X=8 y=4 z=0 w=2 <br><br> W(x-2z)=

Show that the equation x^4/2021 − 2021x^2 − x − 3 = 0 has at least two real roots.

andreev551 [17]

The roots of an equation are simply the x-intercepts of the equation.

See below for the proof that $\mathbf{\frac{x^4}{2021} = 2021x^2 - x - 3 = 0}$ has at least two real roots

The equation is given as: $\mathbf{\frac{x^4}{2021} = 2021x^2 - x - 3 = 0}$

There are several ways to show that an equation has real roots, one of these ways is by using graphs.

See attachment for the graph of $\mathbf{\frac{x^4}{2021} = 2021x^2 - x - 3 = 0}$

Next, we count the x-intercepts of the graph (i.e. the points where the equation crosses the x-axis)

From the attached graph, we can see that $\mathbf{\frac{x^4}{2021} = 2021x^2 - x - 3 = 0}$ crosses the x-axis at approximately <em>-2000 and 2000 </em>between the domain -2500 and 2500

This means that $\mathbf{\frac{x^4}{2021} = 2021x^2 - x - 3 = 0}$ has at least two real roots

Read more about roots of an equation at:

brainly.com/question/12912962

6 0

3 years ago

Please help me on this question

viva [34]

I am stuck on same thing as u

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

Calculate the percent change if a city that used to produce 2050 kilowatt hours has reduced their consumption to 1125 kilowatt h

Crazy boy [7]

The percent change if a city that used to produce 2050 kilowatt hours has reduced their consumption to 1125 kilowatt hours is 45.122% decrease.

<h3>What is percentage change?</h3>

Percent increase and percent decrease are measures of percent change, which is the extent to which a variable gains or loses intensity, magnitude, extent, or value.

we know,

% change = (final- initial) / initial * 100

=(1125-2050)/1125 *100

=45.122%

Hence, percentage change be 45.122% decrease.

Learn more about percentage change here:

brainly.com/question/14656289

#SPJ1

5 0

2 years ago

Can you help me write proofs for these, PLEASE!!!

brilliants [131]

Exterior angle theorem and properties of the isosceles triangles are used

prove the specified relations.

Correct responses:

9. ΔPAT ~ ΔPTB by AA similarity postulate

15. $\overleftrightarrow{HM}$ ║ $\overleftrightarrow{JK}$ by basic proportionality theorem

<h3>Detailed methods used to prove response</h3>

9. A two column proof is presented as follows;

Statement ${}$ Reasons

1. ∠PTA = ∠B ${}$ 1. Given

2. ∠PAT = ∠ATB + ∠B ${}$ 2. Exterior angle of a triangle theorem

3. ∠BTP = ∠ATB + ∠PTA ${}$ 3 Angle addition postulate

4. ∠BTP = ∠ATP + ∠B ${}$ 4. Substitution property of equality

5. ∠PAT = ∠BTP ${}$ 5. Substitution property

6. ΔPAT ~ ΔPTB ${}$ 6. AA similarity postulate

The Angle-Angle, AA, similarity postulate states that two triangles are similar if two angles in one triangle are each equal to two angles in the other triangle.

15. A two column proof is presented as follows;

Statement ${}$ Reasons

$\displaystyle 1. \hspace{0.3 cm} \frac{GJ}{HK} = \frac{GK}{GM}$ ${}$ 1. Given

2. ∠1 ≅ ∠G ${}$ 2. Given

3. ΔKHG is an isosceles triangle ${}$ 3. Definition

4. HK = HG ${}$ 4. Legs of an isosceles triangle

$\displaystyle 5. \hspace{0.3 cm} \frac{GJ}{HG} = \frac{GK}{GM}$ ${}$ 5. Substitution property

6. $\overleftrightarrow {HM}$ ║ $\overleftrightarrow{JK}$ ${}$ 6. BPT, Basic Proportionality Theorem

Basic Proportionality Theorem, BPT, states that if a line parallel to one of the sides of a triangle, intersects the other two sides, then the line divides the other two sides in the same proportion.

Learn more about basic proportionality theorem, AA similarity postulate here:

brainly.com/question/14417137

brainly.com/question/17003791

4 0

2 years ago

Jared bought eighteen doughnuts to share with his coworkers. If each doughnut cost c cents, which expression represents his tota

Snezhnost [94]

18 x c= p
need this to extend fgctdrxdfghbgtyfrtyvfg

7 0

3 years ago

X=8 y=4 z=0 w=2 W(x-2z)=