Solve the quadratic equation below by completing the square. What are the solutions?
x^2 - 16x + 50 = 21
A. X= -8+sqrt 7
B. X= 8 + sqrt 7
C. X= 8 +sqrt 35
D. X= -8+sqrt 35

Answers

Answer 1

By completing squares we will see that the solutions are:

[tex]x =\pm \sqrt{35} + 8[/tex]

How to complete squares?

Here we have the quadratic equation:

[tex]x^2 - 16x + 50 = 21[/tex]

We can rewrite it as:

[tex]x^2 - 2*8*x + 50 - 21 = 0\\\\x^2 - 2*8*x + 29= 0[/tex]

Then we must have a 8² term to complete squares, then we need to add and subtract 35.

[tex]x^2 - 2*8*x + 29 +35 - 35= 0\\\\(x - 8)^2 - 35 = 0\\\\(x - 8)^2 = 35[/tex]

Now we can solve this:

[tex]x =\pm \sqrt{35} + 8[/tex]

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Related Questions

What is the image point of (7, 0) after a translation right 2 units and up 1 unit

Answers

Answer:

(9,1)

Step-by-step explanation:

The required image of the point of (7, 0) after a translation right 2 units and up 1 unit is (9, 1).

As mentioned in the question, the image point of (7, 0) after a translation right 2 units and up 1 unit is to be determined.

What is coordinate?

Coordinate, is represented as the values on the x-axis and y-axis of the graph. while the coordinate x is called abscissa and the coordinate of the y is called ordinate.

Here,
The image point of (7, 0) after a translation right 2 units and up 1 unit is given as,
= (x + x', y + y')
= (7 + 2, 0 + 1)
= (9, 1)

 

Thus, the required image of the point of (7, 0) after a translation right 2 units and up 1 unit is (9, 1).

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⚠️HURRY⚠️
write an equation that matches this graph in Slope-Intercept Form

Answers

Answer:

y = -1/4x+2

Step-by-step explanation:

Answer:

y = -1/4x + 2

Step-by-step explanation:

We can tell that the line passes trough the point (0, 2), so the y-intercept is 2.

Let's calculate the slope by using rise over run. We see for every one unit down, it goes 4 units to the right. It also goes downward, so the slope is negative. So the slope is -1/4. Put it together...

y = -1/4x + 2

Hope this helps!

2-10n plez helppppppppppppppppppppp

Answers

Answer:

2-10n=.............what. We can't figure out n given 2-10n without a solution

Step-by-step explanation:

This doesn’t make sense

plz help me i need it​

Answers

I can't see the choices real well, but I think it's b, 35%.

Answer:

B 35% is the answer

In JL, K is the midpoint. The coordinates of J are (2, 2), and the
coordinates of Kare (10, 11). What are the coordinates of L?

Answers

(6,6.5) u can do the math simply

Which part of the figure shows evidence of the use of a compass?

Answers

Answer:

Whichever line is curved like a semi-circle, arch, or a full circle.

Step-by-step explanation:

A compass is a tool used to draw curved lines.

What is the equation of the line that passes through the point (2,-5) and is
perpendicular to y = 1/4x - 5? *
O y = -4x + 3
O y = 1/4x + 11/2
O y = -4x - 13
O y = -4X - 3

Answers

Answer:

y=-4x+3

if you bring (2,-5) in other three lines.

you will know that it will be unreasonable that

-5=10

-5=-21

-5=-11

Idk how to fill this in .

Answers

Answer:

3, 3, 6,9,12 if that's wrong try 3, 3, 6, 12, 36, 144

Step-by-step explanation:

you just multiply the numbers together to get your answer


Please can anyone help me

Find the missing coordinate if the ordered pair is to be a solution to the given equation.
(-3, ?) for the equation 4x + y = 5

Answers

Answer:

17 (I think)

Step-by-step explanation:

substitue -3 in for x so 4(-3) + y = 5

-12+ y =5

+12        +12

y=17

Miguel completed the division problem below. What is Miguel's error? A.He included a 5 in the quotient, which does not belong. B.He multiplied the divisor by 10 and the dividend by 100. C.He subtracted 208 from 234 incorrectly. D.He multiplied the divisor by 100 and the dividend by 10.

Answers

The image of the division problem is missing, so i have attached it.

Answer:

D: He multiplied the divisor by 100 and the dividend by 10.

Step-by-step explanation:

From the image, we can see from the initial values, they are trying to divide 0.52 by 754.

In Mathematics, it means that 0.52 is the divisor while 754 is the dividend.

Now, the next step sees 0.52 changed to 52 while 754 changes to 7540.

Now, 0.52 to 52 means 0.52 was multiplied by 100.

This means that 754 should also be multiplied by 100 to give 75400 in order to retain the original answer that would have been gotten if we had divided 0.52 by 754.

Yet they used 7540.

Thus,the error is that he multiplied the divisor by 100 while he multiplied the dividend by 10.

Answer :

D - He multiplied the divisor by 100 and the dividend by 10.

What is the distance between (8, -3)and (4,−7)?

Answers

Answer:

+4sqrt(2)

Step-by-step explanation:

Note that the horizontal distance is 8 - 4, or 4 (which is the "run") and that the vertical distance is -3 - (-7), or 4 (which is the "rise").  Applying the Pythagorean Theorem, we get:

distance = length of hypotenuse = +sqrt(4^2 + 4^2) = +4sqrt(2)

Which shows how to best estimate the product of 0.4 x 0.93?

0 x 1 = 0
0.5 x 0.5 = 0.25
0.5 x 1 = 0.5
1 x 1 = 1

Answers

Answer:

b

Step-by-step explanation:

Answer:

C. 0.5 times 1 = 0.5

would you rather drive a car at the rate of 40 kilometers per hour or drive a car at a rate of 15 meters per second, and why? which one is correct

Answers

Answer: 15 meters per second

Step-by-step explanation: Kilometers are 1,000 times larger than meters

Find the minimum value of
C=x+3y

Answers

Answer:

DNE

Step-by-step explanation:

If x and y may be any real number, there is no minimum value for C. It can approach negative infinity.

If C is a constant, and the domain of x is all real numbers, there is no minimum for y. It can approach negative infinity.

We're not sure what you want or what restrictions may exist. The given relation does not suggest any minimum. We'd have to say it Does Not Exist

Hello there,

Use the first constraint to isolate y :

[tex]9x+2y\geq 35[/tex]

[tex]y \geq \frac{35-9x}{2}[/tex]

Now use the second one to isolate x :

[tex]x+3y\geq 14[/tex]

[tex]x\geq 14-3y[/tex]

You know that [tex]x\geq 0[/tex] and [tex]y\geq 0[/tex]

So what's the minimum value of x it's 0 ! Same for y !

So substitute x by 0 and y by 0

[tex]y\geq \frac{35}{2} =17.5[/tex]

[tex]x\geq 14[/tex]

So the minimum value of C is :

[tex]C=14+3*17.5[/tex]

[tex]\boxed{C=66.5}[/tex]

Hope it helps !

Photon

Find three consecutive even integers such that their sum decreased by 34 is equal to the first integer. Find the first integer.

Answers

Answer:

The first number: 14

The second number: 16

The third number: 18

Step-by-step explanation:

Equations

Let's assume:

x=the first even number.

x+2=the second even number

x+4=the third even number

The sum of all three is: x + x + 2 + x + 4

The condition states the sum decreased by 34 equals the first number:

x + x + 2 + x + 4 - 34 = x

Moving all the variables to the left side and the numbers to the right side:

x + x + 2 + x + 4 - 34 - x = 34 - 2 - 4

Simplifying:

2x =  28

Solving:

x = 28 / 2 = 14

The first number: 14

The second number: 16

The third number: 18

713.49 written in standard form

Answers

Answer:

7.1349 * 102

Step-by-step explanation:

Hope this helps. Have a great day!

Find X if PQR is an isosceles triangle. Please

Answers

Answer:

x=9

Step-by-step explanation:

because its isosceles, and as stated PQ = QR

so...

2x+1=3x-8

solve for x

x=9

Hope you are having a good day!

Answer:

The value of X in isosceles triangle is 9

Write the equation of the line passing through the points -2,3 and -1,-2 in slope intercept and point slope form

Answers

Answer:

y=-5x-7

Step-by-step explanation:

y=-5x-7

Hope you are having a good day!

