Write an equation to solve each problem and then solve it. There are two numbers whose sum is 53. Three times the smaller number is equal to 19 more than the larger number. What are the numbers?
According to the order of operations, which of the following should be evaluated first? exponents multiplication or division expressions within parentheses addition or subtraction
the correct answer is the expression with parentheses
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if you laid 9 bolts end-to-end that each measure seven eighths of an inch, how long would that row of bolts be?
In the linear equation y = 2x + 1, if x increases by 4 points, how much will y increase?
If [tex]\(x\)[/tex] increases by 4 points, [tex]\(y\)[/tex] will increase by 8 units.
In the linear equation [tex]\(y = 2x + 1\)[/tex], the coefficient of [tex]\(x\)[/tex] is 2. This means that the slope of the line is 2, and for every one unit increase in [tex]\(x\), \(y\)[/tex] will increase by 2 units.
Given that [tex]\(x\)[/tex] increases by 4 points, the corresponding increase in [tex]\(y\)[/tex] can be found by multiplying the change in [tex]\(x\)[/tex] by the slope:
[tex]\[\Delta y = \text{Slope} \times \Delta x\][/tex]
[tex]\[ \Delta y = 2 \times 4 = 8\][/tex]
Therefore, if [tex]\(x\)[/tex] increases by 4 points, [tex]\(y\)[/tex] will increase by 8 units.
Example:
Let's use the given linear equation [tex]\(y = 2x + 1\)[/tex] and demonstrate how an increase in [tex]\(x\)[/tex] by 4 points results in an increase in [tex]\(y\)[/tex] by 8 units.
Given Linear Equation:
[tex]\[y = 2x + 1\][/tex]
Let's consider an initial point on the line where [tex]\(x = 3\)[/tex]. Find the corresponding [tex]\(y\)[/tex]:
[tex]\[y = 2(3) + 1 = 7\][/tex]
So, when [tex]\(x = 3\), \(y = 7\)[/tex].
Now, if [tex]\(x\)[/tex] increases by 4 points, new [tex]\(x\)[/tex] value will be [tex]\(3 + 4 = 7\)[/tex].
Using the same linear equation to find the new [tex]\(y\)[/tex]:
[tex]\[y_{\text{new}} = 2(7) + 1 = 15\][/tex]
Now, calculate the increase in [tex]\(y\)[/tex]:
[tex]\[\Delta y = y_{\text{new}} - y_{\text{initial}} = 15 - 7 = 8\][/tex]
So, in this example, when [tex]\(x\)[/tex] increases by 4 points (from 3 to 7), [tex]\(y\)[/tex] increases by 8 units (from 7 to 15), confirming that the increase in [tex]\(y\)[/tex] is proportional to the increase in [tex]\(x\)[/tex] with a slope of 2.
What is the answer for 5 3/4+3 1/3 =?
Find the intervals on which f is increasing and decreasing, find the local maximum and minimum values of f, find the intervals of cocavity and inflection f(x) 2x^3 + 3x^2 -36x
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In 2012, the population of a city was 6.81 million. the exponential growth rate was 1.61% per year. a) find the exponential growth function. b) estimate the population of the city in 2018. c) when will the population of the city be 10 million? d) find the doubling time.
If f(x) = x^2 and g(x) = 1/2x + 3, find g(f(-1)).
A.) -1
B.) 1/25
C.) 1/5
D.) 1
what is the answer to the problem above?
A ball is launched into the sky at 272 feet per second from the roof of a skyscraper 1,344 feet tall. The equation for the ball’s height h at time t seconds is h = -16t2 + 272t + 1344. When will the ball strike the ground?
Answer:
Time taken to reach the ball to the ground is 21 seconds.
Step-by-step explanation:
Given : A ball is launched into the sky at 272 feet per second from the roof of a skyscraper 1,344 feet tall. The equation for the ball’s height h at time t seconds is [tex]h = -16t^2 + 272t + 1344[/tex].
To find : When will the ball strike the ground?
Solution :
The equation for the ball's height 'h' at time 't' is given by,
[tex]h(t)= -16t^2 + 272t + 1344[/tex]
When the ball strike the ground the height of the ball became zero.
Substitute h=0 in the given equation,
[tex]-16t^2 + 272t + 1344=0[/tex]
Taking 16 common,
[tex]16(-t^2 + 17t + 84)=0[/tex]
or [tex]t^2-17t-84=0[/tex]
Solve by middle term split,
[tex]t^2-21+4t-84=0[/tex]
[tex]t(t-21)+4(t-21)=0[/tex]
[tex](t-21)(t+4)=0[/tex]
[tex]t=21,-4=0[/tex]
Reject t=-4 as time can never be negative.
Therefore, Time taken to reach the ball to the ground is 21 seconds.
Emily got a newjob that guarantees her a 6% raise every year. If she started out making 25,000, how long will it be before she doubles her current salary
At the end of the past month the cash account of a company had an ending balance of 6750. During the last month the account was debited for a total of 11350 and credited for a total of 10500. What was the balance in the cash account at the of the last month
the local weather forecast has been accurate for 17 of the past 33 days based on this fact what is the relative frequency probability that the forecast for tomorrow will be accurate
Tangerine trees yield 50 pounds of fruit per acre and grapefruit trees yield 75 pounds of fruit per acre. Suppose Josh's farm has t acres of tangerine trees, g acres of grapefruit trees, and yields 1,500 pounds of citrus. What is the constraint equation that represents this scenario?
50t + 75g = 1,500 75t + 50g = 1,500 125c = 1,500 t + g = 1,500
Answer: 50t+75g=1,500
A pound of chocolate costs 7 dollars. Tiffany buys p pounds. Write the equation to represent the total cost c that Tiffany pays.
Final answer:
The equation to represent the total cost c that Tiffany pays for p pounds of chocolate, when a pound costs 7 dollars, is c = 7 × p. This is a simple linear equation with 7 as the price per pound.
Explanation:
The question asks to write an equation to represent the total cost c that Tiffany pays for p pounds of chocolate, with the knowledge that a pound of chocolate costs 7 dollars.
To find the total cost c, we simply need to multiply the cost per pound of chocolate by the number of pounds Tiffany buys. If each pound costs $7, then the equation showing the total cost for p pounds would be:
c = 7 × p
Where:
c represents the total cost
p represents the number of pounds of chocolate
This is a straightforward linear equation with the coefficient 7 representing the price per pound of chocolate.
show this fraction as a decimal 1 1/4
What is the total future value six years from now of $80 received in one year?
Which statistic is used to test a global hypothesis about a multiple regression equation?
In RST , RS=11 ,RT=9 and ST=6 which angle of RST has the smallest measure ?
<R angle of RST has the smallest measure.
The correct option is C.
We have,
RS=11 ,RT=9 and ST=6
Now, from the given lengths it can be seen that the length of ST is shortest and length of RS is longest.
By the definition which states that,
The angle opposite to longest side is largest and the angle oppsite to shortest side is smallest.
From given, <R is opposite to shortest side ST.
Thus, the smallest angle is R.
Learn more about Angle here:
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Which of the following represents the zeros of f(x) = 6x3 − 35x2 + 26x − 5?
the answer choices are
A. -5, one third, one half
B. 5, negative one third, one half
C. 5, one third, negative one half
D. 5, one third, one half
how to Solve for the Missing Side
You roll a standard number cube. Find P(number is not 2).
Select one:
a. 2/3
b. 1/2
c. 5/6
d. 1/6
What is the inequality for this verbal description?Sam has d dollars to spend on grapes and carrots. He wants to buy one bag of grapes for $4.00 and c pounds of carrots that cost $2.00 per pound. Which inequality represents this situation?
Final answer:
The inequality for Sam's expenditures on grapes and carrots, with grapes costing $4 and carrots costing $2 per pound, is 4 + 2c <= d.
Explanation:
The inequality that represents Sam's spending on grapes and carrots, given that he has d dollars to spend, is 4 + 2c ≤ d. This inequality is derived from the cost of one bag of grapes, which is $4, and the cost of carrots, which is $2 per pound. The variable c represents the number of pounds of carrots Sam wants to buy. The total cost of grapes and carrots must be less than or equal to the amount of money Sam has, which is d dollars.
Starting time 7:43 elapsed time 36 min
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Circle P is below
One side of a cube has an area of 25 centimeters squared. What is the surface area of the cube?
Atrap and Bracken are two rival insurance companies. Atrap and Bracken have premiums of $150 and $100 and deductibles of $2,500 and $3,500 respectively. The average expense of surgery is $25,000. If after 5 years, 25 of the 1,000 people registered with Bracken have gone through surgery, where does Bracken stand in terms of gains or losses?
Answer:
Bracken has incurred a loss of $37,500
Step-by-step explanation:
People who have registered with Bracken insurance company pays premium of $100. 1,000 people in total have registered with Bracken. In 5 years Bracken would have earned an income of $500,000 [tex]\left ( $100\times1,000\times5)\right[/tex].
25 among the 1,000 registered have undergone surgery. Average surgery expense is $25,000. $3,500 is deductible. So Bracken's total expense per client is $21,500 (25,000 - 3,500). For 25 patients, it will be $537,500 [tex]($21,500\times25)[/tex].
Since expenses of $537,500 is more than income of $500,000, Bracken incurs a loss of $37,500 (500,000 - 537,500) over 5 years.
Therefore, Bracken's loss over 5 years is $37,500