Answer:
The point at which the line y = 2.5·x + 3 intersect with the circle of radius 4 and center (0, 3) is x = 1.49
Step-by-step explanation:
Here we have the equation of a circle = (x - h)² + (y-k)² = r²
Where (h, k) is the coordinate of the center
Therefore, we have
(x - 0)² + (y - 3)² = 4²
Which gives x² + (y - 3)² = 16
Since the line y = 2.5·x + 3 we have
x² + ( (2.5·x + 3 ) - 3)² = 16
x² + (2.5·x)² = 16
x² + 6.25·x² = 16
7.25·x² = 16
x² = 16/7.25 = 2.21
x = 1.49
That is the line y = 2.5·x + 3 intersect with the circle of radius 4 and center (0, 3) at x = 1.49.
The point of intersection in the first quadrant of the given line y = 2.5x + 3 and the given circle x² + (y - 3)² = 16, can be found by substituting the equation of the line into the equation of the circle and then solving for x and y.
Explanation:The subject of this question is the intersection of a line and a circle in the first quadrant of a coordinate plane. The circle is defined by the equation (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius. For a circle with center at the origin (0, 3) and radius 4, the equation is x² + (y - 3)² = 16.
The line is defined by the equation y = 2.5x + 3. To find the intersection point, we substitute this equation into the equation of the circle, resulting in x² + (2.5x)² - 6x + 9 = 16. Solving this quadratic equation gives the x-coordinates of the intersection points. Since we are only interested in the first quadrant, we pick the positive root. Substituting this value of x into y = 2.5x +3 gives the corresponding y-coordinate, defining the point of intersection in the first quadrant.
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Solve this equation for x. 2x² + 122 – 7= 0
2rº + 12z - 7 = 0
Step 1: What is the first step to solve this equation?
O Combine like terms.
O Factor the trinomial.
Isolate the constant term by adding 7 to both sides
of the equation.
Check
Intro
Answer:
Combine like terms is the first step.
Step-by-step explanation:
Subtract '122-7' on both sides and that gives you [tex]2x^2=-115[/tex]
Trace needs a new carpet for her house the living are is an open floor plan of a dining room 6 feet c 4 feet sitting area 10 feet x 15 feet and a breakfasg nook 5 feet x 5 feet how many square feet of carpet does she need
Answer:
199 square feet
Step-by-step explanation:
Given:
Trace needs a new carpet for her house.
Dimension of dining room = 6 feet by 4 feet.
Dimension of sitting area = 10 feet by 15 feet.
Dimension of breakfast nook = 5 feet by 5 feet.
Question asked:
How many square feet of carpet does she need ?
Solution:
First of all we will calculate the area of each part of the house and then add up.
[tex]Area \ of \ dining\ room=length\times width[/tex]
[tex]=6\times4\\ \\ =24\ square\ feet[/tex]
[tex]Area \ of \ sitting\ part=length\times width[/tex]
[tex]=15\times10\\ \\ =150\ square\ feet[/tex]
[tex]Area \ of \ breakfast\ nook=(side)^{2}[/tex]
[tex]=5^{2} =25\ square\ feet[/tex]
Total carpet needed will be needed = For dining + For sitting area + For breakfast nook
= 24 + 150 + 25
= 199 square feet
Therefore, she needs 199 square feet of a new carpet for her house.
The cost of buying a small piece of land in a remote village since the year 1990 is represented by the following table . Which model c(t) the cost of the piece of land t years since 1990, best fits the data?
Answer:
C(t)=30+3.5t
Step-by-step explanation:
Yeah this is the answer
Answer:
C(t)=30+3.5t
Step-by-step explanation:
Time increases by 2, the average difference in the cost is approximately 7.
So if d is the common difference of the function modeling this relationship, then 2d≈72.
Therefore, d≈ 7/2 = 3.5
Since the initial cost of the land is 30 thousand dollars, the function that best models its cost t years since 1990 is C(t)=30+3.5t
rolls
Which reaction shows that the enthalpy of formation of C2H4 IS A Hp = 52.5
kJ/mol?
A. 2C(s) + 2H₂(g) + 52.5 kJ → C₂H₄ shows that the enthalpy of formation of C₂H₄ is 52.5 kJ/mol.
Step-by-step explanation:
Enthalpy of formation of C₂H₄ is given as 52.5 kJ/mol.
There are 4 options given and they are:
A. 2C(s) + 2H₂(g) + 52.5 kJ → C₂H₄
B. 2C(s) + 4H(g) + 52.5 kJ → C₂H₄
C. 2C(s) + 2H₂(g) → C₂H₄ + 52.5 kJ
D. 2C(s) + 4H(g) → C₂H₄ + 52.5 kJ
Here the reactants absorb some energy from the surroundings and gives the product and it is an endothermic reaction.
So A and B is taken into account, but in B there are 4 H atoms involved in the reaction. So in the reaction A hydrogen molecules are involved and also energy is absorbed by the reactants.
So option A is the answer.
Answer: 2C(s) + 2H₂(g) + 52.5 kJ → C₂H₄
max and some friends shared the cost of a meal. The meal cost $51 and each person contributes $17. How many people share the cost meal?
Answer:
3 people
Step-by-step explanation:
$51/$17 = 3 people
- We know to start with $51 dollars because that is the total price of the meal.
- We also know each meal costs $17.
- Next, ask youself what we are trying to find? We are trying to find how many people are eating.
- Therefore to find that we need to take our starting amount $51 divided by $17 because that is the cost of 1 meal.
- $51/$17 = 3 people (whole cost/individual cost = # of people)
- To check this take 3 x 17 = 51 (Now we know it is correct)
- If you would like a further explanation please let me know.
Casey wants to buy a gym membership. Gym A has a $50 joining fee & costs $40 per month. Gym B has no joining fee & cost $65 per month. When would Casey pay the same amount to be a member of either gym? How much would he pay?
Answer:
1; after 2 months
2; $130
Step-by-step explanation:
In this question, we are trying to compare the fees to be paid in two different gyms, to determine when the amount paid would be equal and also what this amount would be.
Now since we do not know the exact number of months, we can represent this unknown by x
so mathematically, at the end of m months, at the first gym , Casey would have paid a total of 50 + 40m
For the second gym, at the end of the second month, casey would have paid a total of 65m only
now we need to know when these fees would be the same. we simply equate what we have on both ends
mathematically, that is 50 + 40m = 65m
65m-40m = 50
25m = 50
m = 50/25
m = 2 months
The fees to be paid is
50 + 40(2) = 65(2) = $130
If Jacob owns 12 books, how many different ways can he arrange 3 of these books on a single bookshelf
Final answer:
To find the number of different ways Jacob can arrange 3 books on a single bookshelf out of 12 books, we use the concept of permutations. The number of arrangements is 1320.
Explanation:
To find the number of different ways Jacob can arrange 3 books on a single bookshelf out of 12 books, we use the concept of permutations. Permutations calculate the number of ways to arrange objects in a specific order. In this case, we need to find the number of permutations of 3 books out of 12, which can be calculated using the formula:
P(n, r) = n! / (n - r)!
Where n is the total number of books (12) and r is the number of books to be arranged (3).
Substituting the values into the formula, we get:
P(12, 3) = 12! / (12 - 3)! = 12! / 9!
Calculating the factorial, we have:
12! = 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 479,001,600
9! = 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 362,880
Now, dividing the factorial values, we can calculate the number of arrangements:
P(12, 3) = 479,001,600 / 362,880 = 1320
Therefore, Jacob can arrange 3 books on a single bookshelf in 1320 different ways.
Recall that h, the phase shift, is any value of x that occurs at the beginning of a cycle.
The green point begins the –cosine cycle. What value of x corresponds to this point?
Answer:
h=0.748
Step-by-step explanation:
The value of x that corresponds to this point on the phase shift is 0.748.
What is phase shift?The phase shift simply means when the graph of the sine and cosine function is shifted from their usual position.
The phase shift, is any value of x that occurs at the beginning of a cycle. In this case, value of x that corresponds to this point on the phase shift is 0.748.
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-8(5b + 2) -7(b - 5)
Answer:
-47b + 19
Step-by-step explanation:
During her lunch hour, Shawna asked 40 students how many after-school clubs they joneu. THICH WIVE
of clubs that the students joined.
2,2,3,0, 3, 2, 4, 2, 1, 4, 3, 2, 4, 1, 0, 2, 1, 3, 2, 0,
1, 1, 2, 1,0,3,0, 1, 4, 1, 1, 0, 2, 3, 2, 0, 3, 2, 0, 1
If this sample is representative of the student population of 360 students, about how many students in the school joi
clubs?
15 students
63 students
109 students
189 students
O
Answer:
maybe 15 students or 63 students and if not I am sorry of that's wrong
The probability of none will have high blood pressure if twenty percent of Americans age 25 to 74 have blood pressure .If 16 randomly selected Americans age 25 to 74 are selected
Answer:
The probability that none will have high blood pressure is 0.0281
Step-by-step explanation:
The correct question is as follows;
Twenty percent of Americans ages 25 to 74 have high blood pressure. If 16 randomly selected Americans ages 25 to 74 are selected, find each probablility. a. None will have high blood pressure
This is a binomial problem. We shall solve in that line
The probability of success is 20% or 0.2 [(Americans ages 25 to 74 have high blood pressure)] p = 0.2
The probability of failure q is thus 1-p = 1-0.2 = 0.8
The probability of none is thus;
P(X= 0) = 16C0 p^0 q^16
= 16C0 * 0.2^0 * 0.8^16 = 0.0281
Pablo buys a 4 pack of towels for $19.60 .
Find the unit price in dollars per towel.
If necessary, round your answer to the nearest cent.
Answer:
$4.90 per towel
Step-by-step explanation
If each towel costs and equal amount, you divide the full amount of the pack, $19.60, by the number of towels, which is 4, which gives you $4.90 as the answer.
Help pls I need this
Write a function rule for “The output is 6 greater than three times the input.” Use x for the independent variable and y for the dependent variable.
Answer:
y = 6+3x
Step-by-step explanation:
If y = f(x), it means y is depending on x. This shows that y is the independent variable and x is the dependent variable.
y variable will be the output depending on the input variable x.
According to the function rule, “The output is 6 greater than three times the input." This can be expressed mathematically as 3x+6 (x being the input)
Three times the input = 3x
6 greater than three times the input = 6+3x
Since y is output then;
y = 6+3x
The function rule is [tex]\boldsymbol{y=6+3x}[/tex].
Function RuleA function rule is an equation that represents the relationship of the dependent and independent variables.
[tex]\boldsymbol{x}[/tex] is the independent variable.
[tex]\boldsymbol{y}[/tex] is the dependent variable.
The output is [tex]6[/tex] greater than three times the input.
[tex]y=6+3x[/tex].
So, the function rule is [tex]\boldsymbol{y=6+3x}[/tex].
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Anyone know the answer to these?
Step-by-step explanation:
Speakers =£ 31.5
Headphones =£ 4.8
Book =£ 3.85
Mobile phone =£ 36
mouse = £12.75
DVD =£ 10.2
Hope it will help you :)
Given that 10% of the nails made using a certain manufacturing process have a length less than 2.48 inches, while 5% have a length greater than 2.54 inches, what are the mean and standard deviation of the lengths of the nails? Assume that the lengths have a normal distribution.
Answer:
The mean, μ is 2.5063 and
The standard deviation, σ = 2.0499 × 10⁻²
Step-by-step explanation:
Here we have
[tex]z = \frac{x- \mu}{\sigma}[/tex]
[tex]z \sigma ={x- \mu}{}[/tex] and
10% have length < 2.48 in while
5% have length > 2.54 in
and
From the z score table
Critical z at 10% to the left = -1.282
Critical z at 5% to the right = 1.645
Therefore, the equations become
-1.282σ = 2.48 - μ → μ -1.282σ = 2.48
1.645σ = 2.54 - μ → μ + 1.645σ = 2.54
Solving the above equations gives
The mean, μ = 2.5063 and
The standard deviation, σ = 2.0499 × 10⁻².
Final answer:
Using the Z-score method and the percentages provided, two equations are set up and solved simultaneously to determine the mean and standard deviation of the lengths of the nails.
Explanation:
Given the information that 10% of the nails produced are shorter than 2.48 inches and that 5% are longer than 2.54 inches, and assuming the lengths are normally distributed, we can determine the mean (μ) and standard deviation (σ) of the lengths of the nails. We can use the Z-score formula which is (X - μ) / σ, where X is the value of the length, μ is the mean, and σ is the standard deviation.
Here, we have two Z-scores corresponding to the given percentages. For 10%, the Z-score is approximately -1.28, and for 5%, the Z-score is approximately 1.645. Now, setting up two equations,
(2.48 - μ) / σ = -1.28
(2.54 - μ) / σ = 1.645
we have a system of equations with two unknowns. Solving these equations simultaneously gives us the values for the mean and standard deviation of nail lengths.
To solve the system, multiply the first equation by σ to get μ = σ * -1.28 + 2.48 and the second equation by σ to get μ = σ * 1.645 + 2.54. By setting these two equations for μ equal to each other, you can solve for σ and afterwards find μ.
To solve the given system of equations:
1. (2.48 - μ) / σ = -1.28
2. (2.54 - μ) / σ = 1.645
We can use the method of substitution or elimination. Let's use the substitution method.
From equation 1, we can isolate μ :
(2.48 - μ) / σ = -1.28
2.48 - μ = -1.28σ
μ = 2.48 + 1.28σ
Now, we substitute this expression for μ into equation 2:
(2.54 - (2.48 + 1.28σ)) / σ = 1.645
(2.54 - 2.48 - 1.28σ) / σ = 1.645
(0.06 - 1.28σ) / σ = 1.645
0.06 - 1.28σ = 1.645σ
0.06 = 1.645σ + 1.28σ
0.06 = 2.925σ
Now, we solve for σ :
σ = [tex]\frac{0.06}{2.925}[/tex]
σ ≈ 0.0205
Now that we have found the value of \( σ \), we can substitute it back into the expression we found for \( μ \) to find its value:
μ = 2.48 + 1.28σ
μ = 2.48 + 1.28(0.0205)
μ ≈ 2.48 + 0.02628
μ ≈ 2.50628
So, the solution is approximately μ ≈ 2.50628 and σ ≈ 0.0205 .
Find the angle between u = (8,-2) and v = (19,3). Round to the nearest tenth of a degree.
A. 32.5
B. 6.3
C. 42.5
D. 16.3
HELP I NEED HELP ASAP!!
WHAT IS THE VOLUME OF THE CUBE SHOWN?
I WILL GIVE LOTS OF POINT TO THE ONE WHO GIVES THE CORRECT ANSWER!!
Answer:
8/125 ft
Step-by-step explanation:2/5 x 2/5 x 2/5 = 8/125
Answer:
The answer to your question is Volume of a cube = 8/125 ft³
Step-by-step explanation:
Data
length of a side = 2/5 ft
Formula
Volume of a cube = side x side x side
Substitution
Volume of a cube = 2/5 x 2/5 x 2/5
-Just multiply the numerator and multiply the denominators
-Simplification
The Volume of a cube = 8/125 ft³
work out the missing numbers:
a)(-4)x =320
Answer:
x=-80
Step-by-step explanation:
Answer:
[tex]x=-80[/tex]
Step-by-step explanation:
[tex]a) (-4)x=320\\\\x=\frac{320}{-4} \\\\x=-80[/tex]
A deli prepares sandwiches with one type of bread (white or wheat), one type of meat (ham, turkey, or chicken), and one type of cheese (cheddar or Swiss). Each combination is equally likely. Find the probability of choosing a sandwich at random and getting turkey and Swiss on wheat bread.
The probability of choosing a sandwich at random with turkey and Swiss on wheat bread is calculated by multiplying the independent probabilities of selecting each component. With 2 bread choices, 3 meat choices, and 2 cheese choices, the calculated probability is 1/12.
To find the probability of choosing a sandwich at random with turkey and Swiss on wheat bread, we consider the possible options for each category that can be selected independently. We have 2 bread options (white or wheat), 3 meat options (ham, turkey, or chicken), and 2 cheese options (cheddar or Swiss). To find the probability of one specific combination, we multiply the probabilities of each choice.
