Find the minimum value of C=-2x+y subject to the following constraints x≥-5 x≤4 y≥-1 x≤3

Answer: C

Step-by-step explanation:

 f(x) =   2x + 1  ⇒       2x + 1

- g(x) = -(x² - 7) ⇒  -x²     + 7

              (f-g)(x) = -x² + 2x + 8

C

G= - 4t + 100 ( add 4t to both sides )

G + 4t = 100 ( subtract G from both sides )

4t = 100 - G ( divide both sides by 4 )

t = [tex]\frac{100-G}{4}[/tex]

t=(G-100)/4 is the equation that correctly solves the given equation for t. So, option C is the correct answer.

Given that, the number of gallons of water in the pool changes with time t according to the equation.

The given equation is G = -4t + 100.

We need to solve the given equation for t.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

Now, G = -4t + 100

⇒4t=G-100

⇒t=(G-100)/4

Therefore, t=(G-100)/4 is the equation that correctly solves the given equation for t. So, option C is the correct answer.

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Craig practiced 15 hours

Nicki practiced his drums for 11 hours, and considering Craig practiced 4 hours more than Nicki, Craig practiced his drums for 15 hours.

Let's start by figuring out how many hours Nicki practiced his drums. We know that Nicki practiced his drums 5 hours less than Marshal, and Marshal practiced his drums 16 hours. This means that Nicki practiced his drums for 16-5= 11 hours.

Next, we move on to figuring out how many hours Craig practiced his drums. The question tells us that Craig practiced his drums 4 hours more than Nicki. Since we now know that Nicki practiced his drums for 11 hours, this means that Craig practiced his drums for 11+4= 15 hours.

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Answer:

180%

Step-by-step explanation:

Answer:

160piein^3

Step-by-step explanation:

Answer:

Step-by-step explanation:

s=5?

t=5?

3(5) - 3(5) +3

(15) -15 = 0

0 + 3 = 3

The value of 3s - 3t + 3 given that s - t = 5 is 18.

In this problem, we are given that s - t = 5. Now we have to find the value of 3s - 3t + 3. What we can do is factor out the '3' from 3s - 3t, then we can see it as 3(s - t) + 3. Our equation becomes 3 * 5 + 3 which simplifies to 15 + 3, and then 18.

So, the value of 3s - 3t + 3 given that s - t = 5 is 18.

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The values are always interpreted as (x1, y1) and (x2, y2) in order from left to right, so in this case, (7,2) are (x1, y1) and (15, 8) are (x2, y2)

X1 = 7

Y1 = 2

X2 = 15

Y2 = 8

first part: 5% of $94 is 0.05*94=$4.70

second part: 80% of 45 questions is .8*45 = 36

Answer: The correct option is (B) [tex]\left(5,\dfrac{1}{2}\right).[/tex]

Step-by-step explanation: We are given to find the midpoint of the line segment shown in the figure.

From the figure, we see

a line segment with co-ordinates of the endpoints (5, 4) and (5, -3).

We know that

the co-ordinates of the midpoint of a line segment with endpoints (a, b) and (c, d) is given by

[tex]M=\left(\dfrac{a+c}{2},\dfrac{b+d}{2}\right).[/tex]

Therefore, the co-ordinates of the line segment shown is given by

[tex]M=\left(\dfrac{a+c}{2},\dfrac{b+d}{2}\right)=\left(\dfrac{5+5}{2},\dfrac{4-3}{2}\right)=\left(5,\dfrac{1}{2}\right).[/tex]

Thus, (B) is the correct option.

Answers

1.  1,364

2. x⁴ + 2x - 6

3.  x⁵ - 5x⁴ + 4x³ - x² + 5x - 4

4.  x⁴ - 7x³  - 21x² + 63x -108

5.  a(n-1) + 1.4

6. 3/(2× 2ⁿ⁻¹)

Explanation

Q1

Σ4ⁿ = 4¹ + 4² + 4³ + 4⁴ + 4⁵

      = 4 + 16 + 64 + 256 + 1024

       = 1,364

Q2. What is (f−g)(x)?

f(x)=x4−3x2+5x−7

g(x)=x3−3x2+3x−1

(f−g)(x) = (x⁴−3x²+5x−7

) - (x³−3x²+3x−1)

             =x⁴ + 2x - 6

3. What is (f⋅g)(x)?

f(x)=x2−5x+4

g(x)=x3−1

(f⋅g)(x) = (x³−1)(x²−5x+4

)

           = x⁵ - 5x⁴ + 4x³ - x² + 5x - 4

4. Let f(x)=x2−9 ​ and g(x)=x2−7x+12 .

What is (fg)(x)?

(fg)(x) = (x²−9)(x²−7x+12)

           = x⁴ - 7x³  - 12x² - 9x² + 63x -108

            =  x⁴ - 7x³  - 21x² + 63x -108

5. What is the recursive rule for the sequence?

4.4, 5.8, 7.2, 8.6, 10, …

5.8 = 4.4 = 1.4,     10 - 8.6 = 1.4  The sequence is an AP where the common difference is 1.4 and the first term a is 4.4.

We and 1.4 to the previous term in order to get the next term.

an = a(n-1) + d

     = a(n-1) + 1.4

6. Enter the explicit rule for the geometric sequence.

3/2, 3/4, 3/8, 3/16, 3/32, …

common ratio r, = 4/3 ÷3/2 = 1/2

First term a, = 3/2

an =  arⁿ⁻¹

     = (3/2)(1/2)ⁿ⁻¹

      = 3/(2× 2ⁿ⁻¹)

Answer: [tex]4\frac{1}{7} ft[/tex]

Step-by-step explanation:

Area (A): [tex]36\frac{1}{4} = \frac{4(36)+1}{4} = \frac{144+1}{4} = \frac{145}{4}[/tex]

Length (L): [tex]8\frac{3}{4} = \frac{4(8)+3}{4} = \frac{32+3}{4} = \frac{35}{4}[/tex]

width (w): W

A = L x W

[tex]\frac{145}{4}[/tex] = [tex]\frac{35}{4}[/tex] x W

[tex](\frac{4}{35})[/tex][tex]\frac{145}{4}[/tex] = [tex](\frac{4}{35})[/tex][tex]\frac{35}{4}[/tex] x W

[tex]\frac{4(145)}{35(4)} = \frac{145}{35} = \frac{5(29)}{5(7)} = \frac{29}{7} = W[/tex]

[tex]\frac{29}{7} = \frac{7(4) + 1}{7} = 4\frac{1}{7}[/tex]

Trisha has 18 nickels and 14 dimes in her bag worth $2.80. The solution involves solving equations simultaneously to find the number of each coin.

Trisha has 18 nickels and 14 dimes. Let's break it down:

Let N represent the number of nickels and D represent the number of dimes.

We know that N + D = 32 (the total number of coins).

We also know that 0.05N + 0.10D = 2.80 (the total value in dollars).

Solving these two equations simultaneously gives N = 18 and D = 14.

Therefore, Trisha has 18 nickels and 14 dimes.

3. AB = CE

4. CE = AC

5. Transitive property of congruence

6. Definition of isosceles triangle

Triangle ABC Is an isosceles triangle because line AB is equal to line AC .

An isosceles triangle is a triangle with two equal sides and two equal angles. The third side and angle may differ in length and measure.

The symmetry in side lengths and angles gives it distinct geometric properties.

Since line BD is equal to line CE and line CE is equal to line AC, this means that line BC is a bisector of line AD and AE,

Therefore we can say triangle ABC is an isosceles triangle because AB = AC.

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The area of a circle with a radius of 7.5 cm is 176.81 cm² to two decimal places, and the area of a semicircle with a radius of 8.2 cm is 104.8 cm² to one decimal place.

To work out the area of a circle with a radius of 7.5 cm using π (pi) as 3.142, we use the formula A = πr².

First, square the radius: 7.5 cm × 7.5 cm = 56.25 cm².
Then multiply by π: 56.25 cm² × 3.142 = 176.8125 cm².
The area to 2 decimal places is 176.81 cm².

For the area of a semicircle with radius 8.2 cm, we first calculate the area of a full circle and then divide by 2.
Full circle area: 8.2 cm × 8.2 cm × 3.142 = 209.5852 cm².
Area of the semicircle: 209.5852 cm² ÷ 2 = 104.7926 cm², which rounds to 104.8 cm² to 1 decimal place.

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The area of the circle is [tex]177.16[/tex] [tex]cm^2[/tex] and the area of semicircle is [tex]105.0[/tex] [tex]cm^2[/tex].

The area of a circle is given by the formula [tex]\( A = \pi r^2 \)[/tex], where [tex]\( r \)[/tex] is the radius of the circle.

1. For the first question, the radius [tex]\( r \)[/tex] is given as 7.5 cm. Using the formula for the area of a circle:

[tex]\[ A = \pi r^2 \][/tex]

[tex]\[ A = 3.142 \times (7.5 \text{ cm})^2 \][/tex]

[tex]\[ A = 3.142 \times 56.25 \text{ cm}^2 \][/tex]

[tex]\[ A = 177.1625 \text{ cm}^2 \][/tex]

Rounded to two decimal places, the area of the circle is [tex]\( A = 177.16 \text{ cm}^2 \)[/tex].

2. For the second question, the figure is a semicircle with a radius of 8.2 cm. The area of a semicircle is half the area of a full circle.

Therefore, using the formula for the area of a circle and then dividing by 2:

[tex]\[ A_{\text{semi}} = \frac{1}{2} \pi r^2 \][/tex]

[tex]\[ A_{\text{semi}} = \frac{1}{2} \times 3.142 \times (8.2 \text{ cm})^2 \][/tex]

[tex]\[ A_{\text{semi}} = \frac{1}{2} \times 3.142 \times 67.24 \text{ cm}^2 \][/tex]

[tex]\[ A_{\text{semi}} = \frac{1}{2} \times 210.0944 \text{ cm}^2 \][/tex]

[tex]\[ A_{\text{semi}} = 105.0472 \text{ cm}^2 \][/tex]

Rounded to one decimal place, the area of the semicircle [tex]\( A_{\text{semi}} = 105.0 \text{ cm}^2 \)[/tex].

14/25 , 29/50 , 53/100 , 13/20 and 3/5

Solution:

Put your numbers first in decimal form;

0.56 , 0.58 , 0.53 , 0.65 and 0.60

Then arrange them from the least to greatest;

0.53 , 0.56 , 0.58 , 0.60 and 0.65

Then revert your values to fraction form to give a final answer:

53/100 , 14/25 , 29/50 , 3/5 , 13/20

The point-slope form of a line:

[tex]y-y_0=m(x-x_0)[/tex]

We have:

[tex]m=\dfrac{2}{5}\\\\(-4,\ -7)\to x_0=-4,\ y_0=-7[/tex]

Substitute:

[tex]y-(-7)=\dfrac{2}{5}(x-(-4))\\\\y+7=\dfrac{2}{5}(x+4)[/tex]

To find the number, divide 34,400 by 344%

To solve this problem, we need to translate the phrase into an equation and solve for the unknown number.

The phrase "344% of what number is 34,400" can be translated as 344% * x = 34,400.

To solve for x, we divide 34,400 by 344% or 3.44.

Therefore, the number is 10,000.

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To find the number, divide 34,400 by 344% (or 3.44), resulting in the number 10,000.

To solve this problem, we need to find what number 344% of is equal to 34,400. Here's how we can do it step by step:

Step 1:

Translate the problem into a mathematical equation.

Let's denote the unknown number as [tex]\( x \)[/tex]. The problem translates to:

[tex]\[ 344\% \text{ of } x = 34,400 \][/tex]

Step 2:

Rewrite the percentage as a decimal.

[tex]\[ 344\% = \frac{344}{100} = 3.44 \][/tex]

Step 3:

Write the equation using the decimal form of the percentage.

[tex]\[ 3.44 \times x = 34,400 \][/tex]

Step 4:

Solve for [tex]\( x \).[/tex]

[tex]\[ x = \frac{34,400}{3.44} \][/tex]

Step 5:

Perform the division.

[tex]\[ x = 10,000 \][/tex]

So, 344% of 10,000 is 34,400. Thus, the unknown number is 10,000.

Answer:

D. two possible amounts by which the dimensions were increased

Step-by-step explanation:

The solutions to the equation (6 + x)(9 + x) = 88 represent two possible amounts by which the dimensions of the rectangular patio were increased.

The solutions to the equation (6 + x)(9 + x) = 88 represent two possible amounts by which the dimensions of the rectangular patio were increased. The equation represents the area of the larger patio, which is found by multiplying the increased length (6 + x) by the increased width (9 + x), and setting it equal to 88. By solving the equation, you can find the possible values of x, which represent the amounts by which the dimensions were increased.

[tex]x^2+52=\\\\x^2-(-52)=\\\\(x-\sqrt{-52})(x+\sqrt{-52})=\\\\(x-2\sqrt{13}i)(x+2\sqrt{13}i)[/tex]

Answer:

B

Step-by-step explanation:

The two points going to the left that are roots are

(-3,0) and (-1,0)

So the factors are (x + 3)(x + 1)

The points going to the right are

(2,0)(3,0)

So the factors are (x - 2)(x - 3)

The answer is B

the answer to your question is B

Answer:

Each dog will receive [tex]\frac{1}{2}[/tex] pounds of dog food.

Step-by-step explanation:

This is a very straightforward question.

To find the amount each dog gets we have to divide the total number of dog food to 7 equal portions.

Amount of dog food each dog will receive= Total number of dog food / number of dogs

=[tex]\frac{3\frac{1}{2} }{7}[/tex]

=[tex]\frac{\frac{7}{2} }{7}[/tex]

=[tex]\frac{7}{7*2}[/tex]

=[tex]\frac{1}{2}[/tex] pounds

Therefore, each dog will receive [tex]\frac{1}{2}[/tex] pounds of dog food.

Answer:

The correct answer is C. $5.07

Step-by-step explanation:

Answer:

5.07

Step-by-step explanation:

 4 ÷ [tex]\frac{1}{6}[/tex]

= 4 * [tex]\frac{6}{1}[/tex]

= 24

Answer: 24 slices

the correct answer should be (b) 6 is extraneous.

If you look at the second row of the solution you see (x-6) as a factor in one of the denominators. That's a problem: if 6 were a solution this denominator would become 0. But denominators being 0 is bad (undefined), so while 6 comes out of the algebraic manipulation as a solution, it is invalid, or extraneous.

-3 is a fine solution.

The correct statement is B that is "6 is an extraneous solution because it creates a zero in the denominator" as the step 2 has x-6 as a term of denominator of the RHS.

The lower number in a fraction is known as the denominator. It demonstrates the equal division of something into parts. Four would be the denominator, for instance, if the fraction was 3/4. For instance, the fraction bar is the line that separates the numbers 4 and 5, and 4/5 is a fraction. Here, the numerator is the number above the fraction bar, and the denominator is the number below the fraction bar. The denominator, or number of parts out of the whole, is represented by a numerator. The bottom number alone serves as the denominator.

Here,

The right option is B, which means that "6 is an extraneous solution because it creates a zero in the denominator," since the RHS's step 2's denominator term is x-6.

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Answer:

The bee traveled 11.7 meters.

Step-by-step explanation:

A bee flew 840 cm first to land on a flower to collect some pollen and then flew another 330 cm to get back to her hive.

For finding the total distance traveled, we need to just add 840 cm and 330 cm.

So, [tex](840+330) cm = 1170 cm[/tex]

We know that,  1 meter = 100 cm. That means, for converting 'cm' into 'meter' , we need to divide by 100.

Thus,  [tex]1170 cm= \frac{1170}{100} meter = 11.7 meter[/tex]

So, the bee traveled 11.7 meters.

Answer:

11.7

Step-by-step explanation:

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