-3y + 2x = -7
8x - 3y = -1

Answer: x has no solutions, y has no solutions

Step-by-step explanation:

y = x² - 3

x - y = 1

x - x² - 3 = 1

- x² - x - 3 = 1

- x² - x - 4 = 0

- x² - x - 16/4 = 0

- x² - x - 1/4 - 15/4 = 0

- (x² + x + 1/4) - 15/4 = 0

- (x+1/2)^2 - 15/4 = 0

- (x+1/2)^2 = 15/4

(x+1/2)^2 = -15/4 ==> x has no solutions, y has no solutions

any number to an even power, in this case to the power of 2, has to be positive, but -15/4 is negative.

Answer:

a) two parallel lines

Step-by-step explanation:

Two parallel lines have the same slope

Let's take a concrete example:
y = 2x + 4        (slope =2, y-intercept = 4)
y = 2x + 10      (slope = 2, y-intercept = 10)

Lines are parallel to each other

If you try to solve this equation you get

2x + 4 = 2x + 10

Subtracting 2x on both sides gives you  the identity 4 = 10 (a contradiction)

This means the 2 line equations are inconsistent

The equation of the circle (x + 3)^2 + (y - 5)^2 = 81 has a radius of 9 and a center located at (3 , 5).

The standard form of the equation of  circle is given by

(x - h)^2 + (y - k)^2 = r^2

where (h , k) is the location of the center and r is the radius of the circle.

On the other hand, the general form of the equation of  circle is given by

x^2 + y^2 + Dx + Ey + F = 0

where D = -2h, E = -2k, and F = h^2 + k^2 -r^2.

If the equation of the circle, (x + 3)^2 + (y - 5)^2 = 81, is in standard form, then

h = -3

k = 5

r = 9

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The explicit relation between x and y in the form is (x2)2+(y2)2=sin2+cos2.

Given that x=2sin, y=2cos, and 0 are constants,

Simplify the parametric functions that are presented. Add their squares after taking them. The following trigonometric identity can be used:

sin2θ+cos2θ=1sin2⁡θ+cos2⁡θ=1

x=2sinθ,

y=2cosθ,0≤θ≤2πsinθ

=x2cosθ,

=y2x

Y=2sin⁡θ,

y=2cos⁡θ,0≤θ≤2πsin⁡θ=x2cos⁡θ=y2

Square them now and add them:

(Using the trigonometric identity sin2+cos2=1)x24+y24=1, where (x2)2+(y2)2=sin2+cos2)

(Using the trigonometric identity sin2+cos2=1)x24+y24=1, where (x2)2+(y2)2=sin2+cos2)

A parameter in a parametric equation can stand in for anything, including an angle. When a parameter is an angle—as opposed to a non-angle parameter—the plane curve can be graphed by choosing values for the angle and computing the x- and y-values.

Hence, the explicit relation between x and y in the form is (x2)2+(y2)2=sin2+cos2.

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The equation of the line parallel to the first line is y = 3 · x - 9. (Correct choice: B)

In this question we must derive the equation of the line for a given street and look for another equation of the line parallel to the previous one. Lines are first order polynomials of the form y = m · x + b, where m and b are the slope and the y-intercept, respectively.

Now we present the procedure in detail. First, find the equation of the first line:

5 = 4 · m₁ + b₁           (1)

2 = 3 · m₁ + b₁          (2)

(m₁, b₁) = (3, - 7)

Second, determine the equation of the line parallel to the line found in the previous step: (Please notice that two lines are parallel to each other when they share the same slope but have different y-intercepts)

- 3 = 3 · 2 + b₂

b₂ = -3 - 6

b₂ = - 9

The equation of the line parallel to the first line is y = 3 · x - 9. (Correct choice: B)

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Answer: The correct answer is B

I think it's trying to get you to find the side length of the square by using a square root on the area.

Assuming that's the case;

Remember that a square has equal side lengths all around, otherwise it would just be a rectangle. You can actually take the square root of a square to get the side length (hence the name square root). A square root is what number you must multiply by itself to get the root, so for example the square root of 25 is 5 because you can multiply 5 by 5 to get 25. The square root of 100 is 10, because you can multiply 10 by itself to get 100. So you would write this as [tex]\sqrt{100}[/tex], which simplifies down to 10.

y+2=-2(x-1) is in point-slope form, it is neither in slope-intercept form nor standard form.

A line's steepness and direction are determined by the slope of the line. Without actually using a compass, determining a line's slope in a coordinate plane allows one to anticipate whether a line is parallel, perpendicular, or not.

The change in a line's y coordinate relative to its change in x coordinate is referred to as the line's slope. Δy is the net change in the y coordinate, while Δx is the net change in the x coordinate.  

Therefore,

m =  y₂-y₁/x₂-x₁ (where m denotes the slope) can be used to express how the y coordinate changes in relation to the x coordinate.

Be aware that tan ∅ = y/x

We also refer to this tan as the line's slope.

We know that  point-slope form = y₂ - y₁ = m(x₂ - x₁)

the equation looks like this in point-slope form ⇒ y-(-2)= -2(x-1)

Here, the points are (x, y) and the points the line is passing through is

(1, -2)

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An unlimited number of acute triangles can be formed from two sides without an angle measurement, such as a = 10 m and b = 10 m.

As an illustration -

If our side lengths are 10m and 10m, and our angle value goes from 0 to 90 degrees, how many different acute triangles can we create?

Construct a triangle with sides of 10 and 10 metres, an angle of 45 degrees, and a third side that can be extended to the desired length. You have built a triangle.

By changing the third side's length and angle, we can make a whole different triangle that is identical to this one.

Never forget to choose the side lengths and angles. There is a suggestion that you might decide to take a different step. The same angles can be used to make an unlimited number of different triangles.

As a result, with a single angle and a single side length, we can create an endless number of triangles.

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The first five terms of an arithmetic sequence with first term 19 and common difference -4 are 19, 15, 11, 7, 3

The given parameters:

a₁ = 19, d = -4

d is the common difference, hence, the given sequence is an arithmetic sequence.

In an arithmetic sequence, the formula for the nth term is given by:

      a(n) = a(1) + (n - 1) . d

We can also find the terms using recursive formula. The nth term of an arithmetic sequence is equal to the (n-1)th term plus the common difference, d. Mathematically,

      a(n) = a(n -1) + d

Let us start from n = 1

a(1) = 19  (given)

a(2) = a(1) + d = 19 + (-4) = 15

a(3) = a(2) + d = 15 + (-4) = 11

a(4) = a(3) + d = 11 + (-4) = 7

a(5) = a(4) + d = 7 + (-4) = 3

Thus, the first five terms are 19, 15, 11, 7, 3

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A mode can be defined as a statistical term that is used to denote the value that appears most frequently (often) or occurs repeatedly in a given data set. This ultimately implies that, the mode of a data set simply refers to the data point with the highest frequency.

By critically observing the frequencies for the number of TVs shown in the table above, we can logically deduce that the mode is equal to 1.

A mean can be defined as a ratio of the sum of the total number in a data set (population) to the frequency of the data set.

Mathematically, the mean for this data can be calculated by using the following formula:

Mean = [F(x)]/n

Frequency, n = 3 + 15 + 9 + 11 + 1

Frequency, n = 39.

Total number of TVs = 0(3) + 1(15) + 2(9) + 3(11) + 4(1)

Total number of TVs = 0 + 15 + 18 + 33 + 4

Total number of TVs = 70

Substituting the parameters into the formula, we have;

Mean = 70/39

Mean = 1.80.

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According to this the given equation the  correct option is G. 22x - 6 = 8x

Algebra is a field of mathematics that aids in the depiction of issues or situations using mathematical expressions. To construct a meaningful mathematical expression, variables such as x, y, and z are combined with mathematical operations such as addition, subtraction, multiplication, and division.

Algebra is a generalized version of arithmetic in which variables stand in for nonspecific numbers. Its objective seems to be to solve algebraic equations including equation systems.

The equation is = 7x-3(2-5x)=8x

Now simplifying the equation:

7x-3(2-5x)=8x

7x - 6 + 15x = 8x

22x - 6 = 8x

According to this the correct option is G. 22x - 6 = 8x

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The distance from the center to any point on the circle exists comprehended as the radius. The radius is 10cm.

