Answer: x = 3
Step-by-step explanation:
From the question,
5x² – 18 = 27
Collect the like terms
5x² = 27 + 18
5x² = 45
We can th n divide both side by 5 which is the coefficient of x²
5x²/5 = 45/5
x² = 9
To get the value of x, we find the square root of 9
x² = 9
x =✓9
x = 3
The value of x is 3
If x = a cosθ and y = b sinθ , find second derivative
I'm guessing the second derivative is for y with respect to x, i.e.
[tex]\dfrac{\mathrm d^2y}{\mathrm dx^2}[/tex]
Compute the first derivative. By the chain rule,
[tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\mathrm dy}{\mathrm d\theta}\dfrac{\mathrm d\theta}{\mathrm dx}=\dfrac{\frac{\mathrm dy}{\mathrm d\theta}}{\frac{\mathrm dx}{\mathrm d\theta}}[/tex]
We have
[tex]y=b\sin\theta\implies\dfrac{\mathrm dy}{\mathrm d\theta}=b\cos\theta[/tex]
[tex]x=a\cos\theta\implies\dfrac{\mathrm dx}{\mathrm d\theta}=-a\sin\theta[/tex]
and so
[tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{b\cos\theta}{-a\sin\theta}=-\dfrac ba\cot\theta[/tex]
Now compute the second derivative. Notice that [tex]\frac{\mathrm dy}{\mathrm dx}[/tex] is a function of [tex]\theta[/tex]; so denote it by [tex]f(\theta)[/tex]. Then
[tex]\dfrac{\mathrm d^2y}{\mathrm dx^2}=\dfrac{\mathrm df}{\mathrm dx}[/tex]
By the chain rule,
[tex]\dfrac{\mathrm d^2y}{\mathrm dx^2}=\dfrac{\mathrm df}{\mathrm d\theta}\dfrac{\mathrm d\theta}{\mathrm dx}=\dfrac{\frac{\mathrm df}{\mathrm d\theta}}{\frac{\mathrm dx}{\mathrm d\theta}}[/tex]
We have
[tex]f=-\dfrac ba\cot\theta\implies\dfrac{\mathrm df}{\mathrm d\theta}=\dfrac ba\csc^2\theta[/tex]
and so the second derivative is
[tex]\dfrac{\mathrm d^2y}{\mathrm dx^2}=\dfrac{\frac ba\csc^2\theta}{-a\sin\theta}=-\dfrac b{a^2}\csc^3\theta[/tex]
What are the answers to these questions
Answer:
135°
Step-by-step explanation:
You want QRT. So if you look at it you have a straight line, which equals 180°. you already have an angle at 45° so all you do is 180-45 and that equals 135°
help fast please who ever answer correct i will rate them excellent,
which is the correct answer
1) 4x - 7 = 13 *
5
4
3
2
2) 3x + 4 = 25 *
5
4
3
7
3) p/3 +5 =9 *
13
12
10
11
4) m/5 + 2 = 12/5 *
0
1
2
3
5) 4z/5 - 2 =6 *
9
10
11
12
who ever answer correct i will rate them excellent
1. x =5
2. x = 7
3. p = 12
4. m=2
5. z = 10
Answer:
Below in bold.
Step-by-step explanation:
1) 4x - 7 = 13
4x = 20
x = 20/4
x = 5.
2) 3x + 4 = 25
3x = 21
x = 7.
3) p/3 + 5 = 9
p/3 = 9 -5 = 4
Multiply both sides by 3:
p = 3*4
p = 12.
4) m/5 + 2 = 12/5
Multiply through by 5:
m + 10 = 12
m = 12 -10
m = 2.
5) 4z/5 - 2 = 6
4z/5 = 8
Cross multiply:
4z = 5*8
4z = 40
z = 10.
The cost of a large pizza is $10.99. Each additional topping costs $1.25. Write an expression that can be used to find the cost of a pizza when x toppings are included
Answer: 10.99 + 1.25x
Step-by-step explanation:
The cost of a large pizza is $10.99 and each additional topping costs $1.25. The expression that can be used to calculate the cost of a pizza when x toppings are added will be:
Cost of pizza + (number of additional toppings × 1.25)
Since x toppings are included, this will be:
= 10.99 + (1.25 × x)
= 10.99 + 1.25x
A data set has the following six data points: 11, 3, x, x+2, 5, 10. If the median if this data set is 7, then what is the possible value of x?
Answer:
x=6
Step-by-step explanation:
The median is also the number that is halfway into the set. To find the median, the data should be arranged in order from least to greatest. If there is an even number of items in the data set, then the median is found by taking the mean (average) of the two middlemost numbers11, 3, x, x+2, 5, 10
in ascending order the data points:
3, 5, 10, 11, x, x+2, then median >7x, x+2, 3, 5, 10, 11 then median <73, 5, x, x+2, 10, 11 then median is (x+x+2)/2=7 ⇒ x+1=7 ⇒ x=6A=4x/t-p make x the subject
Answer:
x = (A t)/4 + (p t)/4
Step-by-step explanation:
Solve for x:
A = (4 x)/t - p
A = (4 x)/t - p is equivalent to (4 x)/t - p = A:
(4 x)/t - p = A
Add p to both sides:
(4 x)/t = A + p
Multiply both sides by t/4:
Answer: x = (A t)/4 + (p t)/4
Factor the expression completely. 1/4 +11/4
Answer:
3
Step-by-step explanation:
1/4 +11/4
(1+11)/4
12/4
3
Answer:
=3
Step-by-step explanation:
The correct answer to this question is =3. I added the steps down below. I also added a attachment that refer to a number line for this question.
1: =1/4+11/4
2: =1+11/4
3: 12/4
4: =3
Answer: =3
Number line attached.
Hope this helps.
At a store, customers are randomly selected to participate in a survey. On Friday, there were 500 customers at the store. Of those, 90 were selected to participate in the survey. On Saturday, the store manager expects 700 customers in the store. If the probability of being selected to participate in the survey on Saturday is the same as it was on Friday, how many customers will be selected to participate in the survey on Saturday? ______ customers on Saturday (Write the number only***)
Answer:
126
Step-by-step explanation:
The probability is 90/500 = 18%
So, from 700 customers,
700 * 18% = 700 * 18/100 = 126
Therefore, 126 customers will be selected on saturday.
A customer at a restaurant can choose a soup and a salad from the menu choices shown.
Which sample space represents all the possible ways to choose one soup and one salad?
OG, OC, OT, OV, TG, TC, TV, VG, VC, GC
OG, TC, VC
Soup
Salads
Onion (O) Garden (G)
Tomato (U) Chopped (C)
Vegetable (V)
OG, OC, TG, TC, VG, VC
OG, OC, TG, TC, VC
Answer:
OG, OC, TG, TC, VG, VC
Step-by-step explanation:
Soups: O, T, V
Salads: G, C
For each soup, he can choose 2 salads.
OG, OC, TG, TC, VG, VC
The sample space represents all the possible ways to choose one soup and one salad is {OG, OC, TG, TC, VG, VC}.
What is sample space?Sample space is the set of all the possible values or the outcomes of a event.
Let suppose the coin are tossed two times. Then the set of possible outcome or sample space of it can be given as,
[tex]S=\{HH,HT,TH,TT\}[/tex]
Here, H denotes the head and T denotes the tail part of the coin.
A customer at a restaurant can choose a soup and a salad from the menu choices shown.
Soup SaladsOnion (O) Garden (G)Tomato (T) Chopped (C)Vegetable (V)For this menu the customer choose one onion as soup and one garden as salad which can be represented as (OG). Similarly, the sample space of his choice can be,
[tex]\{OG, OC, TG, TC, VG, VC\}[/tex]
Thus, the sample space represents all the possible ways to choose one soup and one salad is {OG, OC, TG, TC, VG, VC}.
Learn more about the sample space here;
https://brainly.com/question/9222927
#SPJ2
7. What fraction of a clockwise revolution does the hour hand of a clock turn through, when it goes
from
(a) 6 to 12
(b) 5 to 8
hi there if you are there
please reply it is a very urgent assignment that I have to send it by today .
Several batches of stew were made yesterday. Each batch required 1 and two-thirds pounds of meat. All together, 10 and StartFraction 5 over 6 EndFraction pounds of meat was used. Janice tried to find the number of batches of stew made. Her work is shown below. 10 and StartFraction 5 over 6 EndFraction divided by 1 and two-thirds = StartFraction 65 over 6 EndFraction divided by five halves = StartFraction 65 over 6 EndFraction times StartFraction 2 over 5 EndFraction = StartFraction 130 over 30 EndFraction = 4 and one-third When she checked the answer by estimating, it did not make sense. What error did Janice make? Janice converted a mixed number to the wrong improper fraction. Janice added the numerators and denominators instead of multiplying. Janice did not change the division problem to multiplication. Janice did not convert the improper fraction to a mixed number correctly in the answer.
Answer:
Janice converted a mixed number to the wrong improper fraction.
Step-by-step explanation:
1 batch of stew uses 1 and 2/3 lb meat
Total amount of meat used - 10 and 5/6 lb
x = number of stew batches made
To get number of batches made, divide total meat used by the amount of meat each batch requires:
x = 10 5/6 ÷ 1 2/3
convert mixed fractions to improper fractions:
x = (10x6+5)/6 ÷ (1x3+2)/3
x = 65/6 ÷ 5/3
The fraction in bold numbers is where Janice got it wrong. She changed 1 2/3 to 5/2. (From the question: 10 and StartFraction 5 over 6 EndFraction divided by 1 and two-thirds = StartFraction 65 over 6 EndFraction divided by five halves). 1 2/3 converted to an improper fraction is 5/3. From this point going forward, the calculations are wrong.
Answer:
A
Step-by-step explanation:
What is the number of sides of a regular polygon whose exterior and interior angles are in the ratio 1:5?
Answer:
12
Step-by-step explanation:
n*30=360
n=360/30
n=12
A man has three white shirts,two blue shirts abd five red shirts.He picks one at random.What is the probability of white.Show workings
Answer: 30% or 3/10.
Step-by-step explanation: To find the probablilty of getting a white shirt, we first have to find the total number of shirts: 3 white + 2 blue + 5 red = 10 total. Out of the ten total, there are 3 white shirts. The probability of getting a white shirt is 3/10, because out of the 10 total shirts, 3 shirts are white.
Answer:
3/10Step-by-step explanation:
[tex]Probability = \frac{Events}{Possible- outcomes} \\Total -no -of -shirts=3+2+5=10\\Event = 3 \\Probability = \frac{3}{10}[/tex]
I hope i am correct
Find the volume of the pyramid below.
Answer: 400 units
Step-by-step explanation:
Volume=1/3a^2h
=1/3(10)^2(12)
=400
The correct answer is 400. I had the same question on a test I took not to long ago.
can anyone help me solve this using exponent rules
(5x4y3)(-2x5y)
Answer:
[tex]-10x^9y^4[/tex]
Step-by-step explanation:
Answer:
-10x9y4
Step-by-step explanation:
When multiplying exponents it's like adding nothing serious. Hope this helps! Plz mark brainliest!!
Can anyone please help me it’s only one question please help me
Answer:
A =7.02 m^2
Step-by-step explanation:
The area of a trapezoid is given by
A = 1/2 (b1+b2)*h where b1 and b2 are the lengths of the bases
A = 1/2 ( 4.5+6.3) * 1.3
A = 1/2(10.8) * 1.3
A =7.02 m^2
calculate the number in the middle of -8 and 31
Step-by-step explanation:
do you mean --8 plus 31
How to find the length when the perimeter and width is given
Answer:
You divide the perimeter by the width to get the length
Step-by-step explanation:
2x+y=5
x - y = 4
Please answer this wuestion
Answer:
x=9
y=5
Step-by-step explanation:
The measure of angle 3 is 42°.
What is the measure of angle 1 in degrees?
Answer:
<1 = 48
Step-by-step explanation:
<1 + <2 + <3 = 180 since they form a line
<1 + 90+ 42 =180
Combine like terms
<1 + 132 =180
Subtract 132 from each side
<1 +132-132 =180-132
<1 = 48
Answer:
48 is the answer
Step-by-step explanation:
I need help on this question
Answer:
x=4
Step-by-step explanation:
Solve the simultaneous equations
3a+2b+1
a+2b=5
a=
b=
Answer: a=-2, b=7/2
Step-by-step explanation:
To solve for a and b, we can use the elimination method for these system of equations.
3a+2b=1
a+2b=5
Since there is a 2b in both equations, we can subtrac the 2 equations.
2a=-4
a=-2
Now that we have found a, we can plug it into ay of the equations to find b.
-2+2b=5
2b=7
b=7/2
slove for x.
3x+15=56
Answer:
13.7
Step-by-step explanation:
3x=41
x is around 13.7
Answer:
x = [tex]\frac{41}{3}[/tex]
x ≈ 13.7
Step-by-step explanation:
[tex]3x+15=56\\3x+15-15=56-15\leftarrow \text {Subtraction Property of Equality} \\3x=41\\\\\frac{3x}{3} =\frac{41}{3} \leftarrow \text {Division Property of Equality}\\\\\boxed {x=\frac{41}{3}}[/tex]
41/3 = 13.66666666....
13.666... ≈ 13.7
Been stuck on this for a while
Answer:
-x^3 -3x+2
Step-by-step explanation:
f(x) = -3x +2
g(x) = x^3
(f-g)(x) = -3x +2 - x^3
= -x^3 -3x+2
Here's a graph of a linear function. Write the
equation that describes that function.
Express it in slope-intercept form. .
Enter the corror answer
Answer:
Y=1/2x-3
Step-by-step explanation:
Down 3 at the y-axis and up 1 right 2.
There are between 24 and 40 students in a class,
The ratio of boys to girls is 4:7
How many students are in the class?
Answer:
There are 33 students
Step-by-step explanation:
Because 7:4 should be in multiple of 11
Triangle ABC is located at A (−2, 2), B (−2, 4), and C (0, 0). The triangle is then transformed using the rule (x+3, y− 2) to form the image A'B'C'. What are the new coordinates of A', B', and C'?
Answer:
In this problem, we have three vertices, namely:
A(-2,2) , B(-2,4) , C(0,0)
Our transformation rule is (x+3,y-2) and this rule forms the image A'B'C'. So:
Step-by-step explanation:
A'=(-2+3,2-2)=(1,0)
B'=(-2+3,4-2)=(1,2)
C'=(0+3,0-2)=(3,-2)
Taking a look in the First Figure, we can see the two triangles. The red one is the triangle ABC and the blue one is A'B'C'. In the Second Figure, the corresponding vertices have been connected with line segments, as indicated the green lines. The characteristics of those three lines are two, namely:
They are parallel.
They have the same length.
please help with question below thank you
Answer:
44/51
Step-by-step explanation:
1 5/6 ÷ 2 1/8
Change to improper fractions
1 5/6 = (6*1+5)/6 = 11/6
2 1/8 = (8*2 +1) /8 = 17/8
11/6 ÷17/8
Copy dot flip
11/6 * 8/17
11/17 * 8/6
11/17 *4/3
44/51
Five times a number is divided by 7 more than the number. If the result is 2 then what was the original number?
the number=A
5xA/7+A=2
5A/7 +A =2
5A/7=2-A/1
7(2-A)=1(5A)
14-7A=5A
14=5A+7A
14/12=12A/12
A=14/12
A=7/6
What is the slope of the linear represents by the equation y = 4/5 x -3
Answer:
4/5
Step-by-step explanation:
y = mx + b
4/5 = m = slope
Answer:
The slope is 4/5.
Step-by-step explanation:
It's a linear equation. Which means that you can graph a "line" out of it.
The format is y=mx+b
mx=slope
b= y-intercept.
The slope is 4/5.
