Mathematics High School

Does the equation x² - 4x + y2 = -3 intersect the x-axis?

a. yes, because the center is on the x-axis.

b. no, because the center is at (2,0) and the radius is 1

c. no, because the circle is entirely in the first quadrant.

d. yes, because the center is at (-2,0) and the radius is 3.

Answers

Answer 1

Answer:  a. yes, because the center is on the x-axis.

========================================================

Explanation:

The x intercepts always occur when y = 0.

Replace y with 0 and solve for x

x^2-4x+y^2 = -3

x^2-4x+0^2 = -3

x^2-4x+0 = -3

x^2-4x = -3

x^2-4x+3 = 0

(x-3)(x-1) = 0

x-3 = 0 or x-1 = 0

x = 3 or x = 1

This shows that the x intercepts are located at (3,0) and (1,0). Refer to the diagram below. The diagram shows that the roots are at points A and B. The center is the midpoint of A and B. The center is also on the x axis.

-----------------

Here's another approach:

The general template of a circle is (x-h)^2 + (y-k)^2 = r^2

Let's complete the square of the original given equation to get it into that template form above.

x^2 - 4x + y^2 = -3

(x^2-4x) + y^2 = -3

(x^2-4x+4) + y^2 = -3+4 ... add 4 to both sides

(x-2)^2 + y^2 = 1

(x-2)^2 + (y-0)^2 = 1^2

The equation is now in the template form mentioned earlier. The center is at (h,k) = (2,0) which is on the x axis.

Does The Equation X - 4x + Y2 = -3 Intersect The X-axis?a. Yes, Because The Center Is On The X-axis.b.

Related Questions

An angle measures 97.2° less than the measure of its supplementary angle. What is the measure of each angle?

Answers

Answer:

41.4º

138.6º

Step-by-step explanation:

x + (x - 97.2) = 180

2x - 97.2 = 180

2x = 277.2

x = 138.6º

x - 97.2 = 41.4º

Need help on these questions ASAP DUE TOMORROW PLEASE

Answers

9514 1404 393

Answer:

  3)  D

  4)  D

  5)  B

  6)  B

Step-by-step explanation:

3) A "Pythagorean triple" is a set of 3 integers that could be the sides of a right triangle. The only triangle shown with integer side lengths is choice D.

__

5) The only triangle for which the square of the hypotenuse is the sum of the squares of the other two sides is choice D.

  11² +2² = (5√5)²

  121 + 4 = 125

__

6) The lengths of sides of each right triangle are 2/3 of those of choice D in problem 4. That is, they are a 7-24-25 triangle, multiplied by 2. That means the height is 24·2 = 48, and the area is ...

  A = 1/2bh

  A = 1/2(28 m)(48 m) = 672 m² . . . . matches choice B

__

7) The side lengths of a 30-60-90 triangle have the ratios 1 : √3 : 2. That is, the short leg is half the hypotenuse, a fact stated in A and D. Those true statements make it clear that statement B is false.

Find the area of a parallelogram with a base of 12cm and a height of 5cm. Giving your answer in square meters​

Answers

The answer will be 0.6Meters
Answer: 0.6 cm


Explanation:

Use the measures of angle 4 and 7 to create
an equation and solve for x:
Equation:
X=
so Angle 4 =
degrees

Answers

(5x + 135) + (45) = (180)

One angle is acute and one is obtuse so they are supplementary and add to 180

Use f(x) = 5x+2 and g(x)=x-3
to find (f+g)(x).
A 5x-1
B 5x^2-6
c 6x-1
D 6x+5

Answers

Answer:

d took test

Step-by-step explanation:

egdgxyzydd7fufyfgdvdvxvxhdfrhrhthrueurgrgrhrhrbr

Fifteen million four hundred and ten thousand five hundred
and sixty eight with commas​

Answers

The answer is 15,410,068

PLEASE HELP
IM BEGGING PLEASE

Lake Pyramid, Nevada is one of the best places in the connected 48 states to
catch trophy cutthroat trout. History shows that about 37% of guest catch a
cutthroat. Let X be a random variable that represents the first trip to Lake
Pyramid on which a guest catches a cutthroat. Let X be a random variable that
represents the first trip to Lake Pyramid on which a guest catches a cutthroat.
Find the probability that it takes the fisher no more than 4 trips to catch a
cutthroat. . *

Answers

If an event occurs 0 times (out of 4, in this case) then it does not occur at least once. So we can find the probability of it not occurring and then subtract that value from 1.

So, what are the chances of it not occurring in 1 trip?

1−.37=.63

What about not occurring in 2 trips?

(1−.37)⋅(1−.37)=.63⋅.63=.3969

Now what about not occurring in 4 trips?

.63^4 = 0.15752961

We must subtract this value from 1

(recall that what we just calculated is the probability of it not occurring, so the probability of it occurring at least once is:

1−0.15752961 = .84247039

TLDR - In 4 trips the chance of a guest catching a cutthroat once in under 4 trips in 0.84.

Dominic took a 20-question online quiz. He received 5 points for every correct answer. For every
question he answered incorrectly, he lost 2 points. The quiz also had a 20-point bonus for
finishing in one hour or less. Since Dominic finished the quiz in less than one hour, his score S is
determined by x, the number of questions answered correctly.
Drag and drop expressions into the function to correctly define S(2).
Х
X + 20
X-20
20 - x
2
5
20
S(x) = 5
-2
+

Answers

Answer:

X+20=2 i think this is a little above my head

Please help me solve what was the original height of the post

Answers

Answer:

2.5 is the original height

Step-by-step explanation:

Hope this helps! :)

Given a polyhedron with 15 faces and 32 edges, how many vertices does it have

Answers

mama ate koya bonso tatay lola

A college cafeteria wants to know which lunch food is least popular. Which of the following groups should be interviewed to ensure that the survey results will not be misleading?

A. students who go out for lunch
B. students who bring their lunch
C. students who eat in the cafeteria
D. students’ families

Answers

Answer:

c. students who eat in the cafeteria

Step-by-step explanation:

it wouldnt help to include people who dont eat the food and therefore wont have an honest opinion about the food. They have to talk to the people who do eat the food, which are those who eat in the cafeteria

The answer is c because the group surveyed will directly relate to the data needed.

Find the mode of the data.
Length (inches) of fish in tank:
2, 3, 1, 4, 5, 2, 2
Mode: [?] in.

Answers

Answer:

The mode is 2 in.

Step-by-step explanation:

The mode of a data set is the number that occurs most frequently in the set which in this case, this data is 2.

Hope this is helpful.

9. Express 20% as a decimal and as a fraction.

Answers

Ok as a decimal it is .20 and as a fraction it could be 2/10

Classify the following triangle check all that apply

Answers

Answer:

Option E, Acute

Option F, Scalene

Hope this helps!

Answer:

Acute & Scalene

Step-by-step explanation:

This triangle has no equal sides. Therefore, it is scalene.

Moreover, this triangle has no angles greater than or equal to 90°. Therefore, it is also acute.

Geometry
Introduction to chord lengths in a circle

Answers

Answer:

x is equal to 6

Step-by-step explanation:

in a circle the perpendicular from centre to any chord bisects the chord into 2 equal parts.

[NO LINKS]
This is Jovan’s solution for the equation x^2-8x-9=0:

x2 – 8x – 9 = 0

x2 – 8x = 9

x2 – 8x + 16 = 9 + 16

(x – 4)2 = 25

x – 4 = 25 and x – 4 = - 25

x = 29 and x = -21

Is Jovan’s solution correct?

Answers

Answer:

No, it's wrong

[tex] {x}^{2} - 8x - 9 = 0 \\ (x - 9)(x + 1) = 0 \\ x = 9 \: and \: - 1[/tex]

Answer:

No

Step-by-step explanation:

x² – 8x – 9 = 0 x² – 8x = 9 x² – 8x + 16 = 9 + 16 (x – 4)² = 25 x – 4 = 25 and x – 4 = - 25 ⇒ Incorrect, should be x - 4 = 5 and x - 4 = -5 x = 29 and x = -21                ⇒ Incorrect, should be x = 9 and x = -1

The green line below Check all that apply. A crosses the x axis B. is parallel to the x-axis O c. crosses the yaxis D D. crosses the origin I E. is in the xy plane D F is perpendicular to the yaxis​

Answers

Answer:

a, c, d, e

Step-by-step explanation:

Which choice is a correct equation for the line graphed below?

Please hurry!!!

Answers

Answer:

y = 3x + 1

Step-by-step explanation:

The y - intercept is +1

And the rise over run = 3/1  (because 3 is also 3/1)

Pictures are attached.

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

A) y=3x+1

1 is the y-intercept (it is on the y axis)

you start at the 1 on the graph where the line passes through, then go 3 squares up and 1 to the right to land on the line again. This is rise over run, which you rise 3 squares up from 1, then run 1 square to the right. 3/1 = 3

Malachy and Paul win some money and share it in the ratio 2:1. Malachy gets £24 more than Paul. How much did they get altogether?

Answers

Step-by-step explanation:

How was Toto an expensive deal for grandfather? Do you think it

was a lesson for grandfather?

PLEASE HELP 50 points

Answers

Answer:

Scalene triangle [any side and angle are not equal]isosceles triangle [two side and two angle are equal]equilateral triangle [all sides and angle are equal]right angled isosceles triangle [having one angle 90° and two other side and two angle are equal]scalene triangleequilateral triangleright angled trianglescalene triangleright angled isosceles triangleright angled isosceles trianglescalene triangleisosceles triangleequilateral triangleright angled triangleright angled isosceles triangleisosceles trianglescalene triangleequilateral triangleright angled isosceles triangleisosceles triangleequilateral trianglescalene triangleisosceles triangleright angled isosceles triangleright angled triangleright angled isosceles triangleisosceles triangle

Of the 25 students who take a standardized test, the minimum score is 98 and the maximum score is 312. The mean score is 216. Standard deviation is 52. What is the number of standard deviations that includes all the data values?

Answers

Answer:

5

Step-by-step explanation:

so we can say that 5 standard deviations include all the data values.

what is the correct answer​

Answers

Answer:

The answer is A (8 inch)

Step-by-step explanation:

All if the sides and angles are the same.

Does anyone know this one !??

Answers

Answer:

I can't see what this says

Step-by-step explanation:

Ranking the correct answer brainliest !

Answers

Answer:

∠ 3 = 115°

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠ 3 is an exterior angle of the triangle, then

∠ 3 = ∠ 1 + ∠ 2 = 68° + 47° = 115°

Now solve this equation for y. Remember the roller coaster is above ground, so you are only interested in the positive root.

Answers

Answer:

[tex]y = \sqrt{ 900 - x\²[/tex]

Step-by-step explanation:

In the complete question, the area of  the roller coaster is:

[tex]x\² + y^2 = 900[/tex]

Required

Solve for y

We have:

[tex]x\² + y^2 = 900[/tex]

Subtract [tex]x\²[/tex] from both sides

[tex]y^2 = 900 - x\²[/tex]

Take positive roots of both sides

[tex]y = \sqrt{ 900 - x\²[/tex]

20 POINTS!
The time t required to drive a certain distance varies inversely with the speed r. If it takes 4 hours
to drive the distance at 50 miles per hour, how long will it take to drive the same distance at 40
miles per hour?

Answers

Answer:

1.78 hours

Step-by-step explanation:

If t varies inversely with the speed, the formula for that is  t= \frac{k}{r} .  If t = 2 and r = 40, then we can solve for k, the constant of variation.  Multiply both sides by 40 to get  k = 80.  Now we need to find the value for t when r = 45.  Using the k value we just solved for, we will fill in the equation as  t= \frac{80}{45}   for a t value of about 1.78 hours

What is the converse of the conditional statement?
If x is even, then x + 1 is odd.
If x is not even, then x + 1 is not odd.
O If x + 1 is odd, then x is even.
Olf x + 1 is not odd, then x is not even.
If x is even, then x + 1 is not odd.

Answers

Its your second answer choice

Answer:

Step-by-step explanation:

it's b

Find the surface area of a cylinder with a height of 11 feet and base radius of 3 feet.
______ square feet​

Answers

Answer:

the surface area is 263.76 feet²

hope this helps

have a nice day

Dan is making a model volcano for the science fair. He wants an awesome eruption, so he
tries different amounts of baking soda and vinegar. First, he tries 2 tablespoons of baking
soda and 6 tablespoons of vinegar. Next, he tries 3 tablespoons of baking soda and 9
tablespoons of vinegar. Did Dan use the same ratio of baking soda to vinegar in both
eruptions?
yes
no

Answers

Answer:

Yes

Step-by-step explanation:

Dan used 2 and 6, and after 3 and 9. If you multiply 2×1.5 = 3, and 6×1.5 = 9, so the ratio is the same and is equal to 1.5

Answer:

Yes

Step-by-step explanation:

2/6 for the first ratio can be reduced to 1/3

3/9 for the second ratio can also be reduced to 1/3

What is the inequality for this verbal description? The value of yis less than or equal to the sum of six times the value of x and three. IN O A. y56x+ 3 O B. ys 3x + 6 O c. yz 6x+ 3 O D. y: 3x + 6 SUBMIT​

Answers

Answer:

y =< 6x + 3

you copypasta looks weird, but I would go for option c if i read this correctly

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