By using the point-slope form, the equation of a line that passes through the point (11, 18) with slope 3 is equal to y - 18 = 3(x - 11).
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁)
Where:
m represents the slope.x and y represents the data points.From the information provided above, we have the following slope and data points on the line:
Points = (11, 18).Slope, m = 3At data point (11, 18), a linear equation of this line can be calculated in point-slope form as follows:
y - y₁ = m(x - x₁)
y - 18 = 3(x - 11)
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Question 4, I need to know the steps to get to the answer
===============================================
Explanation:
We'll use the pythagorean theorem converse.
Consider a triangle with sides a,b,c where c is the longest side.
There are 3 scenarios possible:
If a^2+b^2 > c^2, then the triangle is acute.If a^2+b^2 = c^2, then it is a right triangle.If a^2+b^2 < c^2, then the triangle is obtuse.The middle or second scenario is probably what you're most familiar with. That's the famous pythagorean theorem without the term "converse" attached to it.
--------------
The two given sides are 8 inches and 10 inches.
Let's say the third side was 5 inches (choice F)
This means we have a triangle with sides a = 5, b = 8, c = 10
Then compute the following:
a^2+b^2 = (5)^2 + (8)^2 = 89c^2 = (10)^2 = 100Since 89 < 100, we see that a^2+b^2 < c^2 is the case. Therefore the triangle with sides 5,8,10 is obtuse.
This will allow us to rule out choice F since we're looking for an acute triangle.
--------------
Now onto choice G.
This time the sides are: a = 6, b = 8, c = 10
a^2+b^2 = (6)^2 + (8)^2 = 100c^2 = (10)^2 = 100Both results (a^2+b^2 and c^2) are the same at 100; so we see that a^2+b^2 = c^2.
Therefore we have a right triangle. We can rule out choice G.
--------------
Now onto choice H.
The triangle now has sides: a = 8, b = 10, c = 12
a^2+b^2 = (8)^2 + (10)^2 = 164c^2 = (12)^2 = 144Since 164 > 144, we see that a^2+b^2 > c^2 is the case. Therefore the triangle with side lengths 8,10,12 is acute.
Choice H is the final answer.--------------
For the sake of completeness, let's go over choice J.
a = 8, b = 10, c = 13a^2+b^2 = (8)^2 + (10)^2 = 164c^2 = (13)^2 = 169We find 164 < 169 which leads to the scenario a^2+b^2 < c^2. The triangle for choice J is obtuse. We can rule out choice J.
You can use something like GeoGebra to help visually verify these results.
Stephen and Chelsea want to increase the volume of this prism by 72 cubic centimeters. Chelsea wants to add eight layers, and Stephen says they need to add four layers. Their teacher tells them they are both correct. Explain how this is possible
Chelsea wants to add one layer of 3 x 3 cubics and Stephen wants to add one layer of 3 x 6 cubics.
From given figure, the dimension of the rectangular prism are:
6 cm × 3 cm × 3 cm
The volume of the rectangular prism would be,
V = l × w × h
V = 6 × 3 × 3
V = 54 cm³
Stephen and Chelsea want to increase the volume of this prism by 72 cubic centimeters.
Chelsea wants to add eight layers.
This means 72 = 8 × 3 × 3 cubics, then one layer in this case consists of 3 x 3 cubics;
Whereas Stephen says they only need to add four layers.
This means 72 = 4 × 3 × 6 cubics, then one layer in this case consists of 3 x 6 cubics.
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Find the complete question below.
Fill in the blank question.
Cynthia made 37 out of 48 free throws last season. Based on this relative frequency, how many free throws could she be expected to make this season if she has 58 attempts? Round to the nearest whole number.
free throws
Answer:
45
Step-by-step explanation:
You want to know the expected number of free throws Cynthia will make in 58 attempts, if her success rate is 37 out of 48.
FractionWe assume the number of successful free throws is proportional to the number of attempts:
37/48 = x/58
x = 37/48·58 ≈ 45
Cynthia could be expected to make 45 free throws this season.
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B and C are sets of real numbers defined as follows.
Write B U C and B C using interval notation.
If the set is empty, write .
B= {x|x>3}
C= {x|x≤5}
1. The union of set B and C, BUC using interval notation is (3, ∞) U (-∞, 5]
2. The intersection of set B and C, B∩C using interval notation is (4, 5]
1. How do I determine BUC?We'll begin by obtaining the elements of set B and C. Details below:
B = {x| x > 3} = All numbers greater than 3 to infinity. This is written as: (3, ∞)C = {x| x ≤ 5} = All numbers lesser than or equal to 5 to infinity. This is written as: (-∞, 5]With the above information we can determine BUC in interval notation as follow:
B = (3, ∞)C = (-∞, 5]BUC =?BUC = (3, ∞) U (-∞, 5]
2. How do I determine B∩C?We can obtain B∩C in interval notation as follow:
B = (3, ∞)C = (-∞, 5]B∩C =?B∩C = (3, ∞) ∩ (-∞, 5]
B∩C = (4, 5]
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Complete question:
B and C are sets of real numbers defined as follows.
Write BUC and B∩C using interval notation.
If the set is empty, write Ø.
B= {x|x>3}
C= {x|x≤5}
Select the label of the function g(x) as a vertical stretch or a vertical compression of the parent function, f(x), and whether it is reflected about the x-axis.
g(x) = −1. 4(9)x, f(x) = 9x
A vertical compression, no reflection
B vertical stretch and reflection
C vertical stretch, no reflection
D vertical compression and reflection
g(x) is the vertical stretch and reflection about the x-axis. Hence option (B) is the correct answer.
Vertical compression by a factor M: g(x) = m*f(x) (m<1)
m = -1.4
it means for given value of xg(x) < f(x)
Vertical stretch by a factor m: g(x) = (1/m)*f(x) (|m|>1)
hence given vlaue of x g(x) > f(x)
reflection about x axis : y = -f(x)
So, In the given plot, we can say that g(x) is a reflection of f(x) about the x-axis,
and g(x) > f(x) for any value of x it denotes stretch
Therefore, g(x) is the vertical stretch and reflection about the x-axis.
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Write the equations described below.
A subtraction equation with one variable that has a solution of 2/3.
Answer:
x - 2/3 = 2/3
Answer: x-2/3=2/3
Step-by-step explanation:
What is the total distance Jane travels biking and running? Include units with your answer.
Jane covers a combined 28 miles on her bike and run.
What is an expression?A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. It is possible to multiply, divide, add, or subtract in math.
An expression is a means to include operations like addition, subtraction, multiplication, and division in a statement that has more than two variables or numbers.
An example of an expression is 2 + 3 x y = 7.
Those are
Jane rides a total of 16 miles.
Jane covers 12 miles on her run.
the combined distance Jane covers while jogging and riding.
= 16 + 12
= 28 miles
Thus,
Jane covers a combined 28 miles on her bike and run.
The complete question is:
Jane is training for a triathlon. After swimming a few laps, she leaves the health club and bikes 16 miles south. She then runs 12 miles west. Her trainer bikes from the health club to meet jane at the end of her run. What is the total distance Jane travels biking and running?
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Convert each equation from slope-form to standard form
The conversion of the equation from slope-form to standard form is 2x + y = 1.
What is the slope-intercept form?In Mathematics, the slope-intercept form of a line is generally modeled by using this linear equation:
y = mx + b
Where:
m represents the slope.b represents the y-intercept.x and y are the data points.Generally speaking, the standard form of a linear function is is generally modeled by this mathematical expression:
Ax + By = C
Where:
A, B, and C represents a number, numeral or numerical value.
Next, we would convert the given linear function in slope-intercept form to standard form as follows:
2x + y = 1.
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help pls i need to finish my aleks topics
I need the answers to part B please
A) x² - 2x - 13 in the form of (x + c)² + d is (x - 1)² - 15, and the value of
c = -1, d = -15
B) The solutions of the equation are 1+ √15 and 1- √15.
What is Quadratic equation?A quadratic equation is a type of polynomial equation that has the general form of ax² + bx + c = 0, where x is the variable, a, b, and c are constants, and a is not equal to zero.
a) To write x² - 2x - 13 in the form (x + c)² + d, we can complete the square.
First, we add and subtract (2/2)² = 1 to get:
x² - 2x - 13 = x² - 2x - 13 + 1 - 1
Next, we group the terms:
(x² - 2x) - 14 = (x² - 2x + 1) - 15
Now, we can see that the left side of the equation is a perfect square trinomial. To complete the square, we add the square of half of the coefficient of the x term, which is (1)² = 1 to both sides:
(x - 1)² - 15 = 0
So, x² - 2x - 13 = (x - 1)² - 15
c = -1, d = -15
b) Using the answer from part a, we know that x² - 2x - 13 = (x - 1)² - 15
=0
so (x-1)² = 15
x-1 = ± √15
x = 1 ± √15
The solutions of the equation are 1+ √15 and 1- √15.
In the form a = fg, where f and g are integers:
a = 1, f = 1, g = √15
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factor 26x to the power of 5 - 13x using the greatest common factor
The factored form of 26x^5 - 13x is 13x(2x^4 - 1).
What is the greatest common factor?
The greatest common factor (GCF), also known as the greatest common divisor (GCD) or highest common factor (HCF), is a concept in mathematics that refers to the largest positive integer that divides two or more integers without a remainder.
To factor 26x^5 - 13x using the greatest common factor, we need to find the greatest common factor of the two terms.
26x^5 = 213x^5
13x = 13*x
The greatest common factor of the two terms is 13x.
So we can factor it out:
26x^5 - 13x = (13x) (2x^4 - 1)
Hence, the factored form of 26x^5 - 13x is 13x(2x^4 - 1).
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Michelle bought a car that costs $25,800 and put a down of $8,000 on it. The car loan is for 60 months and has an interest rate of 3.99%. How much will she actually pay for the car? What will her monthly payment be?
Please show you’re work and be specific for both questions. Due at 10 pm!!
Answer:
$20239.6
Step-by-step explanation:
The amount financed for the car is $25,800 - $8,000 = $17,800.
To find the monthly payment, you can use the formula:
M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1]
where M is the monthly payment, P is the amount financed, i is the monthly interest rate (3.99%/12), and n is the number of payments (60 months).
So,
i = 3.99%/12 = 0.00399
n = 60
M = $17,800 [ 0.00399(1 + 0.00399)^60 ] / [ (1 + 0.00399)^60 – 1]
M ≈ $337.31
So, Michelle will make monthly payments of $337.31 for 60 months.
To find the total amount that Michelle will pay for the car, you can multiply the monthly payment by the number of payments:
$337.31 x 60 = $20239.6
So, the total amount that Michelle will pay for the car is $20239.6
hey guys ! I need lots of explaining and help for these type of questions. I have a test tomorrow.. （ ；´Д｀）
Answer:
Step-by-step explanation:
First you go up to your y intercept which in your case would be (0,4) and plot a point.
From there you add your slope. From the point (0,4) go down 2 and left 5 and plot a point there. You do that one p=more time from the new point and then you draw your line.
Hope this helps :)
Question 2 (2 points) ✓ Saved
Mr. and Mrs. Smith went out to dinner. their bill was $84.00. Mr. Smith left a 18%
tip. How much was the tip?
A/
Given: ABCD is a parallelogram and angle ABC is a right angle
Prove: AC is congruent to BD
For the given parallelogram, AC is congruent to BD
The term parallelogram in math is defined as a two-dimensional geometrical shape whose sides are parallel to each other.
Here we have know that ABCD is a parallelogram and angle ABC is a right angle.
And we need to proved that AC is congruent to BD.
=> AC = BD
To show that, ABCD is a rectangle if the diagonals of a parallelogram are equal
To show ABCD is a rectangle we have to prove that one of its interior angles is right angled.
Here we have know that in ΔABC and ΔBAD,
Here we all know that the common side that is BC and BA and here we have also know that the sides AC and AD as Opposite sides of a parallelogram are equal.
Then it can be written as,
=> AC = BD
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What are the answers for questions C and F. Please show an explanation of how you got your answers. Thank you. I will award you with 30 points if you answer these.
Answer:
see below
Step-by-step explanation:
C; slope =1/5. The flame length will increase at 5x of the speed increase
or, the speed increase is 1/5 of the flame length increase.
F: Y intercept in the graph is 0, so nothing has happened yet. no fire, no flame.
...........................
Answer: Number 4
Step-by-step explanation:
5/6 = 0.83333...
-9 5/6 = -9.8333333..., which is number 4
19.2 + X = -60.7
Solve for X
Answer:
-79.9
Step-by-step explanation:
-60.7-19.2=-79.9
Answer: -79.9
Step-by-step explanation:
Subtract 19.2 from both sides of the equation to isolate the X.
0 + X = -60.7 - 19.2
X = -79.9
You can also check your answer by plugging in X into the equation and seeing if it equals -60.7
Write an expression for the number of laps each person swam. Let L represent the number of laps swum by Rita
The number of laps swum by Rita: L
The number of laps swum by John: 3L
The number of laps swum by Rodell: 3L + 25
What is algebra? Algebra is the branch of mathematics that studies the use of symbols, variables, and other mathematical objects to represent and analyze relationships between quantities. Algebra is used to solve many practical problems, such as how much a car costs after taxes, how much gas is needed to travel a certain distance, and how many items must be purchased to stay within a certain budget. Algebraic equations and inequalities can be solved through various techniques, such as substitution, elimination, and graphing. Algebraic equations can also be used to solve problems involving functions, which are equations that represent relationships between two or more variables. Algebraic functions can be used to predict future behavior of a system or to determine the best solution to a given problem.To learn more about algebra refer to:
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what is defined equation 6x−3y=−6
The slope and the intercept of the linear function 6x - 3y = -6 are given as follows:
Slope of 1.Intercept of 2.How to define the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
For which the parameters are given as follows:
m is the slope.b is the intercept.The function in this problem is given as follows:
6x - 3y = -6.
In slope-intercept form, we have that:
3y = 6x + 6
y = x + 2.
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find the sum of these polynomials. (4x^2+3x-1) + (x^2-5x-6)=
The sum of the given polynomials is 5x² - 2x - 7.
What are Polynomials?Polynomials are mathematical expressions which consist of one or more terms involving variables and coefficients connected with operations like multiplication, subtraction, addition and natural number powers of variables.
The given polynomials are 4x² + 3x - 1 and x² - 5x - 6.
We have to add the given polynomials to find the sum.
(4x² + 3x - 1) + (x² - 5x - 6)
Rearranging with adding the like terms,
(4x² + x²) + (3x - 5x) + (-1 - 6) = 5x² - 2x - 7
Hence 5x² - 2x - 7 is the sum of the given polynomials.
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HELP ME PLSSSSSSSSSSSSSSSSSSSSSS;(
Answer:
a= 3/
Step-by-step explanation:
2/3a-1/6=1/3
2/3a=1/3+1/6
2/3a=1/2
a=1/2×3/
a=3/
Does someone mind helping me with this problem? Thank you!
Answer: 12x + 15y = 4140, x+y = 300
Step-by-step explanation:
12x represents $12 tickets, 15y represents $15 tickets, x + y is total tickets
Answer:
that a huge prob but yeah
Which rule describes the transformation shown?
Note that the rule that describes the transformation shown is: (x,y) → (x+7,-y)(Number 2)
A transformation is a broad phrase covering four distinct methods of changing the shape and/or location of a point, line, or geometric figure. The Pre-Image is the original shape of the item, and the Image is the final shape and location of the object after the transformation.
Thus, with regard to the transformation above,
At Point A: The original coordinate of point A was (-6,-6).
The coordinate after the transformation is A'(1,6), which eliminates option 3.
At Point B:
The original coordinate of point B was (-2,4).
After the transformation, we have B'(5,-4), which eliminates option 1 and option 4. It is therefore right to state that (x,y) → (x+7,-y) is the correct representation of the transformation.
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Full Question:
The missing options are:
Which rule describes the transformation shown?
1. (x,y) → (-y, x+7)
2. (x,y) → (x+7,-y)
3. (x,y) → (-x, y+7)
4. (x,y) → (y+7, -x)
△WXY is a right triangle. Find the length of XY.
a. 80mm
b. 60
c. 69. 3
d. 34. 6
The length of the side XY taken out by using trigonometric formulas is 12.208 cm.
Now we know that ΔWXY is a right-angled triangle. With ∠XWY = 90°
Hence we see that we can use the trigonometric formulas to find the length of XY
Since ∠YWX = 35° with XW being the corresponding side and XY being the hypotenuse we can use the formula
cosx = base/hypotenuse
Now using a scientific calculator we can calculate
cos35 to be 0.81915
or, base/hypotenuse = 0.81915
or, WX/XY = 0.81915
or, 10/XY = 0.81915
or, XY = 10/0.81915
or, XY = 12.208 cm
Hence the length of side XY is 12.208 cm.
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Complete Question
(Image Attached)
this table shows the exact temperature at three different times in beltsville md one day last winter
The difference in temperature at 10 a.m. and 3:30 p.m. is -3.3 degree Fahrenheit
How to find the difference in temperatureWhen the time was 10 in the morning the temperature was 1.2 degrees Fahrenheit
When it was 3.30 in the afternoon, the temperature was - 2.1 degrees fahrenheit
The difference that would be in the temperatures that we have here would be:
-2.1 - 1.2
= -3.3 degrees fahrenheit
This tells us that there is a decrease in temperature in this time frame
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complete question
shows the exact temperatures at three different times in Beltsville, Md., one day last
3.30 p.m.
-2.1° F
Noon
10 a.m.
1.2° F
Time
Temperature
winter.
0° F
What is the difference between the temperatures at 10 a.m. and 3:30 p.m.? Indicate whether the
Solve each trigonometric function IN THE INTERVAL [0, 360).
17.) sec x + tan x = 1
The solution of the trigonometric function in the interval is x = 0
What is a trigonometric function?A trigonometric function is an equation that contains the trigonometric ratios.
How to solve the given trigonometric function?Given the trigonometric function secx + tanx = 1, we proceed to solve it as follows.
secx + tanx = 1
Using the trigonometric identity tan²x + 1 = sec²x
⇒ secx = √(1 + tan²x)
So, substituting this into the equation, we have that
secx + tanx = 1
√(1 + tan²x) + tanx = 1
√(1 + tan²x) = 1 - tanx
Squaring both sides of the equation, we have that
√(1 + tan²x) = 1 - tanx
√(1 + tan²x)² = (1 - tanx)²
1 + tan²x = 1 - 2tanx + tan²x
Substracting 1 from both sides, we have that
1 - 1 + tan²x = 1 - 1 - 2tanx + tan²x
0 + tan²x = 0 - 2tanx + tan²x
tan²x = - 2tanx + tan²x
Substracting tan²x from both sides, we have that
tan²x - tan²x= - 2tanx + tan²x - tan²x
0 = -2tanx + 0
0 = -2tanx
tanx = 0/-2
tanx = 0
taking inverse tan, we have that
x = tan⁻¹0
x = 0
So, the solution is x = 0
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A container has a capacity of 20 litres. It is filled with wine whose density is 0.8kg/litre. What is the mass of the wine?
The mass of the wine can be found by multiplying the density of the wine (0.8 kg/litre) by the volume of the wine (20 litres). The mass of the wine is 16 kg.
What makes for an excellent density example?Its density is how much "stuff" can fit into a certain quantity of space. For instance, a block of the more resilient, lighter element gold (Au) will have a higher density than a block of the more substantial element lead (Pb) (Au). Styrofoam blocks are not as dense as bricks. Mass per unit volume serves as its definition.
We use the word "density" to indicate how much space (or "volume") an object or substance occupies in relation to the amount of matter contained therein (its mass). Density can also be defined as the quantity of mass per unit of volume.
mass = density x volume
mass = 0.8 kg/litre x 20 litres
mass = 16 kg
So, the mass of the wine is 16 kg.
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How do you do substitution in algebra
Answer: The method of substitution involves three steps:
Step-by-step explanation:
Solve one equation for one of the variables.
Substitute (plug-in) this expression into the other equation and solve.
Substitute the value into the original equation to find the corresponding variable. here i helped ya
Tomika and Mark had $3,800 in medical expenses and paid an additional $8,009 for medical insurance. The insurance covered 60% of the medical expenses. The IRS allows medical and dental expense deductions for the amount that exceeds 7.5% of a taxpayer's adjusted gross income. If their adjusted gross income is $101,598, how much can they claim as a medical deduction?
Tomika and Mark claim a medical deduction in the amount of $1,839.8.
What is the percentage?
A number or ratio that can be expressed as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The percentage, therefore, refers to a part per hundred. Per 100 is what the word percent means. It is represented by the symbol “%
Given that the gross income is $101,598
Medical insurance = 7.5 % of $101,598
= 7.5% x $101,598
= $7,619.88.
The insurance covered 60% of the medical expenses.
Medical deduction claim = $7,619.88 - (100% - 60%)x $3,800
= $7,619.88 - 40% x $3,800
= $7,619.88 - $1,520
= $6,099.88
Therefore, they can claim a medical deduction in the amount of $1,839.8.
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