Answer:
x^2-x-90=0 x^2-10x+9x-90 x(x-10)+9(x-10)
(x+9)(x-10)=0
Solutions are 0-9=-9 and 0+10=10.
10-9=1= a+b
Step-by-step explanation:
After finding the solutions a and b, The value of a + b is,
⇒ 1
What is Quadratic equation?An algebraic equation with the second degree of the variable is called an Quadratic equation.
We have to given that;
Equation is,
⇒ x² - x - 90 = 0
Now, We can find the factor of the equation as;
⇒ x² - x - 90 = 0
⇒ x² - 10x + 9x - 90 = 0
⇒ x (x - 10) + 9 (x - 10) = 0
⇒ (x + 9) (x - 10) = 0
This gives,
⇒ x - 10 = 0
⇒ x = 10
⇒ x + 9 = 0
⇒ x =- 9
Hence, Value of solutions a + b is,
a + b = 10 + (- 9) = 1
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3.(a) A cylindrical tank for storing oil has a capacity of
1078 cm. If its height and radius are equal, calculate
the depth of oil in the tank when full (Take p = 22/7)
(b) Find the perimeter of a rectangular field which is
10 m by 5 m.
Answer:
a. 7cm
b. 30m
Step-by-step explanation:
b. Formula of perimeter is 2(l + b)
= 2(10 + 5) = 2(15) = 30 m
a. Capacity of the cylinder is 1078 cm^3 but we have equal radius and height
Let’s call the height h which of course is the depth.
The radius is also h too
Using the formula for the volume of a cylinder;
Mathematically we have;
V = pi * r^2 * h
but in this case;
V = pi * h^2 * h
V = pi * h^3
1078 = 22/7 * h^3
h^3 = (1078 * 7)/22
h^3 = 343
h = cube root of 343
h = 7cm
So the depth of the cylindrical tank when full is 7cm
Help!!!!! please!!!!!
Hey there! :)
Answer:
B. The volume of Cylinder B is larger.
Step-by-step explanation:
Find the volumes of each cylinder using the formula V = πr²h:
Cylinder A:
V = π3² · 5
V = 9π · 5
V = 45π units³
Cylinder B:
V = π5²· 3
V = 25π · 3
V = 75π units³
75π u³ > 45π u³, so the volume of Cylinder B is larger.
How do you do this? Please help!
Answer: 7/36
Step-by-step explanation:
As you can see, 7 of the 36 squares are multiples of 5. Also, pls brainliest, this took forever.
A history instructor has given the same pretest and the same final examination each semester. He is interested in determining if there is a relationship between the scores of the two tests. He computes the linear correlation coefficient and notes that it is 1.15. What does this correlation coefficient value tell the instructor?
Answer:
The history instructor has made a computational error.
Step-by-step explanation:
We have that the data represents the linear correlation coefficient and notes it is 1.15
The linear correlation coefficient value which is 1.15 does tell the instructor that the history instructor has made a computational error due to the linear correlation coefficient value falls in the range -1 to +1.
Therefore, the history instructor has made a computational error.
The mean length of 4 childrens' big finger is 14cm. The mean length of 9 adults' big finger is 16.1cm. What is the mean length (rounded to 2 DP) of these 13 people's big finger?
Answer:
The mean length of the 13 people's big finger is 15.45 cm
Step-by-step explanation:
Given;
mean length of 4 childrens' big finger, x' = 14cm
mean length of 9 adults' big finger is 16.1cm, x'' = 16.1cm
Let the total length of the 4 childrens' big finger = t
[tex]x' = \frac{t}{n} \\\\x' = \frac{t}{4}\\\\t = 4x'\\\\t = 4 *14\\\\t = 56 \ cm[/tex]
Let the total length of the 9 adults' big finger = T
[tex]x'' = \frac{T}{N} \\\\x'' = \frac{T}{9}\\\\T = 9x''\\\\T = 9*16.1\\\\T = 144.9 \ cm[/tex]
The total length of the 13 people's big finger = t + T
= 56 + 144.9
=200.9 cm
The mean length of these 13 people's big finger;
x''' = (200.9) / 13
x''' = 15.4539 cm
x''' = 15.45 cm (2 DP)
Therefore, the mean length of the 13 people's big finger is 15.45 cm
I am looking to decrease my bill by 25%. Can you look at my current plan and tell me what I can remove to achieve this reduction in cost? My current bill is $140.00 per month
Answer: $35
Step-by-step explanation:
From the question, we are informed that the current bill of the person is $140.00 per month and that the person wants to decrease the bill by 25%.
To know the amount that the person needs to deduct, we have to calculate 25% of $140.00. This will be:
= 25% of $140
= 25/100 × $140
= 1/4 × $140
= 0.25 × $140
= $35
The person will need to remove $35. The person will now pay ($140 - $35) = $105 monthly.
The amount that could be removed to achieve the specified reduction is $35.00
From the question,
We are to determine what should be removed from the current bill to decrease it by 25%
From the given information,
The current bill = $140.00 per month
Now, we will determine 25% of $140.00
That is,
[tex]\frac{25}{100}\times \$140.00[/tex]
= 25 × $1.40
= $35.00
Hence, the amount that could be removed to achieve the specified reduction is $35.00
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What is the prime factorization of 50?
2x25
2x5
2x5²
Answer:
2x5²
Step-by-step explanation:
[tex]25 = 2 \times 5 \times 5 = 2 \times {5}^{2} \\ [/tex]
Answer:
2x5²
Step-by-step explanation:
Really need helpppp?!
Answer:
6.43
pls follow me and mark brainliest ...thank u
Step-by-step explanation:
length of side x will be
Tan tita = opp/adjacent
tan65 = x/3
tan 65 is 2.14
so...you are left with 2.14=x/3
by cross multiplying
x= 2.14 × 3
= 6.43
Line AB, segment DF, and segment CE are drawn. Segments DF and CE intersect at point Z. Which statement about the diagram is true?
Step-by-step explanation:
A chord is a segment with endpoints on the circle.
A tangent line is a line that touches a circle at only one point.
A diameter is a chord that passes through the center of the circle.
A secant line is a line that touches a circle at two points.
Therefore, AB is a secant line.
The statement related to the diagram is true is that AB is the secant line.
What is a chord, tangent line, diameter, and secant line?A chord should be treated as the segment that contains the endpoints on the circle. A tangent line refers to the line that touches a circle at only one point. A diameter refer to a chord that passes via the center of the circle. A secant line should be a line that touches a circle at two points.
Hence, The statement related to the diagram is true is that AB is the secant line.
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A translation moves A(2,3) onto A′(4,8). If B(4,6), what is the image of B under the same translation?
A. (6,11)
B. (12,18)
C. (6,8)
D. (8,12)
A certain quantity decays exponentially over time. The initial quantity at t = 0 is 1,000. The quantity
decays at a rate of 2%. What is the quantity at t = 4?
A. 0.00016
B. 1.6000
C. 903.9208
D. 922.3682
Answer:
D: 922.3682
Step-by-step explanation:
First you take 1000 and subtract 20 from it.( 2% of 1000 = 1000x0.02x2=20).
You could do this on a calculator by entering 1000 and then subtracting 2% by clicking minus then, 2 then percent, then equals. you get 980. do the same to 980. (click minus, then 2, then percent, then equals). you get 960.4. do the same to 960.4. you get 941.192. do the same one more time since it says t=4 and you get 922.36816 which rounded to the nearest ten-thousandths is 922.3682.
hope this helped!
Based on a recent poll, there is a 50-50 chance that randomly selected adut has pierced ears, Express the indicated degree of likelihood as a proabability value between 0 and 1.
Answer:
1/2 or 0.5
Step-by-step explanation:
Saying that there is a 50-50 chance of an event happening is equivalent to saying there is a 1 in 2 chance. Therefore, expressing that degree of likelihood as a value between 0 and 1:
[tex]\frac{1}{2}=0.50[/tex]
There is a 1/2 or 0.5 chance that a randomly selected adult has pierced ears.
Answer:
1/2 or 0.5
Step-by-step explanation:
50-50 chance between 0-1 means half of 0-1 which is 1/2 or 0.5
1/2 or 0.5!
a group of girls bought 72 rainbow hairbands ,144 brown and black hairbands and 216 bright colored hairbands .what is the largest possible number of girls in the group
Answer:
72
Step-by-step explanation:
We are assuming that all girls in the group bought the same number of items.
Therefore, we need to find the highest common factor of 72, 144 and 216.
HCF
72 = 2 * 2 * 2 * 3 * 3
144 = 2 * 2 * 2 * 2 * 3 * 3
216 = 2 * 2 * 2 * 3 * 3 * 3
The product of the emboldened numbers is the highest common factor.
That is:
2 * 2 * 2 * 3 * 3 = 72
Therefore, the largest possible number of girls in the group is 72.
please help !! what’s the answer? i don’t understand !!
Answer:
992
Step-by-step explanation:
You must convert the meter the kilometer by miltiplying by 1000
and when you do it you must multiply 0.992 by 1000 since it is a fraction .
or you can work it this way :
0.992⇒1m x(the new rate) ⇒1000m x= 0.992*1000= 992A train travels 600 km in one hour .what is the trains Velocity in meters /seconds?
Answer:
166.6666 metres/second
Step-by-step explanation:
1 km/hr = 5m/18s
600*5/18
Please answer i will give thanks and 5 star
Answer:
A, B, and E are all less than 1/8
Here is a Venn diagram. One of the numbers in the Venn diagram is picked at random. Find the probability that this number is in set C'
Answer:
5/6
Step-by-step explanation:
hello
in total there are 12 numbers
C has two items
so C' has 10 items
so the probability that this number is in set C' is 10/12=5/6
hope this helps
The length of a square is 2x cm. The breadth and length of a rectangle are x cm and (2x + 1) cm
respectively. If both have the same perimeter. find the value of x.
Answer:
I hope it will help you.......
find the zero of the following function: f(×)=(×-1)/(×-3)
Answer:
[tex]\boxed{\sf \ \ x = 1 \ \ }[/tex]
Step-by-step explanation:
Hello,
First of all we need to take x different from 3 as dividing by 0 is not allowed
then for x real different from 3
[tex]f(x)=0\\\\<=> \dfrac{x-1}{x-3}=0\\\\<=> x-1 = 0\\\\<=> x = 1[/tex]
hope this helps
Here is a sequence of numbers:
64
49
36
25
16
a)
What is the name given to these numbers?
Answer:
Perfect squares
Step-by-step explanation:
Here, we have a list of some numbers and we want to know the name given to these numbers.
Mathematically, these numbers are referred to as perfect squares.
Although all numbers have square roots, not all numbers have integer square root values.
Numbers having integer square root values otherwise known as whole number square root values are referred to as perfect squares.
What is the slope of the line that contains the points (-1, 2) and (3, 3)?
O A. 4
O B. 4
ОС.
4
OD.
4
Answer:
the answer shoudl be OB 4
Which of the following statements is true for the figures shown?
Answer:
Option D is the correct answer.
Step-by-step explanation:
A-p-e-x :)
Two teaching methods, A and B, are implemented for learning Spanish. There is a 70% chance of successfully learning Spanish if method A is used, and a 85% chance of success if methodB is used. However, method B is substantially more 3. time consuming and is therefore used only 20% of the time (method A is used the other 80% of the time). The following notations are suggested:
A-Method A is used.
B-Method B is used.
L-Spanish was learned successfully Interpret each of the probabilities given in the original problem in probability
a) notation with their respective values (four of these).
b) Draw a Probability Tree representing each of the probabilities mentioned above.
c) What is the likelihood a person does not learn Spanish?
d) A student learned the spanish successfully. What is the probability that they were taught by method B?
Answer:
(a) Shown below.
(b) Shown below.
(c) The probability that a person does not learn Spanish is 0.18.
(d) The probability that method B was used given that a student learned the Spanish successfully is 0.83.
Step-by-step explanation:
(a)
Consider the provided data.
[tex]P(A)=0.20\\P(B)=0.80\\P(L|A)=0.70\\P(L|B)=0.85[/tex]
Then the probability of not learning Spanish using the respective methods are:
[tex]P(L'|A)=1-P(L|A)=1-0.70=0.30\\\\P(L'|B)=1-P(L|B)=1-0.70=0.15[/tex]
(b)
The Probability Tree representing each of the probabilities mentioned above is attached below.
(c)
Compute the probability that a person does not learn Spanish as follows:
[tex]P(L')=P(L'|A)P(A)+P(L'|B)P(B)[/tex]
[tex]=(0.30\times 0.20)+(0.15\times 0.80)\\\\=0.06+0.12\\\\=0.18[/tex]
Thus, the probability that a person does not learn Spanish is 0.18.
(d)
Compute the probability that method B was used given that a student learned the Spanish successfully as follows:
[tex]P(B|L)=\frac{P(L|B)P(B)}{P(L|A)P(A)+P(L|B)P(B)}[/tex]
[tex]=\frac{(0.85\times 0.80)}{(0.70\times 0.20)+(0.85\times 0.80)}\\\\=\frac{0.68}{0.14+0.68}\\\\=0.82927\\\\\approx 0.83[/tex]
Thus, the probability that method B was used given that a student learned the Spanish successfully is 0.83.
Describe how the graph of the parent function
y=
is transformed when graphing y = 8x - 3
The graph is translated 3 units
Answer:
Down
Stretched by a factor of 2
Step-by-step explanation:
The transformed function is translated to the right along the x-axis and stretched by a scale factor of 2.
What is transformation?A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure.
Given is a function, y = [tex]\sqrt[3]{x}[/tex] being transformed into y = [tex]\sqrt[3]{8x} -3[/tex]
We see, that, in the function, 3 is being subtracted from x, we mean the translation is right along the x-axis
And, ∛x is converted into 2∛x, that shows a stretched in the graph,
Hence, The transformed function is translated to the right along the x-axis and stretched by a scale factor of 2.
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Consider the following quadratic equation. -4x^2+bx-11=0 Determine a possible value of b so that the quadratic has two complex solutions.
Answer:
Step-by-step explanation:
hello,
for [tex]ax^2+bx+c=0[/tex]
[tex]\Delta = b^2-4ac[/tex]
so here
[tex]\Delta = b^2-4*(-4)*(-11)=b^2-176[/tex]
to have two complex solutions we need [tex]\Delta < 0\\[/tex]
so [tex]b^2<176[/tex]
[tex]<=> b < \sqrt{176}=13.266...[/tex]
for instance we can take b = 0
hope this helps
Answer:
The correct answer is 12.
Step-by-step explanation:
i got it correct on my test, thanks to comment on the question above.
which is the domain of the function in this table ?
Answer: 1,2,3,4
Step-by-step explanation:
The domain consists of every x value
Can someone please help me I really need help
Answer:
choice c
Step-by-step explanation:
y axis shows value of computer
v-intercept; x axis = 0
show initial value of the computer
Where do the graphs go ?
Answer:
1 goes into not pro
2 goes to not pro
3 goes into pro
and 4 goes into not pro
Step-by-step explanation:
proportional is a straight line
non proportional is not a line
What is the following product? (3 startroot 16x^7 endroot) (3 startroot 12x^9 endroot)
Answer:
72x^8
Step-by-step explanation:
Product of ;
3 √(16x^7) * 3 √(12x^9)
Let’s factor out all perfect squares in the roots
3 √(16 * x^4 * x^3) * 3 √(4 * 3 * x^8 * x)
Taking out the perfect squares, we have;
3 * 4 * x^2 * √(x^3) * 3 * 2 * √3 * x^4 * √(x)
72 * x^(2 + 4) * √(x^3 * x)
72 * x^6 * √(x^4)
72 * x^6 * x^2
72 * x^8
solve this, please prove it with steps in detail
Answer:
2
Step-by-step explanation:
-(1-√2) -(2-√3) + 1/√3 + 2+1/2+√5-(√5-√6)-(√6-√7)+ 1/√7+2√2+1/2√2+3
-1+√2-√2+√3-(√3-2)-(2-√5)-√5+√6-√6+√7-(√7-2√2)-(2√2-3)
-1+√2-√2+√3-√3+2-2+√5-√5+√6-√6+√7-√7+2√2-2√2+3
2