In the figure shown, what is the value of x?

Answer:

Grace will be 32 years old in 2027.

Answer: she will be 32 years old.

Step-by-step explanation:

if a²+b²>c², the triangle is acute, if a²+b2²=c², the triangle is a right triangle,  and if a²+b²<c², the triangle is obtuse.

where a and b are the lengths of the two shorter sides of the triangle and c is the length of the longest side.

A right-angled triangle is a triangle with one of the angles at 90 degrees. A 90-degree angle is called a right angle, and hence the triangle with a right angle is called a right triangle.

An acute triangle has three angles that each measure less than 90°. In an acute-angled triangle, all three internal angles of the triangle are acute, that is, they measure less than 90°.

An obtuse triangle is a triangle with one angle that is greater than 90° degrees, it is not possible for a triangle to have more than one obtuse angle.

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Solving for x and y intercepts when given an equation:

X-intercept:

[tex]2x-5(0)=20[/tex]

[tex]2x=20[/tex]

[tex]x=10[/tex]

x-intercept occurs at (10,0)

Y-intercept

[tex]2(0)-5y=20[/tex]

[tex]-5y=20[/tex]

[tex]y=-4[/tex]

y-intercept occurs at (0,-4)

a) The equation that models Alice's total cost of filling up her car tank using regular unleaded gas and premium gas is 4.65r + 4.95p = 874.80.

b) Based on the above equation, if Alice purchases 87 gallons of regular unleaded gas, it means that she also purchases 95 gallons of premium gas.

An equation is a mathematical statement equating two or more mathematical expressions using the equation sign (=).

The cost per gallon of regular unleaded gas = $4.65

The cost of premium gas per gallon = $4.95

The total cost for gas = $874.80

Let gallons of regular unleaded gas = r

Let gallons of premium gas = p

4.65r + 4.95p = 874.8

If r = 87, the value of p is:

4.65(87) + 4.95p = 874.8

404.55 + 4.95p = 874.8

4.95p = 470.25

p = 95 gallons

Thus, during Alice's first leg from the East Coast to the West Coast, she purchases 87 gallons of unleaded and 95 gallons of premium gas for her car.

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Considering  the given triangle, the information given helped to apply similar triangle principle to determine v to be 3.9

This is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent

Hence assuming the corresponding angles of the triangle are congruent then the side should be in proportions

Examining the figure shows that pair of equivalent sides are

TS and TR , SU and QR

The solution is worked out using sides WX and XV, WY and YU

TS / TR = SU / QR

TS / TR = 1/2 since it is a mid segment

1 / 2 = (19v - 38) / (-5v + 96)

-5v + 96 = 2 * (19v - 38)

-5v + 96 = 38v - 72

96 + 72  = 38v + 5v

168 = 43v

v = 3.9

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Answer: Tom can come up with 13 different wacky personalities for Mr Potato Head.

Step-by-step explanation:

Tom can come up with 3 different hairstyles for Mr Potato Head, 2 sets of eyebrows, 1 pair of googly eyes, 2 sets of ears, and 2 sets of lips. He also has 2 pairs of shoes to choose from. If Mr Potato Head can be bald, Tom can also choose to not include a hairstyle.

In total, Tom can come up with 3+2+1+2+2+2+1=13 different combinations of features for Mr Potato Head. Since each combination represents a different personality, Tom can come up with 13 different wacky personalities for Mr Potato Head.

The answer is that space contains at least four points that are not coplanar or not all coplanar.

Axioms are statements or propositions taken to be established, accepted, or self-evident truths. In other words, a statement or mathematical statement that serves as a starting point from which other statements are logically derived. This is formulated in Hypothesis 1 as follows:

A plane contains at least three points that are not all on a straight line. Space contains at least four points that are not all in one plane. "

Simply put,

"There is at least one plane for every three points. There is exactly one plane for every three non-collinear points."

"There are at least 3 points in the plane that are not co-linear. There are at least 4 points in space that are not co-planar."

Not collinear:

Not all lined up.

Not coplanar:

do not occupy the same area or rectilinear plane

An axiom of Euclidean geometry states that there are at least four points in space that are not in the same plane.

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The if __name__ == '__main__' syntax allows a programmer to specify that certain code should only be executed when the script is run directly, rather than when it is imported as a module into another script.

This can be useful for running code that you only want to execute when you're running the script for testing or development, rather than when you're using it as a library in another program. It also allows to use the same code in multiple script without running the main code.

When a Python script is run, the interpreter assigns the name __main__ to the script's global namespace. Therefore, when the script is run directly, __name__ will be set to __main__. When the script is imported as a module into another script, __name__ will be set to the name of the module, rather than __main__.

So, when a programmer uses the if __name__ == '__main__' syntax, they are essentially checking whether the script is being run directly or imported as a module. If the script is being run directly, the code within the if block will be executed. If the script is being imported as a module, the code within the if block will not be executed.

This allows the programmer to separate code that should only be run when the script is executed directly from code that is intended to be used as a library when the script is imported as a module. It also allows to use the same code in multiple script without running the main code.

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The linear expression that is not equivalent to the other three is D) (-5x-1)+(6x + 7).

A linear expression is an algebraic expression which is composed of constants, variables, and coefficients that are related by only addition and multiplication operations. It usually takes the form of ax + b, where 'a' and 'b' are constants and 'x' is a variable. Linear expressions can be used to describe various mathematical and physical phenomena, such as the slope of a line or the volume of a cylinder.

This linear expression is not equivalent to the other three because it does not have the same coefficient for the x terms and the constant terms. The other three expressions all have the same coefficients for the x terms and the constant terms, making them equivalent.

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The trigonometric ratio as a fraction for sinC is  , and the decimal is 0.80.

The trigonometric functions are actual functions that connect the right-angled triangle's angle to the ratios of its two side lengths.

The widely used trigonometric functions are sine, cosine and tangent. The trigonometric functions also operate the inverse of the functions.

For the given triangle the trigonometric values are as follows:

For angle A the opposite side is CB, the adjacent side is AB and the hypotenuse is AC.

For angle C the opposite side is AB, the adjacent side is CB and the hypotenuse is AC.

[tex]sinC = \frac{\text{Opposite side }}{Hypotenuse} = \frac{4}{5} =0.80\\ \\ cosC = \frac{\text{Adjacent side }}{Hypotenuse} =\frac{3}{5} = 0.60\\\\tanA =\frac{\text{Opposite side }}{Adjacent side} = \frac{3}{4} = 0.75\\\\tanC= \frac{\text{Opposite side }}{Adjacent side} =\frac{4}{3} = 1.33\\\\cosA = \frac{\text{Adjacent side }}{Hypotenuse} =\frac{4}{5} = 0.80\\\\sinA= \frac{\text{Opposite side }}{Hypotenuse}=\frac{3}{5} =0.60[/tex]

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Answer: 0.28 Km^2

Step-by-step explanation:

A= L x W

=0.4x0.7

=0.28

Part (a)

Let one of the angles be [tex]\theta[/tex]. After solving for all of the other angles using the triangle sum theorem, we see that [tex]\triangle CDA \sim \triangle BDC \sim \triangle BCA[/tex].

Part (b)

[tex]\frac{BD}{BC}=\frac{BC}{CA}, \frac{DA}{DC}=\frac{DC}{DB}[/tex]

The perimeter of the parallelogram with the given vertices is 33.

The complete length of a shape's boundary is referred to as the perimeter in geometry. A shape's perimeter is calculated by adding the lengths of all of its sides and edges.

Given that:

A = (3, 6)

B = (-5, 6)

C= (6 , -1)

D = (-2, -1)

The length of side is given by the formula:

[tex]L = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]

Substitute the values in the formula to find the sides of the parallelogram.

[tex]AB= \sqrt{(-5 -3)^2 + (6-6)^2} = 8\\ \\BC = \sqrt{(6+5)^2 + (-1 - 6)^2} = 13\\\\CD= \sqrt{(-2+6)^2 + (-1 +1)^2} = 4\\\\\DA= \sqrt{(3+2)^2 + (6+1)^2} = 8[/tex]

The perimeter is obtained by adding all the sides of the given two-dimensional shape.

P = 8+13+4+8

P = 33

Hence the perimeter of the parallelogram is 33.

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Answer:

x = -4 or x = -1

Step-by-step explanation:

Let's check

x = -4

(-4 + 4)(-4 + 1) = 0

(0)(-3) = 0

0 = 0

Let's check x = -1

(-1 + 4)(-1 + 1) = 0

(-3)(0) = 0

0 = 0

So, x = -4 or x = -1 is correct answer!

Answer:

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

Step-by-step explanation:

The common factor of both -3p^7 and 3p^3 is 3p^3

Divide -3p^7 by 3p^3 and get -p^4

Divide 3p^3 by 3p^3 and get 1

So the factorisation is 3p^3 (-p^4 + 1)

Answer:

19°

Step-by-step explanation:

In this problem, we have complementary angles, which add up to 90° as indicated by the right angle symbol. So, getting x° is as simple as 90°-71°=19°.

Marla is 30 years old.

Let marla age be x and Darla age be y

Given : Marla is four years less than twice as old as Darla

What is equation ?

In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

Marla is four years less than twice as old as Darla can be represented as : 2y - x = 4

sum of their ages is 47 can be represented as : x + y = 47

Solving both the equation using addition we got ,

3y = 51

y = 17

Substituting the value of y in x + y =47 , we get

x + 17 = 47

x = 47 -17

x = 30

Hence , Marla is 30 years old.

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The confidence interval is (22.68,29.52).

In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time. Confidence ranges that include 95% or 99% of anticipated observations are frequently used by analysts. Therefore, it can be concluded that there is a 95% probability that the true value falls within that range if a point estimate of 10.00 is produced using a statistical model with a 95% confidence interval of 9.50 - 10.50.

n = 10

x = 26.1

s = 4.2

Two-sided confidence interval :

CI = [tex](x-\frac{z*s}{\sqrt{n}},x+\frac{z*s}{\sqrt{n} } )[/tex]

    = [tex](26.1-\frac{2.576*4.2}{\sqrt{10}},26.1+\frac{2.576*4.2}{\sqrt{10}} )[/tex]

    = (26.1−3.42,26.1+3.42)

    = (22.68,29.52)

Hence, the confidence interval is (22.68,29.52).

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Answer:

26$

Step-by-step explanation:

¼×48=12

so 12 was spent on calculator

12+14= 26

Answer: William Wordsworth, a prominent figure in the Romantic movement, believed that nature had an immense value and could have a profound impact on the human spirit. In his poem "I Wandered Lonely as a Cloud," he wrote, "Nature never did betray the heart that loved her," which is a claim that nature is a constant source of comfort and inspiration. In this poem he praises nature and its ability to be a source of beauty and joy.

One could argue that Wordsworth's claim is true based on the evidence that nature can have a positive impact on mental and physical health. Studies have shown that spending time in nature can reduce stress, improve mood, and boost overall well-being. Additionally, nature can be a source of inspiration for many artists and poets, including Wordsworth himself, who drew inspiration from the natural world for his poetry.

On the other hand, one could argue that Wordsworth's claim is idealistic and may not apply to everyone or every situation. Some people may not find nature as comforting or inspiring, especially those who live in urban areas with limited access to natural spaces. Additionally, there are negative impacts of human activities on nature, such as pollution and deforestation, which can make it harder for some people to find value in nature.

Overall, while Wordsworth's claim that "Nature never did betray the heart that loved her" is a strong statement, and it holds true for many people, but it's a personal perspective that may not apply to everyone. Each individual has their own relationship with nature and it's not always a constant source of comfort, however, it's a treasure that we should take care of, respect and appreciate in order to achieve a better quality of life.

Step-by-step explanation:

Answer: solving by forming simple algebra equation

Step-by-step explanation:

8x (x is the cost of 1 volleyball)
6y (y is the cost of 1 basketball)

We know that cost of 8 volleyballs is = cost of 6 basketballs
i.e. 8x = 6y

& total money spent to buy 8 volleyballs and 6 basketballs is $960
so we can write;
8x + 6y = 960
= (6y) + 6y = 960
= 12y = 960
= y or cost of 1 basketball is (960/12) = $80

& if we want to know the value of x (cost of 1 volleyball)
8x = 6y
= 8x = 6(80)
& x = 6(80/8)
      = 6 (10) = 60

so the cost of basketball is $80 & 1 volleyball is $60

Hope it helps :)

p.s. that the equation I formed were made as if I was making an assumption & the conditions were kept uniform from the beginning, this is very applicable in day to day scenario; for e.g. when you go out with you friends to eat and have to split the bill - this assumption and division is called algebra - so value this education!

Answer:

120 cm.

Step-by-step explanation:

The perimeter of a rectangle is found by adding up the length of all four sides. In this case, the length is 36 cm and the breadth is 24 cm. Therefore, the perimeter of the rectangular table-top is

2 (length + breadth) = 2 (36 + 24) = 2 × 60 = 120 cm.

A nation cannot have a comparative advantage in the production of every good. Alpha can produce either 18 oranges or 9 apples an hour, while Beta can produce either 16 oranges or 4 apples an hour. The opportunity cost of producing 1 orange for Alpha and Beta, respectively, are: 0.5 apples; 0.25 apples.

A percentage is a component, piece, or amount that is compared to a total. It might be 0 or 1, or any number between 0 and 1. It can be stated numerically or as a percentage. In official statistics, one example would be the proportion of the Canadian population residing in a certain province.

Here,

A country cannot have a competitive advantage in producing every good. Alpha can generate 18 oranges or 9 apples per hour, whilst Beta can produce 16 oranges or 4 apples per hour. The opportunity cost of producing one orange for Alpha and Beta is 0.5 apples and 0.25 apples, respectively.

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Answer:

a 97- (55+80) +250

b Melanie has $212 left in her bank account.

Step-by-step explanation:

55 + 80 = 135

97 - 135 = -38

-38 +250 = 212

The combined volume of the podium and the platform is 64 cubic feet.

This sort of figure offers several choices. We really only need to consider how to divide the front face into appropriate rectangles, since the depth of the figure is 2 feet everywhere.

The volume is the area of the front face times that depth.

1) A 2 ft × 4 ft upright atop a 12 ft × 2 ft horizontal base. The frontal area is

(2 ft)(4 ft) +(12 ft)(2 ft) = 8 ft² +24 ft² = 32 ft

so, the total volume is:

V = frontal area × depth

V= (32 ft²)(2 ft)

V=64 ft³

2) A vertical post of 2 ft × 6 ft at the left side with a horizontal protrusion of 10 ft × 2 ft from its bottom.

The frontal area calculated this way is:

(2 ft)(6 ft) +(10 ft)(2 ft) = 12 ft² +20 ft² = 32 ft²

Again, the total volume is (32 ft²)(2 ft) = 64 ft³.

3) A 6 ft × 12 ft rectangle with a 4 ft × 10 ft cutout from the upper right corner. The area calculated this way is

(6 ft)(12 ft) -(4 ft)(10 ft) = 72 ft² -40 ft² = 32 ft² . . . . . same as above

Again, the total volume is (32 ft²)(2 ft) = 64 ft³.

V=64 ft³.

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Answer:x=20

Step-by-step explanation:5x+9 and 3x+11 must add to 180, so you can set these equal to 180 and get  8x+20 = 180, this can be simplified to 8x=160 or x = 20

Answer:

x = 20°

Step-by-step explanation:

Given angles,

→ 5x + 9

→ 3x + 11

Forming the equation,

→ (5x + 9) + (3x + 11) = 180°

{Because, sum of two angles in a straight line leads to 180°}

Now the value of x will be,

→ (5x + 9) + (3x + 11) = 180°

→ 5x + 3x + 9 + 11 = 180°

→ 8x + 20 = 180°

→ 8x = 180° - 20

→ x = 160/8

→ [ x = 20° ]

Hence, the value of x is 20°.

As you can see, we turned the fraction 10100 into its decimal representation, 0.1, in a single simple computation.

Any number of equal portions, or parts of a whole, are described by fractions. Fractions in standard English indicate the number of pieces of a specific size. 8, 3/4 of .Part of an entire is a fraction. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. When a fraction is true, its numerator is smaller than its denominator.

With 100 as the denominator, decimal fractions in the hundredth place are written. We shall discover how each square is split into 100 equal sections in this section. A tenth is a portion that is just partially shaded. The fraction is expressed as 1/100 in decimal form.

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The number of seconds, it takes for the balloon to drop below 310 feet is 1.25 seconds

To find out how many seconds it will take for the balloon to drop to below 310 feet, we need to use the information provided and some basic algebra.

Given the starting altitude of the balloon, we know:

h(0) = 1200 feet

The rate of change of the altitude, or the speed at which the altitude is changing, is given as:

dh/dt = −712 feet/second

This tells us that the altitude of the balloon is decreasing at a rate of 712 feet per second. To find out how long it will take for the altitude to drop to 310 feet or less, we can set up the following equation:

h(t) = h(0) + dh/dt * t

We know that h(t) must be less than or equal to 310 feet, so we can substitute this value in for h(t) and solve for t:

310 = 1200 + (−712) * t

This equation can be solved for t by isolating t on one side and then dividing both sides by −712:

t = (1200 - 310) / −712

t = (890) / (−712)

t = 1.25 seconds.

So it will take 1.25 seconds for the balloon to drop below 310 feet.

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