Choose the triangle that seems to be congruent to △AEC.



△BFC
△ABD
△EFD

The rectangle with:

Factorize the volume expression

If a > 4, then:

Since the longest dimension is the length, it is

The breadth is the middle dimension,  it is

The height is the smallest dimension, it is

The area of the floor is:

Answer:

i)  length > 9 ft

   breadth > 5 ft

   height > 3 ft

ii)  Area of floor > 45 ft²

Step-by-step explanation:

Volume of a rectangular prism

[tex]\textsf{V}=lbh[/tex]

where:

Given:

Part (i)

To find expressions for the 3 dimensions of the tank, factor the expression for Volume.

Using the Factor Theorem, if V(x) = 0 then (a - p) is a factor:

[tex]\implies \sf V(1)=2(1)^3+(1)^2-2(1)-1=0[/tex]

[tex]\implies \sf V(-1)=2(-1)^3+(-1)^2-2(-1)-1=0[/tex]

Therefore  (a - 1)  and  (a + 1)  are factors:

[tex]\implies \sf 2a^3+a^2-2a-1=(a-1)(a+1)(2a+p)[/tex]

(where p is a constant to be found)

To find the value of p, expand:

[tex]\implies \sf 2a^3+a^2-2a-1=2a^3+pa^2-2a-1[/tex]

and compare coefficients:

[tex]\implies \sf a^2=pa^2 \implies p=1[/tex]

Therefore:

[tex]\implies \sf 2a^3+a^2-2a-1=(a-1)(a+1)(2a+1)[/tex]

If  l > b  and  b > h  then:

If a > 4 ft then:

Part (ii)

The area of the floor can be found by multiplying the found expressions for breadth and length:

[tex]\begin{aligned}\implies \sf Area\:of\:floor & =(a+1)(2a+1)\\& = 2a^2+3a+1\end{aligned}[/tex]

If a > 4 ft then Area of floor > 45 ft²

Answer:

d

Step-by-step explanation:

the fitness grows into bodyness from good

Answer:

2x+4/ x-1 C

Step-by-step explanation:

Because the y-intercept is -4

Equation of the new function -3(x+1)².

The correct option is (B)

An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given function:

f(x) = x²

The given condition are shift one unit right+ 1.

i.e., x+1

Vertically stretch 3 units= -3

i.e., -3(x+1)

So, reflect over x- axis = square the function'

So, new function= -3(x+1)²

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The value of x from the figures are 18 and 26 respectively

13) From the diagram, the angles at the corner is 90 degrees. This shows that the sum of the angles is complementary (sum is 90 degrees)

3x + 2x = 90

5x = 90

x = 90/5

x = 18

15) Since the sum of angles on a straight line is supplementary, hence;

6x + x - 2 = 180

7x = 182

x = 182/7

x = 26

Hence the value of x from the figures are 18 and 26 respectively

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Answer: rhombus

Step-by-step explanation:

By inspection, we can tell that there are no right angles, so we can determine it is not a square or a rectangle.

From the options, it is implied that it is a parallelogram, so to determine if it is a rhombus, we can determine if there is a pair of consecutive congruent sides.

By the distance formula,

[tex]AB=\sqrt{(-1-3)^{2}+(-1-1)^{2}}=\sqrt{16+4}=2\sqrt{5}\\BC=\sqrt{(-1-1)^{2}+(-1-3)^{2}}=\sqrt{4+16}=2\sqrt{5}[/tex]

As AB=BC, there is indeed a pair of consecutive congruent sides, and thus the most specific classification is a rhombus

How much is $100 in ZA rands.

Let the unknown be "x"

[tex]\frac{1}{17}×\frac{100}{x}[/tex]

We'll have to do cross multiplication.

So we'll have to multiply 100 and 17.

[tex]100×17[/tex]

[tex]\huge\boxed{= 1700 \: ZA \: rands}[/tex]

Therefore, $100 is 1700 ZA rands.

Answer:

3x+(4x-1)+90°=180°{sum of angles in a triangle}

3x+4x-1+90°=180°

7x+89°=180°

7x=180°-89°

7x=91°

divide both sides by 7

x=13

Answer:

The answer is x=13

Answer: The answer is 22

Step-by-step explanation: you divide the 36 and the 9 to get 4 then you add the 18 and the 4 to get 22

Answer:

22

Step-by-step explanation:

[tex]18+(\frac{36}{9})=?\\ 18+4=?\\22=?[/tex]

Answer:

A triangle is equal to 540° so you do 112 add 37 which equals 149° then take it away from 540 which gives you 391° as your answer

Step-by-step explanation:

Your Welcome

Answer:

27 I think just divide 81 by 3

Using the distance formula, the length of WX is approximately: 8.5.

Distance formula is, [tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex].

