Let ​ x² + 15x = 49 .​ What values make an equivalent number sentence after completing the square? Enter your answers in the boxes.

x² + 15x + ​= ​ [ ]

Answers

Answer 1

Answer:

Step-by-step explanation:

15/2 = 7.5 and (7.5)^2 = 56.25  so

x^2 + 15x + 56.25 = 49 + 56.25

x^2 + 15x + 56.25 = 105.25.

Answer 2

Answer:

[tex]x^2+15x+\boxed{\dfrac{225}{4}}=\boxed{\dfrac{421}{4}}[/tex]

[tex]x^2+15x+\boxed{56.25}=\boxed{105.25}[/tex]

Step-by-step explanation:

General form of a quadratic equation: [tex]ax^2+bx+c[/tex]

When completing the square, first add the number that is the square of half of [tex]b[/tex].

Given equation:  [tex]x^2+15x=49[/tex]

Therefore, [tex]b=15[/tex]

[tex]\implies \left(\dfrac{b}{2}\right)^2=\left(\dfrac{15}{2}\right)^2=\dfrac{225}{4}[/tex]

So we need to add 225/4 to both sides of the equation:

[tex]\implies x^2+15x+\dfrac{225}{4}=49+\dfrac{225}{4}[/tex]

[tex]\implies x^2+15x+\boxed{\dfrac{225}{4}}=\boxed{\dfrac{421}{4}}[/tex]

In decimal form:

[tex]\implies x^2+15x+\boxed{56.25}=\boxed{105.25}[/tex]

To finish completing the square,

factor the left side of the equation:

[tex]\implies \left(x+\dfrac{15}{2}\right)^2=\dfrac{421}{4}[/tex]

Finally, subtract 421/4 from both sides:

[tex]\implies \left(x+\dfrac{15}{2}\right)^2-\dfrac{421}{4}=0[/tex]

In decimal form:

[tex]\implies (x+7.5)^2-105.25=0[/tex]


Related Questions

Kim is installing blue
white tile in her bathroom. She
made a diagram of
the layout showing the area of both colors. Write two
expressions that describe the area of the blue tile.

Answers

Answer:

4/9, 44.4%

Step-by-step explanation:

16 tiles are blue out of 36

16/36 = 4/9

4 ÷ 9 × 100 = 44.4%

Convert 67,000 pounds to tons. choose the words and numbers to complete the statements. a pound is choose... than a ton, so choose... the number of pounds by choose... to find the number of tons. therefore, 67,000 pounds is choose... tons.

Answers

Answer:

See below

Step-by-step explanation:

A POUND IS   1/2000 of a ton    so  multiply the number of pounds by 1/2000 to find the number of tons   therefore   67 000 pounds is 33.5 tons

Answer:

A pound is (larger) than a ton, so (multiply) the number of pounds by (1000) to find the number of tons. Therefore, 67,000 pounds is  (33.5) tons.

Step-by-step explanation:

when you see ( ) it means it's the answer

CAN SOMEONE HELP PLEASE IM BEGGING YOU PLAS

Answers

Substitute each value and see the answers

The average height of Hillsdale College's student body is 64.8 inches. If the 600 women at the college average 64 inches, what is the average height of the 400 men at the college? Show work.

Answers

Answer:

dont know bro

Step-by-step explanation:

An ecologist wants to know what percent of the 10,000 fish in a lake are cod. She conducts a study in which 50 fish are randomly caught. Of those 50 fish, 15 are cod. Based on this data, using a 95% confidence interval, the researcher can determine that the percent of fish that are cod in the lake is which of the following?

(1) Between 17% and 43%
(2) Exactly 30%
(3) Between 24% and 36%
(4) Between 20% and 40%

Answers

Answer:

3

Step-by-step explanation:

Because there are about 3,000 fish in the lake, 3,000 is 30 percent of 10,000. C or (3) gives the 6 percent each way around 30.

 Which of the following side lengths do not make up a right triangle?

A. 3,4,5
B. 5,12,13
C. 7,22,25
D. 8,15,17

Answers

2/22/55 does not make a right triangle

Answer:

C. 7,22,25

Step-by-step explanation:

A. 3,4,5

=> p² + b² = h²

=> 3²+4² = 5²

=> 9+16 = 25

=> 25 = 25

B. 5,12,13

=> 5² + 12² = 13²

=> 25 + 144 = 169

=> 169 = 169

C. 7,22,25

=> 7² + 22² = 25²

=> 49 + 484 = 625

=> 533 625

D. 8,15,17

=> 8² + 15² = 17²

=> 64 + 225 = 289

=> 289 = 289

so, the side that lengths do not make up right triangle is C. 7,22,25

what is 2+2 divided by 50

Answers

Answer: 2.04

Step-by-step explanation:

2+2=4

4/50 = 2.04

two days of the year on which the noon sun is directly overhead at nearly 23.5 south or north December 21st and June 21

Answers

June 21st - summer solstice

December 21st - winter solstice

hope it helps...!!!

