Express cos A as a fraction in simplest terms.

Answer:

y = 4(x+6)(x-2)

Step-by-step explanation:

y = 4x² + 16x - 48, factor out the 4

y = 4(x² + 4x - 12), find factors of 12

Factors of 12:

1*12, 2*6, 3*4; find a pair that sums to 4x or 4

6-2 = 4, since 12 is a negative number, a number in the factor must be negative, in this case, making 2 negative, would make 6-2 = 4

y = 4(x+6)(x-2)

About 492 pounds of milk and egg were consumed each year

Given the following parameters from the chart

Total consumption = 1640 pounds per person

The percentage of milk and egg = 100 -(38 + 10 + 10 +8 + 4)

The percentage of milk and egg = 30%

Determine the amount consumed each year

Amount of milk and egg consumed = 30% of 1640

Amount of milk and egg consumed = 492 pounds

Hence about 492 pounds of milk and egg were consumed each year

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Answer:

An equation connects two expressions with an equal sign. It shows that the two expressions are equal to each other, like 5 = 5, or for variables, 5x = 2x, which means that x = 0.

Brainliest, please :)

Answer:

An equation is a problem consist sting of many numbers mostly division or mulitiplication

Step-by-step explanation:

To solve this problem, you will use the distributive property to create an equation that can be rearranged and solved using the quadratic formula.

Use the distributive property to distribute 3x into the term (x + 6):

[tex]3x(x+6)=-10[/tex]

[tex]3x^2+18x=-10[/tex]

To create a quadratic equation, add 10 to both sides of the equation:

[tex]3x^2+18x+10=-10+10[/tex]

[tex]3x^2+18x+10=0[/tex]

The quadratic formula is defined as:

[tex]\displaystyle x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]

The model of a quadratic equation is defined as ax² + bx + c = 0. This can be related to our equation.

Therefore:

Set up the quadratic formula:

[tex]\displaystyle x=\frac{-18 \pm \sqrt{(18)^2 - 4(3)(10)}}{2(3)}[/tex]

Simplify by using BPEMDAS, which is an acronym for the order of operations:

Brackets

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

Use BPEMDAS:

[tex]\displaystyle x=\frac{-18 \pm \sqrt{324 - 120}}{6}[/tex]

Simplify the radicand:

[tex]\displaystyle x=\frac{-18 \pm \sqrt{204}}{6}[/tex]

Create a factor tree for 204:

204 - 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102 and 204.

The largest factor group that creates a perfect square is 4 × 51. Therefore, turn 204 into 4 × 51:

[tex]\sqrt{4\times51}[/tex]

Then, using the Product Property of Square Roots, break this into two radicands:

[tex]\sqrt{4} \times \sqrt{51}[/tex]

Since 4 is a perfect square, it can be evaluated:

[tex]2 \times \sqrt{51}[/tex]

To simplify further for easier reading, remove the multiplication symbol:

[tex]2\sqrt{51}[/tex]

Then, substitute for the quadratic formula:

[tex]\displaystyle x=\frac{-18 \pm 2\sqrt{51}}{6}[/tex]

This gives us a combined root, which we should separate to make things easier on ourselves.

Separate the roots at the plus-minus symbol:

[tex]\displaystyle x=\frac{-18 + 2\sqrt{51}}{6}[/tex]

[tex]\displaystyle x=\frac{-18 - 2\sqrt{51}}{6}[/tex]

Then, simplify the numerator of the roots by factoring 2 out:

[tex]\displaystyle x=\frac{2(-9 + \sqrt{51})}{6}[/tex]

[tex]\displaystyle x=\frac{2(-9 - \sqrt{51})}{6}[/tex]

Then, simplify the fraction by reducing 2/6 to 1/3:

[tex]\boxed{\displaystyle x=\frac{-9 + \sqrt{51}}{3}}[/tex]

[tex]\boxed{\displaystyle x=\frac{-9 - \sqrt{51}}{3}}[/tex]

The final answer to this problem is:

[tex]\displaystyle x=\frac{-9 + \sqrt{51}}{3}[/tex]

[tex]\displaystyle x=\frac{-9 - \sqrt{51}}{3}[/tex]

Plug in the points and see if they satisfy the equation.

y = 2x - 3

(1, -1)

-1 = 2(1) - 3

-1 = 2 - 3

-1 = -1

So (1, -1) satisfies the equation.

