find a positive real number such that its square is equal to 15 times the number increased by 286

Answer:

sec squared 55 – tan squared 55  = 1

Explanation:

Given, sec square 55 – tan squared 55

We know that,

[tex]\sec \Theta=\frac{\text {hypotenuse}}{\text {base}}[/tex]

And,

[tex]\tan \theta=\frac{\text { perpendicular }}{\text { base }}[/tex]

where Ө is the angle

Substituting the values

[tex]\left(\frac{\text {hypotenuse}}{\text {base}}\right)^{2}-\left(\frac{\text { perpendicular }}{\text {base}}\right)^{2}[/tex]

Solving,

[tex]\frac{(\text {hypotenuse})^{2}-(\text {perpendicular})^{2}}{(\text {base}) *(\text {base})}[/tex]

According to Pythagoras theorem,

[tex]\text { (hypotenuse) }^{2}-\text { (perpendicular) }^{2}=(\text { base })^{2}[/tex]

Putting this in the equation;

squared 55 - tan squared 55 =

[tex]\frac{(\text {hypotenuse})^{2}-(\text {perpendicular})^{2}}{(\text {base}) *(\text {base})}=\frac{(\text {base})^{2}}{(\text {base}) *(\text {base})}=1[/tex]

Therefore, sec squared 55 – tan squared 55 = 1

The value is always 1.

To solve the expression sec²(55°) - tan²(55°), we can use a trigonometric identity. Recall the Pythagorean identity for tangent and secant:

sec²(θ) - tan²(θ) = 1

Using this identity, we substitute θ with 55°:

This simplifies our expression immediately, as the value is always 1 regardless of the angle, as long as the identity holds.

So, sec²(55°) - tan²(55°) = 1.

Answer:

[tex]x = 1000[/tex] or [tex]x = 0.01[/tex]

Step-by-step explanation:

We are given a logarithmic equation of x and we have to solve it for x.

Given,

[tex]x^{\log x} = 1000000x[/tex]

⇒ [tex]x^{\log x} = 10^{6} \times x[/tex]

Now, taking log on both sides, we get

[tex]\log x^{\log x} = \log 10^{6} \times x[/tex]

⇒ [tex]\log x .\log x = \log 10^{6}  + \log x[/tex]

{Since [tex]\log a^{b} = b\log a[/tex] and [tex]\log ab = \log a + \log b[/tex]}

⇒ [tex](\log x)^{2} = 6 + \log x[/tex]

{Since log 10 = 1}

⇒ a² = 6 + a {Where, a = log x}

⇒ a² - a - 6 = 0

⇒ (a - 3)(a + 2) = 0

⇒ a = 3 or a = -2

⇒ [tex]\log x = 3[/tex] or [tex]\log x = - 2[/tex]

Now, converting logarithm to exponential form, we get,

⇒ [tex]x = 10^{3} = 1000[/tex] or [tex]x = 10^{- 2} = \frac{1}{100} = 0.01[/tex] (Answer)

The value of x in the equation 5 - 3x = - 7 is 4.

The simple algebraic expression consists of numbers and variables. The objective is to determine the value of x in this expression.

From the given information;

Multiply both sides by (-)

Divide both sides by 3

[tex]\mathbf{\dfrac{3x}{3} = \dfrac{12}{3}}[/tex]

x = 4

Therefore, the value of x  in the equation 5 - 3x = -7 is 4.

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Final answer:

The value of x in the equation 5 - 3x = -7 is found to be x = 4 after isolating x through subtraction and division.

Explanation:

To solve the equation 5 - 3x = -7, we need to isolate x. Let's move through the steps together:

The value of x in the equation is 4.

Answer:

The order is as follows:

30, 44, 106

Step-by-step explanation:

Sum of all the three sides = 180°

⇒ (2y + 6)° + (y + 32)° + (8y + 10)° = 180°

⇒ 11y + 48 = 180°

⇒ 11y = 132

⇒ y = 12

Therefore, The angles become 30°, 44° and 106°

They are in the increasing order as well.

Answer:

i think yes it can

Step-by-step explanation:

Answer:

every function is vacuuously both increasing and decreasing at every point because there are no x<y in the "interval" than for all (all zeor of them) x<y we have f(x)≤f(y).

Step-by-step explanation:

Answer:

it saids all that apply its A and what ????

Step-by-step explanation:

The correct options are:

(A) 6 (1/3) cup of flour

(E) 6/5 cups of chopped almonds.

Step-by-step explanation:

Given information:

One batch of cookies requires the ingredients:

2 (1/3) cup of flour.

3/4 of a cup of chocolate chips

2/5 of a cup of chopped almonds

1 (1/2) cup of brown sugar

3/8 of a cup of white sugar

1/2 of teaspoon of salt

Now if Eric wishes to triple the recipe, He needs to triple all the ingredients.

So the new list of ingredients will be triple of pervious one.

That will be:

6 (1/3) cup of flour

3 (3/4) cup of chocolate chips

3 (2/5) cup of chopped almonds

3 (1/2) cup of brown sugar

3 (3/8) cup of white sugar

3 (1/2) tea spoon of salt

So the correct options are:

(A) 6 (1/3) cup of flour

(E) 6/5 cups of chopped almonds.

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Answer:

Share of A is $116 and Share of B is $84.

Step-by-step explanation:

Let the share of A be [tex]x[/tex]

Let the share of B be [tex]y[/tex]

Given:

$200 is shared between A and B

So, [tex]x+y =\$200\ \ \ \ equation \ 1[/tex]

Also given;

twice of A's share is less than 3 times than B's share by $20

[tex]2x= 3y -20\\2x-3y = -20 \ \ \ \ equation \ 2[/tex]

Solution:

Now multiplying equation 1 by 3 we get,

[tex]3x+3y=600 \ \ \ \ equation \ 3[/tex]

Now Adding equation 2 and equation 3 we get

[tex](2x-3y = -20)+ (3x+3y=600)\\5x=580\\\\x=\frac{580}{5}=\$116[/tex]

Now Substituting the value of x in equation 1 we get,

[tex]x+y=200\\116+y=200\\y=200-116 = \$84[/tex]

Hence, Share of A is $116 and Share of B is $84.

Answer:

9.63

Step-by-step explanation:

Answer:

The radius of the circle is 2.4ft

Step-by-step explanation:

circumference of circle = 2πr

circumference = 15ft

2πr = 15

(2×3.14)r = 15

6.28r = 15

r = 2.4ft (near. tenth)

Answer:

The answer is 2.4 ft.

Step-by-step explanation:

C= 2πr

15= 2(3.14)r

15= 6.28r

15÷6.28= 6.28r÷ 6.28

2.4= r

Answer:

y=7x-26

Step-by-step explanation:

Answer:

Step-by-step explanation:

a^2+b^2=400

a^2=400-b^2

a=sqrt(400-b^2) & -sqrt(400-b^2)

-----------------------------------------------

b^2=400-a^2

b=sqrt(400-a^2) & -sqrt(400-a^2)

Answer:

20

Step-by-step explanation:

Picture is posted as and attachnent

We can see here that the reason Gyro went into a bakery was For The Smell Of It.

A bakery is a place where baked goods, such as bread, pastries, cakes, cookies, pies, and other related items, are produced and sold. It is an establishment where baking and the preparation of baked products take place.

Bakeries play a significant role in providing staple food items and indulgent treats, and they contribute to culinary traditions and cultures worldwide. They vary in size and style, ranging from small neighborhood bakeries to larger commercial or industrial operations.

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The profit is $3300 for the month of January.

Step-by-step explanation:

Per hour charge = $40

Total number of tutoring hours = 200

Rent of space = $4000

Electricity = $325

Advertising = $375

Total expenses = 4000+325+375 = $4700

Profit = $40(number of hours) - (expenses)

[tex]Profit=\$40(200)-4700\\Profit=\$8000-4700\\Profit=\$3300[/tex]

The profit is $3300 for the month of January.

Keywords: profit, addition

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Final answer:

To solve the inequality -4x > -24, divide both sides by -4 and flip the inequality sign to obtain x < 6. The solution in interval notation is (-∞, 6).

Explanation:

To solve the inequality -4x > -24, we can divide both sides of the inequality by -4. Remember, when dividing or multiplying both sides of an inequality by a negative number, the inequality sign flips. So, the inequality becomes:

x < 6

The solution in interval notation is (-∞, 6).

Final answer:

The solution is x < 6, which is represented as (-∞, 6) in interval notation.

Explanation:

To solve the inequality -4x > -24, we can start by dividing both sides by -4.

Divide both sides of the inequality by -4. Remember that when you multiply or divide both sides of an inequality by a negative number, the direction of the inequality sign changes.

However, when dividing an inequality by a negative number, the direction of the inequality sign must be flipped. So we have x < 6.

Since the inequality sign is less than, the solution set is all values of x that are less than 6. In interval notation, this is represented as (-∞, 6).

Answer:

Part 1) [tex]LA=220\ ft^2[/tex]

Part 2) [tex]SA=280.5\ ft^2[/tex]

L = 220 ft2 ; S = 280.5 ft2

Step-by-step explanation:

The correct question is

Find the lateral area and surface area of a rectangular prism. The base is a square 5.5 ft by 5.5 ft, and the height is 10 ft

Part 1) Find the lateral area

The lateral area of a rectangular prism is equal to

[tex]LA=Ph[/tex]

where

P is the perimeter of the base

h is the height of the prism

we have

[tex]P=4(5.5)=22\ ft[/tex] ---> the perimeter of a square

[tex]h=10\ ft[/tex] ---> is given

substitute

[tex]LA=22(10)=220\ ft^2[/tex]

Part 2) Find the surface area

The surface area of a rectangular prism is equal to

[tex]SA=2B+LA[/tex]

where

LA is the lateral area

B is the area of the base

we have

[tex]LA=220\ ft^2[/tex]

[tex]B=5.5^2=30.25\ ft^2[/tex] ----> area of a square

substitute

[tex]SA=2(30.25)+220=280.5\ ft^2[/tex]

Answer:

D. L = 220 ; S = 280.5

Step-by-step explanation:

Answer:

The number would be 16.

Step-by-step explanation:

If you have a specific number of apples, and then pluck 3 more, you have 19. So this can be modeled as 19-3, which gives you the original

Answer: 16

steps: 19-3=16

Hope this helps u :)

Answer:

3/5 is greater because when you convert it into decimal it's 0.6 and when you convert 23% into decimal it's 0.23

A real-world problem using 7 groups can be illustrated like a builder constructing 7 buildings each requiring 15 bricks per day. Multiplying these, 7 times 15 gives us 105, which is the total number of bricks needed each day.

Consider a scenario where a builder is constructing 7 buildings. Each building needs 15 bricks per day for construction. We can therefore write a multiplication problem to find out how many total bricks are needed each day.

So, 7 (groups of buildings) multiplied by 15 (bricks per building) equals a total daily brick requirement. To solve this, you simply multiply 7 by 15 which equals 105 bricks needed each day.

This is a simple real-world problem to help understand the concept of multiplication as repeated addition. Here, you're adding 15 bricks 7 times since there are 7 buildings.

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The missing values are [tex]\( a = 2 \), \( b = 0 \), and \( c = -24 \),[/tex] yielding the factored form [tex]\( 2x(x - 24) \).[/tex]

To find the missing values of[tex]\( a \), \( b \), and \( c \)[/tex], we need to expand the polynomial [tex]\( (x+b)(x+c) \)[/tex]and equate it to [tex]\( 2x^3 - 8x^2 - 24x \).[/tex]

Expanding [tex]\( (x+b)(x+c) \),[/tex] we get:

[tex]\[ (x+b)(x+c) = x^2 + (b+c)x + bc \][/tex]

Comparing this to [tex]\( 2x^3 - 8x^2 - 24x \),[/tex]we see that:

[tex]\[ x^2 + (b+c)x + bc = 2x^3 - 8x^2 - 24x \][/tex]

We need to match the coefficients of corresponding terms on both sides of the equation.

From the equation above, we can equate coefficients:

1. Coefficient of [tex]\( x^3 \): \( 2 = 0 \)[/tex] (there is no [tex]\( x^3 \)[/tex] term on the right side).

2. Coefficient of [tex]\( x^2 \): \( 1 = -8 \) (from \( x^2 \) term)[/tex].

3. Coefficient of [tex]\( x \): \( b + c = -24 \) (from \( x \) term).[/tex]

4. Constant term: [tex]\( bc = 0 \)[/tex] (there is no constant term on the right side).

From the last equation, we know that either [tex]\( b \) or \( c \)[/tex]must be zero, or both.

If one of them is zero, then the other must be equal to [tex]\( -24 \)[/tex] for the equation [tex]\( b + c = -24 \)[/tex] to hold true.

Now, we can test some values to satisfy these equations:

1. If [tex]\( b = 0 \)[/tex]

  [tex]\[ c = -24 \][/tex]

2. If [tex]\( c = 0 \):[/tex]

[tex]\[ b = -24 \][/tex]

3. If both [tex]\( b \) and \( c \)[/tex]are non-zero:

  We can solve the equation [tex]\( b + c = -24 \)[/tex] for various values of [tex]\( b \) and \( c \).[/tex]

Therefore, possible combinations are:

1.[tex]\( a = 2 \), \( b = 0 \), \( c = -24 \)[/tex]

2.[tex]\( a = 2 \), \( b = -24 \), \( c = 0 \)[/tex]

3.[tex]\( a = 2 \), \( b = -12 \), \( c = -12 \)[/tex]

So, the possible missing values are:

1. [tex]\( a = 2 \), \( b = 0 \), \( c = -24 \)[/tex]

2. [tex]\( a = 2 \), \( b = -24 \), \( c = 0 \)[/tex]

3.[tex]\( a = 2 \), \( b = -12 \), \( c = -12 \)[/tex]

Answer(1/2)x(2/3)x(4/5)

(1/2x2/3)x(4/5)

(1 1/4x2 1/2)

2 3/4

Step-by-step explanation:

(1/2)x(2/3x4/5)

(1/2x1 3/4)

2 3/4

The right answer is Option D.

Step-by-step explanation:

Distance of Team A = 6x+12

Distance of Team B = 4x-7

Difference between two teams means subtraction, therefore, subtracting the distance of Team B from Team A;

[tex](6x+12)-(4x-7)\\6x+12-4x+7[/tex]

Combining alike terms;

[tex]6x-4x+12+7\\2x+19[/tex]

The difference between two teams is 2x+19.

The right answer is Option D.

Keywords: subtraction

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Answer:

Step-by-step explanation:

Distance of Team A = 6x+12

Distance of Team B = 4x-7

Combining alike terms;

6x-4x+12+7

6x-4x=2x

12+7=19

2x+19

The difference between two teams is 2x+19.

The right answer is Option D.

Answer:

7.5 cm²

Step-by-step explanation:

Note that [tex]\sqrt{120}[/tex] = [tex]\sqrt{4(30)}[/tex] = 2[tex]\sqrt{30}[/tex]

Thus the side s of the square = 2[tex]\sqrt{30}[/tex] ÷ 4 = 0.5[tex]\sqrt{30}[/tex]

Hence

A = s² = (0.5[tex]\sqrt{30}[/tex])² = 0.25 × 30 = 7.5

Answer:

C

Step-by-step explanation:

I don't know exactly why it is C, but I know it isn't the other ones.

