How many solutions exist for the given equation?
12x + 1 = 3(4x + 1) – 2
zero
one
two
infinitely many

Answer:220

Step-by-step explanation:

65+65+ 60+ 30

Answer:

shows correct substitution of the values a, b, and c  from the given quadratic equation    into quadratic formula.

Step-by-step explanation:

Given: The quadratic equation

We have to show the correct substitution of the values a, b, and c from the given quadratic equation    into quadratic formula.

The standard form of quadratic equation is  then the solution of quadratic equation using quadratic formula is given as

Consider the given  quadratic equation

Comparing with general  quadratic equation, we have

a = -3 , b = -2 , c = 6

Substitute in quadratic formula, we get,

Simplify, we have,

Thus,  and x_{2}=\frac{2-\sqrt{76} }{-6}

Simplify, we get,

Thus,  shows correct substitution of the values a, b, and c  from the given quadratic equation    into quadratic formula.

Answer:

shows correct substitution of the values a, b, and c  from the given quadratic equation    into quadratic formula.

Step-by-step explanation:

Given: The quadratic equation  

We have to show the correct substitution of the values a, b, and c from the given quadratic equation    into quadratic formula.

The standard form of quadratic equation is  then the solution of quadratic equation using quadratic formula is given as  

Consider the given  quadratic equation  

Comparing with general  quadratic equation, we have

a = -3 , b = -2 , c = 6

Substitute in quadratic formula, we get,

Simplify, we have,

Thus,  and x_{2}=\frac{2-\sqrt{76} }{-6}

Simplify, we get,

Thus,  shows correct substitution of the values a, b, and c  from the given quadratic equation    into quadratic formula.

Domain: [tex][-2,6][/tex]

Range: [tex][0,5][/tex]

Explanation:

Domain:

The domain of a function is the set of all possible values of the independent variable x. From the graph, we can see that the function has the set of all possible values from -2 to 6. Hence, the domain is from -2 to 6.

Thus, writing the domain in interval notation, we have,

[tex]-2\leq x\leq 6[/tex]

This also can be written as [tex][-2,6][/tex]

Hence, the domain is [tex][-2,6][/tex]

Range:

The Range of a function is set of all possible values of y obtained by substituting the values for x in the function. From the graph, we can see that the function has the set of all possible values from 0 to 5. Hence, the range is from 0 to 5.

Thus, writing the range in interval notation, we have,

[tex]0\leq y\leq 5[/tex]

This also can be written as [tex][0,5][/tex]

Hence, the range is [tex][0,5][/tex]

The domain and range in interval notation represent sets of possible values a function can take. For instance, for the function f(x) = 2x + 3 where x can be any real number, both the domain and range would be (-∞, ∞). Square brackets denote inclusive endpoints, while parentheses denote exclusive endpoints in interval notation.

In mathematics, particularly in functions, the domain and range represent sets of possible input and output values respectively. When expressed in interval notation, domain and range convey a concise representation of these sets.

Let's illustrate with an example. If we have the function f(x) = 2x + 3, and x can be any real number, the domain in interval notation would be (-∞, ∞). As for the range, since the function can also output any real number, the range would also be (-∞, ∞).

To write the domain and range in interval notation, remember that square brackets [ ] represent inclusive endpoints, while parentheses ( ) represent exclusive endpoints. The symbol '∞' is always cloaked by parentheses.

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Answer:

7) -6, -3, 1, 50

9) -18, -11, -8, 11, 18

Answer:

320 liters

Step-by-step explanation:

Each tank = 40 liters

8 tanks = 40 × 8 = 320

Answer:

8 x 40 = 320

Step-by-step explanation:

since 1 fish tank has 40 liters of water, we are trying to find the total of all 8 which is why we multiply 8 x 40

The greatest integer that will divide both 4900 and 168 exactly is 28.

Least Common Multiple is a mathematical term. The smallest number that is a multiple of both of two numbers is called the least common multiple.

For example, the LCM of 6 and 8 is 24. Hence 24 is divisible by both 6 and 8.

First, Prime Factorizing 4900

4900 = 7 x 7 x 2 x 2 x 5 x 5

and, Prime Factorizing 168

168 = 2 x 2 x 2 x 3 x 7

So, the Common multiple of 4900 and 168 is 2 x 2 x 7 = 28.

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Final answer:

The greatest integer that will divide both 4900 and 168 exactly is 4.

Explanation:

The greatest integer that will divide both 4900 and 168 exactly is 4.

To determine this, we can use the concept of greatest common divisor (GCD). The GCD is the largest positive integer that divides two given numbers without leaving a remainder. In this case, the GCD of 4900 and 168 is 4.

One way to find the GCD is to factorize both numbers and determine the common factors. In this case, the prime factorization of 4900 is 2^2 * 5^2 * 7^2, and the prime factorization of 168 is 2^3 * 3 * 7.

The common factors are 2^2 and 7^1, which multiplied together give us 4. Therefore, 4 is the greatest integer that will divide both 4900 and 168 exactly.

Answer:

See explanation

Step-by-step explanation:

Triangle ABC ahs vertices at points A(-4,-4), B(-1,-2) and C(-1,-4).

1 way: First reflect this triangle across the y-axis to form the triangle A''B''C'' which vertices are at points A''(4,-4), B''(1,-2) and C''(1,-4).

Then translate this triangle 7 units up to form the triangle A'B'C' with vertices:

[tex]A'(4,-4+7)=A'(4,3)\\ \\B'(1,-2+7)=B'(1,5)\\ \\C'(1,-4+7)=C'(1,3)[/tex]

2 way: First translate this triangle 7 units up to form the triangle A''B''C'' which vertices are at points A''(-4,3), B''(-1,5) and C''(-1,3).

Then reflect this triangle across the y-axis to form the triangle A'B'C' with vertices:

[tex]A'(-(-4),3)=A'(4,3)\\ \\B'(-(-1),5)=B'(1,5)\\ \\C'(-(-1),3)=C'(1,3)[/tex]

Answer:

Step-by-step explanation:

hello :

the system is :

4x-4<8 ....(*)

9x+5>23...(**)

means :

4x < 12

9x > 18

x<3 and x>2  means : 2<x<3

A- The circumference of the tire is about 7.85 feet

B- The tire will rotate about 672 times to travel 1 mile

Step-by-step explanation:

∵ The diameter of a tire is 2.5 ft

∴ d = 2.5 ft

∵ C = π d, where C is the circumference of tire

∴ C = π(2.5) = 7.85398 ft

∴ C ≅ 7.85 feet

A- The circumference of the tire is about 7.85 feet

∵ The tire have to travel 1 mile

∵ 1 mile = 5280 feet

∴ S = 5280 feet

- To find the number of rotation of the tire divide S by C

∵ n =  [tex]\frac{S}{C}[/tex]

∴ n = [tex]\frac{5280}{7.85}[/tex] ≅ 672 revolution

B- The tire will rotate about 672 times to travel 1 mile

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Answer:

The circumference of the tire is about 7.85 feet

B- The tire will rotate about 672 times to travel 1 mile

Step-by-step explanation:

   The formula of the circumference of a circle is C = π d, where d is the diameter of the circle

   If a circle rotates for n turns and make a distance S, then n =

∵ The diameter of a tire is 2.5 ft

∴ d = 2.5 ft

Step-by-step explanation:

Answer:

3x^4-x^2-x^2-5x^4+3

-2x^4-2x^2+3 is the answer

To simplify the given expression, combine like terms by adding or subtracting the coefficients of the same powers of x.

The given expression is 3x4 - x2 - x2 - 5x4 + 3.

To simplify this expression, combine like terms by adding or subtracting the coefficients of the same powers of x.

Combining like terms, we have: -2x2 - 2x4 + 3.

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Answer:

Step-by-step explanation:

The dollar amount of the reduction was $200 - $140, or $60.

$60 is what percentage of $200?

 $60

---------- = 3/10 = 0.30

$200

The reduction was 30%; the jacket sold for 70% of its original price.

Answer:

Step-by-step explanation: set up a proportion:

140/200 = x/100 answer is 70%

to cross check - .70 multiplied by 200 =140

Answer:

(2+6)*(4-1) = 24

(2-1)*(6*4) = 24

(2-1)*6*4 = 24

(2-1)*(4*6) = 24

(2-1)*4*6 = 24

(6+2)*(4-1) = 24

6*(2-1)*4 = 24

6*(2-1)*4 = 24

6/(2-1)*4 = 24

6/(2-1)*4 = 24

The expression (1.3x + 2.4) - (6.1x - 3.2) simplifies to -4.8x + 5.6 after distributing the negative sign and combining like terms.

To solve the expression (1.3x + 2.4) - (6.1x - 3.2), we'll distribute the negative sign inside the second parentheses and then combine like terms:

(1.3x + 2.4) - (6.1x - 3.2)

Distribute the negative sign:

1.3x + 2.4 - 6.1x + 3.2

Combine like terms:

(1.3x - 6.1x) + (2.4 + 3.2)

Combine the x terms:

-4.8x + 5.6

So, (1.3x + 2.4) - (6.1x - 3.2) simplifies to -4.8x + 5.6.

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The probable question may be:

Simplify (1.3x + 2.4) - (6.1x - 3.2)

angle list: k,l,j:

sides are:  LJ, KJ, KL

To find the sides of triangle JLK in order from smallest to largest, we need to compare the measures of the angles. The side opposite the largest angle is the longest side, so we can determine the order of the sides based on the angle measures.

The triangle JLK has angles J, L, and K with measures 82, 57, and 41 degrees, respectively. To determine the sides of JLK in order from smallest to largest, we can use the fact that the side opposite the largest angle is the longest side. So, we need to identify the largest angle and its corresponding side.

Comparing the measures of the angles, we can see that M∠J is the largest angle. Therefore, the side opposite angle J, which is side JL, is the longest side. Next, we compare the measures of the remaining angles. M∠L is the next largest angle, so the side opposite angle L, which is side LK, is the second longest side. Finally, M∠K is the smallest angle, so the side opposite angle K, which is side JK, is the shortest side.

Therefore, the sides of triangle JLK in order from smallest to largest are JK, LK, JL.

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Answer:

i think its d

Step-by-step explanation:

The question is asking about the inverse of a function, a crucial mathematical concept. We generally calculate this by switching x and y, then solving the new equation for y. Without specific function options, we cannot provide a correct answer.

The question is about determining the inverse of a function, an important concept in Mathematics. Given that the question does not have any specifics about the function itself, it's impossible to determine the correct answer. In general, to find the inverse of a function, we follow a certain procedure: exchange the roles of y and x; once that is done, solve the function for y.

For instance, if you had a function like f(x) = 2x + 3, the inverse would be calculated by flipping x and y and solving the resulting equation for y: x = 2y + 3. Solving for y, you have y = (x - 3) / 2.

Unfortunately, without knowledge of the specific functions mentioned in the options A, B, C, D, we cannot select a correct answer.

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Answer:

a. 157 cm

Step-by-step explanation:

Multiply the diameter times 3.14

3.14 x 50=157 cm.

answer: 157 cm

To find the circumference of a circle given the diameter, multiply the diameter by π (approximately 3.14). Hence, the circumference of the dartboard is approximately 157 cm.

The subject of the question is Mathematics and it covers a topic generally taught in Middle School. When given the diameter of a circle, you can calculate the circumference using the formula C=πd where C is the circumference, π (pi) is about 3.14, and d is the diameter. In this case, the diameter of the dartboard is 50 cm. So, we simply multiply the diameter (50 cm) by π (3.14) to get the circumference. This means the circumference of the dartboard is approximately

157 cm (Option A)

.

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Step-by-step explanation:

Let Jim earned $ x

Therefore, Debbie earned = $(x + 1600)

According to the given information:

[tex]x + (x + 1600) = 7200 \\ \therefore \: 2x = 7200 - 1600 \\ \therefore \: 2x =5600 \\ \\ \therefore \: x = \frac{5600}{2} \\ \\ \therefore \: x =2800 \\ [/tex]

Thus, Jim`s earning = $2800

Debbie`s earning = 2800 + 1600 = $4400

Lets Jim earn $ x

Therefore, Debbie earned=$(x+1600)

calculate Debbie's earnings

According to the given information :

[tex]x+(x+1600)=7200\\$$\therefore 2 x=7200-1600\\$$\therefore 2 x=5600\\$$\therefore x=\frac{5600}{2}\\$$\therefore x=2800\\$[/tex]

thus, Jim's earnings =$2800

Debbie's earnings =2800+1600=$4400

An example of earning is to be paid five dollars for washing a car. An example of earning is getting a promotion for being very good at your job. An example of to earn is to take a vacation after completing a difficult and time-consuming project. To gain (success, reward, recognition) through applied effort or work.

Definitions of earnings. something that remunerates. “they saved a quarter of all their earnings” synonyms: pay, remuneration, salary, wage.

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Answer:

390 miles

Step-by-step explanation:

30 mpg means that he gets 30 miles for every gallon.

If he has 13 gallons means that you multiply 30 by 13.

