Consider the Piece-Wise graph described by the following equation:
Determine the coordinates of the point on the graph where x=3.

(3, 1)

(3, 3)

(3, 5)

(3, 13)

Sarah sold 66 posters

Solution:

Let "a" be the number of shirts sold

Let "b" be the number of posters sold

Sarah sold a total of 178 t shirts and posters at a festival

Therefore,

number of shirts sold + number of posters sold = 178

a + b = 178 ----------- eqn 1

She sold 46 more tshirts than poster

Number of shirts sold = 46 + number of posters sold

a = 46 + b --------- eqn 2

Substitute eqn 2 in eqn 1

46 + b + b = 178

2b = 178 - 46

2b = 132

b = 66

Thus she sold 66 posters

Final answer:

Sarah sold 66 posters at the festival.

Explanation:

Let's represent the number of posters Sarah sold as P. Since she sold 46 more t-shirts than posters, we can represent the number of t-shirts as P + 46. The total number of t-shirts and posters sold is 178, so we can write the equation: P + (P + 46) = 178.

Combining like terms, we get: 2P + 46 = 178. Subtracting 46 from both sides, we have: 2P = 132. Dividing both sides by 2, we find: P = 66.

Therefore, Sarah sold 66 posters at the festival.

Answer:

Center = (0, -4)

Radius = [tex]\sqrt{7}[/tex] units

Step-by-step explanation:

We are given;

The equation of a circle;

[tex]x^2+y^2+4y=3[/tex]

We are required to determine the radius and the center of the circle;

To do this we are going to use completing square method;

[tex]x^2+y^2+4y=3[/tex]

Since we don't have the x term then;

[tex]x^2+ox+y^2+4y=3[/tex]

We add the square of half the coefficients of x and y on both sides of the equation;

That is;

[tex]x^2+0x+(0^2)+y^2+4y + (2^2)=3+0+(2^2)[/tex]

We get;

[tex]x^2+0x+(0^2)+y^2+4y + (2^2)=7[/tex]

Taking the squares;

[tex](x+0)^2+(y+4)^2=7[/tex]

But we know when the equation of a circle is written in the form of;

[tex](x-a)^2+(y-b)^2=r^2[/tex], where (a,b) is the center and r is the radius of the circle.

Thus, in this case;

[tex](x+0)^2+(y+4)^2=7[/tex]

Center = (0, -4)

Radius = [tex]\sqrt{7}[/tex] units

Answer:

H = 21.7

Step-by-step explanation:

A = 1/2 x b x h

26 = 1/2 x2.4xh

26= 1.2h

divide both sides by 1.2

26/1.2 = 1.2/1.2 h

h = 21.7

9514 1404 393

Answer:

  5

Step-by-step explanation:

The evaluation can be easier if terms are collected first.

  3xy+7x^2−3x^2y+3y^2x−2x^2−2xy+4x^2y−2y^2x

  = x^2y(-3+4) +xy^2(3-2) +x^2(7-2) +xy(3-2)

  = x^2y +xy^2 +5x^2 +xy

  = x(xy +y^2 +5x +y)

Filling in the numbers, we have ...

  = (1)(1(-2) +(-2)^2 +5(1) +(-2))

  = -2 +4 +5 -2

  = 5

The value of the polynomial is 5.

Answer:

11.55

Step-by-step explanation:

An equilateral triangle is one which all it sides are equal.

10cm altitude means the height is 10cm.

Using Pythagoras theorem,

x² = 10² + (x/2)²

Assume that the side of the triangle is xcm

x² - x²/4 = 100

3x²/4 = 100

x = √(400/3)

x = 11.55cm

Answer: 7x2−2x+11

Step-by-step explanation:

Distribute the Negative Sign:

7x2+6+−1(2x−5)

7x2+6+−1(2x)+(−1)(−5)

7x2+6+−2x+5

Combine Like Terms:

7x2+6+−2x+5

(7x2)+(−2x)+(6+5)

7x2+−2x+11

Answer:

90°

Step-by-step explanation:

All circles are equal to 360°. Since the pie chart is a circle, if you added all of the central angles for all three sections, it would total to 360°.

Since the circle is not divided into 360 parts for each degree, but 100 parts for each percent %.

You can solve using an equivalent. Write each fraction in the form "Lemonade" over "total". The left side is percentage, the right side is degrees.

Let x be the central angle for lemonade

[tex]\frac{25}{100}=\frac{x}{360}[/tex]

Solve for the central angle of lemonade by isolating 'x'. To isolate x, move  360 over to the other side. When moving numbers in an equivalent, you do the opposite operation to both sides. Since 'x' divides by 360, multiply 360 on both sides.

[tex]\frac{25}{100}=\frac{x}{360}[/tex]

[tex]360*\frac{25}{100}=360*\frac{x}{360}[/tex] 360 cancels out on the right

[tex]\frac{360*25}{100}=x[/tex]         Combined multiplication in numerator

[tex]\frac{9000}{100}=x[/tex]        When dividing, 0s cancel out

[tex]\frac{90}{1}=x[/tex]       Simplify fraction over 1

[tex]x = 90[/tex]      Answer

Therefore the central angle in the Lemonade section is 90°.

Without the markup percentage or discount percentage, it is impossible to calculate the actual cost price the store paid for the trumpet. One needs this additional information to provide a precise answer.

The question "if the price tag on a trumpet says $104, how much did the store pay for it" cannot be answered with the information provided. To calculate how much the store paid for the trumpet, we need additional details such as the markup percentage or the discount percentage. Retail stores typically apply a markup to the cost of the goods they purchase from suppliers to cover their operating expenses and make a profit.

Let's assume the markup percentage is known. For example, if a store generally marks up items by 50%, and the selling price of the trumpet is $104, we can calculate the store's cost using the formula: Cost Price = Selling Price / (1 + Markup Percentage). So the cost would be $104 / (1 + 0.50), which is $69.33.

Without the markup or discount information, it is impossible to determine the exact cost price that the store paid for the trumpet.

Answer:no

Step-by-step explanation:

Because it can not get any smaller

Answer:

70 miles

Step-by-step explanation:

30 minn+30 min=1 hour/60 min

30 min=35 miles

add the minutes together then add the miles together witch will give you

1 hour/60 min=70 miles

Answer:

70 miles

1 hour= 60 minutes

[tex]60 \div 30 = 2[/tex]

Take 35 and multiply it by your first equations sum

[tex]35 \times 2 = [/tex]

=70

Answer:12

Step-by-step explanation:

Answer:

X=-1

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

The similarity statement: FGHI ~ BCDE

Similarity ratio: 5:1

Step-by-step explanation:

The similarity statement is quite obvious, as there are only two rectangles shown, and the other one is "BCDE".

The similarity ratio is 5:1 because everything in the 1st (FGHI) rectangle is multiplied 5 times the values in the 2nd (BCDE) rectangle.

Answer:

1,800

Step-by-step explanation:

Answer:

Step-by-step explanation:

The polynomial f(x)=x^4+2x^3−27x−54 has x+2 as a factor. The complete factorization of f(x) after polynomial division and analysis is (x + 2)(x^2 - 3x + 9)(x + 3).

To show that x+2 is a factor of f(x)=x^4+2x^3−27x−54, we need to use the Factor theorem which states that if a polynomial f(x) has a factor of the form x - k, then f(k) = 0.

So, if x + 2 is a factor of the function, then f(-2) should equal 0. Let's apply this to our function:

f(-2) = (-2)^4 + 2(-2)^3 - 27(-2) -54 = 16 -16+54 -54 = 0. So x+2 is indeed a factor.

To factor f(x) completely, we will perform polynomial division of f(x) by the factor (x+2) which will give us g(x) = x^3 - 27. This can be further factored to x^3 - 3^3 which is a difference of cubes. Consequently, the complete factorization of f(x) would be:

f(x) = (x + 2)(x^2 - 3x + 9)(x + 3).

https://brainly.com/question/34290719

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Answer:

Step-by-step explanation:

-(-3)-[-(-4)]-2+7 = 3 - [4] - 2 + 7 = 3 - 4 - 2 + 7 = (3+7) - (4+2) = 10 - 6 = 4

Answer:

Therefore the overall vertical change is a drop of 300 feet.

Step-by-step explanation:

i) The overall vertical change is given by = -282 feet + 143 feet - 161 feet = -300 feet.

ii) Therefore the overall vertical change is a drop of 300 feet. A drop is represented as negative and a climb is represented as positive.

Answer:

Total cost of the meal is $ 27.32.

Step-by-step explanation:

Given:

Cost of the meal = $25.30

Tax levied on it = 8%

We have to find the total cost.

Total cost of the meal = Summation of cost of the meal and levied tax.

So,

We have to calculate the tax.

⇒ [tex]8\%\ of\ \$25.30[/tex]

⇒ [tex]\frac{8}{100}\times \$25.30[/tex]

⇒ [tex]0.08\times \$25.30[/tex]

⇒ [tex]\$2.024[/tex]

Tax imposed = [tex]\$2.024[/tex]

Now,

Total cost of the meal =Tax + Meal cost

⇒ [tex]\$(2.024+25.30)[/tex]

⇒ [tex]\$27.324[/tex]

Total cost of the meal is $ 27.32.

Answer:

A) -2/3

Step-by-step explanation:

We are given the equation;

5 - 2m - 3m² = 0

We are required to get the sum of the roots of the equation;

Rearranging the equation;

3m² + 2m - 5 = 0

product = -15 m²

sum = 2 m

Terms = 5m and -3m

Therefore;

3m² + 5m - 3m - 5 = 0

Factorizing by pairing

m(3m + 5) - 1 (3m + 5) = 0

Thus;

(m - 1) (3m + 5) = 0

This means;

m - 1 = 0 or 3m + 5 =0

Hence; the roots of the equation are;

m = 1 or m = -5/3

Thus, the sum of the roots is;

= 1 + -5/3

= -2/3

Hence, the sum of the roots of the equation is -2/3

Answer:

Step-by-step explanation:

there is 15 emperor penguins...they make up 30% of all the penguins

so 30% of all the penguins is 15

let x represent all the penguins

turn ur percent to a decimal

0.30x = 15

x = 15 / 0.30

x = 50 <===== 50 total penguins

Answer:

50 penguins

Step-by-step explanation:

there is 15 emperor penguins...they make up 30% of all the penguins

so 30% of all the penguins is 15

let x represent all the penguins

turn ur percent to a decimal

0.30x = 15

x = 15 / 0.30

x = 50 <===== 50 total penguins

Answer:

12.5

Step-by-step explanation:

1) Original equation: 3(2) - 18x +225 = 6

2) Simplify: 6 - 18x + 225 = 6

3) Move 18x over to the right: 6 + 225 = 6 + 18x

4) Move the 6 on the right over to the left: 225 = 18x

5) Divide both sides by 18 to isolate x: 225/18, 18x/18

6) x = 12.5

Answer:

350 people

Step-by-step explanation:

you would cross multiply

98/100 times 343/x

98x = 34300

34300/98= 350

So the answer is 350 people

Perimeter of a rectangle = 6x + 8

Solution:

Given area of a rectangle = [tex]2x^2+7x+3[/tex]

Let us first factor the given polynomial.

[tex]2x^2+7x+3=2x^2+x+6x+3[/tex]

                    [tex]=(2x^2+x)+(6x+3)[/tex]

Taking out common terms in the above expression

                    [tex]=x(2x+1)+3(2x+1)[/tex]

Taking out common term [tex]2x+1[/tex] in the above expression

                    [tex]=(2x+1)(x+3)[/tex]

[tex]2x^2+7x+3=(2x+1)(x+3)[/tex]

Area of a rectangle = l × b

Therefore, [tex]l=2x+1[/tex] and [tex]b=x+3[/tex]

Perimeter of a rectangle = 2(l + b)

                                         [tex]=2[(2x+1)+(x+3)][/tex]

                                         [tex]=2(2x+1+x+3)[/tex]

                                         [tex]=2(3x+4)[/tex]

                                         [tex]=6x+8[/tex]

The answer is same if you take l = x + 3 and b = 2x + 1.

Hence, perimeter of a rectangle = 6x + 8.

Answer:

I believe the answer to this question is: 3/2 simplified to 1  1/2.

Answer: 4/3

Explanation: To write the fraction 8/6 in lowest terms, we divide the numerator and the denominator by the greatest common factor of 8 and 6.

Since the factor of 8 are 1, 2, 4, and 8 and the factors of 6 are 1, 2, 3, and 6, the greatest common factor of 8 and 6 is 3 so we divide the numerator and the denominator of 8/6 by 2 and we get 4/3.

So 8/6 can be simplified to 4/3.

4/3 can also be changed to the mixed number 1 and 1/3.

Good evening

Answer:

RM ≈ 8.25

Step-by-step explanation:

√((10-2)^2+(6-4)^2)

= √(8^2+2^2)

=√(64+4)

=√(68)

=8.246211251235

Distance RM To the nearest hundredth 8.25

:)

Answer:

The Correct option is C ) 25

Therefore the value of x is 25 when y =40.

Step-by-step explanation:

Given:

Variable 'y' is directly proportional to the variable 'x'.

[tex]\therefore y=kx[/tex]     ......Direct Variation

Where,

k = Constant of proportionality

To Find:

value of x = ? when y = 40

Solution:

First we need to find Constant of proportionality

When x = 20 and y = 32

Substituting the values we get

[tex]32=k\times 20\\k=\dfrac{32}{20}=1.6\\\\k=1.6[/tex]

Now when k =1.6 , y = 40 then x will be

[tex]40=1.6\times x\\\\x=\dfrac{40}{1.6}=25\\\\x=25[/tex]

Therefore the value of x is 25 when y =40.

Final answer:

The value of x when y is 40 is C) 25.

Explanation:

The variable y is directly proportional to the variable x.

This means that as x increases or decreases, y does so at a constant rate.

This relationship can be written as y = kx, where k is the constant of proportionality.

To find k, we use the information that y = 32 when x = 20, leading to the equation 32 = k * 20.

Solving this gives us k = 32 / 20 or k = 1.6.

With the constant k known, we can find the value of x when y = 40 by setting up the equation 40 = 1.6x.

Dividing both sides by 1.6 gives us x = 40 / 1.6, which results in x = 25.

Therefore, the correct answer is C) 25.

Answer:

29 1/3

Step-by-step explanation:

1/3 (4 + 18) 4

1/3 (22) 4

7 1/3 x 4

29 1/3

Twenty nine and one third is your answer.

Final answer:

The expression 1/3 (4+18) 4 evaluates to approximately 29.333 following the order of operations; first the addition inside the parentheses, then multiplication by 1/3, and lastly by 4.

Explanation:

When evaluating the expression 1/3 (4+18) 4, it's essential to follow the orders of operation, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication, and Division (from left to right), Addition and Subtraction (from left to right)). Let's break down the problem step by step:

Now, perform the multiplication: 22 * 4 = 88. Since we are multiplying by a division by 3 (22/3), it is the same as dividing 88 by 3, which gives us the final answer: 88 divided by 3 equals 29 with a remainder of 1, or as a decimal, approximately 29.333.

The correct answer to the expression 1/3 (4+18) 4 is therefore approximately 29.333. It is crucial to always follow the order of operations in any math problem to get the correct result.

Answer:

B, hope this helps you!

Both the variable and constant terms in Yari's equation are identical on each side after simplification, leading to the conclusion that both sides are exactly the same.

Analysing Yari's equation step-by-step, we can see that after expanding and simplifying both sides of the equation:

Comparing both sides of the simplified equation 2x + 3 = 3 + 2x, we notice that both the variable terms (2x) and the constant terms (3) are identical on each side.

Therefore, the correct answer is:

B) Both sides are exactly the same.