Answer:
Explained below.
Step-by-step explanation:
Consider the series is a set of first 6 natural numbers.
Sum of first n terms is:
[tex]\text{Sum of n terms}=\frac{n(n+1)}{2}[/tex]
[tex]\text{Sum of first 6 terms}=\frac{6(6+1)}{2}[/tex]
[tex]=3\times7\\=21[/tex]
Consider the series is an arithmetic sequence.
Sum of first n terms is:
[tex]S_{n}=\frac{n}{2} [2a+(n-1)d][/tex]
Here,
a = first term
d = common difference
Consider the series is an geometric sequence.
Sum of first n terms is:
[tex]S_{n}=\frac{a_{1}\cdot(1-r^{n})}{(1-r)}[/tex]
Here,
a₁ = first term
r = common ratio
Answer:
84
Step-by-step explanation:
Correct on edge 2021!!!
what is the value of the discriminators of f f(x)=x^2-3x+18
Answer:
-63
Step-by-step explanation:
Compare ...
f(x) = x^2 -3x +18
to the standard form ...
f(x) = ax^2 +bx +c
and you will see that ...
a = 1, b = -3, c = 18.
__
The value of the discriminant is ...
d = b^2 -4ac
d = (-3)^2 -4(1)(18) = 9 -72 = -63
The discriminant is -63.
Please help me Thank u
Answer:
Step-by-step explanation:
Fist let's have a look :
(AB) is parallel with (CD) and there is a line crossing them both.Now the first question : What is the size x ?
We notice that x and 53° are vertically opposite so they are corresponding angles so the size of x is 53°The second question : what is the size of y ?
We notice that y and 53° are alternate angles so they are corresponding angles with same size y=53°The trick is to khow the situation where we have corresponding angles
Can any one please help me I really need help please help me I need help
Answer:
$8000 worth of sales
Step-by-step explanation:
We know Jack needs to make $1000 in 40 hours. We also know he makes 5% commission, meaning he gets 5% of the money from a sale, and that he makes $15/h.
First, lets find how much made from his hourly pay.
40 * $15 = $600
Now subtract that from how much he needs,
$1000 - $600 = $400
He still needs $400 from commissions. We know he makes 5% commission, so we can find the total value of the sales he'd need by multiplying 400 by 20 since 5% x 20 = 100%, aka the total value. $400 x 20 = $8000 in sales.
Which is the value of g(-5) it g(x) = 3,4x - 8?
Answer:
g(-5)=-25
Step-by-step explanation:
In triangle △JKL, ∠JKL is right angle, and KM is an altitude. JK=24 and JM=18, find JL.
Answer:
JL ≈ 32
Step-by-step explanation:
The triangle JKL has a side of JK = 24 and we are asked to find side JL. The triangle JKL is a right angle triangle.
Let us find side the angle J first from the triangle JKM. Angle JMN is 90°(angle on a straight line).
using the cosine ratio
cos J = adjacent/hypotenuse
cos J = 18/24
cos J = 0.75
J = cos⁻¹ 0.75
J = 41.4096221093
J ≈ 41.41°
Let us find the third angle L of the triangle JKL .Sum of angle in a triangle = 180°. Therefore, 180 - 41.41 - 90 = 48.59
Angle L = 48.59 °.
Using sine ratio
sin 48.59 ° = opposite/hypotenuse
sin 48.59 ° = 24/JL
cross multiply
JL sin 48.59 ° = 24
divide both sides by sin 48.59 °
JL = 24/sin 48.59 °
JL = 24/0.74999563751
JL = 32.0001861339
JL ≈ 32
What is Pascal's triangle.
Answer:
Pascal's triangle is a triangular array of the binomial coefficients. It is used to find combinations.
Answer:
In mathematics, Pascal's triangle is a triangular array of the binomial coefficients.
Step-by-step explanation:
ANSWER ASAP PLEASE!!!!!!!!!!!! THANKS!!!!!!!!! :)
Answer: the answer is A
Step-by-step explanation:
Four consecutive multiples of 3 have a sum of 78? What is the second largest number?
