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. He can only do this if the height of the trapezoid is at least 4.5 feet. What is the length of the f the trapezoid

Answer:

It's minimum value

and the value is :(1 , -2)

Answer:

see explanation

Step-by-step explanation:

Given

f(x) = 3x² - 6x + 1

To express in vertex form

f(x) = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Use the method of completing the square

The coefficient of the x² must be 1, so factor out 3

f(x) = 3(x² - 2x) + 1

add/subtract ( half the coefficient of the x- term )² to x² - 2x

f(x) = 3(x² + 2(- 1)x + 1 - 1) + 1

     = 3(x - 1)² - 3 + 1

     = 3(x - 1)² - 2 ← in vertex form

with vertex = (1, - 2)

To determine if vertex is a max/ min

• If a > 0 then minimum

• If a < 0 then maximum

here a = 3 > 0 ⇒ minimum at (1, - 2)

The minimum value is the y- coordinate of the vertex, that is

minimum value = - 2

Answer: You will need 18 containers of 1-quart to fill the gearbox with 16.3 liters of oil.

Step-by-step explanation:

Knowing that you have 1-quart containers, you need to make the conversion from quarts to liters. This is:

[tex]1\ quart=0.946\ liters[/tex]

Now, since the gearbox holds 16.3 liters of oil, you can divide the volume of oil the gearbox holds by the volume of a container  (which is 0.946 liters or 1-quart) to calculate how many containers of 1-quart you will need to fill the gearbox with 16.3 liters of oil.

 [tex]number\ of\ containers=\frac{16.3\ liters}{0.946\ liters}=17.2[/tex]

Based on the result, you will need 18 containers of 1-quart to fill the gearbox with 16.3 liters of oil.

You will need 17 one-quart containers of oil to fill the 16.3-liter gearbox.

To determine how many 1-quart containers of oil you will need to fill the 16.3-liter gearbox, we can convert the 16.3 liters to quarts by using the conversion factor of 1 liter = 1.05668821 quarts. So, 16.3 liters would be approximately 17.229 quarts. Since each 1-quart container holds exactly 1 quart of oil, you will need 17 of the 1-quart containers to fill the gearbox with 16.3 liters of oil.

https://brainly.com/question/29195599

#SPJ3

Answer:

The correct options are B, C and D.

Step-by-step explanation:

It is given that the figure is a Japanese art of paper folding. It means the figure have many lines of symmetry (i.e., AK, IO, CM and NF).

From the figure it is clear that HV is larger than GW, so segment HV and GW are not pairs of congruent segments.

Therefore option A is incorrect.

[tex]\overline{IJ}\cong \overline{LM}[/tex]        (AK is line of symmetry)

[tex]\overline{AB}\cong \overline{AP}[/tex]        (AK is line of symmetry)

[tex]\overline{BC}\cong \overline{PO}[/tex]        (AK is line of symmetry)

Therefore the correct options are B, C and D.

From the figure it is clear that PO is smaller than ON, so segment HV and GW are not pairs of congruent segments.

Therefore option E is incorrect.

The word "climbing" has 8 letters, so there are [tex]8![/tex] permutations of all the letters.

Nevertheless, the letters are not unique: there are 2 I's. This means that, if we start from a given word and we exchange the positions of the two I's, we'd still get the same word. So, we have to divide the number of possible permutations by [tex]2![/tex], because for any given permutation there are two identical words, given by the interchange of the I's.

So, the number of possible words is

[tex]\dfrac{8!}{2!} = \dfrac{8\times7\times6\times5\times4\times3\times2}{2}=8\times7\times6\times5\times4\times3=40320[/tex]

Answer:

$7 000 was loaned at 10 % and

$10 500 was loaned at 14 %

Step-by-step explanation:

                 Let x = amount loaned at 10 %

Then 17 500 - x = amount loaned at 14 %

                0.10x = interest on 10 % loan

0.14(17 500 - x) = interest on 14 % loan

          2170.00 = total interest

[tex]\begin{array}{rcl}0.10x + 0.14(17 500 - x) & = & 2170.00\\0.10x + 2450 - 0.14x & = & 2170.00\\2450 - 0.04x & = & 2170.00\\-0.04x & = & -280\\\\x & = & \dfrac{-280}{-0.04}\\\\x & = & \mathbf{7000}\\\\\end{array}[/tex]

$7000 was loaned at 10 % and

$10 500 was loaned at 14 %

Check:

\[tex]\begin{array}{rcl}0.10\times 7000 + 0.14(17 500 - 7000) & = & 2170\\700 + 0.14(10 500) & = & 2170\\700 + 1470 & = & 2170\\2170 & = & 2170\\\end{array}[/tex]

OK.

