The formulas for the exponential functions that pass through the two points given are:
f(x) = 6 * 7^x
g(x) = 1280 * 0.125^x
To find the formula for an exponential function that passes through two points, we can use the general form of an exponential function, which is f(x) = a * b^x, where a and b are constants. We can plug in the x and y values from the two points and solve for a and b.
For part a:
f(x) = a * b^x
6 = a * b^0 (from point (0,6))
294 = a * b^2 (from point (2,294))
From the first equation, we can see that a = 6. We can substitute this value into the second equation:
294 = 6 * b^2
49 = b^2
b = 7
So the formula for the exponential function that passes through the two points is f(x) = 6 * 7^x.
For part b:
g(x) = a * b^x
1280 = a * b^0 (from point (0,1280))
20 = a * b^2 (from point (2,20))
From the first equation, we can see that a = 1280. We can substitute this value into the second equation:
20 = 1280 * b^2
0.015625 = b^2
b = 0.125
So the formula for the exponential function that passes through the two points is g(x) = 1280 * 0.125^x.
In conclusion, the formulas for the exponential functions that pass through the two points given are:
f(x) = 6 * 7^x
g(x) = 1280 * 0.125^x
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I bought a toy car for $7.55, a pizza for $3.75 and a pencil for $0.75. How much money did I spend altogether?
Answer:
To find the total amount of money spent on the toy car, pizza, and pencil, we simply need to add the individual prices together:
$7.55 (toy car) + $3.75 (pizza) + $0.75 (pencil) = $12.05
Therefore, you spent $12.05 altogether on the toy car, pizza, and pencil.
 which of the following table, represents a linear relationship that is also proportional?
All of Four table shows the proportionality.
What is Proportionality?Proportionality refers to any relationship that always has the same ratio. For example, the amount of apples in a crop is proportionate to the number of trees in the orchard, with the proportionality ratio being the average number of apples per tree.
To the proportionality we have to find the rate change of each table
Table 1:
Rate of change
= (4-2)/ (4-0)
= 2/4
= 0.5
Again, (6-4)/ (8-4)
= 2/4
= 0.5
As, the rate of change is constant then the table shows the proportionality.
Table 2:
Rate of change
= (1-0)/ (2-0)
= 1/2
= 0.5
Again, = (2-1)/ (4-2)
= 1/2
= 0.5
As, the rate of change is constant then the table shows the proportionality.
Table 3:
Rate of change
= (3-1)/ 5-0)
= 2/5
= 0.4
Again, (5-3)/ (10-5)
= 2/ 5
= 0.4
As, the rate of change is constant then the table shows the proportionality.
Table 4:
Rate of change
= (7-3)/ (3-0)
= 4/3
Again, (11-7)/ (6-3)
= 4/3
As, the rate of change is constant then the table shows the proportionality.
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The exact same experiment was conducted 15 times. How many times should the results have been similar for them to be valid?
A. 6
B. 15
C. 9
D. 8
Convert the following angles measures to degrees or radius.
Answer:
a) [tex]\frac{2\pi }{3}[/tex]
b) 330
Work:
a) To convert degrees to radians you multiply by [tex]\frac{\pi }{180}[/tex]
[tex]\frac{120}{1}[/tex] x [tex]\frac{\pi }{180}[/tex]
= [tex]\frac{6}{1}[/tex] x [tex]\frac{\pi }{9}[/tex]
= [tex]\frac{2\pi }{3}[/tex]
b) To convert radians to degrees you multiply by [tex]\frac{180}{\pi }[/tex]
[tex]\frac{11\pi }{6}[/tex] x [tex]\frac{180}{\pi }[/tex]
= [tex]\frac{11}{1}[/tex] x [tex]\frac{30}{1}[/tex]
= 330
Help similar triangles
The value of x for the similar triangles is 57.5 units.
What is the value of x?The value of x is determined by applying the principle of similar triangles as shown below.
In the given diagram, we can assume the following for the similar triangles;
length 46 is congruent to length (16 + 46)
length 20 + x is congruent to length x
So we will have the following equation;
46/x = (16 + 46 ) / ( 20 + x )
46/x = ( 62 ) / ( 20 + x )
46 ( 20 + x ) = 62x
920 + 46x = 62x
920 = 16x
x = 920 / 16
x = 57.5
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A lithotripter of height 15 cm and diameter 18 cm is to be constructed from a semi-ellipse. High energy underwater shock waves will be emitted from the focus that is closest to the vertex V in order to break down the kidney stone. How far from V in the vertical direction should a kidney stone be located to receive the greatest effect of the shock waves?
Answer:
27 cm
Step-by-step explanation:
You want the distance from the vertex of an ellipse to the opposite focus if the semi-major axis is 15 cm, and the minor axis is 18 cm.
Center to focusThe square of the distance from the center to either focus is the difference of the squares of the semi-axes. The semi-minor axis is half the diameter of the ellipsoid.
c² = 15² -(18/2)² = 225 -81 = 144
c = √144 = 12 . . . . . cm
Vertex to focusThe distance from the vertex (V) to the opposite focus is the distance from vertex to center plus the distance from center to focus:
15 cm +12 cm = 27 cm
The kidney stone should be located 27 cm from the vertex for greatest effect.
If you have a triangle and one of the side is 3cm the other two are 5cm. And the pre-image of that triangle is 8cm and the other two sides are still 5cm what happend to the triangle? Is it a reflection,` reduction, rotation, dilation, or a enlargment? PLEASE ANSWER QUICKLY PLEASE!!!!
Answer:
It is not clear what you mean by "pre-image" in this context. However, based on the given information, we can say that the second triangle is a dilation of the first triangle.
A dilation is a transformation that changes the size of an object, but not its shape. In this case, the second triangle has the same shape as the first triangle, but its sides are scaled up by a factor of 8/3, which is greater than 1. Therefore, the second triangle is an enlargement (or a magnification) of the first triangle.
Answer: Your welcome!
Step-by-step explanation:
The transformation of the triangle is a reduction. This is because the side of the triangle that was 3 cm has been reduced to 8 cm, while the other two sides have stayed the same. This reduction has resulted in the triangle being smaller than the original triangle.
On a certain route, an airline carries 9000 passengers per month, each paying $150. A market survey indicates that for each$1 decrease in the ticket price, the airline will gain 50 passengers. Express the monthly revenue for the route, R, as a function of the ticket price, x.
The monthly revenue for the route, R, as a function of the ticket price, x, can be expressed as R(x) = (9000 + 50(150 - x))x.
The airline carries 9000 passengers per month, and each pays $150, so the initial monthly revenue is R(150) = 9000 x $150 = $1,350,000.
If the ticket price is decreased by $1, the airline will gain 50 passengers, so the new monthly revenue can be calculated by adding the revenue gained from these additional passengers to the initial revenue, and subtracting the revenue lost from the decrease in ticket price. The revenue gained from the additional passengers is 50(x - $150), since each passenger pays the new ticket price x instead of $150. The revenue lost from the decrease in ticket price is 9000($150 - x), since each of the 9000 passengers pays $150 - x instead of the initial price of $150.
Putting these together, we get:
[tex]R(x) = R(150) + 50(x - $150) - 9000($150 - x)[/tex]
R(x) = (9000 x $150) + 50x - 50($150) - 9000($150) + 9000x[tex]R(x) = R(150) + 50(x - $150) - 9000($150 - x)[/tex]
[tex]R(x) = (9000 + 50(150 - x))x[/tex]
Thus, the monthly revenue for the route, R, as a function of the ticket price, x, is [tex]R(x) = (9000 + 50(150 - x))x[/tex]
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(a) Let E be an intermediate field of the extension K⊂F and assume that E=K(u1,…,ur)
where the ui are (some of the) roots of fεK [x]. Then F is a splitting field of f over K if and only if F is a splitting field of f over E. (b) Extend part (a) to splitting fields of arbitrary sets of polynomials.
All the roots of all the polynomials in {f1, ..., fn}.
(a) Let E be an intermediate field of the extension K⊂F and assume that E=K(u1,…,ur) where the ui are (some of the) roots of fεK [x]. Then F is a splitting field of f over K if and only if F is a splitting field of f over E.
(b) We can extend part (a) to splitting fields of arbitrary sets of polynomials by first noting that the field E must contain the coefficients of all the polynomials in the given set. This implies that for a given set of polynomials {f1, ..., fn}, the field F is a splitting field over K if and only if it is a splitting field over E, where E is the smallest field containing the coefficients of {f1, ..., fn}. In other words, F must contain all the roots of all the polynomials in {f1, ..., fn}.
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Find the distance between Point A and Point B. Enter your answer in the box.
51Y
4
-3
2
1
0
X
0 1 2 3 4 5
10
A
Check the picture below.
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{2}~,~\stackrel{y_1}{1})\qquad B(\stackrel{x_2}{5}~,~\stackrel{y_2}{5})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ AB=\sqrt{(~~5 - 2~~)^2 + (~~5 - 1~~)^2} \implies AB=\sqrt{( 3 )^2 + ( 4 )^2} \\\\\\ AB=\sqrt{ 9 + 16 } \implies AB=\sqrt{ 25 }\implies AB=5[/tex]
Help with my home work
Using the given functions: f(x)=2x^(2)-5x-3,g(x)=x-3 and h(x)=2x+5, what is the product of (g*f)(x) ? 2x^(3)+11x^(2)+18x+9 2x^(3)-z^(2)-18x+9 2x^(3)-x^(2)-12x+9
Using the given functions, the product of (g*f)(x) is 2x³ - 11x² + 12x + 9.
A relation between a set of inputs having one output each is called a function. The product of (g*f)(x) can be found by multiplying the functions f(x) and g(x) together.
Since f(x) = 2x² - 5x - 3 and g(x) = x - 3, then the product of (g*f)(x) can be solved as follows:
(g*f)(x) = g(x)*f(x) = (x - 3)(2x² - 5x - 3)
Use the distributive property:
(g*f)(x) = 2x³ - 5x² - 3x - 6x² + 15x + 9 = 2x³ - 11x² + 12x + 9.
Therefore, the correct answer is 2x³ - 11x² + 12x + 9.
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Solve this system of equations: y=x-4 y=6x - 10
The system of equations are solved and the value of x and y are 6/5 and -14/5 respectively
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
y = x - 4 be equation (1)
y = 6x - 10 be equation (2)
On simplifying , we get
x - 4 = 6x - 10
Subtracting x on both sides , we get
5x - 10 = -4
Adding 10 on both sides , we get
5x = 10 - 4
5x = 6
Divide by 5 on both sides , we get
x = 6/5
So , the value of y = ( 6/5 ) - 4
y = -14/5
Hence , the value of x and y are 6/5 and -14/5 respectively and the equations is solved
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log2(9x^10/y²)
Can someone explain it step by step?
Answer:
We can use the properties of logarithms to simplify this expression:
log2(9x^10/y²) = log2(9) + log2(x^10) - log2(y²)
Now we can apply the power rule of logarithms to the second term:
log2(x^10) = 10 log2(x)
Substituting back into the original expression:
log2(9x^10/y²) = log2(9) + 10 log2(x) - log2(y²)
This is the simplified form of the expression.
Evaluate log3 3^(2x+1)
[tex]\begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ \stackrel{ \textit{let's use this one} }{log_a a^x = x}\qquad \qquad a^{log_a (x)}=x \end{array} \\\\[-0.35em] ~\dotfill\\\\ \log_3(3^{2x+1})\implies 2x+1[/tex]
cancelleddddddddddddddddddd
Answer:
Step-by-step explanation:
2
Alice went to a toy store. She paid for 2 jigsaw
puzzles and 4 packs of cards with 3 ten dollar bills.
The price for a pack of cards is $2. She received
$4 in change.
What was the total cost of the 2 jigsaw puzzles?
A $9
B $18
C $22
D $26
Answer:
Alice paid for the 4 packs of cards with 4 x $2 = $8.
She used 3 ten dollar bills, which is 3 x $10 = $30.
Therefore, the cost of the 2 jigsaw puzzles is:
Total cost of the purchase - Cost of the packs of cards
= ($30 + $4 change) - $8
= $26
So, the total cost of the 2 jigsaw puzzles was $26.
The answer is (D) $26.
Answer:
C. $22
Step-by-step explanation:
You have $30, then you multiply 4x2=8(Price of the Cards)
next subtract the $8 from $30 (30-8)
Your final answer is 22
What mass of MgBr₂ in grams are in 215 mL of a 0. 350 M solution of MgBr₂?
Taking into account the definition of molarity, the mass of MgBr₂ in 215 mL of a 0.350 M solution of MgBr₂ is 13.85 grams.
Definition of molarityMolarity is a measure of the concentration of a solution expressed in the number of moles dissolved per liter of solution.
This is, the molarity indicates the number of moles of solute that are dissolved in a given volume.
The molarity of a solution is calculated by dividing the moles of solute by the volume of the solution:
molarity= number of moles of solute÷ volume
Molarity is expressed in units moles/L.
Definition of molar massThe molar mass of substance is a property defined as the amount of mass that a substance contains in one mole.
Mass of MgBr₂In this case, you have:
Molarity= 0.350 MNumber of moles of solute= ?Volume= 215 mL= 0.215 L (being 1000 mL= 1 L)Replacing in the definition of molarity:
0.350 M= number of moles of solute÷ 0.215 L
Solving:
0.350 M× 0.215 L= number of moles of solute
0.07525 moles= number of moles of solute
Being the molar mass of MgBr₂ 184.11 g/mole, the mass of the compound is calculated as:
mass of MgBr₂= 0.07525 moles× 184.11 g/mole
mass of MgBr₂= 13.85 grams
Finally, the mass of MgBr₂ is 13.85 grams.
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The graph of f(x)=x^2 was transformed to create g(x)=2/3x^2 Mark the statement. True or False
The graph of g(x) will be wider than f(x)
Graph of g(x) will be wider than f(x) is false.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
The graph of f(x)=x² was transformed to create g(x)=2/3x².
The transformation applied to f(x) to create g(x) is a vertical compression by a factor of 2/3.
This means that the graph of g(x) will be narrower than the graph of f(x), not wider.
Specifically, the parabola of g(x) will be compressed vertically towards the x-axis by a factor of 2/3, making it more pointy than the original graph of f(x).
Hence, graph of g(x) will be wider than f(x) is false.
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An indoor soccer field can be rented for personal use. The total cost for renting the field can be found by using the equation y= 225x. The x-variable is the number of hours the field is
being rented, and the y-variable is the total cost, in dollars.
Which statement is true based on the given equation?
A) The equation shows a linear relationship, but not a proportional relationship.
B) The equation shows a linear relationship and a proportional relationship
C) The equation does not show a linear relationship or a proportional relationship
D) The equation shows a proportional relationship,but not a linear relationship.
PLS HELP!!
Answer:
The equation y=225x represents a proportional relationship between the number of hours the field is being rented and the total cost. This means that as the number of hours increases, the total cost will increase proportionally. Therefore, statement D) "The equation shows a proportional relationship, but not a linear relationship" is true based on the given equation.
Select all the expressions that have the same value 892 ÷ 7.
answer choices
A. 8920 ÷ 80 =
B. 894 ÷10 =
C. 89.2 ÷ 0.08 =
D. 8.92 ÷ 0.8 =
E. 892 ÷ 0.008 =
Answer: if there is a none of the above answer I would choose that otherwise your best bet might be A.
PLEASE HELP ME PLEASE I BEG YOU THIS IS VERY IMPORTANT!!! Classify the figure using the terms in the boxes. Write the letter of the figure in the correct box. A figure may be classified using more than one term.
Shape A is Convex and Hexagon.
Shape B is Concave and Hexagon.
Shape C is Convex and Pentagon.
Shape D is Concave and Hexagon.
Shape E is Concave and Pentagon.
Shape F is Convex and Pentagon.
What is a Polygon?Polygons are closed figures which has at least three set of line segments joined together.The polygon with the least number of sides is a triangle.
As per the given data:
The shape of the figures is given.
The shapes can be classified as:
Concave, Convex, Hexagon, Pentagon.
Concave polygons are the one with alteast one of the vertices pointing inwards toward the shape.
Convex polygons are the one with all the vertices pointing outwards from the shape.
A Hexagon can be defined as a closed two-dimensional polygon with six sides.
A Pentagon can be defined as a closed two-dimensional polygon with five sides.
Consider the shape A:
It has 6 sides and all vertices pointing outwards.
Shape A is Convex and Hexagon.
Consider the shape B:
It has 6 sides and some vertices pointing inwards.
Shape B is Concave and Hexagon.
Consider the shape C:
It has 5 sides and all vertices pointing outwards.
Shape C is Convex and Pentagon.
Consider the shape D:
It has 6 sides and one vertice pointing inwards.
Shape D is Concave and Hexagon.
Consider the shape E:
It has 5 sides and one vertice pointing inwards.
Shape E is Concave and Pentagon.
Consider the shape F:
It has 5 sides and all vertices pointing outwards.
Shape F is Convex and Pentagon.
Hence, Shape A is Convex and Hexagon. Shape B is Concave and Hexagon. Shape C is Convex and Pentagon. Shape D is Concave and Hexagon. Shape E is Concave and Pentagon. Shape F is Convex and Pentagon.
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A group of friends wants to go to the amusement park. They have no more than $425 to spend on parking and admission. Parking is $14.75, and tickets cost $18.75 per person, including tax. Which inequality can be used to determine x, the maximum number of people who can go to the amusement park? 425 18.75(x + 14.75), 425 14.75 +18.75x 4252 14.75 +18.75, 425 18.75(x + 14.75)
Answer:
14.75 + 18.75x ≤ 425
Step-by-step explanation:
Total amount they have is $425
Parking for the entire group = $14.75
If x is the number of persons in the group, the cost of x tickets at $18.75 per head
= 18.75x
The total cost incurred
= Parking Cost + Ticket Cost
= 14.75 + 18.75x
This has to be less than equal to 425
So the inequality is
14.75 + 18.75x ≤ 425
i cannot make out the given answer choices clearly, it appears the constant 425 is on the left side in each answer choice - choose the one which is closest to the given answer
3/4d-11=1/4d-6 1/2 please help!!!
The solution for d in the one-variable equation as required to be determined is; d = 9.
What is the value of d in the given equation?As evident in the task content; the given equation is;
3/4d - 11 = 1/4d - 6½
¾d - 11 = ¼d - 13/2
Therefore, we have that;
¾d - ¼d = 11 - 13/2
½d = 9/2
d = 9
Ultimately, the value of d which holds true for the given equation is; 9.
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The equations y1 = 2x + 1 and intersect at a point. After three cycles of successive approximation, without rounding the answers, the approximate x-value of the point of intersection is
The intersection point on the graph has an approximate x-value of 1a.
Describe graphs?Making the curve that represents a function on a coordinate plane is the process of graphing a function. If the curve (or graph) represents the function, then each point on the curve will satisfy the function equation.
The line, also called the "curve," has a point at each point that fulfils the function.
The three lines are contemporaneous if they all cross at the same point.
From the second equation,
x = 8y + 19
Putting value of x,
2(8y + 19) + 3y = 0 9(8y + 19) + 5y = 17
16y + 38 + 3y = 0 72y + 171 + 5y = 17
19y = -38 77y = -154
y = -2 y = -2
You'll see that the y value for the answer is the same for the two equations. Simply evaluate the second equation now to find x. Hence, we are aware that the y-coordinate is negative two at some x number.
x = 8(-2) + 19
x = -16 + 19
x = 3
The single point that these three equations share is (3, -2).
