Answer:
[tex]\boxed{\sf Slope( m)=-\cfrac{3}{4}}[/tex]
Step-by-step explanation:
To find the slope between two points we'll use the Slope formula:-
[tex]\boxed{\sf \mathrm{Slope(m)}=\frac{y_2-y_1}{x_2-x_1}}[/tex]
______________
Given:-
(3,-4)(-5,2)Where,
[tex]\mathrm{\left(x_1,\:y_1\right)=\left(3,\:-4\right)}[/tex]
[tex]\mathrm{\left(x_2,\:y_2\right)=\left(-5,\:2\right)}[/tex]
[tex]\mathrm{m=\cfrac{2-\left(-4\right)}{-5-3}}[/tex] ← Subtract
[tex]\sf m=-\cfrac{6}{8}[/tex]
[tex]\sf m=-\cfrac{3}{4}[/tex]
Therefore, the slope of the line is m = - 3/4.
______________________
Hope this helps!
Have a great day!
what is the scale factor of a figure with a shape with a side lengths of 12 and is dilated to a shape with 4
The scale factor of a figure with a shape with a side length of 12 and is dilated to a shape with 4 is 1/3.
What is a scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).
Given that a figure with side length of 12 units is being dilated in a figure with side length of 4.
In this case, the scale factor = 4/12 = 1/3
Hence, The scale factor of a figure with a shape with a side length of 12 and is dilated to a shape with 4 is 1/3.
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A football team has an away game, and the bus breaks down. The coaches decide to drive the players to the game in cars and vans. Four players can ride in each car. Six players can ride in each van. There are 48 players on the team. The equation $4x+6y=48$ models this situation, where $x$ is the number of cars and $y$ is the number of vans
The 4 possible solutions in the context of the problem are (0, 8), (3, 6), (6, 3), and (9, 2)
Given the equation that models the situation expressed as:
4x + 6y = 48
We are to find 4 possible solutions for x and y. Note that the values of x and y must be integers.
If there are no cars i.e. at when x = 0
4(0) + 6y = 48
0 + 6y = 48
6y = 48
y = 48/6
y = 8
One of the solution is (0, 8)
If there are 3 cars, i.e. at when x = 0
4(3) + 6y = 48
12 + 6y = 48
6y = 48 - 12
y = 36/6
y = 6
The second solution will be (3, 6)
If there are 6 cars, i.e. at when x = 6
4(6) + 6y = 48
24 + 6y = 48
6y = 48 - 24
y = 24/6
y = 4
The third solution will be (6, 3)
If there are 9 cars, i.e. at when x = 9
4(9) + 6y = 48
36 + 6y = 48
6y = 48 - 36
y = 12/6
y = 2
The fourth solution will be (9, 2)
Hence the 4 possible solutions in the context of the problem are (0, 8), (3, 6), (6, 3), and (9, 2)
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A scientist is observing two ant colonies. The colonies each have 800 ants when he begins observing them. The population of Colony A increases by 25% each week. The population of Colony B decreases by 25% each week. In each equation, y represents the ant population with respect to a number of weeks, x. Drag each equation to show whether it can be used to represent the ant population of Colony A, Colony B, or neither of these.
In writing the equations that describe each of the colonies A ad B we have;
y = 800e^0.25x (Colony A)y = 800e^-0.25x (colony B )What are the equations?We know that the increase or decrease of population are exponential problems. We such, we must be able to look at the problem form the exponential perspective. This is how we would be able to know how to write the appropriate equation that would be able to be used in each of the cases that have been shown in the problem.
We are told that; a scientist is observing two ant colonies. The colonies each have 800 ants when he begins observing them. The population of Colony A increases by 25% each week. The population of Colony B decreases by 25% each week. In each equation, y represents the ant population with respect to a number of weeks, x.
Thus;
For colony A we can write;
y = 800e^0.25x
For colony B we can write;
y = 800e^-0.25x
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Can somone help me with this will mark u brainliest
The simplest radical form of √(11/(x + 4)) when x is 16 is; ¹/₁₀√55
How to simplify surds in radical form?Surds are actually the expressions of the number, and often use radicals. Meanwhile, the radical is just the symbol used to express the square root.
We are given the expression of the surd as;
√(11/(x + 4))
We want to solve this for when x = 16. Thus, we plug in 16 for x in the surd to get;
√(11/(16 + 4))
= √(11/20)
Now, we can rewrite the fraction in the bracket to have the denominator as a perfect square by multiplying both numerator and denominator by 5 to get;
√(55/100)
Square root of 100 is 10 and as such we now have;
√(55/100) = ¹/₁₀√55
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two foods contain proteins, carbohydrates, and fats. food a costs $1 per pound and contains 30% protein, 10% fat, and 50% carbohydrates. food b costs $1.50 per pound and contains 20% protein, 4% fat, and 75% carbohydrates. what is a combination of x pounds of food a and y pounds of food b that provides at least 1 1 2 pounds of protein, 3 3 4 pounds of carbohydrates, and 1 5 pound of fat at the lowest cost? (x, y)
A combination of x pounds of food a and y pounds of food b that provides at least 1 1 2 pounds of protein, 3 3 4 pounds of carbohydrates, and 1 5 pound of fat lowest cost is at (x,y) is (3,2).
Define function.A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
Given,
Function:
C = x + 1.5y
Subjected to:
30x + 20y ≥ 13/10 ×100 ≥ 130
10x + 4y ≥ 1/5 × 100 ≥ 20
50x + 75y ≥ 3 × 100 ≥ 300
Feasible region:
(0, 13/2), (3,2) (6,0)
C = x + 1.5y
(0, 13/2) ⇒ C = 0+ (1.5)(13/2)
(0.13/2) ⇒ C = 9.75
(3,2) ⇒ C = 3+ (1.5)(2)
(3,2) ⇒ C = 6
(6,0) ⇒ C = 6 + 0
(6,0)⇒ C = 6
A combination of x pounds of food a and y pounds of food b that provides at least 1 1 2 pounds of protein, 3 3 4 pounds of carbohydrates, and 1 5 pound of fat lowest cost is at (x,y) is (3,2).
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Supposed the original quality is 1,500 and the new quality is 1,650 what should be the first step in solving for the percent increase what is the percent increase
The first step is to find the increase in quantity.
The percentage increase is 10%.
How to calculate the percentage?From the information, the original quality is 1,500 and the new quality is 1,650.
The first step is to find the increase in quality will be:
= New quantity - Old quantity
= 1650 - 1500
= 150
The percentage increase will be:
= Increase / Old Quantity × 100
= 150 / 1500 × 100
= 10%
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a point is randomly picked from inside the rectangle with vertices , , , and . what is the probability that ?
The probability that x < y is 1/8 or 0.25 .
What is probability of an event?
The possibility or chance of an event happening is commonly believed to be the probability of it happening. In the most basic scenarios, the probability that a specific event 'A' will occur as a result of an experiment is calculated by dividing the number of ways that 'A' can happen by the total number of possible outcomes.
P(A) = Number of events concerning 'A' / Total events in consideration.
Given, the vertices of the rectangle are (0, 0), (4, 0), (4, 1), (0, 1).
On carefully analyzing and plotting the vertices roughly, we get that the given rectangle has a width of 4 units and a height of 1 unit.
Therefore, the area of the given rectangle = Width*Height = 4*1 = 4 units²
Also, it can be assessed that the line x = y passes through the points of the rectangle at (0, 0) and (1, 1).
Thus, the area for which x < y will be an isosceles triangle with side length of 1 units and co-ordinates of vertices as (0, 0), (0, 1) and (1, 1).
The area of the isosceles triangle thus assumed = 0.5 × 1² = 0.5 units²
Probability that x < y is P(E): 0.5/4 = 1/8 = 0.25
Therefore, the probability that x < y is 1/8 or 0.25 .
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Sheri has $15,200 to invest in mutual funds and in bonds. sheri has selected a mutual fund that earns 1% a year and a bond that earns 4% a year. if she wants to earn $548 at the end of the first year, how much does she need to invest into each type of account?