The radius of a circle is the separation between any two points on the circle and its center. The radius of a circle is the separation between any two points on its circumference. R or r is typically used to indicate it.

The distance along a line connecting a circle's center to a point on its perimeter is known as a circle's radius. Therefore, the radius is equal to half the diameter's length. Therefore, the radius is equal to half the diameter's length.

The radius of a circle is the separation between any two points on the circle and its center.

In this instance (using the Pythagorean Theorem)

r = [tex]\sqrt{(7-1)^{2}+(5-(-3))^{2} }[/tex]

= √(36 + 64)

r = 10

If a circle whose center is at (1, -3) passes through the point (7, 5) then the radius of the circle exists 10.

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The measure of each angle is 23 degrees, 67 degrees, and 90 degrees.

The acute angle can be defined as the angle  less than 90°. Or we can say that the angle which is between 0° and 90° is called as an acute angle of a triangle.

Right triangle is also known as right angled triangle. If a triangle has atleast one 90° angle then the triangle is said to be a right angled triangle. A right angle triangle always follows the Pythagoras theorem.

Now, According to statement given :

Let  smaller acute angle = x,

and measure of larger acute angle = 3x-2

Since, it is right triangle the acute angles must be complementary

x + (3x-2) = 90

4x - 2 = 90

4x = 92

x = 23

i.e. smaller acute angle is 23

now second angle = 3x-2 = 3(23) - 2 = 67

and third angle is 90 , as this is a right angled triangle.

Thus, The measurement of each angle is 23 degrees, 67 degrees, and 90 degrees.

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Answer:

A. Is the correct answer

Step-by-step explanation:

Step 1: Multiply (3 x 4 = 12)

Step 2: Add (12 + 2 = 14)

I hope i was able to help you out :)

Answer:

Step-by-step explanation:

division is ÷

addition is +

product is the word for the answer of multiplying numbers together

difference is the word for the answer of subtracting numbers

in this problem, any variable is called a number.

4 d : this is the product. you can write 4 x d, but a shortcut is to exclude the multiplication

y - 4 : this is subtraction, so the difference

4 + x : this is addition

4 ÷ n : this is division

Write the first five numbers of two different patterns in which 12 is the third number.

Pattern 1= 4, 8, 12, 16, 20

Pattern 2= 2,4,12,48,240

How to calculate the patterns?

Pattern 1=multiples of 4

4*1=4

4*2=8

4*3=12

4*4=16

4*5=20

Pattern 2= tn=(tn-1)*n

t1=2

t2=2*2=4

t3=4*3=12

t4=12*4=48

t5=48*5=240

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The location of point P under the translation is (2, 4)

The complete question is added as an attachment

The location of point P is

P = (-1, 3)

The translation is given as:

(x+3, y+1)

So, we have

P' =(-1 + 3, 3 + 1)

Evaluate

P' = (2, 4)

Hence, the location of point P under the translation is (2, 4)

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The solution of the equation (3x -2)/12 -1/6 = 1/6 is at x = 2.

According to the given question.

We have an equation (3x -2)/12 -1/6 = 1/6 .

As we know that, an equation is a condition on a variable such that two expressions in the variable should have equal value.

Therefore, the solution of the equation (3x -2)/12 -1/6 = 1/6 is given by

(3x -2)/12 -1/6 = 1/6

⇒ (3x -2)/12 = 1/6 + 1/6 (adding 1/6 both the sides)

⇒ (3x -12)/12   = 2/6

⇒ (3x -2)/12 = 1/3

⇒ (3x -2)    = (1/3)12

⇒ 3x -2 = 4

⇒ 3x = 4 + 2

⇒ 3x = 6

⇒ x = 6/3

⇒ x = 2

Hence, the solution of the equation (3x -2)/12 -1/6 = 1/6 is at x = 2.

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Answer:

A and E (top left and bottom middle)

Step-by-step explanation:

Unit rates are found when a ratio has a denominator of 1.  For the sake of simplicity, I will give the options in the image letter designations. A, B, and C are the top three from left to right, and D, E, and F are the bottom 3 from left to right.

A

[tex]\frac{9}{5} miles:\frac{5}{6}hour[/tex]
Because ratios can be written as fractions, this ratio can be written:

[tex]\frac{\frac{9}{5}}{\frac{5}{6}}[/tex]
That's a mess! Another way to divide fractions is to multiply by the reciprocal of the denominator:

[tex]\frac{9}{5}*\frac{6}{5}[/tex]

Since none of the terms can be cross-cancelled, multiply!

[tex]=\frac{54}{25}[/tex]
Since the numerator is greater than the denominator, the unit rate is greater than one!

B

[tex]4miles:3\frac{1}{3}hours[/tex]

Start by turning the mixed number into an improper fraction:

[tex]3\frac{1}{3}=\frac{10}{3}[/tex]

Now compare by multiplying 4 over 1 by the reciprocal of 10 thirds:

[tex]\frac{4}{1}*\frac{3}{10}[/tex]

Cross-cancel and multiply:

[tex]=\frac{2}{5}[/tex]

Since the numerator is less than the denominator, the unit rate is less than one!

C

[tex]2\frac{1}{2} miles:3hours[/tex]
Convert the mixed number into an improper fraction:

[tex]2\frac{1}{2} =\frac{5}{2}[/tex]
Multiply by the reciprocal of 3:

[tex]\frac{5}{2}*\frac{1}{3}[/tex]
Multiply!

[tex]\frac{5}{6}[/tex]
Since the numerator is less than the denominator, the unit rate is less than one!

D

[tex]\frac{9}{5} miles :3hours[/tex]

Multiply by the reciprocal of 3:

[tex]\frac{9}{5}*\frac{1}{3}[/tex]

Cross cancel and multiply!

[tex]=\frac{3}{5}[/tex]

Since the numerator is less than the denominator, the unit rate is less than one!

E

[tex]7 miles :\frac{3}{4}hour[/tex]

Multiply by the reciprocal of 3 fourths:

[tex]\frac{7}{1}*\frac{4}{3}[/tex]

Multiply:

[tex]=\frac{28}{3}[/tex]

Since the numerator is greater than the denominator, the unit rate is greater than one!

F

[tex]\frac{1}{3}mile:2\frac{3}{8}hours[/tex]

Convert the mixed number into an improper fraction:

[tex]2\frac{3}{8}=\frac{19}{8}[/tex]

Multiply one third by the reciprocal of 19 eighths:

[tex]\frac{1}{3}*\frac{8}{19}[/tex]
Multiply!

[tex]=\frac{8}{57}[/tex]

Since the numerator is less than the denominator, the unit rate is less than one!

We can find whether three points are coplanar by using vector approach.

In geometry, a of group points in space are coplanar if there exists a geometric plane that contains them all. For instance, three points are always coplanar, and if the points are distinct and non-collinear, the plane they exist is unique.

We can check whether the given point F,Q and P are coplanar by first forming vectors of the each given point. The vector form for general point (a,b,c) can be written as [tex]a\hat{i}+b\hat{j}+c\hat{k}[/tex].

The vector forms of point F,Q and P can be given as 'f', 'q' and 'p'. The scalar triple product of the vectors 'f', 'q' and 'p' can be found out by finding the scalar product of vector 'f' with the cross product of the vectors 'q' and 'p' .

For the points F,Q and P to be coplanar the triple scalar product must be zero else the points are not coplanar.

This implies f·(q×p)=0 must be satisfied for three points to lie on the same plane.

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The correct question is " How can you say points F, Q and D are coplanar?"

The value of √12 is equals to 3.46, and the number 4 is larger than the number 3.46.

The value of √12 = 3.46, and the number 4 is larger than the number 3.46.

Therefore, 4 > √12.

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   The equation that defines the parabola with vertex at the point (0, 0) and focus at (0, 7) is:

y = x²/28

  A parabola is a quadratic function that can move on any axis, it is composed of:

   The equation that defines a parabola can be given by:

  This will depend on its aperture

  In this case we have the vertex of the parabola at the point (0, 0) and the focus at the point (0, 7) this is displaced on the y-axis upward, so the parabola is of the form y = x²

(x - 0)² = 4p(y - 0)

Focus

f = (0, 0  + p)

(x- 0)² = 4*7(y - 0)

(x - 0)² = 28(y - 0)

y = x²/28

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Angle is mistaken because triangles of two pairs of congruent sides and one pair of congruent angles do not always satisfy the SAS criterion.

In the given situation:

Therefore, the angle is mistaken because triangles of two pairs of congruent sides and one pair of congruent angles do not always satisfy the SAS criterion.

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The coordinate of point P is -8.

We are given that the endpoints of AB are -16 and -4.

This means that A is at -16 and B is at -4

Therefore, the total length of the line AB will be-

-16 - (-4) = -12 units

But since length cannot be negative, we take only the absolute value, the length of AB comes out to be 12 units.

Now, point P divides AB in the ratio 2:1

The length of these two parts will be

12 × 2/3 and 12 x 1/3

= 8 units and 4 units

This means that AP = 8 units and PB = 4 units

Hence the coordinate of P will be (-16 + 8) or (-4 - 4)

Thus, the coordinate of point P is -8.

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The length of a segment ab is 16 units.

Given that, a= -7 and b=9.

We need to find the length of a segment ab.

In geometry, a line segment is a part of a straight line that is bounded by two distinct end points and contains every point on the line that is between its endpoints.

The length of the line segment is fixed, which is the distance between two fixed points. The length here can be measured by metric units such as centimetres (cm), millimetres (mm) or by conventional units like feet or inches.

Now, the length of a segment ab=a+b

=7+9=16

Therefore, the length of a segment ab is 16 units.

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The height of house to ladder reach  is 17 ft

The Pythagoras theorem states that the square of the longest side must be equal to the sum of the square of the other two sides in a right-angle triangle.

|AC|^2 = |AB|^2 + |BC|^2    

Given data; ladder = 18 ft

The base  = 5 ft

In order to find out the height of house.

we know this is triangle shape so we apply here so we consider here x is ladder and y is base and z is height

By pythagoras theorem;

z² + y² = x²

z² = x² -y²

Then put value

z² = 18² - 5²

z² = 299

z = 17.29

z = 17

Therefore, the height of house to ladder reach is 17 ft

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If you had 250 minutes left on your cell phone and you talk an hour a week, then the algebraic expression is 250-60x

Given,

The conditions

Consider the number of weeks as x

We know 1 hour = 60 minutes

Then, the algebraic expression = 250-60x

Hence, if you had 250 minutes left on your cell phone and you talk an hour a week, then the algebraic expression is 250-60x

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The result of true and false is-

a) True: J and J' are opposite of y axis.

b) False: Location of L' is (-3, -4).

c) True: N and N' are at same distance.

d) False: L' is at 3 unit above x axis.

As per the given graph;

Part a: True: J and J' are opposite of y axis.

It is clear from the graph that J and J' lies on the opposite side of Y-axis.

The coordinate of J = (2, -6) and J' = (2, 6).

Part b: False: The location of L' is not (-3, -4)

The correct Location of L' is (3, 4) as seen from the graph.

Part c: True: N and N' are at same distance.

The coordinates of N and N' are (5, -5) and (5, 5).

Thus, they are at the same distance from the both axis.

Part d: False: L' is at 3 unit above x axis.

Point L' lies at the distance of 4 units from the x axis.

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Answer:

x = 8

Step-by-step explanation:

the area (A) of the triangle is calculated as

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

where a and b are 2 sides of the triangle and C the angle between them

here a = 13 , b = x , C = 30° and A = 26 , then

[tex]\frac{1}{2}[/tex] × 13 × x × sin30° = 26 ( multiply both sides by 2 to clear the fraction )

13x × sin30° = 52 ( using the exact value of sin30° = [tex]\frac{1}{2}[/tex] )

13x × [tex]\frac{1}{2}[/tex] = 52 ( multiply both sides by 2 to clear the fraction )

13x = 104 ( divide both sides by 13 )

x = 8