Answer:
Step-by-step explanation:
Equations
x + y = 29
x^2 + y^2 = 425
Solution
y = 29 - x
x^2 + (29 - x)^2 = 425
x^2 + (841 - 58x + x^2 ) = 425
x^2 - 58x + x^2 + 841 - 425 = 0
2x^2 - 58x +416 = 0
a = 2
b = - 58
c = 416
You get two answers that look valid
2x^2 - 58x + 416 = 0
x^2 - 29x + 208 = 0 This factors
(x - 16)(x - 13) = 0
x = 16
y = 13
Now check it
16^2 + 13^2 = ? 425
256 + 169 = 425
5. The average weight of a blue whale is 4 x 105 pounds. The average weight of an elephant is 1 x 10 pounds. How many more times heavier is a blue whale than an elephant in pounds?
Answer:
42 more times
Step-by-step explanation:
1) 4×105=420 (pounds)-blue whale
2) 1×10=10 (pounds)- elephant
3) 420:10=42
The amount of times that the blue whale is more heavier than the elephant in pounds is; 40 times heavier.
We are given;Average weight of blue whale; W_w = 4 × 10^(5) pounds
Average weight of elephant; w_e = 1 × 10⁴ pounds
Now, we want to find how much more heavier the blue whale is than the elephant. Thus we will just divide W_w by W_e to get;W_w/W_e = (4 × 10^(5))/(1 × 10⁴)
According to laws of exponents;
a¹²/a³ = a¹² ¯ ³ = a^(9)
Applying that to our question gives;
4(10^(5 - 4)) = 4 × 10 = 40
Read more about exponents at; https://brainly.com/question/18248071
The derivative of f(x) = x3 – 12x + 5 is 3x2 – 12 . Find the coordinates of the turning points of f(x)
Answer:
(-2, 21) and (2, -11) let me know if anything didn't make sense
Step-by-step explanation:
Try and put the symbols in, so for x to the third power write x^3 just makes it all much easier.
The turning point is when a graph changes from increasing to decreasing, or the other way around. What this means is that its slope is changing from positive to negative, or the other way around.
The derivative allows you to find the slope at any point of a graph. If you are unfamiliar witht his concept let me know and I can go more into it.
Since the derrivative tells you the slope, if you find a spot where it equals 0 then you know before that point it was positive or negative, and then after that point it was the opposite. In other words it changes, so it's exactly what we are looking for. Also if a derrivative is ever non existant, like in the square root function the numbers under the square root cannot be negative, so any x value that makes them negative doesn't exist, this means you would want to check these point too because they can be turning points as well.
There are certain special cases where a derivative does not coss 0, and if that happens then the original function does not have a turning point. So keep that in mind.
The derivative is 3x^2 - 12. So we want to find when this equals 0. We also know it always exists so only need to worry about the 0s. Hopefully you are familiar with quadratics having two zeroes, if not let me know.
3x^2 - 12 = 0
3x^2 = 12
x^2 = 4
x = 2 and-2
So these are the turning points. You should double check though and choose an x value below -2, then between -2 and 2, then larger than 2 and make sure the signs swap.
These are the x values of the turning points. Solve f(x) at these points to find the y values. so f(-2) = (-2)^3 - 12(-2) + 5 = 21 and f(2) = -11 so now we know the turning points are (-2, 21) and (2, -11)
The coordinates of the turning points of f(x) are (-2, 21) and (2, -11).
What is differential equation?An equation containing derivatives of a variable with respect to some other variable quantity is called differential equations. The derivatives might be of any order, some terms might contain product of derivatives and the variable itself, or with derivatives themselves.
The turning point is when a graph changes from increasing to decreasing, or the other way around that means, its slope is changing from positive to negative.
Given that the derivative of f(x) = x³ – 12x + 5 is 3x² - 12.
Since the derrivative tells the slope, if you find a spot where it equals 0 then before that point it was positive or negative, and then after that point it was the opposite.
The derivative is 3x² - 12.
3x² - 12 = 0
3x² = 12
x² = 4
Thus, x = 2 and-2
So, these are the turning points.
Now Solve f(x) at these points to find the y values.
so f(x) = x³ – 12x + 5
f(-2) = (-2)³ - 12(-2) + 5 = 21
f(2) = -11
Hence, the coordinates of the turning points of f(x) are (-2, 21) and (2, -11).
Learn more about equations here;
https://brainly.com/question/25180086
#SPJ2
Find the HCF of: 5a²b² and 9x³y³
Answer:
1
Step-by-step explanation:
To do this, we can first look at each factor of each number.
For 5a²b², we can split this up into three parts: 5, a², and b². The factors of 5 are 1 and 5, the factors of a² are 1, a, and a² (because a*a = a² and a²*1 = a²), and the factors of b² are 1, b, and b²
For 9x³y³, the factors for 9 are 1, 3, and 9, the factors of x³ are 1, x, x², and x³ (because x * x² = x³ and x³ * 1 = x³), and the factors of y³ are 1, y, y², and y³.
The only number that is a factor of at least 1 item in each number is 1. Therefore, 1 is the HCF
Another way of looking at this is seeing that a, b, x, and y are all different variables with nothing to connect them, so as a result, they will have no common factors except for 1
help me please I'm bad at math
Answer:
123
Step-by-step explanation:
Large rectangle:
8 - 3 = 5
5 × 4 × 3 = 20 × 3 = 60
Smaller rectangle:
3 × 3 × 7 = 9 × 7 = 63
Both:
63 + 60 = 123
Hope this helped.
A certain shampoo is available in two sizes. A 14.2 ounce bottle costs $3.98. A 33.9 ounce bottle costs $9.98. Find the unit price for each size. Then state which size is the better buy based on the unit price. Round your answers to the nearest cent. Thank you!
Answer:
A 14.2 ounce bottle costs $3.98 is the better buy
Step-by-step explanation:
Find the price per ounce for each
A 14.2 ounce bottle costs $3.98
3.98 /14.2 =.28028169 = .28 per ounce
A 33.9 ounce bottle costs $9.98
9.98/33.9 =.29439528 = .29 per ounce
If you have the time mind helping me on this
you can go for option g cause ans is 14:5
find the value of x
3+x/4=5
Step-by-step explanation:
it think it will help you
Answer:
the value of x = 8
Step-by-step explanation:
3+x/4 = 5
x/4 = 5 - 3
= 2
X = 2 ×4
=8
whats the figures and how do I find the area?
Answer:
This is trapezium.
Area of this figure =1/2h(d1-d2)
1/2×5(14-8)
=30/2
=15cm^2
PLS HELP Leo is looking at two different savings plans. The first plan requires an initial deposit of $500 and grows at an annual interest rate of 2.5%. The second plan requires an initial deposit of $400 and interest grows continuously at a rate of 2% per year. Leo wrote a system of equations to represent the account balance of either plan, y, after x years. Which two equations are part of the system?
OPTIONS ARE BELOW
Answer:
First and Second option choices
Step-by-step Explanation:
1st case:
Initial deposit (P) = 500
Annual interest rate (r) = 2.5%
Account balance after x years, y = P(1+r/100)×
y = 500(1+2.5/100)×
y = 500(1+0.025)×
y = 500(1.025)×
2nd case:
Initial deposit (P) = 400
Annual interest rate (r) = 2%
Account balance after x years, y = P(1+r/100)×
y = 400(1+2/100)×
y = 400(1+0.02)×
y = 400(1.02)×
The correct option is (A) and (B)
What are Equations?Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign. It shows the relationship of equality between the expression written on the left side with the expression written on the right side. In every equation in math, we have, L.H.S = R.H.S (left hand side = right hand side).
Parts of an EquationThere are different parts of an equation which include coefficients, variables, operators, constants, terms, expressions, and an equal to sign. When we write an equation, it is mandatory to have an "=" sign, and terms on both sides. Both sides should be equal to each other. An equation doesn't need to have multiple terms on either of the sides, having variables, and operators. An equation can be formed without these as well, for example, 5 + 10 = 15. This is an arithmetic equation with no variables. As opposed to this, an equation with variables is an algebraic equation. Look at the image below to understand the parts of an equation.
Initial deposit (P) = 500
Annual interest rate (r) = 2.5%
Account balance after x years, y = P(1+r/100)^×
y = 500(1+2.5/100^)×
y = 500(1+0.025)^×
y = 500(1.025)^×
again,
Initial deposit (P) = 400
Annual interest rate (r) = 2%
Account balance after x years, y = P(1+r/100)×
y = 400(1+2/100)^×
y = 400(1+0.02)^×
y = 400(1.02)^×
Learn more about Algebra here:
https://brainly.com/question/10413253
#SPJ2
Someone please help with this
Answer:
g(-3) = 1
Step-by-step explanation:
We use the top piece of the function since x = -3
g(-3) = x+4 and x = -3
g(-3) = -3 +4 = 1
write down the first 3 term of each sequence described by the sequence with first term 8 and difference -7
Answer:
8,1,-6
Step-by-step explanation:
8 + (-7)
= 8-7 = 1
1 + (-7) = 1 - 7 = -6
The first three terms are 8, 1,-6
Answered by Gauthmath
Write the following expression
as a
simplified polynomial in standard form.