(I realize this is not a very concrete answer and it may be wrong, but good luck!)

Answer:

8

Step-by-step explanation:

By fives go up 1 number for eggs

Answer:

6

Step-by-step explanation:

3 times 2

Is 6 and 5 times 2 is 10

Final answer:

To find the number of blue bags, we calculate based on the 5 to 3 ratio with 10 black bags. Each part corresponds to 2 bags, hence there are 6 blue bags.

Explanation:

The question concerns the calculation of the quantity of blue bags based on a given ratio to the quantity of black bags. If the ratio of black bags to blue bags is 5 to 3, and there are a total of 10 black bags, then we can set up a proportion to find the number of blue bags.

To solve this, we assume the number of black bags (5 parts) equals 10, which means each part corresponds to 10 / 5 = 2 bags. Since there are 3 parts of blue bags in the ratio, we then multiply the number of bags per part by 3 (the number of blue parts), which gives us 3 * 2 = 6 blue bags.

Answer:

The width of the rectangular space  = 5 ft.

Step-by-step explanation:

The area of the rectangular space = 70 sq ft.

The length of the rectangular space = 14 ft

The width of the rectangular space - m ft

Now, AREA OF THE RECTANGLE  = LENGTH x WIDTH

⇒  70 sq ft.  =  14 ft x m ft

or, m =  70 / 14  = 5 ft

or, m = 5 ft

Hence the width of the rectangular space  = 5 ft.

Answer: 64

Step-by-step explanation:

the absolute value of a positive number is that number , the absolute value of a negative number is that numbers opposite .

The absolute value is a concept in mathematics that signifies the magnitude of a number, disregarding its positive or negative sign.  The absolute value of a number refers to its magnitude, regardless of its sign. Thus, the absolute value of 64 is itself, which is 64.

The absolute value is a concept in mathematics that signifies the magnitude of a number, disregarding its positive or negative sign. Think of it as a number's distance from zero. Considering your question, the absolute value of 64 is simply 64. This is because 64 is already a positive number, and the absolute value of a positive number is the number itself.

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HEY DEAR

Answer:

45p^5 + 3p^4

step by step explanation:-

3p^4( 4p+7p+4p+1)

3p^4 (11p + 4p) +1

3p^4 (15 p +1)

multiplying 3p^4 to both 15p and 1 we get:-

3p^4× 15p +3p^4× 1

=45p^5 +3p^4

HOPE ITS HELPFULL

Answer:

Dr. Banks Has 164 toothbrushes left to give away or to keep :)

Step-by-step explanation:

subtract 330-53-67-46= 164! Please mark brainliest :)

Answer:

164

Step-by-step explanation:

he had 330 toothbrushes

he gave away 53+67+46

which means he gave away

166 toothbrushes

so we subtract the toothbrushes that he had and the toothbrushes that he gave away.

330-166=164

Answer:

[tex] ME=1.64\sqrt{\frac{0.07(1-0.07)}{370}}=0.0218[/tex]

Step-by-step explanation:

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

[tex]p[/tex] represent the real population proportion of interest

[tex]\hat p=0.07[/tex] represent the estimated proportion for the sample

n=370 is the sample size required (variable of interest)

[tex]z[/tex] represent the critical value for the margin of error

The population proportion have the following distribution  

[tex]p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})[/tex]  

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 90% of confidence, our significance level would be given by [tex]\alpha=1-0.90=0.10[/tex] and [tex]\alpha/2 =0.05[/tex]. And the critical value would be given by:  

[tex]z_{\alpha/2}=-1.64, z_{1-\alpha/2}=1.64[/tex]  

The margin of error for the proportion interval is given by this formula:  

[tex] ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex] (a)  

And replacing into formula (a) the values provided we got:

[tex] ME=1.64\sqrt{\frac{0.07(1-0.07)}{370}}=0.0218[/tex]

The margin of error on this case would be ME=0.0218