135
55
Triangle ABC is a right triangle. The length of one leg is 117 inches, and the
length of the hypotenuse is 125 inches. What is the length of the other leg?

A- 8 inches
B- 44 inches
C- 121 inches
D- 171 inches

The solutions for the quadratic equation:

x^2 - 8x = -3

Are:

Here we want to solve the quadratic equation:

x^2 - 8x = -3

First we can move all the terms to the left side so we get:

x^2 - 8x + 3 = 0

Using the quadratic formula (or Bhaskara's formula) we can get the solutions for x as:

\(x = \frac{8 \pm \sqrt{(-8)^2 - 4*¨1*3} }{2*1} \\\\x = \frac{8 \pm 7.2 }{2}\)

Then the two solutions for the quadratic equation are:

x = (8 + 7.2)/2 = 7.6

x = (8 - 7.2)/2 =0.4

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The dimensions of the rectangle with a perimeter of 52 ft and given parameters is; Width = 4 ft and Length = 22ft

The formula for the perimeter of a rectangle is;

Perimeter = 2(Length + Width)

We are given;

Perimeter = 52 ft

Length is 2ft more than 5 times the width . Thus;

Length = 2 + 5(W)

Thus, perimeter formula expression is now;

2[2 + 5W + W] = 52

2(2 + 6W) = 52

2 +6W = 26

6W = 24

W = 4 ft

L = 2 + 5(4)

L = 22ft

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Answer:

55

Step-by-step explanation:

WRONG ANSWER I WANT THE RIGHT ANSWER

Solution:

Given:

Using the diagonal property of a rectangle,

The two diagonals bisect each other and divide the rectangle into two equal parts.

Hence, the diagonal divides the area of the rectangle into two equal parts. Each part is a triangle.

Thus,

Therefore, the area of the shaded triangle is 22 square centimeters.

The missing variables on item 2 are given as follows:

The three trigonometric ratios are the sine, the cosine and the tangent of an angle, and they are obtained according to the formulas presented as follows:

For the angle of 60º, we have that:

Hence the length o is given as follows:

tan(60º) = o/12.

\(\sqrt{3} = \frac{o}{12}\)

\(o = 12\sqrt{3}\)

Applying the Pythagorean Theorem, the length i is given as follows:

i² = 12² + \((12\sqrt{3})^2\)

i² = 576

i² = 24²

i = 24.

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Answer:

o = 12√3

i = 24

Step-by-step explanation:

From observation of the given right triangle, we can see that two of its interior angles measure 60° and 90°. As the interior angles of a triangle sum to 180°, this means that the remaining interior angle must be 30°, since 30° + 60° + 90° = 180°. Therefore, the triangle is a special 30-60-90 triangle.

The side lengths in a 30-60-90 triangle have a special relationship, which can be represented by the ratio formula a : a√3 : 2a, where "a" represents a scaling factor that can be any positive real number.

In triangle #2, the shortest leg is 12 units.

As "a" is the shortest leg, the scale factor "a" is 12.

The side labelled "o" is the longest leg opposite the 60° angle. Therefore:

\(o = a\sqrt{3}=12\sqrt{3}\)

The side labelled "i" is the hypotenuse of the triangle. Therefore:

\(i= 2a = 2 \cdot 12=24\)

Therefore:

Answer:

Step-by-step explanation:

Step 1. The point estimate is the difference between the the mean amount of mail-order purchases and the mean amount of internet purchases. It becomes

74.9 - 87.3 = - 12.4

Step 2. The formula for determining margin of error is expressed aa

Margin of error = z√(s1²/n1 + s2²/n2)

Where

z = z score

s1 = sample standard deviation for data 1

s2 = sample standard deviation for data 2

n1 = number of samples in group 1

n2 = number of samples in group 2

For a 95% confidence interval, the z score is 1.96

From the information given,

s1 = 21.75

n1 = 18

s2 = 19.75

n2 = 9

z√(s1²/n1 + s2²/n2) = 1.96√(21.75²/18 + 19.75²/9) = 1.96 × 8.343

= 16.35

Step 3. Confidence interval = (x1 - x2) ± z√(s²/n1 + s2²/n2)

95% Confidence interval = - 12.4 ± 16.35

a = 1, b = 2 is a counterexample, and with that, we conclude that the conjecture is false.

Here we have the conjecture:

"For any two integers a and b, (a - b)^2 = (a^2 - b^2)"

Notice that if we find a single pair of integers a and b such that the equality in the conjecture is false, then we have found a counterexample and that is enough to conclude that the conjecture is false.

If we define=

a = 1

b = 2

Replacing that in the equation of the conjecture we get:

(1 - 2)^2 = (1^2 - 2^2)

(-1)^2 = 1 - 4

1 = -3

This is false, then a = 1, b = 2 is a counterexample, and with that we conclude that the conjecture is false.

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Two factors that need to be controlled to keep this test fair are the temperature and the sample volume.

The control variables are those variables that should be kept constant in order to avoid interfering with the free flow of the experiment.

For the provided test, it is important that the temperature of the environment where the test sample is kept is controlled throughout the duration of the experiment so that some results are not affected by this. Also, the sample volume should be controlled for fair outcomes.

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Based on the information, EFH and GHF does not have to be congruent.

Congruents angles are presented in the figure below. Congruent angles are angles that have the same measure or size. When two angles are congruent, they look exactly the same, even if they are in different orientations.

The symbol used to represent congruence is an equals sign with a tilde above it, like this: ≅. For example, if angle A and angle B have the same measure, we can write it as:

angle A ≅ angle B

Congruent angles play an important role in geometry because they allow us to compare and analyze different shapes and figures. In particular, when two angles are congruent, we can use this fact to make conclusions about other angles and sides of a shape.

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In circle O shown, points E, F, G, and H lie on the circle asshown and chords FH and GE intersect at J. Based on thisinformation alone, which two angles below do not have tobe congruent?m(1) angle FJE and angle HJG(2) angle EFH and angle HGE(3) angle EFH and angle GHF(4) angle FEG and angle FHG

Answer:

\(x + 1 + \frac{4}{x - 1} \)

Answer:

9

Step-by-step explanation:

The reciprocal of 1/9 is 9/1 which is just 9.

Answer: Product: 0.1111111... Reciprocal: 9

Step-by-step explanation:

One can be able to  test to see if a diagram made using digital tools is a construction or just a drawing based on estimation by:

Digital Construction is known to be a term that connote  the act of using digital technologies to be able to make construction to be more better and  with higher quality.

Note that  a lot of the new technologies have been seen to have proven themselves and gives  a lot of opportunities for the construction,

In the use of the digital tools, one can Construct a line or a line segment and then uses the move tool to drag some points around, and then watch to see what happens.

Therefore,  One can be able to  test to see if a diagram made using digital tools is a construction or just a drawing based on estimation by:

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Answer:

0.275 thats the answer no cap

Step-by-step explanation:

The decimal form of the given fraction is 0.275 lb.

Given that, a bowl weighs 11/40 lb.

We need to express the given fraction in decimals.

When a number is present in a fraction form i.e., p/q, we use the long division method to convert it into a decimal form. In such a case we divide the numerator by the denominator. Let us understand the steps involved in fraction to decimal conversion by the long division method with the help of an example.

Now, the fraction 11/40 can be written in decimal as 11/40=0.275 lb

Therefore, the decimal form of the given fraction is 0.275 lb.

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Answer:

488

Step-by-step explanation:

You divide 28453 by 58.3053278689 and get 488.

Answer:    x=67

Step-by-step explanation:

All of the angles add up to 180 for a triangle

38 + 75 + x = 180               >combine like terms (the numbers)

113 + x = 180                       >subtract 113 from both sides

x=67

Answer:

Step-by-step explanation:

We know that,

\( \sf \: By \: Using \: Angle \: sum \: property \: of \: triangle\)

\( \large \sf \: → x +38° + 75° = 180°\)

\( \large \sf \: → x + 113 = 180°\)

\( \large \sf→ x = 180°- 113°\)

\( \boxed{\large \bf→ x = 67° }\)

GIVEN

Two isosceles triangles with two equal pairs of sides are drawn.

SOLUTION

The two triangles have similar sides. The remaining pair of sides are 27 and 26 units respectively.

Note that the angle that subtends the longer side should be greater than the angle that subtends the smaller side. Therefore:

Solving the inequality:

The smaller angle must be greater than 0. This means that:

Solving the inequality:

Combining both inequalities:

Answer:

18% off

Step-by-step explanation:

i just took the test

Answer:

x = 155

Step-by-step explanation:

\(\sqrt{x-11} +7=19\)

\(\sqrt{x-11} =12\)

\((\sqrt{x-11} )^2=12^2\)

\(x-11=144\)

x = 155

Answer:

x=5

Step-by-step explanation:

Answer:

x = 5

Step-by-step explanation:

Answer: 3 ≤ 47

Step-by-step explanation:

The inequality given is 3 ≤ 47.

To determine the solutions to this inequality, we need to find the values of x that satisfy the inequality.

Looking at the options provided:

x = 24: This is not a solution because 24 is less than 47.

x = 51: This is a solution because 51 is greater than or equal to 47.

x = 6: This is not a solution because 6 is less than 47.

x = 99: This is a solution because 99 is greater than or equal to 47.

Therefore, the solutions to the inequality 3 ≤ 47 are x = 51 and x = 99.

Answer: 16/1 8 of 2 is 8 times 2 so you get 16 and as a fraction it’s 16/1

Step-by-step explanation:

Answer:

5/8

Step-by-step explanation:

Only C is the polynomial function among the given equations.

In mathematics, a polynomial is an equation that solely uses the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are also known as indeterminates in this context.

A function that only uses non-negative integer powers or only positive integer exponents of a variable in an equation is referred to as a polynomial function.

Thus among the given equations, there is only one equation whose variable's exponent is not negative.

Therefore, Among the provided equations, only C is a polynomial function.

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Answer:

339.4cm³

Step-by-step explanation:

V

=

π

r

2

h

3

22/7×6²×9/3= 339.42

The volume of the ark is about 1.44 million cubic feet.

What is unit conversion mean?

A unit conversion expresses the same property as a different unit of measurement. For instance, time can be expressed in minutes instead of hours, while distance can be converted from miles to kilometers, or feet, or any other measure of length.

First, we need to convert the measurements from cubits to inches.

We know that one cubit is equal to six palms and that one palm is equal to 2.5 inches. So, we can convert the measurements of the ark by multiplying the number of cubits by the number of inches per cubit:

Length of ark = 300 cubits x 6 palms/cubit x 2.5 inches/palm = 4500 inches

Width of ark = 50 cubits x 6 palms/cubit x 2.5 inches/palm = 750 inches

Height of ark = 30 cubits x 6 palms/cubit x 2.5 inches/palm = 450 inches

Next, we can find the volume of the ark by multiplying these dimensions together:

Volume of ark = 4500 inches x 750 inches x 450 inches = 1.42 x 10^9 cubic inches

Finally, we can convert cubic inches to cubic feet by dividing by the conversion factor of 1 cubic foot = 12 x 12 x 12 cubic inches.

1.42 x 10^9 cubic inches / (12x12x12 cubic inches/cubic foot) = 1.44 x 10^6 cubic feet

Hence, the volume of the ark is about 1.44 million cubic feet.

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Answer:

75

Step-by-step explanation:

f(4) means to use 4 in place of x.

f(x) = 3(5)^(x-2)

fill in 4 for

f(4) = 3(5)^(4-2)

do the 4-2 subtraction first

f(4) = 3(5)^2

do the 5 to the 2nd power next.

f(4) = 3(25)

last, multiply.

f(4) = 75

This is just following the typical order of operations.

Answer:

X= 7

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

7+8=15

5×3=15

4/5×15=12

if that makes sense