Answer:
Step-by-step explanation:
In an arithmetic sequence, the consecutive terms differ by a common difference. The formula for determining the nth term of an arithmetic sequence is expressed as
Tn = a + (n - 1)d
Where
a represents the first term of the sequence.
d represents the common difference.
n represents the number of terms in the sequence.
From the information given,
a = - 5
d = 6
n = 21
We want to determine the value of the 21th term, thus, n = 21. Therefore,
T21 = - 5 + (21 - 1)6
T21 = - 5 + 120
T21 = 115
Answer:
115
Step-by-step explanation:
I had this on my test and I got 100%
The length of a rectangle is 2 less than 3 times its width. If the area of the rectangle is 96cm², what is the length of the rectangle?
Answer:
[tex] \boxed{\sf Length \ of \ the \ rectangle = 16 \ cm} [/tex]
Given:
Area of the rectangle = 96 cm²
Length of the rectangle = 2 less than 3 times it's width
To Find:
Length of the rectangle
Step-by-step explanation:
Let the width of the rectangle be 'w'.
So,
Length of the rectangle = 3w - 2
[tex]\sf \implies Area \ of \ rectangle = Length \times Width \\ \\ \sf \implies 96 = (3w - 2) \times w \\ \\ \sf \implies 96 = 3 {w}^{2} - 2w \\ \\ \sf \implies 3 {w}^{2} - 2w = 96 \\ \\ \sf \implies 3 {w}^{2} - 2w - 96 = 0 \\ \\ \sf \implies 3 {w}^{2} - (18 - 16)w - 96 = 0 \\ \\ \sf \implies 3 {w}^{2} - 18w + 16w - 96 = 0 \\ \\ \sf \implies 3w(w - 6) + 16(w - 6) = 0 \\ \\ \sf \implies (w - 6)(3w + 16) = 0 \\ \\ \sf \implies w - 6 = 0 \: \: \: \: \: \: \: \: \: or \: \: \: \: \: \: \: \: 3w + 16 = 0 \\ \\ \sf \implies w = 6 \: \: \: \: \: \: \: \: or \: \: \: \: \: \: \: \: \: 3w = - 16 \\ \\ \sf \implies w = 6 \: \: \: \: \: \: \: \: \: or \: \: \: \: \: \: \: \: w = - \frac{16}{3} [/tex]
Width can't be negative. So,
Width of the rectangle = 6
Length of the rectangle = 3w - 2
= 3(6) - 2
= 18 - 2
= 16 cm
The length of the rectangle is 16 cm
The width of the rectangle is 6 cm
What is the Area of a Rectangle?
The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle
Area of Rectangle = Length x Width
Given data ,
Let the area of the rectangle be = 96 cm²
Let the length of the rectangle be = L
Let the width of the rectangle be = W
Now ,length of a rectangle is 2 less than 3 times its width
Substituting the values in the equation , we get
L = 3W - 2
Now , the area of the rectangle = L x W
So ,
96 = ( 3W - 2 ) x W
On simplifying the equation , we get
96 = 3W² - 2W
Subtracting 96 on both sides of the equation , we get
3W² - 2W - 96 = 0
3W² - 18W + 16W - 96 = 0
Taking 3W as the common factor , we get
3W ( W - 6 ) + 16 ( W - 6 ) = 0
( W - 6 ) ( 3W + 16 ) = 0
Now , the width of the rectangle cannot be negative , so
W - 6 = 0
Adding 6 on both sides of the equation , we get
W = 6 cm
Now , the length of the rectangle L = 3W - 2
L = 3 ( 6 ) - 2
L = 18 - 2
L = 16 cm
Therefore , the value of L is 16 cm
Hence , the length of the rectangle is 16 cm
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$5000 was invested into an investment that pays 4.25% simple interest. The total value of the investment amounted to $6593.75. How long was principal invested for?
Answer:
7.5 years
Step-by-step explanation:
P = $5000,
R = 4.25%,
A = $6593.75,
N =?
SI = A - P = 6593.75 - 5000 =$1593. 75
[tex] \because \: SI = \frac{ PNR}{100} \\ \\ \therefore \: 1593.75 = \frac{5000 \times N \times 4.25}{100} \\ \\ \therefore \: 1593.75 \times 100 = 21,250 \times N \\ \\ N = \frac{159375}{21250} \\ \\ N = 7.5 \: years \: [/tex]
(-3)(-)-4+ (-2)(09-11)
Slove the problem
Answer:
The answer is -8
Step-by-step explanation:
(3)(-4)=-12 (-2)(-2)=4
identify the variable expression that is not a polynomial.
A. y+23
B. 3\sqrt(x)-2
C. x^3
D. 13
Answer:
B. 3\sqrt(x)-2
Step-by-step explanation:
A polynomial cannot have a variable in the denominator
A constant is a polynomial
3\sqrt(x)-2 and this cannot be simplified to get rid of the variable in the denominator so it is not a polynomial
please help me I am very confused.
Answer:
1/2
Step-by-step explanation:
Square root as a exponent or power with a base is 1/2.
z^1/2 = √z
Michael has 3 quarters, 2 dimes, and 3 nickels in his pocket. He randomly draws two coins from his pocket, one at a time, and they are both dimes. He says the probability of that occurring is 1 4 because 2 of the 8 coins are dime
Answer: No. Choosing two dimes are dependent events. The probability of choosing the first dime is 1/4 and the probability of choosing the second dime is 1/7. The probability that both coins are dimes is (1/4)(1/7) = 1/28.
Step-by-step explanation:
Answer:
Step-by-step explanation:
2/8×1/7=1/28
Mario writes the equation (x+y ) 2 = z 2 +4( 1 2 xy) (x+y)2=z2+4(12xy) to begin a proof of the Pythagorean theorem. Use the drop-down menus to explain why this is a true equation.
Answer:
For the drop down menu:
i) x + y
ii) z²
iii) ½ xy
The complete question related to this found on brainly (ID:16485977) is stated below:
Mario writes the equation (x+y)² = z² +4( 1/2 xy) to begin a proof of the Pythagorean theorem. Use the drop-down menus to explain why this is a true equation.
_____finds the area of the outer square by squaring its side length.
_____finds the area of the outer square by adding the area of the inner square and the four triangles.
These expressions are equal because they both give the areas of outer space.
Find attached the diagram of the question.
Step-by-step explanation:
Pythagoras theorem is a formula that shows the relationship between the sides of a right angled triangle.
Pythagoras theorem
Hypotenuse ² = opposite ² + adjacent ²
From the diagram of the question.
Hypotenuse = z
Opposite = y
Adjacent = x
z² = x² + y²
Area of outer square = area of inner square + 4(area of triangles)
area of inner square = length² = (x+y)²
Expanding area of the outer square:
(x+y)² = (x+y)(x+y) = x²+xy+xy+y²
(x+y)² = x²+y²+2xy
= z² + 2xy
Area of inner square = length² = z²
Area of triangle = ½ base × height
= ½ × x × y = ½ xy
Area of outer square = area of inner square + 4(area of triangles)
(x + y)² = z² + 4(½xy )
Therefore, it is a true equation.
( x + y )² finds the area of the outer square by squaring its side length.
z² + 4( 1/2xy ) finds the area of the outer square by adding the area of the inner square and the four triangles.
These expressions are equal because they both give the areas of outer space.
So for the drop down menu:
i) x + y
ii) z²
iii) ½ xy
Find the measures of the supplementary angles that satisfy each case.
The measure of the first angle is 45° more than the measure of the second.
Please help meeeee!
Answer:
67.5 degrees, and 112.5 degrees.
Step-by-step explanation:
Let's make the second angle "x"
Supplementary angles always add up to 180 degrees.
So the first angle is 45 degrees more than the second, so you do:
x+x+45=180
Solve that and you get 67.5. That is the second answer. To find the first answer, add 45 to that. The answer is correct. Please give me branliest.
help plz i will make u brainllest
Answer:
C. 3√7
Step-by-step explanation:
As we know, the product of projections is equal to square of altitude in the right triangle. Applied to the given triangle, we get:
9×7= y²y= √9×7y=3√7Choice C. 3√7 is the correct one
Answer: C. 3√7
Step-by-step explanation:
-3(x-1) + 8(x-3) = 6x + 7 - 5x
Answer:
x=7
Step-by-step explanation:
-3(x-1)+8(x-3)=6x+7-5x
-3x+3+8x-24=6x+7-5x
5x-21=x+7
4x=28
x=7
Answer:
x=7
Step-by-step explanation:
-3(x-1) + 8(x-3) = 6x + 7 - 5x
Distribute
-3x +3 +8x -24 = 6x +7 -5x
Combine like terms
5x -21 = x+7
Subtract x from each side
5x-x-21 = 7
4x -21 =7
Add 21 to each side
4x-21+21 = 7+21
4x = 28
4x/4 = 28/4
x=7
what is -5c plus 2 less than or equal to 27. I need this for very difficult homework if anyone can help :)
Answer:
c ≥ -5
Step-by-step explanation:
-5c +2 ≤ 27
Subtract 2 from each side
-5c +2-2 ≤ 27-2
-5c ≤25
Divide by -5, remembering to flip the inequality
-5c/-5 ≥25/-5
c ≥ -5
Answer: [tex]x\geq 5[/tex]
Step-by-step explanation:
[tex]-5x+2\leq 27\\Subtract\\-5x\leq 25\\Divide\\x\geq 5[/tex]
It's important to remember that when you divide both sides of an inequality by a negative number to flip the sign.
Hope it helps <3
Please answer this question fast in two minutes
Answer:
∠CGA or ∠DGF
Step-by-step explanation:
Supplementary angles add up 180°
∠CGD + ∠CGA = 180°
∠CGD + ∠DGF = 180°
what is the surd of these two right angled triangles
Answer:
a = √157b = √85First QuestionTo find a we Pythagoras theorem
That's
[tex] {a}^{2} = {6}^{2} + {11}^{2} \\ {a}^{2} = 36 + 121 \\ \\ {a}^{2} = 157 \\ \\ a = \sqrt{157} \\ [/tex]
Second question[tex] {11}^{2} = {b}^{2} + {6}^{2} \\ \\ {b}^{2} = 121 - 36 \\ \\ {b}^{2} = 85 \\ \\ \\ b = \sqrt{85} [/tex]
Hope this helps you
Answer:
Below in bold.
Step-by-step explanation:
The first one a^2 = 6^2 + 11^2 ( By the Pythagoras Theorem)
a^2 = 157
a = √157.
The second triangle:
b^2 = 11^2 - 6^2
b^2 = 85
b = √85.
if y varies inversely as x and y=6 when x=8 find y when x=7
Answer:
y = 5 1/4
Step-by-step explanation:
For direct or inverse variation relation
relation between two variable and y can be expresses in form of
y = kx where k is constant of proportionality .
Only thing happens in inverse relation is that when x increases then y decreases and vice versa. That is care by constant of proportionality
__________________________________
Thus, let the inverse relation be
y = kx
given
when y = 6 then x = 8
we will plug this value in y = kx
6 = k*8
=>k = 6/8 = 3/4
Thus,
relation is
y = 3/4 x
we have to find y when x = 7 ,
lets put x = 7 in y = 3/4 x
y = 3/4 *7 = 21/4 = 5 1/4
Thus, when x = 7 then y = 5 1/4
A basket of fruit contains 4 bananas, 3 apples, and 5 oranges. You intend to draw a piece of fruit from the basket, keep it, draw a 2nd piece of fruit from the basket, keep that, and then draw a third piece of fruit from the same basket.What is the probability of selecting one banana, then one apple, then one orange, in that order, from the basket if you are blindfolded?
Answer:
The probability that the fruits will be selected in the order of banana then apple then orange is 0.1094
Step-by-step explanation:
The given information are;
The number of bananas = 4
The number of apples = 3
The number of oranges = 5
The total number of fruits are 4 + 3 + 5 = 12
The probability of selecting a banana, p(b) = 4/12 = 1/3
The probability of selecting an apple, p(a) = 3/12 = 1/4
The probability of selecting an oranges, p(o) = 5/12
The probability of selecting one banana, then one apple, then one orange, in that order, from the basket with replacement is the product of the individual probabilities found as follows;
p(p(b) then p(a) then p(o)) =
The number o
The probability that the first fruit is a banana = ₁₁C₃×(1/3)^(3)×(2/3)^8 = 0.2384
The probability that the second fruit is an apple = ₁₁C₃×(1/4)^(3)×(3/4)^8 = 0.258
The probability that the third fruit is an apple = ₁₁C₃×(5/12)^(3)×(7/12)^8 = 0.16
The total probability = 0.2384 + 0.285 + 0.16 = 0.657
The number of ways in which the three can be selected = 3 × 2 × 1 = 6 ways
Therefore, the probability that the fruits will be selected in the order of banana then apple then orange = 0.657/6 = 0.1094.
CAN SOMEONE TUTOR ME PLSSSSS ????
Answer:
[tex] \frac{105}{4} [/tex]
please see the attached picture for full solution..
hope it helps...
Good luck on your assignment..
Jose’s school has 426 students. His principal has promised the Student Council that their idea will be carried out if they can get at least 25% of the student population to sign a petition. So far, 82 students have signed the petition. Jose used the following steps to write an inequality that can be used to determine the number of student signatures still needed: Step 1. Declare the variable: Let x = the number of student signatures still needed. Step 2. Create a ratio equivalent to StartFraction total number of signatures needed over total number of students in the school EndFraction : StartFraction x + 82 over 426 EndFraction. Step 3. Convert 25% to a decimal: 25% = 0.25. Step 4. Write the inequality: StartFraction x + 82 over 426 EndFraction less-than-or-equal-to 0.25. What is Jose’s error? In Step 1, x should be equal to the total number of students in the school. In Step 2, the ratio should be StartFraction x over 426 EndFraction. In Step 3, the decimal should be 0.025. In Step 4, the inequality should
Answer: Step 4
Step-by-step explanation:
1. Define variable x as student signatures still needed (Correct)
[tex]2)\ \dfrac{x+82}{426}[/tex] (Correct)
3. 25% = 0.25 (Correct)
[tex]4)\ \dfrac{x+82}{426}\leq 0.25[/tex] (Error)!
The inequality symbol should be GREATER THAN or equal to (≥) because Jose needs 25% or more (not less).
Answer:
In Step 4, the inequality should be StartFraction x + 82 over 426 EndFraction greater-than-or-equal-to 0.25.
¯\_ _/¯
( ﾉ ﾟｰﾟ)ﾉ ＼(ﾟｰﾟ＼)
USE THE IMAGE ATTACHED BELOW please help me with my work answer it correctly I HAVE SO MUCH WORK DURING QUARANTINE
Answer:
Question 1:
a. The answer is B because the graph inclined really quickly and then it inclined at a much slower pace, suggesting that the person was running and then walking.
b. The answer is C because you can see on the graph that after a while, the distance from the starting point goes back to 0, indicating that the person forgot something at home.
Question 2:
a. The dashed line reaches the bottom at 15:30 so the answer is C.
b. Siobhan travels 8 km to go from home to school so the answer is 2 * 8 = 16 which is option D.
Question 3:
The answer is C because after the distance from the starting point increased, it then decreased and came back to the original point suggesting that he walked, turned around and walked back to the starting point.
Answer:
first page : a) A because it is the shortest time with no stop
b) C the graph goes up and return to the start point after a while
second page : it is at 3:30 0r 15:30
b): 8 km going to schools and 8 coming back is 16
third page it is C because he walk up a certain distance and come back to the starting point
PLEASE HELP ME! can someone explain this to me pls?
PLEASE HELP ME I WILL MAKE YOU THE FAMOUS
Which description matches the graph of the inequality y<-1/2x+5 A.a shaded region above a dashed boundary line B.a shaded region below a dashed boundary line C.a shaded region below a solid boundary line D.a shaded region above a solid boundary line
Answer:
B
Step-by-step explanation:
dashed line above the shaded area, shaded area below dashed boundary line
Multiple the polynomials (3x^2+4x+4) (2x-4)
Answer:
6x³ - 4x² - 8x - 16
Step-by-step explanation:
Step 1: Distribute the 2x
6x³ + 8x² + 8x
Step 2: Distribute the -4
-12x² - 16x - 16
Step 3: Combine the 2 distributions
6x³ + 8x² + 8x - 12x² - 16x - 16
Step 4: Combine like terms
6x³
8x² - 12x² = -4x²
8x - 16x = -8x
-16
Step 5: Rewrite
6x³ - 4x² - 8x - 16
━━━━━━━☆☆━━━━━━━
▹ Answer
6x³ - 4x² - 8x - 16
▹ Step-by-Step Explanation
(3x² + 4x + 4) (2x - 4)
Distribute
3x²(2x - 4) + 4x(2x - 4) + 4(2x - 4)
Remove parentheses
6x³ - 12x² + 4x(2x - 4) + 4(2x - 4)
Collect like terms
6x³ - 12x² + 8x² - 16x + 8x - 16
6x³ - 4x² - 16x + 8x - 16
Solve
6x³ - 4x² - 8x - 16
Hope this helps!
CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
Write the decimal 4.06 in word form and expanded form. Please
Answer:
four and six one hundredths
406/100
Step-by-step explanation:
Amad was curious if triangles \triangle ABC△ABCtriangle, A, B, C, and \triangle EDF△EDFtriangle, E, D, F were congruent. He was able to map one figure onto the other using a reflection and a rotation. Amad concluded: "I was able to map \triangle ABC△ABCtriangle, A, B, C onto \triangle EDF△EDFtriangle, E, D, F using a sequence of rigid transformations, so the figures are congruent."
Answer:
There is no error, Amad is correct.
Step-by-step explanation:
Khan Academy Checked.
Amad had done no error. His conclusion is true.
What is Congruency?Two triangles are said to be congruent if their sides are equal in length, the angles are of equal measure, and they can be superimposed on each other.
For example,
In the figure given above, Δ ABC and Δ PQR are congruent triangles. This means that the corresponding angles and corresponding sides in both the triangles are equal.
Sides: AB = PQ, BC = QR and AC = PR;
Angles: ∠A = ∠P, ∠B = ∠Q, and ∠C = ∠R.
Therefore, Δ ABC ≅ Δ PQR
The following are the congruence theorems or the triangle congruence criteria that help to prove the congruence of triangles.
SSS (Side, Side, Side)SAS (side, angle, side)ASA (angle, side, angle)AAS (angle, angle, side)RHS (Right angle-Hypotenuse-Side or the Hypotenuse Leg theorem)As, from the given cases the prediction of congruency of two triangles is correct. There is no error he made.
Hence, Amad had not made any error.
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Solve: 3/x-4 >0 A.x -4 C.x>4 D.x<-4
Answer:
C. x>4
Step-by-step explanation:
3/(x-4) > 0
3>0, so
x-4 >0
x > 4
Solve for x 6 x − 9 = 2 x + 7 can u plz help me
Answer:
x=4
Step-by-step explanation:
some come in clutch and do this for me
Answer:
68cm²Step-by-step explanation:
The total surface area of the bite= total surface area of the sphere + total surface area of the rectangular prism
Total surface area of a sphere Ss = 4πr²
r = radius of the sphere = diameter/2
Given diameter of the sphere= 3cm; r = 3/2 cm
Ss = 4π(3/2)²
Ss = 4π*9/4
Ss = 9πcm²
For the rectangular prism
Total surface area Sr = 2WL + 2LH + 2HW
W = width of the prism
L = length of the prism
H = height of the prism
Given W = 4cm, L = 4cm, H = 0.5cm
Sr = 2(4)(4) + 2(4)(0.5) + 2(0.5)(4)
Sr = 32+4+4
Sr = 40cm²
Surface area of the bite = 9π + 40
Surface area of the bite = 68.27cm²
Surface area of the bite = 68cm² (to nearest square of a centimetre)
The equation of a line is y = 4x + 15. what is the y-intercept of the line.
Answer:
15
Step-by-step explanation:
[tex]y = 4x + 15 \\ equating \: it \: with \\ y = mx + b \\ we \: find \\ b = 15 \\ \implies \: y - intercept = 15[/tex]
Answer:
Y intercept = 15
Step-by-step explanation:
Formula we use,
→ y = mx + b
→ b = y intercept
Then the y intercept will be,
→ y = mx + b
→ y = 4x + 15
→ [ b = 15 ]
Thus, required answer is 15.
Bidmas 7+8 divided 5-2
Answer:
Step-by-step explanation:
7 + 8 = 15
5 - 2 = 3
∴ 7 + 8 ÷ 5 - 2
= 15 / 3
= 5
Hope this helps
plz mark as brainliest!!!!!!
Answer:
5
Step-by-step explanation:
:)
Question is down below
Answer:
a ) [tex]2 / n[/tex],
b ) [tex]15[/tex]
Step-by-step explanation:
This is a nice and short question we have here.
Given that a bag has n counters, and that one counter is blue, respectively the rest is red, if two counters are taken at random there isn't a definite percentage that one of the counters chosen is red or blue, but there is a fractional representation of this.
We could express n ( number of counters ) to form a probability of 2 / n. As you can see, two counters are taken at random over n counters, and thus we derived this fraction.
a ) [tex]2 / n[/tex]
____
Now we have this second part -
[tex]2 / n = 2 / 16,\\16 - 1 = 15[/tex]
Therefore, there are 15 red counters. Hope that helps!
Factor completely.
a 2 + 28 a + 27
Hey there! :)
Answer:
(x + 27)(x + 1)
Step-by-step explanation:
Given:
a² + 28a + 27
Find numbers that add up to 28 and multiply to 27:
We can find that the numbers 27 and 1 add up to 28 and multiply to form 27. Therefore, the equation in factored form is:
(x + 27)(x + 1)
Answer:
(a+27)(a+1)Solution,
[tex] {a}^{2} + 28a + 27 \\ = {a}^{2} + (27 + 1)a + 27 \\ = {a}^{2} + 27a + a + 27 \\ = a(a + 27) + 1(a + 27) \\ = (a + 27)(a + 1)[/tex]
Hope this helps..
Good luck on your assignment..