Factorise completely:

Applying the knowledge of congruent triangles, the measures are solved as:

6. X = 14; AC = 11; T = 14; WZ = 16; WY = 60; AB = 60; m∠A = 64°; m∠Y = 64°; m∠W = 50°

7. X = 7; YZ = 28; T = 9; WZ = 10; WY = 11; AB = 28; m∠A = 31°; m∠C = m∠W = 99°

To solve for the missing measures of triangles that are congruent to each other, recall that triangles that are congruent will have corresponding sides that are equal and also corresponding angles that are equal.

6. Triangles ABC and YWZ are congruent, therefore:

m∠A = m∠Y; m∠B = m∠W; m∠C = m∠Z

AB = WY; AC = YZ; BC = WZ

Therefore:

5X - 4 = 66

Solve for X

5X = 66 + 4

5X = 70

X = 14

AC = YZ = 11

AB = WY

5T - 10 = 4T + 4

5T - 4T = 10 + 4

T = 14

BC = WZ = 16

WZ = 16

WY = 4T + 4 = 4(14) + 4

WY = 60

AB = WY = 60

AB = 60

m∠A = m∠Y

m∠A = 180 - 50 - 66

m∠A = 64°

m∠Y = 64°

m∠B = m∠W = 50°

m∠W = 50°

7. Triangles ABC and ZYW are congruent, therefore:

m∠A = m∠Z; m∠B = m∠Y; m∠C = m∠W

AB = YZ; AC = WZ; BC = WY

Therefore:

5X - 4 = 3X + 10

Solve for x

5X - 3X = 4 + 10

2X = 14

X = 7

AB = YZ

2T + 10 = 4T - 8

2T - 4T = -10 - 8

-2T = -18

T = 9

YZ = 4T - 8 = 4(9) - 8

YZ = 28

AC = WZ = 10

WZ = 10

WY = 11

AB = YZ = 28

AB = 28

m∠A = m∠Z = 3X + 10 = 3(7) + 10

m∠A = 31°

m∠C = m∠W = 180 - 31 - 50 = 99°

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Answer:

121.5

Step-by-step explanation:

1.5 x 9 x 9 (the equation for volume (minus the 1/2 inch that Isaac's grandmother said to leave out) = 121.5

Answer: x=18

Step-by-step explanation:

It just does ok

The solution to the inequality is X  > 4

Inequality  is a set of mathematical expression which the individual side is not equal to other side

To solve for  x  in the inequality  x - 1 . 5 > 2, we followed the step;

Step 1: Add 1.5 to both sides

x - 1.5 + 1.5 > 2 . 5 + 1.5

X  > 4

Therefore, the solution to the inequality is X  > 4

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Answer:

that is a quadratic function so yes it is a function

Step-by-step explanation:

it is a function becausr you can write an equation with it. Hope I could help!

According to the integer N,

a) The smallest possible value of N is 6.5 if N >= 6.5

b) The largest possible value of N is -2 if N < - 3

c) The possible value of N is {-2, -1, 0, 1} if N >= -2 and N < 2.

Integer

Integer refers a collection of whole numbers and negative numbers.

Given,

Here we have the integer N.

And we need to find the following:

a. the smallest possible value of N if N >= 6.5

b. the largest possible of N if N < -3

c. the possible values of N if N >= -2 and N <2.

Part a). smallest possible value of N if N >= 6.5

Here the smallest number is 6.5 because other value are greater than this one.

Part b). the largest possible of N if N < -3

The largest possible number is -2, because the other values on N are less than -2.

Part c). the possible values of N if N >= -2 and N <2.

Here the possible values between these are {-2, -1, 0, 1}.

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Answer:

35 square inches

Step-by-step explanation:

21x15=315

315/9=35

Therefore, the answer is 35 square inches

The distance of segment AX sis found to be 8.6 units using the distance formula.

Given: A(-4, 5), X (1, −2)

We need to find the distance of the segment AX.

Distance of AX is given as :

[tex]\sqrt{[1-(-4)]^{2} + [-2-5]^{2} } \\= \sqrt{25 + 49}\\ = \sqrt{74}\\ =8.6[/tex]

Therefore, the distance of segment AX sis found to be 8.6 units using the distance formula.

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For the given four congruent parallelograms and the shaded area of 192cm² then value of x is equal to 8cm.

As given in the question,

Given four congruent parallelograms

Shaded area of the parallelogram is 192cm²

As four parallelograms are congruent

Let the area of each parallelogram is A

4A = 192

⇒A = 48cm²

For two parallelogram base length = 24cm

Base length of each parallelogram = 12cm

Area of parallelogram = base × height

48 = 12 × height

⇒ height = 4cm

Value of x = 2 times of height

                = 2 (4)

                = 8cm

Therefore, for the given four congruent parallelograms and the shaded area of 192cm² then value of x is equal to 8cm.

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Answer:

4.5

Step-by-step explanation:

45/10=4.5

The function, changes from f(x) = (3x)³ - 8 to g(x) = (9x)³ - 8 when it is dilated, the statementr which best describes the graph is,  the graph is streched towards the x axis by a factor of 1/3

When an object is dilated the image formed is larger or smaller, but there is a difference in the size of the shape.

the rule of function change f(x) = (3x)³ - 8 to g(x) = (9x)³ - 8

3x = 9xk

k = 1/3

Therefore, the function, changes from f(x) = (3x)³ - 8 to g(x) = (9x)³ - 8 when it is dilated, the statement which best describes the graph is,  the graph is streched towards the x axis by a factor of 1/3

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The minimum score needed to receive a grade of 'a' is 87.92

Given that,

At a nearby university, a professor noticed that her students' exam results were regularly distributed, with a mean of 73 and a standard deviation of 11. 8.75 percent of the professor's students achieved grades of A, she told us.

Mean = μ = 73

Standard deviation = σ =  11

Using the standard normal table,

⇒ P(Z > z) = 8.75%

⇒ 1 - P(Z < z) = 8.75%

= 1 - P(Z < z) = 0.0875

= P(Z < -1.36) =1- 0.0875

= P(Z < 1.3563) =0.9125

∴ Z = 1.3563                              ( Using standard normal z-table )

Using z-score formula ;

x= z * σ + μ

x=1.3563 * 11 + 73

x=87.92

So, the minimum score needed to receive a grade of 'a' is 87.92

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The number of views in the four weeks round to the whole number is 48.

Here it is given that the initial number of views for a reader board was 25 and it gets increased at the rate of 18% per week.

We have to find the number of views in the fourth week.

On the first week the increase = 25 + 25× 18%

                                                   = 25 + 25 × 18/100

                                                   = 25 + 4.5

                                                   = 29.5

The second week increase = 29.5 + 29.5 × 18%

                                              = 29.5 + 5.31

                                                = 34.81

The third week increase = 34.81 + 34.81 × 18%

                                         = 34.81 + 6.2658

                                         = 41.0758

The fourth week increase = 41.0758 + 41.0758 × 18%

                                           = 41.0758 + 7.393644

                                            = 48.469444

Therefore the number of views in the four weeks is 48.

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The representation of the composite function (fg)(x) is (fg)(x) = 10x

From the question, we have the following function definitions

f(x) = √2x

g(x) = √50x

The function to calculate is given as (fg)x

This can be calculated using

(fg)(x) = f(x) * g(x)

Substitute √2x for f(x) and √50x for g(x) in the above equation

So, we have

(fg)(x) = √2x  * √50x

Evaluate the products

(fg)(x) = √100x²

Evaluate the exponents

(fg)(x) = 10x

Hence, the possible equation is (fg)(x) = 10x

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Each text will cost Hassan $0.09

A rate is a special ratio in which the two terms are in different units. It can also be defined as the amount of money that is charged for goods or services. For example, if a 12 malt can of costs 69¢, the rate is 69¢ for 12 malt. Then 1 malt will cost ¢69/12.

Similarly $5.31 is the cost of 59 text messages

Therefore a text message will cost $5.31/12=$0.09

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The probability of Sid takes at random counters from the bag is 24/55

The total number of counters = 11

Total number of green counters = 8

Total number of blue counters = 3

Probability = Number of favorable outcomes / Total number of outcomes

Total number of outcome = 55

Number of outcome that Sid will get both green = 28

Number of outcome that Sid will get both blue = 3

Number of favorable outcome = 55 - 28 - 3

= 24

Probability = Number of favorable outcomes / Total number of outcomes

= 24/55

Hence, the probability of Sid takes at random counters from the bag is 24/55

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If he arranges them into 6 equal rows, 4 posters will be in each row.

One of the fundamental arithmetic operations in mathematics is the division, which is the process of dividing a group of items into equal pieces. Every day, we might employ the division approach in various situations. Fraction division differs significantly from natural number division. We must change the division operator into a multiplication operator when dividing fractions. Therefore, the dividend should be multiplied by the inverted divisor.

Given,

Total posters = 24

Arranging them into 6 equal rows,

Dividing:

24÷ 6

Reciprocating,

24 × 1/6

4

If he arranges them into 6 equal rows, 4 posters will be in each row.

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Answer:

Hi! I'm pretty sure the question is: Two cities are 45 miles apart. Two trains, with speeds of 70 mph and 60 mph, leave the two towns at the same time so that one is catching up to the other. How long after the trains leave will they be 10 miles apart for the first time? How long after the trains leave will they be 10 miles apart for the second time?

I have had a similar question before, and I will answer yours. :)

Step-by-step explanation:

T1 - the time the trains are moving to each other.

For time T1, the first train will go the distance of 70*t.

The second train, for time t, will go the distance 60*t.

Both for time t1  - 70t+60(t1) =  (70+60)*(t1).

45 - (70+60)*t is the distance between trains that left after t hours.

For the first time, they will be 10 miles apart when they are moving into each other

45 - (70+60)*t = 10

45-10 = (70+60)*t

35 = 130*t

t=35/130 h =7/26 h = 0.27 h

The train meets when distance = 0

45 - (70+60)*t = 0

45 = 130t

t  =45/130 h = 9/26 h = 0.35 h when trains met.

Trains began to move apart from each other after 9/26 h moving,

After t2 time trains will be (70+60)*(t2) = 130*(t2) mi apart from each other.

130*(t2) =  10

t2 = 1/13h = 0.08h after they met, they are apart from each other 10 mi.

So after the beginning of the movement, it will be time when they met + time when they were moved  10 mi apart from each other

9/26 h+1/13h = 11/26 h = 0.42 h

Answer:

2 , 3 , 4

Step-by-step explanation:

Corresponding angles:  When two parallel lines are intersected by a transversal, the angles on the same side and same position of the transversal are same.

            ∠3 = ∠1

Vertically opposite angles: When two lines intersect, the opposite angles are congruent.

             ∠2 = ∠1

            ∠4 = ∠3

So, ∠1 = ∠2 = ∠3 = ∠4 = 60°

Answer:

thats correct

Step-by-step explanation:

The sum of the geometric progression with the features stated in the text is given as follows:

S = 2.62 x 10^(43).

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

The nth term of a geometric sequence is given by:

[tex]a_n = a_1q^{n-1}[/tex]

In which [tex]a_1[/tex] is the first term.

The sum of a finite geometric sequence with n terms is given as follows:

[tex]S_n = \frac{a_1(1 - r^n)}{1 - r}[/tex]

In this problem, the first term and the common ratio are given as follows:

[tex]a_1 = 2, n = 3[/tex]

Hence the equation is:

[tex]a_n = 2(3)^{n - 1}[/tex]

The nth term is of 1458000, hence the number of terms of the sequence is obtained as follows:

[tex]a_n = 2(3)^{n - 1}[/tex]

[tex]1458000 = 2(3)^{n - 1}[/tex]

[tex]3^{n - 1} = 729000[/tex]

[tex]3^{n - 1} = 3^{90}[/tex]

Then:

n - 1 = 90

n = 91.

Thus the sum of the sequence is given as follows:

[tex]S_n = \frac{a_1(1 - r^n)}{1 - r}[/tex]

[tex]S_{91} = \frac{2(1 - 3^{91})}{1 - 3}[/tex]

S = 2.62 x 10^(43).

The problem is solvable with an nth term of 1,450,800, not 145,800, as 145,800/2 is not a root of 3.

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The amount of fat in Cherry ice-cream is 24 grams.

The amount of fat in the Mint Chocolate Chunk ice-cream is 12 grams.

Writing data into equations using Algebra,3C + M = 84...(1)C + 3M = 60...(2)

Multiplying equation (2) by 3 and then subtracting equation (1) from

the result gives, 3 * (C +3M) = 3 × 603C + 9M = 180...(3)(3C + 9M = 180) - (3C + M = 84) = 8M =96M= 12

The amount of fat in the Mint Chocolate Chunk ice-cream, M = 12  

grams C + 12*3 = 60C = 60-36 = 24

The amount of fat in Cherry ice-cream C = 24 grams As a result, Cherry ice cream contains 24 grams of fat and Mint Chocolate Chunk ice cream contains 12 grams of fat.

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The point (9,7) is the image of the point after a rotation of 90° counterclockwise.

Given that,

The points (-7,9).

We have to find the image of the point after a rotation of 90° counterclockwise.

Because the hands of a clock move in a clockwise manner, we can rotate a point either in that direction or in the opposite direction when we rotate it. In mathematics, clockwise is defined as a negative rotation and counterclockwise as a positive rotation.

Consider the point on the coordinate plane (x,y). You may always swap the x- and y-coordinates and then multiply the new x-coordinate by -1 to rotate this point by 90 degrees around the origin in a clockwise orientation.

(x,y)→(y,-x)

(-7,9)→(9,7)

Therefore, The point (9,7) is the image of the point after a rotation of 90° counterclockwise.

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Answer:

a = 4.52 km

Step-by-step explanation:

Formula we use,

→ (AC)² = (BC)² + (AB)²

Now the value of a will be,

→ (7.2)² = a² + (5.6)²

→ 51.84 = a² + 31.36

→ a² = 51.84 - 31.36

→ a = √20.48

→ [ a = 4.52 km ]

Hence, value of a is 4.52 km.

Answer:

3.6

................................

Answer: 1.01% sale tax.

Step-by-step explanation:

First you must take your tax price before and the tax price after and divide them. This gets you 1.01.

To be sure this is your answer you can multiply the 1.01% by 53 and it gives you 53.53$ (If you don't understand I suggest looking at a video from khan academy they explain things much better than I do.)

Hope that helped in some way :)

1. The angles measures are larger than the original angle measures is a false statement.

2. If two sides parallel in the original figure, then those sides are parallel in the final figure is true statement.

3. The final angle measure are the same as the original angle measure is false statement.

4. The original figure and the final figure may not be congruent is true statement.

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Answer:

7 cents:$0.45

Step-by-step explanation:

(whatever you do to one side you do the same to the other)

35 divided by 5= 7

2.25 divided by 5= 0.45

They bought  15 acres at $ 4000 per acre and  8 acres at  $6300 per acre

Let,

They bought x acres at $ 4000

and ( 23-x ) acres at $ 6300

From information,

By using algebra,

4000x + 6300(23-x) = 110,400

4000x - 6300x+ 144900 = 110,400

-2300x = 110,400-144900

- 2300x  = - 34500

x =34500 /2300

x = 15

x = 15

They bought 15 acres at $ 4000 per acre

(23 - 15 ) = 8 acres at  $6300 per acre

Hence, they purchased 8 acres for $6300 per acre and 15 acres for $4,000 each.

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With the help of trignometric identities we can say that the answer is = 0.672355, nearly.

acc to our question-

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