I need to write this equation that has a infinite number of solutions

So we need to solve the following equation for x:

The first step would be substracting 8 from each side of the equation:

The next step is to square

Answer:

The length of the base is:

The resulting quadratic is

Step-by-step explanation:

Base = x

Height = 4x

Area, A = 1/2* base * Height

           A = (1/2) * (x) * (4x)

          A = 2x²           (1)

But,    A = 6              (2)

Since (1) = (2);

2x²= 6

x²= 3

Resulting quadratic:

x² - 3= 0

For the difference between 2 squares:

a² - b² = (a-b)(a+b)

Using that identity, we can factorize our quadratic:

(x-3)(x+3) = 0

So, we have 2 roots:

x = 3 and x = -3

Now, noting that length must take a positive value, we go for the first:

x = 3

The length of the base is:

The resulting quadratic is

we have that

the area of parallelogram is equal to

A=b*h

we have

b=14 mm

Find the value of h

tan(60)=h/7 -----> by opposite side divided by the adjacent side

Remember that

so

h=7√3 mm

substitute

A=14(7√3 )

We are asked to identify the types of symmetries found in the given geometrical figure. Let's remember that asymmetry is a transformation that maps the figure onto itself. In this case the object has symmetry under reflections, also has symmetry under rotations around its center

Okay, here we have this:

Considering the provided data set, we are going to calculate the requested data, so we obtain the following:

Mean:

It corresponds to the result of adding all the data and dividing it by the amount of data, then we have:

Mean=(89+81+96+85+93+70+66+64+68+70)/10

Mean=782/10

Mean=78.2

Median:

First we will order the data from smallest to largest and the value that is in the center will be the median:

Sorted Data Set: 64, 66, 68, 70, 70, 81, 85, 89, 93, 96

Since 70 and 81 are in the middle, the median will be their average.

Median=(70+81)/2=151/2=75.5

Mode:

It is the data that is repeated the most, in this case it is 70 because it is twice

Range:

It is the difference between the smallest and largest value, then:

Range=96-64=32

we have the following:

Solution

For this case since we want to verify if a circle can be circumscribed in the quadrilateral we can use the following Theorem:

Theorem: If a quadrilateral is incribed in a circle then the opposite sides are supplementary

And we cna verify:

105+ 98= 203

82 +75= 157

Then we can conclude that the answer is:

False

The number line always goes from negative to positive :

It increases from left to right

SInce negative is always on the left side of the zero

Snumber greater than zero are always positive

i.e. x > o

we have

7 3/4 + 1 5/6​

step 1

Convert mixed number to an improper fraction

7 3/4=7+3/4=31/4

Remember taht

If you multiply 31/4 by (1.5/1.5) you obtain an equivalent fraction

so

(31/4)(1.5/1.5)=46.5/6

multiply by 10/10

465/60

1 5/6=1+5/6=11/6

multiply by 10/10

(11/6)(10/10)=110/60

step 2

Adds the fractions

465/60+110/60=575/60

simplify

Convert to mixed number

575/60=540/60+35/60=9+35/60

simplify the fraction 35/60

35/60=7/12

so

we have

9+7/12=9 7/12

Solution of an inequality

We can express the solution (s) of inequalities in several forms.

Here we will use two of them: The set-builder notation and the interval notation.

Let's solve the inequality

x - 1 ≤ 9

Adding 1 to both sides of the inequality:

x ≤ 10

The solution in words is "all the real numbers less than or equal to 10"

In set-builder notation:

{x | x <= 10}

In interval notation: (-inf, 10]

The number of black bears in the national park is 36

Here, given the ratio of black bears to grizzly bears, and the number of grizzly bears, we want to find the number of blackbears the national park has

Let the number of black bears be x

what this mean is that the total number of bears in the park is (x + 12)

The total ratio of the two is 3 + 1 = 4

Matematically;

Answer:

Question 1: 3

Question 2: $120

Step-by-step explanation:

Set up a proportion

[tex]\frac{inches}{miles}[/tex] = [tex]\frac{inches}{miles}[/tex]  fill in the numbers that you know and solve for the unknow.

[tex]\frac{5}{2}[/tex] =[tex]\frac{7.5}{m}[/tex]  Cross multiply

5x =7.5(2)

5x = 15  Divide both sides by 5

x = 3

If we take 40% off that means that we leave 60% on

Percent means per hundred

[tex]\frac{60}{100}[/tex]  When you divide by hundred, you move the decimal two places to the left.

200(.6)

$120.00

1) To find each unit price, let's find out the unit rate. Setting a proportion.

Option A

cupcakes price

12 ------------------- 29

1 --------------------x

Cross multiplying it:

12x = 29 Divide both sides by 12

x =2.42

Each cupcake costs $ 2.42

Option B

24 ------------ 56

1 ------------ y

24y = 56

y =$2.33 per cupcake.

2) The best deal for buying cupcakes is found in Option B. Since the price is lower per cupcake

3) Hence, the answers are:

Option A = $2.42 per cupcake

Option B =$2.33 per cupcake

Best Deal: Option B

Given:

A bee produce 0.05 ml of honey per day

We will find how many liters of honey can the bee produce in its lifetime if they live for 28 days

Let it produces x ml

So, using the ratio and proportions

Solve for x:

Convert ml to liters

1 liter = 1000 ml

So, 1.4 ml = 0.0014 liters

So, the answer will be

The bee can produce honey in its lifetime = 0.0014 liters

Answer:

• Plan B, by $4

• 140 minutes

Explanation:

Part A

From the graph, at 40 minutes, the costs of the plans are:

• Plan A: $4

• Plan B: $8

Plan B costs more by $4.

Part B

The point where the costs are the same is the time at which the two graphs intersect.

When the number of minutes = 140 minutes

• Cost of Plan A = $14

• Cost of Plan B = $14

Thus, the two plans cost the same for 140 minutes of long-distance call.

• If the time spent is less than this amount, Plan B costs more.

Given:

A diver starts at 342 feet below the surface, which means -342 feet.

Now, she swims 237 feet upward.

It shows that she is moving in a positive direction.

So, the current depth of diver is,

The depth is -105 feet, which shows that the diver is still 105 feet below the surface.

Answer: The factor of the above function is (2x + 3) (3x + 4)

We are given the below function

This function can be factor using factorization method

The co-efficient of x^2 = 6

Multiply 6 by 12 to get the constant of the function

12 x 6 = 72

Next, find the factors of 72

Factors of 72 : 1 and 72, 2 and 36, 6 and 12, 9 and 8, 3 and 24

The only factor that will give us 17 when add and give us 72 when multiply is 8 and 9

The new equation becomes

The factor of the above function is (2x + 3) (3x + 4)

We have to calculate the volume of the pyramid with the following dimensions:

We can express and calculate the volume as:

Answer: the volume is 128 dm³

The scenarios that demonstrate a proportional relationship for each person's income are :

Consider the income as y in each scenario

Scenario 1

Millie works at a car wash and earns $17.00 per car she washes.

Consider the number of car she washes as x

y = 17x

y ∝ x

This is a proportional relationship

Scenario 2

Bryce has a cleaning service and charges $25.00 plus $12.50 per hour.

The relationship will be

y = 25 +12.50x

where x is the number of hours

This is not a proportional relationship

Scenario 3

Carla makes sandwiches at her job and earns $7.85 per hour.

The relationship will be

y = 7.85x

y ∝ x

Where x is the number of hours

This is a proportional relationship

Scenario 4

Tino is a waiter and makes $3.98 per hour plus tips.

The relationship will be

y = 3.98x + tips

Where x is the number of hours

This is not a proportional relationship

Hence, the scenarios that demonstrate a proportional relationship for each person's income are

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Answer:

68

Step-by-step explanation:

100-68-12-11=9

12+11=23

100-23-9=68

Divide side R'O' (8) by th scale factor (2/3)

8 : 2/3= 12

The cost for 1 liter of premium gasoline is $0.43 greater than the regular gasoline.

This is referred to as the total amount of money and resources which are used by companies in other to produce a good or service.

In this scenario, we were given 25 liters of regular gasoline for $58.98 or 25 liters of premium gasoline for $69.73.

Cost per litre of premium gasoline is = $69.73 / 25 = $2.79.

Cost per litre of regular gasoline is = $58.98/ 25 = $2.36.

The difference is however $2.79 - $2.36 = $0.43.

Therefore the cost for 1 liter of premimum gasoline is $0.43 greater than the regular gasoline.

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If the polynomial function be P(x) = [tex]x^4[/tex] − 3x³ + 2x² then Zeros exists at x = 0, 0, 1, 2.

A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.

An expression that consists of variables, constants, and exponents that exists combined utilizing mathematical operations like addition, subtraction, multiplication, and division exists directed to as a polynomial (No division operation by a variable).

Let the polynomial function be P(x) = [tex]x^4[/tex] − 3x³ + 2x²

P(x) = x²(x² - 3x + 2)

factoring the above polynomial function, we get

P(x) = x·x(x - 1)(x - 2)

Zeros exists at x = 0, 0, 1, 2

P(x) exists degree 4, so it will contain four roots. You only entered three which exists probably why it came up as wrong. The x² term contains a multiplicity of 2, so it counts twice.

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Given

Solution

Formula

Now

The midpoint M of the line segment joining the points C=(6,2) and D=(2,8). is

Answer:

q = -1

Step-by-step explanation:

We are given the inequality [tex]11-\frac{64}{q} > 60[/tex]

We want to find out which value of q is a solution to the inequality. In other words, which value of q makes the statement true?

We can substitute the values given for q into the inequality to see this.

Let's start with q=2.

Replace q with 2.

[tex]11-\frac{64}{2} > 60[/tex]

Divide 64 by 2.

64/2= 32

11 - 32 > 60

Subtract 32 from 60

11-32 = -21

-21 > 60

The inequality reads "-21 is greater than 60", which is false (negative numbers are less than positive ones).

This means q=2 is NOT an answer.

Next, let's try q=-2

[tex]11 - \frac{64}{-2 } > 60[/tex]

64/-2 = -32

11 - - 32 > 60

- - 32 means subtracting a negative, which is the same as adding 32 to 11.

11 + 32 > 60

43 > 60

This is also NOT true (it reads "43 is greater than 60").

So q=-2 is also NOT an answer.

Now, let's try q = -1

[tex]11-\frac{64}{q} > 60[/tex]

[tex]11-\frac{64}{-1} > 60[/tex]

64/-1=-64

11 - -64 > 60

11 + 64 > 60

75 > 60

This reads "75 is greater than 60".

This is a true statement, meaning q = -1 IS an answer.

We are technically done, but just to be sure, we can check q=1 as well.

[tex]11 - \frac{64}{q} > 60[/tex]

[tex]11 - \frac{64}{1} > 60[/tex]

11 - 64 > 60

-53 > 60

This reads "-53 is greater than 60", which is false.

So this confirms that q = -1 is the only option that is an answer.

GIVEN

The time left before the store closes is 3/4 h while the time taken to find one item is 1/8 h.

QUESTION A

Let the number of items that can be gotten before the store closes be N.

The number of items can be calculated using the formula:

Therefore, the equation to get the number of items will be:

QUESTION B

The solution can be obtained by division.

Apply the fraction rule:

Hence, the solution will be:

The answer is 6.

QUESTION C

Jane can find 6 items before the store closes.

The perimeter of a triangle is given by the sum of all it is sides.

Now, we have the next measures:

- The longest side of a triangle is 5in longer than the shortest side.

- The medium side is 4 inches longer than the shortest side

Then, the perimeter is given by:

P = (s+5)+(s+4)+s

If the perimeter is P=21 inches:

21 = (s+5)+(s+4)+s

Solve for s:

21 = s+5+s+4+s

21 = 3s + 9

21-9 = 3s

12 = 3s

s = 12/3

s= 4

Therefore,

The shortest side of the triangle is 4 inches.

The medium side is s+ 4 = 4+ 4 = 8 inches

The longest side is s+5 = 4+5 = 9 inches

the graph of a line passing through point

with gradient m

is given by

ANSWER:

D. the exponential function grows faster than the quadratic function over two intervals; 2 < x ≤ 4

STEP-BY-STEP EXPLANATION:

We can see from the graphs that the growth is the same from 0 to 2 and then the exponential function grows faster, therefore, strictly speaking, the correct answer is D. the exponential function grows faster than the quadratic function over two intervals; 2 < x ≤ 4

a) Given:

The length of the side of a square is,

To find:

The area of the square.

Explanation:

Using the formula of the area of the square,

Final answer:

The area of the square is,