four less than the quotient of a number cubed and seven, increased by three

[tex]\huge{\boxed{\frac{12}{14}}} \huge{\boxed{\frac{18}{21}}} \huge{\boxed{\frac{24}{28}}} \huge{\boxed{\frac{30}{35}}} \huge{\boxed{\frac{36}{42}}}[/tex]

One really simple way to find an equivalent fraction is just to multiply the numerator and denominator.

For example, for the first answer, [tex]\boxed{\frac{12}{14}}[/tex], I simply multiplied the numerator and denominator each by 2.  This gives you an equivalent fraction.

You can then continue with this process using numbers such as 3, 4, 5, and 6 as your multiplication factor.

Step-by-step explanation:

[tex]\dfrac{6}{7}=\dfrac{6\cdot2}{7\cdot2}=\dfrac{12}{14}\\\\\dfrac{6}{7}=\dfrac{6\cdot3}{7\cdot3}=\dfrac{18}{21}\\\\\dfrac{6}{7}=\dfrac{6\cdot4}{7\cdot4}=\dfrac{24}{28}\\\\\dfrac{6}{7}=\dfrac{6\cdot5}{7\cdot5}=\dfrac{30}{35}\\\\\dfrac{6}{7}=\dfrac{6\cdot6}{7\cdot6}=\dfrac{36}{42}\\\\\dfrac{6}{7}=\dfrac{6\cdot7}{7\cdot7}=\dfrac{42}{49}\\\vdots\\\dfrac{6}{7}=\dfrac{6\cdot10}{7\cdot10}=\dfrac{60}{70}\\\vdots\\\dfrac{6}{7}=\dfrac{6\cdot100}{7\cdots100}=\dfrac{600}{700}\\\vdots[/tex]

Answer:

Option D. is the answer.

Step-by-step explanation:

Option A.

From the table we can see that for the value of x = 3, there are two values of y (14 and 19).

Which is not possible for a function. It should be one to one.

So option A is not a function.

Option B.

In this option again we have two values of y = 0, -5 for the value of x = 3.

For a function values of x and y should be one to one.

Therefore, it's not a function.

Option C.

Here for x = -1, there are two values of y (y = -11 and 5).

Therefore, it's not a function.

Option D.

In the given graph we find that there are different values of y for every value of x.

Therefore, Option D is the answer.

The discriminant of the quadratic function f(x) = 25x² - 10x + 1 is equal to zero. Hence, the graph of this function has only one x-intercept.

The student is asking for the value of the discriminant of the quadratic function f(x) = 25x² - 10x + 1 and the number of x-intercepts the function has. In a quadratic function ax²+bx+c, the value of the discriminant, denoted as D, is calculated using the formula D = b² - 4ac. In this case, a = 25, b = -10, and c = 1.

Therefore, the discriminant D = (-10)² - 4(.25)(1) = 100 - 100 = 0. The quadratic equation will have exactly one root if the discriminant is zero.

Thus, "the graph of the function f(x) = 25x² - 10x + 1 has one x-intercept".

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The value of the discriminant is 0, and the graph of \(f\) has one repeated x-intercept.

1. The value of the discriminant [tex](\(\Delta\))[/tex] of the quadratic function [tex]\(f(x) = 25x^2 - 10x + 1\)[/tex] is [tex]\(b^2 - 4ac\),[/tex] where a, b and c are coefficients in the quadratic equation [tex]\(ax^2 + bx + c = 0\)[/tex].

2. The number of x-intercepts the graph of \(f\) has is determined by the discriminant:

  - If [tex]\(\Delta > 0\)[/tex], there are two distinct x-intercepts.

  - If [tex]\(\Delta = 0\)[/tex], there is one repeated x-intercept (the graph touches the x-axis but does not cross it).

  - If [tex]\(\Delta < 0\)[/tex], there are no x-intercepts (the graph does not intersect the x-axis).

1. Calculate [tex]\(\Delta\)[/tex]: In the given function [tex]\(f(x) = 25x^2 - 10x + 1\)[/tex], [tex]\(a = 25\),[/tex] [tex]\(b = -10\),[/tex]and [tex]\(c = 1\)[/tex]. Plug these values into the discriminant formula: [tex]\(\Delta = b^2 - 4ac\).[/tex]

[tex]\[\Delta = (-10)^2 - 4(25)(1) = 100 - 100 = 0\][/tex]

2. Analyze the number of x-intercepts based on \(\Delta\):

  - Since [tex]\(\Delta = 0\)[/tex], there is one repeated x-intercept.

Therefore, the value of the discriminant is 0, and the graph of \(f\) has one repeated x-intercept.

The only option that is a triangle from the given options is; 4cm, 8cm, 10 cm

A triangle is a plane shape with three sides which could all be equal or have 2 equal or have no equal sides.

Now, we know a triangle to be one if the sum of two smallest sides is greater than the longest side.

Thus, only option B can B a triangle because the sum of 4cm and 8cm is 12 cm which is greater than 10 cm.

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Answer:

[tex]x_{1}=\frac{+3+\sqrt{5} }{2}\\\\x_{2}=\frac{+3-\sqrt{5} }{2}[/tex]

Step-by-step explanation:

Using:

[tex]x=\frac{-b+-\sqrt{b^{2}-4*a*c} }{2*a}[/tex]

we will have two solutions.

x^2-3x+1=0

So, a=1   b=-3  c=1

[tex]x_{1}=\frac{+3+\sqrt{-3^{2}-4*1*1} }{2*1}\\\\x_{2}=\frac{+3-\sqrt{-3^{2}-4*1*1} }{2*1}[/tex]

We have two solutions:

[tex]x_{1}=\frac{+3+\sqrt{5} }{2}\\\\x_{2}=\frac{+3-\sqrt{5} }{2}[/tex]

The answer is in the picture below! :)

|

V

Answer:

D.

Step-by-step explanation:

The data is symmetric for Shop A but not for Shop B ( note the values 10 and 11 for Shop B which are a lot lower than the other values).

Mean for Shop A and Median for Shop B.

Answer:

The correct option is B.

Step-by-step explanation:

The number of lattes sold daily by two coffee shops is shown in the table.

The data set for shop A is

55, 52, 56, 48, 57, 30, 45, 41

Arrange the data in ascending order.

30, 41, 45, 48, 52, 55, 56, 57

Mean of shop A is

[tex]Mean=\frac{\sum x}{n}=\frac{30+41+45+48+52+55+56+57}{8}=48[/tex]

[tex]Median=\frac{(\frac{n}{2})th+(\frac{n}{2}+1)th}{2}=\frac{48+52}{2}=50[/tex]

The data set for shop B is

45, 42, 57, 48, 11, 10, 46, 43

Arrange the data in ascending order.

10, 11, 42, 43, 45, 46, 48, 57

Mean of shop A is

[tex]Mean=\frac{\sum x}{n}=\frac{10+11+42+43+45+46+48+57}{8}=37.75[/tex]

[tex]Median=\frac{(\frac{n}{2})th+(\frac{n}{2}+1)th}{2}=\frac{43+45}{2}=44[/tex]

Both data distribution are not symmetric, so it is better to describe the centers of distribution in terms of median for both coffee shops. Therefore the correct option is B.

Answer:

[tex] 27^{\frac{1}{5}} = \sqrt[5]{27} [/tex]

Step-by-step explanation:

Rule of exponents:

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

Apply the rule to this case:

[tex] 27^{\frac{1}{5}} = \sqrt[5]{27} [/tex]

Answer:

[tex]3-\sqrt{11}[/tex]

Step-by-step explanation:

If you want rational coefficients then you would want the conjugate of any irrational zero given.

The question is equivalent to what is the conjugate of [tex]3+\sqrt{11}[/tex].

The conjugate of [tex]3+\sqrt{11}[/tex] is [tex]3-\sqrt{11}[/tex].

In general, the conjugate of a+b is a-b

or the conjugate of a-b is a+b.

Or maybe you like this explanation more:

Let [tex]x=3+\sqrt{11}[/tex]

Subtract 3 on both sides:

[tex]x-3=\sqrt{11}[/tex]

Square both sides:

[tex](x-3)^2=11[/tex]

Subtract 11 on both sides:

[tex](x-3)^2-11=0[/tex]

Use difference of squares to factor. I apply [tex]u^2-v^2=(u-v)(u+v)[/tex].

[tex]([x-3]-\sqrt{11})([x-3]+\sqrt{11})=0[/tex]

So you have either

[tex][x-3]-\sqrt{11}=0[/tex] or [tex][x-3}+\sqrt{11}=0[/tex]

Solve both for x-3 and then x.

Add sqrt(11) on both sides for first equation and subtract sqrt(11) on both sides for second equation:

[tex]x-3=\sqrt{11}[/tex] or [tex]x-3=-\sqrt{11}[/tex]

Add 3 on both sides:

[tex]x=3+\sqrt{11}[/tex]  or [tex]x=3-\sqrt{11}[/tex]

Answer:

the answer is C.

Step-by-step explanation:

Answer:

option D

Step-by-step explanation:

As the sample space is for first rolling a number cube and then shooting a basketball, it should be a number n , and X/O

where n= 1,2,3,4,5,6

of the given options

A) 0,2 is incorrect as O of basketball is first and then there is 2

of cube

B) X,O is incorrect because both are from shooting basket ball

C)1,T is incorrect as T is not from the basketball.

only D is correct 6,X!

Option D.) 6, X correctly represents an element of the sample space for rolling a number cube followed by shooting a basketball, including an outcome of rolling a 6 and then making the shot

The question relates to an understanding of sample spaces in probability. The sample space is a set of all possible outcomes of a probability experiment. In this case, the experiment consists of two independent actions: rolling a number cube (commonly a six-sided die) and shooting a basketball with two possible outcomes (making a shot 'X' or missing 'O').

A correct element of the sample space would include one outcome from rolling the die (1 through 6) and one outcome from shooting the basketball (X or O). For example, rolling a 1 on the die and making the basketball shot (X) would be represented as (1, X). Therefore, the correct answer to the question is option D.) 6, X, which shows an outcome of rolling a 6 on the die followed by making the basketball shot

The perimeter of a rectangle with sides of 14 ft and 8 ft is 44 ft.

The perimeter of a rectangle is calculated by adding all its sides. For a rectangle with sides of 14 ft and 8 ft, the perimeter is found by adding twice the length and twice the width:

Perimeter = 2(length + width)
Perimeter = 2(14 + 8) = 2(22) = 44 ft

Answer:

Mary: 16

Kevin: 22

Ahmed: 88

Step-by-step explanation:

This could be written as the following formula.

Mary + Kevin + Ahmad = 126

and we know that

Mary + 6 = Kevin

Kevin * 4 = Ahmed

so Ahmed = (Mary + 6) * 4

When filling this in you get

Mary + Mary + 6 + (Mary + 6) * 4 = 126

Mary + Mary + 6 + 4Mary + 24 = 126

6Mary + 30 = 126

6Mary = 96

Mary = 16

So Mary served 16 orders.

Using the earlier formulas you get

Kevin = Mary + 6 = 16 + 6 = 22

Ahmed = Kevin * 4 = 22 * 4 = 88.

Now we just need to double check it.

Mary + Kevin + Ahmad = 16 + 22 + 88 = 126. Which matches what it should be.

Answer:

Is a Mean, Median and Mode

Is also a summary statistics that presents the center point or typical value off a dataset.

Answer is attached in the image provided.

Answer:

1. Length when found = length at birth + (age when found × growth each year); 2. 6.3 yr

Step-by-step explanation:

1. The word equation

Length when found = length at birth + (age when found × growth each year)

2. The calculations

                            5 m = 2.6 m + (age when found × 0.38 m/yr)  

Do the multiplication first (PEMDAS)

                            5 m = 2.6 m + 0.38 × age when found m/yr

Subtract 2.6 m from each side of the equation

                           2.4 m = 0.38 × age when found m/yr

Divide each side by 0.38 m/yr

                           6.3 yr = age when found

The killer whale is 6.3 yr old.

Step-by-step explanation:

x - y = 7...eqn 1

x^2 + y = 125...eqn 2

making y the subject of the formula in eqn 1

=> y = x -7...eqn 3

subst for y from eqn 3 in eqn 2

=> x^2 + x-7 = 125

=> x^2 + x - 132 = 0

=> (x + 12) (x -11) =0

x = 11 or -12

when x = 11, y = 4

when x = -12, y = -19

Answer:

The largest numbers is either -12 or 11

Step-by-step explanation:

Let the numbers be a and b and a be the largest number.

The difference of two numbers is 7

        a - b = 7 ------------------------- eqn 1

The sum of the smaller number and the square of the larger number is 125

        a² + b = 125 ------------------------- eqn 2

eqn 1 + eqn 2

       a² + a - 132 = 0

       ( a + 12 ) (a - 11) = 0

        a = -12 or a  = 11

So the largest numbers is either -12 or 11

Answer:

33 feet

Step-by-step explanation:

We can draw a triangle in this situation.

Note:

The height of the tree is the side "opposite" of the 35 angle. The squirrel's distance of 47 feet from the base of the tree is the side "adjacent" to the angle.

Which trig ratio relates "opposite" and "adjacent"?

It is Tan

Thus we can write and solve (let height of tree be h):

[tex]Tan(35)=\frac{h}{47}\\h=Tan(35)*47\\h=32.91[/tex]

To the nearest foot, the height of tree is about 33 feet

The graph shows the solutions:

x1 = -3    ⇒  x + 3 = 0

x2 = 1     ⇒  x - 1 = 0

x3 = 5     ⇒  x - 5 = 0

The polynomial follows:   y = (x + 3)(x - 1)(x - 5)

.

Answer:

y= (x+3) (x-1) (x-5)

Step-by-step explanation:

The graph crosses the x axis at the points -3,1,5

These are also called the zeros

f(x) =k (x-a) (x-b) (x-c) .....

where a,b,c,... are the zeros of the function and k is a constant

f(x) = k * (x--3) (x-1) (x-5)

f(x) = k(x+3) (x-1) (x-5)

To help determine the value of k

Take another point  at x = 0, we know the value is positive

f(0) = k(3) (-1) (-5)

f(0) = k(15)

That means k must be greater than 0  Looking at the graph, it should be around 1

f(x) = (x+3) (x-1) (x-5)

Answer:

[4, 1]

Step-by-step explanation:

Here we have four rows and one column, so the order of A + B is [4, 1].

The two lines are parallel, which means they never touch, cross or meet.

Answer: No solution

Answer:

no solution

Step-by-step explanation:

The sum of the geometric series is approximately 435.4, according to the formula for geometric series summation.

To find the sum (Sn) of a geometric series, you can use the formula:

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

Where:

[tex]- \( a_1 \) is the first term\\- \( r \) is the common ratio\\- \( n \) is the number of terms[/tex]

Given:

[tex]\( a_1 = 0.28 \)\( a_5 = 362.88 \)\( r = 6 \)[/tex]

We need to find [tex]\( n \)[/tex]. Since [tex]\( a_5 \)[/tex] is the fifth term, we can use the formula for the nth term of a geometric series:

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

Substitute the values we have:

[tex]\[ 362.88 = 0.28 \cdot 6^{(5-1)} \]\[ 362.88 = 0.28 \cdot 6^4 \]\[ 362.88 = 0.28 \cdot 1296 \]\[ 362.88 = 363.648 \][/tex]

So, [tex]\( n = 5 \).[/tex]

Now, plug the values into the sum formula:

[tex]\[ S_5 = \frac{{0.28 \cdot (1 - 6^5)}}{{1 - 6}} \]\[ S_5 = \frac{{0.28 \cdot (1 - 7776)}}{{-5}} \]\[ S_5 = \frac{{0.28 \cdot (-7775)}}{{-5}} \]\[ S_5 = \frac{{-2177}}{{5}} \]\[ S_5 = -435.4 \][/tex]

Since the sum of a series cannot be negative, the correct answer is option:

a. 435.4

Answer:

You would click (1,-5)

Step-by-step explanation:

The absolute minimum is the lowest point of the graph.

In all graphs, if it says minimum, it almost certainly means that lowest point, and if there are more than one, you would simply click on those.

It does not matter how many points there are, only that they are the lowest.

Therefore, it would be 1,-5.

Answer:

Step-by-step explanation:

If you accept that this is a function or even a relationship then and is connected then the minimum should be (1,-5).  

Answer:

-2

Step-by-step explanation:

Within the provided points list for the graph, there is the coordinate (1, -2). Hence, by definition of a function and how to read graphs, f(1) is -2.

In this scenario, you're being asked to read the value of f(1) from a given graph. The line passing through the listed points is irrelevant provided one of the plotted points has an x-coordinate of 1. You directly read this from the graph - not calculate it or interpolate it. The list of points you've provided includes (1, -2), so, in your case, f(1) = -2. This is exactly how you would refer to the y-value at x=1 on a visual graph.

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Answer:

204 in^3

Step-by-step explanation:

The volume of the base square is V=lwh.

When we substitute our givens, it becomes V=6(4)(2). This equals 48 in^3.

The volume of the triangle is V=.5lwh.

When we substitute our givens, it becomes V=.5(6)(4)(15-2). This equals 156 in^3.

When we add 48 and 156, we get 204 in^3.

Hope this helps :)

Answer:

11.43

Step-by-step explanation:

10 divided by 7/8

Set the expression:

(10/(7/8))

To solve, flip the denominator fraction, and make the division into multiplication:

((10 x 8)/7)

Multiply across, then divide:

(80)/7

Divide:

80/7 = 11.43 (rounded)

11.43 is your answer.

~

Answer:

{x = -3 , y=2  (Isolved for both variables be elimination)

Step-by-step explanation:

Solve the following system:

{3 x + 5 y = 1 | (equation 1)

7 x + 4 y = -13 | (equation 2)

Swap equation 1 with equation 2:

{7 x + 4 y = -13 | (equation 1)

3 x + 5 y = 1 | (equation 2)

Subtract 3/7 × (equation 1) from equation 2:

{7 x + 4 y = -13 | (equation 1)

0 x+(23 y)/7 = 46/7 | (equation 2)

Multiply equation 2 by 7/23:

{7 x + 4 y = -13 | (equation 1)

0 x+y = 2 | (equation 2)

Subtract 4 × (equation 2) from equation 1:

{7 x+0 y = -21 | (equation 1)

0 x+y = 2 | (equation 2)

Divide equation 1 by 7:

{x+0 y = -3 | (equation 1)

0 x+y = 2 | (equation 2)

Collect results:

Answer:  {x = -3 , y=2

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}3x+5y=1&\text{multiply both sides by 7}\\7x+4y=-13&\text{multiply both sides by (-3)}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}21x+35y=7\\-21x-12y=39\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad23y=46\qquad\text{divide both sides by 23}\\.\qquad\qquad y=2[/tex]

If you want to solve it to the end, put the value of y in the first equation and solve it for x.

3x + 5(2) = 1

3x + 10 = 1         subtract 10 from both sides

3x = -9           divide both sides by 3

x = -3

Answer:

180

Step-by-step explanation:

180-120 = 60 this is one of all the congruent angles

of the top of my head i know a regular triangle has three 60 degree angles meaning it is 60*3 = 180

Answer:

Wrong

Step-by-step explanation:

The student is wrong. Two angles are coterminal if and only if the difference between their measures is a multiple of 360°.

The difference between the angles 180° and –180° is 360°, and they are coterminal. Therefore the student is WRONG.

Answer:

The student is wrong. Two angles are coterminal if and only if the difference between their measures is a multiple of 360°.

The difference between the angles 180° and –180° is 360°, and they are coterminal. Therefore the student is WRONG.

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]p\%=\dfrac{p}{100}\\\\14\%=\dfrac{14}{100}=0.14\\\\3540\%=\dfrac{3540}{100}=35.40=35.4\\\\14\%\ of\ 3540\%\ of\ 35\to(0.14)(35.4)(35)=173.46[/tex]

Answer: B. Rhombus.

Step-by-step explanation: B. Rhombus is the answer because a rectangle has 2 pairs of equal sides. A pentagon has 5 sides. A trapezoid doesn’t have all equal sides. A rhombus is like a squished square.

Answer:

B. take up less space than when the data set is not organized

Step-by-step explanation:

Well, in this question, you can analyze one answer after the other.

In A see important values in the data set, this makes sense when determining mode and median of a data set.Median is the center value in a data set, while mode is the repeated value in the set.When data set is arranged from smallest to the largest, the median and mode can be seen clearly.These can be the important values in the data set

In C. More easily see the maximum and minimum values in the data set, is possible especially when data is arranged in an increasing order.The smallest value will start, where as the largest value will be at the end.This applies to D too.

However in B, it will depend with the manner you would like to analyze the data.For example organizing data using tables will make your data easy to understand and present your analysis.Another person will group the data in intervals to identify the frequency of in data set.So, you see, its not about space taken by data but how you would like to present your data when analyzing it.

Hope this helps.

The end behavior of the function y = 10x9 – 4x is such that as x approaches infinity, y approaches infinity, and as x approaches negative infinity, y approaches negative infinity. This is because the degree of the polynomial is odd and the leading coefficient is positive.

The end behavior of a polynomial function describes what happens to the function values (y-values) as x approaches infinity and negative infinity. In your function, y = 10x9 – 4x, the highest power of x is 9, and it's coefficient is positive.

According to the rules of end behavior, if the degree (highest power) of the polynomial is odd, and the leading coefficient (the number in front of the highest power) is positive, as x approaches positive infinity, y also approaches positive infinity, and as x approaches negative infinity, y approaches negative infinity.

In simpler terms, this means that the graph of your function starts in the third quadrant (bottom-left) and ends in the first quadrant (top-right). Hence, the end behavior of this function can be described as: as x approaches infinity, y approaches infinity; and as x approaches negative infinity, y approaches negative infinity.

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Answer: C

Step-by-step explanation: the answer is C on edge :)