Answer:

Multiply all the sides

Step-by-step explanation:

Multiply every side together and you should get your answer just make sure you put the right unit hope this helped :)

The ratio for the expression "4 added to the difference of d minus 3" can be represented as: (d - 3) + 4.

Expression: "The difference of d minus 3"

This means subtracting 3 from d:

d - 3

Expression: "4 added to the difference of d minus 3"

Add 4 to the result of the previous expression:

(d - 3) + 4

This gives us the entire expression "4 added to the difference of d minus 3.":

(d - 3) + 4

Combine like terms:

d + 1

Therefore, the simplified form of the given expression is (d + 1).

Answer:

pi as a value of 3.14 or 3.14159.

Step-by-step explanation:

Please mark brainliest and have a great day!

Answer:

B

Step-by-step explanation:

Ratio of sides = a : b , then

Ratio of volumes = a³ : b³

Here the ratio of volumes = 27 : 729, hence

Ratio of sides = [tex]\sqrt[3]{27}[/tex] : [tex]\sqrt[3]{729}[/tex] = 3 : 9

Ratio of sides = 3 : 9 = 1 : 3 ← in simplest form

Hence sides of larger cube are 3 times sides of smaller cube → B

Answer:

Step-by-step explanation:

This is impossible to figure out because 0 = 0x, as defined by the Zero Property of Multiplication. I apologize.

Answer:

3.46 x [tex]10^{10}[/tex]

Step-by-step explanation:

Number of cows 6.4 million = 6.4 x [tex]10^{6}[/tex]

production rate for each cow per year = 5400 = 5.4 x 10³

Total amount of milk produced per year,

= 6.4 x [tex]10^{6}[/tex] x 5.4 x 10³

= (6.4) (5.4) x [tex]10^{6+3}[/tex]

= 34.56 x [tex]10^{9}[/tex]

= 3.46 x [tex]10^{10}[/tex]

y=4

the values of x changes while the y doesn't so it's y=4

Answer:

[tex]y=4[/tex]

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

[tex]y=mx+b[/tex]

Where "m" is the slope and "b" is the y-intercept.

The equation of the line in Standard form is:

 [tex]Ax + By =C[/tex]

Where A, B, and C are integers.

We can find the slope of this line with this formula:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Given the points K(6, 4) and L(-6, 4), we get:

[tex]m=\frac{4-4}{-6-6}=0[/tex]

Substituting the value of "m" and the coordinates of any point on the line into the equation and solving for "b", you get:

[tex]4=0(6)+b\\b=4[/tex]

Therefore, the equation of this line is:

[tex]y=4[/tex]

Answer:

[tex]x=19[/tex]

Step-by-step explanation:

We have the following equation

[tex]3(x+6)=5(x-4)[/tex]

Notice that in this equation the variable that we want to find is x.

Then the equation for the variable x must be solved

After applying the distributive property and simplifying the equation Maria obtained the following result

[tex]19=x[/tex]

This is the same as:

[tex]x=19[/tex]

That means that the value of x for which equality is met is [tex]x = 19[/tex]. Therefore the solution of the equation is [tex]x = 19[/tex]

Answer:

The third quartile is:

[tex]Q_3=29[/tex]

Step-by-step explanation:

First organize the data from lowest to highest

4, 5, 10, 12, 14, 16, 18, 20, 21, 21, 22, 22, 24, 26, 29, 29, 33, 34, 43, 44

Notice that we have a quantity of n = 20 data

Use the following formula to calculate the third quartile [tex]Q_3[/tex]

For a set of n data organized in the form:

[tex]x_1, x_2, x_3, ..., x_n[/tex]

The third quartile is  [tex]Q_3[/tex]:

[tex]Q_3=x_{\frac{3}{4}(n+1)}[/tex]

With n=20

[tex]Q_3=x_{\frac{3}{4}(20+1)}[/tex]

[tex]Q_3=x_{15.75}[/tex]

The third quartile is between [tex]x_{15}=29[/tex] and [tex]x_{16}=29[/tex]

Then

[tex]Q_3 =x_{15} + 0.75*(x_{16}- x_{15})[/tex]

[tex]Q_3 =29 + 0.75*(29- 29)\\\\Q_3 =29[/tex]

Answer:

29

Step-by-step explanation:

Answer:

Option B: 49 square units.

