What is the solution to the system of equations below?



y= -1/3 and x = –6

Answer:

A

Step-by-step explanation:

Consecutive nnumbers are spaced 1 units apart.

Such as 4,5,6,...

or 12,13,14,...

Thus,

if smaller number is n, then the next number (consecutive) is n+1

Since, half of the product of them is 105, we can write the equation as:

[tex]\frac{1}{2}((n)(n+1))=105[/tex]

We can do some algebra and make it in quadratic form as shown below:

[tex]\frac{1}{2}((n)(n+1))=105\\\frac{1}{2}(n^2 + n)=105\\n^2+n=2*105\\n^2+n=210\\n^2+n-210=0[/tex]

Answer choice A is right.

Answer:

A.) n^2 + n – 210 = 0

Step-by-step explanation:

just took edg 2022. hope this helps!

A tangent line will have a couple of characteristics:

Substituting for x in the equation of the circle, we have ...

  (2y+5)^2 +y^2 = 5

  5y^2 +20y +20 = 0 . . . . simplify, subtract 5

  5(y +2)^2 = 0 . . . . . . . . . factor

This equation has exactly one solution, at y = -2. The corresponding value of x is ...

  x = 2(-2) +5 = 1

So, the line intersects the circle in exactly one point: (1, -2).

__

The center of the circle is (0, 0), so the line through the center and point of intersection is ...

  y = -2x . . . . . . . . . slope is -2

The tangent line is ...

  y = 1/2x -5/2 . . . . . . slope is 1/2

The product of slopes of these lines is (-2)(1/2) = -1, indicating the lines are perpendicular.

__

We have shown ...

Hello There!

We know that the formula of a triangle is "Base Multiplied By Height And Then Divide It By 2"

First, let's plug in our numbers. Our base is going to be 10 inches so we have 10 multiplied by our height which is 14 inches and we get a product of 140.

Next, we divide 140 by 2 to get a quotient of 70.

Finally, our answer is 70in squared

Answer:

5

Step-by-step explanation:

Answer:

[tex]z =3\sqrt{13}[/tex]

Step-by-step explanation:

In the figure you can identify up to 3 straight triangles.

To solve the problem, write the Pythagorean theorem for each triangle.

Triangle 1

[tex]13^2 = z^2 + x^2[/tex]

Triangle 2

[tex]z^2 = y^2 + 9^2[/tex]

Triangle 3

[tex]x^2 = y^2 + 4^2[/tex]

Now substitute equation 2 and equation 3 in equation 1 and solve for y.

[tex]13^2 = y^2 + 9^2 + y^2 + 4^2[/tex]

[tex]13^2 = 2y^2 + 9^2 + 4^2[/tex]

[tex]169 = 2y^2 + 81 + 16[/tex]

[tex]2y^2 =72[/tex]

[tex]y^2 =36[/tex]

[tex]y =6[/tex]

substitute the value of y in the second equation and solve for z

[tex]z^2 = 6^2 + 9^2[/tex]

[tex]z^2 = 36 + 81[/tex]

[tex]z^2 = 117[/tex]

[tex]z = \sqrt{117}[/tex]

[tex]z =3\sqrt{13}[/tex]

For this case we have that the total of objects is given by:

Large blue objects, small blue objects, large red objects and small red objects.

In total we have: [tex]17 + 3 + 8 + 12 = 4[/tex]0 objects.

If we want to find the probality of obtaining small and blue objects we have to:

[tex]p = \frac {3} {40}[/tex]

ANswer:

[tex]p = \frac {3} {40}[/tex]

Answer:

  TUW ~ UTV, TWV ~ UVW

Step-by-step explanation:

An isosceles trapezoid is symmetrical about the perpendicular bisector of its bases. A triangle formed by deleting a vertex on one side of that line of symmetry will be similar to the corresponding triangle formed by deleting the symmetrically opposite vertex on the other side. The two pairs listed above are the possibilities.

Answer:

  B. Place the compass on the point of intersection and mark an arc through the transversal and y-axis

Step-by-step explanation:

Creating a parallel line through a point involves copying the angle a transversal makes with the given line. The copied angle has the given point as its vertex, and the transversal as one side.

Copying an angle uses the steps of ...

The step this question is referring to is the first bullet above. The given angle is the angle between the transversal and the y-axis.

Answer:

  the two signs are the same

Step-by-step explanation:

Whenever the quotient or product of two operands is positive, the signs of the operands are both the same, both negative or both positive.

__

Comment on the general case

Whenever the product of any number of operands is positive, the number of negative signs among the factors is even.

A quotient is the product of one operand and the reciprocal of another (the denominator). A number and its reciprocal have the same sign.

Answer:

The total number of points you score is dependent variable Because it change when x is change.

The number of question you answer correctly is independent variable Because it can change itself when you got more correct answers.

Answer:

The function y= sec(x-2)+2 is shifted two units to the right and 2 units upwards., compared to y=sex(x).

Step-by-step explanation:

To solve this problem we need to know the rules for translation of graphs:

Given the function y = f(x):

In this case, our main function is y=sec(x). And the function y= sec(x-2)+2 is shifted two units to the right and 2 units upwards.

Answer:

D. it is shifted two units up and two units right

Step-by-step explanation:

this is the correct answer on ed-genuity, hope this helps! :)

Answer:

2r (1 + √3)

Step-by-step explanation:

Circle O₁ is tangent to AB.  Let's call the point of intersection point D.  If we draw a radius from the center O₁ to D, we know this forms a right angle.

△ABC is an equilateral triangle, so we know m∠A = 60°.  If we draw a line from A to O₁, we know that bisects the angle, so m∠DAO₁ = 30°.

So △DAO₁ is a 30-60-90 triangle.  We can find the length AD:

AD = r √3

Now on the other side, circle O₃ is tangent to AB.  Let's call the point of intersection point E.  We know it's the same triangle we found earlier, so:

EB = r √3

And finally, we can draw a rectangle connecting O₁, O₃, E, and D.  The distance between O₁ and O₃ is 2r, so:

DE = 2r.

Therefore:

AB = r√3 + 2r + r√3

AB = 2r√3 + 2r

AB = 2r (1 + √3)

Here's a graph showing the steps.  Hopefully this helps, let me know if you have questions!

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Answer:

  d.  1/4

Step-by-step explanation:

The ratio of adjacent terms is the common ratio:

  (3/12)/(3/3) = 3/12 = 1/4

Answer: 1/8

Step-by-step explanation:

First Bag   and      Second Bag

[tex]\dfrac{3\ blue}{8\ total}[/tex]        x            [tex]\dfrac{2\ blue}{6\ total}[/tex]        =  [tex]\dfrac{6}{48}[/tex]

which reduces to [tex]\boxed{\dfrac{1}{8}}[/tex]

Answer:

6

Step-by-step explanation:

The opposite of squaring a number is taking the square root. They are inverse operations.

The opposite of squaring a number is taking the square root of the number. They are inverse operations.

A perfect square is a number system that can be expressed as the

square of a given number from the same system.

Perfect squares are those integers whose square root is an integer.

Let x-a be the closest perfect square less than x,

Let x-a be the closest perfect square less than x, and let x+b be the closest perfect square more than x, then we get x-a < x < x+b (no perfect square in between x-a and x+b, except possibly x itself).

Then, we get:

[tex]\sqrt{x-a} < \sqrt{x} < \sqrt{x+b}[/tex]

Thus, these are the closest integers, less than and more than the value of[tex]\sqrt{x}[/tex]. (assuming x is a non-negative value).

The opposite of squaring a number is taking the square root of the number. They are inverse operations.

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Answer:

She got a 87 on her chemistry test

Step-by-step explanation:

(72 + 85 + 92 + x)/4 = 84

249 + x = 336

x = 87

Answer:

Correct me if I am wrong, but I believe it is B.

Step-by-step explanation:

Answer:

C. 28

Step-by-step explanation:

From the diagram diagram; [tex]\angle BAC=(x+6)\degree[/tex] and [tex]\angle ABD=2x\degree[/tex].

The pair of co-interior angles are [tex]\angle BAD[/tex] and [tex]\angle ABC[/tex].

Also the diagonals of a rhombus bisect corner angles.

This implies that:

[tex]\angle BAD=2(\angle BAC)\implies \angle BAD=2(x+6)\degree[/tex].

[tex]\angle ABC=2(\angle ABD)\implies \angle ABC=2(2x)\degree[/tex].

The co-interior angles are supplementary  so we form the equation:

[tex]\angle BAD+\angle ABC=180\degree[/tex]

[tex]\implies 2(x+6)\degree+2(2x)\degree=180\degree[/tex]

Expand the parenthesis to get:

[tex]\implies 2x+12+4x=180\degree[/tex]

Group the similar terms:

[tex]\implies 2x+4x=180-12[/tex]

Simplify

[tex]\implies 6x=168[/tex]

Divide both sides by 6.

[tex]\implies \frac{6x}{6}=\frac{168}{6}[/tex]

[tex]\therefore x=28[/tex]

The correct answer is C.

Answer:

  3.  15 units

Step-by-step explanation:

When medians intersect, the point of intersection divides the median into parts in the ratio 2:1. That is ...

  OC : CR = 2 : 1 = 4 units : 2 units . . . . . . OR = (4+2) units = 6 units

  MC : CT = 2 : 1 = 6 units : 3 units . . . . . . MT = (6+3) units = 9 units

The sum of lengths OR + MT is ...

  6 units + 9 units = 15 units

The given question is incomplete. Without information about dimensions or additional information of the triangle or the lines, we cannot solve for lengths.

Unfortunately, the question is incomplete, so it is impossible to answer it accurately. In the given situation, we have a triangle △MNO and points R and T are the midpoints of their respective sides. The lines MT and OR intersect at a point C. However, without explicit dimensions or additional information about the triangle or the lines, we cannot determine the length of any line segment. In geometry problems like this, it's crucial to have a complete set of given information before proceeding with the solution.

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The inequality used in this situation will be 14x + 58 < 150.

The word inequality means a mathematical expression in which the sides are not equal to each other.

Let the no. of T-shirts Lisa can buy be = X

Cost of each T-shirt = $14

No. of jeans she bought = 1

Cost of jeans = $58

Total money she has = $150

Hence, the inequality will be 14X + 58 < 150.

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Lisa can spend a maximum of $92 on T-shirts after buying jeans, and with each T-shirt costing $14, she can buy up to 6 T-shirts as represented by the inequality 14t <= $92, where t is the number of T-shirts.

To create an inequality representing the number of T-shirts Lisa can purchase, let's define the variable t to represent the number of T-shirts. Lisa has $150 to spend, and she wants to buy a pair of jeans for $58, leaving $150 - $58 = $92 for T-shirts. Each T-shirt costs $14, so if Lisa buys t T-shirts, the cost for the T-shirts is 14t. The inequality to represent the maximum number of T-shirts Lisa can buy is 14t ≤ $92.

Now, to solve for t, we divide both sides of the inequality by 14: t ≤ $92 / $14, which simplifies to t ≤ 6.57. Since Lisa cannot buy a fraction of a T-shirt, the maximum number of T-shirts she can buy is 6.

Answer:

19 minutes

Step-by-step explanation:

cost = .45+.36m

If we take 6.93 minus .45 for the minute, we get 6.48. We take 6.48 and divide it by .36 for each additional minute, which is 18. We take the 18 and add one more minute to it since .45 was covered for the first minute.

The long-distance phone call that cost $6.93 was 19 minutes long. This was calculated by first deducting the cost of the first minute from the total cost, then dividing the remaining cost by the cost of each additional minute, and finally adding back the first minute.

The subject of this question is mathematics, and it involves understanding the cost structure of a long-distance phone call. So here's how we solve the problem:

Therefore, the duration of the long-distance phone call that cost $6.93 was 19 minutes.

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Answer:

The measure of arc DEF is 204° ⇒ answer C

Step-by-step explanation:

* Lets talk about some facts in the circle

- If the vertex of an angle on the circle and the two sides of the

 angle are chords in the circle, then this angle is called  

 an inscribed angle

- Each inscribed angle subtended by the opposite arc, the arc name

 is the starting point and the ending point of the angle

- The measure of any circle is 360°

# Ex: ∠CAB is inscribed angle subtended by arc CB

- There is a relation between the inscribed angle and its  

  subtended arc, the measure of the inscribed angle equals half

  the measure of its subtended arc

* Now lets solve the problem

- ∠DEF is an inscribed angle subtended by arc DF

∴ m∠DEF = (1/2) measure of arc DF

∵ The measure of ∠DEF = 78°

∴ 78° = (1/2) measure of arc DF ⇒ multiply both sides by 2

∴ The measure of arc DF = 78° × 2 = 156°

∵ The measure of arc DF + The measure of arc DEF = The measure of

   the circle

∵ The measure of the circle = 360°

∵ The measure of the arc DF = 156°

∴ 156° + measure of arc DEF = 360° ⇒ subtract 156 from both sides

∴ The measure of arc DEF = 360° - 156° = 204°

* The measure of arc DEF is 204°

Answer: OPTION C.

Step-by-step explanation:

By definition:

[tex]Inscribed\ Angle = \frac{1}{2} Intercepted\ Arc[/tex]

Then we can calculate the measure of DF. This is:

[tex]78\°=\frac{1}{2}DF\\\\DF=(2)(78\°)\\\\DF=156\°[/tex]

We know that there are 360 degrees in a circle, therefore, in order to find the measure of DEF, we need to make the following subtraction:

[tex]DE[/tex][tex]F[/tex][tex]=360\°-156\°[/tex]

[tex]DE[/tex][tex]F[/tex][tex]=204\°[/tex]

 You can observe that this matches with the option C.

Answer:

Missing side=25 units.

Area of the figure= 470 sq units.

Step-by-step explanation:

The figure is made up of a rectangle and a triangle.

To get the base of the triangle, we find the difference between the two parallel sides, that is, 16ft and 31 ft.

31ft-16ft=15ft  

The height of the triangle is 20 since it is parallel and equal to the length of the rectangle.

We therefore use pythagoras theorem to find ?

a²+b²=c²

15²+20²=c²

625=c²

c=25

ii. The figure is a trapezium therefore we use the following formula to find the area.

A= 1/2(a+b)h, where a and b are the two parallel sides. and h the distance between them.

=(1/2)(31+16)×20

=470 sq units

Answer: 614° and -106°

Step-by-step explanation:

You have this angle in degrees:

254°

Then, in order to find  the measure of a positive angle conterminal with the given angle in degrees (254°), you need to add  360 degrees. Therefore, the measure of the positive angle is:

[tex]254\°+360\°=614\°[/tex]

Now, to find the measure of a negative angle coterminal with the given angle in degrees (254°), you need to subtract  360 degrees. Therefore, this is:

[tex]254\°-360\°=-106\°[/tex]

Answer:  c

Step-by-step explanation:

Notice the pattern (vowel, consonant, vowel, consonant):

A: first vowel            z: last consonant

e: second vowel                                        b: first consonant      

i: third vowel             y: second to the last consonant

o: fourth vowel                                           c: second consonant

Answer:

  -4x² +6x⁴y

Step-by-step explanation:

Deal with it term by term, factor by factor.

[tex]\dfrac{48x^4y-72x^6y^2}{-12x^2y}=\dfrac{48x^4y}{-12x^2y}+\dfrac{-72x^6y^2}{-12x^2y}\\\\=\dfrac{48}{-12}\cdot\dfrac{x^4}{x^2}\cdot\dfrac{y}{y}+\dfrac{-72}{-12}\cdot\dfrac{x^6}{x^2}\cdot\dfrac{y^2}{y}=-4x^2+6x^4y[/tex]

Final answer:

To divide the binomial by the monomial, divide each term's coefficients and subtract their exponents, resulting in the quotient [tex]-4x^2 + 6x^4y[/tex].

Explanation:

To divide the given binomial by the monomial, we divide each term in the numerator by the term in the denominator. In this case, we need to divide both terms of the binomial [tex]48x^4y - 72x^6y^2[/tex] by the monomial[tex]-12x^2y[/tex]. This involves dividing the coefficients (the numbers in front of the variables) and subtracting the exponents for like bases according to the rules of division of exponentials.

Starting with the first term:

[tex]\frac{48x^4y}{ -12x^2y} = -4x^{(4-2)}y^{(1-1)} = -4x^2y^0 = -4x^2[/tex]

Now the second term:

[tex]\frac{-72x^6y^2}{-12x^2y } = 6x^{(6-2)}y^{(2-1)} = 6x^4y[/tex]

The final quotient of dividing the binomial by the monomial is:

[tex]-4x^2 + 6x^4y[/tex]

The figure is attached to show the shapes Ben could have drawn

He could have drawn  2 four angled polygon , 1 triangle and  1 pentagon , 2 triangles .

The shapes which lie on two coordinate axis and has length ,and breadth are called Two dimensional shapes.

A polygon is included in two dimensional shapes.

It is given in the question that

Ben drew 3 two-dimensional shapes that had 11 angles in all.

11 angles mean

2 quadrilaterals ( rectangle , square , rhombus etc.) and a triangle

A figure is attached  for the above stated answer .

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The volume of a pyramid is one-third of the volume of a prism with the same base area and height, yielding the formula V = (1/3)Bh for the volume of a pyramid.

When comparing the volume of a prism and a pyramid with the same base and height, the volume of a pyramid is one-third of the volume of the prism. Therefore, the formula for the volume of a prism is V = Bh, where B is the base area and h is the height. Applying this to the pyramid, the pyramid's volume becomes V = (1/3)Bh. This formula tells us that the volume of a pyramid is equal to one-third of the product of the area of its base and its height.

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Answer:

[tex]x\geq 29,000[/tex]  and  [tex]x\leq 41,000[/tex]

Step-by-step explanation:

Let

x -----> the altitude of a commercial aircraft

we know that

The expression " A minimum altitude of 29,000 feet" is equal to

[tex]x\geq 29,000[/tex]

All real numbers greater than or equal to 29,000 ft

The expression " A maximum altitude of 41,000 feet" is equal to

[tex]x\leq 41,000[/tex]

All real numbers less than or equal to 41,000 ft

therefore

The compound inequality is equal to

[tex]x\geq 29,000[/tex]  and  [tex]x\leq 41,000[/tex]

All real numbers greater than or equal to 29,000 ft and less than or equal to 41,000 ft

The solution is the interval ------> [29,000,41,000]

option 1 : x ≥ 29,000 and x ≤ 41,000 represents the most fuel-efficient altitudes using compound inequality.

We need to identify the correct compound inequality describing the altitude at which the aircraft operates most efficiently. The best fuel efficiency altitudes range from 29,000 ft to 41,000 ft, meaning the altitude must be at least 29,000 ft and at most 41,000 ft.

So, to represent that the altitude must be at least 29000 ft we use the mathematical expression:

[tex]x\geq 29,000[/tex]

To represent that the altitude must be 41000 ft at most we use the mathematical expression:

[tex]x\leq 41,000[/tex]

These two expression can be represented as a compound inequality as follows:

[tex]x\geq 29,000\[/tex] and [tex]x\leq 41,000[/tex]

Therefore, option 1 : x ≥ 29,000 and x ≤ 41,000 represents the most fuel-efficient altitudes using a compound inequality.

[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ X(\stackrel{x_1}{x}~,~\stackrel{y_1}{y})\qquad Z(\stackrel{x_2}{11}~,~\stackrel{y_2}{-5}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{11+x}{2}~~,~~\cfrac{-5+y}{2} \right)=\stackrel{\stackrel{midpoint}{y}}{(3,-1)}\implies \begin{cases} \cfrac{11+x}{2}=3\\[1em] 11+x=6\\ \boxed{x=-5}\\ \cline{1-1} \cfrac{-5+y}{2}=-1\\[1em] -5+y=-2\\ \boxed{y=3} \end{cases}[/tex]

We define midpoint formula as

[tex]Y(x_m, y_m)=Y(\dfrac{x_2+x_1}{2}, \dfrac{y_2+y_1}{2})[/tex]

Also here are the coordinates of every point in variables so you won't get confused.

[tex]

Y(x_m, y_m) \\

X(x_1, y_1) \\

Z(x_2, y_2)

[/tex]

Which means there are two equations. One to find x of point X and one to find y of point X.

[tex]

x_m=\dfrac{x_2+x_1}{2}\Longrightarrow 3=\dfrac{11+x_1}{2} \\

6=11+x_1\Longrightarrow\underline{x_1=-5} \\ \\

y_m=\dfrac{y_2+y_1}{2}\Longrightarrow-1=\dfrac{-5+y_1}{2} \\

-2=-5+y_1\Longrightarrow\underline{y_1=3}

[/tex]

So point X has coordinates: [tex]\boxed{X(-5, 3)}[/tex]

Hope this helps.

r3t40