

Do 2(5) and do y^4 times y^3!

2(5)=10

if you have to write out what y^4 means and y^3...

How many factors of y do you have 7... so y^4*y^3=y^7

The answer is 10y^7

Answer:

18 + -3

Step-by-step explanation:

It is not really an estimate because it is obviously seen that +- = -.

Answer:

2

Step-by-step explanation:

m² = 4² + 8²  

m² = 16 + 64

m² = 80

l² = k² + 4²

l² = k² + 16

m² + l² = (k + 8)²   m² = 80,  (b)

80 + k² + 16 = k² + 16k + 64

k² - k² - 16k = 64 - 80 -16

-16k = -32

k = -32/-16

k = 2

Answer:

B x^9 ∛ y

Step-by-step explanation:

(x^27 y) ^ (1/3)

x^27^(1/3) y^(1/3)

We can distribute the exponent a^b ^c = a^(b*c)

x^(27*1/3) y^(1/3)

x^9 y^(1/3)

Answer:

a system of equations has 1 solution. if 4x-y=5 is a new of the equations which could be the other equation

The question asks for an algebraic expression. Based on the phrases used, the expression can be written as (5x³ - 4)/x.

The subject of your question involves algebra, which is a branch of mathematics. When the question asks for the 'quotient of the difference of 5 times x cubed and 4 and x', it is asking for an algebraic expression. This expression can be written as (5x³ - 4)/x. This expression cannot be simplified further as the terms in the numerator are not like terms.

Remember that the 'difference' refers to subtraction, 'quotient' refers to division, and 'times' refers to multiplication in algebra. Also, 'x cubed' means x is being raised to the power of 3.

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Answer: 28

Step-by-step explanation:

7/8 = m/32

cross multiply the expression

8m = 224

m = 224/8 = 28

Hope it helped!

[tex]\huge{\boxed{m=28}}[/tex]

[tex]\frac{7}{8}=\frac{m}{32}[/tex]

Since [tex]8[/tex] is multiplied by [tex]4[/tex] to get 32, you also multiply [tex]7[/tex] by [tex]4[/tex] to get [tex]m[/tex].

[tex]7*4=28[/tex]