slope = - [tex]\frac{5}{2}[/tex]
the equation of a line in slope-intercept form is
y = mx + c ( m is the slope and c the y-intercept )
y = - [tex]\frac{5}{2}[/tex] x - 5 is in this form
with slope m = - [tex]\frac{5}{2}[/tex]
The slope of the equation
[tex]Y=\dfrac{-5}{2}x-5[/tex] is [tex]-\dfrac{5}{2}[/tex] .
A line's steepness or inclination can be measured by a line's slope. It specifies the amount of rise or fall a line experiences for each unit of horizontal distance. In other words, it measures how quickly the vertical (y) and horizontal (x) coordinates of points on a line change with time.
Given equation is
[tex]Y=\dfrac{-5}{2}x-5[/tex] consider it as equation (1)
This is in the form of slope-intercept equation y = mx +b consider it as equation (2).
Where m represents the slope and b represents the intercept term.
On comparing the equation (1) and equation (2)
[tex]m=-\dfrac{5}{2}[/tex]
Hence, the slope of the given equation is given by [tex]-\dfrac{5}{2}[/tex] .
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Find 5x − 3y − z if x = −2, y = 2, and z = −3
What is the product of -2x^3 + x - 5 and x^3 - 3x - 4? Are the products equal to those of x^3 - 3x - 4 and -2x^3 + x - 5? Explain
I am soooo lost on working this out.
Answer:
Step-by-step explanation:
( -2x³ + x - 5) × ( x3 - 3x - 4)
= ( -2x³)×( x3 - 3x - 4) +(x)×( x3 - 3x - 4) - (5)( x3 - 3x - 4)
= - 2x^6 +6x^4 +8x³ + x^4 - 3x² -4x - 5x³ +15x + 20
= - 2x^6 +7x^4 +3x³-3x²+11x +20
Will make brainliest!
Parallel lines r and s are cut by two transversals, parallel lines t and u.
Which angles are corresponding angles with angle 8?
4 and 12
2 and 10
6 and 14
3 and 9
Answer:
∠4 and ∠12
A is correct
Step-by-step explanation:
Parallel lines r and s are cut by two transversals, parallel lines t and u
r || s and t || u
We are four parallel line. Two parallel line cuts two another parallel line.
Angle 8 is form by intersection of s and t line.
Corresponding angle: When two parallel lines are crossed by transversal line, the angles at matching corners are called corresponding angles.
For angle 8, t || u with s is transveral line.
Thus, ∠8 = ∠12 (By definition of corresponding angle)
For angle 8, s || r with t is transveral line.
Thus, ∠8 = ∠4 (By definition of corresponding angle)
Hence, ∠4 and ∠12 are corresponding angle of ∠8
-(1-5x)=8x+25 please help
63 less than four times a number is equal to the number. what is the number?
If y = 2x^3 + 4x and dx/dt = 2, find dy/dt when x = 4.
dy/dx = 6x² +4 . . . . . using the power rule
dy/dt = (dy/dx)×(dx/dt) = (6(4²) +4)×2
dy/dt = 200 . . . at x=4
I need a little help with the second part of b and part c! + can y'all check my explanations please
a. (my answer for context) The system for this word problem is x+y=14; 11.99x+24.99y=245.86 (x is shirts and y is pants)
b. 1. Explain, without solving, which method is most efficient in solving this system: substitution, elimination, graphing, or making a table?
(my answer is substitution, because the solutions to x and y can easily be substituted into the first equation).
b. 2. Explain why the other methods are not as sufficient.
(I need a little help but I'm thinking it's because for this system solving method you basically only have to solve the second equation and then just substitute)
c. How could you simplify the numbers used in this system to simplify the system? Does this new system change your answer to part b? Explain. (What does this mean? How can I answer it?)
Answer:
b. Your answer is appropriate.
c. The decimals can be eliminated by multiplying by 100. (You can also add 0.14 to the problem, adding .01 to each individual price and 0.14 to the total. This will make the second equation be 12x +25y = 246, which makes the numbers slightly easier to work with.) Unfortunately, there don't seem to be any common factors that would reduce the size of the numbers.
Step-by-step explanation:
a. We assume you're finding quantities of shirts and pants for a purchase of 14 total items costing $245.86. If so, your equations are appropriate.
b. The solution for one variable or the other can be found in 6 arithmetic operations using your suggested method. Any other method takes as many or more. (Multiplying the first equation by -11.99 and adding to the second gets you the equivalent of substituting for x in as many operations.)
Graphing can be quick and easy with the right tool. Since you know the solutions are integers, just about any graphing tool will get you close enough.
Another method (using only 5 arithmetic operations) is to calculate the average price of an item as 245.86/14, then figuring the ratio of the difference from the lower price to the total difference in price. Multiplying this ratio by the number of items gives the number of the higher-priced item (pants). (245.86/14 -11.99)/(24.99 -11.99)·14 = 6 This method treats the problem as a "mixture" problem, finding the numbers of each consitutuent that make the average come out what it is.
c. See above for how to simplify the numbers. Done properly, the answer is not changed. (Some people don't work well with decimals or fractions, so like to see those eliminated from the problem. Some folks work better with small integers than with large ones, so like to see the numbers be made as small as possible.)
how to solve this m<3=(x+1)(x+4) and m<5= 16(x+3)-(x^2-2)
Answer:
x = 2.75+√30.5625
∠3 = ∠5 ≈ 113.923°
Step-by-step explanation:
We are given that ∠3 = (x+1)(x+4) and ∠5 = 16(x+3)-(x²-2) are corresponding angles, hence equal. We can equate the two angle expressions and solve the resulting quadratic for x.
... (x+1)(x+4) = 16(x+3)-(x²-2)
... x² +5x +4 -16x -48 +x² -2 = 0 . . . . . subtract the right side, eliminate parentheses
... 2x² -11x -46 = 0 . . . . . . . . . . . . . . . . . collect terms
Using the quadratic formula, we want to find
... x = (-b±√(b²-4ac))/(2a) . . . . for a=2, b=-11, c=-46
... x = (11 ±√((-11)² -4(2)(-46)))/(2(2)) = (11 ±√489)/4 = 2.75 ± √30.5625
The negative solution results in negative values for the angles, so only the positive solution is useful for this problem.
... x = 2.75+√30.5625 ≈ 8.27834
Using this value for x in either expression for the angle value, we get
... ∠3 = ∠5 = (8.27834+1)(8.27834+4) ≈ 113.923 . . . degrees
_____
It seems a little odd that this problem should result in irrational values for the variables. If we take ∠3 and ∠5 to be a linear pair, then the solution is x=6 and the angle measures are 70° and 110°. The solution is done basically the same way, except that you use the equation
... ∠3 + ∠5 = 180
and substitute the given expressions. The x² terms will cancel, leaving a linear equation easily solved.
(Since this is not the problem described here, the detailed working is left to the reader.)
53% of what number is 384
Answer:
The answer is 384 is 53% of 724.53
Step-by-step explanation:
Calculation:
384/53% = 724.53
formula:
value1/% = value2
Hope this helps!
Answer:
The answer is 384 is 53% of 724.53
3. A town's population has been decreasing at a constant rate, In 2010, the population was 5,900 By 2012 the population jad dropped to 4,700 Assume the tren contiues
a. Predict te population in 2016
b. Identify the year in which the population will reach 0
4. A town has an initial population of 75,000. It grows at a constant rate of 2,500 per year for five year
a. Find the linear function that models the town's population P as a function of the year, t where t is the number of years since the model began
b. Graph y==p(t) Interpret the meaning of the Intercepts.
c. When does the model expect the population to reach 100,000?
5. The weight of a newborn baby is 7.5 pounds. The baby gained one-half pound a month in its first year.
a. Find the linear function that models the baby's weight W as a function of the age of the baby t, in months
b. Fine a reasonable domain and range for the function W
The population of the first town decreases at a rate of 600 people per year, and is predicted to be 2,100 in 2016. The town with an initial population of 75,000 grows at a linear rate, represented by the function P(t) = 75000 + 2500t, with the population expected to reach 100,000 after 10 years.
Explanation:For the first part of your question regarding the town's decreasing population, we need to establish a rate of decrease. The town's population went from 5,900 in 2010 to 4,700 in 2012—this is a decrease of 1,200 over two years, or 600 people per year. Therefore, we can predict that the population will continue to decrease by 600 people per year. In 2016, this suggests the population would be 4,700 (population in 2012) - 600*4 (4 years from 2012 to 2016), which equals 2,100. For identifying the year when the population will reach 0, we use the same rate and find it by using the formula (current population / rate of decrease) + current year. As for the part about the town with an initial population of 75,000 growing at a constant rate, we can model this as a linear function such as P(t) = 75000 + 2500t. This equation states that the population at any given year is the initial population plus the annual growth times the number of years since the model began. In terms of the graph of this function, the y-intercept represents the initial population, while the slope is the constant rate of growth. The model expects the population to reach 100,000 after (100,000 - 75,000) / 2,500 = 10 years.
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Every month, Ms. Thomas pays her car loan through automatic payments (withdrawals) from her savings account. She pays the same amount on her car loan each month. At the end of the year, her savings account balance changed by −$2,931 from payments made on her car loan. Describe the total change to Ms. Thomas’ savings account balance after making six monthly payments on her car loan. Model your answer using a number sentence.
Answer: -$1465.5
Ms. Thomas pays the 'same' amount as her car loan each month through car payments.
Total amount payed at the end of the year for car loan = -$2931
Change in Ms. Thomas' savings account each month (with respect to car loan) =
-2931/12 = -$244.25
So, to to calculate the total change to Ms. Thomas's savings account balance after paying for car loan for six months, we will simply multiply one month's amount with 6:
-$244.25 x 6 = -$1465.5
Answer:
Answer: -$1465.5
Ms. Thomas pays the 'same' amount as her car loan each month through car payments.
Total amount payed at the end of the year for car loan = -$2931
Change in Ms. Thomas' savings account each month (with respect to car loan) =
-2931/12 = -$244.25
So, to to calculate the total change to Ms. Thomas's savings account balance after paying for car loan for six months, we will simply multiply one month's amount with 6:
-$244.25 x 6 = -$1465.5
Step-by-step explanation:
NEED HELP NOW 70 POINTS! Divide. 2/3 ÷ 4/5 A.2/8 B.8/15 C.56 D.8/8
Hi,
Solution:
Find Common Denominators,
2/3 = 10/15
4/5 = 12/15
Divide,
10/15 ÷ 12/15 = 0.8333...
Turn into fraction;
0.8333... = 5/6
Answer - C. 5/6
Use mathematical induction to prove the statement is true for all positive integers n. 8 + 16 + 24 + ... + 8n = 4n(n + 1)
8++16+...+8n = 4n(n+1)
and, using regular Algebra, you can change it into the formula for (n+1):
8++16+...+8n+8(n+1) = 4(n+1)((n+1)+1)
simplify (8c^4w^2)^2 show work
Exponents are not particularly mysterious. They show repeated multiplication. That is ...
... c⁴ = c·c·c·c
... w² = w·w
Then the factor inside parentheses is ...
... 8·c·c·c·c·w·w
The exponent outside parentheses tells you the number of times this is repeated as a factor:
... (8c⁴w²)² = (8·c·c·c·c·w·w)(8·c·c·c·c·w·w)
... = 8·8·c·c·c·c·c·c·c·c·w·w·w·w = 64c⁸w⁴
_____
You can take advantage of the fact that multiplication is repeated addition, so the exponents of the various factors can be found by multiplying the outside exponent by the inside exponents.
[tex]\displaystyle\left(8c^{4}w^{2}\right)^{2}=8^{2}\cdot c^{4\cdot 2}\cdot w^{2\cdot 2}\\\\=64c^{8}w^{4}[/tex]
The population of a town is 6500 and is increasing at a rate of 4% each year. Create a function for this scenario. At this rate, approximately what will the town's population be in 4 years?
Answer:
[tex]P_4 = 7604.08[/tex]
Step-by-step explanation:
If the population increases at a rate of 4% per annum, then:
In year 1:
[tex]P_1 = P_0 + 0.04P_0[/tex]
Where [tex]P_0[/tex] is the initial population and [tex]P_n[/tex] is the population in year n
In year 2
[tex]P_2 = P_1 + 0.04P_1[/tex]
It can also be written as:
[tex]P_2 = P_0 + 0.04P_0 + 0.04 (P_0 + 0.04P_0)[/tex]
Taking out common factor [tex]P_0[/tex]
[tex]P_2 = (1 + 0.04) (P_0) + 0.04P_0 (1 + 0.04)[/tex]
Taking out common factor (1 + 0.04)
[tex]P_2 = (1 + 0.04) (P_0 + 0.04P_0)[/tex]
Taking out again common factor [tex]P_0[/tex]
[tex]P_2 = (1 + 0.04) (1 + 0.04) P_0[/tex]
Simplifying
[tex]P_2 = P_0 (1 + 0.04) ^ 2[/tex]
So
[tex]P_n = P_0 (1 + 0.04) ^ n[/tex]
This is the equation that represents the population for year n
Then, in 4 years, the population will be:
[tex]P_4 = P_0 (1 + 0.04) ^ 4\\P_4 = 6500(1 + 0.04) ^ 4\\P_4 = 7604.08[/tex]
A company developed a student survey so that students could share their thoughts about school. In 2011, 78,234 students across the United States were administered the survey. In 2012, the company planned to administer the survey to 10 times as many students as we're surveyed in 2011. About how many surveys should the company have printed in 2012? Explain how you found your answer.
Answer:
Company needs to print [tex]782,340[/tex] surveys in 2012.
Step-by-step explanation:
In 2011, 78,234 students participated in the survey.
Now in 2012 it is to be increased by 10 times. So there will be 10 times more students participating in the survey. Therefore they will need as 10 times more surveys.
Number of surveys needed in 2012 = [tex]78,234*10[/tex]
=[tex]782,340[/tex]
Company needs to print [tex]782,340[/tex] surveys in 2012.
Point C is the center of the circle. angle ACB measures 49. What is the of arc ADB
If arc ADB is that portion of the circle that is not arc AB, then its measure is ...
... 360° -49° = 311°
_____
The sum of the measures of the arcs of a circle is 360°.
Solve for x.
4 - 3x
---------- = 5
2
Answer:
x=-2
Step-by-step explanation:
We are given an equation as
[tex]\frac{4-3x}{2} =5[/tex]
and asked to solve for x
Simplify by multiplying both sides by 2. This will get rid of fraction on left side.
4-3x = 10
Grouping like terms by taking 4 to right side
we get right side 10-4 = 6
-3x = 6
To get exact value of x, we divide by -3 on both the sides
x = 6/-3 = -2
Since this is an equation, we get a single value for x
x=-2
and answer is -2
Given fractional expression:
{(4-3x)/2} = 5
→ 4-3x = (5)2
→ 4-3x = 10
→ -3x = 10-4
→ -3x = 6
Therefore, x = -(6/3) = -2
If you ever swam in a pool and your eyes began to sting and turn red, you felt the effects of an incorrect pH level. pH measures the concentration of hydronium ions and can be modeled by the function p(t) = −log10t. The variable t represents the amount of hydronium ions; p(t) gives the resulting pH level.
Water at 25 degrees Celsius has a pH of 7. Anything that has a pH less than 7 is called acidic, a pH above 7 is basic, or alkaline. Seawater has a pH just more than 8, whereas lemonade has a pH of approximately 3.
Create a graph of the pH function either by hand or using technology. Locate on your graph where the pH value is 0 and where it is 1. You may need to zoom in on your graph.
The pool maintenance man forgot to bring his logarithmic charts, and he needs to raise the amount of hydronium ions, t, in the pool to 0.50. To do this, he can use the graph you created. Use your graph to find the pH level if the amount of hydronium ions is raised to 0.50. Then, convert the logarithmic function into an exponential function using y for the pH.
Recall from 07.02 how to convert a log to an exponential function. The equation y equals b to the power of x is written on the left. The equation x equals log base b of y is written on the right. A double-ended arrow points to both equations. The word exponent is written above the equations with arrows pointing to the x on the left and the x on the right. The word base is written below the equations with arrows pointing to the b on the left and the b on the right.
The pool company developed new chemicals that transform the pH scale. Using the pH function p(t) = −log10t as the parent function, explain which transformation results in a y-intercept and why. You may graph by hand or using technology. Use complete sentences and show all translations on your graph.
p(t) + 1
p(t + 1)
−1 • p(t)
Hello,
Please, see the attached files.
Thanks.
Answer:
hey i think the answer is 7
Step-by-step explanation:
why is it useful to write a ratio of fractions as a unit rate
A "unit rate" has a denominator of 1. That will often simplify any subsequent math operations.
_____
The choice of the form of a ratio should be made based on what you need to do with it. Sometimes, a denominator other than 1 is appropriate to follow-on operations you may need to perform.
Answer:
It is useful to write a ratio of fractions as a unit rate because it makes it easier to compare other unit rates to the corresponding unit rate.
Work the following area application problem.
You own a swimming pool elliptical in shape. You wish to cover it at night to retain its warmth. If the pool measures 18 ft. across at its minor axis and 25 ft. across at its major axis, how much plastic material will you need to cover the pool, assuming you need a 1.5 ft. overhang all around the pool?
Area (to the nearest tenth) = ______ sq. ft.
SInce you need 1.5 feet of overhang, add 3 feet to each axis dimension 1.5 on each side):
Minor Axis = 18 + 3 = 21 feet
Major axis = 25 + 3 = 28 feet
The area of an ellipse is found by multiplying half the minor axis by half the major axis by PI.
1/2 minor axis = 21 / 2 = 10.5
1/2 major axis = 28 / 2 = 14
Using 3.14 for PI
Area = 10.5 x 14 x 3.14 = 147 x 3.14 = 461.6 sq ft
This problem is not as simple as it may appear at first. The area of an ellipse is ...
... A = πab
where a and b are the semi-axes.
Here, it looks like you're expected to choose these to be 1.5 ft longer than half the given axes, so the area of the pool cover is about ...
... A = π(9 ft + 1.5 ft)(12.5 ft +1.5 ft)
... A = 147π ft² ≈ 461.8 ft²
_____
However, adding 1.5 ft of material to an ellipse results in a shape that is not an ellipse, but is slightly larger than the ellipse with the dimensions used above. The area of that may be about 462.5 ft² (found numerically).
HOW DO I DOOO THISS IDEK!!!!! HELLLPPPPP
Rex galore is taking his written test to get his license. there is an 85% probability of passing the test.
a. what is the probability that he will pass on his first try?
85% is the answer, because it is an 85% chance of him passing, now the chance of him passing twice in a row would be 72.25% because you would multiply 0.85 and 0.85 together.
I thought of a number, added 4 5/7 to it, and got the number equal to the original one times 12. What was the original number?
Answer:
x=3/7
Step-by-step explanation:
x+4 5/7 = 12x
4 5/7 = 11x
x = 3/7
Answer:
3/7
Step-by-step explanation:
The perimeter of an isosceles triangle is 15.6 m. Find the lengths of its sides, if: The base is 3 m bigger than a leg.
So, an isosceles triangle has 2 equal sides, we will call them x.
The base can be modeled by 3+x
So, the perimeter is equal to x + 3+x + x
So
15.6 = 3x + 3
12.6 = 3x
4.2 = x
So, the lengths of the sides are 4.2, 4.2, 7.2
Answer:
6.2, 6.2, 3.2
Step-by-step explanation:
im himothy
This is the variable, usually shown on the y-axis, that gets its value from the one on the x-axis.
The Hint say's it starts with (De)
Jordan and Sharla are saving money to go on a study abroad trip. They must provide a down payment of $650 to sign up for the trip, and they can pay the remaining balance later. Jordan raises money by mowing lawns in his neighborhood and charges $25 per lawn. Sharla raises money by selling handmade necklaces for $15 each. Sharla raises less money than Jordan does because Sharla 3. only has enough materials to make 40 necklaces. (A) write two constraints to model the problem. Let x respresent the number of lawns Jordan mows and y represent the number of necklaces Sharla sells. (B) can sharla afford the down payment with the money she earns selling her necklaces? Explain your answer . PLEASE HELP its due NOW! I’ll make you brainliest
to get to a dog show, mr luna first drives 7 miles west from his home and then 3 miles north. next he turns east and drives 11 miles. finally he turns north and drives 4 miles to the dog show. how far north of mr. luna's home is the dog show?
Answer:
7 miles
Step-by-step explanation:
Mr. Luna's travels east and west are irrelevant to the question. He drives 3 miles north, then he drives 4 more miles north. 3 + 4 = 7, so Mr. Luna ends up 7 miles north of his home.
Find the distance between 4 2/3 and −5 1/3
Answer:
The distance between these two is 10.
Step-by-step explanation:
In order to find this, we simply need to subtract the values from one another. If the value is then negative, we take the absolute value to find the distance.
4 2/3 - -5 1/3
4 2/3 + 5 1/3
10
ain ABC, AB=x, because=y, and CA=2x. A similarity transformation with a scale factor of 0.5 Maps ABC to MNO, such that vertices M,N and O correspond to A,B,C respectively. If OM=5, what is AB?
We are given: Triangle ABC sides, AB = x, BC = y and CA = 2x.
Another triangle MNO whose vertices M,N and O correspond to A,B,C respectively.
Therefore, AB corresponding to sides MN , BC corresponding to sides NO and CA corresponding to sides OM.
Also, we are given " A similarity transformation with a scale factor of 0.5 Maps ABC to MNO".
That means triangle ABC is dilated by a factor of 0.5.
Each side of the triangle MNO is 0.5 times(half) of Triangle ABC.
We could also say that each side of Triangle ABC is two times of sides of triangle MNO.
We are given side OM = 5 units.
CA = Times of OM = 2 * 5 = 10 units.
CA = 2x = 10 units or 2x=10.
Dividing both sides by 2, we get
[tex]\frac{2x}{2}=\frac{10}{2}[/tex]
x=5.
AB = x.
Therefore, AB = 5 units.
Answer:
Step-by-step explanation: