may someone help me with this question? Thank you!

(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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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

Answer:

2x+4/ x-1 C

Step-by-step explanation:

Because the y-intercept is -4

The information shows that:

It should be noted that the mean is the average of the numbers that are given.

The median is the number in the middle when they are arranged in ascending or descending order. The mode is the number that appears most.

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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:

After considering the given data we come to the conclusion that the two other cards are 6 and 10, under the condition that Neyha has six number cards. Here are four of Neyha's cards. 8;8;8;8.

Let us assume that the other two cards x and y.
The given mean of all six cards is 8. Then, the sum of all six cards is 48 (8×6). We have that four of the cards are 8s.
So, the summation of these four cards is 32 (8×4).
The dedicated range of all six cards is 4. Therefore, the difference between the largest and smallest card is 4.
Furthermore, we know that four of the cards are 8s, the other two cards must be different from 8.
Hence, we can consider that x and y are the smallest and largest numbers in the set.
Here we have to apply basic algebraic expression
We can perform the setting up two equations:
x + y = 48 - 32 = 16 (the summation of x and y is equivalent to the summation of all six cards minus the summation of the four 8s)
y - x = 4 (the difference considering y and x is equal to the range of all six cards)
Evaluating these equations simultaneously gives us:
y = 10
x = 6
Therefore, the other two cards are 6 and 10.
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Answer:

27 I think just divide 81 by 3

The equivalent expression of [tex]\frac{(5ab)^3}{30ab^{-7}}[/tex] is [tex]\frac{25a^{2}b^{10}}{6}[/tex]

The expression is given as:

[tex]\frac{(5ab)^3}{30ab^{-7}}[/tex]

Expand the numerator

[tex]\frac{(5ab)^3}{30ab^{-7}} =\frac{125a^3b^3}{30ab^{-7}}[/tex]

Divide 125 and 30 by 5

[tex]\frac{(5ab)^3}{30ab^{-7}} =\frac{25a^3b^3}{6ab^{-7}}[/tex]

Apply the law of indices

[tex]\frac{(5ab)^3}{30ab^{-7}} =\frac{25a^{3-1}b^{3+7}}{6}[/tex]

Evaluate the exponent

[tex]\frac{(5ab)^3}{30ab^{-7}} =\frac{25a^{2}b^{10}}{6}[/tex]

Hence, the equivalent expression of [tex]\frac{(5ab)^3}{30ab^{-7}}[/tex] is [tex]\frac{25a^{2}b^{10}}{6}[/tex]

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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:

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:

11,676 M&M's

Step-by-step explanation:

A dozen is 12

the problem is saying that in the jar, there are 973 (12-M&M's)

973 * 12 is 11676

There are 11,676 M&M's in the jar

Answer:

they are 11,676

Step-by-step explanation:

A dozen is 12 so since there are 973 dozen, we multiply by 12.

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

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 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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Answer:

hope you can understand

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.

Answer:

y=x+4

Step-by-step explanation:

pretty sure

Answer:

d

Step-by-step explanation:

the fitness grows into bodyness from good

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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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.

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:

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: 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

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

The measure of central tendency that is most affected by the lowest score is; A: The mean.

The points table is missing and so I have attached it.

The 3 main measures of central tendency are called mean, median and mode.

Now, from the table attached, if we find the average which is the mean, we will get 56.6.

Now, the mode is the number that occurs the most times. In this case, there is no mode because no number appears more than the other.

For the median, if we arrange in ascending order, we have;

42, 48, 49, 53, 55, 56, 58, 66, 68, 71.

The median = (55 + 56)/2 = 55.5

Now, if we remove the lowest score, the measure that will be most affected will be the mean as the median will only change by 0.5 to 56.

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Answer:

B

Step-by-step explanation: