Answer:
D. x = 3+i√5 or 3-i√5
Step-by-step explanation:
Given the equation x² - 6x = -14, on rewriting the equation in the firm if a quadratic equation ax²+bx+c = 0 will give x² - 6x + 14= 0.
Required
Use the quadratic formula to solve the equation.
The quadratic formula is expressed as x = (-b±√b²-4ac)/2a
From the equation given, a = 1, b = -6 and c = 145.
x = (-(-6)±√(-6)²-4(1)(14))/2(1)
x = = (6±√36-56)/2
x = = (6±√-20)/2
x = (6±√20*√-1)/2
Since √-1= i
x = (6±√20 i)/2
x = (6±√5*4 i)/2
x = (6±2√5 i)/2
x = 6/2 ± 2√5 i/2
x = 3±√5 i
x = 3+i√5 and 3-i√5
Hence the solution to the quadratic equation is x = 3+i√5 and 3-i√5
Once you have completed the above problems and checked your solutions, complete
the above photos is the solution
A farmer is packing eggs. Each box holds six eggs. The farmer has 860 eggs to pack. I. How many boxes can the farmer fill? 2. How many eggs will be leftover?
Answer:
1. boxes filled= 860/ 6
=143.3
= 143 boxes will be filled.
2. leftover eggs = 2
Step-by-step explanation:
Answer:
1. 143 2. 3
Step-by-step explanation:
860 divided by 6 is 143.3, so the .3 will be 3 leftover eggs
Write the equation for the following table:
Answer:
y = 10x + 20
Step-by-step explanation:
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Slope-Intercept Form: y = mx + b
Step 1: Find slope m
m = (20 - 10)/(0 - -1)
m = 10/(0 + 1)
m = 10/1
m = 10
y = 10x + b
Step 2: Find y-intercept
(0, 20) is y-int from graph
Step 3: Plug into form
y = 10x + 20
Select the correct answer. The edges of a cube are 5 centimeters each and the diagonal of a face is approximately 7 centimeters. What is the approximate area of the cross section passing through the diagonals of opposite faces of this cube? A. 12 square centimeters B. 25 square centimeters C. 35 square centimeters D. 49 square centimeters Reset Next
C : 35
---------------------
Find the average rate of change of g(x)= – x2 over the interval [ – 8, – 2]. Write your answer as an integer, fraction, or decimal rounded to the nearest tenth. Simplify any fractions.
Answer:
[tex]Average\ Rate = 10[/tex]
Step-by-step explanation:
Given
[tex]g(x) = -x^2[/tex]
[tex](-8,-2)[/tex]
Required
Determine the average rate of change;
Average rate of change is calculated as thus;
[tex]Average\ Rate = \frac{g(b) - g(a)}{b - a}[/tex]
Where
[tex](a,b) = (-8,-2)[/tex]
i.e. a = -8 and b = -2
[tex]Average\ Rate = \frac{g(b) - g(a)}{b - a}[/tex] becomes
[tex]Average\ Rate = \frac{g(-2) - g(-8)}{-2 - (-8)}[/tex]
[tex]Average\ Rate = \frac{g(-2) - g(-8)}{-2 + 8}[/tex]
[tex]Average\ Rate = \frac{g(-2) - g(-8)}{6}[/tex]
Calculating g(-2)
Substitute -2 for x in [tex]g(x) = -x^2[/tex]
[tex]g(-2) = -(-2)^2[/tex]
[tex]g(-2) = -4[/tex]
Calculating g(-8)
Substitute -8 for x in [tex]g(x) = -x^2[/tex]
[tex]g(-8) = -(-8)^2[/tex]
[tex]g(-8) = -64[/tex]
Substitute values for g(-2) and g(-8)
[tex]Average\ Rate = \frac{g(-2) - g(-8)}{6}[/tex]
[tex]Average\ Rate = \frac{-4 - (-64)}{6}[/tex]
[tex]Average\ Rate = \frac{-4 + 64}{6}[/tex]
[tex]Average\ Rate = \frac{60}{6}[/tex]
[tex]Average\ Rate = 10[/tex]
Hence, the average rate of change is 10
Helllllpppppp!
I went to Starbucks and purchased three coffees and two cake pops with a total cost of $7 dollars. Then I
went to Einstein Bagels and purchased two coffees and four cake pops for $8 dollars. What is the price for a
single coffee and single cake pop?
x=cost of a single coffee
y= cost of a cake pop
3x+2y+7
2x+4y+8
Answer:
Step-by-step explanation:
The system of equations is:
● 3x + 2y = 7
● 2x + 4y = 8
Where x is the price of a single coffee and y is the price of a single coffee
We will solve this simultaneous equations using the graphing method:
The solutions is the intersection point of to the lines.
(Picture below)
The intersection point is (1.5,1.25)
Answer:
x = 1.5
y =1.25
Step-by-step explanation:
3x+2y=7
2x+4y=8
Multiply the first equation by -2
-2(3x+2y=7 )
-6x-4y = -14
Add this to the second equation
-6x-4y = -14
2x+4y=8
----------------
-4x = -6
Divide by -4
-4x/-4 = -6/-4
x = 1.5
Now find y
3x+2y=7
3(1.5) + 2y = 7
4.5 +2y = 7
Subtract 4.5 from each side
2y = 2.5
Divide by 2
y = 1.25
Liam tried to define a translation. - Point A maps to point A' - Every point P maps to point P' such that PP' is parallel to AA' and points in the same direction as AA' Which counterexample shows that Liam's definition does not fully define a translation?
Answer:
B
Step-by-step explanation:
This is the correct answer.
From The diagrams shown here, the option that does not fully define a translation is B.
What is a translation in mathematics?
In mathematics, this is another word for a transformation. What the translation does is that it helps to move a shape in different ways without altering the appearance of the shape.
The translation in this question is option B given the definition that we have above.
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please help me find the nth term of this sequence 0, 3, 8, 15, 24
Answer:
80
Step-by-step explanation:
0, 3, 8, 15, 24, 35, 48, 63, 80 which is the nth term
first step you have to find how many steps the sequence was going with.
examples= from 0 to 3 the steps were 3
=from 3 to 8 the steps were 5
= from 8 to 15 the steps were 7
you will recognize that the steps the sequence is going with is odd numbers.
so you will use the odd numbers until you find what you need. which leads you to 80 which is the nth number in the sequence.
Answer:
80
Step-by-step explanation:
What is the mode of the data represented in the dot plot shown in the image? A. 0 B. 1 C. 2 D. 3 Show all work!
Answer:
2
Step-by-step explanation:
The mode is the number that appear most often
The number with the most dots is 2
The mode is 2
The mode in any data set is the number that gets represented the most.
As you can see on the plot, the number that gets represented the most is 2.
Best of Luck!
Amir drove from Jerusalem down to the lowest place on Earth, the Dead Sea, descending at a rate of 12 meters per minute. He was at sea level after 30 minutes of driving. Graph the relationship between Amir's altitude relative to sea level (in meters) and time (in minutes).
Answer:
Graph these two points: (0, 360), (30, 0)
Step-by-step explanation:
Since Amir drove for 30 minutes at a rate of 12 meters, that means that he started at an elevation of 360 feet. The easiest way to graph this, is to place one dot at (0, 360), and at (30, 0).
The straight line joining the points (0, 360) and (30, 0) will be the graph.
What is the equation of a straight line? What do you mean by domain and range of a linear function?The general equation of a straight line is -
y = mx + c
where -
[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.
Other possible equations of lines are -
(y - y₁) = m(x - x₁) {Point - slope form}
(y - y₁) = (y₂ - y₁) × (x - x₁)/(x₂ - x₁) {Two point - slope form}
x/a + y/b = 1 {intercept form}
x cos(β) + y sin(β) = L {Normal form}
For any function y = f(x), Domain is the set of all possible values of [y] that exists for different values of [x]. Range is the set of all values of [x] for which [y] exists.
We have Amir who drove from Jerusalem down to the lowest place on Earth, the Dead Sea, descending at a rate of 12 meters per minute. He was at sea level after 30 minutes of driving.
We can write the equation of graph as -
y = - 12t + 360
At t = 0 -
y = 0 + 360
y = 360
and
at t = 30 minutes -
y = - 12 x 30 + 360
y = - 360 + 360
y = 0
The straight line joining the points (0, 360) and (30, 0) will be the graph.
Therefore, the straight line joining the points (0, 360) and (30, 0) will be the graph.
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Which of the following statements is true for a function with equation Ax) = 5(3)*?
The graph has y-intercept (0,5) and increases with a constant ratio of 3.
The graph has y-intercept (0, 3) and decreases with a constant ratio of 3.
The graph has y-intercept (0, 3) and increases with a constant ratio of 5.
The graph has y-intercept (0,5) and decreases with a constant ratio of 3.
Answer:
Hey there!
The graph has a y-intercept of (0,5), and increases with a common ratio of 5. (For example, it increases from 3, 15, 75, and the common ratio is 5.
Hope this helps :)
What is the solution to -5 + z = -12 A. z = -17 B. z = -7 C. z = 7 D. z = 17
Answer: -7
Step-by-step explanation:
Complete the statement. The line x = −2 is _______.
Answer:
see explanation
Step-by-step explanation:
The line x = - 2
Is a vertical line parallel to the y- axis
It passes through all points with an x- coordinate of - 2
The function f is defined by f(x) = (x + 3)(x + 1).
The graph of f in the xy-plane is a parabola. Which
of the following intervals contains the x-coordinate
of the vertex of the graph of f?
Answer:
Below in bold.
Step-by-step explanation:
The zeroes ( = x-intercepts) are x = -3 and x = -1.
So the x -coordinate of the vertex is between x = -3 and x = -1.
The actual x-coordinate is halfway between these value: at x = -2.
Answer:
x = -3 or x = -1
Step-by-step explanation:
f(x) = (x + 3)(x + 1)
⇒ x = -3 or x = -1
does the following table shows a proportional relationship between the variables g & h
*the table being referred to is attached below
Answer:
The table does not show a proportional relationship between variable g and h.
Step-by-step explanation:
For a proportional relationship to exist between two variables, there must be a constant, of which serves like a unit rate, when comparing two variables.
Thus, in the table attached below, there is no obvious constant of proportionality between variable g and variable h.
Thus, [tex] \frac{9}{3} [/tex] ≠ [tex] \frac{36}{6} [/tex] ≠ [tex] \frac{81}{9} [/tex]
1) A furlong is 1/8 of a mile. What part of a mile is 6 furlongs?
Answer:
6/8 of a mile,
Step-by-step explanation:
if one furlong is 1/8 of a mile, the 6 shall be 1/8 added to itself 6 times, therefore it shall be 6/8.
Answer:
3/4 of a mile
Step-by-step explanation:
1 furlong = 1/8 mile
======== ====
6 forlongs = x
cross multiply
1*x = 6 * (1/8)
x = 6/8
reduce 6/8. Divide top and bottom by 2
x = 3/4
Easy question
I need the answers only for (d) and (e) parts.
plz help
will give the brainliest
Need explanation.
Please answer correctly.
Answer:
d)33
e)80
Step-by-step explanation:
I'm sorry I don't really know how to explain this.
If for [tex] x[/tex] cumulative frequency the marks are $y$ (as given on the graph), we have $x$ students with marks equal to or less than $y$
d)
Total students are $140$. Hence three-fifths of that is $140\times \frac{3}{5}=84$. Find the marks at $84$ in the graph for the passing marks.
e)
From the graph we have $60$ students having less than or equal to $30$ marks. Total students are $140$.
Subtracting, $140-60=80$ we get the numbee of students achieving more than 30 marks.
Find the length of MK¯¯¯¯¯¯ A. 7 B. 47 C. 19 D. 34
Answer:
19
Step-by-step explanation:
JH = 47 (70 - 23)
HM = 23
MK = 19 (42 - 23)
KU = 34 (81 - 47)
UC = 7 (47 - 40)
CN = 40
Answer:
19
Step-by-step explanation:
HM + MK = HK
23 + MK = 42
Subtract 23
MK = 42-23
MK =19
Nine and one-half less than four and one-half times a number is greater than 62.5. Which of the following represents the solution set of this problem?
(16, positive infinity)
(Negative 16, positive infinity)
(Negative infinity, 16)
(Negative infinity, Negative 16)
Answer:
{16, +infinity}
Step-by-step explanation:
Represent the number with n
Required
Find the solution set
From the question, we have that;
4½n - 9½ > 62.5
Convert all numbers to decimal
4.5n - 9.5 > 62.5
Add 9.5 to both sides
4.5n - 9.5 + 9.5 > 62.5 + 9.5
4.5n > 72
Multiply both sides by 2
2(4.5n) > 72 * 2
9n > 144
Multiply both sides by ⅑
⅑ * 9n > 144 * ⅑
n > 16
This implies that n ranges to infinity from positive 16;
Hence, the correct answer is {16, +infinity}
PLEASE HELP! Will mark brainliest! Find the slope of each line:
Answer:
6/7
Step-by-step explanation:
First, find two points that fall on the line and are coordinates on the graph.
The two points I found were (3,5) and (10,11).
Use the slope formula to come up with the slope.
[tex]slope = \frac{change in y}{change in x}[/tex]
slope = [tex]\frac{11-5}{10-3}[/tex] = [tex]\frac{6}{7}[/tex]
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the
correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag
the item to the trashcan. Click the trashcan to clear all your answers.
Type the expressions as radicals
y3/5
Answer:
[tex]\sqrt[5]{y^3}[/tex]
Step-by-step explanation:
[tex]y^{3/5}[/tex] is simply [tex]\sqrt[5]{y^3}[/tex]
help me plz I really need this thanks I will give a lot of points
Answer:
see the picture below
Step-by-step explanation:
There is 19, 13, 8, 4, 7, 14, 7, 9.
There is 1 number between 0 and 5.
and there's 4 on between 6 to 10.
and so far.
Step-by-step explanation:
Taller bars show that more data falls in that range.
19, 13, 8, 4, 7, 14, 7, 9 stay in order = 1,2,3,4,5,6,7,8
Add 2 more months to make 8 months
Then go vertical if using this histogram so that numbers of feathers above are vertical shaped bars. |--------------| stacked on top of each other.
Or///
Copy the diagram and swap the names ie) months so they go at the bottom and feathers go along the side axis.
What is the value of i 20+1?
1
- т т .-
Me need big brain to answer this question c:
Answer:
[tex]y=\dfrac{3}{2}x\ ...(i)\\\\ z=\dfrac{5}{2}x\ ...(ii)\\\\ z=x+y\ ....(iii)[/tex]
Step-by-step explanation:
Let x be the amount of dough required for small pizza, y be the amount of dough required for medium pizza and z be the amount of dough required for large pizza.
As per the question , we have
[tex]y=\dfrac{3}{2}x\ ...(i)\\\\ z=\dfrac{5}{2}x\ ...(ii)\\\\ z=x+y\ ....(iii)[/tex]
Hence, the equation for the question with the variable representing the amount of dough needed for small pizza.
[tex]y=\dfrac{3}{2}x\ ...(i)\\\\ z=\dfrac{5}{2}x\ ...(ii)\\\\ z=x+y\ ....(iii)[/tex]
How many numbers between 1 and 1000 do not contain the digits 8, and 9 ?
Answer:
998
Step-by-step explanation:
I haven't included the 1 or the 1000
Answer:
There are 200 numbers between 1 and 1000 that do not contain the digits 8, and 9.
Step-by-step explanation:
1-100
=(8,9,18,19,28,29,38,39,48,49,58,59,68,69,78,79,88,89,98,99)=20
101-200
=(108,109,118,119,128,129,138,139,148,149,158,159,168,169,178,179,188,189,198,199)=
201-300=20
.......
100*10=1000
20*10=200
A percent is the numerator of a ratio whose denominator is A. 25 B. 50 C. 75 D. 100
I am sure the answer is D
Answer:
D 100
Step-by-step explanation:
60% = 60/100
70% =70/100
WILL GIVE BRAINLY PLEASE HELP!!!!
A quadratic equation of the form 0=ax2+bx+c has a discriminant value of -16. How many real number solutions does the equation have?
A) -1
B) 0
C) 1
D) 2
Answer:
the answer is c. One real number solution
Step-by-step explanation:
Hey There!!
I think the best answer will be is (D) 2.
Because, The discriminant is the expression b2 - 4ac, which is defined for any quadratic equation ax2 + bx + c = 0. Based upon the sign of the expression, you can determine how many real number solutions the quadratic equation has. If you get a positive number, the quadratic will have two unique solutions. Im not a 100% sure this right... Hope This helps!! By ~♡Itsbrazts~♡
what is (7*7*7*7*7*7) * (7*7) in exponential form?
Answer:
7^8
Step-by-step explanation:
Answer:7^8
Step-by-step explanation:
Remove all perfect squares from inside the square root√ 72
Answer:
8.48
Step-by-step explanation:
After removing the perfect square inside √72 we get,
6√2
The given square root is,
√72
Since we know that,
A perfect square is a number that is stated as the product of an integer multiplied by itself. The perfect square is also represented as the second exponent of an integer since the same number is multiplied twice. The squares of all integers are hence referred to as perfect squares.
Simplify the square root of 72.
Factor 72 into 36 and 2,
Giving us the square root of 36 times the square root of 2.
Therefore,
√72 = √36 x √2
We know that the square root of 36 is 6,
So we can substitute that in:
√72 = 6 x √2
Hence after removing the perfect square inside √72 we get,
6√2.
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What will come in the circle
I will even rate who ever answer
And give brainliest
Answer:
1st circle: 1.25
Second circle: 2
Step-by-step explanation:
We can use the cross product property here to find the value of what's in the circles.
Let's first look at the first two fractions.
[tex]\frac{x}{5} = \frac{1}{4}[/tex]
We can multiply the cross values and divide by the number that is diagonal to the variable.
[tex]5\cdot1 = 5\\5\div4 = 1.25[/tex]
So 1.25 goes in the first circle.
Now let's look at the last two circles and use the same property to find the missing value.
[tex]\frac{1}{4} = \frac{0.5}{x}\\ 4\cdot0.5 = 2\\2\div1 = 2[/tex]
So 2 goes in the second circle.
Hope this helped!
Answer:
x = 5/4
Step-by-step explanation:
Use the variable 'x' instead of 'the circle.' Then:
x 1
----- = ------
5 4
Cross-multiplying, we get
4x = 5, and so x = 5/4
