One side of a triangle is 9 cm shorter than the base, x. The other side is 17 longer than the base.
What lengths of the base will allow the perimeter of the triangle to be at least 32 cm? Write your
answer as an interval.

Answer:

1.D

2.D

3.D

4.A

5.A

6.B

7.A

8.B

hope those are right

Step-by-step explanation:

1.D

2.D

3.B

4.A

5.A

6.B

7.A

8.B

Deandre invested $22,000 in the 10% account and $30,000 - $22,000 = $8,000 in the 5% account.

percentage, a relative value indicating hundredth parts of any quantity.

Let's call the amount Deandre invested in the 10% account x.

The amount he invested in the 5% account is $30,000 - x.

The interest he received from the 10% account is 0.10x and the interest he received from the 5% account is 0.05($30,000 - x).

The total interest received is $2600, so we can set up the equation:

0.10x + 0.05($30,000 - x) = $2600

0.10x + 0.05 * $30,000 - 0.05x = $2600

0.10x - 0.05x + 0.05 * $30,000 = $2600

0.05x = $2600 - 0.05 * $30,000

0.05x = $2600 - $1,500

0.05x = $1100

x = $1100 / 0.05

x = $22,000

Hence, Deandre invested $22,000 in the 10% account and $30,000 - $22,000 = $8,000 in the 5% account.

To learn more on Percentage click:

https://brainly.com/question/28269290

#SPJ1

The set is {0, 1, 2, 3, 5, 6, 8}. and the truth set is {0, 1, 2, 3, 5}

From the question, we have the following parameters that can be used in our computation:

ID = 01238586

So, the roster notation for the set is

{0, 1, 2, 3, 5, 6, 8}.

We have:

The statement is x ∈ S, (x prime) ∨ (x + 1 ∈ S)

This means that

Using the above as a guide, we have the following:

So, the truth set is {0, 1, 2, 3, 5}

Read more about set at

https://brainly.com/question/24713052

#SPJ1

By using trigonometry formula, The value of variable y is 63.6396103.

In the field of mathematics known as trigonometry, correlations between angles and length ratios are studied.

Trigonometry has a wide variety of identities. In order to simplify an expression, identify a more practical version of an expression, or solve an equation, trigonometric identities are frequently employed to rewrite trigonometrical expressions.

Given that, the angle is 45°.

the height is 45.

from the formula Sin A = height/ hypotenuse

⇒ Sin45° = 45/ y

⇒ y = 45 / Sin45°

⇒ y = 45 / 0.7071067

⇒ y = 63.6396103

The value of variable y is 63.6396103.

To learn more about height and distance visit:

brainly.com/question/28845883

#SPJ1

The variable that can be used to represent the number of points scored before is x and the algebraic expression would be equal to (3x - 2).

Algebra refers to the system for computation using letters or other symbols to represent numbers, with rules for manipulating these symbols.

let the Number of points scored before = x

3 times the number of points scored before

= 3 × x

= 3x

Thus, two points fewer than 3 times the number of points scored before;

= 3x - 2

The examples of algebraic expression are:

2t - 5 + 3t

65x + y - 8y + 5x

In conclusion, the expression can be written as; 3x - 2

Read more on algebraic expression:

brainly.com/question/4344214

#SPJ1

Answer:

I think it is 4.5 length
area= 20.25

Step-by-step explanation:

Step 1: I square rooted 324 to get 18

Step 2: I divided that number by 2 twice to get 4.5
18/2 = 9/2 = 4.5
multiply 4.5 by 4.5 to get 20.25!


Hope this is correct!

The expression for r and h are 9 and x⁸ respectively.

A cone is a three-dimensional geometric shape with a smooth and curving surface and a flat base, with an increase in the height radius of a cone decreasing to a certain point.

The volume of a cone is (1/3)πr²h.

The total surface area of a cone is πr(r + l).

The curved surface area is πrl.

Given, The volume of a cone is 27πx⁸.

We know, The volume of a cone is (1/3)πr²h.

Therefore,  (1/3)πr²h = 27πx⁸.

r²h = 81x⁸.

h = x⁸ and r² = 81 ⇒ r = 9

learn more about cones here :                                      

https://brainly.com/question/23863102

#SPJ1

The sample mean of the number of movies watched by 25 students is 2.8 and the approximate sample standard deviation is 1.15.

(a) The sample mean X can be calculated by taking the average of the number of movies watched by all 25 students.

Step 1: Sum up the number of movies watched by all 25 students:

[tex]0 * 1 + 1 * 2 + 2 * 4 + 3 * 10 + 4 * 6 + 3 * 2 = 0 + 2 + 8 + 30 + 24 + 6 = 70[/tex]

Step 2: Divide the sum from Step 1 by the number of students (25):

70 / 25 = 2.8

So the sample mean X = 2.8

(b) The sample standard deviation s can be calculated using the formula:

[tex]s = \sqrt{\frac{ \sum(X - X_{mean})^2}{(n-1)} }[/tex]

Where [tex]X_{mean}[/tex] is the sample mean, n is the sample size, and Σ represents the sum of all values.

Step 1: Calculate [tex](X - X_{mean})^2[/tex]for each data point and sum up the values:

[tex](0 - 2.8)^2 * 1 + (1 - 2.8)^2 * 2 + (2 - 2.8)^2 * 4 + (3 - 2.8)^2 * 10 + (4 - 2.8)^2 * 6 + (3 - 2.8)^2 * 2\\ = 7.84 + 3.24 + 0.64 + 9.6 + 1.44 + 7.84\\ = 31.36[/tex]

Step 2: Divide the sum from Step 1 by (n - 1) = 24:

31.36 / 24 = 1.31

Step 3: Take the square root of the result from Step 2:

[tex]\sqrt{1.31} = 1.15[/tex]

So the approximate sample standard deviation s = 1.15 (rounded to two decimal places).

Learn more about deviation :

https://brainly.com/question/23907081

#SPJ4

The graph of the function is added as an attachment

From the question, we have the following parameters that can be used in our computation:

2x−y=−8​

Make y the subject

y = 2x + 8

The above equation is a linear equation

A linear equation is represented as

y = mx + c

Where

slope = m

y-intercept = c

This means that the slope is 2 and the y-intercept is 8

Next, we plot the graph of the equation

See attachment for the graph

Read more about linear equation at

brainly.com/question/2030026

#SPJ1

The equation for the horizontal asymptote will be y = -2.

Since the degree of the numerator and denominator of f(x) is the same both being 1, therefore horizontal asymptote exists and is given by:

y = Leading coefficient of numerator of f(x) / Leading coefficient of denominator of f(x)

=> y = -2/1

=> y = -2

The vertical asymptote will be f(x) = -2x / (x + 3). To find the vertical asymptote we will equate the denominator of f(x) = 0

=> x + 3 = 0

=> x = -3

Learn more about asymptote on:

brainly.com/question/4138300

#SPJ1

A dynamic array is an array with a big improvement: automatic resizing.

How does dynamic array works?

A random access, variable-size list data structure called a dynamic array, growable array, resizable array, dynamic table, or array list allows elements to be added or removed. It comes with standard libraries for many current, widely used programming languages.

A value of type array is stored in a static array variable. A pointer to an array value is stored in a dynamic array variable. The code you write to use either type of array differs very little because of automatic pointer dereferencing and automatic index padding.

Resizable dynamic arrays offer random access to its elements. They can have variable size initializations, and the software can change their size at a later time.

Initial Values:

n = 2

arr[0] = [ ]

arr[1] = [ ]

Query 0: Append 5 to arr[( 0 ⊕ 0 ) % 2 )] = arr[0]

last answer = 0

arr[0] = [5]

arr[1] = [ ]

Query 1: Append 7 to arr[( 1 ⊕ 0 ) % 2 )] = arr[1]

arr[0] = [5]

arr[1] = [7 ]

Query 2: Append 3 to arr[( 0 ⊕ 0 ) % 2 )] = arr[0]

last answer = 0

arr[0] = [5, 3]

arr[1] = [7 ]

learn more about of array here

https://brainly.com/question/30324928

#SPJ4

The trigonometry ratios are tan(∅) = 2/3√10 and

csc(∅) = 7√10/20

From the question, we have the following parameters that can be used in our computation:

0°≤ ∅ ≤ 180°

Also, we have

cos(∅) = -3/7

The tangent is calculated as

tan(∅) = √[1/cos²(∅) - 1]

Substitute the known values in the above equation, so, we have the following representation

tan(∅) = √[1/(-3/7)² - 1]

So, we have

tan(∅) = √[49/9 - 1]

This gives

tan(∅) = √40/9

So, we have

tan(∅) = 2/3√10

Also, we have

cos²(∅) + sin²(∅) = 1

So, we have

(-3/7)² + sin²(∅) = 1

Evaluate

sin²(∅) = 1 - (-3/7)²

sin²(∅) = 1 - (9/49)

sin²(∅) = 40/49

Take the inverse of both sides

csc²(∅) = 49/40

So, we have

csc(∅) = 7/(2√10)

Rationalize

csc(∅) = 7√10/20

Read more about trigonometry function at

https://brainly.com/question/24349828

#SPJ1

Any field if is also a vector space over itself, with the field addition used as vector addition, and the field multiplication used as scalar multiplication is True.

A set whose elements, frequently termed vectors, can be added to and multiplied ("scaled") by figures known as scalars is referred to as a vector space (also known as a linear space). Real numbers make up scalars most of the time, but they can also be complex numbers or, more broadly, components of any field.

If V and W are both sub spaces of the vector space U, then their intersection is also a subspace of U.

According to the definition of a subspace, we can say that {0} belongs to both V and W.

So, {0} will also belong to the intersection of V and W.

That is, {0} ∈ V ∩ W.

Now, let a, b are scalars and v, w∈ V ∩ W.

So, we get

v, w ∈ V  and  v, w ∈ W.

Since V and W are sub spaces of V and W, so we get

av + bw ∈ V  and  av + bw ∈ W.

Therefore, av + bw ∈ V ∩ W.

Thus, V ∩ W is also a subspace of U.

Learn more about Vector space:

https://brainly.com/question/13045843

#SPJ4

The square is shown in the complex plane, where each vertex can be represented as a complex number.

If we let the first vertex be 0, then the next vertex [tex]$a$[/tex] is at a distance of 1 unit along the real axis. The complex number representing [tex]$a$[/tex] is [tex]$1 + 0i$[/tex]. The vertex [tex]$b$[/tex] is at a distance of 1 unit along the imaginary axis, so its complex representation is [tex]$0 + 1i$[/tex]. Finally, the vertex [tex]$c$[/tex] is at a distance of 1 unit along the negative real axis, so its complex representation is [tex]$-1 + 0i$[/tex].

To find [tex]$b/a$[/tex], we divide the complex number representing [tex]$b$[/tex] by the complex number representing [tex]$a$[/tex]. We get [tex]$b/a = (0 + 1i) / (1 + 0i) = 0 + 1i$[/tex].

Similarly, to find [tex]$c/a$[/tex], we divide the complex number representing [tex]$c$[/tex] by the complex number representing [tex]$a$[/tex]. We get [tex]$c/a = (-1 + 0i) / (1 + 0i) = -1 + 0i$[/tex].

So, the values of [tex]$b/a$[/tex] and [tex]$c/a$[/tex] in rectangular form are [tex]0 + 1i[/tex] and [tex]-1 + 0i[/tex], respectively.

You can learn more about complex number at

https://brainly.com/question/29747771

#SPJ4

Answer: w=-7/4, x = 3 , z = 8.
You were only incorrect on one which I will provide an image on how I solved that one so you can maybe see what you did wrong. hope it helps !

The polynomial function for the cars manufactured in thousands since 1990, where x represents the number of years since 1990 the fourth option

P(x) = 0.2·x³ + 0.5·x² + 0.4·x + 0.3

A polynomial consists of an expression that has two or more terms of (the same) variables with different powers or index.

The possible table in the question, obtained from a similar question on the internet is presented as follows;

Year;              [tex]{}[/tex]                1991     1993       1995        1997         1999

Cars Manufactured; [tex]{}[/tex]      1.4       11.4         39.8         96.2         190.2

(thousands)

The details in the table indicates that we get;

When x = 1991 - 1990 = 1, P(x) = 1.4

Which, based on the coefficients of x³, x², and x, corresponds with the first and the fourth polynomial.

p(x) = 0.5·x³ + 0.2·x² + 0.3·x + 0.4...(1)

p(1) = 0.5 × 1³ + 0.2 × 1² + 0.3 × 1 + 0.4 = 1.4

P(x) = 0.2·x³ + 0.5·x² + 0.4·x + 0.3...(4)

p(1) = 0.2 × 1³ + 0.5 × 1² + 0.4 × 1 + 0.3 = 1.4

When x = 1993 - 1990 = 3, we get in equation (1);

p(3) = 0.5 × 3³ + 0.2 × 3² + 0.3 × 3 + 0.4 = 16.6

The polynomial in equation (4) indicates that we get;

p(3) = 0.2 × 3³ + 0.5 × 3² + 0.4 × 3 + 0.3 = 11.4

Therefore, the polynomial in the fourth equation best represents the polynomial function for the cars manufactured in thousands where x represents the years since 1990

Verifying, we get;

When x = 5; p(5) = 0.2 × 5³ + 0.5 × 5² + 0.4 × 5 + 0.3 = 39.8

When x = 7; p(7) = 0.2 × 7³ + 0.5 × 7² + 0.4 × 7 + 0.3 = 96.2

When x = 9; p(9) = 0.2 × 9³ + 0.5 × 9² + 0.4 × 9 + 0.3 = 190.2

Learn more about polynomials here: https://brainly.com/question/29257478

#SPJ1

Using Factorization, The solution of the algebraic fraction is [tex]\frac{10}{p-4}[/tex].

Due to the fact that they have polynomials on both sides of the equality sign, algebraic equations are also known as polynomials. Variables, coefficients, constants, and algebraic operations like addition, subtraction, multiplication, division, and exponentiation are all components of algebraic equations.

Numbers are factored using formulas for factorization. Decomposing an entity into the result of another entity or factors that, when multiplied together, produce the original number is known as factorization. Simple factorization formulas are used in factorization procedures to simplify algebraic or quadratic equations. Instead of expanding parentheses, expressions are expressed as the sum of their constituent parts. Each equation may have factors that are algebraic expressions, variables, or .

[tex]\frac{p - 8}{8 p²-12p+32} \div \frac{1}{10}[/tex]

first we factorize the denominator and using invert Endo to the other fraction.

[tex]\frac{p - 8}{8 p²-12p+32} \times \frac{10}{1}\\\frac{p - 8}{(p - 8)(p - 4)} \times 10[/tex]

= [tex]\frac{10}{p-4}[/tex]

Hence the simplified fraction is [tex]\frac{10}{p-4}[/tex]

To learn more about Factorization from given link

https://brainly.com/question/10718512

#SPJ1

The equation of the relation between x and y is y= 2x

From the question, we have the following parameters that can be used in our computation:

The table of values

On the table of values, we can see that

y is twice of x

When represented as an equation, we have

y = 2x

Hence, the equation is y = 2x

Read more about equation at

brainly.com/question/2972832

#SPJ1

Complete question

Without performing any algebraic manipulations, can you define the relation between x and y?

X (input) 7 8 9 10

y (output) 14 16 18 20

Answer: 0.17193742185

Step-by-step explanation:

Answer:

0.171937422

Step-by-step explanation:

Answer:

hi !!

Step-by-step explanation:

34.70 - 34.70/100*10 = 34.70 - 3.47 = $31.23

The arc lengths of the given circles are 8π/3, 14π/3 and 4π

Arc length is the distance between two points along a section of a curve.

Given are circles, with radii 4, 3 and 3 units, we need to find the arc length of each,

Since, angles are in radian, convert them into degree by multiply them by π/180°

1) radius = 2π/3 × 180°/π

= 120°

2) radius = 7π/6 × 180°/π

= 210°

3) radius = 4π/3 × 180°/π

= 240°

Arc length = θ/360° × 2π × radius, where θ is the central angle,

1) Arc length = 120°/360° × 2π × 4

= 8π/3

2) Arc length = 210°/360° × 2π × 3

= 14π/3

3) Arc length = 240°/360° × 2π × 3

= 4π

Hence, the arc lengths of the given circles are 8π/3, 14π/3 and 4π

Learn more about arc lengths, click;

https://brainly.com/question/16403495

#SPJ1

The number of hours spent walking dogs is 3 hours and 5 hours was spent landscaping.

The first step is to form a system of equations using the information provided in the question:

x + y = 8 equation 1

6x + 13y = 83 equation 2

Where:

The elimination method would be used to solve the equations.

Multiply equation 1 by 6

6x + 6y = 48 equation 3

Subtract equation 3 from equation 2:

7y = 35

Divide both sides of the equation by 7:

y = 35 / 7

y = 5

Substitute for y in equation 1:

x + 5 = 8

8 - 5 = x

x = 3

To learn more about system of equations, please check: https://brainly.com/question/25875552

#SPJ1

Approximately 524 calories are contained in each of the eight slices of a 16-inch pizza (note: this makes good sense since it has a little less than the area as a complete 6-inch pizza).

The diameter of a circle is equal to the number of inches in a pizza's size.

The area of a circle is calculated using the formula: [tex]\pi r^{2} = \pi (d/2)^{2}[/tex].

Assume that a pizza's calories are evenly distributed over its surface (even though we know there is a crust ring around the outsize). C calories per square inch, as an illustration.

The number of calories in a 6-inch pizza is

[tex]CA_{6} = C\pi (6/2)^{2} =9C\pi =590[/tex]      [eq1]

Calories in a 16-inch pizza are calculated as follows:

[tex]CA_{16}=C\pi (6/2)^{2} =64C\pi[/tex]

The number of calories in one of those pizza's eight slices is:

[tex]X=CA_{16} /8=8C\pi[/tex]   [eq2]

math:

[tex]C\pi =590/9[/tex]   [from eq1]

[tex]X=8(C\pi )[/tex]    [from eq2]

[tex]X=8(590/9)[/tex]

[tex]X=524[/tex]        [estimated]

Approximately 524 calories are contained in each of the eight slices of a 16-inch pizza (note: this makes good sense since it has a little less than the area as a complete 6-inch pizza).

Learn more about diameter of a circle here:

https://brainly.com/question/732113

#SPJ4

The point D on the graph shows that the rider has stopped moving.

What is a graph?

Graph is a line or curve of a line with represents the relation between two quantities.

There are two axis in graph each axis represents different quantity in a graph.

Two axis are X-axis and Y-axis. Generally quantity which increases gradually is kept on X-axis.

By using graph we can calculate many different things like in distance time graph if we calculate the area of the graph we can get the speed for that region.

Graph is a very helpful took as its a pectoral representation of data and we all know action speak louder than words so graphs can explain more information with less data.

Now for the given question:

In graph section D shows that bicycle rider has stopped because the distance of rider from its house is not increasing while the time increases due to of which this interval has a straight line.

Hence, rider has stopped moving at region D.

To know more about Graphs visit:

https://brainly.com/question/9644332

#SPJ1

The complete Question is:

The graph shows the position (distance from home) of a bicycle rider on a 42-minute trip. Letters A through E are time intervals during the trip. The key defines the length of each interval. Which of the following best explains how the graph shows that the rider stopped during time interval D?

Answer:

Step-by-step explanation:

y = mx +c

1 = m0 + c

1=0+c

c=1

5-1=4

3-1=2

4/2=2

m=2

y=2x+1

Applying the corresponding angles theorem, m<DEG = 33°.

The Corresponding Angles Theorem states that if two lines are cut by a transversal, then corresponding angles are equal. This means that if two lines intersected by a transversal form a pair of corresponding angles, then those angles are congruent (have the same measure).

Given that:

m<HBC = 33 degrees

m<ABE = m<HBC [vertical angles are congruent]

m<ABE = 33° [substitution property]

Therefore, based on the corresponding angles theorem, we have:

m<DEG = m<ABE

Substitute:

m<DEG = 33°

Learn more about corresponding angles theorem on:

https://brainly.com/question/2009183

#SPJ1

The improved high-speed mixer that allows bakers to produce cookies in less time will result in an increase in production, a decrease in cost, an increase in demand, and an increase in price of chocolate chip cookies.

Point A to Point B illustrates an increase in the production of chocolate chip cookies. This can be calculated using the formula: Change in Output = Output at Point B - Output at Point A. For example, if the output of chocolate chip cookies at Point A is 25 cookies per hour, and the output at Point B is 40 cookies per hour, then the change in output is 40-25=15 cookies per hour.

Point C to Point B illustrates a decrease in the cost of production of chocolate chip cookies. This can be calculated using the formula: Change in Cost = Cost at Point C - Cost at Point B. For example, if the cost of production at Point C is $2 per cookie, and the cost at Point B is $1 per cookie, then the change in cost is $2 - $1 = $1 per cookie.

Point C to Point D illustrates an increase in the demand for chocolate chip cookies. This can be calculated using the formula: Change in Demand = Demand at Point D - Demand at Point C. For example, if the demand for chocolate chip cookies at Point C is 100 cookies per hour, and the demand at Point D is 150 cookies per hour, then the change in demand is 150 - 100 = 50 cookies per hour.

Point A to Point D illustrates an increase in the price of chocolate chip cookies. This can be calculated using the formula: Change in Price = Price at Point D - Price at Point A. For example, if the price of chocolate chip cookies at Point A is $1 per cookie, and the price at Point D is $2 per cookie, then the change in price is $2 - $1 = $1 per cookie.

The improved high-speed mixer that allows bakers to produce cookies in less time will result in an increase in production, a decrease in cost, an increase in demand, and an increase in price of chocolate chip cookies.

Learn more about change in cost here:

https://brainly.com/question/19075809

#SPJ4

The claim of Carly is correct that the sum of the deviations for a data set will always be 0.

Mean of a set of data is defined as the average of all the values. It gives the exact middle point of the data set.

Sum of the deviations of a data set is always 0.

This is because that the sum of the positive deviations is equal to the sum of the negative deviations.

Let a data set be 3, 2, 4, 5, 1

Mean = (3 + 2 + 4 + 5 + 1) / 5 = 3

Values     Deviations

3               3 - 3 = 0

2               2 - 3 = -1

4               4 - 3 = 1

5               5 - 3 = 2

1                1 - 3 = -2

Sum of the deviations = 0 - 1 + 1 + 2 - 2 = 0

Hence the sum of the deviations for a data set will always be 0.

Learn more about Mean here :

https://brainly.com/question/29895356

#SPJ1

Answer:

224 millimeters

or

2.24 cm

Step-by-step explanation:

Scale is 8 millimeters = 1 meter

So 28 meters = 28 x 8 millimeters = 224 millimeters

224 millimeters = 224/10 cm = 22.4 cm

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 9000\\ P=\textit{original amount deposited}\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &4 \end{cases}[/tex]

[tex]9000 = P\left(1+\frac{0.04}{4}\right)^{4\cdot 4} \implies 9000=P(1.01)^{16} \\\\\\ \cfrac{9000}{(1.01)^{16}}=P\implies \boxed{7675.39\approx P}[/tex]