Answer:
Explanation:
Given:
[tex]\begin{gathered} 2x^2+32=0 \\ \text{The answer is x=}+-4i \end{gathered}[/tex]To fully understand how we get the given answer, we simplify the equation first:
[tex]\begin{gathered} 2x^2+32=0 \\ \text{Simplify and rearrange} \\ 2x^2=-32 \\ x^2=-\frac{32}{2} \\ x^2=-16 \\ \end{gathered}[/tex]Next, we apply the rule:
[tex]\begin{gathered} \text{For x}^2=f(a),\text{ the solutions are } \\ x=\sqrt[]{f(a)} \\ x=-\sqrt[]{f(a)} \end{gathered}[/tex]So,
[tex]\begin{gathered} x^2=-16 \\ x=\sqrt[]{-16},x=-\sqrt[]{-16} \end{gathered}[/tex]Then, we also apply the radical rule:
[tex]\begin{gathered} \sqrt[]{-a}=\sqrt[]{-1}\sqrt[]{a} \\ So, \\ x=\sqrt[]{-16} \\ =\sqrt[]{-1}\sqrt[]{16} \\ \text{Then, apply the imaginary number rule:} \\ \sqrt[]{-1}=i \\ \text{Hence,} \\ x=4i \end{gathered}[/tex]For
[tex]\begin{gathered} x=-\sqrt[]{-16} \\ Use\text{ the same steps} \\ x=-4i \end{gathered}[/tex]Therefore the x-values are: x=4i, x=-4i. The i on the answer means imaginary number. It is a number that, when squared, has a negative result.
Finding Slope From Two Points
Find the slope of the line through each pair of points.
1) (19,-16), (-7, -15)
The slope of a line from given points (19,-16), (-7, -15) is - 1/26
Slope :
In Mathematics, Slope of a line defined as the direction of the line and the change in y-coordinate with respect to x - coordinate. Slope of a line is denoted by 'm'
The formula for slope of a line which passes through the points (x₁, y₁) and (x₂, y₂) is given by Slope (m) = (y₂– y₁)/(x₂ – x₁)
Here, we have pair of points (19,-16), (-7, -15)
Take (x₁, y₁) = (19,-16) and (x₂, y₂) = (-7, -15)
Slope (m) = [-15 -(-16) ] / [ -7 -19 ]
= [ - 15+16] / [ -26 ]
= [ 1 ] / [ -26 ]
= - 1/26
Therefore,
The slope of line from given points (19,-16), (-7, -15) is - 1/26
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A 90% confidence interval is found to be (72, 78). What is the margin of error?
In order to find the margin of error, we need to know that the width of the confidence interval is equal to 2 times the margin of error.
The width of this confidence interval is given by:
[tex]\begin{gathered} width=upper\text{ }limit-lower\text{ }limit\\ \\ width=78-72\\ \\ width=6 \end{gathered}[/tex]If the width is 2 times the margin of error, we have:
[tex]\begin{gathered} width=2\cdot E\\ \\ 6=2\cdot E\\ \\ E=\frac{6}{2}\\ \\ E=3 \end{gathered}[/tex]The margin of error is equal to 3, therefore the correct option is D.
WILL MARK BRAINLIEST PLS HELP
⇒For m=2 and n=-3 in the equation 3m-4n In the place of m plug in 2 and in the place of n plug in -3 and simplify.
[tex]=3(2)-4(-3)\\=6+12\\=18[/tex]
Option C is the answer.
show each quadratic equation by factoring (show your solution)
7x^2+25x+12
PLEASE HELP
Answer:or a polynomial of the form
a
x
2
+
b
x
+
c
, rewrite the middle term as a sum of two terms whose product is
a
⋅
c
=
7
⋅
−
12
=
−
84
and whose sum is
b
=
25
.
7
x
2
−
3
x
+
28
x
−
12
Factor out the greatest common factor from each group.
Tap for more steps...
x
(
7
x
−
3
)
+
4
(
7
x
−
3
)
Factor the polynomial by factoring out the greatest common factor,
7
x
−
3
.
(
7
x
−
3
)
(
x
+
4
)
Step-by-step explanation:
a survey was given to people who owned a certain type of car.what percent of the people surveyed were completely satisfied with the car.blue:compleletely satisfiedpurple: somewhat satisfiedgreen:not satisfied
The percent of people that were completely satisfied (%PS) can be calculated with the formula:
[tex]\text{ \%PS=}\frac{PS}{TP}\times100\text{\%}[/tex]Where PS is the number of persons that were completely satisfied and TP is the total number of persons, in this case, the total number of persons is the sum of each number of persons from each category:
[tex]TP=160+740+1100=2000[/tex]And as we can see from the figure, the number of completely satisfied people is 1100, then the percent of people that were completely satisfied is:
[tex]\begin{gathered} \text{\%PS=}\frac{PS}{TP}\times100\text{\%} \\ \text{\%PS=}\frac{100}{2000}\times100\text{\%} \\ \text{\%PS=}0.55\times100\text{\%}=55\text{\%} \end{gathered}[/tex]The percent of people that were completely satisfied is 55%
You just have to divide 1100 by the total people which is 2000, and then just multiply by 100, and that's it
Rectangle ABCD is shown. What is the length of diagonal BD? Round to the nearest tenth if needed
THe diagonal, BD divides the rectangle into two right angle triangles.
BD represents the hypotenuse
BC represents the opposite side
DC represents the adjacent side
We would determine BD by applying the pythagorean theorem which is expressed as
[tex]\begin{gathered} \text{hypotenuse}^2=oppositeside^2+adjacentside^2 \\ BD^2=7^2+12^2=49\text{ + 144 = 193} \\ BD\text{ = }\sqrt[]{193} \\ BD\text{ = 13.9 } \end{gathered}[/tex]The length of the diagonal, BD is 13.9m to the nearest tenth
Hello what is ALL of the answers to this question
Answer
The function that describes the height of the rocket in terms of the is
[tex]h(t)=-16t^2+224t+68[/tex]
The height of a trapezoid can be expressed as x - 4, while the bases can be expressed as x + 4 and x + 9. If the area of the trapezoid is 99 cm², find the length of the larger base.
Answer: 19 cm
Step-by-step explanation:
Substituting into the formula for the area of a trapezoid,
[tex]\frac{1}{2}(x-4)(x+4+x+9)=99\\\\\frac{1}{2}(x-4)(2x+13)=99\\\\(x-4)(2x+13)=198\\\\2x^2 +5x-250=0\\\\(2x+25)(x-10)=0\\\\x=-12.5, 10[/tex]
However, as x must be positive (since length must be positive), x=10. This means the length of the longer base is 19 cm.
what is 42/100 of x over 35?
The value of x in 42/100 of x over 35 based on the computation is 14.7.
How to calculate the fraction?It should be noted that a fraction simply means a number that's not a whole number.
Based on the information, we want to calculate 42/100 × x/35. This will be illustrated thus:
= 42/100 × x/35.
Cross multiply
(100 × x) = (42 × 35)
100x = 1470
Divide through by 100
100x / 100 = 1470 / 100
x = 14.7
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Find the perimeter of the figure shown. Round your answer to the nearest centimeter. This is for problem number 9
I need help with this question please?
[tex]t=100 \left(1-\frac{V}{50} \right)^2\\\\\frac{t}{100}=\left(1-\frac{V}{50} \right)^2[/tex]
Since time is positive, we take the positive square root.
[tex]\frac{\sqrt{t}}{10}=1-\frac{V}{50}\\\\\frac{\sqrt{t}}{10}-1=-\frac{V}{50}\\\\50-5\sqrt{t}=V\\\\\therefore f^{-1}(V)=\boxed{50-5\sqrt{V}}[/tex]
The table below gives the material of each item in Maria’s jewelry box. These are the only items in Maria’s jewelry box. Give the contra positive
The contra positive of the conditional statement is given as follows:
If an item is not made from copper, then it is not a pendant.
How to find the contra positive of a conditional statement?A conditional statement is modeled as follows:
p -> q.
In which:
p is the hypothesis.q is the conclusion.Hence the statement is read as:
If p then q.
The contra positive of the statement is given by:
~q -> ~p.
Hence it is read as:
If not q, then not p.
In the context of this statement, the hypotheses and the conclusion are given, respectively, by:
p: Item is a pendant.q: Item is made from copper.Hence the contra positive of the statement is:
If an item is not made from copper, then it is not a pendant.
What is the missing information?The statement is missing and is given as follows:
"If an item is a pendant, then the item is made from copper".
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2) At a party, Karen notices the amount songs being played. The chart shows wh she figured out. Number of hours 50 Number of songs VSJ 3 4 5 6 60 80 A. 85 C. 100 After five hours, how many songs were played? 120 B. 90 D. 110
Answer:
C. 100
Step-by-step explanation:
If 60 songs are played in 3 hours, 80 songs in 4 hours, and 120 songs in 6 hours, you want to know the number played in 5 hours.
Linear functionConsidering the rate of change of songs per hour, we find ...
hours 3-4: 80-60 = 20 songs, over the 1-hour period
hours 4-6: 120 -80 = 40 songs, over the 2-hour period
It appears that the number of songs being played is steady at 20 songs per hour. Then 5×20 = 100 songs were played in 5 hours.
Instructions: For the following sequence, state the common ratio, identify which is the explicit form and which is the recursive form of the rule.
Given that the series is 1, 3, 9, 27, ............
The common ratio will be
[tex]Common\text{ ratio=}\frac{2nd\text{ term}}{1st\text{ term}}=\frac{3}{1}=3[/tex]So the common ratio is 3.
The explicit formula uses starting term and the recursive formula uses the previous term.
As
[tex]\begin{gathered} Explicit\text{ form} \\ a_n=3^{n-1} \\ Recursive\text{ form} \\ a_n=a_{n-1}\times3 \end{gathered}[/tex]These are the required forms.
Suppose that the function f is defined, for all real numbers, as follows.
f(x)= {5x-4 if x≤1
-x+4 if x>1
Graph the function f. Then determine whether or not the function is continuous.
Answer:
F(x)
Step-by-step explanation:
hope it helps
Given the function [tex]f(x) = \left \{ {{5x-4, \ \ \ x\leq 1} \atop {-x+4, \ \ \ \ \ x > 1}} \right.[/tex], the function is not continuous at x = 1.
A function is said to be continuous if it can be drawn without picking up the pencil. Otherwise, a function is said to be discontinuous.
Given function,
[tex]f(x) = \left \{ {{5x-4, \ \ \ x\leq 1} \atop {-x+4, \ \ \ \ \ x > 1}} \right.[/tex]
We need to check the continuity of the function f(x) at x = 1. At all other points, it is continuous.
f(x) at x = 1 : 5x - 4 = 5*1 - 4 = 5 - 4 = 1
f(x) at x < 1 : 5x - 4 = 5*1 - 4 = 5 - 4 = 1
f(x) at x > 1 : -x + 4 = -1 + 4 = 3
Since, f(x) at x < 1 ≠ f(x) at x > 1, therefore, f(x) is not continuous at x = 1.
The same is also visible from the graph attached below. There is a disruption at x = 1, the graph is not a smooth line.
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7. Are the lines represented by the equations below parallel, perpendicular, or neither?
Justify your answer with words and numbers. (3 points)
- 3x + 6y = 12
y =
3x + 10
The two lines are neither parallel nor perpendicular.
What is condition for perpendicular, parallel?
if two given lines are parallel, perpendicular, or neither, we need to compare their slopes. For this, we need to make sure that their equations are in the form y = mx + b. This represents the equation of a straight line in the slope-intercept form, where m is the slope and b is the y-intercept.
If the given lines have the same slope, they’re parallel to one another. On the other hand, if they have slopes that are opposite reciprocals, i.e., the slopes have opposite signs and are flipped fractions of one another, they are perpendicular to each other. Else, they are neither.
The given lines are
- 3x + 6y = 12 or, y = (1/2)x + 2 ... (1)
y = - 3x + 10 ... (2)
The gradient of the lines (1) and (2) are 1/2 and (- 3) respectively.
Since the gradients are not equal, the lines are not parallel and also since (1/2) × (- 3) ≠ - 1, the lines are not perpendicular to each other.
Hence we can conclude that the given two lines are neither parallel nor perpendicular.
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NEED HELP ASAP‼️‼️‼️‼️‼️‼️‼️‼️‼️
simplify 3xy³ + x²y⁵ over xy²
PLEASE SEND QUICK DUE IN 10-15 MINUTES ‼️‼️‼️
Answer:
[tex]4xy^3[/tex]
Step-by-step explanation:
3xy^3 + x^2y^5/xy^2
Find and simplify each of the following for f(x) = 4x2 - 5x + 7.(A) f(x + h)(B) f(x +h)-f(x)f(x+h) – f(x)(C)h
(A) f(x+h)
[tex]\begin{gathered} f(x+h)=4(x+h)^2\text{ - 5(x + h) + 7} \\ =\text{ 4(x + h)(x + h) - 5x - 5h + 7} \\ =4(x^2+2xh+h^2)\text{ - 5x - 5h + 7} \\ =4x^2+8xh+4h^2\text{ - 5x - 5h + 7} \end{gathered}[/tex](B) f(x + h) - f(x)
[tex]\begin{gathered} =4x^2+8xh+4h^2\text{ - 5x - 5h + 7 - }(4x^2\text{ - 5x + 7)} \\ =4x^2+8xh+4h^2-5x-5h+7-4x^2\text{ + 5x - 7} \\ =4x^2-4x^2-5x+5x+7-7+8xh+4h^2\text{ - 5h} \\ \text{ = 0 + 0 + 0 + 8xh + 4h}^2\text{ - 5h} \\ =8xh+4h^2\text{ - 5h} \end{gathered}[/tex](C)
[tex]\begin{gathered} =\text{ }\frac{f(x+h)\text{ - f(h)}}{h} \\ =\text{ }\frac{8xh+4h^2\text{ - 5h}}{h} \\ =\text{ }\frac{8xh}{h}\text{ + }\frac{4h^2}{h}\text{ - }\frac{5h}{h} \\ =\text{ 8x + 4h - 5} \end{gathered}[/tex]Solve each problem below by writing an equation that matches the situation. Then solbe your equation to find the solution to the problem. (It's been almost a day and these two questions baffled me.)
Step 1:
Let the number of hours = m
Flat fee = $25
Fees charge per hour = $30
Step 2:
Money Ronnie made from his first customer = $175
Write an equation.
30m + 25 = 175
Step 3:
Solve the equation.
[tex]\begin{gathered} 30m\text{ + 25 = 175} \\ 30m\text{ = 175 - 25} \\ 30m\text{ = 150} \\ \text{Divide through by 30} \\ m\text{ = }\frac{150}{30} \\ \text{m = 5 hours} \end{gathered}[/tex]Final answer
5 hours
you have 27 teaspoons of peppercorns you need 0.25 teaspoons make one serving of beef brisket how many servings can you make
Given:
Total Number of teaspoons of peppercorns = 27
Amount of teaspoons you need for one serving of brief brisket = 0.25
Let's find the amount of servings can be made.
To find the amount of servings that can be made, apply the formula:
[tex]\text{Number of servings = }\frac{TotalNumber\text{ of teaspoons}}{Teaspooons\text{ for one brisket}}\text{ }[/tex]Thus, we have:
[tex]\begin{gathered} \text{Number of servings = }\frac{27}{0.25} \\ \\ \text{Number of servings = }\frac{27}{\frac{25}{100}} \\ \\ \text{Number of servings = }\frac{27}{25}\ast100=1.08\ast100=108 \end{gathered}[/tex]Therefore, 108 servings can be made.
ANSWER:
108
helppppppppppppp!!!!!!!!!!!!
(5)(3) - (2-7) divided by 4?
Answer:
Step-by-step explanation:
Answer:
[tex]{ \tt{(5)(3) - (2 - 7) \div 4}}[/tex]
- We are going to simplify the expression using BODMAS
B stands for BracketsO stands for OfD stands for DivisionM stands for MultiplicationA stands for AdditionS stands for Subtraction- From our expression, relating it to BODMAS, Brackets come first, so let's first operate the brackets
[tex] = { \tt{(5 \times 3) - ( \frac{2 - 7}{4}) }} \\ \\ = { \tt{15 - ( - \frac{5}{4} )}} \\ \\ = { \tt{15 + 5 \div 4}}[/tex]
- Then in our last expression, Division comes next
[tex] = { \tt{15 + \frac{5}{4} }} \\ [/tex]
- Then addition comes last
[tex] = { \tt{ \frac{65}{4} }} \\ [/tex]
- Simplifying our answer into mixed fraction and decimal format;
[tex] = { \tt{16 \frac{1}{4} \: \: or \: \: 16.25}}[/tex]
[tex]{ \boxed{ \delta}}{ \underline{ \mathfrak{ \: \: beicker}}}[/tex]
If f(x) = -x-11, find -3f(5) x f(2)
Given the function :
[tex]f(x)=-x-11[/tex]we need to find the value of 3f(5) x f(2)
so, to find the value of f(5), substitute with x = 5 at the given function
And to find the value of f(2) , substitute with x = 2 at the given function
so,
[tex]\begin{gathered} f(5)=-5-11=-16 \\ \\ f(2)=-2-11=-13 \\ \\ 3f(5)\cdot f(2)=3\cdot-16\cdot-13=624 \end{gathered}[/tex]I need help solving for x assume that lines which appear tangent are tangent
SOLUTION:
Case: Secant secant theorem
Secant-Secant Power Theorem: If two secants are drawn from an external point to a circle, then the product of the measures of one secant's external part and that entire secant is equal to the product of the measures of the other secant's external part and that entire secant
Method:
[tex]\begin{gathered} 7(7+x+6)=8(8+x+2) \\ 7(x+13)=8(x+10) \\ 7x+91=8x+80 \\ 91-80=8x-7x \\ x=11 \end{gathered}[/tex]Final answer:
x = 11
A pizza shop specializes in deep-dish pizzas. They sell a 14 -inch pizza that is 3 inches deep and a 16-inch pizza that is 2 inches deep. The 14 -inch pizza is cut into 8 slices and the 16-inch pizza is cut into 7 slices, and each slice is sold for the same price. If you are purchasing one slice of pizza, which size should you choose to get the most food? Show all of your work to justify your response.
Answer:
The 14-inch pizza cut into 8 slices.
Explanation:
The deep-dish pizza forms a cylindrical shape.
To make comparisons, we find the volume of each slice of pizza in each case.
[tex]\text{Volume of a cylinder=}\pi r^2h[/tex]Case 1
A 14-inch pizza that is 3 inches deep.
Radius = 14/2 = 7 inches
Height = 3 inches
[tex]\begin{gathered} \text{The volume of the full pizza}=\pi\times7^2\times3 \\ =147\pi\text{ cubic inches} \end{gathered}[/tex]Since it is cut into 8 slices:
[tex]\begin{gathered} \text{The volume of one slice=}\frac{147\pi}{8} \\ =18.375\pi\text{ cubic inches} \end{gathered}[/tex]Case 2
A 16-inch pizza that is 2 inches deep.
Radius = 16/2 = 8 inches
Height = 2 inches
[tex]\begin{gathered} \text{The volume of the full pizza}=\pi\times8^2\times2 \\ =128\pi\text{ cubic inches} \end{gathered}[/tex]Since it is cut into 7 slices:
[tex]\begin{gathered} \text{The volume of one slice=}\frac{128\pi}{7} \\ \approx18.285\pi\text{ cubic inches} \end{gathered}[/tex]Conclusion
The volume of a slice of pizza in the first case (the 14 -inch pizza cut into 8 slices) is larger, therefore it should be chosen to get the most food.
Find the total cost of 12 boxes of cookies if each box costs $3.
each box costs $3 : The cost of one box = $3
12 boxes of cookies : The total number of boxes = $12
For the total cost of 12 boxes : Multiply the cost of one box by the number of boxes
The total cost of 12 boxes = 12 x $3
The cost of 12 boxes = $36
The cost of 12 boxes of cookies ia $36
Answer : $36
need help!! algebra 1
Answer:
Step-by-step explanation:
6a) f(1)=-3
b) x=-5 x=-1 x=1
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For which value of x is therelation not a function?{(3, 1), (x, 0),(9,5),(12, 6)}A) 1. B)3C) 8. D)6
A function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.
Here the domain of the relation is {3,x,9,5}.
The given relation is a function only if x not takes any of the value 3, 9 or 5.
So, option B is correct.
The graph to the right is the uniform probability density function for a friend who is x minutes late.
(a) Find the probability that the friend is between 10 and 20 minutes late.
(b) It is 10 A.M. There is a % probability the friend will arrive within how many minutes?
Using the uniform distribution, it is found that:
a) The probability that the friend is between 10 and 20 minutes late is of 1/3.
b) There is a 30% probability that the friend will arrive within 9 minutes.
Uniform distributionThe uniform has two bounds, a and b, and each outcome of the distribution is equally as likely.
From the image given at the end of the answer, the bounds are given as follow:
a = 0, b = 30.
The probability of finding a value between c and d in the distribution is:
[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]
Hence, the probability that the friend is between 10 and 20 minutes late is given as follows:
P(10 <= X <= 20) = (20 - 10)/(30 - 0) = 1/3.
The 30th percentile of the distribution, which is what item b is asking, is given as follows:
0.3 x (30 - 0) = 0.3 x 30 = 9 minutes.
Missing informationThe complete problem is given by the image at the end of the answer.
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A basketball player scores 14, 16, 20, 5, 22, 30, 16, and 28 points during a
tournament. Make a box-and-whisker plot for the points scored by the player.
The diagram attached shows the box-and-whisker plot for the points scored by the player.
How to Make a Box-and-whisker Plot for a Data Set?A box-and-whisker plot displays the maximum and minimum data values, the upper and lower quartiles, and the median of the data. They are called the five-number summary.
Given the data for the number of points scored by a basketball player is: 14, 16, 20, 5, 22, 30, 16, and 28, the five-number summary for the data would therefore be:
Minimum: smallest data point, which is 5.First Quartile: center of the first part of the data set when ordered, which is 15.Median: The middle data point, which is 18.Third Quartile: center of the second part of the data set, which is, 25Maximum: this represents the highest data point, which is, 30The box-and-whisker plot is shown below.
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