Answer:
[tex]x=2[/tex]
Step-by-step explanation:
-------------------------
Given:
[tex]4x+x-3-9+4x=6[/tex]
---------->>>>
Combine like terms.
[tex]9x-12=6[/tex]
---------->>>>
Add 12 to both sides.
[tex]9x=18[/tex]
---------->>>>
Divide both sides by 9.
[tex]x=2[/tex]
-------------------------
Hope this is helpful.
Solve the system of linear equations below.
6x + 3y = 33
4x + y = 15
A.
x = 2, y = 7
B.
x = -13, y = 7
C.
x = - 2/3, y = 12 2/3
D.
x = 5, y = 1
Answer:
A. x=2 y=7
Step-by-step explanation:
-12x -3 = 3y
6x + 3y = 33
sooo you add them up...
so its
-6x = -12
x=2
and then you plug in the x value into one of the equations
6x + 3y = 33
6(2) + 3y = 33
12 + 3y = 33
3y = 33 - 12
3y = 21
21/3=7
y=7
What is the slope of (-1,3) and (3,1)
Work Shown:
Apply the slope formula
m = (y2-y1)/(x2-x1)
m = (1-3)/(3-(-1))
m = (1-3)/(3+1)
m = -2/4
m = -1/2 is the slope
In decimal form, this converts to -0.5, though usually slopes are in fraction form.
Helpi
Identify the domain of the function shown in the graph.
Answer:
D = all reals (or -7 to 7)
Step-by-step explanation:
If the line continues on for infinity, then the domain is all reals, or negative infinity to positive infinity. If the line ends on the graph that we can see, though, the domain would be [-7 , 7]
On a coordinate plane, 2 triangles are shown. The first triangle has points A (negative 1, negative 2), B (negative 4, negative 2), C (negative 1, negative 4). The second triangle has points A prime (1, 2), B prime (4, 2), C prime (1, 4). What rule describes the rotation about the origin? (x, y) → How many degrees was the figure rotated about the origin?
9514 1404 393
Answer:
(x, y) ⇒ (-x, -y)180°Step-by-step explanation:
Each image point has its signs reversed from the pre-image point.
(x, y) ⇒ (-x, -y) . . . . describes the rotation
Rotation from the third quadrant (A) to the first quadrant (A') is a rotation of 180°.
Answer:
3rd and 2nd option
Step-by-step explanation:
Naval intelligence reports that 4 enemy vessels in a fleet of 17 are carrying nuclear weapons. If 9 vessels are randomly targeted and destroyed, what is the probability that more than 1 vessel transporting nuclear weapons was destroyed
Answer:
0.7588 = 75.88% probability that more than 1 vessel transporting nuclear weapons was destroyed
Step-by-step explanation:
The vessels are destroyed without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x successes is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this question:
Fleet of 17 means that [tex]N = 17[/tex]
4 are carrying nucleas weapons, which means that [tex]k = 4[/tex]
9 are destroyed, which means that [tex]n = 9[/tex]
What is the probability that more than 1 vessel transporting nuclear weapons was destroyed?
This is:
[tex]P(X > 1) = 1 - P(X \leq 1)[/tex]
In which
[tex]P(X \leq 1) = P(X = 0) + P(X = 1)[/tex]
So
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 0) = h(0,17,9,4) = \frac{C_{4,0}*C_{13,9}}{C_{17,9}} = 0.0294[/tex]
[tex]P(X = 1) = h(1,17,9,4) = \frac{C_{4,1}*C_{13,8}}{C_{17,9}} = 0.2118[/tex]
Then
[tex]P(X \leq 1) = P(X = 0) + P(X = 1) = 0.0294 + 0.2118 = 0.2412[/tex]
[tex]P(X > 1) = 1 - P(X \leq 1) = 1 - 0.2412 = 0.7588[/tex]
0.7588 = 75.88% probability that more than 1 vessel transporting nuclear weapons was destroyed
The U.S. average for state and local taxes for a family of four is $4172. A random sample of 20 families in a northeastern state indicates that they paid an annual amount of $4560 with a standard deviation of $1590. At α = 0.05, is there sufficient evidence to conclude that they pay more than the national average of $4172?
Answer:
Calculating p-value from excel
p-value = 0.144458 (From excel =T.DIST.RT(1.091,19))
p-value = 0.144458 > 0.05
So, we failed to reject the null hypothesis. There is sufficient evidence to conclude that they pay not more than the national average of $4172.
Step-by-step explanation:
Here the given de4tails are,
Hypothesized mean = 4172
Sample Standard deviation = 1590
Sample mean = 4560
Sample size n = 20
Formulation of hypothesis
Please help me i will give you brainlest
Answer:
19. - 4/11
21. 14
Step-by-step explanation:
Im sorry but i can't solve 20
The negative effects of a recession would be reduced by which fiscal policy decision?
A. incurring a budget deficit which is used to retire debt held by the public
B. incurring a budget surplus and allowing that surplus to accumulate as idle Treasury balances
C. incurring a budget surplus, which is used to retire debt held by commercial banks
D. incurring a budget deficit by borrowing from the public and increasing expenditures
Incurring a budget surplus and allowing that surplus to accumulate as idle Treasury balances. Then the correct option is B.
What is Recession?A span of transitory negative growth marked by a drop in Income in four quarters.
The negative effects of a recession would be reduced by the fiscal policy decision will be
Incurring a budget surplus and allowing that surplus to accumulate as idle Treasury balances
Then the correct option is B.
More about the Recession link is given below.
https://brainly.com/question/18075358
#SPJ1
There are seven people online and each person uses either a blue, black, or red pen to write while working. How many possible combinations can be made?
A. 49
B. 28
C. 21
D. 10
A S A P!! I DONT WANT MY DAD YELLING AT ME FOR THIS ;^;
Answer:
21 is the answer for this question may be
what is the product of ten and the sum of two and a number is five times the number
How do you complete the other two?
I know how to complete the first one but 3D Pythag confuses me so much
For now, I'll focus on the figure in the bottom left.
Mark the point E at the base of the dashed line. So point E is on segment AB.
If you apply the pythagorean theorem for triangle ABC, you'll find that the hypotenuse is
a^2+b^2 = c^2
c = sqrt(a^2+b^2)
c = sqrt((8.4)^2+(8.4)^2)
c = 11.879393923934
which is approximate. Squaring both sides gets us to
c^2 = 141.12
So we know that AB = 11.879393923934 approximately which leads to (AB)^2 = 141.12
------------------------------------
Now focus on triangle CEB. This is a right triangle with legs CE and EB, and hypotenuse CB.
EB is half that of AB, so EB is roughly AB/2 = (11.879393923934)/2 = 5.939696961967 units long. This squares to 35.28
In short, (EB)^2 = 35.28 exactly. Also, (CB)^2 = (8.4)^2 = 70.56
Applying another round of pythagorean theorem gets us
a^2+b^2 = c^2
b = sqrt(c^2 - a^2)
CE = sqrt( (CB)^2 - (EB)^2 )
CE = sqrt( 70.56 - 35.28 )
CE = 5.939696961967
It turns out that CE and EB are the same length, ie triangle CEB is isosceles. This is because triangle ABC isosceles as well.
Notice how CB = CE*sqrt(2) and how CB = EB*sqrt(2)
------------------------------------
Now let's focus on triangle CED
We just found that CE = 5.939696961967 is one of the legs. We know that CD = 8.4 based on what the diagram says.
We'll use the pythagorean theorem once more
c = sqrt(a^2 + b^2)
ED = sqrt( (CE)^2 + (CD)^2 )
ED = sqrt( 35.28 + 70.56 )
ED = 10.2878569196893
This rounds to 10.3 when rounding to one decimal place (aka nearest tenth).
Answer: 10.3==============================================================
Now I'm moving onto the figure in the bottom right corner.
Draw a segment connecting B to D. Focus on triangle BCD.
We have the two legs BC = 3.7 and CD = 3.7, and we need to find the length of the hypotenuse BD.
Like before, we'll turn to the pythagorean theorem.
a^2 + b^2 = c^2
c = sqrt( a^2 + b^2 )
BD = sqrt( (BC)^2 + (CD)^2 )
BD = sqrt( (3.7)^2 + (3.7)^2 )
BD = 5.23259018078046
Which is approximate. If we squared both sides, then we would get (BD)^2 = 27.38 which will be useful in the next round of pythagorean theorem as discussed below. This time however, we'll focus on triangle BDE
a^2 + b^2 = c^2
b = sqrt( c^2 - a^2 )
ED = sqrt( (EB)^2 - (BD)^2 )
x = sqrt( (5.9)^2 - (5.23259018078046)^2 )
x = sqrt( 34.81 - 27.38 )
x = sqrt( 7.43 )
x = 2.7258026340878
x = 2.7
--------------------------
As an alternative, we could use the 3D version of the pythagorean theorem (similar to what you did in the first problem in the upper left corner)
The 3D version of the pythagorean theorem is
a^2 + b^2 + c^2 = d^2
where a,b,c are the sides of the 3D block and d is the length of the diagonal. In this case, a = 3.7, b = 3.7, c = x, d = 5.9
So we get the following
a^2 + b^2 + c^2 = d^2
c = sqrt( d^2 - a^2 - b^2 )
x = sqrt( (5.9)^2 - (3.7)^2 - (3.7)^2 )
x = 2.7258026340878
x = 2.7
Either way, we get the same result as before. While this method is shorter, I think it's not as convincing to see why it works compared to breaking it down as done in the previous section.
Answer: 2.7Answer:
Qu 2 = 10.3 cm
Qu 3. = 2.7cm
Step-by-step explanation:
Qu 2. Shape corner of a cube
We naturally look at sides for slant, but with corner f cubes we also need the base of x and same answer is found as it is the same multiple of 8.4^2+8/4^2 for hypotenuse.
8.4 ^2 + 8.4^2 = sq rt 141.42 = 11.8920141 = 11.9cm
BD = AB = 11.9 cm Base of cube.
To find height x we split into right angles
formula slant (base/2 )^2 x slope^2 = 11.8920141^2 - 5.94600705^2 = sq rt 106.065
= 10.2987863
height therefore is x = 10.3 cm
EB = 5.9cm
BC = 3.7cm
CE^2 = 5.9^2 - 3.7^2 = sqrt 21.12 = 4.59565012 = 4.6cm
2nd triangle ED = EC- CD
= 4.59565012^2- 3.7^2 = sq rt 7.43000003 =2.72580264
ED = 2.7cm
x = 2.7cm
In the diagram below, trapezoid ABCD maps to trapezoid A’B’C’D’
Which angle corresponds to angle C
Answer:
C'
Step-by-step explanation:
Given
ABCD to A'B'C'D'
Required
Corresponding angle of C
ABCD to A'B'C'D' means that the following angles are corresponding
[tex]A \to A'[/tex]
[tex]B \to B'[/tex]
[tex]C \to C'[/tex]
[tex]D \to D'[/tex]
Hence, C' corresponds to C
Answer:
C
Step-by-step explanation:
I took the test :)
Given the following angles, what ray is the common side of CFD and ZDFE?
Answer:
B. Ray FD
Step-by-step explanation:
A common side of two angles is the side shared by the two angles. It is part of the sides that forms both angles.
The common side of <CFD and <DFE is therefore ray FD. Ray FD is part of the sides that forms <CFD and also <DFE.
Answer:
B. Ray FD
Step-by-step explanation:
A common side of two angles is the side shared by the two angles. It is part of the sides that forms both angles.
The common side of <CFD and <DFE is therefore ray FD. Ray FD is part of the sides that forms <CFD and also <DFE.
you have to find ABC and I'm not sure how to any help is appreciated
Hello,
Since (BD) bissects angle ABC,
18-x=26-3x
2x=8
x=4
18-x=18-4=14
m angle ABC=14°*2=28°
Which expression is equivalent to the difference shown?
Answer:
Option A. -1/20x
Step-by-step explanation:
[tex] \frac{5x + 1}{5x} - \frac{4x + 1}{4x} [/tex]
[tex] = \frac{20x + 4x - 20x - 5x}{20x^{2} } [/tex]
[tex] = \frac{ - x}{20x^{2} } [/tex]
[tex] - \frac{1}{20x} [/tex]
Answered by GAUTHMATH
The half-life of a newly discovered radioactive element is 30 seconds. To the nearest tenth of a second, how long will it take for a sample of 9 grams to decay to 0.72 grams
Answer:
It will take about 109.3 seconds for nine grams of the element to decay to 0.72 grams.
Step-by-step explanation:
We can write a half-life function to model our function.
A half-life function has the form:
[tex]\displaystyle A=A_0\left(\frac{1}{2}\right)^{t/d}[/tex]
Where A₀ is the initial amount, t is the time that has passes (in this case seconds), d is the half-life, and A is the amount after t seconds.
Since the half-life of the element is 30 seconds, d = 30. Our initial sample has nine grams, so A₀ is 9. Substitute:
[tex]\displaystyle A=9\left(\frac{1}{2}\right)^{t/30}[/tex]
We want to find the time it will take for the element to decay to 0.72 grams. So, we can let A = 0.72 and solve for t:
[tex]\displaystyle 0.72=9\left(\frac{1}{2}\right)^{t/30}[/tex]
Divide both sides by 9:
[tex]\displaystyle 0.08=\left(\frac{1}{2}\right)^{t/30}[/tex]
We can take the natural log of both sides:
[tex]\displaystyle \ln(0.08)=\ln\left(\left(\frac{1}{2}\right)^{t/30}\right)[/tex]
By logarithm properties:
[tex]\displaystyle \ln(0.08)=\frac{t}{30}\ln(0.5)[/tex]
Solve for t:
[tex]\displaystyle t=\frac{30\ln(0.08)}{\ln(0.5)}\approx109.3\text{ seconds}[/tex]
So, it will take about 109.3 seconds for nine grams of the element to decay to 0.72 grams.
A humanities professor assigns letter grades on a test according to the following scheme. A: Top 13% of scores B: Scores below the top 13% and above the bottom 60% C: Scores below the top 40% and above the bottom 23% D: Scores below the top 77% and above the bottom 8% F: Bottom 8% of scores Scores on the test are normally distributed with a mean of 70 and a standard deviation of 9.6. Find the minimum score required for an A grade. Round your answer to the nearest whole number, if necessary
Answer:
81
Step-by-step explanation:
Given data:
mean μ = 70.
standard deviation σ, 9.6.
P(Z < 1.123) = 0.13
z = 1.13
Use the z-score formula,
x = z×σ +μ
Substitute the values in the above equation.
x = 1.13 9.6 + 70 = 81
The minimum score required for an A grade is = 81
Use the relationship among the three angles of any triangle to solve. Two angles of a triangle have the same
measure and the third angle is 27° greater than the measure of the other two. Find the measure of each angle.
Please help :)
Answer:
51°,51°,78°
Step-by-step explanation:
The sum of angles in a triangle add up to 180°
The office needs 6 new devices worth $7200. The order consists of new computers (C) which cost $1425 each and printers (P) which cost $750 each. How many of the new devices are computers and how many are printers?
6. Calculate the area of the octagon in the
figure below.
Answer:
[tex]41\text{ [units squared]}[/tex]
Step-by-step explanation:
The octagon is irregular, meaning not all sides have equal length. However, we can break it up into other shapes to find the area.
The octagon shown in the figure is a composite figure as it's composed of other shapes. In the octagon, let's break it up into:
4 triangles (corners)3 rectangles (one in the middle, two on top after you remove triangles)Formulas:
Area of rectangle with length [tex]l[/tex] and width [tex]w[/tex]: [tex]A=lw[/tex] Area of triangle with base [tex]b[/tex] and height [tex]h[/tex]: [tex]A=\frac{1}{2}bh[/tex]Area of triangles:
All four triangles we broke the octagon into are congruent. Each has a base of 2 and a height of 2.
Thus, the total area of one is [tex]A=\frac{1}{2}\cdot 2\cdot 2=2\text{ square units}[/tex]
The area of all four is then [tex]2\cdot 4=8[/tex] units squared.
Area of rectangles:
The two smaller rectangles are also congruent. Each has a length of 3 and a width of 2. Therefore, each of them have an area of [tex]3\cdot 2=6[/tex] units squared, and the both of them have a total area of [tex]6\cdot 2=12[/tex] units squared.
The last rectangle has a width of 7 and a height of 3 for a total area of [tex]7\cdot 3=21[/tex] units squared.
Therefore, the area of the entire octagon is [tex]8+12+21=\boxed{41\text{ [units squared]}}[/tex]
Tourism is extremely important to the economy of Florida. Hotel occupancy is an often-reported measure of visitor volume and visitor activity (Orlando Sentinel, May , ). Hotel occupancy data for February in two consecutive years are as follows. Current Year Previous Year Occupied Rooms 1,400 1,309 Total Rooms 1,750 1,700 a. Formulate the hypothesis test that can be used to determine whether there has been an increase in the proportion of rooms occupied over the one-year period. Let population proportion of rooms occupied for current year population proportion of rooms occupied for previous year - Select your answer - - Select your answer - b. What is the estimated proportion of hotel rooms occupied each year (to decimals)
Answer:
H1 : P1 - P2 = 0
H1 : P1 - P2 > 0
Step-by-step explanation:
The test to be performed on the given data is ; difference in proportion ;
P1 = proportion od rooms in current year
P2 = proportion of rooms
The null hypothesis ``, H0 : p1 - p2 (this onstage null hypothesis and it is the initial truth, representing the notion that no difference in proportion exists.
H1 : P1 - P2 = 0
The alternative hypothesis takes takes the side that there is an increase on proportion of rooms occupied :
H1 : P1 - P2 > 0
Name the following segment or point.
Given:
L, M, N are midpoints
orthocenter of triangle ABC
Answer:
P
Step-by-step explanation:
It's where the altitudes meet
PLEEEASEEEE HEEELPPP!!!
Answer: About 72%
Step-by-step explanation:
It's a conditional probability.
(Number of graduates on financial aid)/(Number of graduates)
[tex]\frac{1879}{2610} =0.7199[/tex]
0.7199 = 71.99% ≈ 72%
giving brainiest Elinor solved this problem. Is her answer correct?
8.93 times 0.15 = 4465. 4465 + 8930 = 13.395
No, Elinor should have placed the decimal point between the 1 and the 3.
No, she should have placed the decimal point between the 3 and the 9.
No, she did not align the place values in the partial products correctly.
Yes. Elinor did not make an error. giving Branniest
Answer:
its a
Step-by-step explanation:
trust did test
suppose △abc≅△xyz. what is the corresponding congruent part for each segment or angle?
Answer:
See below
Step-by-step explanation:
Hi there!
We're given that ΔABC≅ΔXYZ
When two triangles are congruent, their corresponding parts are congruent
Because of that, it means vertex A in ΔABC is congruent to vertex X in ΔXYZ, vertex B is congruent to vertex Y, and vertex C is congruent to vertex Z
Since we don't have a picture of the triangles given, we can use the names of the triangles to find the corresponding parts
so, to find the corresponding congruent angle to <BCA:
B is the first letter in the angle, and the corresponding letter in ΔXYZ is Y.
C is the second letter in the angle, and the corresponding letter is Z.
A is the last letter in the angle, and the corresponding letter is X
so that means <YZX is congruent to <BCA
now let's do the same for <ZYX
Z is the first letter in the angle, and the corresponding letter that's in the same place in ΔABC is C
Y is the second letter in the angle, and the corresponding letter is B
X is the last letter in the angle, and the corresponding letter is A
So that means <CBA is congruent to <ZYX
Now to find corresponding sides:
We can still use the names of the triangles, ΔABC and ΔXYZ
so to find the corresponding side to AB,
in ΔABC, AB makes up the first and second letter of the name of the triangle
The corresponding side must also make up the first and second letter of the name of the triangle
in ΔXYZ, the letters X and Y make up the first and second letter
so that means XY must be corresponding to AB
finally,
we need to find the segment congruent to YZ
in ΔXYZ, YZ makes up the second and third letter of the name of the triangle
the corresponding side must also make up the second and third letter of the name of the triangle
in ΔABC, the letters B and C make up the second and third letter in the triangle
So that means BC must be congruent to YZ
Hope this helps!
Can someone help please ??
Answer:
x=40
Step-by-step explanation:
In the picture, it seems that angles BHC, CHD, and DHE form a line, 180 degrees. So to solve, set up an equation:
[tex](2x+5)+55+40=180[/tex]
Take off the parentheses and solve.
Subtract 5, 55 and 40 from both sides, or add them together, then subtract.
5+55+40=100
You get:
[tex]2x=80[/tex]
Divide both sides by 2
You get:
[tex][x=40][/tex]I hope this helps!
Which of the following is equivalent to the expression log2a=r? 2a = r logr2 = a 2r = a log2r = a
9514 1404 393
Answer:
(c) 2^r = a
Step-by-step explanation:
The relationship between log forms and exponential forms is ...
[tex]\log_2(a)=r\ \Leftrightarrow\ 2^r=a[/tex]
__
Additional comment
I find this easier to remember if I think of a logarithm as being an exponent.
Here, the log is r, so that is the exponent of the base, 2.
This equivalence can also help you remember that the rules of logarithms are very similar to the rules of exponents.
Answer: Choice C) [tex]2^r = a[/tex]
This is the same as writing 2^r = a
==========================================================
Explanation:
Assuming that '2' is the base of the log, then we'd go from [tex]\log_2(a) = r[/tex] to [tex]2^r = a[/tex]
In either equation, the 2 is a base of some kind. It's the base of the log and it's the base of the exponent.
The purpose of logs is to invert exponential operations and help isolate the exponent. A useful phrase to help remember this may be: "if the exponent is in the trees, then we need to log it down".
The general rule is that [tex]\log_b(y) = x[/tex] converts to [tex]y = b^x[/tex] and vice versa.
What are the solutions of the quadratic equation 49x2 = 9?
A. x = 1/9 and x = -1/9
B. x = 3/7 and x = -3/7
C. x = 3/4 and x = -3/4
D. x = 9/49 and x = -9/49
Brainliest if you explain how. got stumped on this one
Answer:
B
Step-by-step explanation:
49x^2=9
solve for x
x^2= 9/49
x=± [tex]\sqrt{9/49\\}[/tex]
which is x = ±3/7 (B)
Answer: b x=1/9 and x=-1/9
Step-by-step explanation:
What are the slope and the y-intercept of the linear function that is represented by the graph?
Answer:
The slope is -3/4 because it rises goes down 3 and runs 4. the Y-intercept or where the line meets the y line is 3.
a Given: △CDE, DK ⊥ CE ,CD=DE Area of △CDE = 29cm2 m∠CDE=31° Find: DK
Answer:
DK = 10.23 units (approx)
Step-by-step explanation:
(DK * (CK + KE))/2 = 29
DK * CK = 29
180 - 31 = 149
149/2 = 74.5 --> degree of other angles
tan 74.5 = DK/CK
CK * tan 74.5 = DK
CK * CK * tan 74.5 = 29
CK = 2.83591462
2.83591462 * tan 74.5 = DK
DK = 10.22597776
So DK is approximately 10.23 units.
Hope this helps!