The perimeter of a rectangular garden is 306 feet. If the length of the garden is 99 feet, what is its width?
feet
Х
5
?

Answer: The vertex form is h(x)=(x-3)^2-6

Step-by-step explanation:

Using the complete the square method, first complete any squares

X^2-6x+(-3)^2-(-3)^2+3

Use the binomial formula

(x-3)^2 - (-3)^2 +3

Simplify

(x-3)^2-6

Answer:

100

Step-by-step explanation:

Since the inscribed angle of a circle is always half of its corresponding, the measure of this angle is 200/2=100 degrees. Hope this helps!

Answer:

100

Step-by-step explanation:

Answer:

The summands are 4 and 5. The sum is 9.

Step-by-step explanation:

In the binary system, the digits, starting at the right and moving to the left are:

1's

2's

4's

8's

etc.

100 = 0 units + 0 2's + 1 four = 0 + 0 + 4 = 4

101 = 1 unit + 0 2's + 1 4's = 1 + 0 + 4 = 5

In decimal, the addition is:

4 + 5 = 9

The summands are 4 and 5. The sum is 9.

The decimal equivalent  of the sum is 9.

It is required to write decimal equivalent of the summand and sum.

Positional numeral system employing 2 as the base and so requiring only two different symbols for its digits, 0 and 1.It is used for representing binary quantities which can be represented by any device that has only two operating states or possible conditions.

Given:

In the binary system, the digits, starting at the right and moving to the left.

The binary numeral system or base-2 numeral system which represents numeric values using two different symbols: typically 0 (zero) and 1 (one). The base-2 system is a positional notation with a radix of 2.

1's  2's  4's   8's  etc.

[tex]100\\\\0*2^{0} +0*2^{1}+1*2^{2}\\\\=0+0+4\\\\=4[/tex]

[tex]101\\\\=1*2^{0} +0*2^{1} +1*2^{2} \\\\=1+0+4\\\\=5[/tex]

In decimal, the addition is:

4 + 5 = 9

∴The summands are 4 and 5.

Therefore, the decimal equivalent  of the sum is 9.

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Answer:

option D

Step-by-step explanation:

x/-3≤3

multiply by (-1) on both sides

x/3≥-3

x>=-9

Answer:

Letter D

Step-by-step explanation:

Answer:

-40*h+280

Step-by-step explanation:

Let s define the function f which represents Emily's distance from home

at h = 0 Emily is 280 miles away from home

so f(0)=280

as she is traveling back at a rate of 40 miles per hour

f(h)=-40*h+280

the graph is below

The required equation for the distance is y = 280 - 40h and graph is shown below.

In unit time, the distance covered by any object is called speed.

In mathematical term, Speed is express as S = D/T,

where S=speed, D=distance, T= time.

Given that,

Distance of Emily from her home = 280 miles,

The speed of Emily of coming back = 40 miles per hour.

In h hours, the distance covered by Emily = 40h

Let the remaining distance is y,

So the equation can be written as,

y = 280 - 40h.

The graph of the equation represented below.

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Answer:

y=x+ 3

Step-by-step explanation:

The given equation is y = x, which is parallel to y = x + 3

Also, the equation I chose has an x-intercept of -3.

The equation of the line that is parallel to the given line and has an x - intercept of - 3 is,

⇒ y = 2/3x - 1

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Two points on the line are (3, 1) and (0, -1).

Now,

Since, The equation of line passes through the points (3, 1) and (0, -1).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (- 1 - 1) / (0 - 3)

m = - 2 / - 3

m = 2/3

Thus, The equation of line with slope 2/3 is,

⇒ y - 1 = 2/3 (x - 3)

⇒ y - 1 = 2/3x - 2

⇒ y = 2/3x - 1

Therefore, The equation of the line that is parallel to the given line and has an x - intercept of - 3 is,

⇒ y = 2/3x - 1

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Answer:

Median = 3.5

Step-by-step explanation:

Median is the middlemost number.