Answer:
26
Step-by-step explanation:
Let x be the first number
the second one is x+1 the third one is x+2 the sum is : x+ (x+1)+(x+2)= 78so : 3x+3 = 78 then : 3x = 75 finally x = 25 the second larger number is x+1 = 25+1 = 26consider a polynomial f(x)=ax^3 + bx^2 + x + 2/3.if x + 3 is a factor of f(x) and f(x) is divided by x + 2, then we get remainder as 5. find the values of a and b.
Answer:
a = 2/27
b = 13/27
Step-by-step explanation:
The given polynomial is presented as follows;
f(x) = a·x³ + b·x² + x + 2/3
Given that x + 3 is a factor, we have;
f(-3) = 0 = a·(-3)³ + b·(-3)² - 3 +2/3 = 0
-27·a + 9·b - 3 + 2/3 = 0
-27·a + 9·b = 7/3........(1)
Also we have
(a·x³ + b·x² + x + 2/3) ÷ (x + 2) the remainder = 5
Therefore;
a·(-2)³ + b·(-2)² + (-2) + 2/3 = 5
-8·a + 4·b - 2 + 2/3 = 5
-8·a + 4·b = 2 - 2/3 = 4/3........(2)
Multiplying equation (1) by 4/9 and subtracting it from equation (2), we have;
-8·a + 4·b - 4/9×(-27·a + 9·b) = 4/3 - 4/9 × 7/3
-8·a + 12·a = 8/27
4·a = 8/27
a = 2/27 ≈ 0.0741
imputing the a value in equation (1) gives;
-27×2/27 + 9·b = 7/3
-2 + 9·b = 7/3
9·b = 7/3 + 2 = 13/3
b = 13/27 ≈ 0.481.
Hey ya'll, DONT DO THE WORK FOR ME just check it for me please, my assignment asked me.....Evan spent 20 hours doing homework last week. This week he spent 25 hours doing homework. He says that he spent 125% more time doing homework this week. Is he correct? Show your work to justify your decision.
Then, i answered with:
To find a percentage you just have to put the percent in decimal form then you multiply. 125% = 125/100 125% = 125/100 = 1.25 By doing this, we get 1.25, which is the same as 125% in decimal form. Therefore, Evan was correct. He spent 125% more time doing homework this week.
WAS MY ANSWER CORRECT OR NOTTTT
Answer:
No it was not
why... well he spent 25% time.
Step-by-step explanation:
Help please! Figure JKLM is a parallelogram. The measures of line segments MT and TK are shown. What is the value of MT? A.) 7 B.) 24 C.) 74 D.) 100
Hey there! :)
Answer:
C) 74 units.
Step-by-step explanation:
MT is congruent to KT because the diagonals of a quadrilateral bisect each other. Therefore:
8y + 18 = 12y - 10
Subtract 8y from both sides:
18 = 4y - 10
Add 10 to both sides:
28 = 4y
Divide both sides by 4:
28/4 = 4y/4
y = 7 units. Plug this into the equation for MT:
8(7) + 18 = 74 units.
Answer:
74
Step-by-step explanation:
Set up the equations
8y + 18 = 12y -10
Combine like terms
28 = 4y
Divide each side by 4
y=7
Plug in the value of y in the equation of 8y + 18 since that's the value for MT
8(7) + 18 = 74
Hope this helps!
work out 5^-2 x 3 square root 8
Answer:
6root(2)/25
Step-by-step explanation:
5^-2 = 1/25
3(root(8)) = 6(root(2))
so you get 6(root(2))(1/25)
= 6(root(2))/25
The required simplified value of the given expression is 0.34 or 6√2 / 25.
Given that,
Expression to simply ios given,
5⁻² x 3√8
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
Simplification =>
= 5⁻² x 3√8
= 1/ 5⁻² x 3 x 2 √2
= 6√2 / 25
= 0.34
Thus, the required simplified value of the given expression is 0.34 or 6√2 / 25.
Learn more about arithmetic here:
brainly.com/question/14753192
#SPJ2
Find the inequality represented by the graph
Answer:
y ≥ -2/3x +3
Step-by-step explanation:
incline is -2/3
and intercept with y-axis is 3
so the equation of the line is
y = -2/3x +3
Since the intended area in the graph I above the line, we now know enough to find the right one question:
y ≥ -2/3x +3
Answer: y>-2/3x+3 because the line is dotted its >
pleaseeeeeeeeeee helllllllllpppppppppppp
Answer:
a)16 (2*2*2*2= 16)
b)16 (-4*-4-16)(-+-=+)
c)500 (5*5*5=125 125*4=500)
d)0.49 (0.7*07)
e)480 (4^=16 9^=81 121^0=1 16+81 -1 =96 96*5=480)
f)5^2 or 25 (a^m/ a^n=a^m-n)
g) 11^14 (reason same as the f one)
h)8.20
i) 4(-4*16=64)
j)900
If ∠R is given and the values of r and q are given, then explain whether the Law of Sines or the Law of Cosines should be used to solve for ∠Q.
Answer:
To solve a triangle is to find the lengths of each of its sides and all its angles. The sine rule is used when we are given either a) two angles and one side, or b) two sides and a non-included angle. The cosine rule is used when we are given either a) three sides or b) two sides and the included angle.
Step-by-step explanation:
We just saw how to find an angle when we know three sides. It took quite a few steps, so it is easier to use the "direct" formula (which is just a rearrangement of the c2 = a2 + b2 − 2ab cos(C) formula). It can be in either of these forms:
cos(C) = a2 + b2 − c22ab
cos(A) = b2 + c2 − a22bc
cos(B) = c2 + a2 − b22ca
Answer:
Law of cosines, two sides and the included angle known
Step-by-step explanation:
double check that the question is exactly the same to make sure you get the question correct
"If ∠P is given and the values of r and q are given, then explain whether the Law of Sines or the Law of Cosines should be used to solve for p."
What is the solution to the following equation? 3(7x – 12) + 26 = 3x – 10
Answer:
x=0
Step-by-step explanation:
3(7x – 12) + 26 = 3x – 10
Distribute
21x -36 +26 = 3x-10
21x -10 = 3x-10
Add 10 on each side
21x-10+10 = 3x-10+10
21x = 3x
Subtract 3x from each side
21x-3x = 0
18x =0
x=0
Answer:
x=0
Step-by-step explanation:
3(7x – 12) + 26 = 3x – 10
21x-36+26-3x+10=0
18x-10+10=0
18x+0=0
18x=0
x=0
check : 3(7(0)-12)+26=3(0)-10
: -36+26=-10
-10=-10 it is correct
HELP 25 PTS ASAP!!!!!! BRAINLIEST
We can solve for the y-intercepts of both f(x) and h(x) by plugging in 0 as x. f(0) = -6(0)-3 = -3
h(0) = -2cos(pi)-1 = -2(-1)-1 = 1
So the y-intercept of f(x) is -3 and of h(x) is 1. We can then conclude that h(x) has a greater y-intercept than f(x) because 1>-3.
Please answer this now in two minutes
Answer:
[tex]7\sqrt{2}[/tex] meters
Step-by-step explanation:
This is a 45 45 90 triangle. This means that two sides of the triangle are equivalent. In this type of triangle, the two equal sides are represented by [tex]a[/tex] and the hypotenuse that you are trying to find (u) is represented by [tex]a\sqrt{2}[/tex]
Therefore, your answer is [tex]7\sqrt{2}[/tex] in simplest radical form.
Answer:
u= 7[tex]\sqrt{2}[/tex]
Step-by-step explanation:
The missing side is u
sin 45°=7/u switch u and sin 45°u = 7/sin°45sin 45° = [tex]\frac{\sqrt{2} }{2}[/tex]
so :
u = 7*[tex]\frac{2}{\sqrt{2} }[/tex] u = 14/√2 u = [tex]\frac{7*\sqrt{2} ^{2} }{\sqrt{2} }[/tex] u = 7[tex]\sqrt{2}[/tex]Please answer this question now in two minutes
Answer:
y=x+5
Step-by-step explanation:
Every proof needs Given and Prove statements. Use the endpoints on the diagram to write a Given statement indicating the down tube is longer than the top tube. Prove the relationship between the opposite angles of the given sides. (2 points; 1 point for the Given statement, 1 point for the Prove statement)
Answer:
m<ABC > m<ACB (angle property of a triangle)
Step-by-step explanation:
Given that: ΔABC
AB = AX
Prove: m<ABC > m<ACB
From the given diagram,
ΔABX is an isosceles triangle (two congruent sides and angles)
<AXB = m<ABX = [tex]90^{o}[/tex] (isosceles triangle property)
AC = AX + XC
Thus,
AC > AB
m<ABC = m1 + m3 ≥ [tex]90^{o}[/tex]
m<ACB < [tex]90^{o}[/tex] (acute angle property)
Therefore since in a triangle the longest side is opposite to the greatest angle, then;
m<ABC > m<ACB (angle property of a triangle)
In triangle △JKL, ∠JKL is right angle, and KM is an altitude. JK=24 and JM=18, find JL.
Answer:
JL = 32
Step-by-step explanation:
We are told in the above question that:
In triangle △JKL, ∠JKL is right angle, and KM is an altitude. JK=24 and JM=18, find JL.
From the attached diagram, we can see that
JL : JK = JK: JM
Therefore,
JL/ JK = JK /JM
Where JL = Unknown
JK = 24
JM = 18
JL/ 24 = 24/18
Cross Multiply
24 × 24 = JL × 18
Divide both sides by 18
JL = (24 × 24) /18
JL = 576/18
JL = 32
Triangles X Y Z and E G F are shown. Side X Y is 3.0 inches and angle Y Z X is 107 degrees. Side F G is 2.4 inches and side E F is 1.3 inches. Angle G E F is 48 degrees. Given ΔXYZ ≅ ΔEGF, find the measurements of the unknown sides and angles. ZX = in. EG = in. M∠X = ° m∠G = °
Answer:
ZX = 1.3 in
EG = 3.0 in
M∠X = 48°
M∠G = 25°
Step-by-step explanation:
As we can see in the attached figure that these two triangles are identical i.e their corresponding sides and angles are equal
Therefore if we say that
ZX = EF
So ZX = 1.3 in.
Now the same is applied for other sides and angles
EG = XY
So, EG = 3.0 in
M∠X = M∠E
hence, M∠X = 48°
For the M∠ G,
The angle is
= 180° - 107° - 48°
= 25°
Hence, the M∠ G is 25°
without using a calculator, choose the statement that best describes the value of \sqrt{10}
10
square root of, 10, end square root.
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
The value of \sqrt{10}
10
square root of, 10, end square root is between 222 and 2.52.52, point, 5.
(Choice B)
B
The value of \sqrt{10}
10
square root of, 10, end square root is between 2.52.52, point, 5 and 333.
(Choice C)
C
The value of \sqrt{10}
10
square root of, 10, end square root is between 333 and 3.53.53, point, 5.
(Choice D)
D
The value of \sqrt{10}
10
square root of, 10, end square root is between 3.53.53, point, 5 and 444.
Answer:
square root of,10,end square root is between 2.52.52,point,5and333
Answer:
Its choice B
Step-by-step explanation:
I got it from khan academy :)
Between 4.5 and 5
Liam wants to treat some friends to lunch. He has $50 and knows that lunch will cost about $8 per person, p. How many people can Liam buy lunch for?Part A- Write and solve an inequality to represent the Situation
Answer:
T ≥ 8x
50 ≥ 8x .......1
x ≤ 6
Liam can buy lunch for 6 people.
Step-by-step explanation:
Let x represent the number of people Liam can buy lunch for.
Given;
Lunch cost per person r = $8 per person
The total amount he has T = $50
The cost of buying lunch for c people is;
C = $8 × x
C = 8x
Therefore, to be able to buy lunch for them, the total cost C must be less than the total amount he has.
T ≥ C
Substituting C, we have;
T ≥ 8x
50 ≥ 8x ,.......1
Solving the inequalities;
8x ≤ 50
x ≤ 50/8
x ≤ 6.25
To the nearest whole number;
x ≤ 6
Liam can buy lunch for 6 people.
Franklin's grandmother opened a savings account with $275 to help him save money for college. Franklin will deposit $55 each month. His grandmother will deposit $40 each month. If Franklin makes no additional deposits or withdrawals, which equation can be used to find A, the amount of money in Franklin's savings account after p months?
Answer:
X = 275 + 95p
Step-by-step explanation:
Hello,
This question requires us to write an expression to find how much he would've saved over a certain period of time.
Initial deposit = $275
Franklin's monthly deposit = $55
Franklin grandmother's deposit = $40
Let the amount he would've saved over a certain period of time p = x
X = 275 + (55 + 40)p
X = 275 + 95p
Eg, how much would he have saved in 5 months
X = 275 + 95(5)
X = 275 + 475
X = $750
I.e in 5 months, he would've saved $750
Please please please urgent help❤️❤️❤️
Answer:
its G(2)
Step-by-step explanation:
Gg
..........help lol xD
Answer:
equilateral
acute
Step-by-step explanation:
equilateral = all equal angles
acute = all angles less than 90
Answer:
D. Equilateral
Step-by-step explanation:
An equilateral triangle is a three sided shape with sides of the same size. Since all the sides in the image are 9cm, it is considered as an equilateral triangle.
Hope this helps
Write an equation of the line that is perpendicular to y = 1/2x +3 and passes through the point
(10,-5)
Answer:
y = -2x+15Step-by-step explanation:
[tex]y = 1/2x +3\\m =1/2\\m_1m_2 = -1\\1/2m_2 =-1\\m_2= -2\\(10 ,-5)\\x = 10\\y = -5\\y = mx+b \\-5 = -2(10) + b\\-5=-20+b\\-5+20 =b\\b = 15\\m = -2\\Substitute -given -values- into- slope -intercept-form\\y = mx+b\\y = -2x+15[/tex]
Tim has 39 pairs of headphones and 13 music players. Tim wants to sell all the headphones and music players in identical packages what is the greatest number of packages time can make
Answer:
He will have 13 packages containing 3 pairs of headphones and 1 music player each.
Step-by-step explanation:
He has 39 pairs of headphones and 13 music players.
He wants to sell both set of items in identical packages.
To do this he has to divide them in such a way that the same number of both set of objects are in every box.
Let us find the ratio of the pairs of headphones to music players:
39 : 13 = 3 : 1
Therefore, dividing the pairs of headphones into 3 parts and the music players into 1 part, he can have identical packages.
So, he will have 13 packages containing 3 pairs of headphones and 1 music player each.
Find x
a) 21 √2
b)7
c)21 √2/2
d)21 √3/2
Answer:
C
Step-by-step explanation:
Use the sine ratio in the left, right triangle to find the common side to both triangles and the exact values
sin60° = [tex]\frac{\sqrt{3} }{2}[/tex] , cos45° = [tex]\frac{1}{\sqrt{2} }[/tex] , thus
sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{opp}{7\sqrt{3} }[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )
2 × opp = 21 ( divide both sides by 2 )
opp = [tex]\frac{21}{2}[/tex]
Now consider the right triangle on the right, using the cosine ratio
cos45° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{\frac{21}{2} }{x}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )
x = [tex]\frac{21}{2}[/tex] × [tex]\sqrt{2}[/tex] = [tex]\frac{21\sqrt{2} }{2}[/tex] → C