2. When three or more lines intersect at one point, they are

Answer:

This implies that

x2+2ax=4x−4a−13

or

x2+2ax−4x+4a+13=0

or

x2+(2a−4)x+(4a+13)=0

Since the equation has just one solution instead of the usual two distinct solutions, then the two solutions must be same i.e. discriminant = 0.

Hence we get that

(2a−4)2=4⋅1⋅(4a+13)

or

4a2−16a+16=16a+52

or

4a2−32a−36=0

or

a2−8a−9=0

or

(a−9)(a+1)=0

So the values of a are −1 and 9.

Step-by-step explanation:

Answer:

[tex]\frac{492}{65}[/tex]

Step-by-step explanation:

Using the trigonometric identity

sin²A + cos²A = 1 , then

sinA = [tex]\sqrt{1-cos^2A}[/tex] thus

sinA = [tex]\sqrt{1-(5/13)^2}[/tex]

        = [tex]\sqrt{1-\frac{25}{169} }[/tex]

        = [tex]\sqrt{\frac{144}{169} }[/tex] = [tex]\frac{12}{13}[/tex] , then

tanA = [tex]\frac{sinA}{cosA}[/tex] = [tex]\frac{\frac{12}{13} }{\frac{5}{13} }[/tex] = [tex]\frac{12}{5}[/tex]

Thus

2tanA + 3sinA

= 2 × [tex]\frac{12}{5}[/tex] + ( 3 × [tex]\frac{12}{13}[/tex] )

= [tex]\frac{24}{5}[/tex] + [tex]\frac{36}{13}[/tex]

= [tex]\frac{312}{65}[/tex] + [tex]\frac{180}{65}[/tex]

= [tex]\frac{492}{65}[/tex]

Answer:

f(g(5)) = 4

Step-by-step explanation:

It says to find the value of f(g(5)). In this case, we first have to find g(5).

Plug 5 into g(x) = -x+5

g(5) = 0

Now, f(g(5)) is f(0), since g(5) was found out to be 0.

Plug in 0 into 2x² + 7x + 4

2(0)² + 7(0) + 4 = 0 + 0 + 4 = 4

So the answer is 4.

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + b

where m is the slope and b the y- intercept

Answer:

m is the slope of the line and b is constant / y intercept value which shows that the line is passing through origin

Answer:

X can be anything above

2

Answer:

Yes

Step-by-step explanation:

the equation for Bruce would be 3b+3b-2= numbers of tiles used.

and Felocias equation would be 5b+5= numbers of tiles used

so therefore if there were 7 tiles in each box they both could have used the same number of tiles

Sin(α)=opposite leg/hypotenuse

Sin(63°)=ya/35

ya=35xSin(63°)

ya=31.2

Area(a)= (15.9x31.2)/2

Area(a)=248.0

Now, we proceed to find the area of "b". We already have the length x=15.9, so:  

Tan(α)=opposite leg/adjacent leg

yb=15.90xTan(42°)

yb=14.3

Area(b)=15.9X14.3/2

Area(b)=113.7

The total Area (At) is:  

At=Area(a)+Area(b)

At=248.0+113.7

At=361.7

10) Triangle "a":

-Adjacent leg of the triangle "a":

Cos(α)=adjacent leg/hypotenuse  

Cos(30°)=xa/48

xa=48xCos(30°)  

xa=41.6

-Opposite leg of the triangle "a":

Sin(α)=opposite leg/hypotenuse

Sin(30°)=y/48

y=48xSin(30°)

y=24.0

-Area of the triangle "a":

Area(a)=41.6x24.0/2

Area(a)=499.2

Triangle "b":

-We have the value of i(y=24).

-Adjacent leg of the triangle "b":

Tan(α)=opposite leg/adjacent leg

Tan(45°)=24/xb

xb=24/Tan(45°)

xb=24

-Area of the triangle "b":

Area(b)= 24x24/2

Area(b)=288

-Total area of the triangle (At) is:

At=Area(a)+Area(b)

At=499.2+288

At=787.2

11) To find the area of the triangle shown in this exercise, we have to apply the same procedure as in exercise 10:

-Adjacent leg of the triangle "a":

Cos(α) = adjacent leg/hypotenuse  

Cos(56°)=xa/14

xa=14xCos(56°)

xa=7.8

-Opposite leg of the triangle "a":

Sin(α)=opposite leg/hypotenuse

Sin(56°)=y/14

y=14xSin(56°)

y=11.6

-Area of the triangle "a":

Area(a)=7.8x11.6/2

Area(a)=45.2

Triangle "b":

-The value of its opposite leg is y=11.6.

-Adjacent leg of the triangle "b":

Tan(α)=opposite leg/adjacent leg

Tan(46°)=11.6/xb

xb=11.6/Tan(46°)

xb=11.2

-Area of the triangle "b":

Area(b)= 11.6x11.2/2

Area(b)=65.0

-Total area of the triangle (At) is:

At=Area(a)+Area(b)

At=45.2+65.0

At=110.2

12)-Adjacent leg of the triangle "a":

Cos(α)=adjacent leg/hypotenuse  

Cos(54°)=xa/13

xa=13xCos(54°)

xa=7.6

-Opposite leg of the triangle "a":

Sin(α)=opposite leg/hypotenuse

Sin(54°)=y/13

y=13xSin(54°)

y=10.5

-Area of the triangle "a":

Area(a)=7.6x10.5/2

Area(a)=39.9

Triangle "b":

-Adjacent leg of the triangle "b":

Tan(α)=opposite leg/adjacent leg

Tan(42°)=7.6/xb

xb=7.6/Tan(42°)

xb=8.4

-Area of the triangle "b":

Area(b)=7.6x8.4/2

Area(b)=31.9

-Total area of the triangle (At) is:

At=Area(a)+Area(b)

At=39.9+31.9

At=71.8First, it is important to remember that the formula to calculate the area of a triangle is: A=bxh/2

As we can see in the exercises, all the triangles are divided in two triangles. So, let's call "a" to the triangle on the left and "b" to the triangle on the right.

9)To find the area of the triangle "a", we need the lenght of the adjacent leg (x) and the opposite leg (ya):

Cos(α)=adjacent leg/hypotenuse  

Cos(63°)=x/35

x=35xCos(63°)

x=15.9

Sin(α)=opposite leg/hypotenuse

Sin(63°)=ya/35

ya=35xSin(63°)

ya=31.2

Area(a)= (15.9x31.2)/2

Area(a)=248.0

Now, we proceed to find the area of "b". We already have the length x=15.9, so:  

Tan(α)=opposite leg/adjacent leg

yb=15.90xTan(42°)

yb=14.3

Area(b)=15.9X14.3/2

Area(b)=113.7

The total Area (At) is:  

At=Area(a)+Area(b)

At=248.0+113.7

At=361.7

10) Triangle "a":

-Adjacent leg of the triangle "a":

Cos(α)=adjacent leg/hypotenuse  

Cos(30°)=xa/48

xa=48xCos(30°)  

xa=41.6

-Opposite leg of the triangle "a":

Sin(α)=opposite leg/hypotenuse

Sin(30°)=y/48

y=48xSin(30°)

y=24.0

-Area of the triangle "a":

Area(a)=41.6x24.0/2

Area(a)=499.2

Triangle "b":

-We have the value of i(y=24).

-Adjacent leg of the triangle "b":

Tan(α)=opposite leg/adjacent leg

Tan(45°)=24/xb

xb=24/Tan(45°)

xb=24

-Area of the triangle "b":

Area(b)= 24x24/2

Area(b)=288

-Total area of the triangle (At) is:

At=Area(a)+Area(b)

At=499.2+288

At=787.2

11) To find the area of the triangle shown in this exercise, we have to apply the same procedure as in exercise 10:

-Adjacent leg of the triangle "a":

Cos(α) = adjacent leg/hypotenuse  

Cos(56°)=xa/14

xa=14xCos(56°)

xa=7.8

-Opposite leg of the triangle "a":

Sin(α)=opposite leg/hypotenuse

Sin(56°)=y/14

y=14xSin(56°)

y=11.6

-Area of the triangle "a":

Area(a)=7.8x11.6/2

Area(a)=45.2

Triangle "b":

-The value of its opposite leg is y=11.6.

-Adjacent leg of the triangle "b":

Tan(α)=opposite leg/adjacent leg

Tan(46°)=11.6/xb

xb=11.6/Tan(46°)

xb=11.2

-Area of the triangle "b":

Area(b)= 11.6x11.2/2

Area(b)=65.0

-Total area of the triangle (At) is:

At=Area(a)+Area(b)

At=45.2+65.0

At=110.2

12)-Adjacent leg of the triangle "a":

Cos(α)=adjacent leg/hypotenuse  

Cos(54°)=xa/13

xa=13xCos(54°)

xa=7.6

-Opposite leg of the triangle "a":

Sin(α)=opposite leg/hypotenuse

Sin(54°)=y/13

y=13xSin(54°)

y=10.5

-Area of the triangle "a":

Area(a)=7.6x10.5/2

Area(a)=39.9

Triangle "b":

-Adjacent leg of the triangle "b":

Tan(α)=opposite leg/adjacent leg

Tan(42°)=7.6/xb

xb=7.6/Tan(42°)

xb=8.4

-Area of the triangle "b":

Area(b)=7.6x8.4/2

Area(b)=31.9

-Total area of the triangle (At) is:

At=Area(a)+Area(b)

At=39.9+31.9

At=71.8

Step-by-step explanation:

Answer:

1 inch = 3ft

Step-by-step explanation:

If you divided 51 feet  by 17 inch  you will get 3 feet. So 1 inch = 3 feet

NOOB

Answer:

he could run 240 miles in 30 days

Step-by-step explanation:

your welcome

Answer/Step-by-step explanation:

8 (x) = m

-----------------------

8 miles (days of the month) = total miles ran

Answer:

The answer is 1 9/19

Step-by-step explanation:

Answer:

16n + 41

Step-by-step explanation:

2(-n - 3) - 7(5 + 2n) (Given)

-2n - 6 - 35 - 14n (Distribute)

-16n - 41 (Add like terms)

16n + 41 (Divide by a factor of -1)

Answer:

B. -16n - 41

Step-by-step explanation:

Use the distributive property:

2(-n - 3) - 7(5 + 2n)

-2n - 6 - 35 - 14n

Combine like terms:

(-2n - 14n) + (-6 - 35)

-16n - 41

Answer:

The statement BI = BK is true from the given information ⇒ B

Step-by-step explanation:

If a line is a perpendicular bisector of a line segment, then

Let us find the true statement

∵ Line AB is the perpendicular bisector of segment IK

→ By using the 1st note above

∴ AB ⊥ IK

∴ ∠IJA, ∠KJA, ∠IJB, ∠KJB are right angles

→ By using the 2nd note above

∴ J is the mid-point of IK

∴ IJ = JK

∵ Any point on line AB is equidistant from The endpoints of IK ⇒ 3rd note

∴ AI = AK

∴ BI = BK

∴ The statement BI = BK is true from the given information

Answer:

x=11

Step-by-step explanation:

3x+28+5x+52+12=180

8x+92=180

-92 on both sides

8x=88

/8 on both sides

x=11

Answer:

he can play 12 games

Step-by-step explanation:

but he is gonna have some tokens left over.

Answer:

im 99.99999% sure its c

Step-by-step explanation:

Answer:

128%

Step-by-step explanation:

Because -5/4 is a negative, no matter what is in front of the % in the128%, as long as it's a positive, it is bigger than -5/4

Answer:

[tex]x^3 + 3x\²y + 3xy^2 + y[/tex] [tex]=283[/tex]

[tex]When\ x = 3\ and\ y = 4[/tex]

Step-by-step explanation:

Given

[tex]x^3 + 3x\²y + 3xy^2 + y[/tex]

Required

Solve when x = 3 and y = 4

To do this, we simply substitute  3 for x and 4 for y in [tex]x^3 + 3x\²y + 3xy^2 + y[/tex]

[tex]3^3 + 3 * 3^2 * 4 + 3 * 3 * 4^2 + 4[/tex]

[tex]27 + 3 * 9 * 4 + 3 * 3 * 16 + 4[/tex]

[tex]27 + 108 + 144+ 4[/tex]

[tex]283[/tex]

Hence:

[tex]x^3 + 3x\²y + 3xy^2 + y[/tex] [tex]=283[/tex]

[tex]When\ x = 3\ and\ y = 4[/tex]

Answer:

x = 7

Step-by-step explanation:

Since the 2 legs are congruent, then

3x + 12 = 33 ( subtract 12 from both sides )

3x = 21 ( divide both sides by 3 )

x = 7

Answer:

2893.14/321.46=9

Step-by-step explanation:

in 9 months he will run out of money

Answer:

B = Blue paint = 3.5 gallons

Y= Yellow paint = 24.5 gallons

Step-by-step explanation:

Let B = Blue paint

Y= Yellow paint

Your mixing blue paint and yellow paint to get a total of 28 gallons.

B + Y = 28 gallons

You want to use 7 times yellow paint as blue.

This means, 7B = Y

How many gallons of each should you use ?

Hence,

B + Y = 28

B + 7B = 28

8B = 28

B = 28/8

B = 3.5 gallons

B + Y = 28 gallons

Y + 3.5 gallons = 28 gallons

Y = 28 gallons - 3.5 gallons

Y = 24.5 gallons

B = Blue paint = 3.5 gallons

Y= Yellow paint = 24.5 gallons

Answer:

The value of [tex]4x+12-x^2[/tex] is 16.

Step-by-step explanation:

The given expression is [tex]4x+12-x^2\ at\ x=2[/tex].

Put x = 2 in the above expression as follows :

[tex]4x+12-x^2=4(2)+12-(2)^2\\\\=8+12-4\\\\=16[/tex]

Hence, the final answer is 16.

Answer:

The amount of cookies in the small tray = x = 19 cookies

The amount of cookies in the Large tray = y = 40 cookies

Step-by-step explanation:

Let

The amount of cookies in the small tray = x

The amount of cookies in the Large tray = y

We are told:

A caterer is making cookie trays for upcoming holiday parties.

This morning, she made 4 small trays and 4 large trays, which contain a total of 236 cookies.

This is represented Mathematically as:

4x + 4y = 236..... Equation 1

In the afternoon, she made 4 small trays and 1 large tray, which contain a total of 116 cookies.

This is represented Mathematically as:

4x + y = 116 ........ Equation 2

y = 116 - 4x

We solve the above equations using the substitution method

We substitute 116 - 4x for y in Equation 1

4x + 4y = 236..... Equation 1

4x + 4(116 - 4x) = 236

4x + 464 - 16x = 236

Collect like terms

4x - 16x = 236 - 464

-12x = -228

x = -228/-12

x = 19 cookies

Solving for y

y = 116 - 4x

y = 116 - 4 × 19

y = 116 - 76

x = 40 cookies

The number of cookies the different sized trays contained is given as:

The amount of cookies in the small tray = x = 19 cookies

The amount of cookies in the Large tray = y = 40 cookies

Answer:

(Choice A) A 16:10

(Choice C) C 48:30

(Choice D) D 32:20

Step-by-step explanation:

Given ratio

8 : 5

Select three ratios that are equivalent to 8:5

Check all options

(Choice A) A 16:10

= 16 / 10

Dividing by 2

= 8 / 5

= 8 : 5

(Choice B) B 50:80

= 50 / 80

Dividing by 10

= 5 / 8

= 5 : 8

(Choice C) C 48:30

= 48 / 30

Dividing by 6

= 8 / 5

= 8 : 5

(Choice D) D 32:20

= 32 / 20

Dividing by 4

= 8 / 5

= 8 : 5

(Choice E) E 64:35

= 64 / 35

The equivalent ratios to 8 : 5 are

(Choice A) A 16:10

(Choice C) C 48:30

(Choice D) D 32:20

Step-by-step explanation:

Side length of heptagon = 20.3cm / 7 = 2.9cm.

The heptagon is made out of 7 congruent triangles, each with height 3.0cm and base 2.9cm

Hence area of heptagon

= 7 * [(0.5)(3.0cm)(2.9cm)]

= 7 * 4.35cm²

= 30.45cm².

Answer:

First choice, 47/100

Step-by-step explanation:

16 + 9 + 22 + 26 + 15 + 12 = 100

The even numbers are 2, 4, and 6. They rolled two 9 times, four 26 times, and six 12 times. Added together and they're 47, so 47/100

There's no simplification of this fraction as theres no number that can be used to divide both 47 and 100

Answer:

The account will take 7 years to reach a value of $4,020

Step-by-step explanation:

Compound Interest

When it occurs interest in the next period is then earned on the principal sum plus previously accumulated interest.

The formula is:

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

Where:

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

Ella invested P=$2,700 in an account with an interest rate of r=5.4% (0.054) compounded monthly. Since there are 12 months in a year, n=12.

It will be calculated when will the account have a value of A=$4,020. Substituting all the values in the formula:

[tex]{\displaystyle 4,020=2,700\left(1+{\frac {0.054}{12}}\right)^{12t}}[/tex]

Calculating:

[tex]{\displaystyle 4,020=2,700\left(1.0045)^{12t}}[/tex]

Dividing by 2,700:

[tex]{\displaystyle \frac{4,020}{2,700}=\left(1.0045)^{12t}}[/tex]

To solve this equation for t, we need to apply logarithms:

[tex]{\displaystyle \log\frac{4,020}{2,700}=\log\left(1.0045)^{12t}}[/tex]

Applying the logarithm power rule:

[tex]\displaystyle \log\frac{4,020}{2,700}=12t\log 1.0045[/tex]

Dividing by 12log 1.0045:

[tex]\displaystyle t=\frac{\log\frac{4,020}{2,700}}{12\log 1.0045}[/tex]

Calculating:

t= 7.39 years

Rounding to the nearest year, the account will take 7 years to reach a value of $4,020

Answer:

7  

Step-by-step explanation:

Answer: Distributive Property

30(4p+6c+12p+40)

=(30)(4p+6c+12p+40)

=(30)(4p)+(30)(6c)+(30)(12p)+(30)(40)

=120p+180c+360p+1200

=180c+480p+1200

Step-by-step explanation: Hope this help