what two expressions are equivalent to 3/5 x - 3
a. 3/5 ( x - 1)
b. 3/5 (x - 5)
c. 3(1/5 x - 1)
d. 3 - 3/5 x

Answer:

c= -2

Step-by-step explanation:

Perpendicular lines imply that the product of the gradient of the two lines is -1.

So let's find the gradient of each lines.

[tex]gradient = \frac{y1 - y2}{x1 - x2} [/tex]

Gradient of 1st line

= 1-(-4)/ -3-2

= 5/-5

= -1

(gradient of 1st line)(gradient if 2nd line)= -1

(-1)(gradient of 2nd line)= -1

gradient of 2nd line= -1 ÷ (-1) =1

Now make use of the gradient formula to find an expression of the gradient of the second line.

Gradient of 2nd line= c-1/ -2-1

subst. gradient of second line and simplify:

1= c-1/-3

c-1= -3 (multiply by -3 on both sides)

c= -3+1 (add 1 on both sides)

c= -2

Answer:

There are no like terms for all 3 variables for 9a-3b+4ab

Answer:

<1 = 93 (vertical opposite angle are equal)

Step-by-step explanation:

Answer: I can confirm, Josshyaby is correct I took the test

Step-by-step explanation:

Answer:

What is n?

Step-by-step explanation:

Answer:14

Step-by-step explanation:

figure out 5x20,, which gives you 100 points

use trial and error is my method :)

if he answered 10 correct, he would get 50 points and lose 10. this gives 40 points. its an error

we now know its between 11 right and 19 right

we continue to do this till we get it right

14 x 5 = 68. - 4 makes 64.

Sammy answered 14 questions correctly on his test, as determined by setting up and solving the equation 5x - (20 - x) = 64, where x represents the number of correct answers.

Sammy is taking a test where each correct question awards him 5 points and each incorrect one deducts a point. With 20 questions in total and a score of 64, we can set up an equation to find out how many questions he answered correctly. Let x represent the number of correct answers. Then, the number of incorrect answers would be 20-x. The scoring system gives us the following equation:

5x - (20 - x) = 64

By solving this equation, we can find out how many questions Sammy answered correctly:

Combine like terms: 5x - 20 + x = 64

Simplify: 6x - 20 = 64

Add 20 to both sides: 6x = 84

Divide both sides by 6: x = 14

Thus, Sammy answered 14 questions correctly on his test.

Answer:

p^10.

Step-by-step explanation:

(p^2)^5

= p^(2*5)

= p^10.

Answer:

Step-by-step explanation:

(P²)^5 = P^(2×5) = P^10

Answer:

yes

Step-by-step explanation:

(1)  [tex]1\frac{7}{8}[/tex] pounds of soil   (2) [tex]\frac{35}{2}[/tex]   (3)  33

Solution:

(1) Number of pots = 5

Quantity of soil each pot can hold = [tex]\frac{3}{8}[/tex] pounds

Quantity of soil need to fill all the pots = [tex]5\times \frac{3}{8}[/tex]

                                                               = [tex]\frac{15}{8}[/tex] pounds

                                                               = [tex]1\frac{7}{8}[/tex] pounds

Therefore, [tex]1\frac{7}{8}[/tex] pounds of soil need to fill all of the pots.

(2) To find the product of [tex]4\frac{2}{3}[/tex] and [tex]3\frac{3}{4}[/tex].

Let us first convert the mixed fraction into improper fraction.

[tex]4\frac{2}{3}\times3\frac{3}{4}=\frac{(4\times3)+2}{3}\times\frac{(3\times4)+3}{4}[/tex]

             [tex]=\frac{14}{3}\times\frac{15}{4}[/tex]

             [tex]=\frac{210}{12}[/tex]

This can be simplified. Divide both numerator and denominator by 6.

             [tex]=\frac{35}{2}[/tex]

[tex]4\frac{2}{3}\times3\frac{3}{4}=\frac{35}{2}[/tex]

(3) To evaluate the expression 12x + 6 for [tex]x=2\frac{1}{4}[/tex].

Let us first convert the mixed fraction into improper fraction.

[tex]x=\frac{(2\times4)+1}{4}=\frac{9}{4}[/tex]

[tex]12x+6=12(\frac{9}{4})+6[/tex]

            [tex]=(\frac{108}{4})+6[/tex]

            [tex]=27+6[/tex]

12x + 6 = 33

Answer:

(1, - 2 )

Step-by-step explanation:

Given the 2 equations

10x + 6y = - 2 → (1)

2x + 6y = - 10 → (2)

Multiplying (2) by - 1 and adding to (1) will eliminate the y- term

- 2x - 6y = 10 → (3)

Add (1) and (3) term by term

(10x - 2x) + (6y - 6y) = (- 2 + 10), that is

8x = 8 ( divide both sides by 8 )

x = 1

Substitute x = 1 into either of the 2 equations.

Substituting x = 1 into (1)

10(1) + 6y = - 2

10 + 6y = - 2 ( subtract 10 from both sides )

6y = - 12 ( divide both sides by 6 )

y = - 2

Solution is (1, - 2 )

Answer: She isn't correct.

Step-by-step explanation: The BODMAS rule must be strictly followed and as such gives different answers to the two expressions.

(12-3)*2 basically gives:

9*2 (Dealing with the bracket first)

18.

While 12-(3*2) while dealing with the bracket first will give:

12-6; which would eventually give

6.

Answer:

it's dilation by 2 because the purple one is 2x bigger

Answer:653.8

Step-by-step explanation:

467 /5=93.4 miles in five hours.   93.4 *7 =653.8

Answer:

29/112

Step-by-step explanation:

3 5/8=29/8

(29/8)/14

(29/8)(1/14)=29/112

Answer:

6/7

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(7-1)/(5-(-2))

m=6/(5+2)

m=6/7

Answer:

The slope is [tex]m=\frac{6}{7}[/tex]

Step-by-step explanation:

The translation is The figure moves left and down.

Option:B.

Step-by-step explanation:

The given coordinate  (x,y) is mapped and it gets translated using mapping (x+a,y+b).

Also, we are given with information that the value of a and also value of b is negative (-a,-b).

⇒the mapping coordinate = (x+(-a),y+(-b)).

The mapping coordinate = ( x-a, y-b).

The coordinate points will be decreasing in x and y axis. So it will move towards the left and downside of the graph.

For example,

Consider that a= -3 and b= -2.

∴The translating coordinate will be (x-3,y-2).

Choose a coordinate point ( 2,2) initially.

Substitute the x,y coordinate in the translating coordinate.

⇒ (x-3,y-2) = (2-3,2-2).

=(-1,0).

After translation the points will be (-1,0).

∴The figure will move towards left and downwards.

Answer:

b} The figure moves left and down

Step-by-step explanation:

i took the test

The trains are 275 km apart when both are at their first stop

Solution:

The tracks make an angle of 130°, with the station as a vertex

Therefore, from given figure in question,

Angle at station = 130 degree

Let "c" be the point at station

The first train  travels 100 km and makes its first stop at point A

Distance between A and station c = 100 km

Let a = 100 km

The second train travels 200 km and makes it first stop at point B

Distance between B and station c = 200 km

Let b = 200 km

We have to find the value of "d"

We can use the law of cosine

The square of a side of a plane triangle equals the sum of the squares of the remaining sides minus twice the product of those sides and the cosine of the angle between them.

From given figure in question,

Side opposite "d" to 130 degree is equal to sum of square of other sides a and b minus twice the product of those sides and the cosine of the angle between them which is 130 degrees

Therefore,

[tex]d^2 = a^2 + b^2 - 2ab\ cos\ d[/tex]

[tex]d^2 = 100^2 + 200^2 - 2(100)(200)cos 130\\\\d^2 = 10000 + 40000 - 40000cos 130\\\\d^2 = 50000 - 40000 \times -0.6427\\\\d^2 = 50000 + 25711.5\\\\d^2 = 75711.5\\\\\text{Take square root on both sides }\\\\d = 275.15 \approx 275[/tex]

Thus trains are 275 km apart when both are at their first stop

Answer:

D. 275 km

Step-by-step explanation:

Answer:

The value of 'x' is 7 that will make make L║M.

Step-by-step explanation:

Given,

Line segment L and line segment M are cut by a transversal line.

We can name it as 't' transversal line and also the given angle measures as ∠1 and ∠2.

So, ∠1 = [tex]7x+9[/tex]

∠2 = [tex]8x+2[/tex]

We have to find the value of 'x'.

Solution,

Since L and M are two line segment which is cut by another line segment 't'.

For L║M, the measure of ∠1 and ∠2 must be equal according to corresponding angle property.

"When the measure of a pair of same side corresponding angle is equal, then the line segments are parallel".

[tex]\therefore \angle1=\angle2[/tex]

On substituting the values, we get;

[tex]7x+9=8x+2[/tex]

Combining the like terms, we get;

[tex]8x-7x=9-2\\\\x=7[/tex]

Now we will find out the measure of  ∠1 and ∠2.

[tex]\angle1=7x+9=7\times7+9=49+9 =58[/tex]

[tex]\angle2=8x+2=8\times7+2=56+2=58[/tex]

Hence The value of 'x' is 7 that will make make L║M.

Answer:

Step-by-step explanation:

10m^2 and 15mk

common factor is 5m

HCF is 5m

[tex]\frac{1}{6}[/tex] or 0.167 pounds more butter was used than sugar

Solution:

Given that, Desmond's Desserts made a batch of fresh scones with 2/3 of a pound of butter and 1/2 of a  pound of sugar

To find: Amount of butter used than sugar

From given information,

[tex]\text{Butter used} = \frac{2}{3} \text{ pound }[/tex]

[tex]\text{Sugar used } = \frac{1}{2} \text{ pound }[/tex]

To find how much butter is used than sugar, find the difference between them

[tex]Difference = Butter\ used - Sugar\ used[/tex]

[tex]Difference = \frac{2}{3} - \frac{1}{2}\\\\Difference = \frac{2 \times 2-1 \times 3}{3 \times 2}\\\\Difference =\frac{4-3}{6}\\\\Difference =\frac{1}{6} = 0.167\\\\[/tex]

Thus [tex]\frac{1}{6}[/tex] or 0.167 pounds more butter was used than sugar

Answer:the mean score would decrease more than the median score

Step-by-step explanation:

i did the quiz

Adding a score of 0 would decrease the mean more than the median, with the new mean being 100 and the new median 120.

Adding a score of 0 to the data set of game scores will impact both the mean and the median of the distribution. However, the way each measure of central tendency is affected will be different.

For the mean, which is the arithmetic average, adding a score of 0 will bring the average down. To find the new mean, you would add 0 to the sum of the existing scores and divide by the new total number of scores. Since 0 is lower than any of the existing scores (100, 120, 130, and 150), the mean will decrease.

The initial mean is 125, which is the sum of all the scores (500) divided by the number of scores (4).

Calculating the new mean after including the score of 0, we get (500 + 0) / (4 + 1) = 500 / 5 = 100. This shows the mean would decrease as a result of the 0 score.

As for the median, if we incorporate the score of 0 into the data set, it will become the new lowest score. With an odd number of scores (5), the median will be the middle value.

The scores in order would be 0, 100, 120, 130, and 150. So the new median would be 120. The median is less influenced by extreme values, especially when they are an outlier like the 0 in this case.

Therefore, the correct answer is that the mean score would decrease more than the median score when adding a 0 to the data set.

Answer:

7^2*5^2

Step-by-step explanation:

The equation contains two 7's and two 5's. 7 squared and 5 squared can be written like this, so the answer is 7^2*5^2

Answer:

c&d

Step-by-step explanation:

because they are connected

Answer:

Quadrant 4

Step-by-step explanation:

sinA < 0 in quadrants 3 and 4

cosA > 0 in quadrants 1 and 4

Thus sinA < 0 and cosA > 0 in quadrant 4

Final answer:

The correct statement regarding the interior and exterior angles of the triangle is 'm∠3 + m∠4 + m∠5 = 180°'. Option b

Explanation:

When considering the properties of interior and exterior angles in a triangle, several theorems are useful to determine the correct statement among the choices provided.

Specifically, one important theorem to recall is: The exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles. Additionally, the sum of all interior angles in a triangle is always 180 degrees.

With these principles in mind, we can examine the provided statements:

m∠5 + m∠6 = m∠1 - Incorrect. The exterior angle at a vertex of a triangle is the sum of the two opposite interior angles, not an addition of an interior and its adjacent exterior angle.

m∠3 + m∠4 + m∠5 = 180° - Correct. This is true because m∠4, being an exterior angle, is equal to m∠2 + m∠5, and since the sum of the interior angles of a triangle is 180 degrees, m∠2 + m∠3 + m∠5 = 180 degrees. Replacing m∠2 + m∠5 with m∠4 gives us the correct equation.

m∠1 + m∠2 = 180° - Incorrect. This statement would imply that angle 1 and angle 2 are on a straight line, which is not the case in a triangle's exterior and interior angles.

m∠2 + m∠3 = m∠5 - Incorrect. There is no direct theorem that supports this statement as a relationship between these angles in a triangle.

