if you are solving a system of equations and you came to a statement like for equals four, what do you know about the solution to the system?

Example with temperature:

The temperature -3 degrees is warmer than -5 degrees. This applies to celsius or fahrenheit. You might also write "negative 3 degrees" as "3 degrees below zero"; the same applies for -5. The absolute difference between the two temperatures is 2 degrees.

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Example with money:

If your bank balance is -3 dollars and your friend's bank balance is -5 dollars, then your friend owes more money to the bank (s/he owes $2 more than you do).

Negative balances mean you are in debt. Another way to look at this is to consider you want to buy an item worth $10 but you only have $7. If the store owner lends you the difference, which you pay back later, then 7-10 = -3 is the amount of money on your balance sheet indicating you are in debt $3. The order of subtraction is important. Saying 10-7 = 3 shows a positive bank balance and you wouldn't be in debt (and still have $3 in your pocket).

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In either example, the value -3 is to the right of -5 on the number line so we would write the inequality -3 > -5 to say that -3 is larger than -5. Have a look at the image attached below.

Answer:

-2.32193...

Step-by-step explanation:

log.5 (5)

Answer:

[tex]\log_{\frac{1}{2}} 5=-2.32193[/tex]

Step-by-step explanation:

Given : Expression [tex]\log_{\frac{1}{2}} 5[/tex]

To find : The solution of the given expression ?

Solution :

We have given expression [tex]\log_{\frac{1}{2}} 5[/tex]

Applying logarithmic property,

[tex]\log_b a=\frac{\log_e a}{\log_e b}=\frac{\ln a}{\ln b}[/tex]      

Where, [tex]\log _e[/tex] is the natural logarithm indicated as [tex]\ln[/tex]

[tex]\log_{\frac{1}{2}} 5=\frac{\ln (5)}{\ln {\frac{1}{2}}}[/tex]

[tex]\frac{\ln (5)}{\ln {\frac{1}{2}}}=\frac{1.60943}{ -0.69315}[/tex]

[tex]\frac{\ln (5)}{\ln {\frac{1}{2}}}=-2.32193[/tex]

Therefore, [tex]\log_{\frac{1}{2}} 5=-2.32193[/tex]

Answer: [tex]50^{\circ}[/tex]

Step-by-step explanation:

By the definition  of quadrilateral,

A quadrilateral has four interior angles and the sum of all interior angle of a quadrilateral is always equal to [tex]360^{\circ}[/tex]

Here the measurements of three interior angles are [tex]85^{\circ}[/tex], [tex]105^{\circ}[/tex] and [tex]120^{\circ}[/tex]

Let the measurement of fourth angle is x degree.

Thus,  [tex]85^{\circ}+105^{\circ}+120^{\circ}+x=360^{\circ}[/tex]

[tex]310^{\circ}+x=360^{\circ}[/tex]

[tex]x = 360^{\circ}-310^{\circ}=50^{\circ}[/tex]

Thus, the measure of fourth angle is [tex]50^{\circ}[/tex]

The measure of the 4th angle is 50 degrees.

To find the measure of the fourth angle of a quadrilateral, we need to know that the sum of all the interior angles of a quadrilateral is always 360 degrees. Therefore, to find the measure of the fourth angle, we can subtract the sum of the other three angles from 360. In this case, the given angles are 85, 105, and 120 degrees, so the sum of these three angles is 85 + 105 + 120 = 310 degrees. To find the measure of the fourth angle, we subtract 310 from 360: 360 - 310 = 50 degrees.

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Answer:

Bowl B contains 2 apples more than Bowl A and Bowl A contains 1 mango more than Bowl B.

Step-by-step explanation:

Number of apples in Bowl A = 6

Number of mangoes in Bowl B = 8

Difference in apples = 8 - 6 = 2

So, Bowl B contains 2 apples more than Bowl A.

Number of mangoes in Bowl A = 3

Number of mangoes in Bowl B =2

Difference in mangoes = 3 - 2 = 1

So, Bowl A contains 1 mango more than Bowl B.

Bowl B has 2 more apples and 1 fewer mango compared to Bowl A. Thus, the primary differences are in the quantities of apples and mangoes in each bowl.

Step by Step Solution:

To understand the differences between Bowl A and Bowl B, let's break down the contents of each bowl:

Bowl A contains 6 apples and 3 mangoes.

Bowl B contains 8 apples and 2 mangoes.

Now, let's find the differences in the number of apples and mangoes between the two bowls:

Difference in Apples: Bowl B has 8 apples, and Bowl A has 6 apples. Therefore, the difference is 8 - 6 = 2 apples. Bowl B has 2 more apples than Bowl A.

Difference in Mangoes: Bowl A has 3 mangoes, and Bowl B has 2 mangoes. Therefore, the difference is 3 - 2 = 1 mango. Bowl A has 1 more mango than Bowl B.

In summary, Bowl B has 2 more apples and 1 fewer mango compared to Bowl A.

The hypotenuse of the ΔBAD is the side BD.

The longest side in a right angled triangle is called hypotenuse, it is the side which is opposite to 90° angle.

Step 1 : In the given cube, we should look at the face ABCD

Step 2 : Let us draw an imaginary line between the point B and D

Step 3 : Now the face ABCD is split into two triangles ΔBAD and ΔBCD respectively

Step 4 : The side opposite to the 90° angle of ΔBAD is BD

Hence the side BD is hypotenuse of ΔBAD.

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Answer:

8.4444...

Step-by-step explanation:

So it's easier if we can write it first in mixed fractions. 9 x 8 is 72 and th is the highest we can go. So it becomes [tex]8\frac{4}{9}[/tex]. Then, if you just long divide 4 by 9 you get .44444.... So it is 8.4 repeating.

8.444 decimal is equivalent to fraction 76/9.

The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.

Given a fraction of 76/9

Simplifying the above fraction,

=> 76/9

=> (72 + 4)/9

=> 8 + 4/9

=> 8 + 0.444

=> 8.444

Therefore, 8.444 decimal is equivalent to fraction 76/9.

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Answer:

A: [tex]7x+y=801[/tex]

B: [tex]18x+3y=1949[/tex]

Step-by-step explanation:

we are given system of equations as

[tex]84x+12y=9612[/tex]

[tex]126x+21y=13643[/tex]

We can simplify each system of equations

[tex]84x+12y=9612[/tex]

we can factor out common terms

[tex]12\times 7x+12\times y=12\times 801[/tex]

[tex]12(7x+y)=12\times 801[/tex]

we can divide both sides by 12

[tex]7x+y=801[/tex]

now, we can simplify second system of equation

[tex]126x+21y=13643[/tex]

Firstly, we can factor

[tex]7\times 18x+7\times 3y=7\times1949[/tex]

[tex]7(18x+3y)=7\times1949[/tex]

we can divide both sides by 7

[tex]18x+3y=1949[/tex]

so, we get

A: [tex]7x+y=801[/tex]

B: [tex]18x+3y=1949[/tex]

Answer:

Difference of cubes polynomial identity prove that 117 =125-8

Step-by-step explanation:

Difference of cubes:- A polynomial in the form of [tex]a^3 -b^3[/tex] is called  the difference of cubes.

The formula for difference of cubes is;

[tex]a^3 -b^3 = (a-b)(a^2+b^2+ab)[/tex]

To prove: 117 = 125 - 8

Take RHS

[tex]125-8 = 5^3 -2^3[/tex]

Apply difference of cubes;

[tex]5^3-2^3 = (5-2)(5^2+2^2+5\cdot 2)[/tex]

                     =[tex]3(25+4+10) = 3(39) = 117[/tex] = LHS       hence proved!

Therefore, difference of cubes polynomial identity will prove that 117 = 125-8

Answer:

$12.00

Step-by-step explanation:

If they paid $0.72 in tax and tax is 6% or .06 then you could create an equation like this: x * .06 = .72 with x representing the original cost of the bracelet. Now you can just solve for x like so:

x * .06 = .72

÷.06       ÷.06

x = 12

Answer:

$12.00

Step-by-step explanation:

The A) (5 + 3) × 20 is another expression to calculate the total amount spent

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Given that Cindy bought 5 dresses for $20 each and 3 pairs of shoes for $20 each. She used this expression to calculate the total amount she spent.