Answer:

-26

Step-by-step explanation:

-23 + (-1-2) = -26

15!!! POINTS!!! PLS ANSWER THIS IM HAVING WAY TOO MUCH TROUBLE WITH IT. I’m in 10th grade and this is compound interest. PLS HELP ME IXLS SO FRUSTRATING!!! If you don’t know PLS don’t comment I’ve been doing this for over 2 hours pls

Answers

Answer:

well im in 7th sorry i cant help

Step-by-step explanation:

Answer:

6 years

Step-by-step explanation:

if we want to know how much i will get with interest

simple interest amount = principal amount × (rate / m) × n

plus the initial quantity

where m is 12 months per year

and n is the number of months

[tex]4451=2887(\frac{0.09}{12months/year})(n)+2887\\\\4451=2887[\frac{0.09}{12}(n)+1]\\\\(\frac{0.09}{12}\cdot n)+1=\frac{4451}{2887}\\\\\frac{0.09}{12}\cdot n=1.54-1\\\\n(0.09)=12(0.54)\\\\n=\frac{12(0.54)}{0.09}\\\\n=72.23\longleftarrow months[/tex]

so we need to convert it to years

[tex]72.23=12(6)+0.019[/tex]

6 years and 0 months

I apologize if there is some mistake in my answer

ASAP ASAP ASAP
PLEASE HELP ME

Answers

Answer:

d

Step-by-step explanation:

Answer:

I rlly don't know how to help you bruh

Step-by-step explanation:

Why I can't understand the question and as to what they mean by if you fold it as shown though i know they probably mean where the shapes on the side are I say find someone else or take a wild guess.

A man drove 13 mi directly east from his home, made a left turn at an intersection, and then traveled 5 mi north to his place of work. If a road was made directly from his home to his place of work, what would its distance be to the nearest tenth of a mile?

Answers

Answer:

13.93 miles

Step-by-step explanation:

From the given information:

we are being told that a drove 13 miles towards east from home.

and make a left turn due north, thus travel 5 miles.

The objective is to find the man's distance from his starting point(i.e. his home) to his place of work.

Let the horizontal base distance be x = adjacent side = 13 miles

Let the vertical distance be y = opposite side = 5 miles

Let the slant distance be z = hypotenuse side =  ??? (unknown)

Therefore, using the pythagoras theorem.

(hypotenuse)² = (opposite)² + (adjacent)²

z² = y² + x²

z² = 5² + 13²

z² = 25 + 169

z² = 194

[tex]z = \sqrt{194}[/tex]

z = 13.93 miles

the amount of money in a bank account

Answers

Answer:

I currently have $-68

Step-by-step explanation:

2-83. Build, simplify, and solve each equation. Record your work. Drag the tiles below into the equation mat.
a. -x+ 2 = 4​

Answers

Answer:

you need to add 2 to the x and convert it to negative   X=-2

Step-by-step explanation:

The equation P=$3.90+$0.10x represents the hourly pay(P) a worker receives for loading x number of boxes onto a truck. What is the slope of the line represented by the given equation?

Answers

Answer:

The slope of the line is 0.1.

-0.8 x +40 - 8x -35 i need help ASAP

Answers

Answer:

-8.8x + 5

Step-by-step explanation:

See the attached picture.

Hope this helps!!!

The value of x is 0.57 in the given expression -0.8 x +40 - 8x -35

What is Expression?

An expression is combination of variables, numbers and operators.

The given expression is -0.8 x +40 - 8x -35

Minus zero point eight times of x plus forty minus eight times of x minus thirty five

-0.8 x +40 - 8x -35

Add the like terms

-0.8x-8x+40-35

-8.8x+5

Isolate the variable x

-8.8x=-5

Divide both sides by 8.8

x=5/8.8

x=0.57

Hence, the value of x is 0.57 in the given expression -0.8 x +40 - 8x -35

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What is x (in degrees)

Answers

Answer: 4

Step-by-step explanation:

By the exterior angle theorem,

[tex]11x+32x=172\\\\43x=172\\\\x=\boxed{4}[/tex]

You are doing chores to earn your allowance. For each chore you do, you earn $3. In the equation below, C is the
number of chores you do, and d is the number of dollars you earn.
The relationship between these two variables can be expressed by the following equation:
d=3c
Identify the dependent and independent variables.
Dependent variable
Independent variable
The number of chores you do
The number of dollars you earn

Answers

The independent variable is d because it is alone or independent. The dependent variable is c because it stands with the number three.

Answer:

Independent- c (number of chores)

Dependent- d (number of dollars)

Step-by-step explanation:

0.52 X 2.1 =
Help i don’t understand

Answers

Answer:

1.092

Step-by-step explanation:

What is the slope of a line parallel to the line whose equation is 6x-y=1. Fully reduce your answer.

Answers

Answer:

0, -1

1, 5

(Hope it helped)

Answer:

I believe the slope is 6  

Step-by-step explanation:

6x - y = 1

- y = - 6x + 1

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

y = 6x + 1

6 = slope

common factor the GCF of 27y^2 and 36^3​

Answers

9 because it is the highest number that it can go it both 27 and 36
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