Can the sides of a triangle have lengths 2, 6, and 7?

Answer:

x ≥ 4

Step-by-step explanation:

Given:

[tex]\displaystyle \large{3x-1\geq 11}[/tex]

Add both sides by 1:

[tex]\displaystyle \large{3x-1+1\geq 11+1}\\\displaystyle \large{3x\geq 12}[/tex]

Divide both sides by 3:

[tex]\displaystyle \large{\dfrac{3x}{3} \geq \dfrac{12}{3}}\\\displaystyle \large{x\geq 4}[/tex]

Hence, the solution is x ≥ 4

Answer: y = 4.5

scale factor = 4/3

Answer:

a joke and a cartoon together cost $80

c=$15   j=$65

Step-by-step explanation:

j=joke

c=cartoon

8j +6c = 610

6j+8c = 510

    Multiply the first by 8

    Multiply the second by -6

64j +48c = 4880

-36j -48c = -3060

      ADD both (c will cancel)

28j = 1820

j= 65

       PLUG j

8(65) + 6c = 610

520+6c = 610

6c= 90

 c = 15

       j + c   = 65+15 = 80

Answer:

1/162

Step-by-step explanation:

first spin 1/9

land heads 50/50

second spin 1/9

so (9 x 2) x 9

= 162

    1

Answer:

1/162 or 0.62 % to the nearest hundredth.

Step-by-step explanation:

Prob(spinning a 4) = 1/9

Prob(spinning a 7) = 1/9

Prob(flipping a head) = 1/2

Required Probability = 1/9 * 1/2 * 1/9

1/162.

[tex]\text{If}~ \alpha ~\text{and}~ \beta~ \text{are the roots,}\\ \\x^2 -(\alpha + \beta)x +\alpha\beta = 0\\\\\text{For}~ x^2+3x-2=0\\\\\alpha +\beta=-\dfrac ba=-3\\ \\\alpha \beta = \dfrac ca = -2\\\\[/tex]

[tex]\text{So,~} \alpha^3+\beta^3 = (\alpha + \beta)(\alpha^2 + \beta^2 -\alpha \beta)\\ \\~~~~~~~~~~~~~~~~=(\alpha+\beta)\left[(\alpha +\beta)^2 -2\alpha \beta - \alpha \beta\right]\\\\~~~~~~~~~~~~~~~~=(\alpha+\beta)\left[(\alpha +\beta)^2 -3\alpha \beta \right]\\\\~~~~~~~~~~~~~~~~=-3\left[(-3)^2-3(-2)\right]\\\\~~~~~~~~~~~~~~~~=-3(15)\\\\~~~~~~~~~~~~~~~~=-45\\\\\text{And}~~~\alpha^3 \beta^3= (\alpha \beta )^3 = (-2)^3 = -8\\\\[/tex]

[tex]\text{Hence the equation whose roots are}~ \alpha^3 ~\text{and}~ \beta^3~ \text{is:}\\ \\ x^2-(\alpha^3 + \beta^3)x +\alpha^3 \beta^3 =0\\\\\implies x^2 -(-45)x+(-8)=0\\\\\implies x^2 +45x -8=0[/tex]

Answer:

1 3/4, 0

Step-by-step explanation:

You have to go 1 3/4 to the right and 0 up.

Answer:

Hope the picture will help you

Answer:  Difference between 21 1/4 - 18 2/4 =2 3/4

Step-by-step explanation:

Step-by-step explanation:

the inner angle of 2 crossing segment lines is half of the sum of the 2 arc angles.

55 = (arc angle IG + arc angle JH)/2 = (76 + JH)/2

110 = 76 + JH

arc angle JH = 34°

The required arc angle JH measures 34 degrees.

In geometry, a chord is a line segment that connects two points on the circumference of a circle. The two endpoints of the chord lie on the circle, and the chord divides the circle into two segments - the major segment and the minor segment.

Given the problem, we are given that the inner angle measures 55 degrees. Thus, we can set up an equation using the formula and solve for the unknown value.

