Question 11 of 18
What is the length of the diagonal of the square shown below?
5
45
90°
5
5
S
OA. 5,2
B. 5
OC. √5
OD. 5√5
OE. √10
OF. 25
SUBMIT

The value of the trigonometric function secθ  is 3/4.

Given the value of the trigonometric function sinθ is 4/5

we know that sinθ = Perpendicular (P)/Hypotenuse(h)

Therefore, sinθ = 4/5;

perpendicular (p) = 4 and

hypotenuse (h) = 5

In trigonometry, the secant function is a periodic function. The ratio of the hypotenuse's length to the base's length in a right-angled triangle is known as the secant function, or sec function. It is also written as sec x = 1 / cos x since it is the reciprocal of the cosine function.

secθ = base(b) / perpendicular(p)

Therefore, Base (b) = √(h² ₋ p²)

= √(5² ₋ 4²)

= √(25 ₋ 16)

= √9

= 3

Now, therefore secθ =  base(b) / perpendicular(p)

= 3/4

Hence we get the value of secθ as 3/4.

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Recall the definition of absolute value.

[tex]|x| = \begin{cases} x & \text{if } x \ge 0 \\ -x & \text{if } x < 0 \end{cases}[/tex]

Now,

[tex]x<1 \implies x-9 \le -8 < 0 \implies |x-9| = -(x-9) = 9 - x[/tex]

and

[tex]x<1 \implies x-6 \le -6 < 0 \implies |x-6| = -(x-6) = 6 - x[/tex]

so that

[tex]|x-9| + |x-6| = (9-x) + (6 - x) = \boxed{15 - 2x}[/tex]

The term, coefficient and constant in the expression are 11q, 11 and 2 respectively.

The parts of an algebraic expression are;

Terms:  A term can be defined as a number, a variable, or the product of two or more variables or that of a product of a number and a variable.

The term is 11q

Coefficients: A coefficient is  defined as an integer multiplied by the variable.

The coefficient is 11

Constants: A constant is a number that do not change.

The constant is 2

Thus, the term, coefficient and constant in the expression are 11q, 11 and 2 respectively.

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The compound inequality is  60 < n < 104.

Let 'x' denote the amount of money saved by Julian.

Then x is between $30 and $52.

I.e., x>30 and x<52.

This can be written as a single inequality by combining the both.

i.e., 30 < x < 52

His friend Daniela saved twice as much as Julian.

Let 'n' denotes the amount of money Daniela saved.

Then n = 2x

We need to write the compound inequality for the money saved by Daniela.

As Daniela saved twice as much as Julian, it will be between 2 x 30 = $60 and 2 x 52 = $104

So the compound inequality is 60 < n < 104.

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The two integers which the length of one side is in between are 72 yards and 73 yards

The given parameters are

Area = 5280 square yards

Shape = Square

The area of a shape is calculated using

Area = Length^2

So, we have

Length^2 = 5280 square yards

Take the square root of both sides

Length = 72.66 yards

72.66 yards is between 72 yards and 73 yards

Hence, the two integers which the length of one side is in between are 72 yards and 73 yards

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When the number given of 15,587,252 is rounded off to the nearest 10 thousand, the result would be 15,590,000.

When rounding to the nearest ten thousand, you would look at the thousands number which is the 4th number before the decimal.

If this digit if more than 5, then you round the ten thousandth digit up to the nearest whole number. If the digit is less than 5, then you round down.

The number 15,587,252 has the thousands number as 7 which is more than 5 so the ten thousands number will be round up to:

= 15,590,000

Rest of the question:

Find out 15,587,252 to the nearest 10 thousand.

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Answer:

y=-2

Step-by-step explanation:

5(2y-3)=40y

10y-15=40y

-15=30y

-2 = y

y = -2

Using proportions, the correct statement is given as follows:

Between 2010 and 2013, Mr. Jones' student loan balance decreased by 4750 dollars.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

His balance is only 100 - 71.4 = 28.6% of the initial balance of $6,400, hence it is currently of:

0.286 x 6400 = $1830.

The decrease was of:

6400 - 1830 = $4750.

Hence the correct statement is:

Between 2010 and 2013, Mr. Jones' student loan balance decreased by 4750 dollars.

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Answer:

  translation 3 units up: g(x) = f(x)+3

Step-by-step explanation:

You are given graphs of f(x) and g(x) and want to know the transformation that gives g(x) from f(x).

The sorts of transformations of graphs that we study are translation, scaling (horizontally or vertically), and reflection about an axis.

Here, both graphs have the same shape, but one is in a different place than the other. The applicable transformation is one of translation.

The vertex of f(x) is at (0, -1). The vertex of g(x) is at (0, 2). We note the x-value has not changed, but the y-value has had 3 added to it. (-1 +3 = 2)

  g(x) = f(x) +3 . . . . . . the function f is translated 3 units upward.

The amount he is expected to have due to interest in the bank after a year is; $2603.16

We are given the equation;

w²/25 + 45w + 155

where;

w is number of weeks

Now, this equation above represents the function of the amount he is expected to have due to interest in the bank. Thus;

After 1 year, the number of weeks is 52 weeks. Thus, we now have;

A(52) = 52²/25 + 45(52) + 155

A(52) = $2603.16

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Answer:

65°

Step-by-step explanation:

  Exterior angle of a triangle equals the sum of opposite interior (remote) angles.

 3x - 10 = x + 15 + 25

 3x - 10 = x + 40

Add 10 to both sides,

       3x = x + 40 + 10

       3x = x +50

Subtract 'x' from both sides,

     3x- x = 50

         2x = 50

Divide both sides by 2

           x = 50÷ 2

           x = 25

Exterior angle = 3x -10

                        = 3*25 - 10

                        = 75 - 10

                        = 65°

The amount invested at 4% is $4,333.33

The amount invested at 7% is $8,666.67

What represents the amount invested at 4%?

Let assume that x is the amount invested in the bank certificate of deposit (CD account)  which earns 4%, in essence, the interest earned at 4% is the amount of money invested multiplied by 4%

interest at 4%=4%*x=0.04x

amount invested at 7%=13000-x

interest at 7%=7%*(13000-x)

interest at 7%=910-0.07x

total interest=0.04x+910-0.07x

total interest=910-0.03x

total interest earned=780

780=910-0.03x

0.03x=910-780

0.03x=130

x=130/0.03

x=amount invested  at 4%=$4,333.33

amount invested at 7%=$13,000-$4,333.33

amount invested at 7%=$8,666.67

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Answer:

5x - 8y = -2

Step-by-step explanation:

m = 5/8, x = 0, y = 1/4

so y = mx + b

1/4 = 5/8(0) + b

b = 1/4

so y = 5/8x + 1/4

8y = 5x + 2

5x - 8y = -2

The number of outfits she can buy is 3.

The The first step is to determine the total cost of all the items already bought.

Total cost = cost of new bicycle + (cost of one reflector x number of reflectors) + cost of the gloves

$488.20 + (2 x $11.17) + 19.05

$488.20 + 19.05 + $22.34 = $529.59

Now, determine the amount that is left to buy the outfits :

$660 - $529.59 = $130.41

Here are inequality signs and what they mean:

> means greater than

< means less than

≥ means greater than or equal to

≤ less than or equal to

The inequality sign that would be used is ≤

(cost of one outfit x number of outfits)  ≤ amount left

$37.26x ≤ $130.41

x  ≤ 130.41 / 37.26

x  ≤ 3.5

x = 3

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Answer:

Step-by-step explanation:

its A. If julie ran 2 minutes more, then your simply adding 2 minutes to whatever teri got to get 28 (what julie got).

If a right triangular prism's height is 1 inch. The produced solid has the following surface area: = 2,930.05 in².

A polyhedron with six vertices, nine edges, and five faces is a right triangular prism. Regular prisms have all of their triangles faces equilateral. The prism's rectangular faces will be congruent in this situation.

A triangular prism's total surface area is the sum of the areas of its three lateral faces (rectangles) as well as two bases (triangles). For something like the surface area of any prism, the most generic formula is:

Given:

Hight = 1 inches

Base of the prism = 10 inches.

The Hight if the base = 82 inches.

Surface area = (Perimeter of the base × Length of the prism) + (2 × Base Area)

Surface area = 5(10× 10) + (0.5÷ 10 × 1) + 3(10× 82)

Surface area = 5(100) +0.05+ 3(810)

Surface area = 500 +0.05 + 2430

Surface area = 2,930.05 in²

The produced solid has a surface area of approximately = 2,930.05 in².

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$525

Step-by-step explanation:

Ben bought the house for $78,850 so 78,850 divided by 0.15 equals 525. So the answer is $525.

Circles are related to Pythagorean theorem in the sense that the equations are alike and the sides conforms to:

The distance between the two cities is 116.62 units (ignoring curvature)

If the curvature is not ignored then we sort for the angle subtended

The Pythagorean theorem relates the square of hypotenuse, square of the opposite, and the square of the adjacent as follows

hypotenuse^2 = opposite^2 + adjacent^2       equation 1

Representing a circle in a coordinate axis will give it values in coordinate form. Assuming the coordinate of the center is (x1, y1) and a point in the circumference is (x2, y2). The radius of the circle, r is given as

r^2 = (x2 - x1)^2 + (y2 - y1)^2                              equation 2

comparing equation 1 and 2 shows that

radius ≅ hypotenuse,  (x2 - x1)^2 ≅ opposite, and (y2 - y1)^2 ≅ adjacent

say A = (45, -123)

say B = (53.65, -6.7)

Let the distance between the two cities be d

d^2 = (53.65 - 45)^2 + (-6.7 - (-123) )^2

d^2 = 8.65^2 + 116.3^2

d = √13600.5125

d = 116.62 units (ignoring the earth curvature)

if the curvature is not ignored then we look for the angle subtends

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If the overall percentage of the defective panels from the two plants is 5% then plant B produced 4000 panels in total.

This question can be solved by formulating the problem into the form of a linear equation having two variables. Linear equation in two variables can be represented in the form of ax+by+c=0 where a, b and c are real numbers and x, y are variables or the coefficients, and a, b ≠ 0.

Let the production from plant A be x, and according to the question x=10000.

Also, let the production from plant B be y.

Now, as 3% of products are found defective from plant A and 10% of products are found defective from plant B and overall defective products is 5%.

Thus, 0.03x+0.1y=0.05(x+y)

As x=10000 then

0.03×10000+0.1y=0.05(10000+y)

300+0.1y=500+0.05y

0.05y=200

=>y=4000

Thus, the total number of panels produced by plant B is equal to 4000.

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Answer: 6,249,715

Step-by-step explanation:

The number sequence is built like this:

Millions , hundred thousands + ten thousands + thousands , hundred + tens

+ ones

The millions place is the greatest value here, and the ones place is the least value in every situation involving whole numbers.

Value for  the 3 straight  lines are 180,28 , 152.

What is a straight line, exactly?

Simply put, a straight line is a line devoid of bends. A straight line is one that does not curve and reaches to infinity on both sides.

CBE = 28 + 90 = so the angle is 118 degrees

ABF = you already got the answer written down, 28

CBA = this is not 180 like you wrote, CBA = ABD - CBD

Straight lines = 180, so ABD = 180

You already found out that CBD = 28

so CBA = 180 - 28 so the answer CBA = 152

So,  answers for the 3 lines are 180,28 , 152

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System of liner equation [tex]x+3y-z=2[/tex],[tex]x+y-z=0[/tex] and [tex]3x+2y-3z=-1[/tex] has no solution.

What do you mean by system of linear equation?

A set of two linear equations with two variables is a system of linear equations.

Given:

[tex]x+3y-z=2[/tex]           ---1

[tex]x+y-z=0[/tex]             ---2

[tex]3x+2y-3z=-1[/tex]     ---3

Rearranging the equation 2

[tex]z=x+y[/tex]   ---4

Putting equation 4 in equation 1

⇒ [tex]x+3y-(x+y)=2[/tex]

⇒ [tex]x+3y-x-y=2[/tex]

⇒ [tex]2y=2[/tex]

⇒ [tex]y=1[/tex]

Putting equation 4 in equation 3

⇒ [tex]3x+2y-3(x+y)=-1[/tex]

⇒ [tex]3x+2y-3x-3y=-1[/tex]

⇒ [tex]-1y=-1[/tex]

⇒ [tex]y=1[/tex]

Putting value of y above

⇒ [tex]1=1[/tex]

Therefore, system of liner equation has no solution.

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So solutions of the linear quadratic systems are (-5,-3) and (1,3)

Given,

y = x²+5x -3 . . . . . . . . . .. ..1

y-x= 2 . . . . . .. . . . . . . . . . . 2\

From 1 and 2

y=x+2

substitute y=x+2 in 1

x+2= x²+5x -3

x²+5x -x-3-2 = 0

x²+4x -5=0

x²+5x-x -5=0

x(x+5) -1(x+5) = 0

(x+5)(x-1)=0

x= -5 and x=1

at x=-5

y=x+2=-5+2=-3

at x=1

y=x+2=1+2=3

So solutions of the linear quadratic systems are (-5,-3) and (1,3)

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It's 47. I used a calculator.

h: The domain

-5 ≤ x ≤ 5