Answer:
x = -6
y = 4
Step-by-step explanation:
Rewriting the equations :
2x + y = -84x - 3y = -36Now, solving the two equations using substitution method, we get :
x = -6
y = 4
Answer:
y = 4
x = -6
Step-by-step explanation:
1/2 x + 1/4 y= -2 first equation
-2/3 x + 1/2 y = 6 second equation
solution:
from the first equation:
8(1/2 x + 1/4 y) = -2*8
8x*1/2 + 8y*1/4 = -16
8x/2 + 8y/4 = -16
4x + 2y = -16 third equation
from the second equation
6(-2/3 x + 1/2 y) = 6*6
6x*-2/3 + 6y*1/2 = 36
-12x/3 + 6y/2 = 36
-4x + 3y = 36 fourth equation
from the third & fourth equation:
4x + 2y = -16
-4x + 3y = 36
0 + 5y = 20
5y = 20
y = 20/5
y = 4
from the fourth equation:
-4x + 3y = 36
-4x + 3*4 = 36
-4x + 12 = 36
-4x = 36 - 12
-4x = 24
x = 24/-4
x = -6
Check:
from the first equation:
1/2 x + 1/4 y = -2
1/2 *-6 + 1/4 * 4 = -2
-3 + 1 0 -2
from the second equation:
-2/3 x + 1/2 y = 6
-2/3 * -6 + 1/2 * 4 = 6
4 + 2 = 6
Given x – 5 < One-fourth (y – 8)2, which graph represents the inequality?
Step-by-step explanation:
x - 5 < 2 (y - 8) • 1/4
x - 5 < (y - 8) / 2
2 (x - 5) < y - 8
2x - 10 < y - 8
2x - 10 + 8 < y
y > 2x - 2
graph 2x - 2 and shade the section above
The graph of (y - 8)² > 4x - 20 is the same as the graph of x - 5 < 1/4(y - 8)²
How to determine the graph of the inequality?The inequality of the graph is given as:
x - 5 < 1/4(y - 8)²
Multiply both sides by 4
4x - 20 < (y - 8)²
Rewrite the inequality as:
(y - 8)² > 4x - 20
Hence, the graph of (y - 8)² > 4x - 20 is the same as the graph of x - 5 < 1/4(y - 8)²
See attachment for the graph
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2sin^2(2x) + 1 = 3sin(2x) Solve for x with exact answers. The domain is 0 ≤ x ≤ π
Answer:
x = π/12 and x = π/4.
Step-by-step explanation:
2sin^2(2x) + 1 = 3sin(2x)
2sin^2(2x) - 3sin(2x) + 1 = 0
(2sin(2x) - 1)(sin(2x) - 1) = 0
2sin(2x) - 1 = 0
2sin(2x) = 1
sin(2x) = 1/2
When there is a variable n = π/6, sin(π/6) = 1/2 [refer to the unit circle].
2x = π/6
x = π/12
sin(2x) - 1 = 0
sin(2x) = 1
When there is a variable n = π/2, sin(π/2) = 1 [refer to the unit circle].
2x = π/2
x = π/4
Hope this helps!
Problem 1. (1 point) A steel ball weighing 128 pounds is suspended from a spring. This stretches the spring 128101 feet. The ball is started in motion from the equilibrium position with a downward velocity of 2 feet per second. The air resistance (in pounds) of the moving ball numerically equals 4 times its velocity (in feet per second) . Suppose that after t seconds the ball is y feet below its rest position. Find y in terms of t. (Note that this means that the positive direction for y is down.)
Answer:
seeed
Step-by-step] explanation:
ddd~!`
which statement correctly describes the relation between the variable in the equation C = nd
Answer:
nd is c
Step-by-step explanation:
Let X denote the day she gets enrolled in her first class and let Y denote the day she gets enrolled in both the classes. What is the distribution of X
Answer:
X is uniformly distributed.
Step-by-step explanation:
Uniform Distribution:
This is the type of distribution where all outcome of a certain event have equal likeliness of occurrence.
Example of Uniform Distribution is - tossing a coin. The probability of getting a head is the same as the probability of getting a tail. The have equal likeliness of occurrence.
A chicken soup recipe calls for 13 cups of chicken stock how much is this in quarts
Answer:
3.25 US Quarts
Step-by-step explanation:
4
If Randy flips a coin 3 times, what is the probability that it will come up heads 3 times?