Sheri should invest $2000 in mutual fund and $13,200 in bond.
Let the amount to be invested in mutual fund be x. So, the amount to be invested in bond will be (15,200 - x). Forming the equation now -
1%×x + 4%×(15,200 - x) = 548
x/100 + 60,800/100 - 4x/100 = 548
60,800 - 3x = 54800
3x = 60800 - 54800
3x = 6000
x = 6000 ÷ 3
x = 2000
Amount to be invested in mutual fund = $2000
Amount to be invested in bond = 15,200 - 2000
Amount to be invested in bond = $13,200
Sheri should invest $2000 and $13,200 in mutual fund and bond respectively.
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The double number line shows that the distance from the start of a hiking trail to a cave entrance is 700\,\text{m}700m700, start text, m, end text.
Answer: 92
Step-by-step explanation:
Terry sees this offer.
Refurbished phone
35% OFF
Now only £78
How much was the phone before the discounted price?
Answer: The phone was £120 before the discount.
The price of products may increase due to inflation and decrease due to depreciation. Marco is studying the change in the price of two products, A and B, over time. The price f(x), in dollars, of product A after x years is represented by the function below: f(x) = 12500(0.82)x Part A: Is the price of product A increasing or decreasing and by what percentage per year? Justify your answer. (5 points) Part B: The table below shows the price f(t), in dollars, of product B after t years: t (number of years) 1 2 3 4 f(t) (price in dollars) 5600 3136 1756.16 983.45 Which product recorded a greater percentage change in price over the previous year? Justify your answer. (5 points)
Step-by-step explanation:
so, after clarification from your side, we know
f(x) = 12500 × (0.82)^x
so, with every new year we are multiplying the value of the previous year by 0.82.
in other words
f(n) = f(n-1) × 0.82
with f(0) = 12500
because anything to the power of 0 equals 1.
A
so, the price is decreasing every year, because any multiplication with a positive value smaller than 1 decreases the original number.
multiplying an amount by a decimal number like 0.82 creates exactly 82% of the original amount because 1 represents 100%.
that means the value decreases every year by 100 - 82 = 18% compared to the value of the previous year.
B
1 5600
2 3136
3 1756.16
4 983.45
remember, Part A showed always an 18% decrease over the previous year.
from 5600 to 3136, this was a change of
100% = 5600
1% = 100%/100 = 5600/100 = $56
the price difference was 5600 - 3136 = 2464
how many % was that decrease ?
as many as how often 1% fits into 2464 :
2464 / 56 = 44%
that was much more than Part A.
from 3136 to 1756.16, this was a change of
100% = 3136
1% = $31.36
the price difference was 3136 - 1756.16 = $1,379.84
how many %
1,379.84 / 31.36 = 44%
again.
from 1756.16 to 983.45, this was a change of
100% = 1756.16
1% = $17.5616
the price difference was 1756.16 - 983.45 = 772.71
hire many %
772.71 / 17.5616 = 43.99997722...%
and again 44% (just a little rounding uncertainty).
so, product B recorded a much greater percentage change in value over the previous year than product A :
44% to 18%
Help me please!!!!!
The matrix
[tex]MN = \left[\begin{array}{ccc}-2&1&0\\17&2&-3\\11&12&-5\end{array}\right][/tex]
The given matrix is
[tex]M = \left[\begin{array}{ccc}1&0\\-4&3\\2&5\end{array}\right][/tex]
[tex]N = \left[\begin{array}{ccc}-2&1&0\\3&2&-1\\\end{array}\right][/tex]
The Order of M = (3×2)
The Order of N = (2×3)
Since the number of columns of M is equal to the number of rows, the multiplication of M and N is possible,
The order of the matrix formed is MN = ( 3 × 3 )
So,
[tex]MN = \left[\begin{array}{ccc}-2+0&1+0&0+0\\8+9&-4+6&0-3\\-4+15&2+10&0-5\end{array}\right] \\\\MN = \left[\begin{array}{ccc}-2&1&0\\17&2&-3\\11&12&-5\end{array}\right][/tex]
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How many kilometres is 6.5cm
Answer:
0.000065 km
Step-by-step explanation:
To get from cm to km you need to divide 6.5 by 0.000001 which equals 0.000065km
E
<
15
Question 15/15
0
B) (-6,-5)
(6,5)
SUBMIT
BOOKMARK
Point G, located at (-5, 6) is rotated 270° counterclockwise. Find the coordinates of G' after the rotation.
(5,-6)
The coordinates of G' after the rotation = (6, 5)
In this question we have been given a point G, located at (-5, 6) is rotated 270° counterclockwise.
We need to find the coordinates of G' after the rotation.
a point (-5, 6) is located in the second quadrant.
First 90° counterclockwise rotation gives (-6, -5) because x & y are interchanged and in Quadrant III both coordinates will be negative.
Second 90° counterclockwise rotation yields (5,-6) because x & y are interchanged and in Quadrant IV the y coordinate will be negative.
Last 90° counterclockwise rotation yields (6, 5) because x & y are interchanged and in Quadrant I both coordinates will be positive.
Therefore, the coordinates of G' after the rotation = (6, 5)
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Which of the following rules describes the function graphed below?
PLEASE ANSWER FOR BRAINLEST!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!1 asap!!!!!!!!!!!
The rule which describes the function graphed in the attached image as required to be identified is; Output = 8 - input.
Which rule represents the function graphed?It follows from the task content that the rule which is a representative of the function which is as graphed in the attached image is to be identified.
By observation, the relation which best describes the graph is; (7, 1), (6, 2), (5, 3).....
The inference which can therefore be drawn from the given graph is that;
The output value is the subtraction of the input value from 8 in each case.
Ultimately, the required rule which represents the function is; Output = 8 - input.
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Find 40th term for 4,8,12
Answer: 160
Step-by-step explanation:
because you times 40 by 4 as 4 is the first term and 4x10=40 <3
hope this helped <3
22. A box containing 40 marbles weighs 280 grams. When 30 marbles are added, the box weighs 430 grams. How many grams does the box weigh when empty? A 80 B 120 C 150 D 490 E 710
Answer:
A/ 80 grams
Step-by-step explanation:
We know that 430 - 280 = 150, so each marble weights 5 grams. Then we take 5 times 40 = 200 grams. Then we take 280 subtract 200 = 80 grams
Determine which integer will make the inequality 5x + 6 ≤ 2x + 15 false.
S:{−2}
S:{5}
S:{2}
S:{−5}
Answer:
the correct she answer should be 5
Step-by-step explanation:
31 <= 25 is falseThe solution set for the given inequality is {.......-4, -3, -2, -1, 0, 1, 2, 3}, so the for x=5 the inequality is false. Therefore, the correct answer is option B.
The given inequality is 5x+6≤2x+15.
Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Here, the inequality can be solved as follows
5x+6≤2x+15
Subtract 6 on both the sides of the inequality, we get
5x+6-6≤2x+15-6
5x≤2x+9
Subtract 2x on both the sides of the inequality, we get
5x-2x≤2x+9-2x
3x≤9
Divide 3 on both the sides of the inequality, we get
x≤3
Here, solution set is {.......-4, -3, -2, -1, 0, 1, 2, 3}
So, the for x=5 the inequality is false.
Therefore, the correct answer is option B.
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Find the length of X using law of cosines.
The length of the X using law of cosine is 34.30yd.
What is cosine?
In a right angled triangle, the cosine of an angle is:
The length of the adjacent side divided by the length of the hypotenuse.
The abbreviation is cos
cos(θ) = adjacent / hypotenuse
Consider that;
[tex]X = \sqrt{a^2+b^2-2abcosX}[/tex] (using law of cosine)
[tex]X = \sqrt{21^2+18^2-2\times 21\times 18\times cos(123 ^\circ)}[/tex]
[tex]X = \sqrt{441+324-756\times (-0.5446)}[/tex]
X = 34.30 yd
If A, B, and C are the measures of the angles of an oblique triangle, and a, b, and c are the lengths of the sides opposite the corresponding angles, then the square of a side of the triangle is equal to the sum of the squares of the other two sides minus twice the product of the two sides and the cosine of the included angle.
[tex]c^2 = a^2+ b^2- 2abcos C[/tex]
We have to the value of X which is present on the side c,
so, from the above formula we modified for the X,
and the formula become,
[tex]X = \sqrt{a^2+b^2-2abcosX}[/tex](using law of cosine)
rest of the solutions are only calculation which is elaborated above which provide us the value of X = 34.30 yd.
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Having trouble solving this
Answer:
[tex]r = 2279.41[/tex]
12 mushrooms $3 How much for one
Answer:
4
Step-by-step explanation:
12÷3=4
Estimate the answer to 4.8 x 47.1
Answer:
235
Step-by-step explanation:
When estimating the product of two decimals, first round the decimals to their nearest whole numbers.
If the number in the tenth place is less than 5, round down to the nearest whole number.If the number in the tenth place is 5 or more, round up to the nearest whole number.Therefore,
4.8 ≈ 547.1 ≈ 47So an estimate of the product of the two decimals is:
[tex]\implies 4.8 \times 47.1 \approx 5 \times 47[/tex]
Partition 47 into tens and units:
[tex]\implies 5 \times 47 = 5 \times (40 + 7)[/tex]
Apply the distributive property of multiplication over addition:
[tex]\begin{aligned}\implies 5 \times (40 + 7) &= (5 \times 40) + (5 \times 7)\\&=200+35\\&=235\end{aligned}[/tex]
Therefore:
[tex]\boxed{4.8 \times 47.1 \approx 235}[/tex]
Identify the domain of the function shown in the graph
The domain of the graph is (d) all set of real values
How to determine the domain of the relation in the graph?The graph represents the given parameter
This graph represents a function
Say the graph represents the function f(x)
The x values represent the domain
i.e domain = Set of all x values
On the graph, we can see that the graph extends across the x-axis till infinity on both sides
This means that
Domain = All set of real values
Hence, the domain of the relation is (d) all set of real values
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F(x)=x^2+1 what is f(f(x))?
Answer:
f(f(x)) = [tex]x^{4}[/tex] + 2x² + 2
Step-by-step explanation:
to evaluate f(f(x)), substitute x = f(x) into f(x)
f(f(x))
= f(x² + 1)
= (x² + 1)² + 1 ← expand factor using FOIL
= [tex]x^{4}[/tex] + 2x² + 1 + 1
= [tex]x^{4}[/tex] + 2x² + 2
Answer:
[tex]f[f(x)]=x^4+2x^2+2[/tex]
Step-by-step explanation:
Given function:
[tex]f(x)=x^2+1[/tex]
To find the composite function f[f(x)], substitute the function f(x) in place of the x in function f(x):
[tex]\begin{aligned}\implies f[f(x)]&=f(x^2+1)\\&=(x^2+1)^2+1\\&=(x^2+1)(x^2+1)+1\\&=x^4+x^2+x^2+1+1\\&=x^4+2x^2+2\end{aligned}[/tex]
HELP the price of gasoline purchased varies directly with the number of gallons purchased if 10 gallons of gasoline are purchased for$23 what will be the price of 50 gallons be?
Answer:
Step-by-step explanation:
It will be 115$
Answer: the answer is $21.7391304348 or round to $21.74 is the cost for 50 gallons
Step-by-step explanation: I did the calculations and it costs $2.30 a gallon
The probability that a male’s foot is between 10 and 12. 5 inches is ___%
P(10
The probability of a foot of male being between 10 and 12. 5 inches is 59%.
Define the term normal distribution?The normal distribution approximates any real-valued random distribution which clusters around one single mean value. A cumulative frequency is a procedure that determines if the total amount of information in such a data set is less than and equal to a specific value.The z score of the distribution is found as-
z = (x - μ)/σ
In which,
μ = mean = (11)
σ = standard distribution (1.5)
The likelihood that a male's foot measures between 10 and 12. 5 inches.
