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Answer:                                  -7=0 --> Impossible

Step-by-step explanation:  

2x-7+x-11= 3x-11

2x+x-7-11=3x-11

3x-18=3x-11

3x-18+11=3x

3x-7-3x=0

-7=0

Impossible

We combined like terms on both sides to solve 2x - 7 + x - 11 = 3x - 11. However, this led to the false equation -18 = -11, indicating a potential error in the given problem.

The equation to solve is 2x - 7 + x - 11 = 3x - 11. The goal is to find the value of x.

The first step is to combine like terms on the left side of the equation. We combine 2x and x to get 3x and -7 and -11 to get -18. So, the problem becomes 3x - 18 = 3x - 11.

From here, we subtract 3x from both sides to isolate x on one side. This gives us -18 = -11. This equation is, however, incorrect.

This discrepancy could arise from a mistake in the original problem, notably, the content loaded 2x - 7 + x - 11 = 3x - 11.

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Answer:

Step-by-step explanation:

Seems to be a

The only correct statement that identifies the right angle is:

Option A: ∠DEF is a right angle

To identify the true statements of the diagram, we will need to look at each of the options to get:

Option A: ∠DEF is a right angle:

We see that the line FA is a straight line and we also see that the line DE is perpendicular to FA and as such we can say that:

∠DEF = ∠DEA = 90°

Option B: m∠DEA = m∠FEC:

This is not true because we can clearly see that m∠DEA is a right angle while  m∠FEC is an acute angle.

Option C: m∠BEA = m∠BEC:

We can't really say if they are equal because we are not told it ED is a bisector of ∠AEC

Option D: EB bisects  ∠AEF

This is wrong as it is not a bisector

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the answer is going to be C

circumference = pi times the diameter , so i used 3.14 as pi and used the values in the answer choices to determine the diameter

12 is the closest because 12 times 3.14 is 37.68 which is very close to 37.5

pls mark brainliest

Answer:

5

Step-by-step explanation:

Final answer:

Using the GCF of 10 and 15, which is 5, we cross-cancel the fractions 5/15 and 5/10 to reduce them to 1/3 and 1/2 respectively. Multiplying these reduced fractions, we obtain the final answer of 1/6.

Explanation:

To solve the fraction 5/15 × 5/10, we first identify the Greatest Common Factor (GCF) of the numerators and denominators. The GCF of 10 and 15 is 5. Using this GCF, we cross-cancel to reduce the fractions before multiplying.

Firstly, we divide both 10 and 15 by the GCF, which gives us:

10 ÷ 5 = 2

15 ÷ 5 = 3

Applying cross-cancellation to the original expression, we get:

(5 ÷ 5) / (15 ÷ 5) × (5 ÷ 5) / (10 ÷ 5)

1/3 × 1/2

Multiplying these reduced fractions gives us:

1/3 × 1/2 = 1/6

Thus, the result of multiplying 5/15 by 5/10, after cross-cancelling the common factors, is 1/6.

Answer:

Step-by-step explanation:

Put x = 5 and y = 7 to the equation ax - 2y = 1 and solve for a:

(a)(5) - (2)(7) = 1

5a - 14 = 1       add 14 to both sides

5a - 14 + 14 = 1 + 14

5a = 15        divide both sides by 5

5a : 5 = 15 : 5

a = 3

Answer:

The only possible numbers are 6 and 0.

Step-by-step explanation:

We are given the following information in the question:

Let x and y be the two numbers whose difference is 6 and whose sum is also 6.

We can write it in the form of the equation:

[tex]x - y = 6\\x+y =6\\\\\text{Adding the two equations}\\(x-y) + (x+y) = 12\\2x =12\\x = 6\\\\\text{Putting this value of x in one of the equations}\\6 + y = 6\\y = 0[/tex]

Hence, the only possible numbers are 6 and 0.

It is possible as the numbers are 0 and 6.

Let the numbers be a and b.

Based on the question, the equation to solve the question will be:

a - b = 6 ........ i

a + b = 6 ........ ii

From equation i, a = 6 + b

Put the above into equation ii

a + b = 6

(6 + b) + b = 6

6 + 2b = 6

2b = 6 - 6.

2b = 0

b = 0/2

b = 0

Therefore, the value of a will be:

a = 6-0 = 6.

The numbers are 0 and 6.