(5 × 20) + (3 × 20)          

Multiply in the parentheses first

100 + 60                        

Now Add

= $160 total

Thus She spent $160 total

The A) (5 + 3) × 20 is another expression to calculate the total amount spent.

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i always use 3.1415 but just to be safe use the pi symbol  :)

Answer:

The answer is A

Step-by-step explanation:

5x + 18 = 7x - 12

Subtract 7x from both sides

5x + 18 - 7x = 7x - 12 - 7x

-2x + 18 = -12

Subtract 18 from both sides

-2x + 18 - 18 = -12 - 18

-2x = -30

Divide both sides by -2

-2x/-2 = -30/-2

x = 15

Answer:

75% increase in price

Explanation:

75% of $1 is 75 cents

Answer:

X=5 (Or (5,0))

Step-by-step explanation:

The Y intercept is when X=0

The X Intercept is when Y=0

Our equation is y=-4200x+21000

So let's rewrite it... First subtract 21,000 (Also, remember Y is 0)

0-21000=-4200x

-21000=-4200x

Now to get X alone, divide -21000 by -4200

This will give us 5=x, which is the same as x=5. There is your answer!

The slope means that the value decreases by -4,200 per year.

Here we have the linear equation:

y = -4,200x + 21,000

We know that this equation relates the value of something, y, after x years.

So a slope will tell us how many units does the value increase or decraeses each year.

Here the slope is -4,200, which means that the price decreases by -4,200 dollars each year.

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Answer:

[tex]x=3-\sqrt{6},x=3+\sqrt{6}[/tex]

Step-by-step explanation:

we are given equation as

[tex]2x^2-12x=-6[/tex]

Since, we have to solve it by using complete square

so, firstly we will complete square

and then we can solve for x

step-1:

Factor 2 from both sides

[tex]2(x^2-6x)=-3\times 2[/tex]

step-2:

Simplify it

[tex]x^2-6x=-3[/tex]

step-3:

Add both sides 3^2

[tex]x^2-6x+3^2=-3+3^2[/tex]

now, we can complete square

[tex](x-3)^2=6[/tex]

step-4:

Take sqrt both sides

[tex](x-3)=-\sqrt{6},(x-3)=\sqrt{6}[/tex]

step-5:

Add both sides by 3

we get

[tex]x=3-\sqrt{6},x=3+\sqrt{6}[/tex]

Answer:

A

Step-by-step explanation:

this is a standard right triangle 30-60-90

with legs 1 and [tex]\sqrt{3}[/tex] and hypotenuse 2, hence

s = [tex]\sqrt{3}[/tex] and h = 2

Answer:

A. [tex]\sqrt{3}[/tex] ; 2

Step-by-step explanation:

Since We have all the angles of the triangle and one side we can use SIN, COS, and TAN to find the missing side lengths. SIN which is [tex]sin(x) = \frac{opposite}{hypotenuse}[/tex] can be used to find the hypotenuse

[tex]sin(30) = \frac{1}{h}[/tex]

[tex]\frac{1}{sin(30)} = \frac{h}{1}[/tex] ..... inverse both sides

[tex]\frac{1}{sin(30)} = h[/tex]

[tex]2 = h[/tex]

Now we can use the Pythagorean theorem to find the missing length. The Pythagorean Theorem is [tex]a^{2} +s^{2} = h^{2}[/tex]. So we just plug in the values we already have and solve for s.

[tex]1^{2} +x^{2} = 2^{2}[/tex]

[tex]1+s^{2} = 4[/tex]

[tex]s^{2} = 3[/tex]

[tex]s = \sqrt{3}[/tex]

In Conclusion, s = [tex]\sqrt{3}[/tex] and h = 2

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.

Answer: E

Step-by-step explanation: 1 gallon is equal to 4 quarts. If Sally needs to fill and refill a 2 quart pitcher with 6 gallons of water, multiply 6 by 4 to get 24.

Answer:

D

Step-by-step explanation:

Under a rotation about the origin of 180°

a point (x, y ) → (- x, - y) → D

Note this only happens if the rotation is about the origin

Answer:

88 cm

Step-by-step explanation:

The side of the square = 6 cm, so the shorter side of each rectangle = 6 cms.

The area of each rectangle =  36 *  1 1/3

= 36 * 4/3 = 48 cm^2

So the longer side of each rectangle = 48 / 6 =  8 cms

Therefore, the perimeter of the whole figure

=  4( shorter sides ) + 8(longer sides)

= 4*6 + 8*8

= 24 + 64

= 88 cm   (answer)

Answer:

[tex]x=7.5[/tex]

Step-by-step explanation:

If you look at the large triangle, you will see that the side [tex]x[/tex] is opposite of 30° angle and the side 15 is opposite of 90° angle (side opposite of 90° angle is called the hypotenuse).

We have the angle, we have the side opposite and the hypotenuse. Which trigonometric ratio relates opposite side and hypotenuse? SINE!

So we use the sin ratio and cross multiply and solve for [tex]x[/tex]:

[tex]Sin(A)=\frac{Opposite}{Hypotenuse}\\Sin(30)=\frac{x}{15}\\x=15*Sin(30)\\x=15*(0.5)\\x=7.5[/tex]

Hence, [tex]x=7.5[/tex]

Answer:

a=3.75 un., b=11.25 un.

[tex]x=7.5\ un.[/tex]

[tex]y=\dfrac{15\sqrt{3}}{4}\ un.[/tex]

[tex]z=\dfrac{15\sqrt{3}}{2}\ un.[/tex]

Step-by-step explanation:

Given triangle is special 30°-60°-90° right triangle. The leg that is opposite to the angle of measure 30° is always equal to half of the hypotenuse. The hypotenuse is of length 15 units, the leg that is opposite to the 30° angle is leg with length of x units, then

[tex]x=\dfrac{15}{2}=7.5\ un.[/tex]

In right triangle with hypotenuse x and legs y and a, angle opposite to the leg a is 30°, then

[tex]a=\dfrac{x}{2}=\dfrac{7.5}{2}=3.75\ un.[/tex]

and

[tex]b=15-a=15-3.75=11.25\ un.[/tex]

By the Pythagorean theorem,

[tex]x^2=y^2+a^2,\\ \\7.5^2=3.75^2+y^2,\\ \\y^2=\left(\dfrac{15}{2}\right)^2-\left(\dfrac{15}{4}\right)^2=\dfrac{225}{4}-\dfrac{225}{16}=\dfrac{675}{16},\\ \\y=\dfrac{15\sqrt{3}}{4}\ un.[/tex]

In right triangle with legs y and b and hypotenuse z, leg y is opposite to 30° angle, then

[tex]z=2y=\dfrac{15\sqrt{3}}{2}\ un.[/tex]

Answer: $286.50

If the AP (Annual Premium) $1000 for 30 yr male with 10 yr policy; $3.82...

75000/1000 = 75

75 x $3.83 = $286.50 AP

The premium for a 10-year, $75000 life insurance policy for a healthy 30-year-old male typically ranges from $10 to $20 per month. Actual pricing can vary based on health status, lifestyle, occupation and the specific insurance company's underwriting process. To get the most accurate premium, it's beneficial to shop around and compare quotes.

The premium for a life insurance policy varies based on several factors including the age of the individual, the amount of coverage, policy term, and the individual's health status. The question doesn't provide enough information for an exact calculation as we do not know the general health status of the 30-year-old male, his occupation, lifestyle factors or the premium rates of the specific insurance company. However, we can give a general idea.

Assuming this individual is in good health, for a 30-year-old male, a $75000, 10-year term life insurance policy would typically cost between $10 to $20 per month. This is an average and the actual cost can vary greatly based on the factors mentioned.

Also, each insurance company has different pricing and underwriting processes, so it's important to shop around and compare quotes from different companies to ensure you're getting the best rate.

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Answer:

x-value is 6.87

Step-by-step explanation:

we are given

Polynomial as

[tex]y=2x^2+7[/tex]

Exponential as

[tex]y=5^{x-4}[/tex]

Firstly, we can draw graph

We can see that intersection point is (6.87,101.392)

so, x=6.87

At (6.97, 101.392) the exponential function surpasses the polynomial function.

Graphical solutions of a system of equations are way of finding the intersection points of all the equations given.

A system with two or more than two equations has a solution only when they have a common intersection point.

Given, A system of equation y = 2x² + 7 and y = 5^(x - 4).

Now by graphing these two equations we observe that at 6.87 the exponential function surpasses the polynomial function.

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Answer:

Solution to system is

x = 6 and y= 4

S.set={6,4}

Step-by-step explanation:

The given equations are

x + 3y = 18                      ................(i)

x + 2y=14                        .................(ii)

Subtracting both equation

(x+3y)-(x+2y)=18-14

x+3y-x-2y = 4

y = 4

put the value of y in equation (i)

the equation becomes

x + 3(4) = 18

x + 12 = 18

subtracting 12 from both sides

x + 12 -12 = 18-12

x =6

Solution to system is

x = 6 and y= 4

S.set={6,4}                            

Answer:

2 pens

Step-by-step explanation:

Let x represent the number of pens Linda buys.  Since they cost $2.65 each, this gives us the expression 2.65x.

Adding the cost of the card to this gives us the expression 2.65x+1.17.

She has a total of $9.00; this gives us the equation

2.65x+1.17 = 9.00

Subtract 1.17 from each side:

2.65x+1.17-1.17 = 9.00-1.17

2.65x = 7.83

Divide both sides by 2.65:

2.65x/2.65 = 7.83/2.65

x = 2.95

We cannot buy a portion of a pen, so the most she can buy is 2 pens.

Answer:

The answer is 2 pens.

Step-by-step explanation:

Total amount Linda has in her wallet = $9

Amount spent on buying a card = $1.17

So, amount left with Linda = [tex]9-1.17=7.83[/tex]

Now, she wants to buy pens that cost $2.65, so the maximum number of pens she can buy are = [tex]\frac{7.83}{2.65}= 2.9[/tex]

But, pens cannot be in decimal, so the maximum pens she can buy are 2.

Answer:

M=3.5

Step-by-step explanation:

7x-2y=0.2

-7x        -7x

-2y = -7x + .02

/-2      /-2     /-2

y= 3.5x+ 0.01

slope is 3.5

Question

what's the answer to this  

4 (w+1)-4w

Answer:

Step-by-step explanation:

4 (w+1)-4w =

4w + 4 - 4w =

4

The largest decimal is :

0.68

Because: In the tenths place, 6 is the biggest number.  Now we go to the hundredths to see which one is the biggest.  8 Is the largest one out of them.  But what about the 0's?  The 0's at the end don't really matter.  They are there to confuze you or to add more extra 0's.  The 0 at the front of the decimal is also smaller then the 6.  For example:  0.0175  < 0.68

Hope helps!-Aparri

The largest decimal among 0.0688, 0.667, 0.68, and 0.6 is 0.68. This can be determined by comparing each digit from left to right in the numbers. Hence, 0.68 is the highest.

To determine which is the largest decimal among 0.0688, 0.667, 0.68, and 0.6, we compare each decimal value:

We start from the leftmost digit and compare:

Therefore, the largest decimal among the given numbers is 0.68.

Answer:

(6, -3)

Step-by-step explanation:

I will solve this system using elimination.

[tex][tex]\left \{ {{-x+2y=-12} \atop {2x+3y=3}} \right.[/tex][/tex]

I will multiply [tex]-x+2y=-12[/tex] by 2 so that -x becomes -2x.

2(-x + 2y = -12)

Distribute.

-2x + 4y = -24

Now subtract this from the other equation.

2x + 3y = 3

-2x + 4y = -24

        7y  =  -21

Divide both sides by 7.

y = -3

Now that we have the value of y, plug it into the original equation.

-x + 2(-3) = -12

Simplify.

-x - 6 = -12

Add 6 to both sides.

-x = -6

Divide both sides by -1.

x = 6

(6, -3)

Answer:

Divided by 3.

They are all divided by 3.

Answer:

b(1)= 27

b(n)=b(n-1)* (-1/3)

Step-by-step explanation: