Find a linear equation satisfying the conditions:
x-intercept at (-2,0) and y-intercept at (0, -3).

CPCTC = corresponding parts of congruent triangles are congruent

BA and CA are corresponding sides for both triangles, namely twins, BA ≅ CA.

Answer: [tex]\overline{BA}\cong\overline{CA}[/tex]

Step-by-step explanation:

Given : [tex]\triangle {BAT}\cong\triangle{CAT}[/tex]

The CPCTC property of congruent triangles says that the corresponding parts of congruent triangles are congruent.

Therefore, the the corresponding angles and sides of [tex]\triangle {BAT}\text{ and }\triangle{CAT}[/tex] are congruent.

i.e. [tex]\angle {BAT}\cong\angle{CAT}[/tex]

[tex]\angle {ATB\cong\angle{ATC}\\\\\[/tex]

[tex]\angle {TBA}\cong\angle{TCA}[/tex]

and

[tex]\overline{BA}\cong\overline{CA}\\\\\overline{AT}\cong\overline{AT}\\\\\overline{TB}\cong\overline{TC}[/tex]

So, from all the options [tex]\overline{BA}\cong\overline{CA}[/tex] is the true option.

Answer:

C

Step-by-step explanation:

Oblique. The other three are used to describe a polyhedron. They are related by the following formula

V + F - E = 2.

Where

For example consider a common cube, like a sugar cube.

It has 6 faces (f)

It has 8 vertexes (V)

It has 12 edges. E

6 + 8 - 12 = 14 - 12 = 2

Answer:

$96.75

Step-by-step explanation:

Answer:

1.7

Step-by-step explanation:

Given:

Area of polygon=10.4

sides of polygon=2

Formula for area of a regular polygon= 1/2 (apothem x perimeter )

Putting value, we get

10.4= 1/2 ( a x 12 )

10.4=6a

a=10.4/6

a=1.73

the measure of the apothem, rounded to the nearest tenth of an inch=1.7!

Answer:

1.7 inches

Step-by-step explanation:

If the area of the regular hexagon is 10.4 in.2, the measure of the apothem, rounded to the nearest tenth of an inch is  1.7 inches

Answer:

y = -16

Step-by-step explanation:

f(x)=3/4x+12 (replace f(x) with y)

y =3/4x+12  (rearrange to express x in terms of y)

y - 12=3/4 x

3/4 x = y - 12

3x = 4(y - 12)

x = (4/3)(y - 12)

x = (4/3)y - (4/3)(12)

x = (4/3)y - 16

[tex]f^{-1}[/tex] (y) = (4/3)y - 16

[tex]f^{-1}[/tex] (x) = (4/3)x - 16

comparing to general form

y = mx + b where b is the y-intercept

b = -16

Hence the y-intercept is y = -16

The value of the y-intercept will be given as y = -16

The equation in mathematics is the relationship between the variables and the number and establishes the relationship between the two or more variables.

f (x)  = 3/4x  +  12 (replace f(x) with y)

y     =   3/4x  +  12  (rearrange to express x in terms of y)

y - 12  =  3/4 x

3/4 x  =  y - 12

3x    =   4(y - 12)

x     =  (4/3)(y - 12)

x    =    (4/3)y - (4/3)(12)

x    =    (4/3)y - 16

(y)  =  (4/3)y - 16

(x) =   (4/3)x - 16

Compared to the general form

y = mx + b where b is the y-intercept

b = -16

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Answer:

[tex]w \ne0[/tex]

Step-by-step explanation:

The area of a rectangle is given by:

[tex]Area = L \times \: W[/tex]

In this case, we have the height replacing the length.

[tex]Area=H\times w[/tex]

The area of the rectangle is 70.

[tex]H\times w = 70[/tex]

Dividing through by w gives:

[tex]H = \frac{70}{w} [/tex]

Or to show that H is dependent on w, we write

[tex]H (w)= \frac{70}{w} [/tex]

[tex]w \ne \: 0[/tex]

Domain is the set of all real numbers for which the function is defined.

Therefore the domain is all real numbers except 0.

Answer:

w>0

Step-by-step explanation:

Answer:

x - 4y = 8

Step-by-step explanation:

We are given point slope form of the equation of the line that passes through the point [tex](-4, -3)[/tex] and [tex](12,1)[/tex] which is [tex]y-1=\frac{1}{4} (x-12)[/tex].

We are to write this equation in its standard form.

From the given equation, we know that the slope is [tex]\frac{1}{4}[/tex] so we will find the y intercept.

[tex]y=mx+c[/tex]

[tex]1=\frac{1}{4}\times (12) +c[/tex]

[tex]c=-2[/tex]

Substituting the given values and the y intercept in the standard form of equation.

[tex]y=mx+c[/tex]

[tex]y=\frac{1}{4} x-2[/tex]

Rearranging this to get:

x - 4y = 8

Answer:

x - 4y = 8.

Step-by-step explanation:

y - 1 = 1/4(x - 12)

y = 1/4x - 3 + 1

y = 1/4x - 2

1/4x - y - 2 = 0

1/4x - y = 2

Multiply through by 4:

x - 4y = 8 is standard form.

Answer:

Step-by-step explanation:

(x²-6x-3)(7x²-4x+7)= ?

Multiply each term of 2nd bracket with the 1st bracket:

=7x²(x²-6x-3) -4x(x²-6x-3) +7(x²-6x-3)

=7x^4-42x^3-21x^2-4x^3+24x^2+12x+7x^2-42x-21

Now solve the like terms:

=7x^4-46x^3+10x^2-30x-21

Therefore the answer is (x²-6x-3)(7x²-4x+7)=7x^4-46x^3+10x^2-30x-21 ....

Answer:

{f ∈ R : f≥-8}

Step-by-step explanation:

The range is the output values

f(x) = |x+5| - 8​

The smallest value the absolute value part can take is 0

f (min) = 0-8

The largest value is infinity

f(max) = infinity -8 = infinity

The range is -8 to infinity

Answer:

Answer is D - $45.75

Step-by-step explanation:

(6 x $4.25) + (3 x $6.75) = $45.75

Answer:

    D) $45.75

Step-by-step explanation:

Step One: Multiply 6 times 4.25 and get 25.5

Step Two: Multiply 3 times 6.75 and get 20.25

Step Three:  Add both answers together: 25.5 + 20.25 and get 45.75 which is your answer.

Answer:

Option d. (-2,-5)

Step-by-step explanation:

we know that

The equation of a vertical parabola in vertex form is equal to

[tex]y=a(x-h)^{2} +k[/tex]

where

a is a coefficient

(h,k) is the vertex of the parabola

In this problem we have

[tex]y=x^{2} +4x-1[/tex]

This is the equation of a vertical parabola open up

The vertex is minimum

Convert the equation in vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

[tex]y+1=x^{2} +4x[/tex]

Complete the square. Remember to balance the equation by adding the same constants to each side.

[tex]y+1+4=x^{2} +4x+4[/tex]

[tex]y+5=x^{2}+4x+4[/tex]

Rewrite as perfect squares

[tex]y+5=(x+2)^{2}[/tex]

[tex]y=(x+2)^{2}-5[/tex] -----> equation in vertex form

therefore

The vertex is (-2,-5)

Answer:

Part A) Annual [tex]\$66,480.95[/tex]  

Part B) Semiannual [tex]\$66,862.38[/tex]  

Part C) Monthly [tex]\$67,195.44[/tex]  

Part D) Daily [tex]\$67,261.54[/tex]

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

Part A)

Annual

in this problem we have  

[tex]t=5\ years\\ P=\$47,400\\ r=0.07\\n=1[/tex]  

substitute in the formula above  

[tex]A=47,400(1+\frac{0.07}{1})^{1*5}\\A=47,400(1.07)^{5}\\A=\$66,480.95[/tex]

Part B)

Semiannual

in this problem we have  

[tex]t=5\ years\\ P=\$47,400\\ r=0.07\\n=2[/tex]

 substitute in the formula above  

[tex]A=47,400(1+\frac{0.07}{2})^{2*5}\\A=47,400(1.035)^{10}\\A=\$66,862.38[/tex]

Part C)

Monthly

in this problem we have  

[tex]t=5\ years\\ P=\$47,400\\ r=0.07\\n=12[/tex] 

substitute in the formula above  

[tex]A=47,400(1+\frac{0.07}{12})^{12*5} \\A=47,400(1.0058)^{60}\\A=\$67,195.44[/tex]

Part D)

Daily

in this problem we have  

[tex]t=5\ years\\ P=\$47,400\\ r=0.07\\n=365[/tex] 

substitute in the formula above  

[tex]A=47,400(1+\frac{0.07}{365})^{365*5}\\A=47,400(1.0002)^{1,825}\\A=\$67,261.54[/tex]

Answer:

Step-by-step explanation:

Answer:

The mathematical expression is : (15 - 4) x (14 - 6) square feet.

The evaluation of this expression gives 88 sq ft.

Step-by-step explanation:

The length of the shaded region is (15 - 4) feet

The width of the shaded region is (14 - 6) feet

hence the expression for area is

(15 - 4) x (14 - 6) square feet.

fyi, if you work this out, you will get

(15 - 4) x (14 - 6)

=11 x 8

= 88 square feet.

