Write a function g whose graph represents the indicated transformation of the graph of f. f(x)= | 4x+3| + 2 translated 2 units down is g (x)

Answer:

Step-by-step explanation:

The orthocenter of a triangle is the point at which the perpendicular lines drawn from the vertices to the opposite sides of the triangle intersect. The coordinates of the orthocenter of ΔJKL is (5, -1).

The orthocenter of a triangle is the point at which the perpendicular lines drawn from the vertices to the opposite sides of the triangle intersect. The orthocenter of an acute angle triangle is located within the triangle. The orthocenter of the obtuse angle triangle is located outside the triangle.

The slope of JK is (6+2)/(5-3) or 4.

So, the slope of the altitude, which is perpendicular to JK is -1/4.

Now, the equation of the altitude from L to JK is:

y + 2 = -1/4 (x - 9)

y = -1/4x + 1/4

Use the same method to find the equation of the altitude from J to KL. That is, y + 2 = 1/2 (x - 3) or y = 1/2x - 7/2.

Solve the equations to find the intersection point of the altitudes.

-1/4x + 1/4 = 1/2x - 7/2

simplifying the above equation, we get

-1/4x - 1/2x = - 7/2 - 1/4

-3/4x = - 15/4

x = 5

y = -1/4(5) + (1/4)

simplifying the above equation, we get

= -4/4

y = -1

Therefore, the coordinates of the orthocenter of ΔJKL is (5, -1).

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Answer:

21

Step-by-step explanation:

i got it from that little mathemetician

Triangle XYZ with vertices X(-3 , -2), Y(-1 , 0), and Z(0 , -1) is a right triangle.

First, using the distance formula, find the length of each side of the triangle: side XY, side XZ, and side YZ.

d = √(x2 - x1)^2 + (y2 - y1)^2

side XY : d = √(-1 - -3)^2 + (0 - -2)^2 = √4 + 4 = 2√2

side XZ : d = √(0 - -3)^2 + (-1 - -2)^2 = √9 + 1 = √10

side YZ : d = √(0 - -1)^2 + (-1 - 0)^2 = √1 + 1 = √2

Next, check if it follows the Triangle Inequality Theorem which states that the sum of any two sides must be greater than the third side, such that a + b > c, a + c > b, and b + c > a.

let a = XY = 2√2, b = XZ = √10, and c = YZ = √2

a + b > c     2√2 + √10 > √2     5.99 > 1.41     True

a + c > b     2√2 + √2 > √10     4.24 > 3.16     True

b + c > a     √10 + √2 > 2√2     4.58 > 2.83     True

Lastly, to know what type of triangle based on the length of its side,

1. Take the sum of the squares of the two smaller sides.

(√2)^2 + (2√2)^2 = 10

2. Compare it to the square of the largest side.

(√10)^2 = 10

10 = 10

If the sum of the squares of the 2 is larger than the square of the 3rd, it is an acute triangle.

if they are equal, it is a right triangle.

if they are smaller, then it is an obtuse triangle.

Hence, triangle XYZ is a right triangle.

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Answer: x=-2/3    x=-4

Step-by-step explanation:

[tex]|x-1|=|2x+3|\\[/tex]

Equate the submodular functions to zero:

x-1=0

x-1+1=0+1

x=1

2x+3=0

2x+3-3=0-3

2x=-3

Divide both parts of the equation by 2:

x=-1.5

Thus,

-∞____-1.5_____1____+∞

x∈[1,+∞)

x-1=2x+3

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

-4=x∉[1,+∞)

x∈(-1.5,1)

-(x-1)=2x+3

-x+1=2x+3

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

-2=3x

Divide both parts of the equation by 3:

x=-2/3∈(-1.5,1)

x∈(-∞,-1.5]

-(x-1)=-(2x+3)

-x+1=-2x-3

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

x=-4∈(-∞,-1.5]

Answer:

2y²+2z

Step-by-step explanation:

y² raise y to the second power

y²+z add result to z

(y²+z)(2) double it

2y²+2ź

3/2 < x <3/2 is the inequality for the equation |2 x|+4<7

For positive case

⇒ |2 x|+4 < 7

⇒ 2 |x| < 3

⇒ x < 3/2

And for negative case

⇒ x > -3/2

Thus, -3/2 < x <3/2

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

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Answer:

x = -3

Step-by-step explanation:

6(3x-4) + 54 = -3(x+11)

18x-24+54 = -3x-33       Multiply 3x and -4 by 6 this means distributive  

                                          property. Next, multiply x and 11 by -3.