4x - 3y = 13 eq1
-6x + 2y = -7 eq2
Use the elimination method. Multiply eq1 by eq2 and multiply eq2 by eq3.
8x - 6y = 26 eq1
-18 + 6y = -21 eq2
Adding the equations to eliminate the y terms.
-10x = 5
x = -1/2
Substituting this value of x into any of the equations to solve for the value of y.
Substituting the first equation into the second equation. In terms of x, this will translate the second equation. From that freshly created equation, find x. Once you solved for x, substitute that value of x into the first equation to solve for y.
You have a vertical line that passes all points that have the x coordinate 7 and you have a horizontal line that passes all point that have the y coordinate -5.
If you were to graph these two lines, they will be intersecting at (7, -5).
Now, draw the following lines on a coordinate system:
i) A vertical line passing through the points (3, 0).
ii) A horizontal line passing through the point (0, 6).
iii) A line passing through the points (0,0) and (1, -3).
Once you have drawn these lines, look for 3 points of intersection.
Area = (base × height) / 2
Lines that have the same slope never intersect. Put both equations in y=mx+b form where the slope is the coefficient of x.
2x + 3y = > 3y = -2x + 23
y = (-2 / 3) x + 23/3
7x + py = 8
py = -7x + 8
y = (-7 / p) x + 8/p
Set the slopes equal to each other.
-2 / 3 = -7 / p
Cross-multiply.
-2p = -21
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A machine can fill 24 jars of honey in 30 seconds create an equation that represents filling y jars of honey in c seconds move the correct answer to each box not all answers will be used
The equation representing filling y in x seconds is given as;
y = 0.8x. Option B
What are algebraic expressions?Algebraic expressions are defined as expressions that are composed of terms, variables, constants, coefficients and factors.
They are expressions that are also identified with some mathematical operations, they are;
SubtractionMultiplicationDivisionBracketParenthesesAdditionFrom the information given, we have that;
24 jars are filled in 30 seconds
Then, for y number of jars of honey, we have x seconds
cross multiply the values, we have;
y = 24x /30
divide the values
y = 0. 8x
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Look for a pattern in the table. Find the missing addends and sums
Looking at the table, we can see that the addends follow a pattern where each subsequent pair of addends adds up to 1/5. Specifically, the missing addend is 2/5 - 3/10, which equals 1/10. The missing sums are 1/2 and 4/10.
The addends in the table are as follows:
1/10 + 1/5 = 3/10, 1/5 + 1/5 = 2/5
3/10 + 1/5 = 1/2
We can observe that the first two pairs of addends add up to 1/5 less than the subsequent sums. This pattern indicates that the missing addend must be
1/5 - 1/10 = 1/10
which would make the third pair of addends add up to
1/2 - 1/10 = 4/10
Therefore, the missing sums are 1/2 and 4/10, respectively. This pattern can be helpful in solving similar problems where pairs of addends add up to a specific sum or difference.
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Does someone mind helping me with this problem? Thank you!
Answer:
832
Step-by-step explanation:
The first step is to add 1 + 0.65 which is 1.65. Then you do 1.65 times itself 7 times which equals 33. You multiply 33 • 25 which is 832.
What is the height (in inches) of a triangle with an area of 720
square inches and base of 32 inches?
The height (in inches) of a triangle with an area of 720 square inches and base of 32 inches is 45 inches.
The height of a triangle can be found using the formula for the area of a triangle: A = (1/2)bh, where A is the area, b is the base, and h is the height.
In this case, we are given the area (720 square inches) and the base (32 inches) and are asked to find the height.
First, we can plug in the given values into the formula:
720 = (1/2)(32)(h)
Next, we can simplify the equation by multiplying both sides by 2:
1440 = 32h
Finally, we can solve for the height by dividing both sides by 32:
h = 45 inches
Therefore, the height of the triangle is 45 inches.
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For every tile you draw in a game, you lose 5 points. For every tile you play, you gain 3 points. What is your score if you draw 9 tiles and play 12 tiles?
Answer:
Your score is -9.
Step-by-step explanation: