John has a rectangular picture which is 43 inches long and 27 inches wide. He wants to build a wooden gram for the picture but she only has 800 square inches of wood available. How wide will the border be?

Answer:

Part A) [tex]15x+25y\geq 700[/tex] and [tex]x> 3y[/tex]

Part B) The point (45,10) and the point (40,5)  satisfy the system

Step-by-step explanation:

Part A) Determine which inequalities represent the constraints for this situation

Let

x -----> the number of small prints sold

y -----> the number of large prints sold

we know that

The system of inequalities that represent this situation is equal to

[tex]15x+25y\geq 700[/tex] ----> inequality A

[tex]x> 3y[/tex] ----> inequality B

Part B) With combinations of small prints and large prints satisfy this system?

we know that

If a ordered pair is a solution of the system, then the ordered pair must satisfy both inequalities

Verify each case

case 1) (45,10)

For x=45, y=10

Inequality A

[tex]15x+25y\geq 700[/tex]

[tex]15(45)+25(10)\geq 700[/tex]

[tex]925\geq 700[/tex] ----> is true

Inequality B

[tex]x> 3y[/tex]

[tex]45> 3(10)[/tex]

[tex]45> 30[/tex] ----> is true

therefore

The point (45,10) satisfy the system

case 2) (35,15)

For x=35, y=15

Inequality A

[tex]15x+25y\geq 700[/tex]

[tex]15(35)+25(15)\geq 700[/tex]

[tex]900\geq 700[/tex] ----> is true

Inequality B

[tex]x> 3y[/tex]

[tex]35> 3(15)[/tex]

[tex]35> 45[/tex] ----> is not true

therefore

The point (35,15) does not satisfy the system

case 3) (30,10)

For x=30, y=10

Inequality A

[tex]15x+25y\geq 700[/tex]

[tex]15(30)+25(10)\geq 700[/tex]

[tex]700\geq 700[/tex] ----> is true

Inequality B

[tex]x> 3y[/tex]

[tex]30> 3(10)[/tex]

[tex]30> 30[/tex] ----> is not true

therefore

The point (30,10) does not satisfy the system

case 4) (40,5)

For x=40, y=5

Inequality A

[tex]15x+25y\geq 700[/tex]

[tex]15(40)+25(5)\geq 700[/tex]

[tex]725\geq 700[/tex] ----> is true

Inequality B

[tex]x> 3y[/tex]

[tex]40> 3(5)[/tex]

[tex]40> 15[/tex] ----> is true

therefore

The point (40,5)  satisfy the system

The question refers to the relationship between x (number of small prints sold) and y (number of large prints sold), in an uncertain context. Constraints would be limitations or restrictions on the values that x and y can take, often expressed as inequalities. As this problem lacks specific details (like total prints or budget limits), it's impossible to define specific inequalities representing these constraints without them.

In this situation, x and y are variables that represent the quantities of small and large prints sold respectively. As such, they can also be understood as independent and dependent variables. In Mathematics, an independent variable is one that stands alone and isn't changed by the other variables you are trying to measure. In contrast, the dependent variable is what you measure in the experiment and what is affected.

In this context, constraints would be limitations or restrictions on the values that x and y can have, often represented by inequalities.

Without specific detail in the context such as the total prints available, thus giving a limit on total sales, or the price information for small and large prints leading to a budget constraint, it is impossible to define any specific inequalities to represent these constraints. Additional information such as these is required to formulate appropriate inequalities.

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Answer:

|-5| is the answer.

Step-by-step explanation:

The opposite of 5 is -5. The absolute value of a number is always positive (e.g: |-10| = 10 because the negative sign is inside the absolute value bars).

-|5| and -|-5| both equal -5 because there is a negative sign outside of the bars. Since |-5| has a negative sign inside the bars, it equals 5.

I tried hard to explain this, so I hope it makes sense! :)

Hey there Brainly Student! Your answer is   I-5I !! I hope this helped! Have a great day!!

The conclusion If AC = AB + BC and AB + BC = 13, then AC = 13 is justified by the transitive property of equality.

The property that justifies the conclusion If AC = AB + BC and AB + BC = 13, then AC = 13 is the transitive property. In mathematics, the transitive property of equality states that if a=b and b=c, then a=c. Here, AB + BC = 13 is equal to AC, hence AC=13 according to the transitive property.

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The transitive property justifies the given conclusion because it dictates that if two values are both equal to a third value, they are equivalent to each other.

The property that justifies the conclusion If AC = AB + BC and AB + BC = 13, then AC = 13 is the transitive property of equality. The transitive property says that if two things are both equal to a third thing, then they are congruent to each other. In this case, because AB + BC equals 13 and AC equals AB + BC, you can conclude that AC must equal 13.

Answer:

=14.69km²

Step-by-step explanation:

We can use the Hero's formula to calculate the area

A= √(s(s-a)(s-b)(s-c))

s is obtained by adding the lengths of the three sides of the triangle and then dividing by 2, a, b and c are the ides of the triangle.

S=(5+6+7)/2

=9

A=√(9(9-6)(9-5)(9-7))

=√(9×3×4×2)

=√216

=14.69km²

Ex: 96 hours ≈ 4 days

This is one way to convert dates.

I am joyous to assist you anytime.

Converting dates involves understanding time zones and the International Date Line. When crossing the date line from west to east, the date decreases by one day, and when crossing from east to west, the date increases by one day.

Converting dates can be done by understanding the concept of time zones and the International Date Line. Time zones are regions that have the same standard time, while the International Date Line is an imaginary line that marks where the date changes by one day. When crossing the date line from west to east, the date is decreased by one day, and when crossing from east to west, the date is increased by one day.

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Answer:

Step-by-step explanation:

[tex]3x^2+x-5=0\\\\\text{Use the quadratic formula for}\ ax^2+bx+c=0\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\\text{For the given equation:}\\\\a=3,\ b=1,\ c=-5\\\\b^2-4ac=1^2-4(3)(-5)=1+60=61\\\\x=\dfrac{-1\pm\sqrt{61}}{(2)(3)}=\dfrac{-1\pm\sqrt{61}}{6}\notin\mathbb{N}[/tex]

Answer:

two real,irrational roots.

GOOD LUCK!

Step-by-step explanation:

Answer:

If there are 5 persons and at a time only 3 can be arranged, the total number of arrangements is 60

Option C is correct

Step-by-step explanation:

There are 5 persons and at a time only 3 can be arranged.

The total number of arrangements = nPr = n!/(n-r)!

Here n = 5 and r = 3

nPr = n!/(n-r)!

nPr = 5!(5-3)!

nPr = 5!/2!

nPr = 5*4*3*2!/2!

nPr = 5*4*3

nPr = 60

So, if there are 5 persons and at a time only 3 can be arranged, the total number of arrangements is 60

Option C is correct.

Answer:

2(n-6)=12

(I went too far in my explanation; I'm not going to erase it because I think it is important to have an example on solving these)

Step-by-step explanation:

Twice the difference of a number and 6 is the same as 12.

Twice means 2 times

Difference means the result of subtracting something.

is the same as means equal to (=).

So we are given 2(n-6)=12.

You can start by dividing 2 on both sides are distributing 2 to terms in the ( ).

I will do it both ways and you can pick your favorite.

2(n-6)=12

Divide both sides by 2.

 n-6  =6

Add 6 on both sides

 n     =12

OR!

2(n-6)=12

Distribute 2 to both terms in the ( )

2n-12=12

Add 12 on both sides

2n    =24

Divide both sides by 2

n       =12

Answer:

6 pounds of potatoes = $9

3 pounds of onions = $9

The onions cost $3 per pound

and the potatoes cost $1.50 per pound

Step-by-step explanation:

Answer:

Unit price of  potatoes = $1.50.

Unit price of onions - $3.

Step-by-step explanation:

The system of equations is

6p + 3n = 18

n = 2p

Substitute  n = 2p in the first equation:

6p + 3(2p) = 18

6p + 6p = 18

12p= 18

p = 18/12 = $1.50 .

Now plug p = 1.50 into the second equation:

n = 2*1.50 = $3.

Answer:

[tex]y+3=\frac{1}{2} \left(x-6)[/tex]

Step-by-step explanation:

Point slope form:

[tex]y-y_1=m\left(x-x_1\right)[/tex]

Note:

Our answer would be [tex]y+3=\frac{1}{2} \left(x-6)[/tex]

Answer:  Our equation will take the form of a linear equation, this is: Y = A*X +B passes through the point (6,-3)

this means that -3 = A*6 + B, and also the slope is 1/2, so A =1/2.

So we only need to know the value of B.

then if :

-3 = 1/2*6 - B = 3 + B

B = - 3 - 3 = -6

So our equation is: Y = 1/2*X - 6

Answer:

(4, - 7)

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

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

f(x) = (x - 4)² - 7 ← is in vertex form

with (h, k) = (4, - 7 ) ← vertex

I tried solving the problem and it didn't make sense until assuming that 22540.75 was a typo for 2540.75.

