Express sin6θ + sin4θ as a product.

The correct conclusion based on the data is that 10% of all eighth-grade students at the High Achievers Charter School are reading below grade level.

Based on the information provided in the question, the most accurate conclusion we can make is that 10% of all eighth-grade students at High Achievers Charter School (HACS), specifically, are reading below grade level. This is because the sample data was only collected from eighth-grade students at HACS. Therefore,

answer C

is correct. That being said, these results only apply to this specific school and grade level and cannot be generalized for all students at HACS or all other schools.

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x+y=8 and 25x+10y=170 are the linear equations.

x+y≤8 and 25x+10y≤170 are the inequalities.

Step-by-step explanation:

Given,

Worth of coins = $1.70 = 1.70*100 = 170 cents

Number of coins = 8

1 quarter = 25 cents

1 dime = 10 cents

Let,

x represent the number of quarters

y represent the number of dimes

1. Write an equation to represent the amount of coins Karen has.

x+y = 8

2.Write an equation to represent the value of the coins Karen has.

25x+10y=170

x+y=8 and 25x+10y=170 are the linear equations.

For inequalities, the amount cannot increase number of coins and worth but it can be less, therefore,

x+y≤8

25x+10y≤170

x+y≤8 and 25x+10y≤170 are the inequalities.

Keywords: linear equations, addition

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Answer:

Yes, because (−1, −5) is below the line.

Step-by-step explanation:

The given inequality is [tex]y \leq  -\frac{3}{4} x - 1[/tex] .......... (1)

Now, rearranging this equality relation we get,

4y = - 3x - 4

⇒ 3x + 4y = - 4

⇒ [tex]\frac{x}{- \frac{4}{3} } + \frac{y}{- 1} = 1[/tex] .......... (2)

This equation is in intercept form and the line represented by this equation passes through the x-intercept [tex](- \frac{4}{3}, 0)[/tex] and y-intercept (0,-1).

Now, it is clear that (0,0) point is above the equation.

But (0,0) point does not satisfy the inequality equation (1).

Hence, the solution of the inequality equation (1) is below and including line (2).

Now, point (-1,-5) is below the line (2) and hence, it is a solution of the inequality (1) as it is below the line. (Answer)

Answer:

the answer is [yes, because (-1, -5) is below the solid line].

Step-by-step explanation:

I took the test and got it right

To divide the given polynomial by a binomial, use polynomial long division, resulting in a quotient of -2x² - 10x - 30 and a remainder of 92.

Dividing a Polynomial by a Binomial

To divide the polynomial -2x³ – 4x² + 3x + 2 by the binomial x - 3, we will use polynomial long division, which is a process similar to long division with numbers. It involves subtracting multiples of the divisor from the dividend to get a quotient and possibly a remainder.

First, divide the first term of the dividend, -2x³, by the first term of the divisor, x, to get -2x².

Multiply the divisor x - 3 by the first term of the quotient, -2x², to get -2x³ + 6x².

Subtract this result from the dividend to obtain the new dividend -4x2 (adjusting the original terms), which becomes -10x².

Repeat this process with the remaining terms of the new dividend.

Continue until all terms of the dividend have been divided.

This process results in the quotient -2x² - 10x - 30 and a remainder of 92. The complete division statement is -2x³ – 4x² + 3x + 2 = (x - 3)(-2x² - 10x - 30) + 92.

Density of wooden block is 850 kilogram per cubic meter

Solution:

Given that wooden block immersed partially into water

There were 15% of the total volume of the block  exposed and 85% of the total volume immersed in water

To find: density of the wooden block

The upward force exerted by any fluid upon a body placed in it is called buoyant force

Buoyant force is balanced by weight force of block

Buoyant force is weight of water displaced by block

Buoyant force = [tex]\rho_{w} V_{2} g[/tex]

Density of water = [tex]\rho_w[/tex] = 1000 kg/m3

[tex]V_2[/tex] = volume of block in water = 0.85 V

[tex]V_1[/tex] = Volume of block in air = 0.15 V

Weight of block = [tex]\rho V g[/tex]

Therefore,

[tex]\rho V g = \rho_{w} V_{2} g\\\\\rho V = \rho_{w} V_{2}\\\\ \rho V = 1000 \times 0.85V\\\\\rho = 1000 \times 0.85\\\\\rho = 850[/tex]

Thus density of wooden block is 850 kilogram per cubic meter

Answer:

x = -4 , y = 3

Step-by-step explanation:

5x - 7y = -41 ... (i)

-3x - 5y = -3 ... (ii)

Multiplying (i) by -3 and (ii) by 5 ;

-15x + 21y = 123 ... (i)

-15x - 25y = -15 ... (ii)

Subtracting (i) by (ii) ;

0 + 46y = 138

46y = 138

y = 138 ÷ 46 = 3

Returning to equation (ii) ;

-3x - 5(3) = -3

-3x = -3 + 15

-3x = 12

x = -4

Answer: The values of x and y in the given equations are [tex]x=-4[/tex] and [tex]y=3[/tex]

Step by step explanation:

Given system of equations are

[tex]5x-7y=-41\hfill (1)[/tex]

[tex]-3x-5y=-3\hfill (2)[/tex]

To find the values of x and y :

by using Elimination method

Now multiplying the equation (1) into 3 we get

[tex]15x-21y=-123[/tex]

Now multiplying the equation (2) into 5 we get

[tex]-15x-25y=-15[/tex]

Adding the above two equations

[tex]15x-21y=-123[/tex]

[tex]-15x-25y=-15[/tex]

_________________

[tex]-46y=-138[/tex]

_________________

[tex]46y=138[/tex]

[tex]y=\frac{138}{46}[/tex]

[tex]y=3[/tex]

Therefore [tex]y=3[/tex]

Substitute y value in equation (1)

[tex]5x-7y=-41[/tex]

[tex]5x-(7\times 3)=-41[/tex]

[tex]5x-21=-41[/tex]

[tex]5x=21-41[/tex]

[tex]5x=-20[/tex]

[tex]x=-\frac{20}{5}[/tex]

[tex]x=-4[/tex]

Therefore [tex]x=-4[/tex]

The values of x and y are [tex]x=-4[/tex] and [tex]y=3[/tex]

Answer:

606 and 612

Step-by-step explanation:

A number is a multiple of 6 if:

1. the sum of its integers can be divided by 3

2. The number is even (ending in 0, 2, 4, 6, 8

With this rule in mind, you have to play around with the numbers. Of course, all odd numbers are out.

606:

6 is even

6 + 6 = 12

12 divided by 4 is 3

612:

2 is even

6 + 1 +  2=  9

9 divided by 3 is 3

Step-by-step explanation:Given that Carter lives on a street where all the house numbers are multiples of 6. We are given to name any two possible house numbers between 601 and 650.The numbers lying between 601 and 650 are602, 603, 604, 605, . . . ,648, 649.And the numbers among these which are multiples of 6 are606, 612, 618, 624, 630, 636, 642, 648.So, any two of these eight numbers can be possible.Thus, the numbers are 606 and 650.

Answer:

4

Step-by-step explanation:

Answer:

Dave:

$20 + 8% of 20 = $21.6

Dave payed a total of $21.6 for the basketball.

Mel

$28 + 8% of 28 = $30.2

Mel payed a total of $30.2 for the football.

$30.2 - $21.6 = $8.6

The difference is $8.6.

Final answer:

To simplify the expression 7[63 ÷ (52 – 22) – 1], perform the operations inside the parentheses first, followed by division, subtraction, and multiplication in that order. The simplified form of the expression is 14.

Explanation:

To find the simplified form of the expression 7[63 ÷ (52 – 22) – 1], we need to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction).

Within the parentheses, we first simplify the exponent, so we calculate 52 – 22 which is 25 – 4.

Perform the subtraction inside the parentheses: 25 – 4 equals 21.

Next, we divide 63 by 21, which equals 3.

Subtract 1 from 3 to get 2.

Finally, multiply 7 by 2 to get the simplified expression, which is 14.

Thus, the simplified form of the expression is 14.

Answer:

53.702

Step-by-step explanation:

You split the two numbers into two.

24, 0.41, 2, and 0,2

Then multiply each one by each other

2 x 24

2 x 0.41

0.2 x 24

0.2 x 24

24 x 2

24 x 0.2

0.41 x 2

then add all of them together and you get your answer

Answer:

Therefore the equation dor nth term is,

[tex]a_{n} =a_{1} + (n-1)\times d[/tex]   and

[tex]a_{30} =-18[/tex]

Step-by-step explanation:

Given:

Arithmetic Sequence as

11 , 10 , 9 , 8 , ..........

∴   First term     = a₁ = 11

   Second term = a₂ = 10

∴ Common Difference = d =  a₂ - a₁ = 10 - 11 = -1

∴ d = -1

To Find:

[tex]a_{n} = ?\\and\\a_{30} = ?[/tex]

Solution:

An equation for the nth term of the arithmetic sequence is given by

[tex]a_{n} =a_{1} + (n-1)\times d[/tex]

Substitute n= 30 for [tex]a_{30}[/tex] and a₁ and d we get

[tex]a_{30} =11 + (30-1)\times -1\\\\a_{30} =11+29\times -1\\\\a_{30} =11-29\\\\a_{30} =-18\\\\\therefore a_{30} =-18\ \textrm{as required}[/tex]

Therefore,

[tex]a_{30} =-18[/tex]

The nth term of the given arithmetic sequence can be represented by the equation an = 12 - n. The 30th term of this sequence is -18.

In order to write an equation for the nth term of an arithmetic sequence, we need to know the first term (a1) and the common difference (d). In the given arithmetic sequence 11, 10, 9, 8, ..., the first term a1 is 11 and the common difference d is -1 (because each term reduces by 1).

The general formula for the nth term (an) of an arithmetic sequence is: an = a1 + (n-1) * d. Substituting the values of a1 and d in the equation, we get: an = 11 + (n-1) * -1 = 12 - n.

To find a30, substitute n = 30 in the equation, we get a30 = 12 - 30 = -18.

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Answer:

the first one is "perpendicular"

the second one is also  "perpendicular"

Step-by-step explanation:

Answer:

1. Perpendicular; 2, perpendicular  

Step-by-step explanation:

1. Segments JK and LM

(a) Calculate the slopes of the segments

(i) Segment JK

[tex]m_{1} = \dfrac{4 - 9 }{7 - 1} = -\dfrac{5}{6}[/tex]

(ii) Segment LM

[tex]m_{2} = \dfrac{13 - 1 }{8 - (-2)} = \dfrac{12}{8 + 2} = \dfrac{12}{10 } = \dfrac{6}{5}[/tex]

(b) Compare their slopes

[tex]m_{2} =\dfrac{6}{5} = -\dfrac{1}{m_{1}}[/tex]

The two segments are perpendicular.

Their graphs are shown in Figure 1.

2. Equations

(a) Calculate the slopes of the segments

(i) First equation

4x + 5y = 10

5y = 10 - 4x

y = 2 - ⅘x

m₁ = -⅘

(ii) Second equation

5x - 4y = -28

-4y = -28 - 5x

y = 7 + ⁵/₄x

m₂ = ⁵/₄

(b) Compare the slopes

m₂ = ⁵/₄ = -1/m₁

[tex]m_{2} =\dfrac{5}{4} = -\dfrac{1}{m_{1}}[/tex]

The two lines are perpendicular.

The graphs are shown in Figure 2.

Answer:

8.9 thats rounded if it wasnt rounded it'll be 8.944

Step-by-step explanation

AB = 14.42

If you plot these points on a graph, they will not be in a straight line, so we'll need to do a little more math here. Draw a diagonal line connecting both points, and use this line as the hypotenuse, so you can draw a right triangle. Count the lengths of each side (except the long, diagonal line called the hypotenuse). Use the equation a^2 + b^2 = c^2 to find the length of side c.

Since side a is 8 units long, square it to get 64.

And side b is 12 units long, and if we square it we get 144.

64 + 144 = 208.

One last step. Now we need to find the square root of 208.

It is 14.42.

So, the distance between points a and b is 14.42 units.

Answer:

[tex]361\dfrac{1}{9}[/tex] tons of high steel and [tex]138\dfrac{8}{9}[/tex] tons of low steel

Step-by-step explanation:

Let x be the number of tons of high grade steel and y be the number of tons ow low grade steel needed.

In x tons of high grade steel there are

[tex]0.85x[/tex] tons of iron

[tex]0.15x[/tex] tons of magnese

In y tons of low grade steel there are

[tex]0.67y[/tex] tons of iron

[tex]0.33y[/tex] tons of magnese

NASA orders 500 tons of steel, so

[tex]x+y=500[/tex]

and specifies that it must be in the proportion 80% iron and 20% magnese, so

[tex]0.85x+0.67y=500\cdot 0.8\\ \\0.85x+0.67y=400[/tex]

From the first equation,

[tex]x=500-y[/tex]

Substitute it into the second equation:

[tex]0.85(500-y)+0.67y=400\\ \\425-0.85y+0.67y=400\\ \\-0.18y=-25\\ \\y=\dfrac{2,500}{18}=138\dfrac{8}{9}\ tons\\ \\x=361\dfrac{1}{9}\ tons[/tex]

Answer:

A = (90°, 1)

B = (270°,-1)

Step-by-step explanation:

if we don't use a calculator, we can explain by reasoning.

Observation 1:

recall y=sin x and y=cos x take values between -1 ≤ y ≤ 1, hence we know that the largest possible value for both functions is 1 and the smallest possible value is -1.

Observation 2:

we also know that both sin and cos functions are cyclic, which means that at some point, the function repeats itself every 360 degrees.

in question 1, we see that point A is located at the top most part of the curve, by observation 1, we can conclude that the y-value must be the maximum value of 1.

We also see that point A is 1/4 of the distance between the starting point of the curve at x=0 and to the end of the curve at x=360 before the curve begins to repeat itself,

hence the x - value is 1/4 of 360 = 90 degrees

Similarly, for point B, we see that B is at the lowest point of the curve, hence by observation 1, we can say that at B, y = -1.

B is also 3/4 of the distance between the start point and the end of the curve before it repeats itself,

hence the x-value of B is 3/4 x 360 = 270 degrees

Answer:

Step-by-step explanation:

a₂ = 14

a₃ = 18

d = a₃ -a₂ = 18 - 14 = 4

a₁ = 14 - 4 = 10

nth term = a + (n-1)d

a₅₁ = 10 +  50 * 4

  = 10 + 200

 = 210

Answer:

The Option D (x ≥ - 53) is correct for the given graph.

Step-by-step explanation:

As shown in the graph blue part is from - 53 to -50 including -53.

therefore x ≥ - 53.

Answer:

On that day 1500 children and 700 adults attended.

Step-by-step explanation:

Given:

There is a carnival. Children are $1.50 and adults are $4.

The total amount of money raised was $5050.

On this particular day there 2200 in attendance.

Now, to find the children and adults attended on that day.

Let the children attended be [tex]x[/tex].

And the adults attended be [tex]y[/tex].

The total number in attendance:

[tex]x+y=2200[/tex]

⇒ [tex]x=2200-y[/tex]........( 1 ).

Now, the total amount of money raised:

[tex]1.50x+4y=5050[/tex]

Putting the equation ( 1 ) in the place of [tex]x[/tex] we get:

⇒ [tex]1.50(2200-y)+4y=5050[/tex]

⇒ [tex]3300-1.50y+4y=5050[/tex]

⇒ [tex]3300+2.50y=5050[/tex]  

Subtracting both sides by 3300 we get:

⇒ [tex]2.50y=1750[/tex]

Dividing both sides by 2.50 we get:

⇒ [tex]y=700.[/tex]

The adults attended = 700.

Now, putting the value of [tex]y[/tex] in equation ( 1 ) we get:

[tex]x=2200-700[/tex]

⇒ [tex]x=1500.[/tex]

The children attended = 1500.

Therefore, on that day 1500 children and 700 adults attended.

Answer: 13

Step-by-step explanation: In this problem we're asked to rewrite as addition and then evaluate.

It's important to understand that minus a negative means the same thing as plus a positive so we can change 5 - (-8) to 5 + (+8).

Now we can simply add to get a sum of 13.

Therefore, 5 - (-8) or 5 + (+8) = 13

Answer: 13

Step-by-step explanation: We originally have the equation 5-(-8).

Flip everything around.

5 + (+8)

5 + (+8) = 13.

When it gives the keywords "rewrite as addition" you should know that you need the rewrite the equation an opposite way of what it was written.

In this case it was 5-(-8).

Flip the signs, 5+(+8).

Add 5 to 8 and get 13.

Answer:

The cost of 1 hat = $2.24

The coat of 1 pair of oven mitten = $2.06

Step-by-step explanation:

Let us assume the cost of 1 hat = $ x

The cost of 1 pair of oven mitten = $y

Case 1:   5 hat and 4 pairs of mittens for $30

Cost of 5 hats  =5 x ( cost of 1 hat) = 5 x    = $ (5 x)

Cost of 4 mittens  =4 x ( cost of 1 mittens) = 4 (y)    = $ (4 y)

Total cost of 5 hats + 4 mittens  = 5x  + 4 y

⇒ 5 x + 4 y = $30 ....... (1)

Case 2:   2 hat and 5 pairs of mittens for $30

Cost of 2 hats  =2 x ( cost of 1 hat) = 2 x    = $ (2 x)

Cost of 5 mittens  =5 x ( cost of 1 mittens) = 5 (y)    = $ (5 y)

Total cost of 2 hats + 5 mittens  = 2 x  + 5 y

⇒2 x + 5 y = $19 ....... (2)

Now, solving (1) and (2) , we get:

5 x + 4 y = $30     (multiply by -2)

2 x + 5 y = $19      (multiply by 5)

Add both equations, we get:

-10 x  - 8 y + 10 x + 25 y = -60 + 95

or, 17 y =  35

or, y =  35/17 =  2.05

or, y  = $2.06

Now, 5 x +  4y = 30

⇒ 5 x + 4 (2.06) = 30

or, 5 x = 30 - 8.24 =  21.76

so, x =  21.76/5 = 2.24

or, x =  $2.24

Hence, the cost of 1 hat = $2.24

And the coat of 1 pair of oven mitten = $2.06

Answer:

A.

The cruise ship will travel 8 nautical miles in 152 minutes.

Step-by-step explanation:

Distance covered by the cruise ship in 342 minutes = 18 nautical miles

Distance covered in 1 minute = [tex]\frac{18}{342}[/tex] nautical miles

                                                = [tex]\frac{1}{19}[/tex] nautical miles

Distance covered in 152 minutes = [tex]\frac{1}{19}\times152[/tex] nautical miles

                                                       = 8 nautical miles

So, distance covered by cruise ship in 152 minutes is 8 nautical miles.

∴ The correct answer is option A.

Answer:

y = 2x - 14

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 2x + 3 ← is in slope- intercept form

with slope m = 2

Parallel lines have equal slopes, thus

y = 2x + c ← is the partial equation

To fid c substitute (5, - 4) into the partial equation

- 4 = 10 + c ⇒ c = - 4 - 10 = - 14

y = 2x - 14 ← equation of parallel line

Answer:

58+54=112

Step-by-step explanation:

The solution is 112 objects

The total number of objects the 7 people from Pia's Pottery shop and Jason's Craft shop is A = 112 objects

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total number of objects be = A

Let the number of mugs in Pia's shop be = m₁

Let the number of bowls in Pia's shop be = b₁

Now , the value of m₁ = 29 mugs

The value of b₁ = 18 bowls

And ,

Let the number of mugs in Jason's shop be = m₂

Let the number of bowls in Jason's shop be = b₂

m₁ = m₂ and b₂ = 2 x b₁

Now , the value of m₂ = 29 mugs

The value of b₂ = 36 bowls

So , the total number of objects A = number of mugs in Pia's shop + number of bowls in Pia's shop + number of mugs in Jason's shop + number of bowls in Jason's shop

Substituting the values in the equation , we get

The total number of objects A = 29 + 18 + 29 + 36

The total number of objects A = 112 objects

Therefore , the value of A is 112 objects

Hence , the total number of objects is 112 objects

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The composite function (f o g)(x) is found by substituting g(x) into the f(x) expression. Upon simplification, (f o g)(x) when f (x) = x²+6x+5 and g(x) = 1/(x+1) is: 1/(x² + 2x + 1) + 6/(x+1) + 5.

To find the composite function (f o g)(x) when f (x) = x²+6x+5 and g(x) = 1/(x+1), we substitute g(x) into f(x). That is, wherever you see 'x' in f(x), replace it with what g(x) is equal to.

Start with f(g(x)) = f(1/(x+1)). In f(x), replace x with 1/(x+1), which gives us: (1/(x+1))² + 6*(1/(x+1)) + 5. This is the composite function (f o g)(x).

To simplify further: the first term '(1/(x+1))²' becomes '1/(x² + 2x + 1)', the second term '6*(1/(x+1))' becomes '6/(x+1)', and the third term is just '+5'. So the composite function (f o g)(x) simplifies to: 1/(x² + 2x + 1) + 6/(x+1) + 5.

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Answer:

9 lawns

Step-by-step explanation:

If she already has $25 of the $115 dollars needed for the ticket, she only needs to make $90 more. If she makes $10 each lawn, she would need to mow 9 lawns in order to get the $90 dollars.

Answer:

Step-by-step explanation:

105/5= 21

21m=b

feel free to ask any question

[tex]\[b = 21m\][/tex] This equation indicates that the number of blinks [tex]\( b \)[/tex] is equal to [tex]21[/tex]times the number of minutes [tex]\( m \)[/tex]

To find a linear equation that represents the number of times Maribel blinks in a given number of minutes, we can use the information provided and assume a constant rate of blinking.

Given:

Maribel blinks [tex]105[/tex] times in [tex]5[/tex] minutes.

To find the rate of blinking per minute, we divide the total number of blinks by the total number of minutes:

[tex]\[\text{Rate of blinking} = \frac{105 \text{ blinks}}{5 \text{ minutes}} = 21 \text{ blinks per minute}\][/tex]

Let [tex]\( b \)[/tex] represent the number of blinks, and let [tex]\( m \)[/tex] represent the number of minutes. Since Maribel blinks at a constant rate, the relationship between [tex]\( b \)[/tex] and [tex]\( m \)[/tex] is linear and can be described by the equation:

[tex]\[b = 21m\][/tex]

Answer:

0.0555555556

Step-by-step explanation:

Answer:

1/18 or 0.055...

Step-by-step explanation:

2/36=1/18

Answer:

1377 minutes

Step-by-step explanation:

645 + 732 = 1377 min