Can someone explain this?

The slope and y-intercept are both [tex]\bf{1}[/tex].

This equation is written in slope-intercept form, or [tex]y=mx+b[/tex], where [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept.

Since there is no coefficient to [tex]x[/tex], which would have been [tex]m[/tex], [tex]m=1[/tex], so the slope is [tex]1[/tex].

[tex]b=1[/tex], so the y-intercept is also [tex]1[/tex].

Answer:

The coordinates of vertex D are (1,2).

Step-by-step explanation:

Let the coordinates of D are (a,b).

It is given that ABCD is a parallelogram and the vertices of the parallelogram are A(-2,4), B(1,3) and C(4,1).

According to the property of parallelogram, the diagonals of the parallelogram bisect each other.

AC and BD are diagonals of the parallelogram ABCD.

Midpoint formula:

[tex]Midpoint=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]

Using midpoint formula, the midpoint of AC is

[tex]Midpoint_{AC}=(\frac{-2+4}{2},\frac{4+1}{2})=(1,\frac{5}{2})[/tex]

Using midpoint formula, the midpoint of BD is

[tex]Midpoint_{BD}=(\frac{1+a}{2},\frac{3+b}{2})[/tex]

Midpoint of both diagonals is the intersection point of the diagonals.

[tex]Midpoint_{AC}=Midpoint_{BD}[/tex]

[tex](1,\frac{5}{2})=(\frac{1+a}{2},\frac{3+b}{2})[/tex]

On comparing both the sides we get

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

[tex]2=1+a[/tex]

[tex]2-1=a[/tex]

[tex]1=a[/tex]

The value of a is 1.

[tex]\frac{5}{2}=\frac{3+b}{2}[/tex]

[tex]5=3+b[/tex]

[tex]5-3=b[/tex]

[tex]2=b[/tex]

The value of b is 2.

Therefore the coordinates of vertex D are (1,2).

The coordinates of point D in the parallelogram formed by points A(-2,4), B(1,3), and C(4,1) are (7,2), calculated based on the property of parallelograms, where opposite sides are congruent.

In order to find the coordinates of point D forming a parallelogram with points A(-2,4), B(1,3), and C(4,1), we can use the property of a parallelogram that opposite sides are equal. This means the vector from A to B is equivalent to the vector from D to C. The vector AB is calculated through subtraction of the coordinates: B minus A (1-(-2), 3-4) = (3, -1).

Applying the same vector (movement) to point C to find point D (since D to C equals B to A), we get D as C plus the vector (4+3, 1-(-1)) = (7,2). So, the coordinates of point D in the parallelogram are (7,2).

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Answer : The length of the rectangle (a) is, 8 cm

Step-by-step explanation :

As we are given that,

Area of rectangle = [tex]24cm^2[/tex]

Length of rectangle = a

Breadth of rectangle = a - 5

As we know that,

Area of rectangle = Length × Breadth

Now put all the given values in this formula, we get the value of 'a'.

[tex]24cm^2=(a)\times (a-5)[/tex]

[tex]24cm^2=a^2-5a[/tex]

[tex]a^2-5a-24=0[/tex]

By the solving the term 'a', we get the value of 'a'.

a = 8

Thus,

Length of rectangle = a = 8 cm

Breadth of rectangle = a - 5 = 8 - 5 = 3 cm

Therefore, the length of the rectangle (a) is, 8 cm

The length a of the rectangle is 8 cm

To solve the above questions, we need to recall some of the formulas as follows:

Area of Square = (Length of Side)²

Perimeter of Square = 4 × (Length of Side)

Area of Rectangle = Length × Width

Perimeter of Rectangle = 2 × ( Length + Width )

Area of Rhombus = ½ × ( Diagonal₁ + Diagonal₂ )

Perimeter of Rhombus = 4 × ( Length of Side )

Area of Kite = ½ × ( Diagonal₁ + Diagonal₂ )

Perimeter of Kite = 2 × ( Length of Side₁ + Length of Side₂ )

Let us now tackle the problem !

Given:

Area of Rectangle = A = 24 cm²

Length of Rectangle = L = a cm

Width of Rectangle = W = (a - 5) cm

Unknown:

Length of Rectangle = a = ?

Solution:

This problem is about Area of Rectangle.

