Evaluate ab for a = -2 3/4 and b= - 4/6

Answer:

The quadrilateral is not a rectangle

Step-by-step explanation:

we know that

If a quadrilateral ABCD is a rectangle

then

Opposite sides are congruent and parallel and adjacent sides are perpendicular

Remember that

If two lines are parallel, then their slopes are the same

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

The formula to calculate the slope between two points is equal to

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

we have

A(-5,5), B(1,8), C(4,2), and D(-2,-2)

Plot the figure to better understand the problem

see the attached figure

Find the slope of the four sides and then compare

step 1

Find slope AB

A(-5,5), B(1,8)

substitute in the formula

[tex]m=\frac{8-5}{1+5}[/tex]

[tex]m=\frac{3}{6}[/tex]

[tex]m_A_B=\frac{1}{2}[/tex]

step 2

Find slope BC

B(1,8), C(4,2)

substitute in the formula

[tex]m=\frac{2-8}{4-1}[/tex]

[tex]m=\frac{-6}{3}[/tex]

[tex]m_B_C=-2[/tex]

step 3

Find slope CD

C(4,2), and D(-2,-2)

substitute in the formula

[tex]m=\frac{-2-2}{-2-4}[/tex]

[tex]m=\frac{-4}{-6}[/tex]

[tex]m_C_D=\frac{2}{3}[/tex]

step 4

Find slope AD

A(-5,5), D(-2,-2)

substitute in the formula

[tex]m=\frac{-2-5}{-2+5}[/tex]

[tex]m=\frac{-7}{3}[/tex]

[tex]m_A_D=-\frac{7}{3}[/tex]

step 5

Verify if the opposites are parallel

Remember that

If two lines are parallel, then their slopes are the same

The opposite sides are

AB and CD

BC and AD

we have

[tex]m_A_B=\frac{1}{2}[/tex]

[tex]m_C_D=\frac{2}{3}[/tex]

so

[tex]m_A_B \neq m_C_D[/tex]

It is not necessary to continue verifying, because two of the opposite sides are not parallel

therefore

The quadrilateral is not a rectangle

The phrase 'decreased by 4' refers to a mathematical operation where you take an integer and subtract 4. Without a specified starting point, it could represent various integers depending upon the starting integer.

The phrase 'decreased by 4' in the context of mathematics usually requires a starting point or reference integer. Suppose the starting point was 0, 'decreased by 4' would result in -4. However, if the starting integer isn't mentioned, it could be indicating a function where you take an input integer and subtract 4. Therefore, the phrase 'decreased by 4' could represent an operation applied to integers, resulting in an integer that is four less than the original.

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Answer:

x = -4, y = 8.

Step-by-step explanation:

Question 16.

8x + y = -24    ........(A)

-3x - 2y = -4    ........(B)

Multiply (A) by 2:

16x + 2y = -48   Adding this to equation (B):

13x = -52

x = -4

Substituting this value of x in Equation (A):

8(-4) + y = -24

y = -24 + 32 = 8.

Answer:

Answer for the first part of question 16 is y =-24 - 8x

1st subtract 8x from both sides: 8x + y - 8x = -24 - 8x

2nd simplify: -24 - 8x

Answer for the 2nd part of Q. 16 is y = -(-4+3x)/2

1st add 3x to both sides: -3x - 2y + 3x = -4 + 3x

2nd simplify: -2y = -4 + 3x

3rd divide both sides by -2: -2y ÷ -2 = 4 ÷ -2 +3x ÷ -2

4th simplify: (-4 + 3x)/2

Answer to the 1st part of Q. 17 is y = (-1 - 2x)/3

1st subtract 2x from both sides 2x + 3y - 2x = -1 - 2x

2nd simplify: -3y= -1 - 2x

3rd divide both sides by -3: -3y ÷ -3 = 1 ÷ -3 - 2x ÷ -3

4th simplify: y = (-1 - 2x)/3

Answer to 2nd part of Q.17: y = 6 + 7x ÷ 10

1st Add 7x to both sides: -7x + 10y + 7x = 6 + 7x

2nd simplify: 10y=6+7x

3rd divide both sides by 10: 10y ÷ 10 = 6 ÷ 10 + 7x ÷ 10

4th simplify: y = 6 + 7x ÷ 10

sorry, but I don't know the answer to Q.18 but I hope I helped on questions 16 and 17 :)

Answer:

A.

[tex]\dfrac{6}{55}[/tex]

B.

[tex]\dfrac{6}{55}[/tex]

C.

