A simple question:


Is a vector made like or ?

Answer:

Annual rate of interest is 8%.

The answer is -.75 because y=mx+b, and the slope is m.

Answer:

Each box has 800 spoons.

Step-by-step explanation:

4800/6=800

Answer:

[tex]\large\boxed{\dfrac{11}{14}}[/tex]

Step-by-step explanation:

[tex]\dfrac{\frac{11}{2}}{7}=\dfrac{11}{2}\div7=\dfrac{11}{2}\div\dfrac{7}{1}=\dfrac{11}{2}\cdot\dfrac{1}{7}=\dfrac{(11)(1)}{(2)(7)}=\dfrac{11}{14}[/tex]

Answer:

Step-by-step explanation:

[tex]\frac{\frac{11}{2}}{7} = \frac{11}{14}[/tex]

[tex]\frac{11}{14} = 0.7857142...[/tex]

I hope this helps!

Answer:

False

True

Step-by-step explanation:

Initially, there were 50 bacteria. It is observed that the bacteria triple in population every 8 hours.

Therefore, the situation can be interpreted as  

[tex]f(x) = 50\times (3)^{\frac{x}{8} }[/tex] .......... (1)

where, f(x) represents the population of bacteria after x hours.

So, the model equation [tex]f(x) = 3 (50)^{\frac{x}{8}}[/tex] is false. (Answer)

Again, from the equation (1) we get, after 36 hours, the bacteria population will be given by [tex]f(36) = 50 \times (3)^{\frac{36}{8}} = 7014.8[/tex] ...... (2)

So, 7014.8 ≈ 7015 is the population of bacteria after 36 hours.  

Hence, this statement is true. (Answer)

Answer:

3

Step-by-step explanation:

11-8=3

3 saves were left out of the 11 for the second game

Answer:

He has made 3 saves in the second game

Step-by-step explanation:

594.15

Step-by-step explanation:

To find the sale price of the iPhone 11, we first calculate the amount of discount which comes to $104.85 and subtract this from the original price. The sale price of the iPhone 11 is therefore $594.15.

The question is about computing the sale price of an iPhone 11 which originally costs $699.00, given that a discount of 15 percent is provided. In mathematical terms, you would be required to find 15% of $699.00 and subtract that amount from the original price to get the sale price.

So, first, determine the amount of discount: 15 / 100 * $699.00 = $104.85. Next, subtract this discount from the original price: $699.00 - $104.85 = $594.15. So, the sale price of the iPhone 11 would be $594.15.

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Answer:

k is -1

Step-by-step explanation:

-12(k+4) = 60

-12k-48=60

-12k=12

k=-1

Answer:

k= -9

Step-by-step explanation:

[tex] - 12(k + 4) = 60 \\ - 12k + - 48 = 60 \\ - 12k = 108 \\ k = - 9[/tex]

Answer:

2/5

Step-by-step explanation:

if one red ball was pulled that mean that now we have 2 red balls 2 green balls and 1 blue ball

and the sum of them is 5 and we have 2 . Soo it is 2/5

Answer:

cos60° = [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Using the trigonometric identity

sin²x + cos²x = 1 ⇒ cos x = [tex]\sqrt{1-sin^2x}[/tex]

Given

sin60° = [tex]\frac{\sqrt{3} }{2}[/tex], then

cos60° = [tex]\sqrt{1-(\frac{\sqrt{3} }{2})^2 }[/tex] = [tex]\sqrt{1-\frac{3}{4} }[/tex] = [tex]\sqrt{\frac{1}{4} }[/tex] = [tex]\frac{1}{2}[/tex]

Final answer:

The cosine of 60 degrees is 1/2.

Explanation:

To find cos 60 degrees, we can use the trigonometric identity: cos² 0 = 1 - sin² 0. Since sin 60 degrees = √3/2, we can substitute this value into the equation:

cos² 60 degrees = 1 - (√3/2)²

cos² 60 degrees = 1 - (3/4)

cos² 60 degrees = 1/4

cos 60 degrees = ±√(1/4)

cos 60 degrees = ±1/2

However, since 60 degrees is in the first quadrant, cos 60 degrees is positive:

cos 60 degrees = 1/2

Answer:

Yes 1/3 is a rational number.

Explanation:

in mathematics, a rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. Hence, 1/3 is a rational number.

Answer:

Yes, it is a rational number.

Step-by-step explanation:

A rational number is any number that can be expressed as a ratio of integers. Even a fraction in which both the numerators and denominators are both integers but the denominator can never ever be less than 0.

I hope this helped you!

Answer:

Length = 25 inches and width = 15 inches.

Step-by-step explanation:

Let us assume that the length of the rectangle is L inches and the width of the rectangle is W inches.

Now, the area of the rectangle is A = LW = 375 sq. inches ........... (1)

Now, given that the length to width ratio of the rectangle is 5 : 3.

Let L = 5x and W = 3x, then from equation (1) we get,

(5x)(3x) = 375

⇒ 15x² = 375

⇒ x² = 25

⇒ x = 5 {Neglecting the negative root, as length can not be negative}

Now, Length = L = 5x = 25 inches and Width = W = 3x = 15 inches. (Answer)

Answer:

5/2 is the scale factor.

Step-by-step explanation:

To calculate scale factor, divide the similar sides.

According to the problem, EFGH is the drawing, or the "result".

Divide a side of the result by the original.

EFGH / ABCD = scale factor

We can use the widths.

Width of EFGH / Width of ABCD

= 10 / 4

= 5/2

Check using the lengths:

Length of EFGH / Length of ABCD

= 20 / 8

= 5/2

The scale factor is 5/2.

Answer:

Step-by-step explanation:

Answer:

The two numbers are 12 , 10

Step-by-step explanation:

Given as :

The least common multiple of two numbers = LCM = 60

The ratio of the greater number to lesser number = 6 : 5

let the greater number = 6 x

And The smaller number = 5 x

∵ The LCM of numbers = 60

So, 6 × 5 × x = 60

Or,  30 × x = 60

∴  x = [tex]\frac{60}{30}[/tex]

I.e x = 2

So The greater number = 6 x = 6 × 2 = 12

And  The smaller number = 5 x = 5 × 2 = 10

Hence The two numbers are 12 , 10 Answer

Answer:

$75.26

Step-by-step explanation:

base cost = $49.95

total mile cost = 1.19*18 =$21.42

gas cost = $3.89

total cost =$(49.95 +21.42+3.89)=$75.26

The expression to represent total cost of the trip is $49.95 + $1.19m + (m/18)($3.89).

Given that, the rental has a base cost of 49.95, plus an additional cost of 1.19 per mile driven.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

If we let m = total distance, then we can set up an equation to find the total cost.

The additional cost for distance would be $1.19m

The cost for gas would be (m/18)($3.89)

So the total cost of the trip could be represented by $49.95 + $1.19m + (m/18)($3.89).

Therefore, the expression to represent total cost of the trip is $49.95 + $1.19m + (m/18)($3.89).

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Required polynomial of degree four having zeros as -2 , 4 , 4 , 8 is [tex]f(x)=x^{4}-14 x^{3}+48 x^{2}+32 x-256[/tex]

Need to determine a polynomial of degree 4 and the zeros are -2, 4 , 4 and 8

Let the required polynomial be represented by f(x)

The factor theorem describes the relationship between the root of a polynomial and a factor of the polynomial.

If the polynomial p(x) is divided by cx−d and the remainder, given by p(d/c), is equal to zero, then cx−d is a factor of p(x).

-2 is zero of a polynomial means when x = -2, f(-2) = 0, so from factor theorem we can say that  

=> x = -2 that is x + 2 = 0 is factor of polynomial f(x)

4 is zero of a polynomial means when x = 4, f(4) = 0 , so from factor theorem we can say that  

=> x = 4 that is x -4 = 0 is factor of polynomial f(x)

4 is zero of a polynomial means when x = 4, f(4) = 0 , so from factor theorem we can say that  

=> x = 4 that is x -4 = 0 is factor of polynomial f(x)

8 is zero of a polynomial means when x = 8, f(8) = 0 , so from factor theorem we can say that  

=> x = 8 that is x -8 = 0 is factor of polynomial f(x)

So now we have four factors of polynomial f(x) that are (x + 2), (x -4) , (x -4) and (x – 8)

And as given that degree of polynomial f(x) is 4  

Now f(x) is equal to product of factors

[tex]\begin{array}{l}{\Rightarrow f(x)=(x+2)(x-4)^{2}(x-8)} \\\\ {=>f(x)=(x+2)\left(x^{2}-8 x+16\right)(x-8)} \\\\ {=>f(x)=(x+2)\left(x^{3}-8 x^{2}+16 x-8 x^{2}+64 x-128\right)} \\\\ {=>f(x)=(x+2)\left(x^{3}-16 x^{2}+80 x-128\right)} \\\\ {=>f(x)=x\left(x^{3}-16 x^{2}+80 x-128\right)+2\left(x^{3}-16 x^{2}+80 x-128\right)} \\\\ {=>f(x)=x^{4}-16 x^{3}+80 x^{2}-128 x+2 x^{3}-32 x^{2}+160 x-256} \\\\ {=>f(x)=x^{4}-14 x^{3}+48 x^{2}+32 x-256}\end{array}[/tex]

Hence required polynomial of degree four having zeros as -2 , 4 , 4 , 8 is [tex]f(x)=x^{4}-14 x^{3}+48 x^{2}+32 x-256[/tex]

To find equivalent fractions, multiply the numerator and denominator of a given fraction by the same number to achieve the desired denominator. For example, 3/4 becomes 9/12 and 1/2 becomes 3/6 when transformed to have denominators of 12 and 3 respectively.

To solve the question of completing each equation so that it shows equivalent fractions, we will use the concept of multiplying the numerator and denominator of a fraction by the same number to find an equivalent.

For the fraction 3/4, to find its equivalent with a denominator of 12, we would multiply both the numerator and denominator by 3, because 4 times 3 equals 12. Thus, we get the equivalent fraction: 3/4 = 9/12.

To find an equivalent fraction for 1/2 with a denominator of 3, we multiply both the numerator and denominator by 3/6 because 2 times 3 equals 6. The equivalent fraction is 1/2 = 3/6.

If we need an equivalent for 2/1 with a denominator of 4, we multiply both the numerator and denominator by 4 because the common denominator we are aiming for is 4. The equivalent fraction is then 2/1 = 8/4.

Note that we always ensure the multiplication factor makes the denominators equal, since that is the requirement for fractions to be equivalent.

The equivalent fractions are:

1. [tex]\( \frac{1}{4} = \frac{3}{12} \)[/tex]

2. [tex]\( \frac{4}{5} = \frac{8}{10} \)[/tex]

3. [tex]\( \frac{1}{6} = \frac{2}{12} \)[/tex]

To complete each equation and show equivalent fractions, we need to find the missing numerator or denominator that, when filled in, will make the fractions equivalent.

1. [tex]\( \frac{1}{4} = \frac{3}{12} \)[/tex]

  Explanation: To find an equivalent fraction for [tex]\( \frac{1}{4} \)[/tex] with a denominator of 12, we notice that we can get from 4 to 12 by multiplying 4 by 3 (4 * 3 = 12). So, to make the fractions equivalent, we also multiply the numerator by 3 (1 * 3 = 3). This gives us [tex]\( \frac{3}{12} \)[/tex], which is equivalent to [tex]\( \frac{1}{4} \)[/tex].

2. [tex]\( \frac{4}{5} = \frac{8}{10} \)[/tex]

  Explanation: To find an equivalent fraction for [tex]\( \frac{4}{5} \)[/tex] with a denominator of 10, we notice that we can get from 5 to 10 by multiplying 5 by 2 (5 * 2 = 10). So, to make the fractions equivalent, we also multiply the numerator by 2 (4 * 2 = 8). This gives us [tex]\( \frac{8}{10} \)[/tex], which is equivalent to [tex]\( \frac{4}{5} \)[/tex].

3. [tex]\( \frac{1}{6} = \frac{2}{12} \)[/tex]

  Explanation: To find an equivalent fraction for [tex]\( \frac{1}{6} \)[/tex], we want the denominator to be 12. To do this, we notice that we can get from 6 to 12 by multiplying 6 by 2 (6 * 2 = 12). So, to make the fractions equivalent, we also multiply the numerator by 2 (1 * 2 = 2). This gives us [tex]\( \frac{2}{12} \)[/tex], which is equivalent to [tex]\( \frac{1}{6} \)[/tex].

The complete question is given below:

Complete each equation below so that it shows equivalent fractions.

1/4 = __/12

4/5 = __/10

1/6 = __/__

Answer:

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36.

Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42.

Step-by-step explanation:

Answer:

6,3,2,1

Step-by-step explanation:

the factors of 36 are 36, 18, 12, 9, 6, 4, 3, 2, 1

The factors of 42 are 42, 21, 14, 7, 6, 3, 2, 1

The factors that they have in common are therefore 6,3,2, and 1 when compared

Answer:

150=6x

Step-by-step explanation:

Let x = height of the tree.

Set up the ratio %28Height%29%2F%28Shadow%29+=5%2F6=x%2F30

Since a%2Fb=c%2Fd means ad=bc,

5%2F6=x%2F30 means 5%2A30=6%2Ax

150=6x

Answer:

The answer is 300. Use an online calculator.

Step-by-step explanation:

Answer:300

Step-by-step explanation:

Write your equation down in long division format and the see how many times you can get 7 into 2,100 and then you put 300 at the top and that’s how you solve a perfect division equation.

RootIndex 12 StartRoot 8 EndRoot Superscript x

12th root of 8^x = (12th root of 8)^x

[tex]\sqrt[12]{8^{x}} = \left(\sqrt[12]{8}\right)^{x}[/tex]

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

Explanation:

The general rule is

[tex]\sqrt[n]{x} = x^{1/n}[/tex]

so any nth root is the same as having a fractional exponent 1/n.

