[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { \: x = - 1 \: + \: i \sqrt{6} \:(or) \: \: x = - 1 \: -\: i \sqrt{6} }}}}}}[/tex]
And[tex]\implies {\blue {\boxed {\boxed {\purple {\sf {x\:=\:2}}}}}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
[tex] \: {x}^{3} + 3x - 14 = 0[/tex]
➺[tex] \: {x}^{2} (x + 1) - x(x + 1) + 4(x + 1) = 18[/tex]
➺[tex] \: (x + 1)( {x}^{2} - x + 4) = 18[/tex]
➺[tex] \: {x}^{2} - x + 4 = \frac{18}{(x + 1)} [/tex]
➺[tex] \: {x}^{2} - x + 4 - 6 = \frac{18}{(x + 1)} - 6[/tex]
➺[tex] \: (x - 2)(x + 1) = \frac{18 - 6(x + 1)}{(x + 1)} [/tex]
➺[tex] \: (x - 2)(x + 1) = \frac{18 - 6x - 6}{(x + 1)} [/tex]
➺[tex] \: (x - 2)(x + 1) = \frac{12 - 6x}{(x + 1)} [/tex]
➺[tex] \: (x - 2)(x + 1) = \frac{ - 6(x - 2)}{(x + 1)} [/tex]
➺[tex] \: (x + 1 )² = \frac{ - 6(x - 2)}{(x + 1)(x - 2)} [/tex]
➺[tex] \: (x + 1)² = \frac{ - 6}{(x + 1)} [/tex]
[tex]\sf\pink{Error\:corrected\:here. }[/tex]
➺[tex] \: {x}^{2} + 2x + 1 = - 6[/tex]
➺[tex] \: {x}^{2} + 2x + 7 = 0[/tex]
By quadratic formula, we have
➺[tex] \: x = \frac{ - b± \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]
➺[tex] \: x = \frac{ - 2± \sqrt{ {2}^{2} - 4.1.7} }{2 \times 1} [/tex]
➺[tex]x = \frac{ - 2± \sqrt{ - 24} }{2 } [/tex]
➺[tex] \: x = \frac{ - 2± \sqrt{ - 1 \times 4 \times 6} }{2} [/tex]
➺[tex] \: x = \frac{ - 2± \sqrt{ - 1} \times \sqrt{4} \times \sqrt{6} }{2} [/tex]
➺[tex] \: x = \frac{ - 2 \: ± \: i \times 2 \times \sqrt{6} }{2} [/tex]
➺[tex] \: x = \frac{ - 2 \: ± \:i \: 2 \sqrt{6} }{2} [/tex]
➺[tex] \: x = \frac{ 2 \: ( - 1 \: ± \: i \: \sqrt{6}) }{2} [/tex]
➺[tex] \: x = - 1 \: ± \: i \sqrt{6} [/tex]
Therefore, the two values of [tex]x[/tex] are ([tex] \: - 1 \: + \: i \sqrt{6}[/tex]) and ([tex] \: - 1 \: -\: i \sqrt{6}[/tex]).
Let us look at another method.[tex]x[/tex]³ + 3 [tex]x[/tex] - 14 = 0
➼ [tex]x[/tex]³ + 3 [tex]x[/tex] = 14
➼ [tex]x[/tex] ( [tex]x[/tex]² + 3 ) = 14
Factors of 14 = 1, 2, 7 and 14.
a) Substituting [tex]x\:=\:1[/tex], we have
➼ 1 ( 1 + 3 ) ≠ 14
➼ 1 x 4 ≠ 14
➼ [tex]\boxed{ 4\: ≠ \:14 }[/tex]
b) Substituting [tex]x\:=\:2[/tex], we have
➼ 2 ( 2² + 3 ) = 14
➼ 2 ( 4 + 3 ) = 14
➼ 2 x 7 = 14
➼ [tex]\boxed{ 14 \:= \:14 }[/tex]
c) Substituting [tex]x\:=\:7[/tex], we have
➼ 7 ( 7² + 3 ) ≠ 14
➼ 7 ( 49 + 3 ) ≠ 14
➼ 7 x 52 ≠ 14
➼ [tex]\boxed{ 364\: ≠ \:14 }[/tex]
d) Substituting [tex]x\:=\:14[/tex], we have
➼ 14 ( 14² + 3 ) ≠ 14
➼ 14 x 199 ≠ 14
➼ [tex]\boxed{ 2786\: ≠ \:14 }[/tex]
Hence, our only real solution is 2.
