Can you have a triangle with sides 6, 7, and 2?

The solution to the system of equation is (-1, -6)

Given the system of equations

2x - 3y = 16

5x - 3y = 13

Subtract to have:

2x-5x = 16 - 13

-3x = 3

x = -3/3

x = -1

Substitute x = -1 into 1 to have:

2(-1) - 3y = 16

-2 - 3y = 16

-3y = 16 + 2

-3y = 18

y = -6

Hence the solution to the system of equation is (-1, -6)

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Answer:

Hello yeily, I think and believe they are all rational..

Step-by-step explanation:

Hope it helps <=/

Answer:

[tex]12 > x[/tex]

Step-by-step explanation:

[tex]20 > .75x + 4[/tex]

Is the equation you need to set up.

Then you want to subtract four from both sides ehich ends up giving you

[tex]16 > .75x[/tex]

Then divide 16 by 4 (this gives you a fourth) you get four

Then multiple 4 by 3 to get .75 of 16 which is 12

Hope this helps!

If yoy have any other questions feel free to ask!

Answer:

Tanner can play 20 games in the arcade and will have 50 cents left over.

Step-by-step explanation:

20 = 4.50 + 0.75x

Subtract 4.5 from both sides.

15.5 = 0.75x

Plug in numbers for x until it is equal more that 15.5

x = 20

0.75(20) = 15

0.75(21) = 15.75 < too much

This rate in lb/s is 833.33 lb/s if a large dump truck can move 1,500 tons/h of gravel from one point to another on a work site.

The term "ton-hour" refers to a cooling service that provides 12,000 BTU of cooling, measured as a function of the amount of chilled water that flows through the Energy Transfer Station, the temperature difference between the chilled water at the Delivery Point, and the Return Point and the total BTU gain that occurs.

The imperial and US customary systems of measurement both utilize the unit of mass known as the pound (symbol: lb). The precise weight of the international avoirdupois pound, or today's standard pound, is 0.45359237 kilos. 16 avoirdupois ounces make up an avoirdupois pound.

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Answer:

18

Step-by-step explanation:

∠BCD=2x (alternate interior angles)

∠BCD+∠CDE=180° (same side interior angles)

Thus, 10x=180, meaning x=18.

The cost of each spiral notebook is $3 and the cost of each book cover is $2

Given that Alexis and her sister bought school supplies. Alexis bought 5 spiral notebooks and 6 book covers for $27. Her sister bought 4 spiral notebooks and 2 book covers for $16 and asked to find out the cost of each spiral notebook and each book cover.

Let's assume spiral notebooks as "x"  and book covers as "y".

As a result, two linear equations in two variables will be formed.

⇒5x+6y=$27; Let's assume this equation as A

⇒4x+2y=$16; Let's assume this equation as B

Multiply equation B with 3

⇒12x+6y=$48; Let's assume this equation as C

Equation c- Equation A

⇒$48-$27=7x

⇒7x=$21

⇒x==$3

The cost of the spiral notebook is $3

From equation A

⇒5($3)+6y=$27

⇒$15+6y=$27

⇒6y=$12

⇒y=$2

The cost of the book cover is $2

Therefore,The cost of each spiral notebook is $3 and the cost of each book cover is $2

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The area of the parallelogram ABCD with the vertices is 40 square units

The vertices are given as

(2, 3), B (7, 3), C (8, -5), and D (3, -5)

From the graph, we have the following dimensions

Base = 5 units i.e. distance AB

Height = 8 units i.e. the distance between the parallel sides

The area of the parallelogram is then calculated as

Area = Base * Height

So, we have

Area = 5 * 8

Evaluate

Area = 40

Hence, the area of the parallelogram ABCD with the vertices is 40 square units

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Answer:

83/100

Step-by-step explanation:

You move 2 times to the right your answer will be 83/100  

Answer:

B

it is the right equation

The largest integer whose square has exactly digits when written in base is 28 in base 9 .

An integer is the number zero, a positive natural number or a negative integer with a minus sign. The negative numbers are the additive inverses of the corresponding positive numbers. In the language of mathematics, the set of integers is often denoted by the boldface Z .

Largest base 9 three digit number = 888  

And it can be represented as 728 in base 10, largest square is 26^2       26 that is 28 in base 9.

Therefore the largest integer whose square has exactly digits when written in base is 28 in base 9 .

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20867

[tex]0.7\times10^{-2}[/tex] times as long as the small virus cell is the white blood cell.

Given that, the length of a white blood cell is [tex]1.4\times10^{-5}[/tex] meter and the length of a small virus cell is [tex]2.0\times10^{-7}[/tex] meter.