Hi there! :)
Answer:
[tex]P(heads) = \frac{1}{8}[/tex]
Step-by-step explanation:
Probability of a coin landing on heads:
[tex]P(heads) = \frac{1}{2}[/tex]
Find the probability of getting heads 3 times:
[tex]\frac{1}{2} * \frac{1}{2} * \frac{1}{2} = \frac{1}{8}[/tex]
Therefore, the probability of the coin showing heads for 3 tosses is:
[tex]P(heads) = \frac{1}{8}[/tex]
20 POINTS! You are planning to use a ceramic tile design in your new bathroom. The tiles are equilateral triangles. You decide to arrange the tiles in a hexagonal shape as shown. If the side of each tile measures 9 centimeters, what will be the exact area of each hexagonal shape?
Answer:
210.33 cm^2
Step-by-step explanation:
We know that 6 equilateral triangles makes one hexagon.
Also, an equilateral triangle has all its sides equal.
If the tile of each side of the triangular tile measure 9 cm, then the height of the triangular tiles can be gotten using Pythagoras's Theorem.
The triangle formed by each tile can be split along its height, into two right angle triangles with base (adjacent) 4.5 cm and slant side (hypotenuse) of 9 cm. The height (opposite) is calculated as,
From Pythagoras's theorem,
[tex]hyp^{2} = adj^{2} + opp^{2}[/tex]
substituting, we have
[tex]9^{2} = 4.5^{2} + opp^{2}[/tex]
81 = 20.25 + [tex]opp^{2}[/tex]
[tex]opp^{2}[/tex] = 81 - 20.25 = 60.75
opp = [tex]\sqrt{60.75}[/tex] = 7.79 cm this is the height of the right angle triangle, and also the height of the equilateral triangular tiles.
The area of a triangle = [tex]\frac{1}{2} bh[/tex]
where b is the base = 9 cm
h is the height = 7.79 cm
substituting, we have
area = [tex]\frac{1}{2}[/tex] x 9 x 7.79 = 35.055 cm^2
Area of the hexagon that will be formed = 6 x area of the triangular tiles
==> 6 x 35.055 cm^2 = 210.33 cm^2
What is the solution to this system of linear equations?
y-x = 6
y + x = -10
(-2,-8)
(-8.-2)
(6.-10)
(-10.6)
Answer:
The correct answer is A
Step-by-step explanation:
Answer:
(-8, -2)
Step-by-step explanation:
y-x = 6
y + x = -10
Add the two equations together to eliminate x
y-x = 6
y + x = -10
--------------------
2y = -4
Divide by 2
2y/2 = -4/2
y = -2
Now find x
y+x = -10
-2+x = -10
x = -8
Mixture Problem A solution contains 15 milliliters of HCI
and 42 milliliters of water. If another solution is to have
the same concentration of HCl in water but is to contain
140 milliliters of water, how much HCI must it contain?
Answer:
Step-by-step explanation:
This is a straight proportion problem.
15/42 = x/140 Cross Multiply
15*140 = 42 * x
2100 = 42x Divide by 42
2100/42 = x
x = 50 ml of HCl will be needed.
Michelle is 7 years older than her sister Joan, and Joan is 3 years younger than their brother Ryan. If the sum of their ages is 64, how old is Joan?
16
22
18
19
Answer:
(C) 18
Step-by-step explanation:
We can create a systems of equations. Assuming [tex]m[/tex] is Michelle's age, [tex]j[/tex] is Joan's age, and [tex]r[/tex] is Ryan's age, the equations are:
[tex]m = j + 7[/tex]
[tex]j = r-3[/tex]
[tex]m+j+r = 64[/tex]
We can use substitution, since we know the "values" of m and j.
[tex](j+7)+(r-3)+r = 64\\(j+7)+(2r-3)=64\\2r + j + 4 = 64\\2r + j = 60\\\\[/tex]
[tex]r = 21, j = 18[/tex]
So we know that Joan is 18 years old.
Hope this helped!
Two sides of a triangle are 24 inches in length, what is the length of the third side
pls help !
hopefully you can read the whole thing :))
Answer:
answer is A
Step-by-step explanation:
option A is the answer
Which is greater than 4?
