What is the radius of a sphere with a surface area of 100cm??

Final answer:

The discriminant of a quadratic equation informs us about the nature of its roots. By calculating the discriminant for each given equation, we categorize them accordingly: equations with discriminant greater than zero have two distinct real roots, equal to zero have one repeated real root, and less than zero have two complex roots.

Explanation:

The discriminant of a quadratic equation ax² + bx + c = 0 is given by the expression b² - 4ac. The value of the discriminant determines the nature of the roots of the equation. To find the type of roots for each given equation:

x² − 4x + 2: The discriminant is (-4)² - 4(1)(2) = 16 - 8 = 8, which is greater than zero, so this equation has two distinct real roots.

5x² − 2x + 3: The discriminant is (-2)² - 4(5)(3) = 4 - 60 = -56, which is less than zero, indicating two complex roots.

2x² + x − 6: The discriminant is (1)² - 4(2)(-6) = 1 + 48 = 49, also greater than zero, leading to two distinct real roots.

13x² − 4 = 0 has a discriminant equivalent to that for x² − 4/13 = 0, which is 0² - 4(1)(-4/13) = 16/13, which is greater than zero, so this equation will have two distinct real roots.

x² − 6x + 9: The discriminant is (-6)² - 4(1)(9) = 36 - 36 = 0, indicating one repeated root.

x² − 8x + 16: The discriminant is (-8)² - 4(1)(16) = 64 - 64 = 0, which means this equation has one repeated root.

4x² + 11 = 0 has a discriminant equivalent to that for x² + 11/4 = 0, which is 0² - 4(1)(11/4) = -11, less than zero, thus resulting in two complex roots.

Through the method of using the discriminant, we can determine the types of roots each quadratic equation will have.

Answer:

C- Negative Slope

This is because it you stated it is decreasing and it is proportional.

Negative slope best describes a condition in which a quantity decreases at a rate that is proportional to the current value of the quantity .

The slope of a line is the measure of the steepness and the direction of the line. Finding the slope of lines in a coordinate plane can help in predicting whether the lines are parallel, perpendicular, or none without actually using a compass.

Depending upon the relationship between the two variables x and y and thus the value of the gradient or slope of the line obtained.

There are 4 different types of slopes, given as,

According to the question

A quantity decreases at a rate that is proportional to the current value of the quantity

As,

Slope decreases i.e when x increases, y decreases.

and the rate at which it is decreasing is proportional to the current value of the quantity .

Therefore ,

It best describes the negative slope .

Hence, the Negative slope best describes a condition in which a quantity decreases at a rate that is proportional to the current value of the quantity .

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Answer:

Yes, it's undefined.

The slope is undefined.

Step-by-step explanation:

Slope formula:

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

[tex]\displaystyle \frac{5-(-3)}{6-6}=\frac{8}{0}=0[/tex]

Therefore, the slope is undefined.

Hope this helps!

Answer:

undefined

Step-by-step explanation:

To find the slope of a line, we use the equation

m = (y2-y1)/(x2-x1)

    = (5--3)/(6-6)

   = (5+3)/(6-6)

  =8/0

 Anything divided by 0 is undefined, so the slope is undefined

[tex]\bf -\sqrt{225}+4.8~~ \begin{cases} 225=&3\cdot 3\cdot 5\cdot 5\\ &3^2\cdot 5^2\\ &(3\cdot 5)^2\\ &15^2 \end{cases}\\\\\\ -\sqrt{15^2}+4.8\implies -15+4.8\implies -10.2[/tex]

Answer:

it may be e=c+12

Step-by-step explanation:

common sense

For this case we have:

e: Variable representing the number of eggs

c: Variable representing the number of cartons of eggs.

So, if in each carton there are 12 eggs we can write the following equation:

[tex]e = 12c[/tex]

Answer:

The equation is: [tex]e = 12c[/tex]

For this case we have the following system equations:

[tex]x + 2y = 11\\6x + 4y = 34[/tex]

To use the elimination method we must multiply the first by -2. So:

[tex]-2x-4y = -22\\6x + 4y = 34[/tex]

In this way, if we add the equations, the variable y is eliminated.

Answer:

-2

Option C

For this case we have that by definition, the point-slope equation of a line is given by:

[tex]y-y_ {0} = m (x-x_ {0})[/tex]

We have the following points:

[tex](x_ {1}, y_ {1}) :( 2,6)\\(x_ {2}, y_ {2}) :( 4,0)\\m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {0-6} {4-2} = \frac {-6} {2} = -3[/tex]

We chose a point:

[tex](x_ {0}, y_ {0}) :( 4,0)[/tex]

Substituting in the equation we have:

[tex]y-0 = -3 (x-4)\\y = -3 (x-4)[/tex]

Finally, the equation is: [tex]y = -3 (x-4)[/tex]

Answer:

OPTION C

Answer:

Third option:  [tex]y=-3(x-4)[/tex]

Step-by-step explanation:

The equation of the line in Point-Slope form is:

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

Where "m" is the slope and [tex](x_1,y_1)[/tex] is a point on the line.

Given the points  (4, 0) and (2, 6), we can find the slope with this formula:

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

Substituting values, we get:

 [tex]m=\frac{0-6}{4-2}=-3[/tex]

Finally, substituting the slope and the point (4,0) into  [tex]y-y_1=m(x-x_1)[/tex], we get:

 [tex]y-0=-3(x-4)[/tex]

 [tex]y=-3(x-4)[/tex]

Answer:

The coordinates of point B are (-7 , -2)

Step-by-step explanation:

* Lets explain how to solve the problem

- The mid-point (x , y) of the line whose endpoints are (x1 , y1) and

 (x2 , y2) is [tex]x=\frac{x_{1}+x_{2}}{2},y=\frac{y_{1}+y_{2}}{2}[/tex]

∵ M is the midpoint of AB

∵ The coordinates of point A are (-3 , 6)

∵ The coordinates of point M are (-5 , 2)

- Let the coordinates of point A are (x1 , y1) , The coordinates of

 point B are (x2 , y2) and The coordinates of point M are (x , y)

∴ x = -5 , x1 = -3 and y = 2 , y1 = 6

- Lets use the rule of the mid point to find x2 , y2

∵ [tex]-5=\frac{-3+x_{2}}{2}[/tex] ⇒ multiply both sides by 2

∴ [tex]-10=-3+x_{2}[/tex] ⇒ add 3 to both sides

∴ -7 = x2

∵ [tex]2=\frac{6+y_{2}}{2}[/tex] ⇒ multiply both sides by 2

∴ [tex]4=6+y_{2}[/tex] ⇒ subtract 6 from both sides

∴ -2 = y2

∵ The coordinates of point B are (x2 , y2)

∴ The coordinates of point B are (-7 , -2)

Answer:

The x-intercepts are the points (-4,0). (2,0) and (9,0)

The location of the x-intercepts in the attached figure

Step-by-step explanation:

we know that

The x-intercepts of a function are the values of x when the value of the function is equal to zero

we have

[tex]f(x)=x^{3}-7x^{2}-26x+72[/tex]

using a graphing tool

The x-intercepts are the points (-4,0). (2,0) and (9,0)

see the attached figure

Answer:

(-4,0), (2,0), (9,0)

Step-by-step explanation:

Correct on Plato

Answer:

716 yards

Step-by-step explanation:

Circumference = π × Diameter

2 × Radius = Diameter

2 × 114 = 228

Circumference = π × Diameter

Circumference = π × 228 = 228π = 716.283125018

Answer:

716 yd

Step-by-step explanation:

The circumference of a circle is 2*pi*radius.

The radius is 114 yd so the circumference is 2*pi*114 yd.

Put into the calculator and you obtain 716.283 yd.

The answer to the nearest yard is 716.

Answer:

k = - 9

Step-by-step explanation:

Given that y varies directly as x then the equation relating them is

y = kx ← k is the constant of variation

To find k use any ordered pair from the given table of values

Using x = 1, y = - 9, then

k = [tex]\frac{y}{x}[/tex] = [tex]\frac{-9}{1}[/tex] = - 9

Answer:

-9.

Step-by-step explanation:

y varies directly as x so y = kx where k is the constant of variation.

Inserting the values of x and y.

0 = k*0

-9 = k*1 so k = -9

-18 = 2*k so k = -9

-27 = 3 *k so k = -9.

Answer:

[tex]\large\boxed{(x-3)(2x^2-5x+1)=2x^3-11x^2+16x-3}[/tex]

Step-by-step explanation:

Use the distributive property: a(b + c) = ab + ac:

[tex](x-3)(2x^2-5x+1)=(x-3)(2x^2)+(x-3)(-5x)+(x-3)(1)\\\\=(x)(2x^2)+(-3)(2x^2)+(x)(-5x)+(-3)(-5x)+x-3\\\\=2x^3-6x^2-5x^2+15x+x-3\qquad\text{combine like terms}\\\\=2x^3+(-6x^2-5x^2)+(15x+x)-3\\\\=2x^3-11x^2+16x-3[/tex]

Answer:

910$

Step-by-step explanation:

It's easiest if we just add the width and length together to start which would be 2 sides of the fence so we multiply by 2 to complete the whole perimeter.

80+60 = 140 x 2 = 280

Now you need to multiply 280 by 3.25 because that is what it will cost in the end since the 280 is all of the feet together and the 3.25 is each foot's price.

3.25 x 280 = 910

910$

Answer:

A. -2, -5

Step-by-step explanation:

x^2 + 7x + 10 = 0

Factor the equation

What 2 numbers multiply to 10 and add to 7

2*5 =10

2+5 = 7

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

Using the zero product property

x+2 =0  x+5 =0

x=-2       x = -5

Answer:

{-4, 8, 5, 1, 5}

Step-by-step explanation:

In a set of ordered pairs, the domain is the set of the first number in every pair.

If the set of ordered pairs is {(-4,8), (8,10), (5,4), (1,6), (5,-9)},

                      the domain is {  -4,     8,        5,     1,      5}

10

If you treat the number as x, then [tex]\frac{1}{2}x=x+5\to-5=\frac{1}{2}x\to-10=x[/tex].

The value of y = 30°

By alternating interior property, alternate angle of 150° is equal to 150°.

Straight line has angle 180°

So, y + 150° = 180°

y = 30°

Hence the value of y = 30°

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Answer:

4) x

Step-by-step explanation:

The expression on the left side simplifies to:

-4(x - 2) + 5x =

= -4x + 8 + 5x

= x + 8

To have an equation with no solution, you need the same x term on the right side but a different constant term. The x term on the left side is x. You need x on the right side but with a constant term different than 8.

Answer: 4) x

Answer:

D) x

Step-by-step explanation:

When simplified, the answer will result to a=b which means that it has no solution

The graph located in the upper right corner of the image attached shows the graph of y = 3[x]+1.

In order to solve this problem we have to evaluate the function y = 3[x] + 1 with a group of values.

With x = { -3, -2, -1, 0, 1, 2, 3}:

x = -3

y = 3[-3] + 1 = -9 + 1

y = -8

x = -2

y = 3[-2] + 1 = -6 + 1

y = -5

x = -1

y = 3[-1] + 1 = -3 + 1

y = -2

x = 0

y = 3[0] + 1 = 0 + 1

y = 1

x = 1

y = 3[1] + 1 = 3 + 1

y = 4

x = 2

y = 3[2] + 1 = 6 + 1

y = 7

x = 3

y = 3[3] + 1 = 9 + 1

y = 10

 x     y

-3    -8

-2    -5

-1     -2

0      1

 1     4

 2    7

 3   10

The graph that shows the function y = 3[x] + 1 is  the one located in the upper right corner of the image attached.

Answer:

The answer you picked was correct. I just took the test and that's it.

Step-by-step explanation:

Answer:

[tex]\large\boxed{\left\{\begin{array}{ccc}x\leq\dfrac{20}{a}&\text{for}\ a>0\\\\x\geq\dfrac{20}{a}&\text{for}\ a<0\end{array}\right }[/tex]

Step-by-step explanation:

[tex]ax-8\leq12\qquad\text{add 8 to both sides}\\\\ax-8+8\leq12+8\\\\ax\leq20\qquad\text{divide both sides by}\ a\neq0\\\\(1)\ \text{if}\ a>0,\ \text{then:}\\\\x\leq\dfrac{20}{a}\\\\(2)\ \text{if}\ a<0,\ \text{then you must flip the sign of inequality:}\\\\x\geq\dfrac{20}{a}[/tex]

Final answer:

To solve the inequality Ax - 8 ≤ 12 for x in terms of a, add 8 to both sides to get Ax ≤ 20, and then divide by A (assuming A > 0) to find x ≤ 20/A.

Explanation:

To solve the inequality for x in terms of a, we start with the given inequality:

Ax - 8 ≤ 12.

First, we add 8 to both sides to isolate the term with x on one side:

Ax ≤ 20

Next, assuming A is not zero, we divide both sides by A to solve for x:

x ≤ 20 / A

This is the solution to the inequality, with the understanding that it only applies if A is positive, because if A were negative, we would need to reverse the inequality sign when dividing by A.

Answer:

B

Step-by-step explanation:

The graph of g(x) has its vertex at (1, - 3)

The equation of a parabola in vertex firm is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

here (h, k) = (1, - 3), thus

g(x) = (x - 1)² - 3 → B

Answer:

B.f(x)=(x-1)²-3

Step-by-step explanation:

apex

Answer:

The measure of the smaller angle is 62°

Step-by-step explanation:

we know that

If two angles form a linear pair, then their sum is equal to 180 degrees (supplementary angles)

so

(2x-30)°+(x-12)°=180°

Solve for x

3x=180°+42°

3x=222°

x=74°

The measure of the angles are

(2x-30)°=2(74)-30=118°

(x-12)°=74-12=62° -----> smaller angle

Answer:

[tex]\large\boxed{y=-\dfrac{2}{3}x-\dfrac{13}{3}}[/tex]

Step-by-step explanation:

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

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

The formula of a slope:

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

From the graph we have two points (-5, -1) and (-2, -3).

Look at the picture.

Calculate the slope:

[tex]m=\dfrac{-3-(-1)}{-2-(-5)}=\dfrac{-2}{3}=-\dfrac{2}{3}[/tex]

Put it to the equation in slope-intercept form:

[tex]y=-\dfrac{2}{3}x+b[/tex]

We can't read the y-intercept from the graph. Therefore put the coordinates of the point (-5, -1) to the equation and calculate b:

[tex]-1=-\dfrac{2}{3}(-5)+b[/tex]

[tex]-1=\dfrac{10}{3}+b[/tex]         subtract 10/3 from both sides

[tex]-\dfrac{3}{3}-\dfrac{10}{3}=b\to b=-\dfrac{13}{3}[/tex]

Finally:

[tex]y=-\dfrac{2}{3}x-\dfrac{13}{3}[/tex]

Answer:

8

Step-by-step explanation:

The question is on interquartile range which is the median of the upper half of the data minus the median of the lower half of data

First arrange the data in an increasing order;

8,15,9,18,9,17,22,10,11,9,13

8,9,9,9,10,11,13,15,17,18,22

Find the median, which is the center value in the data set

8,9,9,9,10,11,13,15,17,18,22⇒the median is 11

Place brackets around the numbers above and below the median

(8,9,9,9,10)11 (13,15,17,18,22)

Find the median in the lower half of the data,Q1

(8,9,9,9,10) ⇒median is 9=Q1

Find the median in the upper half of the data,Q3

(13,15,17,18,22)⇒median is 17=Q3

Subtract Q1 from Q3 to get the interquartile range

Q3=17, and Q1=9

Q3-Q1=17-9=8

The diagram that represents the contrapositive of the statement "If it is an equilateral triangle, then it is an isosceles triangle" is: B. Figure B.

In Mathematics, a conditional statement is a type of statement that can be written to have both a hypothesis and conclusion. This ultimately implies that, a conditional statement has the form "if P then Q."

P → Q

Where:

P and Q represent sentences or statements.

Generally speaking, the contrapositive of a conditional statement involves interchanging the hypothesis and conclusion, and negating both hypothesis and conclusion;

~Q → ~P

In this context, the contrapositive of the given statement "If it is an equilateral triangle, then it is an isosceles triangle" can be written as follows;

"If it is not an isosceles triangle, then it is not an equilateral triangle."

Therefore, only figure correctly represent the contrapositive of the statement.

Complete Question:

Which of the diagrams below represents the contrapositive of the statement

"If it is an equilateral triangle, then it is an isosceles triangle"?

A. Figure A

B. Figure B

Answer:

A) 6^2 + 11^2 is not equal to 15^2

Step-by-step explanation:

To find out if a right triangle is a right triangle you have to use the Pythagorean Theorem, like it is used in A.

6^2 + 11^2 = 15^2

36 + 121 = 225

157 does not equal 225

So this is not a right triangle

Answer:

Option A

Step-by-step explanation:

Given in the picture is a triangle ABC with three sides given as 6,11 and 15

By the picture itself we can say that the largest angle is obtuse and hence the triangle is not right angled.

Using the converse of Pythagorean theorem that in a right triangle sides square add upto square of hypotenuse let us check whether this applies to this triangle.

Small sides are 6 and 11

Squaring and adding gives

[tex]6^2+11^2 = 187[/tex]

Large side = 11 and square is

[tex]15^2 =225 > 121[/tex]

Hence this is not a right triangle but obtuse

So option A is right

Answer:

The parent function f(x) is equal to [tex]f\left(x\right)=\left|x\right|[/tex]

The translations is 3 units to the left and 5 units down

Step-by-step explanation:

we have

[tex]h\left(x\right)=\left|x+3\right|-5[/tex]

The vertex of the function h(x) is the point (-3,-5)

we know that the parent function f(x) is equal to

[tex]f\left(x\right)=\left|x\right|[/tex]

The vertex of the function f(x) is the point (0,0)

so

The rule of the transformation of f(x) to h(x) is equal to

(x,y) -----> (x-3,y-5)

That means ----> The translations is 3 units to the left and 5 units down

Answer:

[tex]\frac{50}{3}[/tex]

Step-by-step explanation:

Similar shapes have corresponding sides that are proportional.

So 20 corresponds to x (big to small).

So 12 corresponds to 10 (big to small).

Your information is already lined up for you to setup your proportion:

[tex]\frac{20}{12}=\frac{x}{10}[/tex]

Cross multiply:

[tex]20(10)=12(x)[/tex]

Simplify both sides:

[tex]200=12x[/tex]

Divide both sides by 12:

[tex]\frac{200}{12}=x[/tex]

Simplify by dividing top and bottom by 4:

[tex]\frac{50}{3}=x[/tex]

Add the totals of each item together:

189.99 + 249.95 + 493.68 + 98.75 + 98.75 = 1,131.12

Now multiply that by the tax rate as a decimal:

1131.12 x 0.0725 = 82.01

Now add that to the total of the items:

1,131.12 + 82.01 = $1,213.13 total

For this case we have that the total of the purchase is given by:

Coffee table: $ 189.99

Loveseat: $ 249.95

Sofa: $ 493.68

2 chairs: 2 * $ 98.75 = $ 197.5

Adding up we have: $ 1131.12

Now, we must find the tax amount:

$ 1131.12 ----------> 100%

x ------------------------> 7.25%

Where "x" represents the value of the tax:

[tex]x = \frac {7.25 * 1131.12} {100}\\x = 82.0062[/tex]

Finally, the amount to be paid is:

$ 1131.12 + $ 82.0062 = $ 1213.13

Answer:

Option B

Answer:

Ratio of the number of votes that were not for mayor Jackson to the total number of votes is 3:7

Step-by-step explanation:

Votes of Mayor Jackson = 32,000

Total Votes = 56,000

Votes not for Mayor Jackson = 56000 - 32000

Votes not for Mayor Jackson = 24000

ratio of the number of votes that were not for mayor Jackson to the total number of votes = Votes not for Mayor Jackson:Total Votes

= 24,000:56,000

=24:56 (divide numerator and denominator by 8)

=3:7

So, ratio of the number of votes that were not for mayor Jackson to the total number of votes is 3:7

Answer:

3 : 7

Step-by-step explanation:

It is given that,

In an election 32,000 people voted for Mayor Jackson

A total of 56,000 people voted in the election.

To find the ratio

Total number of people voted = 56000

Number of people voted for Mayor Jackson = 32000

Number of  votes that were not for mayor Jackson = 56000 - 32000 = 24000

The ratio of the number of votes that were not for mayor Jackson to the total number of votes = 24000 : 56000

 = 3 : 7