What is the unit rate for 98.4 miles on 4.8 gallons of gas? 2.05 20.5 25 205

Why do you think rates are usually written as unit rates?

stellarik [79]

Coooooooooooooooooooooool

6 0

3 years ago

The hypotenuese of an isosceles right triangle is 13 inches. The midpoints of its sides are connected to form an inscribed trian

Georgia [21]

Answer:

The Sum of the areas of theses triangles is 169/3.

Step-by-step explanation:

Consider the provided information.

The hypotenuse of an isosceles right triangle is 13 inches.

Therefore,

$x^2+x^2=169\\2x^2=169\\x=\frac{13}{\sqrt{2} }$

Then the area of isosceles right triangle will be: $A=\frac{1}{2} x^2$

Therefore the area is: $A=\frac{169}{4}$

It is given that sum of the area of these triangles if this process is continued infinitely.

We can find the sum of the area using infinite geometric series formula.

$S=\frac{a}{1-r}$

Substitute $a=\frac{169}{4} \ and\ r=\frac{1}{4}$ in above formula.

$S=\frac{\frac{169}{4}}{1-\frac{1}{4}}$

$S=\frac{\frac{169}{4}}{\frac{3}{4}}$

$S=\frac{169}{3}$

Hence, the Sum of the areas of theses triangles is 169/3.

7 0

3 years ago

In the diagram below,AB is the diameter of the circle with centre P.Point C lies on the y-axis.Given the coordinates of A and B

Step2247 [10]

Answer:

The coordinates of P are (-2,0)

The radius of the circle is 5.

Step-by-step explanation:

Analytic geometry

The diagram shows a circle with center P, and two points A(-6,3) and B(2,-3) that form the diameter of the circle.

a)

The center of the circle lies at the midpoint of A and B. The midpoint (xm,ym) can be calculated by:

$\displaystyle x_m=\frac{x_1+x_2}{2}$

$\displaystyle y_m=\frac{y_1+y_2}{2}$

Substituting x1=-6, x2=2, y1=3, y2=-3:

$\displaystyle x_m=\frac{-6+2}{2}=\frac{-4}{2}=-2$

$\displaystyle y_m=\frac{3-3}{2}=0$

Thus, the coordinates of P are (-2,0)

b) The radius of the circle is the distance from the center to any point in its circumference. We can use the distance from P to A or B indistinctly.

Given two points A(x1,y1) and P(x2,y2), the distance between them is:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Substituting x1=-6, x2=-2, y1=3, y2=0:

$r=\sqrt{(-2+6)^2+(0-3)^2}$

$r=\sqrt{4^2+(-3)^2}$

$r=\sqrt{16+9}=\sqrt{25}=5$

The radius of the circle is 5.

4 0

3 years ago

The slope-intercept form given (6,-5) & perpendicular to -5x - 7y = -17.

tatuchka [14]

Answer:

$y=\dfrac{7}{5}x-\dfrac{67}{5}$

Step-by-step explanation:

Slope-intercept form of a linear equation:

$y=mx+b$

where:

m is the slope.
b is the y-intercept.

Rearrange the given equation so that it is in slope-intercept form:

$\implies -5x-7y=-17$

$\implies -7y=5x-17$

$\implies y=-\dfrac{5}{7}x+\dfrac{17}{7}$

Therefore, the slope of the given equation is -⁵/₇.

If two lines are perpendicular to each other (at right angles), the product of their slopes will be -1. Therefore, their slopes will be negative reciprocals of each other.

Therefore, the slope of the line perpendicular to the given equation is:

$\sf m=\dfrac{7}{5}$

Substitute the found slope and the given point (6, -5) into the slope-intercept formula and solve for b:

$\implies -5=\dfrac{7}{5}(6)+b$

$\implies -5=\dfrac{42}{5}+b$

$\implies b=-\dfrac{67}{5}$

Substitute the found slope and the found value of b into the slope-intercept formula to create the equation for the perpendicular line:

$\implies y=\dfrac{7}{5}x-\dfrac{67}{5}$

Learn more about slope-intercept form here:

brainly.com/question/27317293

brainly.com/question/27926846

8 0

1 year ago

Charlie paid 660 for 6 shirts and four belts. One shirt costs three times as much as one belt. If Sam bought 5 shirts and 2 suck

Cerrena [4.2K]

Sam would have to pay $510 to buy 5 shirts and 2 suck belts.

Step-by-step explanation:

Let,

Cost of one shirt = x

Cost of one belt = y

According to given statement;

6x+4y = 660 Eqn 1

x = 3y Eqn 2

Putting value of x from Eqn 2 in Eqn 1

$6(3y)+4y=660\\18y+4y=660\\22y=660$

Dividing both sides by 22

$\frac{22y}{22}=\frac{660}{22}\\y=30$

Putting y=30 in Eqn 2

$x=3(30)\\x=90$

One shirt costs $90 and one belt cost $30.

Price of 5 shirts = 90*5 = $450

Price of 2 belts = 30*2 = $60

Total = 450+60 = $510

Sam would have to pay $510 to buy 5 shirts and 2 suck belts.

Keywords: linear equation, addition

Learn more about addition at:

#LearnwithBrainly

6 0

3 years ago