Write an equation of the line passing through each of the following pairs of points. (5, 7), (−6, −3)

Final answer:

To find the total amount of the two components, add the fractions together. The total amount of the two components combined is 7/24 cup.

Explanation:

To find the total amount of the two components, we need to add the fractions together. The common denominator of 6 and 8 is 24. So, we have 1/6 cup of water which is equivalent to 4/24 cup, and 1/8 cup of the secret component which is equivalent to 3/24 cup. Adding these fractions together, we get a total of 7/24 cup of the two components combined.

Answer: D(2,6)

Step-by-step explanation:

To find  the values of x and y that maximize the objective function

x+y≤8....(line 1)

2x+y≤10.......(line 2)

x≥0......(3)

y≥0.......(4)

we need need to plot them by the following steps.

Step 1: Find coordinates(x,y) of line(1) x+y=8

Put x=0 , we get y =8

Put y=0, we get x=8

by this we got points (0,8) and (8,0) to plot line (1)........(a)

Step 2: Find coordinates (x,y) of line(2) 2x+y=10

Put x=0 , we get y =10

Put y=0, we get 2x=10⇒x=5

by this we got points (0,10) and (5,0) to plot line (2)...........(b)

so with the help of (a) , (b) ,(3) and (4) ,we plot the given graph .

By the graph we can find  that at (x,y)=(2,6) the objective function is maximized , so option D is right.

I believe it is D.

hope it helps

p = number of items sold (note: this is not the profit)

1 item sells for $855, so p items sell for 855p dollars

Subtract off the cost of 6780 and we have the expression 855p-6780 which is the profit for that given month.

Now plug in p = 250 because 250 items were sold in that given month

855*p - 6780 = 855*250 - 6780 = 206,970

The company earns $206,970 in profit for that month. Apply 15% to this value

15% of 206,970 = (15/100)*206,970 = 0.15*206,970 = 31,045.50

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Answer: $31,045.50 which is choice C

It will take approximately 1.25 hours for the snowfall of the two towns to be equal.

To find the number of hours in which the snowfall of the two towns will be equal, we can set up an equation: 3 + 6h = 8 + 2h

where h represents the number of hours.

Simplifying the equation, we get 4h = 5

Dividing both sides by 4, we find h = 5/4 = 1.25 hours.

Therefore, it will take approximately 1.25 hours for the snowfall of the two towns to be equal.

5/9, when square rooting fractions like these, you square root them seperatly. Square root of 25 is 5 and square root of 81 is 9.

the temp at 2 am is -6.7 degrees

Answer:

The length of Ms. Ford's kitchen is 57.5 feet.

Step-by-step explanation:

1. You have the following information given in the problem above:

- The kitchen is rectangular.

- Ms. Ford wants to buy 5 extra feet of wallpaper border.

- She buys a total of 62.5 feet of wallpaper border.

2. Therefore, to calculate the length of Ms. Ford's kitchen, you only need to substract 62.5 feet and the 5 extra feet of wallpaper border. Therefore, the result is:

[tex]62.5ft-5ft=57.5ft[/tex]

Answer: It would be y-intercept: (0,-45), x-intercept:(-10,0)

In the given diagram of the coordinate plane , the x-intercept is (-10, 0) and the y-intercept is (0,-45 ).

To find the x-intercept of a line, we set y = 0.

To find the y-intercept of a line, we set x = 0.

This can be verified by looking at the graph. The line intersects the x-axis at (-10, 0) and the y-axis at (0, -45).

To find the intercepts of a line using algebra:

X-intercept:

To find the x-intercept of a line, we set y = 0 and solve the resulting equation for x.

For example, the equation of the line in the image is y = x  + 10. To find the x-intercept, we set y = 0 and solve for x as follows:

0 = x + 10

x = -10

Therefore, the x-intercept of the line is (-10, 0).

Y-intercept:

To find the y-intercept of a line, we set x = 0 and solve the resulting equation for y.

For example, the equation of the line in the image is y = x - 45. To find the y-intercept, we set x = 0 and solve for y as follows:

y = 0 - 45

y = -45

Therefore, the y-intercept of the line is (0, -45).

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22. 28 minus(eats) 6 is 22.

He saves $96, The Equation I did for this is 196 Divided by 2

[tex]\frac{441}{4}[/tex]

change the mixed numbers to improper fractions and multiply the numerators / denominators

10 [tex]\frac{1}{2}[/tex] = [tex]\frac{21}{2}[/tex]

[tex]\frac{21}{2}[/tex] × [tex]\frac{21}{2}[/tex] = [tex]\frac{441}{4}[/tex] = 1110 [tex]\frac{1}{4}[/tex]

[tex]\dfrac{\partial }{\partial x}(y+4x^2)=0+8x=8x[/tex]

First one

[tex]\frac{-7}{9} \times \frac{3}{5}[/tex]

We cancel out common factors before multiplying out.

[tex]=\frac{-7}{3} \times \frac{1}{5}[/tex]

[tex]=\frac{-7\times 1}{3\times 5}[/tex]

[tex]=\frac{-7}{15}[/tex]

Second Question

[tex]=\frac{-2}{5} \times -1\frac{1}{4}[/tex]

We need to change the mixed numbers to improper fraction first.

[tex]=\frac{-2}{5} \times \frac{-5}{4}[/tex]

We now cancel out common factors.

[tex]=\frac{-1}{1} \times \frac{-1}{2}[/tex]

We multiply out now to obtain,

[tex]=\frac{-1\times -1}{1 \times 2}[/tex]

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

Third Question

[tex]=1\frac{3}{4} \times -1\frac{1}{4}[/tex]

We need to change the mixed numbers to improper fraction first.

[tex]=\frac{7}{4} \times \frac{-5}{4}[/tex]

[tex]=\frac{7 \times -5}{4\times 4}[/tex]

[tex]=\frac{-35}{16}[/tex]

[tex]=-2\frac{3}{16}[/tex]

Fourth Question

[tex]=1\frac{3}{4} \times \frac{-3}{4}[/tex]

[tex]=\frac{7}{4} \times \frac{-3}{4}[/tex]

[tex]=\frac{7\times -3}{4\times 4}[/tex]

[tex]=\frac{-21}{16}[/tex]

[tex]=-1\frac{5}{16}[/tex]

Fifth Question

[tex]=-\frac{7}{8} \times -1\frac{3}{7}[/tex]

[tex]=-\frac{7}{8} \times \frac{-10}{7}[/tex]

[tex]=-\frac{1}{8} \times \frac{-10}{1}[/tex]

[tex]=\frac{10}{8} [/tex]

[tex]=\frac{5}{4} [/tex]

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

Answer:

10,12,14

Step-by-step explanation:

Two consecutive integers will have difference of 2.

Let 3 consecutive even integers be a-2, a, a+2

Smallest number = a-2 and middle number = a

Sum of the smallest number and twice the middle number

= a-2+2a =3a-2

20 more than the largest number = 20+a+2 =a+22

i.e. 3a-2 = a+22

2a = 24

Or a =12

Hence three integers even consecutive are 12-2, 12, 12+2

=10,12,14

First, multiply -6*-5. This equals (positive) 30 because the negative signs cancel out.

This leaves you with:

30+12

Doing the addition leaves you with 42.

The answer is 42.

I hope this helps :)

-6(-5)+12

Do first the parenthesis

30+12

Add 30 &12

42

[tex]a=\dfrac{bh}{2}\qquad|\text{multiply both sides by 2}\\\\2a=bh\qquad|\text{divide both sides by}\ b\neq0\\\\\boxed{h=\dfrac{2a}{b}}[/tex]

Answer: c)

Answer:

c

Step-by-step explanation:

i just did it :)

THE ANSWER IS IN A RED BOX BELOW

To evaluate [tex]\log _{\frac{1}{3}}27[/tex] note that:

Use following properties:

1) [tex]\log_ab^k=k\log_ab;[/tex]

2) [tex]\log_{a^k}b=\dfrac{1}{k}\log_ab.[/tex]

Then

[tex]\log _{\frac{1}{3}}27=\log_{3^{-1}}3^3=3\log_{3^{-1}}3=3\cdot \dfrac{1}{-1}\log_33=-3\log_33.[/tex]

Since [tex]\log_aa=1,[/tex] you have

 [tex]\log _{\frac{1}{3}}27=-3.[/tex]

Answer:

a on edge

Step-by-step explanation:

let x be the name for that number, write the inequalities:

[tex]0.5x+3>0 \\0.5x>-3\\x>-6\\\mbox{OR}\\0.5x+3\leq -3\\0.5x\leq -6\\x\leq -12\\[/tex]

This number x can be anything, except anything in the interval (-12, 6]    (excluding -12, and including 6). Lmk if you have questions.

Answer:

The solutions of given inequalities are [tex]x>-6[/tex] and [tex]x\leq -12[/tex] respectively.

Step-by-step explanation:

It is given that one half a number increased by three is greater than zero or less than or equal to negative three.

Let x be the unknown number.

[tex]\frac{1}{2}x+3>0[/tex] or [tex]\frac{1}{2}x+3\leq -3[/tex]

On solving first inequality,

[tex]\frac{1}{2}x+3>0[/tex]

Subtract 3 from both sides.

[tex]\frac{1}{2}x>-3[/tex]

Multiply both sides by 2.

[tex]x>-6[/tex]

On solving second inequality,

[tex]\frac{1}{2}x+3\leq -3[/tex]

Subtract 3 from both sides.

[tex]\frac{1}{2}x\leq -6[/tex]

Multiply both sides by 2.

[tex]x\leq -12[/tex]

Therefore, the solutions of given inequalities are [tex]x>-6[/tex] and [tex]x\leq -12[/tex] respectively.

The answer to your problem is -6

Answer:

If you were to complete the square here and then factor, it would look like this: (x + 12)^2 = 177

Step-by-step explanation:

In order to complete the square, you have to take the coefficient of x (24) and cut it in half (12). Then you have to take that number and square it (144). Once you have this, you add it to both sides of the equation.

x^2 + 24x = 33

x^2 + 24x + 144 = 33 + 144

x^2 + 24x + 144 = 177

(x + 12)^2 = 177

The equation is (x + 12)² = 177, which results from completing the square and then factoring the equation x² +24x=33.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

In order to complete the square, you have to take the coefficient of x (24) and cut it in half (12). Then you have to take that number and square it (144). Once you have this, you add it to both sides of the equation.

x² + 24x = 33

x² + 24x + 144 = 33 + 144

x² + 24x + 144 = 177

(x + 12)²= 177

Therefore, the equation is (x + 12)² = 177, which results from completing the square and then factoring the equation x² +24x=33.

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Simplify

10/3

Convert to a mixed fraction

3 1/3

the value of n is 4 because you have to subtract 7n from both sides and then subtract 16 from both sides then the last step is to divide -4 from both sides and you get 4

Answer:

4

Step-by-step explanation:

3n + 16 = 7n is to be solved for n.  Subtract 3n from both sides, obtaining 16 = 4n.

Now divide both sides by 4, obtaining n = 4.

Hello!

To look for squareroots, we need to find a solution for us that can help us solve the problem.

The most common way to solve for a squareroot is by factoring.

If this case, we can see that D. 7.1 is the closest approximation to the root of 51.

Answer: [tex]\angle CAD = 83^\circ [/tex] Option D

Step-by-step explanation:

In this question we use properties of parallelogram and angle sum property of a triangle.

In parallelogram ABCD

[tex] \angle ABC=40^\circ [/tex]

As, we know that opposite angles of parallelogram are equal

Therefore,

[tex] \angle ABC =\angle ADC =40^\circ [/tex]

Now, in triangle ADC

We know that sum of all the angles of a triangle is [tex]=180^\circ[/tex]

[tex]\angle ACD +\angle ADC +\angle DAC =180^\circ[/tex]

[tex]57^\circ +40^\circ +\angle DAC =180^\circ[/tex]

[tex]97^\circ + \angle DAC = 180^\circ [/tex]

Subtracting 97 from both sides we get

[tex] \angle DAC = 180^\circ - 97^\circ [/tex]

[tex] \angle DAC = 83^\circ [/tex]

Measure of [tex]\angle CAD = 83^\circ [/tex]

In a parallelogram, the measure of angle CAD can be found by subtracting the measure of angle ACD from 180°.

In parallelogram ABCD, we have AC as the diagonal. Given that angle ABC is 40° and angle ACD is 57°, we need to find the measure of angle CAD.

In a parallelogram, opposite angles are congruent. So, angle ACD is also equal to 57°.

Now, angle CAD can be found by subtracting angle ACD from 180° (since the sum of the interior angles of a triangle is 180°). So, angle CAD = 180° - 57° = 123°.

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Solving for this equation is 25.

Answer:

49:5

Explanation

Write the quantity of fans in the order of which you are doing the ratio for (TIP - Replace the word "to" with ":") = Football Fans : Hockey Fans = 49:5

The correct ratio of football fans to hockey fans is 49:5 according to the survey results provided, which makes the answer D. 49 to 5.

The survey of sports fans revealed different preferences for various sports. The question asks for the ratio of football fans to hockey fans. According to the survey results provided, 49 people say their favorite sport is football and 5 say it's hockey. Therefore, the ratio of football fans to hockey fans is simply the number of football fans divided by the number of hockey fans.

The calculation would be 49 football fans divided by 5 hockey fans, which simplifies to a ratio of 49:5. Hence, the correct answer is D. 49 to 5. This ratio signifies that for every 5 hockey fans, there are 49 football fans based on the survey results.