18x+30 = -3x-33            Next, combine -24 and 54 which equals 30.

     -30          -30       Next, subtract 30 from both sides to leave 18x by itself.

18x = -3x-63

+3x   +3x                   Next, add 3x to both sides to leave -63 by itself.

21x = -63

/           /

21       21                 Divide 21 on both sides to leave x by itself.

x = -3

solve for n:  n>0,x=0

or

solve for x : x=0,n>0

Yes, the given set of numbers can be the measures of the sides of a triangle. The triangle is acute.

By the triangle inequality theorem, the sum of the lengths of any two sides should be greater than the length of the third side.

6.2 + 13.8 > 20

13.8 + 20 > 6.2

20 + 6.2 > 13.8

Hence, these set of numbers can be the measures of the sides of a triangle.

According to the Pythagorean Inequality Theorem, a triangle whose sides measure a, b, and c where c is the largest, the triangle can be characterized as:

acute if [tex]a^{2} + b^{2} < c^{2}[/tex]

obtuse if  [tex]a^{2} + b^{2} > c^{2}[/tex]

right if  [tex]a^{2} + b^{2} = c^{2}[/tex]

∴The longest side is 20.

Hence, a = 6.2, b = 13.8 and c = 20;

Consider [tex]a^{2} + b^{2}[/tex]  :

= [tex]6.2^{2} + 13.8^{2}[/tex]

= 228.88.

Now consider [tex]c^{2}[/tex] :

= [tex]20^{2}[/tex]

= 400.

Thus,  [tex]a^{2} + b^{2} < c^{2}[/tex].

Hence, the triangle is acute.

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Answer:

x = 16

z = 90°

Step-by-step explanation:

The angle with the measure (10x - 70) and the angle with measure (5x+10) are supplementary angles and their sum is equal to 180 so it's safe to write the following equation:

10x - 70 + 5x + 10 = 180 add like terms

15x - 60 = 180 add 60 to both sides

15x = 240 divide both sides by 15

x = 16

The angle represented with z and the angle with measure (10x - 70) are also supplementary because they are on a straight line so we can write the following equation to find the value of z:

z + (10*16-70) = 180 calculate inside the parenthesis

z + 90 = 180 subtract 90 from both sides

z = 90°

The probability that a family vacations in the mountains is 0.3

A Venn diagram is a diagram that uses circles to depict the relationships between things or finite collectives of things. Circles that overlap share characteristics, whereas circles that don't overlap do not.

Refer the Venn diagram.

The probability of a family vacationing at the beach is P(B) [the a whole blue circle] = 0.6,

The probability of a family vacationing at both locations is P(B∩M) [the red/blue overlapping intersection of a two circles] = 0.2.

P(only B) [the blue just background] = 0.6 - 0.2 = 0.4 is the probability which a family vacationed only on the beach.

P(neither) [a white background] = 0.1 is the possibility that a family vacationed at none of location.

Remember that the probability sum is 1.

P(M) [a entire red circle] = 1 - 0.1 - 0.4 = 0.5 is the probability which a family vacationed with in mountains.

As a result, the probability of a family vacationing only in the mountains is P(only M) [a red only background] = 0.5 - 0.2 = 0.3.

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If circle J has a radius of 10 units and BC = 5.4 units then the measure of CK is 2.6 units.

A radius of a circle or sphere is any of the line segments from its center to its perimeter in classical geometry, and in more modern usage, it is also their length. The name is derived from the Latin radius, which means both rays and spoke of a chariot wheel.

The radius of a circle is the distance between the circle's center and any point on its circumference. It is usually represented by the letters 'R' or 'r'. This number is significant in almost all circle-related formulas. A circle's area and circumference are also measured in terms of radius.

Since the radius of K is 8 units, BK = 8.

CK + BC = BK

Where the value of BC = 5.4, we get

substitute the value of BC in the above equation, then we get

CK + 5.4 = 8

subtract 5.4 from both sides

CK + 5.4 - 5.4 = 8 - 5.4

simplifying the above equation,

CK = 2.6

Therefore, the measure of CK is 2.6 units.

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Answer: f(-1)=-13

Step-by-step explanation:

f(0) = -5

f(n) = f(n - 1) + 8

f(0) = f(0 - 1) + 8

-5 =f(-1) + 8

f(-1)=-13

Using conversion from fraction to decimal and rational numbers, we have that:

7. The fraction that has a corresponding decimal greater than 1 is 4/3.

8. One rational number between 7 and 8 is given by option a, which is 7.83838383...

A fraction is converted to decimal dividing the numerator by the denominator.

In item 7, we consider fraction 4/3, for which:

Hence the corresponding decimal is given as follows:

4/3 = 1.333, which is the result of the division of 4 by 3, and is greater than 1.

The set of rational numbers is composed by all numbers that can be represented by fractions, such as integer, terminating decimals and repeating decimals.

In item 8, option a, we have the number 7.83, with the bar at 83. This means that 83 is the repeating decimal part, that is, the rational number is 7.83838383...

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If Johnson & Johnson sold $12,949,847 of hand lotion in 2009 and $3,150,367 of the sales was spent by mothers of Hispanic children, the percentage of Johnson & Johnson's profits due to Hispanic mothers is 24.43%.

A percentage is a ratio of one variable to the whole value or number.

Like ratios, probabilities, and proportions, percentages are expressed over 100.

The total sales revenue in 2009 = $12,949,847

The total sales revenue from Hispanic mothers = $3,150,367

The percentage of Hispanic sales over the total sales revenue = 24.43%($3,150,367/$12,949,847 x 100)

Thus, the percentage of Johnson & Johnson's profits due to Hispanic mothers is 24.43%.

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The equation of the line passing through the points (3 , 5) and (7 , 1) is x + y = 8.

The equation of a line can be expressed in different forms: standard form, slope-intercept form, and point-slope form

The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).

Given two points, (3 , 5) and (7 , 1), use the point-slope form to generate the equation of the line. But, first, get the slope of the line using the two points.

m = (y2 - y1)/(x2 - x1)

m = (1 - 5)/(7-3)

m = -4/4

m = -1

Substitute the value of the slope and one point to the point-slope form.

(y - y1) = m(x - x1)

y - 5 = -1(x - 3)

y - 5 = -x + 3

Combining the variable(s) in one side and the constant(s) in the other.

y - 5 = -x + 3

x + y = 3 + 5

x + y = 8

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Answer: 1st image: option 2

2nd image: (x, y) ==> (x+4, y-9) ==> option 4

Step-by-step explanation:

1st image: Reflection over the y-axis means that all x-coordinates are negated while the y-coordinates remain the same.

A: (2, -2) ==> A' (-2, -2)

B: (-2, 5) ==> B' (2, 5)

C: (-4, 2) ==> C' (4, 2)

Answer: option 2

A to A', B to B', C to C'

Purple to Blue

2nd image: 1st, the purple triangle moves 4 units to the right (x ==> x+4)

Then, the purple triangle moves 9 units down to become the blue triangle (y ==> y-9)

(x, y) ==> (x+4, y-9) ==> option 4

Answer: its b

Step-by-step explanation:

Solve the first equation for [tex]x[/tex].

[tex]x+3y = -2 \implies x = -3y - 2[/tex]

Substitute this into the second equation and solve for [tex]y[/tex].

[tex]-3(-3y-2) + y = 6 \implies 9y + 6 + y = 6 \implies 10y = 0 \implies y=0[/tex]

Now solve for the value of [tex]x[/tex].

[tex]x = -3\cdot0 - 2 = -2[/tex]

So the solution to the system is the point [tex](x,y) = \boxed{(-2,0)}[/tex]

Answer:

[tex]\left( \: \boxed{-2}\:, \: \boxed{0} \: \right)[/tex]

Step-by-step explanation:

Given system of equations:

[tex]\begin{cases}x+3y=-2\\-3x+y=6 \end{cases}[/tex]

To solve using the method of substitution, solve one equation for one of the variables.

Solving equation 2 for y:

[tex]\implies -3x+y=6[/tex]

[tex]\implies -3x+y+3x=3x+6[/tex]

[tex]\implies y=3x+6[/tex]

Substitute this expression into the other equation and solve for x:

[tex]\implies x+3y=-2[/tex]

[tex]\implies x+3(3x+6)=-2[/tex]

[tex]\implies x+9x+18=-2[/tex]

[tex]\implies 10x+18=-2[/tex]

[tex]\implies 10x+18-18=-2-18[/tex]

[tex]\implies 10x=-20[/tex]

[tex]\implies 10x \div 10=-20 \div 10[/tex]

[tex]\implies x=-2[/tex]

Substitute the found value of x into the expression for y, and solve for y:

[tex]\implies y=3x+6[/tex]

[tex]\implies y=3(-2)+6[/tex]

[tex]\implies y=-6+6[/tex]

[tex]\implies y=0[/tex]

Therefore, the solution to the given system of equations is:

[tex]\left( \: \boxed{-2}\:, \: \boxed{0} \: \right)[/tex]

The value of the function is x = 3 is 11

Functions are expressions that consists of dependent and independent variables. This variables are represented using letters. For instance, f(x) is a function of x.

Given the function below

f(x) = 3(x-1)² + 2x - 7

Given that the value of x is 3, hence;

f(x) = 3(3-1)² + 2(3) - 7

Expand to have:

f(3) = 3(2)² + 2(3) - 7

f(3) = 3(4) + 6 - 7

f(3) = 12 - 1

f(3) = 11

Hence the value of the function is x = 3 is 11

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The algebraic expression models for the word phrase two times the sum of a and b is 2(a+b)

Given,

The word phrase : Two times the sum of a and b.

Sum of a and b = a+b

2 times the sum of a and b = 2(a+b)

Hence, the algebraic expression models for the word phrase two times the sum of a and b is 2(a+b)

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Answer:

y=8

Step-by-step explanation:

The equation: y=mx+c

First you have to turn this equation into a proper equation (y=mx+c).

m = gradient

c = y-intercept (where the line goes through the y-axis).

To turn this into a proper equation, you have to isolate the y by subtracting 5 from both sides (because whatever you do to one side, you have to do the same to the other side).

So you subtract 5 by 5 and subtract 5 from 13. *You do not subtract 5 from 6x.

This will give you and answer of y=6x+8.

m = gradient = 6

c = y-intercept = 8

So the value of y is 8.

Answer: x = -5

Step-by-step explanation:

The angle of the parallelogram is mZDCF= 61°

DF= EB and EF = AD

DF =18, mZDEF =61°

□CDEF is parallelogram, so mZDEF =61°

With two sets of parallel sides, a parallelogram is a quadrilateral. A parallelogram has opposite sides that are the same length and angles that are the same size. Additionally, the internal angles on the same transverse side are supplementary. The total internal angles add up to 360 degrees.

The term "parallelepiped" refers to a three-dimensional shape with parallelogram-shaped faces. The parallelogram's base (one of its parallel sides) and height (the distance between its top and bottom elevations) determine its area. The lengths of the four sides determine a parallelogram's perimeter.

A parallelogram's characteristics are shared by the shapes of a square and a rectangle. Rhombus: A parallelogram is a rhombus if all of its sides are congruent or equal to one another.

Hence, the angle of the parallelogram is mZDEF =61°

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Answer:

Eli has the faster speed than Jess.

Answer:

78m

Step-by-step explanation:

6×13

78

not too sure tho

The common ratio of the geometric sequence can be determined by finding the dividing any of the given term in the geometric sequence, n by the preceding term n-1.

The geometric sequence from part a is 2,4,8,…

Geometric sequence is a series of number that increases or decreases by a constant ratio called a common ratio. Each term in the sequence is the product of the common ratio and the previous term.

Hence, common ratio r = nth term/n-1 term

For the given geometric sequence,

r=2nd term/1st term=3rd term/2nd term

r=4/2=2 or

r=8/4=2

The common ratio of the geometric sequence 2,4,8,… is 2

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Answer:

The answer is 40. If you divide 4000 by 100 you get 40. Hopefully this is what you were looking for.

Step-by-step explanation:

4000/100=40

Answer:

_00 x 10 = _000 (100 x 10 = 1000 basically).

40 x 100 = 4000

so..

40 hundreds is the same as 4 thousands.