Which of the following choices must be true in order for ΔABC ≅ ΔEDC by the AAS congruency theorem? ∠B ≅ ∠D ∠A ≅ ∠E AC ≅ EC AB ≅ DE

Answer:

B. 5

Step-by-step explanation:

[tex] \tan(30 ) = x \div 5 \sqrt{3} = \tan(30) \times 5 \sqrt{3} = 5[/tex]

Answer:

Step-by-step explanation:

To get the value f x, we need to use SOH, CAH, TOA identity on ΔAEB but first we need to know any of the sides EB or AB.

From ΔBED, sum of the the angle in the triangle is 180° i.e ∠BED+∠EDB+∠EBD = 180°

65+55+∠EBD  = 180

∠EBD  = 180-120

∠EBD  = 60

Also ∠DBC = 90- ∠EBD

∠DBC = 90- 60

∠DBC = 30°

Applying sine rule on ΔBCD;

52/sin∠DBC = DB/sin115

52/sin30 = DB/sin115

DB = 52sin115/sin30

DB = 52sin115/0.5

DB = 104sin115

DB = 114.75 m

Also applying sine rule on ΔBED to get side BE;

BE/sin55 = 114.75/sin65

BEsin65 = 114.75sin55

BE =  114.75sin55/sin65

BE = 93.998/0.906

BE = 103.75m

Finally, applying the trigonometry identity SOH on  ΔABE

sinΔEAB = opp/hyp

sin70° = BE/AE

Since AE = x;

sin70° = 103.75/x

x = 103.75/sin70°

x = 110.41m

Hence, the value of x missing is approximately 110.41m

Answer:

x= -4

Step-by-step explanation:

2x+4=6x+20

so 2x-6x=20-4

divide both sides by -4

-4x/-4 = 16/4

=-4

Answer: 15π m³

Step-by-step explanation:

Volume of a cone = 1/3πr²h

where,

r = radius = 3 meters

h = height = 5 meters

Volume = 1/3πr²h

Volume = 1/3 × π × 3² × 5

Volume = 1/3 × π × 9 × 5

Volume = 1/3 × π × 45

Volume = 45π/3

Volume = 15π m³

Answer:

6n(n³ - 4n² + 3)

Step-by-step explanation:

Given

6[tex]n^{4}[/tex] - 24n³ + 18n ← factor out 6n from each term

= 6n(n³ - 4n² + 3) ← which may be factored further if required

6n(n³ - 4n² + 3)  is the factored form.

Expressions is the defined as mathematical statements that have a minimum of two terms containing variables or numbers.

Given that,

⇒6n⁴ - 24n³ + 18n

factor out 6n from each term

⇒6n(n³ - 4n² + 3)

There are two factors 6n and (n³ - 4n² + 3) of given expression.

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Answer:

The answer is D.

Step-by-step explanation:

The lateral surface area of a 3-D figure is the area of each face that is NOT a base.

Answer:

I think it's 1/2 because it might be right

Answer:

36°

Step-by-step explanation:

Let m∠8 = x°

Therefore, m∠7 = 4x°

Since, ∠7 and ∠8 are linear angles.

Therefore,

m∠7 + m∠8= 180°

4x° + x° = 180°

5x° = 180°

x° = 180°/5

x° = 36°

x = 36

Hence,

m∠8 = 36°

Answer: height = 1.16 ft

Step-by-step explanation:

14 inches = 1.17 feet

Height of the oven =

Height = volume / lw

H = 1.59 / 1.17*1.17

H = 1.16 feet

Answer:

a. 3.25 m

b.1.2 ft

Solution,

a. Let 'h' be the height of cylinder

Given,

Radius(r)=0.7 m

Volume(v)=5 m^3

Formula to find volume of cylinder

[tex]\pi {r}^{2} h[/tex]

where r= radius and h= height

so,

[tex] \frac{22}{7} \times 0.7 \times 0.7 \times h = 5 \\ or \: h = \frac{5 \times 7}{22 \times 0.7 \times 0.7} \\ or \: h = \frac{35}{22 \times 0.49} \\ or \: h = \frac{35}{10.78} \\ h = 3.25 \: m[/tex]

b.

[tex]volume = 1.59 = \frac{14}{12} \times \frac{14}{12} \times h \\ 1.59 = \frac{ {14}^{2} }{144} \times h \\ h = \frac{1.59 \times 144}{196} \\ h = 1.168 \: ft \\ h = 1.2 \: ft[/tex]

hope this helps...

Good luck on your assignment...

Answer:

140 square units

Step-by-step explanation:

The areas of the three right triangles are subtracted from the area of the entire box. This gives you 140 square units.

Answer:

6 + 6y + 6 = 12 + 6

Step-by-step explanation:

2(3) + 6y = 12

Multiply 2(3).

6 + 6y = 12

Subtract 6 on both sides, so y variable is isolated.

6 + 6y - 6 = 12 - 6

6y = 6

Divide by 6 on both sides.

6y/6 = 6/6

y = 1

Answer:

About 157 meters

Step-by-step explanation:

The circumference of a circle is [tex]2\pi r[/tex]. In this case, this means that one loop around the roundabout would be a distance of:

[tex]2\cdot \pi \cdot 12.5\approx 78.5[/tex]

Multiplying this by 2, you get a distance of about 157 meters. Hope this helps!

Answer:

Solution,

1 round = circumference

[tex]2\pi \: r[/tex]

[tex] = 2 \times \frac{22}{7} \times 12.5[/tex]

[tex] = \frac{44}{7} \times 12.5[/tex]

Required distance covered:

[tex]2 \times \frac{44}{7} \times 12.5 \\ = \frac{88 \times 12.5}{7} \\ = 157.14 \: m[/tex]

hope this helps..

Good luck on your assignment...

Answer:

The correct answer is 260

Step-by-step explanation:

Also known as B

Answer:

260 so Answer B

Step-by-step explanation:

Answer:  NO. He had an increase of 25%

Step-by-step explanation:

To find the percentage increase, use the following formula where New (this week) = 25 and Original (last week) = 20.

[tex]\% Change=\dfrac{\text{New - Original}}{\text{Original}}\\\\\\.\qquad \qquad =\dfrac{25-20}{20}\\\\\\.\qquad \qquad =\dfrac{5}{20}\\\\\\.\qquad \qquad =\dfrac{1}{4}\qquad \rightarrow \qquad =0.25[/tex]

Convert the decimal into percentage by moving the decimal point two places to the right.  0.25 = 25%

Evan spent 25% more time this week than last week.

It can also be stated that this week Evan did 125% of homework compared to last week.

If Even spent 125% more than last week, he would have spent 100% (20 hours) + 25% (4 hours) = 24 hours.

Answer: angles EBA and HBI are congruent

Step-by-step explanation:

they are the congruent because they are verticle angles

Answer:

Step-by-step explanation:

The length PN is the diagonal of a rectangle that is 33 m by 60 m. Its length can be found from the Pythagorean theorem.

  PN² = 33² +60² = 4689

  PN = √4689 ≈ 68.476 . . . meters

Diagonal NS is the hypotenuse of triangle PNS. Once again, the Pythagorean theorem can be used to find its measure.

  NS² = PN² +PS² = 4689 +1600 = 6289

  NS = √6289

  NS ≈ 79.3 . . . meters

__

We have the side adjacent (PN) and the side opposite (PS) to angle PNS, so we can use the tangent function to find the angle:

  tan(PNS) = NS/PN = 40/68.476

  ∠PNS = arctan(40/68.476)

  ∠PNS ≈ 30.3°

Answer:

y = -2/3x + 1

Step-by-step explanation:

Step 1: Find slope

m = (-1 - 3)/(3 + 3)

m = -2/3

y = -2/3x + b

Step 2: Find b

-1 = -2/3(3) + b

-1 = -2 + b

b = 1

Step 3: Write equation

y = -2/3x + 1

Answer:

x² + 13x + 50 + [tex]\frac{57}{x-5}[/tex]

Step-by-step explanation:

Using Synthetic division

divisor is (x - 5) , thus evaluate at h = 5

5 | 1  8  - 25  - 193

        5     65   250

  -----------------------------

    1  13   50     57 ← remainder = 57

The coefficients of the quotient are 1, 13,  50 , that is

x² + 13x + 50

Thus

[tex]\frac{x^3+8x^2-25x-193}{x-5}[/tex] = x² + 13x + 50 + [tex]\frac{57}{x-5}[/tex]

Answer:

Number of lawns mow in 49 hours = 31.5 lawns

Step-by-step explanation:

Given:

Number of lawns mow = 9

Time taken = 14 hours

Find:

Number of lawns mow in 49 hours

Computation:

Time taken for 1 lawn = 14 / 9

Number of lawns mow in 49 hours = 49 / Time taken for 1 lawn

Number of lawns mow in 49 hours = 49 / (14/9)

Number of lawns mow in 49 hours = 31.5 lawns

Answer:

a.) 7/20

b.) 0.375

c.) 1/15

Step-by-step explanation:

a. 0.35 is out of 1, so to find 0.35 in fraction form: 35/100.

Simplify that down by dividing both top-bottom by 5 and you get 7/20

b. 1/8th of anything is 0.125, so 0.125(3) = 0.375. Alternatively you can use a calc to calculate the decimal.

c. Find the area of the rectangular carpet: 60m. Then find the area of the square rug: 4m

Find the fraction: 4/60

Simplify by dividing top-bottom by 4 and you get 1/15

Answer:

The reason is because linear functions always have real solutions while some quadratic functions have only imaginary solutions

Step-by-step explanation:

An asymptote of a curve (function) is the line to which the curve is converging or to which the curve to line distance decreases progressively towards zero as the x and y coordinates of points on the line approaches infinity such that the line and its asymptote do not meet.

The reciprocals of linear function f(x) are the number 1 divided by function that is 1/f(x) such that there always exist a value of x for which the function f(x) which is the denominator of the reciprocal equals zero (f(x) = 0) and the value of the reciprocal of the function at that point (y' = 1/(f(x)=0) = 1/0 = ∞) is infinity.

Therefore, because a linear function always has a real solution there always exist a value of x for which the reciprocal of a linear function  approaches infinity that is have a vertical asymptote.

However a quadratic function does not always have a real solution as from the general formula of solving quadratic equations, which are put in the form, a·x² + b·x + c = 0 is  [tex]\dfrac{-b \pm \sqrt{b^{2} - 4\cdot a\cdot c}}{2\cdot a}[/tex], and when 4·a·c > b² we have;

b² - 4·a·c < 0 = -ve value hence;

√(-ve value) = Imaginary number

Hence the reciprocal of the quadratic function f(x) = a·x² + b·x + c = 0, where 4·a·c > b² does not have a real solution when the function is equal to zero hence the reciprocal of the quadratic function which is 1/(a·x² + b·x + c = 0) has imaginary values, and therefore does not have vertical asymptotes.

Step-by-step explanation:

it's simple:

Answer:

See attached graph for the first part

Answer to second part: The end part of the graph show the slowest increase

Step-by-step explanation:

The attached picture represents the number of infected people, starting with a relatively small number at the origin of the horizontal axis (x=0, or time=0) then increasing abruptly in the center of the graph with steep slope. and then infection slowing down (although still slowly increasing) in the region highlighted in yellow to the right of the graph.

Answer:

The length of the arc is 89 yards

Step-by-step explanation:

Mathematically, to find the length of an arc, we use the formula below;

Length of an arc = Theta/360 * 2 * pi * r

In this case, Theta = 300 and r = 17 yards

Length of the arc = 300/360 * 2 * 22/7 * 17 = 89.047619047583 which is 89 yards to the nearest yard

Answer:

1) 2 (11) - 1/2

Step-by-step explanation:

Given the following:

A line “t” is parallel to 3y = 6x + 9

Equation of a line;

y = mx + c

Where the Coefficient of x, 'm' is the gradient or slope and c is the intercept.

From the equation;

3y = 6x + 9

Divide through by 3

y = 2x + 3

Comparing the line equation with the equation provided :

Coefficient of x = 2, therefore 2 = slope

Since line t is Parallel to y = 2x + 3

Then, slope of line 't' is the same as that of y:

Slope of line 't' = 2

(11) For perpendicular lines :

Slope of original line : 3y = 6x + 9

Divide through by 3

y = 2x + 3

Compare to line equation:

y = mx + c

m = gradient/ slope, c = intercept

Gradient of original line, m = 2

For a line 'r' perpendicular to y = 2x + 3

Gradient, m of line r equals to the negative reciprocal of the gradient of original line

Therefore, gradient of r equals :

-1/2

Answer:

715

Step-by-step explanation:

The total milliliters of water is 715 if the birdbath contains 1\2 liters of water. A rainy day adds 215 milliliters.

It is defined as the conversion from one quantity unit to another quantity unit followed by the process of division,and  multiplication by a conversion factor.

We have:

A birdbath contains 1\2 liters of water. A rainy day adds 215 milliliters.

1/2 liters = 0.5 liters

We know,

1 lter = 1000 ml

0.5 liters = 0.5×1000 = 500 ml

Total water = 215 ml + 500 ml = 715 ml

Thus. the total milliliters of water is 715 if the birdbath contains 1\2 liters of water. A rainy day adds 215 milliliters.

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Hey there!

Let's think of this with a simpler example. Let's say one package is 4 pounds and one is 2 pounds. How many times heavier is the first than the second?Well, two, because the first package is double the weight of the second package! It's twice as heavy! And to get to that number, we divide four by two!

So, in our actual problem, we just divide 3.92 (bigger package) by 2.8 (smaller package).

3.92÷2.8=1.4

So, the first package is 1.4 times heavier than the first one!

Have a wonderful day!

none of the above

Step-by-step explanation:

Answer:

option c

Step-by-step explanation:

Answer: 2398.72

Step-by-step explanation:

Simply do 3100*0.95*0.95*0.95*0.95*0.95 ≈ 2398.72

Hope it helps <3

Answer:

$2398.72( I cannot use your dollar sign).

Step-by-step explanation:

If it decreases by 5% every year, then 3100*0.95=2945. Then 2945*0.95=2797.75. Then the 3rd year is 2797.75*0.95=2657.8625. Then 2,657.8625*0.95=2524.96938. Lastly, in the fifth year, it is 2524.96938*0.95=2398.72091. Then, I round off to the nearest penny(hundredths). The answer I get is $2398.72!