Find the value of x
26 26 6

The vector form of the general solution of the given system of linear equations is given by:

{x} = {x1, x2, x4} = s { -1, 1, 0} + t { -2, 0, 1}

where s and t are arbitrary constants.

To find the vector form of the general solution, we need to find the null space of the coefficient matrix of the system of linear equations. The coefficient matrix of the system is:

A = [ 1 1 0 1; 1 2 0 4; 2 0 0 -4]

The null space of A is the set of all vectors x such that Ax = 0. We can find the null space of A by reducing A to its reduced row echelon form:

A = [ 1 0 0 -2; 0 1 0 1; 0 0 0 0]

From the reduced row echelon form of A, we can see that x1 and x2 are the leading variables and x4 is the free variable. Therefore, the general solution of the system of linear equations is given by:

x1 = -2x4
x2 = x4
x4 = x4

We can write the general solution in vector form as:

{x} = {x1, x2, x4} = x4 { -2, 1, 1}

Since x4 is an arbitrary constant, we can write the general solution in terms of two arbitrary constants s and t as:

{x} = {x1, x2, x4} = s { -1, 1, 0} + t { -2, 0, 1}

Therefore, the vector form of the general solution of the given system of linear equations is:

{x} = {x1, x2, x4} = s { -1, 1, 0} + t { -2, 0, 1}

Learn more about vector at https://brainly.com/question/30465708

#SPJ11

The value of b that makes the area between the two functions equal to 50.5 on the interval [-6.2, 6.2] is 29.64355.

To find the value of b that makes the area between the two functions equal to 50.5 on the interval [-6.2, 6.2], we need to set up an integral and solve for b.

First, we need to find the difference between the two functions:
x2 - x1 = b - y^2

Next, we need to integrate this difference over the given interval:
∫[-6.2, 6.2] (b - y^2) dy

Using the power rule for integration, we get:
[b*y - (y^3)/3] from -6.2 to 6.2

Plugging in the values for the interval and simplifying, we get:
(6.2b - 158.488) - (-6.2b - 158.488)

Simplifying further, we get:
12.4b - 316.976

Now, we can set this equal to the given area and solve for b:
12.4b - 316.976 = 50.5

12.4b = 367.476

b = 367.476/12.4

b = 29.64354839

Rounding to five decimal places, we get:
b = 29.64355

So, the value of b that makes the area between the two functions equal to 50.5 on the interval [-6.2, 6.2] is 29.64355.

Learn more about Decimal

brainly.com/question/29765582

#SPJ11

The standard deviation of the given data set is 825.87.

The standard deviation of a data set is a measure of how spread out the data is from the mean (average) of the data set. It is calculated using the following formula:

Standard Deviation = √(Σ(x - mean)^2 / n)

Where:

- x is each individual data point

- mean is the average of the data set

- n is the number of data points in the data set

- Σ is the sum of all the values

To calculate the standard deviation of the given data set, we first need to calculate the mean:

Mean = (200 + 1200 + 300 + 350 + 500 + 55 + 10 + 500 + 800 + 850 + 1300 + 2000 + 2100 + 340 + 760 + 830 + 2670 + 9 + 3000) / 20 = 833.45

Next, we need to calculate the sum of the squared differences between each data point and the mean:

Σ(x - mean)^2 = (200 - 833.45)^2 + (1200 - 833.45)^2 + ... + (3000 - 833.45)^2 = 1.365E7

Finally, we can calculate the standard deviation:

Standard Deviation = √(1.365E7 / 20) = 825.87

Therefore, the standard deviation of the given data set is 825.87.

Learn more about standard deviation at

https://brainly.com/question/29758680

#SPJ11

Using the Gaussian elimination method, the general solution is:               [tex]\[ x = -31t + 6 \][/tex], [tex]\[ y = 5 \][/tex], [tex]\[ z = 31t \][/tex].

To solve this system of equations, we can use the Gaussian elimination method. This method involves creating a matrix with the coefficients of the equations and using row operations to reduce the matrix to a form that can be easily solved.