Answer:

(15 ft - 4 ft) * (14 ft - 6 ft)

Step-by-step explanation:

The shaded area is a rectangle.

area of rectangle = length * width

Length of outer rectangle = 15 ft

Length of shaded rectangle = 15 ft - 4 ft

Width of outer rectangle = 14 ft

Width of shaded rectangle = 14 ft - 6 ft

Area of shaded rectangle = length * width = (15 ft - 4 ft) * (14 ft - 6 ft)

Answer:

8 pounds of peanuts, 6 pounds of raisins and 6 pounds of chocolate chips

Step-by-step explanation:

Let x be the number of pounds of peanuts and y be the number of pounds of raisins and chocolate chips.

Peanuts cost $2 per pound, then x pounds cost $2x.

Raisins cost $2.50 per pound, then y pounds cost $2.50y.

Chocolate chips cost $4 per pound, then y pounds cost $4y.

In total, x+y+y=20 and those 20 pounds cost

2x+2.50y+4y=20·2.75.

Solve the system of two equations:

[tex]\left \{ {{x+2y=20} \\ \\ \\ \\ \\ \\ \atop {2x+6.5y=55}} \right.[/tex]

From the first equation:

[tex]x=20-2y[/tex]

Substitute x into the second equation:

[tex]2(20-2y)+6.5y=55\\ \\40-4y+6.5y=55\\ \\2.5y=15\\ \\25y=150\\ \\y=6\\ \\x=20-2\cdot 6=8[/tex]

Answer:

C

Step-by-step explanation:

For the given intervals

( - ∞, - 5) ← use any value < - 5 but not - 5, the parenthesis ) indicates that x is less than - 5 but not equal to - 5

(- 5, - 1) ← - 4, - 3, - 2 can be used but not - 5 or - 1

(- 1, 4) ← 0, 1, 2, 3 can be used but not - 1 or 4

(4, ∞ ) ← use any value > 4 but not 4

Hence

3 can be used in (- 1, 4)

- 6 can be used in (- ∞, - 5)

zero can be used in (- 1, 4)

- 5 cannot be used in any of the given intervals

Answer:

A

Step-by-step explanation:

A:  The student incorrectly divided both sides by 35.  The student should first add 10 to both sides, obtaining 35x = 15, and then divide 15 by 35, obtaining the final answer 3/7.

Answer:

[tex]\large\boxed{-3x+2y\geq7}[/tex]

Step-by-step explanation:

<, > - dotted line

≤, ≥ - solid line

<, ≤ - shaded region below the line

>, ≥ - shaded region above the line

====================================

We have solid line (≤, ≥).

Shaded region is above the line (>, ≥)

Therefore, the inequality sign must be: ≥

Finally, your answer is -3x + 2y ≥ 7.

Check the equation of a line.

The point-slope form of an equation of a line:

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

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

From the graph we ahve the points (3, 8) and (1, 5) - look at the picture.

Substitute:

[tex]m=\dfrac{5-8}{1-3}=\dfrac{-3}{-2}=\dfrac{3}{2}[/tex]

[tex]y-8=\dfrac{3}{2}(x-3)[/tex]

Convert to the standard form [tex]Ax+By=C[/tex]:

[tex]y-8=\dfrac{3}{2}(x-3)[/tex]            multiply both sides by 2

[tex]2y-16=3(x-3)[/tex]           use the distributive property

[tex]2y-16=3x-9[/tex]             subtract 3x from both sides

[tex]-3x+2y-16=-9[/tex]           add 16 to both sides

[tex]-3x+2y=7[/tex]         CORRECT :)

Answer:

A line of best fit is a straight line that best represents the data on a scatter plot. This line may pass through some of the points, none of the points, or all of the points. A real world example would be a scatter plot of the number if balloons bought each year and a straight line going diagonally representing the average or goal of the number of balloons bought. The points may be above (signaling that the number of balloons purchased was higher than normal or exceeded the goal) or they may be below (signaling that balloon sales are lower than normal or didnt meet there goals). I hope this helps, if not then I apologize

Answer with explanation:

Line of best fit is the line which describes the relationship between two variables with the help of Linear Equation in two variables.

 The equation of line of best fit is:

   y= a x + b

Where, y and x are related with each other,that is with increase in one other may decrease or with decrease in one other may increase or Both increases in same way.

Real life Example

There are ten bulbs which have to be arranged in a rectangular room.Switch off all the Bulbs.Now you have to arrange the bulbs in the room in such a way that room has maximum intensity of light.

As ceiling of room is like two dimensional coordinate plane.Now you have arranged the bulb.You have to draw a line which is called line of best fit such that as the number of bulbs increases intensity of room increases.The line of best fit may pass all the points where bulb is located  or none of the points where bulb is located or may be single or two or three or more than these points where bulb is located.

Answer:

10 inches

Step-by-step explanation:

All the sides are the same.

Answer:

B)

B)

D)

Step-by-step explanation:

1. [tex]7x^3y+14x^2y^3-7x^2y^2[/tex]

The GCF of all the term of the above polynomial is [tex]7x^2y[/tex] , hence we take it outside and form a bracket

[tex]7x^2y(x+2y^2-y)[/tex]

The polynomial within the bracket can not be factorized further hence this is our final answer. Option (B) is the right answer

2. [tex]5x(x+3)+6(x+3)[/tex]

The GCF of all the term of the above polynomial is [tex](x+3)[/tex] , hence we take it outside and form a bracket

[tex](x+3)(5x+6)[/tex]

The polynomial within the bracket can not be factorized further hence this is our final answer. Option (B) is the right answer

3. [tex]8x^5+2x^4+4x^2[/tex]

The GCF of all the term of the above polynomial is [tex]2x^2[/tex] , hence we take it outside and form a bracket

[tex]2x^2(4x^3+x^2+2)[/tex]

The polynomial within the bracket can not be factorized further hence this is our final answer. Option (D) is the right answer

The answer is 2+2√3 or 2-2√3

Answer:

[tex]x = 2[/tex]±[tex]\sqrt{12}[/tex]

Step-by-step explanation:

Given the following equation ax^2 + bx + c = 0, the quadratic formula states that the solution to that equation is going to be given by:

[tex]x1 = \frac{-b+\sqrt{b^{2}-4ac } }{2a}[/tex]

[tex]x1 = \frac{-b-\sqrt{b^{2}-4ac } }{2a}[/tex]

In this case, a=1, b=-4 and c=-8. Therefore:

[tex]x1 = \frac{4+\sqrt{(-4)^{2}-4(1)(-8)} }{2}[/tex]

[tex]x1 = \frac{4+\sqrt{48}}{2}[/tex]

[tex]x1 = 2+\sqrt{12}[/tex]

[tex]x2 = \frac{4-\sqrt{(-4)^{2}-4(1)(-8)} }{2}[/tex]

[tex]x2 = \frac{4-\sqrt{48}}{2}[/tex]

[tex]x2 = 2-\sqrt{12}[/tex]

Therefore the solutions are:

[tex]x = 2[/tex]±[tex]\sqrt{12}[/tex]

Answer:

Step-by-step explanation:

This is an absolute value equation.

Firstly we will remove absolute value:

Absolute value always gives the positive result. Hence to remove the absolute value we will take both positive and negative:

|x+4|=2

x+4=2

Move the constant value to the R.H.S

x=2-4

x= -2

x+4 = -2

Move 4 to the R.H.S

x= -2 -4

x= -6

Therefore x = (-2, -6)....

Answer:

a^ (13)

Step-by-step explanation:

We know x^b* x^c = x^ (b+c)

a^8 * a^5 = a^ (8+5) = a^ (13)

Answer:

Step-by-step explanation:

The answer would be A^13, because when multiplying exponents with the same base, you just have to adfd the exponents.

Answer:

Step-by-step explanation:

The smallest number is 0.6. A fractional amount is always less that a whole number.

6.0 is the next smallest amount in some form. 6.009 The 0.009 is very tiny compared to the other numbers

then comes 6.08 That has only 2 decimal places, but those two places are bigger than 6.009

0.009 has 3 decimal places.

========

Finally 6.24 is larger than anything else. The 2 is in the tenths place.

Answer:

$950

Step-by-step explanation:

(500*6*15)/100 = 450 (applying the formula of simple interest)

450 + 500 ( adding the interest to the initial investment or princlple)

= 950 (bank balance after 15 years)

Hope this helps! :)

Answer:

x = -5

Step-by-step explanation:

It just is :)

For this case we must find the value of "x" of the following expression:

[tex]2x-3 + 3x = -28[/tex]

We add similar terms:

[tex]5x-3 = -28[/tex]

We add 3 to both sides of the equation:

[tex]5x = -28 + 3[/tex]

Different signs are subtracted and the sign of the major is placed:

[tex]5x = -25[/tex]

We divide between 5 on both sides of the equation:

[tex]x = \frac {-25} {5}\\x = -5[/tex]

ANswer:

[tex]x = -5[/tex]