30 * 13 = 390 miles

Final answer:

Mark can travel 390 miles on 13 gallons of gas, as his car gets 30 miles per gallon and distance is calculated by multiplying fuel efficiency by the number of gallons.

Explanation:

To calculate the distance Mark can travel on 13 gallons of gas, we use the formula: Distance = Fuel Efficiency  imes Number of Gallons.

Mark's car gets 30 miles per gallon. Thus, the distance he can cover on 13 gallons of gas is calculated by multiplying 30 miles/gallon by 13 gallons, which equals 390 miles.

This is a straightforward multiplication problem involving units of fuel efficiency (miles per gallon) and quantity of fuel (gallons).

The solution directly gives us the total number of miles Mark can travel on 13 gallons of gas.

Answer:

[tex]\large \boxed{\text{c. 405.3 ft}}[/tex]

Step-by-step explanation:

[tex]\begin{array}{rcr}\angle A + \angle B + \angle C & = & 180^{\circ}\\82^{\circ} + 78^{\circ} +\angle C & = & 180^{\circ}\\160^{\circ} + \angle C & = & 180^{\circ}\\\angle C & = & 20^{\circ}\\\end{array}[/tex]

[tex]\begin{array}{rcl}\dfrac{\sin A}{a} & = &\dfrac{\sin C}{c}\\\\\dfrac{\sin82^{\circ}}{a} & = &\dfrac{\sin20^{\circ}}{140}\\\\\dfrac{0.9903}{a} & = &\dfrac{0.3420}{140}\\\\a & = & \dfrac{0.9903 \times140}{0.3420}\\\\& = & \mathbf{405.3 ft}\\\end{array}\\\text{The distance from Ship B to the signal fire is $\large \boxed{\textbf{405.3 ft}}$}[/tex]

Answer:

D) -73

Step-by-step explanation:

(-21)+(-37)+(-15)

-21-37-15

-58-15

-73

Answer:

False

Step-by-step explanation:

Factors of 10 and 14:

10:  1 , 2, 5, 10

14:  1, 2, 7, 14

As you can see, 5 is not a common factor of 10 and 14

The greatest common factor is two

So the answer is false, 5 is not the greatest common factor of 10 and 14

Hope this helps :)

The greatest common factor of 10 and 14 is 2, not 5. The statement is false as 5 is not a factor of 14.

The greatest common factor (GCF) of two numbers is the largest number that divides both of them without leaving a remainder. To find the GCF of 10 and 14, we list the factors of each number:

The common factors of 10 and 14 are 1 and 2. Therefore, the GCF of 10 and 14 is 2, not 5. The statement that the greatest common factor of 10 and 14 is 5 is false.

Hey there!

When we say (f + g)(2), we are adding both functions together and plugging in 2 for x.

Since f(x) is equal to 2x + 210 and g(x) is equal to 2x + 125, (f + g)(x) is equal to (2x + 210) + (2x + 125).

That can be simplified to 4x + 335.

So, (f + g)(x) = 4x + 335.

Let's plug 2 in for x and solve.

(f + g)(2) = 4(2) + 335

Multiply.

(f + g)(2) = 8 + 335

Add.

(f + g)(2) = 343

The x value is consistent for the values of both equations, in both x is defined as the number of hours spent exercising.

So, (f + g)(2), which is 343, is the amount of calories burned and the calorie deficit on a diet when 2 hours are spent exercising.

Hope this helps!

Answer:

Its D

Step-by-step explanation:

Answer:

Cost of each cherry pie = $6

Cost of each blackberry pie = $16

Step-by-step explanation:

Let x be the cherry pies and y be the blackberry pie.

Solution:

From the above statement Jasmine sold 12 cherry pies and 4 blackberry pies for a total of $136.

So, we write the first equation as.

[tex]12x+4y = 136 ------(1)[/tex]

And Stephanie sold 8 cherry pies and 1 blackberry pie for a total of $64.

So, we write the second equation as.

[tex]8x+y = 64 --------(2)[/tex]

First we solve equation 2 for y.

[tex]y = 64-8x[/tex] ------------------------(3)

Substitute [tex]y = 64-8x[/tex]  in equation 1.

[tex]12x+4(64-8x) = 136[/tex]

[tex]12x+256-32x=136[/tex]

[tex]12x-32x=136-256[/tex]

[tex]-20x=-120[/tex]

[tex]x=\frac{120}{20}[/tex]

x = 6

Substitute x = 6  in equation 3.

[tex]y = 64-8(6)[/tex]

[tex]y=64-48[/tex]

y = 16

Therefore, cost of each cherry pie = $6 and cost of each blackberry pie = $16

By solving the system of equations, it is determined that the cost of one cherry pie is $6 and the cost of one blackberry pie is $16. These findings are crucial for pricing strategies in the school fundraiser.

To solve the system of equations for the cost of cherry and blackberry pies sold by Jasmine and Stephanie for a school fundraiser, we can set up two equations based on the given information:

Let's denote the cost of one cherry pie as c and the cost of one blackberry pie as b. Therefore, we can form the following equations based on the problem statement:  

Using the method of substitution or elimination, we solve for c and b.

For simplicity, let's use elimination. To eliminate b, we can multiply the second equation by -4 and add to the first:

-32c - 4b = -256
12c + 4b = 136

Combining these, we get -20c = -120, thus c = $6. Substituting c = 6 into the second equation, 8*6 + b = 64, gives us b = $16.

In real-life terms, this means one cherry pie costs $6, and one blackberry pie costs $16, which would be important for pricing and accounting in the fundraiser.

z(5 , 3) = 10

Step-by-step explanation:

x = 5

y = 3

z(x,y) = x/ y(x-y)

z (5, 3) = 5/ 3(5-3)

            = 4x5/ 2

            = 20/2

z (5- 3) = 10

Answer: X = 28

Step-by-step explanation: The diagram shows a triangle which is actually in fact, two triangles placed into each other. The first one is triangle APR (the larger one) while the second one is triangle CDR (the smaller one).

Also the diagram shows line AP as being parallel to line CD. That makes triangle APR similar to triangle CDR.

We can now determine the ratios of the similar sides

If triangle APR = triangle CDR, then

Line PD/DR = AC/CR or

PD/PR = AC/AR or

CD/RD = AP/RP

Therefore to calculate X, we use the ratio,

PD/DR = AC/CR

15/42 = 10/x

{we reduce the left hand side to it's simplest form}

5/14 = 10/x

When we cross multiply we now have

5x = 14 × 10

5x = 140

Divide both sides of the equation by 5

x = 28

Answer:

2.4

Step-by-step explanation:

Final answer:

The equation that does not support the fact that polynomials are closed under multiplication is 1x⋅x=1. To multiply and simplify [tex]x^2⋅x⋅x^5[/tex]onents are added. To multiply and simplify[tex](3x+7)8x^2,[/tex]ive property is used.

Explanation:

The equation that does not support the fact that polynomials are closed under multiplication is 1x⋅x=1. When multiplying two polynomials, the degree of the resulting polynomial is the sum of the degrees of the two original polynomials. In this case, the degree of the resulting polynomial would be 2, but the equation implies a polynomial of degree 0, which is not possible.

To multiply and simplify[tex]x^2⋅x⋅x^5[/tex]he exponents when multiplying the same base. So,[tex]x^2⋅x⋅x^5 = x^(2+1+5) = x^8.[/tex]

To multiply and simplify [tex](3x+7)8x^2,[/tex] distributive property. We multiply each term in the first polynomial by each term in the second polynomial. So, [tex](3x+7)8x^2 = 24x^3 + 56x^2.[/tex]

Final answer:

The total surface area of a square prism with a base edge of 6 km and height of 5 km is 192 km².

Explanation:

The question is about finding the surface area of a square prism (also known as a rectangular prism where the base is a square). A square prism has six faces: two square bases and four rectangular sides. To find the total surface area, we calculate the area of each face and sum them up.

The formula for the area of a square is side × side. Since the base of the prism is a square with each side measuring 6 km, the area of one square base is:

Since there are two square bases:

The formula for the area of a rectangle is length × width. The four rectangular sides each have one dimension that is the height of the prism (5 km), and the other dimension is the length of a side of the base (6 km), so:

There are four such sides:

Adding the areas of the bases and the sides:

The measure of the third angle is 119 degrees

Step-by-step explanation:

The given is:

We need to find the measure of the third angle in the triangle

The sum of the measures of the interior angles of a triangle is 180°

∵ The measure of an angle = 26°

∵ The measure of another angle = 35°

∵ The some of measures of the 3 angles = 180°

∴ 26° + 35° + x° = 180°, where x is the measure of the 3rd angle

- Add the like terms in the left hand side

∴ 61° + x° = 180°

- Subtract 61 from both sides

∴ x = 119°

The measure of the third angle is 119 degrees

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