Sara is 33 years younger than Rolando. The sum of their ages is 105. Select the system of equations if Sara’s age is represented by S and Rolando’s age is represented by R.

Considering the given fractions

You have to find the least common denominator between the denominators "20" and "50"

For these values, the least common denominator is the least common multiple between both values:

So, the least common denominator is 100.

We have a rigth triangle, where we have to find the measure of x.

We can use trigonometric ratios to relate the lengths of the sides and the measure of x.

The lengths we know are from the hypotenuse and the adyacent side of x, so we can use the following trigonometric ratio:

Answer: x = 51.4°

Given:

Passing grade = 70

Formula for adjusted grade, A:

Given a passing adjusted grade of 70, let's find the raw score, R.

To solve for R, substitute 70 for A and solve for R.

We have:

Divide both sides by 10:

Take the square of both sides:

Therefore, the raw score a student would need to have a passing adjusted grade of 70 is 49

ANSWER:

49

Answer:

a: a produces vertical stretch

b: b produces a horizontal stretch

h: h produces a translation to the left of the X-axis

k: k produces a translation on the new function upward of the Y-axis

Step-by-step explanation:

An intermediate function is produced by adding each variable in the following order:

1) f(x) to f(bx):

Effect:

the horizontal stretch of f(x) along the x-axis with stretch factor b

2) f(bx) to f(bx+h):

Effect:

translation of f(bx) to the left of the X-axis by h units

3) f(bx+h) to a*f(bx+h):

Effect:

vertical stretching of f(bx+h) by a factor equal to a

4) Finally, a*f(bx+h) to a*f(bx+h)+k:

Effect:

vertical translation of a*f(bx+h) by h units upwards along the Y-axis.

Blaise M.

Answer:

[tex]\frac{5}{2}[/tex] or 2.5cm

Step-by-step explanation:

Hello! Let's help you with your question here!

Let's start by working out what we know and what we need. So, we know that P is a circle and Q is the shape of a quarter circle with a radius of 20cm. The area of Q is 9 times the area of P and we must find the radius of P.

To start, we're looking for area, so we should at least start looking at the area of a circle, given radius, which is:

[tex]A=\pi r^2[/tex]

Now, we don't necessarily know r (radius) and the area either. However, we can try to use the quarter circle as our guide for the full circle. So, we want to find the area of the quarter circle, we can do that by using this formula!

[tex]A=\frac{1}{4} \pi r^2[/tex]

The reason why we put a [tex]\frac{1}{4}[/tex] at the front of [tex]\pi r^{2}[/tex] is because we're only solving for a quarter of a circle instead of the entire circle.

Now that we have our formula! We can calculate the area of the quarter circle as follows:

[tex]A=\frac{1}{4}\pi 15^2[/tex]

[tex]A=\frac{\pi 15^2}{4}[/tex]   -We combine the fraction [tex]\frac{1}{4}[/tex] into the rest of the equation.

[tex]A=\frac{225\pi }{4}[/tex]   - Evaluating [tex]15^2[/tex]

Now that we have the area of the quarter circle, we can now work on the full circle. What we know is that the area of A is 9 times of B, since we're finding the radius of B, we can essentially plug in the area and solve for the radius of the full circle. That would be as such:

[tex]A=9\pi r^2[/tex]   -We're using the area of circle A to find the radius of B.

[tex]\frac{225\pi }{4} =9\pi r^2[/tex]   - Plugging in the area of the quarter circle.

[tex]\frac{225\pi }{4}/9\pi =\frac{9\pi r^2}{9\pi }[/tex]   - We divide [tex]9\pi[/tex] to get rid of it on the right side.

[tex]\frac{25}{4} =r^2[/tex] - When dividing by [tex]\pi[/tex], the numerator [tex]\pi[/tex] gets cancelled out.

[tex]\sqrt{\frac{25}{4} }=r[/tex]   -We square root to get rid of the squared.

[tex]\frac{5}{2}=r[/tex]    - Square rooted both numerator and denominator.

And there we have it! We finally get a radius of [tex]\frac{5}{2}[/tex] or 2.5cm.

Multiplication of coefficients and variable

It's given the expression:

Given that the price is $140 , and the tax rate is 7.5% (0.075 in decimal form)

we can find the amount in taxes by the product :

0.075 times 140

0.075 * 140 = 10.5

so $10.5 is the amount to be paid in taxes

A scatter plot uses dots to represent values for two different values

(16,15)

(20,12)

(14,20)

(15,18)

(19,14)

(18,21)

Where the x value is boys and the y value is girls

Let the trip by car be c and the trip by plane be p.

The missionary travelled 9 times as far by plane as he did by car. This means if his trip by car is modelled by c, then the trip by plane would be 9c.

Hence, knowing that the entire trip of 2300 miles is by plane and by car;

Solution

We can do the following operation_

17-50 = -33 ft

And that represent the distance between te heron and the squirrel

And since the actual height is -23 ft

Then the answer would be given by:

17 -(-23) = 40 ft

The distance from the squirrel and the bird is 40 ft

The coterminal of angle with measure x is x + 360 degrees

Example:

If x = 30 degrees, then

The coterminal of x is 30 + 360 = 390 degrees

The coterminal of 128 degrees is 128 + 360 = 488 degrees

Then the answer is D

Perimeter = sum of outer lengths

Lenght of the triangle sides = 5ft

perimeter of a semicircle = π d; half = π d / 2

5 ft + 5ft + π r

5 + 5 + (3.14*3) = 19.42 ft

We have to find the length of AB.

We can use the Law of sines the tell us that the quotient between the sine of an angle and the length of the opposite side is constant for each of the three angles.

So we can write:

Answer: AB = 4.7

Answer:

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Class 11

>>Applied Mathematics

>>Straight lines

>>Various forms of the equation of a line

>>Find the equation of the line that passe

Question

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Find the equation of the line that passes through the points (7,5) and (−9,5)

Hard

Updated on : 2022-09-05

Solution

verified

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Correct option is A)

Since slope of line passing through two points (x

1

,y

1

) and (x

2

,y

2

) is m=

x

2

−x

1

y

2

−y

1

We now find the slope of the line passing through the points (7,5) and (−9,5) as shown below:

m=

−9−7

5−5

=

−16

0

=0

Therefore, the slope of the line is 0.

Now use the slope and either of the two points to find the y-intercept.

y=mx+b

5=(0)(7)+b

b=5

Write the equation in slope intercept form as:

y=mx+b

y=(0)x+5

y=5

Hence, the equation of the line is y=5.

Answer:

Step-by-step explanation:

A horizontal line with evenly spaced numerical increments is referred to as a number line. How the number on the line can be answered depends on the numbers present. The use of the number is determined by the question that it corresponds to, such as when graphing a point.

The visual depiction of numbers, such as fractions, integers, and whole numbers, spread out uniformly along a single horizontal line is known as a number line. A number line can be used as a tool for operations like addition and subtraction as well as comparison and sorting of numbers.

Given:

As from the Figure we have

-1 3/4 = -7/4 = -1.75, which is represented by point 1 on the number line.

and, 14/8 = 1.75, which is represented by point 7 on the number line.

and, 1.125, which is represented by point 6 on the number line.

and, -0.875, which is represented by point 4 on the number line.

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Answer:

=========================

The difference between odd and even functions is that:

Let's test this property for the given functions.

we have the equation

x+8=14

step 1

subtract 8 both sides

x+8-8=14-8

x=6

therefore the answer is the last option

I have 42 dimes in my piggy bank according to the given condition of 66 coins and amount $10.20 and used the system of equation as well as substitution method.

A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, also known as a system of equations or an equation system. A group of two or more equations that share the same variables is known as a system of equations. A set of values for a variable that simultaneously satisfy each equation is the solution to a system of equations.

Finding the value of any variable from one equation in terms of another variable is the first step in the substitution method. For instance, if there are two equations, x+y=7 and x-y=8, we can deduce that x=7-y from the first equation. Applying the substitution method begins with this.

Here,

x+y=66    ......(1)

1 dime values 10 cents.

1 quarter values 25 cents.

10x+25y=1020       ........(2)

x=66-y

10(66-y)+25y=1020

660-10y+25y=1020

15y=360

y=360/15

y=24

x=66-24

x=42

I used the system of equations and the substitution method to determine that I have 42 dime coins in my piggy bank in accordance with the requirement of 66 coins totaling $10.20.

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Given the two sets:

we can write the product set of A and B in the following form:

next, we have that the number of elements in A is 2 and the number of elements in B is 3, then, we have:

finally, the equation that involves the numerals of the previous parts is:

where n(A) and n(B) represents the number of elements in A and B respectively.

According to the given data we have the following function:

f(x)=3x-6

To determine f(8)​ we would have to plug in into the equation the 8 and then proceed to calculate it, so:

If f(x)=3x-6

Then, f(8)=3(8)-6

f(8)=24-6

f(8)=18

Volume of object = 42 cubic cm

Surface area of object = 96 square cm

The given figure is a triangular prism.The formula for calculating its volume is expressed as:

where:

B is the base area

H is the height of prism

Determine the surface area of the prism

The surface area if the sum of all the faces of the prism.The faces consists of 3 rectangles and 2 triangles. The surface area is calculated as:

Hence the surface area of the object shown is 96 square cm

SOLUTION

The Point of a co-ordinate is always written as

Giving a point

For instance x=2 and y=2, the point will be

If the coordinate of x and y are reversed, the point will remain the same

Hence

the points with the same x- and y-coordinates will give the same location if the coordinate is reversed.

Therefore The Third option is correct (c)

The standard deviation for a total of 200 games is 5.3735.

Let X = number of home runs of this player in 200 games played by him.

p = probability that a this player hits a home run in a single game and this is given to be 0.175.

Where np = Mean of X and √{np(1 - p)} is the standard deviation of X.

Here n = 200 and p = 0.175. So, the standard deviation for a total of 200 games is the standard deviation for a total of X

= √(200 x 0.175 x 0.825) / 2

= 5.3735

The value is 5.3735.

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Question:

Solution:

This computer program carries out a single mathematical operation in

then, to complete 2.5 x 10^3 mathematical operations the program will take a time of:

thus, the correct answer is:

The symmetry of a quadratic equation is given by the line that passes through its vertex, so in order to find the axis of symmetry we need to find the coordinate of the vertex, which is done below.

Where "a" is the number multiplying the square factor and "b" is the number multiplying the factor that isn't squared. To find these two constants we need to expand the equation given.

We have that a = 1 and b = 4, therefore:

The axis of symmetry for this quadratic equation is x=-2.

From the information given, the mean monthly water bill for 82 residents in a local apartment complex is 137 dollars. The best estimate for the mean monthly water bill is the sample mean. Since 137 dollars is the sample mean, the correct answer is 137

Answer: i donno

Step-by-step explanation:

ask Professor Ahmad Shaoki

Given:

A pound of chocolate costs 7 dollars.

To find:

The equation represents the total cost c for buying p pounds of chocolate.

Solution:

It is given that a pound of chocolate costs 7 dollars. So,

Since the cost of p pounds of chocolate is c. So,

Thus, the answer is c = 7p.