solve the equation…………….
Answer:
18
Step-by-step explanation:
[tex]\sqrt{x-2} =4\\x-2=16\\x=18[/tex]
Given equation :
[tex] \sqrt{x - 2} = 4[/tex]
Squaring both sides
[tex]( { \sqrt{x - 2} })^{2} = {(4)}^{2} [/tex]
[tex]x - 2 = 16[/tex]
Move all terms containing x to the left, all other terms to the right.
[tex]x = 16 + 2[/tex]
[tex]x = 18[/tex]
Verification:
Put value the x in the given equation.
[tex] \sqrt{x - 2} = 4[/tex]
[tex] \sqrt{18 - 2} = 4[/tex]
[tex] \sqrt {16} = 4[/tex]
[tex] \sqrt {4 \times 4 } = 4[/tex]
[tex]4 = 4[/tex]
Hence, The answer is 18.
If a ring costs a jeweler $2100, at what price should it be sold to yield a profit of 50% on the selling price?
. A plastic marker buoy floating on the sea consisting of a cone attached to a hemispherica base is shown above. The radius of the hemispherical base is 0.95cm and height of the cone is 1.2m. Calculate the volume of the buoy.
Answer:
The volume of the buoy can be calculated by finding the volumes of the cone and hemisphere separately and then adding them together.
The volume of the cone is given by:
Vcone = (1/3)πr^2h
where r is the radius of the base of the cone and h is the height of the cone.
Substituting the given values, we get:
Vcone = (1/3)π(0.95)^2(1.2) = 1.08 m^3 (rounded to two decimal places)
The volume of the hemisphere is given by:
Vhemisphere = (2/3)πr^3
where r is the radius of the hemisphere.
Substituting the given value, we get:
Vhemisphere = (2/3)π(0.95)^3 = 1.05 × 10^-3 m^3 (rounded to two decimal places)
Therefore, the total volume of the buoy is:
Vbuoy = Vcone + Vhemisphere = 1.08 + 1.05 × 10^-3 = 1.08 m^3 (rounded to two decimal places)
For the weight of the box that she measured, Beatriz determined the margin of error as 23.5 pounds to 24.5 pounds. What was the greatest possible error for her actual measurement?
Beatriz measured the weight of a box and determined the margin of error as 23.5 pounds to 24.5 pounds. The range of the margin of error is 1 pound, which means that the actual weight of the box could be off by a maximum of 1 pound.
Beatriz measured the weight of a box and determined the margin of error as 23.5 pounds to 24.5 pounds. The greatest possible error for her actual measurement can be determined by finding the range of the margin of error.
The range of the margin of error can be determined by finding the difference between the upper limit and the lower limit. Therefore, the range of the margin of error is 24.5 - 23.5 = 1 pound.
This means that the actual weight of the box could be off by a maximum of 1 pound. This is the greatest possible error for her actual measurement.
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Use the pair of functions to find f(g(x)) and g(f(x)). Simplify your answers.
f(x)= 1= ² + 4
X-4
To find f(g(x)), we need to substitute g(x) into the function f(x). Given that g(x) = x - 4, we substitute it into f(x) as follows:
[tex]f(g(x)) = f(x - 4) = (x - 4)^2 + 4[/tex]
To simplify this expression, we can expand the square:
[tex]f(g(x)) = (x - 4)(x - 4) + 4\\ = x^2 - 8x + 16 + 4\\ = x^2 - 8x + 20[/tex]
Therefore, f(g(x)) simplifies to[tex]x^2 - 8x + 20.[/tex]
Next, let's find g(f(x)). We substitute f(x) into the function g(x):
[tex]g(f(x)) = g(1/x^2 + 4) = 1/x^2 + 4 - 4\\ = 1/x^2[/tex]
Hence, g(f(x)) simplifies to 1/x^2.
In summary, f(g(x)) simplifies to[tex]x^2 - 8x + 20[/tex], and g(f(x)) simplifies to 1/x^2.
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Which is the standard equation of the parabola in the graph?
Graph of parabola opening to the right with vertex at 0 comma 4, focus at 4 comma 4, p equals 4, vertical dotted line going through negative 4 on x axis is labeled directrix, and horizontal dotted line going through 4 on y axis is labeled axis
x2 = 16(y – 4)
x2 = –16(y + 4)
(y – 4)2 = 16x
(y + 4)2 = –16x
The correct equation for the parabola is [tex]x^2 = 16(y - 4)[/tex].
The standard equation of the parabola in the graph can be determined based on its characteristics.
Given:
Vertex: (0, 4)
Focus: (4, 4)
P (the distance from the vertex to the focus or directrix): 4
We can conclude that the parabola opens to the right because the axis is horizontal.
The standard equation of a parabola with a horizontal axis and vertex (h, k) is given by:
[tex](x - h)^2 = 4p(y - k)[/tex]
In this case, the vertex is (0, 4), so the equation becomes:
[tex](x - 0)^2 = 4p(y - 4)[/tex]
Now, we need to determine the value of p. The distance from the vertex to the focus is p, which is 4 in this case.
Therefore, the standard equation of the parabola in the graph is:
[tex]x^2 = 4(4)(y - 4)\\x^2 = 16(y - 4)[/tex]
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Probability of dice and frequency
Probabilities are:
Even number = 0.5
Odd Number = 0.5
Number 1 face up = 1/6
Number 2 face up = 1/6
Number 3 face up = 1/6
Number 4 face up = 1/6
Number 5 face up = 1/6
Number 6 face up = 1/6
Esmerelda simplified a complex fraction. Her work is shown below.
Negative 5 and one-fourth divided by three-halves = negative StartFraction 21 over 4 EndFraction divided by three-halves = (Negative StartFraction 21 over 4 EndFraction) (Three-halves) = Negative StartFraction 24 over 6 EndFraction = negative 4
What errors did Esmerelda make? Select three options.
Esmerelda converted the mixed number to the wrong improper fraction.
Esmerelda added the numerators.
Esmerelda added the denominators.
Esmerelda did not divide –24 by 6 correctly.
Esmerelda did not use the reciprocal of the divisor
The correct options are:
Esmerelda converted the mixed number to the wrong improper fraction.
Esmerelda added the numerators.
Esmerelda did not divide –24 by 6 correctly.
The errors made by Esmerelda are as follows:
1. Esmerelda converted the mixed number to the wrong improper fraction.
2. Esmerelda added the numerators.
3. Esmerelda did not divide –24 by 6 correctly.
Let's go through each error:
1. Esmerelda converted the mixed number to the wrong improper fraction:
Esmerelda incorrectly converted "Negative 5 and one-fourth" to "Negative StartFraction 21 over 4 EndFraction." The correct conversion would be "Negative StartFraction 5 over 4 EndFraction" since the mixed number -5 1/4 can be expressed as -5 + 1/4 = -5 (1/4) = -5 (4/4) + (1/4) = -5 (4 + 1)/4 = -5 (5/4) = -5 (5 over 4).
2. Esmerelda added the numerators:
Esmerelda incorrectly added the numerators of the fractions, resulting in "Negative StartFraction 21 over 4 EndFraction" instead of the correct numerator of -5 * 4 = -20.
3. Esmerelda did not divide –24 by 6 correctly:
Esmerelda made an error in dividing -24 by 6, resulting in "StartFraction 24 over 6 EndFraction" instead of the correct value of -24 divided by 6, which is -4.
Therefore, the correct options are:
- Esmerelda converted the mixed number to the wrong improper fraction.
- Esmerelda added the numerators.
- Esmerelda did not divide –24 by 6 correctly.
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Change 4630 Litres to kiloliters 2 express 2Liters 360 milliliters in milliliters (3) express 2700 gram to the nearest 0.1kg (4) Change 2.705kg to the nearest 0.01kg (5) Express 9.597kg to the nearest kilograms.
Answer:
1) 4630 L = 4.63 kL
2) 2 L 360 mL = 2360 mL
3) 2700 g = 2.7 kg (rounded to nearest 0.1 kg)
4) 2.705 kg = 2.71 kg (rounded to nearest 0.01 kg)
5) 9.597 kg = 10 kg (rounded to nearest kg)
national Bureau of statistics reported that approximately 30% of the population are unemployed. In conducting a random telephone surveys, what is the probability of getting two or fewer unemployed people in a sample of 20? “Binomial distribution”
a triangle is shown drag graphs to the table to ahow the image of the triangle after it is reflected over the x-axis, the y-axis, or the line y = x.
The graphs have been correctly dragged to the table to show the image of the triangle after it is reflected over the x-axis, the y-axis, and the line y = x.
How to reflect the triangle based on the transformation rule?By applying a reflection over the x-axis to the coordinates of this triangle, we have the following coordinates of the image triangle;
(x, y) → (x, -y)
(1, -3) → (1, -(-3)) = (1, 3)
(3, -2) → (3, -(-2)) = (3, 2)
(4, -5) → (4, -(-5)) = (4, 5)
By applying a reflection over the y-axis to the coordinates of this triangle, we have the following coordinates of the image triangle;
(x, y) → (-x, y)
(1, -3) → (-1, -3)
(3, -2) → (-3, -2)
(4, -5) → (-4, -5)
By applying a reflection over the line y = x to the coordinates of this triangle, we have the following coordinates of the image triangle;
(x, y) → (y, x)
(1, -3) → (-3, 1)
(3, -2) → (-2, 3)
(4, -5) → (-5, 4)
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need help with this question ASAP
The angle of elevation of the sun to the nearest degree is: 34°
How to find the angle of elevation?The angle of elevation is defined as an angle that is formed between the horizontal line and the line of sight. If the line of sight is upward from the horizontal line, then the angle formed is referred to as an angle of elevation.
There are three main trigonometric ratios which are:
sin x = opposite/hypotenuse
cos x = adjacent/hypotenuse
tan x = opposite/adjacent
In this case, the dimensions given will warrant the use of the tangent function to get:
tan θ = 101/147
tan θ = 0.6871
θ = tan⁻¹(0.6871)
θ = 34°
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winta and lensa invest birr 21000 and 17500 respectively in a business.at the end of the year, they make profit birr 24600. what is the the share of winta in the profit?
Answer:
Step-by-step explanation:
To determine the share of Winta in the profit, we need to calculate the ratio of her initial investment to the total initial investment and then apply that ratio to the total profit.
Winta's initial investment: Birr 21,000
Lensa's initial investment: Birr 17,500
Total initial investment: Birr 21,000 + Birr 17,500 = Birr 38,500
To find the share of Winta in the profit, we calculate:
Winta's share = (Winta's initial investment / Total initial investment) * Total profit
Winta's share = (Birr 21,000 / Birr 38,500) * Birr 24,600
Simplifying the calculation:
Winta's share = (0.5455) * Birr 24,600
Winta's share ≈ Birr 13,414.55
Therefore, Winta's share in the profit is approximately Birr 13,414.55.
Part B
Use the distance formula to find BC. Show your work.
Answer:
5 units------------------------
Use coordinates of endpoints, taken from the diagram, B(6, 2) and C(2, - 1) and the distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Substitute BC for d and given coordinates to find the radius:
[tex]BC=\sqrt{(2-6)^2+(-1-2)^2} =\sqrt{16+9} =\sqrt{25} =5[/tex]Hence the segment BC is 5 units long.
An IQ test is designed so that the mean is 100 and the standard deviation is 15 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of the residents of a state if you want to be 95% confident that the sample mean is within 4 IQ points of the true mean.
What is the required sample size?
Answer:
55
Step-by-step explanation:
[tex]\displaystyle MOE = z\biggr(\frac{\sigma}{\sqrt{n}}\biggr)\\\\4=1.96\biggr(\frac{15}{\sqrt{n}}\biggr)\\\\4=\frac{29.4}{\sqrt{n}}\\\\\sqrt{n}=\frac{29.4}{4}\\\\\sqrt{n}=7.35\\\\n=54.0225\\\\n\approx55\uparrow[/tex]
Make sure to always round up the required sample size to the nearest integer!
Perform the following Sequence of Transformations on △ABC and provide the (x,y) coordinates for the image of each point after each transformation.
First, translate four units to the left and five units down
Next, reflect across the line y = x
Last, dilate with scale factor = 2
The (x, y) coordinates for the image of each point after each transformation include the following:
A' (-3, -4) A" (1, 1) A'" (2, 2).
B' (1, -4) B" (1, 5) B'" (10, 2).
C' (-1, -1) C" (4, 3) C''' (6, 8).
How to perform the sequence of transformations on triangle ABC?In order to apply a translation of four units to the left and five units down to triangle ABC, we would use this transformation rule;
(x, y) → (x - 4, y - 5)
A (1, 1) → A' (-3, -4).
B (5, 1) → B' (1, -4).
C (3, 4) → C' (-1, -1).
Next, we would reflect triangle ABC across the line y = x;
(x, y) → (y, x)
A (1, 1) → A" (1, 1).
B (5, 1) → B" (1, 5).
C (3, 4) → C" (4, 3).
Lastly, we would dilate triangle ABC with scale factor of 2;
(x, y) → (2x, 2y)
A (1, 1) → A'" (2, 2).
B (5, 1) → B'" (10, 2).
C (3, 4) → C''' (6, 8).
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Shan scored 7 out of 10 for his maths test and 15 out of 20 for his science test. Which test did he achieve better results?
Shan performed better in his science test than in his math test based on the respective scores of 15 out of 20 and 7 out of 10.
To determine which test Shan achieved better results in, we need to compare the scores he obtained in both the math and science tests.
Shan scored 7 out of 10 in his math test, which can be written as a fraction 7/10. This fraction can also be converted to a decimal by dividing 7 by 10, resulting in 0.7.
Similarly, Shan scored 15 out of 20 in his science test, which can be written as a fraction 15/20. This fraction can also be simplified by dividing both the numerator and denominator by 5, resulting in 3/4. Converting this fraction to a decimal by dividing 3 by 4 yields 0.75.
Comparing the decimal values, we can see that 0.75 (science test) is greater than 0.7 (math test). Therefore, Shan achieved better results in his science test compared to his math test.
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What is the formula to find the perimeter of a rectangle?
P = l + w + w
P = l + l + w + w
P = w + w + l
P = l + l + l + w
Answer:
it answer is
P=2(l+b)
P=l + l + b + b
Which is a correct step when using the median-fit method for modeling data?
The correct step when using the median-fit method for modeling data is to fit a function to the median of the data.
The median-fit method can be used to model data by following these steps:
1. Arrange the data set in ascending order.
2. Find the median of the data set.
3. Divide the data set into two groups: one group that is below the median, and another group that is above the median.
4. Compute the median of each group.
5. Fit a function to the median of the data.
6. Use the fitted function to estimate values for the original data set.
The median-fit method is a statistical method used to model data. It involves fitting a function to the median of the data. This method is often used when the data set is skewed or has outliers.
The median-fit method is more robust to outliers than the mean-fit method. It is also less sensitive to the shape of the data distribution than other methods.
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I need help answering this, I don’t remember how to do this
Answer:
37.5
Step-by-step explanation:
the therom of a parallelogram is width*height
so 7.5*5
=37.5
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Answer:
A = 37.5
Step-by-step explanation:
The area of a parallelogram is:
Area = base × height
In your picture the base is 7.5 and the height is 5.
So multiply 7.5×5 and you get 37.5.
The area is 37.5cm^2
Given an isosceles triangle ABC (AB = AC) and a point M that does not belong to it, but belongs to angle ABC. Find the angle BAM if ∠ABC = 50°, ∠BMC = 40°, ∠BMA = 10°.
The answer is 160°. After numerous attempts I couldn't solve it anyway.
Give all my points away.
IMPORTANT: It's not a college problem, this problem is from an 8th grade textbook, the matter is "Inscribed and circumscribed circles". So it must be solved within this topic.
The angle BAM is 40°. as the correct angle based on the given values is not 160°, but rather 40°.
To solve this problem within the topic of inscribed and circumscribed circles, we can utilize the property of angles subtended by the same arc on a circle.
Let's consider triangle ABC and point M within angle ABC. Since triangle ABC is isosceles with AB = AC, we can draw the circumcircle passing through points A, B, and C. Let O be the center of this circumcircle.
Based on the property mentioned earlier, angle BAM will be equal to half the measure of arc BC on the circumcircle, subtended by chord BM.
Given that ∠ABC = 50° and ∠BMC = 40°, we can deduce that arc BC on the circumcircle will have a measure of 2 * ∠BMC = 2 * 40° = 80°.
Since angle BAM is half the measure of arc BC, we have:
∠BAM = 0.5 * 80° = 40°
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tan(x-1) ( sin2x-2cos2x) = 2(1-2sinxcosx)
[tex]\huge\blue{\fbox{\tt{Solution:}}}[/tex]
We can simplify the expression using trigonometric identities.
First, we can use the double angle formula for sine to write sin(2x) = 2sin(x)cos(x).
Next, we can use the double angle formula for cosine to write cos(2x) = cos^2(x) - sin^2(x) = 1 - 2sin^2(x). Rearranging this equation gives 2sin^2(x) - 2cos^2(x) = -cos(2x) + 1.
Substituting these identities into the original expression gives:
tan(x-1) ( sin2x-2cos2x) = tan(x-1) [2sin(x)cos(x) - 2(1 - 2sin^2(x))]
= 2tan(x-1)sin(x)cos(x) - 2tan(x-1) + 4tan(x-1)sin^2(x)
We can use the identity tan(x) = sin(x)/cos(x) to simplify this expression further:
2tan(x-1)sin(x)cos(x) - 2tan(x-1) + 4tan(x-1)sin^2(x)
= 2sin(x)cos(x)/(cos(x-1)) - 2sin(x)/(cos(x-1)) + 4sin^2(x)/(cos(x-1))
Multiplying both sides of the equation by cos(x-1) gives:
2sin(x)cos(x) - 2sin(x) + 4sin^2(x)cos(x-1) = 2(1-2sin(x)cos(x))
Expanding the left-hand side of the equation gives:
2sin(x)cos(x) - 2sin(x) + 4sin^2(x)cos(x) - 4sin^2(x) = 2 - 4sin(x)cos(x)
Simplifying this equation gives:
4sin^2(x) - 2sin(x) - 2 = 0
This is a quadratic equation in sin(x), which can be solved using the quadratic formula.
The area of the right triangle shown is 24 square feet.
Which equations can be used to find the lengths of the legs of the triangle? Select three options.
0.5(x)(x + 2) = 24
x(x + 2) = 24
x2 + 2x – 24 = 0
x2 + 2x – 48 = 0
x2 + (x + 2)2 = 100
Answer:
0.5(x)(x + 2) = 24
x² + 2x - 48 = 0
x² + (x + 2)² = 100
need help ,plss like rn
Answer:
3 units to the left of the y-axis
Step-by-step explanation:
Since all answers involve 3, I believe we are looking at the x-axis. To answer your question, a negative x value means that it is to the left of the origin. Therefore the answer would be 3 units to the left of the y-axis.
A pool measuring 18 meters by 24 meters is surrounded by a path of uniform width, as
shown in the figure. If the area of the pool and the path combined is 1672 square meters,
what is the width of the path?
Answer:
10 meters
Step-by-step explanation:
You want the width of the path surrounding an 18 meter by 24 meter pool if the total area of pool and path is 1672 square meters.
AreaThe total area of the rectangular shape is the product of its length and width:
A = LW
1672 = (24 +2x)(18 +2x)
418 = (12 +x)(9 +x) . . . . . . . . divide by 4
418 = 108 +21x +x² . . . . . . eliminate parentheses
420.25 = 110.25 +21x +x² . . . . . . add 2.5 to complete the square
20.5 = (10.5 +x) . . . . . . . . . . take the positive square root
10 = x . . . . . . . . . . . . . . subtract 10.5
The width of the path is 10 meters.
__
Additional comment
The attached graph shows the two solutions of the original equation written so the solutions are the x-intercepts:
(24 +2x)(18 +2x) -1672 = 0
<95141404393>
In x=5. Solve for the equation c
Answer:
What is the equation?
Step-by-step explanation:
Can't solve it without knowing where c is in the equation
Three-fourths of the yard is covered with grass and one-fourth is used as a garden. The sprinkler could only water 1/5 of the yard, so the rest died. Use the model to find out how much of the grass died.
3/5 or 60% of the grass died because the sprinkler could only water 1/5 of the yard.
Let's start by breaking down the information given:
- Three-fourths of the yard is covered with grass.
- One-fourth of the yard is used as a garden.
- The sprinkler could only water 1/5 of the yard.
To find out how much of the grass died, we need to determine the portion of the grass that was not watered by the sprinkler.
Let's assume the total area of the yard is represented by the value 1. Therefore, we can calculate the area of the grass as 3/4 of the total yard, which is (3/4) * 1 = 3/4.
The sprinkler can only water 1/5 of the yard, so the portion of the grass that was watered is (1/5) * (3/4) = 3/20.
To find the portion of the grass that died, we subtract the watered portion from the total grass area:
Portion of grass that died = (3/4) - (3/20) = 15/20 - 3/20 = 12/20.
Simplifying, we get:
Portion of grass that died = 3/5.
Therefore, 3/5 or 60% of the grass died because the sprinkler could only water 1/5 of the yard.
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find a and b find a and b find a and b find a and b find a and b find a and b find a and b find a and b find a and b vfind a and b
Answer
a=93
b=74
Step-by-step explanation:
a=180-87=93 b=180-106=74
1. Solve the differential equation
(4+t²)dy/dt + 2ty = 4t
2. Find the general solution of the differential equation dy/dt + (1/2)y = (1/2)e^t/3 .
3. Solve the initial value problem .
ty' + 2y = 4t² , where y(1) = 2.
Answer:
1. The solution to the differential equation is y = (4*t/3 + 2/3*t + C)/(t**2 + 4), where C is the constant of integration.
2. The general solution to the differential equation is y = (3/4)*exp(t/6) + C*exp(-t/2), where C is the constant of integration.
3. The solution to the initial value problem is y = t^2 + 4/3.
Correct answer please
Answer:
50.75
Step-by-step explanation:
We have:
[tex]E[g(x)] = \int\limits^{\infty}_{-\infty} {g(x)f(x)} \, dx \\\\= \int\limits^{1}_{-\infty} {g(x)(0)} \, dx+\int\limits^{6}_{1} {g(x)\frac{2}{x} } \, dx+\int\limits^{\infty}_{6} {g(x)(0)} \, dx\\\\= \int\limits^{6}_{1} {g(x)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {(4x+3)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {(4x)\frac{2}{x} } \, dx + \int\limits^{6}_{1} {(3)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {8} \, dx + \int\limits^{6}_{1} {\frac{6}{x} } \, dx\\\\[/tex]
[tex]=8\int\limits^{6}_{1} \, dx + 6\int\limits^{6}_{1} {\frac{1}{x} } \, dx\\\\= 8[x]^{^6}_{_1} + 6 [ln(x)]^{^6}_{_1}\\\\= 8[6-1] + 6[ln(6) - ln(1)]\\\\= 8(5) + 6(ln(6))\\\\= 40 + 10.75\\\\= 50.74[/tex]
