Answer:
[tex]\sf t_{20}= 0[/tex]
Step-by-step explanation:
Arithmetic sequence:[tex]\sf \boxed{\bf n^{th} \ term = a + (n-1)d}\\\\\text{Here, a is the first term ; d is the common difference }[/tex]
6th term is 14 ⇒ [tex]\sf t_6 = 14[/tex]
a + (6 - 1)d = 14
a + 5d = 14 --------------(I)
14th term is 6 ⇒[tex]\sf t_{14} = 6[/tex]
a + (14-1)d = 6
a + 13d = 6 ----------------(II)
Subtract equation (II) from equation(I)
(I) a + 5d = 14
(II) a + 13d = 6
- - -
-8d = 8
d = 8 ÷(-8)
[tex]\sf \boxed{\bf d= (-1)}[/tex]
Plugin d = -1 in equation (I)
a + 5(-1) = 14
a -5 = 14
a = 14 + 5
[tex]\sf \boxed{\bf a = 19}[/tex]
20th term:
[tex]\sf t_{20}= 19 + 19*(-1)[/tex]
= 19 - 19
[tex]\sf \boxed{\bf t_{20} = 0}[/tex]
Answer:
0
Step-by-step explanation:
The number of terms of an Arithmetic progressions has the formular.
Tn = a + ( n - 1 ) d
From the question,
6th term = 14
14th term = 6
Therefore,
a + 5d = 14 -----------(1)
a + 13d = 6 ----------(2)
subtracting
-8d = 8
dividing bothsides by -8
[tex] \frac{ - 8d}{ - 8} = \frac{8}{ - 8} \\ d = - 1[/tex]
Therefore,
common difference= -1
substituting the value of d into equation (1)
a + 5 ( -1) = 14
a - 5 = 14
a = 14 + 5 = 19
First term = 19
For the 20th term
T 20 = a + 19d
19 + 19 ( -1 )
19-19 = 0
Therefore,
20th term = 0
HELP QUICK!!
The Top-Notch Middle School had athletes from all the grades playing on a sports team.
6th grade 7th grade 8th grade
Basketball 2 4 7
Baseball 1 6 5
Soccer 7 4 4
Football 8 15 10
Explain what the ratio 5:73 represents.
The ratio 5:73 represents the ratio of 8th grade baseball players to total athletes.
The ratio 5:73 represents the ratio of 7th grade football players to total athletes.
The ratio 5:73 represents the ratio of total athletes to 7th grade football players.
The ratio 5:73 represents the ratio of 6th grade athletes to total athletes.
The ratio 5:73 represents A. The ratio 5:73 represents the ratio of 8th grade baseball players to total athletes.
What is the ratio about?Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).
Number of 8th grade baseball players = 5
Total number of athletes = 73
Therefore the ratio will be:
= 5 / 73
= 5:73.
The correct option is A
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Help please! Brainly?
Answer:
-8/4 or -2
Step-by-step explanation:
First of all notice the graph is negative. Meaning that this will be a negative slope.
Now we can use rise over run, counting up 8 spaces, and to the left 4.
Since the graph is negative make the rise negative. -8/4.
To simplify this fraction divide -8 by 4, and receive an answer of -2.
-Hope this helped
simplify to radical form the square root of 40 and then divide by 6
The simplified expression of the radical is √10/3
How to evaluate the expressionFrom the question, we have the following parameters that can be used in our computation:
the square root of 40 and then divide by 6
This statement can be mathematically represented as
√40/6
Simplify the numerator
So, we have the following representation
2√10/6
Divide 2 and 6
√10/3
Hence, the solution is √10/3
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HELP PLSS!! Find cos (A) given the triangle!!
Answer:
77.3
Step-by-step explanation:
Cos = Adjacent/Hypotenuse
Adjacent = 2.25 & Hypotenuse = 10.25
So that means...
Cos = 2.25/10.25
*When you type in the calculator type Cos-1 (2.25/10.25).
The answer is 77.319....
When you round it, it would become 77.3°.
Hope it's helpful.
How many inches of the width of the box
The width of the box is 4 inches wide
How to determine the number of inches of the widthFrom the question, we have the following parameters that can be used in our computation:
Area = 20 square inches
Height = 5 inches
The width of the box can be calculated using the following equation
Width = Area/Height
substitute the known values in the above equation, so, we have the following representation
Width = 20/5
Evaluate the quotient
Width = 4
Hence, the width is 4 inches
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Complete question
The side of a box has an area of 20 square inches and a height of 5 inches. How many inches is the width of the box?
How much is the cost per ticket?
Ride Tickets Cost
5 $7.50
7 $10.50
9 $13.50
10 $15.00
A company launches two new products. The market price, in dollars, of the two products after a different number of years, x, is shown in the following table
Based on the data in the table, for which product does the price eventually exceed all others, and why? (1 point)
Product 1, because the function is exponential
Product 2, because the function is exponential
Product 1, because it has a greater start value
Product 2, because it has a greater Year 3 value
Answer:
Product 1, because the function is exponential
Step-by-step explanation:
An exponential function, such as f(x) = 3^x, grows very quickly.
Answer: Product 1, because the function is exponential
Dawson Christian Academy have 1200 people attend a music festival on either Friday or Saturday night if 60% attended Friday night how many people attended Friday night
There are 720 people (60 percent) attended a music festival on Friday night in Dawson Christian Academy.
What is the percentage?A percentage is a figure or ratio that shows a portion of one hundred. A dimensionless relationship between two numbers can be represented in a variety of ways, such as through ratios, fractions, and decimals. The symbol "%" is frequently written after the number to indicate percentages. Additionally, you can indicate them by adding "percent" or "pct" after the number.
Given that Dawson Christian Academy have people to attend a music festival is 1200
out of these people to attend a music festival on friday is 60%
No. of people to attend a music festival on friday is 60% of 1200
⇒ (60/100)*1200
⇒ 0.60*1200
⇒ 720 people
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Help me quick please
Answer:
y = 3x + 2
Step-by-step explanation:
1. Work out the gradient of the line segment: change in y/change in x: -2 - -6/ -8 - 4 = 4/-12 = -1/3
2. Work out the gradient of the perpendicular bisector: the gradient of the line segment and the perpendicular bisector should multiply to get -1. This means that we can do -1 ÷ -1/3 to work out the gradient which is 3
4. Find the midpoint of the line segment: (-8 + 4) ÷ 2 = -2, and (-2 + -6) ÷ 2 = -4, so the midpoint is (-2, -4)
3. The equation will be in the format y = 3x + c and will go through (-2, -4), so we can substitute those values into the equation to find c:
y = 3x + c-4 = 3(-2) + c-4 = -6 + cc = -4 + 6c = 2The equation of the line is y = 3x + 2
Hope this helps!
What is the formula of image of a line?
The formula of the image of a line is( l−p)/a = (m−q)/b = -2(ap+bq+c)/√a²+b²
What is the image of a line?
Typically, a little dash is used to identify a point's reflection, such as A'. This is said with a "prime." As a result, line AB's reflection is known as A'B'. The reflection is referred to as line AB's "image."
Here,
We have to determine the formula of the image of a line.
We concluded that
The mirror's "reflection" of the specified point P causes it to appear at an equal distance away on the opposite side of the line. To see this, move point P. According to tradition, the "image" of point P is the reflection of point P across the line, which is designated by the term P' (pronounced "P prime").
Hence, the formula of the image of a line is( l−p)/a = (m−q)/b = -2(ap+bq+c)/√a²+b²
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A company produced 600 parts during first shift. The second shift produced 564 parts.
What is the percent change from first to second shift?
Reduced by 6%
In the first shift, they purchased 600 parts
the second time they purchased 564 parts
Percent = output/ total* 100here the second year they purchased a percentage
-> second shift/first shift*100 of the first year
564/600*100 ---> 564/6which gives 94%so it shows there is a reduction of 100-94 = 6%
As the second shift purchased 94 of them as compared to 100 in the first shift, So by this we can draw the inference that there is a drop of 6%.
Percent is the number out of 100 so here 36 parts are less than in the case of 600 which shows 6%. Moreover, the percentage gives a clear idea in terms of 100 which is more familiar as compared to their figures.
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What is the value of x? round to the nearest tenth, if necessary. responses x = 6 x, = 6 x = 11 x, = 11 x = 11.5 x, = 11.5 x = 13.6
Round to the nearest tenth , if necessary the value of x is 11.5.
What is right triangle ?
A right triangle is a type of triangle in which one angle is equal to 90 degrees. The side opposite this 90-degree angle is known as the hypotenuse, and the other two sides are known as the legs. The Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs, applies to all right triangles.
Triangle ABC is a right angle triangle,
We can apply the Pythagorean Theorem to get,
[tex]x^{2} +8^{2} = 14^{2} \\x^{2} = 14^{2}-8^{2} \\x^{2} = 196-64\\x^{2} =132[/tex]
x ≈ 11.5
So , Round to the nearest tenth , if necessary the value of x is 11.5.
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3) Mr. Kelly, Mr. Brust and Mr. Sullivan all met by one common interest, THE BOBSLED! In fact they were pretty darn
good. In fact they were just one-thousandth of second from qualifying for the medals at the 1998 Nagano, Japan Winter
Olympics. While bobsledding they had to maintain a balance in terms of weight. The weight of the bobsled combined
with the weight of the three men couldn't be over 1200 pounds.
a) Make an inequality where x represents the weight of the bobsled and y represents the weight of the three men.
b) If the bobsled weighed 480 pounds what are all the possible weights of the three men combined?
c) Could the bobsled weigh 520 pounds and the men weigh 685 pounds? Why or why not?
Create an inequality where x represents the weight of the bobsled and y represents the weight of the three men. Graph the inequality below. Include proper labeling on each axis, units and shading.
How do you graph inequalities ?To graph an inequality, treat the <, ≤, >, or ≥ sign as an = sign, and graph the equation. If the inequality is < or >, graph the equation as a dotted line. If the inequality is ≤ or ≥, graph the equation as a solid line.To plot an inequality, such as x>3, on a number line, first draw a circle over the number (e.g., 3). Then if the sign includes equal to (≥ or ≤), fill in the circle. If the sign does not include equal to (> or <), leave the circle unfilled inWhen solving an inequality: • you can add the same quantity to each side • you can subtract the same quantity from each side • you can multiply or divide each side by the same positive quantity If you multiply or divide each side by a negative quantity, the inequality symbol must be reversed.To learn more about graph inequalities refers to:
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If 2 1/4 + y= 5 3/4, what does y equal?
Answer:
y= 3 2/4
Step-by-step explanation:
2 1/4 + 3 2/4 = 5 3/4
Answer: y= 7/2 = 3 1/2 = 3.5
Step-by-step explanation:
2 1/4 +y=5 3/4
Multiply both sides of the equation by 4.
2×4+1+4y=5×4+3
Multiply 2 and 4 to get 8.
8+1+4y=5×4+3
Add 8 and 1 to get 9.
9+4y=5×4+3
Multiply 5 and 4 to get 20.
9+4y=20+3
Add 20 and 3 to get 23.
9+4y=23
Subtract 9 from both sides.
4y=23−9
Subtract 9 from 23 to get 14.
4y=14
Divide both sides by 4.
y= 14/4
Reduce the fraction 14/4 to lowest terms by extracting and canceling out 2.
y= 7/2
It is a property of exponents that if ax = ay and a is not 0 or 1, then x = y. You used this property to solve the equation in Question 1. Now use this same property to solve the equation 3x = 729 by rewriting to get a common base number
Using the property of exponents, the value of x for the formula 3x=729 is 6.
What is exponents?The number of times a number is multiplied by itself is referred to as its exponent. For instance, 2 to the third (written as 23) means: 2 x 2 x 2 = 8. 2 x 3 = 6 does not equal 23. Keep in mind that a number raised to the power of one is itself. Exponentiation is the process of expressing huge numbers in terms of powers. That is, exponent refers to the number of times a number has been multiplied by itself. For example, 6 is multiplied by itself four times, yielding 6 6 6 6. This is written as 64. The exponent is 4 and the base is 6.
Here,
3ˣ=729
3ˣ=3⁶
x=6
The value of x for expression 3ˣ=729 is 6 using property of exponents.
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Do the lengths 18cm 24cm and 30cm form a right triangle?
It is possible to construct a triangle whose sides are 18 cm 24 cm and 30 cm because the sum of two sides are greater than three sides.
In the given question, we have to check that it is possible to construct a triangle whose sides are 18 cm 24 cm and 30 cm.
The sum of the two sides must always be greater than the third side in order to determine whether or not the given sides may form a triangle.
To check this we firstly add the 18 and 24
18 + 24 > 30
42 > 30
Now we add 18 and 30
18 + 30 > 24
48 > 24
Now we add 24 and 30
24 + 30 > 18
54 > 18
It is possible to construct a triangle whose sides are 18 cm 24 cm and 30 cm because the sum of two sides are greater than three sides.
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Find the y-value that will make the equations below true by
graphing the lines on a coordinate plane and determining
where they intersect.
3x + y = -3
-2x + y = 2
NEED DONE BY 5:PM!!
Answer:
(-1,0)
Step-by-step explanation:
See attached graph. Use a free site such as DESMOS for graphing.
plssss i’ll give points?
Perpendicular is an angle of 90° to a given line, plane, or surface means.
the equation is : y = ax+b
the equation is : y = ax+b
the slope is a : a×(1/4) = -1......( perpendicular to a line with a slope of 1/4) because
y=x/4 -2 means y = (1/4)x -2... the slope is : 1/4
but : a×(1/4) = -1 so : a = - 4 y= - 4x+b
the line that passes through (4, -1)
-1 =-4(4)+b
b = 15
the equation is : y = - 4x+15
19) Solve for "x" using an inverse operation.
3x = 48
20) Solve for "x" using an inverse operation.
4x = 64
The value of x in the equation 3x = 48 is 16 and for equation 4x = 64 is 16.
What is equation ?
A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used. A lot of specialists, such as air traffic controllers, architects, computer programmers, and carpenters, employ equations on a daily basis.
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.
3x = 48
As it is multiplication we divide it by 3
3x / 3 = 48 / 3
x = 16
4x = 64
As it is multiplication we divide it by 4
4x / 4 = 64 / 4
x = 16
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Evaluate the expression, use calculator if needed.
Answer:
1/128 or 0.0078125, round as needed
Step-by-step explanation:
✨calculator✨
What is the value of |238| + |−28| − |−14|?
224
196
280
252
Answer:
Step-by-step explanation:the answer is d
Answer:
252 my guy
Step-by-step explanation:
238 after absolute value is 238
-28 after absolute value is 28
-14 after absolute value is 14, but theres a negative infront of the number
therefore:
238+28-14
= 252
Julie has 15 nails. she uses 8 to build a birdhouse she subtracts to find the number of nails left. which addition sentence can she use to check her work
Answer:A
Step-by-step explanation:
.
I need help with this! L, M belong on line KN
The value of x in the triangle is 38 degrees.
How to find angles in a triangle?A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.
The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle.
The exterior angle theorem can be used to find the angle x in the triangle.
Hence,
x + (180 - 84) = 134
x + 96 = 134
subtract 96 from both sides of the equation
x = 134 - 96
Therefore,
x = 38 degrees
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Answer: x=38
Step-by-step explanation:
x=38
a cabinet holds shelves that are 12 1/2 inches apart. On one shelf, Katherine stacked a CD player that is 4 5/8 in. high on top of an amplifier that is 6 3/4 in. high. How much space was left above the CD player?
The space left above the CD player of height 4 5/8 in. stacked on the amplifier of height 6 3/4 in. in the cabinet which has shelves of 12 1/2 in. apart calculated as mixed fractions is 1 1/8 inches.
What is a mixed fraction?A mixed fraction is a fraction that is specified using the value of the quotient (the whole number part) and a fraction consisting of the remainder divided by the divisor.
The distance between the shelves of the cabinet = 12 1/12 inches
The height of the amplifier on a shelve of the cabinet on top of which Katherine stacks the CD player = 6 3/4 inches
The height of the CD player placed on top of the amplifier = 4 5/8 inches
The dimensions of the distance between the shelves and the heights of the CD player and amplifier are specified in fractions.
The space left above the CD player can be found in fractions as follows;
The combined height of the CD player and the amplifier is therefore;
[tex]H = 4\frac{5}{8} +6\frac{3}{4} = (4 + 6) + \left(\dfrac{5}{8}+\dfrac{3}{4} \right)[/tex]
[tex](4 + 6) + \left(\dfrac{5}{8}+\dfrac{3}{4} \right)=10 + \left(\dfrac{5+2\times 3}{8} \right) = 10 + \dfrac{11}{8}[/tex]
[tex]10 + \dfrac{11}{8} = 10 + 1\dfrac{3}{8} = 11\frac{3}{8}[/tex]
The space above the CD player is therefore;
[tex]12\frac{1}{2} - 11\frac{3}{8} = 12 - 11 + \left(\dfrac{1}{2} - \dfrac{3}{8} \right) = 1 + \left(\dfrac{4 - 3}{8} \right)[/tex]
[tex]1 + \left(\dfrac{4 - 3}{8} \right) = 1\frac{1}{8}[/tex]
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A rock climber climbs at a rate of 720 feet per hour. Write and solve an equation to find the number of minutes
m it takes for the rock climber to climb 288 feet.
An equation that represents this situation is
The equation is y=12x.
It takes 24 minutes for the rock climber to get to 288 feet.
The calculation is as follows:
here we know that
One hour = 60 minutes
so, by dividing 720 from 60 we get 12
here we assume the time in minutes be x
So, the equation is
y = 12x
288=12x
288/12 = 12x/12
24 = x
The length of the hypothesis of an isosceles right triangle is 8. Find the perimeter of the triangle with a picture
An isosceles right triangle has a perimeter of 16 square centimeters since the hypotenuse is 8 length.
what is perimeter ?A boundary is a closed path that surrounds, delimits, or includes a two-dimensional shape or a one-dimensional length. The outermost part of a circle or an ellipse is called the perimeter. The perimeter calculation has numerous real-world applications. A shape's perimeter is the measurement of its edge's radius. Discover how to calculate the perimeter by adding together the lengths of the sides of various forms. The perimeter of any shape can be calculated by multiplying its side lengths. An object's perimeter is the region that surrounds it. A good illustration of this at your house is a closed-off garden. Its perimeter is the space encircling something. For a 50 by 50 foot yard, a 200 foot fence will be required.
given
AC (hypotenuse) = 8 cm. ,
AB^2+BC^2 = AC^2
x^2+x^2 = 8^2
2x^2 = 64
x^2= 64/2=32
x = 4.2^1/2 cm.
Perimeter = {8 +4.(2)^1/2+4.(2)^1/2}
= {8+8.(2)^1/2}
=8(1+2^1/2) cm.
Area =( base×altitude)/2= (4.2^1/2×4.2^1/2)/2 = 16sq.cm.
An isosceles right triangle has a perimeter of 16 square centimeters since the hypotenuse is 8 length.
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Is 3x³ a polynomial?
So on solving the provided question we can say that 3x³ is a polynomial as it have exponential power
what are polynomials?A mathematical expression made up of coefficients and uncertainty that only makes use of additions, subtractions, multiplications, and positive integer powers of variables is known as a polynomial. The formula x2 4x + 7 denotes a single indeterminate x polynomial. An expression in mathematics known as a polynomial is made up of variables (also known as indeterminates) and coefficients that may be added, subtracted, multiplied, and raised to negative integer powers of non-variables. An algebraic statement with variables and coefficients is called a polynomial. An expression can only contain the operations addition, subtraction, multiplication, and non-negative integer exponents. Polynomials are the name for these expressions.
here,
3x³ is a polynomial
as it have exponential power
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Brianna surveyed a representative sample of students at her school to collect data about the numbers of Internet-compatible devices they own. Brianna wants to know how many Internet-compatible devices are owned, on average, by people in her town. Can she use her sample data to form a valid inference about the town? Use the drop-down menus to explain your answer.
Brianna
Choose...
use her sample data to form a valid inference about the town because her school
Choose...
represent her town’s entire population.
I apologize for any confusion. Based on the information given, Brianna cannot use her sample data to form a valid inference about the town because it is not specified that her sample is random or representative of the entire population. Additionally, it is not clear what the population of the town is or how many people live in the town. The question is asking whether or not she can use her sample data to form a valid inference about the town based on the information given in the question. The answer is no, she cannot use her sample data to form a valid inference about the town.
someone please helppp
The shape forms a pentagon. The value of y is 84°.
What is a polygon?
In geometry, a polygon is any closed curve made up of a series of line segments (sides) joined so that no two segments cross. Triangles (three sides), quadrilaterals (four sides), and pentagons are the simplest polygons (five sides).
The shape ABCDE forms a petagon.
The interior angle of a pentagon is 108°
The interior angle of a hexagon is 120°.
The ∠ABC is an angle of a regular hexagon, thus ∠ABC = 120°.
The ∠BCD is the angle of a regular hexagon, thus ∠BCD =120°.
The ∠BAE is an angle of a regular pentagon, thus ∠BAE=108°.
The ∠AED is an angle of a regular pentagon, thus ∠AED=108°.
The sum of all interior angle of a pentagon is 540°
Therefore,
∠ABC + ∠BCD + ∠BAE + ∠AED +∠EDC = 540°
120° + 120° + 108° + 108° + y = 540°
456° + y = 540°
y = 540° - 456°
y = 84°
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Calculate the geometric mean return of the following data set: (Negative value should be indicated by a minus sign. Round your intermediate calculations to 4 decimal places and final answer to 2 decimal places.)
The geometric mean return of the given data set is 0.02.
The geometric mean return measures the compound rate of return over a period of time. It is calculated by taking the product of all the returns and then taking the nth root of the product, where n is the number of returns.
Formula: GMR = ((1+r1)(1+r2)…(1+rn))^1/n – 1
In this case, the data set is as follows:
r1 = 0.05
r2 = 0.03
r3 = -0.02
Using the formula above, the geometric mean return is calculated as:
GMR = ((1+0.05)(1+0.03)(1-0.02))^1/3 - 1
GMR = ((1.05)(1.03)(0.98))^1/3 - 1
GMR = (1.1394)^1/3 - 1
GMR = 0.0204
Therefore, the geometric mean return of the given data set is 0.02.
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