When a is divided by 7, the remainder is 5; and when b is divided by 7, the remainder is 4. What is the remainder when a + b is divided by 7? When a is divided by 7 , the remainder is 5 ; and when b is divided by 7 , the remainder is 4. What is the remainder when a + b is divided by 7 ? ​

Option c) 2x-3y ≥ 3 is correct inequality which has a shaded area below the boundary line.

Attempting all the equation on the graph to get the solutions

Inequality can be define as the relation of equation contains the symbol of ( ≤, ≥, <, >) instead of equal sign in an equation.

Since, while attempting all the option on graph. The one equation that satisfies the condition is 2x-3y ≥ 3 of having shaded area below the boundary line.

Thus, the option c) 2x-3y ≥ 3 is correct implification on graph which shows the shaded area below the boundary line.

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The graph of the function. f(x)=−|x+2|+1 is illustrated.

The given function is f(x)=−|x+2|+1.

We will have to draw the graph of the function.

When x = 1, f(1) will be -2. When x = 2, f(2,) will be -3

The points are illustrated based on the information given and the appropriate graph is illustrated and attached.

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Answer:

960

Step-by-step explanation:

(if i made any typos, sorry it is kind of hard to type on computer over writing on paper.)

A=2AB+(a+b+c)h

AB=s(s﹣a)(s﹣b)(s﹣c)

s=(a+b+c)/2

Solving forA

A=ah+bh+ch+1/2 sqrt(﹣a^4+2(ab)^2+2(ac)^2﹣b4+2(bc)^2﹣c^4)=10·12+24·12+26·12+1

2·﹣104+2·(10·24)2+2·(10·26)2﹣244+2·(24·26)2﹣264=960

The equation of a parabola that has intercepts of x=-2 and x=6 and passes through point (8,6) is f(x) = 3/10(x+2)(x-6)

The standard equation of a parabola is in the form f(x) = (x-a)(x-b)

where a and b are the intercepts of the graph. Given the parabola that has intercepts of x=-2 and x=6, the resulting equation will be:

f(x) = a(x-(-2))(x-6)

f(x) = a(x+2)(x-6)

If the parabola passes through (8, 6), then;

6 = a(8+2)(8-6)

6 = a(20)

a = 6/20

a = 3/10

Substitute

f(x) = 3/10(x+2)(x-6)

Hence the equation of a parabola that has intercepts of x=-2 and x=6 and passes through point (8,6) is f(x) = 3/10(x+2)(x-6)

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Answer:

5.5 in

Step-by-step explanation:

First we will calculate the total lawn grown after 8 weeks.

Grow Rate = [tex]2\frac{1}{8} in/2 weeks[/tex]

Total lawn grown after 8 weeks = [tex]2\frac{1}{8} *4\\=8.5 in[/tex]

Next we will calculate the total lawn mown after 8 weeks.

Mowing Rate = [tex]1\frac{3}{4} in/2weeks[/tex]

Total lawn mown after 8 weeks = [tex]1\frac{3}{4} *4\\=7 in[/tex]

Lawn Height after 8 weeks = Initial Lawn Height + Total lawn grown - Total lawn mown

= 4 in + 8.5 in - 7 in

= 5.5 in

Answer:

False

Step-by-step explanation:

The slope is 0.

The perimeter of the triangle is 30 units

The vertices are (−7,−1), (5,−1), and (5,4).

Start by calculating the distance between the vertices using:

[tex]d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2[/tex]

So, we have:

[tex]d1 = \sqrt{(-1 + 1)^2 + (5 + 7)^2[/tex]

d1 = 12

[tex]d2 = \sqrt{(-1 - 4)^2 + (5 - 5)^2[/tex]

d2 =5

[tex]d3 = \sqrt{(-1 - 4)^2 + (-7 - 5)^2[/tex]

d3 = 13

The perimeter is then calculated as:

P = d1 + d2 + d3

This gives

P = 12 + 5 + 13

Evaluate

P = 30

Hence, the perimeter of the triangle is 30 units

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Answer:

yes I think I'm new to this but I think that's a yes

Answer:

Step-by-step explanation:

The alternate interior angles theorem, and the angle sum theorem can be used here.

Alternate interior angles are found on either side of a transversal where it crosses a pair of parallel lines. They are between the parallel lines. Their vertices are at the junction of the transversal and the parallel lines. Alternate interior angles are congruent.

In this diagram, there are two pairs of alternate interior angles where the two transversals AD and BD cross parallel lines AB and CD.

At points A and D, the alternate interior angles are 70° and x, respectively. This tells you ...

  x = 70° . . . . alternate interior angles theorem

At points B and D, the alternate interior angles are w and 70°, respectively. This tells you ...

  w = 70° . . . . alternate interior angles theorem

The angle sum theorem tells you the sum of angles in a triangle is 180°. This fact can be used to find the measure of angle y.

  70° +w +y = 180°

  y = 180° -70° -w = 110° -70°

  y = 40° . . . . angle sum theorem

There is not enough information to determine the measure of angle z.

  z = indeterminate

[tex]im \: guessing \: its \: 4x {}^{2} - 3x + 1 \\ (correct \: me \: if \: im \: wrong)[/tex]

[tex](a - b) {}^{2} = a {}^{2} - 2ab + {b}^{2} [/tex]

[tex]4x {}^{2} = a {}^{2} \: \: \: \: \: \: \: \: \: \: \: b {}^{2} = 1 \\ a = 2x \: \: \: \: \: \: \: \: \: \: \: \: \: \: b = 1[/tex]

[tex](2x - 1) {}^{2} = 4x {}^{2} -4x + 1[/tex]

[tex]we \: need \: to \: add \: a \: - x \\ \: to \: the \: original \: equation[/tex]

Inequalities help us to compare two unequal expressions. The inequality that represents the given statement is 45≤x≤ 65.

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.

It is mostly denoted by the symbol <, >, ≤, and ≥.

Given the maximum legal speed on the highway is 65 MPH, therefore, the value of x must not exceed 65 MPH.

x ≤ 65

Also, the minimum legal speed on the highway is 45 MPH, therefore, the value of x must not be less than 45 MPH.

45≤x

By combining the two inequalities, we will get,

45≤x≤ 65

Hence, the inequality that represents the given statement is 45≤x≤ 65.

The complete question is:

Write an inequality that accurately represents the following statement: "Bobby, you should know that the minimum legal speed for this highway is 45 MPH, and the maximum legal speed is 65 MPH."

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Answer:

The answer is D. 7x-8

Step-by-step explanation:

We can solve this problem by finding the area of the rectangle, which is equal to the length times the width. In this case, the length is 2x-3 feet and the width is 5 feet. Therefore, the area of the rectangle is (2x-3)(5), or 7x-8.

In 11.76 months, the value of the population will be 15000.

We have given that,

At the end of January 2003, the population of my town was 11,212.

the population is increased by 322 every month

So at the end of the second-month population will be 11534.

suppose x represents the year and  y represent the population

The population increased by 322 every month

Therefore the value of m =322

[tex](x_1,y_1)=(0,11212)[/tex]

We have m=332

[tex](x_2,y_2)=(x_2,15000)[/tex]

We have to determine the value of the x_2

[tex](y_2-y_1)=m(x_2-x_1)[/tex]

[tex]322\left(x_2-0\right)=15000-11212[/tex]

[tex]322\left(x_2-0\right)=3788[/tex]

[tex]\frac{322\left(x_2-0\right)}{322}=\frac{3788}{322}[/tex]

[tex]x_2=\frac{1894}{161}[/tex]

[tex]x_2=11.76[/tex]

Therefore in 11.76 months, the value of the population will be 15000.

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Answer:

Two solutions exist for the system of equations in the graph.

Step-by-step explanation:

Solutions are when the two graphs intersect.

Answer: 4a^2-2b^2 (I think this is right)

Step-by-step explanation:

Using the order of operations I started by multiplying both of the sides separately. The left side of the equation becomes 2a^2-b^2-ab while the right becomes 2a^2-b^2+ab. Then I put the sides together to add them and after combining like terms it becomes 4a^2-2b^2.

Answer:

14

Step-by-step explanation:

CB/AB = CE/ET

3/7 = 6/ET

ET = 14

Based on the account balances at the end of year, the retained earnings are $5,000.

First, find the net income:

= Service revenue - Salaries

= 35,000 - 29,000

= $6,000

Then find the assets:

= 22,000 + 14,000 + 5,200

= $41,200

Then the liabilities:

= 2,200 + 16,000

= $18,200

Retained earnings:

= Assets - Liabilities - Net income - Common stock

= 41,200 - 18,200 - 6,000 - 12,000

= $5,000

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Answer:

g(f(-2)) = -15

Step-by-step explanation:

• f(x) = x³

Then

f(-2) = (-2)³ = -8

• When x = -2 → g(f(x)) = g(f(-2)) = g(-8)

Since -8 ≤ 0 then g(-8) = 2×(-8) + 1 = -16 + 1 = -15

Conclusion:

g(f(-2)) = -15

Answer:

Infinite Number of Solutions

Step-by-step explanation:

Hello!

We can solve for y in the first equation, and plug that value in for y in the second equation.

Now that we know the equation for y, we can plug that in for y into the second equation to solve for x.

Since the equations match, there are an infinite number of solutions.

If we take a close look at the equations, we can also see that they are the same equation, but with flipped signs.

Answer:

2. (3+4) should be (3*4)

3. x is also x^1, so it should be x^(6+3+1)

4. you have to do 3^4 and 2^3 before timing them together

The number of the sample that is necessary is 171. The number of employees that would be selected if E is 30 = 476

The standard deviation = 398

error E = 50

Alpha is = 1-0.90 = 0.10

a. We are to find the value of the size of the sample

Z∝/2 = Z0.05

= 1.645

sample size,n >= [Za/2 *(sigma/E)]^2

n >= [1.645 * (398/50)] ^2

n >= 171.46

n = 171

b.

error,E = 30

n >= [1.645 * (398/30)] ^2

n >= 476.27

n = 476

A survey is planned to determine the mean annual family medical expenses of employees of a large company. The management of the company wishes to be 90% confident that the sample mean is correct to within ±$50 of the population mean annual family medical expenses. A previous study indicates that the standard deviation is approximately $398. a. How large a sample is necessary?

b. If management wants to be correct to within ±$30, how many employees need to be selected?

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Answer:

-960

Step-by-step explanation:

1) Expand [tex](x - 2y)^{10}[/tex] using the binomial theorem.

Binomial Theorem: [tex]\left(a+b\right)^n=\sum _{i=0}^n\binom{n}{i}a^{\left(n-i\right)}b^i[/tex]

1.1) Substitute the values into the theorem.

[tex]\sum _{i=0}^{10}\binom{10}{i}x^{\left(10-i\right)}\left(-2y\right)^i[/tex]

1.2) Expand summation.

[tex]=\frac{10!}{0!\left(10-0\right)!}x^{10}\left(-2y\right)^0+\frac{10!}{1!\left(10-1\right)!}x^9\left(-2y\right)^1+\frac{10!}{2!\left(10-2\right)!}x^8\left(-2y\right)^2+\frac{10!}{3!\left(10-3\right)!}[/tex]

[tex]x^7\left(-2y\right)^3+\frac{10!}{4!\left(10-4\right)!}x^6\left(-2y\right)^4+\frac{10!}{5!\left(10-5\right)!}x^5\left(-2y\right)^5+\frac{10!}{6!\left(10-6\right)!}x^4\left(-2y\right)^6+\frac{10!}{7!\left(10-7\right)!}x^3\left(-2y\right)^7+\frac{10!}{8!\left(10-8\right)!}x^2\left(-2y\right)^8+\frac{10!}{9!\left(10-9\right)!}x^1\left(-2y\right)^9+\frac{10!}{10!\left(10-10\right)!}x^0\left(-2y\right)^{10}[/tex]

1.3) Simplify them.

1.4) You will get:

[tex]=x^{10}-20x^9y+180x^8y^2-960x^7y^3+3360x^6y^4-8064x^5y^5+13440x^4y^6-15360x^3y^7+11520x^2y^8-5120xy^9+1024y^{10}[/tex]

2) We are told to find the coefficient of [tex]x^{7} y^{3}[/tex]. Find it from the simplified expansion. The coefficient is -960.

The required height of window of the glass 2.4 meters.

Tony is installing a window that is shaped like a parallelogram. He has 6 square meters of glass and knows that the base of the window needs to be 2 and 1 half meters.

parallelogram is a quadrilateral consist of pairs of parallel side.

Area of parallelogram = base x height
                                    6 = 2.5 x height

               height = 2.4 m

Thus the required height of window is given by 2.4 meters.

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Answer is (4,7)

Step-by-step explanation:

The dot plot that represents the library book data is shown in the image below.

To construct a dot plot, each data point is represented as a dot. The number of dots one data point has represents the frequency at which that data point occurs in the data set.

The data set given in the table will have the following data points and frequencies:

1: 1

2: 3

3: 4

4: 4

5: 4

6: 0

7: 2

8: 2

The dot plot for the data is shown in the image below.

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