The point slope and the intercept form is y = -3x + 11
What is the slope intercept form?One of the most popular ways to represent a line's equation is in the slope intercept form of a straight line. When the slope of the straight line and the y-intercept are known, the slope intercept formula can be used to determine the equation of a line ( the y-coordinate of the point where the line intersects the y-axis).
This written in the form of y = ax + b
where a is the slope and b is the intercept
We have the equation as
y + 4 = - 3 ( x - 5 )
we would have to open the bracket and then take the like term
this is going to be
y + 4 = -3x + 15
From here we would get the like term
y = -3x + 15 -4
y = -3x + 11
The slope is -3 and the intercept is 11.
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Kelly grows potatoes.
She has 2500 kg of potatoes, correct to the nearest 10kg.
Kelly is going to put the potatoes into sacks.
Each sack will contain 12. 5 kg of potatoes.
Kelly assumes that 12. 5 kg is measured correct to the nearest 0. 1 kg.
(a) Does Kelly definitely have enough potatoes to fill 200 sacks?
You must show how you get your answer
Kelly fill 200 sacks with the weight of 2000 kg potatoes and in each sack, she can fill up to 12.5 kg of potatoes.
What is weight?The gravitational attraction of an item near the Earth or another celestial body toward the center of the body. The weight of an item is determined by its mass and the strength of the gravitational force. We use the following generic formula to compute weight: W = mg. Where 'W' is the object's weight,'m' is the object's mass, and 'g' is the acceleration due to gravity. The value of g on Earth is 9.8 m/s2. The most frequent definition of weight is the force imposed by gravity on a body.
Here,
weight of potatoes she has=2500 kg
weight of each sack that contain the potatoes=12.5 kg
with this, she can fill,
=2500/12.5
=200 sacks
Kelly fills 200 sacks with 2000 kg of potatoes, and each sack can hold up to 12.5 kg of potatoes.
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a car travels 75 miles in the same amount of time that it takes another car, moving 10 mph faster that has traveled 100 miles. what is the number of miles per hour in the speed of the faster car?
The speed of the faster car is 40 miles/hr.
both cars travel for same time , so let that time be 't'
car 1 :
distance travelled = 75 miles
let the speed of the car be = x miles/hr
∴ time (t) = distance / speed
t = 75 / x .............(1)
car 2 :
distance travelled = 100 miles
speed of the car is = x + 10 miles/hr ( already provided )
∴ time ( t) = distance / speed
t = 100/ (x+10) ..............(2)
now as the time for both the cases is same , so we equate eqn (1) and eqn (2) .
∴ 75/x = 100/ (x+10)
3x + 30 = 4x
x = 30
so the speed of the 1st car will be 30 miles / hr
and the speed of the 2nd car ( faster car ) will be x + 10 = 40 miles/hr
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Solve the equation for x. Show each step of the solution for full credit. (3 points - 2 points showing work, 1 point correct answer)
3.5(x +2) = 17
Answer:2.86
Step-by-step explanation:
3.5(x +2) = 17
3.5x + 7 = 17
3.5x =17 - 7
3.5x =10
x = 10/3.5
x = 2.86
Find two consecutive positive odd integers such that three times the sum of the largest number plus 22 is equal to the product of both numbers.
Answer:
Step-by-step explanation:
Let's say your consecutive numbers are A and B with A+2=B. Using the information we have been given, we can get the linear equation; AB=3B+22. A=B-2, so we can replace A with B-2 to get (B-2)(B)=3(B+22). Multiplying this out, we get B^2-2B=3B+66. Simplifying, we get B^2-5B-66=0. This is a quadratic equation. Using the quadratic formula, we get B=11,-6. B has to be positive, so B=11. A+2=11, so A=9
Translate "eight more than the sum of y and x" into a variable expression.
Answer:
(y+x)+8
it is expressed like that i think
Answer:
(Y+x)+8
Step-by-step explanation:
A landscaper has 105 small shrubs to plant on the grounds of a park. he wants to plant the shrubs in equal groups. what different sized groups could he make
The different-sized groups are three groups of each size (35), five groups of each size (21), and seven groups of each size (15).
Given that;
A landscaper must plant 105 little bushes on a park's grounds. He intends to divide the bushes into equal groups.
We are asked to find what different-sized groups could a landscaper can make.
Here, we use Prime factorization;
Let,
∴ 105 = 3 * 5 * 7
From the above factors, we can find different groups as;
3 groups of each sized 35.
5 groups of each sized 21.
7 groups of each sized 15.
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Ahmad decided to increase his homework time of 8 hours per week by 15%,
Calculate his new homework time.
Give your answer in hours and minutes.
Answer:
it's a answer done bro
125 in the ratio 2:3
Answer:
50:75
Step-by-step explanation:
let the ratio of 2:3 be x
now,
125=2+3x
or,5x=125
therefore,x=125/5
x=25
now,
2x=25*2
=50
3x=25*3
=75
At the craft store, Tara bought 12 yards of fabric to make tote bags. Each bag requires 1.25 yards of fabric.
Write an equation that shows how the number of yards of fabric remaining, y, depends on the number of tote bags Tara sews, x.
The number of yards of fabric remaining, y, depends on the number of tote bags Tara sews, x is y = 12 - 1.25x.
What is an equation?An equation is written in the form of variables and constants separated by the operation of multiplication and division,
An equation states that terms in different forms on both sides of the equality sign are equal.
Multiplication and division do not separate the terms of an equation.
Given, Tara bought 12 yards of fabric to make tote bags and each bag requires 1.25 yards of fabric.
The equation that describes the number of yards of fabric remaining, y, depends on the number of tote bags Tara sews, x is
y = 12 - 1.25x.
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Part A Write a paragraph proof to prove ABC ≌ ABD. Explain in complete sentences each statement and reason. Be sure to give the reason the two triangles are congruent.
Part B Now that you have proven the two triangles are congruent, can you show that ∠CBA ≌ ∠DBA? Explain your reasoning in a complete sentence.
A. Both triangles have two pairs of corresponding sides and a pair of included angles, therefore, ΔABC ≌ ΔABD by SAS.
B. ∠CBA ≌ ∠DBA by CPCTC.
What is the SAS Congruence Theorem?The SAS congruence theorem state that if we have two triangles that we can show that they posses two pairs of corresponding sides that are equal and a pair of included angles that are also equal, then we can state that the two triangles are congruent to each other
When two triangles are proven to be congruent to each other, every corresponding parts of both triangles will be equal to each other based on CPCTC.
Part A:
We are given that AC ≌ AD, and ∠CAB ≌ ∠DAB.
Also, AB ≌ AB based on the reflexive property.
Therefore, both triangles are congruent to each other based on SAS.
ΔABC ≌ ΔABD
Part B:
Since both triangles are congruent, therefore ∠CBA ≌ ∠DBA by CPCTC.
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a client who weighs 70 kg is receiving a solution of 0.9% sodium chloride (normal saline) 500 ml with dopamine 800 mg at 5 ml/hour. how many mcg/kg/minute is the client receiving? (enter the numeric value only. if rounding is required, round to the nearest tenth.)
1.904 mcg/kg/min is what the client receives.
The number of mcg/kg/minute = flow rate × concentration ÷ mass of client
Flow rate = 12 ml/ hour = 12 /60 = 1/5 = 0.2 ml/min
Formula:
Concentration = mass of dopamine/volume
mass of dopamine = 800mg
volume = 500ml
Concentration = 800/ 500
= 1.6 mg/ml
= 1.6 × 1000 mcg/mg
= 1600 mcg/mg
Here the mass of the client = 70kg
Now calculating mcg/kg/minute = flow rate× concentration÷ mass of client
= 0.08 ml/min × 1600mcg/ml ÷70 kg
= 320/70
= 1.904 mcg/kg/min
Therefore mcg/kg/min is 1.904.
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Equation 1: y = 2²
Equation 2: y=2x-5
Equation
3: y = x² +6
Equation 4: y=
Witch one is non linear
From the given three options the equation y = x^2 + 6 is non - linear.
What is linear equation?
A linear equation is one in which the variable's maximum power is consistently 1. A one-degree equation is another name for it. A linear equation with one variable has the formula Ax + B = 0, which is its standard form. x is a variable, A is a coefficient, and B is constant in this situation. A linear equation with two variables has the formula Ax + By = C as its standard form. Here, the variables are x and y, the coefficients are A and B, and the constant is C.
Consider, the first equation
y = 2^2
⇒ y = 4
Since, the constant equations are linear.
So, first equation is linear.
Consider, second equation
y = 2x - 5
Here, the variable x and y both having degree 1.
So, second equation is also linear.
Consider, third equation
y = x^2 + 6
Here, the variable y having degree 1, but the variable x having degree 2.
Therefore, equation (3) is non - linear.
Hence, the equation y = x^2 - 5 is non - linear.
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What do you need to multiply the subtotal by in order to get the total?
Given: Subtotal: 42.00
Total: 45.99
Tax rate: 9.5%
Sales tax: $3.99
Can anyone answer question 8?
if the probability of pulling a four of hearts from a randomly shuffled deck is 1 / 52, and the probability of pulling a spade from a randomly shuffled deck are 1 / 4, then the probability of pulling a spade or a four of hearts from a randomly shuffled deck is:
The probability of pulling a spade or a four of hearts is 0.264 .
we have , from a deck of cards
probability of pulling a spade = 1/4 = 13/52
probability of not pulling a spade 3/4 = 39/52
probability of pulling a 4 of hearts = 1/52
probability of not pulling a spade = 51/52
we have to find the probability of pulling a spade or a four of hearts from a random shuffled deck
So we can get three cases :
case A :
getting a spade and not getting four of hearts
∴ P (A) = [tex](\frac{13}{52} ) (\frac{51}{52} )[/tex] = 663/2704
case B :
not getting a spade and getting four of hearts
P(B) = [tex](\frac{39}{52}) (\frac{1}{52} )[/tex] = 39/2704
case C :
getting a spade and getting four of hearts
P(C) = [tex](\frac{13}{52})(\frac{1}{52} )[/tex] = 13/2704
therefore , the required probability will become
P = P(A) +P(B) + P(C)
P = 715/ 2704
P = 0.264
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What is the inverse of this function? f(x)=1/3x-2
The inverse of the function f(x) = 1/3x-2 is f^-1(x) = (1 + 2x)/3x.
Inverse of a functionA function f is has an inverse if it is both one-to-one and onto.
Given the function f(x) = 1/3x-2
we replace f(x) with y and make x the subject of the formula to derive the inverse function f^-1(x) as follows ;
y = 1/3x - 2
by cross multiplication
3x - 2 = 1/y
add 2 to both sides of the equation
3x = 1/y + 2
3x = (1 + 2y)/y
divide both sides of the equation by 3
x = (1 + 2y)/y ÷ 3
x = (1 + 2y)/3y
So, f^-1(x) = (1 + 2x)/3x
Therefore, the inverse of the function f is derived by interchanging the value of x for y and vice versa, that is f^-1(x) = (1 + 2x)/3x.
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386666666667/100000000000 simplest fraction
Answer: ___________________________________________
58/15
A famous piece of artwork was up for bid at a museum auction. The minimum bid was $25,000.
Determine which inequality represents the bid for the artwork.
b ≥ 25,000
b ≤ 25,000
b < 25,000
b > 25,000
The inequality that represents the bid for the artwork is A. b ≥ 25,000.
What is an inequality?Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.
In this case, the famous piece of artwork was up for bid at a museum auction and the minimum bid was $25,000.
Let the minimum bid be b. This will be b ≥ 25,000.
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this shows that the percentage in a normal distribution that is at most 1.65 sds above average is about 95%. explain why 1.65 is the right number of sds to use when constructing a 90% confidence interval. (6 points)
The correct number of Standard deviation to generate a confidence interval is therefore 1.65.
Given that;
This shows that the percentage in a normal distribution that is at most 1.65 standard deviation above average is about 95%.
Percentage above 1.65 SD equals 100 - 95 = 5.
Now, because of the symmetric distribution,
Percentage above 1.65 SD = % below 1.65 SD is what we can see:
Below 1.65 SD + between 1.65 SD below and 1.65 above + above 1.65 SD + % above 1.65 SD = 100%
=> 5% + between -1.65 SD below and 1.65 above + 5% = 100%
=> % between -1.65 SD and 1.65 SD above mean = (100 - 5 - 5)% = 90%
The correct number of SDs to generate a confidence interval is therefore 1.65.
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Find the slope of the line passing through the points (4, -2) and (9, -2).
slope:
Find the slope of the line passing through the points (2, 9) and (2, - 7).
slope:
Answer:
x1 y1 x2 y2
1. 0 - explanation - (4, -2) (9, -2) -2 - -2
4 - 9 (put a fraction bar when you put the y2 and y1 together and put the x2 and y2 in the denominator spot) basically -2 subtract -2 equals 0
2. it would be defined or 0
a fruit stand has to decide what to charge for their produce. they need \$10$10dollar sign, 10 for 444 apples and 444 oranges. they also need \$12$12dollar sign, 12 for 666 apples and 666 oranges. we put this information into a system of linear equations. can we find a unique price for an apple and an orange?
No, we cannot find a unique price for an apple and an orange
Let the price of an apple be $x and that of orange be $y.
Condition 1.
They need $10 for 4 apples and 4 oranges.
Then, 4x + 4y = 10
or, 2x + 2y = 5 .....(1)
Condition 2.
They need $12 for 6 apples and 6 oranges.
Then, 6x + 6y = 12
or, 2x + 2y = 5 .....(2)
Two identical linear equations have been discovered.
