Answer:
x^2-6x+9
Step-by-step explanation:
for f=x^2 subsititude x with g(x) = x-3 in which will give you (x-3)^2 using the perfect square formula ((a-b)^2=a^2-2ab+b^2) in which a=x, b=3. you shall then get x^2 -2x · 3 + 3^2 to get x^2-6x+9
In countries that use the metric system of measurement, corn yields are sometimes expressed in quintals per hectare (q/ha) instead of bushels per acre (bu/ac). 1 quintal = 220.462 lbs 1 bushel of corn = 56 lbs In field trials in one of these countries, a particular corn hybrid yielded 151 q/ha. What is this in bushels per acre (bu/ac)? Margin of Error: +/- 1 bu/ac
Answer:
The answer is below
Step-by-step explanation:
Different countries have different metric system of measurement, but the metric system of measurement accepted all over the world is the international system of unit (SI unit)
1 quintal = 220.462 lbs and 1 bushel of corn = 56 lbs.
151 q/ha = (151 × 220.462) lbs/ha = 33289.762 lbs/ha
But 1 hectare = 2.471 acre, hence:
33289.762 lbs/ha = [tex]\frac{33289.762\ lbs}{1\ ha*\frac{2.471\ acre}{1 \ ha} } =13472.182\ lbs/acre[/tex]
Since 1 bushel of corn = 56 lbs, hence:
[tex]13472.182\ lbs/acre=\frac{13472.182\ lbs*\frac{1\ bushels}{56\ lbs} }{acre}=240.6\ bushels/acre[/tex] = 240.6 bu/ac
For a Margin of Error: +/- 1 bu/ac, the bushels per acre = (239.6 bu/ac, 241.6 bu/ac)
At 5pm the total rainfall is 3cm. At 11 pm the total rainfall is 13cm.What is the mean hourly rainfall?
Answer:
2.16 cm
Step-by-step explanation:
5 through 11 = 6 hours
total of cms = 13
13/6 = 2.16
Find the gradient of the straight line joining (1, 2 + 4p) to (1 – 2p, 2).
Answer:
2
Step-by-step explanation:
The gradient of the straight line is equal to (y2-y1)/(x2-x1), where
(x1,y1) and (x2,y2) coordinates of the points A and B which belong to the line.
So y2=2 ,x2=1-2p , y1=2+4p, x1=1
k=(2-(2+4p))/((1-2p)-1)= (2-2-4p)/(1-2p-1)= (-4p)/(-2p)=2
The gradient of the straight line joining (1, 2+4p) to (1-2p, 2) is 2 and this can be determined by using the two-point slope formula.
Given :
Points -- (1,2+4p) and (1-2p,2)
The following steps can be used in order to determine the gradient of the straight line joining (1, 2+4p) to (1-2p, 2):
Step 1 - According to the given data, the points on the straight line are (1, 2+4p) to (1-2p, 2).
Step 2 - The two-point slope formula can be used in order to determine the gradient of the straight line joining (1, 2+4p) to (1-2p, 2).
Step 3 - The two-point slope formula is given below:
[tex]\rm m = \dfrac{y_2-y_1}{x_2-x_1}[/tex]
Step 4 - Substitute the values of [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] in the above expression.
[tex]\rm m = \dfrac{2-(2+4p)}{1-2p-1}[/tex]
Step 5 - Simplify the above expression.
[tex]\rm m = \dfrac{-4p}{-2p}[/tex]
m = 2
For more information, refer to the link given below:
https://brainly.com/question/3605446
The length of a rectangle is 99 meters and the width is 87 meters. Find the area. Give your answer without units.
Answer:
Area = 8613Step-by-step explanation:
Area of a rectangle = l × w
where
l is the length
w is the width
From the question
length = 99 m
width = 87 m
Substitute the values into the above formula and solve for the area
That's
Area = 99 × 87
We have the final answer as
Area = 8613
Hope this helps you
3.a. Use the distributive property to rewrite the equation.
Enter the new equation as your answer.
3(2x - 1) + 4 = 7
Enter your answer
4.b. Combine any like terms to rewrite the equation that you entered as an answer in part a.
Enter the new equation as your answer.
Enter your answer
5.c. Use addition or subtraction to rewrite the equation that you entered as an answer in part b.
Enter the new equation as your answer.
Enter your answer
6.d. Use multiplication or division to rewrite the equation that you entered as an answer in part c.
Enter the new equation as your answer.
Answer:
Hey there!
Part A
3(2x-1)+4=7
6x-3+4=7
Part B
6x+1=7
Part C.
6x+1-1=7-1
6x=6
Part D.
6x/6=6/6
x=1
Let me know if this helps :)
Answer:
3. 6x -3 +4 = 7
4. 6x +1 = 7
5. 6x = 6
6. x = 1
Step-by-step explanation:
3. The distributive property allows you to eliminate parentheses by multiplying the outside factor by every term inside.
3(2x -1) +4 = 7 . . . . . . given
3(2x) +3(-1) +4 = 7 . . . . using the distributive property
6x -3 +4 = 7 . . . . . . . finishing the evaluation of those products
__
4. The only like terms that can be combined are the two constant terms on the left side. We simply add them up.
6x +1 = 7
__
5. Using the subtraction property of equality, we can subtract 1 from both sides of the equation. We choose to do this so that the x-term is by itself.
6x +1 -1 = 7 -1
6x = 6
__
6. Using the division property of equality, we can divide both sides of the equation by 6. We choose to do this so the new coefficient of x is 1.
6x/6 = 6/6
x = 1
______
Additional comment
You're told to apply these steps without any explanation as to why or what the goal may be. We assume you're supposed to realize that you can use these steps to solve the equation. Of course, you can use different values for addition (or subtraction) or multiplication (or division). Doing so may satisfy the literal interpretation of the question, but won't get you a solution to the equation.
Round the given number to the nearest tenth. 560.294
Answer:
560.3
hope it helps
Solve s=2b+lw for l. Show all work
Answer:
l = (2b-s)/w
Step-by-step explanation:
s=2b+lw
s-2b=lw
(s-2b)/w= l
Explain the difference between observed frequency and expected frequency as it relates to Chi-Square test.
Answer:
Step-by-step explanation:
A Chi-square test is used to test the test of independence between rows and columns, contingency tables. It is a test related to frequencies. The observed frequency is a given statistical frequency known as the actual frequency, the expected frequency is known as the theoretical frequency is derived from the study by using the sum total of the row and total in the column divided by their corresponding sample size.
find the area of the given triangle a = 19, c= 14, B=60°. Round your answer to the nearest tenth.
Answer: 115.2 units²
Step-by-step explanation:
Since you know the length of two sides and the measure of the included angle, you can use the following trig formula:
[tex]Area=\dfrac{1}{2}ac \sin B[/tex]
Given: a = 19, c = 14, B = 60°
[tex]A=\dfrac{1}{2}(19)(14) \sin 60^o\\\\.\quad =133\sin 60^o\\\\.\quad =115.2[/tex]
Answer:
[tex]\huge \boxed{\mathrm{115.2 \ units^2 }}[/tex]
Step-by-step explanation:
We can solve for the area of the triangle when two sides are given and the angle in between the two sides.
[tex]\displaystyle A=\mathrm{\frac{1}{2}ac \cdot sinB }[/tex]
[tex]\displaystyle A=\mathrm{\frac{1}{2} \cdot 19 \cdot 14 \cdot sin60 }[/tex]
[tex]\displaystyle A=\mathrm{\frac{133\sqrt{3} }{2} }[/tex]
[tex]\displaystyle A=\mathrm{115.18137870...}[/tex]
The area of the triangle is 115.2 units².
Find the radius and the center of the circle with the given equation x2+y2−6x−8y−30=0.
Answer:
Center is (3,4)
Radius is √55 which is approximately 7.42
Step-by-step explanation:
First, recall the equation for a circle. The equation for a circle is given by:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Where (h,k) is the center and r is the radius.
We have the equation:
[tex]x^2+y^2-6x-8y-30=0[/tex]
Thus, we want to turn this into the circle equation.
To do so, we need to complete the square.
First, put all the x-terms together and all the y-terms together. Also, add 30 to both sides:
[tex](x^2-6x)+(y^2-8y)-30=0\\(x^2-6x)+(y^2-8y)=30[/tex]
Now, complete the square for both of the variables. Recall how to complete the square. If we have:
[tex]x^2+bx[/tex]
We divide b by 2 and then square it. Then we will have a perfect square trinomial. To keep things balanced, we must also subtract what we added.
Thus, for the first term:
[tex](x^2-6x)\\=(x^2-6x+9)-9\\(x-3)^2-9[/tex]
And for the second term:
[tex](y^2-8y)\\=(y^2-8y+16)-16\\=(y-4)^2-16[/tex]
Replace the two terms:
[tex]((x-3)^2-9)+((y-4)^2-16)=30[/tex]
Simplify. Add -9 and -16:
[tex](x-3)^2+(y-4)^2-25=30[/tex]
Add 25 to both sides:
[tex](x-3)^2+(y-4)^2=55[/tex]
This is now in the form of the circle equation.
Thus, the center is (3,4).
And the radius is √55 which is approximately 7.42
Answer:
to be honest I'm not sure
Use the Pythagorean Theorem to find the length of the leg in the triangle shown below. The figure shows a right triangle with one leg marked 15. The hypotenuse is marked 39.
Answer:
36
Step-by-step explanation:
you would just to 39^2-15^2 which is 1296 and the square root of that is 36 so 36 would be the answer
Which ordered pair is a solution bf 2x = y? . (-1,-2) (-1,-1) (1,1) (1.-1)
Answer:
(-1,-2)
Step-by-step explanation:
Ordered pairs go in the order x,y so the 2x would be the first number that then equals the second number. The answer is (-1,-2) because when you multiply 2*-1 you get -2 and what's the y? -2. Does -2 = -2? Yes.
The function D ( p ) D(p) gives the number of items that will be demanded when the price is p. The production cost, C ( x ) C(x) is the cost of producing x items. To determine the cost of production when the price is $5, you would:
A. Solve C(D(p)) = 7 for p
B. Evaluate D(C(7))
C. Evaluate C(D(7))
D. Solve D(C(x)) = 7 for x
Answer:
[tex]C(D(5))[/tex]
Step-by-step explanation:
Given:
D(p): Items demanded when price is P
C(x): Production cost of x items
Required
Cost of producing when price is $5
First, we need to get the number of items demanded;
To do this, we substitute 5 for P in D(p)
This gives;
[tex]D(5)[/tex]
Next, we determine the production cost;
To do this, we substitute D(5) for x in C(x)
This gives;
[tex]C(D(5))[/tex]
None of the listed options answer the question
Given: Point K is between points H and J, HK = x − 5, KJ = 5x − 12, and HJ = 25. Find the value o
Answer:
[tex]\huge\boxed{\sf x = 7}[/tex]
Step-by-step explanation:
According to the given statement
HJ = HK + KJ
Given that HJ = 25 , HK = x - 5 and KJ = 5x-12
[tex]\sf 25 = x-5+5x-12[/tex]
Adding like terms
[tex]\sf 25 = 6x-17\\Adding \ 17\ to\ both\ sides\\25 + 17 = 6x\\42 = 6x\\Dividing \ both \ sides \ by \ 6\\7 = x\\OR\\x = 7[/tex]
Which of the following statements says that a number is between -3 and 3? A. |x|< 3 B. |x| =3 C. |x| >3
Answer:
A
Step-by-step explanation:
|x|< 3 translates to
x < 3 AND -x < 3
which simplifies to
x < 3 AND x > -3
so, yes, -3 < x < 3
find the area of the triangle given a = 14, c=21, and B=87°. Round your answer to the nearest tenth.
Answer: 143.8 units²
Step-by-step explanation:
Since you know the length of two sides and the measure of the included angle, you can use the following trig formula:
[tex]Area=\dfrac{1}{2}ac \sin B[/tex]
Given: a = 14, c = 21, B = 87°
[tex]Area=\dfrac{1}{2}(14)(21) \sin 87^o\\\\.\qquad =147\sin 87^o\\\\.\qquad =143.8[/tex]
Answer:
[tex]\huge \boxed{\mathrm{146.8 \ units^2 }}[/tex]
Step-by-step explanation:
We can solve for the area of the triangle when two sides are given and the angle in between the two sides.
[tex]\displaystyle A=\mathrm{\frac{1}{2}ac \cdot sinB }[/tex]
[tex]\displaystyle A=\mathrm{\frac{1}{2} \cdot 14 \cdot 21 \cdot sin87 }[/tex]
[tex]\displaystyle A=\mathrm{147 \cdot sin87 }[/tex]
[tex]\displaystyle A=\mathrm{146.79854160...}[/tex]
The area of the triangle is 146.8 units².
Which of the following fractions converts to a terminating decimal greater than one?
A. 4/3
B.7/2
C. 1/4
D.13/11
Answer:
B.7/2
Step-by-step explanation:
4/3 = 1.3333...
The number is greater than one, but it is NOT a terminating decimal.
7/2 = 3.5
The number is greater than one and terminating.
1/4 = 0.25
The number is terminating but less than one.
13/11 = 1.181818...
The number is greater than one, but it is NOT a terminating decimal.
Option B is the correct answer.
Hope this helps.
Considering that a fraction is a division, the correct option is:
B.7/2
---------------------------------
To convert the fraction to decimal, we divide the numerator by the denominator.
---------------------------------
Option A:
[tex]\frac{4}{3} = 1.333333....[/tex]
Greater than one, but non-terminating.
---------------------------------
Option B:
[tex]\frac{7}{2} = 3.5[/tex]
Greater than one and terminating, thus this is the correct option.
---------------------------------
Option C:
Denominator greater than the numerator, thus less than one.
---------------------------------
Option D:
[tex]\frac{13}{11} = 1.1818181818....[/tex]
Greater than one, but non-terminating.
A similar problem is given at https://brainly.com/question/17772407
Write down at least five number
pairs to solve the equation
(r - 2)(s + 1) = 100.
Answer:
(52,1)
(4,49)
(27,3)
(6,24)
(7,19)
(22,4)
key: (r,s)
.3% of what number is 4.8?
Answer:
1600
Step-by-step explanation:
0.3% of 1600 will result to 4.8
PLS HELP ASAP NEED ANSWER NOW FOR TIMED WORK!
Answer: A
Step-by-step explanation:
Since we know that T is the midpoint of SU, we know that it bisects SU. Now, we know that it cuts SU in half. With that, we know that ST and TU are equal.
3x=2x+20 [subtract both sides by 2x]
x=20
Now that we know x, we can plug them in to solve for each segment.
ST
3x [plug in x=20]
3(20) [multiply]
60
----------------------------------------------------------------------------------------------------------
TU
2x+20 [plug in x=20]
2(20)+20 [multiply]
40+20 [add]
60
----------------------------------------------------------------------------------------------------------
SU
60+60=120
We know that SU is ST and TU combines, therefore, we add the values of ST and TU.
Two teaching methods and their effects on science test scores are being reviewed. A random sample of 18 students, taught in traditional lab sessions, had a mean test score of 78.3 with a standard deviation of 6.4 . A random sample of 11 students, taught using interactive simulation software, had a mean test score of 84.3 with a standard deviation of 5.3 . Do these results support the claim that the mean science test score is lower for students taught in traditional lab sessions than it is for students taught using interactive simulation software? Let μ 1 be the mean test score for the students taught in traditional lab sessions and μ 2 be the mean test score for students taught using interactive simulation software. Use a significance level of α=0.1 for the test. Assume that the population variances are equal and that the two populations are normally distributed.
Step 2 of 4 :
Compute the value of the t test statistic. Round your answer to three decimal places.
Answer:
the value of the t test statistic is - 3.419
Step-by-step explanation:
Given that;
n₁ = 18, u₁ = 78.3, s₁ = 6.4
n₂ = 11, u₂ = 84.3, s₂ = 5.3
α = 0.1
Now The hypothesis are;
H₀ : u₁ = u₂
H₁ : u₁ < u₂
To compute the value of the t test statistic;
t = [(x₁ - x₂) / s × √(1/n₁ + 1/n₂)]
where
s = √ [ ((n₁-1) × s₁² + (n₂ - 1 ) × s₂²) / ( n₁ + n₂ - 2)]
s = √ [ ((18-1) × 6.4² + (11 - 1 ) × 5.3²) / ( 18 + 11 - 2)]
s = √ [ (7 × 40.96 + 10 × 28.09 ) / 27 ]
s = √ [ (286.72 + 280.9) / 27 ]
s = √(567.62/27)
s = √21.0229
s = 4.585
Now t test statistics t = [(x₁ - x₂) / s × √(1/n₁ + 1/n₂)]
t = [(78.3 - 84.3) / 4.585 × √(1/18 + 1/11)]
t = -6 / (4.585 × 0.3827)
t = - 6 / 1.7546795
t = - 3.419
Therefore the value of the t test statistic is - 3.419
as as level of significance α = 0.1
df = 18+11-2 = 27
∴ T(csal) = t(0.1, 27) = -1.313
That is
t(statistics) < t(cal)
{ - 3.419 < -1.313 }
Estimate. Then find the difference 300,980 -159,000
Answer:
142,000
Step-by-step explanation:
I would round 300,980 to the nearest thousands place = 301,000
Subtract 301,000 and 159,000 = 142,000
бx - 6 = 24х +6
Help
Answer: [tex]x=-2/3[/tex]
Subtract 24x from both sides
[tex]6x-6-24x=24x+6-24x\\-18x-6=6[/tex]
Add 6 to both sides
[tex]-18x-6+6=6+6\\-18x=12[/tex]
Divide both sides by -18
[tex]-18x/-18=12/-18\\x=-2/3[/tex]
Answer: x=-2/3.
Step-by-step explanation:6x-6 = 24х+6
6x-6-24x=6 -18x-6+6=6+6 -18x/-18=12/-18 x=-2/3
A raffle game has a single gran prize that will be drawn randomly from among all the tickets. A total of 500 tickets are sold. If a man buys 25 tickets, what is the probability that he will win the grand prize?
Step-by-step explanation:
P = 25/500
P = 1/20, or 5%
an angle measures 76° . what is the measure of its supplement
Answer:
The answer is
104°Step-by-step explanation:
Let the measure of it's supplement be x
Supplementary angles sum up to 180° which means the sum of 76° and it's supplement is 180°
To find its supplement add 76° and it's supplement and equate it to 180° to find x
So we have
76 + x = 180
x = 180 - 76
We have the final answer as
x = 104°Hope this helps you
YOU HAVE 30 GALLONS OF GAS AND YOU USE 5 GALLONS ER DAY FOR D DAYS
Answer:
d = 6 days
Step-by-step explanation:
We only have a total of 30 gallons.
We are told that we use 5 gallons per day.
So:
d - days
5d = 30
*Divide both sides by 5*
d = 6
What are the coordinates of the midpoint of a segment AB , if: A(–3, 4), B( 1, 2)
Hi there! :)
Answer:
[tex]\huge\boxed{(-1, 3)}[/tex]
Use the midpoint formula to derive the midpoint of the segment:
[tex](x_{m} ,y_{m}) = (\frac{x_{1}+x_{2} }{2} , \frac{y_{1}+y_{2} }{2} )[/tex]
Substitute in the coordinates:
[tex](x_{m} ,y_{m}) = (\frac{-3+1 }{2} , \frac{4+2 }{2} )[/tex]
Simplify:
[tex](x_{m} ,y_{m}) = (-1 , 3 )[/tex]
The coordinates of the midpoint are:
[tex](-1, 3)[/tex]
Which of the following is the method used to determine whether or not a proportion is
true?
O Inverse operations
O Simplifying
O Prorating
O Cross multiplication
Answer:
Cross multiplication
Step-by-step explanation:
5х – 11 = 3х + 3
Solve for x
Answer:
Hello☺️!
Step-by-step explanation:
[tex]5 x - 11 = 3x + 3[/tex]
[tex]5x - 3x = 3 + 11[/tex]
[tex]2x = 14[/tex]
[tex]x = \frac{14}{2} [/tex]
[tex]x = 7[/tex]
The daily demand for ice cream cones at a price of $1.20 per cone is 50 cones. At a price of $2.20 per cone, the demand is 30 cones. Use linear interpolation to estimate the demand at a price of $1.50 per cone.
Answer:
The demand at a price of $1.50 per cone is 44 conesStep-by-step explanation:
let us apply the interpolation formula to solve this problem
we have
[tex]\frac{y-y1}{x-x1} =\frac{y2-y1}{x2-x1}[/tex]
Now let us set the values to the notation above
x= $1.20
x1= $2.20
x2= $1.50
y = 50 cones
y1= 30 cones
y2= ?
[tex]y2= \frac{(y-y1)}{(x-x1)} (x2-x1)+y1[/tex]
Substituting our given data we have
[tex]y2= \frac{(50-30)}{(1.2-2.2)} (1.5-2.2)+30\\\\y2= \frac{20}{-1} (-0.7)+30\\\\y2= (20*0.7)+30\\y2= 14+30\\y2= 44[/tex]
the demand at a price of $1.50 per cone is 44 cones