Solve for x.
.
Simplify your answer as much as possible.

(1) is correct. [tex]\mathbf u\cdot\mathbf v=(-14)(0)+(8)(11)=0+88=88[/tex]

(2) is correct. I assume you just computed the dot product as above, but another way to do it is to notice that [tex]\mathbf v\cdot\mathbf v=\|\mathbf v\|^2[/tex] (that is, the dot product of a vector with itself is the square of its magnitude). Then since [tex]\|\mathbf v\|=\sqrt{1^2+2^2}=\sqrt5[/tex], we have [tex]\mathbf v\cdot\mathbf v=\|\mathbf v\|^2=5[/tex].

(3) is not correct. Since [tex]\mathbf u\cdot\mathbf u=\|\mathbf u\|^2=\sqrt{45}[/tex], we have [tex]\|\mathbf u\|=\sqrt{\sqrt{45}}[/tex].

(4) is correct.

[tex]2\mathbf u\cdot\mathbf v=2(\mathbf u\cdot\mathbf v)=2((-3)(1)+(6)(2))=2(-3+12)=2(9)=18[/tex]

Answer: D) y = - 1 /2 x + 1

Step-by-step explanation:

Got this right on USA test prep

The equation of the perpendicular line that passes through (6, -2) will be y = - (1/2)x + 1. Then the correct option is D.

If the slope of the line is m, then the slope of the perpendicular line will be negative 1/m.

The equation of the line is given as,

y = 2x + 8

Then the slope of the line is 2, then the slope of the perpendicular line will be - 1/2. Then the equation is given as,

y = - (1/2)x + c

The equation of the line is passing through (6, -2). Then we have

- 2 = - (1/2)6 + c

- 2 = - 3 + c

c = 1

Then the equation of the line is given as,

y = - (1/2)x + 1

The equation of the perpendicular line that passes through (6, -2) will be y = - (1/2)x + 1. Then the correct option is D.

More about the equation of a perpendicular line link is given below.

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Answer:

6-y

Step-by-step explanation:

Six less than y means you take away y from six.

Hope this helps

Answer:

30 divided by 2+3 is 6.

Step-by-step explanation:

The first thing you need to do is add 2 and 3, which is five, and then divide 30/5. The quotient is 6.

The quotient of 30 and the sum of 2 and 3 is 6.

The quotient of 30 and the sum of 2 and 3 can be found by dividing 30 by the sum of 2 and 3.

Step 1: Calculate the sum of 2 and 3. 2 + 3 = 5.

Step 2: Divide 30 by 5. 30 ÷ 5 = 6.

Therefore, the quotient of 30 and the sum of 2 and 3 is 6.

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Answer:

2(4x - 3)

Step-by-step explanation:

Factor 3(x-2) + 5x

8x - 6

= 2(4x - 3)

Answer:

The answer is 8 1/3.

The answer will be 8 1/3

Answer:

Greece had a larger difference ($7.07)

Step-by-step explanation:

Brazil -

18.33 - 12.25 = 6.08

Greece-

16.55 - 9.48 = 7.07

Answer:

Greece has the larger difference between categories

Step-by-step explanation:

Difference in categories of Brazil

[tex]= 18.33 - 12.25\\= 6.08\\[/tex]

Difference in categories of Greece

[tex]= 16.55 - 9.48\\= 7.07\\[/tex]

Thus, Greece has the larger difference between categories

Answer:

976 421; 124 679

Step-by-step explanation:

Part A. Largest number

Leslie's number was 976 421.

This is because the largest numbers are in the positions of largest value.

For example, 9 in the hundred thousands place, the next largest number in the ten thousands place, and so on.

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

Part B. Smallest number

The smallest possible number is 124 679.

The value of the 4 is greater than the value of the 6 because the 4 is in the thousands place and the 6 is only in the hundreds place.

4000 > 600.

Answer:

The cost of soft pretzel is $1.25

Step-by-step explanation:

Let $x be the price of one slice of pizza and $y be the price of one soft pretzel.

1. 9 slices of pizza cost $9x and 5 soft pretzels cost $5y. Together they cost $33.25, then

9x+5y=33.25.

2. 4 slices of pizza cost $4x and 6 soft pretzels cost $6y. Together they cost $19.50, then

4x+6y=19.50.

3. Solve the system of two equations:

[tex]\left\{\begin{array}{l}9x+5y=33.25\\4x+6y=19.50\end{array}\right..[/tex]

Multiplythe first equation by 4, the second equation by 9 and subtract them:

[tex]4(9x+5y)-9(4x+6y)=4\cdot 33.25-9\cdot 19.50,\\ \\36x+20y-35x-54y=133-175.5,\\ \\-34y=-42.5,\\ \\y=\$1.25.[/tex]

Then

[tex]4x+6\cdot 1.25=19.50,\\ \\4x=19.50-7.50,\\ \\4x=12,\\ \\x=\$3.[/tex]

Answer: Each soft pretzel cost $1.25

Step-by-step explanation:

Hi, we have to write an equation for each case:

9 x + 5 y = 33.25

4x +6 y = 19.50

Where x is the price of 1 slice of pizza, and y is the price of each soft pretzel.

Multiplying the first equation by 4, and the second equation by 9

36x +20y =133

36x +54y =175.5

And subtracting the first equation to the second equation

36x +54y =175.5

-

36x +20y =133

____________

34 y = 42.5

Solving for y  

y =42.5/34

y = $1.25

Each soft pretzel cost $1.25

The point-slope form:

[tex]y-y_1=m(x-x_1)[/tex]

We have the slope m = 4 and the point (-1, -3). Substitute:

[tex]y-(-3)=4(x-(-1))\\\\\boxed{y+3=4(x+1)}[/tex]

Answer:

Step-by-step explanation:

About Point Slope Form:

Y - 3 = 4 (x - -1)

The formula of a distance between two points:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

We have the points (3, 5) and (4, 6). Substitute:

[tex]d=\sqrt{(4-3)^2+(6-5)^2}=\sqrt{1^2+1^2}=\sqrt{1+1}=\sqrt2\approx1.4[/tex]

The distance between the two points is 1.4.

Option D is the correct answer.

The distance between two points of a line is given as:

Distance =  √(c - a)² + (d - b)²

We have,

To find the distance between the two points (3, 5) and (4, 6)

We can use the distance formula:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.

Substituting the given values, we get:

d = √((4 - 3)² + (6 - 5)²)

d = √(1² + 1²)

d = √2

To the nearest tenth, the distance is approximately 1.4.

Therefore,

The distance between the two points is 1.4.

Learn more about the distance of a line here:

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[tex]\dfrac{o+4m+p}{6}=e\qquad\text{multiply both sides by 6}\\\\o+4m+p=6e\qquad\text{subtract o and 4m from both sides}\\\\\boxed{p=6e-o-4m}[/tex]

Answer:

[tex]\frac{C}{2\pi } =r[/tex]

Step-by-step explanation:

Recall to find the circumference of a circle the formula is [tex]C=\pi d[/tex] or [tex]C=2\pi r[/tex]. Since we need r, we will use the second formula for circumference.

We start by solving for r in the Circumference formula. using inverse operations. We divide both sides (as the inverse of multiply) by 2pi.

[tex]C=2\pi r\\\frac{C}{2\pi } =r[/tex].

Answer: C

Step-by-step explanation:

First find the difference

160-40=120

Take the difference and divide it by the original number

120/160=0.75

Multiply by 100

75

Answer:

Linear

Step-by-step explanation:

This can be written in slope intercept form (y=-5x+7) and there are no exponents.

20 cents per apple

1/5=.20

Answer: Option 'c' is correct.

Step-by-step explanation:

Since we have given that

Number of students who are interested in being on the team = 9

Number of positions to fill on his basket ball team = 3

So, the combinations of the three positions he can choose for the team is given by

[tex]3\times 9=27[/tex]

Hence, Option 'c' is correct.

The coach can choose 84 different combinations of the three positions from 9 interested students for the basketball team.

The coach needs to choose 3 out of 9 students to fill the positions on his basketball team. This is a combination problem, and the number of ways to choose [tex]\( r \)[/tex] items from [tex]\( n \)[/tex] items is given by the combination formula:

[tex]\[ C(n, r) = \frac{n!}{r!(n-r)!} \][/tex]

Here, [tex]\( n = 9 \) (number of students) and \( r = 3 \)[/tex] (number of positions to fill).

[tex]\[ C(9, 3) = \frac{9!}{3!(9-3)!} \][/tex]

[tex]\[ C(9, 3) = \frac{9!}{3!6!} \][/tex]

[tex]\[ C(9, 3) = \frac{9 \times 8 \times 7}{3 \times 2 \times 1} \][/tex]

[tex]\[ C(9, 3) = \frac{504}{6} \][/tex]

[tex]\[ C(9, 3) = 84 \][/tex]

So, the coach can choose from 84 different combinations for the team positions.

The correct answer is:

B: 84

Answer:

I didn’t know you could have more than 2 answers that’s pretty cool

Step-by-step explanation:

Answer:

a ≠ 2b

Step-by-step explanation:

The given expression is

[tex]\frac{8ab^{2}x}{4a^{2}b-8ab^{2}}[/tex]

[tex]=\frac{8ab^{2}x}{4ab(a-2b)}[/tex]

Simplifying it, we have

[tex]\frac{8ab^{2}x}{4a^{2}b-8ab^{2}} = \frac{bx}{a-2b}[/tex]

For the above fraction to exist, the denominator must not be equal to zero.

i.e, a-2b ≠ 0

=> a≠2b

∴ The algebraic fraction exists when a≠2b.

Answer:

A valid exclusion for the algebraic fraction is when a=2b

Step-by-step explanation:

You have:

[tex]8ab^2x/4a^2b-8ab^2[/tex]

First you must to simplify:

Taking out common factor 4ab

[tex]4ab(2bx)/4ab(a-2b)[/tex]

[tex]2bx/a-2b[/tex]

The fraction can be written only if  the denominator is different to zero, then

a-2b[tex]\neq[/tex]0

the excluded values are where  

a-2b=0

this expression is equal to 0 when a=2b

Answer: After about years 27 Account B will have more money than Account A  

Step-by-step explanation:  

Account A: 27(50) + 500 = $1850

Account B: 500(1.05^27) = $1866.73  

Hope this help

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Answer:

[tex]A=8.2 cm^2[/tex] or [tex]A=\frac{81}{\pi }[/tex]

Step-by-step explanation:

Since the the formula for the circumference of a circle is [tex]C=2\pi r[/tex] and C is 18, we can substitute and solve for r. After we solve for r, we substitute it into the area formula.

[tex]18=2\pi r\\\frac{18}{2\pi } =\frac{2\pi r}{2\pi }\\2.866=r[/tex]

The formula for the area is [tex]A=\pi r^{2} \\A=\pi 2.866^{2} \\A=8.2 cm^2[/tex]

As a fraction, we would not simplify to a decimal and the solution would be:

[tex]A=\pi r^{2} \\A=\pi (\frac{9}{\pi }) ^{2} \\A=\frac{81}{\pi }[/tex]

Answer:

Estimate is 150 and actual product is 138.

Step-by-step explanation:

To estimate products, we round the numbers to nearest unit place, 10th, 100th, 1000th, and so on.

Given are the numbers 3 and 46.

We can round 46 ≈ 50.

So Estimation would be 3 x 46 ≈ 3 x 50

3 times 5 is 15 and we can add zeros after it.

So estimation is 3 x 46 ≈ 150.

Now actual product would be...

3 times 6 is 18, so we note down 8 and 1 goes to carry over 4.

3 times 4 is 12 and carry 1 will be added in it, so 12 + 1 = 13.

It means the actual product is 3 x 48 = 138.

Final answer:

The equation of the line with an x-intercept of -4 and a y-intercept of 2 is y = 0.5x + 2. We found this by calculating the slope using the two given points and then using the slope-intercept form to construct the equation.

Explanation:

To write the equation of the line with an x-intercept of -4 and a y-intercept of 2, we can use the two intercepts as points on the line: (-4,0) and (0,2). We can find the slope using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are points on the line. For our points this would be:

m = (2 - 0) / (0 - (-4)) = 2 / 4 = 0.5

Once we have the slope, we can use the slope-intercept form of a line, which is y = mx + b, where m is the slope and b is the y-intercept. Since the y-intercept is given as 2, we can write:

y = 0.5x + 2

This is the equation of the line with the given intercepts.

Answer:

Intercept form  y=-5/64 (x) (x-160)

Vertex form  y =  -5/64 (x-80)^2 + 500

Step-by-step explanation:

The equation for a parabola in intercept form is y =a(x-p) (x-q)

where p and q are the intercepts.  We know that it intersects the x axis at 0 and 160, so we can substitute these in

y = a(x-0) (x-160)

y = a(x) (x-160)

We have to calculate the value of a.

Using the point (80, 500)

500 = a(80) (80-160)

500 = a (80) *(-80)

500 = a *-6400

Divide each side by -6400

a = -500/6400

a = -5/64

So the equation in intercept form is

y = -5/64 (x) (x-160)

The equation for a parabola in vertex  form is

y = a(x-h)^2 +k    

We know the vertex is (80,500)

y = a(x-80)^2 + 500

We need to pick a point to solve for a.  (0,0)

0 = a(0-80)^2 + 500

Subtract 500 from each side.

-500 = a(-80)^2

-500 = a (6400)

Divide by 6400

-500/6400 = a

-5/64 = a   ( Does this look familiar?)

y = -5/64 (x-80)^2 + 500

Answer:$5.1

Step-by-step explanation: so since theres the 1 in 1.2 we know we have $3.40 right?, yeah so, half of $3.40 is 1.7 so jus add $1.7 to $3.40 wich is $5.1

Answer:

X^2 y

Step-by-step explanation:

So now you can make this x^2 y because the ^3 cancels it out

Answer:

x^6/27y

Step-by-step explanation:

(x^2/3y^1/3)^3

x^2 ^3/  (3^3 y^1/3 ^3)

Using the power of power rule, when a power is raised to a power, we multiply the powers.

x^ (2*3)/ (3^3 y^(1/3*3))

x^6/(27 y^1)

x^6/27y

Answer:

The width of the rectangle is [tex]5xy^3[/tex].

Step-by-step explanation:

The area of a rectangle is the product of length and width of the rectangle.

[tex]A=length\times width[/tex]

It is given that the area of the rectangle is [tex]15x^3y^4[/tex] square meters and the length of the rectangle is [tex]3x^2y[/tex].

[tex]15x^3y^4=3x^2y\times width[/tex]

[tex]width=\frac{15x^3y^4}{3x^2y}[/tex]

[tex]width=\frac{3\times 5\times x^2\times xy^3\times y}{3x^2y}[/tex]

Cancel out common factors 3x²y.

[tex]width=5xy^3[/tex]

Therefore the width of the rectangle is [tex]5xy^3[/tex].

Answer:

12.=0.06

13. =-5.12

14. =0.5

Step-by-step explanation:

12. .1 + .2 -.3 x.4/.5

.1+.2 -.12/.5

.1+.2-.24

.3-.24=.06

13. 3.2^2

10.24-15.36=-5.12

14. 4.2 x5/6 /10 +3/20

3.5 / 10 + 3/20

0.35+3/20

7/20+3/20=10/20

0.5

Answer:

24 total students

Step-by-step explanation:

multiply 25 times 18 to get 450 then divide 450 by 75 then you get 6, which is the total amount of girls, so 6 + 18 = 24

x = number of students

75% of x = number of boys

(75/100)*x = 18

0.75x = 18

x = 18/0.75 <--- divide both sides by 0.75 to isolate x

x = 24

So there are 24 students in the class

Note how 18/24 = 3/4 = 0.75 = 75% represents the percentage of boys

Answer: (B) a=3, b=3

Step-by-step explanation:

   [tex]\dfrac{(2xy)^4}{4xy}[/tex]

[tex]=\dfrac{2^4x^4y^4}{4xy}[/tex]

[tex]=\dfrac{16x^4y^4}{4xy}[/tex]

[tex]=4x^{4-1}y^{4-1}[/tex]

[tex]=4x^3y^3[/tex]

Answer:

b

Step-by-step explanation: