Simplify the expression –3(x + 3)2 – 3 + 3x. What is the simplified expression in standard form?

–3x2 – 18x – 27
–3x2 – 15x – 30
–3x2 + 3x + 6
–3x2 + 3x – 30

Answer:

The minimum value of the width is 15 ft and the maximum value of the width is 30 ft

Step-by-step explanation:

Let

x -----> the length of the deck

y ----> the width of the deck

we know that

The perimeter of the deck is equal to

[tex]P=2(x+y)[/tex]

[tex]P=90\ ft[/tex]

so

[tex]90=2(x+y)[/tex]

[tex]45=(x+y)[/tex]

[tex]x=45-y[/tex] -----> equation A

The area is equal to

[tex]xy\geq 450[/tex] -----> inequality B  

[tex](45-y)y\geq 450\\ \\-y^{2} +45y-450\geq 0[/tex]

Solve the quadratic equation by graphing

The possible width of the deck are the values of y in the interval

[15,30]

All real numbers greater than or equal to 15 ft and less than or equal to 30 ft

see the attached figure

The minimum value of the width is 15 ft and the maximum value of the width is 30 ft

[tex]2x+7x=747\\9x=747\\x=83\\\\2x=166\\7x=581[/tex]

Tom - [tex]\pounds166[/tex]

Ben - [tex]\pounds581[/tex]

Answer:

-12-14i

Step-by-step explanation:

subtract real from real number and imaginary from imaginary number

Answer:

-12 -14i

Step-by-step explanation:

(2 + 2i) - (14+ 16i)

Distribute the negative sign

2+2i -14-16i

Subtract the real part

2-14 = -12

Subtract the imaginary part

2-16 = -14

Put them back together in the form a + bi where a is the real part and b is the imaginary part

-12 -14i

Answer:

The height of the trapezoid is [tex]4.5\ ft[/tex]

Step-by-step explanation:

we know that

The area of a trapezoid is equal to

[tex]A=\frac{1}{2}(b1+b2)h[/tex]

In this problem we have

[tex]A=33.75\ ft^{2}[/tex]

[tex]b1=5\ ft[/tex]

[tex]b2=10\ ft[/tex]

substitute in the formula and solve for h

[tex]33.75=\frac{1}{2}(5+10)h[/tex]

[tex]67.5=15h[/tex]

[tex]h=67.5/15=4.5\ ft[/tex]

Answer:

[tex]h=4.5\text{ feet}[/tex]

Step-by-step explanation:

We have been given that a plot of land has an area 33.75 square feet. Jackson wants to put a 4-foot by 4 foot shed on the land. Jackson wants to put a 4-foot by 4 foot shed on the land. He can only do this if the height of the trapezoid is at least 4.5 feet.

We will use area of trapezoid to find the height of trapezoid.

[tex]\text{Area of trapezoid}=\frac{1}{2}(a_1+a_2)\times h[/tex], where,

[tex]a_1\text{ and }a_2=\text{ Parallel sides or bases of trapezoid}[/tex],

[tex]h=\text{Height}[/tex].

We can see that parallel sides are 5 feet and 10 feet. We have been given that area of trapezoid is 33.75 square feet.

[tex]33.75\text{ feet}^2=\frac{1}{2}(\text{ 5 feet + 10 feet})\times h[/tex]

[tex]33.75\text{ feet}^2=\frac{1}{2}(\text{ 15 feet})\times h[/tex]

Switch sides:

[tex]2\times\frac{1}{2}(\text{ 15 feet})\times h=2\times 33.75\text{ feet}^2[/tex]

[tex]\text{ 15 feet}\times h=67.50\text{ feet}^2[/tex]

[tex]\frac{\text{ 15 feet}\times h}{\text{ 15 feet}}=\frac{67.50\text{ feet}^2}{\text{ 15 feet}}[/tex]

[tex]h=4.5\text{ feet}[/tex]

Since the height of trapezoid is 4.5 feet, therefore, Jackson can put a 4 foot by 4 foot shed on the land.

Answer:

29/50 is the same as 0.580

Step-by-step explanation:

0.580 is the same as 0.58

.58=58/100

I knew to put 58 over 100

because the decimal terminates in the hundredths spot

58/100 can be reduced

58 and 100 are both even so they are both divisible by 2

58/2=29

while

100/2=50

so 58/100 is the same as saying 29/50

Answer:

29/50

Step-by-step explanation:

0.58 = 58/100 = 29/50

Answer:

[tex]12.5 \div 100 \times 6000 \times 0.5 = 375.00[/tex]

you have to convert six months to years by dividing six by 12 because it must be in years

Step-by-step explanation:

6÷12=0.5years

%/rate × money × years

12.5 ÷100 always divide by 100 because it is percentages over 100

12.5÷100 ×6000 ×0.5=Rs375.00

Answer:

Rs 375.00

Step-by-step explanation:

12.5 ÷ 100 × 6000 × 0.5 = 375.00

Answer:

-55

Step-by-step explanation:

A debt is a negative value

-55

Answer:

[tex]-55[/tex].

Step-by-step explanation:

We are asked to write an integer for the given situation.

Situation: Greg has a debt of $55.

As Greg has a debt of $55, this means that Greg owes $55 to someone.

So the balance of Greg's account would be [tex]-55[/tex].

Therefore, our required integer would be [tex]-55[/tex].

Answer:

Segment JK is a chord in circle H

Line LM is a secant to circle H

Step-by-step explanation:

* Lets revise some definition in the circle

- The radius of the circle is a line segment drawn from the center of  

 the circle to a point on the circumference of the circle

- The chord of a circle is a line segment whose endpoints lie on the

 circumference of the circle

- The secant is a line intersect the circle in two points

- The tangent is a line touch or intersect the circle in one point

* Now lets solve the problem

- In circle H

∵ JK is a segment in circle H

∵ Point J lies on the circumference of circle H

∵ Point K lies on the circumference of circle H

∴ Segment JK is a chord in circle H

∵ LM is a line

∵ LM intersect circle H in two points L and M

∴ Line LM is a secant to circle H

Answer:

98 ft  and   38 ft

Step-by-step explanation:

We know that the initial length of the piece is  136 feet

Then the piece is cut into two pieces.

Let's call x the length of the first piece  of cable and call z the length of the second piece of cable.

So we know that

[tex]x + z = 136[/tex]

and

[tex]x = 3z-16[/tex]

Now we substitute the second equation in the first one and solve for the variable z

[tex]3z-16 + z = 136[/tex]

[tex]4z-16= 136[/tex]

[tex]4z= 136+16[/tex]

[tex]z= \frac{152}{4}[/tex]

[tex]z=38\ ft[/tex]

Now we find the length x

[tex]x + 38 = 136[/tex]

[tex]x= 136-38[/tex]

[tex]x= 98\ ft[/tex]

Answer:

x=6

x=2

Step-by-step explanation:

Fortunately for us, the function is written in factorized terms, so it is easier to find its roots.

The roots are the values for the 'x' variables that makes the functions goes to zero.

They are x=6 and x=2, any of those value make the function equals zero, or in other words, they are the points of interception with the 'y' axis.

To obtain these value

lets study the following condition

(x-6) * (x-2)=0

The above is accomplish when (x-6)=0 or (x-2)=0

We have two independent equations from where we obtain that x=6 and x=2

To find the x-intercepts of a parabola with given vertex and y-intercept, we can use the vertex form of the equation. Substituting the given values, we find the value of a, and then substitute the values again to find the x-intercepts. The x-intercepts of this parabola are approximately (0.55, 0) and (1.45, 0).

To find the x-intercepts of a parabola, we need to find the values of x when y is equal to zero. Starting with the equation of the parabola in vertex form, y = a(x-h)^2 + k, where (h,k) is the vertex, we can substitute the given values for the vertex (1,1) into the equation. This gives us y = a(x-1)^2 + 1. Next, we substitute the y-intercept (-3) into the equation, so we have -3 = a(0-1)^2 + 1. Solving for a, we get a = -2.

Now we can substitute a and the given values into the equation again to find the x-intercepts. Plugging in a = -2, we have 0 = -2(x-1)^2 + 1. Simplifying this equation and solving for x, we get x = 1 ± √(3/2). Rounding to the nearest hundredth, the x-intercepts are approximately (0.55, 0) and (1.45, 0).

https://brainly.com/question/29158613

#SPJ12

Answer:

y=-4x

Step-by-step explanation:

You can graph it.. It might be easier for you to count than to use the formula for slope. We are counting from (0,0) to (2,-8)... I'm doing rise/run... I have to go down from (0,0) 8 units so the rise is -8 and the run is 2. So the slope is -8/2=-4.

We know the y-intercept is (0,0)... so the equation is y=-4x+0 or just y=-4x

Maybe you seen that this was proportional because it was a straight diagonal line going through the origin which we knew then that the line was already in the form of y=kx

Then you can look at the point (2,-8) and see what you need to do 2 to get -8 multiplication-wise.

2(-4)=-8

so

x(-4)=y

or

y=-4x

Answer:

[tex]a=0.1\\b=0.85[/tex]

Step-by-step explanation:

In this problem we are calculating the relative frequency conditional by columns.

Therefore the sum of the frequencies of each column must be equal to 1.

Then we use this condition to calculate the values of a and b

So:

[tex]0.9 + a = 1\\a = 1-0.9\\a = 0.1[/tex]

[tex]b +0.15 = 1\\b = 1-0.15\\b = 0.85[/tex]

Finally

[tex]a=0.1\\b=0.85[/tex]

Answer:

Values of a and b are:

a=0.1

and b=0.85

Step-by-step explanation:

As we can clearly see from the table that sum of each column is equal to 1.0

i.e. 0.9+a=1.0

and b+0.15=1.0

Hence, a=1.0-0.9

              = 0.1

and b=1.0-0.15

        =0.85

Hence, Values of a and b are:

a=0.1

and b=0.85

[tex]|\Omega|=3+4+5=12\\|A|=3+5=8\\\\P(A)=\dfrac{8}{12}=\dfrac{2}{3}\approx66.7\%[/tex]

Answer:

3:2

Step-by-step explanation:

To answer questions like this I would makeup an age for Alan

Like say Alan is 10 years old

John is 3 times the age of 10 so he is 30

Ralph is twice the age of 10 so he is 20

so 30/20 can be simplified to 3/2

There are other ways to solve it but that is how I would solve it

I hope it helped you

Answer:

3:2 or 3/2

Step-by-step explanation:

Let Alan's age be x

So according to the assumed variable, John's age will be three times of Alan's age

John's Age = 3x

Similarly,

Twice of Alan's age = 2x

so, Ralph's age = 2x

Since we have to find the ratio of John's age to Ralph's age that will be equal to

3x : 2x

which can also be written as:

3:2 or 3/2 ..

Answer:

supplementary angle sum = 180°

EOG + EOF = 180°

71° +EOF = 180°  

EOF = 180° -71°

EOF = 109°

Step-by-step explanation:

Answer:

m<EOF = 109 deg

Step-by-step explanation:

Definition of supplementary angles:

Two angles are supplementary if the sum of their measures is 180 degrees.

Angles EOF and EOG are supplementary, so the sum of their measures is 180 degrees.

m<EOF + m<EOG = 180

We are given the measure of <EOG: m<EOG = 71 deg.

We substitute that measure in our equation and solve the equation for m<EOF.

m<EOF + 71 deg = 180 deg

Subtract 71 deg from both sides.

m<EOF = 109 deg

Answer:

f(x)=(x-12)^2

Step-by-step explanation:

We know that the function f(x+m) equals to the function f(x) translated 'm' times to the left. Therefore, to translate the function f(x) = x^2 twelve units to the right, we have to:

f(x-12) = (x-12)^2

Therefore, the new function is: f(x)=(x-12)^2

Answer:

f(x)=-1(x+4)(x-3)

or  f(x)=-(x+4)(x-3)

Step-by-step explanation:

We see zeros at x=-4 and x=3.

So the factors are (x+4) and (x-3).

So we have a function that looks like

f(x)=A(x+4)(x-3).

y=A(x+4)(x-3)

I see the point (1,10) is on the curve.

So that means

10=A(1+4)(1-3)

10=A(5)(-2)

10=A(-10)

A=-1

So the function is f(x)=-1(x+4)(x-3)

or                          f(x)=-(x+4)(x-3)

Answer:

0.3x = 100

x = 1000/3 = 333 and 1/3

To solve this you must use a proportion like so...

[tex]\frac{part}{whole} = \frac{part}{whole}[/tex]

65 is a percent and percents are always taken out of the 100. This means that one proportion will have 65 as the part and 100 as the whole

We want to know out of what number is 78 65%. This means 78 is the part and the unknown (let's make this x) is the whole

[tex]\frac{78}{x} =\frac{65}{100}[/tex]

Now you must cross multiply

78*100 = 65*x

7800 = 65x

To isolate x divide 65 to both sides

7800/65 = 65x/65

120 = x

This means that 65% of 120 is 78

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer: 120

It is because google said so

Answer:

You multiply

Step-by-step explanation:

The base: 12 in times 12 in

Each side (There are four, so multiply by 4!): 10 in times 12 in divided by 2

Answer:

Answer: A (first option)

Step-by-step explanation:

E2020

The angles formed by the diagonals and sides of the rhombus are

x + y = z.

Option A is correct.

As, When the diagonals of a rhombus are perpendicular, the angle z must be exactly 90 degrees (z=90).

Any triangle's interior angles must add up to 180 degrees.

Using Angle Sum Property

x + y + z = 180°

(x+y+z)=180°

x+y+z=180

As, z=90

x + y + 90 = 180

x + y = 90

So, the angles formed by diagonals is x + y = z.

Learn more about Rhombus here:

https://brainly.com/question/4910909

#SPJ7

Answer:

[tex]\large\boxed{\left[\begin{array}{ccc}1&26&7\end{array}\right] }[/tex]

Step-by-step explanation:

[tex]\left[\begin{array}{ccc}-1&2&4\end{array}\right] \times\left[\begin{array}{ccc}3&6&1\\2&4&0\\0&6&2\end{array}\right]\\\\=\left[\begin{array}{ccc}(-1)(3)+(2)(2)+(4)(0)&(-1)(6)+(2)(4)+(4)(6)&(-1)(1)+(2)(0)+(4)(2)\end{array}\right]\\\\=\left[\begin{array}{ccc}-3+4+0&-6+8+24&-1+0+8\end{array}\right] \\\\=\left[\begin{array}{ccc}1&26&7\end{array}\right][/tex]

Option B [1 26 7] is the product of given matrix.

What is matrix multiplication formula?

Consider matrix A which is a × b matrix and matrix B, which is a b ×c matrix.

Then, matrix C = AB is defined as the A × B matrix.

An element in matrix C, Cxy is defined as Cxy = Ax1By1 +….. + AxbBby =

AxkBky  for x = 1…… a  and y= 1…….c

How to multiply given matrix?

[tex]\left[\begin{array}{ccc}-1&2&4\end{array}\right][/tex]×[tex]\left[\begin{array}{ccc}3&6&1\\2&4&0\\0&6&2\end{array}\right][/tex]

=[ -1×3+2×2+4×0   -1×6+2×4+4×6   -1×1+2×0+4×2  ]

=[-3+4+0   -6+8+24   -1+0+8]

=[1  26 7 ]

Learn more about matrix : https://brainly.com/question/14490203

#SPJ2

Answer: w = 4

Step-by-step explanation:

Subtract 1w from each side of the equation to get 5w = 20.

Divide both sides of the equation by 5 to get w = 4.

Hello!

Answer:

[tex]\boxed{w=4}\checkmark[/tex]

Answer should be positive sign.

Step-by-step explanation:

First, you subtract by w both sides of an equation.

[tex]6w-w=w+20-w[/tex]

Simplify.

[tex]5w=20[/tex]

Then, you divide by 5 both sides of an equation.

[tex]\frac{5w}{5}=\frac{20}{5}[/tex]

Finally, simplify and then solve.

[tex]20\div 5 = 4[/tex]

[tex]\boxed{w=4}[/tex], which is our final answer.

Hope this helps!

Thanks!

Have a nice day! :)

Answer:

5x - 1

Step-by-step explanation:

(f + g)(x) = f(x) + g(x)

f(x) + g(x) = 3x - 2 + 2x + 1 ← collect like terms

               = 5x - 1

[tex](f+g)(x)=3x-2+2x+1=5x-1[/tex]

there are 50 states, NY is the 27th largest so before NY there are other 26 states that are larger than NY.

if we take 50 to be the 100%, what is 26 off of it in percentage?

[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 50&100\\ 26&x \end{array}\implies \cfrac{50}{26}=\cfrac{100}{x}\implies \cfrac{25}{13}=\cfrac{100}{x}\implies 25x=1300 \\\\\\ x=\cfrac{1300}{25}\implies x=52[/tex]

Answer:

Step-by-step explanation:

Givens

Let Phoebe = P

Let Andy = A

Let Polly = Po

Total = 270

Equations

P = 3*A

A = 2*Po

P + A + Po = 270

Solution

P + 2Po + Po = 270

P = 3*A                                       But A = 2Po. Substitue 2Po for A

P = 3(2*Po)                                 Combine the right

P = 6Po                                      Substitute 6Po for P  

6Po + 2Po + Po = 270               Combine the left

9*Po = 270                                 Divide by 9

9Po/9 = 270/9                           Do the division

Po = 30

==========================

A = 2*Po = 2* 30 = 60

A = 60

==========================

P = 3*A

P = 3*60

P = 180

Answer

Phoebe gets 180

Andy gets       60

Polly gets        30

Answer:

3 < third side < 13

Step-by-step explanation:

The third side must be greater than the difference of the two other sides

and less than the the sum of the two sides

8-5 < third side < 8+5

3 < third side < 13

Answer:

there was an increase and it increased by 6.9%

Answer:

y = 4x + b, where b is any number

Step-by-step explanation:

Adrian, you need to share the possible answer choices.

Every line parallel to y = 4x + 1 has the slope 4.

This is true for any y-intercept, that is, for any b in y = mx + b.

Final answer:

An equation of a line parallel to y=4x+1 would have the same slope of 4 and can be expressed as y=4x+b, where b is any y-intercept not equal to 1.

Explanation:

An equation of a line parallel to the line represented by y=4x+1 would have the same slope as the given equation. This is because parallel lines have identical slopes. In the equation y=4x+1, the slope is 4, as this is the coefficient of x. Therefore, any line that has a slope of 4 will be parallel to y=4x+1. The general form for such a parallel line would be y=4x+b, where b is the y-intercept, which can be any number different than 1 to ensure the lines are not the same.