Answer:
sum is 1275
Step-by-step explanation:
[tex]sum = \frac{n}{2} [2a + (n - 1)d] \\ \\ sum = \frac{50}{2} [(2 \times 1) + (50 - 1) \times 1] \\ \\ sum = 25(51) \\ sum = 1275[/tex]
The functions q and r are defined as follows
g(x) = -2x-2
r(x) = x² – 2
Find the value of r(q(4)).
r(9 (4)) =
Answer:
98
Step-by-step explanation:
So we have the two functions:
[tex]g(x)=-2x-2\text{ and } r(x)=x^2-2[/tex]
And we want to find the value of r(g(4)).
To do so, first find the value of g(4):
[tex]g(x)=-2x-2\\g(4)=-2(4)-2\\[/tex]
Multiply:
[tex]g(4)=(-8)-2[/tex]
Subtract:
[tex]g(4)=-10[/tex]
Now, substitute this into r(g(4)):
[tex]r(g(4))\\=r(-10)[/tex]
And substitute this value into r(x):
[tex]r(-10)=(-10)^2-2[/tex]
Square:
[tex]r(-10)=100-2[/tex]
Subtract:
[tex]r(-10)=98[/tex]
Therefore:
[tex]r(-10)=r(g(4))=98[/tex]
Answer:
Step-by-step explanation:
For what values of does the equation (2 + 1)^2 + 2 = 10 − 6 have two real and equal roots?
Answer:
it isn't the equation so it can't be any roots...
Step-by-step explanation:
[tex](2+1)^2+2=10-6\\4+4+1+2=10-6\\11\neq 4[/tex]
consider the polynomial 8x^3+2x^2-20x-5 factor
Answer:
(4x + 1)(2x² - 5)
Step-by-step explanation:
Given
8x³ + 2x² - 20x - 5 ( factor the first/second and third/fourth terms )
= 2x²(4x + 1) - 5(4x + 1) ← factor out (4x + 1) from each term
= (4x + 1)(2x² - 5)
Answer:
blank 1 is -20-5
blank 2 is 4x+1
blank 3 is -5
blank 4 is 2x^2-5
Step-by-step explanation:
Vanessa uses the expressions (3x2 + 5x + 10) and (x2 – 3x – 1) to represent the length and width of her patio. Which expression represents the area (lw) of Vanessa’s patio?
To get the area simply multiply the length by the width.
(3x^2+5x+10)(x^2-3x-1) = 3x^4 - 4x^3 - 8x^2 - 35x - 10
Answer:
the answer is A
Step-by-step explanation:
got it right on edge
The temperature in Anchorage, Alaska at 6:00 am was 2°C. If the temperature drops 2 degrees each hour, what is the temperature in degrees celsius at 2:00 pm
Answer:
-12°C
Step-by-step explanation:
6AM = 2°C
8AM= -2°C
10AM= -6°C
12AM= -8°C
2PM= -12°C
the temperature in degrees Celsius at 2:00 pm would be -14°C.
To find the temperature in degrees Celsius at 2:00 pm, we need to determine the number of hours that have passed from 6:00 am to 2:00 pm, and then calculate the temperature decrease accordingly.
From 6:00 am to 2:00 pm, a total of 8 hours have passed (6 hours from 6:00 am to 12:00 pm, and 2 hours from 12:00 pm to 2:00 pm).
Given that the temperature drops 2 degrees Celsius each hour, we can multiply the number of hours (8) by the rate of temperature decrease (2 degrees/hour):
Temperature decrease = 8 hours × 2 degrees/hour = 16 degrees
Starting with a temperature of 2°C at 6:00 am, if the temperature drops 16 degrees Celsius over 8 hours, we can subtract 16 from the initial temperature:
Temperature at 2:00 pm = 2°C - 16°C = -14°C
Therefore, the temperature in degrees Celsius at 2:00 pm would be -14°C.
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stagg high school has a rectangular swiming pool the area of the water in the pool is 1,800 meters squared the length is twice the width what is the perimeter of the pool find the length and width. SHOW WORK
Step-by-step explanation:
L*b=1800m^2
L=2b
2b*b=1800
2b^2=1800
b^2=900
b=30m
L=2*30
=60m
Perimeter=2(l+b)
=2(60+30)
=2*90
=180m
A bag contains 5 pieces of string. The lengths of the pieces of string are 1 inch, 3 inches, 5 inches, 7 inches, and 9 inches. Suppose you pick three pieces of string from the bag at random and all pieces are equally likely to be chosen. What is the probability you can form a triangle with the three pieces
Answer:
30%
Step-by-step explanation:
There are 10 possible combinations of sticks that can be drawn from a group of 5 strings
5C3 = (5*4*3)/(3*2) = 10 combinations, which are
1,3,5 ; 1,3,7 ; 1,3,9 ; 1,5,7 ; 1,5,9 ; 1,7,9 ; 3,5,7 ; 3,5,9 ; 3,7,9 ; 5,7,9
to make a triangle, the sum of any two sides must be greater than the third side and if you look at the possible combinations there are only three cases where that is true
so the probability for drawing three sticks that would make a triangle is 3/10 or 30%
This table represents a quadratic function.
y
x
0
14
1
10.5
2
8
3
6.5
4
5
6.5
What is the value of a in the function's equation?
A.2
B.1/2
C.-1/2
D.1
Answer:
B. 1/2
Step-by-step explanation:
y = ax^2 + bx + c
14 = a(0)^2 + b(0) + c
c = 14
10.5 = a(1)^2 + b(1) + 14
10.5 = a + b + 14 ____(i)
8 = a(2)^2 + b(2) + 14
8 = 4a + 2b + 14
4 = 2a + b + 7 ___ (ii)
i - ii
10.5 - 4 = -a + 7
6.5 = -a + 7
a = 7- 6.5
a = 0.5
Value of a in the quadratic function is 0.5
What is Quadratic function?In algebra, a quadratic function, a quadratic polynomial, a polynomial of degree 2, or simply a quadratic, is a polynomial function with one or more variables in which the highest-degree term is of the second degree
Given,
Quadratic function
y = [tex]ax^{2}+bx+c[/tex]
Consider values in the table x= 0 and y =14
[tex]14=a(0)^{2}+b(0)+c\\ c=14[/tex]
Consider x=1 and y = 10.5
[tex]10.5=a(1^{2})+b(1)+c\\ a+b=10.5-14\\a+b=-3.5[/tex]
Consider x=2 and y =8
[tex]8=a(2^{2})+b(2)+c\\ a\\8=4a+2b+14\\4a+2b=-6\\2a+b=-3[/tex]
Subtract a + b= -3.5 from 2a + b= -3
a=-3--3.5=0.5
Hence, the Value of a in the quadratic function is 0.5
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Solve 8
Given quadrilateral MATH is similar to quadrilateral ROKS calculate the value of MH Picture is below
=====================================================
Explanation:
The double tickmarks for quadrilateral MATH show that MA = TH. Since TH is 5 units long, this makes MA the same length as well.
For quadrilateral ROKS, we have RO = 15. For "MATH" and "ROKS" we have "MA" and "RO" as the first two letters of each four-letter sequence; meaning that MA and RO correspond together.
The ratio of the corresponding segments is RO/MA = 15/5 = 3.
The larger quadrilateral has each side length 3 times longer than the smaller quadrilateral's corresponding side lengths.
--------------
In short,
larger side = 3*(smaller side)
--------------
Using this scale factor of 3, we can find MH
larger side = 3*(smaller side)
RS = 3*(MH)
21 = 3*MH
3*MH = 21
MH = 21/3
MH = 7
simplify 6(x - 4) +9
To simplify use the distributive property first. Multiply 6 by each value inside the parentheses:
6(x-4) + 9
6x -24 + 9
Now combine like terms to get the final answer:
6x - 15
Express in terms of power =(3x) ×(3x)× (3x)× (3x)
Answer:
3x^4
Step-by-step explanation:
3x • 3x • 3x • 3x = 3x^4
said like “3x to the 4th power”
Answer:
[tex](3x)^4}[/tex]
Step-by-step explanation:
further it can represent as [tex]3^{4} x^{4}[/tex]
If 3sinA+4cosA=5 then find the value of cosA
Answer:
cos(A) = 4/5
Step-by-step explanation:
3sinA+4cosA=5
Divide by 5 on both sides
(3/5)sinA+(4/5)cosA = 1 .................(1)
from which sin(A) = 3/5, cos(A) = 4/5 by inspection, since
(3/5)^2+(4/5)^2 = 1
For more details,
Let
cos(B) = (3/5), then
sin(B) = (4/5)
Substitute in (1)
cos(B)sin(A) + sin(B)cos(A) = 1 substitute trigonometric sum
sin(A+B) = 1 => A & B are complementary
cos(A) = sin(B) = 4/5
what is the square and square root of 9x⁸
Answer:
square: (9x^8)^2= 81x^16
square root: (9x^8)^1/2 = 3x^4
Step-by-step explanation:
the ^ mean that the following num should be like this ⁸
Q4) Using Euclid's algorithm, find the HCF of 240 and 228
[tex] \LARGE{ \underline{ \boxed{ \purple{ \rm{Solution : )}}}}}[/tex]
Euclid's division lemma : Let a and b are two positive integers. There exist unique integers q and r such that
a = bq + r, 0 [tex]\leqslant[/tex] r < b
Or We can write it as,
Dividend = Divisor × Quotient + Remainder
Work out:
Given integers are 240 and 228. Clearly 240 > 228. Applying Euclid's division lemma to 240 and 228,
⇛ 240 = 228 × 1 + 12
Since, the remainder 12 ≠ 0. So, we apply the division dilemma to the division 228 and remainder 12,
⇛ 228 = 12 × 19 + 0
The remainder at this stage is 0. So, the divider at this stage or the remainder at the previous age i.e 12
[tex] \large{ \therefore{ \boxed{ \sf{HCF \: of \: 240 \: \& \: 228 = 12}}}}[/tex]
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Find the first three terms of the sequence given by the following.
a
n = 25-3(n − 1), n= 1, 2, 3, ...
A. 28, 25, 22
B. 25, 22, 19
C. 25, 28, 31
D. 28, 31, 34
the answer is
A. 28, 25, 22
Find the distance between the origin and the points (-8,4)
Hi, I'm happy to help!
To solve this, we need to find the distance from the origin to the y coordinate value, x coordinate value, then use the Pythagorean Theorem.
The origin of a graph (center) has the coordinates (0,0), so this will be our other coordinates.
First, let's find the x coordinate distance change. We move from the x coordinate 0, to the x coordinate -8, so we move 8 x units.
Next, let's find the y coordinate distance change. We move from the y coordinate 0, to the y coordinate 4, so we move 4 y units.
Now that we have these two leg lengths, let's imagine this as a right triangle. Moving from the origin, we draw a line from (0,0), to (-8,0). Then, we draw a line from (-8,0) to (-8,4). Now, draw a direct line from (0,0), to (-8,4). We have the length of the first(8) and second(4) lines, and we need to find the third line length to find our answer. To do this, we use the Pythagorean Theorem, which states that a²+b²=c². This says that, in a right triangle, the square of the two shorter lengths equals the square of the longest length. The longest length is what we are solving for.
Let's say x distance is a, and y distance is b. Now, apply the values:
8²+4²=c²
64+16=c²
80=c²
Now, we need to find the value of c, so we need to find the square root of 80.
√80=c
8.9442...=c
Since the number goes on forever, we need to round it. For this example, let's round it to the nearest tenth, which would be 8.9.
To summarize the distance between the origin and the coordinates (-8,4), is about 8.9.
I hope this was helpful, keep learning! :D
The basic unit in which data are stored in an accounting system is called an __________. These storage units should be so constructed as to readily receive money measurements of the __________ or ___________ in the items for which they are established. The basic unit in which data are stored in an accounting system is called an __________. These storage units should be so constructed as to readily receive money measurements of the __________ or ___________ in the items for which they are established.
Answer:
an accounts; credit or debit.
Step-by-step explanation:
Remember, accounting involves activities done to keep financial records. Interestingly, a similar term is used to refer to the basic unit in which data are stored in an accounting system called accounts.
Also, we need to bear in mind that this financial records written as storage units would include incoming or outgoing money measurements often called debit or credit transactions in the items for which they are established.
An orchardist is to plant apple trees and pear trees in the ratio 3:11. If he intends to plant 150 apple trees, how many pear trees will he need to plant?
The ratio 2:11 means for every 3 apple trees they will plant 11 pear trees.
They are planting 150 apple trees. Divide total apple trees by the ratio: 150/3 = 50
Multiply that by the ratio of pear trees:
50 x 11 = 550
They need to plant 550 pear trees.
Xian and his cousin Kai both collected stamps. Xian has 56 stamps, and Kai has 80 stamps. They boys recently joined different stamp-collecting clubs. Xian’s club will send him 12 new stamps per month. Kai’s club will send him 8 new stamps per month. after how many months will Xian and Kai have the same number of stamps? How many stamps will each have?
Answer:
After 4 months Xian will have 104 stamps,
But after three months Kai will also have 104 stamps
Step-by-step explanation:
Write an equation for the line in the graph that passes through the points (0,4) and (12,16).
Answer:
We have,
y-y1=m(x-x1)
or,y-4=-1(x-0)
or,y-4=-x
or,x+y=4 is the required equation
Step-by-step explanation:
it it helps u ...plz mark it as brainliest
Write all the possible two-digit numbers which can be formed using the digits 0,3,5
Answer:
i) where the digits can repeat
1. 30
2. 50
3. 33
4. 55
5. 35
6. 53
ii) where the digits cannot be repeated
1. 30
2. 50
3. 35
4. 53
find the distance between (3,3) and (3,4)
Answer:
1
Step-by-step explanation:
√(4-3²+(3-3)²
√1¹+0
√1
1
Answer:
1 unitStep-by-step explanation:
Since x- coordinates are same, the distance is the difference of the y-coordinates:
4 - 3 = 1Serena hits a tennis ball downward from the top of the net at which the angle of
depression is 20°. If the net is 0.9 m high, how far from the net does the ball land to
the nearest tenth of a metre?
Answer:
2.5 meter
Step-by-step explanation:
in a right triangle, tan of an angle = opposite side /adjacent side
tan 70° = x/ 0.9 , multiply both sides by 0.9
0.9 * tan 70° = x, solve on a calculator
x ≈ 2.5 m
Convert the improper fraction 17⁄5 into a mixed number The denominator is 5 So the denominator of the ______number will be 5 This is from Seneca Learning:
Answer:
3 wholes 2/5
I hope this helps you!
HELP ASAP!!!!! Which statement is not always true for a parallelogram?
Answer:
D
Step-by-step explanation:
The consecutive angles in a parallelogram are supplementary.
Thus statement D is not always true.
whats the squareroot of 72 needs to be simplified
Answer: 6√2
Step-by-step explanation: The easiest way to do this problem is to factor 72 as 2 · 36, then recognize 36 as a perfect square, 6 · 6.
There's no need to factor further because the 6's pair up
so a 6 comes out of the radical leaving a 2 inside.
So our answer is 6√2.
Always be on the lookout for perfect squares!
Work is attached below.
URGENT HELP I REALY NEED AN EXPERT HERE
Hi
P and Q only intersect for 2 as 2 is common for P and Q . So P U Q = 2
For the diagram :
One big circle name U with 1 on the
Far corner left and 9 on the far right corner.
Then on the left, a circle within circle U with the number Of P
Same with Q on the right.
But P and Q must intersect on number 2 as 2 is in both circles.
ps : nothing oblidge you to set the number on mathematical order. Of it'esasier to do the circles, do it whatever you like as long as you respect what is said.
help me Complete each sentence to describe the algebraic expression 9 + y. The variable in the expression is . The operation in the expression is . The constant in the expression is .
Answer:
'y', "addition", '9'.
Step-by-step explanation:
The variable is an unknown value in an algebraic equation or expression. It is represented by a letter.
'y' would be the variable in the given equation.
The operation in the expression is addition. The '+' sign represents addition, which means 9 and 'y' would be added together to get the sum.
Constants are terms in a expression or equation that contains no variables. This means that constants are only numbers.
'9' would be the given constant in the expression.
Hope this helps.
Answer:
y
+
9
Step-by-step explanation:
Melissa put her $500 In a savings account that earns 4% interest compounded annually. How much will be in the account after 3 years? Round your answer to the nearest hundredth
Work Shown:
A = P*(1+r/n)^(nt)
A = 500*(1+0.04/1)^(1*3)
A = 562.432
A = 562.43
Answer: $562.43
Step-by-step explanation:
The initial start up amount is 500 and we want to expressed this as an exponential function. So since we know the initial value we need to find the rate of change. So if you earn 4% interest you are earning 4% percent more on top the actual 100%.
So 100% + 4 % = 104% = 1.04
The common difference is 1.04.
so 500 * 1.04^n= A where n is the number of years and A is the total amount.
A = 500 * [tex]1.04^{3}[/tex]
A= 562.43