1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Masteriza [31]
3 years ago
13

The line x = k intersects the graph of the parabola x = -2y^2 - 3y + 5 at exactly one point. What is k? Thank you! :)

Mathematics
1 answer:
bearhunter [10]3 years ago
6 0

Answer:

49/8 is the value of k

Step-by-step explanation:

We have the system

x = -2y^2 - 3y + 5

x=k

We want to find k such that the system intersects once.

If we substitute the second into the first giving us k=-2y^2-3y+5 we should see we have a quadratic equation in terms of variable y.

This equation has one solution when it's discriminant is 0.

Let's first rewrite the equation in standard form.

Subtracting k on both sides gives

0=-2y^2-3y+5-k

The discriminant can be found by evaluating

b^2-4ac.

Upon comparing 0=-2y^2-3y+5-k to 0=ax^2+bx+c, we see that

a=-2, b=-3, and c=5-k.

So we want to solve the following equation for k:

(-3)^2-4(-2)(5-k)=0

9+8(5-k)=0

Distribute:

9+40-8k=0

49-8k=0

Add 8k on both sides:

49=8k

Divide both sides by 8"

49/8=k

You might be interested in
Find a​ point-slope form for the line with slope
Katen [24]

Answer:

It is Third quardant in Graph

7 0
2 years ago
In the figure, and bisect each other. Complete the statements to prove that quadrilateral ABCD is a parallelogram.
Alisiya [41]

Observe the figure below.

    Statement                                                                          Reason

1. AC and BD bisect each other                                             Given

2. AE = EC and BE = ED                                                         Definition of bisection

3. m \angle AEB = m \angle CED                       Vertical angle theorem

Vertical angle theorem states " When two lines intersect each other, the vertically opposite angles are always equal".

4. \Delta ABE \cong \Delta CDE                         SAS criterion for congruence

5. m \angle ACD = m \angle CAB           Corresponding angles of congruent triangles are congruent

6. AB \parallel CD                                 Converse of alternate interior angle theorem

7.  m \angle BEC = m \angle AED                   Vertical angle theorem

8.  \Delta BEC \cong \Delta DEA            SAS criterion for congruence

9.  BC \parallel AD                                 Converse of alternate interior angle theorem

As, \Delta BEC \cong \Delta DEA, so m \angle CBD = m \angle BDA as corresponding parts of corresponding triangles are equal. As these angles are alternate interior angles, so the lines BC and AD are parallel by  "Converse of alternate interior angle theorem".

5 0
3 years ago
What is the overtime rate for lifeguard who regularly earns $8.75 per hour?
TEA [102]
The overtime rate is an added percentage to the regular rate. By how much percentage, this would depend on the place you're working. If your work in USA, under US federal labor and tax law, the rate would be 150%. Thus, the overtime rate would then be:

Overtime rate = $8.75/hour * 1.50 = $13.125/hour
3 0
3 years ago
What’s the formula to find the shaded area?
trapecia [35]

<em>shaded</em><em> </em><em>area</em><em> </em><em>=</em><em> </em><em>area</em><em> </em><em>of</em><em> </em><em>outer</em><em> </em><em>figure</em><em> </em><em>-</em><em> </em><em>area</em><em> </em><em>of</em><em> </em><em>inner</em><em> </em><em>figure</em><em>.</em><em>.</em><em>.</em><em>.</em><em>.</em><em>.</em><em>.</em><em>.</em>

3 0
2 years ago
Read 2 more answers
he equation of a line is y=2/3 x + 5. What is an equation of the line that is perpendicular to the given line and that passes th
Levart [38]
2/3 × m2 = - 1
m2 = - 3/2

2 = - 3/2(4) + c
4 = - 12 + 2c
2c = 16
c = 8
y = - 3/2x + 8
5 0
3 years ago
Other questions:
  • I thought it was 25/100 buts it’s wrong
    10·1 answer
  • Find the rate of change for this linear function Y equals MX plus be
    11·1 answer
  • Which statement is correct?
    7·1 answer
  • The measure of the angles of triangle ABC are given by the expressions in the table.
    12·2 answers
  • What is the distance between (8, -3)(4,−7)
    6·1 answer
  • The graph of the equation y=2x^2-2 is shown which equation will shift the graph up 3 units
    7·1 answer
  • HELP! WILL GIVE BRANLIEST!!!
    11·2 answers
  • Decide if the answer to 8/7 x 12 is less than, greater than, or equal to 12.
    14·2 answers
  • Kassie recorded the favorite sport of students at her school. She surveyed 800 students. How many more students chose Baseball t
    14·1 answer
  • Janie and Jasmine are playing three games at an arcade. Each of the games requires either 2, 3, or 4 tokens. The girls plan to p
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!