The correct statement, based on the theorems regarding triangle angles, is m∠3 + m∠4 + m∠5 = 180°.

Answer:

a) [tex]\log 52[/tex]

b) [tex]\log_57[/tex]

Step-by-step explanation:

Use logarithm properties:

[tex]\log_ab+\log_ac=\log_a(b\cdot c)\\ \\\log_ab-\log_ac=\log_a\dfrac{b}{c}[/tex]

Then

a) [tex]\log 13+\log 4=\log 13\cdot 4=\log 52[/tex]

b) [tex]\log_514-\log _52=\log _5\dfrac{14}{2}=\log _57[/tex]

Answer:

  [tex]y^4\sqrt{39y}[/tex]

Step-by-step explanation:

[tex]\displaystyle\sqrt{39y^9}=\sqrt{39y(y^4)^2}=y^4\sqrt{39y}[/tex]

To simplify √(39y¹¹), rewrite y¹¹ as (y²)·(y²)·(y²) and take out the perfect square. The simplified expression is 3y√(39y).

To simplify the expression √(39y¹¹), we need to remove the perfect square from inside the square root. Since y is raised to the power of 9 and is positive, it is a perfect square. We can rewrite y¹¹ as (y²)·(y²)·(y²).

Therefore, √(39y¹¹) = √(39(y²)·(y²)·(y²)) = √(39)·(y²)√(y²)√(y²) = √(39)·y²·y²·y² = √(39)·y¹ = 3y√(39y).

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The missing length [tex]x=\frac{12}{5}[/tex].

Solution:

The image of the answer is attached below.

In figure ABCD,  AB = 4, BC = 10

In figure PQRS, PQ = x, RS = 6

Given figures are similar.

If two figures are similar, then the sides are proportionate to each other.

⇒ [tex]\frac{AB}{BC}= \frac{PQ}{QR}[/tex]

⇒ [tex]\frac{4}{10}= \frac{x}{6}[/tex]

Do cross multiply.

⇒ [tex]4 \times 6 = x \times 10[/tex]

⇒ [tex]24 = 10x[/tex]

⇒ [tex]x=\frac{24}{10}[/tex]

To reduce the length, divide both numerator and denominator by 2.

⇒ [tex]x=\frac{12}{5}[/tex]

Hence, the missing length [tex]x=\frac{12}{5}[/tex].

Answer:

Interest rate tend to be lower in weak economy than in strong economy to encourage people to borrow money to invest in businesses, the lower the interest rate, the more willing people are to borrow money to make big purchases and this will make economic growth tend to be faster.

Moreso a weak economy tends to have low inflation, so interest rates drop to match.

The product of the two binomials is (y + 1)(y - 5)

Step-by-step explanation:

To write a polynomial as a product of two binomials

∵ The polynomial is (y - 5) - y(5 - y)

- Multiply y by the bracket (5 - y)

∵ y(5 - y) = y(5) - y(y)

∴ y(5 - y) = 5y - y²

- Substitute 5(5 - y) by (5y - y²)

∴ (y - 5) - y(5 - y) = (y - 5) - (5y - y²)

- Multiply (-) by the bracket (5y - y²)

∵ (-)(5y) = -5y

∵ (-)(-y²) = y²

∴ (y - 5) - y(5 - y) = y - 5 - 5y + y²

- Add the like terms

∴ (y - 5) - y(5 - y) = -4y - 5 + y²

- Arrange the terms from greatest power of y

∴ (y - 5) - y(5 - y) = y² - 4y - 5

Now let us factorize y² - 4y - 5 into two factors

∵ y² = y × y

∵ -5 = -5 × 1

- Multiply y by 1 and y by -5, then add the product the sum

   must be equal the middle term of the polynomial above

∵ y(1) + y(-5) = y - 5y = -4y ⇒ as the middle term

- Now write the two bracts

∴ y² - 4y - 5 = (y + 1)(y - 5)

The product of the two binomials is (y + 1)(y - 5)

Learn more:

You can learn more about the polynomials in brainly.com/question/12700460

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