Find the discriminant and the number of real roots for this equation. x^2 + 2x + 8 = 0
A. -28; no real roots B. 32; one real root C. 32; two real roots D.-28; one real roof​

Answer: The value of x is 5.970.

Step-by-step explanation:

Given: The square has sides length of X cm.

Let r be the radius of the circle.

The square fits exactly inside a circle with each of the vertices being on the circumference of the circle.

Then diagonal of square = diameter of circle

i.e. [tex]\sqrt{2}x= 2r[/tex]    [Diagonal of square = [tex]\sqrt{2}[/tex](side)]

i.e. [tex]r=\dfrac{x}{\sqrt{2}}[/tex]

area of circle =[tex]\pi r^2[/tex]

i.e. [tex]56=\frac{22}{7}(\frac{x}{\sqrt{2}})^2[/tex]

[tex]56=\frac{22}{7}\times\frac{x^2}{2}\\\\\Rightarrow\ x^2= \dfrac{7}{11}\times56\\\\\Rightarrow\ x^2=35.636\\\\\Rightarrow\ x=\sqrt{35.636}\approx5.970[/tex]

Hence, the value of x is 5.970.

Answer:

(4, 0)

Step-by-step explanation:

D is clearly (1, 2).

so, for D' we have (1+3, 2-2) = (4, 0).

that's it. there is nothing more to it.

Answer:

y = ( x-4)(x+7)

Step-by-step explanation:

When we know the zeros of the equation, we can write the equation in the form

y= a(x-z1) (x-z2)   where a is a constant and z1 and z2 are the zeros (solutions)

y = a( x-4)(x--7)

y =a( x-4)(x+7)

Since its says write an equation, we can pick a and I will let a=1

y = ( x-4)(x+7)

Answer:

a,

Step-by-step explanation:

Answer:

58.33%

Step-by-step explanation:

A's Contribution = 2700

B's Contribution= 1800

Ratio = 7:5

Profit = 900

Total Ratio = 7+5 = 12

First , Calculate both share of the profit.

A's Share= 7/12 ×900

525

B's share= 5/12 ×900

375

Now , express A's Share as a percentage

A's Share= 525/900 ×100

58.33%

Answer:

Step-by-step explanation:

4986 ounces/m³

Step-by-step explanation:

1 kilogram = 35.274 ounces

1 cubic foot = 0.0283 cubic metre

We are converting kg/ft³ to ounces/m³

Hence:

4kg/ft³ × 35.274 ounces/ 1 kg × 1 ft³/0.0283m³

= 4985.7243816 ounces/m³

Approximately to the nearest whole number = 4986 ounces/m³

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The density of the material is approximately 123 ounces per cubic meter.

Density [tex](\(D\))[/tex] is defined as mass [tex](\(m\))[/tex] per unit volume [tex](\(V\))[/tex], and it is calculated using the formula:

[tex]\[ D = \frac{m}{V} \][/tex]

In this case, the density is given in kilograms per cubic foot. To convert this to ounces per cubic meter, we need to perform the following steps:

Step 1: Convert kilograms to ounces:

1 kilogram = 35.27396 ounces

Step 2: Convert cubic feet to cubic meters:

1 cubic foot = 0.0283168 cubic meters

Now, let's substitute the given values and perform the conversion:[tex]\[ \text{Density in ounces per cubic meter} = \frac{4 \, \text{kg} \times 35.27396 \, \text{ounces/kg}}{1 \, \text{cubic foot} \times 0.0283168 \, \text{cubic meters/cubic foot}} \][/tex]

Solving this equation gives us the density in ounces per cubic meter:

[tex]\[ \text{Density} \approx 123 \, \text{ounces/m}^3 \][/tex]

Rounded to the nearest whole number, the density of the material is approximately 123 ounces per cubic meter.

In summary, we converted the given density from kilograms per cubic foot to ounces per cubic meter using unit conversions.

This involved converting the mass units and volume units before performing the calculation to obtain the final density value in the desired units.

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Answer:

The area of the circular garden is approximately 7.1 square yards

Step-by-step explanation:

The given parameters are;

The area surrounding the circular garden = A rectangular grassy area

The area of the circular garden ≈ (1/2) × The base of the grassy rectangular area

The dimensions of the base of the rectangular grassy area = 6 yards by 3 yards

The diameter of the circle, D = 3 yards

The area of the rectangular grassy area = 6 yards × 3 yards = 18 yards²

∴ The approximate area of the circular garden = (1/2) × 18 yards² = 9 yards²

The area of the circular garden, A = π·D²/4

∴ A = 3.14 × (3 yards)²/4 = 7.065

The area of the circular garden, A ≈ 7.1 yd².

Answer:

-2

Step-by-step explanation:

x = the number

difference refers to subtraction

(8*x) - 3 = -19

8x - 3 = -19

      + 3   + 3

8x = -16

/ 8    /8

x = -2

Hope that helps!

Answer:

- 2

Step-by-step explanation:

let the number be n , then

8n - 3 = - 19 ( add 3 to both sides )

8n = - 16 ( divide both sides by 8 )

n = - 2

The number is - 2

Answer:

TN = 13 units

MP = 22 units

TQ = 6.93 units

PT = 13 units

Step-by-step explanation:

If T is a circumcenter of the given triangle MNP,

Measure of TN = Measure of TM = Measure of TN

By applying Pythagoras theorem in ΔMRT,

MT² = TR² + MR²

MT² = (12)² + 5²

MT = [tex]\sqrt{169}[/tex]

MT = 13

Measure of TN = 13 units

Since, TQ, TS and RT are the perpendicular bisectors of the sides MP, NP and MN respectively,

Measure of MP = 2(PQ)

                         = 2(11)

                         = 22 units

By applying Pythagoras theorem in ΔTQM,

MT² = TQ² + MQ²

(13)² = TQ² + (11)²

TQ = [tex]\sqrt{169-121}[/tex]

TQ = [tex]\sqrt{48}[/tex]

TQ = 6.93

Measure of PT = Measure of TN = 13 units

Answers:

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

Explanation:

Answer:

Simultaneous equations

Step-by-step explanation:

4a + 7m = 17.75

2a + 5m = 10.75

Double the 2nd equation and then subtract the two equations to cancel the 4a out

Work with the 'm' terms and find the value of m

After finding the value of 'm', substitute it into one of the original equations (the ones given in the question) and solve to find the value of 'a'

Hope this helped

Answer:

34 units

Step-by-step explanation:

Perimeter of ∆ABC is,

2(6+4+7)

= 2×(17)

= 34

Answered by GAUTHMATH

Answer:

[tex]8\sqrt{5}+3\sqrt{30}[/tex]

Step-by-step explanation:

When we have any quantity being multiplied to an expression, we can use the distributive property.  The distributive property says that [tex]a(b+c)=ab+ac[/tex].  In other words, we can distribute the outer number inside the parentheses.  

Using the distributive property, we can then simplify the given equation as follows:

[tex]\sqrt{5}(8+3\sqrt{6})=8\sqrt{5}+3\sqrt{6}\sqrt{5}[/tex]

Finally, you should recall that when multiplying square roots, you can simply bring all the numbers inside of one root.  For instance, [tex]\sqrt{2}*\sqrt{3}=\sqrt{2*3}=\sqrt{6}[/tex] (note, this does not work for addition or subtraction, only multiplication or division).  Therefore, we can simplify [tex]\sqrt{6}\sqrt{5}=\sqrt{6*5}=\sqrt{30}[/tex].  

Finally, we can combine our answer into [tex]\sqrt{5}(8+3\sqrt{6})=8\sqrt{5}+3\sqrt{6}\sqrt{5}=8\sqrt{5}+3\sqrt{30}[/tex]

Answer:

The height of the tree is 6.12 meters and the height of the building is 33.12 meters.

Step-by-step explanation:

Since the person is 1.8 meters tall, HC = 1.8

And since their shadow is 10 meters long, HD = 10.

We are also given that GH is 24 meters and that FG is 150 meters.

Height of the Tree:

The height of the tree is given by GB.

Again, since m∠BGD = m∠CHD = 90°, ∠BGD ≅ ∠CHD.

Likewise, ∠D ≅ ∠D. So, by AA-Similarity:

[tex]\displaystyle \Delta BGD\sim \Delta CHD[/tex]

Corresponding parts of similar triangles are in proportion. Therefore:

[tex]\displaystyle \frac{GB}{GD}=\frac{HC}{HD}[/tex]

Note that:

[tex]GD=GH+HD[/tex]

Find GD:

[tex]GD=(24)+(10)=34[/tex]

Substitute the known values into the proportion:

[tex]\displaystyle \frac{GB}{34}=\frac{1.8}{10}[/tex]

Cross-multiply:

[tex]10GB=61.2[/tex]

Therefore:

[tex]GB=6.12\text{ meters}[/tex]

The height of the tree is 6.12 meters.

Height of the Building:

The height of the building is given by FA.

Since m∠AFD = m∠CHD = 90°, ∠AFD ≅ ∠CHD.

∠D ≅ ∠D. So, by AA-Similarity:

[tex]\Delta AFD\sim \Delta CHD[/tex]

Corresponding parts of similar triangles are in proportion. Therefore:

[tex]\displaystyle \frac{FA}{FD}=\frac{HC}{HD}[/tex]

Note that:

[tex]FD=FG+GH+HD[/tex]

Find FD:

[tex]FD=(150)+(24)+(10)=184[/tex]

Substitute the known values into the proportion:

[tex]\displaystyle \frac{FA}{184}=\frac{1.8}{10}[/tex]

Cross-multiply:

[tex]10FA=331.2[/tex]

Therefore:

[tex]FA=33.12\text{ meters}[/tex]

The height of the building is 33.12 meters.

Answer:

The answer would be B

Answer:

-2

Step-by-step explanation:

We know that the object is at 12 on a horizontal line.

The horizontal line of a graph is the x axis, so lets think of 12 as 12x

On a graph, left is negative, and right is postive.

In this case we need to move 14x to the right, or -14x.

We start at 12x, so its going to be:

12x-14x=-2x

So -2 is the postition of the object on the x axis.

This is answer B.

Hope this helps!

Answer:

Step-by-step explanation:

100 sq cm

The value of x is 13 in the rhombus ABCD

A quadrilateral is a four-sided polygon, having four edges and four corners

In figure ABCD is a rhombus

Given as Angle ∠ A = (5x + 25)

Angle ∠ D = (7x - 1)

Since adjacent angles of a rhombus add up to 180°

(5x + 25) + (7x - 1) = 180 and both equal

So, 5x + 25 = 7x - 1

Rearrange the terms in the equation,

7x - 5x = 1 +25

2x = 26

x = 13

Hence, the value of x is 13 in given figure.

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Answer:

The answer is no.d b= 2a + 1

Explanation:

Each time b goes up by 4, 'a' goes up by 2. The rate of change or slope is 4/2 = 2. This lets us see that the answer must be choice D, as no other answer choice has 2 as a slope.

Answer:

Step-by-step explanation:

2(9a - 6) = 2*9a - 2*6 = 18a - 12    

Yes, it is equivalent.

6*(3a-2) = 6*3a - 6*2 = 18a - 12

Yes, it is equivalent.

-3(6a+4)= -3*6a + 4*(-3) = -18a - 12

No, not equivalent

3(6a+4) = 3*6a + 3*4 = 18a + 12

No, not equivalent

-3(4-6a) = -3*4  - 6a*(-3 )  = -12 + 18a = 18a - 12

Yes, it is equivalent.

Answer:

Step-by-step explanation:

2(9a - 6) = 2 × 9a + 2 × (-6)

= 18a - 12

6(3a - 2) = 6 × 3a + 6 × (-2)

= 18a - 12

- 3( 4 - 6a ) = - 3 × 4 + (-3) × (- 6a)

= - 12 + 18a = 18a - 12

Step-by-step explanation:

When X is - 5 then y is 3

When X is-1 then y is - 2

When X is 3 then y is -4

From the graph we get, when x is - 5 then y is 3, when x is -1 then y is - 2, and when x is 3 then y is -4.

A point is a dot in space used to indicate an exact location in space.

Consider the first line, which has constant y values. its x value ranges from -1 to negative infinity.

The second line is starts from (-1,-2) point and tend towards positive infinity but its y values and x values are varying.

Hence, when x = -5 y is 3 and at x = -1 the y values is -2. Similarly, when x = 3 then y = -4.

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Answer:

Between 32 and 37

Step-by-step explanation:

Here, we simply want to get the data portion represented by the box alone

we can see that the box starts from 32

It ends at the number 37

Note;

between each individual number on the plot, we have 5 small lines indicating an extra point

Answer:

∅ = 44.9º

Step-by-step explanation:

sin = opp/hyp

Assuming ∅ is the top angle

∅ = arcsin(353/500)

use calculator

∅ = 44.910389254710144

∅ = 44.9º

Answer:

k = ±4

Step-by-step explanation:

Equation of the circle is:

x² + y² = 5​

This means from the general form of equation of a circle;

Centre coordinates is (0, 0) and radius is; √5.

The line 2x - y + k = 0 touches the circle. Thus, perpendicular distance from centre of the circle to this line is equal to the circle radius;

Thus;

|((2 - 0) - (1 × 0) + k)|/(√(2² + 1²)) = √5

|(1 + k)|/√5 = √5

Multiply both sides by √5 to get;

|1 + k| = 5

|k| = 5 - 1

k = ±4

Answer:

i guess you'll get that answer

Step-by-step explanation:

if xy is 3cm then y is 3 divide by 2

where y=

then if xyz=30 to get z you divide 30 by 3

where z=

then x will surely be the same value as y

so u solve for yz=x

Answer:

triangle - 7

Step-by-step explanation:

Because Evan has 7 less pencils than isiah, the number of pencils evan has can be determined by subtracting 7 from the number of pencils isaish has

triangle - 7

If evan had 7 more pencils : triangle +  7