Step-by-step explanation:

The irregular polygon consists of a rhombus a square.

Area of rhombus = 0.5*(product of diagonals).

Area of square = length * length = l^2.

The diagonals of the rhombus measure 8 units and 6 units respectively. The diagram shows the length of half of the diagonals, so doubling both the lengths gives us the required lengths. The side of the square measures 5 units. Substituting all the information in the formula:

Total Area = Area of rhombus + Area of square.

Total Area = 0.5*8*6 + 5^2.

Total Area = 24 + 25

Total Area = 49 square units.

Therefore, Option B is the correct answer!!!

Answer:

Step-by-step explanation:

The question is asking for a system of equations, which make explanations easy. :)

Define the variables. Setting [tex]x[/tex] to the number of clubhouse seats sold and [tex]y[/tex] to the number of grandstand seats sold will be sufficient. The "let statement[s]" will be:

The number of equations shall be no less than the number of variables for the solution to be unique. There are two variables. It will take at least two equations to find a unique solution.

Everyone at the race need a seat. The number clubhouse seats plus the number of grandstand seats shall be the same as the number people at the race. There were 36,000 people. Therefore the first equation shall be:

[tex]x + y = 36000[/tex].

Every clubhouse seat will add $12.00 to the receipt. [tex]x[/tex] clubhouse seats will add $[tex]12\;x[/tex] to the receipt. Similarly, [tex]y[/tex] grandstand seats will add $[tex]5\;y[/tex] to the receipt. The two values shall add up to $250,000.

Drop the dollar sign to get the second equation:

[tex]12\;x +5\;y =250000[/tex].

Hence the system:

[tex]\displaystyle \left\{\begin{aligned}& x + y = 36000 && \textcircled{\raisebox{-0.9pt}1}\\ & 12\;x + 5\;y = 250000 && \textcircled{\raisebox{-0.9pt}2}\end{aligned} \phantom{\small credit for the raisebox hack: tex[dot]stackexchange[dot]com/questions/7032/good-way-to-make-textcircled-numbers}[/tex].

Solve this system.

The first non-zero coefficient in equation [tex]\textcircled{\raisebox{-0.9pt}1}[/tex] is already one. That's the coefficient for [tex]x[/tex]. Use multiples of equation [tex]\textcircled{\raisebox{-0.9pt}1}[/tex] to get rid of [tex]x[/tex] in other equations (equation [tex]\textcircled{\raisebox{-0.9pt}2}[/tex] in this case.)

[tex]-12[/tex] times equation [tex]\textcircled{\raisebox{-0.9pt}1}[/tex] is

[tex]-12 \;x - 12\;y = -432000[/tex].

Add [tex]-12\times \textcircled{\raisebox{-0.9pt}1}[/tex] to [tex]\textcircled{\raisebox{-0.9pt}2}[/tex] to get:

[tex]0\;x + -7\;y = -182000[/tex].

Divide both sides by -7 to get:

[tex]y = 26000[/tex].

Add -1 times this equation to equation [tex]\textcircled{\raisebox{-0.9pt}1}[/tex] to get:

[tex]x = 10000[/tex].

That is:

[tex]\displaystyle \left\{\begin{aligned}&x = 10000\\&y = 26000\end{aligned}[/tex].

In other words,

Answer:

4 3/8 yards.

Step-by-step explanation:

1 7/8 + 2 1/2

= 15/8 + 5/2

Make the denominator 8 in both cases ( The LCM = 8):

= 15/8 +  20/8

= 35/8

= 4 3/8.

Answer:

[tex]a_{11} = 14336[/tex]

Step-by-step explanation:

The general formula for the twelfth term of a geometric sequence is:

[tex]a_n = a_1(r)^{n-1}[/tex]

Where [tex]a_1[/tex] is the first term and r is the common ratio

In this case we know that:

[tex]a_1 = 14\\r=-2[/tex]

The equation is:

[tex]a_n = 14(-2)^{n-1}[/tex]

So for [tex]n = 11[/tex] we look for [tex]a_{11}[/tex]

[tex]a_{11} = 14(-2)^{11-1}[/tex]

[tex]a_{11} = 14(-2)^{10}[/tex]

[tex]a_{11} = 14336[/tex]

Answer:

[tex]11^{th}[/tex] term = 14336

Step-by-step explanation:

We are given the first term [tex] a _ 1 = 1 4 [/tex] and  common ratio [tex] r = - 2 [/tex] of a geometric sequence and we are to find the [tex]11^{th}[/tex] term of this sequence.

We know that the formula to find the [tex]n^{th}[/tex] term in a geometric sequence is given by:

[tex]n^{th}[/tex] term = [tex] a r ^ { n - 1 } [/tex]

Substituting the given values in the above formula:

[tex]11^{th}[/tex] term = [tex]14 \times(-2)^{11-1}[/tex]

[tex]11^{th}[/tex] term = [tex]14 \times(-2)^{10}[/tex]

[tex]11^{th}[/tex] term = 14336

Answer:

Option C. x=7

Step-by-step explanation:

we know that

If PQ is parallel to BC

then

triangles APQ and ABC are similar

Remember that

If two figures are similar them the ratio of its corresponding sides is proportional

so

[tex]\frac{AP}{AB}=\frac{AQ}{AC}[/tex]

substitute the values

[tex]\frac{x}{x+7+x}=\frac{x-3}{x-3+x+1}[/tex]

Solve for x

[tex]\frac{x}{2x+7}=\frac{x-3}{2x-2}\\ \\x(2x-2)=(2x+7)(x-3)\\ \\2x^{2}-2x=2x^{2}-6x+7x-21\\ \\3x=21\\ \\x=7\ units[/tex]

Answer:

The answer should be A.

Answer: The Answer is A.) AG=6

Step-by-step explanation:

Answer:

Step-by-step explanation:

The answer is A

Answer:

250 students would

prefer chocolate ice cream

Step-by-step explanation:

50 of 200

+50   +200

100 of 400

+50    +200

150 of 600

+50     +200

200 of 800

+50      +200

250 of 1000

Answer:

the answer is 1/12

Step-by-step explanation:

it is 1/12 because if there are only a pair you would have 2 dice. and since each die has numbers all the way up to 6 all you have to do is add them. and don't count all the numbers. like add 1+2+3+4+5+6. that's just plain wrong just do add the highest number on each die (6+6)

Answer:

acute

Step-by-step explanation:

ANSWER

(C) y

EXPLANATION

We have two equations:

The first one is

[tex]x + y = z...(1)[/tex]

The second equation is

[tex]y - z = x...(2)[/tex]

Let us make z the subject of this second equation:

[tex] \implies \: -x +y = z...(3)[/tex]

We now add equation (1) and (3) to get:

[tex](-x + x) + (y + y) = z + z[/tex]

We simplify to get:

[tex]0+2y= 2z[/tex]

[tex]2y= 2z[/tex]

Divide throu by 2.

[tex] \frac{2y}{2} = \frac{2z}{2} [/tex]

[tex]y= z[/tex]

[tex] \therefore \: z = y[/tex]

The correct answer is C

Answer:

Step-by-step explanation:

The pentagon RSTYZ is a regular polygon. Therefore all angles are congruent.

If m∠RST = 108°, then m∠STY = 108°.

We have the equation:

m∠UTY + m∠STY + m∠STU = 360°.

Substitute m∠STY = 108° and m∠UTY = 115°.

115° + 108° + m∠STU = 360°

223° + m∠STU = 360°          subtract 223° from both sides

m∠STU = 137°

Answer: Area of Square = 81m^2

Step-by-step explanation:

To find the area of a square you just need to know the side length on one side, and since we know that the perimeter is 36, and all sides of a square are equal we can divide 36/4, to get 9 is your side length.

Now to actually find the area you can just square your side length, so basically 9x9, which gives you 81, your answer!!

Answer:

Area = 81m^2

Step-by-step explanation:

Square has 4 equal sides so 36/4 =  9

9(9) = 81

Hope this helps :)

Answer:

[tex]15x+60\leq 100[/tex]

Step-by-step explanation:

Let

x -----> the number of hours that the painter works

we know that

The inequality that represented this situation is equal to

[tex]15x+60\leq 100[/tex]

solve for x

Subtract 60 both sides

[tex]15x\leq 100-60[/tex]

[tex]15x\leq 40[/tex]

Divide by 15 both sides

[tex]x\leq 40/15[/tex]

[tex]x\leq 2.67\ hours[/tex]

The maximum number of hours is 2

Answer:

When Harold wrote his equation, the point he used was (7,0).

Step-by-step explanation:

we know that

The equation of a line into point slope form is equal to

[tex]y-y1=m(x-x1)[/tex]

where

(x1,y1) is the point

m is the slope

In this problem we have

[tex]y=3(x-7)[/tex]

therefore

the point is (x1,y1)=(7,0)

the slope is m=3