Here, there are two middlemost numbers, 5 and 2

So, we'll take the mean of them to find out the median

Median = 5+2/2

Median = 7/2

Median = 3.5

Answer:

-20

Step-by-step explanation:

f(x)= 2x^2 + 5x - 17,

f(-1)

Let x = -1

f(-1)= 2 *(-1)^2 + 5(-1) - 17

     = 2 *1   -5 -17

    = 2 -22

   = -20

Answer:

-20

Step-by-step explanation:

f(x)= 2x² + 5x - 17

Put x as -1.

f(-1)= 2(-1)² + 5(-1) - 17

Solve for the powers.

f(-1)= 2(1) + 5(-1) - 17

Multiply the terms.

f(-1)= 2 + -5 - 17

Add or subtract the terms.

f(-1)= -20

Answer:

The maximum height the projectile reaches is 100 feet

Step-by-step explanation:

Notice that the given equation representing the height of the projectile is a quadratic equation which negative leading coefficient (-16). Such type of equations would have a parabola that branches downwards as its graph.

therefore, what we need to find is the coordinates of the top vertex of that parabola. We can use for such the typical formula for the x-position of the vertex of a parabola with standard equation:

[tex]f(x)=ax^2+bx+c[/tex]

with x-position of the vertex given by:

[tex]x_v=\frac{-b}{2a}[/tex]

Then in our case  ([tex]H(t)=-16t^2+16t+96[/tex])  we have:

Horizontal position of the vertex given by:

[tex]t_{vertex}=\frac{-16}{2(-16)} =\frac{1}{2}[/tex]

and now we can find the maximum height plugging this value into the height expression:

[tex]H(t)=-16(\frac{1}{2}) ^2+16\,(\frac{1}{2})+96=-4+8+96=100\,\,ft[/tex]

Answer:

Hi there!

The correct answer is: True

Step-by-step explanation:

If there is a line, there are infinite planes that pass through that line, therefore since the 4 points are in a line, they are coplanar .

Answer:

Step-by-step explanation:

An x value of 0 can only be plugged into the equation that has a domain that includes 0. The first function's domain is between -2 and -4, so 0 is not included in that domain. In the third function, the domain is between 1 and 3, so 0 is not included in that domain, either. The middle function's domain does include 0 (0 falls between -2 and 1) so we can only evaluate this function at an x value of 0.

g(0) = -0 - 1 so

g(0) = -1

Answer:

B

Step-by-step explanation:

-1

Answer:

21,845

Step-by-step explanation:

The sum of geometric sequence:

S n = a 1 * ( q^n - 1 ) / ( q - 1 )

where:  a 1 = 1,

q = a 2 : a 1 = 4 : 1 = 4

S 8 = 1 * ( 4^(8) - 1 ) / ( 4 - 1 ) =

= ( 65,536 - 1 ) / ( 4 - 1 ) = 65,535 / 3 = 21,845

Answer:

V = 1072.3 cm³

Step-by-step explanation:

Volume of a hemisphere = [tex]\frac{2}{3} \pi r^3[/tex] [Because it's half of a sphere's volume]

V = [tex]\frac{2}{3} (3.14)(8)^3[/tex]

V = [tex]\frac{2}{3} (3.14)(512)[/tex]

V = [tex]\frac{3216.99}{3}[/tex]

V = 1072.3 cm³

Answer:

The resultant velocity is 12.21 m/s.

Step-by-step explanation:

We are given that the water from a fire hose follows a path described by y equals 2.0 plus 0.9 x minus 0.10 x squared ​(units are in​ meters).

Also, v Subscript x is constant at 10.0 ​m/s.

The water from a fire hose follows a path described by the following equation below;

[tex]y=2.0 + 0.9x-0.10x^{2}[/tex]

The velocity of the [tex]x[/tex] component is constant at =  [tex]v_x=10.0 \text{ m/s}[/tex]

and the point at which resultant velocity has to be calculated is (9.0,2.0).

Let the velocity of x and y component be represented as;

[tex]v_x=\frac{dx}{dt} \text{ and } v_y=\frac{dy}{dt}[/tex]

Now, differentiating the above equation with respect to t, we get;

[tex]y=2.0 + 0.9x-0.10x^{2}[/tex]

[tex]\frac{dy}{dt} =0 + 0.9\frac{dx}{dt} -(0.10\times 2)\frac{dx}{dt}[/tex]

[tex]\frac{dy}{dt} = 0.9\frac{dx}{dt} -0.2\frac{dx}{dt}[/tex]

[tex]v_y = 0.9v_x -0.2v_x[/tex]

[tex]v_y = 0.7v_x[/tex]

Now, putting [tex]v_x=10.0 \text{ m/s}[/tex] in the above equation;

[tex]v_y = 0.7 \times 10.0[/tex] = 7 m/s

Now, the resultant velocity is given by = [tex]v=\sqrt{v_x^{2}+v_y^{2} }[/tex]

                            [tex]v=\sqrt{10^{2}+7^{2} }[/tex]

                               = [tex]\sqrt{149}[/tex] = 12.21 m/s

See attached graph: v is on the y-axis and t is on the x-axis

Answer:

D

Step-by-step explanation:

subsitute each of the x and y values for each of the equations and if they both equal each other It is correct.