(-3, 0)

0 = 2(-3) - 3

0 = -6 - 3

0 = -9

So (-3, 0) does not satisfy the equation.

(5, 4)

4 = 2(5) - 3

4 = 10 - 3

4 = 7

So (5, 4) does not satisfy the equation.

Therefore your answer is (1, -1).

Answer:

the answer is 5,4

Answer:

the equivalent fractions for 2/5 are:

(2/5) × (2/2) = (2 × 2) / (5 × 2) = 4/10

(2/5) × (3/3) = (2 × 3) / (5× 3) = 6/15

(2/5) × (4/4) = (2 × 4) / (5 × 4) = 8/20

Answer:

4/10, 6/15, 8/20, etc.

Step-by-step explanation:

I hope you got some idea

THE ANSWER IS -> b. x > 1

hope it helps

thanks

Answer: c. x>0

Step-by-step explanation:

The greatest height is 9 feet.

What is projectile?

A projectile is any object thrown into space upon which the only acting force is gravity.

As, from the graph we can see that

The highest point the ball reaches shown by the coordinates (0.75, 9)

As, the maximum height is shown by y- axis(vertical axis).

Hence, the greatest height is 9 feet.

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Answer:

25/36

Step-by-step explanation:

put 2500 over 3600 and you get 2500/3600 but you can simplify to get 25/36 but removing the 0's

Answer:

8 in the box.

Step-by-step explanation:

As, it is given that 35 students study Biology.

So, in Biology circle,

15+7+5+x=35

27+x=35

x=35-27

x=8

Answer:

f(2) =  18

Step-by-step explanation:

Put '2' into the equation where 'x' is to get :

f(2)  =  2 (2^2) + 5 (sqrt(2+2)

        =  8        + 5 (2)   =  18

Answer: $12.96

Given:

1305 bags of carrots purchased

Total cost = $16,910

Step-by-step explanation:

To find the unit cost, divide 16910 by 1305 to find the cost of one bag of carrots:

[tex]\frac{16910}{1305} = 12.96[/tex]  (rounded to nearest hundredth)

Assuming average cost of $55.5, the cost of goods sold by Olympic Enterprises for the June 14 sale is equal to $444.

In Financial accounting, the cost of goods sold for a business firm can be calculated by multiplying the total quantity of goods by an average cost. Mathematically, this is given by:

Cost of goods = quantity × average cost

Note: We would assume an average cost of $55.5.

Substituting the parameters into the formula, we have:

Cost of goods sold = 8 × 55.5

Cost of goods sold  = $444.

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Answer:

Looks to me like it should be -2

The line of music is refered to as the bracket

It should be noted that music simply means a vocal or instrumental sounds that are combined to produce beauty of harmony and expression if emotions.

When When both of these staves are connected with this symbol, it's called a brace.

Lastly, the things inside the box are voice, piano, and guitar.

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The volume of the given figure is 104 m³.

We need to find the volume of the given figure.

Volume is a scalar quantity expressing the amount of three-dimensional space enclosed by a closed surface.

Divide the given figure into two convenient cuboids. That is one with dimensions length=4 m, breadth=4 m and height=3 m. Another with length=4 m,  breadth=7 m and height=2 m.

We know that, the volume of cuboid =l×b×h cubic units.

Now, the volume of cuboid=4×4×3=48 m³ and the volume of another

cuboid=4×7×2=56 m³.

The volume of the given figure=48+56=104 m³.

Therefore, the volume of the given figure is 104 m³.

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Answer:

expression for (g + h)([tex]x\\[/tex]) = [tex]2x[/tex] + [tex]3x^2\\[/tex] and for (g - h)([tex]x[/tex]) = [tex]2x[/tex] - [tex]3x^2[/tex]

value of (g .h)(2) = 24

Step-by-step explanation:

function operations: Functions with overlapping domains can be added, subtracted, multiplied and divided. If f(x) and g(x) are two functions, then for all x in the domain of both functions we can find the sum, difference, product and quotient

given :

g([tex]x[/tex]) = [tex]2x[/tex]

h([tex]x[/tex]) = [tex]3x^2[/tex]

we know that ;

(g + h)([tex]x[/tex]) = g([tex]x[/tex]) + h([tex]x[/tex])

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

similarly;

(g - h)([tex]x[/tex]) = g([tex]x[/tex]) - h([tex]x[/tex])

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

now,  

(g . h)([tex]x[/tex]) = 2([tex]3x^2\\[/tex])

             = 6[tex]x^2\\[/tex]

for (g .h)(2) = 6([tex]2^2[/tex])

                  = 6 × 4

                  = 24

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The school bus will take 5.34 seconds to travel 95.1 m if the bus is moving 26.8 m/s on flat ground when it begins to accelerate at 4.73 m/s².

Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

As we know, the formula for the roots of the quadratic equation is given by:

[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]

We have:

A school bus is moving 26.8 m/s on flat ground when it begins to accelerate at 4.73 m/s².

From the second equation of motion:

[tex]\rm s = u + \dfrac{1}{2}at^2[/tex]

We have given:

s = 95.1 m

u = 26.8 m/s

a = 4.73 m/s²

[tex]\rm 95.1 = 26.8 + \dfrac{1}{2}(4.73)t^2[/tex]

The above equation is a quadratic equation:

After simplification:

[tex]\rm \dfrac{4.73}{2}t^2=68.3[/tex]

[tex]\rm t^2=28.879[/tex]

t = 5.373 seconds ≈ 5.34 seconds

Thus, the school bus will take 5.34 seconds to travel 95.1 m if the bus is moving 26.8 m/s on flat ground when it begins to accelerate at 4.73 m/s².

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As x decreases without bound, the graph of f(x)  approaches y = 0

As x increases without bound, the graph of f(x)  increases without bound

An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given:

f(x)=5^(x−1)

When x -> -∞

[tex]lim_{ x- > -\infty.[/tex] f(x)= 5 ^(x-1) = 0

When x -> ∞

[tex]lim_{ x- > \infty.[/tex] f(x)= 5 ^(x-1) = ∞

Hence,

As x decreases without bound, the graph of f(x) approaches y = 0

As x increases without bound, the graph of  f(x) increases without bound

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Step-by-step explanation:

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Question

Bookmark

The value of the expression x

4

−8x

3

+18x

2

−8x+2, when x=2+

3

, is:

Medium

Solution

verified

Verified by Toppr

Correct option is B)

Let f(x)=x

4

−8x

3

+18x

2

−8x+2

Substituting x=2+

3

, we get

f(2+

3

)=(2+

3

)

4

−8(2+

3

)

3

+18(2+

3

)

2

−8(2+

3

)+2

=(2+

3

)

2

((2+

3

)

2

+18)−8(2+

3

)((2+

3

)

2

+1)+2

=(7+4

3

)(4

3

+25)−8(2+

3

)(8+4

3

)+2

=175+48−128−96+2

=1

Hence, option B is correct.

a) The test statistic is given as t = [tex]\dfrac {14-12}{\dfrac{4.32}{\sqrt25}}}[/tex]= 2.315

b) The pa value will be P = P( t₂₄ > 2.315 ) = 0.015

c) If we compare the p-value and the significance level is given we see that  so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is higher than 12 at 1% of significance

In null hypotheses, there is no relationship between the two phenomena under the assumption that it is not associated with the group. And in alternative hypotheses, there is a relationship between the two chosen unknowns.

X= represents the sample mean

s = represent the sample standard deviation

n = 25 sample size  

[tex]\mu_o[/tex] = 12 represent the value that we want to test

[tex]\alpha[/tex] = 0.05 represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

[tex]p_v[/tex] represent the p-value for the test (variable of interest)  

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the mean is higher than 12, the system of hypothesis would be:  

Null hypothesis:  ≤ 12

Alternative hypothesis: > 12

If we analyze the size for the sample is > 30 but we don't know the population deviation so is better to apply a t-test to compare the actual mean to the reference value, and the statistic is given by:  

[tex]t=\dfrac{X-\mu_o}{\dfrac{\sigma}{\sqrt{n}}}[/tex]

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to a specified value".  

Calculate the statistic

We can replace in formula (1) the info given like this:  

[tex]\dfrac {14-12}{\dfrac{4.32}{\sqrt25}}}[/tex]= 2.315    

P-value:-

The first step is calculate the degrees of freedom, on this case:  

 df = n - 1 =25 - 1 = 2

Since is a one side right tailed test the p value would be:  

[tex]p_v[/tex] =  P( t₂₄ > 2.315 ) = 0.015

Conclusion  

If we compare the p-value and the significance level is given [tex]\alpha[/tex]= 0.05  we see that [tex]p_v < \alpha[/tex]  so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is higher than 12 at 1% of significance.

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Answer:  90 degrees clockwise

This is equivalent to 270 degrees counterclockwise

The rule for either rotation is [tex](x,y) \to (y,-x)[/tex]

The x and y coordinates swap places, and the new second coordinate flips from positive to negative (or vice versa).

The diagram below shows an example of this for the point (-4,-2) rotating to (-2, 4). The center of the rotation is the origin (0,0).

The equation of the line is y = 3x +3 .

A straight line equation is that can be represented by y = mx +c , where m is the slope and c is the intercept on y axis.

The points given are (2,3) and (5,9)

m = (9-3)/(5-2) = 3

m = 3

Therefore the equation becomes

y = 3x +c

Te equation is given by

(y-y₁) = m(x-x₁)

y-3 = 3(x - 2)

y-3 = 3x -6

y = 3x +3

Therefore the equation of the line is y = 3x +3 .

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Answer:

The total money we have to pay is $69.

Step-by-step explanation:

MARKUP is the amount added to the cost price.

MARKUP formula = 100*profit / cost

Cost of the item = $60.00

put the value in the formula

15 = 100*profit/60

profit = 60 × 15 ÷ 100 = 9

the total money  is  cost + profit

which is 60 + 9 = $69.

So the total money we have to pay is $69.

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The probability that a boy is selected is 0.5357 or 53.57%

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

P(boy) is asking for the probability that a boy will be chosen to read a poem out loud. Since there are 15 boys, we can get the probability by dividing this by the total number of students.

This is because out of all the students, there is an equal possibility that each of the 15 boys will be chosen.

P = ( 15 ) / ( 15+13)

P = 15 / 28

P = 0.5357

Therefore the probability that a boy is selected is 0.5357 or 53.57%

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Answer:

53.57%

Step-by-step explanation:

Answer:

D) 8[tex]\frac{1}{2}[/tex]

Step-by-step explanation:
5[tex]\frac{2}{3}[/tex] ÷ [tex]\frac{2}{3}[/tex] = 8[tex]\frac{1}{2}[/tex]

She has 45% of the original amount left

Fractions are written as a ratio of two integers

Given the following

Initial amount. = ∈4000

Amount given to her sister = 1/4 * 4000 = 1000

Amount given to her brother = 40% of 3000 = 1200

Amount left = 4000 - (1000+1200)

Amount left = ∈1800

Determine the percentage left

x * 4000 = 1800

x = 1800/4000

x = 0.45

x = 45%

Hence she has 45% of the original amount left

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Answer:

740 miles

Step-by-step explanation:

$415-$230=$185

$185÷0.25 per miles =740 miles