(a) 5,
(b) -5,
(c) -1/2,
(d) -25.
round to
237 divide by 4 = (hundredths)
An aluminum bar 4 feet long weighs 24 pounds. What is the weight of a similar bar that is 3 feet 3 inches long? WILL MARK BL
Answer:
19.5 pounds
Step-by-step explanation:
1 foot = 12 inches
3 inches = 3/12 = 0.25 feet
3 feet 3 inches = 3.25 feet
then:
24 pounds is 4 feet
A pounds is 3.25 feet
A = 24*3.25/4
A = 19.5 pounds
Answer:
19.50 pounds
Step-by-step explanation:
1 foot = 12 inches
3 inches = 3/12 = 0.25 feet
3 feet 3 inches = 3.25 feet
then:
24 pounds is 4 feet
A pounds is 3.25 feet
A = 24*3.25/4
A = 19.50 pounds
find the measure of c
Answer:
A. 149
Step-by-step explanation:
When a quadrilateral is inscribed in a circle, the sum of the opposite angles in the quadrilateral equal (180) degrees. Applying this theorem here, one can state the following:
c + 31 = 180
Inverse operations,
c + 31 = 180
c = 149
Thus, option (A) is the correct angles: ( c = 149°)
Six people attend the theater together and sit in a row with exactly six seats.
a. How many ways can they be seated together in the row?
b. Suppose one of the six is a doctor who must sit on the aisle in case she is paged. How many ways can the people be seated together in the row with the doctor in an aisle seat?
c. Suppose the six people consist of three married couples and each couple wants to sit together with the husband on the left. How many ways can the six be seated together in the row?
Answer
A. 720 ways
B. 240 ways
C. 6 ways
There are 720 ways they can be seated in a row together, 120 ways can the people be seated together in a row with the doctor in an aisle seat, and 6 ways can the six be seated together in a row.
What is a permutation?A permutation is defined as a mathematical process that determines the number of different arrangements in a set of objects when the order of the sequential arrangements.
It is assumed that six people will attend the theater together and sit in a row of six.
The following are the various ways they can be seated in a row together:
⇒ 6!
⇒ 6 × 5 × 4 × 3 × 2 × 1
⇒ 720
If the doctor sits in the aisle seat, the remaining 5 persons can sit in the remaining 5 seats 5! ways
The total possibilities are as follows:
⇒ 5 × 4 × 3 × 2 × 1
= 120
Consider that the six persons are made up of three married couples.
In addition to the aforementioned, divide the six chairs into three groups of two seats each.
There is one choice in each block for the husband to be placed on the left and the wife to be positioned on the right and the 3 couples can be seated in the 3 blocks in 3! ways.
⇒ 3 × 2 × 1
The required answer is 6.
Thus, there are 720 ways they can be seated in a row together, 120 ways can the people be seated together in a row with the doctor in an aisle seat, and 6 ways can the six be seated together in a row.
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GIVING BRAINLIEST!!!!! AND ALL POINTS!!!!!!!!!!!!!!!!!!!
A right rectangular prism is packed with cubes of side length fraction 1 over 4 inch. If the prism is packed with 12 cubes along the length, 8 cubes along the width, and 5 cubes along the height, what is the volume of the prism?
fraction 2 and 3 over 4 cubic inches
fraction 3 and 3 over 4 cubic inches
fraction 7 and 1 over 4 cubic inches
fraction 7 and 1 over 2 cubic inches
Answer:
7 and 1 over 2 cubic inches ( 7 1/2 in³
Step-by-step explanation:
The height = 1/4 * 5 = 1 1/4 = 1.25
The width = 1/4 * 8 = 2
The length = 1/4 * 12 = 3
Volume = 1.25 * 2 * 3 = 2.5 * 3 = 7.5
0.5 is represented as 1/2
So answer : fraction 7 and 1 over 2 cubic inches or 7 1/2 in³
if my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
What is the size of each piece in square units?
What is the area of the shaded rectangle in square units?
Answer Asapp plezz
Answer:
8 pieces are shaded
Size of one square is (1/3)*(1/5)=1/15
The area of shaded region is basically (2/3)*(4/5)=8/15
The Size of one square is 1/15. The area of the shaded region rectangle is 8/15.
What is the area of the rectangle?The area of the rectangle is the product of the length and width of a given rectangle.
The area of the rectangle = length × Width
From the given figure we can see that 8 pieces of the square makes a shaded region.
The area of a square = side x side
[tex]= \dfrac{1}{3}\times\dfrac{1}{5}\\\\=\dfrac{1}{15}[/tex]
Therefore, the Size of one square is 1/15.
The area of the shaded region rectangle = length × Width
[tex]= \dfrac{2}{3}\times\dfrac{4}{5}\\\\=\dfrac{8}{15}[/tex]
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PLEASE HELP!! WHOEVER HELPS FIRST AND GETS IT CORRECT GETS BRAILIEST!!
Answer:
16 rotations
Step-by-step explanation:
500/32 = 15.625
15.625 rounded = 16
hope it helps!
the number of times n a ball bounces
Choose the correct answer below.
O rational numbers
O integers
o irrational numbers
O natural numbers
The number of times n a ball bounces is a natural number
How to determine the category of the statement?The mathematical statement is given as:
The number of times n a ball bounces
A ball cannot bounce in decimal times or negative times
Also, it can not bounce in 0 times
This means that the number of bounce is a positive integer
A positive integer is also a natural number
Hence, the number of times n a ball bounces is a natural number
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how many hours are there from 10:30 on Monday to 11:30 on Tuesday
Answer:
25 hours.
Step-by-step explanation:
We are to find the number of hours from:
Monday at 10:30
to
Tuesday at 11:30
Since the question does not state whether the times are in A.M / P.M ,
There are 24 hours upto 10:30 on Tuesday.
Adding 1 hour gives 11:30
So the answer = 24 + 1 = 25 hrs
Answer:
25 hours
Step-by-step explanation:
1 day=24 hours
11.30-10.30=1 hour
----------------------------
add the total 25 hours
What is the corresponding index of the random matrix of 7 criteria for checking consistency of random judgment? Group of answer choices 0.58 1.45 1.32 .90
Corresponding Index is one which creates a random matrix index based on the values.
The random consistency index has values lesser than 1 therefore the value for the random matrix of 7 the consistency index will be 0.58.
Random Index maximum value will be 0 and its minimum value will be 0.01. The values will depend on the matrix consistency Index.
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A geometric sequence is a sequence of numbers where the next term equals to
the previous term multiplied by a common factor (for example, (3, 6, 12, 24, ...)
is a geometric sequence with the first term ”3” and the common factor ”2”). If
the 5th term of a geometric sequence is 24 and the 7th term is 144, what is the
first term of the sequence?
(A) 2
(B) 3/2
(C) 2/3
(D) 1/3
(E) 1/4
Answer:
C
Step-by-step explanation:
Let the first term be a and the common ratio be r.
ATQ, ar^4=24 and ar^6=144, r=sqrt(6) and a=24/(sqrt(6))^2=24/36=2/3
Difference between 5429 and 5907 to the greatest place.
Given numbers
54295907Inorder to find the difference between them we have to substarct them.
[tex]\\ \sf\longmapsto 5907-5429[/tex]
[tex]\\ \sf\longmapsto 478[/tex]
Answer:
478
Step-by-step explanation:
To solve the problem
5907 -
5429 =
478
What are the approximate solutions of the graphed function?
Answer:
x = -2.6, x = 2.6
Step-by-step explanation:
The graph crosses the x-axis at approximately 2.6 and -2.6.
The required approximate solution of the function graphed is x = -2.6 and 2.6.
Given that,
A graph of a function is plotted, and the solution of the function is to be determined.
What are functions?
Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
What is a graph?The graph is a demonstration of curves that gives the relationship between the x and y-axis.
Here, the solution of the function is that value of x where the function terminates to zero, So the given curve terminates to zero at two places at x = -2.6 and x = 2.6 from the observation of the graph.
Thus, the required approximate solution of the function graphed is x = -2.6 and 2.6.
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What is the value of the mean from the following set of data: 12,10, 11, 8, 6, 5, 3, 7, 9. Round to the nearest hundredth.
Answer:
7.88 or 7.9
Step-by-step explanation:
To find the mean, we need to do:
=> (12 + 10 + 11 + 8 + 6 + 5 + 3 + 7 + 9) / 9
=> 71/9
=> 7.88 or 7.9
I divided the sum of all numbers by 9 because we added 9 numbers.
In the diagram, XY bisects ZWXZ.
1
z
2
w
(5x + 3)
(7x - Y
х
mWYZ
type your answer.
In provided diagram angle WXY = angle YXZ
Angle WXY =( 7x-7)°
Angle YXZ = ( 5x +3)°
We have to find out the value of Angle WXZ
→ 7x-7 = 5x +3
→ 7x - 5x = 7+3
→ 2x = 10
→ x = 10/2
→ x = 5 .
Putting the value of x .
→ Angle WXY = 7(2)-7
→ 14-7 = 7°
→ Angle YXZ = 5(2)+3
→ 10+3 = 13°
Angle WXZ = 13° + 7 ° → 20°
So 20° is the required answer .
Answer:
SI
Step-by-step explanation:
Find the total amount in the compound interest account.
$10000 is compounded semiannually at a rate of 9% for 22 years.
(Round to the nearest cent.)
Answer:
$69,361.23
Step-by-step explanation:
[tex] A = P(1 + \dfrac{r}{n})^{nt} [/tex]
[tex] A = 10000(1 + \dfrac{0.09}{2})^{2 \times 22} [/tex]
[tex]A = 10000(1.045)^{44}[/tex]
[tex] A = 69361.23 [/tex]
Answer: $69,361.23