-2a(a+b-5)+3(-5a+2b)+b(6a+b-8) the coefficient of the a^2 term is

Answer:

The lateral edge is [tex]7\ in[/tex]

Step-by-step explanation:

we know that

The surface area of a cube is equal to

[tex]SA=6b^{2}[/tex]

where

b is the length side of the cube

we have

[tex]SA=294\ in^{2}[/tex]

substitute in the formula and solve for b

[tex]294=6b^{2}[/tex]

[tex]b^{2}=294/6[/tex]

[tex]b^{2}=49[/tex]

[tex]b=7\ in[/tex]

Answer:

7

Step-by-step explanation:

294/6 = 49

square root of 49 is 7

Answer:

2in

Step-by-step explanation:

Let's call the original side "x". so x² (area of a square) is = x² (as we can't simplify it). Then we got a 4 added to each side. So now we redefine each side as "x+4". So now we can make an equation of the area of the square. x² + 4² = 36. Now you realize that 36 is 6² so you write it. x² + 4² = 6² . Since everything is now a square just square root everything (√) So Now x + 4 = 6. Now you have a 1st degree equation now solve simple math. x = 6 - 4 = 2. The side of original square is 2in

Answer:

Step-by-step explanation:

Ok so first we need to look and rule out the ones that are not correct like 9m and 5m. ok now we ruled out 2 of the wrong ones and now we have 90m and it looks like a 45m. now we multiply 5 x 2 x 9 which equals 90. so the answer is 90.

                        Hope it helps!

Answer:

45

Step-by-step explanation:

with triangles you have to do base times height and divide by 2 so 5*9*2=90 and 90 divided by 2 is 45

A nine cubic millimeters

The volume of a cube with each dimension being 3 mm is obtained by multiplying the length, width, and height which results in 27 cubic millimeters. So the correct answer is C) 27 cubic millimeters.

To solve for the volume of a cube, the formula Volume = Length x Width x Height is used. In the case given, all three dimensions (length, width, and height) are 3 mm. This results in Volume = 3 mm x 3 mm x 3 mm which simplifies to 27 cubic millimeters.

Hence, the correct option is C) 27 cubic millimeters.

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Answer:

C.Ralph would save more, since he has $30,000 more in principal

Step-by-step explanation:

The amount of interest each will pay (or save) on his loan is proportional to the amount of principal. Since Ralph's principal of $98000 is more than David's principal of $68000, Ralph will save more by paying off the loan early.

#1 : reflected over y-axis, so x changes signs and becomes negative (-5, -2)

translated 4 units up, so move the point up 4 units/squares  (-5, 2)

#2 translated right 10 units, so the points move right 10 squares (15, -2)

reflected over x-axis, so y changes signs (15, -2)

#3 translated left 10 units (-5, -2)

up 4 units (-5, 2)

#4 reflected over the y -axis (-5, -2)

translated down 4 units (-5, -6)

Answer:

1 and 3

Step-by-step explanation:

Answer:

The range of a function is the set of all possible output values.

Answer: any numbers along the x axis

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Given a complex number x + yi then the conjugate is x - yi

Note the real part remains unchanged while the sign of the imaginary part is negated.

here z = 1 - 2i hence conjugate is 1 + 2i

and the product is

(1 - 2i)(1 + 2i) ← expand factors

= 1 - 4i² [ i² = - 1 ]

= 1 + 4

= 5

The product of z and its conjugate will be 5.

The complex number is the combination of the real part and the imaginary part. Then the complex number is given as

⇒ a+bi

In the graph, z is a complex number represented as a vector from the origin.

Then the complex number will be

z = 1 – 2i

Then the conjugate of z will be

⇒ 1 + 2i

Then the product of z and its conjugate will be

⇒ (1 – 2i)(1 + 2i)

⇒ 1² – 2²i²

We know i² = -1

⇒ 1 – 4(-1)

⇒ 1 + 4

⇒ 1² – 2²i²

⇒ 5

More about the complex number link is given below.

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The equation x = 3 represents a vertical line, but not a linear function, as it violates the definition of a function. Thus, the correct choice is D.

The equation x = 3 describes a vertical line passing through the point where x equals 3 on the coordinate plane.

While it represents a line, it fails to meet the criteria of a function because it violates the one-to-one mapping between inputs (x-values) and outputs (y-values).

For every value of x, the y-value remains constant at 3, meaning multiple x-values map to the same y-value, thus failing the vertical line test for functions.

Therefore, although it represents a line, it does not represent a linear function. Thus, the correct choice is D.

Complete Question:

Which statement best describes the equation x = 3?

A. The equation can not be graphed.

B. The equation represents a function, but not a linear function.

C. The equation represents a linear function.

D. The equation represents a line, but not a linear function.

Answer:

x > -5

Step-by-step explanation:

-5(x+7)<-10

Divide each side by -5.  Remember to flip the inequality

-5/-5(x+7)>-10/-5

x+7 > 2

Subtract 7 from each side

x+7-7>2-7

x > -5

Answer:

x^(4)+2x^(2)y^(2)+y^4)

Hope This Helps!  Have A Nice Day!!

The binomial expansion of (x²+y²)² is x⁴ +y⁴ + 2x²y²

The theorem states that any power of a binomial (a + b)ⁿ can be expanded as a specific sum of products (), such as (a + b)² = a² + 2ab + b².

Given

The given expression is (x² + y²)² and we have to simplify it to find the binomial expansion.

(x ²+ y²)² is in the form of (a + b)².

When we expand (a + b)² we get the binomial expression

(a + b)² = a² + b² + 2ab

Now we put the value of a = x² and b = y²

(x² + y²)² = (x²)² + (y²)² + 2(x²)(y²)

              = x⁴ + y⁴ + 2x²y²

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Answer:

Yes, because the total will be $37.50

(cool profile pic)

Step-by-step explanation:

Yes, because the total will be $37.50

To simplify 4(6r+3) + 2(r + 2), distribute the coefficients, combine like terms, resulting in the simplified expression 26r + 16.

To simplify the expression 4(6r+3) + 2(r + 2), we need to distribute the multiplication over the addition inside the parentheses and then combine like terms.

Distribute the 4 into the first set of parentheses: 4 × 6r = 24r and 4 × 3 = 12.

Do the same with the 2 into the second set of parentheses: 2 × r = 2r and 2 × 2 = 4.

Now, combine the individual terms: The expression becomes 24r + 12 + 2r + 4.

Combine like terms (24r and 2r) and constants (12 and 4): 24r + 2r = 26r and 12 + 4 = 16.

The simplified expression is therefore 26r + 16.

Answer:

Step-by-step explanation:

The perimeter is the arc length plus the two radius lines.

Arc length is:

s = (θ/360) 2πr

So the perimeter is:

P = (θ/360) 2πr + 2r

Given that θ=135 and r = 11:

P = (135/360) 2π(11) + 2(11)

P = 8.25π + 22

P ≈ 47.9

So the perimeter is greater than 47.5 cm.

Step-by-step explanation:

Answer:

32 with 11 handkerchief left over

Step-by-step explanation:

Handkerchief = 811

Quits for 1 handkerchief = 25

Number of quits

= 811 ÷ 25

= 32 Remainder 11

Answer:

32 reminder of 11

Step-by-step explanation:

Answer:

Step-by-step explanation:

4 (10)

5 (13)

6 (16)

7 (19)

Answer:

On the first picture

1 goes to 16.

2 goes to 13

3 goes to 10

4 goes to 19

On the second picture

1 goes to 9

2 goes to 11

3 goes to 13

4 goes to 15

Answer:

16 beta fish

Step-by-step explanation:

Take the starting number of fish: 25, and subtract it by the number of fish being taken away: 9.

Answer:

16

Step-by-step explanation:

if we have 25 bettas and then 9 were taken that means we should subtract 9 from 25 to get 16 bettas left

Answer:

in april

Step-by-step explanation:

Keep track of every 1, 2, 3, or 4 rolled in 30 rolls and repeat this process 100 times to represent the days the temperature is above 80°F in June.

The BEST way to perform the simulation in this scenario would be to keep track of every 1, 2, 3, or 4 rolled in 30 rolls, as these represent the number of days the temperature is above 80°F in June. Repeat this process 100 times.

By simulating the number of days the temperature is above 80°F in June for 30 rolls and repeating it 100 times, you will obtain a larger sample size and a more accurate estimate of the probability. This approach allows for more data points and reduces the impact of random variations that can occur in smaller sample sizes.

Therefore, option 3 is the best way to perform the simulation: Keep track of every 1, 2, 3, or 4 rolled in 30 rolls and repeat this process 100 times to represent the days the temperature is above 80°F in June.

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Answer:

5 miles per hour

Step-by-step explanation:

You divide 15/3 and get 5.

Answer:

5 miles per hour

Step-by-step explanation:

To determine how fast he can run per hour, take the miles and divide by the number of hours

15 miles / 3 hours

5 miles per hour

Answer:

narrower than and opens in the same direction as

Step-by-step explanation:

Answer:

narrower than and opens in the same direction as

Step-by-step explanation:

The graph of y = 5x2 is narrower than and opens in the same direction as the graph of y = x2.

Answer:

a = 70°

Step-by-step explanation:

a and 110 form a straight angle, thus

a + 110 = 180 ( subtract 110 from both sides )

a = 70°

Answer:

a =70

Step-by-step explanation:

Angle a and 110 are supplementary, which means they add to 180 degrees

a+ 110 = 180

Subtract 110 from each side

a+110-100=180-110

a = 70

Answer:

greater than 67,124

Step-by-step explanation:

since you are multiplying 67,124 with a variable(x) and multiplication only increases the value, the answer is greater than since you are multiplying 67,124 with a variable, which will only increase  the product value

Answer:

[tex]x=4,y=-3[/tex], or as an ordered pair: (4, -3)

Step-by-step explanation:

We have the system of equations

[tex]x^2+y^2=25[/tex] (1)

[tex]x-y^2=-5[/tex] (2)

Let's solve our system step-by-step:

Step 1. Solve for [tex]y^2[/tex] in equation (1)

[tex]x^2+y^2=25[/tex]

[tex]y^2=25-x^2[/tex] (3)

Step 2. Replace equation (3) in equation (2) and solve for [tex]x[/tex]

[tex]x-y^2=-5[/tex]

[tex]x-(25-x^2)=-5[/tex]

[tex]x-25+x^2=-5[/tex]

[tex]x^2+x-20=0[/tex]

[tex](x+5)(x-4)=0[/tex]

[tex]x+5=0,x-4=0[/tex]

[tex]x=-5,x=4[/tex]

Remember that in the fourth quadrant x is positive and y is negative, so we are taking the positive value of x; in other words [tex]x=4[/tex] (4)

Step 3. Replace equation (4) (the positive value of x) in equation (1)

[tex]x^2+y^2=25[/tex]

[tex]4^2+y^2=25[/tex]

[tex]16+y^2=25[/tex]

[tex]y^2=25-16[/tex]

[tex]y^2=9[/tex]

[tex]y=\sqrt{9} ,y=-\sqrt{9}[/tex]

[tex]y=3,y=-3[/tex]

Since y is negative in quadrant IV, we take [tex]y=-3[/tex]

We can conclude that the solution of our system of equations that lies in the quadrant IV is [tex]x=4,y=-3[/tex], or as an ordered pair: (4, -3)

Answer:

if you type (4,-3) is wrong

First, let's get out common denominators.

8/12 and 3/12.

We then minus the 8 and 3 = 5/12.

We have 5/12.

That's your answer.

Answer:

190,208

Step-by-step explanation:

732,178 + 167 = 732345

732345 -  542,137 = 190,208

190,208

Step by Step

732178+167=732345

732345-542137=190208

Answer:

Step-by-step explanation:

First triangle is a 45-45-90 triangle.  In most basic form, the two equal sides have length 1 and the hypotenuse has length √2.  Do not write x√2.

Second triangle:  The shortest side is 1, the longer side is √3 and the hypotenuse is 2.  You could verify this using the Pythagorean Theorem:

2² = 1² + (√3)² is true.

Please, no more than 2 problems per post.  Please re-post the remaining problems and either I or someone else will help you with them.

Answer:

The position P is:

[tex]P = 87\^x + 75\^y[/tex] ft     Remember that the position is a vector. Observe the attached image

Step-by-step explanation:

The equation that describes the height as a function of time of an object that moves in a parabolic trajectory with an initial velocity [tex]s_0[/tex] is:

[tex]y(t) = y_0 + s_0t -16t ^ 2[/tex]

Where [tex]y_0[/tex] is the initial height = 0 for this case

We know that the initial velocity is:

82 ft/sec at an angle of 58 ° with respect to the ground.

So:

[tex]s_0 = 82sin(58\°)[/tex] ft/sec

[tex]s_0 = 69.54[/tex] ft/sec

Thus

[tex]y(t) = 69.54t -16t ^ 2[/tex]

The height after 2 sec is:

[tex]y(2) = 69.54 (2) -16 (2) ^ 2[/tex]

[tex]y(2) = 75\ ft[/tex]

Then the equation that describes the horizontal position of the ball is

[tex]X(t) = X_0 + s_0t[/tex]

Where

[tex]X_ 0 = 0[/tex] for this case

[tex]s_0 = 82cos(58\°)[/tex] ft / sec

[tex]s_0 = 43.45[/tex] ft/sec

So

[tex]X(t) = 43.45t[/tex]

After 2 seconds the horizontal distance reached by the ball is:

[tex]X (2) = 43.45(2)\\\\X (2) = 87\ ft[/tex]

Finally the vector position P is:

[tex]P = 87\^x + 75\^y[/tex] ft

Answer:

[tex]A=34\ units^2[/tex]

Step-by-step explanation:

Suppose we have a general triangle like the one shown in the figure.

We know the angle A, the angle B and the length b.

[tex]A = 30\°\\\\B = 45\°\\\\b = 10[/tex]

By definition I know that the sum of the internal angles of a triangle is always equal to 180 °.

So

[tex]A + B + C = 180\\\\30 + 45 + C = 180[/tex]

We solve the equation and thus we find the angle C.

[tex]C = 180 - 30-45\\\\C = 105[/tex]

We already know the three triangle angles.

Now we use the sine theorem to calculate the sides c and a.

The  sine theorem says that:

[tex]\frac{sin(A)}{a}=\frac{sin(B)}{b}=\frac{sin(C)}{c}[/tex]

Then

[tex]\frac{sin(30)}{a}=\frac{sin(45)}{10}[/tex]

[tex]\frac{sin(30)}{\frac{sin(45)}{10}}=a[/tex]

[tex]a=7.071[/tex]

Also

[tex]\frac{sin(105)}{c}=\frac{sin(45)}{10}[/tex]

[tex]\frac{sin(105)}{\frac{sin(45)}{10}}=c[/tex]

[tex]c=13.660[/tex]

Finally, we use the Heron formula to calculate the triangle area

[tex]A=\sqrt{s(s-a)(s-b)(s-c)}[/tex]

Where s is:

[tex]s=\frac{a+b+c}{2}[/tex]

Therefore

[tex]s=\frac{7.071+10+13.660}{2}[/tex]

[tex]s=15.37[/tex]

[tex]A=\sqrt{15.37(15.37-7.071)(15.37-10)(15.37-13.66)}[/tex]

[tex]A=34\ units^2[/tex]

The answer choice is D because sin7pi/6 which it’s exact form is -1/2 the only answer choice which the same exact form is D.

For this case we must find an expression equivalent to:

[tex]Sin (\frac {7 \pi} {6})[/tex]

According to the unit circle, [tex]\frac {7 \pi} {6}[/tex] is in the third quadrant and equals 210 degrees.

Then, we must find an expression equivalent to:

[tex]Sin (210) = - \frac {1} {2} = - 0.5[/tex]

We have to:

[tex]\frac{11 \pi} {6}[/tex]

It is in the fourth quadrant and is equivalent to 330 degrees, according to the unit circle.

[tex]Sin (330) = - \frac {1} {2} = - 0.5[/tex]

Answer:

Option D