Help me with this question….

The equation that can be used to find the length of the remaining side is z² = 14² - 9²

Using the Pythagorean theorem that states that the square of the hypotenuse side is equal or equivalent to the sum of square of the other two sides.

This is represented as;

x² = y² + z²

Given that the parameters are enumerated as;

Now, substitute the values

14² = 9² + z²

collect like terms

z² = 14² - 9²

Hence, the equation is z² = 14² - 9²

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The length of the remaining side can be calculated using 14² = x² + 9² is 10.7 units

An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.

Pythagoras theorem is used to show the relationship between the sides of a right angled triangle. It is given as:

hypotenuse² = adjacent² + opposite²

Let x represent the missing side.

The hypotenuse of a right triangle has a length of 14 units and a side that is 9 units long. Hence:

14² = x² + 9²

x² = 14² - 9²

x² = 115

x = 10.7 units

The length of the remaining side is 10.7 units

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The percentage decrease for the sale of the house is 0.27%.

What are the nearest two places?

The second place to the right of the decimal point, or the hundredth place, is used to round a decimal number to two decimal places. For instance, you can round 2.83620364 to two decimal places as 2.84 and 0.7035 to two decimal places as 0.70.

Given that the initial cost of a home is  369,000.

The cost of a house decreases from 369,000 to 368,000.

The formula of percentage change is

(Final value - initial value)/ initial value × 100

= [(368,000 - 369,000)/369,000] × 100

= (-1000)/369,000 × 100

= 0.27

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Answer: 4x = 64 or -32/-2

Step-by-step explanation:

you could multiply both sides by 2.

4x = 64

4x/4 = 64/4

x = 16

OR

-2x or -32 to both sides

-32 = -2x

divide both sides by -2

x = -32/-2

x = 16

hope this helps

Answer:

To approximate the area between the x-axis and the graph of f(x) = x^2 + 4 over the interval [0, 2], we can use the right rectangle method, where the heights of the rectangles are given by the value of the function at the right endpoint of each subinterval. If we divide the interval [0, 2] into 4 equal subintervals of width 0.5, the right endpoint of each subinterval would be 0.5, 1, 1.5, 2.

The height of the first rectangle would be f(0.5) = 0.5^2 + 4 = 4.25, the height of the second rectangle would be f(1) = 1^2 + 4 = 5, the height of the third rectangle would be f(1.5) = 1.5^2 + 4 = 6.25, and the height of the fourth rectangle would be f(2) = 2^2 + 4 = 8.

The sum of the areas of the rectangles is equal to (0.5) × (4.25 + 5 + 6.25 + 8) = (0.5) × 24 = 12.

So, the approximate area between the x-axis and the graph of f(x) = x^2 + 4 over the interval [0, 2] is 12.

Answer:

1.75

Step-by-step explanation:

1. Algebraic equation: 8x - 9 = 5

2. Add 9 on both sides; 8x=14

3. Divide both sides by 8

4. x=1.75

Answer:

Number = 1/2

Step-by-step explanation:

9 - 8a = 5

9 - 5 = 8a

4 = 8a

4/8 = a

a = 1/2

Check:

9 - 8*1/2 = 5

9 - 4 = 5

Answer:

BL

Step-by-step explanation:

because it goes in both directions infintely

Hi there, here's your answer:

To find the answer to this question, let us review all the options given in the question.

a) BL

BL being two ends of a given line that extends infinitely along its axis, forms a line.

b) GK

GK being two distinct lines do not join and hence do not form an independent line.

c) EB

E being a point on the line BL and B being one end of a larger line form a ray.

d) HI

HI being two points on a line GJ form a line segment, which is finite and has definite end points.

Thus, the answer to this question is (a).

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The average rate of change over the interval (-1, 2) is; 3

The formula for the average rate of change over an interval (a, b) is expressed as;

f'(x) = [f(b) - f(a)]/[b - a]

We want to find the average rate of change over the interval (-1, 2). Thus;

a = -1 and b = 2

Thus;

f(-1) = -4

f(2) = 5

Thus;

f'(x) = (5 - (-4))/(2 - (-1))

f'(x) = 9/3

f'(x) = 3

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Answer:

x=2

y=0

Step-by-step explanation:

2x=4

x=4/2

x=2

again,

y-1 =2y -1

1-1 =2y -y

0=y

The area of the shape given which is a circle is; 38.465 in²

The area of a circle is π multiplied by the square of the radius. The area of a circle(A) when the radius 'r' is given is πr².

Area = πr²

The parameters are;

radius; r = 3¹/₂ inches = ⁷/₂ inches

Thus;

Area = π * (⁷/₂)²

Area = π * 49/4

Area = 3.14 * 49/4

Area = 38.465 in²

That's the area of the circle shape given.

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Answer: range is (-4,0,28)

Step-by-step explanation:

Graph the line using the slope and the y-intercept, or the points.

The correct answers are:

The word "domain" is used with other related meanings in some areas of mathematics. In topology, a domain is a connected open set. In real and complex analysis, a domain is an open connected subset of a real or complex vector space.

The slope-intercept form is y =mx + b where m is the slope and b is the y-intercept:

→ y = mx + b

Find the values of m and b using the form y = mx + b:

m = 4

b = 12

Therefore, Graph the line using the slope and the y-intercept, or the points.

The correct answers are:

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Answer:

Step-by-step explanation:

To put a ratio in its lowest terms, we need to divide both terms of the ratio by their greatest common divisor (GCD). The GCD of 1500 and 1200 is 300, which is the largest number that divides both numbers evenly.

Dividing both terms of the ratio by 300, we get:

1500 / 300 : 1200 / 300 = 5 : 4

So, the ratio 1500:1200 in its lowest terms is 5:4.

The perimeter of the triangle is 23x + 17.

Perimeter is simply the sum of all sides of a polygon.

Given the sides of the triangle;

Side one = 10x + 19

Side two = 12x - 2

Side three = x

To find the perimeter, we add the sides

Perimeter = Side one + Side two + side three

Perimeter = 10x + 19 + 12x - 2 + x

Collect and add like terms

Perimeter = 10x + 12x + x - 2 + 19

Perimeter = 23x - 2 + 19

Perimeter = 23x + 17

Therefore, the perimeter is 23x + 17.

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Answer:

∠1 and ∠3

Step-by-step explanation:

The other pair of vertical angles are ∠2 and ∠4

The number line of the inequality is (d)

from the question, we have the following parameters that can be used in our computation:

3x+2≤4x+5≤9

When this is expanded, we have

3x + 2 ≤ 4x + 5 and 4x + 5 ≤ 9

Evaluate the like terms

So, we have the following representation

-x ≤ 3 and 4x ≤ 4

Divide by the coefficient of x

x ≥ -3 and x ≤ 1

When combined, we have

-3 ≤ x ≤ 1

So x is between -3 and 1, inclusive.

This is represented by the number line (d)

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The reason why AC must be congruent to BD is the hypotenuse - leg theorem and CPCTC

According to the hypotenuse-leg (HL) theorem, a right triangle is congruent if each of its hypotenuse and one leg are congruent with their corresponding hypotenuse and one leg in another right triangle.

The problem have the hypotenuse and a leg of the two triangles stated to be equal. This completes the requirement for the theorem and hence the two triangles are said to be equal

Then applying the CPCTC theorem which says that if two triangles are congruent, every corresponding part of one triangle is congruent to the other side hence, the sides AC = BD

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we get two possible solutions: L = 6 and W = 4. Therefore, the length of the land could be 6 meters.

If the rectangular plot has length L and width W, then we know that 2L + 2W = 20 since 20 meters of wire mesh were used. We also know that L × W = 24 since the area of the plot is 24 square meters. Solving these two equations simultaneously, We have the equations:

2L + 2W = 20

L × W = 24

From the first equation, we can solve for L in terms of W:

2L = 20 - 2W

L = 10 - W

Substituting this into the second equation, we get:

(10 - W) × W = 24

Expanding the brackets, we get: 10W - W² = 24

Rearranging and setting equal to zero, we get: W² - 10W + 24 = 0

We can solve this quadratic equation by factoring: (W - 6) × (W - 4) = 0

So the possible solutions for W are: W = 6 or W = 4

If W = 6, then L = 10 - W = 4, so the rectangular plot has dimensions 4 meters by 6 meters. If W = 4, then L = 10 - W = 6, so the rectangular plot has dimensions 6 meters by 4 meters. Therefore, the length of the land is 6 meters. because the length is assumed as the longer side of a shape or an object.

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Complete Question

To enclose a rectangular plot of 24 m², 20 m of wire mesh were used, what is the length of the land?

The tables of x- and y-values that represents a function include the following: C. table C.

In Mathematics, a function is a mathematical expression which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair in tables or relations.

This ultimately implies that, a function is typically used in mathematics for uniquely mapping an input variable (domain) to an output variable (range) representing a given scenario or situation such as the following:

x  1   3   7   5   2  4

y  6  6   6   6   6  6

In conclusion, we can reasonably infer and logically deduce that only table C represent a function.

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The solutions of the quadratic equation are;

1) x = 1 or -1/2

2) x = 11 or -1

We know that the quadratic formula is one of the ways that we can use to solve for the variables that we have in a quadratic equation. We can be able to obtain x by using the formula;

x = -b ±√b^2 - 4ac/2a

To use the discriminant;

√b^2 - 4ac

√(-5)^2 - (4 * 4 * 10)

√-135

The roots are imaginary

√18^2 - 4(1 * 81)

= 0

The roots are equal

√(-4)^2 - (4 * 4 * -24)

=20

The equation roots are real and different

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Answer:

Step-by-step explanation:

To calculate 8% of 350, we can first calculate 1% of 350 and then multiply it by 8.

1% of 350 is equal to 0.01 times 350 which can be calculated as:

0.01 * 350 = 3.5

Since 1% of 350 is equal to 3.5, 8% of 350 can be calculated as follows:

8 * 3.5 = 28

So, 8% of 350 is equal to 28.

The solution of the radical expression ∛(4+3) will be 1.91.

Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication, and division.

The radical sign, which may be read as either the nth root of x or x radical n, expresses the root of a number. The vinculum, or horizontal line that encircles the number, and the radicand, or number beneath it, are both technical terms.

Given that the expression is ∛(4+3). The solution of the medical expression will be,

E = ∛ ( 4 + 3)

E = ∛(7)

The value of the cube root of the number 7 will be,

E = 1.91

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The 55th term of the arithmetic sequence is 131.

An arithmetic sequence is a sequence of numbers where the differences between every two consecutive terms is the same. The general form an arithmetic sequence is aₙ=a+(n-1)d.

Given that, the nth term of the sequence is aₙ= -1+3(n−1)

Here, the 55th term in the sequence is

a₅₅= -1+3(55-1)

= -1+132

= 131

Therefore, the 55th term is 131.

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Hakeem made 10 shots. The solution has been obtained by using proportions.

What is proportion?

Two numbers are compared. It is known as a proportion in mathematics. The law of proportion states that if two sets of given numbers rise or decrease in the same ratio, they are considered to be directly proportionate to one another.

We are given that Hakeem made 5% of his free throws over the season.

He shot 200 free throws and was able to make 5% from them.

So,

Number of throws he made = Number of free throws x Percentage made

Using this, we get

⇒Number of throws he made = 200 x 5%

⇒Number of throws he made = 10

Hence, Hakeem made 10 shots.

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Answer:

41°

Step-by-step explanation:

We know that,

y°+49°= 90°

y° = 90°-49°

y=41°

So, the value of y is 41°

The equation of the straight line is 2x+5y=340.

The x-intercept point of that line is (170,0).

A straight line has different forms like point-slope form, standard form, slope-intercept form, and others. A specific form is used according to the given data for convenience.

here, we have,

As f(-10)=64 and f(15)=54, two points can be wriiten as (x₁,y₁)=(-10,64) and (x₂,y₂)=(15,54).

Now, use the two-point form of the equation of a line.

(y-y₁)/(x-x₁)=(y₂-y₁)/(x₂-x₁)

(y-64)/(x-(-10))=(54-64)/(15-(-10))

(y-64)/(x-10)=-10/25

25(y-64)=-10(x-10)

5(y-64)=-2(x-10)

5y-320=-2x+20

2x+5y=340

Therefore, the required equation of the line is 2x+5y=340.

To find the x-intercept, substitute y=0 into the equation of the line.

2x+5×0=340

2x=340

x=170

Therefore, the x-intercept point is (170,0).

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Answer: y > 8

Step-by-step explanation:

6 - 5y < -34

-5y < -40

y > 8

[tex]6-5y < -34[/tex]

Simplify:

[tex]-5y+6 < -34[/tex]

Subtract 6 from both sides:

[tex]-5y+6-6 < -34-6[/tex]

[tex]-5y < -40[/tex]

Since we are dividing by a negative number, the sign will reverse.

Divide both sides by -5:

[tex]\dfrac{-5y}{-5} > \dfrac{-40}{-5}[/tex]

[tex]\boxed{y > 8}[/tex]

Answer:

5/2 hours      or      2 hours and 30 minutes

Step-by-step explanation:

The x represents the time it took Mrs. Ritts to mow the front yard. We don't know this time so put it as a variable. We also know that the time to mow her backyard is equal to 2 times the variable and then minus 2.

Equation:   3 = (2x) - 2  

Now we just isolate the x. First, start by adding 2 to both sides.

5 = 2x

Now just divide both sides by 2.

5/2 = x

5/2 as a mixed number would be 2 and 1/2 so that means the time would be 2 and a half hours.

The absolute humidity is 500g/m³, specific humidity = 16.67% and mixing ratio = 20%.

Absolute humidity is a measure of the amount of water vapor in a given volume of air, regardless of the total mass of the air. It is expressed as the mass of water vapor per unit volume of air, typically in units of grams per cubic meter (g/m³).

First, we need to find the mass of dry air in the package. Since the total volume of air is 1m³ and the volume of dry air is 2.5m³, the volume of water vapor is 1 -2.5 = -1.5 m³. This means that the water vapor must have condensed and become liquid water, which we can ignore for the purposes of this problem. So the mass of dry air is:

mass of dry air = density of air * volume of dry air

mass of dry air = 1000g/m³ × 2.5m³

mass of dry air = 2500 g

Now we can use this value, along with the given mass of water vapor, to calculate the three measures of humidity:

       absolute humidity = 500g/ 1m³

       absolute humidity =  500g/m³

       specific humidity = 500g/(2500g + 500g)

       specific humidity = 0.1667 (or 16.67% as a percentage)

       mixing ratio = 500g/2500g

       mixing ratio = 0.2 (or 20% as a percentage)

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Answer:B

Step-by-step explanation:

5x+15=55

5x=40

x=8