[tex]\dfrac{4}{165}[/tex]

Step-by-step explanation:

Dustin has a bag of marbles with 4 blue marbles, 4 white marbles, and 3 red marbles. There are 11 marbles in total.

A. The probability that the first marble drawn is blue marble is

[tex]\dfrac{4}{11},[/tex]

the probability that the second marble drawn is red marble is

[tex]\dfrac{3}{10}[/tex]

The probability that the first marble drawn is blue and the second is red is

[tex]\dfrac{4}{11}\cdot \dfrac{3}{10}=\dfrac{12}{110}=\dfrac{6}{55}[/tex]

B. The probability that the first marble drawn is red marble is

[tex]\dfrac{3}{11},[/tex]

the probability that the second marble drawn is white marble is

[tex]\dfrac{4}{10}[/tex]

The probability that the first marble drawn is red and the second is white is

[tex]\dfrac{3}{11}\cdot \dfrac{4}{10}=\dfrac{12}{110}=\dfrac{6}{55}[/tex]

C. The probability that the first marble drawn is blue marble is

[tex]\dfrac{4}{11},[/tex]

the probability that the second marble drawn is blue marble is

[tex]\dfrac{3}{10},[/tex]

the probability that the third marble drawn is blue marble is

[tex]\dfrac{2}{9},[/tex]

The probability that the first, second and third marbles drawn are blue is

[tex]\dfrac{4}{11}\cdot \dfrac{3}{10}\cdot \dfrac{2}{9}=\dfrac{24}{990}=\dfrac{4}{165}[/tex]

Answer:

Step-by-step explanation:

16 miles in it

Answer: Should be 16 miles.

I'm not a genius but I know partial of math in my grade. Hope this helped.

Answer:

The original cost of the pair of shoes before tax is $48.95

Step-by-step explanation:

* Lets explain how to solve the problem

- Assume that the cost of the pair of shoes is 100% before taxes

∵ The cost of the pair of shoes is 100% before taxes

∵ The tax is 7.25%

∴ The price of the pair of shoes after tax = 100% + 7.25% = 107.25%

- This 107.25% equivalent to the price of the pair of shoes including

  the tax

∵ The cost of the pair of shoes including tax is $52.50

- Lets use the cross multiplication to find the cost of the pair of

 shoes before  tax

∵     100%  ⇒  107.25%

         ?       ⇒  52.50

- ? represents the cost of the pair of shoes before tax

∴ ? = [tex]\frac{100*52.50}{107.25}=48.95[/tex]

∴ The original cost of the pair of shoes before tax is $48.95

Answer:

3 and 4

Step-by-step explanation:

Consider squares on either side of 15, that is 9 and 16, so

[tex]\sqrt{9}[/tex] < [tex]\sqrt{15}[/tex] < [tex]\sqrt{16}[/tex], that is

3 < [tex]\sqrt{15}[/tex] < 4

Answer:

[tex]3<\sqrt{15}<4[/tex]

Step-by-step explanation:

We are asked to find the integers such that square root of 15 lies between them.

We know that perfect square less than 15 is 9 and perfect square greater than 15 is 16.

We can represent this information in an inequality as:

[tex]\sqrt{9}<\sqrt{15}<\sqrt{16}[/tex]

[tex]\sqrt{3^2}<\sqrt{15}<\sqrt{4^2}[/tex]

[tex]3<\sqrt{15}<4[/tex]

Therefore, the square root of 15 lies 3 and 4.

Answer:

The answer is 5r^2s^3t^4 (the last answer) because it is the only monomial in the bunch.

Step-by-step explanation:

Answer:

24,12,6

Step-by-step explanation:

48 is even, so you can factor out 2, your first prime factor

Final answer:

The prime factors of 48 are 2 to the power of 4 and 3. You divide 48 by 2 repeatedly until only prime numbers are left, which are 2´ and 3.

Explanation:

Finding Prime Factors

The prime factors of a number are the prime numbers that multiply together to equal the original number. To find the prime factors of 48, you start by finding the smallest prime number that divides 48. In this case, it would be 2. So, you divide 48 by 2 to get 24. You then repeat this process until you are only left with prime numbers.

Here's a step-by-step breakdown:

48 ÷ 2 = 24

24 ÷ 2 = 12

12 ÷ 2 = 6

6 ÷ 2 = 3

Now, you're left with 2, 2, 2, 2, and 3, all of which are prime numbers. So the prime factors of 48 are 2´ (2 raised to the power of 4) and 3.

The number is 3.6

Algebra is a branch of mathematics that deals with symbols and the arithmetic operations across these symbols. These symbols do not have any fixed values and are called variables. In our real-life problems, we often see certain values that keep on changing. But there is a constant need to represent these changing values.

Given statement:

Five times the sum of a number and 6 is 48.

Let the number be x.

5(x+6)=48

x+6= 9.6

x= 9.6-6

x= 3.6

Hence, the number is 3.6.

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Answer:

50 mins

Step-by-step explanation:

Set up the following equation:

80-0.6m=100-1m

1) Add 1m to both sides:

80+0.4m=100

2) Subtract 80 from both sides:

0.4m=20

3) Divide both sides by 0.4:

m=50

Let me know if you have any difficulty understanding how I set up the equation!

Answer:

The number of lemon cookies is 75

Step-by-step explanation:

we know that

The total cookies are 300

Let

x ----> the number of lemon cookies

[tex]x=300(1-\frac{1}{2} -\frac{3}{20}-\frac{1}{10})[/tex]

Multiply by 20 both sides to remove the fractions

[tex]20x=300(20)-300(10)-300(3)-300(2)[/tex]

[tex]20x=1,500[/tex]

[tex]x=75[/tex]

therefore

The number of lemon cookies is 75

Answer:the geezer is right

Step-by-step explanation:

I'm not good with intigers, but if you added two negative intigers together wouldn't it still be negative? If you added -1 to -2 you'd get -3. It would always be less than the two original integers.

Answer:

The Answer is 4

Step-by-step explanation:

75 Miles divided by 5 Gallons is 15. Take that and divide 60 miles by 15. Your answer is 4 Gallons.

Hank's pickup consumes gas at a rate of 15 miles per gallon. To travel 60 miles, it would need 4 gallons of gas.

To solve this problem, you need to first establish the rate of gas consumption for Hank's pickup. According to the data given, we know that Hank's pickup travels 75 miles with 5 gallons of gas which gives us a rate of 15 miles per gallon. The next step is to find out how much gas Hank's pickup will consume to travel 60 miles. So you divide the 60 miles by the rate of consumption which is 15 miles per gallon. The result is 4 gallons. Therefore, Hank's pickup will need 4 gallons of gas to travel 60 miles.

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Answer: Yep! I agree

Step-by-step explanation: Ok to shows the 10 and 30 are proportional... This means 8 and n would be too

Answer:

The solution for x and y in (2x - 1) + (3y + 2)i = 5 – 4i cannot be determined.  

Solution:

From question, the equation given is

(2x - 1) + (3y + 2)i = 5 – 4i

Multiplying the terms inside the bracket (3y + 2) with i, the above equation becomes,

(2x – 1) + 3iy + 2i = 5 – 4i  

Removing the parenthesis in (2x – 1), the above equation becomes,

2x -1 + 3iy + 2i = 5 - 4i

2x – 1 + 3iy + 2i – 5 + 4i = 0  

Rearranging the terms, the above equation becomes

2x + 3iy + 4i + 2i -1 -5 = 0

2x + 3iy + 6i – 6 = 0

The above equation cannot be simplified further. Hence the solution for x and y cannot be determined.

Answer:

Option C.) 6x=320

Step-by-step explanation:

we know that

The Multiplication Property of Equality states that if you multiply both sides of an equation by the same number, the sides remain equal

we have

[tex]\frac{6x}{8}=40[/tex]

Apply the multiplication property of equality

Multiply by 8 both sides

[tex]\frac{6x}{8}(8)=40(8)[/tex]

[tex]6x=320[/tex]

therefore

The answer is the Option C

Answer:

Option C.

Step-by-step explanation:

Multiplication property of equality states that "if a number is multiplied to one side of the equation then other side of the equation should be multiplied with the same number".

The given equation is [tex]\frac{6x}{8}=40[/tex]

By the multiplication property of equality,

[tex]\frac{6x}{8}\times 8=40\times 8[/tex]

6x = 320

Option C will be the correct option.

Answer:

C=10π

Step-by-step explanation:

Circumference formula: C=πd (or C=2πr)

all of them except the last one is correct, the last one is C). -8, 5, 6, |-7|, 8, because it says least to greatest, the one you picked wasn't even put in greatest to least, but I think where you went wrong is the absolute value of -7, the absolute value of a number is shown with | ? |.

I hope you understand your mistake and won't make it again :)

Right for the most part but, 5 is C. –8, 5, 6, |–7|, 8

Good job overall tho :)

Answer:

53 students on each bus

Step-by-step explanation:

506-29=477 (take out the students that went by car)

477/9 = 53 (distribute 477 students evenly in 9 buses)

Answer:

-3

Step-by-step explanation:

Take negative 11 and add positive 8 to it because you are going in the positive direction.

The ratio of cranberry juice to apple juice to orange juice, when the drink consists of 1/3 apple juice and 1/2 orange juice, is 1:2:3.

The student asked for the ratio of cranberry juice to apple juice to orange juice in its simplest form, knowing that 1/3 of the drink is apple juice and 1/2 is orange juice. To find the fraction of the drink that is cranberry juice, we subtract the other two parts from the whole (which is 1):

1 - (1/3 + 1/2) = 1 - (2/6 + 3/6) = 1 - 5/6 = 1/6

So the ratio of cranberry juice to apple juice to orange juice can be written as:

Cranberry : Apple : Orange = 1/6 : 1/3 : 1/2

To compare ratios, we need to have the same denominator. Multiplying each part of the ratio by 6 (the least common multiple of 6, 3, and 2) gives us:

Cranberry : Apple : Orange = 1 : 2 : 3

Therefore, the ratio of cranberry juice to apple juice to orange juice in its simplest form is 1:2:3.

A)

5x+y=13

−x+2y=−7

Multiply each  term in the first equation by -2:

5x + y = 13 x -2 = -10x - 2y = -26

Now add that to the second equation:

-10x - 2y = -26 + −x+2y=−7

= -11x = -33

Divide each side by -11

X = -33 / -11

X = 3

Now you have x, replace it in the first equation and solve for y:

5(3) + y = 13

Simplify:

15 + y = 13

Subtract 15 from both sides:

y = 13 -15

y = -2

Solution = (3,-2)

B)

4x+5y=35

−3x+2y=−9

Multiply each term in the second equation by -2.5:

7.5x -5y = 22.5

Add this to the first equation:

4x+5y=35  + 7.5x -5y = 22.5

= 11.5x = 57.5

Divide both sides by 11.5:

x = 57.5 / 11.5

x = 5

Now you have x, replace x in one of the equations to solve for y:

4(5) + 5y = 35

Simplify:

20 + 5y = 35

Subtract 20 from both sides:

5y = 15

Divide both sides by 5:

y = 15/5

y = 3

Solution = (5,3)

Andre's Mistake in reasoning is assuming that 7 4/8 is equal to 7 1/2. Drawing a number line can prove that the fractions may be equivalent, but the whole numbers are not.

Andre made a mistake in his reasoning.

He incorrectly assumed that 7 4/8 is equal to 7 1/2. The fractions 4/8 and 1/2 are actually equivalent, but the whole numbers 7 and 7 are not.

To prove this, you can draw a number line and divide it into equal parts.

Taking the fractions 4/8 and 1/2, you will see that they represent the same distance, but they start at different points on the number line.

Therefore, 5 3/4 + 2 1/4 is not equal to 7 1/2.

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Answer:

Yes, it is divisible by three. The answer would be 280,249

Step-by-step explanation:

Answer:

<1

Step-by-step explanation:

I think its <1 as well

Answer:

Step-by-step explanation:

(x + 3)² − 5   because :

(x + 3)² − 5 = x² +6x+9 -5 =x²+6x+4

Answer:

B) [tex](x + 3)^2 - 5[/tex]

Step-by-step explanation:

the equation is: [tex]x^2 + 6x + 4[/tex]

we have an equation of the form

[tex]ax^2+bx+c[/tex]

where

[tex]a=1,b=6,c=4[/tex]

and we must complete the square to obtain a perfect square binomial,

we must add and substract the following:

[tex](\frac{b}{2a} )^2[/tex]

which is:

[tex](\frac{6}{2*1} )^2=3^2[/tex]

and then the equation becomes:

[tex]x^2 + 6x + 4+3^2-3^2[/tex]

where the terms [tex]x^2+6x+3^2[/tex] are the components of the perfect square binomial: [tex](x+3)^2[/tex]

and thus, the equation now is:

[tex](x+3)^2+4-3^2\\=(x-3)^2+4-9\\=(x+3)^2-5[/tex]

the answer is: B) [tex](x + 3)^2 - 5[/tex]

Answer:

option D is correct

the collection of all points on the same plane located 12cm from point Q

Answer:

Option D is correct

Step-by-step explanation:

A circle is a planar shape which has a point called center. All the points on the circle keep equal distance from the centre and the equal distance is called radius.

Here given that radius is 12 cm.  Since it is a circle it should be in a plane only.  Otherwise this will form a sphere.  So this lies in a plane with all points keeping equal distance of [tex]12 cm[/tex] from the center

Option D) the collection of all points on the same plane located 12 centimeters from point Q