y=1/4x+7 y=1/2x+5 The y-coordinate of the solution to the system shown is _____.

Answer:

The correct option is B) zero x = -2.

Step-by-step explanation:

Consider the provided graph y = x + 2

The zeros of a function are the point on which graph intersects the x axis or we can say the value of x when y = 0.

Substitute y = 0 in the provided equation.

0 = x + 2

x = -2

The coordinate is (-2,0). Also the zero of the graph is at x = -2 because it follows the definition of zeros.

Now substitute x = 0 in the provided equation.

y = 0 + 2

y = 2

The coordinate is (0,2).

Now, draw a line passing through the point (-2,0) and (0,2).

The required line is shown in figure 1.

Now consider the provided options only option A and B have the same graph.

But the correct option is B as the zero of the option B is x = -2.

Hence, the correct option is B) zero x = -2.

Explanation of graphing y=x+2 and finding its zero. Find the correct graph and x-intercept.

Graph: First, graph the equation y = x + 2. This is a straight line with a slope of 1 (rise of 1, run of 1) and y-intercept at 2.

Zero of the function: To find the zero of the function (where y = 0), set x + 2 = 0 and solve for x. In this case, x = -2.

[tex]\bf 8n^2-4n+2=5n\implies 8n^2-4n-5n+2=0\implies 8n^2-9n+2=0 \\\\[-0.35em] ~\dotfill\\\\ \qquad \qquad \qquad \textit{discriminant of a quadratic} \\\\\\ \stackrel{\stackrel{a}{\downarrow }}{8}n^2\stackrel{\stackrel{b}{\downarrow }}{-9}n\stackrel{\stackrel{c}{\downarrow }}{+2}=0 ~~~~~~~~ \stackrel{discriminant}{b^2-4ac}= \begin{cases} 0&\textit{one solution}\\ positive&\textit{\underline{two solutions}}\\ negative&\textit{no solution} \end{cases} \\\\\\ (-9)^2-4(8)(2)\implies 81-64\implies 17[/tex]

Answer:

2 real distinct roots.

Step-by-step explanation:

8n^2 - 4n + 2 = 5n

Rearranging to standard form:

8n^2 - 9n + 2 = 0

The discriminant = b^2 - 4ac

= (-9)^2 - 4 * 8 * 2

= 17.

So there will be 2 real distinct roots.

Answer:

0

Step-by-step explanation:

Integers are counting numbers, opposite of counting numbers, and 0.

Answer:

The dimensions of the garden are

Length [tex]25.5\ ft[/tex]  and Width [tex]16.5\ ft[/tex]

Step-by-step explanation:

Let

x----> the length of the rectangular garden

y ---> the width of the rectangular garden

Aw ----> the area of the walkway

we know that

[tex]x=y+9[/tex] ----> equation A

[tex]Aw=(x+8)(y+8)-xy[/tex]

[tex]Aw=400\ ft^{2}[/tex]

so

[tex]400=(x+8)(y+8)-xy\\400=xy+8x+8y+64-xy[/tex]

[tex]400=8x+8y+64[/tex] ----> equation B

Substitute equation A in equation B

[tex]400=8(y+9)+8y+64[/tex]

[tex]400=8y+72+8y+64[/tex]

[tex]400=16y+136[/tex]

[tex]16y=400-136[/tex]

[tex]y=16.5\ ft[/tex]

Find the value of x

[tex]x=16.5+9=25.5\ ft[/tex]

therefore

The dimensions of the garden are

Length [tex]25.5\ ft[/tex]

Width [tex]16.5\ ft[/tex]

Here is your answer in the picture

Answer:

6

Step-by-step explanation:

Divide -12/-2 to get 6.

Simplify -12\div -2−12÷−2 to 66.

Answer:

y = -x - 2.

Step-by-step explanation:

The function rule that describes the patter in the table is: y = -x - 2.

To prove that, we're going to test each given point:

For x= -2 ⇒  y = -(-2) - 2 = 0  ✅

For x = -1 ⇒ y = -(-1) - 2 = -1 ✅

For x = 0 ⇒ y = -(0) - 2 = -2 ✅

For x = 1 ⇒ y = -(1) - 2 = -3 ✅

For x = 2 ⇒ y = -(2) - 2 = -4 ✅

Then, we have just proved that the function rule that describes the patter in table is y = -x - 2

Answer:

See below in bold.

Step-by-step explanation:

The 40 is the adjacent side of the triangle that can be drawn and the 9 is the opposite side.

The hypotenuse =  sqrt (40^2 + 9^2) = 41.

sine = opp/hyp = 9/41 = 0.2195.

cosine = 40/41 = 0.9756.

tangent = 9/40 =0.2250.

cosec = 1/ sine =  41/9 = 4.5556.

secant = 1  / cosine = 41/40 = 1.0250.

cotangent = 1 / tangent =  40/9 = 4.4444.

The decimal forms are  correct to the nearest ten thousandth.

The values of the six trigonometric functions are:

sin θ = 9/41, cos θ = 40/41, tan θ = 9/40, cot θ = 40/9, sec θ = 41/40, cosec θ = 41/9.

The values of all trigonometric functions dependent on the value of the ratio of sides of a right-angled triangle are known as trigonometric ratios. The trigonometric ratios of a right-angled triangle's sides with regard to any of its acute angles are known as that angle's trigonometric ratios.

The three sides of the right-angled triangle are:

Hypotenuse (the longest side)

Perpendicular (opposite side to the angle)

Base (Adjacent side to the angle)

The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

The trigonometry ratios for a specific angle ‘θ’ is given below:

Trigonometric Ratios:

Sin θ =  Perpendicular/Hypotenuse

Cos θ = Base/Hypotenuse

Tan θ = Perpendicular/Base or Sin θ/Cos θ

Cot θ = Base/Perpendicular or 1/tan θ

Sec θ = Hypotenuse/Base or 1/cos θ

Cosec θ = Hypotenuse/Perpendicular or 1/sin θ

According to the Pythagoras theorem, we can say that in a right-angled triangle:

Hypotenuese² = Base² + Perpendicular²

We have to find the six trigonometric functions of an angle in standard position if the point with coordinates (40, 9) lies on its terminal side.

With the angle being θ, we have drawn a figure of the case. (attached)

In the right-angled triangle AOB, with respect to angle θ,

Hypotenuse: AO, Perpendicular: AB, and Base: BO

First we derive the value of AO, using the Pythagoras theorem,

AO² = AB² + BO² = 9² + 40² = 81 + 1600 = 1681 = 41²

∴ AO = 41 units.

Now we find the value of the six trigonometric functions, with respect to the angle θ.

sin θ = Perpendicular/Hypotenuse = AB/AO = 9/41

cos θ = Base/Hypotenuse = BO/AO = 40/41

tan θ = sin θ/cos θ = (9/41)/(40/41) = 9/40

cot θ = 1/tan θ = 1/(9/40) = 40/9

sec θ = 1/cos θ = 1/(40/41) = 41/40

cosec θ = 1/sin θ = 1/(9/40) = 40/9.

∴ The values of the six trigonometric functions are:

sin θ = 9/41, cos θ = 40/41, tan θ = 9/40, cot θ = 40/9, sec θ = 41/40, cosec θ = 41/9.

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Answer:

x=2

Step-by-step explanation:

y = x^2 -4x-8

This is in the form y = ax^2 + bx +c

The axis of symmetry, h is found by h=-b/2a

We know a = 1, b=-4

h = -(-4)/ (2*1)

  =4/2

  =2

The axis of symmetry is x=2

Final answer:

To calculate the area of triangle ABC with sides measuring 8, 11, and 15 units, Heron's formula is used. The semiperimeter s is 17 units, which leads to an area of the square root of 1836 or approximately 42.8 square units.

Explanation:

To find the area of triangle ABC with sides a = 8, b = 11, and c = 15, we can use Heron's formula, which is a method of finding the area of a triangle when you know the lengths of all three sides. The formula states that the area of a triangle is the square root of s(s-a)(s-b)(s-c) where s is the semiperimeter of the triangle, or half of the triangle's perimeter. First, we calculate the semiperimeter: s = (a + b + c) / 2. Then, we substitute the values of a, b, and c into the formula to find the area.

The semiperimeter s is (8 + 11 + 15) / 2 which equals 17. Using Heron's formula, the area is the square root of 17(17-8)(17-11)(17-15). Therefore, the area of triangle ABC is equal to the square root of 17  imes 9  imes 6  imes 2, which simplifies to the square root of 1836, resulting in an area of 42.8 square units.

answer is 2nd equation

30x 6/100x6=180/600

Answer:

19.25 tons = 38500 lbs

Step-by-step explanation:

We are to convert the following given amount of tons in pounds.

We know that, 1 ton = 2000 pounds. So using the ration method, we can convert 19.25 tons into pounds.

[tex]\frac{1 ton}{19.25 tons} =\frac{2000 lbs}{x}[/tex]

[tex] x = 2 0 0 0 \times 1 9 . 2 5 [/tex]

[tex] x = 3 8 5 0 0 lbs[/tex]

Therefore, 19.25 tons = 38500 lbs.

Answer: [tex]38,500\ lbs[/tex]

Step-by-step explanation:

In order to answer the question, it is necessary to make the corresponding conversion from 19.29 tons (t) to pounds (lbs).

Then, for this conversion it is important to remember that:

[tex]1\ t=2,000\ lbs[/tex]

Finally, knowing this, you can make the conversion:

[tex](19.25\ t)(\frac{2,000\ lbs}{1\ t})=38,500\ lbs[/tex]

Therefore, you get this result:

[tex]19.25\ t=38,500\ lbs[/tex]

Answer:

A. 1/x = 2/6

Step-by-step explanation:

Given the sides of the smaller parallelogram:

1 in and 2 in

Given the sides of the bigger parallelogram:

x in and 6 in

By Comparison of similar sides

I.e. the slant sides (1in and x in) and the base (2in and 6in) of both parallelogram.

1/x = 2/6

Hence, the scale factor proportion for the enlargement is 1/x = 2/6.

Solving further to get the value of x

Simplify both sides

1/x = ⅓

Multiply both sides by x

1/x * x = ⅓ * x

1 = ⅓x

Multiply both sides by 3

1 * 3 = ⅓x * 3

3 = x

So x = 3 in

Answer:

A. 1/x = 2/6

Step-by-step explanation:

Answer:

D=[tex]\sqrt{(147-30\sqrt{10}}[/tex]

Step-by-step explanation:

Here we are required to find the distance between two coordinates. We will use the distance formula to find the distance

The distance formula is given as

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

Here we are given two coordinates as

[tex](6,5\sqrt{5} ) , (4,3\sqrt{2} )[/tex]

Substituting these values in the Distance formula given above we get

[tex]D=\sqrt{(6-4)^2+(5\sqrt{5} -3\sqrt{2}) ^2}[/tex]

[tex]D=\sqrt{(2)^2+(5\sqrt{5})^2+(3\sqrt{2})^2-2*5\sqrt{5}*3\sqrt{2}}\\[/tex]

[tex]D=\sqrt{4+125+18-2*15\sqrt{10}}\\D=\sqrt{147-30\sqrt{10}}\\[/tex]

Hence this is our answer

answer :

2 square of 3 is the answer

step-by-step explanation :

[tex]\sqrt({x} _{2} - x_{1})^{2} + (y_{2} - y_{1})^{2} \\\\\sqrt({4} - 6})^{2} + (3\sqrt{2} - 5\sqrt{2} )^{2} \\\\= \sqrt(-2})^{2} + (-2\sqrt{2} )^{2} \\\\\\= \sqrt4 + 8 \\\\\\\\\\= \sqrt12 \\\\\\\\= 2\sqrt{3}[/tex]

Final answer:

To find the sum of one gross, a quarter of a dozen, and two scores, you add 144 (one gross), 3 (a quarter of a dozen), and 40 (two scores) to get a total of 187.

Explanation:

The sum of one gross, a quarter of a dozen, and two scores can be calculated as follows:

One gross = 144

A quarter of a dozen = 3

Two scores = 40

Therefore, the sum = 144 + 3 + 40 = 187

Answer: 187

Step-by-step explanation:

First, we need to define what these words mean numerically.

      One gross = 144

      A quarter of a dozen = 12/4 = 3

      Two scores = 2 * 20 = 40

Now, we can find the sum of one gross, a quarter of a dozen, and two scores. Sum means addition.

      144 + 3 + 40 = 187

Answer:

Dist = 45 m/h * x h

Step-by-step explanation:

We know a speed is a measure of distance over time:  speed = dist / time

In this case, we are looking for a distance expressed in terms of time.

So, we only need to modify the formula a bit: dist = speed * time

We don't know the time (which will be a variable), but we know their speed.  So, the formula becomes:

Dist = 45 m/h * x h

Enter the number of hours in the formula and that will give you an approximation of the distance traveled within that time (approximation since our result will be rely on an average).

Answer:

Beena = 19 years old

Seema = 28 years old

Step-by-step explanation:

Beena = x

Seema = x + 9

x + 9 + 10 = 2x

19 + x = 2x

2x - x = 19

x = 19

Answer:

y = -2x + 1

Step-by-step explanation:

Then any equation of the form y = -2x + b, b≠1 will create a system with no solution.  Hence the values of m and b are m = -2, b ≠ 1.

hope i helped

Answer:

Option B and E

Step-by-step explanation:

As we know a system of two parallel lines has no solution.

In other words two lines having same slope will have no solution.

In this question equation of one line is

y = -2x + b

So another line having same slope (-2) will have no solution.

Option B and E are the correct options.

The value of n and the distance from Point B to Point C cannot be determined without specific coordinates for these points. Given that B is the midpoint between points A and C, the x-coordinate for Point B should be n/2. The distance between the points would be calculated using the distance formula derived from the Pythagorean Theorem.

To calculate the distance between points in a graph, we typically use the distance formula, which is derived from the Pythagorean Theorem. From our given information, Point A lies on the y-axis and has the same y-coordinate as Point B. Point C is graphed at (n, -3). Given that the distance is the same from Point B to both points A and C, this implies that Point B is the midpoint between Points A and C. The coordinates of the midpoint are obtained by averaging the x and y coordinates of the two points. Therefore, the x-coordinate of Point B must be n/2.

The distance from Point B to Point C (or similarly to Point A) can be obtained using the distance formula: sqrt((x2−x1)² + (y2−y1)²), where x1, y1 are the coordinates of one point and x2, y2 are the coordinates of the other point.

However, without concrete values for some of these points in the given equation, we cannot provide a specific numerical value for the distance or n. This calculation depends specifically on the placement of the points on the graph.

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1. Only constraint 2 would be met if 18 pairs of leather boots and 36 pairs of running  shoes were ordered.

2. Only constraint 1 would be met if 12 pairs of leather boots and 36 pairs of running shoes were ordered.

Data and Calculations:

Total pairs of shoes required = 48 pairs

Running shoes required (r) = 2 of leather boots

Leather boots required (b)= 1/2 of running shoes

Constraint 1:

The total pairs of different shoes required:

Running shoes = 32r

Leather boots = 16b

Total pairs = 32r + 16b = 48

Constraint 2:

Ratio equation:

Running shoes = 2r

Leather boots = b

Equation = 2r + b = 48

Thus, Constraint 2 satisfies the first order, while Constraint 1 satisfies the second order. The two constraints do not satisfy the two orders.

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Amanda needs 48 pairs of shoes total, with twice as many running shoes as leather boots. Constraint 1 is x + y = 48, and constraint 2 is y = 2x. An order of 18 boots and 36 running shoes meets only constraint 2, while 12 boots and 36 running shoes meet both constraints.

Amanda needs to order a total of 48 pairs of shoes, with twice as many pairs of running shoes as leather boots. To set up the equations, let x represent the number of pairs of leather boots and y represent the number of pairs of running shoes.

Constraint 1:

The total number of pairs of shoes:

x + y = 48

Constraint 2:

The ratio of the number of running shoes to leather boots:

y = 2x

To check which constraints are met by given orders:

1. For 18 pairs of leather boots (x = 18) and 36 pairs of running shoes (y = 36):

Using constraint 1: 18 + 36 = 54. This does not meet constraint 1.

Using constraint 2: 36 = 2(18). This meets constraint 2.

2. For 12 pairs of leather boots (x = 12) and 36 pairs of running shoes (y = 36):

Using constraint 1: 12 + 36 = 48. This meets constraint 1.

Using constraint 2: 36 = 2(12). This meets constraint 2.

Find the volume of a cylinder, we need to follow the formula:

Volume = πr2h

Following the formula, we substitute for:

π×82×10

π=3.14, so we multiply it:

= 640π

= 2010.6192982975 feet3

To identify geometric figures in a diagram, know the definitions and characteristics of each shape like a circle, triangle, and rectangle. By recognizing these characteristics, you can determine which shapes are in the diagram.

In order to identify which geometric figures are drawn in a diagram, you need to know the basic definitions and characteristics of geometric shapes. For instance, a circle is a figure in which all points are equidistant from a single point in the center. A triangle is a figure formed by three straight lines. A rectangle has four sides and all the angles are right angles. A square is a special type of rectangle where all four sides are equal. By identifying these various characteristics, you can determine which geometric shapes are represented in the diagram.

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Answer:

19600

Step-by-step explanation:

140 squared = 140 x 140 = 19600

Answer:

ALL REAL NUMBERS

Step-by-step explanation:

Any quadratic function is ALWAYS R.

9+1/2x=35

x=52

hope this helps

Answer:

Option A is correct i.e 2R2+R3 -> R3

Step-by-step explanation:

The given matrix is:

[tex]\left[\begin{array}{ccc}-4&1&2&4\\0&-1&3&1\\3&2&4&5\end{array}\right][/tex]

If we perform the operation 2R2 + R3 we get the result given i.e

[tex]\left[\begin{array}{cccc}-4&1&2&4\\0&-1&3&1\\3&0&10&7\end{array}\right][/tex]

The operations performed are:

2R2 i.e. we multiply the row 2 with 2

we get 0  -2  6  2

now add it with row 3

0  -2   6   2

3   2   4   5

___________

3  0   10    7

So, Option A is correct i.e 2R2+R3 -> R3

Answer:

x = 10

Step-by-step explanation:

The axis of symmetry is the vertical line that passes through the vertex.  We can readily see that the x-coordinate of the vertex is 10.

Therefore, the axis of symmetry here is x = 10.

Answer:

The line will be going 'uphill' from left to right

Step-by-step explanation:

we know that

The equation of the line into slope intercept form is equal to

y=mx+b

where m is the slope

b is the y-intercept

If the coefficient of the x-term is positive

then

the slope is positive

therefore

If the values of x increases, the values of y increases

If the values of x decreases, the values of y decreases

The line will be going 'uphill' from left to right

Answer: the line slants up

Step-by-step explanation:

X being positive will cause a “ rise “ in the positive x,y plane.

Answer:

1. Option C is correct

2. Option A is correct

3. Option C is correct

4. Option B is correct

5. Option D is correct

Step-by-step explanation:

1. x^2-3x-18/x+3

Factorize the numerator

x^2-6x+3x-18/x+3

x(x-6)+3(x-6)/x+3

(x+3)(x-6)/x+3

x-6

x-6 where x≠6

Option C is correct.

2. x-2/x^2+4x-12

Factorizing the denominator

x-2/x^2+6x-2x-12

x-2/x(x+6)-2(x+6)

x-2/(x-2)(x+6)

1/x+6

1/x+6 where x≠-6

Option A is correct.

3. 5x^3/7 x^3+x^4

5x^3/7x^3+x^4

5x^3/x^3(7+x)

5/7+x

Option C is correct

5/7+x where x≠-7

4. Simplify x/6x-x^2

x/6x-x^2

x/x(6-x)

1/6-x

Option B is correct

1/6-x where x≠6

5. 2/3a * 2/a^2

Multiplying both terms

4/3a^3

Option D is correct.

4/3a^3 where a≠0

Answer:

4x^2 - 12x + 9

Step-by-step explanation:

Please use " ^ " to denote exponentiation:  4x^2 - 12x + 9.

This 4x^2 - 12x + 9 factors into (2x - 3)^2, and is thus a perfect square trinomial.

The polynomial [tex]4x^2-12x + 9[/tex] is a perfect square trinomial. It has a binomial factor (2x - 3).

The product of a binomial by itself gives the perfect square trinomial.

A trinomial is a polynomial that has only three terms and A binomial is a polynomial that has only two terms.

A. Trinomial  [tex]4x^2-12x+9[/tex]

⇒ [tex](2x)^2-2(2x)(3)+(3)^2[/tex]

This is in the form of [tex]a^2-2ab+b^2[/tex] . So, we can write [tex](a - b)^2[/tex]

⇒ [tex](2x - 3)^2[/tex] or (2x - 3)(2x - 3)

Thus, this is a perfect square trinomial.

B. Trinomial [tex]16x^2+24x-9[/tex]

⇒ [tex](4x)^2+2(4x)(3)-(3)^2[/tex]

Since it cannot split into a binomial square, this trinomial is not a perfect square trinomial.

C. Trinomial [tex]4a^2-10a+25[/tex]

⇒ (2a)^2-2(5a)+(5)^2

This cannot be split into a binomial square, this is not a perfect square trinomial.

D. Trinomial [tex]36b^2-24b-16[/tex]

⇒ [tex](6b)^2-2(6b)(2)-(4)^2[/tex]

So, this is not a perfect square trinomial.

Therefore, the trinomial at option A is a perfect square trinomial.

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Answer:

for value 36

c makes the perfect square

x2 - 12x +36

= x2 - 2*6x +6^2

= (x-6)^2 #

Answer:  The required value of c is 36.

Step-by-step explanation:  We are given to find the value of c so that the following expression becomes a perfect square trinomial :

[tex]E=x^2-12x+c~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

To find the value of c, we proceed as follows :

[tex]E\\\\=x^2-12x+c\\\\=(x^2-2\times x\times6+6^2)+c-6^2\\\\=(x-6)^2+c-36.[/tex]

So, for E to be a perfect square trinomial, we must have

[tex]c-36=0\\\\\Righatrrow c=36.[/tex]

Thus, the required value of c is 36.