Carlos is using a number line to add another integer to –4. He begins by showing –4 on the number line, as shown below. Carlos adds the other integer on the number line and says that the sum is negative.Which is true of the number Carlos added to –4?

To find the height of the original oil tank from the sample, you set up a proportion using the scale given. The calculation shows that the original tank is 25 meters tall, corresponding to answer A.

The question is asking us to find the height of the original oil tank given that the sample tank is [tex]\frac{1}{25}th[/tex] the size of the original and that the sample is 1 meter tall. Since the sample is a scaled-down version of the original, we can set up a proportion to find the original height.

To set up the proportion, we assume the scale is such that 1 meter on the sample represents 25 meters on the original. Therefore, we can write the proportion as:

[tex]\frac{1\ meter}{ x\ meters} = \frac{1}{25}[/tex]

We can then cross-multiply to solve for x:

1 * x = 25 * 1

x = 25 meters

Thus, the height of the original oil container tank is 25 meters, which corresponds to answer choice A.

Answer: The difference is,

[tex]m^2n^2-mn-11[/tex]

Step-by-step explanation:

Given expression is,

[tex](m^2n^2-7)-(mn+4)[/tex]

By distributive property,

[tex]m^2n^2-7-mn-4[/tex]

Combine like terms( that have the same variables and powers ),

[tex]m^2n^2-mn-11[/tex]

Which is the required result.

Hence, option third is correct.

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:

khan academy

You need to send 360 texts to earn 1800 points and get the prize.

To figure out how many texts you need to send to obtain the prize from your cell phone company's reward club, you'll want to set up a proportion because you earn a set number of points for every several texts sent. In this case, you get 15 points for every three texts.

Let's use the variable T to denote the total number of texts needed to be sent. We know that:

3 texts = 15 points

T texts = 1800 points

To find T, we can set up a ratio and solve for the variable:

[tex]\(\frac{3 texts}{15 points} = \frac{T texts}{1800 points}\)[/tex]

Cross multiply to solve for T:

3 texts * 1800 points = 15 points * T texts

T = [tex]\(\frac{3 * 1800}{15}\)[/tex]

T = 360 texts

Therefore, you need to send 360 texts to earn 1800 points and get the prize.

A Pythagorean triplet is a set of 3 positive integer numbers which may be the sides of a right triangle, i.e. they meet the Pythagorean theorem c² = a² + b².

You can check that the numbers on your table are Pythagorean triplets by substituting them in the Pythagorean equation:

Now, lets look for the pattern:

x-value     Pythagorean

                 triple    

3               (6, 8, 10)              6/2 = 3

                                            3² - 1 = 9 - 1 = 8

                                            3² + 1 = 9 + 1 = 10

----------------------------------------------------------------------

4               (8, 15, 17)              8/2 = 4

                                             4² - 1 = 16 - 1 = 15

                                             4² + 1 = 16 + 1 = 17

---------------------------------------------------------------------

5               (10, 24, 26)              10/2 = 5

                                                 5² - 1 = 25 - 1 = 24

                                                 24² + 1   = 25 + 1 = 26

--------------------------------------------------------------------------

6               (12, 35, 37)              12/2 = 6

                                                6² - 1 = 36 - 1 = 35

                                               6² + 1   = 36 + 1 = 37

----------------------------------------------------------------------

From which you find the pattern: the first number is 2x, the second number is x² - 1, and the third number is x² + 1

                                            ⇒ (2x)² + (x² - 1)² = (x² + 1)², or

                                                (x² - 1)² + (2x)² = (x² + 1)².

Other example of a Pythagorean triple is (3, 4, 5). You migth think that it does not follow the pattern, but if you do x = 2, you end with:

Hence, (3, 4, 5) also follows the pattern.

Only  right triangles with non-integer sides do not form Pythagorean triples.

Of course you may proof that (x² - 1)² + (2x)² = (x² + 1)² is an identity (always true):

Left hand side: (x⁴ - 2x² + 1) + 4x² = x⁴ + 2x² + 1

Right hand side: x⁴ + 2x² + 1

∴ The equation is always true.

At the end, the pattern is true for any Pythagorean triplet, but a more formal proof is beyond the scope of this question.

This isn't even the full question

Answer:

2539.63

Step-by-step explanation:

A = 1400(1 + 0.06/4)^(4*10)

 =  2539.63

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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I think it's degrees or like something to do with translating?!

It is function composition. If you have one function f(x), and another function g(x), then we can create a new function named g∘f (read as: "gg composed with ff") that is defined as(g∘f)(x)=g(f(x))(g∘f)(x)=g(f(x))For example, if f(x)=x+1f(x)=x+1, and g(x)=2x−1g(x)=2x−1, then(g∘f)(x)=g(f(x))=g(x+1)=2(x+1)−1=2x+1

Since, area of square patch of fabric = 2.25 square inches

Area of square of side 's' = [tex]s^2[/tex]

Since, area of square patch of fabric = 2.25 square inches

[tex]2.25 = s^2[/tex]

[tex]s = \sqrt{2.25}[/tex]

s = 1.5 inches

Therefore, the side length of the patch is 1.5 inches.

Final answer:

To determine the side length of a square with an area of 2.25 square inches, take the square root of the area, which is 1.5 inches.

Explanation:

To find the side length of a square patch of fabric that is 2.25 square inches, we need to understand that the area of a square is given by the formula Area = side × side (or side2). Given that the area is 2.25 square inches, we set up the equation side2 = 2.25.

Now, to find the side, we take the square root of both sides of the equation:

Therefore, the side length of the square patch is 1.5 inches.

20 - 6 + 4k = 2 - 2k

    14   + 4k = 2 - 2k    added like terms (20 and -6)

           +2k        +2k

     14 + 6k  =  2

    -14           -14

             6k = -12

             [tex]\frac{6k}{6} = \frac{-12}{6}[/tex]

               k = -2

Answer: k = -2

The solution to the equation is k = -2.

To solve for k in the equation 20 - 6 + 4k = 2 - 2k, we can start by simplifying both sides of the equation.

Combining like terms on each side:

14 + 4k = 2 - 2k

Next, we can isolate the variable k by moving all terms containing k to one side of the equation.

Adding 2k to both sides:

14 + 4k + 2k = 2 - 2k + 2k

14 + 6k = 2

Now, we'll isolate the variable k by subtracting 14 from both sides:

14 + 6k - 14 = 2 - 14

6k = -12

To solve for k, we'll divide both sides by 6:

(6k)/6 = (-12)/6

k = -2

Therefore, the solution to the equation is k = -2.

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Answer:

5

Step-by-step explanation:

The total number of bags of mixed nuts with Carmela are 5.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given is Carmela who mixes 3/4 kilogram of walnuts, 1/2 kilogram of almonds, and 1/4 kilogram of pecans together. She divides the mixed nuts into 3/10 kilogram bags.

We can write the equation as -

(3/4 + 1/2 + 1/4) x 1000 = (3/10) x 1000 x n

1.5 x 1000 = 3 x 100 x n

1.5 x 10 = 3n

15 = 3n

n = 5

Therefore, the total number of bags of mixed nuts with Carmela are 5.

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6 is your answer good luck

Step 1. Expand

q + 12 - 2q + 44 > 0

Step 2. Simplify q + 12 - 2q + 44 to -q + 56

-q + 56 > 0

Step 3. Regroup terms

56 - q > 0

Step 4. Subtract 56 from both sides

-q > -56

Step 5. Multiply both sides by -1

q < 56

To solve the inequality q + 12 – 2(q – 22) > 0, distribute the negative sign, isolate the variable, and divide by -1 with a flipped inequality sign to find q < 56.

To solve the inequality q + 12 – 2(q – 22) > 0, we can start by distributing the negative sign to the terms inside the parentheses: q + 12 - 2q + 44 > 0. Simplifying, we have -q + 12 + 44 > 0, which becomes -q + 56 > 0. Next, we isolate the variable by subtracting 56 from both sides: -q > -56. Finally, we divide both sides by -1, remembering to flip the inequality sign when dividing by a negative number: q < 56.

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For the shown graph, we need to find the value of h(2).

h(2) represents the value of h function for x=2.

We need to check the value of function on the graph where h is 2.

From the graph, we can see for x=2, we have a solid dot for y coordinate at 0 and a hollow dot at y coordinate at 3.

Because hollow dot represents excluded value.

Therefore, we would take y coordinate of solid dot of the graph at x=2.

Therefore, f(2) = 0.

 4 ÷ [tex]\frac{1}{6}[/tex]

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

= 24

Answer: 24 slices

The answer to your question  is B.

Ok so here it is:

-67 ≥ 5 + 3n -21

-67+ 21 ≥ 5 + 3n -21 + 21

the 21 cancel each other out

now add -67 and 21

-46 ≥ 5 + 3n

-46 -5 ≥ 5 -5 +3n

the 5 cancel each other out

now subtract -5 from -46

-51 ≥ 3n

-51 / 3 ≥ 3n / 3

3 cancel each other out

now divide -51 and 3

n ≤ -17

B

Jon is selling tickets for the school talent show. On the 1st day, he sold 3 senior tickets and 12 child tickets for $195. On the 2nd day he sold 13 senior tickets for $299. Find the price of a senior citizen ticket.

Create a system of equations to help you solve this problem. The system of equations will look like: 3s + 12c = 195 and 13s = 299. The variable s represents the cost of senior tickets and the variable c represents the cost of children tickets.

[tex]\left \{ {{3s~+~12c~=~195} \atop {13s~=~299}} \right.[/tex]

Solve the second equation for the variable s as this is the easiest way to solve the problem. Solve the second equation for s by dividing both sides of the equation by 13 to isolate the variable s.

s = 23

Since the question was only asking for the price of a senior citizen ticket, you are technically done. The first equation was only put there to confuse you or allow you to check your work if you needed to. The price of a senior citizen ticket (variable s) is $23.

The solution to ax² + bx + c = 0  is [tex]x=-\frac{b}{2a}\pm\sqrt{\frac{b^2-4c}{4a} }[/tex]

A quadratic function is an equation of degree 2.  

Given the equation:

ax² + bx + c = 0

Subtracting c from both sides to get:

ax² + bx = -c

Dividing through by a:

x² + (b/a)x = -c/a

Add to both sides the square of half of the coefficient of x that is (b²/4a):

x² + (b/a)x + (b²/4a)= -c/a + (b²/4a)

(x + b/2a)² = (b²-4c/4a)

[tex]x=-\frac{b}{2a}\pm\sqrt{\frac{b^2-4c}{4a} }[/tex]

The solution to ax² + bx + c = 0  is [tex]x=-\frac{b}{2a}\pm\sqrt{\frac{b^2-4c}{4a} }[/tex]

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Final answer:

Next, Florence should complete the square on the quadratic equation by dividing by 'a' (if applicable), moving the constant term to the other side, and adding the square of half the coefficient of 'b' to both sides. This is a precursor step toward factoring and ultimately deriving the quadratic formula.

Explanation:

The step Florence should do next in deriving the quadratic formula from the equation ax² + bx + c = 0 is to complete the square. To do this, Florence first needs to divide the entire equation by a to normalize the coefficient of x² to 1, assuming a≠0. Then she should move the constant term to the other side of the equation to get x² + (b/a)x = -c/a. The next step is to add the square of half of the coefficient of x to both sides of the equation, which is (b/2a)². This process sets the stage for factoring the left side of the equation as a perfect square.

Once the perfect square is created, the equation can be written in the form (x + b/2a)² = (b² - 4ac)/4a². Then, by taking the square root of both sides and isolating x, Florence will arrive at the quadratic formula: x equals minus ‘b’, plus-or-minus the square root of ‘b’ squared minus four ‘a’ ‘c’, all over two 'a'.

587 rounded to the nearest ten is 590, and 92 is 90. Then, take 590 times 90 to get 53100. The two answers are in the same ballpark, so yes, the answer is reasonable.

Answer:

x ≤ 8

Step-by-step explanation:

Will first used 16 of the 144 ounces for his own water bottle.  This leaves 144-16 = 128 ounces.

Dividing that equally amount 16 plastic cups, each cup would have at most

128/16 = 8 ounces.

This means each one would have x ≤ 8 ounces.

The correct inequality is 8 > 6 .

To solve this problem, we need to figure out how many ounces of water Will could pour into each cup. He started with a cooler filled with 144 ounces of water.

Then, he took out 16 ounces for his own water bottle. So, he had 144 - 16 = 128 ounces left.

