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Answer:

1) true

2) false

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Answer:

Length of hypotenuse of given triangle

= sqrt(356)   (exact value)

= 18.87 (to 2 decimal places)

Step-by-step explanation:

Using the pythagorean Theorem,

The hypotenuse

c = sqrt(a^2+b^2)

= sqrt(16^2+10^2)

= sqrt(356)   (exact value)

= 18.87 (to 2 decimal places)

The length of the hypotenuse of the right triangle is approximately

18.9 cm.

Pythagorean theorem states that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

We can apply this theorem only in a right triangle.

Example:

The hypotenuse side of a triangle with the two sides as 4 cm and 3 cm.

Hypotenuse side = √(4² + 3²) = √(16 + 9) = √25 = 5 cm

We have,

The length of the hypotenuse of a right triangle can be found using the Pythagorean theorem:

c² = a² + b²

where c is the length of the hypotenuse, and a and b are the lengths of the other two sides (the base and the height in this case).

Plugging in the given values, we get:

c² = 16² + 10²

c² = 256 + 100

c² = 356

c ≈ 18.9

Rounding the answer to the nearest tenth of a centimeter, we get:

c ≈ 18.9 cm

Therefore,

The length of the hypotenuse of the right triangle is approximately

18.9 cm.

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Answer:

b. 5 + 17i

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

identify two points on the graph:

1. (0, 4)

2. (-2, 2)

use slope formula: (y² - y¹) / (x² - x¹)

1. (2 - 4) / (-2 - 0) = -2 / -2 = 1

slope = 1

Answer:

c

Step-by-step explanation:

Answer:

(3, 1/2)

Step-by-step explanation:

set the equation up

x+2y=4

2x-2y=5

then solve

The correct option is B.[tex](3,\frac{1}{2})[/tex]

Given equations,

[tex]x+2y=4.....(1)\\2x-2y=5.....(2)[/tex]

The standard form for linear equations in two variables is [tex]Ax+By=C[/tex].

On comparing equation 1 and equation 2 with the standard form we get,

[tex]a_{1}=1, b_{1}=2, c_{1}=4\\a_{2}=2, b_{2}=-2,c_{2}=5[/tex]

Here,

[tex]\frac{a_{1} }{a_{2} } =\frac{1}{2} \\[/tex] and [tex]\frac{b_{1} }{b_{2} } =\frac{2}{-2} =-1[/tex]

Since [tex]\frac{a_{1} }{a_{2} } \neq \frac{b_{1} }{b_{2} }[/tex], So the given system of equation has a unique solution.

Now Adding equation 1 and 2 we get,

[tex]3x=9\\x=3[/tex]

putting the value of x in equation 1 we get,

[tex]3+2y=4\\2y=1\\y=\frac{1}{2}[/tex].

Hence the required solution of equation is [tex](3,\frac{1}{2})[/tex]. the correct option is B.[tex](3,\frac{1}{2})[/tex]

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Answer:

its a! sorry im so late

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

Angle C is equal to the 1/2 the difference of the two arcs

C = 1/2 ( large DC - small DC)

Large DC = ( 360 - 5x - 2)   sum of a circle is 360 degrees

Small DC = 5x-2  the central angle is equal to the intercepted arc

C = 1/2 ( 360 - 5x-2 - ( 5x -2))  Angle Formed by Two Intersecting Chords

C = 1/2 ( 360 - 2 ( 5x-2))

Distributing the 1/2

C = 180 - (5x-2)

Replacing the C with 2x+7

2x+7 = 180 - (5x-2)

Add 5x-2 to each side

2x+7  +5x-2  = 180

Antonio is correct

Combine like terms

7x +5 = 180

7x = 175

Divide by 7

x =25

Then solve for A = 5x-2

A = 5*25-2

   = 125-2

   = 123

Answer:

20

Step-by-step explanation:

2 get well cards

4 anniversary cards

6 greeting cards

8 birthday cards

Answer:

Step-by-step explanation:

Let x represent the number of cases of 16-oz cups produced.

Let y represent the number of cases of 20-oz cups produced.

The limitation imposed by available production time is ...

  x + y ≤ 15·8 = 120 . . . . maximum number of cases produced in a day

The limitation imposed by raw material is ...

  14x +18y ≤ 1800 . . . . . maximum amount of resin used in a day

__

The point of intersection of the boundary lines for these inequalities can be found using substitution:

  14(120- y)+18y = 1800

  4y = 120 . . . . . subtract 1680, simplify

  y = 30

  x = 120 -30 = 90

This solution represents the point at which production will make maximal use of available resources. It is one boundary point of the "feasible region" of the solution space.

__

The feasible region for the solution is the doubly-shaded area on the graph of these inequalities. It has vertices at ...

  (x, y) = (0, 100), (90, 30), (120, 0)

The profit for each of these mixes of product is ...

  (0, 100): 25·0 +20·100 = 2000

  (90, 30): 25·90 +20·30 = 2850 . . . . uses all available resources

  (120, 0): 25·120 +20·0 = 3000 . . . . maximum possible profit

The family can maximize their profit by producing only 16-oz cups at 120 cases per day.

Answer:

90 16-oz cases and 30 20-oz cases will maximize resin and time use

120 16-oz cases will maximize profit

Step-by-step explanation:

Answer: y = 3(x - 5)² + 4

Step-by-step explanation:

Use the Vertex form:  y = a(x - h)² + k to find the a-value

Given: (x, y) =(0, 79) and (h, k) = (5, 4)

79 = a(0 - 5)² + 4

79 = 25a + 4

75 = 25a

3 = a

Input a = 3 and (h, k) = (5, 4) into the Vertex form:

y = 3(x - 5)² + 4

Answer:

36.33

Step-by-step explanation:

The given figure is pentagon

The sum of angles of polygon is (2n-4)*90 where n is number of sides of polygon

for pentagon number of sides is 5

thus, n = 5

\

sum of angles of pentagon = (2*5-4)*90 = 6*90 = 540

Given angles of pentagon

t, 149 , t+144, 3t -11 , t+40

Thus, sum of all these angles should be equal to 540

t + 149 + t+144 + 3t -11 + t+40 = 540

=> 6t + 322 = 540

=> 6t = 540 - 322 = 218

=> t = 218/6 = 36.33

Thus, t = 36.33

Answer:

1. Always translate the question stem, set up equations (limit the number of variables) and breakdown the question stem of possible

2. Never overlook the constraints the question provides.

Now the question stem tells us that on the

1st day Joe earned = x

2nd day = 2x

3rd day = 4x

4th day = 8x

Question stem: Did Joe earn less than $35 on the 4th day -----> 8x < 35 ----> x < 4.375

Since x is an integer, the question becomes 'Is x <= 4

Statement 1 : Joe earned more than $120 in total for the first five days he worked in December.

x + 2x + 4x + 8x + 16x > 120

31x > 120 ---> x > 3.9....

This gives us both a YES and a NO since x can be 4 or any integer greater than 4

Statement 2: Joe earned less than $148 on the 6th day he worked in December

32x < 148 ----> x < 4.625

Since x is an integer, x <=4. Sufficient.

hope this helps

-lvr

Answer:

[tex]x=-1[/tex]

Step-by-step explanation:

[tex]2x-3x-1=0\\(2x-3x)+(-1)=0\\-x-1=0\\-x-1+1=0+1\\-x=1\\\frac{-x}{1}=\frac{1}{-1}\\ x=-1[/tex]

Answer:

[tex]\frac{5x - 8}{3}[/tex]

Step-by-step explanation:

Find the LCM of the denominators and then solve:

[tex]\frac{4x - 5}{2} - \frac{2x - 1}{6} \\\\[/tex]

[tex]\frac{4x - 5}{2} - \frac{2x - 1}{6} \\\\\frac{3(4x - 5) - 2x - 1}{6} \\\\\frac{12x - 15 - 2x - 1}{6}\\\\\frac{10x - 16}{6}\\\\ \frac{2(5x - 8)}{2 * 3} \\\\ \frac{5x - 8}{3}[/tex]

Answer:

Step-by-step explanation:

m : n = 2 : 1

R (-3, 3 )  ;  x1 = -3 & y1 = 3

S(6 , -3)   ; x2 = 6 & y2 = -3

Formula for the point that divides a line m:n = [tex](\frac{mx_{2}+nx_{1}}{m+n} , \frac{my_{2}+ny_{1}}{m+n})[/tex]

[tex]Q(\frac{2*6+1*(-3)}{2+1}, \frac{2*-3 + 1*3}{2+1})\\\\\\Q(\frac{12-3}{3} , \frac{-6+3}{2+1})\\\\\\Q(\frac{9}{3} , \frac{-3}{3})\\\\[/tex]

=Q(3, -1)

Answer:

D.) (3,-1)

Step-by-step explanation:

I got it correct on founders edtell

Answer:

Step-by-step explanation:

If BD║CE then ΔADB and ΔAEC a similar triangles

so:

     [tex]\frac{AE}{AD}=\frac{AC}{AB}\\\\\frac{AE}{7}=\frac{6}{4}\\\\AE=\frac32\cdot7\\\\AE=\frac{21}2\\\\AE=10.5[/tex]

Container + cement = 78.1

Container + sand = 25.5

Difference( cement - sand) = 78.1 -25.5 = 52.6

4 x Sand = 52.6

Sand = 52.6/4 = 13.15

Container = 25.5 - 13.15 = 12.35 kg

Answer:

99,290

Step-by-step explanation:

99,200 + 10(18/2)

= 99,200 + 10(9)

= 99,200 + 90

= 99,290

Sara works 46 hours per week

9 hours are overtime and 37 hours are regular time

pay rate at time and a half: 10.20∗1.5=15.30

regular hours plus overtime pay

37∗10.20=377.40

9∗15.30=137.70

Income due to tips

Total hours worked∗60per hour∗20%

46∗60∗.20=552

Weekly Income=Hourly income + tips

Weekly Income=377.40+137.70+552.00

Weekly Income=1067.10

Annual income=Weekly income∗52

Annual income=55489.20

Answer:

Height of stone face is : 56.7 ft

Step-by-step explanation:

Kindly refer to the attached image for the diagram of the given conditions and values.

Let C be the base of mountain.

D be the point from where two sightings are taken.

AB be the stone face.

Angle of elevations:

[tex]\angle BDC =35^\circ\\\angle ADC =38^\circ[/tex]

To find:

Height of stone face = ?

AB = ?

Solution:

We can use trigonometric function of tangent here in two triangles [tex]\triangle BCD\ and\ \triangle ACD[/tex]:

[tex]In\ \triangle BCD :[/tex]

[tex]tan(\angle BDC) = \dfrac{Perpendicular}{Base} = \dfrac{BC}{CD}\\\Rightarrow BC = 700 \times tan35 ..... (1)[/tex]

[tex]In\ \triangle ACD :[/tex]

[tex]tan(\angle ADC) = \dfrac{Perpendicular}{Base} = \dfrac{AC}{CD}\\\Rightarrow AC = 700 \times tan38\\\Rightarrow AB +BC = 700 \times tan38\\\\\text{Using equation (1):}\\\Rightarrow AB + 700 \times tan 35 = 700 \times tan 38\\\Rightarrow AB = 700 \times tan 38-700 \times tan35\\\Rightarrow AB = 700 \times (tan 38-tan35)\\\Rightarrow AB = 700 \times 0.081\\\Rightarrow AB = \bold{56.7}\ ft[/tex]

So, Height of stone face is : 56.7 ft

Answer: B

Step-by-step explanation:

The domain of a function is every x-value, and the range is every y-value.

Hope it helps <3

Answer:

B

Domain: (-∞,∞)

Range: (-∞,5]

Step-by-step explanation:

The domain is (-∞,∞) because the graph as you can see, is continuously going outwards forever.

The range is (-∞,5] because the graph as you can see, is always going down forever and the top point is at 5. The 5 is in a bracket because it is a defined number while ∞ is undefined!

Hope this helped and good luck :)

Answer:

here,

money spent in 1st year =$250

money spent in 2nd year=$295

total inflated amount=$295- $250

=$45

Then,

inflation rate= ($45/ $250)×100%

=18%

Answer:

x = 1/3 , y = 10/3

Step-by-step explanation:

Solve the following system:

{y = x + 3 | (equation 1)

y = 7 x + 1 | (equation 2)

Express the system in standard form:

{-x + y = 3 | (equation 1)

-(7 x) + y = 1 | (equation 2)

Swap equation 1 with equation 2:

{-(7 x) + y = 1 | (equation 1)

-x + y = 3 | (equation 2)

Subtract 1/7 × (equation 1) from equation 2:

{-(7 x) + y = 1 | (equation 1)

0 x+(6 y)/7 = 20/7 | (equation 2)

Multiply equation 2 by 7/2:

{-(7 x) + y = 1 | (equation 1)

0 x+3 y = 10 | (equation 2)

Divide equation 2 by 3:

{-(7 x) + y = 1 | (equation 1)

0 x+y = 10/3 | (equation 2)

Subtract equation 2 from equation 1:

{-(7 x)+0 y = -7/3 | (equation 1)

0 x+y = 10/3 | (equation 2)

Divide equation 1 by -7:

{x+0 y = 1/3 | (equation 1)

0 x+y = 10/3 | (equation 2)

Collect results:

Answer: {x = 1/3 , y = 10/3

Answer:

[tex]\boxed{x=\frac{1}{3} }[/tex]

[tex]\boxed{y=\frac{10}{3} }[/tex]

Step-by-step explanation:

[tex]y=x+3\\y=7x+1[/tex]

Plug y as x+3 in the second equation.

[tex]x+3=7x+1\\7x-x=3-1\\6x=2\\x=\frac{1}{3}[/tex]

Plug x as 1/3 in the second equation.

[tex]y=7(\frac{1}{3} )+1\\y=\frac{7}{3}+1\\y=\frac{10}{3}[/tex]

Answer:

3 degrees F

Step-by-step explanation:

if the temperature rose 1* for 7 hours, times 1 by 7. which is 7 and add to -10. which is -3. then, since the temperature rose by 2* for 3 hours, times 2 by 3 which is 6 and add to -3, which is 3.

i hope this helped?

Answer:

Step-by-step explanation:

12) p & q are parallel lines , n is transversal

4z = 108  { corresponding angles are congruent}

Divide both sides by 4

z = 108/4

z = 27°

n & m are parallel lines , p is transversal

3y = 4z  { corresponding angles are congruent}

3y =  4 * 27

y = [tex]\frac{4*27}{3}[/tex]

y = 4*9

y = 36°

n & l are parallel lines,  q is transversal

6x   = 108 { corresponding angles are congruent}

x = 108/6

x = 18°

Answer:

(500,0) , (300,0), (200,200) and (300,200)

Step-by-step explanation:

The region of the graph we are concerned with is that small portion which is shaded.

We need the coordinates that bounds this portion of the graph.

These coordinates are four in number and they are as identified by noticing the four points that surround the portion then making tracings from these points to the x and y axes respectively.

We proceed as follows;

The four points we are looking at in no particular order are;

(500,0) , (300,0), (200,200) and (300,200)

The points having coordinates that have y = 0 are those that are domiciled on the x-axis

We have two of these points which are on the x-axis.

Answer:

720 seating arrangments

Step-by-step explanation:

There are eight people but driver is always the same so we only have to deal with combinations of the other 7 seats.

the combination of the five seats has 5! times 2 combinations for each of the 3 passengers willing to ride in the two boat seats thus the total number of different seating arrangements is 5! times 3! or 720

hope this helps :)

Using the Fundamental Counting Theorem, it is found that there are 5760 possible seating arrangements.

It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

In this problem:

Hence:

[tex]N = 8 \times 6 \times 5! = 5760[/tex]

There are 5760 possible seating arrangements.

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Large-size shirts should be brought more of which is more likely to be sold.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

                  Sales       Sold

Small            180          126

Medium        220          270

Large            284           315

x-large           95            135

Now,

The percentage of small size sold.

= 126/180 x 100

= 70%

The percentage of medium size sold.

= 220/270 x 100

= 81.5%

The percentage of large size sold.

= 284/315 x 100

= 90%

The percentage of x-large size sold.

= 95/135 x 100

= 70%

Thus,

Large-size shirts are sold more.

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