Tom would like to take out a secured loan to help pay for a vacation this summer. he has offered his car as collateral. his car is worth $3,500. his bank can offer loans for 80% of collateral value. the vacation he has planned will cost $4,750. approximately how much additional collateral will tom need to offer in order to borrow enough to go on his vacation as planned? a. $1,000.00 b. $1,362.50 c. $2,437.50 d. $2,800.00 please select the best answer from the choices provided a b c d

The missing side of a right triangle x is 24 units.

A right triangle has one of its angles as 90 degrees. The side of a right angle triangle can be found using trigonometric ratios.

The side x can be found using similar triangle ratios,

Hence,

x / 400 = 144 / x

cross multiply

x × x = 400 × 144

x² = 57600

square root both sides

√x² = √57600

x = 240

Therefore, the value of x in the right triangle is 240 units.

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(p p) would produce Tautology.

Tautology:

It is needless repetition of an idea, statement, or word Rhetorical repetition, tautology ('always and for ever'), banal metaphor, and short paragraphs are part of the jargon.— Philip Howard. b : an instance of such repetition The phrase "a beginner who has just started" is a tautology.

A tautology is an expression or phrase that says the same thing twice, just in a different way. For this reason, tautology is usually undesirable, as it can make you sound wordier than you need to be and make you appear foolish.

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The radius of the circular swimming pool is 17.20 feet.

The distance round the  circular swimming pool is the circumference of the circle.

Radius = circumference / (pi x 2)

108 / (3.14 x2)

108 / 6.28 = 17.20 feet

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Answer:

FP is 70 degrees 35 times 2 so PD is 180 half a turn minus 70 = 110 degrees

Step-by-step explanation:

The length of the side of the octagon is 4.142 inches.

Let the length of the congruent sides of the isosceles triangle be x.

The hypotenuse of the triangle is given by:

√x+x = √2x

This is also the length of the sides of the octagon. It is given that the sides of the octagon are equal.

It is also given that the length of the square side is 10 inches.

This means that:

x + √2x + x = 10

2x + √2x = 10

(2 + √2)x = 10

(2 + 1.414)x = 10

3.414x = 10

x = 10/3.414

x = 2.929 inches.

The side of the octagon is given by:

√2 × 2.929 = 4.142 inches

Therefore, we have found that the length of the sides of the octagon is 4.142 inches.

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The density in pounds per cubic meter is 83 pounds per cubic metre.

The density is mass of a unit volume of a material substance.

In other words, density is the ratio between mass and volume or mass per unit .

Therefore, density can be represented mathematically as follows:

density = mass / volume

Hence,

mass = 5 ounces

5 ounces = 0.3125 pounds

1 gallon = 0.00378541 pounds

Therefore,

density = 0.3125 / 0.00378541

density = 82.5538052681

density = 83 pounds per cubic metre.

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Answer:

410 Miles

Step-by-step explanation:

Please refer to the photo attached. (Apologies for the legitimately terrible drawing)

The Shortest Distance between any 2 points is the distance thats connects the 2 points directly.

In this case, we can use Pythgoras's Theorem to find AB which is the shortest distance between A and B.

By Pythagoras's Theorem,

[tex] {c}^{2} = {a}^{2} + {b}^{2} \\ {ab}^{2} = {ac}^{2} + {cb}^{2} \\ {ab}^{2} = {90}^{2} + {400}^{2} \\ab = \sqrt{ {90}^{2} + {400}^{2} } \\ = 410 \: miles[/tex]

Miami gets 6.12 more inches of rainfall more than Tampa.

The annual amount of precipitation that we anticipate is known as normal or typical rainfall (in a given area).

It is calculated and set by estimating the average (mean) of precipitation that has been observed in a region over a long period of time ( at least 30 years). The total amount of daily precipitation in a year is referred to as annual precipitation.

Calculation for the average rainfall-

The average rainfall (in inches) in Miami for 5 months are-

1.61, 2.24, 2.99, 3.15, 5.35, and 9.68,

Thus, the total rainfall in Miami in 5 months,

Total average rainfall = 1.61 +2.24 +2.99 +3.15 +5.35 + 9.68 = 25.02 inches

Similarly,

The average rainfall (in inches) in Tampa for 5 months are-

2.24, 2.8, 3.03, 2.05, 2.09, and 6.69.

Thus, the total rainfall in Tampa in 5 months,

Total average rainfall = 2.24 +2.8 +3.03 + 2.05 + 2.09 + 6.69 = 18.9 inches.

The difference between the total rainfall in Miami and Tampa is

25.02 - 18.9 = 6.12 inches

The total rainfall in Miami is 25.02 inches while the total rainfall in Tampa in the same time period is 18.9 inches.

Therefore, Miami gets 6.12 inches more rainfall during the same time period.

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Considering the definition of an inequality, the inequality that expresses the previous relationship is 12 < x ≤ 12.2

An inequality is the existing inequality between two algebraic expressions, connected through the signs:

An inequality contains one or more unknown values ​​called unknowns, in addition to certain known data.

Solving an inequality consists of finding all the values ​​of the unknown for which the inequality relation holds.

In this case, you know that to fit in an existing frame, the length, x, of a piece of glass must be longer than 12 cm but not longer than 12.2 cm.

It means that the length has to be strictly greater than 12 cm but less than or equal to 12.2 cm. In other words, length of frame must be longer than 12 cm means that x>12, while ength of frame not longer than 12.2 cm means x≤12.2

Finally, the inequality that expresses the previous relationship is

12 < x ≤ 12.2

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Answer:

The triangles are Congruent for the same reason as the answer above

Step-by-step explanation:

Answer: Correct

Step-by-step explanation:

The conclusion is valid. Since [tex]\overline{AB} \parallel \overline{DC}[/tex] and [tex]\overline{AD} \parallel \overline{BC}[/tex], we know that ABCD is a parallelogram because it has two pairs of parallel sides. Also, since [tex]\overline{AB} \cong \overline{BC}[/tex], we know that ABCD is a parallelogram with a pair of consecutive congruent sides, making it a rhombus.

The results of the given task 8.8 ÷ 4 is 2.2.

8.8 ÷ 4

= 2.2

Therefore, 8.8 ÷ 4 = 2.2

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Answer: 18 years

Work Shown:

[tex]f(\text{x}) = 2.56(1.04)^\text{x}\\\\5 = 2.56(1.04)^\text{x}\\\\5/2.56 = (1.04)^\text{x}\\\\1.953125 = (1.04)^\text{x}\\\\\log(1.953125) = \log(1.04^\text{x})\\\\\log(1.953125) = \text{x}*\log(1.04)\\\\\text{x} = \frac{\log(1.953125)}{\log(1.04)}\\\\\text{x} \approx 17.0682937693249\\\\[/tex]

The steps above show f(x) replaced with 5. Then you'd use logarithms to isolate the variable x. The relevant useful log rule is [tex]\log(A^B) = B\log(A)[/tex] so we can pull down the exponent.

From here it seems your teacher wants you to round up to the nearest integer.

If we plugged in x = 17, then f(x) = 4.99 which is one cent too small.

While x = 18 leads to f(x) = 5.19

Therefore, x = 18 has the price reach or exceed $5

Answer:

Step-by-step explanation:

 5x² - 6x - 2 = 0

a = Coefficient of x² = 5

b = coefficient of x = -6

c = constant = -2

Discriminant = D = b² - 4ac

                           = (-6)² - 4 * 5 * (-2)

                           = 36 +  40

                           = 76  > 0

So, the quadratic equation has two distinct real roots.

[tex]\sf \boxed{\bf x = \dfrac{-b \± \sqrt{D}}{2a}}\\\\[/tex]

     [tex]\sf = \dfrac{-[-6] \± \sqrt{76}}{2*5}\\\\= \dfrac{6 \±8.7}{10}\\\\=\dfrac{6+8.7}{10} \ ; \ or \ x =\dfrac{6-8.7}{10}\\\\=\dfrac{14.7}{10} \ ; \ or \ x = \dfrac{-2.7}{10}[/tex]

x = 1.47  or x = -0.27

Answer: x = 1.5 or (-0.3)

b) x² + 3x = 40

x² + 3x - 40= 0

We can solve the quadratic equation using factor method.

Sum = 3

Product = -40

Factors = 8 , (-5)

 When we add, 8 + (-5) = 3 , we get 5and when we multiply 8 *(-5) = -40, we get -(-40).

Rewrite the middle term of the quadratic equation using the factors.

 x² + 8x - 5x - 40 = 0

x(x + 8) - 5(x + 8)= 0

 (x + 8) (x - 5)    = 0

 x + 8 = 0   or x - 5 = 0

     x = -8   or       x = 5

Answer : x = -8 , 5

The quadrilateral is a parallelogram because both pairs of opposite sides are parallel and since the product of the slopes of both pairs of adjacent segments is -1, the quadrilateral is a rectangle

Answer:

The guy above is somewhat right.

Hope this helps!

Step-by-step explanation:

The quadrilateral is a rectangle.

Answer:

B

Step-by-step explanation:

Answer:

x = 20°

f = 40°

Step-by-step explanation:

4x + 5x = 180°

because a straight line is 180°

so 9x = 180°

1x = 180 ÷ 9

1x = 20

all angles in a triangle add together is 180°

so 7x + f = 180°

1x = 20

7x = 20 × 7

7x = 140°

f = 180° - 140 °

f = 40°

Answer:

x = 20 , f = 40

Step-by-step explanation:

4x and 5x are a linear pair and sum to 180° , then

4x + 5x = 180

9x = 180 ( divide both sides by 9 )

x = 20

then

5x = 5 × 20 = 100° and 3x = 3 × 20 = 60°

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

5x is an exterior angle of the triangle , then

f + 3x = 5x , that is

f + 60 = 100 ( subtract 60 from both sides )

f = 40

Answer:

x = -4/3 or x = 3/2

Step-by-step explanation:

Let's solve your equation step-by-step.

6x^2−x−12=0

Step 1: Factor left side of equation.

(3x+4)(2x−3)=0

Step 2: Set factors equal to 0.

3x+4=0 or 2x−3=0

x = -4/3 or x = 3/2

Answer:

x = -4/3 or x = 3/2

Answer:

okay he's saying that each student gets 25 points to start with and then they get five more like 25 / 25 * 5 or like 25 + 5 or 25 - 5 like represent those numbers and like get the number or something like that

Using proportions, it is found that the federal tax rate is of 10%.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The tax rate is the proportion that $17.50 is of $175, hence:

r = 17.50/175 = 0.1 = 10%.

The federal tax rate is of 10%.

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Answer:

<x = 55 degrees

<y = 55 degrees

<z = 70 degrees

Step-by-step explanation:

The 125 degree angle and x are supplementary since they form a straight line, which means that their degrees add up to 180. To find x, the interior angle, we must subtract 125 from 180.

180 - 125 = 55

Angle x is 55 degrees. Since the sides opposite x and y are marked with lines, they are congruent, and since the sides are congruent, the angles must be, too. So, y is also 55 degrees.

Finally, the angles in any triangle add up to 180 degrees. To find z, we must subtract the values of x and y from 180.

180 - 55 - 55 = 70, so z is 70 degrees.

Brainliest, please :)

❄Hi there,

the external angle & the interior angle form a linear pair, which means, if you add these angles together, you'll arrive at 180°.

Using this knowledge let's set up an equation and find x:

[tex]\triangleright \ \sf{125+x=180}[/tex]. We let x be the desired angle.

[tex]\triangleright \ \sf{x=180-125=55}[/tex]

So the interior angle is [tex]\angle\sf{55}\textdegree[/tex].

❄

Number of rooms left excluding a quarter of 140 is: 105 rooms.

A quarter is one-fourth. A quarter of a number is therefore, one-fourth of that number or 1/4 part of the number.

Therefore, number of rooms cleaned = 1/4(140) = 35.

A quarter of the 140 rooms is: 35.

Number of rooms left for cleaning in the afternoon = 140 - 35

Number of rooms left for cleaning in the afternoon = 105 rooms.

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Answer:

23.53

Step-by-step explanation:

OK so we got sin 52°=0.8 and the cos 52°=0.6

but we need tan 52° because we don't want to spend our time on calculating hypothenuse so

[tex] \frac{ \sin(52) }{ \cos(52) } = 1.3 = \tan(52) [/tex]

so

[tex]1.3 = \frac{x}{18.1} = = = > x = 23.53[/tex]

The time restriction faced by ABC Corporation for it to buy back its newly issued shares is 4 weeks

What is share buyback?

Share buyback means that the company would repurchase its own shares in the stock market by paying investors holding the shares, then reduce its number of shares outstanding by the number of shares bought back.

The shares repurchased are known as Treasury stocks, which are held until the company decides to reissue them or cancel them.

The restriction placed on a company before it can repurchase its shares is that the shares must be in issue 4 weeks, in other words, the new issued shares through Initial Public Offer(IPO) must be existence for 4 weeks before being repurchased by the company after having issued an IPO.

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The graphs of the reciprocal functions are related to their corresponding original functions based on the information illustrated below.

It should be noted that the trigonometric functions are the real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

There are six functions of an angle. They are sine (sin), cosine (cos), tangent (tan), cotangent, secant, and cosecant (csc).

It should be noted that all the y-coordinates of a reciprocal function will be the reciprocals of the y-coordinates of the original function. Then, the graph of a reciprocal function has a vertical asymptote at each zero of the original function. For example, y=arcsinx reflects against y=sinx.

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3 roada andy to billy

5 road billy to willies

3×5 =15 it's the answer 15

The percent increase to the nearest tenth is 22.2%

Percent increase is the percent it takes from a value to change from its initial value

Given the following

Initial value = 558,000

Final value = 718,000.

Determine the percent increase

% increase = (718,000-558000)/718,000 * 100

% increase = 160000/718000 * 100

% increase = 22.2%

Hence the percent increase to the nearest tenth is 22.2%

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