Since he poured the same amount of water into each of the 16 cups, we can divide the total remaining ounces by the number of cups to find out how many ounces each cup contains:

[tex]\[ \frac{128}{16} = 8 \][/tex]

So, Will could have poured 8 ounces of water into each cup.

Therefore, the correct inequality is:

8 > 6

Answer:

The cost of 10 cm and 70 cm are  £0.55 and £3.85 respectively.

Step-by-step explanation:

Material for a dress costs £5.50 per meter.

We know that,  1 meter = 100 cm.

Suppose, the cost of 10 cm material is [tex]x[/tex] and the cost of 70 cm material is [tex]y[/tex]

Now, according to the ratio of "cost" to the "length of material" , we will get.......

[tex]\frac{x}{10} =\frac{5.50}{100}\\ \\ 100x=10*5.50=55\\ \\ x=\frac{55}{100}=0.55[/tex]

and

[tex]\frac{y}{70} =\frac{5.50}{100}\\ \\ 100y=70*5.50=385\\ \\ x=\frac{385}{100}=3.85[/tex]

So, the cost of 10 cm material is £0.55 and the cost of 70 cm material is £3.85

Answer:

first we will multiply -3/10 and 60,

-3/10 x 60 = -18    

(one-tenth of 60 is 6, and because we are multiplying -3/10 and not -1/10 we can multiply 6 by -3 to get 18.)

then multiply the exponents

x(x) = x^2

y(y^6) = y^7

we can then multiply all terms together to form one single term

-18(x^2)y^7=-18x^2y^7

our final answer is:

-18x^2y^7

The answer to the given question is [tex]\[ \boxed{-18x^2y^7} \][/tex]

First, we need to multiply the numerical coefficients and the literal coefficients (variables) separately. The numerical coefficients are -3 and 60, and the literal coefficients are 1/10, x, y, x, and [tex]y^6[/tex].

Multiplying the numerical coefficients:

[tex]\[ -3 \times 60 = -180 \][/tex]

Multiplying the literal coefficients (variables):

[tex]\[ \frac{1}{10} \times x \times y \times x \times y^6 \][/tex]

Since we have two x's and one y to the power of 6, we can simplify this as:

[tex]\[ \frac{1}{10} \times x^2 \times y^7 \][/tex]

Now, we combine the numerical and literal coefficients:

[tex]\[ -\frac{180}{10} \times x^2 \times y^7 \][/tex]

Simplifying the numerical fraction:

[tex]\[ -18 \times x^2 \times y^7 \][/tex]

Therefore, the final simplified expression is:

[tex]\[ -18x^2y^7 \][/tex]

The answer is: [tex]-18x^2y^7[/tex].

Answer: C

Step-by-step explanation:

 f(x) =   2x + 1  ⇒       2x + 1

- g(x) = -(x² - 7) ⇒  -x²     + 7

              (f-g)(x) = -x² + 2x + 8

Answer:

The correct option is:  B

Step-by-step explanation:

The x-axis is labeled Time driving, and the y-axis is labeled Distance driven.

Segment B is a horizontal line from x equals 0.5 until 1.75.

So, the value of [tex]y[/tex] is constant in the interval [tex]x=0.5[/tex] to [tex]x=1.75[/tex] is 0.

Thus, the distance traveled in the time interval 0.5 to 1.75 will be 0, which means the car was in the same position in that time interval.

So, the interval B on the graph indicates she is stuck in a traffic jam.

Answer:

B

Step-by-step explanation:

To work this out we have to do 16.9  hours - 13.2 hours = 3.7 hours so there is a 13.7hour difference and to show it as an addition equation you do 13.2 hours + 3.7hours = 16.9 hours

The difference in time spent online by teens in Brooklyn, NY and Charlotte, NC is 16.9 hours.

To find the difference in time spent online by teens in Brooklyn, NY and Charlotte, NC, we can write and solve an addition equation.

Let's define:

The equation is: x + y = difference in time spent online

Given that teens in Brooklyn, NY spend 16.9 hours per week online and teens in Charlotte, NC spend 13.2 hours per week online, we can substitute these values into the equation:

16.9 + 13.2 = difference in time spent online

Simplifying the equation, we get:

difference in time spent online = 30.1 - 13.2

Therefore, the difference in time spent online by teens in Brooklyn, NY and Charlotte, NC is 16.9 hours.

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