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An exterior angle of a triangle is equal to the sum of its adjacent angle and one remote interior angle

An isosceles triangle is an equilateral triangle

An equilateral triangle is an isosceles triangle

Step-by-step explanation:

It is given that,

The height of the sail on a boat is 7 feet less than 3 times the length of its base.

Let the length of the base is x.

ATQ,

Height = (3x-7)

Area of the sail is 68 square feet.

Formula for area is given by :

[tex]A=lb\\\\68=x(3x-7)\\\\3x^2-7x=68\\\\3x^2-7x-68=0[/tex]

x = 8 feet and x = -3.73 feet

So, length is 8 feet

Height is 3(8)-7 = 17 feet.

So, its height and the length of the base is 17 feet and 8 feet respectively.

Answer:

(2a, b )

Step-by-step explanation:

Given the endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

[ [tex]\frac{1}{2}[/tex](x₁ + x₂ ), [tex]\frac{1}{2}[/tex](y₁ + y₂ ) ]

Here (x₁, y₁ ) = N(2a, 2b) and (x₂, y₂ ) = P(2a, 0), thus

midpoint = [ [tex]\frac{1}{2}[/tex](2a + 2a), [tex]\frac{1}{2}[/tex](2b + 0 ) ] = (2a, b )

Answer:

5

Step-by-step explanation:

Let be blank be a

-4=a-9

-4+9=a

9-4=a

a=5

Proof:

-4=a-9

-4=5-9

-4=-4

Hope this helps ;) ❤❤❤

The value of BLANK in the given expression is 5.

To solve the equation "-4 = BLANK - 9",

Isolate the variable on one side of the equation.

To do this, we can add 9 to both sides of the equation:

-4 + 9 = BLANK - 9 + 9

This simplifies to:

5 = BLANK

So the value of BLANK is 5.

To solve the equation "-4 = BLANK - 9",

We can add 9 to both sides of the equation to isolate the variable.

This gives us the solution of BLANK = 5.

To learn more about equations visit:

https://brainly.com/question/29174899

#SPJ2

Answer:

A

Step-by-step explanation:

[tex] \sin(2 \alpha ) = 2 \sin( \alpha ) \cos( \alpha ) [/tex]

[tex] \sin( \alpha ) \cos( \alpha) = \frac{1}{2} \sin( 2\alpha ) [/tex]

Answer:

5(x-7)

Step-by-step explanation:

5(x-7) or 5x-35

Hope this helps!

P.S. Please give me brainliest. Thanks :)

Answer: 5*(x-7)

Step-by-step explanation:

no work needed

difference of a number means x

Answer:

Step-by-step explanation:

This study investigated three mathematics teachers' construction process of geometric structures using compass and straightedge. The teacher-student-tool interaction was analysed. The study consists of the use of a compass and straightedge by the teachers, the ideas of the teachers about their use, and the observations regarding the learning process during the construction of the geometric structures. A semi-structured interview was conducted with the teachers about the importance of the use of a compass and straightedge to construct geometric structures. It was found that teachers taught compass and straightedge constructions in a rote manner where learning is little more than steps in a process. The study concludes with some suggestions for the use of a compass and straightedge in mathematics classes based on the research results. SUMMARY Purpose and significance: For more than 2,000 years, the way in which geometric structures could be constructed with the help of compasses and straightedges has caught the attention of mathematicians. Nowadays, mathematics curriculums place an emphasis on the use of the compass and straightedge. The compass and straightedge is more important in constructing geometric structures than other drawing tools such as rulers and protractors. Because steps taken with a compass and straightedge cannot be seen at first glance and this situation become a problem for students. However, 'doing compass and straightedge construction early in the course helps students to understand properties of figures'

Answer:

234 people

Step-by-step explanation:

1 fish = 3 people

Multiply each side by 78

1*78 = 3 *78

78 fish = 234 people

Answer:

234 traveling people

Step-by-step explanation:

78 times 3 equals 234

Answer:

The formula for the lateral surface area (LSA) of a right cone is:

LSA = π x r x l

where: r as radius, and l as the slant height of the cone

If NASA need to do two coats of the sealant, the number of square feet that they are painting is: 2 x LSA = 2 x π x r x l

Step-by-step explanation:

Answer:

56.5 ft^2

Step-by-step explanation:

After you calulate the the surface area and double it, subtract the area of the circle.

Answer:

73.5in³

Step-by-step explanation:

You multiply the three numbers.

3.5x5.25x4=73.5in³

Answer:

D

Step-by-step explanation:

End behaviour refers to the asymptotes, which both exponential functions have the same one at y = 2. However, they have different y - intercepts. The first one has a y - intercept of 4 and the second one has a y - intercept of 6. Thus, the answer is D.

Answer:

Step-by-step explanation:

Let's name the function from graph: f

for f:

y-intercept = f(0) = 4

for x → ∞,  f(x)→2

for g:

y-intercept = f(0) = 4(¹/₄)⁰+2 = 4•1+2 = 4+2 = 6 ≠4

f(1) =  4(¹/₄)¹+2 = 4•¹/₄+2 = 1+2 = 3

f(2) =  4(¹/₄)2+2 = 4•¹/₁₆+2 = ¹/₄+2 = 2¹/₄

f(3) =  4(¹/₄)³+2 = 4•¹/₆₄+2 = ¹/₁₆+2 = 2¹/₁₆

f((5) =  4(¹/₄)⁵+2 = 4•¹/₁₈₂₄+2 = ¹/₅₁₂+2 = 2¹/₅₁₂

....

so for x x → ∞,  f(x)→2

Answer:

Value of x = 20°

Angle B = 60°

Exterior angle to B = 300°

Step-by-step explanation:

Given:

Angles of triangle.

A = 2x

B = 3x

C = 4x

We know that,

A + B + C = 180°

2x + 3x + 4x = 180°

9x = 180°

x = 20°

Value of x = 20°

Angle B = 3x

Angle B = 3(20°)

Angle B = 60°

Exterior angle to B = 360° - 60°

Exterior angle to B = 300°

Answer:

The graph is attached below.

Step-by-step explanation:

The volume of the box containing the coffee mugs is,

[tex]V=x^{3}[/tex]

Then the function representing the side length, in inches, for the box is:

[tex]g(x)=x[/tex]

Now, it is provided that the company decides to double the volume of the box.

That is, the new volume will be:

[tex]V_{n}=2x^{3}[/tex]

Then the side length, in inches, for the box will be:

[tex]g_{n}(x)=\sqrt[3]{2x^{3}} =\sqrt[3]{2}x[/tex]

Then the graph representing the function, formed using the following points is:

[tex]x\ \ \ \ \ \ \ \ \ g_{n}(x)\\\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\\0\ \ \ \ \ \ \ \ \ \ \ 0\\1\ \ \ \ \ \ \ \ \ \ \ 2^{1/3}[/tex]

Answer:

c

Step-by-step explanation:

Answer:

The answer is D. A reflection, a rotation and a translation will prove that shape 2 is congruent to shape 1.

Answer:

Increase

Step-by-step explanation:

Since your not including the bad mark, it'd increase.

Answer:

Step-by-step explanation:

Each weekday repeats every 7 days.

51 = 49 + 2 = 7•7 + 2

So 49 days from now also will be Friday .

Two days later will be Sunday.

So in 51 days will be Sunday.

Answer: 14%

Step-by-step explanation:

Complete question is provided in the attachment below:

Probability that members of the junior varsity swim team wear glasses = 55%=0.55

Given: P(wear glasses) = 0.55

P(not wear glasses) = 1-0.55 = 0.45

P(member in 10th grade | not wear glasses) = 30%

Using conditional probability formula:

[tex]P(B|A)=\dfrac{P(A\text{ and } B)}{P(A)}[/tex]

[tex]\Rightarrow\ 0.30=\dfrac{P(\text{not wear glasses and in 10th grade})}{0.45}\\\\\Rightarrow\ P(\text{not wear glasses and in 10th grade})=0.45\times0.30\\\\0.135=13.5\%\approx14\%[/tex]

Hence, the probability that a randomly chosen member of the JV swim team does not wear glasses and is in the 10th grade = 14%.

So, the correct option is "14%".

Answer:

Step-by-step explanation:

1) (-13)* .......(-13) for 35 times = (-13)³⁵

2) (2/3) *  ...... * (2/3) for 4 times = (2/3)⁴

3)(-3.1)* ......(-3.1) for 4 times = (-3.1)⁴ = 92.2531

[tex]\{2,3\}[/tex] is a set containing two elements - numbers 2 and 3

[tex]\{\{2,3\}\}[/tex] is a set containing one element - a set [tex]\{2,3\}[/tex]

Answer:

The first and third polynomials have roots in x = 3 and x = -i. (A, C)

Step-by-step explanation:

The quickest form to determine if [tex]x = 3[/tex] and [tex]x = -i[/tex] are roots consist in evaluating each polynomial and proving that result is zero.

A. [tex]f(x) = x^{3}-3\cdot x^{2}+x-3[/tex]

x = 3

[tex]f(3) = 3^{3}-3\cdot (3)^{2}+3-3[/tex]

[tex]f(3) = 27-27+3-3[/tex]

[tex]f(3) = 0[/tex]

x = -i

[tex]f(-i) = (-i)^{3}-3\cdot (-i)^{2}-i-3[/tex]

[tex]f(-i) = i + 3-i-3[/tex]

[tex]f(-i) = 0[/tex]

B. [tex]f(x) = x^{5}+9\cdot x^{4}+28\cdot x^{3} + 36\cdot x^{2}+27\cdot x +27[/tex]

x = 3

[tex]f(3) = 3^{5}+9\cdot (3)^{4}+28\cdot (3)^{3}+36\cdot (3)^{2}+27\cdot (3)+27[/tex]

[tex]f(3) = 2109[/tex]

x = -i

[tex]f(-i) = (-i)^{5}+9\cdot (-i)^{4}+28\cdot (-i)^{3}+36\cdot (-i)^{2}+27\cdot (-i)+27[/tex]

[tex]f(-i) = -i+9 -28\cdot i +36-27\cdot i +27[/tex]

[tex]f(-i) = -56\cdot i +64[/tex]

[tex]f(-i) = 64 -56\cdot i[/tex]

C. [tex]f(x) = x^{5}-9\cdot x^{4}+28\cdot x^{3} - 36\cdot x^{2}+27\cdot x -27[/tex]

x = 3

[tex]f(3) = (3)^{5}-9\cdot (3)^{4}+28\cdot (3)^{3}-36\cdot (3)^{2}+27\cdot (3)-27[/tex]

[tex]f(3) = 0[/tex]

x = -i

[tex]f(-i) = (-i)^{5}-9\cdot (-i)^{4}+28\cdot (-i)^{3}-36\cdot (-i)^{2}+27\cdot (-i)-27[/tex]

[tex]f(-i) = -i - 9+28\cdot i+36-27\cdot i-27[/tex]

[tex]f(-i) = 0[/tex]

D. [tex]f(x) = x^{3}+3\cdot x^{2}+x+3[/tex]

x = 3

[tex]f(3) = (3)^{3}+3\cdot (3)^{2}+(3)+3[/tex]

[tex]f(3) = 60[/tex]

x = -i

[tex]f(-i) = (-i)^{3}+3\cdot (-i)^{2}+(-i)+3[/tex]

[tex]f(-i) = -i+3-i+3[/tex]

[tex]f(-i) = 6-i\,2[/tex]

The first and third polynomials have roots in x = 3 and x = -i. (A, C)

Answer:

Step-by-step explanation:

We first need to figure out what the equation is for this set of circumstances before we can answer any questions. We will use the equation

[tex]A(t)=P(1+r)^t[/tex] which is just another form of an exponential equation where

(1 + r) is the growth rate, P is the initial investment, and t is the time in years. We will fill in the values we know first to create the equation:

[tex]A(t)=4000(1+.11)^t[/tex] which simplifies to

[tex]A(t)=4000(1.11)^t[/tex]

Now we'll just sub in a 1 for t and solve, then a 2 for t and solve.

When t = 1:

A(t) = 4000(1.11) so

A(t) = 4440

When t = 2:

[tex]A(t)=4000(1.11)^2[/tex] which simplifies to

A(t) = 4000(1.2321) so

A(t) = 4928.40

Answer:

- All real numbers are rational numbers.   FALSE

- Some rational numbers are natural numbers. TRUE

- No real numbers are irrational numbers. FALSE

- All whole numbers are integers. TRUE

- Some integers are natural numbers. TRUE

- No rational numbers are integers. FALSE

Answer: B,D, and E

Step-by-step explanation:

A. All real numbers are rational numbers.

B. Some rational numbers are natural numbers

C.No real numbers are irrational numbers.

D.All whole numbers are integers.

E. Some integers are natural numbers.  

F. No rational numbers are integers.

Answer:

Step-by-step explanation:

2x ( -3y - 4) + 8 ( -3y - 4 )

= -6xy - 8x - 24y - 32

Hope this helps

plz mark as brainliest!!!

Answer:

Step-by-step explanation:

Use FOIL method

(2x + 8)(-3y -4) = 2x*(-3y) + 2x*(-4) + 8*(-3y) + 8*(-4)

                       = -6xy - 8x - 24y - 32

Answer:

-4

Step-by-step explanation:

6 − 4x − 8 + 2

The variable is x

The coefficient is the number in front of the variable ( it will include the sign)

-4 is the coefficient

Answer:

-4

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

point on left is -1 and 3/6 = -9/6 = -3/2

point on right is 5/6

Difference 5/6 - -3/2 = 14/6 = 7/3

Answer:

x2 # of farmers

y2 # of hours

x1# unknown workers

x2# amount wanted

x1 y1 = x2 y2

x1 (8) = 12(20)

x1 = 12(20)/8

x1 = 30

30 Farmers needed to complete the same work in 8 hours.

Answer:

a = 2, b = 3

Step-by-step explanation:

The diagonals of a rectangle bisect each other, thus

5a² = 4a² + 4 ( subtract 4a² from both sides )

a² = 4 ( take the square root of both sides )

a = [tex]\sqrt{4}[/tex] = 2

Also

6b - 8 = 4b - 2 ( subtract 4b from both sides )

2b - 8 = - 2 ( add 8 to both sides )

2b = 6 ( divide both sides by 2 )

b = 3

Answer:

B. f(n) = 56(0.5)^n-1

Step-by-step explanation:

 First, You have to find out the starting population, if you look at the problem you see the population starts at 56

f(x) = 56

Second, you know that the population goes down 50% each week so it has a decay of 0.5

f(x) = 56(0.5)

 Third,  you need to add the exponent of n to make it exponential.  But, if you just add n then the the population would be 28 on week 1 which is incorrect. To fix that you make the exponent n-1 so when you are on week 1 it doesn't become 28 but it stays on 56, and on week 2 it's 28, ect

f(x) = 56(0.5)^n-1

Answer:

[tex]\large \boxed{\mathrm{B. \ 84}}[/tex]

Step-by-step explanation:

[tex]LU[/tex] bisects [tex]RU[/tex] and [tex]UA[/tex].

[tex]RU=UA[/tex]

[tex]3m+21=6m[/tex]

Solve for m.

Subtract 3m from both sides.

[tex]21=3m[/tex]

Divide both sides by 3.

[tex]7=m[/tex]

Calculate [tex]RA[/tex].

[tex]RA=3m+21+6m[/tex]

[tex]RA=9m+21[/tex]

Put m = 7.

[tex]RA=9(7)+21[/tex]

[tex]RA=63+21[/tex]

[tex]RA=84[/tex]

Answer:

B) 84

Step-by-step explanation:

ΔLRU ≅ ΔLAU   {SAS congruent}

Therefore, UA = UR    {CPCT}

 6m = 3m +21

Subtract 3m from both sides

6m - 3m = 3m + 21 -3m

        3m = 21

Divide both sides by 3

    3m/3 = 21/3

m = 7

RA = RU + UA

    = 3m + 21 + 6m {add like terms}

    = 9m + 21   {Plug in m =7}

    = 9*7 + 21

    = 63 + 21

RA = 84 units

Answer:

h=6.003 cm

Step-by-step explanation:

[tex] \frac{1}{3} \pi {r}^{2} h \: \: is \: the \: volume \: of \: cone[/tex]

1/3×22/7×7×7×h=308

h=308/51.3

Answer:

h = 6 cm

Step-by-step explanation:

r = 7 cm

Volume of cone = 308 cm³

[tex]\frac{1}{3}\pi r^{2}h=308\\\\\\\frac{1}{3}*\frac{22}{7}*7*7*h=308\\\\\\h=\frac{308*3*7}{22*7*7}\\\\\\h=2*3[/tex]

h = 6 cm

Answer:

Step-by-step explanation:

3 is the constant term.

Constant term is the term without any variables

Answer:

3

Step-by-step explanation:

The constant number is the number that has no variable and just a number.