A-18. Evaluate the expressions below for the given values.
a. 4d +3 if d=-1
b. x² + y2 if x = 7 and y = 5

Using linear functions, we have that:

a. Sara will have driven 2.25 hours when Pedro catches up with her.

b. They are 146.25 miles from home when Pedro catches up with Sara.

A linear function is modeled by:

y = mx + b

In which:

We have to consider the starting time as when Pedro leaves, when Sara will be at position 45 miles. Considering the velocities as the slope, the functions are:

Pedro will catch up with Sara when:

P(t) = S(t)

Hence:

65t = 45t + 45

20t = 45

t = 45/20

t = 2.25 hours.

Sara will have driven 2.25 hours when Pedro catches up with her.

The distance from home will be given by:

P(2.25) = S(2.25) = 65(2.25) = 45(2.25) + 45 = 146.25.

They are 146.25 miles from home when Pedro catches up with Sara.

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In Wednesday, the stock market had its biggest loss.

Over the course of a day, the stock market will fluctuate in value due to a number of factors. These include political news and economic data. Over the first four days of the week, this means that Monday through Thursday there is more volatility because these are typically the busiest trading days for stocks.

10.45 - (-18.75) = +29.2

-34.75 - (10.45) = -45.2

-40.89 - (-34.75) = -6.14

On Wednesday the stock value lost -45.2 of its value.

When the stock market loses value, it is usually because there are concerns about a company's future prospects. This can be due to changes in the business environment, new technologies that negatively impact the company's performance, or regulatory issues.

Hence, the stock market lost its most value on Wednesday .

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Answer:

1400

Step-by-step explanation:

10² is 100 so 100*14 is 1400

The unit rate is $9.50 per hour

As the rate for 6 hrs. is $57,

the rate is 57/6=(3×19) / (3×2)

=19/2

=9.50

The unit rate is $9.50 per hour

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Answer:

number of years worked, salary, salary, number of years worked, M(x)=4,000x+60,000, M(9)=96,000, switch your very last answer

Step-by-step explanation:

The dependant veriable depends on whatever the independent variable is.

Ryan was offered a job after college earning a salary of $60,000. He will get a raise of $4,000 after each year working for the company.

In this problem, the dependant variable is the salary, because his salary depends on the number of years he's worked.

If you think about it as if it's really happening, it'll make more sense--the longer you work at a job, the more raises you'll get over time.

To put this into an equation, we have to use slope-intercept form: y=mx+b

y is the same as M(x), m is your dependent variable, x is your independent variable, and b is the amount you start with.

Then we just plug the numbers in:

the dependant variable is 4000, independent is the years (which we don't need yet, so it stays as x) and the amount he will start with is 60000

M(x)=4,000x+60000

for M(9), you just plug 9 into x and solve

M(9)=4,000(9)+60000=96,000

Finally, 9 years after being hired, his salary will be 96000 (dollars? I don't know what answer goes here but what you put doesn't really fit)

I really hope I didn't explain that too badly or completely wrong because it's been a bit since I learned this so sorry, but fun fact, I remember doing this exact delta math, and I also remember hating it so good luck

:D

Answer:

0.000000072

Step-by-step explanation:

Assuming you mean Regular Notation, that's your answer.

Answer:720,000,000

Step-by-step explanation:

1. Convert to decimal notation

More Icon

The exponent is 8, making it 10 to the power of 8. As the exponent is positive, the solution is a number greater than the origin or base number. To find our answer, we move the decimal to the right 8 time(s):

7.2 -> 720,000,000

If Samantha works in a department store selling clothing and she makes a guaranteed salary of $500 per week but is paid a commission on top of her base salary equal to 25% of her total sales for the week, then Samantha would make $662.5 in a week in which she made $650 in sales and she would make 500 + 0.25 xx in a week in which she made xx dollars in sales.

The amount of money Samantha makes in a week can be given by an algebraic expression.

Amount of money Samantha makes in a week = Salary per week + 25% of her total sale

Amount of money Samantha makes in a week = 500 + 0.25 x

Here x is the sales Samantha made in a week

If she made $650 in sales in a week :

Amount of money Samantha makes in a week = 500 + 0.25(650)

Amount of money Samantha makes in a week = 500 + 162.5

Amount of money Samantha makes in a week = $662.5

If she made xx dollars in sales in a week :

Amount of money Samantha makes in a week = 500 + 0.25 x

Amount of money Samantha makes in a week = 500 + 0.25 xx

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If Lisa's father randomly pick a tie among his 16 ties, the probability it will be a blue one is 3/8

Probability is a measure how likely an event will happen. The probability of an event A is defined as the number of event A divided by the number of all possible outcomes. Mathematically,

P(A) = n(A)/n(S)

Where:

n(A) = number of event A

n(S) = number of all possible outcomes or sample space.

In the given problem:

Number of all ties = 16

Number of blue ties = 6

Hence, when a tie is picked up randomly, the probability it will be a blue one is:

P(blue) = (number of blue ties) / (number of all ties)

P(blue) = 6/16 = 3/8

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The Percent of Aileen's bi-weekly gross pay has been withheld for tax is 81 %.

A part of a whole expressed in hundredths a high percentage of students attended. Also the result obtained by multiplying a number by a percent the percentage equals the rate times the base.

Given:

Aileen's bi-weekly gross pay = $799.80

Deducted for taxes=$151.96

According to given question we have

Percent of Aileen's bi-weekly gross pay has been withheld for tax

[tex]\frac{799.80-151.96 }{799.80} *100\\\\=81 %[/tex]

Therefore, the Percent of Aileen's bi-weekly gross pay has been withheld for tax is 81 %.

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Answer: 19%

Step-by-step explanation: Just took the test. 799.80 x .19= 151.96

Answer:

the answer is 6.43 × 10-5

Answer:

B

Step-by-step explanation:

The distance between the coordinates G(8, -2) and H(-1, 4)is; 10.82

We are given the two coordinate points as;

G(8, -2) and H(-1, 4)

The formula to find the distance between these two given coordinates is;

d = √[(x2 - x1)² + (y2 - y1)²]

Plugging in the relevant values gives;

d = √[(-1 - 8)² + (4 - (-2))²]

d = √(81 + 36)

d = √117

d = 10.82

Thus, the distance between the coordinates G(8, -2) and H(-1, 4)is; 10.82

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Take the difference in y coordinates and divide that by the difference in the x coordinates. That's the slope, sometimes called the "rise over run"  For a straight line or a linear function the slope is a constant

(6-10)(7,10) = 2/3 = slope

the line is

y-h = m(x-k) where m=2/3 and (k,h) = (10,10) or either point

to get y-10 = (2/3)(x-10)

3y -30 = 2x-20

2x-3y = -10

or use (k,h) as (7,8)

y-8 = (2/3)(x-7)

3y-24 = 2x-14

2x-3y = -10

or if you write it in y=mx + b form

it's y=(2/3)x + 10/3  where 10/3 is the y-intercept and 2/3 = slope

In this form, take the derivative of (2/3)x + 10/3

to get y' = 2/3,  the derivative is the slope

Answer:

1: is in the million

6: is in the hundred thousand

7: is in the ten thousand

5: is in the thousand

8: is in the hundred

9: is in the ten

2:is in the one

Graph the coordinates J(-2,-0.5) K(0,2) L(-4,-2) is attached.

Given that

Three points

To do

So, according the question

We have

Three points J,K AND .L

For Showing that all points in graph, We have to follow some points

So, from question

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Answer:

option 3

Step-by-step explanation:

4x² - 100 = 0 ( add 100 to both sides )

4x² = 100 ( divide both sides by 4 )

x² = 25 ( take square root of both sides )

x = ± [tex]\sqrt{25}[/tex] = ± 5

then

x = - 5 , x = 5

Answer:

purple. (said with British ascent)

Answer:

1100. because the 4% and 44 are the same thing 4% goes into 100% 25 times then 44 times 25 is 1100

Answer:

12:1

Step-by-step explanation:

1 purple bead for every 12 pink beads

Answer: The answer is triangle ABC ~ triangle EDC because m<3=m<4 and m<1=m<5.

Step-by-step explanation: The reason this would be is that both triangles are equilateral, so all the sides are the same.

Now that we know that the triangles are similar to each other, then we can eleminate the last two answers. The best possible answer would be triangle ABC ~ triangle EDC because m<3=m<4 and m<1=m<5.

When carpet sells for $4 per square foot and will cost you $616 to carpet your rectangular room, if you room is 14 feet long then the width is 11 feet

Given,

The cost of Carpet per square foot = $4

Total cost of the carpet = $616

We know

Area of the rectangle = Length × Width

Length = 14 feet

Consider the width of the rectangular room as x

Then the area of the room = 14x

Total cost of carpet = Area of the rectangular room× Cost of carpet per foot

Substitute the values

14x×4=616

14x=154

x=11 feet

Hence, When carpet sells for $4 per square foot and will cost you $616 to carpet your rectangular room, if you room is 14 feet long then the width is 11 feet

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The answers are as follows -

(a) f(x) = 0.15 + 0.89x

(b) $ 10.83.

(c) 7 donuts

(a) Firstly, forming the function using given information. Let x be the number of donuts. Adding the one-time fee and cost per donut.

f(x) = 0.15 + 0.89x

(b) As per the known fact, 1 dozen = 12 quantities. Hence, there will be 12 donuts. Keeping the values in formula to find the price of box.

f(12) = 0.15 + 0.89 × 12

f(12) = 0.15 + 10.68

f(12) = 10.83

Thus, the price of box containing one dozen donuts is 10.83.

(c) Now, finding the value of x as per given cost.

6.38 = 0.15 + 0.89x

0.89x = 6.38 - 0.15

0.89x = 6.23

x = 6.23 ÷ 0.89

x = 7

Thus, a box costing $6.38 will contain 7 donuts.

Hence, (a) f(x) = 0.15 + 0.89x, (b) $ 10.83 and (c) 7 donuts.

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The linear function that gives the cost of spending h hours at the park is given by:

C(h) = 2 + mh.

In which m is the hourly rate.

Two separate but related concepts are referred to as linear functions in mathematics: A polynomial function of degree 0 or 1 is referred to as a linear function in calculus and related fields if its graph is a straight line.

A straight line makes up the graph of a linear function. The following expression describes a linear function. Y equals f(x) = a + bx. Both the independent and dependent variables of a linear function are one. X is an independent variable, whereas Y is a dependent variable.

The three main types of linear equations are the slope-intercept form, standard form, and point-slope form.

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Answer:

[tex]y = \frac{ac}{a - b - c} [/tex]

35-25/7-5

10/2= 5

5 trees per hour

Factors estimate 5,897 times 67

The estimate product of the factors 5897 times 67 is 383500.

We have to use strategies to estimate the products.

We can round each factor to the greatest place value which is the place value farthest to the left.

we can use compatible numbers.

compatible numbers are friendly numbers they are easy to compute numbers.

Given 5897[tex]\times[/tex]67=395099

This is the actual factor

But the estimation product is

We use mental math and compatible numbers here.

step1: 5900[tex]\times\\[/tex]70=413000

step2:5900[tex]\times[/tex]65=383500

Both the step1 and step2 are reasonable because the factor are close to the actual factor.

But 5900[tex]\times[/tex]65=383500 is better because it is very close to the actual factor compared to 5900[tex]\times\\[/tex]70=413000.

Therefore, The estimate product of the factors 5897 times 67 is 383500.

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Answer:

x>=27

Step-by-step explanation:

You have to remove the -3 from the left side by adding 3 to both sides, 4x=108 then 108/4 to get x. x=27

Answer:

I already checked the question .I think it is correct