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4 years ago

Are negative numbers bigger than positive numbers?

1 answer:

5 0

Nope. Negative numbers are smaller that positive numbers.

the number line looks like this.

-5_-4_-3_-2_-1_0_1_2_3_4_5

So the further the number is to the right the bigger the number. (positives)
The further a number to the left is a smaller number (negatives)

Good Luck! :)

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Please help... How many odd perfect squares are between 5 and 211?

frez [133]

Answer:

we conclude that the total number of perfect odd squares between 5 and 211 will be: 6

Step-by-step explanation:

Let us check by taking squares

3² = 9

5² = 25

7² = 49

9² = 81

11² = 121

13² = 169

As taking 14² = 256 would exceed 211, and 1² = 1 is smaller than 5.

Therefore, we conclude that the total number of perfect odd squares between 5 and 211 will be: 6

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3 years ago

Figure ABCD is a parallelogram.

Aleonysh [2.5K]

Answer:

13.

Step-by-step explanation:

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4 years ago

Read 2 more answers

What type of triangle is shown in the image?

frutty [35]

The triangle is an Obtuse triangle

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3 years ago

Read 2 more answers

1. $239 television; 10% discount 2. $72 game; 20% discount

Fiesta28 [93]

These are 16 questions and 16 answers

Answer:

See below and the attachment.

Explanation:

From 1 to 10, find the sale price to the nearest cent:

1. $239 television; 10% discount

$Sale\text{ }price=Orignal\text{ }price-discount\\ \\ Sale\text{ }price=\$239-10\%\times \$239=\\\\ Sale\text{ }price=\$239-0.10\times \$239=\\\\ Sale\text{ }price=\$239-\$23.9=\$215.10$

2. $72 game; 20% discount

You can also multiply by the factor (1 - % discount);

For instance for 20% discount, the factor is 1 - 20% = 1 -0.20 = 0.80. Which means that you can multiply the original price by the factor 0.80 to get the sale price:

$Sale\text{ }price=Orignal\text{ }price\times factor\\ \\ Sale\text{ }price=\$72\times(1-0.20)=\\\\ Sale\text{ }price=\$72\times0.80=\\\\ Sale\text{ }price=\$57.60$

3. $18.95 football; 15% discount

$Sale\text{ }price=Orignal\text{ }price\times factor\\ \\ Sale\text{ }price=\$18.95\times(1-0.15)=\\\\ Sale\text{ }price=\$18.95\times0.85=\\\\ Sale\text{ }price=\$16.11$

4. $10.99 CD; 25% discount

$Sale\text{ }price=Orignal\text{ }price\times factor\\ \\ Sale\text{ }price=\$10.99\times(1-0.25)=\\\\ Sale\text{ }price=\$10.99\times0.75=\\\\ Sale\text{ }price=\$8.24$

5. $149 MP3 player; 40% discount

$Sale\text{ }price=Orignal\text{ }price\times factor\\ \\ Sale\text{ }price=\$149\times(1-0.40)=\\\\ Sale\text{ }price=\$149\times0.60=\\\\ Sale\text{ }price=\$89.40$

6. $213 ski jacket; 30% discount

$Sale\text{ }price=Orignal\text{ }price\times factor\\ \\ Sale\text{ }price=\$213\times(1-0.30)=\\\\ Sale\text{ }price=\$213\times0.70=\\\\ Sale\text{ }price=\$149.10$

7. $595 refrigerator; 20% discount

$Sale\text{ }price=Orignal\text{ }price\times factor\\ \\ Sale\text{ }price=\$595\times(1-0.20)=\\\\ Sale\text{ }price=\$595\times0.80=\\\\ Sale\text{ }price=\$476.00$

8. $64 video game; 25% discount

$Sale\text{ }price=Orignal\text{ }price\times factor\\ \\ Sale\text{ }price=\$64\times(1-0.25)=\\\\ Sale\text{ }price=\$64\times0.75=\\\\ Sale\text{ }price=\$48.00$

9. $119 croquet set; 50% discount

You should not have problems with this: 50% discount means that you will pay half the price.

Hence, the sale price is:

$Sale\text{ }price=Orignal\text{ }price/2 \\\\ Sale\text{ }price=\$59.50$

10. $14.99 clock; 10% discount

$Sale\text{ }price=Orignal\text{ }price\times factor\\ \\ Sale\text{ }price=\$14.99\times(1-0.10)=\\\\ Sale\text{ }price=\$14.99\times0.90=\\\\ Sale\text{ }price=\$13.49$

11. A radio is on sale for $50. If this price represents a 10% discount from the original price, what is the original price to the nearest nickel? Hint: need to use a proportion to find the whole.

First note that if the discount is 10%, the sale price is 100% - 10% = 90% of the original price.

Let's set the proportion that represents the proportionality between the two ratios, starting with the fact that $ is the 90% and original price is the 100% (the whole part):

First ratio: $50/90

Second ratio: x /100

Proportion: first ratio = second ratio

$\$50/90=x/100$

Solve for x:

$x=100\times\$50/90=\$55.55$

Hence, the original price is $55.55

12. A box of laundry detergent is on sale for $6.50. If this price represents a 40% discount from the original price, what is the original price to the nearest cent?

Use the same hint used in the question above: set a proportion.

Remember a 40% discount means that the sale price is 60% of the original price:

$\$6.50/60=x/100\\ \\ x=100\times\$6.50/60=\$10.83$

13. Determine the price of a $35 basketball that is on sale for 50% off the regular price.

Again, 50% discount means that the sale price will be half of the original price, or the original price will be double of the sale price.

Here, the original price is $35, hence the sale price is $35/2 = $17.50

14. Dominic bought a new alarm clock that was on sale for $18.75. If this price represents a 30% discount from the original price, what is the original price to the nearest cent?

Since the price is after a 30% discount, the sale price is a 70% of the original price, and you set the proportion:

$\$18.75/70=x/100$

Solve for x:

$x=100\times\$18.75/70=\$26.79$

15. Michael bought a new fishing rod. The regular price of the fishing rod was $125.99. He bought it on sale with a 15% discount. Sales tax of 3% is applied to the discounted total. What was the sale price with tax of Michael’s fishing rod to the nearest cent?

First find the the sale price after the 15% discount:

$\$125.99\times(1-0.15)=\$125.99\times0.85=\$107.09$

Now add the 3% tax:

$\$107.09\times1.03=\$110.30$

Hence, the sale price with tax is $110.30

The last answer (# 16) is in the attached file, since this already exceeds the number of characters allowed.

7 0

4 years ago

X^2 - 10x + 21 = 0 which number would have to be added to complete the square

salantis [7]

Answer:

x = -3

x = -7

Step-by-step explanation:

Factoring x2+10x+21

The first term is, x2 its coefficient is 1 .

The middle term is, +10x its coefficient is 10 .

The last term, "the constant", is +21

Step-1 : Multiply the coefficient of the first term by the constant 1 • 21 = 21

Step-2 : Find two factors of 21 whose sum equals the coefficient of the middle term, which is 10 .

-21 + -1 = -22

-7 + -3 = -10

-3 + -7 = -10

-1 + -21 = -22

1 + 21 = 22

3 + 7 = 10 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 3 and 7

x2 + 3x + 7x + 21

Step-4 : Add up the first 2 terms, pulling out like factors :

x • (x+3)

Add up the last 2 terms, pulling out common factors :

7 • (x+3)

Step-5 : Add up the four terms of step 4 :

(x+7) • (x+3)

Which is the desired factorization

Equation at the end of step

(x + 7) • (x + 3) = 0

STEP

Theory - Roots of a product

2.1 A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one o

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation:

2.2 Solve : x+7 = 0

Subtract 7 from both sides of the equation :

x = -7

Solving a Single Variable Equation:

2.3 Solve : x+3 = 0

Subtract 3 from both sides of the equation :

x = -3

Supplement : Solving Quadratic Equation Directly

Solving x2+10x+21 = 0 directly

Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula

Parabola, Finding the Vertex:

3.1 Find the Vertex of y = x2+10x+21

Parabolas have a highest or a lowest point called the Vertex . Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) . We know this even before plotting "y" because the coefficient of the first term, 1 , is positive (greater than zero).

Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.

Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.

For any parabola,Ax2+Bx+C,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is -5.0000

Plugging into the parabola formula -5.0000 for x we can calculate the y -coordinate :

y = 1.0 * -5.00 * -5.00 + 10.0 * -5.00 + 21.0

or y = -4.000

Parabola, Graphing Vertex and X-Intercepts :

Root plot for : y = x2+10x+21

Axis of Symmetry (dashed) {x}={-5.00}

Vertex at {x,y} = {-5.00,-4.00}

x -Intercepts (Roots) :

Root 1 at {x,y} = {-7.00, 0.00}

Root 2 at {x,y} = {-3.00, 0.00}

Solve Quadratic Equation by Completing The Square

3.2 Solving x2+10x+21 = 0 by Completing The Square .

Subtract 21 from both side of the equation :

x2+10x = -21

Now the clever bit: Take the coefficient of x , which is 10 , divide by two, giving 5 , and finally square it giving 25

Add 25 to both sides of the equation :

On the right hand side we have :

-21 + 25 or, (-21/1)+(25/1)

The common denominator of the two fractions is 1 Adding (-21/1)+(25/1) gives 4/1

So adding to both sides we finally get :

x2+10x+25 = 4

Adding 25 has completed the left hand side into a perfect square :

x2+10x+25 =

(x+5) • (x+5) =

(x+5)2

Things which are equal to the same thing are also equal to one another. Since

x2+10x+25 = 4 and

x2+10x+25 = (x+5)2

then, according to the law of transitivity,

(x+5)2 = 4

We'll refer to this Equation as Eq. #3.2.1

The Square Root Principle says that When two things are equal, their square roots are equal.

Note that the square root of

(x+5)2 is

(x+5)2/2 =

(x+5)1 =

x+5

Now, applying the Square Root Principle to Eq. #3.2.1 we get:

x+5 = √ 4

Subtract 5 from both sides to obtain:

x = -5 + √ 4

Since a square root has two values, one positive and the other negative

x2 + 10x + 21 = 0

has two solutions:

x = -5 + √ 4

x = -5 - √ 4

Solve Quadratic Equation using the Quadratic Formula

3.3 Solving x2+10x+21 = 0 by the Quadratic Formula .

According to the Quadratic Formula, x , the solution for Ax2+Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by :

4 0

3 years ago