6 points are place on the line a, 4 points are placed on the line b. How many triangles is it possible to form such that their verticies will be the given points, if a ∥b?

Answer:

The sum of the series is Sₙ = n/2 [2·a + (n - 1)·d] where a = 8 and d = 8, therefore 8 + 16 + 24 + ... + 8·n = 4·n·(n + 1)

Step-by-step explanation:

The parameters given are;

8 + 16 + 24 + ... + 8·n = 4·n·(n + 1)

The given series of numbers can be checked to find;

16 - 8 = 24 - 16 = 8

Therefore, the series of numbers is an arithmetic progression with first term = 8, and common difference = 8, we have;

The sum of n terms of an arithmetic progression, Sₙ, is given as follows;

Sₙ = n/2 [2·a + (n - 1)·d]

Where;

a = The first term of the series of numbers = 8

d = The common difference = 8

∴ Sₙ = n/2 × [2×8 + (n - 1)×8] = n [2×8/2 + (n - 1)×8/2]  =  n × [8 + (n - 1)×4]

Sₙ =  n × [8 + (n - 1)×4] =  n × [8 + 4·n - 4] = n × [8  - 4 + 4·n] = n × [4 + 4·n]

Sₙ =n × [4 + 4·n] = 4 × n×(n + 1) = 4·n·(n + 1).

Answer:

y=3/4x-2

Step-by-step explanation:

two points from graph (0-2) and (8,4)

find slope m: y2-y1/x2-x1

m=4+2/8-0

m=6/8=3/4

x=0 then y=b=-2

y=3/4x-2

Answer:

The rate charged by first mechanic per hour= x =$85

The rat charged by second mechanic per hour =y = $70

Step-by-step explanation:

Two mechanics worked on a car. The first mechanic worked for 10 hours, and the second mechanic worked for 15 hours. Together they charged a total of $1900. What was the rate charged per hour by each mechanic if the sum of the two rates was $155 per hour?

Solution

Let

x= hourly rate of the first mechanic

y= hourly rate of the second mechanic

Derive two equations to solve for the two unknowns

10x + 15y = 1900 (1)

x + y = 155 (2)

From (2)

x + y = 155

x=155-y

Substitute x=155-y into (1)

10x + 15y = 1900

10(155-y) + 15y =1900

1550 -10y + 15y =1900

5y =1900-1550

5y=350

Divide both sides by 5

y= 70

Substitute y=70 into (2)

x + y = 155

x + (70) =155

x=155 - 70

= 85

x= 85

The rate charged by first mechanic per hour= x =$85

The rat charged by second mechanic per hour =y = $70

Answer:

(f*g)(x) = 4x⁵ - 16x³ + x² - 4

Step-by-step explanation:

To find (f*g)(x), you need to multiply f(x) with g(x).  Use FOIL to multiply.

f(x) = 0.5x² - 2

g(x) = 8x³ + 2

(f*g)(x) = (0.5x² - 2)(8x³ + 2)

(f*g)(x) = 4x⁵ + x² - 16x³ - 4

(f*g)(x) = 4x⁵ - 16x³ + x² - 4

Answer:

The answer is below

Step-by-step explanation:

The ratio of Keith's height and his nephew's height is 15:7. Let keith height be x cm and his nephews height be y cm.

[tex]\frac{x}{y}=\frac{15}{7} \\x=\frac{15}{7}y[/tex]

Keiths height increased by 16% , therefore Keith new height is (100% + 16%) × x = 1.16x

The nephew height is doubled, therefore his new height is 2y.

Given that Keith is now 34 cm taller than his nephew

1.16x = 2y + 34

but x = (15/7)y

[tex]1.16(\frac{15}{7} )y=2y+34\\\\\frac{87}{35} y=2y+34\\\\\frac{87}{35} y-2y=34\\\\\frac{17}{35}y=34\\ \\y=\frac{34*35}{17}\\ \\y=70\ cm[/tex]

The nephews new height = 2y = 2(70) = 140 cm

Keith new height = 2y + 34 = 140 + 34 = 174 cm

Their total current height = 140 cm + 174 cm = 314 cm

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

Explanation:

The diagonal cuts the rhombus into two congruent isosceles triangles. We know they are isosceles because the non-diagonal sides are equal in length (since all four sides of a rhombus are the same length).

Let x be the measure of angle 1. This is one base angle. The other base angle is also x as well. The third angle of the bottom triangle is angle 3, which is given to us at 80 degrees. For any triangle the three angles always add to 180.

x+x+80 = 180

2x+80 = 180

2x = 180-80

2x = 100

x = 100/2

x = 50

Angle 1 is therefore 50 degrees.

Angle 2 is also 50 degrees because angles 1 and 2 are congruent alternate interior angles. Any rhombus is a parallelogram (but not the other way around) so the top and bottom lines of the rhombus are parallel, allowing the alternate interior angles to be congruent.

Answer:

m<2 = m<1 = 50°

Step-by-step explanation:

In a Rhombus, Diagonals intersect at 90° as well bisect angles.

Therefore, in a triangle formed by <1, 90° at the diagonal intersection and angle bisection of <3 = 40°.

m<1 = m<2 = 50°

Work Shown:

f(x) = 50(0.952)^x

f(9) = 50(0.952)^9

f(9) = 32.1146016801717

f(9) = 32 approximately

Side note: the exponential function is in the form a*b^x with b = 1+r = 0.952, which solves to r = -0.048. The negative r value means we have a 4.8% decrease each year.

Another note: you don't even need to use math to answer this question. Note how 50 is the starting population and the population is declining. Only choice B has a value smaller than 50, so we can rule out the others right away.

Answer:

  32

Step-by-step explanation:

The initial value of the population is f(0) = 50(0.952^0) = 50. If the population is declining, it must be less than 50 in 9 years. The only answer choice that is less than 50 is ...

  about 32 feral cats

_____

You can evaluate f(9) to choose the same answer:

  f(9) = 50(0.952^9) ≈ 32.114 ≈ 32

Answer:

91

Step-by-step explanation:

Let x be the smallest one:

● x is the first number

● x+1 is the second number

● x+2 is the third number

The sum of these numbers is 276

● x+(x+1)+(x+2) =276

● x+x+1+x+2 = 276

● 3x + 3 = 276

Substract 3 from both sides:

● 3x+3-3 = 276-3

● 3x = 273

Divide both sides by 3

● (3x)/3 = 273/3

● x = 91

So the smallest one is 91

Answer:

v = 6

Step-by-step explanation:

3/v = 2/4

We can use cross products to solve

2v = 3*4

2v = 12

Divide each side by 2

2v/2 = 12/2

v =6

Answer:

v=6

Step-by-step explanation:

If this is making them equal, then you should know that 2/4 is 1/2 , so you could just multiply 3 by both the 1 and the 2 in 1/2 and 1 times 3 is 3 which is what we have and 2 times 3 is 6 which is v.

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               Hi my lil bunny!

   ❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

[tex]\frac{3}{7}+\frac{5}{21}[/tex]

[tex]= \frac{3}{7}+\frac{5}{21}[/tex]

[tex]= \frac{9}{21}+\frac{5}{21}[/tex]

[tex]= \frac{9 + 5}{21}[/tex]

[tex]= \frac{14}{21}[/tex]

[tex]= \frac{2}{3}[/tex] (Decimal: 0.666667)

Answer : [tex]\boxed{\frac{2}{3} }[/tex] (Decimal: 0.666667)

 ❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

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        Have a great day/night!

                   ❀*May*❀

Answer:

b

Step-by-step explanation:

Answer:

The answer is D or (10,-9)

Step-by-step explanation:

Since y is already given (and you have to use the substitution method) substitute y into one of the equations. So you should have something like this:

-2x+11=3x+21

After that merely solve for x which should get you x=10. After you get your x value plug 10 in either (of the original) equation and your y value should be -9. For example if you chose y=-2x+11 you should have y= -2(10)+11. In the end your answer should be (10,-9).

If you want to check your work merely plug your answer into both equations (ex: -9=-2(10)+11 --> -9=-9), therefore you know your answer is correct).

Hope this helped!

Answer:

546 - 25 x 13 (divided by) 13

546 - (25 x 13) / 13

Step-by-step explanation:

25 x 13 = 325

546 - 325 = 221

221 / 13 = 17

17 mens teams can register.

Answer:

[tex]25(13)+13m\leq 546[/tex]

A

Step-by-step explanation:

Each team can only consists of thirteen players. Therefore, by letting w represent the number of women's teams and m the number of men's teams, the total number of players is represented by the equation:

[tex]13w+13m[/tex]

The total number of players cannot surpass 546. In other words, it must be less than or equal to. Therefore:

[tex]13w+13m\leq 546[/tex]

We are given that that 25 women's teams have already signed up. To find out the possible number of men's teams that can sign up, we can substitute 25 for w and then solve for m.

Therefore:

[tex]25(13)+13m\leq 546[/tex]

In conclusion, the answer is A.

Answer:

y=x-1

Step-by-step explanation:

Answer:

Cylinder has a formula

π×r²×h

so of it is open

π×r²×h - π×r²

Answer:

pls give brainiest

Step-by-step explanation:

A=2πr×h(r+h)

Step-by-step explanation:

Since this is a rectangle these two equations for the length have to equal each other.

2x+4=7x-1

We now need to get all of the x's on one side and constant numbers on the other side.

add 1 to both sides and subtract 2x from both sides.

5=5x

divide 5 from both sides.

x=1

Answer:

u should put this also in English then type it in so it will translate

Answer:

Parallelogram

Step-by-step explanation:

Answer:

Parallelogram

Step-by-step explanation

Answer:

99% confidence interval will be wider because as the level of confidence increase the width increases as well and the standard error decreases

Step-by-step explanation:

The  confidence interval is directly proportional to the sample size  hence the 99% confidence interval will be wider than the 95% confidence interval of the sample of 120 college students

using a 99% confidence interval gives a more accurate result than a 95% confidence because the standard error decreases with increase in confidence interval

Answer:

B, f(x) = ( x+2) ^2(x-1) (x+3)

Step-by-step explanation:

Looking at the x- intercepts, the line passes at 2, -1, and 3, so B is you answer (:

Answer:

the positive integers or whole numbers include 1, 2, 3, and etc. sometimes zero.

Whole numbers are 0, 1, 2, 3, 4, 5, 6. Whole numbers include positive integers along with 0.

17, 99, 267, 8107 and 999999999 are examples of whole numbers.

A rational number is a number that can be express as the ratio of two integers. A number that cannot be expressed that way is irrational. For example, one third in decimal form is 0.33333333333333

A real number that can NOT be made by dividing two integers (an integer has no fractional part). "Irrational" means "no ratio", so it isn't a rational number.

Example: π is an irrational number.

The real numbers include all the rational numbers, such as the integer −5 and the fraction 4/3, and all the irrational numbers, such as √2.

Included within the irrationals are the transcendental numbers, such as π

Answer:

[tex]\huge\boxed{\sf y = 2x -4}[/tex]

Step-by-step explanation:

The given equation is:

y = 2x + 3

Where Slope = m = 2 , Y-intercept = b = 3

Parallel lines have equal slopes

So, Slope of new line = m = 2

Now, Finding y-intercept:

Given Point = (x,y) = (1,-2)

So, x = 1 , y = -2

Putting m, x and y in standard form of equation to get b:

[tex]\sf y = mx+b[/tex]

[tex]\sf -2 = (2)(1) + b\\-2 = 2 + b\\[/tex]

Subtracting 2 to both sides

[tex]\sf b = -2-2\\[/tex]

b = -4

So, the standard form og equation for the new line is :

[tex]\sf y = mx+b[/tex]

[tex]\sf y = 2x -4[/tex]

Answer:

y = 2x - 4

Step-by-step explanation:

the problem is called (slope-intercept form)

the equation of the line is y = mx + b

the equation of a line is given as y = 2x + 3

slope = 2

b = y-intercept is where the line crosses the y-axis = 3

so point (x1, y1)  = (1, -2)

by using the equation.

y = mx + b

-2 = 2 (1) + b

-2 -2 = b

therefore b = -4

writing the new equation using the slope intercept form

y = mx + b  would be y = 2x + 4

so the equation parallel to the equation y = 2x + 3 is y = 2x - 4

Answer:

Lin drank more water

Step-by-step explanation:

Given

Elena = 3 litres

Jada = ¾ of Elena

Lin = 2 times of Jada

Required

Determine if Lin drank more or less water than Elena

First, we have to get the actual amount of water Jada drank.

Jada = ¾ of Elena

Substitute 3 litres of Elena

[tex]Jada = \¾ * 3 litres[/tex]

[tex]Jada = 9/4 litres[/tex]

[tex]Jada = 2\¼\ litres[/tex]

Lin = 2 * Jada

Substitute 2¼ litres for Jada

[tex]Lin = 2 * 2\¼\ litres[/tex]

[tex]Lin = 2 * 9/4 litres[/tex]

[tex]Lin = 9/2 litres[/tex]

[tex]Lin = 4\frac{1}{2} litres[/tex]

Recall that Elena drank 3 litres

Comparing 3 Litres to [tex]4\frac{1}{2}[/tex] litres, we can conclude that Lin drank more water.

Answer:

h= 24 inches

Step-by-step explanation:

(Volume)= (Base Area) * (Height)

6,912= 288h

h=

Answer: [tex]x+y=45\\\\1000 x + 500y = $2500[/tex]

Step-by-step explanation:

Let x =  Number of employees taking technology training

y= Number of employees taking customer service training

Given, The technology training costs $1,000 per person. The customer service training costs $500 per person.

Total cost = 1000 x + 500y

Since, Total cost = $25,000 and total employee to attend training= 45 .

That means , the required equations are:

[tex]x+y=45\\\\1000 x + 500y = $2500[/tex]

Answer:

1,000x + 500y = 45

x + y =45

Step-by-step explanation:

So that means answer b is the correct answer, also I took the test.

Answer:

Option (B)

Step-by-step explanation:

From the figure attached,

ΔABC is a right triangle.

Cosine and Sine ratios from the given triangle will be,

SinA = [tex]\frac{\text{Opposite side}}{Hypotenuse}[/tex]

        = [tex]\frac{a}{c}[/tex]

CosB = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]

         = [tex]\frac{a}{c}[/tex]

Therefore, both the ratios (Sine and Cosine) will be equal as [tex]\frac{a}{c}[/tex]

Option (B) will be the correct option.

Answer:

[tex]\bold{x = 66.42^\circ, 70.53^\circ}[/tex]

Step-by-step explanation:

Given equation is:

[tex]15sin^2 x+11cosx-17=0[/tex]

To find:

Values of [tex]x[/tex] in the range [tex]0^\circ\leq x\leq180^\circ[/tex].

Solution:

First of all, let us recall one identity of square of sine and square of cosine.

Sum of square of sine of an angle and square of cosine of the same angle is equal to 1.

[tex]\bold{sin^2\theta+cos^2\theta=1}[/tex]

So

Putting [tex]sin^2x=1-cos^2x[/tex] in the given equation.

[tex]15(1-cos^2x)+11cosx-17=0\\\Rightarrow 15-15cos^2x+11cosx-17=0\\\Rightarrow -15cos^2x+11cosx-2=0\\\Rightarrow 15cos^2x-11cosx+2=0\\\Rightarrow 15cos^2x-5cosx-6cosx+2=0\\\Rightarrow 5cosx(3cosx-1)-2(3cosx-1)=0\\\Rightarrow (5cosx-2)(3cosx-1)=0\\\Rightarrow cosx=\dfrac{2}{5}, \dfrac{1}{3}[/tex]

So, in the range [tex]0^\circ\leq x\leq180^\circ[/tex]

[tex]\bold{x = 66.42^\circ, 70.53^\circ}[/tex]

The statement that is true about the given figure, a limaçon, is c. It has no rotational symmetry, with an angle of rotation of 90 degrees.

Let's examine each option and explain why they are true or false:

a. It has reflectional symmetry with one line of symmetry: This option is false. To have reflectional symmetry with one line of symmetry, the figure must be identical on both sides when divided by a line. The given figure, a limaçon, does not exhibit this property.

b. It has no rotational symmetry: This option is true. Rotational symmetry means that the figure remains unchanged after rotation by certain angles. The limaçon does not have any rotational symmetry because it does not appear the same after any rotation.

c. It has no rotational symmetry, with an angle of rotation of 90 degrees: This option is true. A figure with rotational symmetry of 90 degrees would appear the same after a 90-degree rotation. However, the limacon does not exhibit this property.

d. It has no reflectional symmetry: This option is true. Reflectional symmetry requires the figure to have a line of symmetry dividing it into two identical halves. The limaçon does not possess such a line of symmetry.

Based on the explanations above, the correct statement is that the limaçon has no rotational symmetry with an angle of rotation of 90 degrees (option c).

Learn more about symmetry here:

https://brainly.com/question/32342060

#SPJ4

Answer:

Astronomers directly use geometry in their work rather than accountants , judges, pharmacist and politicians.

They used geometry to measure velocity , direction, distance, relativity, momentum, and probability. They used it to look at objects in the sky with a telescope by setting a required angle to get a proper view .

But Accountants, judges, pharmacist and politicians are not in use of geometry directly or frequently.

Hence, Option 'B' is correct.

Step-by-step explanation:

Answer: b

Step-by-step explanation:

Answer:

B= -3

Step-by-step explanation:

Move the terms that do not contain b to the right then solve. Hope this helps!

Answer:

[tex]\large \boxed{{b=-3}}[/tex]

Step-by-step explanation:

[tex]-11b +7=40[/tex]

Subtract 7 from both sides.

[tex]-11b +7-7=40-7[/tex]

[tex]-11b=33[/tex]

Divide both sides by -11.

[tex]\displaystyle \frac{-11b}{-11} =\frac{33}{-11}[/tex]

[tex]b=-3[/tex]

Answer:

[tex]\boxed{\pink{0.27945}}[/tex]

Step-by-step explanation:

[tex]3.45 \times 0.27 \\ = 0.9315 \times 0.3 \\ = 0.27945[/tex]

Answer: thousandths place

Step-by-step explanation:

                                      ↓

3.45 x 0.27 x 0.3 = 0.27945

The place values to the right of the decimal point are:

one to the right (2): tenths

two to the right (7): hundredths

three to the right (9): thousandths

four to the right (4): ten thousandths

five to the right (5): hundred thousandths