what are the roots of the quadratic equation below 2x ^ 2 - 12x + 13=0 PLEASE HELP

Hi there! :)

Answer:

a = -9

Step-by-step explanation:

Starting with:

2/3a = -15 - a

Solve for 'a' by isolating the variable:

2/3a = -15 - a

On the right-hand side of the equal sign, make 'a' have a common denominator of 3 to make the simplifying easier:

2/3a = -15 - 3/3a

Add 3a/3 to both sides:

5/3a = -15

Divide both sides by 5/3, or multiply by its reciprocal (3/5)

5/3a(3/5) = -15(3/5)

a = -9

Answer:

x = 35/22

y = 3/22

Step-by-step explanation:

y= 2/5x-1/2 ................(1)

y=-1/3x+2/3 ...............(2)

10*(1)

10y = 4x -5 ...................(1A)

3*(2)

3y = -x +2  ....................(2A)

To find intersection, solve for y & x

4(2A) + (1A)

12y+10y = -4x+4x +8-5

22y = 3

y = 3/22

Substitute in (1)

3/22 = 2/5x -1/2

multiply by 110

15 = 44x - 55

70 = 44x

x = 70/44 = 35/22

Answer:

Step-by-step explanation:

hello,

how many students ? 14 + 2 + 5 +3 = 24

how many students who had C and S ? 14 + 2 + 5 = 21

so P(C∪S)=21/24=(7*3)/(8*3)=7/8

hope this helps

Answer:

The answer is option B.

The second graph.

Hope this helps you

Answer:

20 cm^2.

Step-by-step explanation:

If the scale factor is 2 each of the sides of the figure will be increased by a factor 2.

So each side will have a length of 2 * 1 = 2 centimeters.

It will consist of 5 squares of dimension 2*2 =  an area of 4 cm^2

So the area of the new cross  is 5*4 = 20 cm^2.

We can also calculate the area directly by multiplying  by 2^2 ( the scale factor)squared.)

The original area = 5 so the area of the enlarged figure = 5 * 2^2 = 20 cm^2.

Answer:

A

Step-by-step explanation:

Here, we are tasked with finding the order of magnitude.

What we are basically asked here is to write the number in powers of ten.

Thus

4,000,000 = 4 * 10^6

We can see that 10 is raised to the power of six here and thus we can say that the order of magnitude here is simply 6

Answer:

0.667

Step-by-step explanation:

According to Bayes theorem:

Since there are three cards, the probability that the side is green = 1/3

For the first card, if one side is green, the probability that the other side is also green = 1 (both sides are green)

For the second card, if one side is green, the probability that the other side is also green = 0 (both sides are red)

For the third card, if one side is green, the probability that the other side is also green = 1/2 (one side is green and the other side is red)

[tex]P(G_k/A)=\frac{P(G_k)P(A/G_k)}{\Sigma_{i=1\ to\ m} P(G_i)P(A/G_i)} \\P(B_1/A)=\frac{P(G_1)P(A/G_1)}{P(G_1)P(A/G_1)+P(G_2)P(A/B_2)+P(G_3)P(A/G_3)}\\ P(B_1/A)=\frac{1/3*1}{(1/3*1)+(1/3*0)+(1/3*1/2)=\frac{1/3}{1/2} }=0.667[/tex]

Answer:

D. The data are discrete because the data can only take on specific values.

Step-by-step explanation:

Continuous variables are variables that can take on any value in an interval. Examples of continuous variables are length, time, etc.

Discrete variables on the other hand are variables that can only take on specific values.

The durations of movies in minutes can only take on integer values from 0 to 60. Therefore, it is a discrete data.

The correct option is D.

Answer:

A.louis drive a chevolet

Step-by-step explanation:

from the question three different people drive different cars . since two out of the three people has been excluded from driving a particular car i.e the third person is the one driving Chevrolet

Answer:

A

Step-by-step explanation:

To determine if a point lies on the curve, substitute the x- coordinate into the equation. If the value obtained is equal to the y- coordinate then the point lies on the curve, that is

A

y = ([tex]\frac{3}{2}[/tex] )² = [tex]\frac{9}{4}[/tex] ≠ [tex]\frac{9}{2}[/tex] ← not on line

B

y = (- 1)² = 1 ← lies on line

C

y = 4² = 16 ← lies on line

D

y = ([tex]\frac{1}{2}[/tex] )² = [tex]\frac{1}{4}[/tex] ← lies on line

Answer:

(2 a - b) (18 a - 9 b - 4)

Step-by-step explanation:

Factor the following:

9 (2 a - b)^2 - 4 (2 a - b)

Factor 2 a - b out of 9 (2 a - b)^2 - 4 (2 a - b):

(2 a - b) (9 (2 a - b) - 4)

9 (2 a - b) = 18 a - 9 b:

Answer: (2 a - b) (18 a - 9 b - 4)

Answer:

A. 12 for every 7

Step-by-step explanation:

There are 12 peas in her bowl.

There are 7 peas in her hair.

The ratio of peas in her bowl to peas in her hair is 12 for every 7.

Answer:

(3) =  119

(4) =  119

Step-by-step explanation:

Given isosceles triangle with vertex angle 58.

Need exterior angles of base angles 1 & 2.

Solution:

Vertex angle = 58.

Base angle = x

Sum of triangles = 180 =>

x + x + 58 = 180

Solve for x

x = (180-58)/2 = 122/2 = 61

Exterior angles are supplementary to interior (base) angles, so

(3) = 180-(1) = 180 - 61 = 119

(4) = 180-(2) = 180 - 61 = 119

* note: supplementary means sum of two angles = 180.

The measurements of angle 3 and angle 4 are​ 119degrees and 119degrees respectively.

The sum of the interior angle of the triangle is 180degrees.

According to the diagram shown:

m<1 + m<2 + 58 = 180

Since <1 = <2, hencce:

m<1 + m<1 + 58 = 180

2m<1 = 180 - 58

2m<1 = 122

m<1 = 122/2

m<1 = 61 degrees

Since <1 = <2, thereofore m<3 = m<4

Get the measure of m<3

m<1 + m<3 = 180 (supplementary angles)

61 + m<3 = 180

m<3 = 180 - 61

m<3 = 119 degrees

Recall that m<3 = m<4, hence m<4 = 119degrees

The measurements of angle 3 and angle 4 are​ 119degrees and 119degrees respectively.

Learn more here: https://brainly.com/question/21680544

I hope this helps you

Sphere Surface Area Formula is

4.pi.r^2

4.pi.13^2

4.pi.169

676.pi

The surface area of the sphere with radius 13 units is S = 676π units²

A sphere is a three-dimensional geometrical object that is perfectly round in shape. A sphere is a fully spherical, three-dimensional geometrical object. Every point on its closed surface is equally spaced from the centre, which is the only point on the surface.The distance from the center to any point on the surface of the sphere is known as the radius of the sphere..

Surface Area of a Sphere = 4πr²

Volume of a Sphere = ( 4/3 ) πr³

where r is the radius of the sphere

They are used to represent many natural and man-made objects such as planets, basketballs, and molecules.

Let the data be ,

Let r = 13 units be the sphere's radius.

Let S be the sphere's surface area.

And , Surface Area of a Sphere = 4πr²

On simplifying , we get

S = 4π ( 13 )²

S = 4π ( 169 )

S = 676π units²

Thus, the sphere's surface area is S = 676 units2.

Click here to discover more about spherical.

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Answer:

no, it does not

Step-by-step explanation:

Hello

-x+4y=-5

so

[tex]4y = x-5\\<=> y=\dfrac{1}{4}x-\dfrac{5}{4}[/tex]

we say that y varies directly with x if y=kx

in this example we have an additional constant, the graph is not a line through the origin so this is not a direct variation

hope this helps

Answer:

the true statements are A. The range for this function is the set (-5) D. The domain for this function is the set(-5)

Answer:

Hey there!

Your answer would be x/2 - 9

Answer:

2 ÷ x - 9

Step-by-step explanation:

Quotient of two is written as = 2 ÷ x

Nine less is written as = -9

Final answer = 2 ÷ x - 9

Hope this helped! :)

Answer:

B(3.5, 0.5)

Step-by-step explanation:

Given:

A(5,5), Xa=5, Ya=5

C(3,-1), Xc=3, Yc=-1

To find point B, we can use the partition rule, where AB = 3BC, so AB occupies k=3/4 of the distance AC.

B(x,y) = ((1-k)Xa+kXc, (1-k)Ya+kYc)

=(Xa/4+3Xc/4, Ya/4+3Yc/4), substitute values

=(5/4+3*3/4, 5/4+3*(-1)/4)

=(14/4,2/4)

=(3.5, 0.5)

Answer:

(3.5, 0.5) or A

Step-by-step explanation:

Got it right

Answer: ABFE or ABJCDI

Step-by-step explanation: Any points that are in the same plane or face of a 3D figure

Answer:

6 granite, 3 marble, 14 sandstone, 1 slate

ratio of sandstone to marble

how many sandstone does she have .....14

how many marble does she have......3

so the ratio would be 14:3

Answer:

C. 14:3

Step-by-step explanation:

Dana has 14 pieces of sandstone.

Dana has 3 pieces of marble.

The ratio of pieces of sandstone to pieces of marble is 14:3.

The ratio cannot be simplified further.

Answer:

[tex]x=1[/tex]

Step-by-step explanation:

[tex]\sqrt{x-1} =2-\sqrt{x+3}[/tex]

Square both sides.

[tex]\left(\sqrt{x-1}\right)^2=\left(2-\sqrt{x+3}\right)^2[/tex]

[tex]x-1=x+7-4\sqrt{x+3}[/tex]

Subtract x on both sides.

[tex]x-1-x=x+7-4\sqrt{x+3}-x[/tex]

[tex]-1=-4\sqrt{x+3}+7[/tex]

Subtract 7 on both sides.

[tex]-1-7=-4\sqrt{x+3}+7-7[/tex]

[tex]-8=-4\sqrt{x+3}[/tex]

Square both sides.

[tex]\left(-8\right)^2=\left(-4\sqrt{x+3}\right)^2[/tex]

[tex]64=16x+48[/tex]

Subtract 48 on both sides.

[tex]64-48=16x+48-48[/tex]

[tex]16=16x[/tex]

Divide both sides by 16.

[tex]\frac{16}{16} =\frac{16x}{16}[/tex]

[tex]1=x[/tex]

Switch sides.

[tex]x=1[/tex]

Answer:

320 people

Step-by-step explanation:

[tex]\frac{2 people}{5 people}[/tex]=[tex]\frac{x}{800 people}[/tex]

solve for x by using cross multiplication

     -multiply 2 by 800 to get 1,600

     -divide 1,600 by 5 people to get 320

your answer is 320 people

Answer:

a) [tex]\angle G = 125^\circ[/tex]

b) AG = 15 units

c) Perimeter of polygon SUBAG = 78 units

Step-by-step explanation:

Given:

Polygon ROTFL ~ Polygon SUBAG

Similar polygons mean they have similar angles and the ratio of corresponding sides and ratio of their perimeter are equal.

Part A:

Given that

[tex]m\angle R = 100^\circ\\m\angle O = 120^\circ\\m\angle T = 75^\circ\\M\angle L = 60^\circ[/tex]

[tex]m\angle L+M\angle L = 180^\circ\\\Rightarrow m\angle L=180-60=120^\circ[/tex]

Sum of all interior angles of a pentagon is [tex]540^\circ[/tex]

[tex]m\angle R+m\angle O+m\angle T+m\angle F+m\angle L=540^\circ\\\Rightarrow 100+120+75+m\angle F+120=540^\circ\\\Rightarrow m\angle F=125^\circ\\[/tex]

Due to similarity property of the two pentagons, [tex]\angle F =\angle G = 125^\circ[/tex]

Part B:

Ratio of corresponding sides is equal.

Given the sides SU = 12, RO = 8 and FL = 10 units respectively.

[tex]\dfrac{SU}{RO}=\dfrac{AG}{FL}\\\dfrac{12}{8}=\dfrac{AG}{10}\\\Rightarrow AG = 15\ units[/tex]

Part C:

Ratio of corresponding sides must be equal to ratio of perimeter of the two polygons:

[tex]\dfrac{RO}{SU} = \dfrac{\text{perimeter of ROTFL}}{\text{perimeter of SUBAG}}\\\Rightarrow \dfrac{8}{12} = \dfrac{52}{\text{perimeter of SUBAG}}\\\Rightarrow \text{perimeter of SUBAG} = 52 \times 1.5\\\Rightarrow \text{perimeter of SUBAG} = 78\ units[/tex]

So, the answers are:

a) [tex]\angle G = 125^\circ[/tex]

b) AG = 15 units

c) Perimeter of polygon SUBAG = 78 units

Answer:

29

Step-by-step explanation:

Let the smaller integer be x.

The other integer is 1 greater than 3 times x, or 3x + 1.

The product is 154.

x(3x + 1) = 154

3x^2 + x - 154 = 0

157 = 2 * 7 * 11

14 * 11 = 154

22 * 7 = 154

(3x + 22)(x - 7) = 0

3x + 22 = 0 or x - 7 = 0

3x = -22 or x = 7

x = -22/3 or x = 7

-22/3 is not a positive integer, so we discard that solution.

The smaller integer is 7.

3x + 1 = 3(7) + 1 = 22

The greater integer is 22.

The sum of the integers is 7 + 22 = 29

Answer: 29

Step-by-step explanation:

Answer:

The graph g(x) is vertically shrunk by a factor of 1/9.

Step-by-step explanation:

Parent Graph: f(x) = a√(bx - c) + d

Since we are only modifying a, we are dealing with vertical shrink (a < 1) and stretch (a > 1). Since 1/9 < 1, we have a vertical shrink by a factor of 1/9.

The correct description is:

"The graph of g(x) is shrunk vertically by a factor of 1/9"

There are two types of dilations.

Vertical dilation:

For a function f(x), a vertical dilation of scale factor k is written as:

g(x) = k*f(x).

Where if k > 1, we have a dilation, if 0 < k < 1, we have a contraction.

Horizontal dilation:

For a function f(x), a horizontal dilation of scale factor k is wrtten as:

g(x) = f(x/k).

Where if k > 1, we have a dilation, if 0 < k < 1, we have a contraction.

Here we have:

So we can see that g(x) is a vertical contraction of scale factor 1/9.

Then the correct option is:

"The graph of g(x) is shrunk vertically by a factor of 1/9"

If you want to learn more about dilations, you can read:

https://brainly.com/question/3457976

Answer:

The answer is A.

Step-by-step explanation:

I hope this helps!

Answer:

a: 3

b. 6973568802

Step-by-step explanation:

a₁ = 6 , r = 3 , a₂₀ =?

Result:

a₂₀ = 6973568802

Explanation:

To find a₂₀ we use the formula

aₙ = a₁ · r ^ⁿ⁻¹

In this example we have a₁ = 6 , r = 3 , n = 20. After substituting these values to above

formula, we obtain:

aₙ = a₁ · r ^ⁿ⁻¹

a₂₀ = 6 · 3 ^²⁰⁻¹

a₂₀ = 6 · 1162261467

a₂₀ = 6973568802

Answer:

The missing reason in step 5 is;

The linear pair postulate

Step-by-step explanation:

The information given are;

Column 1,                                                 Column 2

Statements,                                             Reasons

Line AB intersect DE at C,                      Given

∠DCB and ∠BCE are linear pair,           Definition of linear pair

∠DCB is supplementary to ∠BCE,         Linear pair postulate

∠BCE and ∠ECA are linear pair,           Definition of linear pair

∠BCE is supplementary to ∠ECA,         Linear pair postulate

∠DCB ≅ ∠ECA,                                      Congruent to supplementary theorem  

Therefore, the missing reason in step 5 is the linear pair postulate.

Answer:

itS A

Step-by-step explanation:

Answer:

(x-5)(x-8)(x+2)=0

Step-by-step explanation:

first look at the x intercept to find the factor

x:-2,5,8

x=-2 then x+2=0

x=5 then x-5=0

x=8 then x-8=0

(x-5)(x-8)(x+2)=0

check for y in the polynomial when x=0

x^3-11x^2+14x+80

x=0 y=80 ( correct according to the graph

Answer:

C. Negative three-fourths

Step-by-step explanation:

Given two fractions -1 1/4 and 1/2, the sum of the fractions is expressed as shown below:

-1 1/4 + 1/2

Converting the improper fraction -1 1/4 to mixed fraction will give -5/4. The expression will now become:

-5/4 + 1/2

Taking the LCM of the expression

= (-5+2)/4

= -3/4

Hence the sum of fraction Negative 1 and one-fourth and one-half is negative three-fourths

Answer:

-3/4

Step-by-step explanation:

-1 1/4 +1/2

-5/4    +    2/4

-3/4