Answer:
A
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = - 3 and crosses the y- axis at (0, - 7 ) ⇒ c = - 7
that is the y- intercept c = - 7
Find the area of the sas triangle with side lengths 29 and 36 and included angle 62 degrees.
Answer:
1323.3
Step-by-step explanation:
Write a division equation that represents the question: how many 3/8s are in 5/4
The division equation is x * 3/8 = 5/4 and there are (10/3) times 3/8s there in 5/4.
Let's assume that x times 3/8 are in 5/4.
So, calculating a division equation for the value of x.
x * 3/8 = 5/4
=> x = 5/4 * 8/3
=> x = 40/12
Dividing the numerator and denominator by 4.
We get, the value of x equal to
=> x = 10/3
Division equation: A division equation is a mathematical expression containing a division operator. Division equations are useful not only in math class but also in everyday life.
For example, if we want to share a bundle of papers equally with our friends, we can use this solution to find the given question. 100 papers and we have 10 friends. To find out how many papers each person gets, divide 100 by 10. The solution is 10. This means that each friend receives 10 papers.
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Write an algebraic expression for the following scenario in terms of total money saved:
“you start with $400 and save $100 a week”
Answer:
y = 100x + 400
Step-by-step explanation:
What we know:
- You started with 400
- You get 100 a week
What we need to find out:
- The equation or rate to know how much money acquired in specific time
Step 1 ( of 1 ): Equation
- if you let y represent the total of money you acquire then the equations starts as
y=
- Then we know that we get 100 a week so let x represent the amount of weeks so
y = 100x
- Lastly we know that we started with 400 so then we just add that to the equation to make it
y = 100x + 400
help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The amount owed by the debtor is $10865
How to determine the amount owed in six years?The given parameters about the compound interest are
Principal Amount, P = $5300
Interest Rate, R = 8%
Time, t = 6 years
To calculate the amount owed, we make use of the following formula
A = P + CI
Where
Compound interest, CI = P(1 + R)^t - P
So, the equation becomes
A = P + P(1 + R)^t - P
Evaluate the like terms
A = P(1 + R)^t
In this question, the formula is given as
A = P(1 + r/n)^nt
Where
n = 12, i.e compounded monthly
Substitute the known values in the above equation
A = 5300 * (1 + 8%/12)^(6*12)
Express 8% as decimal
A = 5300 * (1 + 0.08/12)^(6*12)
Evaluate the sum
A = 5300 * (1.01)^(6*12)
Evaluate the exponent
A = 5300 * 2.05
Evaluate the product
A = 10865
Hence, the value of the amount after 6 years is $10865
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pls helpp!! ixl is so frustrating and i can't get this question wrong itll drop me like 20 points i don't understand this question
Answer:
oof try adding dem
Step-by-step explanation:
hope you git 20 points
Kira and Hector each performed as soloists for a concert. Each person performed for the same amount of time. Kira sang three solos and played a piano piece. Hector sang 2 solos and played a piano piece that lasted twice as long as Kira's. Each of the solos Kira and Hector sang was 3.5 minutes long.
a. Define a variable and write an equation to represent the situation. Solve the equation and interpret the solution of your equation in the context of the situation.
b. How long did each student perform?
A variable can be any number or alphabet that may constantly vary and the equation to represent the given situation for Kira is (3x+y) and for Hector is (3x+z) where x is the time for solos and y and z are times for piano. The value of x and y is 3.5 minutes and that of z is 7 minutes.
According to the question,
We have the following information:
Each person performed for the same amount of time. Kira sang three solos and played a piano piece. Hector sang 2 solos and played a piano piece that lasted twice as long as Kira's. Each of the solos Kira and Hector sang was 3.5 minutes long.
Now, let's take time for solos to be x min and time for Kira's piano to be y min and that for Hector is z min.
So, we have the following equations:
Kira:
3x+y
Hector:
2x+z
Now, z = 2y
x = 3.5 minutes
Time is equal:
3x+y = 2x+z
3x+y = 2x+2y
3x-2x = 2y-y
x = y
y = 3.5 min
z = 2*3.5
z = 7 min
Hence, a variable can be any number or alphabet that may constantly vary and the equation to represent the given situation for Kira is (3x+y) and for Hector is (3x+z) where x is the time for solos and y and z are times for piano. The value of x and y is 3.5 minutes and that of z is 7 minutes.
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Find the slope of the line graphed below.
Answer: -1
Step-by-step explanation:
Answer:
By counting, to go from one point to another, we go down 4, over 4. This means the slope is -4/4. This can then be simplified.
-4/4 = -1
So, the slope is -1
Determine the distance between the points (−6, −3) and (0, 5).
22 units
10 units
8 units
5 units
By using the distance formula, The distance between the points (−6, −3) and (0, 5) is 10 units.
In geometry, we use the distance formula to evaluate the distance between two points whose coordinates are given,
The coordinates of the points are given as [tex](x_{1} ,y_{1})( x_{2} ,y_{2} )[/tex]
Then, the distance (D) between them is given by :
[tex]D = \sqrt{(x_{1} -x_{2} )^{2} -(y_{1} -y_{2} )^{2} }[/tex]
Now, the given points are (−6, −3) and (0, 5).
Putting these values in the distance formula, we have
[tex]D = \sqrt{(-6-0)^{2}+ (-3 -5)^{2} }\\ \\D = \sqrt{36 +64 \\\\ \\D = 10[/tex]
Hence, the distance between the points (−6, −3) and (0, 5) is 10 units.
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Answer: 10 units
Step-by-step explanation: i took the test and got it right
These are the answer choices though
Answer:
[tex]m= -2\frac{1}{13}[/tex]
Step-by-step explanation:
2m-27/3=5m
x3. x3
2m-27=15m
-2m. -2m
-27=13m
/13. /13
-27/13=m
-2 1/13=m
Hopes this helps please mark brainliest
A state imposes a sales tax on items of clothing that cost more than $175. The tax applies only to the difference of the price of the item and $175.
Use the receipt shown to find the tax rate (as a percent).
The tax rate is _%.
Answer:
2.543%
Step-by-step explanation:
295x1.02543=$302.50
295+2.543%=302.50
Brad and john met up for lunch when they were done brad traveled 6 blocks east and john traveled 4 blocks west how many blocks .away from brad was john
Answer:10 blocks
Step-by-step explanation: East And West are in a straight line
[tex]3x-1=1/3(9x-5)[/tex]
write expression in terms of log of x , and z
log x√z
The equation in terms of log(x) and log(z) is, [tex]logx\sqrt{z} = logx + \frac{1}{2} log(z)[/tex].
What is logarithmic expression?
A logarithmic equation is one in which a variable-containing expression's logarithm is used as a solution. If you can write both sides of the equation as powers of the same number, that will help you answer exponential equations.
Consider, the given logarithmic expression,
[tex]logx\sqrt{z}[/tex]
By using the logarithmic rule: log(ab) = log(a) + log(b)
So,
[tex]logx\sqrt{z} = log(x) + log\sqrt{z}[/tex] ..(1)
Replace [tex]\sqrt{z}[/tex] by [tex]z^\frac{1}{2}[/tex].
So,
[tex]log\sqrt{z} = logz^\frac{1}{2}[/tex]
Apply the rule: [tex]loga^b = b log(a)[/tex]
Therefore, [tex]log(\sqrt{z}) = \frac{1}{2}log(z)[/tex]
Substitute this value in equation (1).
[tex]logx\sqrt{z} = logx + \frac{1}{2} log(z)[/tex].
Hence, the expression in terms of x and z is, [tex]logx\sqrt{z} = logx + \frac{1}{2} log(z)[/tex].
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-3√7r³-6√7r²
How do I solve this step by step?
The solution of the expression -3√7r³-6√7r² is -3√7r²(r+3)
Expression:
An expression also known as the algebraic expression consists of unknown variables, numbers and arithmetic operators.
Given,
Here we have the expression -3√7r³-6√7r²
Now, we have to solve this expression step by step.
In order to solve this expression, we have to write the given expression as,
=> - 3√7r³- 6√7r²
Here the value √7 is common, so we have to take it as the common term and then rewrite the given expression as,
=> √7(-3r³-6r²)
Now, we have to take the number -3, as the common term then we get he expression like the following,
=> -3√7(r³+3r²)
Now we have to take the variable r² as the common term, then we get,
=> -3√7r²(r+3)
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a fifth grade teacher assumes that 30% of her students are late for class. if the teacher is correct, what is the probability that the proportion of late students in a sample of 449 students would differ from the population proportion by less than 5%? round your answer to four decimal places.\
Answer:
9
How I got the Answer:
We have,
p = 0.30
q = 1 - p = 0.70
n = 449
Here,
npq = 4449*0.3*0.7 = 9
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A rental car company charge $63. 25 per day to rent a car and $0. 07 for every mile driven. Ella want to rent a car, knowing that: She plan to drive 50 mile. She ha at mot $130 to pend
Answer:
it would be 66.75 for one day if ella plans to drive for 1 day with 50 miles, and if you need how much money she has left it is 63.25
Step-by-step explanation:
hope it helped:)
consider the following graph. the x y coordinate plane is given. the curve begins at the origin, goes up and right becoming less steep, the curve changes direction at (1, 3), goes down and right becoming more steep, passes through (2, 2), goes down and right becoming less steep, changes directions at (3, 1), goes up and right becoming more steep, passes through the point (4, 3), goes up and right becoming less steep, passes through (5, 4) almost horizontally, goes up and right becoming more steep, passes through the approximate point (6, 4.2) and ends at (7, 6). (a) find the interval(s) on which f is increasing. (enter your answer using interval notation.) incorrect: your answer is incorrect. (b) find the interval(s) on which f is decreasing. (enter your answer using interval notation.) correct: your answer is correct. (c) find the interval(s) on which f is concave upward. (enter your answer using interval notation.) incorrect: your answer is incorrect.
A) The interval(s) on which f is increasing is; (1,3) ∪ (4,6).
B) The interval(s) on which f is decreasing is; (0,1) ∪ (3,4).
(C) The interval(s) on which f is concave upward is; (0,2) ∪ (3,5).
How to find the increasing or decreasing interval?
A) A function is said to be increasing on an interval if for every point on that interval we see that the first derivative is positive. Thus, from the attached graph, we see that the function is increasing on the intervals (1,3) and (4,6).
B) If the value of the derivative f' (x) ≤ 0 of the function, then we can say that the interval is a decreasing interval. From the graph, we can say that the function is decreasing on intervals (0,1) and (3,4).
C) The graph is concave upward on the intervals (0,2) and (3,5).
D) The graph is concave downward which means convex on the interval (3,4).
e) The points of inflection are defined as the points located on a smooth plane curve that the curvature changes sign. In this graph, the points of inflection are x=3 and x=5.
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The midpoint of line AB is M(3,−3). If the coordinates of A are (2,−8), what are the coordinates of B?
Answer:
The coordinates of B are (4, 2)
Step-by-step explanation:
The coordinates of B can be calculated as follows ?
The midpoint of line AB is M(3,-3) is derived from the formula
[tex]M=(\frac{x_{1}+x_{2}}{2} ,\frac{y_{1}+y_{2}}{2})[/tex]
Where [tex]x_1[/tex] and [tex]y_1[/tex] are the coordinates of A and [tex]x_{2}[/tex] and [tex]y_{2}[/tex] are the coordinates of B
Since the coordinates of A are (2, -8), then the value of [tex]x_1[/tex] is 2 and the value of [tex]y_{1}[/tex] is -8.
Since the [tex]x[/tex]-coordinate of M is 3, then the equation to follow is
[tex]\frac{x_{1}+x_{2}}{2}=3[/tex]
Substitute 2 for [tex]x_{1}[/tex], then it follows that
[tex]\frac{2+x_{2}}{2}=3[/tex]
Multiply both sides of the equation by 2
[tex]\frac{2+x_{2}}{2}\times 2=3\times 2[/tex]
Simplify both sides of the equation
[tex]2+x_{2}=6[/tex]
Substract 2 from both sides of the equation
[tex]2-2+x_{2}=6-2[/tex]
Simplify the equation
[tex]x_{2}=4[/tex]
Since the [tex]y[/tex]-coordinate of M is -3, then the equation to follow is
[tex]\frac{y_{1}+y_{2}}{2}=-3[/tex]
Substitute -8 for [tex]y_{1}[/tex], then it follows that
[tex]\frac{-8+y_{2}}{2}=3[/tex]
Multiply both sides of the equation by 2
[tex]\frac{-8+y_{2}}{2}\times 2=-3\times 2[/tex]
Simplify both sides of the equation
[tex]-8+y_{2}=-6[/tex]
Add 8 to both sides
[tex]-8+8+y_{2}=-6+8[/tex]
Simplify the equation
[tex]y_{2}=2[/tex]
Since the value of [tex]x_{2}[/tex] is 4 and the value of [tex]y_{2}[/tex] is 2, then the coordinates of B are (4,2).
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the value of 1. 35⁷
Give your answer correct to 5 significant figures.
Answer:
1.35⁷ = 8.1722 (to 5sf)
Brianna is very good at keeping her school binder organized. Every time her teacher returns an assignment, Brianna puts it in the right section. Brianna has 113 assignments in the history, science, and art sections combined. The rest of her assignments are in the math section. Brianna has 182 assignments in total.
Using equation, the number of math assignment is 69 .
How to use equation to find the number of math assignment?Brianna has 113 assignments in the history, science, and art sections combined. The rest of her assignments are in the math section. Brianna has 182 assignments in total.
Using equation, the number of assignments in the math section of Brianna's binder can be calculated as follows:
She has 113 assignments in the history, science, and art sections combined.
Let x be the number of assignments that are in math section.
There are 182 assignments in total.
Therefore,
x + 113 = 182
subtract 113 from both sides of the equation
x + 113 = 182
x + 113 - 113 = 182 - 113
x = 69
Therefore, the number of math assignment is 69.
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What is the area of trapezoid abcd? enter your answer as a decimal or whole number in the box. do not round at any steps. units²
The area of trapezoid ABCD is 37.5 units^2.
Trapezoid is a type of quadrilateral with at least one pair of parallel sides. The area of trapezoid is given by:
Area = ½(a + b)*h
Where a and b are the length of two parallel sides and h is the perpendicular length between the length of two parallel sides.
In the given trapezoid ABCD, which is defined by coordinates of A, B, C, and D, the distance of each side is given by: √((x2 – x1)^2 + (y2 – y1)^2)
The length of a (DA) = √((x2 – x1)^2 + (y2 – y1)^2) = √((-3 – 0)^2 + (2 – (-2))^2) = √((-3)^2 + (4)^2) = √(9 + 16) = √25 = 5 units
The length of b (BC) = √((x2 – x1)^2 + (y2 – y1)^2) = √((7 – 1)^2 + (-3 – 5)^2) = √((6)^2 + (-8)^2) = √(36 + 64) = √(36 + 64) = √(100) = 10 units
The length of h (AB) = √((x2 – x1)^2 + (y2 – y1)^2) = √((1 – (-3))^2 + (5 – 2)^2) = √((4)^2 + (3)^2) = √(16 + 9) = √(25) = 5 units
Hence, the area of trapezoid:
Area = ½ (5 + 10) * 5 = 7.5 * 5 = 37.5 units^2
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1/6x^2=1/2x+7/6x^2
Rational Equation
Answer: x = -2
Step-by-step explanation:
[tex]\frac{1}{6x^2} =\frac{1}{2x} +\frac{7}{6x^2}[/tex]
[tex]\frac{1}{6x^2} = \frac{3x}{6x^2} + \frac{7}{6x^2}[/tex] (work with common denominators)
[tex]\frac{1}{6x^2} = \frac{3x+7}{6x^2}[/tex]
[tex]1 = 3x + 7[/tex] (remove the 6x^2 because they'll cancel out when you cross multiply)
[tex]-6 = 3x[/tex]
[tex]-2 = x[/tex]
In the accompanying diagram, parallel lines HE and AD are
cut by transversal BF at points G and C, respectively. If
mLHGF = 5n and m/BCD = 2n +66, find n.
The value of n is 22.
In this question, we have been given the parallel lines HE and AD are
cut by transversal BF at points G and C, respectively.
Consider the following diagram.
If m∠HGF = 5n and m∠BCD = 2n +66, we need to find n.
∠HGF and ∠BCD are alternate exterior angles.
We know that alternate exterior angles are congruent.
So, m∠HGF = m∠BCD
5n = 2n +66
5n - 2n = 66
3n = 66
n = 66/3
n = 22
Therefore, the value of n is 22.
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someone help step by step
Step-by-step explanation:
we know, the area of a rectangle is
length × width
so, we have here
length × (x - 5) = x² - 7x + 10
therefore,
length = (x² - 7x + 10) / (x - 5)
so, just by looking at it (with experience) I see that length is (x - 2).
but let's do the actual polynomial division, which seems to be the desired exercise here.
x² - 7x + 10 ÷ x - 5 =
it is very similar to actual number divisions.
we go from left to right.
we start with the first term (x²) and see how many times (x - 5) would fit into it. for that we look only at the first term in x - 5 (that is x).
x² / x = x
that is already our first term of the result (quotient) :
x² - 7x + 10 ÷ x - 5 = x
now, we multiply that result with the divisor (x - 5) and subtract that from the dividend.
x² - 7x + 10 ÷ x - 5 = x
- x² - 5x
--------------
0 - 2x
and now we pull down the next term from the dividend :
x² - 7x + 10 ÷ x - 5 = x
- x² - 5x
--------------
0 - 2x + 10
and we repeat the process with that new dividend :
-2x / x = -2
that is our next term of the quotient.
x² - 7x + 10 ÷ x - 5 = x - 2
- x² - 5x
--------------
0 - 2x + 10
we repeat the process of multiplying that term (-2) with the divisor (x - 5) and subtracting that result from the dividend :
x² - 7x + 10 ÷ x - 5 = x - 2
- x² - 5x
--------------
0 - 2x + 10
- -2x + 10
-------------
0 0
there is no remainder, and there is no more term to pull down. we are finished.
the result of the division is (as expected) : x - 2
the expression to describe the length is therefore
x - 2
Kirsty changes $380.80 into pounds (£) when £1 = $1.19. Calculate the amount Kirsty receives.
Answer:
320 pounds sterling
Step-by-step explanation:
All you have to do is $380.80 divided by $1.19 which is equal to one pound sterling. Hope this helps!
logan is constructing a scaled model of his town. the city's water tower stands 40 meters high, and the top portion is a sphere that holds 100 , 000 liters of water. logan's miniature water tower holds 0.1 liters. how tall, in meters, should logan make his tower?
Answer:
0.4 m = 40 cm
Step-by-step explanation:
You want the height of a model water tower with a volume of 0.1 liters that models a city water tower 40 m high with a volume of 100,000 liters.
Scale factorThe scale factor for volume is the cube of the scale factor for linear dimensions, such as height. Conversely, the scale factor for height is the cube root of the scale factor for volume.
This lets us write a proportion for the height of the model tower:
[tex]\dfrac{h}{40\text{ m}}=\sqrt[3]{\dfrac{0.1\text{ L}}{100000\text{ L}}}\\\\h=(40\text{ m})\sqrt[3]{10^{-6}}=\boxed{0.40\text{ m}}[/tex]
Logan should make his tower 0.4 meters, or 40 cm high.
Chicken and rabbit are placed in the ame cage. There are 35 head and 94 feet. How many rabbit are there?
Based on heads and feet of chicken and rabbits, there are 12 rabbits in the cage.
Let us represent chicken by x and rabbit by y. So, we all know that chicken and rabbit have 1 head each. We also know that chicken has 2 feet and rabbit has 4 legs. Now forming the equation accordingly.
Equation for head -
x + y = 35 : Equation 1
Equation for feet -
2x + 4y = 94 : Equation 2
Rewriting equation 1 according to x
x = 35 - y : Equation 3
Keep the value of x from equation 3 in equation 2
2(35 - y) + 4y = 94
Preforming multiplication on Left Hand Side
70 - 2y + 4y = 94
Performing subtraction
2y = 94 - 70
2y = 24
y = 24 ÷ 2
Performing division
y = 12
Thus, there are 12 rabbits in the cage.
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PLEASE NEED HELP ASAP
Answer:
-1
Step-by-step explanation:
The number never changes when you divide by 1. So -1/1=-1.
-Hope this helped
The school needs to purchase a new refrigerator for student rewards. Lowes is
having a 15% off. If the original price is $700, what is the discount amount?
Mari cella has a bag containing 35 nickels and quarters. The total value of these coins is less than $2.50. What is the maximum number of quarters that meets these conditions
From the given numbers nickels and quarters ,total value of given coins is less than $2.50 then maximum number of quarters to meet the given condition is equal to 3.
As given in the question,
Let x represents the number of nickels
And y represents the number of quarters
Total number of nickels and quarters are 35
Total value of given coins = $2.50
Required equation for the given condition is:
x + y = 35 ___(1)
1 nickel = 0.05 dollars
1 quarter = 0.25 dollars
0.05x + 0.25y <2.50 ___(2)
Substitute x = 35 - y in (2) we get,
0.05 ( 35 - y ) + 0.25y < 2.50
⇒1.75 - 0.05y + 0.25y < 2.50
⇒ 0.2y < 2.50 - 1.75
⇒ 0.2y < 0.75
⇒ y < 3.75
Maximum number of quarters for the given condition is equal to 3.
Therefore, for the given numbers nickels and quarters ,total value of given coins is less than $2.50 then maximum number of quarters to meet the given condition is equal to 3.
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