Alex is saving money because she would like to purchase the new video gaming system that everyone has been talking about. After two weeks of saving, she had $47. After 24 weeks of saving, she had $430. Approximately how many dollars per week did Alex save on average between weeks 2 and 24? (2 points)

$15.96 per week
$17.41 per week
$17.91 per week
$19.88 per week

Answer:

200 dollars

Step-by-step explanation:

Let's say p equals the cost price of the article. Since the man made 25% profit, that means he got 100% of what he originally paid plus another 25% of what he originally paid. In other words, he sold the article for 125% of the original price. Converting that to a decimal we get:

250=p*1.25

Some simple division gets us a cost price of 200 dollars.

The resultant speed of the plane is 100 mi/hr along the northeast direction.

Speed can be calculated as the ratio of distance traveled to the time taken

First, we need to find our coordinate axis, we will define the x-axis as the east and the y-axis as the north.

We are given that the plane travels at 150 mi/hr at 100° east of north, notice that if we measure from the positive x-axis, this is equivalent to an angle of -10°.

Then the x-component of the velocity ;

150mi/hr x cos(-10°) = 147.7 mi/hr

The y-component of the velocity;

150mi/hr x sin(-10°) = -26 mi/hr.

So, the vector is:

V = 147.7 mi/hr, -26 mi/hr

Now we know that the wind blowing at 50mi/hr at southwest, exactly southwest would be at an angle of 225°,

Thus, the components of the vector are:

x-component: 50mi/hr x cos(225°) = -35.4 mi/hr

y-component: 50mi/hr x sin(225°) = -35.4 mi/hr.

So, the vector is:

W = < -35.4 mi/hr, -35.4 mi/hr>

The sum of the vectors gives the total velocity of the plane in the wind is;

V + W = < 147.7 mi/hr -35.4 mi/hr , -26 mi/hr -35.4 mi/hr >

V + W = <112.3 mi/hr, -61.4 mi/hr>

The direction of a vector is;

θ = Atan(y/x)

Then, in this case the direction of the plane is:

θ = Atan(-61.4 mi/hr/112.3 mi/hr) = -28.7°

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Answer:

Step-by-step explanation:

Depending on whether or not the g(x) is x^2 or 2x, I have both ways.

If g(x) is x^2 - 9...

--> (3x^2 + 2) - (x^2 - 9) = 2x^2 + 11

If g(x) is 2x...

--> (3x^2 + 2) - (2x - 9) = 3x^2 - 2x + 11

Hope this helps!

1. Height of the equilateral triangle is: √3 units

2. Area of the equilateral triangle = √3 units²

3. Area = √3/4 x², when each side is x.

A triangle that has all its three sides equal in length, is referred to as an equilateral triangle.

1. Given the each side measures 2 units, and h is the height, applying the Pythagorean theorem, we would have:

h = √(2² - 1²)

h = √(4 - 1)

h = √3

2. Area of the equilateral triangle = 1/2bh = 1/2(2)(√3)

Area of the equilateral triangle = √3 units²

3. If x is the side length of the equilateral triangle, we would have:

height (h) = √[x² - (x/2)²] = √[x² - x²/4] = √(3x²/4) = √3/2x

Area = 1/2bh = 1/2(x)(√3/2x) = √3/4 x²

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Mrs. Potter’s class was more consistent because their standard deviation of 3 points was lower.

A statistical dispersion is also referred to as degree of dispersion and it can be defined as a measure of the extent to which a numerical value (data) is likely to vary about a mean or an average value.

In Mathematics, there are four measures of dispersion for a data set and these include the following:

In this scenario, we can infer and logically conclude that Mrs. Potter’s class was more consistent than Mr. Jones class because their standard deviation of 3 points was lower.

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Answer:

No solution.

Step-by-step explanation:

[tex]\textbf{Given that,}\\\\~~~~~~~~3x = 3(x-1)\\\\\\\implies \dfrac{3x}3 = \dfrac{3(x-1)}{3}~~~~~~~~~~~~~~~~~;\textbf{Dividing both sides by 3}\\\\\\\implies x = x-1\\\\\\\implies x-x = x-1-x~~~~~~~~~~~~~;\textbf{Subtracting}~ x ~ \textbf{from both sides} \\\\\\\implies 0 = -1\\\\\\\textbf{Which is not true, so there are no solutions.}[/tex]

71 and the blank angle are a linear pair/supplementary angles, meaning that their sum is 180 degrees.

71 + y = 180

y = 109

The sum of the interior angles of a triangle is 180 degrees. Therefore, all of the angles inside of the triangle will add up to 180.

109 + 46 + x = 180

x = 25

Answer: x = 25 degrees

Hope this helps!

Answer:

f(x)=19

Step-by-step explanation:

2(3)²+1

2(9)+1

19

The value of function at x = 3 is,

⇒ f (3) = 19

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

The function is,

⇒ f (x) = 2x² + 1

Now, Substitute x = 3 in above function,

⇒ f (x) = 2x² + 1

⇒ f (3) = 2 × 3² + 1

⇒ f (3) = 19

Thus, The value of function at x = 3 is,

⇒ f (3) = 19

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Answer:

i might just be mind numb right now but you don't use pie on rectangles for area

Area = 6510

Step-by-step explanation:

A = L x W

A = 93 x 70

A = 6510

Answer:

3

Step-by-step explanation:

blue, white, and red colors

[tex] \frac{2}{3} (x - 4) = 2x \\ \frac{2}{3} x - \frac{8}{3} = 2x \\ \frac{2}{3} x - 2x = \frac{8}{3} \\ \frac{2}{3} x - \frac{6}{3} x = \frac{8}{3} \\ \frac{ - 4}{3} x = \frac{8}{3} \\ - 12x = 24 \\ x = \frac{24}{ - 12} \\ x = - 2[/tex]

Answer:

[tex]x = 49degrees[/tex]

Step-by-step explanation:

[tex]131 + x = 180( \: < \: on \: str \: line = 180) \\ x = 180 - 131 \\ x = 49[/tex]

The required value of x for the given figure is 49°.

A straight line can be defined as a locus of points satisfying the equation ax + by + c = 0 for two coordinates x and y.

The sum of the angles on a straight line is always 180°.

In the given figure the angles 131° and x° are on the same straight line.

Since, the sum of the angles on a straight line is 180°.

The following equation can be written for the given figure,

x + 131 = 180

=> x = 180 - 131

       = 49

Hence, the value of x for the given figure is 49°.

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Let's see

[tex]\\ \rm\Rrightarrow (x^{22}-3x^5+x^{-2}-7)5x^4[/tex]

Use distributive law

[tex]\\ \rm\Rrightarrow 5x^{22+4}-15x^{5+4}+5x^{-2+4}-35x^4[/tex]

[tex]\\ \rm\Rrightarrow 5x^{26}-15x^9+5x^2-35x^4[/tex]

Answer:

[tex]5x^{26}-15x^{9}+5x^{2}-35x^4[/tex]

Step-by-explanation:

Given expression:

[tex](x^{22}-3x^5 + x^{-2} - 7) (5x^4)[/tex]

Use the Distributive Property Law  (b ± c)a = ab ± ac
to remove the parentheses:

[tex]\implies 5x^4 \cdot x^{22}-5x^4 \cdot 3x^5+5x^4 \cdot x^{-2}-5x^4 \cdot 7[/tex]

Simplify by multiplying the coefficients of each term:

[tex]\implies 5x^4 \cdot x^{22}-15x^4 \cdot x^5+5x^4 \cdot x^{-2}-35x^4[/tex]

[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}[/tex]:

[tex]\implies 5x^{4+22}-15x^{4+5}+5x^{4-2}-35x^4[/tex]

[tex]\implies 5x^{26}-15x^{9}+5x^{2}-35x^4[/tex]

Answer: 5/6, 3/4, 4/12

Step-by-step explanation:

Convert them all into a common denominator, 12.

5/6=10/12, 3/4=9/12, and 4/12 stays the same. 10>9, and 9>4

Question 13

[tex]{12x+2}=\frac{18+34}{2}\\\\12x+2=26\\\\12x=24\\\\x=\boxed{2}[/tex]

Question 14

Base angles of an isosceles trapezoid are congruent, so:

[tex]73x+1=74\\73x=73\\x=\boxed{1}[/tex]

Answer:

one of them is two trapezoids

Step-by-step explanation:

Answer:

Given:

To Find:

Solution:

According to the question:

(1) The product of 7 & x

➝ 7x

(2) The sum of 9 and 3 and 2

➝ 9 + 3 + 2

➝ 14

From (1) and (2) , we get:

➝ 7x = 14

➝ x = 14 ÷ 7

➝ x = 2

Let's check whether our answer is correct or not:

• To check our answerer, let's putting the value of x :

♣ 7(2) = 14

♣ 14 = 14 ✅

Thus, our answer is correct....The value of x is 2.

The probability that the selected element is a member of A n B is 2/9

The elements of the set are given as:

E = {1,2,3,4,5,6,7,8,9}

A = {1,3,4,8,9}

B = {2,4,9}

Using the above parameters, we have:

A only = {1, 3, 8}

B only = {2}

A and B = {4, 9}

None = {5,6,7}

The above dataset is the represented using the attached Venn diagram

In (a), we have:

A and B = {4, 9}

E = {1,2,3,4,5,6,7,8,9}

The probability is then calculated as:

P(A n B) = n(A n B)/n(E)

This gives

P(A n B) = 2/9

Hence, the probability is 2/9

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then for 5 tablespoons you use 12.5 ounces of milk

Answer:

positive

Step-by-step explanation:

(-a) (-a) (-a) (-a) = a

(-a)(-a) = a

a (-a) = -a

-a (-a) = a --> positive sign

If you multiply four negative numbers, what is the sign of the product?

You can test this with numbers, the easiest with -1:

(-1)(-1)(-1)(-1) = (1)(-1)(-1) = (-1)(-1) =  1

General:

(-a)(-b)(-c)(-d) = abcd

The sign of the product of four negative numbers is positive.

If you multiply five negative numbers, what is the sign of the product?

Testing with -1:

(-1)(-1)(-1)(-1)(-1) = (1)(-1)(-1)(-1) = (-1)(-1)(-1) = (1)(-1) -1

General:

(-a)(-b)(-c)(-d)(-e) = -abcde

The sign of the product of five negative numbers is negative.

General rule: The product of an even number of negative numbers is positive. The product of an odd number of negative numbers is negative.

The growth of the plant is 25 inches last year.

Explanation:

Suppose the growth of the plant last year was y.

From the given situation, the normal growth was 10  inches more than twice the amount of last year.

So the equation will be

= 10 + 2y = 60

= 2y = 50

= y= 25 inches.

Therefore , the growth of the plant was 25 inches last year.

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Answer:

a) 150

b) 2650

Step-by-step explanation:

6% of 2500 is 150

150 + 2500 = 2650

Answer:

x = 68

Explanation:

⇒ log₈(x - 4) = 2

apply log rules: logₐN = x then N = aˣ

⇒ (x - 4) = 8²

simplify

⇒ x - 4 = 64

add 4 on both sides

⇒ x = 64 + 4

add the integers

⇒ x = 68

Answer:

x = 68

Step-by-step explanation:

Given equation:

[tex] \rm log_{8}(x - 4) = 2[/tex]

To Find:

Value of x

Solution:

Rewrite the equation in exponential form which is equivalent to b^y = x.

[tex] \implies {8}^{2} = x - 4[/tex]

Now find the value of x.

[tex] \implies \:64 = x - 4[/tex]

Transpose 4 from RHS to LHS, make sure to change its sign from (-) to (+) .

[tex] \implies \: 64 + 4 = x[/tex]

Overturn the equation

[tex] \implies \: x = 68[/tex]

Thus, value of x is 68.

The correct statement is that it is done by the converse of the triangle parts relationship theorem. The correct answer is option D.

The complete answer is given below and the figure is attached with the answer.

Consider the diagram and proof by contradiction.

Given: △ABC with ∠B ≅ ∠C

Prove: AB ≅ AC

It is given that ∠B ≅ ∠C. Assume AB and AC are not congruent. If AB > AC, then m∠C > m∠B by ________. If AC > AB, then m∠B > m∠C for the same reason. However, using the given statement and the definition of congruency, we know that m∠B = m∠C. Therefore, AB = AC and AB ≅ AC.

What is the missing reason in the proof?

the converse of the triangle parts relationship theorem

substitution

definition of congruency

the converse of the isosceles triangle theorem

Triangle is a polygon that has three sides and three angles. The sum of the angle of the triangle is 180 degrees.

Isosceles triangle two sides of the triangle are equal and their opposite angles too.

Given

△ABC with ∠B ≅ ∠C

Prove that

AB ≅ AC

How to give a conclusion?

From the definition of the Isosceles triangle, it is proved that if ∠B ≅ ∠C Then AB ≅ AC. We know that if the length o the side increases then the opposite angle decreases. It is done by the converse of the triangle parts relationship theorem.

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Check the picture below, so the parabola looks more or less like so, with a "p" distance of 3 and the vertex at the origin, keeping in mind the vertex is half-way between the focus point and the directrix.

[tex]\textit{horizontal parabola vertex form with focus point distance} \\\\ 4p(x- h)=(y- k)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h+p,k)}\qquad \stackrel{directrix}{x=h-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{"p"~is~negative}{op ens~\supset}\qquad \stackrel{"p"~is~positive}{op ens~\subset} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{cases} h=0\\ k=0\\ p=3 \end{cases}\implies 4(3)(x-0)~~ = ~~(y-0)^2\implies 12x=y^2\implies x=\cfrac{1}{12}y^2[/tex]