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12. Answer:  $9.50

Step-by-step explanation:

4 tickets plus 1 popcorn equals 44.25

    4t         +       1(6.25)       =       44.25

4t + 6.25 = 44.25

   -  6.25   -6.25     Subtraction Property of Equality

4t            = 38.00

÷4             ÷4           Division Property of Equality

t             = 9.50  

13. Answer:

Step-by-step explanation:

4.9x - 1.9 = 27.5

       +1.9    +1.9        Addition Property of Equality

4.9x         = 29.4

÷4.9           ÷4.9        Division Property of Equality

     x          =   6

GgAnswer:

Step-by-step explanation:

gg

To determine if a set of measurements could be the side lengths of a right triangle, we need to check if the Pythagorean theorem holds true. Option D, with side lengths 54 in, 72 in, and 90 in, satisfies the theorem and represents a right triangle.

In a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. This is known as the Pythagorean theorem: a^2 + b^2 = c^2.

So, to determine if a set of measurements could be the side lengths of a right triangle, we need to check if the Pythagorean theorem holds true. Let's check each option:

Therefore, the correct answer is option D: 54 in, 72 in, 90 in.

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Answer:

Option B. [tex]R(2,4)[/tex]

Step-by-step explanation:

we know that

If a ordered pair lie on the circle. then the ordered pair must satisfy the equation of the circle

step 1

Find the equation of the circle

we know that

The equation of the circle in center radius form is equal to

[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]

where

r is the radius of the circle

(h,k) is the center of the circle

substitute the values

[tex](x-6)^{2}+(y-1)^{2}=5^{2}[/tex]

[tex](x-6)^{2}+(y-1)^{2}=25[/tex]

step 2

Verify each case

case A) [tex]Q(1, 11)[/tex]

substitute the value of [tex]x=1, y=11[/tex] in the equation of the circle and then compare the results

[tex](1-6)^{2}+(11-1)^{2}=25[/tex]

[tex]25+100=25[/tex] ------> is not true

therefore

the ordered pair Q not lie on the circle

case B) [tex]R(2,4)[/tex]

substitute the value of [tex]x=2, y=4[/tex] in the equation of the circle and then compare the results

[tex](2-6)^{2}+(4-1)^{2}=25[/tex]

[tex]16+9=25[/tex] ------> is true

therefore

the ordered pair R lie on the circle

case C) [tex]S(4,-4)[/tex]

substitute the value of [tex]x=4, y=-4[/tex] in the equation of the circle and then compare the results

[tex](4-6)^{2}+(-4-1)^{2}=25[/tex]

[tex]4+25=25[/tex] ------> is not true

therefore

the ordered pair S not lie on the circle

case D) [tex]T(9,-2)[/tex]

substitute the value of [tex]x=4, y=-4[/tex] in the equation of the circle and then compare the results

[tex](9-6)^{2}+(-2-1)^{2}=25[/tex]

[tex]9+9=25[/tex] ------> is not true

therefore

the ordered pair T not lie on the circle

y=mx+b where m is the slope and b is the y intercept.

Final answer:

Linear equations are written as y = mx + b or y = a + bx, where 'm' or 'b' in the first form and 'b' in the second represents the slope and 'b' in the first form and 'a' in the second represents the y-intercept. The equation can model relationships where 'y' changes at a constant rate with 'x', forming a straight line graph.

Explanation:

Understanding Linear Equations

Linear equations represent relationships between variables that result in a straight line when graphed on a Cartesian plane. These equations are typically written in the form y = mx + b or in a statistical context as y = a + bx. Here, 'y' is the dependent variable and 'x' is the independent variable. The constant 'm' or 'b' in the first equation and 'b' in the second represents the slope of the line, which indicates the rate of change of 'y' with respect to 'x'. The constant 'b' in the first equation and 'a' in the second equation represents the y-intercept, which is the point where the line crosses the y-axis, at which point 'x' equals zero.

Graphically, the slope denotes the steepness and the direction of the line, while the y-intercept gives us the starting point of the line on the graph. For example, in the equation y = 6x + 8, the slope is 6 and the y-intercept is 8. This means that for every one unit increase in 'x', 'y' will increase by 6 units, and when 'x' is 0, the value of 'y' is 8.

Different scenarios can be modeled using linear equations, such as calculating the total number of hours required based on the square footage (y = x + 4), determining the total payment based on the number of students (y = 100(x) + 2,000), or finding the total cost of attendance over a number of years (y = 3,000(x) + 500).

The linear equation is also applicable in understanding real-world issues, such as tracking the number of flu cases over the years, where the number of cases depends on the year.

The constant variation is k=-13/2

Answer:

k = - 6.5

Step-by-step explanation:

Given that y varies directly with x then the equation relating them is

y = kx ← k is the constant of variation

To find k use the condition x = 4 when y = - 26, hence

k = [tex]\frac{y}{x}[/tex] = [tex]\frac{-26}{4}[/tex] = - [tex]\frac{13}{2}[/tex] = - 6.5

Hey there!

Answer:

A. -4

Explanation:

All you do is evaluate:

[tex]-(-(-4))\\= -4[/tex]

= A. -4

Therefore, that is how you got your answer.

Hope this Helps!

Answer:

A. -4

Explanation:

All you do is evaluate:

= A. -4

Therefore, that is how you got your answer.

Hope this Helps

To fill a rectangular prism with dimensions 9in. by 4in. by 1.5in. using half-inch cubes, you need to divide the volume of the prism (54in.^3) by the volume of a cube (0.125in.^3), resulting in 432 cubes needed.

To determine how many half-inch cubes are needed to fill the rectangular prism, we must first calculate the volume of the prism and then the volume of a single cube. Next, we divide the volume of the prism by the volume of a cube to find the number of cubes needed.

Calculating the Volume of the Rectangular Prism

The volume of a rectangular prism is found by multiplying its length by its width by its height. Volume of the prism = length × width × height = 9in. × 4in. × 1.5in. = 54in.3.

Calculating the Volume of a Cube

The volume of a cube is found by raising the length of an edge to the third power. Volume of a cube = edge length3 = (0.5in.)3 = 0.125in.3.

Number of Cubes Needed

To find the number of cubes needed to fill the prism, divide the volume of the prism by the volume of a cube. Number of cubes needed = Volume of the prism / Volume of a cube = 54in.3 / 0.125in.3 = 432.

Therefore, 432 half-inch cubes are needed to fill the rectangular prism.

Answer:f(x)=x

Step-by-step explanation:

Answer:

[tex]y = \frac{2}{3}x + \frac{23}{3}[/tex]

Step-by-step explanation:

To write the equation of a line with a point and a slope, use the point-slope form of a linear equation. Substitute m = 2/3 and the point (-4,5) into the equation.

[tex]y - y_1 = m(x-x_1)\\y - 5 = \frac{2}{3}(x --4)\\y - 5 = \frac{2}{3}(x+4)[/tex]

Convert to slope intercept form by using the distributive property.

[tex]y - 5 = \frac{2}{3}(x+4)\\y - 5 = \frac{2}{3}x +\frac{8}{3}\\y = \frac{2}{3}x + \frac{8}{3} + 5\\y = \frac{2}{3}x + \frac{23}{3}[/tex]

Answer:

The initial temperature is 80 °F.

The final termperature is 20°F.

During this period, fell 60 °F which represents a percentage of

[tex]\frac{60}{80} \times 100= 75\%[/tex]

We repeat the process for the rest.

From -13 °F to 9 °F, the temperature arose 22 °F, which is equivalent to

[tex]\frac{22}{13} \times 100= 169.23 \%[/tex]

From -5 °F to 8 °F, the temperature fell 13 °F, which is equivalent to

[tex]\frac{13}{5} \times 100= 260 \%[/tex]

Answer:

Step-by-step explanation:

y-intercept is for x = 0. Substitute x = 0 to the equation of a function

[tex]y=3\left(\dfrac{8}{9}\right)^x[/tex]

[tex]y=3\left(\dfrac{8}{9}\right)^0=3(1)=3[/tex]

Answer:

7

Step-by-step explanation:

Since these two points are straight left and right from each other it's really easy.  Think of it as just moving so many spaces left or right on the x axis.  We are moving from point (-5,5) along the line y=5 to the point (2,5), which is moving 7 units.

Answer:

y = -3x² has the narrowest graph

Step-by-step explanation:

D)  y = -3x² has the narrowest graph.  That coefficient "3" stretches the graph of x² vertically.

On the other hand, B) has the widest graph.

Hello. The answer to your problem is (3, 1). I've included a screenshot of the graph.

Answer:  F) 7 mph

Step-by-step explanation:

The line you drew is correct but you read the graph wrong.  

The line drawn from 15 hours of training (bottom axis) meets the "line of best fit" at the average running speed (left axis) between 6 and 8, which is 7.

Answer:   [tex]\bold{x^{\frac{1}{3}}y^{\frac{1}{2}}}[/tex]

Step-by-step explanation:

[tex]\sqrt[6]{x^2y^3} =x^{\frac{2}{6}}y^{\frac{3}{6}}=x^{\frac{1}{3}}y^{\frac{1}{2}}[/tex]

Answer:

A. They are the only values that make both equations true.

Step-by-step explanation:

Equation A: 4y-3x=4

Equarion B: -2x-8y=8

Put x=-2, y=-0.5 in those two equations.

Equation A: 4(-0.5)-3(-2)=4

                     -2+6=4

                         4=4

Equation B: -2(-2)-8(-0.5)=8

                      4+4=8

                          8=8

So it's not B and C.

For D, you can tell that they are didferent lines by put them in to F(x)=kx+b format, and it tell you it's not D.

Answer:A

Step-by-step explanation:A P E X

Answer:

1

Step-by-step explanation:

Change of Y is 0 and change of x is any number.

0/any number = 0

Answer:

h(x) =  x - 5

set of all integers except 3

-∞ ≤ x ≤ ∞ and x ≠ 3

Step-by-step explanation:

Given the two equations in the question

Equation 1

f(x) = x² − 8x + 15

Equation 2

g(x) = x − 3

To find equation 3 that is h(x) we need to divide f(x) by g(x)

f(x) / g(x)

x² − 8x + 15 /  x − 3

By using quadratic factorisation  

(x-3)(x-5) / (x-3)

Cancel (x-3) from both numerator and denominator

h(x) = x-5

set of all integers except 3

-∞ ≤ x ≤ ∞ and x≠3

Answer:

first blank is x-5

second blank is -infinity, 3

third blank is 3, infinity

Answer:  [tex]x=2[/tex]

Step-by-step explanation:

To solve this exercise you must apply the Intersecting secan theorem.

Then, according to this theorem, you can know that:

[tex]EC*ED=EB*EA[/tex]

Therefore, you must substitute the values shown in the figure attached, as following:

[tex](x+4)(x+4+1)=(x+1)(x+1+11)[/tex]

Now you can solve for x, as you can see below:

[tex](x+4)(x+4+1)=(x+1)(x+1+11)\\\\(x+4)(x+5)=(x+1)(x+12)\\\\\\x^2+5x+4x+20=x^2+12x+x+12\\\\x^2+9x+20=x^2+13x+12\\x^2-x^2+9x-13x=12-20\\-4x=-8\\x=2[/tex]

Answer:

see explanation

Step-by-step explanation:

Using the rule of exponents

[tex]a^{m}[/tex] ÷ [tex]a^{n}[/tex] = [tex]a^{(m-n)}[/tex], then

[tex]a^{x^2-5x}[/tex] = [tex]a^{6}[/tex], hence

x² - 5x = 6 ( subtract 6 from both sides )

x² - 5x - 6 = 0 ← in standard form

(x - 6)(x + 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 6 = 0 ⇒ x = 6

x + 1 = 0 ⇒ x = - 1

Answer:

Step-by-step explanation:

Using the rule of exponents:

a^{m} ÷ a^{n} = a^{(m-n)} , then

aˣ² ÷ a^{5x}  = a⁶

⇒ a^{x^2 - 5x} = a⁶

⇒ x² - 5x = 6

x² - 5x - 6 = 0

(x - 6)(x + 1) = 0 [middle term splitting]

Equate each factor to zero and solve for x

x - 6 = 0 ⇒ x = 6     ║     x + 1 = 0 ⇒ x = -1

Answer:

11 days

Step-by-step explanation:

Answer:

[tex]\frac{5(x-3)}{6}[/tex]

No excluded values.

Step-by-step explanation:

To simplify the fraction expression, multiply by the reciprocal.

[tex]\frac{5}{x+2} * \frac{x^2-x-6}{6}  =\frac{5(x^2-x-6)}{6(x+2)}=\frac{5(x-3)(x+2)}{6(x+2} = \frac{5(x-3)}{6}[/tex]

Excluded values are values which make the denominator 0 but since there is no variable in the denominator then there are none.

Final answer:

It will take 72 minutes to fill the pool using only 3 taps.

Explanation:

To find out how many minutes it will take to fill the pool using only 3 taps, we can set up a proportion.

If it takes 120 minutes to fill the pool using 5 taps, then the rate at which water flows from the taps is 1 pool/120 minutes/tap.

Using this rate, we can set up the proportion:

5 taps / 3 taps = 120 minutes / x minutes

Cross-multiplying and solving for x gives us:

x = (3 taps * 120 minutes) / 5 taps = 72 minutes

So, it will take 72 minutes to fill the pool using only 3 taps.