Using that rule we can say the cube root of 8 is equivalent to 8^(1/3)

[tex]\sqrt[3]{8} = 8^{1/3}[/tex]

-----

Raising this to the power of (1/4)x will have us multiply the exponents of 1/3 and (1/4)x like so

(1/3)*(1/4)x = (1/12)x

In other words,

[tex]\left(8^{1/3}\right)^{(1/4)x} = 8^{(1/3)*(1/4)x}[/tex]

[tex]\left(8^{1/3}\right)^{(1/4)x} = 8^{(1/12)x}[/tex]

-----

From here, we rewrite the fractional exponent 1/12 as a 12th root. which leads us to this

[tex]8^{(1/12)x} = \sqrt[12]{8^{x}} [/tex]

[tex]8^{(1/12)x} = \left(\sqrt[12]{8}\right)^{x} [/tex]

Answer:

C 8 x/3

Step-by-step explanation:

For this case we have that by definition, the equation of the line in the slope-intersection form is given by:

[tex]y = mx + b[/tex]

Where:

m: It is the slope of the line

b: It is the cut-off point with the y axis

We have two points through which the line passes:

[tex](x_ {1}, y_ {1}) :( 8,5)\\(x_ {2}, y_ {2}): (- 6,5)[/tex]

We found the slope:

[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {5-5} {- 6-8} = \frac {0} {- 14} = 0[/tex]

The slope is zero.

Thus, the equation is of the form:

[tex]y = b[/tex]

We substitute one of the points and find b:

[tex](x, y) :( 8,5)\\5 = b\\b = 5[/tex]

Finally, the equation is:

[tex]y = 5[/tex]

Answer:

[tex]y = 5[/tex]

Answer:

y=5

Step-by-step explanation:

Answer:

1.25 miles/hr

Step-by-step explanation:

5miles in 4 hours, this means  5miles/ 4hrs

To find the rate per hour:

5/4 = 1.25 miles/hr

Hope this helps!

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Answer:

5/4

Step-by-step explanation:

Divide the miles by the hours. It gives you the ratio.

Answer:

The original fraction was less than 1/2. Since the result was a mixed number, the original fraction must have contained less than 1 unit of 1/2.

Step-by-step explanation:

The fraction will be less than 1/2. An example will be 1/2 divided by 1/3. You'll need to do 1/2 x 3/1, which will result in 3/2, or 1 1/2.

The original fraction was greater than 1/2. Dividing by 1/2 is the same as doubling, so for the result to be a mixed number, the original fraction must have exceeded 1/2.

The original fraction was greater than 1/2. Since the result was a mixed number, the original fraction must have contained more than 1 unit of 1/2.

This is because when you divide a fraction by 1/2, you are essentially doubling that fraction. If the original fraction were less than or equal to 1/2, doubling it would still result in a fraction that is less than or equal to 1 (not a mixed number). Therefore, in order for the result to be a mixed number, the original fraction must have been more than 1/2. For example, if the original fraction was 3/4 (which is greater than 1/2), when divided by 1/2, the result would be 1 1/2, a mixed number.

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Answer:

The answer would be 3; 1.3

the answer is 173 square units

Answer: 84 un squared

Step-by-step explanation:

area of parallelogram = bh

area = 14 x 6 = 84 un squared

Answer:

9.4(3.5 - 2.6x) = -0.4(5.5 + 4.85x)​

Step-by-step explanation:

x = 1.56

Sorry I didn't show my work, my computer won't let me upload pictures right now. I hope this helps!

It takes 3.2 pounds of steel to make one pot.

Step-by-step explanation:

Given,

It takes 800 pounds to manufacture 250 steel pots, therefore,

250 pots = 800 pounds

For calculating steel used for making one pot,

1 steel pot = [tex]\frac{800}{250}[/tex]

[tex]1\ steel\ pot=3.2\ pounds[/tex]

It takes 3.2 pounds of steel to make one pot.

Keywords: division, unit rate

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Answer:

The answer is 25/31 because it equals 56

Final answer:

The smaller number is 25 and the larger number is 31, obtained by setting up an equation with x for the smaller number and x + 6 for the larger one, to represent the described relationship.

Explanation:

To solve the problem, let's denote the smaller number as x and the larger number as x + 6, because the problem states that the larger number is 6 more than the smaller number. The sum of the two numbers is given as 56, so we can set up the following equation:

x + (x + 6) = 56

This simplifies to:

2x + 6 = 56

Subtract 6 from both sides to get:

2x = 50

Now, divide both sides by 2 to find x:

x = 25

Since x is the smaller number, the larger number would be x + 6. Plugging in the value of x, we get:

Larger number = 25 + 6 = 31

Therefore, the smaller number is 25 and the larger number is 31.