P(10 < x < 12.5)
For x = 10
z = (10 - 11) / 1.5
z = -0.67
check the p-value fro z score table.
p (z = -0.67) = 0.2514
For x = 12.5
z = (1.5 - 11)/1.5
z = 1
p (z = 1) = 0.8413
P(10 < x < 12.5) = 0.8413 - 0.2514
P(10 < x < 12.5) = 0.5899
P(10 < x < 12.5) = 58.99%
P(10 < x < 12.5) = 59%.
Thus, the likelihood of a male's foot being between 10 and 12. 5 inches is 59%.
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The complete question is attached in figure.
How long will it take for $3, 900 to double if it is invested at 8% annual interest compounded 2 times a year?
Enter in exact calculations or round to 3 decimal places.
It will take___years to double.
How long will it take if the interest is compounded continuously?
Compounded continuously, it would only take___ years.
The number of years to double the investment is 8.824 years.
What is compound interest?It is the interest we earned on the interest.
The formula for the amount earned with compound interest after n years is given as:
A = P [tex](1 + r/n)^{nt}[/tex]
P = principal
R = rate
t = time in years
n = number of times compounded in a year.
We have,
P = $3,900
R = 8%
n = 2
A = 2P = 2 x 3,900 = $7,800
Now,
A = P [tex](1 + r/n)^{nt}[/tex]
7,800 = 3,900 [tex](1 + 0.04)^{2t}[/tex]
78/39 = [tex](1.04)^{2t}[/tex]
2 = [tex](1.04)^{2t}[/tex]
Taking logs on both sides.
log 2 = 2t log(1.04)
0.30 = 2t x 0.017
0.30/0.017 = 2t
17.65 = 2t
Divide both sides by 2.
t = 17.65 / 2
t = 8.824 years.
Thus,
The number of years to double the investment is 8.824 years.
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A printing service charges a set-up fee of $14.50 for each order and 10 cents more for each copy. The total cost, C (in dollars), for an order of x copies is given
by the following function.
C(x)=0.10x+14.50
What is the total cost for an order of 30 copies?
The total cost for an order of 30 copies is $17.50.
What is a function?A formula, rule, or legislation specifies how one variable (the independent variable) and another variable are related (the dependent variable).In the given function cost is the dependent variable and x is the independent variable.So, calculate the total cost as follows:
We have:
C(x)=0.10x+14.50 → equation 1Here, x implies a number of orders of copies and in question, it says the order of 30 copies.
So, Substitute x=30 in equation 1,
C(x)=0.10x+14.50C(30) = 0.10(30)+14.50 = 3.00+14.50 = 17.50Hence, the total cost for an order of 30 copies is $17.50.
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in a recent study, it was found that 87.3% of all homes have a large-screen tv. a sample of 28 homes is selected. the data follows a binomial distribution. a) what is the mean of the distribution? (round your answer to 3 decimals.)
The mean of the distribution is 24.444.
Given, that 87.3% of all homes have a large-screen tv. a sample of 28 homes is selected.
Now, we have to find the mean of the distribution
As, we know
E(x) = np
where, n is the sample and p is the probability of success
So, n = 28 and p = 87.3% = 0.873
Now, on using the formula we get,
E(x) = (28)(0.873)
E(x) = 24.444
So, the mean of the distribution is E(x) = 24.444
Hence, the mean of the distribution is 24.444.
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A bag contains 8 beads.
. 2 of the beads are blue.
. 1 of the beads is green.
. 3 of the beads are purple.
. The rest of the beads are red.
Jules takes a bead from the bag at random. Optional working
c) What is the probability that this bead
is purple or red?
Answer:
the probability would be taking a purple one. there are only 2 red beads
3/2 or 2/3
The probability that the two beads selected from the bag at random is purple or red is 5/8.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
We have,
Total number of beads = 8
2 of the beads are blue.
1 of the beads is green.
3 of the beads are purple.
Red beads = 8 - (2 + 1 + 3) = 8 - 6 = 2
Now,
The probability that the two beads selected are purple or red.
= Probability that the two beads are purple + Probability that the two beads are red.
= 3/8 + 2/8
= 5/8
Thus,
The probability that the two beads selected are purple or red is 5/8.
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