100 POINTS AND BRAINLIEST

For what values of c does the quadratic equation -x^2+4x+c=0


1. Have no real roots?

2. Have two roots with the same sign?

3. Have one negative root and one root equal to 0?

4. Have two roots with opposite sides?

Answers

Answer 1

Answer:its c

Step-by-step explanation:

Answer 2

Answer:

1.  c < -4

2.  -4 < c < 0

3.  c = 0

4.  c > 0

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{6.8 cm}\underline{Discriminant}\\\\$b^2-4ac$ \quad when $ax^2+bx+c=0$\\\\when $b^2-4ac > 0 \implies$ two real roots.\\when $b^2-4ac=0 \implies$ one real root.\\when $b^2-4ac < 0 \implies$ no real roots.\\\end{minipage}}[/tex]

Given quadratic equation:

[tex]-x^2+4x+c=0[/tex]

Question 1

If the quadratic equation has no real roots, then the discriminant is less than zero:

[tex]\implies b^2-4ac < 0[/tex]

[tex]\implies (4)^2-4(-1)(c) < 0[/tex]

[tex]\implies 16+4c < 0[/tex]

[tex]\implies 4c < -16[/tex]

[tex]\implies c < -4[/tex]

Question 2

If the quadratic equation has two real roots, then the discriminant is greater than zero:

[tex]\implies b^2-4ac > 0[/tex]

[tex]\implies (4)^2-4(-1)(c) > 0[/tex]

[tex]\implies 16+4c > 0[/tex]

[tex]\implies 4c > -16[/tex]

[tex]\implies c > -4[/tex]

Using Descartes' Rule of Signs, if c > 0 there would be one sign change and so a maximum of one positive root.  If c < 0 there would be 2 sign changes and therefore a maximum of 2 negative roots.

Therefore, for the two roots to have the same sign, -4 < c < 0.

Question 3

If c = 0 then:

[tex]\implies -x^2+4x=0[/tex]

[tex]\implies -x(x+4)=0[/tex]

[tex]\implies x(x+4)=0[/tex]

Therefore, the roots would be 0 and -4 so there would be one negative root and one root equal to zero.

Question 4

Using Descartes' Rule of Signs, if c > 0 there would be one sign change and so a maximum of one positive root.

Therefore, for the equation to have two roots with opposite signs, c > 0.


Related Questions

Write the equation of the line in fully simplified slope-intercept form.



I dont know what im doing wrong

Answers

The equation of the straight line in fully simplified slope-intercept form: [tex]y = 2x-6[/tex]

What is straight line?

A straight line is just a straight line with no bends. A straight line is one that has no bends and continues to infinity on both sides.

A straight line's equation is y=mx+c, where m is the gradient and c is the height at which the line crosses the y axis, commonly known as the y -intercept.

The drawn line cut the x-axis at (3,0) and y-axis at (0,-6)

So, the equation of line is:

    [tex]\frac{x}{3} + \frac{y}{-6} = 1[/tex]

or, [tex]\frac{x}{3} - \frac{y}{6} = 1[/tex]

or, [tex]\frac{2x-y}{6} = 1[/tex]

or, [tex]2x-y =6[/tex]

or, [tex]y = 2x-6[/tex]

Thus, slope-intercept form is: [tex]y = 2x-6[/tex]

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Find the missing number.
n/5 = 7/8

Answers

Answer:

3!

Step-by-step explanation:

Hope this helped ! :D

NEED ANSWERS ASAP PLEASE HELP!!! THE NUMBERS ARE THE QUESTION #

Answers

Area of the parallelogram is 882 square units

the solution of the inequality is plotted in the last number line

area o the glass window is 144π cm²

the second number line is the correct plot

the water left after the serving is 2 gallons 3 quart 1 pint

How to find the area of the parallelogram

Area of a parallelogram is given by the formula

= base *  height

= 63 * 14

= 882 square units

The solution of the number line is b/2 ≥  4

= b ≥  8

the last option is correct

Area of circle is solved by

= πd² / 4

= π * 24² / 4

= 144π cm²

The inequality 4 > -y

= -4 < y

The second option is correct

total fluid ounces used

= 68 * 4 = 272 ounces

272 ounces = 2.125gallons

5 - 2.125 = 2.825 gallons

2.875 gallons

0.875 gallons = 3.5 quart

2 gallons 3.5quart

0.5 quart = 1 pint

2 gallons 3 quart 1 pint

Water left in the cooler is 2 gallons 3 quart 1 pint

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Given z, find |z|.

z=-2-6i

Answers

Answer:

[tex] \Large{\boxed{\sf | \sf z| = \sf \sqrt{40} = 2\sqrt{10} }} [/tex]

[tex] \\ [/tex]

Explanation:

We are given a complex number in algebraic form, and we would like to find its modulus, |z|.

[tex] \\ \\ [/tex]

Modulus of a complex number

[tex] \\ \\ [/tex]

Let's recall that a complex number in algebraic form is written as [tex] \sf z = a + ib [/tex] , where a is its real part and b is its imaginary part.

[tex] \\ [/tex]

The modulus of said complex number is calculated as follows:

[tex] \sf | \sf z| = \sqrt{a^2 + b^2} [/tex]

[tex] \\ [/tex]

[tex] \hrulefill [/tex]

[tex] \\ [/tex]

Let's identify our values:

[tex] \sf z = -2 - 6i \Longleftrightarrow z = \underbrace{\sf -2}_{\sf a} + (\underbrace{\sf -6}_{\sf b})i [/tex]

[tex] \\ [/tex]

Now, substitute these values into our formula:

[tex] \sf | \sf z | = \sqrt{(-2)^2 + (-6)^2} = \sqrt{4 + 36} = \boxed{\sf \sqrt{40}} [/tex]

[tex] \\ [/tex]

While this may be optional, the result can be simplified by using the following property:

[tex]\green{\begin{gathered}\begin{gathered} \\ \boxed { \begin{array}{c c} \\ \blue{ \star \: \sf{\boxed{ \sf Product \: rule \: of \: square \: roots\text{:}}}} \\ \\ \sf{ \diamond \: \sqrt{ab} = \sqrt{a} \times \sqrt{b} } \\ \end{array}}\\\end{gathered} \end{gathered}}[/tex]

[tex] \\ [/tex]

[tex] \sf \sqrt{40} = \sqrt{4 \cdot 10} = \sqrt{4} \cdot \sqrt{10} = \boxed{\boxed{\sf 2\sqrt{10}}} [/tex]

[tex] \\ [/tex]

[tex] \hrulefill [/tex]

[tex] \\ [/tex]

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PQ has endpoints P(-3,2) and Q(3,-2). Find the coordinates of the midpoint of PQ

Answers

Answer:

(0,0)

Step-by-step explanation:

For this, you need to use the midpoint formula.

(-3) + 3                      2 + (-2)

--------------      ,       ----------------

     2                               2

This leads to:

-3 + 3 = 0 -> 0/2

x = 0

3 + (-3) = 0 -> 0/2

The answer is:

(0, 0)

Select 3 correct and answer?

___ l

___ m

___ n

___ j

___ no lines are parallel

___ Corresponding Angles Converse

___ Alternate interior Angles Converse

___ Alternate Exterior Angles Converse

___ Consecutive interior Angles Converse

Answers

These sentences are correct among all the given sentences & in terms of a given diagram.

 Corresponding Angles Converse

 Alternate interior Angles Converse

 Alternate Exterior Angles Converse

What are the corresponding angles?

In geometry, corresponding sides and corresponding angles of polygons are compared as part of the tests for congruence and resemblance. In these tests, the order of adjacency is maintained by pairing each side and each angle of one polygon with a side or angle of the other polygon.

We have,

no lines are parallel

Corresponding Angles Converse

Alternate interior Angles Converse

Alternate Exterior Angles Converse

Consecutive interior Angles Converse

By considering the given diagram the correct sentences are:

 Corresponding Angles Converse

 Alternate interior Angles Converse

 Alternate Exterior Angles Converse

Hence, these sentences are correct among all the given sentences & in terms of a given diagram.

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Answer:

Line l is parallel to line n.

Alternate interior angle converse.

Step-by-step explanation:

Angles 8 and 19 are alternate interior angles of lines l and n cut by transversal k.

Since angles 8 and 19 are congruent, then by alternate interior angle converse, lines l and n are parallel.

Suppose megan wants to run more sprints and laps. How many of each could she run so that her total sprints and total laps are in the ratio that the coach wanted?

Answers

Answer:

2

Step-by-step explanation:

PLEASE IT DUE SOON!!! DONT EVEN KNOW WHERE TO START IM SO CONFUSED!!!

QUESTION DOWN BELOW!! ONLY HAVE 20MIN SO PLEASE SOMEONE!!

Answers

A test point which is in the solution set for the linear inequality is: C. (-2, 4).

How to determine the true test point?

In order to determine which ordered pairs is a true solution based on the given linear inequality, we would have to test each of the ordered pairs by substituting their values into the linear inequality as follows;

For ordered pair (-2, -4), we have:

2x - 9y < 0

2(-2) - 9(-4) < 0

-4 + 36 < 0

32 < 0 (False).

For ordered pair (-1, -5), we have:

2x - 9y < 0

2(-1) - 9(-5) < 0

-2 + 45 < 0

43 < 0 (False).

For ordered pair (-2, 4), we have:

2x - 9y < 0

2(-2) - 9(4) < 0

-4 - 36 < 0

-40 < 0 (True).

For ordered pair (-1, -1), we have:

2x - 9y < 0

2(-1) - 9(-1) < 0

-2 + 9 < 0

7 < 0 (False).

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The complex fifth roots of 5-5sqrt3i

Answers

The required fifth roots of the given complex number as ⁵√3i = ⁵√3·⁵√i.

What is a complex number?

A complex number is a combination of real values and imaginary values. It is denoted by z = a + ib,

where a, and b are real numbers and i is an imaginary number.

The complex number is given in the question following as

3i

We have to determine the fifth roots of the given complex

As per the given question, we have

⇒ ⁵√3i

Apply the radical rule ⁿ√ab = ⁿ√aⁿ·√b,  (Assuming a ≥ 0, b ≥ 0)

⇒ ⁵√3·⁵√i

Thus, the required fifth roots of the given complex number as ⁵√3i = ⁵√3·⁵√i.

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5. Find the value of x. Round the length to the nearest tenth. 18 yd 309 2?. ​

Answers

By Trigonometric formula - Tan(∅) =  [tex]\frac{opposite}{adjacent}[/tex] , we got that answer - x= 10.4 yard (On rounding to tenth place)

what are trigonometric equations?

An equation containing one or more trigonometric ratios of unknown angles is known as a trigonometric equation. In terms of angles, it is written as ratios of the sine, cosine, tangent, secant, and cotangent angles. A trigonometric equation is, for instance, cos2 x + 5 sin x = 0.

For angle 30 degrees adjacent side is 18 yard and opposite side is x.

=>  Tan(∅) =  [tex]\frac{opposite}{adjacent}[/tex]

=>  Tan(30) = [tex]\frac{x}{18}[/tex]

=>  x=Tan 30 (18)

=>  x= 10.39

=>  x= 10.4 yard (On rounding to tenth place)

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50 POINTS! I GIVE BRAINLIEST ANSWERR!!! PLEASE HELP !!!!! David is standing 500 feet away from the base of a cell phone tower. the angle of elevation from his eyes to the top of the tower is 78°. if David’s eyes are 6 feet above the ground how tall is the tower (EXPLAIN PLEASE)

Answers

The height of the tower is 2358.3 feet

What are trigonometric relations?

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data ,

Let the height of the tower be = A

Let the base of the tower be at a distance of = 500 feet

Now , the angle of elevation is θ = 78°

The height of David's view = 6 feet above

So , the total height of the tower be = A + height of David's eyes

Now , A right angle triangle is formed between the tower, the angle of elevation of David's eyes and his distance from the tower

And , the opposite side = A

Adjacent side = 500 feet

So , from the trigonometric relations

tan θ = opposite side / adjacent side

tan θ = A / 500

Multiply by 500 on both sides , we get

A = tan θ x 500

Substituting the value for θ

A = tan 78° x 500

A = 4.7046 x 500

A = 2352.3 feet

Now , the total height of the tower = A + height of David's eyes

                                                          = 2352.3 + 6

                                                          = 2358.3 feet

Hence , The height of the tower is 2358.3 feet

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The ratio of nitrogen to potassium in a sample of soil is 12:9. The sample has 36 units of nitrogen. How much potassium does the sample have?
Group of answer choices

48 units

21 units

27 units

33 units

Answers

Answer:

27 units

Step-by-step explanation:

12 over 4

36 over x

x = 27

linear equation

Answer:alt  account

Step-by-step explanation:

If f(1)=7, f(5)=-3, f(11)=-9, g(7)=11, g(-3)=6 and g(-9)=1, then find g(f(11))

Answers

Answer:

1

Step-by-step explanation:

g(f(11))

It says in the problem that f(11) = -9

So:

g(-9)

It says again in the problem that g(-9) = 1

So the answer is 1

A marching band needs to raise $13,500 for a trip to the Rose Bowl. The director told the band members that one-third of the amount that has been raised so far is equal to half of the amount that is still needed. How much more money needs to be raised for the trip?​

Answers

Answer: $5400

Step-by-step explanation:

x =  amount raised so far

13500 - x = amt. still needed

x/3 = (13500 - x)/2

2x = 3(13500 - x)

2x = 40500 - 3x

5x = 40500

x = 40500/5 = 8100 (amt. raised so far)

13500 - 8100 = 5400 (amt. still needed)

An airline passenger fell asleep halfway to her destination. When she awoke, the distance remaining was half the distance travelled while she slept. How much of the entire trip did she sleep?​

Answers

Answer:

1/4 of the trip

Step-by-step explanation:

The questions is asking what is 1/2 of 1/2 and that would b 1/4

Adenan makes a scale drawing of a rectangular flower box. The length is 5 in., and the width is 3 in. Adenan changes the scale of the drawing from 1 in. : 4 ft to 1 in. : 6 ft. Which statement about the dimensions of the flower box is true?

Answers

The previous length and width are 20 ft and 12 ft, new length and width are 30 ft and 18 ft thus, option (C) is correct.

What is the scale factor?

You must specify the extent of the shape's enlargement when describing one.

The scale factor is the ratio of two dimensions such that one figure is large and another is small.

The scale factor is done due to the unpractical measurement of any figure.

As per the given scale factor 1 in 4ft

Previous length   = 5 × 4 = 20 feet

Previous width = 3 ×4 = 12 ft

As per the given scale factor 1 in 6ft

Previous length = 5×6  = 30 feet

and New width  = 3 × 6 = 18 feet

Hence" the Previous length and width are 20 ft and 12 ft, new length and width are 30 ft and 18 ft".

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The complete question is below,

Adenan makes a scale drawing of a rectangular flower box. The length is 5 in., and the width is 3 in. Adenan changes the scale of the drawing from 1 in. : 4 ft to 1 in. : 6 ft. Which statement about the dimensions of the flower box is true?

The length of the flower box under the new scale is 15 ft.

The length of the flower box under the old scale is 30 ft.

The width of the flower box under the old scale is 12 ft.

The width of the flower box under the new scale is 24 ft.

Jean Conrad is an amateur bowler with an average score of 187. She recently bowled a perfect 300 score. Write an equation that can be used to find how much the perfect score was above her average score and then solve the equation.

Answers

The equation to find out his score is above average is  x = 300 - 187

and it is 113.

What is a numerical expression?

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, Jean Conrad is an amateur bowler with an average score of 187. She recently bowled a perfect 300 score.

Let the score above her average score be x,

x = 300 - 187.

x = 113.

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Determine the equation of the parabola that opens up, has vertex (7, 7), and a focal
diameter of 16.

Answers

Answer:

Step-by-step explanation:

Question: Determine the equation of the parabola that opens up, has vertex (7,7), and a focal diameter of 16 . This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts.

Answer: ((x2)−14x+87)/16

Step-by-step explanation:

  focal diameter = 16,

  4a=16;

  a=4.

(h,v)=(7,7-a)

==> (h,v)=(7,3)

the equation of the parabola =  ((x-7)^2)=16(y-3)

                                                => y = ((x^2)-14x+87)/16.

Which pair of numbers has an lcm of 16​

Answers

Answer:4 and 16

Step-by-step explanation:

4 = 4, 8, 12, 16, 20

16 = 16, 32..

LCM = 16

After adding the two equations to eliminate x you are left with 4y=-8. Solve for y: y =

Answers

Answer:  -2

Step-by-step explanation:

4y/4 = -8/4

     y = -2

Answer:

Step-by-step explanation:

Answer is -2

-2(12-2(-4) )^2 please help. ​

Answers

Answer: -800

Step-by-step explanation:

-2(12+8)^2

-2(20)^2

-2(400)

-800

(i think)

help me with this you need to do associative property of addition, identity property of addition, associative property of multiplication, and identity of multiplication also tell what Properties are shown. due tomorrow morning​

Answers

Answer:

12 x 12

Step-by-step explanation:

(12+0)=12

(12 x 1)= 12

Cuántos metros cuadrados mide la superficie de un salón de fiestas infantiles con forma de rombo cuyas diagonales miden 12 y 18 metros

Answers

The area of the rhombus is 108m²

Surface Area of Rhombus

The area of a rhombus can be defined as the amount of space enclosed by a rhombus in a two-dimensional space. A rhombus is a type of quadrilateral projected on a two dimensional (2D) plane, having four sides that are equal in length and are congruent.

The formula of a rhombus is given as

A = (d₁ * d₂) ÷ 2

where d₁ and d₂ are the diagonals

d₁ = 12m

d₂ = 18m

A = (12 * 18) / 2

A = 108m²

The area is 108 squared meter

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Translation: How many squared meters does the surface of a rhombus-shaped children's party room whose diagonals measure 12 and 18 meters?

sorry its blurry but here are the numbers just in case

-3x-3
-------- =7
6

Answers

Answer: x=-15

Step-by-step explanation:

First you want to get rid of the fraction.
you multiply by 6 on each side so you get -3x-3=42. After that you add 3 to get 45, and lastly you divide 45 by -3 which gets you -15

50 points! Which expression is equivalent to 7(y - 4)? * 1 point
7y - 28
7y - 4
3y
7y - 3
I have to explain also!

Answers

The answer is 7y - 28. You use the distributive property. So you multiply 7 and y and multiply 7 and -4. Therefore the answer is 7y - 28

The vertex angle of an isosceles triangle measures
15 degrees more than one of its base angles. How
many degrees are there in a base angle of the
triangle?

Answers

The required three angle is 55 , 55 and 70

What is an angle ?

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.

When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together. The Latin word "angulus," which means "corner," is where the term "angle" originates.

Let each of the base angle of isosceles triangle = x

Vertex angle = (x+15)

Sum of the angle = 180

x + x + (x + 15) = 180

3x + 15 = 180

3x = 180 - 15

x = 165 / 3

x = 55

Each base angel = 55

Vertex angle = x + 15

                      = 55 + 15

                      = 70

Required three angles = 55 , 55 and 70

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.............................

Answers

The answer is 1,200

First you need to add . + . to get 1.5M and then you need to subtract the rest ( 1.5M - one million four hundred ninety-eight thousand eight hundred )

So then you get 1,200

Hope this helped!

What is the range of the function f(x)=2x^3−3x for the domain {−1, 1, 2}?

Answers

The range of the function is {1,-1,10} for function f(x)=2x³−3x .

What is a function?

A relation is a function if it has only One y-value for each x-value.

In a function what can go into a function is called the Domain. What may possibly come out of a function is called the Codomain. What actually comes out of a function is called the Range.

The given function is f(x)=2x³−3x

The domain is {-1,1,2}

Now f(-1)=2(-1)³-3(-1)

=-2+3=1

f(1)=2(1)³-3(1)=2-3=-1

f(2)=2(2)³-3(2)=16-6=10

Hence, the range of the function is {1,-1,10} for  f(x)=2x³−3x .

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You decide to buy a refurbished computer for $550.00 plus 6% sales tax. BB Electronics allow you to take out a no-interest loan for 12 months, and after that the interest rate is a 13.25% APR. You must make payments of $25/month, and if you miss one payment you are assessed a late fee of $29.00 plus 13.25% APR interest beginning from the date of purchase. How much is due the first month?

Answers

$25 due the first month

rotate (2,-3) 270 degree counterclockwise around (1,-2) then translate (x-2,y+5)

Answers

The image point of the transformation is (-1, 6)

How to determine the image of the transformation?

The coordinate of the point is given as

(2, -3)

The transformations are given as

270 degree counterclockwise around (1,-2) Translation by (x-2,y+5)

The rotation is around the point (1,-2)

So, the point becomes

Point = (2 - 1, -3 + 2)

Evaluate

Point = (1, -1)

The 270 degrees rotation has the algebraic rule of its rotation to be changed from (x, y) to (-y, x) i.e.  (x, y) => (-y, x)

So, we have

(x, y) = (1, 1) after the rotation

The translation is given as

(x - 2, y + 5)

So, we have

(x, y) = (1 - 2, 1 + 5)

Evaluate

(x, y) = (-1, 6)

Hence, the coordinates of the image is (-1, 6)

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If the economy is experiencing less than full-employment, the keynesian model recommends that the government. which artist painted summer's day, a depiction of two well-dressed women in a boat, using the open brushwork and the plein air lighting characteristic of impressionism? Mr. Brown is making a total of n wooden frames. If he has made two-thirds of them so far, what would be an expression to represent the number of frames he has left to make? researchers have noted that many children who appear to have been reading well in the third grade show a dip in reading performance in the fourth grade. this may be explained by for the given scenario, determine the type of error that was made, if any. (hint: begin by determining the null and alternative hypotheses.) a new whitening toothpaste advertises four shades as the mean number of shades the toothpaste whitens your teeth. one user claims that the mean number of shades the toothpaste whitens your teeth is less than four shades. the user conducts a hypothesis test and fails to reject the null hypothesis. assume that in reality, the mean number of shades the toothpaste whitens your teeth is three shades. was an error made? if so, what type? rahim is looking for ways to increase communication with customers through his company's website. which of the following would be most helpful? --Fatty acid molecules with single bonds between some carbons and double bonds between some carbons are ______________.--A molecule made up of glycerol connected to three fatty acid chains is a ________________.--A chemical reaction in which an ester is converted into a new type of ester is a ____________.--Fatty acid molecules with single bonds between all carbons are ________________.--A type of fuel synthesized by breaking down lipids from natural sources is _______________. which of the following statements are correct regarding viruses? a) all viruses have nucleic acid b) all viruses have proteins c) all viruses have lipid envelopes x/7= -10 what is the answer???? Fill in the blank: A data analyst is working with the World Happiness data in Tableau. To get a better view of Moldova, they use the _____ tool.Single Choice Question. Please Choose The Correct Option ARadialBPanCLassoDRectangular Mihir has 14,203 beads. He uses 36 beads tomake one necklace. How many necklaces canhe make? Hannah is grieving the death of her mother, so she is experiencing extreme stress. She is likely to engage in social distancing. a fight-or-flight response. a tend-and-befriend pattern. an aggressive behavior. Ann recently saw an ad for Claritin, a medicine perfect for counteracting her allergy symptoms. She immediately went to the store to purchase the product. In terms of the communication process, the Claritin ad created a(n) __________.a. stimulusb. exposurec. field of experienced. subconscious impulsee. response benevolence, a charity organization, wants to hire welfare officers who will interact with representatives of the public. apart from the right qualifications and experience, the candidate must be cooperative and altruistic to be able to perform the job well. which of the big five personality traits is benevolence seeking? Consider how sedimentary rocks are formed; from sediments! sediments are composed of particles that often come from existing rocks. How are these particles produced?. as online interaction becomes more common, so too do online friendships. within an online environment, which conceptual element within sociology becomes unavailable to us? Based on what you know and have seen, do you think either of the two broad theories of intelligencegeneral intelligence or modularityis more plausible than the other? why? the energy released by the sun is the result of a) natural radioactivity. d) photosynthesis. b) nuclear fusion. e) nuclear fission. c) combustion of hydrogen. Give an example of a function that is a dilation and a reflection of the parent function. in most states, the seller of a new house warrants that it is fit for habitation even if the deed does not include such a warranty. true false