Find the 96th term of the arithmetic sequence 1, -12, -25,

The graph that matches the data on the table, representing the altitude and time of a hawk is the straight line graph in the second option.

A straight line graph is the graph of a linear function or relationship

From the he values in the given, we have;

The difference between the consecutive altitude values (the first difference) = 70 - 80 = 60 - 70 = 50 - 60 = -10 is constant

The difference between consecutive time values = 1

Therefore;

The relationship is a linear relationship and the graph is a straight line.

Slope of the graph = -10/1 = -10

The equation in point and slope form is therefore;

(y - 80) = (-10) × (x - 1) = -10•x + 10

(y - 80) = -10•x + 10

y = 80 + 10 - 10•x = 90 - 10•x

y = 90 - 10•x

The y–intercept = 90

The slope = -10

The correct option is therefore the second graph that has the altitude (ft) on the the vertical axis and the time (s) on the horizontal axis, with a straight line decreasing from left to right starting at the point (0, 90) on the left

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The volume of a pyramid is v = 1/3base area × height

height = 3volume/ base area

height = 3×168cm^3/ 36cm^2

height = 14cm

A pyramid is a three-dimensional shape. It has a flat polygon base. All the other faces are triangles which are called lateral faces. The number of lateral faces equals the number of sides on its base.

The volume of a pyramid is given by

v= 1/3base area × height

= 3×168 = 36h

therefore the height =3x168/36

= 14cm

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The area of the rectangle is  [tex]b^2[/tex] +9b square feet

The rectangle is the quadrilateral whose opposite sides are parallel and equal. The rectangle is a four sided shape that all the angles are 90 degrees

The area is defined as the total space occupied by the two dimensional shape like rectangle, triangle, circle etc..

The length of the rectangle = (5/3)b+15 feet

The width of the rectangle = (3/5)b feet

The area of the rectangle = The length of the rectangle × The width of the rectangle

Substitute the values in the equation

The area of the rectangle  = [(5/3)b+15] ×(3/5)b

Apply the distributive property in the equation

[(5/3)b+15] ×(3/5)b = [tex]b^2[/tex] +9b square feet

Hence, the area of the rectangle is  [tex]b^2[/tex] +9b square feet

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The ratio of the number of history majors to the number of mathematics majors is 3 to 2.

When two objects are related using numbers or amounts, the relationship is known as a ratio.

Let E be the number of English majors, H be the number of history majors, and M is the number of math majors.

Now,

There are twice as many English majors as history majors.

E = 2 × H

There are three times as many English majors as mathematics majors.

E = 3 × M

Now, let's assume E = 6.

Then,

6 = 2 × H

H = 3 and,

6 = 3 × M

M = 2

Therefore, the ratio of the number of history majors to the number of mathematics majors will be:

H: M = 3 : 2

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Using the graph obtained value of k is 1/3. Option C is correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that

f(x) and g(x) = f(k-x),

The standard equation of a line is,

y = mx + b

The slope of the line for the coordinate points are (1, 2) and (1.5, 5)

m = 5-2/1.5-1

m = 3/0.5

m = 6

The y-intercept of the line is,

2 = 6(1) + b

2 - 6 = b

b = -4

As a result the obtained  equation is g(x) = 6x - 4

For the other coordinate point (3, 2) and (2, 0), the slope is

m = 0-2/2-3

m = -2/-1

m = 2

The y-intercept of the line is,

2 = 2(3) + b

2 - 6 = b

b = -4

As a result the obtained equation will be f(x) = 2x - 4.

Substitute xk at the place of x in the function as

f(xk) = 2(xk)- 4

If g(x) to f(k⋅x)

6x + 4 = 2(xk)- 4

6x = 2xk

6 = 2k

k = 1/3

Thus, using the graph obtained value of k is 1/3. Option C is correct.

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Answer:

5

Step-by-step explanation:

If Alex is 14 and he's 9 years older than his sister Kristen,then Kristen is 5

14-9=5

Answer:

14-9 = 5, so Kristen is 5 years old

Answer:

The original price was $864

Step-by-step explanation:

if the ring is now $840 $40 u do $40 - %40 = %24

$24 + $840 = $864

Juniper spends $1300 out of the monthly income of $3250 on rent

Total income of Juniper = 3250 each month

Income is the money that an individual or organization receives in return for their services or goods. Depending on the context—such as taxation, financial accounting, or economic analysis—income may have a variety of definitions.

Percentage of expenditure on rent = 40%

Percentage of expenditure on food = 15%

Percentage of expenditure on utilities = 18%

The percentage for savings = 15%

Percentage of expenditure for personal items = 8%

Money Juniper spends on rent each month out of total income:

= Income per month*40%

3250*40%

= $1300

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Answer:

[tex]y=x+3[/tex]

Step-by-step explanation:

Using Point-Slope form: Y-y1=m(X-x1)

Slope(m) = 1, Point(x1,y1) = (-2,1)

y-1=1(x+2)

y=x+2+1

y=x+3

:]

(ps. Brainliest would be greatly appreciated lol)

Step-by-step explanation:

1.given gradient (slope) make formula of straight line

[tex]y = 1x + c[/tex]

2.substitute in y and x values in order to work out c

[tex]1 = 1( - 2) + c[/tex]

[tex]c = 3[/tex]

3. equation of line is

[tex]y = 1x + 3[/tex]

Answer:

(3×6)÷5

Step-by-step explanation:

We are given the following expression:

(3/5)*6

The 6 can also be written as a fraction(6/1).

So we have a multiplication of fractions, is which we multiply the numerators and denominators.

So

(3*6)/5

The fraction sign means division

So the answer is:

(3×6)÷5

The price of one candy box was $2.50 if the popcorn were of $3.20 and the total amount was $18.20.

The price of one candy box can be determined using an algebraic expression. An algebraic expression can be defined as one that consists of both numbers and letters.

As he ordered 6 boxes of candy and a bucket of popcorn and the popcorn was of $3.20 and the total was $18.20, an algebraic expression can be given as;

6(x) + 3.20 = 18.20

Here x is the price of one candy box

Solving for x;

6x = 18.20 - 3.20

6x = 15

x = 15 / 6

x = 2.50

Hence the price of one candy box is calculated to be $2.50.

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Step-by-step explanation:

5 - (-7) = 5 + 7

because 2 negatives added together make positive.

Answer:

+ 7

Step-by-step explanation:

the rule of signs for addition/ subtraction

a + (- b ) = a - b

a + (+ b) = a + b

a - (+ b) = a - b

a - (- b) = a + b

Then

5 - (- 7 ) = 5 + 7

6561m⁴ is the value of the expression (9m)⁴ without applying the exponent property.

What is an exponent?

The type of mathematical shorthand known as exponential notation enables us to write complex expressions more concisely. The base, which can be either a number or letter, is an exponent. It implies that the base is to be raised to a specific level of power. While n is the power, X is the base.

The expression is (9m)⁴.

The value of the expression (9m)⁴ without applying the property of the exponent will be

→ 9m × 9m × 9m × 9m

(we've simply expanded  (9m)⁴ )

which on further simplifying gives,

→ 6561m⁴

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The probability that the next chew Aaden removes from the bag will be a flavor other than apple is 24/31.

Probability is a branch of mathematics concerned with determining the likelihood of an event occurring. Probability assesses the likelihood of an event occurring and is equal to the number of favorable events divided by the total number of events.

Given:

Number of times Aaden performs the experiment = 31 times

A strawberry chew was selected 4 times.

An apple chew was selected 7 times.

A watermelon chew was selected 20 times.

So,

Probability of selecting a strawberry chew = 4/31

Probability of selecting an apple chew = 7/31

Probability of selecting a watermelon chew  = 20/31

So, the probability that the next chew Aaden removes from the bag will be a flavor other than apple i.e. it can be strawberry or watermelon chew.

Probability of selecting a strawberry chew + Probability of selecting a watermelon chew

= 4/31 + 20/31 = 24/31

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Answer:

24/31

Step-by-step explanation:

Based on these results, express the probability that the next chew Aaden removes from the bag will be a flavor other than apple as a fraction in simplest form.

The experiment occurred 31 times, a flavor other than apple was selected 4+20=24 times. Probability the next chew will be a flavor other than apple:

24/31

=

The probability as a fraction in simplest form is

24/31

The domain of the given question is; 20 to 25.  

If she is paid $9 per hour, the range is; $180 to $225.

The independent quantity is defined as the quantity that causes a change in the dependent quantity.  

Now, In this question, the defined quantities are hours worked and weekly pay.  Applying the concept of independent and dependent quality, the number of hours she works causes her weekly pay to change. This means that hours worked is the independent quantity and weekly pay is the dependent quantity.

We are told that she plans to work between 20 and 25 hours. This means that;

The domain is 20 to 25.  

Now, as she is paid $9 per hour, this makes the range;

9(20) = $180 to 9(25) = $225.

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1) 20 percent of 60 is 12

2) 25 percent of 24 is 6

3) 4 percent of 600 is 24

4) 88 is 110 percent of 80

5) 18 is 20 percent of 90

To calculate the proportion of value to the original value, the percentage concept is employed. For calculating a company's profit or loss percentage , percentages are frequently employed in business. Additionally, it's a common way for universities and schools to display the grades that pupils have earned. An estimation of the pupils' grades can be made using a percentage calculation. A ratio of any value to the total value multiplied by 100 is how percentages are typically defined. The percentage is shown as % in symbols.

1) [tex]\frac{20}{100}[/tex]×x=12

x=[tex]\frac{1200}{20}[/tex]

x = 60

2) x ×[tex]\frac{24}{100}[/tex] = 6

x=25%

3)[tex]\frac{4}{100}[/tex]×600 = 24

4) [tex]\frac{110}{100}[/tex]×x = 88

x =[tex]\frac{8800}{110}[/tex]

x= 80

5) [tex]\frac{x}{100}[/tex]×90 = 18

x = 20

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Answer: k = 13

Step-by-step explanation:

The solution is ; 5/6 = 0.833... (recurring decimal)

The graph of an exponential function has a y-intercept of 9 and contains the point (2,144). the function that describes the graph.

y=9(4)^x

This is further explained below.

Generally, the Standard form of an exponential function

y=a b^x

Where

y= is the y component of the graph

x=  is the x component of the graph

a and b are equation vaiables

Given the y-intercept (0,9) and the point (2,144) Applying both.

a=9,

144=9 b^2

Solve further by making b the subject of formular

b^2=144/9

b^2=16

b[tex]= \sqrt{ 16}[/tex]

Therefore  b=4

So, y=9(4)^x

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Answer:

[tex]2\sqrt{2}[/tex]

Step-by-step explanation:

x^2+x^2=16

x^2=8

x= 2sqrt2

:]

I l over here and I have no idea

Answer: 9

Step-by-step explanation:

I am assuming that the grid units equal 1 inch.

We have to solve for x. For the width,

60 = 20/3 x

To divide by a fraction is to multiply by its reciprocal.

x = 60 * 3/20 = 180/20 = 9

Answer:

-3

Step-by-step explanation:

f(x) = (x^2 - 4)/(x + 2)

Substituting x = -1,

f(-1) = (1 - 4)/(-1 + 2)

f(-1) = -3

Answer:

1 , 7 , 7

Step-by-step explanation:

to evaluate f(- 2) means what is the value of y when x = - 2

locate x = - 2 on the x- axis , go vertically up to meet the graph at (- 2, 1)

f(- 2) = 1

similarly

f(0)

locate x = 0 , at the origin, go vertically up to meet the graph at (0, 7 )

f(0) = 7

f(3)

locate x = 3 on the x- axis , go vertically up to meet the graph at (3, 7 )

f(3) = 7

The area of a triangle is 1/2bh. We know the area, a, the base, b, and we are attempting to find the height, h. So, we simplify the area formula with the value of b and solve for h, given a.

1/2(6)h = 30
3h = 30

Isolate h.

3h/3 = 30/3
h = 10

The value of x is 43.

As per the property of exterior angles, the exterior angle is equal to sum of opposite interior angles. Also, the rightmost interior angle of triangle will be 35°. This will be according to the property that opposite angles are equal. Now, forming the equation for sum of exterior angles.

109 = x + 31 + 35

Performing addition on Right Hand Side of the equation

109 = x + 66

Rearranging the equation

x = 109 - 66

Performing subtraction on Right Hand Side of the equation

x = 43

Therefore, as per the angles of triangle, the value of x is 43.

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Answer:

Supplementary: 2,3

Complementary: 1,4,5

Vertical Angles (VA): 1 is equivalent to 4

Step-by-step explanation:

Supplementary angles are angles that equal up to 180 degrees.

Complementary angles are angles that are 90 degrees.

VA (Vertical Angles) are angles that are basically across from other (take a look at 1 and 4) AND NO, 2,3 or 5 would be considered as Vertical angles as they do not Aline.

An answer choice shows these weights in order from least to greatest is:

A numerical data can be defined as a data set that is primarily expressed in numbers only. This ultimately implies that, a numerical data refers to a data set consisting of numbers rather than words.

In order to arrange the given numerical data (weights) in order from least to greatest, we would convert the fractions into a decimal number as follows:

Now, we can arrange the numerical data in order from least to greatest based on the weight of each item:

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length×width = 108

length + 2×width = 30

length = 30 - 2×width

using that in the first equation

(30 - 2×width)×width = 108

-2×width² + 30×width - 108 = 0

the general solution to such a quadratic equation like

ax² + bx + c = 0

is

x = (-b ± sqrt(b² - 4ac))/(2a)

so,

width = (-30 ± sqrt(30² - 4×-2×-108))/(2×-2) =

= (-30 ± sqrt(900 - 864))/-4 =

= (-30 ± sqrt(36))/-4 = (-30 ± 6)/-4

width1 = (-30 + 6)/-4 = -24/-4 = 6 ft

width2 = (-30 - 6)/-4 = -36/-4 = 9 ft

for width = 6 ft

length = 30 - 2×width = 30 - 12 = 18 ft.

for width = 9 ft

length = 30 - 2×width = 30 - 18 = 12 ft

given the request that the length sound be as long as possible,

width = 6 ft

length = 18 ft

is our solution.

The angle subtended by an arc is twice the angle it subtends.

The angle is 90 degrees.

What is diameter of circle?

diameter is circle is twice the radius of circle.

The theorem to solve the given statement is :

The angle subtended by an arc is twice the angle it subtends.

let suppose, O be the center of circle,

The diameter AB forms on the circle and point P on the periphery of circle ,

so we have:

To prove : ∠APB=90°

We know that angle subtended by an arc at center is double the angle subtended at any point or circumference.

that is:

Angle subtended by arc AB at O = Double the angle subtended at P

⇒∠AOB=2∠APB

∵AOB is a straight line.

∠AOB=180°

2∠APB=180°

∠APB=90°

Angle formed by arc AB or semi circle is 90°

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