A class used cars and vans to go on a field trip because of the buses were already in use the use 12 vehicles to go on the trip each car holds for students in each van holds 11 students if 83 students went on the trip and how many of each type of vehicle did the class use
Please answer

Answer:

2 2/5

Step-by-step explanation:

5/6 x-4 = -2

Add 4 to each side

5/6 x-4+4 = -2+4

5/6 x = 2

Multiply by 6/5 to isolate x

6/5 *5/6 x = 6/5 *2

x = 12/5

Changing this from an improper fraction

5 goes into 12   2 times with 2 left over

x = 2  2/5

Answer:

H

Step-by-step explanation:

Solve each equation for y.

First equation:

8x + 6 = 2y

2y = 8x + 6

y = 4x + 3

This line has y-intercept 3, and slope 4.

Second equation:

12x - 3 = 3y

3y = 12x - 3

y = 4x - 1

This line has y-intercept -1 and slope 4.

Since the two lines have the same slope and different y-intercepts, they are parallel lines.

Answer: H

Answer:

The correct answer is H.

Step-by-step explanation:

In order to solve this exercise we have two paths. The first one uses less calculation than the second.

First way of solution: Isolate the variable [tex]y[/tex] in the right hand side of each equation. To do this you only need to divide the first equation by 2, and then divide the second equation by 3. Thus, you will obtain [tex]4x+3=y[/tex] and [tex]4x-1=y[/tex].

Now, notice that both lines have the same slope, so they are parallel. But before to give a definite answer we need to check if both lines are the same or not. Evaluate at [tex]x=0[/tex], in the first equation you have [tex]y=3[/tex] and in the second one [tex]y=-1[/tex]. As they have different intercepts with the X-axis, they parallel.

Second way of solution: Solve the system of equations. Isolate [tex]y[/tex] in the first equation:

[tex]4x+3=y[/tex].

Then, substitute this expression in the second equation:

[tex]12x-3=3(4x+3)[/tex]

[tex]12x-3=12x +9[/tex].

Which is equivalent to [tex]0=9+3[/tex] and this is impossible. Hence, the system of equations has no solution and the lines are parallel.

Answer:

B

Step-by-step explanation:

The function is

[tex]y=\sqrt{x-4}[/tex]

use the graph tool to visualize the graph as below

Answer:

B

Step-by-step explanation:

The given equation is :

[tex]y=\sqrt {x-4}[/tex]

This is a equation of a half parabola because general equation of a parabola with its as x-axis is:

[tex]y^2={x-a}[/tex]

Where a is the vertex of the parabola. If square root is taken, then there will be one positive and one negative. So,

The positive represents the upper side of the parabola.

Hence,  [tex]y=\sqrt {x-4}[/tex] represents upper parabola with x -axis is its axis and vertex at (4,0). Option B is correct.

Answer:

It's the last choice.

Step-by-step explanation:

1.  (3x - 2y)(3x -2y)

= 9x^2 - 12xy + 4y^2

The product is  (9x^2 - 4y^2) (9x^2 - 12xy + 4y^2)

which is neither a  difference of 2 squares  or perfect square trinomial.

2.  (3x - 2y)(3x + 2y)

= 9x^2 - 6xy + 6xy - 4y^2

= 9x^2 - 4y^2

and (9x^2 - 4y^2(9x^2 - 4y^2) is a perfect square.

Statement 4 is true about the product (9x² – 4y²)(3x – 2y) that if it is multiplied by (3x + 2y), the product of all of the terms will be a perfect square trinomial. This can be obtained by multiplying the product in the question with each term in the question and check whether the it is a  difference of squares or  a perfect square trinomial.

Difference of squares can be factored using the identity

    a²-b²=(a+b)(a-b)

Algebraic expressions in which there are three terms that can be obtained by multiplying a binomial with itself.

Formulas required,

  (a + b)² = a² + 2ab + b²

  (a - b)² = a² - 2ab + b²

Given product is, (9x² – 4y²)(3x – 2y)

Using difference of squares it can be written as, ((3x)² – (2y)²)(3x – 2y)

=(3x + 2y)(3x – 2y)(3x – 2y)

=(3x + 2y)(3x – 2y)²

(3x + 2y)(3x – 2y)²× (3x – 2y)

=(3x + 2y)(3x – 2y)³

This is not in the form of difference of squares.

(3x + 2y)(3x – 2y)²× (3x – 2y)

=(3x + 2y)(3x – 2y)³

This is not in the form of a perfect square trinomial.  

(3x + 2y)(3x – 2y)²× (3x + 2y)

=(3x + 2y)(3x – 2y)³

This is not in the form of difference of squares.

(3x + 2y)(3x – 2y)²× (3x + 2y)

=(3x + 2y)²(3x – 2y)²

=[(3x + 2y)(3x – 2y)][(3x + 2y)(3x – 2y)]

=(9x² – 4y²)(9x² – 4y²)

=(9x² – 4y²)² = (a - b)², where a = 9x² and b = 4y²

This is in the form of a perfect square trinomial.

Hence statement 4 is true about the product (9x² – 4y²)(3x – 2y) that if it is multiplied by (3x + 2y), the product of all of the terms will be a perfect square trinomial.

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Answer:

The correct answer option is A. $4,400.

Step-by-step explanation:

Cost of the tuition and fees for 1 year = $12,500

Grants and scholarships for 1 year = $6500

Cost of room and board for 1 year = $8200

Cost for work study for 1 year = $9800

So basically, Marcel pays = (tuition and fees + cost of room and board)

                                          = $12,500 + $8,200 = $20,700

He can pay through the (grants and scholarships + cost for work-study) =  $6,500 + $9,800 = $16,300

Therefore, Marcel needs to borrow = $20,700 - $16,300 = $4,400

Answer:

The answer is A

Step-by-step explanation:

Answer:

1/5

Step-by-step explanation:

There are 30 contestants.  16 are men, which means 14 are women.

All 14 women wear glasses.  Since 20 of the contestants wear glasses, that means there are 6 men who wear glasses.

So the probability that a randomly selected contestant will be a male with glasses is 6/30 or 1/5.

Answer:

20% markup

Step-by-step explanation:

10,000 x 1.20 = 12,000

Answer:

20%

Step-by-step explanation:

10,000×120%=12,000

Answer:

[tex]y+1=\dfrac{1}{3}(x+2)[/tex] - point-slope form

[tex]f(x)=\dfrac{1}{3}x-\dfrac{1}{3}[/tex] - function notation

Step-by-step explanation:

The point-slope form of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

From the graph we have the points (-2, -1) and (1, 0).

Substitute:

[tex]m=\dfrac{0-(-1)}{1-(-2)}=\dfrac{1}{3}[/tex]

[tex]y-(-1)=\dfrac{1}{3}(x-(-2))[/tex]

[tex]y+1=\dfrac{1}{3}(x+2)[/tex] - point-slope form

[tex]y+1=\dfrac{1}{3}(x+2)[/tex]          use the distributive property

[tex]y+1=\dfrac{1}{3}x+\dfrac{2}{3}[/tex]           subtract 1 = 3/3 from both sides

[tex]y=\dfrac{1}{3}x-\dfrac{1}{3}[/tex]

Answer:

Point slope form : [tex]y-0=\frac{1}{3}(x-1)[/tex]

Function notation : [tex]f(x)=\frac{1}{3}(x-1)[/tex]

Step-by-step explanation:

If a line passes through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], then the point slope form of line is

[tex]y-y_1=m(x-x_1)[/tex]

Where, m is slope.

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

From the given graph it is clear that he line passes through the points (-2,-1) and (1,0). Slope of the line is

[tex]m=\frac{0-(-1)}{1-(-2)}=\frac{1}{3}[/tex]

The point is (1,0) and slope is 1/3. So, the point slope form of the line is

[tex]y-0=\frac{1}{3}(x-1)[/tex]

[tex]y=\frac{1}{3}(x-1)[/tex]

Therefore the point slope form is [tex]y-0=\frac{1}{3}(x-1)[/tex].

Replace y by f(x) to write the equation in function notation.

[tex]f(x)=\frac{1}{3}(x-1)[/tex]

Therefore the function notation is [tex]f(x)=\frac{1}{3}(x-1)[/tex].

Answer:

B. All real numbers

Step-by-step explanation:

I assume the function is f(x) = 3^x, where x is an exponent.

Since an exponent can be a positive number, a negative number, and zero, x can be any real number. The domain of a function is the set of values that can be used for x.

Answer: B. All real numbers

For f(x) = 3*x

Domain of given function is B. All real numbers

It is a set of all values that gives a valid value if we put it in a function.

Any value which can be substituted in function and doesn't return infinity or  complex form is part of domain.

Check for which value f(x) can return infinite?

Answer is none.

for which value f(x) can give complex number?

Answer is none.

since there exists no such value for which f(x) return infinity or complex number, Domain of f(x) is all real numbers.

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Answer:

c. x = 6 only

Step-by-step explanation:

In order to calculate the zeros of f(x), we need to set it equal to zero and find the corresponding values of x.

[tex]x^{2}-12x+36=0[/tex]

Using the midterm breaking, we can split -12x into two such terms whose sum will be -12x and product will be 36x². These two terms are -6x and -6x

So, the above expression can be written as:

[tex]x^2-6x-6x+36=0\\\\ x(x-6)-6(x-6)=0\\\\ (x-6)(x-6)=0\\\\ (x-6)^{2}=0\\\\ x-6=0\\\\ x=6[/tex]

This means, the zero of f(x) occurs at x = 6 only.

Answer:

I believe it's A, because all triangles have 3 vertices.

Step-by-step explanation:

Answer:

Figure A

Step-by-step explanation:

We are given that a  statement

''If is is an triangle , then it has three vertices.

We have to find that which diagram represents the given statement

From first diagram

If triangle then it have three vertices because intersection of triangle and three vertices is triangle.

From second diagram

Intersection region of three vertices and triangle is three vertices.

So, from second diagram we cannot say if a triangle then it has three vertices.

Hence, figure A represent the given statement.

2 x 10^(10 - 2)

2 x 10^(8)

2 x 100,000,000

200, 000, 000

C. x=2

To complete the table, let's plug in the x-values into [tex]f(x)[/tex] and [tex]g(x)[/tex], so:

For [tex]f(x)[/tex]:

[tex]If \ x=0: \\ \\ f(0)=9(0)+7=7 \\ \\ \\ If \ x=1: \\ \\ f(1)=9(1)+7=16 \\ \\ \\ If \ x=2: \\ \\ f(2)=9(2)+7=25[/tex]

For [tex]g(x)[/tex]:

[tex]If \ x=-2: \\ \\ g(-2)=5^{-2}=0.04 \\ \\ \\ If \ x=-1: \\ \\ g(-1)=5^{-1}=0.2 \\ \\ \\ If \ x=2: \\ \\ g(2)=5^{2}=25[/tex]

From this, the complete table is:

[tex]\left|\begin{array}{c|c|c}x & f(x)=9x+7 & g(x)=5^{x}\\-2 & -11 & 0.04\\-1 & -2 & 0.2\\0 & 7 & 1\\1 & 16 & 5\\2 & 25 & 25\end{array}\right|[/tex]

From the table, you can see that [tex]f(x)=g(x)=25[/tex] when [tex]x=2[/tex] so the correct option is C. x=2. But what does [tex]x=2[/tex] mean? It means that at this x-value, the graph of the linear function [tex]f(x)[/tex] and the graph of the exponential function [tex]g(x)[/tex] intersect and the point of intersection is [tex](2,25)[/tex]

Step-by-step explanation:

Six less than five times a number is at least thirty- four

n - number

a)

5n - 6 ≥ 34           add 6 to both sides

5n ≥ 40           divide both sides by 5

n ≥ 8

b) in the attachment

c) n ∈ [8, ∞)

Answer:

-1 edge

Step-by-step explanation:

...

1st-1

2nd –i

I just did it on edge :D

Answer:

4(r+4)(r-4)

Step-by-step explanation:

If you factor it out, then it will be 4(r+4)(r-4). You can double check by multiplying it.

For this case we must factor the following expression:

[tex]4r ^ 2-64[/tex]

We take common factor 4:

[tex]4 (r ^ 2-16)[/tex]

We factor the expression within the parenthesis:

[tex]4 [(r-4) (r + 4)][/tex]

Finally we have that the factored expression is:

[tex]4 [(r-4) (r + 4)][/tex]

Answer:

[tex]4 [(r-4) (r + 4)][/tex]

Answer:

-19/40

Step-by-step explanation:

-3/8-1/10

Convert -3/8 to -15/40

Convert 1/10 to 4/40

-15/40-4/40=-19/40

Answer:

-19/40

Step-by-step explanation:

First thing to notice is they don't have a common denominator.

It is easy to see that 8 and 10 both go into 80 because 8(10)=80.

Let's see if we can think of smaller number 8 and 10 both go into.

8=2(2)(2)

10=2(5)

The greatest common factor of 8 and 10 is 2.

The least common multiple of 8 and 10 is 2(2)(2)(5)=40.

That first 2 was what they had in common and then I wrote down all the left over numbers from when we did the greatest common factor.

So 8 and 10 both go into 40.

8(5)=40 and 10(4)=40.

[tex]\frac{-3}{8}-\frac{1}{10}[/tex]

Multiply first fraction by 5/5 and second fraction by 4/4:

[tex]\frac{-3(5)}{8(5)}-\frac{1(4)}{10(4)}[/tex]

Simplify/Multiplied a little:

[tex]\frac{-15}{40}-\frac{4}{40}[/tex]

Wrote as one fraction since they had the same denominator:

[tex]\frac{-15-4}{40}[/tex]

Time to add 15 and 4 since they are both negative and their result also be negative:

[tex]\frac{-19}{40}[/tex]

Answer:

Step-by-step explanation:

Parallel lines have the ame slope.

The slope-intercept form of an equation of a line:

y = mx + b

m - slope

b - y-intercept

We have the line y = 3x → m = 3.

Therefore:

y = 3x + b            convert it to the standard form Ax + By = C

y = 3x + b                subtract 3x from both sides

-3x + y = b           change the signs

3x - y = -b      where b is any real number except 0.

The required standard of the parallel line to the line y = 3x is y = 3x + c.

Given that,

What is the standard form of the line parallel to the given line y=3x is to be determined.

A line can be defined by the shortest distance between two points is called a line.

The slope of the line is the tangent angle made by the line with horizontal. i.e. m =tanx where x in degrees.

Here, there is a property of the parallel lines that the slope of the equation is always the same. Thus
The equation of the line,
y = 3x
the slope of the above line is m = 3
A standard form of parallel line
y = mx +c

put the value of m in above equation,
Now the equation of the parallel lines can be given as y =3x + c

Thus, the required standard of the parallel line to the line y = 3x is y = 3x + c.

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Answer:

D)150 ≤ w ≤ 500

Step-by-step explanation:

Let  be the number of word in Kylie's essay.

We know that the essay has to have a minimum word count of 150, so the length of the essay must be greater or equal than 150 words; remember that in mathematics we say greater or equal with the sign: ≥, so we can express the statement as:

Which is equivalent to

We also know that the essay has to have a maximum word count of 500 words, so the length of the essay must be lest or equal than 500 words; remember that we can say the same using the symbol ≤, so we can express the statement as:

Now, we can join our tow inequalities in a compounded one:

The length w of an essay is typically represented by a compound inequality of form a < w < b, where a and b represent the range of acceptable lengths. Without specific details, we can't provide a more precise inequality.

From the question, it seems that the length w of the essay might be compared to a word count that is too short or too long. This could translate into an inequality such as a < w < b, where a and b represent the acceptable range of the essay length in words. Unfortunately, without specific values for 'too short' and 'too long', we cannot give a more precise answer. However, the type of compound inequality we are talking about is known as a 'conjunction' or 'and' inequality, represented by a < w < b or a ≤ w ≤ b if including the exact lower and upper bounds.

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Answer:

So we have (-1,3), (-2,2) and (-5,-1).

Step-by-step explanation:

So we need to find the equation of the line that is parallel to the blue line going through point P.

The slope of the blue line (count the rise/run) is 1/1=1.

Parallel lines have the same slope.  

So y=mx+b is the slope-intercept form where m is the slope and b is the y-intercept.

So since the blue line has slope 1 and parallel lines have the same slope then the line going through point P will have slope 1 too.

Point P is actually the y-intercept of the line going through P.

So the equation that is parallel to the blue line going through point P is y=1x+4. b was 4 because it was the y-intercept.

You can also just write y=1x+4 as y=x+4.

Testing the points:

(-4,2)?

Does y=x+4 for this point?  2=-4+4 which gives us 2=0 so no for this point.

(-1,3)?

Does y=x+4 for this point?  3=-1+4 which gives us 3=3 so yes for this point.

(-2,2)?

Does y=x+4 for this point?  2=-2+4 which gives us 2=2 so yes for this point.

(4,2)?

Does y=x+4 for this point?  2=4+4 which gives us 2=8 so no for this point.

(-5,-1)?

Does y=x+4 for this point?  -1=-5+4 which gives -1=-1 so yes for this point.

So we have (-1,3), (-2,2) and (-5,-1).

Answer:BCE

Step-by-step explanation:I jus did it on EDGE

Answer:

3 and 4: B

Step-by-step explanation:

As per the property of traversal lines, when two parallel lines are cut by traversal then the corresponding angles formed are equal.

In given case ∠6 is corresponding angle of ∠8 and ∠8 is corresponding to ∠18.

Hence option B is correct for 3 and statements!

If lines are ||, corresponding angles are equal.

Answer:

If lines are ||, corresponding angles are equal.

Step-by-step explanation:

yep

Answer:

∠DFE=119°

Step-by-step explanation:

step 1

Find the measure of angle BFD

we know that

The measure of the inner angle is the semi-sum of the arcs comprising it and its opposite.

so

∠BFD=(1/2)[arc BD+arc CE]

substitute the given values

∠BFD=(1/2)[38°+84°]

∠BFD=61°

step 2

Find the measure of angle DFE

we know that

∠BFD+∠DFE=180° -----> linear pair (supplementary angles)

substitute

61°+∠DFE=180°

∠DFE=180°-61°=119°

Answer:

d. the quantity of negative twenty plus sixteen i all over forty one.

Step-by-step explanation:

We want to simplify the complex number:

[tex]\frac{\sqrt{-16} }{(3-3i)+(1-2i)}[/tex]

We rewrite to obtain:

[tex]\frac{\sqrt{16}\times \sqrt{-1} }{(3+1)+(-3i-2i)}[/tex]

Recall that: [tex]\sqrt{-1}=i[/tex] and  [tex]-1=i^2[/tex]

We simplify to get:

[tex]\frac{4i}{4-5i}[/tex]

We rationalize to get:

[tex]\frac{4i}{4-5i}\times\frac{4+5i}{4+5i} [/tex]

[tex]\frac{4i(4+5i)}{(4-5i)(4+5i)}[/tex]

[tex]\frac{16i+20i^2}{4^2+5^2}[/tex]

[tex]\frac{16i-20}{16+25}[/tex]

[tex]\frac{-20+16i}{41}[/tex]

The correct answer is D

Answer:

t>2

Step-by-step explanation:

We are given:

3t+9>15.

Subtract 9 on both sides:

3t+9-9>15-9

Simplify:

3t+0>6

3t>6

Divide both sides by 3:

t>6/3

Simplify:

 t>2

Answer:

t > 2.

Step-by-step explanation:

3t + 9 > 15

3t + 9 - 9 > 15 - 9

3t  > 6

t > 2.

Answer:

f(x) = x

Step-by-step explanation:

f(x) = x is of the form y = mx + b.

y = mx + b is the slope-intercept form of the equation of a line, so its graph is a line.

f(x) = x^2 has a variable to the second power, so its graph is a parabola, and not a line.

f(x) = |x| has an absolute value, so its graph is shaped like a V. It is not a line.

Answer:

f(x) = (x+2)³(x²−7x+3)⁴

Step-by-step explanation:

The fundamental theorem of algebra (in its simplest definition), tells us that a polynomial with a degree of n will have n number of roots.

recall that the degree of a polynomial is the highest power that exists in any variable.

i.e.

polynomial, p(x) = axⁿ + bxⁿ⁻¹ + cxⁿ⁻² + .........+ k

has the degree (i.e highest power on a variable x) of n and hence has n-roots

In our case, if we expand all the polynomial choices presented, if we consider the 2nd choice:

f(x) = (x+2)³(x²−7x+3)⁴   (if we expand and simplify this, we end up with)

f(x) = x¹¹−22x¹⁰+150x⁹−116x⁸−2077x⁷+3402x⁶+11158x⁵−8944x⁴−10383x³+13446x²−5076x+648

we notice that the term with the highest power is x¹¹

hence the polynomial has a degree of 11 and hence we expect it to have exactly 11 roots

Answer:

B

Step-by-step explanation:

Just did it on edge2020

Answer:

A. 111.65

Step-by-step explanation:

This scenario can be interpreted like a triangle ABC where A and B are islands and C is the point from where the captain is 160 miles from island B.

a = 160

b = 260

c = 250

Law of cosines

[tex]c^2 = a^2 + b^2 - 2(ab)Cos(C)\\Arranging\ as\\2ab \ cos\ C = a^2+b^2-c^2\\2(160)(260)\ cos\ C = (160)^2+(260)^2- (250)^2\\83200\ cos\ C=25600+67600-62500\\83200\ cos\ C=30700\\cos\ C= \frac{30700}{83200}\\cos\ C=0.36899\\C = arccos\ (0.36899)\\C = 68.35[/tex]

The internal angle is 68.35°

We have to find the external angle to find the bearing the captain should turn

Using the rule of supplimentary angles:

The external angle = 180 - 68.35 = 111.65°

Therefore, the captain should turn 111.65° so that he would be heading straight towards island B.

Hence, option 1 is correct ..

Answer: Option 'a' is correct.

Step-by-step explanation:

Since we have given that

AB = 250 feet

AC = 260 feet

BC = 160 feet

We need to find the angle C that is heading straight towards island B.

We will apply "Law of cosine":

[tex]\cos C=\dfrac{a^2+b^2-c^2}{2ab}\\\\\cos C=\dfrac{160^2+260^2-250^2}{2\times 160\times 260}\\\\\cos C=0.368\\\\C=\cos^{-1}(0.368)\\\\C=68.40^\circ[/tex]

Exterior angle would be

[tex]180-68.40=111.65^\circ[/tex]

Hence, Option 'a' is correct.

No Solution

Brainliest Please :)

Answer:

6

Step-by-step explanation:

9^3 ÷2 the inverse is 9÷3×2 =9÷3=3×2=6 the answer is 6

Answer:

1) Parabola is opened up with no x-intercepts so the graph is fully above the x-axis which means all the y-coordinates in our points are positive so that is why the solution is all real numbers because it asked you to solve y>0 for x.

2) Parabola is opened up with no x-intercepts so the graph is fully above the x-axis which means all the y-coordinates in our points are positive so that is why the solution is all real numbers because it asked you to solve y>=0 for x.

3) Parabola is opened up with no x-intercepts so the graph is fully above the x-axis which means all the y-coordinates in our points are positive so that is why the solution is none because we are looking for when y<0 for x.  (y<0 means y is negative)

4) Parabola is opened up with no x-intercepts so the graph is fully above the x-axis which means all the y-coordinates in our points are positive so that is why the solution is none because we are looking for when y<=0 for x.  (y<=0 means negative or 0)

Step-by-step explanation:

[tex]y=ax^2+bx+c[/tex forms a parabola when graph assuming [tex]a \neq[/tex].

If [tex]a=0[/tex], we would have a parabola.

Anyways here are few things that might help when solving these:

1) Write ax^2+bx+c in factored form; it can lead to the x-intercepts quickly once you have it

2) The discriminant b^2-4ac:

    A) It tells you if you have two x-intercepts if b^2-4ac is positive

    B)  It tells you if you have one x-intercept if b^2-4ac is zero

    C)  It tells you if you have zero x-intercepts if b^2-4ac negative

3) If a>0, then the parabola opens up.

   If a<0, then the parabola opens down.

4)  You might choose to test before and after the x-intercepts too, using numbers between or before and after.

Let's look at questions labeled (1)-(4).

(1)  x^2-x+2>0

a=1

b=-1

c=2

I'm going to use the discriminant to see how many x-intercepts I have:

b^2-4ac

(-1)^2-4(1)(2)

1-8

-7

Since -7 is negative, then we have no x-intercepts.

The parabola is also opened up.

So if we have no-x-intercepts and the parabola is opened up (a is positive), then the parabola is above the x-axis.

So the y values for x^2-x+2 where y=x^2-x+2 is positive for all real numbers.

The solution to x^2-x+2>0 is therefore all real numbers.

(2)  x^2+5x+7>=0

a=1

b=5

c=7

b^2-4ac

(5)^2-4(1)(7)

25-28

-3

Since -3 is negative, we have no x-intercepts.

The parabola is also opened up because a=1 is positive.

So again x^2+5x+7>=0 has solutions all real numbers.

(3)  x^2-4x+5<0

a=1

b=-4

c=5

b^2-4ac

(-4)^2-4(1)(5)

16-20

-4

Since -4 is negative, we have no x-intercepts.

The parabola is opened up because a=1 is positive.

All the y-coordinates for our points are positive.

So y=x^2-4x+5<0 has no solutions because there are no y's less than 0.

(4)  x^2+6x+10<=0

a=1

b=6

c=10

b^2-4ac

6^2-4(1)(10)

36-40

-4

Since -4 is negative, the parabola has no x-intercepts.

The parabola is opened up because a=1 is positive.

All the y-coordinates on our parabola are positive.

So y=x^2+6x+10<=0 has no solutions because there are no y's less than 0 or equal to 0.