The equation is given as follows:

55 = (arc angle IG + arc angle JH)/2

We know that the arc angle IG measures 76 degrees, so we can substitute this value into the equation:

55 = (76 + arc angle JH)/2

Multiplying both sides of the equation by 2 yields:

110 = 76 + arc angle JH

Subtracting 76 from both sides of the equation gives:

arc angle JH = 34°

Therefore, the arc angle JH measures 34 degrees.

Learn more about chords here:

https://brainly.com/question/30009947

#SPJ2

Answer:

The answer is 72

Step-by-step explanation:

because you take the 8 times it by the 9

9×8=72 square³

Answer:

2x = 26, x = 13

Step-by-step explanation:

Write and solve an equation twice a number is 26

x = unknown number

Equation: 2x = 26

Solve:

2x = 26

/2    /2 <== divide both sides by 2

x = 13

Check your answer:

2x = 26

2(13) = 26

26 = 26

This stament is correct

Hope this helps!

Answer:

median is 20

Step-by-step explanation:

due to both of them having it in there 1 time

Answer:

The Median Age: Yoga Class (31)      Dance Class (30)

The Range: Yoga Class (17-44)        Dance Class (20-47)

Step-by-step explanation:

Answer: 35

Step-by-step explanation:

     The average can be found by adding their ages together and dividing by the number of ages.

     Given:

[tex]\frac{19+20+20+21+x}{5}[/tex] = 23

     Multiply both sides of the equation by 5:

19 + 20 + 20 + 21 + x = 115

     Combine like terms:

80 + x = 115

     Subtract 80 from both sides of the equation:

x = 35

                    Erica is 35.

the length of the line would be 1 inch

Answer:

solution 1= 40ml

solution 2= 160ml

Step-by-step explanation:

%alcohol= amount of alcohol/total solutionx100

0.52x200=104ml of alcohol present

0.2x L=0.2Lml of alcohol in solution one

0.6 x M=0.6Mml of alcohol in solution two

1st equation

0.2L+0.6M=104ml alcohol

times 10 to get whole

2L+6M=1040ml

2nd

same for this equation

10L+10M=2000ml

10L+10M=2000

2L+6M=1040

elimination method

=20L+20M=4000

-

=20L+60M=10400

-40M=-6400

M=160ml

2L+6 (160)=1040

2L=1040-960

2L=80

L=40ml

Step-by-step explanation:

what is that called into the comet or ok

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

Work Shown:

[tex]n = \hat{p}*(1-\hat{p})\left(\frac{z}{E}\right)^2\\\\n \approx 0.5*(1-0.5)\left(\frac{1.96}{0.03}\right)^2\\\\n \approx 1067.111\\\\n \approx \boldsymbol{1068}\\\\[/tex]

Notes:

The approximate diameter of the rug with an area of 40 ft² is 7.14 feet.

Area is the amount of space occupied by a two dimensional shape or object.

The area of a circle is given by:

Area = π * diameter²/4

The rug has an area of 40 square feet. Hence:

40 = π * diameter²/4

Diameter = 7.14 feet

The approximate diameter of the rug with an area of 40 ft² is 7.14 feet.

Find out more on area at: https://brainly.com/question/25292087

Answer:

88 + 30[tex]\sqrt{7} \\[/tex]

Step-by-step explanation:

Expand to make easier:

(3[tex]\sqrt{7} \\[/tex] + 5) x (3[tex]\sqrt{7} \\[/tex] + 5)

FOIL:

9(7) + 15    [tex]\sqrt{7}[/tex] + 15[tex]\sqrt{7}[/tex] + 25

Simplify:

63 + 30[tex]\sqrt{7}[/tex] + 25

88 + 30[tex]\sqrt{7}[/tex]

Answer:

tan m‹G = 28.2/45.8

m‹G= 31.62°

Hello!

x + y = 9,

x=  9-y

x - y + 3z = 2

x= 2+y -3z

4y - 32 - 5 = 0.​

4y = 32+5

4y = 37

y = 37/4

Answer:

  see attached

Step-by-step explanation:

When the signs of the x^2 and y^2 terms of a relation quadratic in both x and y are different, the relation represents a hyperbola. The graph of the hyperbola is shown in the attachment.

__

If the signs are the same, the relation represents an ellipse. If the coefficients of the squared terms are also the same, then that ellipse is a circle.

Since no diagram attached there are two possible options.

Option 1

The quadrilateral is parallelogram.

In this case ∠A and ∠D sum up to 180°, therefore:

Option 2

The quadrilateral is isosceles trapezoid.

In this case ∠A is congruent with ∠D, therefore:

Answer:

115

Step-by-step explanation:

Answer:

4 ,-5

Step-by-step explanation:

Answer:

Below in bold.

Step-by-step explanation:

The ratio of theire areas is  1^2 : 3^2

= 1:9.

So the area of triangle A = 28 * 9

= 252 cm^2.

Answer:

[tex]252cm {}^{2} [/tex]

step by step explanation:

[tex]since \: \: dimension \: of \: traiangle \: a \: = 3 times \: dimension \: of \: triangle \: b \\ note \: that \: area \: is \: square \: of \: dimension \: \\ therefore \: area \: of \: triangle \: a \: = 3 {}^{2} \: area \: of \: triale \: \: b \\ area \: of \: trianle \: a = 9 \times 28 = 252cm {}^{2} [/tex]

Answer:

no

Step-by-step

Use the slope-intercept form to find the slope and y-intercept.

Tap for fewer steps...

The slope-intercept form is

y

=

m

x

+

b

, where

m

is the slope and

b

is the y-intercept.

y

=

m

x

+

b

Find the values of

m

and

b

using the form

y

=

m

x

+

b

.

m

=

4

b

=

−

6

The slope of the line is the value of

m

, and the y-intercept is the value of

b

.

Slope:

4

y-intercept:

(

0

,

−

6

)

Any line can be graphed using two points. Select two

x

values, and plug them into the equation to find the corresponding

y

values.

Tap for fewer steps...

Find the x-intercept.

Tap for fewer steps...

To find the x-intercept(s), substitute in

0

for

y

and solve for

x

.

0

=

4

x

−

6

Solve the equation.

Tap for fewer steps...

Rewrite the equation as

4

x

−

6

=

0

.

4

x

−

6

=

0

Add

6

to both sides of the equation.

4

x

=

6

Divide each term by

4

and simplify.

Tap for fewer steps...

Divide each term in

4

x

=

6

by

4

.

4

x

4

=

6

4

Cancel the common factor of

4

.

Tap for fewer steps...

Cancel the common factor.

4

x

4

=

6

4

Divide

x

by

1

.

x

=

6

4

Cancel the common factor of

6

and

4

.

Tap for fewer steps...

Factor

2

out of

6

.

x

=

2

(

3

)

4

Cancel the common factors.

Tap for fewer steps...

Factor

2

out of

4

.

x

=

2

⋅

3

2

⋅

2

Cancel the common factor.

x

=

2

⋅

3

2

⋅

2

Rewrite the expression.

x

=

3

2

x-intercept(s) in point form.

x-intercept(s):

(

3

2

,

0

)

Find the y-intercept.

Tap for fewer steps...

To find the y-intercept(s), substitute in

0

for

x

and solve for

y

.

y

=

4

(

0

)

−

6

Solve the equation.

Tap for fewer steps...

Remove parentheses.

y

=

4

(

0

)

−

6

Simplify

4

(

0

)

−

6

.

Tap for fewer steps...

Multiply

4

by

0

.

y

=

0

−

6

Subtract

6

from

0

.

y

=

−

6

y-intercept(s) in point form.

y-intercept(s):

(

0

,

−

6

)

Create a table of the

x

and

y

values.

x

y

0

−

6

3

2

0

Graph the line using the slope and the y-intercept, or the points.

Slope:

4

y-intercept:

(

0

,

−

6

)

x

y

0

−

6

3

2

0

Answer: HELLO THERE!  Here's what I found from study dot  com            "4 divided by 5 is equal to 0.8. This decimal can also be written as a fraction. 0.8 = eight tenths or 8/10 (4/5 in its reduced form)."

Step-by-step explanation:

Hope this helps, have a good day!

The sum we want is

[tex]\displaystyle \sum_{n=0}^\infty \frac{(-1)^{T_n}}{(2n+1)^2} = 1 - \frac1{3^2} - \frac1{5^2} + \frac1{7^2} + \cdots[/tex]

where [tex]T_n=\frac{n(n+1)}2[/tex] is the n-th triangular number, with a repeating sign pattern (+, -, -, +). We can rewrite this sum as

[tex]\displaystyle \sum_{k=0}^\infty \left(\frac1{(8k+1)^2} - \frac1{(8k+3)^2} - \frac1{(8k+7)^2} + \frac1{(8k+7)^2}\right)[/tex]

For convenience, I'll use the abbreviations

[tex]S_m = \displaystyle \sum_{k=0}^\infty \frac1{(8k+m)^2}[/tex]

[tex]{S_m}' = \displaystyle \sum_{k=0}^\infty \frac{(-1)^k}{(8k+m)^2}[/tex]

for m ∈ {1, 2, 3, …, 7}, as well as the well-known series

[tex]\displaystyle \sum_{k=1}^\infty \frac{(-1)^k}{k^2} = -\frac{\pi^2}{12}[/tex]

We want to find [tex]S_1-S_3-S_5+S_7[/tex].

Consider the periodic function [tex]f(x) = \left(x-\frac12\right)^2[/tex] on the interval [0, 1], which has the Fourier expansion

[tex]f(x) = \frac1{12} + \frac1{\pi^2} \sum_{n=1}^\infty \frac{\cos(2\pi nx)}{n^2}[/tex]

That is, since f(x) is even,

[tex]f(x) = a_0 + \displaystyle \sum_{n=1}^\infty a_n \cos(2\pi nx)[/tex]

where

[tex]a_0 = \displaystyle \int_0^1 f(x) \, dx = \frac1{12}[/tex]

[tex]a_n = \displaystyle 2 \int_0^1 f(x) \cos(2\pi nx) \, dx = \frac1{n^2\pi^2}[/tex]

(See attached for a plot of f(x) along with its Fourier expansion up to order n = 10.)

Expand the Fourier series to get sums resembling the [tex]S'[/tex]-s :

[tex]\displaystyle f(x) = \frac1{12} + \frac1{\pi^2} \left(\sum_{k=0}^\infty \frac{\cos(2\pi(8k+1) x)}{(8k+1)^2} + \sum_{k=0}^\infty \frac{\cos(2\pi(8k+2) x)}{(8k+2)^2} + \cdots \right. \\ \,\,\,\, \left. + \sum_{k=0}^\infty \frac{\cos(2\pi(8k+7) x)}{(8k+7)^2} + \sum_{k=1}^\infty \frac{\cos(2\pi(8k) x)}{(8k)^2}\right)[/tex]

which reduces to the identity

[tex]\pi^2\left(\left(x-\dfrac12\right)^2-\dfrac{21}{256}\right) = \\\\ \cos(2\pi x) {S_1}' + \cos(4\pi x) {S_2}' + \cos(6\pi x) {S_3}' + \cos(8\pi x) {S_4}' \\\\ \,\,\,\, + \cos(10\pi x) {S_5}' + \cos(12\pi x) {S_6}' + \cos(14\pi x) {S_7}'[/tex]

Evaluating both sides at x for x ∈ {1/8, 3/8, 5/8, 7/8} and solving the system of equations yields the dependent solution

[tex]\begin{cases}{S_4}' = \dfrac{\pi^2}{256} \\\\ {S_1}' - {S_3}' - {S_5}' + {S_7}' = \dfrac{\pi^2}{8\sqrt 2}\end{cases}[/tex]

It turns out that

[tex]{S_1}' - {S_3}' - {S_5}' + {S_7}' = S_1 - S_3 - S_5 + S_7[/tex]

so we're done, and the sum's value is [tex]\boxed{\dfrac{\pi^2}{8\sqrt2}}[/tex].

Answer:

A

Step-by-step explanation: