(a) [tex]a_{n}[/tex] = 4n + 8
(b) row 13 has 60 seats
(a)
the sequence of seats is an arithmetic sequence whose n th term is
[tex]a_{n}[/tex] = [tex]a_{1}[/tex] + (n - 1 )d
where [tex]a_{1}[/tex] is the first term and d the common difference
here the sequence is 12, 16, ....
with [tex]a_{1}[/tex] = 12 and d = 16 - 12 = 4, thus
[tex]a_{n}[/tex] = 12 + 4( n - 1 ) = 12 + 4n - 4 = 4n + 8
(b)
calculate the number of rows n when 60 seats
solve 4n + 8 = 60 ( subtract 8 from both sides )
4n = 52 ( divide both sides by 4 )
n = 13 ← number of rows
One of the angles formed by two intersecting lines is 30°. What is the measure of the other three angles? please help i need this asap 20 POINTS
Answer: the angles are if the 30° is in the first quadrant:
30°, 150°, 30°, 150° (from quadrant one to quadrant four)
Step-by-step explanation:
If two lines intersect, and one of the angles that form is 30°, we have that:
Now, suppose that you have only a line, this is the representation of a 180° angle, then if you divide it with a line and one of the angles created is 30°, the other angle must be equal to 150°
and on the other side of the line we will have a mirrored image, right next to the 150° we should see another 30° angle, and after that another 150° angle.
what is the length of the missing side
Answer:
The answers are:
m = 9 and n = 15
Step-by-step explanation:
m/15 = n/25 = 12/20
m/15 = 12/20
m/15 = 3/5
5m = 45
m = 9
n/25 = 12/20
n/25 = 3/5
5n = 75
n = 15
m = 9 and n = 15
Find the length( l ) of the leg in the large right triangle using Pythagoras' identity
l = √(25² - 20²) = √225 = 15
the outer and inner right triangles are similar hence the ratios of corresponding sides are equal
[tex]\frac{25}{n}[/tex] = [tex]\frac{15}{m}[/tex] = [tex]\frac{20}{12}[/tex]
using [tex]\frac{25}{n}[/tex] = [tex]\frac{20}{12}[/tex] (cross-multiply )
20n = 300 ( divide both sides by 20 )
n = 15
using [tex]\frac{15}{m}[/tex] = [tex]\frac{20}{12}[/tex] ( cross-multiply )
20m = 180 ( divide both sides by 20 )
m = 9
A movie theater charges $5 per ticket and averages 300 customers each night. If prices are raised to $7 per ticket, the theater estimates that average nightly ticket sales will be $1,750. What is the percentage change in the average number of customers the theater has each night? (Express your answer in whole numbers; round decimals up or down).
Attendance with the higher ticket price is ...
... $1750/$7 = 250
So the percentage change in attendance is ...
... change = (new - original)/original × 100%
... = (250 -300)/300 × 100% = -1/6×100% ≈ -17%
Final answer:
The percentage change in the average number of customers after the movie theater raises ticket prices is approximately -17%.
Explanation:
The movie theater originally charges $5 per ticket and has an average of 300 customers each night. After raising the price to $7, the average nightly ticket sales amount to $1,750. To find the new number of customers, divide the total sales by the price per ticket: $1,750 / $7 = 250 customers.
The change in the number of customers is the new amount minus the original amount, which is 250 - 300 = -50. To find the percentage change, divide the change by the original amount and multiply by 100: (-50 / 300) x 100 = -16.67%. After rounding the decimal, the percentage change is approximately -17%.
Manuel's bus ride to school is 9/10 of a mile and Jessica's bus ride is 3/10 of a mile. How much longer is Manuel's bus ride than Jessica's?
A)
6
0
of a mile
Eliminate
B)
12
0
of a mile
C)
6
10
of a mile
D)
12
20
of a mile
The answer us C. 9/10 minus 3/10 is 6/10 simplified to 3/5 if you need it.
Jessica is making gift baskets.each basket has 1 jarof salsa and 1 bag of tortilla chips.she buys the salsa in cases of 6 jars.she buy the tortilla chips in cases of 4 bags what is the least numbers of baskets Jessica can make
The least number of gift baskets Jessica can make, given that she has 6 jars of salsa and 4 bags of tortilla chips in each case, is 12. This is calculated by finding the Least Common Multiple of 6 and 4.
Explanation:Jessica is working with two different quantities: 6 jars of salsa in a case and 4 bags of tortilla chips in a case. In each gift basket, she places 1 jar of salsa and 1 bag of tortilla chips, meaning that she needs the same number of jars and bags for an even number of gift baskets.
Therefore, to find the least number of baskets she can make, we need to find the Least Common Multiple (LCM) of 6 and 4, which the smallest number that both numbers divide evenly into. The LCM of 6 and 4 is 12. Hence, the least number of gift baskets Jessica can make is 12.
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Find the missing number of each unit rate 24/4=?/1 and 40/5=?/1
24/4 = 6/1
40/5 = 8/1
The answer is 6/1 and 8/1.
Best of luck.
The missing number unit rate of 24/4=?/1 is 6 and 40/5=?/1 is 8.
We have to determineThe missing number of each unit rate is 24/4=?/1 and 40/5=?/1.
According to the questionLet the missing number be x.
The missing number is determined by cross multiply and then solving for the value of x.
The missing number is,
[tex]\rm \dfrac{24}{4} = \dfrac{x}{1}\\\\24 \times 1 = x \times 4\\\\24 = 4x\\\\x = \dfrac{24}{4}\\\\x = 6[/tex]
And another missing number is,
[tex]\rm \dfrac{40}{5} = \dfrac{x}{1}\\\\40 \times 1 = 5 \times x\\\\40 = 5x\\\\x = \dfrac{40}{5}\\\\x = 8[/tex]
Hence, the missing number unit rate of 24/4=?/1 is 6, and 40/5=?/1 is 8.
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if quadrilateral RESP is is reflected across the line y = 2x +7 and again across the line y = -12x + 5, what will be the resulting image?
A. The resulting image will be a translation of the pre-image
B. The resulting image will be a rotation of the pre-image
C. The resulting image will be a reflection of the pre-image
D. The resulting image cannot be determined
The first reflection reverses the orientation and alters the direction of the vectors representing the sides of the quadrilateral. The second reflection does the same thing. The end result is that the orientation is unchanged by two reflections, and the direction of the sides of the quadrilateral is changed.
The appropriate choice is ...
... B. The resulting image will be a rotation of the pre-image.
_____
The center of rotation will be the point where the lines cross. (That is the invariant point.)
In the attachment, the green quadrilateral RESP is reflected across the line y=2x+7 (blue) to form the blue quadrilateral R'E'S'P'. That is then reflected across the line y = -12x +5 (orange) to give the orange quadrilateral R"E"S"P", which is a rotation of the pre-image.
The amount of rotation is double the angle between the lines, about 62.7°.
What is the remainder of (x 3 + 5x 2 − 32x − 7) ÷ (x +3)
a store sells rope by the meter The equation p=0.8L represents the price p (in dollars) of a piece of nylon rope that is L meters long. a. How much does the nylon rope cost per meter. b. How long is a piece of nylon rope that costs $1.00
(a) $0.80
(b) 1.25 m
Step-by-step explanation:(a) Put 1 where L is, and evaluate the equation.
... p = 0.8·1 = 0.8
The cost for 1 meter of rope is $0.80.
(b) Put 1 where p is and solve for L.
... 1 = 0.8L
... 1/0.8 = L = 1.25
The length of rope that costs $1 is 1.25 meters.
Answer:
a. $ 0.8
b. 1.25 meters.
Step-by-step explanation:
Given equation that represents the price p (in dollars) of a piece of nylon rope having length L meters,
[tex]p=0.8L[/tex]
a. If L = 1 meter,
The cost of the rope would be,
[tex]p=0.8(1) = \$ 0.8[/tex]
b. if p = $ 1.00,
[tex]\implies 1 = 0.8L[/tex]
[tex]\implies L=\frac{1}{0.8}=1.25[/tex]
Thus, the length of the rope would be 1.25 meters.
a.) Describe a transformation sequence that will transform quadrilateral ABCD into quadrilateral A’B’C’D’.
b.) There is more than one way to transform quadrilateral ABCD into quadrilateral A’B’C’D’. Describe a second sequence of transformations that will accomplish this goal. Explain what tool you used as an aid in identifying a transformation sequence.
a.) The orientation of ABCD is clockwise, as is the orientation of A'B'C'D'. This means the transformation involves a even number of reflections (may be 0). The orientation of AB is North, and the orientation of A'B' is West, so a rotation of 90° CCW (or equivalent) is involved. We can find the point of intersection of the perpendicular bisectors of AA' and BB' (at (-1, -1)) to determine a suitable center of rotation.
ABCD can be transformed to A'B'C'D' by ...
rotation 90° CCW about the point (-1, -1)b.) Rotation by 90° can also be accomplished by reflection across a diagonal line. Since we want the orientation to remain unchanged, we need another reflection to put the figure into its final position. A suitable alternate sequence for mapping ABCD to A'B'C'D' is ...
reflection across the line y=xreflection across the line x=-1The tables show the high and low temperatures in Chicago over a 15-day period. Which set of data has the greatest RANGE?
I would say the low I’m just guessing so get it checked
Answer:
the answer is C
Step-by-step explanation:
The low temperatures have the greater range. The range for the highs is 6, the range for the lows is 8.
Let x = a + bi and y = c + di and z = f + gi Which statements are true? Check all of the boxes that apply. x + y = y + x (x × y) × z = x × (y × z) x – y = y – x (x + y) + z = x + (y + z) (x – y) – z = x – (y – z)
The usual rules of addition and multiplication apply to complex numbers as well as to real numbers. The true statements are ...
x + y = y + x . . . . . . . . . . . . . . . commutative property of addition(x × y) × z = x × (y × z) . . . . . . . . associative property of multiplication(x + y) + z = x + (y + z) . . . . . . . . associative property of additionThe true statements after evaluating the expression based on principle of commutativity and associativity are :
x + y = y + x(x × y) × z = x × (y × z)(x + y) + z = x + (y + z)x = a + bi
y = c + di
z = f + gi
Recall :
Commutative property establishes that, if the ordering of the numbers an addition or multiplication expression, is changed, the result is unchanged : a + b = b + a The Associative property maintains that, the grouping of values in a multiplication operation does not affe t the result of the product. : a × ( b × c) = b × (a × c) = c × (b × a)Evaluating the options :
x + y = y + x ; This is true (Commutative property of addition) (x × y) × z = x × (y × z) (True according to the Associative property) x - y = y - x (False) (x + y) + z = x + (y + z) (True ; Commutative property) (x – y) – z = x – (y – z) (False)Hence, only 3 of the given statements are true, according to the Commutative or Associative rule.
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The cost of making 15 handbags is 1,615. The cost of making 27 handbags is 2,635. What is the cost per handbag ?
In ∆ABC, the altitudes from vertex B and C intersect at point M, so that BM = CM. Prove that ∆ABC is isosceles.
Answer:
Given: ∆ABC with the altitudes from vertex B and C intersect at point M, so that BM = CM.
To prove:∆ABC is isosceles
Proof:-Let the altitudes from vertex B intersects AB at D and from C intersects AC at E( with reference to the figure)
Consider ΔBMC where BM=MC
Then ∠CBM=∠MCB......(1)(Angles opposite to equal sides of a triangle are equal)
Now Consider ΔDMB and ΔCME
∠D=∠E.......(each 90°)
BM=MC...............(given)
∠CME=∠BMD........(vertically opposite angles)
So by ASA congruency criteria
ΔDMB ≅ ΔCME
∴∠DBM=∠MCE........(2)(corresponding parts of a congruent triangle are equal)
Adding (1) and (2),we get
∠DBM+∠CBM=∠MCB+∠MCE
⇒∠DBC=∠BCE
⇒∠B=∠C⇒AB=AC(sides opposite to equal angles of a triangle are equal)⇒∆ABC is an isosceles triangle .
Answer:
m∠MBC = m∠MCB
by reason: Base Angles
Step-by-step explanation:
:)
PLZ HELP ASAP! ILL MARK BRAINLEST!
Factor completely 12x4 + 6x3 + 18x2.
Prime
3(4x4 + 2x3 + 6x2)
3x2(4x2 + 2x + 6)
3x(4x3 + 2x2 + 6x)
Factor completely 7x3y +14x2y3 − 7x2y2.
7x2(xy + 2y3 – y2)
7x2y(x + 2y2 – y)
7(x3y +2x2y3 − x2y2)
Prime
What is the Greatest Common Factor of x6 and x3?
x4
x3
x2
x
Question 1.) Factor completely [tex]12x^{4}+ 6x^{3}+18x^{2}[/tex]
Since [tex]6[/tex] divides all the three terms of the equation, so we take [tex]6[/tex] common out from the equation.
i.e., [tex]6(2x^{4}+ 1x^{3}+3x^{2})[/tex]
Now, since [tex]x^{2}[/tex] divides all the three terms of the equation, so we take [tex]x^{2}[/tex] common out from the equation.
i.e., [tex]6x^{2}(2x^{2}+ 1x+3)[/tex]
Now, this cannot be factored further as [tex]2x^{2}+ 1x+3[/tex] is a quadratic equation and taking out discriminant of it is:
[tex]D = (1)^2 - 4(2)(3)\\ \ \ = 1- 24\\ \ \ = -23<0[/tex]
Since, the discriminant is less than zero. Therefore, the factored form of the given equation : [tex]12x^{4}+ 6x^{3}+18x^{2}[/tex] is : [tex]6x^{2}(2x^{2}+ 1x+3)[/tex]
Question 2.) [tex]7x^{3}y+ 14x^{2} y^{3} - 7x^{2}y^{2}[/tex]
Since [tex]7[/tex] divides all the three terms of the equation, so we take [tex]7[/tex] common out from the equation.
i.e., [tex]7(x^{3}y+ 2x^{2} y^{3} - x^{2}y^{2})[/tex]
Now, since [tex]x^{2}y[/tex] divides all the three terms of the equation, so we take [tex]x^{2}y[/tex] common out from the equation.
i.e., [tex]7x^{2}y(x+ 2y^{2} - y)[/tex]
Therefore, the factored form of the given equation : [tex]7x^{3}y+ 14x^{2} y^{3} - 7x^{2}y^{2}[/tex] is : [tex]7x^{2}y(x+ 2y^{2} - y)[/tex]
Question 3.) What is the Greatest Common Factor of [tex]x^{6}[/tex] and [tex]x^{3}[/tex] ?
The Greatest Common Factor of two numbers is the biggest number which divides both the given numbers completely.
Now, for the expressions [tex]x^{6}[/tex] and [tex]x^{3}[/tex]:
Since, [tex]x^{3}[/tex] divides both the expressions completely and it is the biggest expression which divides both the expressions.
Therefore, [tex]x^{3}[/tex] is the Greatest Common Factor of [tex]x^{6}[/tex] and [tex]x^{3}[/tex]
Answer:
#2 is definatly B
Step-by-step explanation:
Which relation is a function?
the diagram on the top left hand side is a function
For each value of x on the domain (x- axis ) there can only be one corresponding value of y in the range (y- axis)
Apart from the diagram on the top left side, the other 3 all fail this definition
g(x) = 2x − 1 h(x) = 1 − g(x) The functions g and h are defined above. What is the value of h(0)?
Answer:
h(0) is equal to 2.
Step-by-step explanation:
In order to find this, we first put 0 in for x in the g(x) equation.
g(x) = 2x - 1
g(0) = 2(0) - 1
g(0) = -1
Now that we have this, we can stick the answer for g(x) into the f(x) equation.
f(x) = 1 - g(x)
f(x) = 1 - -1
f(x) = 1 + 1
f(x) = 2
The value of [tex]h(0)[/tex] is 2.
It is given that,
[tex]g(x)=2x-1[/tex][tex]h(x)=1-g(x)[/tex]Explanation:
We have,
[tex]h(x)=1-g(x)[/tex]
[tex]h(x)=1-(2x-1)[/tex]
[tex]h(x)=1-2x+1[/tex]
[tex]h(x)=2-2x[/tex]
Substitute [tex]x=0[/tex] in the above function.
[tex]h(0)=2-2(0)[/tex]
[tex]h(0)=2-0[/tex]
[tex]h(0)=2[/tex]
Thus, the value of [tex]h(0)[/tex] is 2.
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write a two column proof
given 4y = 2x - 10 y=6
prove x=17
please help me with this
[tex]4y=2x-10[/tex] and [tex]y=6[/tex]
use the second expression to calculate the left-hand side of the first equation:
[tex]4\cdot 6 = 2x -10\\24 = 2x -10[/tex]
Add 10 to both sides if this equation to get
[tex]34 = 2x[/tex]
and divide both sides by 2
[tex]17 = x[/tex]
this proves that x = 17, give the two initial equations
baseball field.....................
Umm. What is the question?
The design and layout of a Baseball Field Design to the game experience by affecting play flow and ensuring visibility, vital for both players and fans. Elements like the diamond infield and the extensive outfield reflect American sports culture, which emphasizes strategy and skill, and has historically fostered community engagement and identity.
The design and layout of a baseball field significantly impact the experience of the game by determining the flow of play and the visibility of actions, which is crucial for player performance and fan engagement.
Specific elements, such as the diamond shape of the infield and the expansive outfield, align with the American sports culture, which values a balance between strategy and physical skill, offering a variety of play styles from power hitting to meticulous base running.
The historical evolution of professional baseball teams and their ballparks reflects a facet of American identity through sports, as communal spaces like Fenway Park and Forbes Field facilitated a collective civic pride and a space for social interaction among diverse groups including immigrants.
Moreover, participation in sports, even at the informal level of pickup games, represents an integral part of cultural dynamics in American society, aligning with the practice of community building and local support within the cultural geography framework.
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The probable question may be:
How does the design and layout of a baseball field contribute to the overall experience of the game, and what specific elements align with the principles of American sports culture as taught in the curriculum?
What is the value of cosA ?
Answer:
cos(A) = 24/25 = 0.96
Step-by-step explanation:
SOH CAH TOA tells you that ...
... cos(A) = AB/AC
We are given AB = 24, but we must calculate AC using the Pythagorean theorem.
... AC² = AB² + BC²
... AC² = 24² + 7² = 576 + 49 = 625
... AC = √625 = 25
Now, we have sufficient information to find cos(A):
... cos(A) = 24/25 = 0.96
The value of cosA is used in trigonometry and physics to calculate the horizontal component of vectors or the angle of right triangles. For example, if we have a vector A, at an angle θ, then Ax = A cos θ, where Ax is the horizontal component of the vector. So in this way, cosA provides a crucial part in vector calculations.
Explanation:The value of cosA refers to the cosine of angle A. In trigonometry, this is often used in the context of right triangles or in the calculation of vectors. For example, if you have a vector A and an angle θ (theta), the horizontal component of that vector can be found by multiplying the magnitude of the vector (Ax) by cos(θ). This is often denoted as Ax = A cos θ.
To use an example, let's say we have a vector A with a magnitude of 10.3 blocks and an angle of 29.1° from the x-axis. We can find the x-component (Ax) of that vector by calculating (10.3 blocks) * cos(29.1°), which gives us a value of approximately 9.0 blocks.
Therefore, the value of cosA in this context would be used to provide a component part of a vector based on an associated angle.
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Which expression is equivalent to the expression 2/3(3 - 1/3)(-1)?
(i'm doing a giveaway worth 25 points if you get the right.)
2/3 (5/3)(-1) = -10/9
Answer:
-7/9
Step-by-step explanation:
2/3(3 - 1/3)(-1) = (1-2/9)(-1) = -1+2/9 = -7/9
expand the expression 4(3/2x+5)
M is the midpoint of segment AB. A has the coordinates (-5,4) and M is at the origin. Find the coordinates of B
Using geometry:
Since M is the origin, point B is the mirror image of point A with respect to the origin. From the origin to point A, you go 5 units left and 4 units up. For the mirror image, start at the origin, and go 5 units right and 4 units down.
Answer: B(5, -4)
Using the midpoint formula:
[tex] x_m = \dfrac{x_1 + x_2}{2}~~~and~~~y_m = \dfrac{y_1 + y_2}{2} [/tex]
[tex] 0 = \dfrac{-5 + x_2}{2}~~~and~~~0 = \dfrac{4 + x_2}{2} [/tex]
[tex] 0 = -5 + x_2~~~and~~~0 = 4 + x_2 [/tex]
[tex] -x_2 = -5~~~and~~~-4 = x_2 [/tex]
[tex] x_2 = 5~~~and~~~x_2 = -4 [/tex]
Answer: B(5, -4)
As you can see, both methods give you the same answer.
A piece of copper weighed 4⁄5 of a kilogram and a piece of nickel weighed 3⁄5 of a kilogram. How much more did the piece of copper weigh?
You find the difference in weight by subtacting the weight of the nickel from the weight of the copper.
... (4/5 kg) - (3/5 kg) = (4 -3)/5 kg = 1/5 kg
The piece of copper weighed 1/5 kg more than the piece of nickel.
I need help with finding X's value.
Please help it's geometry.
See attachment
The marks on the line segments tell you they are the same length, and that the triangle is an equilateral triangle. That tells you the angles are the same size, and all are 60°. This lets you find x and y.
(7x+4)° = 60°
7x = 56 . . . . . . . . divide by °, subtract 4
x = 8 . . . . . . . . . . divide by 7
_____
(8y+12)° = 60°
8y = 48 . . . . . . . . divide by °, subtract 12
y = 6 . . . . . . . . . . divide by 8
Write the equation of a line that is perpendicular to x = 3 and that passes through the point ( 0 , − 4 )
We have to write the equation of a line that is perpendicular to the line [tex]x=3[/tex] and that passes through the point [tex](0,-4)[/tex].
The general equation of a line in the slope-intercept form is given by:
[tex]y=mx+b[/tex]
Where, 'm' is the slope and 'b' is the y-intercept.
Now, we need to find the slope first,
The required line is perpendicular to the line [tex]x=3[/tex]. Slope of the line [tex]x=3[/tex] is undefined. A line perpendicular to that must have slope of '0'. That implies, our required line is parallel to the x-axis.
Therefore, m=0
Now that line is passing through the point [tex](0, -4)[/tex].
We can plug in the points to the find the value of y-intercept. After plugging the values, we get:
[tex]y=0 \times 0+(-4)=-4[/tex]
Hence, the equation of the required line is [tex]y=-4[/tex].
What is the solution of sqrt2x+4=15
Answer:
x = 126
Step-by-step explanation:
Square both sides of the equation. (sqrt2x+4)^2 = 16^2
2x+4 = 256
Then you should solve for x. (First Subtract 4 from both sides; Then simplify; Next divide both sides by 2; Finally, simplify once more)
This should give you your answer. (x = 126)
Hope this helps! ^-^
Answer:
x = 72
Step-by-step explanation:
sqrt {2x} +4 = 16
sqrt {2x} = 12
2x = 12 ^ 2
x = 144/2
x = 72
If you wanted to write:
sqrt {2x + 4} = 16
2x + 4 = 16 ^ 2
2x + 4 = 256
2x = 252
x = 252/2
x = 126
Use the given information to find the lengths of the other two sides of the right triangle if side a is opposite angle A, side b is opposite angle B, and side c is the hypotenuse.
cos(B) = 4/5, a = 8
SOH CAH TOA tells you
... cos(B) = a/c
... 4/5 = 8/c
... c = 10 . . . . . multiply by 5c/4
By the Pythagorean theorem,
... b = √c² -a²) = √(10² -8²) = √36 = 6
The lengths of the other two sides are: b = 6, c = 10.
_____
You can tell from the value of the cosine that this is a 3-4-5 right triangle. You can tell from the value of "a" that the scale factor is 2. That means the other two sides are 6 and 10.
To find the lengths of the other two sides of the right triangle, we can use the Pythagorean theorem and the cosine function. Side a is given as 8 and the cosine of angle B is given as 4/5. Using the cosine function, we can find the length of side b. Then, using the Pythagorean theorem, we can find the length of side c. The lengths of the other two sides are approximately 6.4 and 10.24, respectively.
Explanation:To find the lengths of the other two sides of the right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse. In this case, we are given that side a is opposite angle A and has a length of 8, and we are given the cosine of angle B, which is 4/5. We can use the cosine function to find the length of side b, and then use the Pythagorean theorem to find the length of side c.
Step 1: Use the cosine function to find the length of side b:
cos(B) = 4/5
b/a = cos(B)
b/8 = 4/5
b = (4/5) * 8
b = 32/5
b = 6.4
Step 2: Use the Pythagorean theorem to find the length of side c:
a² + b² = c²
8² + 6.4² = c²
64 + 40.96 = c²
104.96 = c²
c = √104.96
c ≈ 10.24
Therefore, the lengths of the other two sides of the right triangle are approximately 6.4 and 10.24, respectively.
A line is drawn so that is passes through the points (-4,0) and (2,3) what is the slope of the line
-1/2
1/2
-2
2
you would use the form y2-y1/x2-x1 so in this case it would be 3-0/2+4 which would be 3/6 but simplify your answer and you get would be 1/2 so your answer is 1/2
slope = [tex]\frac{1}{2}[/tex]
to calculate the slope m use the gradient formula
m = ( y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 4, 0 ) and (x₂, y₂ ) = (2, 3)
m = [tex]\frac{3-0}{2+4}[/tex] = [tex]\frac{3}{6}[/tex] = [tex]\frac{1}{2}[/tex]
Luna's monthly mortgage payment was $2100 last year, and on average, 9% of each payment was interest. If Luna itemizes deductions on her federal income tax return, how much can she deduct for mortgage interest?
Answer:
$2268
Step-by-step explanation:
Luna's total mortgage payments for the year would be
... (monthly payment)×(number of months in a year)
... = $2100×12 = $25,200
Of that, 9% went to interest, so the interest amount is ...
... $25,200×9% = $2268
_____
About percentages
Your calculator may do percentages directly. If not, it can be helpful to realize that the percent symbol (%) means the same thing as /100 (divided by 100). So, 9% = 9/100 = 0.09
Answer:
$2268
Step-by-step explanation:
did it on apXX