Which answer choice correctly represents an algebraic expression for the sum of 15 and a number?

i)

Factor using completing square method

[tex]\dashrightarrow \sf y = -x^2+16x-64[/tex]

[tex]\dashrightarrow \sf y = -(x^2-16x+64)[/tex]

[tex]\dashrightarrow \sf y = -(x^2-8x-8x+64)[/tex]

[tex]\dashrightarrow \sf y = -(x(x-8)-8(x-8))[/tex]

[tex]\dashrightarrow \sf y = -((x-8)(x-8))[/tex]

ii)

Find zeros of a function, f(x) = 0

[tex]\dashrightarrow \sf -((x-8)(x-8))=0[/tex]

[tex]\dashrightarrow \sf (x-8)=0, \ (x-8)=0[/tex]

[tex]\dashrightarrow \sf x = 8[/tex]

iii)

In order to find vertex use the formulae : x =  -b/2a

[tex]\dashrightarrow \sf x = \dfrac{-(16)}{2(-1)}[/tex]

[tex]\dashrightarrow \sf x = 8[/tex]

Then find y:

[tex]\dashrightarrow \sf y = -(8)^2+16(8)-64[/tex]

[tex]\dashrightarrow \sf y = 0[/tex]

coordinates: (8, 0)

iv) Sketched Below:

#1

#2

Zeros are the x intercepts

Here they are

#3

Vertex form of parabola:-y=a(x-h)²+k

#4

Attached

6x + 3 = 2

its the answer

easy peasy

Answer:

3 + 6(x) =  2

Step-by-step explanation:

Given statement:

3 more than the product of a number and six is equal to 2​

Converting the statement into an equation:

{3} {more} than {the product of a number and six} is {equal to} {2​}

↓      ↓                                          ↓                                      ↓           ↓

3      +                                        6 × x                                   =           2

⇒ Equation formed: 3 + (6 × x) =  2

⇒ Equation formed: 3 + 6(x) =  2

Answer:

x = 18

By Pythagoras Theorem:

[tex] {(x + 7)}^{2} = {(7)}^{2} + {(24)}^{2} \\ \\ \implies \: (x + 7)^{2} = 49 + 576 \\ \\ \implies \: (x + 7)^{2} = 625\\ \\ \implies \: x + 7 = \pm \sqrt{625}\\ \\ \implies \: x + 7 = \pm \: 25\\ \\ \implies \: x + 7 = 25 \: \: or \: \: x + 7 = - 25 \\ \\ \implies \: x = 25 - 7 \: \: or \: \: x = - 25 - 7 \\ \\ \implies \: x = 18 \: \: or \: \: x = - 32 \\ \\ x \: can \: not \: be \: negative \\ \implies \: x \neq \: - 32 \\ \implies \: x = 18[/tex]

Hey there!

7t - 3 = -59

ADD 3 to BOTH SIDES

7t - 3 + 3 = -59 + 3

CANCEL out: -3 + 3 because it give you 0

KEEP: -59 + 3 because it help solve for the t-value

NEW EQUATION: 7t = -59 + 3

SIMPLIFY IT!

7t = -56

DIVIDE 7 to BOTH SIDES

7t/7 = -56/7

CANCEL out: 7/7 because it give you 1

KEEP: -56/7 because it help solve for the t-value

NEW EQUATION: t = -56/7

SIMPLIFY IT!
t = -8

Therefore, your answer is: t = -8

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

First box, second from the left,

Second box, first on the left.

Third box, third from the left.

Fourth box, Last on the right.

Step-by-step explanation:

Welcome.

Answer: 256,1

Step-by-step explanation:

[tex]\sqrt{x} - \sqrt{y} =15\\\sqrt{y} = 49-3\sqrt{x} \\\\\sqrt{x} -(49-3\sqrt{x} ) =15 \\so, x=256\\substitute \{x}\ :\\\\\sqrt{y} = 49-3\sqrt{256} =y=1[/tex]

so, 256=x

and, y=1

Hope this Helped!

Answer:

1, 4 or -1, -4

Step-by-step explanation:

Let the two numbers be x and such that x > y.

According to the first condition:

[tex]x^2 -y^2= 15[/tex]

[tex]\implies x^2 =y^2+15[/tex]......(1)

According to the second condition:

[tex]3x^2 +y^2= 49[/tex]

[tex]\implies 3(y^2+15) +y^2= 49[/tex]

(From equation 1)

[tex]\implies 3y^2+45 +y^2= 49[/tex]

[tex]\implies 4y^2 =49-45[/tex]

[tex]\implies 4y^2 =4[/tex]

[tex]\implies y^2 =\frac{4}{4}[/tex]

[tex]\implies y^2 =1[/tex]

[tex]\implies y =\pm 1[/tex]

When y = 1

[tex]\implies x^2 =(1)^2+15=1+15=16[/tex]

[tex]\implies x =\pm 4[/tex]

When y = -1

[tex]\implies x^2 =(-1)^2+15=1+15=16[/tex]

[tex]\implies x =\pm 4[/tex]

Thus, the required numbers are either 1, 4 or -1, -4

Answer:

Multiply the moduli and add the arguments.Step-by-step explanation:First write out the two terms being multiplied: z1z2= [r1(cos(theta 1) + isin(theta 1))][r2(cos(theta 2)+ isin(theta 2))] z1z2= r1r2 (cos(theta 1) + isin(theta 1))(cos(theta 2)+ isin(theta 2)) z1z2= r1r2(cos(theta 1)cos(theta 2))+(icos(theta 1)sin(theta 2))+(icos(theta 2)sin(theta 1))+(i^2 sin(theta 1)sin(theta 2)) Next group and rewrite the like term with the sums and differences. Your answer is the multiplication of the moduli and the addition of the arguments: z1z2= r1r2[cos(theta 1 + theta 2) + i sin (theta 1 and theta 2)].

The product complex number is [tex]z_1z_2[/tex]= [tex]r_1r_2[/tex][cos (θ1+θ2) + i sin (θ1+θ2)].

A real number and an imaginary number are effectively combined to create a complex number. The complex number is written as a+ib, where a and ib are real and imaginary numbers, respectively.

We have,

z1=r1 (cos θ1 +i sin θ1)

z2=r2 (cos θ2 +i sin θ2)

where r-radius/radii

and, m-modulus/moduli

Now, the product is

[tex]z_1z_2[/tex] = r1 (cos θ1 +i sin θ1) x r2 (cos θ2 +i sin θ2)

[tex]z_1z_2[/tex] = r1 r2(cos θ1 . cos θ2 +i cos θ1 sin θ2 + i sin θ1 cos θ2 + i² sin θ1 sin θ2)

[tex]z_1z_2[/tex] = r1 r2(cos θ1 . cos θ2 +i cos θ1 sin θ2 + i sin θ1 cos θ2 - sin θ1 sin θ2)

We know,

cos (a + b)= cos a cos b - sin a sin b

sin (a+b) = sin a cos b + cos a sin b

Thus, [tex]z_1z_2[/tex] = [tex]r_1r_2[/tex][cos (θ1+θ2) + i sin (θ1+θ2)].

Learn more about complex number here:

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#SPJ2

Answer:

angle 2 and angle 4

Answer:

4x + 15 = 6x - 3

Step-by-step explanation:

Four times an unknown number is 4x, add 15 like it says, then it says three less so it would be - 3 and then it says than six times the [unknown] number, which remains being x

hope this helps!

Answer:

Hi mate

The right angled triangle is the best name for it

Because it has an right angle or 90 degree angke

Step-by-step explanation:

Answer:

because a= 1,1 then 1+1 = 2

The slope of the line is -2.5 and the y-intercept is 2. This shows that the Quantity B is greater that A

The intercept is the point where the line intersects

Determine the slope of the graph using the coordinate points (0, 2) and (0.8, 0)
Slope = -2/0.8
Slope = -2.5

The slope of the line is -2.5 and the y-intercept is 2

This shows that the Quantity B is greater than A

Learn more on equation of a line here:https://brainly.com/question/13763238

Answer:

Step-by-step explanation:

If you multiply 7.2 x 7.2 then you say + 8 * 8 is 64 plus 64 equal to 115

The answer would be ⁻[tex]\frac{19}{x-5\\}[/tex]

Answer:

[tex]\underline{\boxed{\sf \cfrac{-19}{x-5}}}[/tex]

Step-by-step explanation:

[tex]\sf \cfrac{x^2+10+25}{x+5}-\cfrac{x^2-6}{x-5}[/tex]

First, Let's factor the expressions that are not already factored in x^2+10+25/x+5

[tex]\sf \cfrac{(x+5)^2}{x+5}-\cfrac{x^2-6}{x-5}[/tex]

Now, cancel out x+5 in both numerator and denominator:-

[tex]\sf x+5-\cfrac{x^2-6}{x-5}[/tex]

Expand equations to make their denominators the same before adding or subtracting them. Multiply x+5 * x-5/x-5:-

[tex]\sf \cfrac{(x+5)(x-5)}{x-5}-\cfrac{x^2-6}{x-5}[/tex]

Now, Since [tex]\sf \frac{(x+5)(x-5)}{x-5}[/tex] and [tex]\sf \frac{x^2-6}{x-5}[/tex] and similar denominator, we'll subtrac their numerators.

[tex]\sf \cfrac{(x+5)(x-5)-(x^2-6)}{x-5}[/tex]

[tex]\sf \cfrac{x^2-5x+5x-25-x^2+6}{x-5}[/tex]

Combine like tems in [tex]\sf x^2-5x+5x-25-x^2+6[/tex] :-

[tex]\sf \cfrac{-19}{x-5}[/tex]

Therefore, your answer is D.

Answer: 80.00

Step-by-step explanation: To convert minutes into percentages, divide the measured number of ... To write your answer in percentage form, multiply the decimal by 100

hope this helps ig

The equation tan(mx) = sin(mx)/cos(mx)​ is a trigonometry equation

The trigonometry equation tan(mx) = sin(mx)/cos(mx)​ is true

The equation is given as:

tan(mx) = sin(mx)/cos(mx)​

The tangent of an angle is the ratio of the sine and the cosine of the angle.

This means that:

tan(α) = sin(α)/cos(α)

By comparison, we have:

α = mx

Substitute α = mx in tan(α) = sin(α)/cos(α).

So, we have:

tan(mx) = sin(mx)/cos(mx)​

Hence, the trigonometry equation tan(mx) = sin(mx)/cos(mx)​ is true

Read more about trigonometry equations at:

https://brainly.com/question/8120556

Step-by-step explanation:

Below in the attached picture is the proof for tangent

Answer:

How to solve your problem 42+36+814r2+36r+81

Use the sum-product pattern 42+36+814r2+36r+8142+18+18+81

The area of the trapezoid is [tex]\frac{1}{2}(b1+b2)*h[/tex]

Therefore the area is:

   [tex]\frac{1}{2}*(3+5)*9 =\frac{1}{2}*(8)*9=4*9=36km^2[/tex]

Area: 36 square kilometers

Hope that helps!

Answer:

2, 3, 4, 7, 8

Step-by-step explanation:

All correct!

Answer:

Yes it is totally corect you are very smart

Step-by-step explanation:

Juan created 35 long swordsmen, 35 spearmen and 15 crossbowmen.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represnt the number of long swordsmen, y represent the spearmen and z represent the crossbowmen. Hence:

75x + 40y = 4025     (1)

25x + 40z = 1475     (2)

And:

30y + 30z = 1500 (3)

Hence;

x = 35, y = 35 and z = 15

Juan created 35 long swordsmen, 35 spearmen and 15 crossbowmen.

Find out more on equation at: https://brainly.com/question/1214333

The behavior of the function f(x) describes the direction of the function

The behavior of the function is as x -> ∞, f(x) -> 4 and x -> -∞, f(x) -> 4

The function is given as:

f(x)= 8x+1/2x-9

Start by plotting the graph of the function f(x).

From the graph (see attachment), we have the following highlights:

Hence, the behavior of the function is as x -> ∞, f(x) -> 4 and x -> -∞, f(x) -> 4

Read more about function end behaviors at:

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Barbara's net loss on the sale of the stocks she purchased last year is 1245.63.

A net loss is earned when the cost price of purchasing the stock is greater than the selling price.

Net loss = cost price - selling price

Cost price = 8500 + (8500 x 1.25%) = 8606.25

Selling price = 7324 + (7324 x 0.5%) = 7360.62

Net loss = 8606.25 - 7360.62 = 1245.63

Here is the complete question: barbara purchased stock last year for 8500 and paid a 1.25% broker fee. she sold it for 7324 and had to pay a .5% broker fee. Compute her net loss.

To learn more about profit and loss, please check: https://brainly.com/question/26181966

Answer:

[tex] \longrightarrow \sf \purple{ \boxed{ \bold{ \: 12x² + 12x – 18}}}[/tex]

Step-by-step explanation:

Simplify

10x² + 3x – 6 + 2x² + 9x – 12

Steps

1Ox² + 3x- 6 - 2x² + 9x - 12

Step 1:- Group like terms:

= 10x² + 2x²+ 3x + 9x - 6 - 12

Step 2:- Subtract the numbers: – 6–12 = -18

= 10x² + 2x² + 3x + 9x – 18

Step 3:- Add similar elements: 10x² + 2x² – 12x²

= 12x² + 3x + 9x – 18

Step 4:- Add similar elements: 3x + 9x – 12x

= 12x² + 12x – 18

Answer:

Step-by-step explanation:

If the three coins are simultaneously tossed again, compute the probability of 2 heads coming up.Solution:Probability of an event, P(E) = Number of occurrences where the event takes place / Total number of occurrencesThe probability of 2 heads coming up when three coins are tossed simultaneously is given by the ratio of the number of times a particular outcome occurs to the total number of tosses.Total number of tosses = 200Number of 2 heads outcomes = 72Probability of 2 heads outcomes = Number of 2 heads outcomes / Total number of tosses= 72/200= 9/25

Answer: -10 or D

Step-by-step explanation: simplify radical then combine

Answer:

1/81

Step-by-step explanation:

First lets simplfy the equation :

(3^2)^-2

(remember that you can mutiply the exponent outside the paranthesis by the exponent inside so -2*2=-4)

3^-4

Now lets evaluate this further!

3^-4

(negative exponets mean that you have to raise the number but as the denominator of a fraction)

1/3^4

Now we can solve it fully

1/3^4

1/81

Step-by-step explanation:

7x² + 9x² - x²

when you wrote the expression you used the "multiplication ×" and not "x".

anyway, when you have terms of the same variable of the same exponent, then the combination variable and exponent become an item. and the same items can simply be added in an expression.

this is similar to

7 apples + 9 apples - 1 apple

what would you do there ?

see ?

and the same we are doing now for the given expression : we are adding the terms up :

7x² + 9x² - x² = (7 + 9 - 1)x² = 15x²

and in the middle I gave you even the reason why we can do that.

please, let me know, if this is still unclear.

Answer:

C

Step-by-step explanation:

Answer:

6!/3!=6x5x4x3x2/3x2=6x5x4=120

Step-by-step explanation:

There are L, O, O, P, H, O, L, E; 8 letters in LOOPHOLE. However, three letters repeat: OOO. That means we cannot count them as different and use ! for them.

L,P,H,L,E,O are the letters not double counted. There are SIX letters, so 6!, however, you still have to divide since there are the Os you have to consider.

You have to divide by 3! as they repeat 3 times.

Thus, 6!/3!

"There is a subset of permutations that takes into account that there are double objects or repetitions in a permutation problem. In general, repetitions are taken care of by dividing the permutation by the factorial of the number of objects that are identical" -www. ck12. org > probability > lesson > permutation