Mary is four years older than Sue. If the sum of their ages is 16, how old are Mary and Sue?

Graph of two linear functions y=2x+7 and y=-x+4 will intersect at (1,5)

A linear function produces a straight line in the algebraic coordinate plane. It often takes the form of a polynomial function with a maximum degree of 1 or 0.

Calculus and linear algebra are also used to express the linear functions.

The primary distinction can be found in the function notation.

An ordered pair stated in function notation must be understood.

Below is a data table for two distinct linear functions with the identical x values for both functions.

x | y=2x+7 y=-x+4 -3 | 2(-3)+7=-6+7=1| -(-3)+4=3+4=7 -2 | 2(-2)+7=-4+7=3|-(-2)+4=2+4=6 -1 | 2(-1)+7=-2+7=5|-(-1)+4=1+4=5 0 | 2(0)+7=0+7=7 |-(0)+4=0+4=4 1 | 2(1)+7=2+7+9 |-(1)+4=-1+4=3 2 | 2(2)+7=4+7=11|-(2)+4=-2+4=2 3 | 2(3)+7=6+7=13|-(3)+4=-3+4=1

The table demonstrates that the function y = 2x + 7 and the function y = -x + 4 both have values of 5 for x = -1.

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Explanation:

m < 0 tells us m is negative

n > 0 means n is positive

Therefore the product of m and n is always negative due to the rule

negative * positive = negative

Examples:

-2*5 = -10

7*(-3) = -21

The smallest number of kilometers that each must run is 6 kilometers.

From the information, Jim runs 6 kilometers at a time while Maureen prefers to run in blocks of 3 kilometers and at the end of the month, they realize that they have run the same total number of kilometers.

It should be noted that the question simony had to do with finding the least common multiple. This will be:

Multiple of 3 = 3, 6, 9, 12

Multiple of 6 = 6, 12

The least common multiple is 6.

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Answer:

22.5

Step-by-step explanation:

we can use the ratios to turn x+y+z=180 to x+4x+3x= 180

then solve for 180

x = 22.5

Answer: D.) 22.5°

Have a nice day!

The rule for the function g(x) is g(x) = x - 5 when f(x) = 5 and vertical down to 5 units.

Functions:

Function refers the relationship from a set X to a set Y assigns to each element of X exactly one element of Y

Given,

Let g(x) indicated the transformation of f(x)

Here we need to write the rule for g(x) when f(x) = x, and vertical translation down 5 units.

Here we have the function f(x) = x.

Considering the normal graph, we know that, the graph has four parts.

And each part refers difference sign. That is,

Horizontal left indicates the positive where as the horizontal right refers the negative for x axis.

Similarly, vertical up refers the positive and the vertical down represents the negative.

Here we have the vertical down translation of 5 units which refers the negative 5.

So, the rule of g(x) = x - 5.

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Answer:

1.92x5=9.6 pounds everyday.

Step-by-step explanation:

The probability that the sample is less than 8.42 is 0.0029 or 0.29%.

Using the normal distribution and the central limit theorem,

The mean is μ = 8.5

The standard deviation is σ = 0.22 .

A sample of 37 is taken, hence n = 37, s = 0.22/√37 i.e. s = 0.0362

The probability that the sample average is LESS than 8.40 is the p-value of Z when X = 8.4, hence:

Z = X - μ/σ

Z = 8.4 - 8.5/0.0362

Z = 2.76

Z = -2.76 has a p-value 0.0029

0.0029 = 0.29% probability that the sample average is LESS than 8.40.

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Answer:

[tex]y=-\frac{1}{3} x - 6[/tex]

Step-by-step explanation:

3x+9y=-54

9y=-3x-54

y=-1/3x-6

:] good luck

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: y = - \frac{x}{3} - 6[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

The given equation is :

[tex]\qquad\displaystyle \tt \rightarrow \: 3x + 9y = - 54[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: 9y = - 54 - 3x[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: y = \frac{ - 54}{9} - \frac{3x}{9} [/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: y = - \frac{x}{3} - 6[/tex]

And this the equation of same line in its slope intercept form, where slope (m) = -1/3 and y - intercept = -6

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

The cost of the jalapeno poppers was $9.24 if each friend paid $9.73.

The cost of the jalapeno poppers can be determined by using multiplication followed by subtraction.

First, we determine the total amount paid by the three friends;

If each friend paid $9.73, then;

Total amount = 9.73 × 3

Total amount = $29.19

Now to find the cost of jalapeno poppers, we subtract the cost of nachos from the total amount paid by the three friends;

cost of jalapeno poppers = total amount - cost of nachos

cost of jalapeno poppers = 29.19 - 19.95

cost of jalapeno poppers = $9.24

Therefore, the cost of jalapeno poppers is calculated to be $9.24.

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Step-by-step explanation:

hope it helps you

thank you

Answer:

The difference is that the first equation, -2x≥10 -2x can be greater than or equal to 10 but the second equestion is only greater than ten.

Step-by-step explanation:

Comparison symbol makes each inequality statement true is −6.809< −6.812.

The given numbers are −6.809 and −6.812.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

Comparing decimals involves starting with the digits having the highest place value, just like when comparing other whole numbers. We begin the comparison by putting the provided decimal numbers in a place value table. We move on to the digits in the next place to the right if the digits on the biggest place value match. Up till the digits that are different are reached, we continue comparing digits.

−6.809< −6.812

|−6.809|>|−6.812|

Therefore, comparison symbol makes each inequality statement true is −6.809< −6.812.

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Answer:

there is no model linked

Step-by-step explanation:

Answer:

Explanation:

The slope of the given line is 3/2

A line parallel to this has the same line but different y-intercept.

IIn point-slope form, it is:

Where

Using these, we have:

Answer:

Step-by-step explanation:

Answer:

The exact Population of the city Y in 2010 was 160,000.

Step-by-step explanation:

Given that,

1. In the year 2015, the populations of City X and City Y were equal.

2. City X population is increased by 20% and City Y population is decreased by 10% from 2010 to 2015.

3. Also, the population of City X was 120,000 in 2010

With the given data, calculation goes like this,

The population of City X in 2010 is 120000

Population Increased by 20% till 2015,

                = 120000×120/100

                = 144000

As Population of city Xand Y are same,

Population of city Y in 2015 would be 144000.

Population of Y in 2010 was decreased by 10%,

                = 144000×100/90

                =160000

Therefore, the Population of city Y in 2010 was 160,000.

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Answer:

x=16

Step-by-step explanation:

11=x-5

first you need to get x alone on one side so you add 5 on both sides

11=x-5

+5.  +5

11 + 5 is 16, so

16=x

Answer:

-2/5

Step-by-step explanation:

m = (10 - 8)/(31 - 36) = 2/(-5) = -2/5

Answer:

Answer down below!

Step-by-step explanation:

The best way to find the slope of the line is first find a point that rests on the line on an exact point. This exact point is (-1,0)

Then, once you find that point, continue to use rise/run to find the slope.

In this case, it goes up one, and over one

So, your slope would be 1/1 or just 1.

(NOTE: IF YOU CONTINUE TO KEEP GOING ONE UP AND ONE OVER, IT WILL STILL GIVE YOU THE SAME SLOPE, BUT YOU WILL HAVE TO DO MORE WORK!!)

In the given recipe, 1/3 cup of sugar is  needed for 1 cup of flour.

What do you mean by recipe?

A recipe is a set of instructions for preparing a dish or dessert, such as your mother's chocolate chip cookie recipe, which has won numerous awards.

The phrase "recipe" is most frequently used while discussing cookery. It covers both the steps to prepare it as well as a list of the ingredients you'll need. Recipes can be found in cookbooks, newspapers, periodicals, websites, publications, and even passed down via families. A recipe isn't just for cooking; it may also be a formula: the formula for success is a combination of diligence, timing, and a little luck.

As given in the question, In the recipe

For every cup of sugar, 3 cups of flour is needed. we can write it as:

1 cup of sugar = 3 cups of flour

we need to find how many cups of sugar needed for 1 cup of flour.

So, dividing the above equation with 3.

1/3 cups of sugar = 1 cups of flour.

Therefore, In the given recipe, 1/3 cups of sugar is required for 1 cup of flour.

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Line segments DA and BE are parallel to FC.

We need to find all the segments parallel to FC.

Parallel lines are those lines that are equidistant from each other and never meet, no matter how much they may be extended in either directions.

From the given figure, FC parallel to DA and FC parallel to BE.

Therefore, line segments DA and BE are parallel to FC.

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Answer:

2

Step-by-step explanation:

all steps are in the picture

Answer: y=3/4x-4.5

Step-by-step explanation: Looking at the two points on the line, it goes up 3 times and right 4 times, making it 3/4x. To find the y-intercept, you look where the line intersects the y-axis, and it intersects at y=-4.5.

Answer:

7y-20

Step-by-step explanation:

-3y-12+8y-8

7y-20

Answer:

5y - 20

Step-by-step explanation:

 Remove the parenthesis by multiplying each term of (y+ 4) by (-3) and  multiplying each term of (2y - 2) by 4

 -3(y + 4) + 4(2y - 2) = (-3)*y + (-3)*4 + 4*2y - 2*4

                                = -3y - 12 + 8y - 8

                               = -3y + 8y  -12 - 8

Combine like terms (-3y & 8y) and constants (-12 & -8).

                               = 5y - 20

It takes a time of 33 mi 33 sec for the two when they work together

Let x be the overall quantity of papers that must be delivered.

Candy can deliver x/50 papers in a minute.

Tim can deliver x/100 papers in a minute.

Tim and Candy took their time gathering all the papers together =x/ (x/50 +x/100)

= x/ (3x/ 100)

=100/ 3 minutes

=33 minutes 33 seconds

When Tim and Candy collaborate, it takes them 33 minutes and 33 seconds to distribute all the papers.

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Answer:

Step-by-step explanation:

It takes a time of 33 min 33 sec.

Let x be the overall quantity of papers that must be delivered.

Candy can deliver x/50 papers in a minute. Tim can deliver x/100 papers in a minute. Tim and Candy took their time gathering all the papers together =x/ (x/50+x/100) = x/(3x/ 100) =100/ 3 minutes =33 minutes 33 seconds

That is When Tim and Candy collaborate, it takes them 33 minutes and 33 seconds to distribute all the papers.

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Answer:

I'm thinking it's 22, but I could be wrong.

Step-by-step explanation:

Four conditions of congruency are: SSS, ASA, SAS, RHS

Using SSS congruency,

Side: PS = PQ (by the rule, all sides of rhombus are equal)

Side: ST = TQ (by the rule, diagonals bisect each other)

Side: PT = PT (common)

Therefore, Area(PQT) = Area(PST) by SSS congruency

Using ASA congruency,

Angle: ∠TPS = ∠TPQ (diagonals bisect the angles)

Side: PS = PQ (by the rule, all sides of rhombus are equal)

Angle: ∠PST = ∠PQT (opposite angles are equal, and diagonals bisect the angles)

Therefore, Area(PQT) = Area(PST) by ASA congruency

Using SAS congruency,

Side: ST = TQ (by the rule, diagonals bisect each other)

Angle: ∠PTS = ∠PTQ (by the rule, diagonals bisect each other at 90°)

Side: PT = PT (common)

Therefore, Area(PQT) = Area(PST) by SAS congruency.

Using RHS congruency,

Right angle: ∠PTS = ∠PTQ (diagonals bisect each other at 90°)

Hypotenuse: PS = PQ (all sides of rhombus are equal)

Corresponding Side: ST = TQ (by the rule, diagonals bisect each other)

Therefore, Area(PQT) = Area(PST) by RHS congruency

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Find the derivate of the expression using the general procedure to find the derivative of a polynomial function. To do it, multiply the term times the exponent of the variable and raise the variable to the original exponent minus 1:

Now that we have the expression for the derivative of the function, evaluate it at the value of x that is in the question statement, which is 1:

The derivative of the function is -2 at x=1.