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John bought a used truck for $4,500. He made an agreement with the dealer to put $1,500 down and make payments of $350 for the next 10 months. The extra cost paid by taking this deal is equivalent to what actual yearly rate of interest?
A. 36%
B. 63%
C. 33%
D. 3.6%

For any direct variation, the equation is of the form y = kx, where k is the constant of proportionality.

Given the equation: f = 2.5wThe constant of proportionality is 2.5.

This means that the ration of the cups of flour to the cups of water used in the recipe is 2.5

Final answer:

The constant of proportionality in the equation f=2.5w is 2.5, representing the ratio of cups of flour to cups of water for the recipe.

Explanation:

Proportionality Constant:

The constant of proportionality in the equation f=2.5w is 2.5. In this context, the constant of proportionality represents the ratio of cups of flour to cups of water needed for the pizza dough recipe.

Explanation:

The constant 2.5 indicates that for every cup of water (w), you will need 2.5 cups of flour (f) in the pizza dough recipe.

Final answer:

To convert 50 miles per hour to kilometers per hour, multiply by 1.6 to get 80 km/h. In 3 hours, the car will travel 240 kilometers.

Explanation:

The student is asking how to convert a car's speed from miles per hour (mi/h) to kilometers per hour (km/h), and then calculate the distance traveled in kilometers over a period of 3 hours.

Conversion from mi/h to km/h

To convert the car's speed from miles per hour to kilometers per hour, you can use the conversion factor that 1 mile is equal to 1.6 kilometers. Given the car's speed of 50 miles per hour, the calculation would be:

Speed in km/h = Speed in mi/h imes Conversion factor = 50 mi/h imes 1.6 km/mi = 80 km/h.

Distance Traveled in 3 Hours

Now, to compute the distance the car will travel in 3 hours at 80 km/h, use the formula:

Distance = Speed imes Time = 80 km/h imes 3 h = 240 kilometers.

Answer:

first one

Step-by-step explanation:

The number line represents the graph of x ≤ 0 is number line (b)

The inequality expression is given as:

x ≤ 0

The inequality symbol ≤ means that:

Hence, the number line represents the graph of x ≤ 0 is number line (b)

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we have

[tex]x<9[/tex] ------> inequality A

The solution of the inequality A is the interval--------> (-∞,9)

All real numbers less than [tex]9[/tex]

[tex]x\geq14[/tex] -----> inequality B

The solution of the inequality B is the interval--------> [14,∞)

All real numbers greater than or equal to [tex]14[/tex]

The solution Inequality A or Inequality B is equal to

Solution A+Solution B

(-∞,9)U[14,∞)    

The solution of the compound system of inequalities must satisfy inequality A or inequality B

we're going to verify every case

case A) [tex]\$8[/tex]

Substitute the value of x in the inequality A and in the inequality B to verify

Verify inequality A

[tex]8<9[/tex] -------> is true

Therefore

[tex]\$8[/tex] is a possible value for x

You don't need to check for inequality B

case B) [tex]\$9[/tex]

Substitute the value of x in the inequality A and in the inequality B to verify

Verify inequality A

[tex]9<9[/tex] -------> is not true

Verify inequality B

[tex]9\geq14[/tex] ------> is not true

Therefore

[tex]\$9[/tex] is not a possible value for x

case C) [tex]\$11[/tex]

Substitute the value of x in the inequality A and in the inequality B to verify

Verify inequality A

[tex]11<9[/tex] -------> is not true

Verify inequality B

[tex]11\geq14[/tex] ------> is not true

Therefore

[tex]\$11[/tex] is not a possible value for x

case D) [tex]\$13[/tex]

Substitute the value of x in the inequality A and in the inequality B to verify

Verify inequality A

[tex]13<9[/tex] -------> is not true

Verify inequality B

[tex]13\geq14[/tex] ------> is not true

Therefore

[tex]\$13[/tex] is not a possible value for x

case E) [tex]\$14[/tex]

Substitute the value of x in the inequality A and in the inequality B to verify

Verify inequality A

[tex]14<9[/tex] -------> is not true

Verify inequality B

[tex]14\geq14[/tex] ------> is true

Therefore

[tex]\$14[/tex] is a possible value for x

case F) [tex]\$15[/tex]

Substitute the value of x in the inequality A and in the inequality B to verify

Verify inequality A

[tex]15<9[/tex] -------> is not true

Verify inequality B

[tex]15\geq14[/tex] ------> is true

Therefore

[tex]\$15[/tex] is a possible value for x

therefore

the answer is

[tex]\$8[/tex]

[tex]\$14[/tex]

[tex]\$15[/tex]

The required slope of a line will be 5/4 which is perpendicular to line m.

Perpendicular lines are two lines that cross one other and create a 90-degree angle. Two lines are perpendicular if the product of their slopes is -1.

The equation of line m is given in the question below as:

⇒ 4x + 5y = −2

We have to determine the slope of a line that is perpendicular to line m

First, we need to find the slope of line m

To convert to slope-intercept form

⇒ 4x + 5y = -2

⇒ 5y = - 4x - 2

⇒ y = -4/5 x - 2/5

So the slope of this line is -4/5  and the slope of a line perpendicular to it is

⇒ - 1 / (-4/5)

Reciprocal the terms in the numerator,

⇒ 5/4

Therefore, the required slope of a line will be 5/4 which is perpendicular to line m.

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Answer:

Place the point of the compass on point M and draw an arc, using a width for the opening of the compass that is greater than 1/2MN.

Step-by-step explanation:

The site told me that correct answer was B., so it was greater than.

Solution-

1st statement- In a parallelogram, all angles are congruent.

If all the angels are congruent then all angles will be 90° (as summation of all the angles are 360° and 360/4= 90°), then it will be either a rectangle or a square, not a parallelogram.

2nd statement- In a parallelogram, consecutive angles are congruent.

If consecutive angles are congruent, then it will be rectangle or a square, not a parallelogram. In a parallelogram, opposite angles are congruent not consecutive angles.

4th statement- In a parallelogram, all angles are supplementary.

In a parallelogram, all the consecutive angles are supplementary or summation of measurements consecutive angles is 180°, not all the angels are supplementary, because opposite angles can't be supplementary.

3rd statement- In a parallelogram, consecutive angles are supplementary.

This is the reasonable conjecture for a parallelogram, because always the summation of measurement of consecutive angles are 180°.

Answer:

Factor: [tex](x-3)(x-3)[/tex]

Step-by-step explanation:

Given: [tex]x^2-6x+9[/tex]

Factor the given polynomial. It is quadratic equation.

[tex]\Rightarrow x^2-6x+9[/tex]

Using formula: [tex]a^2-2ab+b^2=(a-b)^2[/tex]

So, first we make given polynomial to perfect square.

[tex]\Rightarrow x^2-2\cdot x\cdot 3+3^2[/tex]

[tex]a\rightarrow x[/tex]

[tex]b\rightarrow 3[/tex]

[tex]\Rightarrow (x-3)^2[/tex]

[tex]\Rightarrow (x-3)(x-3)[/tex]

Hence, The factor of given polynomial is [tex]\Rightarrow (x-3)(x-3)[/tex]

Factorizing the polynomial expression x² - 6x + 9 = (x - 3)²

Factorization is the simplification of an expression into a smaller expression using its factors.

To factor the polynomial expression. x² - 6x + 9, we proceed as follows

Since we have the polynomial expression x² - 6x + 9, we multiply x² by 9 to get x² × 9 = 9x².

Now, we desire to find the factors of 9x² so that the sum of those factors equal - 6x

Thus, we have 9x² = -3x × (-3x)

So, -6x = -3x - 3x

Thus, we replace this with -6x, so

x² - 6x + 9 = x² - 3x - 3x + 9

So, factorizing, we have that

x² - 3x - 3x + 9 =  x(x - 3) - 3(x - 3)

= (x - 3)(x - 3)

= (x - 3)²

So, factorizing x² - 18x + 81 = (x - 9)²

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The length of a line with known end point coordinates is given by Pythagoras's theorem

The expression for the length of the diagonal [tex]\overline{PR}[/tex], is [tex]\underline{\sqrt{b^2 + a^2}}[/tex]

The expression for the length of the diagonal  [tex]\overline{QS}[/tex], is [tex]\underline{\sqrt{b^2 + a^2}}[/tex]

Reason:

The given coordinates of the vertices are; P(0, b), Q(a, b), R(a, 0), and S(0, 0)

The lengths of the diagonals are given by the equation for finding the length, l, of a line given the coordinates which is [tex]l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}[/tex]

Where:

(x₁, y₁) = P(0, b), and (x₂, y₂) = R(a, 0), we get;

Where:

(x₁, y₁) = Q(a, b), and (x₂, y₂) = S(0, 0), we get;

Therefore,

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angle a = arctan(5/7) = 35.5

angle b = arctan(7/5) = 54.5

Answer is C

Answer:

(C)35.5° and 54.5°

Step-by-step explanation:

It is given that ABC is a right angled triangle which is right angled at C and AC=7 inches and CB=5 inches.

Now, using the trigonometry, we have

From ΔABC, we have

[tex]\frac{BC}{AC}=tanA[/tex]

[tex]\frac{5}{7}=tanA[/tex]

[tex]0.714=tanA[/tex]

[tex]A=tan^{-1}(0.714)[/tex]

[tex]A=35.5^{\circ}[/tex]

Again, from ΔABC, we have

[tex]\frac{AC}{BC}=tanB[/tex]

[tex]\frac{7}{5}=tanB[/tex]

[tex]1.4=tanB[/tex]

[tex]B=tan^{-1}(1.4)[/tex]

[tex]B=54.5^{\circ}[/tex]

Therefore, the measure of missing angles in triangle ABC are 35.5° and 54.5°respectively.

Thus, option C is correct.

Answer: the answer is 5

Step-by-step explanation:

b