Answer:

x = 2, y= -1

Step-by-step explanation:

12x - y = 25

9x + y = 17

add both equations to eliminate y

21x = 42

divide by 21

x = 42/21

x = 2

sub x in equation i to find y

12(2) - y = 25

24 - y = 25

-y = 1

therefore y = -1, x = 2

Answer:

Jason likely misplaced the decimal, because 3 times 1 = 3, and if the decimal was between the 2 and the 5, the number would be near 3.

Step-by-step explanation:

Jason applied 2 and 82.242 miles

Answer:

b

Step-by-step explanation:

[tex]42 \times 48=2016[/tex]

[tex]24 \times 84 = 2016[/tex]

The answer is 42 × 48 because even when we switch the digits, the product remains the same.

Answer:

The correct option is SSS (Side-Side-Side) Theorem

Step-by-step explanation:

The question is incomplete because the diagrams of ΔLON and ΔLMN are not given. I have attached the diagram of both triangles below for better understanding of the question.

Consider the diagram attached below. We have to find the congruence theorem which can be used to prove that ΔLON ≅ ΔLMN

We can see in the diagram that both triangle have a common side that is LN. It means 1 side of both triangles is congruent because LN≅LN

Consider the sides ON and MN. Both side have a single bar on them, which means that it is given that both of these side are congruent. Hence ON≅MN

Consider the sides LO and LM. Both side have a double bars on them, which means that it is given that both of these side are also congruent. Hence LO≅LM

SSS theorem states that if all sides of the triangles are congruent, then the triangles themselves are also congruent, which is the same case in this question

Answer:

D. SSS

Step-by-step explanation:

I hope this helps.

Answer:

in total she would spend 27.90 so she should bring C i got this by doing 7.80 x 3 because she is buying 3 medium pizzas then i did 0.75 x 6 and got 27.90 so at least bring 25-30 dollars with her

Step-by-step explanation:

Answer:

Step-by-step explanation:

You didn't list any choices here, but it doesn't matter. There's only one way to get to the answer so we'll work it through and you can match it up to your choices. The only thing I don't know is how pens is identified if pencils is "p". So I'm going to use the words "pens" and "pencils" and you can take it from there at the end.

If a pen's cost IS twice as much as a pencil...

the word "is" indicates an equals sign, the words "twice as much" indicates 2 multiplied by something. To put that above sentence into an algebraic expression:

pen = 2 pencils

Now for the money part of this.

The total cost of 11 pens and 11 pencils IS (there's that word again!) 2.10

Therefore,

11 pens + 11 pencils = 2.10

But we know from the first expression that pen = 2 pencils so we make the substitution:

11(2 pencils) + 11 pencils = 2.10

I'm not sure how far you are to go with this. That's the main equation you need to solve this. If you were to go further with it you would distribute the 11 into the set of parenthesis to get:

22 pencils + 11 pencils = 2.10 and combine like terms:

33 pencils = 2.10 so

1 pencil is approximately $.06

Answer:

1. A letter, A, added to a letter, B, equals ten.

2. A letter, x, which is multiplied by 4, then has a number, y, subtracted from it to equal a letter, a.

If you try write these out, I'm sure you'd get the algebraic expression given.

Answer:

AB=6 Units

Step-by-step explanation:

Given the following lengths of rectangle ABCD and its dilation A'B'C'D' respectively

We are to determine the length of AB. To do this, we first determine the dilation factor.

[tex]D$ilation Factor =\dfrac{B'C'}{BC} =\dfrac{9.5}{3.8} =2.5[/tex]

Therefore:

[tex]\dfrac{A'B'}{AB} =2.5\\\\\dfrac{15}{AB} =2.5\\$Cross multiply \\ 2.5 AB =15 \\AB=15 \div 2.5\\$Therefore, AB=6 Units[/tex]

Answer:

6 units

Step-by-step explanation:

edge 2022

Answer:

$6.89

Step-by-step explanation:

To find unit price divide the dollar by the amount. The dollar is 20.67. The amount of socks are 3. The equation would then be 20.67/3. Then solve and the answer would be $6.89.

Answer:

12-y------------> 9

3x-y------------>21

4y-10----------->2

1/4 xy-----------> 6

Solution,

Given,

X=8

y=3

Now,

[tex]1. \: \: 12 - y \\ \: \: \: = 12 - 3 \\ \: \: = 9 \\ 2. \: \: 3x - y \\ \: \: = 3 \times 8 - 3 \\ \: \: = 21 \\ 3. \: \: 4y - 10 \\ \: \: = 4 \times 3 - 10 \\ \: = 12 - 10 \\ \: \: = 2 \\ 4. \: \: \frac{1}{4} xy \\ \: \: = \frac{1}{4} \times 8 \times 3 \\ = 6[/tex]

hope this helps...

Good luck on your assignment...

Answer:

A reflection across the y axis

Step-by-step explanation:

think about it, if you reflect some point across the y-axis it will have a negative x value.  For example, if you reflect (1,2) across the y-axis you will get (-1,2)

Answer:

This type of transformation is called mirroring in the y-axis.

Step-by-step explanation:

By mirroring in the y-axis, you can find the new value, by multiplying the x-coordinate by -1.

Any point (a , b) will be transformed after mirroring in the y-axis, to (-a , b), which is the question here.

This type of transformation is called mirroring in the y-axis.

Answer:

a) 0.68

b) 0.08

c) 0.74

Step-by-step explanation:

Given that:

Probability of hitting bulls eye, P(B) = 0.26

Probability of an inner, P(I) = 0.42

Probability of an outer, P(O) = 0.24

a) Probability of hitting an inner or better (inner or bulls eye):

P(I or B) = P(I [tex]\cup[/tex] B)

Formula for P(P [tex]\cup[/tex] Q)  where P(P) and P(Q) are the probabilities of two mutually exclusive events i.e. having nothing in common:

P(P [tex]\cup[/tex] Q)  = P(P) + P(Q)

P(I [tex]\cup[/tex] B)  = P(I) + P(B) = 0.26 + 0.42 = 0.68

b) Probability of failing to hit the target:

P(F) = 1 - (P(B)+P(I)+P(O))

P(F) = 1 - (0.26 + 0.42 + 0.24)) = 1 - 0.92 = 0.08

c) Probability of failing to score a bulls eye:

P(B)' = 1 - P(B) = 1 - 0.26  = 0.74

So, the answers are:

a) 0.68

b) 0.08

c) 0.74

Answer:

6 1/6 ft

Step-by-step explanation:

12 inches = 1 ft

So 2 inches is 2/12 of a foot

2/12 = 1/6

6 ft 2 inches = 6  1/6 ft

Answer:

Converges

Sum = 20.8333

Step-by-step explanation:

A geometric series has a general formula of:

[tex]\sum ar^n[/tex]

Where 'a' is the initial term, 'n' is the number of terms, and 'r' is the constant ratio. If |r| < 1 than the series converges.

In this particular case, the initial term is a=25, and each term is being divided by -5, or multiplied by -0.2, so the general form would be:

[tex]\sum 25*(-0.2)^n[/tex]

Since 0.2 < 1.0, the series converges.

The sum of the series is given by:

[tex]S=\frac{a}{1-r}\\S=\frac{25}{1-(-0.2)}\\S=20.8333[/tex]

The sum is 20.8333.

The geometric series converges and the sum is equal to 20.83.

A geometric series is the sum of an infinite number of terms that have a constant ratio between successive terms .

A geometric series has a general formula of:

∑arⁿ

Where 'a' is the initial term, 'n' is the number of terms, and 'r' is the constant ratio. If |r| < 1 than the series converges.

In this particular case, the initial term is a=25 and each term is divided by -5 or multiplied by (-0.2)

Therefore r = -0.2 and as it is <1 therefore the series converges

The sum of a convergent series is

S = a/(1-r)

S = 25/(1-(-0.2))

S= 25/1.2

S = 20.83

Therefore the sum of the series is 20.83

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