2(x – 5)^2 + 2(x – 5) + 5
Answer:
2x^2 - 18x + 45
Step-by-step explanation:
Standard form is ax^2 + bx + c
Expand the (x-5)^2 = (x-5)(x-5) --
x^2 - 5x - 5x + 25
x^2 - 10x + 25
So we now have
2(x^2 - 10x + 25) + 2(x-5) + 5
From here, distribute the 2 to each term in x^2 - 10x + 25, and distribute the 2 to each term in x - 5.
2x^2 - 20x + 50 + 2x - 10 + 5
Combine like terms
2x^2 - 20x + 2x + 50 - 10 + 5
2x^2 - 18x + 40 + 5
2x^2 - 18x + 45
Find the surface area of the cylinder in terms of T. 9 cm 19 cm Not drawn to scale O 211.5 cm 2 0 382.57 cm 2. O 333 77 cm2 o 504 лcm
Answer:
hey the answer is cylinder= 211.5л!
EFGH is an isosceles trapezoid and EFGI is a parallelogram. If m∠IEF = 36°, then m∠HGI = ° (Blank 1).
The base angles of an isosceles trapezoid are equal; For EFGI to be a parallelogram, the measure of [tex]\angle HGI[/tex] is: 108 degrees
Given that:
[tex]\angle IEF = 36^o[/tex]
IEF and GHI are the base angles of the trapezoid.
So:
[tex]\angle GHI = \angle IEF = 36^o[/tex]
Also:
[tex]\triangle GHI[/tex] is an isosceles triangle.
This means that:
[tex]\angle GHI = \angle HIG = 36^o[/tex] --- base angles of an isosceles triangle
So:
[tex]\angle GHI + \angle HIG + \angle HGI = 180[/tex] --- sum of angles in a triangle
Substitute known values
[tex]36 + 36+ \angle HGI = 180[/tex]
[tex]72 + \angle HGI = 180[/tex]
Collect like terms
[tex]\angle HGI = 180-72[/tex]
[tex]\angle HGI = 108[/tex]
Learn more about isosceles trapezoids at:
https://brainly.com/question/4333941
The extract of a plant native to Taiwan has been tested as a possible treatment for Leukemia. One of the chemical compounds produced from the plant was analyzed for a particular collagen. The collagen amount was found to be normally distributed with a mean of 61 and standard deviation of 9.8 grams per mililiter. a. What is the probability that the amount of collagen is greater than 60 grams per milliliter
Answer:
45.94%
Step-by-step explanation:
Probability-Above 45.94%
Z =0.1
x= 61
µ 60
σ 9.8
WHERE ARE THE EXPERTS AND ACE!!!!!!! I NEED HELP PLS SHARE YO SMARTNESS!!!!! WILL GIVE BRAINLIEST AND RATE AND VOTE!!!
Answer:
21. C, 24.B
Step-by-step explanation:
Since the y-value for x = 0 is not zero, the function cannot have sine in it because sin of 0 is always 0. Therefore, the function will have cos in it. That leaves only B and C left. Since cos(0) is always 1, and the value of y when x = 0 is 0.5, the function will have 1/2 multiplied by a cos function. The only answer option that has that is C.
Now, for the next problem, we know the values of all three sides, and we need to find one angle. We can use the law of cosines for this and plug the values into the equation:
[tex]55^2=40^2+24^2-2(40)(24)\cos(C)[/tex]
We can subtract 40 squared plus 24 squared from both sides to get
[tex]849=-2(40)(24)\cos(C)[/tex]
Negative two times 40 times 24 equals -1920. Dividing -1920 from both sides gets us
[tex]\frac{849}{-1920}=\cos(C)[/tex]
Plugging this equation into a calculator and solving for C, we get the answer as approximately
C = 116.24353.
This rounds to 116.2
Which monomials are perfect squares? Select three options.
a
25x12
b
16x9
c
6x2
d
36x16
e
9x8
Answer:
a, d and e.
Step-by-step explanation:
A perfect square is one where the coefficient is a perfect square and the exponent is even.
So they are 25x^12, 36x^16 and 9x^8.
Which angles are congruent to each other?
Angle 4 and Angle 3
Angle 3 and Angle 7
Angle 8 and Angle 5
Angle 1 and Angle 3
Answer:
1 and 3 are congruent
Answer:
Angle 1 and angle 3 are congruent
What’s the answer to this?
Answer:
you need to make a line by using the tools
1. Simplifying Equation Below
please help!!
Answer: 0
Step-by-step explanation:
In this equation 0/y would equal 0, no matter what y is. 0/y means that there's 0 items out of y items (ex: substitute y with 2, it would be 0/2). Beginning with 1*0 (one times zero) the answer there would be 0. Since we already know that 0/y equals 0, the rest of the equation would be 0 - 0 which would equal to 0. Hope this explanation helps :)
[tex]\\ \sf\longmapsto 0-\dfrac{0}{y}[/tex]
[tex]\\ \sf\longmapsto \dfrac{0-0}{y}[/tex]
[tex]\\ \sf\longmapsto \dfrac{0}{y}[/tex]
[tex]\\ \sf\longmapsto \infty[/tex]
[tex]\\ \sf\longmapsto 0[/tex]
write down the relation between the scales of temperature i.e degree Fahrenheit and degree Celsius in form of function and also write it's inverse
Answer:
C=（9F-32）/5
inverse：
Step-by-step explanation:
Find the value of b.
A. 57
B. 123
C. 50
D. 61.5
Answer:
please i need educere answers
Step-by-step explanation:
i have one day left and i cannot finish please reply with any way to contact you
2. The ? states that the product of the extremes is equal to the product of the
means.
Answer:
proportion
Step-by-step explanation:
In a proportion, the means or the extremes (or both) may be interchanged. In proportion, the product of the means equals the product of the extremes.
hope it helps :)
mark brainliest!
Write an equation of the line that is parallel to the given line and passes through the given point.
1. y=2x+1; (0,4)
2. y= -x-3; (0,7)
3. y=-8x +9; (0,-2)
If S is the midpoint of RT, RS = 5x + 17, and ST = 8x - 31, find RS. Show work!
Answer:
97
Step-by-step explanation:
Since S is the midpoint of RT, and when you split the line into two you'd get two distances that are equidistant. Therefore, you can make the two distances into an equation. When combined together, the result will be the total length of the line.
5x + 17 = 8x - 31
Now simply just solve for "x"
5x + 17 = 8x - 31
5x + 48 = 8x
48 = 3x
48/3 = 3x/3
16 = x
Once you get x, plug it into the equation "RS = 5x + 17"
5(16) + 17
80 + 17
97, which is our final answer.
After a 15% increase January receives a new salary of R23000. What was his salary before the increase
Answer:
His salory before Increse is 17250
I need help with this
Find the value of x for which ABCD must be a parallelogram
a. 1
b. 94
c. 3
d. 47
Answer:
c. 3
Step-by-step explanation:
BC||AD so <CBD=<BDA
15x+2=9x+20
15x-9x=20-2
6x=18
x=3
solve for x the triangles are the same
Answer: x=8
Step-by-step explanation:
So to begin with we need to find the connection being that they are the same triangle but with a dilation. We need to find the dilation by matching the new angles with each other H=E F=C and D=G. We need to find the relation ship between CD and FG. 65 divided by 24= 2.6 take ED and multiply 2.6 to find HG. HG= 91. Now we need to find x. 8 times x+ 3=91. Find the closest eight multiple to 91 which is 8 times 8= 88 and add 3 to see it makes 91.
8 is your answer.
Find the number of five-digit numbers which are not divisible by 5?
Answer:
72000
Step-by-step explanation:
First five digit number is 10000
And the last five digit number is 99999.
There are 99999-10000+1 five digits in all.
That simplifies to 89999+1=90000.
Any number whose units digit is 5 or 0 is divisble by 5.
10000 is the first five digit number that is divisble by 5.
10000+5k where k is a positive integer can be used to find any after.
The last five digit number divisible by 5 is 99995. What is k then?
10000+5k=99995
5k=89995
k=89995/5
k=17999
How many 5 digit numbers are divisble by 5?
So the first one happens at k=0 and the last one happens at k=17999.
How many numbers is that? 17999+1=18000.
So the number of 5 digit numbers that aren't divisble by 5 is 90000-18000=72000
