PLEASE HELP ME WITH THIS

Answer:

[tex]2a^2 + 3x - 2a[/tex]

Step-by-step explanation:

[tex] (6a^2 + 3x) - (4a^2 + 2a) = [/tex]

The first set of parentheses is unnecessary and can be removed.

[tex] = 6a^2 + 3x - (4a^2 + 2a) [/tex]

To remove the second set of parentheses, you must distribute the negative sign to its left as if it were a -1 multiplying the quantity inside the parentheses.

[tex] = 6a^2 + 3x - 1(4a^2 + 2a) [/tex]

[tex] = 6a^2 + 3x - 4a^2 - 2a [/tex]

Now combine like terms. Like terms are terms with the same variable part.

[tex] = 2a^2 + 3x - 2a [/tex]

Answer:

[tex]sin\theta_1 = \dfrac{\sqrt{217}}{19}[/tex]

Step-by-step explanation:

It is given that:

[tex]cos\theta_1 = -\dfrac{12}{19}[/tex]

And we have to find the value of [tex]sin\theta_1 = ?[/tex]

As per trigonometric identities, the relation between [tex]sin\theta\ and \ cos\theta[/tex] can represented as:

[tex]sin^2\theta + cos^2\theta = 1[/tex]

Putting [tex]\theta_1[/tex] in place of [tex]\theta[/tex] Because we are given

[tex]sin^2\theta_1 + cos^2\theta_1 = 1[/tex]

Putting value of cosine:

[tex]cos\theta_1 = -\dfrac{12}{19}[/tex]

[tex]sin^2\theta_1 + (\dfrac{12}{19})^2 = 1\\\Rightarrow sin^2\theta_1 + \dfrac{144}{361} = 1\\\Rightarrow sin^2\theta_1 = 1-\dfrac{144}{361}\\\Rightarrow sin^2\theta_1 = \dfrac{361-144}{361}\\\Rightarrow sin^2\theta_1 = \dfrac{217}{361}\\\Rightarrow sin\theta_1 = +\sqrt{\dfrac{217}{361}}, -\sqrt{\dfrac{217}{361}}\\\Rightarrow sin\theta_1 = +\dfrac{\sqrt{217}}{19}, -\dfrac{\sqrt{217}}{19}[/tex]

It is given that [tex]\theta_1[/tex] is in 2nd quadrant and value of sine is always positive in 2nd quadrant. So, the answer is.

[tex]\Rightarrow sin\theta_1 = \dfrac{\sqrt{217}}{19}[/tex]

Answer:

−  square root 15/4

Step-by-step explanation:

Answer:

65 = <JKL

Step-by-step explanation:

There are two expressions that represent the same thing.

The diagram shows that <JKL = 45 + x

The question states that JKL = 3x + 5

The two expressions must be equal since they represent the same thing.

3x + 5 = x + 45

Subtract 5 from both sides

3x + 5 -  5 = x + 45 - 5

3x = x + 40                     Subtract x from both sides

3x - x = x - x + 40

2x = 40                          Divide by 2

2x/2 = 40/2

x = 20

So x + 45 = 20 + 45 = 65

or

3x + 5 = 3*20 + 5 = 60 + 5 = 65

Answer:

i think its c idk if im wrong im sorry

Step-by-step explanation:

Answer:

The dimensions of the driveway are 21 ft x 47 ft, which is option "D" in your list of possible answers

Step-by-step explanation:

Notice that the length "L" of the driveway can be written in terms of its width as:

L = 2 w + 5

based on the given information.

Please see the attached diagram to understand the geometry of the problem, and what the area of the brick walkway involves (depicted in brick color) as the addition of the area of two rectangles:

1) one of length L= 2 w + 5 (w being the width of the driveway - depicted in grey) times 3 feet (the width of the brick walkway

and the other one:

2) w + 3 times 3

Therefore the total area of the brick walkway is given by the formula:

(2 w + 5) * 3 +(w + 3) * 3 = 213 square feet

Now we can solve for "w" in the above equation:

6 w + 15 + 3 w + 9 = 213

9 w + 24 = 213

9 w = 213 - 24

9 w = 189

w = 189/9

w = 21 feet

We can now solve for the L of the driveway, using the first formula we created:

L = 2 w + 5

L = 2 (21) + 5

L = 42 + 5

L = 47 feet

Therefore the driveway's width is w = 21 feet

and its length is L = 47 feet

Answer:

$30.74

Step-by-step explanation:

Answer:

The correct answer is the third expression.

Step-by-step explanation:

We have the following equation:

[tex]4*x^2 + 4*y^2 + 16*x - 24*y = 34[/tex]

Let's organize it by variables, putting together the ones that have the same letter or no letter at all. We have:

[tex]4*x^2 + 16*x + 4*y^2 - 24*y = 34[/tex]

We can extract the common factor on the left side by dividing them by 4, we have:

[tex]4*(x^2 + 4*x) + 4*(y^2 - 6*y) = 34[/tex]

We need to complete the squares on the parenthesis without changing the value of the equation, to do that we will sum the proper values inside the parenthesis and those multiplied by four on the other side of the equation, we have:

[tex]4*(x^2 + 4*x + 4) + 4*(y^2 - 6*y + 9) = 34 + 16 + 36\\4*(x + 2)^2 + 4*(y - 3)^2 = 86[/tex]

The correct answer is the third expression.

Answer:

Felipe's answer is 8.

6 divided by 3/4

= 6 * 4/3

= 24/3

= 8

Answer:

8

Step-by-step explanation:

6÷3/4=6×4/3=8

Answer:

Step-by-step explanation:

The area for a trapezoid is

[tex]A=\frac{1}{2}h(b_{1}+b_{2})[/tex]

h is the length of ST, one of the bases is the length of MK, and the other base is the length of AS.  First we'll find h:

The coordinates for S are (0, -2) and T are (1, 2). Using the distance formula:

[tex]d=\sqrt{(1-0)^2+(2-(-2))^2[/tex] and

[tex]d=\sqrt{17}[/tex].  So h = √17

Now for the length of MK. The coordinates for M are (-7, 4) and for K (5, 1). Using the distance formula again:

[tex]d=\sqrt{(-7-5)^2+(4-1)^2}[/tex] and

[tex]d=\sqrt{(-12)^2+(3)^2}[/tex] so

[tex]d=\sqrt{153}[/tex] which simplifies to

[tex]d=3\sqrt{17}[/tex]. So MK = 3√17.

Now for the length of AS. The coordinates for A: (-4, -1) and for S: (0, -2). Using the distance formula one more time:

[tex]d=\sqrt{(-4-0)^2+(-1-(-2))^2}[/tex] and

[tex]d=\sqrt{(-4)^2+(1)^2}[/tex] and

[tex]d=\sqrt{17}[/tex]. So AS = √17.

Now we can fill in our area formula:

[tex]A=\frac{1}{2}(\sqrt{17})(3\sqrt{17}+\sqrt{17})[/tex]

Simplifying a bit:

[tex]A=\frac{1}{2}(\sqrt{17})(4\sqrt{17})[/tex] and simplifying a bit more:

[tex]A=\frac{4*17}{2}[/tex] and

A = 34

Answer:

[tex]131.95[/tex] [tex]cm[/tex]

Step-by-step explanation:

[tex]C=2 \pi r[/tex]

[tex]C=2 \pi \times 21[/tex]

[tex]C=42\pi[/tex]

[tex]C \approx 131.946891451[/tex]

Answer:

Step-by-step explanation:

This problem is on the mensuration of flat shape, a circle.

we know that the circumference of a circle is expressed as

[tex]C= 2\pi r[/tex]

Given that radius = 12 ft

The circumference can be solved for by substituting the value of r in the formula

C=2*3.142*12

C= 75.408ft

to 2 d.p the circumference is 75.41 ft

｡☆✼★ ━━━━━━━━━━━━━━  ☾  

4 : 5

300 : ?

Divide 300 by 4 to find out what '1 part' would count as:

300/4 = 75

Multiply this by 5

75 x 5 = 375

Add the two values together

375 + 300 = 675

There are 675 students

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Step-by-step explanation:

Number of boys=300

Ratio of boys to girls=4:5

let the number of girls=y

300/y=4/5

Cross multiply

300×5=4×y

1500=4y

Divide through both sides by 4

1500/4=4y/4

374=y

Number of girls is 375

Total number of students=Number of boys+Number of girls

Total number of students=300+375

Total number of students=375

Answer:

The equation of the relationship is y = 1.25x + 6.5

Step-by-step explanation:

I graphed the ordered pairs on the graph below and found the slope and y-intercept of the line.

The price per game is $7.75. (If needed)

Answer:

The answer is option D

Took the quiz

Answer: They are equivalent because when x=2, the two expressions have the same value.

Step-by-step explanation:

Answer:

3.2 ft

Step-by-step explanation:

The initial distance from the base of the ladder to the wall is:

[tex]20^2=16^2+d^2\\d=12\ ft[/tex]

After moving the ladder, the distance from the base to the wall is 12 - 2x while the height of the ladder is 16 + x. The distance x is given by:

[tex]20^2 = (12-2x)^2+(16+x)^2\\400 = 144-48x+4x^2+256+32x+x^2\\5x^2-16x=0\\5x=16\\x=3.2\ ft[/tex]

Therefore, the top of the ladder is  3.2 ft higher now.

Answer:

3.2ft higher

Step-by-step explanation:

The expression [tex](8 + 2 \times 6)^2[/tex], following PEMDAS, simplifies to 400.

Let's break down the steps in solving the expression [tex](8 + 2 \times 6)^2[/tex] in more detail (Follow PEMDAS).

Step 1: MultiplicationWe start by evaluating the multiplication operation, which is 2 x 6. The result of this operation is 12.

Step 2: AdditionNext, we evaluate the addition operation, which is 8 + 12. The sum of 8 and 12 is 20.

Step 3: SquaringFinally, we square the result of the addition, which is 20. Squaring a number means multiplying it by itself. In this case, [tex]20^2[/tex] means 20 multiplied by 20, which equals 400.

Therefore, the expression [tex](8 + 2 \times 6)^2[/tex] simplifies to 400.

Learn more about PEMDAS here:

https://brainly.com/question/36185

#SPJ4

Answer:

9 cubic feet

Step-by-step explanation:

Assuming that the garden box is a rectangular prism, its volume is:

[tex]4\dfrac{1}{2} \cdot 4 \cdot \dfrac{1}{2}=9 \text{ ft}^3[/tex]

Hope this helps!

Solution,

Length(L)=4 1/2 ft

Breadth(b)= 4 ft

Height(H)=1/2 ft

Now,

Volume=L*B*H

= 4 1/2*4*1/2

=9/2*4*1/2

= 9 cubic feet

Hope it helps

Good luck on your assignment

Answer:

W

Step-by-step explanation:

The input is the x-axis.

The output is the y-axis.

Make them coordinates. Hope this helped!

Answer:

Step-by-step explanation:

Before we begin this, there are a few things that need to be said and a few formulas you need to know. First is that we need to use the work form of a parabola, which is

[tex]y=a(x-h)^2+k[/tex]

All of the parabolas listed in blue highlight open either up or down, and this work form represents those 2 options. The only thing we need to know is that if there is a negative sign in front of the a, the parabola opens upside down like a mountain instead of up like a cup.

Another thing we need to know is how to find the focus of the parabola. The formula to find the focus for an "up" parabola is (h, k + p) and the formula to find the focus for an upside down parabola is (h, k - p). Then of course is the issue on how to find the p. p is found from the a in the above work form parabola, where

[tex]p=\frac{1}{4|a|}[/tex] .

In order to accomplish what we need to accomplish, we need to put each of those parabolas into work form (as previously stated) by completing the square. I'm hoping that since you are in pre-calculus you have already learned how to complete the square on a polynomial in order to factor it.  Starting with the first one, we will complete the square. I'll go through each step one at a time, but will provide no explanation as to how I got there (again, assuming you know how to complete the square).

[tex]y=-x^2+4x+8[/tex] and, completing the square one step at a time:

[tex]-x^2+4x=-8[/tex] and

[tex]-(x^2-4x+4)=-8-4[/tex] and

[tex]-(x-2)^2=-12[/tex] and

[tex]-(x-2)^2+12=y[/tex]

From this we can see that the h and k values for the vertex are h = 2 and k = 12. Now to find p.

[tex]|a|=1[/tex], ∴

[tex]p=\frac{1}{4(1)}=\frac{1}{4}[/tex]

Using the correct focus formula (h, k - p), we get that the focus is

[tex](2, 12-\frac{1}{4})[/tex] which simplifies to (2, 11.75) which is choice 2 in your options.

Now for the second one (yes, this takes forever...)

[tex]y=2x^2+16x+18[/tex] and completing the square one step at a time:

[tex]2x^2+16x=-18[/tex] and

[tex]2(x^2+8x+16)=-18+32[/tex] and

[tex]2(x+4)^2=14[/tex] and

[tex]2(x+4)^2-14=y[/tex]

From this we can see that the vertex is h = -4 and k = -14. Now to find p from a.

[tex]|a|=2[/tex], ∴

[tex]p=\frac{1}{4(2)}=\frac{1}{8}[/tex] .

Using the correct focus formula for an upwards opening parabola (h, k + p),

[tex](-4, -14+\frac{1}{8})[/tex] which simplifies down to (-4, -13.875) which is choice 3 in your options.

Now for the third one...

[tex]y=-2x^2+5x+14[/tex] and completing the square step by step:

[tex]-2x^2+5x=-14[/tex] and

[tex]-2(x^2-\frac{5}{2}x+\frac{25}{16})=-14-\frac{50}{16}[/tex] and

[tex]-2(x-\frac{5}{4})^2=-\frac{137}{8}[/tex] and

[tex]-2(x-\frac{5}{4})^2+\frac{137}{8}=y[/tex]

From that we can see the vertex values h and k. h = 1.25 and k = 17.125. Now to find p.

[tex]|a|=2[/tex], ∴

[tex]p=\frac{1}{4(2)}=\frac{1}{8}[/tex]

Using the correct focus formula for an upside down parabola (h, k - p),

[tex](1.25, 17.125-\frac{1}{8})[/tex] which simplifies down to (1.25, 17) which is choice 4 in your options.

Now for the fourth one...

[tex]y=-x^2+17x+7[/tex] and completing the square step by step:

[tex]-x^2+17x=-7[/tex] and

[tex]-(x^2-17x)=-7[/tex] and

[tex]-(x^2-17x+72.25)=-7-72.25[/tex] and

[tex]-(x-8.5)^2=-79.25[/tex] and

[tex]-(x-8.5)^2+79.25=y[/tex]

From that we see that the vertex is h = 8.5 and k = 79.25. Now to find p.

[tex]|a|=1[/tex], ∴

[tex]p=\frac{1}{4(1)}=\frac{1}{4}[/tex]

Using the correct formula for an upside down parabola (h, k - p),

[tex](8.5, 79.25-\frac{1}{4})[/tex] which simplifies down to (8.5, 79) and I don't see a choice from your available options there.

On to the fifth one...

[tex]y=2x^2+11x+5[/tex] and again step by step:

[tex]2x^2+11x=-5[/tex] and

[tex]2(x^2+\frac{11}{2}x+\frac{121}{16})=-5+\frac{242}{16}[/tex] and

[tex]2(x+\frac{11}{4})^2=\frac{81}{8}[/tex] and

[tex]2(x+\frac{11}{4})^2-\frac{81}{8}=y[/tex]

from which we see that h = -2.75 and k = -10.125. Now for p.

[tex]|a|=2[/tex], ∴

[tex]p=\frac{1}{4(2)}=\frac{1}{8}[/tex]

Using the correct focus formula for an upwards opening parabola (h, k + p),

[tex](-2.75, -10.125+\frac{1}{8})[/tex] which simplifies down to (-2.75, -10) which is choice 1 from your options.

Now for the last one (almost there!):

[tex]y=-2x^2+6x+5[/tex] and

[tex]-2x^2+6x=-5[/tex] and

[tex]-2(x^2-3x+2.25)=-5-4.5[/tex] and

[tex]-2(x-1.5)^2=-9.5[/tex] and

[tex]-2(x-1.5)^2+9.5=y[/tex]

from which we see that h = 1.5 and k = 9.5. Now for p.

[tex]|a|=2[/tex], ∴

[tex]p=\frac{1}{4(2)}=\frac{1}{8}[/tex]

Using the formula for the focus of an upside down parabola (h, k - p),

[tex](1.5, 9.5-\frac{1}{8})[/tex] which simplifies down to (1.5, 9.375) which is another one I do not see in your choices.

Good luck with your conic sections!!!

Answer:

Step-by-step explanation:

rectangle + semicircle

= 8*6 + pi r^2/2

=48 + 22/7 * 3/2 * 3/2

then simplyn..

Answer:

The figure is a rectangle and a semicircle

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

a = 2 ;  b = -6 ;  c = 5

[-b±√b²-4ac]/2a=[-(-6)±√6²-4*2*5]/2*2

=[6±√√36-40]/4

=[6±√-4]/4

=[6±√i²*2²]/4

=[6±2i]/4

=2[3±i]/4

=3±i/2

= 3+i/2  or 3-i/2

Answer:

400

Step-by-step explanation:

Answer:

g(x) has a greater y intercept than f(x)

Step-by-step explanation:

f(x) = 6x^2 + 18x +3

f(0) = 0+0+3

The y intercept is 3

g(x) crosses the y axis at 6

The y intercept is 6

g(x) has a greater y intercept than f(x)

Answer:

g(x) has a greater y intercept than f(x)

Step-by-step explanation:

f(x) = 6x^2 + 18x +3

f(0) = 0+0+3

The y intercept is 3

g(x) crosses the y axis at 6

The y intercept is 6

g(x) has a greater y intercept than f(x)

hope I could help

Answer:

192 cubes.

Step-by-step explanation:

The volume of each cube  = (side)³  = (1/4)³  = 1/64 units ³

Next is to find how many cubes are needed to fill the prism.

The number of cubes  that will fill the prism  :

Vol. of prism / Vol. of cube = 3 / [tex]\frac{1}{64}[/tex]

                                            =192 cubes.

Therefore, it takes 192 cubes to fill the prism.

Answer:

8/17

Step-by-step explanation:

total balls= 9 + 18 + 2 + 5 = 34

balls drawn should NOT be Orange.

so, 34 - 18 (as there are 18 orange balls)

16 balls

probability= 16/34 = 8/17

answer = 8/17

Answer:

25

Step-by-step explanation:

To find the constant

take the coefficient of x

10

divide by 2

10/2 =5

Square it

5^2 =25

Add this

x^2 +10x+25

Answer:

See explaination:

Graphs are on the right, equations are on the left, and they are color coded.

Step-by-step explanation:

Answer:

easy just find the total of how many people work there then put that no. as a denominator and put 12 on the numerator then times it by 100 and the answer should be 52.2% or 52.17%

Answer:

52.2% or 52.17%

12 men

Total = 23

12 / 23 =

Answer:

9 spoons knives =12

9 spoons cost= £ 82.80

total no of 1 knife = 12x9 = 108

1 knife = 82.80 x 108 = 8,94, 240

so, 1 knife Cost's =£ 8,94,240