Given the endpoints:

W(5,-3) = (x1, y1)

X(-1,-9) = (x2, y2)

Plug in the values:

WX = √[(−1−5)² + (−9−(−3))²

WX = √[(−6)² + (−6)²]

WX = √72

WX ≈ 8.5

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Answer:

6 2 with the little check mark line in the midddle

Step-by-step explanation:

Answer:

See below ~

Step-by-step explanation:

P (first red) :

⇒ Original number of red balls / Total

⇒ 4 / 10

⇒ 0.4

⇒ 40%

===============================================================

Remember the first ball drawn is NOT replaced.

P (second red) :

⇒ Original number of red - 1 / Total - 1

⇒ 4 - 1 / 10 - 1

⇒ 3/9

⇒ 33%

For is mathematically given as

Considering line segments from (0,0,0)origin to (3,0,0) , (3,5,1) and (0,5,1) under the infulence of force

Generally,  the equation for force is mathematically given as

F = z2i + 5xyj + 2y2k

Therefore, Considering u*v

[tex]u * v = (u_1j+u_2j+u_3k) * (v_1i+v_2j+v_3k)[/tex]

[tex]u* v = u_1v_1(i * i) + u_1v_2(i * j)+u_1v_3(i * k) + u_2v_1(j * i) + u_2v_2(j * j)+u_2_3(j* k) + u_3v_1(k * i) + u_3v_2(k * j)+u_3v_3(k * k)[/tex]

Where

[tex]i * i = j *j=k * k=0[/tex]

Hence

[tex]u* v = u_1v_2k-u_1v_3j-u_2v_1k+u_2v_3i +u_3v_1j - u_3v_2i[/tex]

[tex]u = (u_1,u_2,u_3) = (0,5,1)\\\\v = (v_1,v_2,v_3) = (-3,0,0)[/tex]

The normal equation formed

-3y + 15z = 0

z= (1/5)y

Considering the level surface and differential surface area

h(x,y,z) = -y + 5z =0

[tex]dS = |grad(h)| dA[/tex]

In terms of the x and y coordinates of (3,0,0) and (3,5,1) and (0,5,1), we can state that the ranges are 0 to 3 and 5 respectively.

In conclusion,

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Answer:

126

Step-by-step explanation:

The difference between the first two terms of this sequence is 5 (16 - 11 = 5). The difference between the second and third terms of this sequence is also 5 (21 - 16 = 5).

So, we can assume that the difference between each term in this sequence is 5. To get from the first term (11) to the second term (16) we had to add 5 once. (or, add 5  x 1 [time])

To get from the first term (11) to third (21), we had to add 5 twice

(or, add 5 x2)

*repeated addition, such as 5+5+5 is the same thing as multiplication. If we are adding 5 three times, we will get the same outcome as 5 x 3.

So, to get from the first term (11) to the 24th term, we will have to add 5 23 times, or 5 x 23

5 x 23 = 115

11 + 115 = 126

Making 126 the 24th term of the sequence

The value of x and y in the right angle triangle are 6 units and 10.4 units.

The sides of a right triangle can be found as follows:

using trigonometric ratio,

sin 60 = opposite / hypotenuse

sin 60 = y / 12

cross multiply

y = 12 sin 60

y = 10.3923048454

y = 10.4 units

Therefore,

cos 60 = adjacent / hypotenuse

cos 60 = x / 12

x = 12 cos 60

x = 6 units

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So we conclude that x measures 6 units and y measures 10.39 units.

Here we have a right triangle.

x is the adjacent cathetus to the shown angle, and y is the opposite cathetus. We can see that the hypotenuse measures 12.

Then using trigonometric relations we get:

So we conclude that x measures 6 units and y measures 10.39 units.

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Work Shown:

12x+10

2*6x+2*5

2(6x+5)

Effectively, we use the distributive property in reverse when it comes to factoring expressions like this.

The distributive property in general is a*(b+c) = a*b+a*c

1) Find the Greatest Common Factor (GCF).

1 What is the largest number that divides evenly into 12 and 10?

It is 2.

2 What is the highest degree of  that divides evenly into 12and 10?

It is 1, since x is not in every term.

3 Multiplying the results above,

The GCF is 22.

2) Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)

[tex]2(\frac{12x}{2}+\frac{10}{2})[/tex]

3) Simplify each term in parentheses.

2(6x+5)

Answer: 18 kilograms

Step-by-step explanation:

If each pumpkin weighs 3 kilograms and the farmer has 6 pumpkins the equation would be 6x3=18 in order to find the mass of the farmer's pumpkins.

The sum of the cubes of first 15 natural numbers.

[tex]( \frac{(15 \times 16)}{2} {)}^{2} [/tex]

[tex] = (15 \times 8 {)}^{2} [/tex]

=14400

Hence, the sum of the cubes of first 15 natural numbers is 14400

The product of the complex numbers 65(cos(14°)+ i sin(14°)) and 8(cos(4°)+ i sin(4°)) is 520[cos(18) + isin(18)]

An equation is an expression that shows the relationship between two or more numbers and variables.

Complex number is in the form z = a + bi, where a and b are real numbers.

The product of the complex numbers 65(cos(14°)+ i sin(14°)) and 8(cos(4°)+ i sin(4°)) is:

z = 65 * 8 [cos(14 + 4) + isin(14 + 4)] = 520[cos(18) + isin(18)]

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Answer:

Step-by-step explanation:

The numbers of zebrafish and neon tetras can be found by writing an equation relating the numbers of each to their total cost.

__

Let z represent the number of zebrafish Ernesto bought. Then the number of neon tetras is (13 -z), and the total cost of the purchase was ...

  2.10z +1.95(13 -z) = 26.70

  0.15z +25.35 = 26.70 . . . . . . simplify

  0.15z = 1.35 . . . . . . . . . . . . subtract 25.35

  z = 9 . . . . . . . . . . . . . . . divide by 0.15

Ernesto bought 9 zebrafish and 4 neon tetras.

The stems that have the same number of leaves are (c) 4 and 5 each have 3 leaves

The table of values is given as:

Week 1: 12 15 25 45 52 30 31

Week 2: 22 25 46 51 10 19 33

Week 3: 44 21 30 20 10 24 52

Remove the week tags:

12 15 25 45 52 30 31

22 25 46 51 10 19 33

44 21 30 20 10 24 52

Sort the data values in tens

10 10 12 15 19

20 21 22 24 25 25

30 30 31 33

44 45 46

51 52 52

Now, we can now plot the stem-and-leaf graph.

This is represented as follows:

Stem  |   Leaves

1               0 0 2 5 9

2              0 1 2 4 5 5

3              0 0 1 3

4              4 5 6

5              1 2 2

In the above plot, we can see that stems 4 and 5 have 3 leaves each

Hence, the stems that have the same number of leaves are (c)

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The probability of 3 successes is 0.0384

The given parameters are:

The binomial probability is represented as:

[tex]P(x) = ^nC_x * p^x * (1 - p)^{n-x[/tex]

So, the probability of three successes is:

[tex]P(3) = ^4C_3 * 0.4^3 * (1 - 0.4)^{4 -3[/tex]

Evaluate the factors in the expression

[tex]P(3) = ^4C_3 * 0.0384[/tex]

Evaluate the combination expression

P(3) = 1 * 0.0384

Evaluate the product

P(3) = 0.0384

Hence, the probability of 3 successes is 0.0384

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Answer:

0.1536

Step-by-step explanation:

Answer:

-16.

Step-by-step explanation:

2/3 * (-3) * (4*5 + 6 - 2(-3)^2)

= -2(20 + 6 - 18)

= -2 * 8

= -16.

Answer:

hope you can understand

The estimated mean lifetime of a bulb of 154.69

The table is given as:

Lifetime                Frequency

25 < t ≤ 50             47

50 < t ≤ 100            86

100 < t ≤ 150          45

150 < t ≤ 200         36

200 < t ≤ 250        0

250 < t ≤ 300       37

300 < t ≤ 350      50

Calculate the midpoint using:

x = (Lower +Upper)/2

So, we have:

Lifetime                Frequency

37.5                        47

75                           86

125                        45

175                        36

225                        0

275                       37

325                      50

The mean value is calculated as:

[tex]\bar x = \frac{\sum fx}{\sum f}[/tex]

So, we have:

[tex]\bar x = \frac{37.5 * 47 + 75 * 86 + 125 * 45 + 175 * 36 + 225 * 0 + 275 * 37 + 325 * 50}{47 + 86 + 45 + 36 + 0 + 37 + 50}[/tex]

Evaluate

[tex]\bar x = \frac{46562.5}{301}[/tex]

Divide

[tex]\bar x = 154.69[/tex]

Hence, the estimated mean lifetime of a bulb of 154.69

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(x+a)(x+3a)= x²+bx+75

x²+4a+3a²=x²+bx+75

by comparing 3a²=75 and b= 4a

a= ±5

possible values of b= ±20

Two possible values of b are 20 and -20.

What is Mathematical expression?

The combination of numbers and variables by using operations addition, subtraction, multiplication and division is called Mathematical expression.

Given that;

The mathematical expression as;

(x + a)(x + 3a) = x² + bx + 75​

Now,

The mathematical expression is;

(x + a)(x + 3a) = x² + bx + 75​

Solve the expression as;

(x + a)(x + 3a) = x² + bx + 75​

x² + 3ax + ax + 3a² = x² + bx + 75

x² + 4ax + 3a² = x² + bx + 75

After comparison we get;

4a = b  ... (i)

And, 3a² = 75  .. (ii)

Solve the second equation for a as;

3a² = 75

Divide by 3;

a² = 25

Take square root both side, we get;

a = ± 5

So, By equation (i) we get;

b = 4a

Substitute a = 5;

b = 4 x 5

b = 20

And, Substitute b = -5;

b = 4 x -5

b = -20

Thus, Two possible values of b are 20 and -20.

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