The probability of selecting wheat bread is 1/2 because there are 2 options for bread. The probability of selecting turkey as the meat is 1/3 since there are 3 meat options. Finally, the probability of selecting Swiss cheese is 1/2, as there are 2 cheese options.
The combined probability is the product of these probabilities:
(1/2) * (1/3) * (1/2) = 1/12
So, the probability of randomly choosing a sandwich with turkey and Swiss on wheat bread is 1/12.
The probability of randomly selecting a sandwich with turkey and Swiss on wheat bread is 1 out of 12 possible combinations.
To find the probability of choosing a sandwich at random that is turkey and Swiss on wheat, we need to calculate the total number of possible different sandwich combinations and then find the probability of the one specific combination. There are 2 types of bread (white, wheat), 3 types of meat (ham, turkey, chicken), and 2 types of cheese (cheddar, Swiss). The total number of sandwich combinations is the product of the number of choices for each component: 2 * 3 * 2 = 12.
Only one of these combinations is turkey and Swiss on wheat. Therefore, the probability of randomly selecting a turkey and Swiss on wheat sandwich is 1 out of the total number of combinations. Mathematically speaking, the probability (P) is P = 1/12.
The deli sandwich scenario is related to a fundamental concept in statistics and probability, where you assess the outcomes of a certain event given a set of choices.
Help ASAP
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Answer:
Last one: 5x - 3√y + 1
Step-by-step explanation:
8x + √1 - √9y - √9x^2
8x + 1 - 3√y - 3x
5x + 1 - 3√y
5x - 3√y + 1
CAN YOU PLEASE MARK MY ANSWER BRANLIEST
4. A circular aluminum sign has a radius of 28 centimeters. If a sheet of aluminum
costs $0.33 per square centimeter, how much will it cost to make the sign? Use
3.14 to approximate a.
The cost for making the sign is $812.38
Step-by-step explanation:
Radius = 28 cm
Cost of aluminum per square cm = $0.33
Area of the sign = π(r x r)
= (3.14) (28 x 28)
= (3.14) (784)
= 2461.76 square cm
Total cost to make the sign = 2461.76 x 0.33
= 812.38
The cost for making the sign is $812.38
To find the cost of making the circular aluminum sign, first calculate the area of the circle, then multiply the area by the cost per square centimeter. The total cost is $812.65.
To determine the cost to make a circular aluminum sign with a radius of 28 centimeters, we first need to find the area of the circle. The formula for the area of a circle is:
→ A = πr²
Given:
→ Radius, r = 28 cm
→ π ≈ 3.14
We can now calculate the area:
→ A = 3.14 × (28 cm)²
→ A = 3.14 × 784 cm²
→ A = 2,462.56 cm²
Next, we calculate the cost of the aluminum sheet:
→ Cost = Area × Price per cm²
→ Cost = 2,462.56 cm² × $0.33/cm²
→ Cost = $812.65
Therefore, it will cost $812.65 to make the circular aluminum sign.
A person stands 10 meters east of an intersection and watches a car driving towards the intersection from the north at 13 meters per second. At a certain instant, the car is 24 meters from the intersection. What is the rate of change of the distance between the car and the person at that instant (in meters per second)?
Answer:
Therefore the rate change of distance between the car and the person at the instant, the car is 24 m from the intersection is 12 m/s.
Step-by-step explanation:
Given that,
A person stand 10 meters east of an intersection and watches a car driving towards the intersection from the north at 13 m/s.
From Pythagorean Theorem,
(The distance between car and person)²= (The distance of the car from intersection)²+ (The distance of the person from intersection)²+
Assume that the distance of the car from the intersection and from the person be x and y at any time t respectively.
∴y²= x²+10²
[tex]\Rightarrow y=\sqrt{x^2+100}[/tex]
Differentiating with respect to t
[tex]\frac{dy}{dt}=\frac{1}{2\sqrt{x^2+100}}. 2x\frac{dx}{dt}[/tex]
[tex]\Rightarrow \frac{dy}{dt}=\frac{x}{\sqrt{x^2+100}}. \frac{dx}{dt}[/tex]
Since the car driving towards the intersection at 13 m/s.
so,[tex]\frac{dx}{dt}=-13[/tex]
[tex]\therefore \frac{dy}{dt}=\frac{x}{\sqrt{x^2+100}}.(-13)[/tex]
Now
[tex]\therefore \frac{dy}{dt}|_{x=24}=\frac{24}{\sqrt{24^2+100}}.(-13)[/tex]
[tex]=\frac{24\times (-13)}{\sqrt{676}}[/tex]
[tex]=\frac{24\times (-13)}{26}[/tex]
= -12 m/s
Negative sign denotes the distance between the car and the person decrease.
Therefore the rate change of distance between the car and the person at the instant, the car is 24 m from the intersection is 12 m/s.
The rate of change of the distance between the car and the person is [tex]\(-\frac{65}{12}\)[/tex] meters per second, indicating decreasing distance.
To find the rate of change of the distance between the car and the person at the given instant, we can use the concept of related rates. We'll use the Pythagorean theorem to relate the distances involved.
Step 1:
Establish variables.
Let (x) represent the distance the car has traveled north from the intersection, and let (y) represent the distance between the car and the person.
Step 2:
Formulate the equation using the Pythagorean theorem.
[tex]\[x^2 + y^2 = 24^2\][/tex]
Step 3:
Differentiate both sides of the equation with respect to time.
[tex]\[2x\frac{dx}{dt} + 2y\frac{dy}{dt} = 0\][/tex]
Step 4:
Plug in the given values and solve for [tex]\(\frac{dy}{dt}\)[/tex].
Given that the car is traveling north, [tex]\(\frac{dx}{dt} = 13\)[/tex]m/s.
When the car is 10 meters east, [tex]\(x = 10\).[/tex]
At that instant, when the car is 24 meters from the intersection, [tex]\(y = 24\).[/tex]
[tex]\[2(10)(13) + 2(24)\frac{dy}{dt} = 0\]\[260 + 48\frac{dy}{dt} = 0\]\[\frac{dy}{dt} = -\frac{260}{48} = -\frac{65}{12}\][/tex]
The rate of change of the distance between the car and the person at that instant is [tex]\(\boxed{-\frac{65}{12}}\)[/tex] meters per second. The negative sign indicates that the distance is decreasing.
Two of the angles in a triangle measure 90° and 16°. What is the measure of the third angle?
Answer:
74°
Step-by-step explanation:
All interior angles of a triangle add up to 180°, so to find the measure of the third angle here, we can use this:
180 - (90+16)
180 - 106
= 74°
Hope this helps!
Find the quotient
4 / 9/10
Answer:
4 × 10/9 = 40/9 is the solution
Which answer shows 0.05 written in scientific notation?
0.5 times 10 Superscript negative 1
5 times 10 Superscript negative 2
5 times 10 Superscript negative 1
5 times 10 Superscript 2
Answer:
B
Step-by-step explanation:
Answer: B
Step-by-step explanation:
If you have a negative exponent its like you divide it
10^-2 = 0.01 then multiply it by 5 = 0.01 x 5 = 0.05
Which equation represents a proportional relationship?
A. y=-2x
B. -2x+3y=12
C. y=1/2x+3
D. -1x+2y=6
Which equation represents a proportional relationship?
C. y=1/2x+3
I need to know what 2+2 is
Answer:
The answer for this question is 4.
Step-by-step explanation:
2+2=4
A scatterplot is produced to compare the size of a school building to the number of students at that school who play an instrument. There are 12 data points, each representing a different school. The points are widely dispersed on the scatterplot without a pattern of grouping. Which statement could be true?
Answer:
As the size of a school building increases, the number of student musicians increases because the scatterplot has a cluster that increases from left to right.
Step-by-step explanation:
Answer:
a is the answer
Step-by-step explanation:
which graph represents a line with a slope of -2/3 and a y-intercept equal to that of the line y=2/3x-2
Answer: the first one
Step-by-step explanation:
Answer:
A or the first one on the left
Which pair show equivalent expressions