Use the discriminant to determine the number of real solutions to the equation. 8n^2−7n=−7

Answer:

chk photo

Step-by-step explanation:

Answer:

11/12

Step-by-step explanation:

The product of One-fourth times three and two-thirds will be 1 / 2.

Multiplication is the process of determining the product of two or more numbers in mathematics. A product, or an expression that specifies factors to be multiplied, is what happens when you multiply two numbers in mathematics.

Given that, the numbers are one-fourth times three and two-thirds. The product of the numbers will be calculated as,

Product =  ( 1 / 4 ) x ( 3 ) x ( 2 / 3 )

Product = 6 / 12

Product = 1 / 2

Therefore, the product of One-fourth times three and two-thirds will be 1 / 2.

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Answer:

240cm^3

Step-by-step explanation:

3cmx20cmx4cm=240cm^3

Answer:

D (7a-3)/4

Step-by-step explanation:

7a – 4b = 3

Subtract 7a from each side

7a-7a – 4b = 3-7a

-4b = 3 -7a

Divide by -4

-4b/-4 = (3-7a)/-4

b = (7a-3)/4

Answer:

b = (7a - 3)/4

Step-by-step explanation:

7a - 4b = 3

=> -4b = 3 - 7a

=> b = (3 - 7a)/(-4)

=> b = -(3 - 7a)/4

=> b = (-3 + 7a)/4

=> b = (7a - 3)/4

Answer:

2x +11=21 and 2x+11=-21 it has 2 solutions because of the absolute value and to solve you would jist solve for X

Step-by-step explanation:

Let's start by finding the area of figure 1

The square:

15cm×15cm=225cm²

Then we're going to find the area of figure 2

it's a rectangle (A=L×W)

L=60cm-15cm(because those cm have been cut off)=45cm

W=40cm

Area=45cm×40cm

=1800cm²

Then we add up the sum

Area of 1+Area of 2

=225cm²+1800cm²

=2025cm²

Answer:

140 cm is the perimeter of the unshaded shape.

Step-by-step explanation:

Perimeter of the rectangle in whole = 2l + 2w

Where length is 60 cm and width is 40 cm.

P = 2 × 60 + 2 × 40

= 120 + 80

= 200 cm

To find the perimeter of the unshaded square = 4l

Where the length is 15 cm.

P = 4× 15

= 60 cm

To find the perimeter of the shaded shape = Perimeter of rectangle - Perimeter of unshaded square.

P = 200 - 60

= 140 cm

140 cm is the perimeter of the unshaded shape.

Answer:

  D.  $2071.20

Step-by-step explanation:

The table tells you that Bob's monthly payment on a 4-year loan at 6.5% will be $23.71 per thousand borrowed. The sum of those 48 payments is ...

  48 × $23.71 = $1138.08

That means, Bob pays $138.08 in total finance charge for each $1000 he borrows. He is borrowing 15 times $1000, so his total finance charge will be ...

  finance charge = 15 × $138.08 = $2071.20 . . . matches choice D

The answer will be 80 degrees

Step-by-step explanation:

50 +50 + x = 180 (Angle sum property of a triangle)

The angle sum property of a triangle:

[tex] \rm \large \rightarrow \: \: x \: + \: 50 \degree \: + \:50 \degree \: = \: 180 \degree[/tex]

[tex] \rm \large \rightarrow \: \: x \: + \: 100 \degree \: = \: 180 \degree[/tex]

[tex]\rm \large \rightarrow \: \: x \: = \: 180 \degree \: - \: 100 \degree[/tex]

[tex]\rm \large \rightarrow \: \: x \: = \: 80 \degree[/tex]

Step-by-step explanation:

Answer:

Step-by-step explanation:

The formula you need to solve for angle x is:

∠x = 1/2(large arc - small arc)

We have enough info to find what we need to solve for the arcs. 58° is an inscribed angle. The rays of the angle cut off an arc on the circle and that arc measure is twice the measure of the angle. So the smaller arc is 58 * 2 = 116. Since around the outside of the circle measures 360°, then the larger arc measures 360 - 116 = 244. So the larger arc is 244. Filling in the formula to solve for the angle x:

∠x = 1/2(244 - 116) and

∠x = 1/2(128) so

∠x = 64

D is your answer.

Answer:

D.) 64

Step-by-step explanation:

I got it correct on founders edtell

Answer:

i think it is 2

Step-by-step explanation:

Answer:

Explained below.

Step-by-step explanation:

(11)

Subtract the sum of (13x - 4y + 7z) and (- 6z + 6x + 3y) from the sum of (6x - 4y - 4z) and (2x + 4y - 7z).

[tex][(6x - 4y - 4z) +(2x + 4y - 7z)]-[(13x - 4y + 7z) + (- 6z + 6x + 3y) ]\\=[6x-4y-4z+2x+4y-7z]-[13x-4y+7z-6z+6x+3y]\\=6x-4y-4z+2x+4y-7z-13x+4y-7z+6z-6x-3y\\=(6x+2x-13x-6x)+(4y-4y+4y-3y)-(4z+7z+7z-6z)\\=-11x+y-12z[/tex]

Thus, the final expression is (-11x + y - 12z).

(12)

From the sum of (x² + 3y² - 6xy), (2x² - y² + 8xy), (y² + 8) and (x² - 3xy) subtract (-3x² + 4y² - xy + x - y + 3).

[tex][(x^{2} + 3y^{2} - 6xy)+(2x^{2} - y^{2} + 8xy)+(y^{2} + 8)+(x^{2} - 3xy)] - [-3x^{2} + 4y^{2} - xy + x - y + 3]\\=[x^{2} + 3y^{2} - 6xy+2x^{2} - y^{2} + 8xy+y^{2} + 8+x^{2} - 3xy]- [-3x^{2} + 4y^{2} - xy + x - y + 3]\\=[4x^{2}+3y^{2}-xy+8]-[-3x^{2} + 4y^{2} - xy + x - y + 3]\\=4x^{2}+3y^{2}-xy+8+3x^{2}-4y^{2}+xy-x+y-3\\=7x^{2}-y^{2}-x+y+5[/tex]

Thus, the final expression is (7x² - y² - x + y + 5).

(13)

What should be subtracted from (x² – xy + y² – x + y + 3) to obtain (-x²+ 3y²- 4xy + 1)?

[tex]A=(x^{2} - xy + y^{2} - x + y + 3) - (-x^{2}+ 3y^{2}- 4xy + 1)\\=x^{2} - xy + y^{2} - x + y + 3 +x^{2}- 3y^{2}+ 4xy -1\\=2x^{2}-2y^{2}+3xy-x+y+2[/tex]

Thus, the expression is (2x² - 2y² + 3xy - x + y + 2).

(14)

What should be added to (xy – 3yz + 4zx) to get (4xy – 3zx + 4yz + 7)?

[tex]A=(4xy-3zx + 4yz + 7)-(xy - 3yz + 4zx) \\=4xy-3zx + 4yz + 7 -xy + 3yz - 4zx\\=3xy-7zx+7yz+7[/tex]

Thus, the expression is (3xy - 7zx + 7yz + 7).

(15)

How much is (x² − 2xy + 3y²) less than (2x² − 3y² + xy)?

[tex]A=(2x^{2} - 3y^{2} + xy)-(x^{2} - 2xy + 3y^{2})\\=2x^{2} - 3y^{2} + xy-x^{2} + 2xy - 3y^{2}\\=x^{2}-6y^{2}+3xy[/tex]

Thus, the expression is (x² - 6y² + 3xy).

Answer:

x = 7

Step-by-step explanation:

y = (x – 7)^2 – 3

This equation is in vertex form

y = a(x-h)^2 +k

where (h,k) is the vertex

For a vertical parabola, the line of symmetry is x=h

x = 7

Answer:

b = 9

Step-by-step explanation:

Step 1: Add b on both sides (Addition Equality)

5/3b + 5 = 20

Step 2: Subtract 5 on both sides (Subtraction Equality)

5/3b = 15

Step 3: Divide both sides by 5/3 (Division Equality)

b = 9

Answer:

We know that the map is of North America:

The probabilities are:

1) North America:

As the map is a map of North America, you can point at any part of the map and you will be pointing at North America, so the probability is p = 1

or 100% in percentage form.

2) New York City.

Here we can think this as:

The map of North America is an extension of area, and New Yorck City has a given area.

As larger is the area of the city, more probable to being randomly choosen, so to find the exact probability we need to find the quotient between the area of New York City and the total area of North America:

New York City = 730km^2

North America = 24,709,000 km^2

So the probability of randomly pointing at New York City is:

P = ( 730km^2)/(24,709,000 km^2) = 3x10^-5 or 0.003%

3) Europe:

As this is a map of Noth America, you can not randomly point at Europe in it (Europe is other continent).

So the probaility is 0 or 0%.

Answer:

North America: certain

New York City: unlikely

Europe: impossible

Step-by-step explanation:

simply

Answer

pretty sure its a or c, sorry I cant be more specific

Step-by-step explanation:

Answer: D [tex]10\sqrt{2}[/tex]

Step-by-step explanation:

It says that the measure of angle B is 45 degrees. So if we were to put in 45 degrees  we could see that is is opposite AC and BC which we needs to find is the hypotenuse. So since we know the opposite of angle B  is 10 ft we can using that to find the length of BC.  Opposite hypotenuse is the sine function so we will use it to calculate the length of BC.

sin(45) = [tex]\frac{10}{BC}[/tex]       multiply both sides by BC  

BC sin(45) = 10      divide both sides by sin(45)

BC = [tex]\frac{10}{sin(45)}[/tex]

BC = [tex]10\sqrt{2}[/tex]

Answer:

[tex]\huge\boxed{Option\ D : \ BC = 10\sqrt{2}\ ft }[/tex]

Step-by-step explanation:

Since it's a right angled triangle, We'll use trigonometric rations.

Given that m∠B = 45°

So,

Sin B = opposite / hypotenuse

Where m∠B = 45°, opposite = 10 ft and hypotenuse = BC

Sin 45 = 10 / BC

[tex]\sf \frac{\sqrt{2} }{2} = \frac{10}{BC}[/tex]

BC = 20 / √2

Multiplying and Dividing by √2

BC = 20√2 / √(2)²

BC = 20 √2 / 2

BC = 10√2 ft

Answer: 4.5 oz/25.5 g = 1 oz/X g  

Step-by-step explanation: Crossed multiplies to solve for X.

Answer:

x > 6

Step-by-step explanation:

2x + 4 > 16

2x > 16 - 4

2x > 12

x > 12/2

x > 6

Answer:

XY = 24

Step-by-step explanation:

In similar triangles, the corresponding sides are in same ratio.

[tex]\frac{AC}{XZ}=\frac{AB}{XY}\\\\\frac{x+6}{30}=\frac{16}{2x-4}[/tex]

Cross multiply,

(x + 6 )(2x-4) = 16*30

Use FOIL method

x*2x + x*(-4) + 6*2x + 6*(-4) = 480

2x² - 4x + 12x - 24 = 480  {Combine like terms}

2x² + 8x - 24 = 480

2x² + 8x - 24 - 480 = 0

2x² + 8x - 504 = 0

Divide the entire equation by 2

x² + 4x - 252 = 0

Sum = 4

Product = -252

Factors = 18 , -14   {18 +(-14) = 4  & 18*(-14) = -254 }

x² + 4x - 252 = 0

x² + 18x - 14x - 252 = 0  {Rewrite middle term}

x(x + 18) - 14(x + 18) = 0

(x + 18)(x - 14) = 0

x - 14 = 0           {Ignore x + 18 = 0 as measurement will not come in negative}

x = 14

XY  = 2x - 4

    = 2*14 -4

     = 28 - 4

       = 24

Answer:

y is 60⁰

because all sides are equal

Answer:

60 degrees

Step-by-step explanation:

In an equilateral triangle, the angles are equiangluar and the sides are equal.

180 degrees in a triangle/3 sides =

= 60 degrees per side

Answer:

-60 and -28

Step-by-step explanation:

-60 + 42= -18

CHECK:

-42-18=-60

-56+-28=-84

CHECK:

-84+28=-56

Hope this helps <3 Need thanks? Comment /hearthelp

Answer:

-60

-28

Step-by-step explanation:

x +42 = -18

Subtract 42 from each side

x+42-42 = -18-42

x = -60

-56 +y = -84

Add 56 to each side

y = -84+56

y = -28

Answer:

The order is 4) → 5) → 6) → 7) → 2) → 1) → 3)

Please find diagram with the arrangements

Step-by-step explanation:

The horizontal width of an hyperbola

For

1) [tex]\dfrac{(y - 11)^2}{7^2} -\dfrac{(x - 2)^2}{6^2} = 1[/tex]

h = 2, k = 11

The widths are;

Horizontal (h - a, k) to (h + a, k) which is (2 - 7, 11) to (2 + 7, 11) = 14 units wide

(h, k - b) to (h, k + b) which is (2, 11 -6) to (2, 11 + 6) = 12 units wide

2)

[tex]\dfrac{(y - 1)^2}{5^2} -\dfrac{(x - 7)^2}{12^2} = 1[/tex]

h = 7, k = 1

(h - a, k) to (h + a, k) which is (7 - 5, 1) to (7 + 5, 1) = Horizontal width 10 units wide

(h, k - b) to (h, k + b) which is (7, 1 -12) to (7, 1 + 12) = 24 units wide

3) [tex]\dfrac{(x - 6)^2}{6^2} -\dfrac{(y + 1)^2}{3^2} = 1[/tex]

h = 6, k = -1

a = 8, b = 3

The widths are;

(6 - 8, -1) to (6 + 8, -1) Horizontal width = 16

(6, -1 - 3) to 6, -1 + 3) width = 6

4) [tex]\dfrac{(x - 4)^2}{2^2} -\dfrac{(y + 2)^2}{5^2} = 1[/tex]

h = 4, k = -2, a = 2, b = 5

(4 - 2, (-2)) to (4 + 2, (-2)) Horizontal width = 4

(4, -2 - 5) to (4, -2 + 5) width = 10

5) [tex]\dfrac{(y + 5)^2}{2^2} -\dfrac{(x + 4)^2}{3^2} = 1[/tex]

h = -4, k = -5, a = 2, b = 3

(-4 - 2, (-5)) to (-4 + 2, (-5)) Horizontal width = 4

(-4, -5 - 3) to (4, -5 + 3) width = 6

6) [tex]\dfrac{(y + 1)^2}{2^2} -\dfrac{(x - 1)^2}{9^2} = 1[/tex]

h = 1, k = -1, a = 2, b = 9

(1 - 2, (-1)) to (1 + 2, (-1)) Horizontal width = 4

(1, -1 - 9) to (1, -1 + 9) width = 18

7) [tex]\dfrac{(x + 7)^2}{4^2} -\dfrac{(y - 9)^2}{9^2} = 1[/tex]

h = -7, k = 9, a = 4, b = 9

(-7 - 4, 9) to (-7 + 4, 9) Horizontal width = 8

(-7,  9 -9) to (-7, 9 + 9) width = 18

Answer:

-3=x <13

Step-by-step explanation:

[tex] - 9 = \frac{2x}{3} - 7 < 5[/tex]

Multiply through by 3

[tex] - 27 = 2x - 21 < 15[/tex]

Add 21 to all sides

[tex] - 6 = 2x < 36[/tex]

Divide through by 2

[tex] - 3 = x < 18[/tex]

The solutin set is

[tex]{- 3 = x < 18}[/tex]

Answer:

[tex]length = x[/tex]

[tex]width = 2x - 3[/tex]

[tex]perimeter = 2(x + (2x - 3))[/tex]

[tex]51 = 2(3x - 3)[/tex]

[tex]51 = 6(x - 1)[/tex]

[tex]x - 1 = 8.5[/tex]

[tex]x = 9.5cm[/tex]

[tex]length = 9.5[/tex]

[tex]width = 2x - 3 = 2(9.5) - 3 = 16cm[/tex]

Answer:

DE = 11

Step-by-step explanation:

DF = DF +EF

4x+2 = x+7 + 7

Combine like terms

4x+2 = x+14

Subtract x from each side

4x+2-x = x+14-x

3x+2 = 14

Subtract 2 from each side

3x+2-2 =14-2

3x=12

Divide by 3

3x/3 = 12/3

x = 4

DE = x+7 = 4+7 =11

Answer:

DE is 11

Step-by-step explanation:

[tex]DE = DF - EF \\ DE = (4x + 2) - 7 \\DE = 4x - 5 [/tex]

But for x:

[tex]4x + 2 = (x + 7) + 7 \\ 4x + 2 = x + 14 \\ 3x = 12 \\ x = 4[/tex]

Therefore:

[tex]DE = (4 \times 4) - 5 \\ = 16 - 5 \\ = 11[/tex]

Number of links = 100

Shape of each link = Circle

Radius = 2.5

Area = πr²

= 3.14×2.5×2.5

= 19.625

Now for 100 links

19.625×100

1962.5Cm²

Cost = 1962.5 × 0.06

= $117.75

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If each link is made of thin silver wire and is in the shape of a circle of radius 2.5 cm, the value of the silver chain is $94.20.

To find the value of the silver chain, we need to calculate the total length of the silver wire used in making the chain and then multiply it by the cost per centimeter.

Each link in the chain is a circle with a radius of 2.5 cm. The circumference of a circle can be calculated using the formula 2πr, where r is the radius.

In this case, the circumference of each link is:

Circumference = 2 * 3.14 * 2.5 cm = 15.7 cm

Since there are 100 links in the chain, we multiply the circumference of each link by 100 to get the total length of the silver wire used:

Total length = 15.7 cm/link * 100 links = 1570 cm

Now, we can calculate the value of the chain by multiplying the total length of the silver wire by the cost per centimeter:

Value of the chain = 1570 cm * $0.06/cm = $94.20

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Answer:

c as in neither.

Step-by-step explanation:

the question does not give enough info because there are not two variables to be dependant on

Answer:  [tex]\sqrt{2}[/tex]

======================================================

Explanation:

Rewrite each trig function terms of sine and/or cosine. Then use the unit circle to find that,

[tex]\cot(90^{\circ})\cos(45^{\circ}) + \sec(45^{\circ})\\\\\frac{\cos(90^{\circ})}{\sin(90^{\circ})}\cos(45^{\circ}) + \frac{1}{\cos(45^{\circ})}\\\\\frac{0}{1}*\frac{\sqrt{2}}{2} + \frac{1}{(\sqrt{2})/2}\\\\\frac{2}{\sqrt{2}}\\\\[/tex]

Now rationalize the denominator

[tex]\frac{2}{\sqrt{2}}\\\\\frac{2\sqrt{2}}{\sqrt{2}*\sqrt{2}}\\\\\frac{2\sqrt{2}}{\sqrt{2*2}}\\\\\frac{2\sqrt{2}}{\sqrt{4}}\\\\\frac{2\sqrt{2}}{2}\\\\\sqrt{2}[/tex]

Which is the exact value of [tex]\sec(45^{\circ})[/tex]

The portion [tex]\cot(90^{\circ})*\cot(45^{\circ})[/tex] evaluates to 0 and goes away.

Answer:

(x+9)(x+9)

Step-by-step explanation:

To factor this expression, we first need to put into standard form, that is, [tex]ax^2 + bx + c[/tex].

So it becomes [tex]x^2 + 18x + 81[/tex]

Now we need to find two numbers that:

A. When multiplied get us c (81)

B. When added get us b (18)

9 and 9 match those requirements, so out product of two binomials for this becomes (x+9)(x+9).

Hope this helped!