f(-10) = 4, ƒ(8) = -5

The distance between the two cars varies at a speed of 65 m/h after two hours.

Let y represent the car's southward travel distance.

Let x be the distance traveled by the westbound automobile.

Allow a to be the distance between the two vehicles.

A right-angled triangle can be used to symbolize these three distances. So, we can state:

a^2 = x^2 + y ^2

Given that the distances vary with respect to time, let's make a distinction.:__________(1)

2a da/dt = 2x dx/dt +2y dy/dt

Rate of distance change between two cars, da/dt

The car is traveling west (dx/dt) at 25 m/h, while the car traveling south (dy/dt) is traveling at 60 m/h.

Therefore:

dy/dt = 60 m/h and dx/dt  = 25 m/h

The separation between the two cars will be after two hours:

y = 3* 60 = 180 miles

x = 3 * 25 = 75 miles

Therefore:

a^2 = x^2 + y ^2

a^2 = 75 ^2+ 180 ^2

a= [tex]\sqrt{5625 + 32400}[/tex]

a= 195

From (1):

195(da/dt) = 75(25) + 180(60)

195(da/dt) = 1875 + 10800 = 12675

da/dt = 12675 / 195 = 65 m/h

As a result, after two hours, the two automobiles' separation is varying at a speed of 65 m/h.

Learn more about distance :

brainly.com/question/15172156

#SPJ4

From the given statements regarding angle the point b) DE is parallel to AC with its reason - AB is a transversal cutting DE and AC will be the correct statement.

DE and AC are parallel for this to work angle 1 is at A, angle 2 is at B and angle 3 is at C. In addition, angle 4 is the alternate interior angle to angle 1 once DE is constructed, as is angle 5 to angle 3. Then the missing reasons are alternate interior angles theorem and definition of congruent angles.

Learn more about angle here

https://brainly.com/question/13954458

#SPJ4

The sample size that should be used is 43.

Given that;

The weight of a cereal box is measured as part of a statistical quality control process for the manufacture of cereal. It is understood that the population standard deviation is 0.06 ounces. To attain a margin of error of and a confidence level of 97% 0.02 ounces.

By considering the confidence level scenario, we get to solve how large a sample should be utilized.

The significance level is (α) = 0.03 ( 97% confidence level )

The critical value is (z*) = 2.17 ( From z-table )

The population standard deviation (σ) = 0.06

The margin of error (E) = 0.02

Therefore, the required sample size is;

n = [(z* × σ)/E ]²

n = 42.383

n ≅ 43

Finally, the sample size that should be used is 43.

To learn more about confidence level click here:

brainly.com/question/9386257

#SPJ4

Answer:

shopkeeper sells a book at INR 960 for a profit of 20% and another book at INR 720 for a loss of 10%. Find the total profit/loss of the shopkeeper

The area of the figure is 1875 sq.in.

In this question, we need to find the area of the given figure.

the area of the figure = area of rectangle + area of two triangles.

For rectangle,

length =  50 inch and width = 30 in.

Using the formula for the area of rectangle,

A1 = length * width

A1 = 50 * 30

A1 = 1500 sq.in.

For triangle,

base = 1/2 * length of rectangle

so, base = 25 in and height = 15 inch

Using the formula for the area of triangle,

A2 = 1/2 * base * height

A2 = 1/2 * 25 * 15

A2 = 187.5 sq.in.

so, the area of the figure would be,

A = A1 + (2 * A2)

A = 1500 + (2 * 187.5)

A = 1875  sq.in.

Therefore, the area of the figure is 1875 sq.in.

Learn more about area of rectangle here:

https://brainly.com/question/20693059

#SPJ1

Converse: If I get sick, I ate too much candy.

Inverse: If I don't eat too much candy, then I will not get sick

Contrapositive: If I do not get sick, I did not eat too much candy.

What is the conditional statement?

'If p, then q's statements are examples of conditional statements. In this case, "p" stands for "hypothesis" and "q" for "conclusion."

A converse statement is one that is produced by flipping a conditional statement's hypothesis and conclusion.

So, Converse: If I get sick, I ate too much candy.

An inverse assertion presupposes that each of the original claims is true.

So, Inverse: If I don't eat too much candy, then I will not get sick.

When you reverse the hypothesis and the conclusion in a statement, you have a contrapositive statement that refutes both propositions.

So, Contrapositive: If I do not get sick, I did not eat too much candy.

To learn more about the conditional statement  from the given link

https://brainly.com/question/21170

#SPJ1

2x + 6 = x - 4

x ≈ -0,67

or

x = -2^3

The fraction of 1/6 is equivalent to this following decimal number:

0.166.

A fraction is represented by the division of a term x by a term y, as follows:

Fraction = x/y.

The terms that represent x and y are given as follows:

In this problem, the fraction is given as follows:

1/6.

1 is less than 6, hence the equivalent decimal can be obtained as follows:

0.10/6.

10 divided by 6 is one with a remainder by 4, hence 1.4/6 = 1.6667.

Thus the equivalent decimal representing the fraction 1/6 is given as follows:

1/6 = 0.1666.

The problem asks for which decimal number the fraction 1/6 is equivalent.

More can be learned about fractions at https://brainly.com/question/1622425

#SPJ1

Answer: x1=π/6 ,x2 = π/4, x3 = 5π/6, x4 5π/4

Step-by-step explanation:

2sin(x)-1=0

tan(x)-1=0

sin(x)=1/2

tan(x)=1

x=π/6

x=5π/6

x=π/4

x=5π/4

x1=π/6 ,x2 = π/4, x3 = 5π/6, x4 5π/4

If a line's angle with the x-axis is then, that line's slope will be tanα, and the new road's slope will be tan(0) = 0.

D Street is depicted as a vertical line with a 90° angle of inclination in the accompanying figure. In other words, D Street has an infinite slope.

The new road will therefore have 0° of inclination if it is perpendicular to D street because if they are perpendicular and D street is vertical, the new road is level and has 0° of inclination.

A horizontal line now has zero slopes.

The new road has a zero slope as a result.

To know more about Slope, refer to this link:

https://brainly.com/question/14548961

#SPJ4

The solution to the linear system of equation is x = 3, y = 5, and z = -0.5

A system of linear equations is a set of linear equations that involve the same variable and which work or are operated (simultaneously) together

The system of linear equation is presented as follows;

2·x - 3·y + 6·z = -12...(1)

5·x + 2·y - 8·z = 29...(2)

7·x + 6·y + 4·z = 49...(3)

Multiplying equation (1) by 5 and equation (2) by 2, we get;

5 × Equation (1) ⇒ 10·x - 15·y + 30·z = -60...(4)

2 × Equation (2) ⇒ 10·x + 4·y - 16·z = 58...(5)

Subtract equation (4) from equation (5), to get;

10·x - 10·x + 4·y - (-15·y) - 16·y - 30·z = 58 - (-60) = 118

19·y - 46·z = 118...(6)

Multiplying equation (1) by 7 and equation (3) by 2, we get;

7 × Equation (1) ⇒ 14·x - 21·y + 42·z = -84...(7)

2 × Equation (3) ⇒ 14·x + 12·y + 8·z = 98...(8)

Subtracting equation (7) from equation (8), we get;

14·x - 14·x + 12·y - (-21·y) + 8·z - 42·z = 98 - (-84) = 182

33·y - 34·z = 182...(9)

Multiplying equation (6) by 33 and equation (9) by 19, we get;

627·y - 1,518·z = 3,894...(10)

627·y - 646·z = 3,458...(11)

Subtracting equation (10) from equation (11), we get;

627·y - 627·y -646·z - (-1,518·z) = 3,458 - 3,894 = -436

872·z = -436

z = -436 ÷ 872 = -0.5

z = -0.5

From equation (6), we have;

19·y - 46·z = 118

19·y - 46 × (-0.5) = 118

19·y - 46 × (-0.5) = 118

19·y = 118  + 46 × (-0.5) = 95

y = 95 ÷ 19 = 5

y = 5

From equation (1), we get;

2·x - 3·y + 6·z = -12

2·x - 3 × 5 + 6 × (-0.5) = -12

2·x = -12 + 3 × 5 - 6 × (-0.5) = 6

x = 6 ÷ 2 = 3

x = 3

Learn more about finding the solution to a system of linear simultaneous equations here:

https://brainly.com/question/12686021

#SPJ1

The correct result would be (x, y) = (5, 17); because both lines pass through this point.

Given,

In the question:

Two lines. C and D are represented by the equations.

We have :

Line C. y = x + 12

Line D. y = 3X + 2

Now, According to the question:

y = x + 12

y = 3X + 2

Substitute into one of the equations

x + 12 = 3x + 2

Solve the equation:

Combine like terms:

x - 3x = 2 - 12

-2x = -10

x = -10/-2

x = 5

Put the value of x in equation of Line C

y = x + 12

y = 5 + 12

y = 17

Hence, The correct result would be (x, y) = (5, 17); because both lines pass through this point.

Learn more about Lines at :

https://brainly.com/question/17188072

#SPJ1

The width is 5 units.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

length = width + 1

let the width be x

length= x+ 1

So, area of rectangle= l x w

30 = x( x+ 1)

x² + x - 30=0

x² + 6x - 5x - 30=0

x( x+ 6) - 5(x +6)= 0

(x+ 6)( x- 5)= 0

x= -6 or 5

Hence, the width is 5 units.

Learn more about Algebra here:

https://brainly.com/question/16104539

#SPJ1

The value of x in the given isosceles triangle is x = 15

From the question, we are to determine the value of x.

From the given information,

The length of the base of the isosceles triangle is x

Also,

The length of a leg is 4x - 3

Since, the length of the legs of an isosceles triangle are equal,

Then,

The length of the other leg is 4x - 3

Also, form the given information,

The perimeter of the triangle is 129

Thus,

x + 4x - 3 + 4x - 3 = 129

Now, solve for x

x + 4x - 3 + 4x - 3 = 129

Collect like terms

x + 4x + 4x = 129 + 3 + 3

9x = 135

Divide both sides by 9

9x/9 = 135/9

x = 15

Hence, the value of x is 15

Learn more on Perimeter of a triangle here: https://brainly.com/question/24696949

#SPJ1

The function rule for each are:

f(x) = -2x - 6

g(x) = 5x - 4

f(x) is less than g(x), in terms of slope, while in terms of y-intercept, f(x) is greater than g(x).

The rule of a function can be written in slope intercept form as, f(x) = mx + b, where the slope is m and the y-intercept is the value of b.

To write the function rule for f(x), substitute m = -2 and b = -6 into f(x) = mx + b:

f(x) = -2x - 6

Find the slope of the function g(x) whose graph is given:

Slope of g(x) = rise/run = 5/1 = 5

m = 5

The y-intercept is at y = -4, therefore b = -4.

To write the function rule for g(x), substitute m = 5 and b = -4 into g(x) = mx + b:

g(x) = 5x - 4

In terms of slope, f(x) is less than g(x)

In terms of y-intercept, f(x) is greater than g(x).

Learn more about function rule on:

https://brainly.com/question/21173462

#SPJ1

Answer:

C

Step-by-step explanation:

If you look at a number line, you can see that numbers with greater values are to the right of numbers with smaller values.

-8 is to the left of -7 on a number line so it is not greater

9 is to the right of 3 on a number line so it is not smaller

0 is to the right of -3 on a number line so it is greater

And lastly, 0 is to the left of 4 on a number line so it is not greater

Turning of head is rooting reflex.

Reflex is defined as the action which is performed without thought. In other words, it is an unconscious behaviour or involuntary movement. Newborns have different reflexes such as rooting reflex, moro reflex, stepping reflex, tonic neck reflex and grasp reflex.

Rooting reflex acts on touch. Based on this, babies feed themself. They start sucking when the roof of their mouth is touched. Moro reflex occurs on sudden sound or movement of high intensity. Tonic neck reflex results in fencing position of baby. Grasp reflex is seen when baby closes their fingers and stepping reflex concerns legs.

Learn more about reflex -

https://brainly.com/question/894334

#SPJ4

Analyzers should use the Alpha aesthetic.

Using the Alpha aesthetic, specific points on a scatterplot are more transparent than others to highlight specific data points.

What is a scatterplot?

A scatter plot is a set of points plotted along a horizontal and vertical axis. In statistics (also known as variables), scatter plots are crucial to demonstrating whether a correlation exists between observational quantities or phenomena.

A scatter plot  plots data points on a horizontal and vertical axis to demonstrate one variable's influence on another. Each row in the data table is represented by a marker whose position is determined by the values of the columns on the X and Y axes.

Using a scatter plot, this line indicates the prevailing direction of a phenomenon. In a scatter plot, a trend line can be used to highlight the direction and speed of price changes.

To Learn more about scatter plot:

https://brainly.com/question/29351385

#SPJ4

Answer:Use the slope-intercept form to find the slope.

m=4

The equation of a perpendicular line to

y

=

4

x

−

9

must have a slope that is the negative reciprocal of the original slope.

m

perpendicular

=

-1/4

Step-by-step explanation:

hii lily how are u

Answer:

67 times

Step-by-step explanation:

33,500 divided by 500 is equivalent to 67

Answer:

h(8) = 2

Step-by-step explanation:

substitute x = 8 into h(x) , that is

h(8) = 2(8 - 7) = 2(1) = 2

A pharmacist wants to mixture of 40 % saline solution with a 12% saline solution to get 119 ml. of a 32% saline solution. He used 85 ml of 40% saline solution and 34 ml of 12% saline solution.

Mixture word problems require you to combine two or more separate items, and then calculate some quantity of the resulting mixture (such as a percentage, price, or number of liters, for example). There will always be some type of "rate," like miles per hour or price per pound. Mixtures are substances that contain two or more distinct substance categories. To separate them, utilize physical tools. Examples include air, different gases, a mixture of sugar and water, a solution of salt and water, and so on.

Given,

A pharmacist wants to mixture of 40 % saline solution with a 12% saline solution to get 119 ml. of a 32% saline solution.

Equation:

X + y = 119

y = 119 - x

0.40x + 0.12y = 119 of 0.32

0.40x + 0.12y = 38.08

Using y = 119 -x

0.40x + 0.12(119 - x) = 38.08

0.40x + 14.28 - 0.12x = 3808  Eq(2)

0.28x = 23.8

x = 85

y = 119 - 85

y = 119 - 85

y = 34

Equating values in equation (2),

0.40(85) + 0.12(34)

34 + 4.08

38.08

A pharmacist wants to mix a 40 % saline solution with a 12% saline solution to get 119 ml. of a 32% saline solution. He used 85 ml of 40% saline solution and 34 ml of 12% saline solution.

To learn more about mixture, visit:

https://brainly.com/question/24898889

#SPJ1

The length and width of the rectangle are 50 feet and 25 feet respectively, the product of which gives the area of the rectangle which is 1250 feet.

Given, 100 feet of fence to make a rectangular play area that is side by side with the wall of your house.

The perimeter of the rectangle is = 2x+2y, since the wall bounds from one side as given in the question perimeter changes to = x+2y.

Perimeter = x+2y

100 = x+2y

100 = 50+2y

2y = 50

y = 25

Using this we found the length and width of the rectangle which is equal to 50 feet and 25 feet respectively. The area which is the final answer comes out to be 1250 feet.

To learn more about area and perimeters,

https://brainly.com/question/11957651

#SPJ4

Answer:

Step-by-step explanation:

so you just have to round where it came from

The age of Marcus now is 20 years as 8 years ago Marcus was 12 years old.

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical sentence with two equal sides separated by an equal sign is called an equation. An example of an equation is 4 + 6 = 10. A mathematical equation that depicts the connection between two expressions on opposite sides of the sign. It generally consists of one variable and one equal to symbol. 2x - 4 = 2 is an example. x is a variable in the preceding example.

Let his age now be x.

x-8=12

x=20

Marcus is currently 20 years old, although he was 12 years old eight years ago.

To know more about equation,

https://brainly.com/question/10413253

#SPJ4

Answer:

2. 25

max = 88 feet

See the attachment photo!

for an ordered pair (x comma y )in a relation, the x element represents the horizontal axis.