find three consecutive positive even integers such that the product of the second and third integers is 20 more than 10 times the first integer.

[tex]\bf \cfrac{1}{1-sin(x)}+\cfrac{1}{1+sin(x)}=\cfrac{2}{cos^2(x)} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{using the LCD of [1-sin(x)][1+sin(x)]}}{\cfrac{[1+sin(x)]1~~+~~[1-sin(x)]1}{\underset{\textit{difference of squares}}{[1-sin(x)][1+sin(x)]}}} \\\\\\ \cfrac{1+sin(x)+1-sin(x)}{1^2-sin^2(x)}\implies \cfrac{1+sin(x)+1-sin(x)}{1-sin^2(x)}[/tex]

recall that 1 - sin²(θ) = cos²(θ).

Answer:

your answer is C

Step-by-step explanation:

vertices neither contain angle nor contain complement

Answer:

C. P, Q and R.

Step-by-step explanation:

In geometry to express verticles, we use only the capital letter for that point.

It's not A because that's the symbol to represent angles.

It's not B because of the right answer in into the options.

it's not D because having both capital letters with the lines above means the line between those points.

The correct answer is C.

Answer

54 degrees

Step-by-step explanation:

Using angle sum property(angles in a triangle add up to 180),

y+y+72=180

2y+72=180

2y=180-72

2y=108

y=108/2

y=54 degrees

pls mark brainliest

hope it helped

Answer:

A 54

Step-by-step explanation:

The sum of the angles of a triangle add to 180 degrees

72+y+y = 180

Combine like terms

72 +2y = 180

Subtract 72 from each side

72-72 +2y = 180-72

2y = 108

Divide by 2 on each side

2y/2 = 108/2

y = 54

Answer:

-6x^4-8x^2 or -2x^2(3x^2+4)

Step-by-step explanation:

Given expression is:

[tex]2x^2(-5x^2-4)+4x^4[/tex]

In order to write the expression in simplest form we have to multiply the terms which needs to be multiplied.

So,

[tex]= -10x^4-8x^2+4x^4[/tex]

Combining alike terms

[tex]= -10x^4+4x^4-8x^2\\=-6x^4-8x^2\\[/tex]

Can also be written as:

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

Answer:

-2x^2(3x^2 + 4).

Step-by-step explanation:

2x^2(-5x^2 - 4) + 4x^4

Distribute the 2x^2 over the parentheses:

= -10x^4 - 8x^2 + 4x^4

= - 6x^4 - 8x^2

=  -2x^2(3x^2 + 4).

Answer:

48 sq. units

Step-by-step explanation:

The area of a trapezoid is given by half sum of the bases multiplied by the height

[tex]=\frac{1}{2} (a+b)h[/tex]

where a and b are the two parallel sides of the trapezoid and h is the height or amplitude of the trapezoid

But you are aware that, the median of a trapezoid is equal to half the sum of the bases, thus the first part of the formulae  is covered by the median

[tex]Median=\frac{1}{2} (a+b)[/tex]

Hence area, A, of a trapezoid is simplified to product of median and amplitude

[tex]A=amplitude*median\\\\A=6*8=48sq.units[/tex]

Answer:

=48 sq. units.

Step-by-step explanation:

Area of a trapezoid =h× (a+b)/2

(a+b)/2 is the median ( half of the sum of the two parallel sides also called the bases.

Median=8 inches

Altitude is the distance between the two parallel sides= 6 inches

A=6 inches×8 inches

=48 sq. units.

Answer:

AC ≈ 12.9 cm

Step-by-step explanation:

Using the ratio

sin40° = [tex]\frac{b}{20}[/tex]

Multiply both sides by 20

20 × sin40° = b, hence

AC = b = 20 × sin40° ≈ 12.9

Answer:

Part 1)  shaded area at left of x=8 (close circle) ---> [tex]-\frac{x}{10}+\frac{1}{5} \geq-\frac{33}{55}[/tex]  

Part 2) shaded area at left of x=-5 (close circle) ---> [tex]-\frac{50x}{3}-\frac{11}{6} \geq \frac{163}{2}[/tex]

Part 3) shaded area at left of x=-6 (close circle) ---> [tex]\frac{3x}{2}+105 \leq 96[/tex]

Part 4) shaded area at left of x=7 (close circle) ---> [tex]-\frac{13x}{18}+\frac{5}{9} \geq -\frac{81}{18}[/tex]

see the attached figure

Step-by-step explanation:

Part 1) we have

[tex]-\frac{x}{10}+\frac{1}{5} \geq-\frac{33}{55}[/tex]  

Multiply by -10 both sides

[tex]x-2 \leq 6[/tex]

Adds 2 both sides

[tex]x \leq 6+2[/tex]

[tex]x \leq 8[/tex]

The solution is the interval -----> (-∞,8]

All real numbers less than or equal to 8

In a number line the solution is the shaded area at left of x=8 (close circle)

Part 2) we have

[tex]-\frac{50x}{3}-\frac{11}{6} \geq \frac{163}{2}[/tex]

Multiply by -6 both sides

[tex]100x+11 \leq -489[/tex]

Subtract 11 both sides

[tex]100x \leq -489-11[/tex]

[tex]100x \leq -500[/tex]

Divide by 100 both sides

[tex]x \leq -5[/tex]

The solution is the interval -----> (-∞,-5]

All real numbers less than or equal to -5

In a number line the solution is the shaded area at left of x=-5 (close circle)

Part 3) we have

[tex]\frac{3x}{2}+105 \leq 96[/tex]

Multiply by 2 both sides

[tex]3x+210 \leq 192[/tex]

Subtract 210 both sides

[tex]3x \leq 192-210[/tex]

[tex]3x \leq -18[/tex]

Divide by 3 both sides

[tex]x \leq -18/3[/tex]

[tex]x \leq -6[/tex]

The solution is the interval -----> (-∞,-6]

All real numbers less than or equal to -6

In a number line the solution is the shaded area at left of x=-6 (close circle)

Part 4) we have

[tex]-\frac{13x}{18}+\frac{5}{9} \geq -\frac{81}{18}[/tex]

Multiply by -18 both sides

[tex]13x-10 \leq 81[/tex]

Adds 10 both sides

[tex]13x \leq 91[/tex]

Divide by 13 both sides

[tex]x \leq 91/13[/tex]

[tex]x \leq 7[/tex]

The solution is the interval -----> (-∞,7]

All real numbers less than or equal to 7

In a number line the solution is the shaded area at left of x=7 (close circle)

Answer:

50.27 units²

Step-by-step explanation:²

The standard equation of a circle with center at the origin is x² + y² = r², where r is the radius.  Substituting 4 for x and 0 for y yields 4² + 0² = r², so we see immediately that r = 4 units.

The formula for the area of a circle is A = πr².

Here, with r = 4, the area is A = π(4 units)² = 16π units², or

50.27 units² to the nearest hundredth.

Answer:

it would be D

Step-by-step explanation:

Answer:

The number line D)

Step-by-step explanation:

Carly withdraws $18 from her bank account.

We assume that Carly has $x in her account. She withdraws $18 from her bank account.

So we have to subtract $18 from $x amount.

Which is $x - 18.

So we are subtracting $18 from her account.

It should be represented by an integer -18.

Now we have to identify the which number line represents -18.

It is D)

Answer:

all pairs are congruent

1) Congruent by SAS (Side-Angle-Side)

2) Congruent by SAS (Side-Angle-Side)

3) Congruent by HL  (Hypotenuse-leg)

Answer:

• Each pair of triangles is congruent

~You can tell that each pair is congruent for the following reasons: (1) The legs, or sides, of the triangles in both #1 & #3 are both the same number. (2) The tick marks in #2 are the same, meaning the side lengths are similar.

• Both triangles in each pair are right triangles.

• The triangle pairs in #1 & #3 are rotations, while the triangle pair for #2 is a translation.

I was unaware of any specific answers, so I hope this is helpful!!!

Answer:

Domain: -∞ < x < ∞

Range: f(x) < 0

Step-by-step explanation:

[tex]f(x)=-2(\frac{1}{4})^x[/tex]

We need to sketch the graph and identify domain and range of the function f(x).

The graph is attached in the figure below.

Domain:

The domain of the function is all the values of x that gives the real values for f(x).

So, in our case all values of x gives real values for f(x). So domain is:

-∞ < x < ∞

Range:

The range of the function is the resulting f(x) values when we put all the values of x.

In our case the value of f(x) will always be less than zero because of the negative sign.

Range is:

f(x) < 0

Answer:

6x^2 -4x +8

Step-by-step explanation:

(6x^2 + 5) - (4x - 3)

Distribute the negative sign

(6x^2 + 5) - 4x + 3

Combine like terms

6x^2 -4x +5+3

6x^2 -4x +8

Answer:

[tex]\boxed{\text{3.0 T}}[/tex]

Step-by-step explanation:

[tex]\begin{array}{rcl}M + T + W + Th + F & = & \text{Total}\\2.4 + 4.4 + 1.8 + 2.8 + F & = & 14.4\\11.4 + F & = & 14.4\\F & = & 3.0\\\end{array}\\\text{Friday's sales of chlorine were }\boxed{\textbf{3.0 T}}[/tex]

Answer: There are 3 tons of chlorine sold on Friday.

Step-by-step explanation:

Since we have given that

Number of tone of chlorine on Monday = 2.4

Number of tone of chlorine on Tuesday = 4.4

Number of tone of chlorine on Wednesday = 1.8

Number of tone of chlorine on Thursday = 2.8

Total number of week's sales = 14.4 tons

So, we need to find the number of tone of chlorine on Friday.

According to question we get that

[tex]14.4=2.4+4.4+1.8+2.8+x\\\\14.4=11.4+x\\\\x=14.4-11.4\\\\x=3[/tex]

Hence, there are 3 tons of chlorine sold on Friday.

The notation of the above inequality:

[tex]-3<n<1[/tex]

Can be written as an interval:

[tex]n\in(-3,1)[/tex]

Or group of points on a line that satisfy the linear inequality.

[tex]n\in\mathbb{G}=\{n; -3<n<1\wedge n\in\mathbb{Z}\}[/tex]

Or simply:

[tex]n\in\mathbb{G}=\{-2,-1,0\}[/tex]

Hope this helps.

r3t40

Answer:

Option C is correct.

Step-by-step explanation:

Option C above the dashed line is correct option.

we will graph the inequality

6y - 3x > 9

6y > 9 +3x

y >9/6 +3x/6

y > 3/2 + x/2

The line is dashed because the values are greater and not equal.

The graph is shown in the figure attached.

Answer: Third option

Above the dashed line

Step-by-step explanation:

First we solve the inequality for the variable y.

[tex]6y - 3x > 9[/tex]

[tex]6y - 3x +3x > 9 +3x[/tex]

[tex]6y> 9 +3x[/tex]

[tex]y> \frac{9}{6} +\frac{3}{6}x[/tex]

[tex]y> \frac{3}{2} +\frac{1}{2}x[/tex]

Notice that the line that limits the region is given by the equation

[tex]y= \frac{3}{2} +\frac{1}{2}x[/tex]

The region is formed by all the points that are greater than the points that are on the line [tex]y= \frac{3}{2} +\frac{1}{2}x[/tex].

Therefore the region does not include the points that are on the line, but those that are above the line. Then the line is dashed.

The answer is the third option

ANSWER

(-6,5)

EXPLANATION

The mapping for 90° counterclockwise rotation has mapping

[tex](x,y)\to (-y,x)[/tex]

The coordinates of M are (5, 6)

To find the coordinates of M' we substitute the coordinates of M into the rule.

[tex]M(5, 6)\to M'(-6,5)[/tex]

Hence the ordered pair of M' after point M (5, 6) is rotated 90° counterclockwise is (-6,5)

Final answer:

The situation with a constant rate of change is the length of a bead necklace compared with the number of identical beads, as it represents a linear relationship with a constant slope.

Explanation:

The situation that is most likely to have a constant rate of change is option C, which describes the length of a bead necklace compared with the number of identical beads.

In this scenario, each bead added to the necklace increases its length by a consistent amount. This defines a linear relationship, where the rate of change, also known as the slope in a linear equation, remains constant.

For example, if one bead adds one centimeter to the necklace, then ten beads will add ten centimeters, indicating that the rate of change is one centimeter per bead.

This can be depicted graphically as a straight line when you plot the number of beads against the length of the necklace.

ANSWER

[tex]y = 3x[/tex]

EXPLANATION

The given function is

[tex]f(x) = {x}^{2} + x + 1[/tex]

To find the gradient function, we find the first derivative;

[tex]f'(x) = 2x+ 1[/tex]

To find the gradient at (1,3), we put x=1 into the gradient function to get;

[tex]f'(1) = 2(1)+ 1 = 3[/tex]

The equation of the tangent line is

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

We substitute the point and the slope to get,

[tex]y-3=3(x-1)[/tex]

This simplifies to

[tex]y = 3x - 3 + 3[/tex]

[tex]y = 3x[/tex]

Final answer:

To verify a proportion solution, substitute the answer back into the original equation, check that the units are consistent, and ensure the answer's reasonableness in terms of magnitude, sign, and units.

Explanation:

To verify that a solution to a proportion is correct, one effective method is to perform a check by substituting the solution back into the original proportion equation. Here's how you can ensure the correctness of the solution step by step:

Answer:

D. alternate interior angles

Step-by-step explanation:

The angles that are formed on opposite sides of the transversal and inside the two lines are alternate interior angles

So p and w are alternate interior angles

ANSWER

{x|x>-12 or x<12}

EXPLANATION

The given inequality is

[tex] |x| \: < \: 12[/tex]

This implies that

[tex] - x \: < \: 12 \: or \: x \: < \: 12[/tex]

Divide the first inequality by -1 and reverse the sign to get;

[tex] x \: > \: - 12 \: or \: x \: < \: 12[/tex]

The correct answer is

{x|x>-12 or x<12}

Answer:

It is A.

Step-by-step explanation:

To solve for b, use the 45-45-90 triangle theorem, in which each of the legs is x, so the legs would be 8. The hypotenuse would therefore be 8√2.

So without further solving the answer is A, since it's the only one with 8√2.

However, I will still solve for A and C. Using the 30-60-90 theorem, we have the sides as x, x√3, and 2x. The second longest side is b. Using this, we find a = 4√6 and c to be 4√2

Answer:

see explanation

Step-by-step explanation:

Let u = x² ( choice of variable is flexible ), then

4u² - 21u + 20 = 0 ← expressed as a quadratic

This can now be solved for u and converted back into terms of x

Answer:

refer the explanation

Step-by-step explanation:

this question can be written as

X^2=y

so,x^4=y^2

so it will be 4y^2-21y+20=0

Answer:

D 2<x

Step-by-step explanation:

The circle is open and the arrow goes to the right so its greater then. The circle is on 2. The answer is D 2<x

Answer:

Last graph on the right.

Step-by-step explanation:

Try substituting some values for x and see which graph is valid.

when x = 0, y = f(0) = 3 [tex](2/3)^{0}[/tex] = 3 (1) = 3

When we compare this to the graphs, we immediately see that the first 2 are not correct because in those cases, when x=0, y = 6 (i.e not 3).

Next we try  x = 1

when x = 1, y = f(1) = 3 [tex](2/3)^{1}[/tex] = 3 ([tex]\frac{2}{3}[/tex]) = 2

Comparing the graphs ones again, show that only the last graph has x=1 and y = 2.

Answer:

D

Step-by-step explanation:

Answer:

Option d) 76.44 units^2

Step-by-step explanation:

The approximate area of the circle is equal to the area of one sector, multiplied by 16

The area of one sector is approximate the area of one triangle

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

we have

[tex]b=1.95\ units[/tex]

[tex]h=4.9\ units[/tex]

substitute

[tex]A=\frac{1}{2}(1.95)(4.9)=4.7775\ units^{2}[/tex]

Multiplied the area of one sector by 16

[tex]4.7775*16=76.44\ units^{2}[/tex]

Answer:

76.44 took test

Step-by-step explanation:

Answer:

If the roots of an equation are x = -1 ± i, it means that the factorized form of that equation is: (x + 1 + i)(x+ 1 - i) = 0.

Using the distributive property, we have:

(x + 1 + i)(x+ 1 - i) = x^2 + x - ix + x + 1 - i + ix + i + 1

Combining like-terms and simplifying:

⇒ x^2 + x + x + 1   + 1 = x^2 + 2x + 2 = 0

Therefore, the stament is correct. If the roots of an equation are x = -1 ± i, then the equation is: x^2 + 2x + 2 = 0.

Answer:

equation are x = -1 ± i, then the equation is: x^2 + 2x + 2 = 0.

Step-by-step explanation:

its correct

To solve this you must use a proportion like so...

[tex]\frac{part}{whole} = \frac{part}{whole}[/tex]

We know that percent's are always taken out of the 100. This means that one proportion will have x (the unknown percent) as the part and 100 as the whole

We want to know out of what percent is 48 in the number 80. This means 48 is the part and  80 is the whole.

[tex]\frac{48}{80} =\frac{x}{100}[/tex]

Now you must cross multiply

48*100 = 80*x

4800 = 80x

To isolate x divide 80to both sides

4800/80 = 80x/80

60 = x

This means that 48 is 60% of 80

Hope this helped!

~Just a girl in love with Shawn Mendes

To find the percentage of 48 in relation to 80, dividing 48 by 80 and multiplying the result by 100 yields the answer of 60%, indicating that 48 is 60% of 80.

A percentage is a way of expressing a portion or fraction of a whole as a value out of 100. It represents a proportion or relative amount in relation to the whole.

The term "percentage" is derived from the Latin words "per centum," which means "per hundred." It is denoted by the symbol "%".

For example, if you say "50 percent," it means "50 out of 100" or "half." It is a way of expressing a quantity or value relative to the whole, where the whole is represented as 100%.

Percentages are commonly used to compare proportions, express ratios, indicate changes, and analyze data. They are widely used in various fields such as mathematics, finance, statistics, science, and everyday life to convey relative information and make comparisons easier.

To find what percent 48 is of 80, you can follow these steps:

Divide 48 by 80:

48/80 = 0.6

Multiply the result by 100 to convert it to a percentage:

0.6 * 100 = 60

Therefore, 48 is 60% of 80.

To learn more about percentages click:

brainly.com/question/14822975

#SPJ6

Final answer:

To find the balance after 5 years with an annual interest rate of 6.92% compounded annually, use the formula A = P(1 + r/n)^(nt). The balance after 5 years will be $13,933.16.

Explanation:

To find the balance after 5 years with an annual interest rate of 6.92% compounded annually, you can use the formula A = P(1 + r/n)^(nt), where A is the final amount, P is the principal (initial deposit), r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

In this case, the principal is $10,000, the annual interest rate is 6.92%, and n is 1 (compounded annually), and t is 5 years.

Calculate (1 + r/n)^(nt): (1 + 0.0692/1)^(1 * 5) = 1.0692^5 = 1.39331595

Calculate the final amount using the formula: A = 10,000 * 1.39331595 = $13,933.16

Therefore, the balance after 5 years will be $13,933.16.