Which of the following is a true proportion of the figure based on the triangle proportionality theorem?

A)
h/j=k/i

B)
j/h=j/k

C)
k/j=i/j

D)
h/k=k/i

Yes, angle 1 is vertically opposite to angle 4 because they are formed due to the intersection of straight lines.

When two lines intersect each other, then the opposite angles formed are called vertical angles or vertically opposite angles. A pair of vertically opposite angles are equal to each other. Also, a vertically opposite angle and its adjacent angle are supplementary angles, i.e., they add up to 180 degrees.

For example, if two lines intersect and make an angle, say X=55°, then its opposite angle is also equal to 55°. And the adjacent angle to angle X will be equal to 180 – 55 = 125°

In the given figure, ∠AOC and ∠BOD form a pair of vertically opposite angles and similarly ∠AOD and ∠BOC form such a pair. Therefore,

∠AOC = ∠BOD

∠AOD = ∠BOC

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B. The function shown on the graph has a smaller rate of change, but a higher starting point.

Rate of change = slope of a linear graph.

Given the linear function, [tex]y=4x+2[/tex] , the rate of change here is represented by the slope of the line, which is 4.

Let's find the rate change of the function represented on the graph using slope formula:

Rate of change = [tex]\frac{y2-y1}{x2-x1}[/tex]

Use coordinates of any two points on the line. Let's take,

[tex](0,4)= (x1,y1)\\(1,7)=(x2,y2)[/tex]

Rate of change = [tex]\frac{7-4}{1-0} = 3[/tex]

Rate of change of the linear function of the graph = 3.

Thus the function on the graph has a smaller rate of change, than the function, y = 4x + 2.

The starting value of a function is the y-intercept, that is, the value of y, when x = 0. It is the point at which the line intercepts the y-axis.

The starting value of the linear function, y = 4x + 2 is 2.

The starting value of the function on the graph is 4. At this point, x = 0.

Thus, the function on the graph has a higher starting point.

The statement that correctly compares the function shown on this graph with the function y= 4x+2 is:

B. The function shown on the graph has a smaller rate of change, but a higher starting point.

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Answer:

[tex]5x^2-3x-7,\,\,f(-2)=19[/tex]

Step-by-step explanation:

[tex]f(x)=2x^2-4x+3x^2+x-7\\f(x)=5x^2-3x-7\\f(-2)=5(-2)^2-3(-2)-7\\f(-2)=5(4)+6-7\\f(-2)=20-1\\f(-2)=19[/tex]

Answer:

x: -8, 0, 8, 16, 24

y: -8, -5, -2, 1, 4

Step-by-step explanation:

For the X values, it is going up by 8.

For the Y values, plug in the X value into the equation.

The number of installations in September were forty that lead to John and Wesley earning same amount of money.

Let the number of installations be x. The equation of be formed for each paycheck will be -

Total paycheck = base pay + number of installations × comission on each installation

The total paycheck and number of installations is same. So equating the equations by keeping x.

2000 + 65.25x = 380 + 105.75x

Rewriting the equation -

105.75x - 65.25x = 2000 - 380

Performing subtraction on each side of the equation

40.5x = 1620

x = 1620/40.5

Performing division on Right Hand Side of the equation

x = 40

There were 40 installations.

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Answer:

11 pounds

Step-by-step explanation:

The ratio of the amount of money Rachel spent on food to clothes is 1/3
She spent: 44 : (1 + 3) x 1 = 11 pounds

Answer:11

Step-by-step explanation:

11 times 3 equals 33(for the clothing)

so 11 is left

The area of the garden whose length and width as given in the task content is; 30 (x + 2) square units.

It follows from the task content that the expression which represents the area of the garden plot whose dimensions are as given.

Recall that Area, A = length × width.

Therefore, since length = 6 (√(x + 2)) units

The width = (5 √(x + 2) ) units

Hence, the area of the garden plot as required in the task content is; 6 (√(x + 2)) × ( 5 √(x + 2) )

= 30 (x + 2) square units

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Answer:

39

Step-by-step explanation:

Answer:

8.1061

8.209

8.26

8.6

Step-by-step explanation:

Answer:

Orange = 4 peers

Blue = 30 peers

Step-by-step explanation:

Orange

Step 1: Find 10% of the total (40): Convert 10% to decimal form

Step 2: Multiply 0.1 by 40

[tex]=0.1\cdot \:40[/tex]

[tex]=4[/tex]

4 total peers said their favorite color was orange

Blue

Step 1: Convert [tex]\frac{3}{4}[/tex] to percentage; [tex]\frac{3}{4} = 75\%[/tex]

Step 2: Find 75% of 40: Convert 10% to decimal form

Step 3: Multiply 0.75 by 40

[tex]=0.75\cdot \:40[/tex]

[tex]=30[/tex]

30 total peers said their favorite color was blue

Purple

Step 1: Convert 0.15 to percentage

[tex]15\%[/tex]

Step 2: Find 15% of 40

[tex]\frac{x}{40}=\frac{15}{100}[/tex]

Step 3: Cross multiply; Multiply 0.15 by 40

[tex]=0.15\cdot \:40[/tex]

[tex]=6[/tex]

Answer:

scale factor(k)=23

A(x,y)=A'(kx,ky)

Let's do by using this formula

C(9,0)=C'(kx,ky)(here x=9 and y=0)

C(9,0)=(23*9,23*0)

C(9,0)=(207,0)

A(0,3)=A'(kx,ky)(here x=0 and y=3)

A(0,3)=A'(23*0,23*3)

A(0,3)=A'(0,69)

Step-by-step explanation:

sorry i dont know how to do B no

There is no shape with exact 3 sides and 3 right angles.

The shape with three sides is a triangle. A triangle is a polygon with three edges and three vertices. It is a basic shape in geometry and can be classified into several types based on the length of its sides and the measure of its angles. Triangles can be classified as acute, right, or obtuse, depending on the measure of their angles.

A right triangle is a triangle with one right angle (90 degrees ). But there can not be a triangle with 2 or more right angle.

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Answer:

That looks good

Step-by-step explanation: wait why is this here?

The equation for dimensions of the rectangle is x(x - 3) = 10 and the width is 2 meters and the length is 5 meters.

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation.

Here,

x(x-3)=10

x²-3x=10

x²-3x-10=0

x²-5x+2x-10=0

(x-5)(x+2)=0

x=-2,5

x=5 units

x-3=5-2

=2 units

The rectangle's dimensions are x(x - 3) = 10, with a width of 2 meters and a length of 5 meters.

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Answer:

[tex]\frac{9}{10}[/tex]

Step-by-step explanation:

In this question, one is asked to multiply a fraction by a whole number, first model the question.

[tex]\frac{3}{10}(3)[/tex]

In a situation like this, one multiplies the whole number by the numerator (number) over the fraction.

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

Simplify,

[tex]\frac{9}{10}[/tex]

A common error that people make is that they will multiply both the numerator and denominator by the whole number, this is the same as multiplying the answer by (1), thus it is incorrect.

Answer:

9/10

Step-by-step explanation:

took test

Answer:

perpendicular

Step-by-step explanation:

perpendicular if the product of their slopes is equal to -1

Parallel lines have equal or identical slopes

Answer:

36

Step-by-step explanation:

I thought I just answered that one.

the first sequence had only numbers that can be divided by 3.

so, what is the first number of the second sequence that can also be divided by 3 ?

36 - it fits both.

The midpoint of the x-intercepts of f(x) = (x - 2)(x - 4) is (3, 0).

The midpoint of a line segment is known as the midpoint in geometry. It is the centroid of the segment and of the ends, and it is equally distant from both of them. It cuts the section in half.

A compass and straightedge setup can be used to locate the midpoint of the line segment they determine given two points of interest. By initially building a lens out of circular arcs with equal radii centered at the two endpoints and joining the cusps of the lens, one can determine the midpoint of a line segment immersed in a plane. The midpoint of the segment is then the place where the line joining the cusps intersects the segment.

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Answer: 7 years

Step-by-step explanation:

Let the number of years be x. Therefore, their ages in x years will be:

Daughter = x

Mother = 27+x

Father = 30+x

Their mean age will then be:

[x + (27+x) + (30+x)]/3 = 26

(3x + 57) / 3 = 26

Cross multiply

3x + 57 = 26 × 3

3x + 57 = 78

3x = 78 - 57

3x = 21

x = 21/3

x = 7

Therefore, the answer will be 7 years

Check: Daughter = x = 7 years

Mother = 27+x= 27+7 = 34 years

Father = 30+x = 30 + 7 = 37 years

Mean= (7+34+37) / 3 = 78/3 = 26 years

Answer:

NOPE

Step-by-step explanation:

The triangle with sides of length 5 cm 3 cm and 4 cm is a right angled triangle because (3, 4, 5) is a Pythagorean triple.

We know that if non zero real numbers a, b, c follows Pythagoras theorem  c² = a² + b², the numbers a, b, c is called as a Pythagorean triple.

And these numbers are nothing but the sides of right triangle.

Here we have been given the triangle with sides of length 5 cm 3 cm and 4 cm

Assume that p = 5 cm, q = 3 cm and r = 4 cm

p² = 25

q² = 9

and r² = 16

Consider q² + r² = 16 + 9

q² + r² = 25

q² + r² = r²

Since given numbers follows Pythagoras theorem, (3, 4, 5) is a  Pythagorean triple.

And p = 5 cm, q = 3 cm and r = 4 cm are the lengths of sides of right triangle.

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Answer:

(20/3,0) is your x-intercept

Step-by-step explanation:

To find x-intercept, let y = 0

[tex] \displaystyle{3x = 20}[/tex]

Solve for x, divide both sides by 3:

[tex] \displaystyle{ \dfrac{3x}{3} = \dfrac{20}{3}} \\ \\ \displaystyle{ x = \dfrac{20}{3}}[/tex]

Hence, the x-intercept is (20/3,0). We write in order pair since it's x-intercept and x = 20/3 at y = 0

Answer:

C.

A traditional 401(k) is tax deferred because the income earned isn't taxed until the money is withdrawn.

Explanation:

There are two types of 401 k plans: traditional 401k and Roth 401k plans. The difference is the way there are taxed.

The traditional 401k plan is an employer-sponsored retirement scheme.  The employer withholds the employee contributions and remits the funds to the employee's 401k savings account. The amount deducted as the employee contribution is not subject to taxation at that point. Contributions to 401k plans reduce the employee's taxable income.

The amounts saved in a 401k plan are invested and generate income. Employees are not expected to pay taxes on the income generated every financial period. All taxes are deferred until the time of withdrawal.

Answer: 73.2

Step-by-step explanation:

78/2 is 39. Now, use the pythagorean theorem to find the hypoteuse (in this case the spine), which is about 73.2

Answer:

15,504 different groups

Step-by-step explanation:

Answer: if they only have 20 patients then there can only be 1 group of 15 people! hope this helps

Step-by-step explanation:

Answer:

its A

Step-by-step explanation: