x²-x-2(area)
x + 1(base)
The triangle above has an area of x2-x-2 and a
base of x + 1. What is the height of the triangle?​

Answer:

√37

Step-by-step explanation:

An irrational number is a number that never terminates nor repeats.

Let's go through each of the answer choices.

1) √100 is just 10. This is not irrational.

2) √81 is just 9. This is again not irrational.

3) √64 is 8. Not irrational.

4) √49 is 7. Again, not irrational.

5) √37 is 6.08276253... This number will never end and it doesn't repeat. Therefore, √37 is irrational.

And this is our answer.

And we're done!

Answer:

D. No. When the discriminant is less than zero, there are no real solutions.

Step-by-step explanation:

We have to notice that quadratic equations are second order polynomials whose standard form is:

[tex]y = a\cdot x^{2}+b\cdot x + c \cdot x[/tex], [tex]\forall \,a,b,c\,\in\,\mathbb{R}[/tex]

The factorized form of this polynomial is:

[tex]y = (x-r_{1})\cdot (x-r_{2})[/tex]

Where [tex]r_{1}[/tex] and [tex]r_{2}[/tex] are the roots of the quadratic equation, which may be real or complex.

If we equalize [tex]y[/tex] to zero and make algebraic handling, we can get the value of each root anatically by the Quadratic Formula:

[tex]r_{1,2} = \frac{-b\pm \sqrt{b^{2}-4\cdot a \cdot c}}{2\cdot a}[/tex]

Where [tex]b^{2}-4\cdot a\cdot c[/tex] is known as the discriminant. Then, we should remember the following rules:

i) If discriminant is greater than zero, then the quadratic equation has two different real roots.

ii) If discriminant is zero, then the quadratic equation has two equal real roots.

iii) If discriminant is less than zero, then the quadratic function has two complex roots.

In consequence, we came to the conclusion that statement is false, as quadratic equation have all roots real or all complex, but not one real and the other complex.

In a nutshell, the correct answer is D.

Answer:

Step-by-step explanation:

In the quadratic formula x = -b±√b²-4ac/2a, the expression b²-4ac inside the square root is called the discriminant. The discriminant is the function that determines the nature of the roots of the equation even without the constant a, b and c

If b²-4ac > 0, the roots of the equation will be real and distinct

If b²-4ac < 0 the roots of the equation will be complex number

If b²-4ac = 0 the roots of the equation will be real and the same

Answer:

-5

Step-by-step explanation:

You divide 80 by -16

Answer:

C

Step-by-step explanation:

(xy^3z^4)^4 =

(x)^4 = x^4

(y^3)^4 = y^12

(z^4)^4 = z^16

Therefore the answer is C. x^4 y^12 z^16

the answer  for your question is y=−2

Answer:

She was initially at a depth of 24.7 feet before she rose

Step-by-step explanation:

To get her initial depth, we need to understand how many feet she sank and rose.

Let us say she was initially at a depth which we can call  = x feet.

After 10 minutes she rose for 24.2 feet.

This means her new depth will be x - 24.2 ft.

We are also told that this new depth is actually 0.5 feet below sea level.

This means

x - 24.2 = 0.5

Now that we have this equation we can simply make x the subject of the formula and solve for x

x = 24.2 + 0.5 = 24.7

She was initially at a depth of 24.7 feet before she rose

Answer:

24.7

Step-by-step explanation:

Add 24.2 and 0.5

Answer:

x=16°

y=25°

Step-by-step explanation:

7x=112

x=112/7

x=16

90+y=115

y=115-90

y=25

Answer:

Probability of choosing 9 of spades = 1/52

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{ - 2x + 28}}}}}[/tex]

Step-by-step explanation:

[tex] \sf{2x + 4(7 - x)}[/tex]

Distribute 4 through the parentheses

[tex] \dashrightarrow{ \sf{2x + 28 - 4x}}[/tex]

Collect like terms

[tex] \dashrightarrow{ \sf{2x - 4x + 28}}[/tex]

[tex] \dashrightarrow{ \sf{ - 2x + 28}}[/tex]

Hope I helped!

Best regards! :D

Answer:

Lines

Step-by-step explanation:

In both linear and vertical pairs share at least one line.

Hope This Helps :)

All linear pairs and vertical pairs share the same supplementary angle.

Linear pairs and vertical pairs are both types of angle pairs formed by intersecting lines or by the intersection of a line and a transversal.

1. Linear Pairs: A linear pair consists of two adjacent angles formed by two intersecting lines. The two angles in a linear pair are always supplementary, meaning their measures add up to 180 degrees. In other words, if one angle in a linear pair measures x degrees, then the other angle will measure (180 - x) degrees.

2. Vertical Pairs: Vertical angles are formed by the intersection of two lines. They are opposite angles that share a common vertex but are formed by different pairs of intersecting lines. Vertical angles are congruent, meaning they have the same measure. If one vertical angle measures x degrees, then the other vertical angle formed by the same pair of intersecting lines will also measure x degrees.

Therefore, both linear pairs and vertical pairs share the same property of having angles with equal measures. In the case of linear pairs, the angles are supplementary (their measures add up to 180 degrees), while in vertical pairs, the angles are congruent (they have the same measure).

To know more about linear pairs, refer here:

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Steps to solve:

-2x = 38

~Divide -2 to both sides

x = -19

Since this equation is solvable, it is a literal equation

Best of Luck!

Answer:

The walk to the park took the longest amount of time

Step-by-step explanation:

In this question, we want to find the location that took Donovan the longest amount of time to work.

We should recall that an hour is 60 minutes

So time spent walking to the mailbox would be 2/15 * 60 = 8 minutes

Time spent walking to the library would be 1/6 * 60 = 10 minutes

Time spent walking to the park = 2/10 * 60 = 12 minutes

So as we can see, the distance taking the longest amount of time to walk is the Park which took a total of 12 minutes

Answer:

the answer is "dilation by a scale factor of 2 and a rotation of 90° counter clock wise about the origin"

Answer:

The sum of 5 times a number x and 8

Step-by-step explanation:

It could also be written as:

The sum of the product of 5 and a number x and 8

Answer:

B

Step-by-step explanation:

So we have the expression:

[tex]15+50[/tex]

Since 5 goes into both 15 and 50, we can factor out a 5. First, rewrite the numbers as:

[tex]5(3)+5(10)[/tex]

Factor out the 5:

[tex]=5(3+10)[/tex]

So, our answer is B

And we're done!

Answer:

31 over -3

Step-by-step explanation:

4.7+1.6=6.3x 5 =31.5-.5=31

Answer: 28

Step-by-step explanation:

Answer:

1 is 5+2a =7 and 2is 14+3a=3 and 3 is 7-2a=5

Answer:

1. 2x+5=7

2. 3x+14=2

3. 2x-7=5

4. 4x+2=-10

6. 3x-8=-14

6. (x/2)+3=7

7. 4x+2=14

8. (x/3)-8=5

9. 2x-3=11

10. 3x+7=25

Answer:

exponential functions.

Step-by-step explanation:

Answer:

x=4

Step-by-step explanation:

y=1/2x+3....equation 1

y=5....equation 2

Sub equation 2 in 1:-

5=1/2x+3

2=1/2x

x=4

Answer:

p=22x-17-15x+12-3x-5

4x-10

Step-by-step explanation:

hope it is helpful for you if it is follow me

Answer:

The maximum height that the football reached = 5.4 yards (16.2 feet)

Step-by-step explanation:

The initial location of the ball = 15 yard line

The final location of the ball = 35 yard line

The equation of the ball's motion can be modeled as follows;

y = -0.054·(x - h)·(x - k)

Where;

h and k are the x-intercepts which are the points where the ball lands or where the ball is in contact with the ground

Given that the kicker kicks the ball from the ground on the 15 yard line and the ball lands on the ground at the 35 yard line, we can write

h = 15 yard line

k = 35 yard line

Therefore;

y = -0.054·(x - 15)·(x - 35) = -0.054·x² + 2.7·x-28.35

The maximum height is found by differentiating the function with respect to x and equating the result to 0 as follows;

d(-0.054·x² + 2.7·x-28.35)/dx = 2.7 - 0.108·x = 0

x = 2.7/0.108 = 25

Therefor, at the maximum point, we have;

x = 25

∴ y = -0.054·(25 - 15)·(25 - 35) = -0.054×10×(-10) = 5.4

The maximum height that the football reached = 5.4 yards = 16.2 feet.

Answer:

[tex]x^3[/tex]

Step-by-step explanation:

To find the greatest common factor of a set of numbers, we need to find the greatest number, that when it's used as a divisor for all the numbers, returns an integer value.

We have the numbers [tex]x^3, x^6,[/tex] and [tex]x^9[/tex].

Exponent rules tell us that [tex]a^b \div a^c = a^{b-c}[/tex].

This means that each of these values must be raised to the power of three. Therefore, each of them can be divided by [tex]x^3[/tex].

[tex]x^3 \div x^3 = 1[/tex]

[tex]x^6 \div x^3 = x^3[/tex]

[tex]x^9 \div x^3 = x^6[/tex]

So [tex]x^3[/tex] is the GCF.

Hope this helped!

Answer:

The square root of 133 is 11.53. The closest to this number would be point D.

Answer:

3

Step-by-step explanation:

Evaluate x/4 + 6 (x - 12) where x = 12:

x/4 + 6 (x - 12) = 12/4 + 6 (12 - 12)

Hint: | Reduce 12/4 to lowest terms. Start by finding the GCD of 12 and 4.

The gcd of 12 and 4 is 4, so 12/4 = (4×3)/(4×1) = 4/4×3 = 3:

3 + 6 (12 - 12)

Hint: | Look for the difference of two identical terms.

12 - 12 = 0:

6×0 + 3

Hint: | Any number times zero is zero.

0×6 = 0:

0 + 3

Hint: | Simplify the expression.

Write 3 + 0 as 3:

Answer: 3

The answer is three.

Explanation:

Answer:

2√13

Step-by-step explanation:

B(1,4) T(4,6)  what is BD

find BT

d=√(x2-x1)²+(y2-y1)²

d=√(4-1)²+(6-4)²

d=√3²+2²

d=√9+4

d=√13 this is haf the distance

BD=2d=2√13

A line segment is also a line but a line with finite length and fixed endpoints. The length of BD is 2√13 units.

The distance or length of any line on the graph,

d = √[(x₂- x₁)² + (y₂- y₁)²]

where,

d = distance/length of the line between points 1 and 2,

(x₁ , y₁) = coordinate of point 1,

(x₂ , y₂) = coordinate of point 2,

Given the coordinate of B and T as (1,4) and (4,6), respectively. Therefore, the length of BT can be written as,

Length of BT = √[(x₂- x₁)² + (y₂- y₁)²]

                      = √[(4 - 1)² + (6 - 4)²]

                      = √[(3)² + (2)²]

                      = √(9 + 4)

                      = √13

Now, we can write the length of BD as the sum of BT and TD,

BD = BT + TD

Since T is the midpoint of BD, therefore, it will divide it into two equal parts, therefore, we can write,

BD = BT + BT

BD = 2(BT)

BD = 2√13

Hence, the length of BD is 2√13 units.

Learn more about the Length of the line here:

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Answer:

16

Step-by-step explanation:

Answer:

7000

Step-by-step explanation:

21000/0.667

=14000

21000-14000

=7000