Tell if each pairs of segments are congruent
Yes/No
A. AB and BC
B. AC and BD

Step-by-step explanation:

x×1/2×1/4×3/4

x×3/32

3/32x

The measure of the central angle is 290 degrees

The measure of arc GI is given as:

mGI = 145 degrees

The measure of the central angle is calculated as:

Central angle = 2 * mGI

Substitute the known values in the above equation

Central angle = 2 * 145

Evaluate the product

Central angle = 290

Hence, the measure of the central angle is 290 degrees

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Answer:

angle <B = 76

Step-by-step explanation:

The measure of an exterior angle is equal to sum of two interior angles that is not adjacent to the exterior angle.

We can write the following equation with this information to find the value of angle <B

<B + 71 = 147 subtract 71 from both sides

<B = 76

The number of years she had her investment is after 3 years

From the question, the given parameters are:

The number of years (T) is calculated from the following simple interest formula

I = PRT

Substitute the given parameters in the above equation

20.64 = 400 * 1.72% * t

Express 1.72% as decimal without percentage

20.64 = 400 * 0.0172 * t

Evaluate the product

20.64 = 6.88 * t

Divide both sides by 6.88

20.64/6.88 = 6.88/6.88 * t

Evaluate the quotient

3 = t

Rewrite the equation as

t = 3

This means that she had her investment after 3 years

Hence, the number of years she had her investment is after 3 years

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Answer:

290 + 5m = 985

Step-by-step explanation:

Given information:

From the given information, we can create the following equation:

Initial payment plus extra amount each month for 5 months equals total payment.

⇒ 290 + 5m = 985

To solve the equation:

Subtract 290 from both sides:

⇒ 290 + 5m - 290 = 985 - 290

⇒ 5m = 695

Divide both sides by 5:

⇒ 5m ÷ 5 = 695 ÷ 5

⇒ m = 139

Therefore, the extra amount George paid each month was $139.

Answer: [tex]\Large\boxed{290+5m=985}[/tex]

Step-by-step explanation:

Given information

Initial cost = $290

Total cost = $985

Number of months = 5 months

Cost each month = ?

Set variable

Let [ m ] be the cost each month

The equation in verble sense

Initial paid + Extra each month = Total cost

Convert verbal equation to mathematical sense

$290 + 5m = $290

Therefore, to find the extra amount paid each month, the equation is [tex]\Large\boxed{290+5m=985}[/tex]

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

EXTRA The following will be solving the derived equation, please ignore this part if it is useless for you.

Given equation

290 + 5m = 985

Subtract 290 on both sides

290 + 5m - 290 = 985 - 290

5m = 695

Divide 5 on both sides

5m / 5 = 695 / 5

m = $139

Hope this helps!! :)

Please let me know if you have any questions

Answer:

  x = 23; not extraneous

Step-by-step explanation:

A solution is extraneous if it does not satisfy the original equation. Extraneous solutions can sometimes be introduced in the process of solving radical and rational function equations.

Squaring both sides of the given equation, we get ...

  √(3x +12) = 9

  3x +12 = 81 . . . . . . square both sides

  x +4 = 27 . . . . . . . divide by 3

  x = 23 . . . . . . . . . . subtract 4

There is only one solution, and it satisfies the equation:

  √(3×23 +12) = √81 = 9

The solution x = 23 is not extraneous.

Answer: x = 23; not extraneous

Step-by-step explanation:

The number of cases after two years is 221.

As a result of the disease, the population of the village would decrease by 95% per year. The number of cases at the village is function of the rate of infection, the number of years and the beginning number of cases.

The exponential function that can be used to represent this situation is:

FV = P( 1 + r)^t

FV = 200 (1.05)^2 = 221

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Answer: Moderate negative association

Step-by-step explanation:

Answer: None of these are correct

Step-by-step explanation:

I believe that the equation is showing transitive property.

See attachment for the graph of the piecewise function h(x)

The function is given as:

h(x) = | -4,    x < 3

         | x + 5,    x >= 3

The above function is a piecewise function.

It has 2 separate functions at two domains

This means that we plot the sub-functions in the piecewise function at their respective domain

See attachment for the graph of the piecewise function h(x)

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The value of x is 70°. The correct option is A. 70

From the question, we are to determine the value of the measure of arc x

From one of the circle theorems, we have that

The angle subtended by an arc at the center is twice the angle subtended by it at any point on the circumference.

First, we will determine the value of the third angle in the triangle formed.

Let the angle be y

y + 15° + 20° = 180°

∴ y = 180° - 15° - 20°

y = 145°

Now, the angle supplementary to this is the angle the arc subtends at the circumference.

Thus,

The angle at the circumference = 180° - 145°

The angle at the circumference = 35°

From the above theorem, we can conclude that the angle subtended by the arc at the center of the circle is 2 × 35° = 70°

∴ The measure of the arc is 70°

This is the value of x

Hence, the value of x is 70°. The correct option is A. 70

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Answer:

[tex]2\frac{2}{3}[/tex]

Step-by-step explanation:

1) Convert [tex]4\frac{1}{3}[/tex] to improper fraction. Use this rule: [tex]a\frac{b}{c} =\frac{ac+b}{c}[/tex].

[tex]\frac{4\times3+1}{3} -1\frac{2}{3}[/tex]

2) Simplify 4 * 3 to 12.

[tex]\frac{12+1}{3}[/tex]

3) Simplify 12 + 1 to 13.

[tex]\frac{13}{3} -1\frac{2}{3}[/tex]

4) Convert [tex]1\frac{2}{3}[/tex]   to improper fraction. Use this rule: [tex]a\frac{b}{c} =\frac{ac+b}{c}[/tex].

[tex]\frac{13}{3} -\frac{1\times3+2}{3}[/tex]

5) Simplify 1 * 3 to 3.

[tex]\frac{13}{3} -\frac{3+2}{3}[/tex]

6) Simplify 3 + 2 to 5.

[tex]\frac{13}{3} -\frac{5}{3}[/tex]

7) Join the denominators.

[tex]\frac{13-5}{3}[/tex]

8) Simplify.

[tex]\frac{8}{3}[/tex]

9) Convert to mixed fraction.

[tex]2\frac{2}{3}[/tex]

(Decimal Form: 2.666667)

Thank you,
Eddie

Answer:

  (c)  Factor

Step-by-step explanation:

The constituents of a product are its factors.

Dividing a product by one of its factors will not leave a remainder.

__

A term is a constant or product of one or more variables and a constant. For example, -4 and 24xy are both terms.

A multiple is a product with one factor being an integer. For example, 3×1.5 = 4.5 is a multiple of 1.5.

A variable is a symbol for an unknown value. Commonly, a variable is a single letter, but may also be a blank (__) or a question mark (?). Sometimes a word or phrase is used as a variable. For example, ...

  3 + x = 5

  3 + __ = 5

  3 + ? = 5

  3 + (some number) = 5

Answer: 30%

Step-by-step explanation:

the first 2 bars < or = to 650 add up to ~29% roughly, cant be 25%, 68%, or 99%. Therefore the only answer available is 30%

Answer:

30%

Step-by-step explanation:

For Connexus students its 30% :)

The sequence of transformation carried out on ABCD is; B: Reflection about the y-axis followed by a translation left by 2 units

As in rotation, reflection and translation the transformed image is congruent to the original figure (i.e all the points undergo same change). Thus, analyzing any one point will give the series of transformation undertaken.

Taking point A(3, 1) into consideration; Reflecting a point (x, y) over y axis, it becomes (-x, y).

Thus, reflecting A(3, 1) over y - axis gives the the new coordinates as (-3, 1)

Now, translating a point (x, y) k units left, gives a new coordinate (x - k, y).

Thus, translating point (-3, 1) 2 units left, gives the new coordinates as A'(-5, 1).

This is the coordinates for A'.

Thus, we can conclude by saying that the sequence of transformation carried out on ABCD is reflected about the y-axis followed by a translation left by 2 units.

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Answer:

252

Step-by-step explanation:

using a brute force method in c++

#include <stdio.h>

int main(){

int a, b, c, n = 0;

for(a = 1; a <= 9; a++)

 for(b = 0; b <= 9; b++)

  for(c = 0; c <= 9; c++)

   if((a==3 || b==3 || c==3)) n++;

printf("%d\n", n);

}

The number of kilometres travelled by the satellite in discuss in which case, the satellite makes 8 revolutions around the earth is; C = 177,271.8 km.

Given from the task content, the earth's diameter is; 6371 km and since, the height at which the satellite orbits the earth is; 343km, it follows that the diameter of orbit if the satellite in discuss is;

D = 6371 + (343)×2

Hence, we have; diameter, D = 7057 km.

Hence, the distance travelled after 8 revolutions is;

C = 8 × πd

C = 8 × 3.14 × 7057

C = 177,271.8 km.

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The number of permutations of picking 4 pens from the box is 30.

There are six different unique colored pens in a box.

We have to select four pens from the different unique colored pens.

We have to find in how many different orders the four pens can be selected.

A permutation is the number of different arrangements of a set of items in a particular definite order.

The formula used for permutation of n items for r selection is:

    [tex]^nP_r = \frac{n!}{r!}[/tex]

Where n! = n(n-1)(n-2)(n-3)..........1 and r! = r(r-1)(r-2)(r-3)........1

We have,

Number of colored pens = 6

n = 6.

Number of pens to be selected = 4

r = 4

Applying the permutation formula.

We get,

= [tex]^6P_4[/tex]

= 6! / 4!

=(6x5x4x3x2x1 ) / ( 4x3x2x1)

= 6x5

=30

Thus the number of permutations of picking  4 pens from a total of 6 unique colored pens in the box is 30.

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The third side of the triangle falls between (50, 60).

Inequality triangle theorem states that the sum of any two sides of a triangle is greater than or equal to the third side.

Therefore, the other two sides are 5 cm and 55 cm. The range of the third side x can be computed using inequality triangle theorem.

Hence,

x < 5 + 55

x < 60

And,

x > 55 - 5

x > 50

Therefore, 50 < x < 60.

Hence, the third side of the triangle falls between (50, 60).

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Answer:

[tex]y=\dfrac{8}{7}x - \dfrac{23}{7}[/tex]

Step-by-step explanation:

Rearranging the terms, we get [tex]7y=8x-23[/tex]. Dividing both sides by 7, we get [tex]\dfrac{7y}{7} = \dfrac{8x-23}{7}[/tex], so [tex]\boxed{y=\dfrac{8}{7}x - \dfrac{23}{7}}[/tex]

Answer:

y = [tex]\frac{8}{7}[/tex]x -[tex]\frac{23}{7}[/tex]

Step-by-step explanation:

You are changing this to the slope-intercept form of a line.

y = mx + b

8x -7y = 23  Subtract 8x from both sides of the equation

-7y = -8x + 23  Divide both sides of the equation by -7

y = [tex]\frac{-8}{-7}[/tex]  - [tex]\frac{23}{7}[/tex]  

[tex]\frac{-8}{-7}[/tex] is the same as [tex]\frac{8}{7}[/tex]

y = [tex]\frac{8}{7}[/tex]x - [tex]\frac{23}{7}[/tex]

Using the relation between velocity, distance and time, it is found that her jogging rate was of 6 mph.

Velocity is distance divided by time, hence:

[tex]v = \frac{d}{t}[/tex]

Jogging, her velocity was of v, while the time was of t, for a distance of 12 miles, hence:

[tex]v = \frac{12}{t}[/tex]

Biking, her velocity was of v + 6, while the time was of 3 - t, for a distance of 12 miles, hence:

[tex]v + 6 = \frac{12}{3 - t}[/tex]

[tex]v = \frac{12}{3 - t} - 6[/tex]

Then:

[tex]\frac{12}{t} = \frac{12}{3 - t} - 6[/tex]

[tex]\frac{12}{3 - t} - \frac{12}{t} = 6[/tex]

[tex]\frac{12t - 36 + 12t}{t(3 - t)} = 6[/tex]

18t - 6t² = 24t - 36

6t² + 6t - 36 = 0

t² + t - 6 = 0

(t + 3)(t - 2) = 0. -> t = 2 hours.

Hence her jogging rate in mph is given as follows:

[tex]v = \frac{12}{2} = 6[/tex]

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Step-by-step explanation:

this just means that the first function with input value x = 0 is calculated. that result becomes the input value x for the second function. and that result becomes the input value x for the 3rd function. and that result is then our result.

to answer a and b we only need to look at the main operation of each function :

the first one uses only basic multiplication and subtraction.

the second one uses squaring.

the third one is a 1/x operation.

a.

since the final result is a negative number (-31), the second function with the square operation cannot be last.

because a square operation always delivers a positive result.

+a × +a = +a²

-a × -a = +a²

remember, for a square operation we multiply the same number by itself. therefore we cannot mix signs like -a × +a, because then they would not be the same numbers anymore.

b.

since the initial input value is 0, the third function (1/x) cannot be the first, because 1/0 is not defined.

c.

because of the "large" -32 term in the first function I guess that this will be the last one to create such a low negative result of -31.

since 1/x cannot be first, (x - 2)² is then first. that makes 1/x second, and (4x - 32) third, as mentioned.

let's try :

x = 0

(x - 2)² = (0 - 2)² = (-2)² = 4

x = 4

1/x = 1/4

x = 1/4

4x - 32 = 4×1/4 - 32 = 1 - 32 = -31

hurrah ! we are correct !

Answer:

788,000 =

788 x 10^3

78.8 x 10^4

7.88 x 10^5

.788 x 10^6

and so on

Answer:

  14(cos(125°) +i·sin(125°))

Step-by-step explanation:

The product of two complex numbers is the product of their magnitudes at an angle equal to the sum of their angles.

For A = a·cis(α) and B = b·cis(β), the product AB is ...

  AB = (a·cis(α))·(b·cis(β)) = ab·cis(α+β)

where "cis(x)" stands for the sum (cos(x) +i·sin(x)).

The product of interest is ...

  Z1·Z2 = (7cis(15°))·(2cis(110°)) = (7·2)cis(15°+110°)

  Z1·Z2 = 14cis(125°) = 14(cos(125°) +i·sin(125°))

The inverse function of the function [tex]f(x)=-3x+3[/tex] will be [tex]x=g(y)=-\frac{y}{3}+1[/tex].

Here, the given function is [tex]f(x)=-3x+3[/tex].

Then we get:

[tex]y=-3x+3\\\Longrightarrow x=-\frac{y}{3}+1[/tex]

Thus, the inverse function of the function [tex]f(x)=-3x+3[/tex] will be [tex]g(x)=-\frac{x}{3}+1[/tex].

The graph representing this inverse function is given as follows:

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Answer:

one of several possible solutions :

18, 75, 105

Step-by-step explanation:

prime factors of 3150 :

3150 ÷ 2 = 1575

1575 ÷ 2 no

1575 ÷ 3 = 525

525 ÷ 3 = 175

175 ÷ 3 no

175 ÷ 5 = 35

35 ÷ 5 = 7

7 ÷ 5 no

7 ÷ 7 = 1

3150 = 2¹ × 3² × 5² × 7¹

these are the product of the longest streaks of prime factors in x, y and z.

the GCF(y, z) = 15.

the prime factors of 15 are simply 3¹×5¹.

so, y and z share only the factors 3 and 5.

the GCF(x, y, z) = 3.

since x is an even number, the elimination of 5 in the GCF is not surprising.

let's try the following :

x = 2¹ × 3² = 2×9 = 18

y = 3¹ × 5² = 3×25 = 75

z = 3¹ × 5¹ × 7¹ = 3×5×7 = 105

that uses all the factors of 3150, and their LCM is as the product of the longest streaks of their prime factors is

2¹ × 3² × 5² × 7¹.

fits.

the GCF(75, 105) is the product of the prime factors they have in common : 3¹ × 5¹ = 15.

fits.

the GCF(18, 75, 105) is the product of the prime factors ask 3 numbers have in common, which is only 3¹ = 3.

fits.

18 < 75 < 105

fits.

18 is an even number greater than 10.

fits.

there are more than 1 solutions.

e.g.

z = 2¹ × 3¹ × 5¹ × 7¹ = 210

is also possible.

Quadrilateral is a family of plane shapes that have four straight sides. Thus the sum of their internal angles is [tex]360^{o}[/tex]. Examples include rectangle, square, rhombus, trapezium, and kite.

A kite is a plane shape that has its adjacent sides to have equal measures.

The given diagram in the question is a kite that has its specific properties compared to other quadrilaterals.

Thus, the required proof is stated below:

Given: ΔCAV and ΔCEV

Prove that: ΔCAV ≅ ΔCEV

Then,

CE ≅ CA (length of side property of a kite)

EV ≅ AV (length of side property of a kite)

<ACV ≅ <ECV (bisected property of a given angle)

<AVC ≅ <EVC (bisected property of a given angle)

CV is a common side to ΔCAV and ΔCEV

Therefore it can be deduced that;

ΔCAV ≅ ΔCEV (Angle-Angle-Side congruent theorem)

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Answer:

please how

Step-by-step explanation:

I will help ypu

1. The sentences translated to equations looks like:

a) 4x = 32.

b) x + 6y = 43.

c) 3x + 7 = 9x - 4.

d) 76 - 2x = 8x.

2. The equations translated to sentences looks like:

a) The sum of 16 and 9 times x is 50.

b) The sum of the square of x and 6 times y is 4 times w.

c) Three times x is 52.

d) Five-sixth is equal to the product of -10 and x.

Practice Part 1: Translate sentence to equation

a)Four times a number is thirty-two.

Assuming the number to be x, we get the equation, 4x = 32.

b)The sum of and six times  is equal to forty-three.

The sentence, when translated to an equation looks like, x + 6y = 43.

c)The sum of 7 and three times  equals the difference of 9 times  and 4.

The sentence, when translated to an equation looks like, 3x + 7 = 9x - 4.

d)Two times  less than 76 is equal to the product of 8 and

The sentence, when translated to an equation looks like, 76 - 2x = 8x.

Practice Part 2: Translate equation into sentence

a) 9x + 16 = 50.

- The sentence for the given equation is, the sum of 16 and 9 times x is 50.

b) x² + 6y = 4w.

- The sentence for the given equation is, the sum of the square of x and 6 times y is 4 times w.

c) 3x = 52.

- The sentence for the given equation is, three times x is 52.

d) 5/6 = -10x.

- The sentence for the given equation is, five-sixth is equal to the product of -10 and x.

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