A bakery sells mocha cupcakes and chocolate cupcakes. One day it sold 238 mocha and 42 chocolate. What percent of the cupcakes sold that day were mocha?

Answers

Answer:

35%

Step-by-step explanation:

The required percentage of the mocha cupcakes that were sold that day is 85%.

Given that,
A bakery sells mocha cupcakes and chocolate cupcakes. One day it sold 238 mochas and 42 chocolate. What percent of the cupcakes sold that day were mocha is to be determined.

What is the percentage?

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,
Number of mocha cupcakes = 238
Number of chocolate cupcakes = 42
Total cupcakes = 238 + 42 = 280
Percentage of mocha sold = 238/280 = 0.85 or 85%

Thus,  the required percentage of the mocha cupcakes that were sold that day is 85%.

Learn more about percentages here:

brainly.com/question/13450942

#SPJ5


What equation is graphed in this figure?
y - 4 = -⅓(x+2)
y - 3 = ⅓ (x+1)
y + 2 = -3(x – 1)
y - 5 = 3(x - 1)​

Answers

to get the equation of any straight line, we simply need two points off of it, let's use those two points in the picture below.

[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{5}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{5}-\stackrel{y1}{2}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{0}}}\implies \cfrac{3}{1}\implies 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_2=m(x-x_2) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_2}{5}=\stackrel{m}{3}(x-\stackrel{x_2}{1})[/tex]

keeping in mind that for the point-slope form, either point will do, in this case we used the second one, but the first one would have worked just the same.

help mah please I give dollar​

Answers

Answer:

45 + X

Step-by-step explanation:

i didnt read it correctly sorry

help please!!!! it makes so sense

Answers

Answer:

(- [tex]\frac{1}{5}[/tex] , 0 )

Step-by-step explanation:

to find where the line crosses the x- axis, let y = 0 in the equation and solve for x

5x - 2(0) + 1 = 0

5x - 0 + 1 = 0

5x + 1 = 0 ( subtract 1 from both sides )

5x = - 1 ( divide both sides by 5 )

x = - [tex]\frac{1}{5}[/tex]

the line crosses the x- axis at (- [tex]\frac{1}{5}[/tex], 0 ) or ( - 0.2, 0 )

Answer:

(-1/5, 0).

Step-by-step explanation:

Where the line crosses the axis the value of y = 0.

5x - 2y + 1 = 0

Let y = 0, then:

5x - 2(0) + 1 = 0

5x + 1 = 0

5x = -1

x = -1/5.

So the point is (-1/5, 0).

Solve the system of equations algebraically show all work.

Y=-x^2+8x+11

Y=5x-7

Answers

Answer:

ummmm..... let's see..

Step-by-step explanation:

using "Almighty formula"

{Y = –x +/– √b^2 – 4ac / 2a}

so we name all the values behind the coefficients which are; –1^2, 8 and 11

so let's assign a,b,c to these values:

a =–1, b =8, c = 11

all you just do now is to add these values to the formula

you should be having Y =1 +/– √8^2 – 4×–1×11

———————————

2×–1

Y =1 +108

———— or Y = 1–108

–2 –––––

–2

now add and divide to get Y.

(your answer will be two)

Help me please I need to get my grade up

Answers

Answer:

Um I can only see a graph

Step-by-step explanation:

Bailey rolls a pair of dice 12 times, and the sum of 6 came up 5 times to calculate the experimental and theoretical probabilities of rolling a sum of six with a pair of dice

Answers

Answers:

Experimental probability =  5/12

Theoretical probability = 5/36

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

Explanation:

The experimental probability, aka empirical probability, is what we observe to happen. The event of rolling a six happens 5 times out of 12 total rolls. That leads directly to the experimental probability of 5/12

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

The theoretical probability is based on predetermined odds, and can be done on paper rather than actually rolling the dice.

There are 6*6 = 36 ways to roll two dice. Of those 36 ways, we have these cases that add to 6

1+5 = 62+4 = 63+3 = 64+2 = 65+1 = 6

There are five ways to add to 6, out of 36 outcomes total.

This means the theoretical probability of getting a sum of 6 is 5/36

Zack sold 3 of his old hockey sticks at Refreeze Secondhand Sports Shop. Before he left, he spent $25 of his earnings on a used pair of hockey gloves. He had $71 remaining. How much did Zack receive for each hockey stick?

Answers

Answer:

Zack received $32 for each hockey stick

Step-by-step explanation:

how I did it:

$71+$25=96

now you divide 96 by 3

      3 2

3    9  6

− 9  

 0 6

−   6

   0  

96 divided by 3 is equal to $32.

Hence, Zack received $32 for each hockey stick.

NO LINKS!!


Find the volume of each sphere, both in terms of p and to the

nearest tenth. Use 3. 14 for p.

r = 6. 12 cm

d = 54 in

Answers

Volumn of 1st Sphere =
4/3 x pi x r^3= 959.7 cm^3
In terms of pi = 305 pi cm^3

Volumn of 2nd sphere =
4/3 x pi x (1/2 diameter of 54)^3
4/3 x 3.14 x 27^3 = 82406.2 in^3
In terms of pi = 26244 pi in^3

pls help me with this

Answers

try 4 vertices and 6 edges

Answer:

4 vertices6 edges

Step-by-step explanation:

A vertex is where three or more edges come together. All of the vertices are shown in the picture, so you can count them. There are 4 vertices.

An edge is where plane faces meet in a line. All of the edges except one are shown as solid lines in the figure. (The remaining edge is shown as a dashed line.) You can count them. There are 6 edges.

What are the least and greatest fractors of 45? of 36? of 60?​

Answers

The GCF for 45,36,60 is 3

The LCM for 45,36,60 is 180

hope this helps

Write the equation of a line in slope-intercept form that passes through the point (0,-7) and has a slope of 3/4.

Answers

Answer:

y=3/4x-7

Step-by-step explanation:

(0,-7) is the y-intercept

3/4 is the slope

y=mx+b

m is the slope

b is the y-intercept

plug it in:

y=3/4x-7

please mark brainliest!

Factor the expression x2 - 36.

Answers

Answer:

x = -6 or 6

Step-by-step explanation:

=> - 36

=> x² - 6²

=>(x + 6 ) (x - 6)

=> x = -6 or x = 6

[tex]x^2-36\\\\=x^2-6^2\\\\=(x+6)(x-6)[/tex]

please help me

Question
A coin is flipped three times, and the following list shows the possible outcomes.

HHH, HHT, HTH, HTT, THH, THT, TTH, TTT

How many outcomes include exactly one head?

Enter your answer as a number, like this: 42

Answers

Answer:

1/8 is the probability to have exactly one head

HELP PLEASE EXPLAIN HOW TO EVALUATE

Answers

Answer:

165

Step-by-step explanation:

The symbol [tex]\sum[/tex]  is used to denote a sum of multiple terms.

The number below [tex]\sum[/tex] is the first term.

The number above [tex]\sum[/tex] is the last term.

Each term can be determined by using the given equation.

[tex]\begin{aligned}\displaystyle \sum_{n=3}^{8}5n & =5(3)+5(4)+5(5)+5(6)+5(7)+5(8)\\ & = 5(3+4+5+6+7+8)\\ & =5(33)\\ & = 165\end{aligned}[/tex]

n=[3,8]

So

[tex]\\ \rm\Rrightarrow \sum^8_{n=3}5n[/tex]

[tex]\\ \rm\Rrightarrow 5(3)+5(4)+5(5)+5(6)+5(7)+5(8)[/tex]

[tex]\\ \rm\Rrightarrow 15+20+25+30+35+40[/tex]

[tex]\\ \rm\Rrightarrow 165[/tex]

Jorge finds that 56% of his 75 classmates like salsa music and 80% of his 60 relatives like salsa music. How many more of Jorge’s relatives, as compared to his classmates, like salsa music?

Answers

Answer: 6

Step-by-step explanation:

Classmate: 56/100 × 75/1 =42

relative: 80/100 × 60/1 = 48

Difference is 6

1. Given: LMN ~ QPR, find RQ.

Answers

Answer:

C. 27

Step-by-step explanation:

If those two triangles are similar then look at how much one side is being increased to the other triangle. ML is similar to PQ and it increases by 1.5 to get there.

So find the side similar to RQ which is LN

1.5(x+7)=2x+5

1.5x+10.5=2x+5

5.5=0.5x

x=11

Then plug in 11 for x to find RQ which will be 27

Please help me solve ma

Answers

VW = 6

HOPE IT HELPS...!!!

So there is one triangle with two sides and the other one has one
XV/SU= VW/ST
u plug in the numbers
8/2=x/1.5
2x=12
X=12/2
X=6

Use the method of elimination to solve the pair of simultaneous equation 2x+5y=4,2x-2y=18​

Answers

[tex]2x+5y= 4~~~...(i)\\\\2x-2y = 18~~~...(ii)\\\\(ii) -(i):\\\\~~~~~2x-2y -2x -5y= 18 -4\\\\\implies -7y = 14\\\\\implies y = -\dfrac{14}7\\\\\implies y= -2\\\\\text{Substitute}~ y=-2~ \text{ in eq (i):}\\\\~~~~~~2x+5(-2) = 4\\\\\implies 2x-10 = 4\\\\\implies 2x = 10+4\\\\\implies 2x =14\\\\\implies x = \dfrac{14}2\\\\\implies x =7\\\\\text{Hence}~ (x,y) =(7,-2).[/tex]

Answer:

              y = -2

              x = 7

Step-by-step explanation:

     Solving simultaneous equation

         2x + 5y = 4 ---------------(I)

         2x - 2y  = 18 -----------(II)

Now, multiply equation (II) by (-1) and then add the equations. So that, 'x' will be eliminated and we can find the value of 'y'

(I)              2x + 5y = 4

(II)*(-1)      -2x  + 2y = - 18 {Now add}

                         7y = -14

                           y = -14/7       {on dividing both sides by 7}

       [tex]\sf \boxed{y= -2}[/tex]

Now plugin y = -2 in equation (I)

        2x + 5*(-2) = 4

           2x - 10   = 4

                    2x = 4 + 10     {on adding 10 to both sides}

                    2x = 14

                       x = 14/2      {Divide both sides by 2}

         [tex]\sf \boxed{x = 7}[/tex]

Answer number 2 please

Answers

6% is .06
Swing decimal by 2 places.
Answer a

-6x+71= -4x-1 procedimiento

Answers

Answer:

[tex]-6x+71= -4x-1[/tex]

[tex]-6x+71-71=-4x-1-71[/tex]

[tex]-6x=-4x-72[/tex]

[tex]-6x+4x=-4x-72+4x[/tex]

[tex]-2x=-72[/tex]

[tex]\cfrac{-2x}{-2}=\cfrac{-72}{-2}[/tex]

[tex]x=36[/tex]

Hope it helps u!! ^-^

Hey ! Buddy .

As the question is in Spanish . So we have provided your answer in English as well as in Spanish language .

( ¡Oye! Amigo, la pregunta es en español. Así que hemos proporcionado su respuesta tanto en inglés como en español. )

Answer:

Value of x is 36 (El valor de x es 36)

Step-by-step explanation:

In this question we have given with an equation that is -6x + 71 = -4x - 1 . And have to find the value of x .

( En esta pregunta hemos dado con una ecuación que es -6x + 71 = -4x - 1 . y hay que encontrar el valor de x )

Solution : -

( Soluciones : - )

[tex] \quad : \implies - 6x + 71 = - 4 - 1[/tex]

Step 1 : Subtracting 71 on both sides :

( Paso 1 : Restando 71 en ambos lados: )

[tex]\quad : \implies - 6x + \cancel{71} - \cancel{71} = - 4x - 1 - 71[/tex]

On calculating further, We get :

( Al calcular más, obtenemos : )

[tex]\quad : \implies - 6x = - 4x - 72[/tex]

Step 2 : Adding 4x on both sides :

( Paso 2 : Sumando 4x en ambos lados: )

[tex]\quad : \implies - 6x + 4x = - \cancel{4x} + \cancel{4x } - 72[/tex]

On calculating further, We get :

( Al calcular más, obtenemos : )

[tex]\quad : \implies \cancel{-} 2x = \cancel{-}72[/tex]

Step 3 : Dividing by 2 on both sides :

( Paso 3 : Dividiendo por 2 en ambos lados: )

[tex]\quad : \implies \frac{ \cancel{2}x}{ \cancel{2} } = \cancel{\frac{72}{2} }[/tex]

On calculating further , We get :

( Al calcular más, obtenemos : )

[tex]\quad : \implies \: \green{ \boxed{ \frak{x = 36}}}[/tex]

Therefore , value of x is 36 . ( Por lo tanto , el valor de x es 36 . )

Verifying : -

( Comprobación :- )

We are verifying our answer by substituting value of x in given equation. So ,

( Estamos verificando nuestra respuesta al sustituir el valor de x en la ecuacióndada. Asi que, )

-6x + 71 = -4x - 1

-6 ( 36 ) + 71 = -4 ( 36 ) - 1

-216 + 71 = -144 - 1

-145 = -145

L.H.S = R.H.S (Lado izquierdo = Lado derecho )

Hence, Verified. ( Por lo tanto, Verificado. )

Therefore, our solution is correct.

( Por lo tanto, nuestra solución es correcta. )

#Keep Learning

Find decimal form root23 and root24

Answers

Answer:

Below.

Step-by-step explanation:

√23 = 4.796

√24 = 4.899.

- both correct to the nearest thousandth,

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