We need to find how many times as long as the small virus cell is the white blood cell.

To determine the power or exponent of 10, let us understand how many places we need to move the decimal point after the single-digit number.

Now, [tex]\frac{1.4\times10^{-5}}{2.0\times10^{-7}}[/tex]

=[tex]0.7\times10^{-2}[/tex]

Therefore, [tex]0.7\times10^{-2}[/tex] times as long as the small virus cell is the white blood cell.

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The measure of angle 2 and angle3 are 133 ad 47 degrees respectively

From the given diagram, the measure of angle 1 and 2 are congruent. (vertical angles)

Given he following parameters

m<1 = 133 degrees

Since m<1 = m<2, hence m<2 = 133 degrees

Also;

m<2 + m<3 = 180

133 + m<3 = 180

m<3 = 180 - 133

m<3 = 47 degrees

Hence the measure of angle 2 and angle3 are 133 ad 47 degrees respectively

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Answer:

(a) 75 minutes

(b) 50 minutes

Answer:      10/3

Step-by-step explanation:

multiply the denominator, "3", by the mixed number "3", then add the numerator "1". So 3*3+1=10/3 (the denominator stays the same)

Answer: [tex]\frac{10}3}[/tex]

Answer:

1. 104F

2. 95F

Step-by-step explanation:

Formula for Celsius to Fahrenheit is

[tex](C*1.8) + 32 = F[/tex]

Question one:

40 times 1.8 = 72

72+32 = 104 Fahrenheit

Question two:

35 times 1.8 = 63

63+32 = 95 Fahrenheit

Answer:niamh gets 15 and jack gets 35

Step-by-step explanation:

think of the raito 3:7 as 3x:7x. then we can do: 3x + 7x = 50, which means 10x = 50. then we can find x by dividing 50 by 10, so x is 5. then we can find 3x, whihc is 3x5 = 15. then find 7x, so 7x5 = 35. so niamh gets 15 and jack gets 35

The length and width of rectangle is 160 feet and 100 feet.

The perimeter of the rectangle is calculated by the formula -

Perimeter = 2 × (length + width)

As per the given information, length = (60 + width)

Keep the values in formula to find the breadth of rectangle.

520 = 2 × (60 + width + width)

520 = 2 × (60 + 2 × width)

(60 + 2 × width) = [tex]\frac{520}{2}[/tex]

(60 + 2 × width) = 260

2 × width = 260 - 60

2 × width = 200

Width = [tex]\frac{200}{2}[/tex]

Width = 100 feet

Keep the value in formula to find the length of perimeter

520 =  2 × (length + width)

Length + 100 = [tex]\frac{520}{2}[/tex]

Length = 260 - 100

Length =  160 feet

Hence, the length and width of rectangle is 160 feet and 100 feet.

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The age of Mrs. Lee when her 2 children's combined age is [tex]\frac{5}{11}[/tex] of her age will be [tex]44[/tex] yrs. old

As per the question statement, Mrs. Lee, who is 40, has a son who is twice as old as her daughter. Mrs. Lee will be thrice her son's age when her daughter is 12-year old. We are asked that how old Mrs Lee be when her two children's combined ages are 5/11 of her own age.

This question is a classic example of forming and solving linear equations.

When Mrs. Lee was 40, her son was twice her daughter's age.

Let d = her daughter's age when Mrs. Lee was 40.

Then her son was 2d yrs. old when Mrs. Lee was 40.

When her daughter is 12, Mrs. Lee will be three times her son's age.

This means [tex](12 - d)[/tex] years have passed since Mrs. Lee was 40.

So, if her daughter was 12 at this time, that means her son was [tex]2d + (12 - d)[/tex]

And, Mrs. Lee's age at this time was [tex]40 + (12 - d)[/tex]

Mrs Lee was thrice her son's age at this time:

[tex]40 + (12 - d) = 3(2d + 12 - d))[/tex]

[tex]40+12-d=6d+36-3d\\4d=16\\d=4[/tex]

So, Mrs. Lee's age when her daughter was 12 is [tex]40 + 12 - 4 = 48[/tex] yrs. old

Her daughter was 8 yrs. old 4 years earlier.

Thus, Mrs Lee's age when her daughter was 20 was [tex]48 - 4= 44[/tex] years old.

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Answer:

y = [tex]\frac{1}{4}[/tex] x + 6

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

4x + y = 7 ( subtract 4x from both sides )

y = - 4x + 7 ← in slope- intercept form

with slope m = - 4

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-4}[/tex] = [tex]\frac{1}{4}[/tex] , then

y = [tex]\frac{1}{4}[/tex] x + c ← is the partial equation of the perpendicular line

to find c substitute )- 4, 5 ) into the partial equation

5 = - 1 + c ⇒ c = 5 + 1 = 6

y = [tex]\frac{1}{4}[/tex] x + 6 ← equation of perpendicular line

The total cost for going to the concert = $90.

The loss of value or benefit that'd result from engaging in a particular activity option in comparison to engaging in such an alternative activity which offers a higher come back on value or benefit is referred to as opportunity cost. The value of the best alternative picked during the decision-making process is provided.

We can select the best option out of all the options available with the aid of the idea of opportunity cost. It helps us use all of our resources as skillfully and productively as possible in order to maximize our financial gains.

For her part-time job, Karen receives a $10 hourly wage. The cost of the concert ticket after the discount is $50, so she decided to go.

It will cost money to take four hours off work. $10 x 4

                                                                           =$40

Opportunity costs of going to the concert = $50 + $40

                                                                      = $90

It is evident that the opportunity cost will be $90.

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I understand that the question you are looking for is:

Karen earn $10 per hour. she wants to go to a concert on Saturday and the price of the ticket is $75, but her friend sold her a ticket for $50. if Karen had to take 4 hours off of work to attend the concert ,What was her opportunity cost of attending the concert?

a.$40

b.$50

c.$75

d.$90

The evaluation of the expression gives -295/24. The correct option is the fourth option-   negative 295 over 24 (-295/24)

From the question, we are to evaluate the given expression

The given expression is,

7 3/8 × -1 2/3

To solve the expression, we will covert the fractions from mixed to improper fractions

7 3/8 × -1 2/3

59/8 × - 5/3

Multiplying, we get

-295/24

Hence, the evaluation of the expression gives -295/24. The correct option is the fourth option-   negative 295 over 24 (-295/24)

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The eight machines can be arranged in the three available spaces in 336 ways.

Here we have 8 screw machines with 3 spaces. To find the different way, permutation will help.

Different ways = 8 P 3

= 8! / (8! -3!)

= 8! / 5!

= 8 x 7 x 6 x 5! / 5!

= 6x7x8 = 336.

Therefore, in 336 different ways the eight machines be arranged in the three spaces available.

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We need to know about logic statements to solve this problem. The solution of the logic statements are 0 and 1 respectively.

Logical operators are used to form logical statements, logical operators compute result based on boolean values true and false or binary 1 and 0. The common logical operators are AND and OR. AND is represented by ^ symbol and OR is represented by v symbol, ' means negation of the value, which means that true becomes false and vice versa. For AND operator, it works like multiplication, 0 and 1 yield 0, 1 and 1 yields 1 and 0 and 0 yields 0. For OR operator it works like addition, 0 and 1 yields 1, 1 and 1 yields 1 and 0 and 0 yields 0. For the logical statements given in the question we need to first compute the logical statement inside the bracket and then compare the inner result with the outer value.

(1'^0)^1 =(0^0)^1=0^1=0

(1v0')^(0v1)=(1v1)^(0v1)=1^1=1

Therefore we found the values of the logical statements to be 0 and 1 respectively.

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Answer: See diagram below

Scale factor = 3

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

Explanation:

The given L shape has a perimeter of 3+1+2+1+1+2 = 10 units. I added up the exterior sides of this shape.

We want the perimeter to be 30 units, so we scale it by a factor of 3. Since 30/10 = 3.

This means we'll triple each side

The vertical side on the left originally 3 units long is now 3*3 = 9 units. The bottom side that is 2 units long is now 2*3 = 6 units. And so on.

See the diagram below.

Notice in the red figure the sides add to 9+3+6+3+3+6 = 30 to help confirm our answer.

GIVEN THE FOLLOWING:

Mario's car rate consumption. R = 24.5mile/gallon

Distance covered each day, D = 32.3 miles

Cost of gas $2.89/gallon

REQUIRED: (a) To calculate how much he spends on gas each week.

We proceed as follow:

Mario uses 1 gallon of gas for every 24.5 miles.

For 32.3 miles, he will use [tex]\frac{32.3}{24.5} ~gallons~ of gas=\frac{325}{245} ~gallons[/tex]

Now, a gallon of gas costs $2.89

[tex]\frac{325}{245}~gallons~will~cost =?[/tex]

[tex]\frac{325}{245} ~*2.89=3.81[/tex]

$3.81 is how much he spends each workday.

There are 5 working days in a week.

Therefore, for a week, he spends:

[tex]3.81~*~5~=19.05[/tex]

therefore, for each work week, he spends $19.05 on gas.

(B) To calculate how many miles he can drive with $15.00 worth of gas

We proceed thus:

A gallon of gas costs $2.89.

$15.00 will amount to:

$15.00/$2.89 = 5.19 gallons

Recall that Mario uses 1 gallon of gas for every 24.5 miles.

Therefore, 5.19 gallons will be used for:

[tex]5.19~*24.5=127.155 ~miles[/tex]

≈ 127 miles

Therefore, with gas worth $15.00, Mario will cover a distance of 127 miles

AshTheNeko

Answer:

Step-by-step explanation:

Givens

Let the Length = L

Let the width = w

w = 2*L - 3

Area = L * w

Area = 193

Solution

Area = 193

193 = L*(2L - 3)

193 = 2L^2 - 3L       Subtract 193 from both sides.

2L^2 - 3L - 193 = 0

You have to use the quadratic formula get the answer. Without going through all all that, I will tell you that the only value you can use for L is 10.6

L = 10.6

w = 2* 10.6 - 3 = 18.4

But you want the diagonal. Use the Pythagorean Theorem to get it.

Diagonal^2 = L^2 + w^2

Diangonal^2 = 10.6^2 + 18.4^2

Diagonal^2 = 450.92                   Take the square root of both sides

√diagonal^2 = √450.92

Answer

The diagonal is 21,23

The amount of silver that  should be added is 48% . A jeweler is said to have 5 rings that weigh 12 g apiece and are composed of an alloy of 20% silver and 80% gold.

What are linear equations?

An equation between two variables that, when plotted on a graph, produces a straight line.

The material will weigh 12 × 5 = 60 grams after melting all 5 rings.

The alloy's 20% silver and 80% gold content have been disclosed to us. Let's further say that the melted material receives an additional x grams of silver, resulting in a composition of 64% gold and 36% silver.

Thus, we can construct the following equation:

Amount of gold before = Amount of gold after mixing

So the equation we get

80% of 60 grams =64% of (X + 60) gram

0.80 × 60 = 0.64 (x + 60)

48 = 0.64x + 38.4

0.64x = 9.6

x = 9.6/0.64

x = 15

So

Amount of silver that needed to be added

= 0.64(15 + 60)

= 0.64(75)

= 48%

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Final answer obtained is 2/3

A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio. For instance, the geometric progression 2, 6, 18, 54, etc. has a common ratio of 3. Similar to that, the geometric series 10, 5, 2.5, 1.25,... has a common ratio of 1/2.

Powers [tex]r^{k}[/tex] of a given non-zero number r, like [tex]2^{k}[/tex] and [tex]3^{k}[/tex], are examples of a geometric sequence. A geometric sequence's basic structure is

[tex]ar,ar^{2},ar^{3}.ar^{4},-----[/tex]

where a is not equal to 0 is a scale factor that is equal to the initial value of the series and r is not equal to 0 is the common ratio.

A series is a sum, whereas a progression is a sequence. This is the difference between the two.

∑[tex]_{i=0}^{n}[/tex] [tex]ar^{i}=\frac{a(1+r^{n+1})}{1-r}[/tex]

We see that n= 99, r= -1/2, a=1

∑[tex]_{i=0}^{99}[/tex] [tex](\frac{-1}{2}) i=[/tex] [tex]\frac{1-(\frac{-1}{2})^{99+1} }{1-\frac{1}{2} }=\frac{1-(\frac{-1}{2})^{100} }{1+\frac{1}{2} }=\frac{1-\frac{1}{2}^{100} }{\frac{3}{2} }[/tex]

[tex]=\frac{\frac{2^{100}}{2^{100}} -\frac{1}{2^{100}} }{\frac{3}{2} } =\frac{2*(2^{100}-1)}{3*2^{100}}[/tex]

[tex]\frac{2*(2^{100}-1)}{3*2^{100}}[/tex]

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Numbers in the first 20 rows of pascal's triangle are 210

Pascal's triangle is a triangular array of the binomial coefficients that arises in probability theory, combinatorics, and algebra.

We have been given that:

Numbers of rows = 20

Pascal's triangle formula

1 + 2 + 3 + ….+ 19 + 20  = n (n + 1) / 2  

n=20

 (20)×(21)/ 2  = 210

Pascal's triangle patterns is its symmetry. Observe that in any row, if we read the consecutive numbers from the left, we will obtain the same as if we read them from the right.

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