Answer:

2540.75 = 6.25x + 5.25y

435 = x + y

x = number of adult tickets

y = number of student and senior tickets

Question is asking to find x

- - - - - - - - - - - - - - - - - -

435 = x + y

2283.75 = 5.25x + 5.25y

Elimination method:

2540.75 = 6.25x + 5.25y

-(2283.75 = 5.25x + 5.25y)

257 = x

257 full priced tickets were sold.

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For any questions, please comment!!

Answer:

Full tickets sold were 257 in count and discounted tickets were 178.

Step-by-step explanation:

Let the full tickets be = f

Let the discounted tickets be = d

Total tickets sold = 435

This can be written as :

[tex]f+d=435[/tex] or[tex]f=435-d[/tex]    .....(1)

The full price of a ticket is $6.25 and discount price is $5.25 and total earning is $2540.75.

In equation form, it can be written as :

[tex]6.25f+5.25d=2540.75[/tex]    ....(2)

Substituting the value of f in (2)

[tex]6.25(435-d)+5.25d=2540.75[/tex]  

[tex]2718.75-6.25d+5.25d=2540.75[/tex]

[tex]-1d=-178[/tex]

so , d = 178

And[tex]f+d=435[/tex]

So,[tex]f=435-178=257[/tex]

Hence, full tickets sold were 257 in count and discounted tickets were 178.

[tex]\bf \begin{array}{ll} \stackrel{year}{term}&value\\ \cline{1-2} a_1&3\\ a_2&3r\\ a_3&3rr\\ a_4&3rrr\\ a_5&3rrrr\\ &3r^4 \end{array}\qquad \qquad \stackrel{\textit{5th year}}{108}=3r^4\implies \cfrac{108}{3}=r^4\implies 36=r^4 \\\\\\ \sqrt[4]{36}=r\implies \sqrt[4]{6^2}=r\implies 6^{\frac{2}{4}}=r\implies 6^{\frac{1}{2}}=r\implies \sqrt{6}=r[/tex]

[tex]\bf n^{th}\textit{ term of a geometric sequence} \\\\ a_n=a_1\cdot r^{n-1}\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{term position}\\ a_1=\textit{first term}\\ r=\textit{common ratio}\\ \cline{1-1} r=\sqrt{6}\\ a_1=3\\ n=11 \end{cases}\implies a_{11}=3(\sqrt{6})^{11-1} \\\\\\ a_{11}=3(\sqrt{6})^{10}\implies a_{11}=3\left(6^{\frac{1}{2}} \right)^{10}\implies a_{11}=3\cdot 6^{\frac{10}{2}} \\\\\\ a_{11}=3\cdot 6^5\implies a_{11}=3\cdot 7776\implies a_{11}=23328[/tex]

Answer:

The investment be worth $23328 after 11 years.

Step-by-step explanation:

It is given that the annual growth reflects a geometric sequence.

An initial investment of $3 is worth $108 after 5 years.

It means the initial value of first term of the gp, a₁ = 3

The 5th term of the gp, a₅ = 108

The nth term of a gp is

[tex]a_n=ar^{n-1}[/tex]              .... (1)

where, a is first term and r is common ratio.

The 5th term of the gp is

[tex]a_5=ar^{5-1}[/tex]

From the given information it is clear that the 5th term of the gp is 108. Substitute a₅ = 108 and a=3.

[tex]108=(3)r^{4}[/tex]

Divide both sides by 3.

[tex]\frac{108}{3}=r^{4}[/tex]

[tex]36=r^{4}[/tex]

Taking fourth root on both the sides.

[tex]\sqrt{6}=r[/tex]

Substitute r=√6, a=3 and n=11 to find the investment worth after 11 years.

[tex]a_{11}=(3)(\sqrt{6})^{11-1}[/tex]

[tex]a_{11}=3(\sqrt{6})^{10}[/tex]

[tex]a_{11}=23328[/tex]

Therefore the investment worth $23328 after 11 years.

Answer:

1024 cm²

Step-by-step explanation:

There are 16 rods.  A square has 4 equal sides, so each side must consist of 4 rods.  The length of each rod is 8 cm, so the length of each of the square's sides is 32 cm.  Therefore, the area of the square is:

A = s²

A = (32 cm)²

A = 1024 cm²

Answer:

[tex]x\sqrt{7} - 49\sqrt{x}[/tex]

Step-by-step explanation:

We have to simplify the following expression: [tex]\sqrt{7x}(\sqrt{x} - 7\sqrt{7})[/tex]

Using distributive property:

[tex]\sqrt{7x}(\sqrt{x} - 7\sqrt{7}) = \sqrt{7x}\sqrt{x} - 7\sqrt{7}\sqrt{7x}[/tex]

⇒ [tex]x\sqrt{7} - 49\sqrt{x}[/tex]

So the most simplified form of the expression is the following: [tex]x\sqrt{7} - 49\sqrt{x}[/tex]

Certainly! To solve this problem, we will need to simplify the expression √(7x)(√x - 7√7).
First, let us consider the individual square root terms: √(7x) and √x. Recall that the square root of a product can be separated into the product of the square roots of the factors, so √(7x) can be expressed as √7 * √x.
Now we have:
√(7x)(√x - 7√7) = (√7√x)(√x - 7√7)
Next, we distribute √7√x into the terms within the parentheses:
(√7√x)(√x) - (√7√x)(7√7)
Simplify each term:
First term: (√7√x)(√x) = √7 * (√x * √x) = √7 * x
This is because the square root of a number multiplied by itself is just the number.
Second term: (√7√x)(7√7) = 7√7 * (√7√x) = 7 * (√7 * √7) * √x
               = 7 * 7 * √x
               = 49√x
This is because the square root of 7 squared is just 7.
Now we combine the two terms:
√7x = √7 * x - 49√x
And that is the simplified form of the given expression.

Answer:

your answer is "18"

Step-by-step explanation:

Formula is:

A= 1/2 (A+B) X H

A = 1/2 (CD + CF) X H

A = 1/2 (5+6) X 3

A = 16.5 CM SQUARED

Hope this is right!

Since ABCF is a rectangle, angle AFC is a right angle. Angle CFE is also a right angle. Since angle DCF is also a right angle, then trapezium CDEF has parallel sides CD and EF.

BC + CD = BD

4 cm + CD = 9 cm

CD = 5 cm

EF = 3 cm

Sides CD and EF are the parallel bases of the trapezium. Side CF is the height of the trapezium.

area of trapezium = (base1 + base2)h/2

area = (5 cm + 3 cm)(6 cm)/2

area = (8 cm)(6 cm)/2

area = 24 cm^2

Answer: 5836200

Step-by-step explanation:

How much does one song cost?

Answer:

[tex]\large\boxed{x^\frac{2}{3}}[/tex]

Step-by-step explanation:

[tex]\left(x^\frac{4}{3}x^\frac{2}{3}\right)^\frac{1}{3}\qquad\text{use}\ a^na^m=a^{n+m}\\\\=\left(x^{\frac{4}{3}+\frac{2}{3}}\right)^\frac{1}{3}=\left(x^{\frac{6}{3}\right)^\frac{1}{3}=(x^2)^\frac{1}{3}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=x^{(2)\left(\frac{1}{3}\right)}=x^\frac{2}{3}[/tex]

Answer:

B and E are the correct answer

Step-by-step explanation:

Because (2,23) and (7,48) are linear

Your question is incomplete and lacks the table. Please check below for the full content.

A group of students is collecting books to add to their library. The table shows the number of books in the library after 1, 3, and 5 days. If the relationship between days and books continues to be linear, which ordered pairs could appear in the table? Check all that apply.

(0, 8)

(2, 23)

(4, 32)

(6, 48)

(7, 48)

The missing table is given below.

The correct options are option 2:(2,23) and 5:(7,48) The ordered pair (2,23),(7,48) will appear in the table.

The equation where highest degree of the variable used in the equation is 1 is called linear equation. Foe example ax+by+c=0

Here given the relationship between days and books is linear.

From the table, it clear that In day 1 the book collected is 18.

in day 3 book collected is 28.

x₁=1,y₁=18

x₂=3,y₂=28

The linear equation will be

(y-y₁)/(x-x₁)=(y₂-y₁)/(x₂-x₁)

⇒(y-18)/(x-1)=(28-18)/(3-1)

⇒(y-18)/(x-1)=10/2

⇒(y-18)/(x-1)=5

⇒y-18=5(x-1)

⇒y-18=5x-5

⇒y=5x-5+18

⇒y=5x+13

So the linear equation will be y=5x+13

By ckecking every option,

1. (0, 8)-  y=5*0+13=13≠8  Option 1 is incorrect.

2. (2,23)-  y=5*2+13=23    Option 2 is correct.

3. (4,32)-   y=5*4+13=33≠32   Option 3 is incorrect.

4.(6,48)-   y=5*6+13=43≠48     Option 4 is incorrect.

5. (7,48)    y=5*7+13=48   Option 5 is correct.

Therefore the correct options are option 2 and 5 i.e. The ordered pair (2,23) , (7,48) will appear in the table.

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Answer:

95

Step-by-step explanation:

(9.5)(-2)(-5)

First multiply the first two terms:

9.5* -2(-5)

9.5* -2 = -19

= -19(-5)

now multiply the product of solved terms by -5

-19(-5)

Negative signs will change into positive because - * - = +

95....

Thus the answer is 95....

Answer:

your answer is 95

Step-by-step explanation:

you multiply (9.5) (-2)(5) and you get 95

Answer:

D. 77.6

Step-by-step explanation:

We have been given a triangle ZYA in which B, C, and D are the midpoints. We are asked to find the perimeter of triangle ZYA.

We will triangle mid-segment theorem to solve our given problem.

The triangle mid-segment theorem states that the segment joining midpoints of two sides of a triangle is parallel to 3rd side and half the measure of parallel side.

[tex]\text{Measure of side YA}=2\times BD[/tex]

[tex]\text{Measure of side YA}=2\times 11.1[/tex]

[tex]\text{Measure of side YA}=22.2[/tex]

[tex]\text{Measure of side YZ}=2\times CD[/tex]

[tex]\text{Measure of side YZ}=2\times 13.7[/tex]

[tex]\text{Measure of side YZ}=27.4[/tex]

[tex]\text{Measure of side ZA}=2\times CB[/tex]

[tex]\text{Measure of side ZA}=2\times 14[/tex]

[tex]\text{Measure of side ZA}=28[/tex]

[tex]\text{Perimeter of triangle ZYA}=22.2+27.4+28[/tex]

[tex]\text{Perimeter of triangle ZYA}=77.6[/tex]

Therefore, the perimeter of triangle ZYA is 77.6 units.

To find the point where the cost of skiing at both ski slopes is the same, set the equations for the total cost of skiing at each resort equal to each other and solve for 'x'.

To determine at what point the cost of both ski slopes is the same, we need to create an equation based on the given information about the costs of each ski resort. Let's assume 'x' is the number of hours of skiing. The total cost of skiing at Black Diamond Ski Resort is given by the equation: Cost = 50 + 15x. The total cost of skiing at Bunny Hill Ski Resort is given by the equation: Cost = 75 + 10x. To find the point where the costs are the same, we can set the two equations equal to each other: 50 + 15x = 75 + 10x. Now we can solve this equation for 'x': 5x = 25, x = 5.

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Answer:

[tex]\large\boxed{y=\dfrac{2}{3}x+7}[/tex]

Step-by-step explanation:

[tex]\text{Let}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2\\\\===================================\\\\y=-\dfrac{3}{2}x+4\to m_1=-\dfrac{3}{2}\\\\m_2=-\dfrac{1}{m_1}\Rightarrow m_2=-\dfrac{1}{-\frac{3}{2}}=\dfrac{2}{3}\\\\\text{Therefore we have the equation:}\ y=\dfrac{2}{3}x+b.\\\\\text{Put the coordinates of the point (3, 9) to the equation:}\\\\9=\dfrac{2}{3}(3)+b\\\\9=2+b\qquad\text{subtract 2 from both sides}\\\\7=b\to b=7[/tex]

Answer:

[tex]4t + 15j > 800[/tex]

Please read explanation below as well.

Step-by-step explanation:

We know the following information:

- The number of T-shirts is represented by the variable [tex]t[/tex]. Each T-shirt costs $4. The total cost depending on the number of T-shirts can be represented by [tex]4t[/tex].

- The number of jeans is represented by the variable [tex]j[/tex]. Each pair of jeans costs $15. The total cost depending on the number of jeans can be represented by [tex]15j[/tex].

- The stores want to sell more than $800. This idea is represented mathematically by writing [tex]>800[/tex].

The total cost of jeans and T-shirts depending on the quantities of each of them is represented as a sum: [tex]4t + 15j[/tex]. This total cost has to be more than $800: [tex]4t + 15j > 800[/tex].

Think for a minute.

Three points are given.

What geometric shape has three points?

Answer: Triangle

Answer:

a. two column proof

Step-by-step explanation:

This is a two column proof, for 2 columns are given to you.

One column is the "Statements" column, which lists everything in mathematical terms.

The other column is the "Reasons" column, which lists everything by definition (either Theorem, Postulate, or Definition).

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