[tex]\text{Area of Rectangle} = \text{Length} \times \text{Width}[/tex]

[tex]A = L \times W[/tex]

[tex]24 = a \times (a - 5)[/tex]

[tex]24 = a^2 - 5a[/tex]

[tex]a^2 - 5a - 24 = 0[/tex]

[tex](a - 8)(a +3) = 0[/tex]

[tex](a - 8) = 0[/tex]

[tex]a = \boxed {8 ~ \text{cm}}[/tex]

Grade: College

Subject: Mathematics

Chapter: Two Dimensional Figures

Keywords: Perimeter, Area , Square , Rectangle , Side , Length , Width

Answer:

B. 4

C. Log₅ 625

Step-by-step explanation:

When given the sum of two logarithms to the same base, let us say

LogₐB +LogₐC, Then, the sum is equivalent to Logₐ(B×C)

=Logₐ BC

The sum given in the question is Log₅5 + Log₅125

This is equivalent to Log₅(5×125)=Log₅625

Log₅625=4 (Since 625=5⁴, the log of 625 to base 5 is 4)

Answer:4 Log5 625 Log5(5^4)

Step-by-step explanation:

Answer:

Step-by-step explanation:

we have the system :

8x+4y=16

7y=15

the easiest unknown to find first is y because we have the second equation contains only y :

7y=15   we divide both sides by 7 we get : y=[tex]\frac{15}{7}[/tex]

then we can substitute this value in the first equation to find x :

8x+4 [tex]\frac{15}{7}[/tex] = 16

means : 8x+[tex]\frac{60}{7}[/tex] = 16

8x=16-[tex]\frac{60}{7}[/tex]

8x = [tex]\frac{52}{7}[/tex]

divide both sides by 8 :

x = [tex]\frac{13}{14}[/tex]

so the solution is ([tex]\frac{13}{14}[/tex],[tex]\frac{15}{7}[/tex])

this is the solution of the system you submitted

Now if you meant this system :

8x+4y=16

7y=15-1    

we get :

7y=14   which gives us y=2

then 8x+4(2)=16   gives us : 8x+8=16

means 8x=8  

means x=1

and in this case the solution will be (1,2)  answer C

Answer:

The correct answer option is: 4.

Step-by-step explanation:

We are given the following two functions and we are to find the value of [tex] ( f - g ) ( 5 ) [/tex]:

[tex]f(x) = x^2 - 5[/tex]

[tex]g(x) = 4x - 4[/tex]

Finding [tex] ( f - g ) ( x ) [/tex]:

[tex] ( f - g ) ( x ) [/tex] [tex]= (x^2-5)-(4x-4) = x^2-4x-5+4[/tex]

[tex]( f - g ) ( x ) = x^2-4x-1[/tex]

So, [tex]( f - g ) ( 5 ) = (5)^2-4(5)-1 = 4[/tex]

Answer:

4

Step-by-step explanation:

f(x) = x^2 - 5

g(x) = 4x - 4

(f-g) (x)= x^2 - 5   - (4x - 4)

Distribute the minus sign

           = x^2 - 5   - 4x + 4

          = x^2 -4x-1

Let x = 5

(f-g) (5) = 5^2 -4(5) -1

            =25 - 20 -1

             =5-1

              =4

Answer:

24

Step-by-step explanation:

36= three part in a length

so, one part=36/3=12

smaller triangle's length=2/3=12×2=24

Answer:

24 millimeters

Step-by-step explanation:

We have 2 triangles with proportional sides. The smaller side has a length of 2/3 of the similar triangle:

[tex]L_1=\frac{2L_2}{3}[/tex]

[tex]L_1=\frac{2*36}{3}[/tex]

[tex]L_1=24 mm[/tex]

24 millimeters

Answer:

x = 12

x = 4

Step-by-step explanation:

Answer:

X=12

X=4

Step-by-step explanation:

Step-1 : Multiply the coefficient of the first term by the constant 1 • 48 = 48

Step-2 : Find two factors of 48 whose sum equals the coefficient of the middle term, which is -16 .

-48 + -1 = -49

-24 + -2 = -26

-16 + -3 = -19

-12 + -4 = -16 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -12 and -4

x2 - 12x - 4x - 48

Step-4 : Add up the first 2 terms, pulling out like factors :

x • (x-12)

Add up the last 2 terms, pulling out common factors :

4 • (x-12)

Step-5 : Add up the four terms of step 4 :

(x-4) • (x-12)

Which is the desired factorization

Answer:

Step-by-step explanation:

[tex]g(x)=x^2-4\\\\g(5)-\text{put}\ x=5\ \text{to the equation of the function}\ g(x):\\\\g(5)=5^2-4=25-4=21[/tex]

The value of the function g(x) = x² - 4 at g(5) is 21. Option C is correct.

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

The expression is solved as:-

g(x) = x² - 4

To calculate the value g(5) put x=5 in the expression.

g(5) = ( 5 )² - 4

g(5) = 25 - 4

g(5) = 21

Therefore, the value of the function g(x) = x² - 4 at g(5) is 21. Option C is correct.

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Answer:

1 and 4

Step-by-step explanation:

There are 2 shaded, and 2 even numbers

There are 2 unshaded, and 2 odd numbers.

Hope this helps

Answer:

Step-by-step explanation:

the base is a square, and then there are four triangles that meet at their tip.

so you need to find the area of the base, and the four triangles.

base-l*w=7*7=49

triangles=1/2*b*h*4=1/2*7*10*4=35*4=140

140+49=189

Final answer:

The surface area of a regular pyramid with a square base of 7 units and a height of 10 units is approximately 197.26 square units. This is calculated by adding the area of the square base to the combined area of the four triangular faces.

Explanation:

To find the surface area of a regular pyramid with a square base, we need to calculate the area of the square base and the area of the four triangular faces. The formula for the area of a square is base x base. If the base is 7 (units unspecified, but assumed to be the same for both height and base), the area of the base is 7 x 7 = 49 square units. To find the area of a triangular face, we use the formula 1/2 x base x slant height.

To calculate the slant height, we need the half of the base of the triangle (which is 3.5 if the base of the square is 7), and the given perpendicular height of the pyramid, in this case, 10 units. We can use the Pythagorean theorem to find the slant height. The slant height (s) can be calculated as s = \\sqrt{(3.5)² + 10²} = \\sqrt{12.25 + 100} = \\sqrt{112.25}, which is approximately 10.59 units.

The area of one triangular face is 1/2 x 7 x 10.59 ≈ 37.065 square units. There are four triangular faces, so their total area is 37.065 x 4 ≈ 148.26 square units. Thus, the total surface area of the pyramid is the sum of the area of the base and the four triangular faces: 49 + 148.26 ≈ 197.26 square units.

Answer:

V=90m³

Step-by-step explanation:

If a rectangular prism has a length of 5 meters, a width of 6 meters, and a height of 3 meters, the volume of the prism is 90m³.

Formula: V=whl

V=whl=6·3·5=90m³

Answer:

B: 1/5

Step-by-step explanation:

If the lines are perpendicular, they have negative reciprocal slopes

s has a slope of -5

t must have a slope of - (1/ -5)

                                    = 1/5

Answer:

The rule for the transformation is (x, y) + (-X, -Y)

The coordinates of L'are (-2,-2).

The coordinates of N' are (-1,-6)

Step-by-step explanation:

90 degree rotation from (x,y) results in (-x, y) and 180 degree results in (-x,-y)

The coordinates will change accordingly

L(2,2) will become L'(-2,-2)

M(4,4) will become M'(-4,-4)

and

N(1,6) will become N'(-1,-6)

So the correct statements are:

The rule for the transformation is (x, y) + (-X, -Y)

The coordinates of L'are (-2,-2).

The coordinates of N' are (-1,-6) ..

The true options are:

The vertices of the triangle are given as:

L(2, 2), M(4,4), and N(1,6).

The rule of transformation is Ro 180°.

This is represented as:

[tex](x, y) \to (-x, -y)[/tex]

So, we have:

[tex]L' = (-2,-2)[/tex]

[tex]M' = (-4,-4)[/tex]

[tex]N' = (-1,-6)[/tex]

Hence, the true options are (a), (b) and (e)

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Answer:

7 inches

Step-by-step explanation:

The dimension of the rectangular gift is 10 by 12 inches so let us find the perimeter of this rectangle.

Perimeter of rectangular gift = 2 (L+ W) = 2 (10 +12) = 44 inches

Since we are to use the same length of ribbon to wrap a circular clock so the perimeter or circumference of the clock should be no more than 44 inches.

[tex]2\pi r=44[/tex]

[tex]r=\frac{44}{2\pi }[/tex]

[tex]r=7.003[/tex]

Therefore, the maximum radius of the circular clock is 7 inches.

Answer:

= 7 inches

Step-by-step explanation:

The ribbon covers the perimeter of the gift.

Perimeter of a rectangle= 2L+2W

=2(12)+2(10)

=44 inches

If the same ribbon is used to frame a circular clock, the perimeter remains to be 44 inches.

Perimeter of a circle= 2πr where r is the radius of the circle.

44 inches= 2×π×r

r=44/2π

=7.0 inches

Radius of the circular clock is 7 inches

Answer:

y=40

Step-by-step explanation:

Step 1: Add 1 to both sides.

3y−1+1=119+1

3y=120

Step 2: Divide both sides by 3.

3y /3  =  120 /3

y=40

Answer:

[tex]a < 0.287[/tex]

Step-by-step explanation:

we have

[tex]13^{4a} < 19[/tex]

Solve for a

Apply log both sides

[tex]log(13^{4a}) < log(19)[/tex]  

Remember the rule

㏒(a^n) = n ㏒(a)

so

[tex](4a)log(13) < log(19)[/tex]

Divide by 4 log(13) both sides

[tex]a < log(19)/[4log(13)][/tex]

[tex]a < 0.2870[/tex]

Answer:

[tex]\%increase = 12\%[/tex]

Step-by-step explanation:

The formula to calculate the percentage of increase is:

[tex]\% = \frac{x_f-x_i}{x_i}*100\%[/tex]

Where

[tex]x_i[/tex] is the initial amount and [tex]x_f[/tex] is the final amount

So:

[tex]\% = \frac{28000-25000}{25000}*100\%[/tex]

[tex]\% = \frac{3000}{25000}*100\%[/tex]

You can write it as:

[tex]\% = \frac{3*1000}{25*1000}*100\%[/tex]

This is:

[tex]\% = \frac{3}{25}*100\%[/tex]

[tex]\%increase = 12\%[/tex]

Answer:

  166 mm²

Step-by-step explanation:

The area is given by ...

  A = (1/2)Pa . . . . . where P is the perimeter and "a" is the apothem

One side of a 6-sided figure is shown as 8 mm, so the perimeter is ...

  P = 6·(8 mm) = 48 mm

Filling in the apothem value, we have ...

  A = (1/2)(48 mm)(4√3 mm) = 96√3 mm² ≈ 166 mm²

The area of the hexagon is about 166 mm².

Answer:

39.34 juniors and 30.1 seniors

Answer:

The closest number of juniors and seniors who were inducted is 69.

Step-by-step explanation:

At Lincoln High School, approximately 7% of enrolled juniors and 5% of enrolled seniors were inducted into the National Honor Society last year.

There were 562 juniors and 602 seniors enrolled at Lincoln High School last year.

We will calculate the number of students as:

[tex]0.07(562)+0.05(602)[/tex]

= [tex]39.34+30.1[/tex]

= 69.44

Therefore, the closest number of juniors and seniors who were inducted is 69.

Answer:

This was occur sometimes in year 2002.4

Step-by-step explanation:

* Lets explain how to solve the problem

- The value of China's exports of automobiles and parts

  (in billions of dollars) is approximately f(x) = 1.8208 e^(0.3387 x)

# You must pay attention about the function is already calculated in

  billions dollars so you will not multiply the value of f(x) by 10^9 to

  change it to billions

∵ The value of x = 0 at 1998

- Remember that e^(0) = 1

∴ f(0) = 1.8208 e^(0) = 1.8208 billion dollars

- You need to calculate the year that the export reaches 8 billion

∵ f(x) = 1.8208 e^(0.3387 x)

∵ f(x) = 8 billion

∴ 8 = 1.8208 e^(0.3387 x)

- Divide both sides by 1.8208

∴ 4.393673111 = e^(0.3387 x)

- Insert ㏑ in both sides

∴ ㏑(4.393673111) = ㏑[e^(0.3387 x)]

- Remember ㏑(e^n) = n ㏑(e), ㏑(e) = 1, then ㏑(e^n) = n

∴ ㏑(4.393673111) = 0.3387 x

- Divide both sides by 0.3387

∴ x = ㏑(4.393673111) ÷ 0.3387

∴ x = 4.37 ≅ 4.4

- Lets add the number of years to 1998

∴ The year is 1998 + 4.4 = 2002.4

∴ This was occur sometimes in year 2002.4

The value of China's exports of automobiles and parts reached $8 billion in approximately the year 2001.8. The mathematical calculation is based on the exponential function representing the export values over time with the base year 1998.

The student has asked to determine the year in which China's exports of automobiles and parts reached $8 billion.

To solve for the year when exports reach $8 billion, we use the given exponential function for the value of China's exports of automobiles and parts, which is f(x) = 1.8208e0.3387x, where x = 0 corresponds to the year 1998. We need to solve the equation f(x) = 8 for x.

Firstly, set f(x) = 8:

Next, divide both sides of the equation by 1.8208 to isolate the exponential part:

Then, take the natural logarithm of both sides to solve for x:

Finally, add the result to the base year 1998 to get the approximate year:

Therefore, the exports reached $8 billion in approximately 2001.8, or the year 2001 when considering just the full year.

Answer:

The measure of the arc x is 80°

Step-by-step explanation:

we know that

The semi-inscribed angle is half that of the arc it comprises

so

40°=(1/2)[arc x]

solve for x

arc x=(2)(40°)=80°

Answer:

5/9, 2/7, 3/10 are all rational numbers

Step-by-step explanation:

Remember that all rational numbers are able to be written as a fraction or ratio of two integers.

Answer:

[tex]\frac{2}{7}+\sqrt{121}[/tex]

Step-by-step explanation:

Since, a real number is called rational number if it can be expressed in the form of [tex]\frac{p}{q}[/tex],

Where, p and q are integers,

S.t. q ≠ 0,

If the number is not a rational number then it is irrational,

Now, the sum or difference of two rational numbers is a rational number,

While, the sum or difference of a rational number and an irrational number is an irrational number.

∵ √18, √11 and [tex]\pi[/tex] are irrational numbers,

Also, [tex]\frac{5}{9}[/tex], [tex]\sqrt{16}[/tex] and [tex]\frac{3}{10}[/tex] are rational number,

[tex]\implies \frac{5}{9}+\sqrt{18},\pi+\sqrt{16}, \frac{3}{10}+\sqrt{11}\text{ are irrational numbers}[/tex]

Now,

[tex]\frac{2}{7}\text{ and }\sqrt{121}\text{ are rational numbers}[/tex]

Hence,

[tex]\frac{2}{7}+\sqrt{121}\text{ is rational number}[/tex]

Answer:

D. 2x + y = -4​

Step-by-step explanation:

Standard form for the equation of a line is Ax + By =C where A is a positive integer and B and C are integers

y + 1 = -2x - 3

Add 2x to each side

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

2x+y +1 = -3

Subtract 1 from each side

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

2x+y = -4

Answer:

y=-2x-4

Step-by-step explanation:

There are many  standard form of any equations. One of them is called the

y intercept form. The standard form is

y=mx+c

where m is the slope and c is the y intercept

Let us see our given equation

y+1= -2x - 3

subtracting 1 from both sides we get

y = -2x - 3 - 1

y= -2x - 4

Here if we compare it with the standard equation we get

m = -2 and c = -4

When A, B, and C are collinear points and B is between A and C, value of AB(x) is 6. Therefore, option A is the correct answer.

If we know that points A, B, and C are collinear, with B between A and C, then we can use the given distances AB and BC to find the total distance AC.

Since AB is given as x, and BC as x+2, and we know AC is the sum of AB and BC< which is equal to 14, we can set up the equation:

AB + BC = AC

x + (x+2) = 14

Combining like terms gives us:

2x + 2 = 14

Subtracting 2 from both sides of the equation, we have:

2x = 12

Dividing both sides by 2 to isolate x:

x = 6

Therefore, the length of segment AB, which is x, is 6 units. Option A. 6 is the correct answer.

Answer:

Step-by-step explanation:

[tex]f(x)=4-x^2,\ g(x)=6x\\\\(g-f)(x)=g(x)-f(x)\\\\(g-f)(x)=6x-(4-x^2)\\\\(g-f)(3)-\text{put x = 3 to the equation}\\\\(g-f)(3)=6(3)-(4-3^2)[/tex]

Answer:

a = 8 ; b = 40

I just took the test and I got it right

Answer:

D

Step-by-step explanation:

D on edge :)

Answer:

2812.5

Step-by-step explanation:

Is means equals and of means multiply

9 = .32% * W

Change the percent to a decimal

9 = .0032 * W

Divide each side by .0032

9/.0032 = .0032W/.0032

2812.5 = W

The number is 2812.5

Answer:

2,812.5

Step-by-step explanation:

Answer:

[tex]3x - y = - 2[/tex]

Step-by-step explanation:

The given line PQ passes through the points P(-5,-13) and Q(5,17) .

Find the slope using the formula:

[tex]m = \frac{y_2-y_1}{x_2-x_1} [/tex]

Plug in the points to get:

[tex]m = \frac{17 - - 13}{5 - - 5} [/tex]

[tex]m = \frac{30}{10} [/tex]

[tex]m = 3[/tex]

Use the point-slope formula :

[tex]y-y_1 = m(x - x_1)[/tex]

Substitute the point (5,17)

[tex]y - 17 = 3(x - 5)[/tex]

Expand:

[tex]y - 17 = 3x - 15[/tex]

The standard form is when the equation is put in the form

[tex]ax + by = c[/tex]

Regroup the terms to get:

[tex]3x - y = - 17 + 15[/tex]

The standard form is

[tex]3x - y = - 2[/tex]