Answer:
Correct option is A)
Given,a,b are distance roots of x
3
+3x
2
−1=0
⇒a
3
+3a
2
−1=0 and b
3
+3b
2
−1=0
let the third root be c
then c
3
+3c
2
−1=0
product of roots =
a
−d
=
1
−(−1)
=1
⇒
abc=1
c=
ab
1
but c is root of x
3
+3x
2
−1=0
⇒c
3
+3x
2
−1=0
⇒
(ab)
3
1
+
(ab)
2
3
−1=0
⇒
1+3ab−(ab)
3
=0
.....(1)
in equation (1)
(ab)
3
−3(ab)−1=0
⇒ab is root of
x
3
−3x−1=0
∴(ab) is root of
x
3
−3x−1=0
Gabrielle is saving money for a vacation. Each week she save $40. Let a represent the total amount of money Gabrielle saves, and let w represent the number of weeks. How much money would she save from 1 to 7 weeks?
Step-by-step explanation:
A = 40w
To Calculate how much she would get in 7 weeks
Substitute w = 7 into A = 40w
⇒ A = 40(7)
⇒ A = 280
Gabrielle would save $280 in 7 weeks
A varies inversely with B.
When A is 0.25, B is 4.
Find the value of B when A is 5.
Answer:80
Step-by-step explanation:if you multiply a times 20 to get 5, you have to multiply b times 20 to get 80
thanks for the question.the the answer is 0.0625
Workers in an office of 60 staff were asked their favourite type of take-away.
The results are summarised in the table.
Pizza=8
Curry=8
Fish & chips=5
Kebab=9
Other=30
Work out the size of each angle to draw a pie chart.
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Please answer to my geometric word problem questions as soon as possible with the best efforts and the best step-by-step explanations in order to get the Brainliest award of all the time! :D
Well anyways, guys, good luck on answering 3 math word problem questions of my my angles, triangles, and quadrilaterals word problem homework package in order to get the best Brainliest award of all of the time, and I will check the answers to see if it’s appropriate for me. :)
Step-by-step explanation:
For question 22: Notice the congruent symbol on sides AB and CB; this shows that the triangle is isosceles, and in an isosceles triangle, the angles opposite congruent sides are congruent. Thus, angle A actually equals angle C.
In other the find B, it is know that all of the interior angles of a triangle must add to 180; thus, this can be written as: angle A + angle B + angle C = 180.
Since you already know angles A and C, subtract angle A and angle C from 180 to get angle B.
For question 23:
Notice that triangle DBC is an isosceles triangle, and that angle D and angle C are opposite of congruent sides, indicating that they are equal. Since the interior angles of a triangle must add up to 180, and you know that angle D equals angle C, you can find angle DBC by doing 180 - (2 * angle D).
Now that you have angle DBC, you can find angle CBA; since these two angles form a straight line, you know they must add to 180 degrees. Thus, 180 - angle DBC equals angle CBA.
Now, notice that triangle CBA is also isosceles, and that angles CBA and angle A are opposite congruent sides, indicating that they are also congruent. Thus, angle A equals angle CBA.
Hope this helps :)
Which is a perfect square?
O 5
O 8
O 36
044
Answer:
6×6=36
36 is the perfect square
Ella traveled by train to visit her friend.
• It took 3 hours for Ella to reach her destination.
• The train averaged a speed of 100 miles per hour.
Enter an equation to express the distance, d, Ella traveled.
Answer:
d = st, d = 100 x 3
Step-by-step explanation:
distance = speed x time
distance = 100 x 3, therefore, distance = 300, but if you just want the equation, it is d = 100 x 3 or d = st
Step-by-step explanation:
d = 100 x 3.
d= 100n
where n = time the journey took.
Help please thank youuu
Answer:
18 mi^2
...
...
...
...
...
Answer:
42 square miles
Step-by-step explanation:
The area of a composite shape can be found by decomposing it into shapes whose area formulas you know. Here, the shape can be decomposed into a triangle and two rectangles. The two rectangles can be formed several ways.
TriangleThe area of the triangle at the top of the figure is ...
A = 1/2bh
A = 1/2(6 mi)(3 mi) = 9 mi²
Overall rectangleThe area of the overall rectangle (including the space at lower right) is ...
A = LW
A = (9 mi)(5 mi) = 45 mi²
Deleted spaceThe area of the rectangle at lower right that is not included in the shaded area is ...
A = LW
A = (4 mi)(3 mi) = 12 mi²
Total areaThe total area of the figure is the sum of the triangle and overall rectangle, less the excluded area at lower right.
total area = 9 mi² +45 mi² -12 mi² = 42 mi²
The area of the figure is 42 square miles.
_____
Additional comment
Other ways to divide the figure into two rectangles are ...
extend the vertical line to make a 9×2 and a 3×5 rectangleextend the horizontal line to make a 4×2 and a 5×5 rectangle80, 60, 45,...
Find the 9th term.
The ninth term of the series [tex]80,60,45.....[/tex] is [tex]50[/tex].
We need to determine the relationship between the consecutive terms of the series to evaluate the succeeding terms of the series.
How to find the terms in a series?
The difference between the first and second terms is [tex]60-80=-20[/tex].
The difference between the second and the third terms is [tex]45-60=-15[/tex]
So, the difference between the third and the fourth terms will be [tex]-10[/tex]. So, the fourth term will be [tex]45-10=35[/tex].
Similarly, the difference between the eighth and the ninth terms will be [tex]-15[/tex]. So, the ninth term will be [tex]35-(-15)=50[/tex].
Thus, the ninth term of the series is [tex]50[/tex].
Learn more about series here- https://brainly.com/question/12707471
#SPJ2
m exponent 2 plus 15 if m =4
Answer:
31
Step-by-step explanation:
[tex]4^{2}[/tex]=16
16+15=31
-5
What is the sign of a.
()
when a = 0 and b < 0?
b
Sos I need help
[tex]\qquad\qquad\huge\underline{\boxed{\sf Answer}}[/tex]
The sign of a will be negative ~
let the value of be be ' -x ' , -x is a negative number (b = -x < 0)
[tex]\qquad \sf \dashrightarrow \: a \times \frac{ - b}{b} [/tex]
[tex]\qquad \sf \dashrightarrow \: a \times \frac{ - ( - x)}{ - x} [/tex]
[tex]\qquad \sf \dashrightarrow \: a \times \frac{ x}{ - x} [/tex]
[tex]\qquad \sf \dashrightarrow \: a \times \frac{ - x}{ x} [/tex]
[tex]\qquad \sf \dashrightarrow \:a \times - 1[/tex]
[tex] \qquad \sf \dashrightarrow \:- a[/tex]
Therefore, the term a, has a negative sign unless it's value is substituted, I.e -a = 0 ( having no sign )
A boy yells in a narrow valley. the sound reflects off of a boulder that is 80 m away. how long will it take to hear the echo if the speed of a sound wave is 320 m/s? (speed = ) 0.25 seconds 0.50 seconds 2.0 seconds 4.0 seconds
Answer:
0.50 seconds
Step-by-step explanation:
The time it takes for an echo to return is the time it takes for the sound to make the round trip between the source and the reflecting object.
The boulder is 80 m away from the source, so the round-trip distance is 2×80 m = 160 m. At a speed of 320 m/s, it takes sound ...
(160 m)/(320 m/s) = 0.50 s
to make the round-trip.
It will take 0.50 seconds to hear the echo.
The time it will take to hear the echo, when the speed of a sound wave is 320 m/s is 0.50 seconds.
What is the speed of sound?
Speed of sound is the rate by which the sound wave travels. The speed of sound depends on the medium by which the sound wave is travelling.
The speed of the wave can be found out using the following formula.
[tex]s=\dfrac{d}{t}[/tex]
Here, (d) is the distance travelled by the wave and (t) is time taken by the wave to cover that distance.
A boy yells in a narrow valley. The sound reflects off of a boulder that is 80 m away.
For the echo, distance travelled will be doubled as it come back.Thus, the distance travelled by sound wave is,
[tex]d=2\times80\\d=160\rm\; m[/tex]
The speed of sound is 320 m/s. Put these value in the above formula as,
[tex]320=\dfrac{160}{t}\\t=0.5\rm\; s[/tex]
Thus, the time it will take to hear the echo, when the speed of a sound wave is 320 m/s is 0.50 seconds.
Learn more about the speed of sound here;
https://brainly.com/question/95976
solve for x and y 13x−28=24
x=4
also uhh where does the y go-
55:26
Square ABCD was translated using the rule (x, y) → (x – 4, y + 15) to form A'B'C'D'. What are the coordinates of point D in the pre-image if the coordinates of point D’ in the image are (9, –8)?
(13, –23)
(5, 7)
(18, 1)
(–6, –4)
the answer is b because you add the two numbers together x + x y + y
Answer:
Its a
Step-by-step explanation:
Edge 22
Find the sine ratio for ∠D.
a. 7/25
b. 24/7
c. 25/24
d. 24/25
Answer:
sin ∠D = 24/25
Step-by-step explanation:
sin = opposite / hypotenuse
Looking at ∠D, the opposite side is 24, hypotenuse is 25
Therefore sin = 24/25
one trillion one hundred eighty-six billion two hundred million in number form
Step-by-step explanation:
1,186,200,000,000 in standard form
help please i don’t know how to do it
Answer:
x + 3y = 15
Step-by-step explanation:
Line is passing through the points [tex](3, \:4) = (x_1,\:y_1)\:and\: (9, 2)=(x_2,\:y_2)[/tex]
Slope of line (m)= (2 - 4)/(9 - 3) = -2/6 = -1/3
Equation of line in point-slope form is given as:
[tex]y-y_1 =m(x-x_1)[/tex]
Plugging the values of [tex]x_1,\: y_1\: and \: m[/tex] in the above equation we find:
[tex]y-4 =-\frac{1}{3}(x-3)[/tex]
[tex]\implies 3y-12 =-x+3[/tex]
[tex]\implies x+ 3y =12+3[/tex]
[tex]\implies \huge {\orange{\boxed{x+ 3y = 15}}}[/tex]
This is the required equation of line in the form [tex]\red{\bold{ax + by = c}} [/tex]
i need help. please
Answer:
[tex]V=\pi r^2h=\pi *6^2*19[/tex] ≈ [tex]2148.8[/tex]
Let me know if you found this helpful! It means a lot!
I need help ASAP...
(reward 10 points)
Answer:
it may be C im sorry if its wrong
Step-by-step explanation:
please mark me the brainiest
Answer:
The answer is a negative correlation.
Step-by-step explanation:
It is a negative correlation because when the y variable tends to decrease as the x variable increases, you can say there is a negative correlation between the variables.
How can this expression be written another way?
60x−24
Factor using the distributive property and the greatest common factor to write an equivalent expression.
Enter your answer by filling in the boxes.
60x−24= __ (__)
Answer:PLEASE BRAINLIEST
factor using 12 (gcf)
12(5x-2)
What is the constant term in the expression 8xy + 9x2 y − 5x − 2?
−5
−2
8
9
Answer:
-2
Step-by-step explanation:
In the expression [tex]8xy + 9x^2y -5x -2[/tex]
[tex]x[/tex] and [tex]y[/tex] are the variablesThe numbers directly before the variables are the coefficientsThe number that it not attached to a variable is the constant termTherefore, the constant term is -2
Answer: -2 is the constant term in the expression 8xy + 9x2 y − 5x − 2
Step-by-step explanation:
A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words.
here, we have,
the expression 8xy + 9x2 y − 5x − 2
now, we know that,
constant is the number with no variable attached to it.
-2 is the constant term in the expression 8xy + 9x2 y − 5x − 2.
Suppose you roll a number cube. What is the probability that you roll the number 5?
Answer:
There is 1/6 chance that you will roll a 5
Step-by-step explanation:
Hope that helps!
PA ANSWERR NEED SOME ANSWERS THNKS
Answer:
16. j = 105 °
17. Q = 68 °
18. s = 97 °
19. t = 70 °
20. r = 125 °
Step-by-step explanation:
16. Name the angle that is supplementary to angle J as K, and label the angle that is next to K as G
Angle G = 105, because it is corresponding to the 105 angle.
Since G is supplementary to K, angle K = 75.
So, J = 105
17. Name the angle that is supplementary to angle Q as R
Angle R = 112, because it is corresponding to the 112 angle.
Since R is supplementary to Q, angle Q = 68.
18. Name the angle that is supplementary to the 83 angle as L
Angle L = 97, since angle L and the 83 angle are supplementary angles
-> Angle S = 97, since S and L are alternate angles
19. Angle T = 70, since angle T and the 70 angle are corresponding angles.
20. Name the angle that are alternate angles with angle R as Q
Angle Q = 125, because it is corresponding to the 125 angle.
Since angle Q and angle R are alternate angles, angle R = 125.
(Note : alternate angles and corresponding angles are equal to each other, supplementary angles add up to 180.)
quadrilateral ABCD is a kita with diagonals AC and BD. determine the area of a kita with diagonals BD = 8 units and AC = 12 units
[tex]\mathsf\blue{♧ANSWER♧}[/tex]
[tex] \mathsf \orange{ \frac{x \times y}{2}} [/tex]
[tex] \mathsf \green{ \frac{8 \times 12}{2} }[/tex]
[tex] \mathsf \orange{ \frac{96}{2} }[/tex]
[tex] \mathsf \green{48 \: square \: units}[/tex]
[tex] \huge \tt \color{pink}{A}\color{blue}{n}\color{red}{s}\color{green}{w}\color{grey}{e}\color{purple}{r }[/tex]
[tex]\qquad\qquad\qquad \large\underline{ \boxed{ \sf{✰\: Information }}}[/tex]
★ Given➣A quadrilateral ABCD shape (kite) with diagonals "AC" and "BD"➣ diagonal BD is of 8units ➣ diagonal AC is of 12units✜ Now let's see about ques ✜question is asking about to find area of kite with the above infosoo we know that[tex]{ \boxed{ ✟ \: \underline{ \boxed{ \sf \: Area \: of \: kite = \frac{ d_1 \times d_2}{2} \: or \blue{ \: \frac{1}{2} \times d_1 \times d_2}}}✟ }}[/tex]
[tex]\rule{80mm}{2.5pt}[/tex]
✜ Let's substitute value according to formula ✜[tex] \qquad \rm{➛Area \: of \: kite = \frac{BD×AC}{2} }[/tex]
[tex]\qquad \rm{➛Area \: of \: kite = \frac{8×12}{2} } \\ \qquad \rm{➛Area \: of \: kite = \frac{ \cancel{96}}{ \cancel2} } \\ \qquad \rm{➛Area \: of \: kite = 48 {units}^{2} }[/tex]
[tex]\rule{80mm}{2.5pt}[/tex]
★Hence area of kite with diagonals BD = 8 units and AC = 12 units is
[tex]\qquad\qquad\qquad{ \boxed{↪ \underline{ \boxed{ \sf{\: 48 {units}^{2} \green✓ }}}↩}}[/tex]
[tex]\rule{80mm}{2.5pt}[/tex]
★ More info regarding this topic ★
➣ Quadrilateral:- A polygon with four sides,sum of it's interior angle is of 360⁰➣ Kite is also a quadrilateral because of four sides.Kite is a quadrilateral which is proved Euclidean geometry.[tex]\rule{80mm}{2.5pt}[/tex]
Hope it helps !
what is the slope between (8, -2) and (-7, 10)?
Answer:
-1/15 is the slope
Use the y2-y1/x2-x1 formula and plug in the variables
Find the area of the figure
Answer:
C. 418 cm²
Step-by-step explanation:
Rectangle
= s × s
= 19 × 19
= 361 cm²
Triangle
= 1/2 × 6 × 19
= 57 cm²
361 + 57 = 418 cm²
So, therefore your answer is 418 cm²
What is the value of x? (Do not put in the degree symbol)
Step-by-step explanation:
x+134=180(straight angle)
x=46
Geoffrey measures the width of his bedroom to determine the largest size bed frame he can have. The wall he plans to place the bed frame against is 13.65 feet wide. He wants there to be 2.25 feet between the wall and the bed frame on each side. What is the maximum width bed frame, in inches, that Geoffrey can put in his bedroom?
Answer:109.8 inches
Step-by-step explanation:
Please help find Find cosR!
Step-by-step explanation:
when we look at the triangle try to reposition it at least in your mind to make R to be the center of the circle. then RP (29) is the radius of the circle and the angle indication of the angle R in this circle.
then we see QP is the sine, and RQ is the cosine of the angle R. but don't forget : all are multiplied by the radius, because the pure sin and cos functions deliver the values for the standard circle with radius 1.
so,
QR = cos(R)×RP
21 = cos(R) × 29
cos(R) = 21/29
the fourth answer is correct.
Answer:
the answer is D I took the test
You draw a rectangular picture that is 8.5 inches wide. It is 3 times as long as it is wide. What
is the area of the picture?
Answer: 216.75 in^2
Step-by-step explanation: area = 8.5 x (8.5x3)
8.5 x25.5
Help I’ll give brainlessly find tqs
Your answer for TQS is 43.
89 - 46 = 43