They do, however, create a system of dependent linear equations that reduces to:
2x + 2y = 5
There are infinite possible solutions to this linear equation.
Thus, we get the conclusion that an apple and an orange cannot have different prices.
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What are the domain and range of the function?
f(x) = -4√x
The domain is x [tex]\geq[/tex] 0. interval notation: [0,[tex]\infty[/tex])
the range is f(x)≤0, interval notation: (-[tex]\infty[/tex],0 ]
What are the domain and range of a function?
The domain is the set of all x-values that can be used to make the function "work" and produce actual y-values.
A function's range is the variety of conceivable y-values (minimum y-value to maximum y-value)
Find domain:
Set the term under the square root [tex]\geq[/tex]0
So, the domain is x [tex]\geq[/tex] 0. interval notation: [0,[tex]\infty[/tex])
Find range:
The range of a radical function of the form -c√(ax+b) +k is f(x)≤k
So, the range is f(x)≤0
interval notation: (-[tex]\infty[/tex],0 ]
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what 29,000 divided by 50,000
Answer:
.58
Step-by-step explanation:
Sofia is 38 years old. Write an equation that relates Sofia's age to Tony's age, t. How old is Tony?
(Sofia’s age is 2 times the combined ages of Carlos and Lily - Carlos’s age is 4 more years than Tony’s age - and Lily’s age is one more than 6 times Tony’s age)
Answer:
Let s, c, y and t represent the ages of Sofia, Carlos, Lily and Tony respectively.
c + y = 2s ------ equation (1)
t + 4 = c ------ equation (2)
6t + 1 = y ------ equation (3)
Since Sofia is 38 years old, substitute s = 38 into equation (1):
c + y = 2(38)
= 76 ------ equation (4)
Substitute equations (2) and (3) into equation (4):
t + 4 + 6t + 1 = 76
7t + 5 = 76
7t = 71
∴ t = 10 (to the nearest whole number)
∴Tony is 10 years old (to the nearest whole number).
when using percentiles with normally distributed scores, differences between raw scores may be .
The percentile rank / score in the setting of statistics denotes the percentage of the population that falls below it when the data is organized in ascending order.
What is meant by normally distributed?The mean and standard deviation of a normal distribution are 0 and 1, correspondingly. It has a kurtosis of 3 and zero skew.Not every symmetrical distributions are normal, but all normal distributions are symmetrical.68.2% of observations would fall within +/- 1 standard deviation of a mean including all normal distributions, 95.4% will fall in +/- two standard deviations, and 99.7% will fall within +/- 3 different deviations.For the given question.
The difference in the percentiles and raw scores is-
When presented in ascending order in statistics, a percentile rank / score signifies the percentage of the population that drops below it. By translating the raw score into an analogous z-score through using empirical z-distribution table, the percentile for such a raw score may be established.To know more about the normally distributed, here
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Determine the total number of Fish food cubes that will fill the shipping box
I hate to leave you without an answer, but there isn't enough information to be able to answer your problem.
What is an equation of the line that passes through the points (-4, -3) and (8, 6)?
Answer:
Y = 3/4x + 0
Step-by-step explanation:
Find the slope of the line = Rise/Run.
[tex]\frac{-3-6}{-4-8}[/tex] = [tex]\frac{-9}{-12}[/tex]
= 0.75 or 3/4.
Therefore, insert into point slope form using one of the corresponding points; (8, 6) for example;
Y-6 = 3/4(x-8)
= Y-6 = 3/4x-6
and simplify the equation;
Y = 3/4x + 0 also just Y = 3/4x.
a telemarketing company is conducting a study of new calling scripts. seventy-five employees will be randomly assigned to three new scripts using a table of random digits. the study leader will assign the subjects to the groups using a table of random digits. how many unique two-digit numbers within the range of 01 to 75 will the study designer need to select from the table? 3 25 50 75
Answer:
50
Step-by-step explanation:
7.69 to the nearest whole number.
Answer: 8
Step-by-step explanation:
7.69 to the nearest whole number is 8
Express 60 as the product of its prime factors.
60 = (Answer here)
Answer:
2x2x3x5= 60
I hope you like it
Answer:
2 X 2 X 3 X 5
Step-by-step explanation:
We divide 60 by 2 as many times as possible to get 60 = 15 x 2 x 2. 2 is a prime number so we don't need to break the 2's down any more. Instead we break 15 down. 15 doesn't divide by 2 so we try the next prime number: 3 Divide 15 by 3 to get 15 = 5 x 3, and so 60 = 5 x 3 x 2 x 2. Now we collect the factors, so our final answer is 60 = 5 x 3 x 22.