Solve the following system of linear equations using elimination. x-y=5 -x-y=-11

The value of the segment a for the similar triangles is equal to 6.

The triangles MNO and YXO are similar, this implies that the length OX of the smaller triangle is similar to the length ON of the larger triangle

and the length OY of the smaller triangle is similar to the length OM of the larger triangle

so;

a/(a + 18) = 4/(4 + 12)

16a = 4(a + 18) {cross multiplication}

16a = 4a + 72

16a - 4a = 72 {collect like terms}

12a = 72

a = 72/12 {divide through by 12}

a = 6.

Therefore, the value of the segment a for the similar triangles is equal to 6.

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Answer:

The coordinates of the image of the point (6,6) under the same  translation is: (9, 2)

Hence, option C is correct.

Step-by-step explanation:

The image of the point (2, 1) under a translation is (5, -3).

It means when we horizontally move 3 units to the RIGHT i.e. adding 3 units to the x-coordinate and vertically move 4 units DOWN i.e. subtracting 4 units from the y-coordinate of the original point (2, 1), we get the coordinates of the image (5, -3).

Thus,

The rule of translation can be formulated such as:

(x, y) → (x + 3, y - 4)

(2, 1) → (2 + 3, 1 - 4) → (5, -3)

Thus,

Under the same rule of translation, we can determine the coordinates of the image of the point (6,6):

(x, y) → (x + 3, y - 4)

(6, 6) → (6 + 3, 6 - 4) → (9, 2)

Therefore, the coordinates of the image of the point (6,6) under the same  translation is: (9, 2)

Hence, option C is correct.

The equation of line passes through the point (6, 4) with a slope 2/3 is, y = 2/3x

Given,

The points which the line passes through = (6, 4)

Slope = 2/3

We have to find the equation of line;

Linear equation;

Y = mx + b is one way to represent a linear equation.

Here,

x is 6 and y is 4

Slope, m is 2/3

Then,

Substitute the values in y = mx + b

Here,

y = mx + b

4 = 2/3 (6) + b

4 = 12/3 + b

4 = 4 + b

b = 4 -4

b = 0

Then,

The equation of line is, y = 2/3x + 0

That is,

The equation of line passes through the point (6, 4) with a slope 2/3 is, y = 2/3x

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Answer:

if that is the ratio the fraction would be 8/14 but if we were to simplify this fraction it would be 4/7

A function that represents a reflection of \(f(x) = \frac{3}{8} (4)^x\) across the y-axis include the following: D. \(g(x) = \frac{3}{8} (4)^{-x}\).

In Mathematics and Geometry, a reflection over or across the y-axis or line x = 0 is represented and modeled by this transformation rule (x, y) → (-x, y).

This ultimately implies that, a reflection over or across the y-axis or line x = 0 would maintain the same y-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive.

By applying a reflection over the y-axis to the parent exponential function, we would have the following transformed exponential function:

(x, y)                                              →                 (-x, y).

\(f(x) = \frac{3}{8} (4)^x\)                               →              \(g(x) = \frac{3}{8} (4)^{-x}\)

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The slope of the perpendicular line would be the negative reciprocal of the other line.

negative reciprocal of 1/2 = -2

answer: -2

Answer:hi

Step-by-step explanation:

Answer:

110 kobo

Step-by-step explanation:

first 18 = 35 kobo

48-18 = 30 words left

30x2.5  = 75 kobo

35 + 75 = 110 kobo

The length AC in the kite is 8.7 cm.

A kite is a quadrilateral that has two pairs of consecutive equal sides and

perpendicular diagonals. Therefore, let's find the length AC in the kite.

Hence, using Pythagoras's theorem, let's find CE.

Therefore,

7² - 4² = CE²

CE = √49 - 16

CE = √33

CE = √33

Let's find AE as follows:

5²- 4² = AE²

AE = √25 - 16

AE = √9

AE = 3 units

Therefore,

AC = √33 + 3

AC = 5.74456264654 + 3

AC = 8.74456264654

AC = 8.7 units

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Answer:

a) 24 minutes

b) 20 mph

Step-by-step explanation:

  time= 12 min

         \(\sf = \dfrac{12}{60} \ hour\)

 speed = 60 mph

\(\sf \boxed{distance =speed * time}\)

                \(\sf = 60 * \dfrac{12}{60}\\\\ = 12 \ m\)    

a) Speed = 30 mph

      \(\sf \boxed{time = \dfrac{distance}{speed}}\)

               \(\sf = \dfrac{12}{30}\\\\ = \dfrac{2}{5} \ hour\\\\ = \dfrac{2}{5}*60\\\\= 2 * 12\\\\= 24 \ minutes\)

It will take 24 minutes.

c) time = 36 minutes

           \(\sf = \dfrac{36}{60} \hour\)

 \(\sf \boxed{speed= \dfrac{distance}{time}}\)

            \(\sf = \dfrac{12}{ \dfrac{36}{60}}\\\\\\ = 12* \dfrac{60}{36}\\\\= 20 \ mph\)

Average speed = 20 mph

Answer:

28/3 or 9 1/3 pounds

Step-by-step explanation:

Let's set up a proportion using the following setup:

pounds/loaves=pounds/loaves

We know that 7 pounds of flour is needed for 3 loaves. We don't know how many pounds are needed for 4 loaves, therefore we can say x pounds are needed for 4 loaves.

7 pounds/ 3 loaves= x pounds/ 4 loaves

7/3=x/4

We want to find out what x (flour needed for 4 loaves) is. We have to get x by itself.

x is being divided by 4. We need to perform the inverse operation. The opposite of division is multiplication. Therefore, we should multiply both sides of the equation by 4.

4*(7/3)=(x/4)*4

4*7/3=x

9.333333=x

x=9.33 or 28/3 or 9 1/3

It will take 28/3 or 9 1/3 pounds of flour to make 4 loaves of bread.

Path A-B-C-E represents the distance traveled, which is 18 meters.

Path A-G-C-E represents the displacement, which is 17 meters.

From the given figure, we can identify the paths and calculate the distance and displacement.

Path A-B-C-E represents the distance traveled, and path A-G-C-E represents the displacement.

Let's calculate the lengths of both paths:

Distance traveled (Path A-B-C-E):

Length of AB = 9m

Length of BC = 3m

Length of CE = 6m

Total distance traveled = Length of AB + Length of BC + Length of CE

= 9m + 3m + 6m

= 18m

Therefore, the distance traveled along path A-B-C-E is 18 meters.

Displacement (Path A-G-C-E):

Length of AG = 5m

Length of GC = 6m

Length of CE = 6m

Total displacement = Length of AG + Length of GC + Length of CE

= 5m + 6m + 6m

= 17m

Therefore, the displacement along path A-G-C-E is 17 meters.

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Answer:

70%

Step-by-step explanation:

the formula for percent of change is:

New value - Old value divided by Old value

we can write this algebraically as:

(6-20)/20 which is -14/20

the negative simply implies a 'decrease' from old to new

14/20 equals 70/100 or 70%

Answer:

The answer to your question is 70% decrease

Step-by-step explanation:

I hope this helps and have a wonderful day!

Answer:

\(\cot(\theta)\)

Step-by-step explanation:

Trig identities:

\(\csc(\theta)=\dfrac{1}{\sin(\theta)}\)

\(sin^2(\theta)+cos^2(\theta)=1\)

\(\cos(2\theta)=cos^2(\theta)-sin^2(\theta)\)

\(\implies \cos(2\theta)=2cos^2(\theta)-1\)

\(\implies2cos^2(\theta)= \cos(2\theta)+1\)

\(\sin(2\theta)=2\sin(\theta)\cos(\theta)\)

Therefore,

\(\dfrac{\cos(2\theta)+\sin(\theta) \times \csc(\theta)}{\sin(2\theta)}\)

\(=\dfrac{\cos(2\theta)+\dfrac{\sin(\theta)}{\sin(\theta)}}{\sin(2\theta)}\)

\(=\dfrac{\cos(2\theta)+1}{\sin(2\theta)}\)

\(=\dfrac{2cos^2(\theta)}{\sin(2\theta)}\)

\(=\dfrac{2cos^2(\theta)}{2\sin(\theta)\cos(\theta)}\)

\(=\dfrac{cos(\theta)}{\sin(\theta)}\)

\(=\cot(\theta)\)

The results of operations between vectors are, respectively:

Case A: u + w = <- 3, - 1>

Case B: - 6 · v = <6, 6>

Case C: 3 · v - 6 · w = <- 21, - 15>

Case D: 4 · w + 3 · v - 5 · u = <39, 4>

Case E: |w - v| = √(4² + 3²) = 5

In this problem we must determine the operations between vectors, this can be done by following definitions:

Vector addition

v + u = (x, y) + (x', y') = (x + x', y + y')

Scalar multiplication

α · v = α · (x, y) = (α · x, α · y)

Norm of a vector

|u| = √(x² + y²)

Now we proceed to determine the result of each operation:

Case A:

u + w = <- 6, - 3> + <3, 2>

u + w = <- 3, - 1>

Case B:

- 6 · v = - 6 · <- 1, - 1>

- 6 · v = <6, 6>

Case C:

3 · v - 6 · w = 3 · <- 1, - 1> - 6 · <3, 2>

3 · v - 6 · w = <- 3, - 3> + <- 18, - 12>

3 · v - 6 · w = <- 21, - 15>

Case D:

4 · w + 3 · v - 5 · u = 4 · <3, - 2> + 3 · <- 1, - 1> - 5 · <- 6, - 3>

4 · w + 3 · v - 5 · u = <12, - 8> + <- 3, - 3> + <30, 15>

4 · w + 3 · v - 5 · u = <39, 4>

Case E:

|w - v| = |<3, 2> - <- 1, - 1>|

|w - v| = |<4, 3>|

|w - v| = √(4² + 3²) = 5

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The set of factors used to factor the given trinomial are -4 and -4. Therefore, option C is the correct answer.

The given trinomial is x²-8x+16.

Factors of 16           Sum of factors

-1 and -16               -1+(-16)=-17

-2 and -8                  -2+(-8)=-10

-4 and -4                  -4+(-4)=-8

The set of factors would used to factor the trinomial are -4 and -4.

Therefore, option C is the correct answer.

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Answer:

7

Step-by-step explanation:

The order of calculate the confidence interval for the mean are as follows:

1. Select sample stat

2. select desired confidence

3. determine margin of error

4. specify upper and lower limits

Now, According to the question:

The order of calculate the confidence interval for the mean are as follows:

1. Select sample stat

2. select desired confidence

3. determine margin of error

4. specify upper and lower limits

Let's know:

What is Confidence Interval?

A confidence interval gives an estimated range of values which is likely to include an unknown population parameter, the estimated range being calculated from a given set of sample data.

The common notation for the parameter in question is θ. Often, this parameter is the population mean μ , which is estimated through the sample mean bar x.

The level C of a confidence interval gives the probability that the interval produced by the method employed includes the true value of the parameter θ.

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Answer:

add 1 Century to divide £6 000 000

Answer:

the answer to your question is 105 I think sorry if it's not

The expression that is always equivalent to sin x when 0° < x < 90° is (1) cos (90° - x). Option 1

To understand why, let's analyze the trigonometric functions involved. In a right triangle, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. Since we are considering angles between 0° and 90°, we can guarantee that the side opposite the angle will always be the shortest side of the triangle, and the hypotenuse will be the longest side.

Now let's examine the expression cos (90° - x). The cosine of an angle is defined as the ratio of the length of the side adjacent to the angle to the length of the hypotenuse. In a right triangle, when we subtract an angle x from 90°, we are left with the complementary angle to x. This means that the remaining angle in the triangle is 90° - x.

Since the side adjacent to the angle 90° - x is the same as the side opposite the angle x, and the hypotenuse is the same, the ratio of the adjacent side to the hypotenuse remains the same. Therefore, cos (90° - x) is equivalent to sin x for angles between 0° and 90°.

On the other hand, options (2) cos (45° - x) and (3) cos (2x) do not always yield the same value as sin x for all angles between 0° and 90°. The expression cos x (option 4) is equivalent to sin (90° - x), not sin x.

Option 1 is correct.

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Answer:

Step-by-step explanation:

this problem is on vector

given the vectors

a = 5i + j, and

b = i − 2j

1. summation of vector a + b

\(= (5i+j)+(i-2j)\\\\=5i+j+i-2j\\\\\)

collect like terms

\(=5i+i+j-2j\\\\=6i-j\\\\\)

2. 2a + 3b

\(= 2(5i+j)+3(i-2j)\\\\=10i+2j+3i-6j\\\\\)

collecting like terms we have

\(=10i+2j+3i-6j\\\\=10i+3i+2j-6j\\\\=13i-4j\)

(3) |a|, and |a − b|.

|a|= |5i+j|

\(=\sqrt{5^2+1^2} \\\\=\sqrt{25+1} \\\\=\sqrt{26} \\\\= 5.1\)

also,

\(|a - b|= |(5i+j) -(i-2j)| \\\\ a-b= 5i+j -i+2j \\\\ a-b=5i-i+j+2j \\\\a-b= 4i+3j\\\\\)

\(|a -b|=\sqrt{4^2+3^2} \\\\|a -b|=\sqrt{16+9} \\\\|a -b|=\sqrt{25} \\\\|a -b|=25\)

Bruce and Felicia would have a unique solution to the given equation. The value of x that satisfies the equation is 15.

To determine if the equation 6x + 2 = 5x + 17 has a unique solution, we need to check if the variable x has a consistent value that satisfies the equation.

By simplifying the equation, we can see that the equation becomes:

6x - 5x = 17 - 2

Simplifying further, we have:

x = 15

Since the variable x has a specific value, in this case, x = 15, the equation does have a unique solution. When x is substituted with 15 in the equation, both sides are equal.

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Using sum of infinite series in a geometric progression, the total number of jumps is 40 inches

A geometric progression or a geometric sequence is the sequence, in which each term is varied by another by a common ratio. The next term of the sequence is produced when we multiply a constant (which is non-zero) to the preceding term.

The jumps are infinite and to find the total distance, we can use the equation given;

S = a(1 / 1 - r)

The first term (a) = 20 in

The common ratio = 10 / 20 = 1/2 = 0.5

Substituting the values into the equation;

S = 20(1 / 1 - 0.5)

S = 20(1 / 0.5)

S = 20 * 2

S = 40 in

The total distance is 40 inches

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Answer:

18 number of daisies and 18 number of roses

Step-by-step explanation:

We are told Darrel has 36 daisies and 54 roses.

And that He wants to put an equal number of daisies and roses into vases.

To get the equal number, it means we have to find the greatest common factor of 36 and 54.

Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36

Factors of 54 = 1, 2, 3, 6, 9, 18, 27, 54

From the factors of both 36 and 54, the greatest common factor to both of them is 18.

Thus, the GREATEST number of daisies and roses Darrel can put in each vase is 18 each

Answer:

18

Step-by-step explanation:

Total number of the adults are 693

Percentage of adults that show that they erase all of their personal information online is 58%

Geberal expression for the percentage is

We need to find the number of adults that erase all of their personal information online.

Substitute the value

Let x=Number of adults who erase thier personal information

Simplify and solve for, x

Round of the x value

Number of adults who erase thier personal information are 402.

Step-by-step explanation:

Arc length formula is

\(s = rx\)

where x is radinas.

A semi circle has a radian measure of

\(\pi\)

The radius is half of the diameter, 12 so the radius is

\(12 \times \frac{1}{2} = 6\)

So the arc length is

\(6 \times \pi = 6\pi\)

Area of semi circle is

\( \frac{1}{2} \pi {r}^{2} \)

where r is the radius.

\( \frac{1}{2} \pi6 {}^{2} \)

\( \frac{1}{2} 36\pi\)

\(18\pi\)

Answer:

Do you need the answer or the factor??

Step-by-step explanation:

Answer: -(5a+16)

Step-by-step explanation: