"Match the vocabulary word with the correct definition. (altitude of a triangle, base angles, base of an isosceles triangle, centroid, median of a triangle, orthocenter, vertex angle )
1. The two angles that include the base of an isosceles triangle.
2. A point on the interior of a triangle in which the three medians of the triangle intersect.
3. A segment from a vertex perpendicular to the opposite side.
4. A point in which the three altitudes of the triangle intersect. It is possible for the orthocenter to occur on the triangle, on the interior of the triangle or on the exterior of the triangle.
5. The angle formed by the two equal sides of an isosceles triangle.
6. A segment from a vertex to the midpoint of the opposite side.
7. The third, unequal side of an isosceles triangle."

Answer:

125 candy bars

Step-by-step explanation:

[tex]\text{Let the number of candy bars sold by Carley is }x\\\text{Then since Beth has sold one less than twice the number of candy bars}\\\text{that Carley has sold, so number of candy bars sold by Beth}=2x-1\\\\\text{also given that they have sold 188 candy bars in all, so we have}\\\\\text{Candy bars sold by Carley + Candy bars sold by Beth}=188\\\\\Rightarrow (x)+(2x-1)=188\\\\\Rightarrow 3x-1=188\\\\\Rightarrow 3x=189\\\\\Rightarrow x=\frac{189}{3}=63[/tex]

[tex]\text{Hence the candy bars sold by Beth are:}\\=2x-1\\\\=2(63)-1\\\\=126-1\\\\=125\\\\\text{Hence, Beth sold 125 candy bars.}[/tex]

Answer: 2⁷

Step-by-step explanation:

                    128

128 = 2 * 2 * 2 * 2 * 2 * 2 * 2

     = 2⁷

Adding the term 8x we will get:

x² + 8x + 4² = (x + 4)²

How to make a perfect square trinomial?

The perfect square trinomial is:

(a + b)² = a² + 2ab + b²

Here we start with:

x² + 16

We can rewrite this as:

x² + 4²

We can see that the term missing is the cross one, which will be:

2*(x)*4 = 8x

Then we will get:

x² + 8x + 4² = (x + 4)²

Answer:

100 yards

Step-by-step explanation:

It takes 4 yards of fabric to make a costume for one student.  She needs to make costumes for every student in chorus, so you just multiply this number by 25 and get 100 yards.

Answer:

100 yards.

Step-by-step explanation:

We have been given that a seamstress uses 12 yards of fabric to make 3 costumes for students in the chorus.

We will use proportions to solve the given problem.

[tex]\frac{\text{Yards of fabric}}{\text{Costumes}}=\frac{12}{3}[/tex]

[tex]\frac{\text{Yards of fabric}}{25}=\frac{12}{3}[/tex]

[tex]\frac{\text{Yards of fabric}}{25}*25=\frac{12}{3}*25[/tex]

[tex]\text{Yards of fabric}=4*25[/tex]

[tex]\text{Yards of fabric}=100[/tex]

Therefore, 100 yards of fabric is needed to make costumes for 25 students.

Answer:

a

Step-by-step explanation:

104 is the only number inside the box

The value of ∠1  is 38 degree , Option B is the correct answer.

Parallelogram is a polygon with four sides , Opposite sides are parallel and equal.

From the figure given

One of the angle is 104 degree

when two lines are parallel and intersected by a transversal

then the sum of the consecutive interior angles is 180 degree

∠1  +  ∠2 =  180 -104 = 76 degree

similarly the other two lines are parallel with each other

so  ∠1  =  ∠4

∠3 =   ∠2

Therefore the diagonals are bisecting the angle and so

the value of ∠1   = 76 / 2 = 38 degree

Therefore , The value of ∠1  is 38 degree , Option B is the correct answer.

To know more about Parallelogram

https://brainly.com/question/1563728

#SPJ2

Answer:

F(t) = 10 +5t

Step-by-step explanation:

Income equals the initial fee plus the hours worked times the hourly rate

We know the initial fee = 10

hours = t

hourly rate =r

F(t) = 10 + r*t

We know a 5 hour job is 35 dollars

35 = 10 + r*5

Subtract 10 from each side

35-10 = 10-10 +5r

25 = 5r

Divide by 5

25/5 = 5r/5

5 =r

The hourly rate is 5

F(t) = 10 +5t

Answer:

12 hours would take emily

Step-by-step explanation:

Read more on Brainly.com - https://brainly.com/question/879403#readmore

[tex]2)\\\\6+5k+2=18\\\\(6+2)+5k=18\\\\8+5k=18\qquad\text{subtract 8 from both sides}\\\\5k=10\qquad\text{divide both sides by 5}\\\\\boxed{k=2}\\\\4)\\\\-8(a-8)=96\qquad\text{divide both sides by (-8)}\\\\a-8=-12\qquad\text{add 8 to both sides}\\\\\boxed{a=-4}[/tex]

[tex]6)\\7m+35=7(5m-3)\qquad\text{divide both sides by 7}\\\\m+5=5m-3\qquad\text{subtract 5 from both sides}\\\\m=5m-8\qquad\text{subtract 5m from both sides}\\\\-4m=-8\qquad\text{divide both sides by (-4)}\\\\\boxed{m=2}[/tex]

Answer:

8

Step-by-step explanation:

Change mixed number to decimal                    6 2/5 = 6.4

Change needed fraction to decimal                  4/5 = 0.8

Divide yogurt by yogurt needed                         6.4 / 0.8 = 8

Working the problem like this will help you with any same type of problem.

If this helped a Brainliest ,Rating ,and/or a thanks will be appreciated

Answer: He can make 8 smoothies.

Step-by-step explanation:

Given : The total amount of yogurt Dean has = [tex]6\dfrac{2}{5}[/tex] cups

In Improper fraction , it will be :

[tex]6\dfrac{2}{5}=\dfrac{6\times5+2}{5}=\dfrac{32}{5}[/tex]

Also, the amount of yogurt required for a fruit smoothie = [tex]\dfrac{4}{5}[/tex]

Now , The number of smoothies he can make = (Total amount of yogurt Dean has) ÷ (amount of yogurt required for a fruit smoothie )

[tex]=\dfrac{32}{5}\div\dfrac{4}{5}\\\\=\dfrac{32}{5}\times\dfrac{5}{4}=8[/tex]

Hence, he can make 8 smoothies.

Answer: A, B, and C

Step-by-step explanation:

root of zero (x = 0) with multiplicity of 1 (x = 0)¹ means that the graph CROSSES the axis at x = 0

root of two (x = 2) with multiplicity of 4 (x = 2)⁴ means that the graph TOUCHES the axis at x = 2

WHY?  

Leading Coefficient (end behavior of right side):

Degree of polynomial (left side behavior):

The given polynomial has a negative leading coefficent and odd degree so the left side goes to +∞ and the right side goes to -∞

OBSERVE INTERVALS:

See graph to confirm statements above

Answer:

A, B, and C

Step-by-step explanation:

Had the same question on Edge :)

Answer:

x = 32

Step-by-step explanation:

This is an equilateral triangle, all three sides equal.  Since all three sides are equal, all three angle are equal.  180/3 = 60.  That means each angle is equal to 60 degrees.

2x-4 = 60

Add 4 to each side

2x-4+4 = 60+4

2x =64

Divide each side  by 2.

2x/2 = 64/2

x = 32

Answer:

Given the table as shown below:

x               y

-3             8/27

-2             8/9

-1             8/3

0              8

1              24

2              72

3              216

Taking any input variable x that are three apart:

i,e x = 0 and x = 3

The output values at x =0 and x = 3 are:

f(0) = 8 and f(3) = 216

Then;

The ratio of outputs is:

[tex]\frac{f(3)}{f(0)} = \frac{216}{8}= \frac{27}{1}[/tex] or 27 : 1

Therefore, the ratio outputs for any two inputs that are three values apart is: [tex]27: 1[/tex]

Answer:

0.5

Step-by-step explanation:

Answer: Other guy is right for 1 & 2 but is wrong for the last question.

I got a 100 on connections.

(1) 0.1992

(2)0.167

(3) 2/5

Step-by-step explanation:

The experimental probability of rolling a 1 on the next roll is 0.1992 (B). The theoretical probability of rolling a 3 on a six-sided die is 0.1667 (A). The odds of an event with a probability of 2/7 are 2 to 5 (D).

The experimental probability of rolling a 1 in this experiment is calculated by dividing the frequency of rolling a 1 by the total number of rolls. There were 245 occurrences of rolling a 1 out of 1230 total rolls. To find the experimental probability, you divide 245 by 1230, which gives you 0.1992.

Part B: The theoretical probability of rolling any particular number on a fair six-sided die is 1/6, because there are 6 possible outcomes and each outcome is equally likely if the die is fair. Therefore, the theoretical probability of rolling a 3 on the next roll is 0.1667 (which is equivalent to 1/6 when rounded to four decimal places).

When the probability of an event is 2/7, the odds of the event are 2 to 5 (not 2/5). This is because odds are expressed as the ratio of the number of successful outcomes to the number of unsuccessful outcomes. Since there are 2 chances of success and 5 chances of failure (7-2=5), the odds are 2 to 5.

https://brainly.com/question/32117953

#SPJ3

Answer:

3000 books

Step-by-step explanation:

We know the author receives a one time fee of $2500. On top of that, the author will receive $1.50 per book sold. This is a constant rate and is linear because of this. We can use y=mx+b. M is the slope or rate of change. M here is $1.50. B is the starting value which is $2500 here.

We write y=1.5x+2500.

This equation will give the amount of money the author earns for x number of books sold. If y=7000 for the author earning 7000. We will use inverse operations to isolate and find x.

7000=1.5x+2500

7000-2500=1.5x+2500-2500

4500=1.5x

4500/1.5=x

3000=x

Answer:

The author must sell 300 books.

Step-by-step explanation:

The total amount earned  = advance + books sold * money per book

We know they want to make 7000

The advance is 2500

They earn 1.50 for each book sold

b= number of books sold

Substituting in

7000= 2500 + 1.5b

Subtract 2500 from each side

7000-2500 = 2500-2500 + 1.5 b

4500 = 1.5 b

Divide each side by 1.5

4500/1.5 = 1.5b/1.5

3000 = b

The volume of the cube would be S^3, where S is the length of the side.

Volume = (5a + 4b)^3

Which becomes:

(5a+4b)(5a+4b)(5a+4b)  

Multiply the first two sets of parenthesis by each other:

(25a^2+40ab+16b^2)(5a+4b)  

Now multiply that by the 3rd set of parenthesis to get:

125a^3+300a^2b + 240ab^2 + b^3

Answer: Choice D) 85.5

Work Shown:

To get the midsegment, we add up the sides parallel to this midsegment, then we divide by 2.

LM = (AB + DC)/2

LM = (46 + 125)/2

LM = 171/2

LM = 85.5

Answer: D is the answerb

The expression for determining the total cost of buying granola and flour is (3.25/g) * g + (0.74/f) * f. The values of g and f represent the number of pounds of each item. To find the total cost, substitute the values into the expression.

The expression that can be used to determine the total cost is:

Total cost = ($3.25/g) * g + ($0.74/f) * f

where 'g' represents the number of pounds of granola and 'f' represents the number of pounds of flour.

For example, if you wanted to find the total cost of buying 5 pounds of granola and 2 pounds of flour, you would substitute g = 5 and f = 2 into the expression to get:

Total cost = ($3.25/5) * 5 + ($0.74/2) * 2 = $16.25 + $1.48 = $17.73

https://brainly.com/question/17747891

#SPJ11

The total cost of buying g pounds of granola at $3.25 per pound and f pounds of flour at $0.74 per pound can be determined using the expression 3.25g + 0.74f.

To determine the total cost of buying g pounds of granola for $3.25 per pound and f pounds of flour for $0.74 per pound, you can use the following expression:

3.25g + 0.74f

Here's a step-by-step explanation:

This expression gives you the total cost based on the quantities of granola and flour you wish to purchase.

Answer: The meaning y-intercept is the initial value of a rare coin is 6.

Step-by-step explanation:

Given : The graph of [tex]f(t) = 6\times 2^t[/tex] shows the value of a rare coin in year t.

The y- intercept is the point on Cartesian plane when the graph intersects y axis. It given the initial value of the function by substituting the value of independent variable as zero.

i.e. , we need to put t=0, we get

[tex]f(0) = 6\times 2^0=6[/tex]

The meaning y-intercept is the initial value of a rare coin is 6.

The roots of the polynomial function F(x)=x^3-3x^2+2 can be found by reducing the function to zero and solving for x, likely by applying synthetic division or the Rational Root Theorem, as the polynomial is of third order.

In Mathematics, especially in algebra, we often encounter the concept of finding the roots of polynomial functions. The roots of the function F(x)=x^3-3x^2+2 can be found by setting the function equal to zero and solving for the variable x:

Note: This explanation suggests general approaches. The actual solution would require longer calculations.

https://brainly.com/question/12158280

#SPJ12

The only root of the polynomial function F(x) = x³ - 3x² + x + 5 is 2 + i.

Let's go through the possible roots of this polynomial function one by one and see which of them will make the function equal to zero. Recall that if a number p is a root of a polynomial, then when we substitute p into the polynomial, the resulting value will be zero.

A. First, let's consider 2+i as a possible root.

We would evaluate F(2+i) = (2+i)³ - 3(2+i)² +(2+i) + 5 = 0.

Upon evaluation, it turns out that F(2+i) does indeed equal 0.

B. Now let's see if -2+i is a root.

We evaluate F(-2+i) = ((-2+i)³ - 3(-2+i)² + (-2+i) + 5. This happens not to equal 0. Therefore, -2+i is not a root.

C. Then, we check if 1 is a root by computing

F(1) = 1³ - 3×1² +1 +5. Upon computing, we find that this doesn't result in 0 either. So, 1 is not a root

D. Finally, let's check if 2 is a root.

We compute F(2)= 2³ - 3×2² +2 +5. This computation also doesn't result in 0, therefore 2 is not a root of the polynomial function.

In conclusion, the only given number that is a root of the function is 2 + i.

https://brainly.com/question/31214281

#SPJ6

Which of the following are roots of the polynomial function below?

F(x)=x³-3x²+x+5

A. 2+i

B. -2+i

C. 1

D. 2

Answer

Average speed of the train = 90 km/h and average speed of the airplane = 360 km/h.

Explanation:-

If speed of train = x then the  speed of airplane = 4x km/h and we have the 2 equations

x = 1440 / (t + 12)                               (t = time taken by the train)

4x = 1440 / t................................(1)       (t = time taken by train)

Multiply the first equation by 4:-

4x = 5760 / (t + 12).....................(2)  

Combining equations (1) and (2):-

1440 / t =  5760 / (t + 12)

Cross multiplying:-

5760t = 1440t + 17,280

4320t = 17,280

t = 17280/4320

t = 4 hours

speed of train = 1440/ (4 + 12) = 90 km/h and speed of plane = 4*90 = 360 km/h.

We know that : In a Triangle, If Two Angles are Equal then Corresponding Sides with Respect to those Two Angles Should be Equal.

In the Given Right Angled Triangle, There are Two Angles which are Equal to 45°. It means The Lengths of the Sides Corresponding to those Equal 45° Angles should be Equal.

It Means The Given Right Angled Triangle is also an Isosceles Triangle

⇒ The Other Side of the Triangle is [tex]3\sqrt{2}[/tex]

As it is a Right Angled Triangle :

[tex]\mathsf{\implies (Hypotenuse)^2 = (3\sqrt{2})^2 + (3\sqrt{2})^2}[/tex]

[tex]\mathsf{\implies (Hypotenuse)^2 = 18 + 18}[/tex]

[tex]\mathsf{\implies (Hypotenuse)^2 = 36}[/tex]

[tex]\mathsf{\implies (Hypotenuse) = 6}[/tex]

The Length of Hypotenuse is 6

Answer:

f^-1(x) = (x +7)/5

Step-by-step explanation:

Set x = f(y) and solve for y.

... x = 5y -7

... x+7 = 5y

... (x+7)/5 = y . . . . this is the inverse function

f^-1(x) = (x +7)/5

Anwser could be 107 because 535/5=107

[tex]\text{The formula of a midpoint:}\\\\\left(\dfrac{x_1+x_2}{2};\ \dfrac{y_1+y_2}{2}\right)[/tex]

[tex]\text{We have}\\\\\text{endpoint}\ (-9,\ -11)\to x_1=-9,\ y_1=-11\\\\\text{midpoint}\ (-18,\ -12)\\\\\text{Therefore we have the equations:}\\\\\dfrac{-9+x_2}{2}=-18\qquad\text{multiply both sides by 2}\\\\-9+x_2=-36\qquad\text{add 9 to both sides}\\\\\boxed{x_2=-27}\\\\\dfrac{-11+y_2}{2}=-12\qquad\text{multiply both sides by 2}\\\\-11+y_2=-24\qquad\text{add 11 to both sides}\\\\\boxed{y_2=-13}\\\\Answer:\ \boxed{(-27,\ -13)}[/tex]

Answer:

This team can lose 6 games and still achieve this goal.

Step-by-step explanation:

In order to find this, we can create a proportion and solve by cross multiplying. The proportion should compare amount of losses to total games.

Ratio = Total  

2/5 = x/15

Now cross multiply

15*2 = 5x

30 = 5x

6 = x

This means the team can lose 6 games and still keep the necessary ratio.

Answer:

54, 52, 26, 24, 22, -6, -4

Step-by-step explanation:

Answer:

Stu makes $338,263 over five years.  

Step-by-step explanation:

In order to find the total amount Stu would make after five years, you need to find out how much he will make each year based on the 2% increase.  Starting with year 1 at $65,000, we need to take his total salary and multiply by 1.02 (or the whole salary plus an increase of 2%).  So, in year 2, he would make $66,300.  Again, we would take his year 2 total salary and multiply by 1.02 to get $67,626 for year 3.  We apply these same steps to years four ($68,978.52) and five ($70,358.10).  To find his income over the five years, we need to add his salary from all five years together to get a total of $338,263.  

Answer:

Option C which is $ 338,263

Step-by-step explanation:

The salary for the first year = $65,000

Increase per year= 2 %

To find total money made in five years = ?

total earned in first year = $65,000

Total increase in money after first year = 2 % of 65,000

                                                                = [tex]\frac{2*65000}{100}[/tex]

                                                                 =$ 1300

Total earned in second year = 65,000 + 1300

                                                = $ 66,300

Total increase in money after second year = 2 % of 66,300

                                                                = [tex]\frac{2*66300}{100}[/tex]

                                                                 =$ 1326

Total earned in third year = 66300 + 1326

                                                = $ 67,626

Total increase in money after third year = 2 % of 67,626

                                                                = [tex]\frac{2*67626}{100}[/tex]

                                                                 =$ 1352.52

Total earned in fourth year = 67626 + 1352.52

                                                = $ 68978.52

Total increase in money after fourth year = 2 % of 68978.52

                                                                = [tex]\frac{2*68978.52}{100}[/tex]

                                                                 =$ 1379.58

Total earned in fifth year = 68978.52 + 1379.58

                                                = $ 70358.1

Total Made in all five years = 65000+66300+67626+68978.52+70358.1

                                             = $ 338262.62

                                             ≅$ 338,263

Answer:

The popcorn buckets each cost around $15.34.

Step-by-step explanation: