Tell whether each system of equations has no solution, one solution, or infinitely many solutions. Show how you arrived at your conclusion for each.
a. y = 5x + 11 and y = 5x
b. y = 6x + 3 and y = 3x
c. x + 4y = 8 and y = -1/4x + 2

The  slope of the table below? 3/8 15/12 9/10 0/7 is 23.8

Slope is defined as the rate of change of y with respect to x.  Invariably, it it the rise in y over the run  in x. put differently, slope is increase over increase in x

The slope of a line is defined

S= (increase in y)/(Increase in x) = Δy/Δx

Slope = (0/7 - 18/12) ÷ (9/10 -3/8)

Slope = 15/12 ÷ 42/80

Simplify the fractions to have

Slope = 15/12 * 80/42

The slope = 1200/504

Slope of the table is given as 23.4

Conclusively, the table gives us a slope approximately 23

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The complete statement is f(2) = 8+5√7

Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given here f(x)=2x²+5√7

Thus f(1) = 2×4+5√7

              = 8+5√7

Hence, The complete statement is f(2) = 8+5√7

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The value of s that makes the inequality true is 6

An inequality can simply be defined as a mathematical relation that makes a non-equal comparison between two variables, numbers, ratios or other mathematical expressions.

It is used in comparing two numbers on the number line on the basis of their size.

The inequality signs are;

From the expression given, we have;

7s < 42

Make 's' the subject by dividing both sides by 7, we have;

s > 42/7

s> 6

Hence, the value is greater than 6

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Answer:

y = -3/4x + 52

y + 6 = -3/4(x-8)

Step-by-step explanation:

y = mx + c

as long as the number is -3/4x , it represents slope -3/

Answer:

B. y = -3/4x + 52, C. y + 6 = -3/4(x - 8), and F. 3x + 4y = 9

Step-by-step explanation:

A. -3x + 4y = -34

y = 3/4x - 17/2

Slope = 3/4

INCORRECT

B. y = -3/4x + 52

Slope = -3/4

CORRECT

C. y + 6 = -3/4(x - 8)

y = -3/4x

Slope = -3/4

CORRECT

D. 4x + 3y = -22

y = -4/3x - 22/3

Slope = -4/3

INCORRECT

E. 4x - 3y = 48

y = 4/3x - 16

Slope = 4/3

INCORRECT

F. 3x + 4y = 9

y = -3/4x + 9/4

Slope = -3/4

CORRECT

G. y - 6 = 3/4(x - 8)

y = 3/4x

Slope = 3/4

INCORRECT

Answer:

D+Q = 31

10D + 25Q = 595

10D + 10Q = 310

subtract to get

15Q = 285 Q = 285/15 = 19 quarters D = 31-19 = 12 dimes

1) The equation of a line of best fit is; y = -1.15x + 102.8

2) The predicted monthly cost for an average temperature of 25°F is $74.05

The equation of a line of best fit is represented by the equation;

y = mx + c

where;

m is the slope

c is the y-intercept

1. To calculate the slope here, we will use the formula;

Slope = (y₂ - y₁)/(x₂ - x₁)

Using two coordinate points on the scatter plot, (72, 20) and (20, 80), we have the slope as;

Slope (m) = (80 - 20)/(20 - 72)

Slope = 60/-52

Slope = -1.15.

Plug in -1.15 for m and (a, b) = (72, 20) into the formula; y = mx + c to get;

20 = -1.15(72) + c

c = 20 + 82.8

c = 102.8

The equation  will now be;

y = -1.15x + 102.8

2. Monthly heating cost, y, for a month with an average temperature of 25°F (x) will be calculated by plugging in 25 for x in the equation of line of best fit gotten earlier to get;

y = -1.15(25) + 102.8

y = 102.8 - 28.75

y = $74.05

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Answer:

The fourth graph since it passes the vertical line test.

Each input has one output.

Hope this helps :)

The design of a simulation that would allow Ian to determine how likely it would

be to guess all answers correctly on this quiz can be Illustrated through a coin.

Ian can design a simulation to determine the likelihood of guessing all answers correctly on the quiz by using a fair coin. He can flip the coin four times, with each flip representing a guess on the quiz. If the coin lands heads up, he marks it as a true answer, and if it lands tails up, he marks it as a false answer.

He can repeat this process a large number of times (e.g. 1000) and count the number of times that the sequence T, T, F, T is generated. The proportion of times that this sequence is generated out of the total number of simulations will be an estimate of the probability of guessing all answers correctly on the quiz by chance.

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Answer:

See the image for marked congruences.

1. JM ≅ LM                           |      Given

2. △JML is isosceles          |      definition of isosceles

3. ∠MJL ≅ ∠MLJ                  |       isosceles triangle theorem

4. m∠MJL = m∠MLJ             |      definition of ≅

5. JK ≅ LK                            |      Given

6. △JKL is isosceles           |      definition of isosceles

7. m∠KJL = m∠KLJ              |       isosceles triangle theorem

8. m∠MJL + m∠KJM = m∠KJL                         |  adjacent angle theorem

9. m∠MLJ + m∠KMJ = m∠KLJ                         |  adjacent angle theorem

10. m∠MJL + m∠KJM = m∠MLJ + m∠KLM      |   transitive property of =

11. m∠MJL + m∠KJM = m∠MJL + m∠KLM      |   substitution

12. m∠KJM = m∠KMJ          |        subtraction

13. ∠KJM ≅ ∠KLM                |        definition of ≅

14. △KJM ≅ △KLM             |        SAS theorem

15. ∠JKM ≅ ∠LKM                |        CPCTC

16. KM bisects ∠JKL            |        definition of bisector

Answer:

3

Step-by-step explanation:

768 can be broken down to:

2×2×2×2×2×2×2×2×3

The part made up of twos is already a perfect square. The 3 needs a partner for it to be a perfect square also.

768 × 3 is 2304.

Sqrt2304 is 48.

Multiply 768 by 3 to make it a perfect square.

Refer To The Given Image

Answer:

x = 4[tex]\sqrt{3}[/tex]

Step-by-step explanation:

using the cosine ratio in the right triangle and the exact value

cos30° = [tex]\frac{\sqrt{3} }{2}[/tex] , then

cos30° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{8}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex]  ( cross- multiply )

2x = 8[tex]\sqrt{3}[/tex] ( divide both sides by 2 )

x = 4[tex]\sqrt{3}[/tex] ( exact value )

Step-by-step explanation:

SOHCAHTOA

CAH-

Cosine●= adj/hyp

cos30= y/8

0.8660=y/8

Cross multiply

0.8660×8=y

y=8×0.8660

y=6.928

the equation in the form of slope interpretation is y = 1/3x -4.

An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation has the conventional form y = mx + c.

Given data in a table such as it makes a linear equation slope-intercept form of the given equation is y = mx +c

Where m is the slope

c is constant

The slope for the given data

m = (y₂ - y₁) / (x₂ - x₁)

m = (-5 + 6 )/ (-3 + 6)

m = 1/3

Hence, the equation would be

y = 1/3x + c

for constant we would satisfy the equation with other coordinates of the line.

Substituting ( 0, -4) in the above equation

-4 = 0 + c

c = -4

thus, the equation of the line is  y = 1/3x  -4

therefore, the linear equation of the given data is y = 1/3x -4.

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Answer:

Step-by-step explanation:

70%=0.7

90 X 0.7 = 63

ANSWER IS 63

The domain of the function f(x, y, z) = ln(144 − 9x² − 16y² − z²) is x ∈ (-4, 4), y ∈ (-3, 3) and z ∈ (-12, 12) which forms an ellipsoid.

Domain of a function is the set of all values possible for the input parameters for real output parameter or output parameter in given range.

Given the function as f(x, y, z) = ln(144 − 9x² − 16y² − z²)

For f(x, y, z) to be real, the function 144 − 9x² − 16y² − z² should be greater than 0. So,

144 − 9x² − 16y² − z² > 0

9x² + 16y² + z² < 144

x²/ 4² + y²/ 3² + z²/ 12² < 1

Therefore, the domain is an ellipsoid.

Therefore x ∈ (-4, 4)

y ∈ (-3, 3)

z ∈ (-12, 12)

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The simplified expression is [tex]c^2 d^2 e^6 / b^8[/tex]

The given expression is [tex](a^0 b^-4 cde^3)^2[/tex]

We know that any number raised to the power of 0 is 1.

Therefore,[tex]a^0 = 1[/tex].

Also, any number raised to the power of -1 is its reciprocal.

Therefore, [tex]b^-4 = 1/b^4[/tex]

Simplifying the above expression we get

[tex](1*1/b^4 * cde^3)^2 = (cde^3/b^4)^2[/tex]

Now, we apply the rule that [tex](a^m * a^n) = a^(m+n)[/tex]

So, [tex](cde^3/b^4)^2 = c^2 d^2 e^6 / b^8)[/tex]

Hence the simplified expression is [tex]c^2 d^2 e^6 / b^8[/tex]

Please note, when an exponent is raised to another exponent, we can multiply the exponents, so [tex](a^m)^n = a^(m*n)[/tex]

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Answer:

The length of the diagonal is 12.53

Step-by-step explanation:

Since we have a rectangle, the diagonal is the hypotenuse of a right triangle. So we can use Pythagorean Theorem.

a^2 + b^2 = c^2

We know the two legs are 6 and 11, so we can find the hypotenuse (which is the diagonal) see image.

See image.

Answer:

Step-by-step explanation:

9.0 × 10-10 I think.....

Answer:

20 ounces of the 63% solution and 80 ounces of the 33% solution.

Step-by-step explanation:

Let x = number of ounces of 63% solution.

Let y = number of ounces of 33% solution.

The total solution to be made is 100 oz.

x + y = 100

x ounces of 63% solution is 0.63x ounces of acid.

y ounces of 33% solution is 0.33y ounces of acid.

100 ounces of 39% solution is 39 ounces of acid

0.63x + 0.33y = 39

The system of equations is

x + y = 100

0.63x + 0.33y = 39

Multiply the both sides of the first equation by -0.33. Then add it to the second equation.

         -0.33x - 0.33y = -33

    +    0.63x + 0.33y = 39

   ---------------------------------

             0.3x             = 6

x = 6/0.3

x = 20

x + y = 100

20 + y = 100

y = 80

Answer:

20 ounces of the 63% solution and 80 ounces of the 33% solution.

The first equation will be multiplied by 3 and that of the second by 4.

An elimination method is a process of solving a system of linear equation, in this we make coefficients of the one variable equal and subtract the equations.

Given that are two equations to be solved by using elimination method,

-4x+4y = 32.....(i)

3x-y = 12......(ii)

To eliminate x, we will multiply eq(i) by 3 and eq(ii) by 4

-12x+12y = 96.....(iii)

12x-4y = 48....(iv)

Solving the equations, we get,

8y = 144

y = 18

Put y = 18 in eq (ii)

3x-18 = 12

3x = 30

x = 10

Hence, the first equation will be multiplied by 3 and that of the second by 4.

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Answer:

All four are equivalent fractions with the LCD of 12

Step-by-step explanation:

Answer: To solve this problem, we can use the information provided to set up and solve an equation. Let x be the number of countries that participated in the 1896 Olympic games.

According to the problem, we know that the number of countries in the 2004 Olympic games was more than 14 times the number of countries in the 1896 games. So we can write the following equation:

x * 14 < 202

To solve for x, we can divide both sides of the inequality by 14:

x < 202/14

x < 14.43

x is the number of countries, it must be an integer.

so x = 14

Therefore, 14 countries participated in the 1896 Olympic games.

Step-by-step explanation:

Answer:

Trapezoid

Step-by-step explanation:

The math

The 5 life examples are:

In all these life examples that are listed above, the number 100 is divided by 20 giving 5 as the result. which is said to be:

100/20

= 5.

Therefore, reason behind this is that the number 20, in these life examples, is a representative of a whole value and the number 5 represents the number of parts it is being divided into, so when you multiply 20 by 5, you get 100, which represents the total of these five parts. So, 100 is related to 20 in this context as the multiple of 20 and 5.

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The student that has the highest reading rate is Student C who has the highest rate of change of the number of words read of 158 words per minute.

The rate of change of a function is the rate at which the output value changes per unit change in the input value.

The possible data and table obtained from a similar question on the website are presented as follows;

Student A

Number of minutes;         [tex]{}[/tex]1              2             3              4

Number of words read; 150        [tex]{}[/tex]300          450          600

Student B

y = 158·x

Where;

x = The time duration in minutes

y = The number of words read by the student

Student C

The points on the graph representing the reading rate of student C are; (2, 280), (3, 420), (5, 700)

The first difference of the number of words read by Student 1 is constant, indicating that the relationship is a linear relationship, with the reading rate obtained by the rate of change of the number of words read as follows;

Reading rate for Student A = (300 - 150)/(2 - 1) = 150

The reading rate for Student A is 150 words per minute

The equation for the reading rate of Student B; y = 158·x, indicates that Student B reads 158 words per minute

The of the straight ling graph for the reading rate of Student C is found as follows;

Slope = (420 - 280)/(3 - 2) = 140

The slope indicates that the number of words read by Student C increases by 140 words every minute, therefore, the reading rate for Student C is 140 words per minute

The student that reads fastest is therefore, Student C who has a reading reading rate of 158 words per minute

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The house is located 6.87 miles to the east of the cell tower.

“In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“.

Given:

Let the center of the town represent the origin (0,0).

Also 1 unit = 1 mile.

Since the cell tower is located 3 miles east and 6 miles north of the center of a small town, it is represented by A(3, 6)

The cell tower has a coverage of radius 4 miles. This can be represented by a circle with equation:

(x - a)² + (y - b)² = r². where (a,b) is the center of the circle and r is the radius.

Then, (x - 3)² + (y - 6)² = 4²

(x - 3)² + (y - 6)² = 16

b) The house is 7 miles north. It can be represented by y = 5 line.

To find the distance east of the house we have to substitute y = 5 and solve for x,

(x - 3)² + (y - 6)² = 16

(x - 3)² + (5 - 6)² = 16

(x - 3)² + 1 = 16

(x - 3)² = 15

(x - 3) = ±3.87

x= 3 ±3.87

x= 6.87 or 0.87.

Hence, the house is located 6.87 miles to the east.

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The inequality g(30) ≥ 20 us that: D. Mona found no more than 20 seashells in the first 30 minutes.

In Mathematics, an inequality simply refers to a mathematical relation that can be used to compare two (2) or more numerical values, numbers, and variables in an algebraic equation, especially based on any of the following inequality symbols:

Assuming the variable g represents the total number of seashells and the variable x represents the total number of time (minutes), an inequality which would model the situation is given by;

g(x) ≥ x

when x = 30, we have;

g(30) ≥ 20

Therefore, Mona found no more than (less than or equal to) 20 seashells in the first 30 minutes.

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Complete Question:

Mona loves the ocean, so she was thrilled to visit the beach and collect some seashells. The function g(x) gives the number of seashells Mona found after x minutes of searching.

What does g(30) ≥ 20 tell you?

It took at least 20 minutes for Mona to find 30 seashells.

Mona found at least 20 seashells in the first 30 minutes.

It took at least 30 minutes for Mona to find 20 seashells.

Mona found no more than 20 seashells in the first 30 minutes.

We will solve the expression:

(3 + 5)*5 - 20*(2 + 5)

Step by step, and we will get the solution -100.

Here we want to solve the following expression:

(3 + 5)*5 - 20*(2 + 5)

The first thing that you need to solve when working in these type of problems, are the operations inside the parenthesis, then we will get:

(3 + 5)*5 - 20*(2 + 5) = (8)*5 - 20*(7)

Now we need to solve the two products, we will get:

(8)*5 - 20*(7) = 40 - 140 = -100

Thus, the solution of that expression is -100.

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Answer:

Triangles DEF and JKL are similar to triangle ABC because they have corresponding angles with the same measure.

Step-by-step explanation:

•Triangles DEF and JKL are similar to triangle ABC because they have corresponding angles with the same measure.

•The Triangle GHI is not similar to triangle ABC because the measure of angle G does not match the measure of angle A.

•The Triangle MNO is not similar to triangle ABC because the measure of angle N does not match the measure of angle B.

• The Triangle POR is not similar to triangle ABC because the measure of angle R does not match the measure of angle A or B.

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The area of the new triangle is  600ft²

To increase the size of a triangle by a scale factor of 10/3, multiply each dimension of the triangle by 10/3.

The new dimensions of the triangle will be:

10/3 × 9ft = 30ft

10/3 × 12ft = 40ft

The area of a triangle is given by the formula A = 1/2  × b  ×h,

where b is the length of the base and h is the height of the triangle.

Thus, the area of the new triangle will be:

A = 1/2  × 30 × 40 = 600ft²

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