First, we create a matrix with the coefficients of the equations:

[tex]\[ \left( \begin{array}{ccc|c} 1 & 1 & 1 & -1 \\ 2 & 3 & 2 & 3 \\ 2 & 1 & 2 & -7 \\ 1 & -3 & 2 & 10 \\ -1 & 3 & -1 & -6 \\ -1 & 3 & 2 & 6 \\ 6 & -2 & 2 & 4 \\ 3 & -1 & 2 & 2 \\ -12 & 4 & -8 & 8 \end{array} \right) \][/tex]

Next, we use row operations to reduce the matrix to a form that can be easily solved:

[tex]\[ \left( \begin{array}{ccc|c} 1 & 1 & 1 & -1 \\ 0 & 1 & 0 & 5 \\ 0 & -1 & 0 & -5 \\ 0 & -4 & 1 & 11 \\ 0 & 4 & 0 & -5 \\ 0 & 4 & 1 & 7 \\ 0 & -8 & -4 & 10 \\ 0 & -4 & -1 & 5 \\ 0 & 8 & 4 & -4 \end{array} \right) \][/tex]

[tex]\[ \left( \begin{array}{ccc|c} 1 & 1 & 1 & -1 \\ 0 & 1 & 0 & 5 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 31 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 27 \\ 0 & 0 & -4 & 50 \\ 0 & 0 & -1 & 25 \\ 0 & 0 & 4 & -44 \end{array} \right) \][/tex]

[tex]\[ \left( \begin{array}{ccc|c} 1 & 0 & 1 & -6 \\ 0 & 1 & 0 & 5 \\ 0 & 0 & 1 & 31 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & -4 \\ 0 & 0 & 0 & 174 \\ 0 & 0 & 0 & 56 \\ 0 & 0 & 0 & -168 \end{array} \right) \][/tex]

From this reduced matrix, we can see that there are infinitely many solutions to this system of equations. The general solution can be written as:
[tex]\[ x = -31t + 6 \][/tex]
[tex]\[ y = 5 \][/tex]
[tex]\[ z = 31t \][/tex]
Where t is any real number.

Know more about Gaussian elimination here:

https://brainly.com/question/14529256

#SPJ11

Martin buys a total of 2(5)/(6) + 4(3)/(4) = 10/6 + 19/4 = 40/24 + 57/24 = 97/24 pounds of nuts.

To find the total amount of nuts Martin buys, we need to add the amount of peanuts and the amount of almonds he buys.

First, we need to convert the mixed numbers to improper fractions. To do this, we multiply the whole number by the denominator and add the numerator. For 2(5)/(6), we multiply 2 by 6 and add 5 to get 10/6. For 4(3)/(4), we multiply 4 by 4 and add 3 to get 19/4.

Next, we need to find a common denominator in order to add the two fractions. The least common denominator for 6 and 4 is 24, so we multiply the numerator and denominator of 10/6 by 4 to get 40/24 and the numerator and denominator of 19/4 by 6 to get 57/24.

Finally, we add the two fractions by adding the numerators and keeping the same denominator: 40/24 + 57/24 = 97/24.

Therefore, Martin buys a total of 97/24 pounds of nuts.

To know more about improper fractions click on below link:

https://brainly.com/question/21449807#

#SPJ11

We will see that the measure of angle z is 70°

First we can get the angle in the right vertex in the triangle in the right side.

We know that the right angle and the 40° one are vertical angles, then the right angle also measures 40°

Also remember that the sum of the interior angles of any triangle is 180°, then:

105° + 40° +x = 180°

x = 180° - 40° - 105° = 35°

Then the right angle of the second triangle (the one that is below the line) also measures 35°

The bottom angle measures:

y + 85 = 180

y = 180 - 85 = 95

And if the last angle is k:

k + 95 + 35 = |80

k = 180 - 35 - 95 = 50

Then the right angle of the last triangle is also 50°, then we can write:

z + 60 + 50 = 180

z = 180 - 50 - 60 = 70°

That is the measure.

Learn more about interior angles at:

https://brainly.com/question/24966296

#SPJ1

Answer:

They have large leaves with holes in them that the Toucan can use to reach the fruit inside. The Toucan's beak is also used to break open hard-shelled fruits, such as coconuts. The Toucan's beak is also used for defence against predators, as it can be used to peck and jab at them. The adaptations of the rainforest plants are examples of convergent evolution. Both the Toucan and Monstera Plants have adapted to their environment in order to survive. The Toucan has a large beak that helps it to reach fruit in the canopy, while the Monstera Plant has long, grooved leaves with drip tips that allow water to run off and prevent mould. Both adaptations are beneficial for the survival of the species in the rainforest.

Step-by-step explanation:

Check the picture below.

[tex]\textit{ellipse, horizontal major axis} \\\\ \cfrac{(x- h)^2}{ a^2}+\cfrac{(y- k)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h\pm a, k) \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} h=-3\\ k=1\\ a=2\\ b=1 \end{cases}\implies \cfrac{(x- (-3))^2}{ 2^2}+\cfrac{(y-1)^2}{ 1^2}=1\implies \cfrac{(x+3)^2}{ 4}+\cfrac{(y-1)^2}{ 1}=1[/tex]

Answer: To find the equation of the ellipse, we need to use the standard form equation of an ellipse:

$\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1$

where (h,k) is the center of the ellipse, a is the distance from the center to the vertices (the major axis), and b is the distance from the center to the co-vertices (the minor axis).

First, let's find the center of the ellipse. The center of the ellipse is the midpoint of the line segment joining the vertices (-5,1) and (-1,1). Using the midpoint formula, we get:

$(h,k) = \left(\frac{-5+(-1)}{2}, 1\right) = (-3,1)$

Now, we need to find the values of a and b. Since the distance between the vertices is 2a, we have:

$2a = |-5-(-1)| = 4$

So, $a = 2$.

Similarly, the distance between the co-vertices is 2b, we have:

$2b = |2-0| = 2$

So, $b = 1$.

Now, we have all the values we need to write the equation of the ellipse:

$\frac{(x+3)^2}{2^2}+\frac{(y-1)^2}{1^2}=1$

Simplifying this equation, we get:

$\frac{(x+3)^2}{4}+(y-1)^2=1$

So, the equation of the ellipse is:

$(x+3)^2/4 + (y-1)^2/1 = 1$

Step-by-step explanation:

Using the %1RM to number of repetitions table, your client's estimated 1RM for the barbell back squat exercise would be 125 lbs, rounded to the nearest whole number.

To estimate the predicted 1RM (one repetition maximum) for the barbell back squat exercise, we can use the %1RM to number of repetitions table from the lecture. According to the table, performing 5 repetitions corresponds to 87% of the 1RM.

To find the estimated 1RM, we can use the following formula:

1RM = weight lifted / %1RM

Plugging in the values from the question:

1RM = 109lb / 0.87

1RM = 125.287lb

Rounding to the nearest whole number, the estimated 1RM for the barbell back squat exercise is 125lb.

Therefore, the answer is 125.

For more such questions on Repetitions.

https://brainly.com/question/16038456#

#SPJ11

The graph of y = [1/2(x -10)] - 3, compared to the graph of 1/x, represents these following transformations:

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

The translations for this problem are given as follows:

Additionally, there was a multiplication by 2 in the domain, meaning that the parent function was horizontally compressed by a factor of 2.

More can be learned about translations at brainly.com/question/28174785

#SPJ1

Evaluating the limit given by [tex]{ lim_{(x- > 9)} } (7x-63)/(x^2-2x-63)[/tex], we will obtain as a result [tex]7/16[/tex]

To evaluate the limit, we need to simplify the expression first. We can do this by factoring the numerator and denominator of the fraction:

[tex]lim_{(x->9)} (7x-63)/(x^2-2x-63) = lim_{(x->9)} (7(x-9))/((x-9)(x+7))[/tex]

Next, we can cancel out the [tex](x-9)[/tex] terms in the numerator and denominator:

[tex]lim_{(x->9)} (7)/(x+7)[/tex]

Now, we can plug in the value of x that the limit is approaching (9) into the expression:

[tex]lim_{(x->9)} (7)/(x+7) = (7)/(9+7) = (7)/(16)[/tex]

Therefore, the limit of the expression as x approaches 9 is 7/16.

Answer: [tex]{ lim_{(x->9)} } (7x-63)/(x^2-2x-63) = 7/16[/tex]

See more about limit at: https://brainly.com/question/23935467

#SPJ11

Answer:

For two linear equations : a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0;

To determine if two such straight lines are parallel, then you should check for the following conditions :

a₁/a₂ = b₁/b₂ ≠ c₁/c₂ , where a,b are coefficients of x and y for each line.

if this condition is true for the coefficients of x,y, and the intercept of lines (c₁ and c₂) then they are parallel.

for instance,

let's say we have two lines :

x + 2y - 4 = 0,

2x + 4y - 12 = 0;

Now to check if they are parallel you simply check if the condition for parallel lines is met or not.

for these two lines :

a₁ = 1 , b₁ = 2, and c₁ = -4;

a₂ = 2, b₂ = 4, and c₂ = -12;

evaluating the values in the condition we have :

[tex]\frac{1}{2}[/tex] = [tex]\frac{2}{4}[/tex] ≠[tex]\frac{-4}{-12}[/tex] ;

since the condition for parallel is true for these two lines, we can conclude they are parallel.

Marco will need 2025 pounds of marble.

The ratio is defined as the relationship between two similar magnitudes in terms of the number of times the first includes the second.

Let's say that Marco mixes 1 bag of quartz with x pounds of marble. Then the ratio of quartz to marble in this bag is:

135 pounds quartz : x pounds marble

3 pounds quartz : x/45 pounds marble

Now we know that the ratio of quartz to marble in one bag is 3: (x/45). Since the ratio stays the same for every bag, we can set up a new proportion using the total amount of quartz and marble:

135 pounds quartz : x pounds marble = total pounds quartz : total pounds marble

We know the total pounds of quartz is 135. Let's call the total pounds of marble "m".

Substituting these values into the proportion, we get:

135 : x = 135 : m/45

To solve for x, we can cross-multiply and simplify:

135(m/45) = 135x

3m = 45x

m = 15x

So, Marco will need 15 times as many pounds of marble as he has of quartz, or:

m = 15 × 135 = 2025 pounds of marble.

Learn more about the ratio here:

brainly.com/question/1504221

#SPJ9

The inverse of the statement is if two angles are vertical, then they are congruent

The statement from the question is:

if two angles are not vertical, then they are not congruent

Given a statement

If a then b

The inverse of the statement is

If not a then not b

To write the inverse statement using the above rule, we have the following statement

The inverse of the given statement is if two angles are vertical, then they are congruent

Read more about inverse statement at

https://brainly.com/question/16901233

#SPJ1

a) The average rate of change of f on [−3,1] is 4.

b) The average rate of change of f on [x,x+h] is 3+16/h.

The average rate of change of a function f(x) on an interval [a,b] is given by the formula:

Average rate of change = (f(b)-f(a))/(b-a)

(a) To find the average rate of change of f on [−3,1], we plug in the values of a=-3 and b=1 into the formula:

Average rate of change = (f(1)-f(-3))/(1-(-3))
= (f(1)-f(-3))/4

Now, we need to find the values of f(1) and f(-3) by plugging in the values of x into the given function:

f(1)=1+3(1)-8=-4
f(-3)=-3+3(-3)-8=-20

Plugging these values back into the formula, we get:

Average rate of change = (-4-(-20))/4
= 16/4
= 4

Therefore, the average rate of change of f on [−3,1] is 4.

(b) To find the average rate of change of f on [x,x+h], we plug in the values of a=x and b=x+h into the formula:

Average rate of change = (f(x+h)-f(x))/(x+h-x)
= (f(x+h)-f(x))/h

Now, we need to find the values of f(x+h) and f(x) by plugging in the values of x and x+h into the given function:

f(x+h)=x+h+3(x+h)-8
=4x+3h-8
f(x)=x+3x-8
=4x-8

Plugging these values back into the formula, we get:

Average rate of change = (4x+3h-8-(4x-8))/h
= (3h+16)/h
= 3+16/h

Therefore, the average rate of change of f on [x,x+h] is 3+16/h.

Learn more about the function: https://brainly.com/question/12431044

#SPJ11

Answer:

To find the total price, we need to add the tip and tax to the total bill amount.

First, we need to find the amount of the tip. To do this, we will multiply the total bill by 22% (or 0.22):

$45.65 x 0.22 = $10.04

This means the tip amount is $10.04.

Next, we need to find the amount of tax. To do this, we will multiply the total bill by 5% (or 0.05):

$45.65 x 0.05 = $2.28

This means the tax amount is $2.28.

Finally, we can find the total price by adding the total bill, tip, and tax together:

$45.65 + $10.04 + $2.28 = $57.97

Therefore, the total price is $57.97.

There are expected to be about 225,000 millipedes in the area of rainforest in 20 years time. Rounded to the nearest 100, this is 225,100.

What is percentage growth rate?

The exponential function with a growth factor has a rate greater than 1

We can use the formula for exponential growth to answer this question:

P(t) = P₀(1 + r)ᵗ

where P₀ is the initial population, r is the annual growth rate as a decimal, t is the number of years, and P(t) is the population after t years.

a) For the first part of the question, we can plug in the given values and solve for P(5):

P₀ = 50

r = 0.62

t = 5

P(5) = 50(1 + 0.62)⁵ ≈ 763

Therefore, there are expected to be about 763 millipedes in the area of rainforest in 5 years time.

b) For the second part of the question, we can plug in the given values and solve for P(20):

P₀ = 50

r = 0.62

t = 20

P(20) = 50(1 + 0.62)²⁰ ≈ 225,000

Therefore, there are expected to be about 225,000 millipedes in the area of rainforest in 20 years time. Rounded to the nearest 100, this is 225,100.

To know more about growth rate visit,

https://brainly.com/question/27161222

#SPJ1

Let the cost of 1 pound of zucchini be 'z' and the cost of 1 pound of tomatoes be 't'. We can set up two equations using the given information:

9z + 6t = 21.15 (equation 1)

4z + 3t = 9.83 (equation 2)

We can solve for 'z' and 't' using the method of substitution:

From equation 2, we can express 4z as 9.83 - 3t:

4z = 9.83 - 3t

Substituting this expression for 4z in equation 1, we get:

9(9.83 - 3t)/4 + 6t = 21.15

Multiplying both sides by 4 to eliminate the fraction, we get:

9(9.83 - 3t) + 24t = 84.6

Expanding the left side, we get:

88.47 - 27t + 24t = 84.6

Combining like terms, we get:

-3t = -3.87

Dividing both sides by -3, we get:

t = 1.29

Substituting this value of 't' in equation 2, we get:

4z + 3(1.29) = 9.83

Simplifying, we get:

4z = 5.56

Dividing both sides by 4, we get:

z = 1.39

Therefore, 1 pound of zucchini costs $1.39 and 1 pound of tomatoes costs $1.29 at the farm stand.

Answer:

z = 1.39

Step-by-step explanation:

a. The greatest possible distance from  Austin to san Antonio is 335.77 mi, b. the Least possible distance to Austin to san Antonio is 120.03 mi.

Distance refers to the physical length or space between two points or objects. It is an important concept in mathematics, physics, and everyday life. Distance can be measured in various units such as meters, feet, kilometers, miles, or light-years, depending on the context and scale of the measurement.

In mathematics, distance is often measured using the Euclidean distance formula, which calculates the distance between two points in a plane or in three-dimensional space. The formula is given by:

d = √((x2 - x1)² + (y2 - y1)²)

where d is the distance between the two points, (x1, y1) and (x2, y2).

In physics, distance is often used to describe the separation between two objects or particles. The distance between two objects can affect the strength of gravitational or electromagnetic forces between them. Distance is also an important concept in special relativity, where it is affected by the relative motion of observers and the distortion of spacetime.

a. Greatest possible distance from  Austin to san Antonio= Distance from Austin →Houston → san Antonio.

Austin - Houston = 146.43 mi

Houston - San Antonio = 189.34 mi

Total  distance= 146.43+ 189.34= 335.77 mi

b. Least possible distance to Austin to San Antonio = the shortest distance = x

By Pythagoras theorem

(189.34)² = (146.43)²+ x²

x² = (189.34)²- (146.43)²

x² = 35849.63- 21441.744

x² = 14407.89

x =√14407.89

x = 120.03

To know more about miles visit:

brainly.com/question/833967

#SPJ1

The complete question is:

1. A person should choose one family pizza.

2. The area of two medium pizza < area of 1 large pizza.

3. The area of two medium pizza is 1413.8 square cm and the area of one large pizza is 1661.9 square cm.

What is area?

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.

I would one family pizza.

I would choose one family because the total area of two medium pizzas is less than the area of a family pizza.

This means that the two medium pizzas will have less pizza to share between the same number of people, so everyone will get a smaller slice of pizza.

To calculate the areas of the pizzas, we need to use the formula for the area of a circle -

Area of a circle = π × (radius)²

For the family pizza with a diameter of 46 cm, the radius is 23 cm. Therefore, the area of the family pizza is -

Area of family pizza = π × (23 cm)² ≈ 1661.9 square cm

For two medium pizzas with a diameter of 30 cm, the radius is 15 cm. Therefore, the area of each medium pizza is -

Area of each medium pizza = π × (15 cm)² ≈ 706.9 square cm

The total area of two medium pizzas is -

Total area of two medium pizzas = 2 × (Area of each medium pizza) ≈ 1413.8 square cm

Since the total area of two medium pizzas is less than the area of the family pizza, it means that two medium pizzas have less pizza to share between the same number of people.

Therefore, choosing one family pizza would be a better option.

To learn more about area from the given link

https://brainly.com/question/25292087

#SPJ1

A family pizza or two medium?

* Each medium pizza is 30 cm in diameter

* The family pizza has only a diameter of 46 cm

1. What do you choose?

2. Why?

3. Please conclude your facts

The area of the composite figure given is 39 cm²

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object. The space enclosed by the boundary of a plane figure is called its area. The area of a figure is the number of unit squares that cover the surface of a closed figure.

Given is a figure with dimensions, 3 cm 4 cm 6 cm 5 cm we need to find the area of the figure,

Since, we can see that the figure is a composite figure, we will first split the figure and find the area of each part separately then, add all of them,

The figure is consisting of two rectangles, with dimensions, 4 cm and 6 cm and the second one with dimensions, 5 cm and 3 cm,

so, the area of the rectangle with dimensions, 4 cm and 6 cm = 4 x 6 = 24 cm²

And,

The area of the rectangle with dimensions, 5 cm and 3 cm = 5 x 3 = 15 cm²

The area of the figure = 15 + 24 = 39 cm²

Hence, the area of the composite figure given is 39 cm²

Learn more about areas, click;

https://brainly.com/question/27683633

#SPJ1

The complete question is attached

Answer:

Air

Step-by-step explanation:

it's asking you to look at the chart and find which substance is densest by comparing it to how fast sound can move through it (the speed of sound in the substance). In my opinion copper is not the densest material because sound moves through it the fastest; which means the particles in copper are not as densely held together. Air however, shows that sound can only travel 330 meters per second which is incredibly slow compared to the other listed materials, so by that logic it must be the densest.  

Answer:

The solution to the inequality is option C. x > -9.

Linear inequalities are defined as those expressions which are connected by inequality signs like >, <, ≤, ≥ and ≠ and the value of the exponent of the variable is 1.

The given inequality is,

-1/3x + 1/2 < 3.5

We have to find the solution of the inequality.

-1/3 x + 0.5 < 3.5

Subtracting both sides by 0.5, we get,

-1/3 x < 3.5 - 0.5

-1/3 x < 3

Multiplying both sides by -3,

x > -9

Hence the solution is x > -9.

Learn more about Inequalities here :

https://brainly.com/question/20383699

#SPJ1

The angle of depression of the escalator is approximately 10.1 degrees.

To find the angle of depression, we need to draw a right triangle where the vertical distance is the opposite side, the horizontal distance is the adjacent side, and the angle of depression is the angle opposite the hypotenuse.

Let's call the angle of depression θ. Then we have

tan(θ) = opposite/adjacent

We know the vertical distance (opposite) is 194.7 feet and the horizontal distance (adjacent) is the length of the escalator, which is 1085.5 feet. So we can plug in these values and solve for θ:

tan(θ) = 194.7/1085.5

θ = tan^-1(194.7/1085.5)

θ ≈ 10.1 degrees

Learn more about angle of depression here

brainly.com/question/13697260

#SPJ4

If the stove's output is greater than or equal to the estimated BTUs, then it should be large enough to heat her basement.

Cary can determine if a stove is large enough to heat her basement by checking the stove's specifications for its heating capacity or output. Typically, a stove's output is measured in British Thermal Units (BTUs) per hour. She can use the following formula to estimate the BTUs required to heat her basement:

BTUs = (Length x Width x Height of basement) x 5

Once Cary has an estimated BTU requirement, she can compare it to the output of the stove she's considering.

To learn more about basement follow the link: brainly.com/question/30630145

#SPJ4

Answer:

To evaluate the function when x = 3, we substitute 3 for x in the given function f(x) = 5x + 2:

f(3) = 5(3) + 2

f(3) = 15 + 2

f(3) = 17

Therefore, when x = 3, the value of the function f(x) = 5x + 2 is 17.

So, the correct answer is option D, 7 is incorrect because 5*3+2 = 17.

The Answers given are incorrect this is because the correct answer is 5.7

f(x) = 5x + 2

f(3)=5(3)+2

3f=15+2

3f=17

3f÷3=17÷3

f=5.66666666667

=5.7

Answer:

Step-by-step explanation:

There is no graph attached.  

Convert the English phrases into expressions:

1.  "A number (Let's call it x) is equal to the sum of half a second number (y) and 3"

2.  "The first number (x) is also equal to the sum of one-quarter of the second number (y) and 5"

Let's rewrite these in standard form:

x = (1/2)y+3

2x = y + 6

y = 2x - 6

and

x = (1/4)y + 5

4x = y + 20

y = 4x - 20

A plot of these two lines is attached.  Match them with the graph.