[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}[/tex]
What is the equation of the line that passes through the point (-7, -4) and has a
slope of 1?
Answer:
Y=x+3
Step-by-step explanation:
we have :
x1= -7
y1= -4
m=1
as we know Y-y1=m(X-x1)
Y+4=(X+7)
Y+4=X+7
Y=X+7-4
Y=X+3
mary is 1 m 15 cm tall. her friend larry is 1 m 30 cm tall. who is taller and by how much?
Answer:
Mary's friend Larry is taller by 15cm.
Step-by-step explanation:
First look for the bigger number.
Then subtract the smaller number from the bigger number.
What is the sum of the interior
angle measures of a polygon
that has 20 sides?
Sum = [?]"
Hint: Sum = (n-2)180
Step-by-step explanation:
if N= given Side then,
(20-2)180
18×180
3240° Answer
Answer:
n=20 side
sum=(n-2)180
=(20-2)180
=(18)180
=3240
The answer I got for this problem was 10.8 (multiplied 18 and 60 then divided by 100) however, it stated that my answer is incorrect. Did I not round correctly or is my entire answer wrong?
9514 1404 393
Answer:
30 mL
Step-by-step explanation:
The meaning of 60% solution is ...
alcohol/(total volume) = 0.60
You are told the amount of alcohol is 18 mL, so you have ...
(18 mL)/(total volume) = 0.60
Multiplying by total volume gives ...
18 mL = 0.60 × (total volume)
Then dividing by 0.60, you have ...
(18 mL)/0.60 = total volume = 30 mL
_____
Additional comment
You need to apply what you know about the real world to consider whether your answer makes any sense. If alcohol is a little more than half of the volume, and the amount of alcohol is 18 mL, then the total volume cannot be less than 18 mL. In fact, you expect it to be not quite double 18 mL.
An answer of 10.8 mL makes no sense in this context. You cannot have less total solution than you have of something that makes up a part of the total solution.
Value of 140 degree in diagrams
Answer:
There are 360º in a circle. 140º has been allocated to one angle.
There are 360-140 = 220º left in the circle.
Step-by-step explanation:
In a math class, there are 6 students with brown hair, 8 students with black hair, and 9 students with blonde hair? One student is selected at random. What is the sample space? *
Brown, black .
Black, blonde.
Brown, black, blonde.
Brown, blonde.
Explanation:
The sample space is simply the list of possible outcomes. We list all the hair colors possible in this class.
if a line intersect x axis at a point (6,0) and y axis at a point (0,-8). then what is equation of a line?
Answer: y = 4/3x -8
Step-by-step explanation:
(6,0) (0,-8)
0-(-8)/6-0 = 8/6 = 4/3
y intercept is given already
A tepee is designed to have a diameter of 10 ft and a volume of 393 ft. At
what height, h, should the support poles cross to assemble the tepee
correctly? Use 3.14 for 1 and round your answer to the nearest foot.
Answer:
15 ft.
Step-by-step explanation:
The tepee is a cone and its volume
= 1/3 pi r^2 h where r = radius and h = height.
The radius r = 1/2 * 10 = 5 ft.
So we have the equation:
393 = 1/3*3.14* 5^2 * h
h = 393 / (1/3*3.14*25)
= 15.02 ft.
At an assembly plant for light trucks, routine monitoring of the quality of welds yields the following data:
Number of Welds
High Moderate Low
Quality Quality Quality
Day Shift
Evening Shift
Night Shift 467 191 42
445 171 34
254 129 17
Can you conclude that the quality varies among shifts?
a. State the appropriate null hypothesis.
b. Compute the expected values under the null hypothesis.
c. Compute the value of the chi-square statistic.
d. Find the P-value. What do you conclude?
Answer:
Kindly check explanation
Step-by-step explanation:
H0 : quality does not vary among shift
H1 : quality varies among shift
The expected values :
(Row * column) / grand total
Given the data:
Observed values :
_________________total
_______467 191 42 __700
_______445 171 34 __650
_______254 129 17 _ 400
Total __ 1166 491 93 _ 1750
Expected value count using the formula :.
Expected Values:
466.4 ____196.4 ______37.2
433.086 _182.371___ 34.5429
266.514_ 112.229____ 21.2571
The Chisquare statistic (χ²) :
χ² = (observed - Expected)²/ observed
χ² = 5.76045
The degree of freedom = (row - 1) * (column - 1)
Degree of freedom = (3-1)*(3-1) = 2*2 = 4
Pvalue = 0.2178
Pvalue > α ; We foal to reject H0 ; Hence, we conclude that quality does not vary among shift
Triangle A'B'C' is the image of triangle ABC after a dilation with a scale factor of 1/2 and centered at point A. Is triangle ABC congruent to triangle A'B'C'? Explain your answer.
Answer:
See below
Step-by-step explanation:
Congruent means having the same size and shape.
If triangle A'B'C' is the image of triangle ABC after a dilation with a scale factor of 1/2 then the two triangles will not acquire the same size
This is because when a shape undergoes a dilation the dilated image is either larger or smaller and can therefore not maintain the same size as the pre image. Hence the triangles are not congruent.
Triangle ABC is not congruent to triangle A'B'C'
How to determine the congruent statement?The triangles are given as:
Triangle ABC and A'B'C'
The other parameters are:
Scale factor, k = 1/2
Center = Point A
Since the scale factor is not 1, then the triangles would not be congruent; but they would be similar
Hence, triangle ABC is not congruent to triangle A'B'C'
Read more about dilation at:
https://brainly.com/question/9791066
Given the triangle below, answer the following:
Answer:
Step-by-step explanation:
question no . 5
ratio of angle L
take angle as reference angle
using cos rule
cos L = base / hypotenuse
= 4/5
ratio of angle N
take angle N as reference angle
using sin rule
sin N = opposite / hypotenuse
= 4/5
for measure of angle L
cos L = 4/5
cos L = 0.8
L = [tex]cos^{-1}(0.8)[/tex]
L = 36.9
for meanure of angle N
sin N = 4/5
sin N = 0.8
N = [tex]sin^{-1}(0.8)[/tex]
N = 53.1
Find the slope of a line that is PRRPENDICULAR to the line that goes between (3,-8) and (5,2).
5
1/5
-5
-1/5
3
-3
1/3
-1/3
Answer:
-1/5
Step-by-step explanation:
Slope of the line = (y2-y1)/(x2-x1)
(2-(-8)/(5-3)
10/2 = 5
Perpendicular line = the slope is opposite of the reciprocal
-1/5
Which of the following represents the factorization of the trinomial below?
X2 - 2x - 48
ANSWER
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { \: (x + 6)(x - 8)}}}}}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
[tex] {x}^{2} - 2x - 48[/tex]
[tex] = {x}^{2} - 8x + 6x - 48[/tex]
Taking [tex]x[/tex] as common from first two terms and 6 from last two terms, we have
[tex] =x \: ( \: x - 8 \: ) + 6 \: ( \: x - 8 \: )[/tex]
Taking the factor [tex](x-8)[/tex] as common,
[tex] = (x + 6)(x - 8)[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}[/tex]
Answer:
(X+6)(x-8)
Step-by-step explanation:
Angle x is conterminal with angle y. If the measure of angle x is greater than the measure of angle y, which statement is true regarding the values of x and y?
x = y - 180n, for any positive integer n
x = y - 360n, for any integer n
x = y + 360n, for any positive integer n
x = y + 180n, for any integer n
9514 1404 393
Answer:
x = y + 360n, for any positive integer n
Step-by-step explanation:
Since x is greater than y, something must be added to y to get x. Angles have the same co-terminal ray at multiples of 360°. Then the amount added to y must be some multiple of 360°:
x = y + 360n . . . . . for positive integer n
If you become a. . what Will you do
Answer:
if you becomes a.. what is this mean
Answer:
i have no idea
Step-by-step explanation:
i dont think turning into a virtual period will let me do anything. If you can clarify please let us know!
4.000.000 x 4.000.000 = ?????
Helpp
I think the answer is 16 but I'm not 100% sure
32
The angles shown are supplementary. What is the value of x? 0
(2 Points)
(5x5°
95°
O 180 degree
• 17 degree
O 22 degree
45 degree
HELPP I NEED THIS ASAP ITS FOR MY FINALSS
Answer:
17degrees
Step-by-step explanation:
The sum of two supplementary angles is equation 180degrees. Hence:
5x+95 = 180
5x = 180-95
5x = 85
x = 85/5
x = 17
Hence the value of x is 17
Find the equation of the line that has a slope of 7 and a y intercept of -10. Write you answer in the form of y = mx + b
Answer:
Step-by-step explanation:
y = mx + b is the slope-intercept form of a line where m is the number value of the slope and b is the number value of the y-intercept. Our slope is given as 7, therefore, m = 7 in our equation. Our y-intercept is given as -10; thus, b = -10. Filling that in gives us y = 7x - 10
help what's the answer??
I would appreciate if someone could answer this :)
Answer:
x = 8
y = 6
Step-by-step explanation:
Recall that one of the properties of a parallelogram is that the diagonals bisect each other, which means they divide each other into equal segments.
Therefore,
LP = PN
x = y + 2 (eqn. 1)
PM = KP
2x - 8 = y + 10 (eqn. 2)
Substitute x = y + 2 into eqn. 2 to find y
Thus:
2(y + 2) = y + 10
2y + 4 = y + 10
Take like terms
2y - y = -4 + 10
y = 6
Substitute y = 6 into eqn. 1 to find x:
x = y + 2 (eqn. 1)
x = 6 + 2
x = 8
a line through (4,2) with slope 1/2
Answer:
Step-by-step explanation:
Use the formula P=MX+B
The ratio of girls to boys in a particular classroom is 4:3. What fraction of the total number of students are boys?
The ratio of boys to the total number of students in a particular classroom is
Answer:
3:7
Step-by-step explanation:
We know that there are 4 girls and 3 boys and 4+3=7.
Two towers A and B are 45m and 30m high. Tower A lies to the west and B to the east of a man 1.5m tall. From the mans eye level, the angle of elevation of the top of A and B are 66° and 28° respectively. Calculate correct to three signigicant fugures the distance between A and B.
Answer:
73.0m
Step-by-step explanation:
see the attachment. Hope it helps.
The length of a rectangle is 5 inches longer than it is wide. If the area is 84 square inches, what are the
dimensions of the rectangle?
The width, or shorter side is i inches
Enter an integer or decimal number (more..
inches
The length, or longer side is
Answer:
b = 7 inches and l = 12 inches
Step-by-step explanation:
Given that,
The area of a rectangle, A = 84 sq inches
Let the width is b.
Length = (5+b)
The area of a rectangle is given by :
A = lb
So,
[tex]84=b\times (5+b)\\\\b^2+5b-84=0\\\\(b-7)(b+12)=0\\\\b=7\ in, b =-12\ in[/tex]
Neglecting negative value,
b = 7 inches
Length, l = 5+b = 5+7
l = 12 inches
If the coordinates of a point p(m-3, -6) = p(-7, -6), then find the value of m
Answer:
[tex]m =-4[/tex]
Step-by-step explanation:
Given
[tex]p(m-3 , -6) = p(-7 , -6)[/tex]
Required
Find m
[tex]p(m-3 , -6) = p(-7 , -6)[/tex]
By comparison:
[tex]m-3 = -7[/tex]
Add 3 to both sides
[tex]m = -7+3[/tex]
[tex]m =-4[/tex]
This are 3 different questions please help me
Nia had a 20 inch by 30 inch enlargement made of a photograph. She wanted to have it framed. How many inches of frame would it take to enclose the photo?
Answer: 100 inches
Step-by-step explanation:
From the question, we are given the information that Nia had a 20 inch by 30 inch enlargement made of a photograph and that she wanted to have it framed.
The number of inches of frame that she would use to enclose the photo will be gotten by calculating the perimeter of the shape and this will be:
= 2(length + width)
= 2(30 + 20)
= 2(50 inches)
= 100 inches
To enclose the photo, 100 inches of frame is needed.
What is the value of x in the equation 1/5x-2/3y = 30, when y = 15
Answer:
x=200
Step-by-step explanation:
(1/5)x-(2/3)y=30, y=15
(1/5)x-(2/3)*15=30
(1/5)x=40
x=200
what is the sum of the rational expressions x-4/2x+3x/2x-1
Answer:
May the ans will help you.
What proportion of families own as opposed to rent their home? To find out, an urban planner selected a random
sample of 400 families in a large city to participate in a survey about homeownership. Of the 362 families that
responded to the survey, 42% reported that they own their home. Which of the following statements about the
survey results is true?
O A suitable estimate of all families who own their home is 42%.
The survey suffers from voluntary response bias and may not accurately represent the population.
O Only 362 responses cannot provide a suitable estimate of families who own their home.
O The survey suffers from undercoverage and may not provide a suitable estimate of homeownership.
Mark this and return
Save and Exit
fyext
Submit
Answer:
A suitable estimate of all families who own their home is 42%.
Step-by-step explanation:
42% reported that they own their home.
This means that the sample proportion is of 42%. So that an estimate for the percentage of all families who own their home is of 42%., and that the first option is correct.
Answer:
The correct answer is: The survey suffers from undercoverage and may not provide a suitable estimate of homeownership.
Step-by-step explanation:
I just took the review test. The person above me is wrong
