The area of the triangle is 128 square inches.
How to find the area of the triangle
To find the area of a triangle, you can use the formula:
Area = (1/2) * base * height
In this case, the base of the triangle is 32 inches and the height is 8 inches.
Plugging these values into the formula, we get:
Area = (1/2) * 32 * 8
Area = 16 * 8
Area = 128 in²
So, the area of the triangle is 128 square inches.
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A triangle is shown in the image. A triangle with a height of 8 inches. The height is perpendicular to the base labeled 32 inches. The side from the top of the perpendicular side to the base is labeled 28 inches. What is the area of the triangle? 256 in2 224 in2 128 in2 112 in2
50 Points! Algebra question, photo attached. Please show as much work as possible. Thank you!
Michio's answer not correct. He made a mistake when he was trying to convert the equation to logarithmic form. The right answer is 2.57
What is the right way Michio could have converted to logarithmic form?Looking at the equation 2(3)ˣ = 34, the best way to convert to logarithm is by isolating x.
we divide 2(3)ˣ = 34 by 2 on both side.
= (3)ˣ = 17
In logarithm form 3 becomes the base of the log
x = log₃(17)
x= 2.578
The answer above is based on the information seen in the picture.
Michio wanted to find the value of x in the equation 2(3)ˣ = 34. He first converted the equation to log₃2x = 17. Next, he wrote 2x = 3¹⁷ and used a calculator to find x = 64,570,081.5. Was his answer correct? If not, what was his mistake and what is the right answer? Justify your answer.
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HELP PLEASE I REALLY NEED HELP ON THIS QUESTION HELP!
The number for which the theoretical probability matches the experimental probability is 2.
What is experimental and theoretical probability?
Experimental probability and theoretical probability are two different ways to determine the likelihood of an event occurring.
Experimental probability is determined by performing an experiment or conducting observations and collecting data to see how often an event occurs. This method involves counting the number of times an event occurs and dividing that number by the total number of trials or observations.
Theoretical probability, on the other hand, is determined by using mathematical principles and calculations to determine the likelihood of an event occurring. It is based on the assumption that all outcomes are equally likely.
In the given table;
For theoretical, P(2) = 1/4
For experimental, P(7) = 7/28 = 1/4
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James is performing statistical analysis to determine whether the effects of the treatment in his experiment might actually have reflected a chance occurrence; Kendra is performing an analysis to combine the results of a number of experiments to yield an overall conclusion. James is performing a _____, Kendra, a _____.
Hello !
James is performing statistical analysis to determine whether the effects of the treatment in his experiment might actually have reflected a chance occurrence; Kendra is performing an analysis to combine the results of a number of experiments to yield an overall conclusion. James is performing a significance test, Kendra, a meta-analysis.
i need answer for this with explanation
Answer:
53yd
Step-by-step explanation:
SA1 = 2(4×2)
= 2×8
= 16
SA2 = 2(4×3)
= 2×12
= 24
SA3 = 2(3×2)
= 2×6
= 12
TOTAL SA
16+24+13
= 53
This is so hard. Can you help me with this?
Answer: 70, 6
Step-by-step explanation:
(a) For <F that is the same as <D. The image has little hash marks to indicates the sides across from those angles are the same; therefore, the angles are the same
All of the angles are = 180 if you subtract <E, you are left with 140 to be split between <F and <D
<F= 70
(b) all of the sides are the same because all the angles are the same
so AB=6
In the first stanza, how does the Pebble's exaggeration of its
accomplishments add to the author's purpose?
It introduces the Pebble's fear of being trampled.
It illustrates the Pebble's disappointment in nature.
It establishes impossible expectations for the Acorn.
It shows a connection between the Acorn and nature.
In the stanza, the exaggeration establishes impossible expectations for the Acorn.
How is exaggeration used here?In the outset, the Pebble boastfully consigns itself as the "boldest" and "hardiest" formation in the woodlands.
On the other hand, the Acorn is portrayed as a feeble and delicate being--establishing unreachable objectives for it to accomplish for transforming into an authoritative and resilient Oak tree.
This distinction evokes a sense of tribulation that need to be overcome by the Acorn in order to attain its full potential.
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If a1 =9 and an n-1 +2 then find the value of a5
Given that a₁ = 9 and aₙ = aₙ₋₁ + 2 , we can find the value of a5 by repeatedly applying the recursive formula to find a₂, a₃, a₄, and a₅.Using this method, we get a₅ is 17.
The given sequence is not defined explicitly. However, we can use the recursive formula to find the value of a5.
a₁ = 9 and aₙ = aₙ₋₁ + 2 for n > 1
To find a₂, we use the recursive formula
a₂ = a₁ + 2 = 9 + 2 = 11
To find a₃, we use the recursive formula
a₃ = a₂ + 2 = 11 + 2 = 13
To find a₄, we use the recursive formula
a₄ = a₃ + 2 = 13 + 2 = 15
To find a5, we use the recursive formula
a₅ = a₄ + 2 = 15 + 2 = 17
Therefore, the value of a₅ is 17.
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What is the standard form of the equation for the circle
A. (X-3)^2+(y-2)^2=32
The standard form of the equation for the circle is (x - 3)² + (y - 2)² = 8.
What is the equation of a circle?In Mathematics and Geometry, the standard form of the equation of a circle is represented by the following mathematical equation;
(x - h)² + (y - k)² = r²
Where:
h and k represents the coordinates at the center of a circle.r represents the radius of a circle.Note: A center that lies on the y-axis simply means the value of h on the x-axis is equal to 0.
Based on the information provided above, we have the following parameters:
Radius, r = √[(3 - 5)² + (2 - 4)²] = √8
Center, (h, k) = (3, 2).
By substituting the given parameters into the equation of a circle formula, we have the following;
(x - h)² + (y - k)² = r²
(x - 3)² + (y - 2)² = (√8)²
(x - 3)² + (y - 2)² = 8.
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Complete Question:
A circle is shown on the coordinate plane. The graph shows a circle with the origin point A at (3, 2), and a point B on its circumference at (5, 4) and intersects the x-axis at 1 and 5 units. What is the standard form of the equation for the circle?
The students in Ms. Deans chemistry class are exploring chemistry by creating milk art with food coloring, milk, and dish soap. Ms. Dean plans to give each of her 28 students 0.5 cups of milk. How many pints of milk does Ms. Dean need
The number of bacteria present after 13 hours
The number of bacteria present after 13 hours is 5,306.
What is the number of bacteria after 13 hours?
The number of bacteria present after 13 hours is calculated by applying half-life equation.
N = N₀ x 2^(t / d)
Where:
N₀ is the initial number of bacteria (3,000)N is the final number of bacteria we want to findt is the time elapsed d is the doubling time of the bacteria populationSince the bacteria population grew from 3,000 to 3,600 in 6 hours, the value of d is calculated as follows;
3,600 = 3,000 x 2^(6 / d)
3600/3000 = 2^(6 / d)
1.2 = 2^(6 / d)
log2 (1.2) = 6/d
0.38 = 6/d
d = 6/0.38
d = 15.8 hours
The number of bacteria after 13 hours is calculated as follows;
N = 3,000 x 2^(13 / 15.8)
N = 5,306.5 ≈ 5,306
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The complete question is below:
A culture started with 3,000 bacteria. After 6 hours, it grew to 3,600 bacteria. Predict how many bacteria will be present in 13 hours. round your answer to the nearest whole number.
help please i need help with this answer
The initial value (a) of the exponential function f(x) = 4ˣ is 1.
How to solve an exponential equation?The standard form of an exponential equation is:
y = abˣ
where a is the initial value and b is the multiplication factor.
If b > 1, it is a growth function and if b < 1, it is a decay function.
Given the exponential function:
f(x) = 4ˣ
The initial value (a) = 1 and the multiplication factor (b) = 4.
The graph of the exponential function f(x) = 4ˣ is attached below.
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Suppose a stock drops in value by 60% one week then increases in value the next week by 75% is the value higher or lower then when u started and by how much
The value of the stock at the end of the two weeks would be 70, which is 30% lower than the starting value of 100.
What is Algebraic expression ?
An algebraic expression is a combination of variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponents, and roots. It typically represents a mathematical relationship or formula and can be used to solve problems and make predictions.
Assuming you started with a value of 100, the value of the stock would be lower after these two weeks.
In the first week, the stock dropped by 60%, which means its value decreased to 40% of its original value. Therefore, the value of the stock at the end of the first week would be:
100 * 0.4 = 40
In the second week, the stock increased in value by 75%. Therefore, the value of the stock at the end of the second week would be:
40 * 1.75 = 70
Therefore, the value of the stock at the end of the two weeks would be 70, which is 30% lower than the starting value of 100.
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How many seconds does the ball reach its maximum height using the equation
h(t)= -0.2t^2 + 2t
5 seconds.
Step-by-step explanation:1. Find the "x" position of the vertex of the equation.In a function expressing altitute (h) in terms of time (t), finding the vertex will provide the time and altitute when the object reaches the maximum height. Therefore, let's use the vertex formula to see exactly when this happens:
"x" vertex value: [tex]-\dfrac{-b}{2a}[/tex]
a) For using that equation, first write the given equation on its standard form.
Standard form of quadratic equations: [tex]ax^{2} +bx+c=0[/tex]
b) You can substitute h(t) by 0 on the origina equation:
[tex]-0.2t^{2} +2t=0[/tex]
c) Idenfity the coefficients.
a= -0.2, beacuse "t²" is being multiplied by -0.2.
b= 2, beacuse "t" is being multiplied by 2.
d) Substitute in the formula and calculate.
[tex]\sf X\,value_{Vertex} =-\dfrac{-b}{2a}=-\dfrac{-(2)}{2(-0.2)}=-\dfrac{-(2)}{-0.4}=5[/tex]
2. Answer.So the "x" value of this h(t) equation is located on x= 5, therefore, the maximum point happens at x= 5. Since this is an equation that expresses altitute in terms of time, this means that 5 seconds after the object starts its movement it reaches its maximum altitute.
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Using the net below, find the surface area
of the pyramid.
7\in.
4 in.
4 in.
Surface Area = [?] in.2
The surface area of the pyramid is approximately 74.24 square inches.
What is a pyramid?
A pyramid is a three-dimensional geometric shape that has a polygonal base and triangular faces that meet at a single point called the apex. The most common type of pyramid is a square pyramid, which has a square base and four triangular faces.
To find the surface area of the pyramid, we need to find the area of each of the four triangular faces and the area of the square base, and then add them up.
The area of each triangular face can be found using the formula:
Area = (1/2) * base * height
where the base is one of the sides of the square base and the height is the slant height of the pyramid.
The slant height of the pyramid can be found using the Pythagorean theorem:
slant height² = height² + (1/2 * base)²
where the height is the height of the pyramid, which is given as 7 inches, and the base is 4 inches.
height = 7 in.
base = 4 in.
slant height² = 7² + (1/2 * 4)² = 49 + 4 = 53
slant height = √53 ≈ 7.28 in.
Now we can find the area of each triangular face:
Area = (1/2) * base * height = (1/2) * 4 * 7.28 ≈ 14.56 in^2
There are four triangular faces, so the total area of the triangular faces is:
4 * 14.56 = 58.24 in²
The area of the square base is:
Area = side² = 4² = 16 in²
Finally, we can find the surface area of the pyramid by adding up the area of the triangular faces and the area of the square base:
Surface Area = 58.24 + 16 = 74.24 in²
Therefore, the surface area of the pyramid is approximately 74.24 square inches.
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A wheelchair ramp is in the shape of a triangular prism. It has a base area (B) of 37.4 and a height of 5 yards. Find the volume of the ramp.
The volume of the ramp ishow many yd3
Answer:
Step-by-step explanation:
The formula for the volume of a triangular prism is:
V = Bh, where B is the base area and h is the height of the prism.
Substituting the given values, we get:
V = 37.4 x 5
V = 187 yd^3
Therefore, the volume of the ramp is 187 cubic yards.
Find the missing variables. Write answer as
number. For example: If answer is 31° type
31
X=
□2°
xº
36°
y=
Z=
yᵒ
75%
78°
The values of missing variables are given by:
x = 51°, y = 105°, z = 90°.
We know that the sum of external and internal angles is 180°.
So from the given figure we can see that y° is the external angle and the corresponding internal angle is 75°.
So, 75° + y° = 180°
y° = 180° - 75° = 105°
And also external angle is right angle that is 90° and the corresponding internal angle is z°.
So, z° + 90° = 180°
z° = 180° - 90° = 90°
This is a pentagon and the sum of all internal angles = (5 - 2)180° = 3*180° = 540°
According to the given figure the sum of all internal angles of the pentagon is = (180° - 36°) + z° + (180° - x°) + (180° - 78°) + 75° = 144° + 90° + 180° - x + 102° + 75° = 591° - x.
So, 591° - x = 540°
x = 591° - 540° = 51°
Hence the value of missing variables are: x = 51°, y = 105°, z = 90°.
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Use the given feasible region to find the maximum possible value of the objective function f=5x+6y
The calculated value of the maximum possible value of the objective function is 46
Finding the maximum possible value of the objective functionFrom the question, we have the following parameters that can be used in our computation:
Objective function, F = 5x + 6y
The coordinates of the feasible region are
(0, 6), (1, 6.5) and (2, 6)
Substitute (0, 6), (1, 6.5) and (2, 6) in the above equation, so, we have the following representation
F(0, 6) = 5(0) + 6(6) = 36
F(1, 6.5) = 5(1) + 6(6.5) = 44
F(2, 6) = 5(2) + 6(6) = 46
The maximum value above is 46 at (2, 6)
Hence, the maximum possible value of the objective function is 46
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1 Place an X in the table to show the solution that makes each equation true. 6+x=15 244 X 9x = 18 x=9
Step-by-step explanation:
| Equation | Solution |
| 6+x=15 | x = 9 |
| 9x = 18 | x = 2 |
The table would look like:
| Equation | Solution |
| 6+x=15 | X |
| 9x = 18 | X |
The solution set of the following equations 2x-y=8 , 3x+2y=5 is ..............
*
Answer:
x = 3,
y = -2
Step-by-step explanation:
Let's write the given equations into a system:
{2x - y = 8,
{3x + 2y = 5;
Let's make y the subject from the 1st equation:
-y = 8 - 2x / × (-1)
y = 2x - 8
Replace y in the 2nd equation with its value from the 1st one:
3x + 2(2x - 8) = 5
Expand the brackets:
3x + 4x - 16 = 5
Collect like-terms:
7x = 5 + 16
7x = 21 / : 7
x = 3
y = 2 × 3 - 8 = -2
Using the information in the table, how many milliliters are in 7 kiloliters?
7,000 mL
700,000 mL
kiloliters (KL) liters (L) milliliters (ml)
3
4
5
3,000
4,000
5,000
3,000,000
4,000,000
5,000,000
70,000 mL
7,000,000 mL
Answer:
7e+6
Step-by-step explanation:
biggest answer
The trajectory of a golf ball hit from a tee on the ground at an angle of 40 degrees with an initial speed of 50 meters per second can be modeled by the parabola f(x) = 0.84x − 0.0033x^2, where the x-axis is the ground. Find the height of the highest point of the trajectory and the horizontal distance the golf ball travels before hitting the ground.
Therefore, the horizontal distance the golf ball travels before hitting the ground is approximately 254.55 meters.
What is equation?In mathematics, an equation is a statement that shows the equality between two expressions, typically separated by an equal sign (=). An equation can contain one or more variables, which are symbols that represent unknown or varying values. The value of the variable(s) can be found by solving the equation.
Here,
The equation of the parabolic trajectory of the golf ball is given by:
f(x) = 0.84x - 0.0033x²
where x is the horizontal distance travelled by the ball and f(x) is the corresponding height at that distance. To find the highest point of the trajectory, we need to find the vertex of the parabola. The x-coordinate of the vertex is given by:
x = -b / 2a
where a and b are the coefficients of the quadratic term and the linear term in the equation of the parabola, respectively. In this case, we have:
a = -0.0033 and b = 0.84
Substituting these values into the formula, we get:
x = -0.84 / 2(-0.0033)
= 127.27
So the horizontal distance at the highest point of the trajectory is approximately 127.27 meters. To find the height of the highest point, we substitute this value of x into the equation of the parabola:
f(127.27) = 0.84(127.27) - 0.0033(127.27)²
f(127.27) ≈ 21.67
So the highest point of the trajectory is approximately 21.67 meters above the ground.
To find the horizontal distance the golf ball travels before hitting the ground, we need to find the two values of x where the height of the ball is zero (i.e., where the ball hits the ground). We can set f(x) = 0 and solve for x:
0 = 0.84x - 0.0033x²
0.0033x² = 0.84x
x = 0 or x = 254.55
So the golf ball hits the ground twice, once at x = 0 (i.e., where it was hit from the tee) and once at x ≈ 254.55 meters.
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You buy a $256,000 home with a down payment of 24%. Find the amount of the down payment and the mortgage amount.
The amount of the down payment and the mortgage amount are $61440 and $194560
Finding the amount of the down payment and the mortgage amount.From the question, we have the following parameters that can be used in our computation:
Buy a $256,000 home with a down payment of 24%
This means that
down payment = 24% * 256,000
So, we have
down payment = 61440
Next, we have
mortgage amount = (1 - 24%) * 256,000
So, we have
mortgage amount = 194560
Hence, the mortgage amount is 194560
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Which line is parallel to the line
and passes through the point (-2, 1)?
The equation of the line parallel is y = mx + (1 + 2m).
We have,
The equation of the line.
y = mx + c
Slope = m
And,
(-2, 1) = (x, y)
So,
1 = m x -2 + c
c = 1 + 2m
Now,
y = mx + c
y = mx + (1 + 2m)
Thus,
The equation of the line parallel is y = mx + (1 + 2m).
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Drag the cards to create a number that matches these rules.
. The number ends in the thousandths place.
2 is the nearest one when rounding
.
A 2 is in the thousandths place
.
1 1 2.2
Answer is 16.4. Hope this helpsAnswer:
Step-by-step explanation:
Rafael finished the Boston Marathon ( 26.2 miles) in 4.75 hours. At this pace, how long would it take him to run a 50 mile marathon in Washington D.C?
The time taken by the runner is equal to 9.064 hours.
How to determine the time taken by a runner
In this problem we find the case of runner taking a time (t), in hours, to run a certain distance (d), in miles, at constant speed (v), in miles per hour. The kinematic equation is now introduced:
v = d / t
Now we proceed to determine the missing time:
(26.2 mi) / (4.75 hours) = (50 mi) / t
t = 9.064 h
The runner takes a time of 9.064 hours to run a distance of 50 miles.
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Help please
The half-life of Radium-226 is 1590 years. If a sample contains 500 mg, how many mg will remain after 1000 years? -----------
after 1000 years, approximately 259 mg of the original 500 mg sample of Radium-226 will remain.
what is approximately ?
Approximately means "about" or "roughly" and is used to indicate an estimated or approximate value or quantity, rather than an exact or precise one. For example, if someone says "the population of the city is approximately 1 million people," it means that the population is around 1 million,
In the given question,
The half-life of Radium-226 is 1590 years, which means that in 1590 years, half of the original sample will have decayed. After another 1590 years (or a total of 2 half-lives), half of the remaining sample will have decayed, leaving 25% of the original sample.
To find how much of the original sample remains after 1000 years, we need to first determine how many half-lives have passed.
Number of half-lives = elapsed time ÷ half-life = 1000 years ÷ 1590 years/half-life = 0.63
So, approximately 0.63 half-lives have passed. Therefore, the fraction of the original sample remaining is:
fraction remaining = (1/2)⁰°⁶³ ≈ 0.518
To find the remaining mass, we can multiply the fraction remaining by the initial mass:
remaining mass = fraction remaining x initial mass
remaining mass = 0.518 x 500 mg ≈ 259 mg
Therefore, after 1000 years, approximately 259 mg of the original 500 mg sample of Radium-226 will remain.
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helppp I need help pleaseeeeeee
The new matrix from an elementary row operation to get a 1, in row 1 column 1 will have:
R₁ = [1 -10 2] and R₂ = [-12 7 -13]
What is a matrix row operationRow operations are a set of operations that can be performed on the rows of a matrix in order to transform it into a row equivalent matrix, which has the same solution set as the original matrix.
The row operation R₁ - 6 — R₁ will be carried out as follows:
7 - 6 = 1 {row 1 column 1}
-4 - 6 = 5 {row column 2}
8 - 6 = -8 {row column 3}
Therefore, the resulting matrix from an elementary row operation to get a 1, in row 1 column 1 will have:
R₁ = [1 -10 2] and R₂ = [-12 7 -13]
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If the sum of a number and 3 is doubled, the result is one less than the number. Find the number.
The unknown number that is summed with 3 and double whose result is one less that the number would be = -7
How to determine the unknown number used above?To determine the unknown number, let the unknown number be = n
From the question statement;
2(n + 3) = n-1
2n + 6 = n-1
Bring the like terms together;
2n-n = -6-1
n = -7
Therefore, the number that represents the unknown number used in the statement above would be = -7.
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The volume of a cube that is 2.9 x 5 x 4
The volume of the cuboid is 58 cubic units.
What is a cuboid?A cuboid is a 3 dimensional figure that has six rectangular faces. So that the volume of a cuboid can be determined by;
volume of cuboid = length x width x height
From the given question, we have;
the volume of a cuboid that is 2.9 x 5 x 4 can be determined as follows;
volume of cuboid = length x width x height
= 2.9 x 5 x 4
= 58
The volume of the cuboid with the given dimension is 58 cubic units.
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how much money does she make all together in one week
needs more explanation