Jackson was solving the problem below for k. However, he made a mistake.
19 - 2k = 3k - 1
+3k +3k
19 +1k = -1
-19 -19
k = -20
Part A: Identify the FIRST mistake Jackson made.
Part B: Solve for k.
⬇️ Which equation has a constant of proportionality equal to 1/4?
Answer:
d
Step-by-step explanation:
i think i helped. have a nice day
How much pizza sauce is needed to cover a 16" pizza? (Note: 16" is the diameter of the pizza.)
Responses
A 200.96 in2200.96 in 2
B 803.84 in2803.84 in 2
C 50.24 in250.24 in 2
D 3215.36 in2
Answer:
It is difficult to give a precise answer without more information, such as the thickness of the sauce and the desired coverage. However, if we assume that the sauce is being applied evenly and that a thin layer is desired, the amount of sauce needed to cover a 16" pizza would be approximately 50.24 in2. This is because the area of a circle with a diameter of 16" is approximately 50.24 in2. To calculate the area of a circle, you can use the formula A = πr^2, where A is the area, π is approximately 3.14, and r is the radius of the circle (which is half the diameter). In this case, the radius would be 8" and the area would be approximately 50.24 in2.
Step-by-step explanation:
The slope of the line with equation y=-3x - 2 is multiplied by 2.
What is the x-intercept of the resulting line?
Step-by-step explanation:
-a/b is slope so here .on comapring slope is 3
after multiply by 2 ans. is 6
x Intercept is where it cut the x-axis so equation of line will have slope 6
X interceptor remain the same
a right cylindrical oil tank is feet tall and its circular bases have diameters of feet each. when the tank is lying flat on its side (not on one of the circular ends), the oil inside is feet deep. how deep, in feet, would the oil have been if the tank had been standing upright on one of its bases? express your answer as a decimal to the nearest tenth.
When the cylindrical tank is standing upright on one of its bases, the oil would be 6 feet deep.
Question: A right cylindrical oil tank is 20 feet tall and its circular bases have diameters of 8 feet each. When the tank is lying flat on its side (not on one of the circular ends), the oil inside is 6 feet deep. How deep, in feet, would the oil have been if the tank had been standing upright on one of its bases? Express your answer as a decimal to the nearest tenth.
To find the depth of the oil when the tank is standing upright on one of its bases, we can use the concept of similar triangles.
Step 1: Find the height of the tank when it is standing upright.
The height of the tank is 20 feet.
Step 2: Find the radius of the tank.
The radius is half of the diameter, so the radius is 8/2 = 4 feet.
Step 3: Find the height of the oil when the tank is upright.
We can set up a proportion using the similar triangles formed by the tank and the oil.
The height of the oil when the tank is lying flat is 6 feet.
Let x represent the height of the oil when the tank is upright.
We can set up the following proportion: 4/6 = 4/x.
Step 4: Solve the proportion to find the height of the oil when the tank is upright.
Cross-multiply: 4x = 6 * 4.
Simplify: 4x = 24.
Divide both sides by 4: x = 24/4.
Simplify: x = 6.
Therefore, when the tank is standing upright on one of its bases, the oil would be 6 feet deep.
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Help plz.. x/6-1=1/3(9-3x)
Step-by-step explanation:
x/6-1=1/3(9-3x)
3(x-1) = 6(9-3x)
3x-3 = 54 - 18x
3x+18x=54+3
21x=57
X=57/21
Two times a number plus ten times a second number is twenty. Thirty times the second number plus three times the first number is 45.
15(123)−72−2⋅7? i need help with this
Answer:
1770.3
Step-by-step explanation:
BODMAS
=15(123)-72-2.7
=1845-72-1.7
=1770.3.
Let u = (1,0, -1), v = (4,3,-2), and w = (2, 3, -2). Find the orthogonal projection of w into the plane spanned by the vectors u and v. Show that the matrix A is orthogonal if and only if its transpose A⁻ is orthogonal.
The transpose of A⁻¹ is the inverse of the transpose of A⁻¹, which implies that if A⁻¹ is orthogonal, then A is orthogonal. Therefore, we have shown that the matrix A is orthogonal if and only if its transpose A⁻¹ is orthogonal.
To find the orthogonal projection of vector w into the plane spanned by vectors u and v, we need to calculate the projection vector proj_w(uv).
First, we calculate the normal vector n of the plane. The normal vector is obtained by taking the cross product of vectors u and v:
n = u x v
= (1, 0, -1) x (4, 3, -2)
The cross product can be calculated as follows:
n = ((0)(-2) - (-1)(3), (-1)(4) - (1)(-2), (1)(3) - (0)(4))
= (-3, -6, 3)
Next, we normalize the normal vector n to obtain the unit normal vector n:
n = n / ||n||
= (-3, -6, 3) / √(9 + 36 + 9)
= (-3, -6, 3) / √54
= (-1/√6, -2/√6, 1/√6)
Now, we can calculate the projection of vector w onto the plane using the formula:
proj_w(uv) = w - ((w · n) / (n · n)) * n
The dot product of w and n is given by:
w · n = (2)(-1/√6) + (3)(-2/√6) + (-2)(1/√6)
= -2/√6 - 6/√6 - 2/√6
= -10/√6
The dot product of n and n is:
n · n = (-1/√6)(-1/√6) + (-2/√6)(-2/√6) + (1/√6)(1/√6)
= 1/6 + 4/6 + 1/6
= 6/6
= 1
Substituting these values into the projection formula, we have:
proj_w(uv) = (2, 3, -2) - ((-10/√6) / 1) * (-1/√6, -2/√6, 1/√6)
= (2, 3, -2) + (10/√6)(-1/√6, -2/√6, 1/√6)
= (2, 3, -2) + (-10/6, -20/6, 10/6)
= (2, 3, -2) + (-5/3, -10/3, 5/3)
= (2 - 5/3, 3 - 10/3, -2 + 5/3)
= (1/3, 1/3, -1/3)
Therefore, the orthogonal projection of vector w into the plane spanned by vectors u and v is (1/3, 1/3, -1/3).
Now, let's prove the statement that the matrix A is orthogonal if and only if its transpose A⁻¹ is orthogonal.
To prove this, we need to show two conditions:
If A is orthogonal, then A⁻¹ is orthogonal:
If A is orthogonal, it means that A · A⁻¹ = I, where I is the identity matrix.
Taking the transpose of both sides, we have (A · A⁻¹)ᵀ = Iᵀ, which simplifies to (A⁻¹)ᵀ · Aᵀ = I.
This shows that the transpose of A⁻¹ is the inverse of the transpose of A, which implies that if A is orthogonal, then A⁻¹ is orthogonal.
If A⁻¹ is orthogonal, then A is orthogonal:
If A⁻¹ is orthogonal, it means that (A⁻¹) · (A⁻¹)ᵀ = I, where I is the identity matrix.
Taking the transpose of both sides, we have ((A⁻¹) · (A⁻¹)ᵀ)ᵀ = Iᵀ, which simplifies to ((A⁻¹)ᵀ) · (A⁻¹) = I.
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A right triangle has a leg length of square root of 5 and a hypotenuse length of 4. Determine the length of the other leg of the right triangle.
square root of 11
square root of 21
3
9
Answer:This Pythagorean theorem calculator will calculate the length of any of the missing sides of a right triangle, provided you know the lengths of its other two sides. This includes calculating the hypotenuse. The hypotenuse of the right triangle is the side opposite the right angle, and is the longest side. This side can be found using the hypotenuse formula, another term for the Pythagorean theorem when it's solving for the hypotenuse.
Step-by-step explanation:
Find X in this question
Answer:
Step-by-step explanation:
∠1 = 38 {Vertically opposite angles}
∠2 = 39 + 36 = 75
Exterior angle equals the sum of opposite interior angles.
x = ∠1 +∠2
= 38 + 75
x = 113
It tells to round to the nearest hundredth. Can anybody help?
Answer:
I can't see it very clearly but its
288m^2
Answer:
90m is the area. (not sure why it says hundredth we do not have any decimals)
Step-by-step explanation:
find the area of both the triangle and he rectangle
triangle - 18 (area = 0.5 * b * h)
rectangle =72. ( L x W)
add em together
if x is positive, is x > 3 ? (1) (x – 1)2 > 4 (2) (x – 2)2 > 9
The answer is "yes," if x is positive, then x is greater than 3, x is greater than 3 when x is positive, we need to examine the two statements given in the problem.
Statement (1) tells us that (x – 1)2 is greater than 4. This means that (x – 1) is either greater than 2 or less than -2. However, this does not give us enough information to determine whether x is greater than 3 or not. For example, if x = 2, then (x – 1)2 is equal to 1, which is greater than 4, but x is not greater than 3. Statement (2) tells us that (x – 2)2 is greater than 9. This means that (x – 2) is either greater than 3 or less than -3. Again, this does not give us enough information to determine whether x is greater than 3 or not. For example, if x = 0, then (x – 2)2 is equal to 4, which is greater than 9, but x is not greater than 3.
Therefore, neither statement alone is sufficient to answer the question. However, if we combine the two statements, we can determine whether x is greater than 3 or not. If (x – 1)2 is greater than 4 and (x – 2)2 is greater than 9, then we know that (x – 1) is greater than 2 and (x – 2) is greater than 3. Adding these two inequalities gives us (x – 1) + (x – 2) > 5, which simplifies to 2x – 3 > 5, or 2x > 8, or x > 4. Therefore, we can conclude that if both statements are true, then x is greater than 4, which means that x is also greater than 3.
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Find the base of a parallelogram with a hight of 10.5 feet and an area of 189 square feet?
Base=18
Step-by-step explanation:
I have used area equals to base times height that's the formula of a parallelogram and I've gotten that base equals to 18 hope this helps.
Je m'échauffe
1 QUESTIONS FLASH
Déterminer la moyenne, la médiane et l'éten-
due de chacune des séries :
2
a. série 1 : 4; 5; 12;
b. série 2: 0; 1; 2; 3;
c. série 3:3; 7; 9:11; 20;
d. série 4:2; 3; 4; 5; 6; 7.
Si quelqun pourrais m’aider sur les 3 question sa serais génial ! Silvouplais
Answer:
yookiiii8bubub7bssh8ss
Which of the following can be used to express the total area of a figure?
A. (5)(4x)(3x)
B. 12x^2 + 15x
C. (3x + 4x) (5)
D. 3x (4x + 5)
Answer:
The answer is option BStep-by-step explanation:
The figure above is a rectangle
Area of a rectangle = length × width
From the question
The total length of the rectangle = 3x
The total width of the rectangle = 4x + 5
So the area of the figure is
A = 3x( 4x + 5)
Expand
We have the final answer as
A = 12x² + 15xHope this helps you
Suppose two females are randomly selected. What is the probability both survived
The probability that both females survived is 0.2961
What is the probability both survivedThe table of values is given as
Male Female Child Total
survived 230 339 54 623
died 1190 102 52 1344
total 1420 441 106 1967
For females that survived, we have
P(Female) = 339/623
For two females, we have
P = 339/623 * 339/623
Evaluate
P = 0.2961
Hence, the probability is 0.2961
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Steven and his family ordered a meal that cost $136.50. Steven paid 14% sales tax and left a 20% tip on $136.50. What was the total cost?
this is a one step equation pls help
Answer:
$58
Step-by-step explanation:
James needs $125 total but needs $67 more for it.
You can find how much he has by doing 125 - 67 = 58
The two triangles are congruent. Find the unknown variables. PICTUCE PROVIDED WILL GIVE BRAINLISET
How is the sample variance computed differently from the population variance?
only one formula includes a computation for SS
the calculation in the numerator is different
the calculation in the denominator is different
both B and C
The sample variance computed differently from the population variance is the calculation in the numerator is different and the calculation in the denominator is different
The sample variance is computed differently from the population variance in that the calculation in the numerator is different and the calculation in the denominator is different. Specifically, in the numerator, the sample variance formula includes a computation for SS (sum of squared deviations from the mean), while the population variance formula does not.
Additionally, in the denominator, the sample variance formula divides by n-1 (sample size minus one) instead of by the denominator (population size) in the population variance formula.
The sample variance is computed differently from the population variance in the following ways:
1. The calculation in the numerator is the same for both sample and population variance, as they both involve computing the sum of squared differences (SS) between each data point and the mean.
2. The calculation in the denominator is different. For the population variance, the denominator is the number of data points in the population (N), while for the sample variance, the denominator is the number of data points in the sample (n) minus 1.
So, the correct answer is: the calculation in the denominator is different (Option C).
Here are the formulas for each variance:
Population variance: σ² = Σ(x - μ)² / N
Sample variance: s² = Σ(x - X)² / (n-1)
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A riverbank has been colonized by mink. They are an alien species that attacks local wildlife. The river authority traps and removes the minks. Each year it reduces the number by 60%. What percentage of the mink remain after 4 years?
Answer:
24%
Step-by-step explanation:
it is easy when you multiply 6 and 4 to know how many minks remain
What are the coordinates of point s after a dilation with the center at the origin and a scale factor of 12?
The new coordinates of point s after the dilation are (12x, 12y)
A dilation is a type of transformation that changes the size of an object. It can be thought of as a resizing or stretching of the object. In this case, we are dilating a point with a center at the origin (0,0) and a scale factor of 12.
The center of dilation is the point around which the dilation occurs. In this case, the center of dilation is the origin. This means that the point will be resized relative to the origin.
The scale factor is a number that determines the amount by which the object is resized. In this case, the scale factor is 12. This means that the point will be enlarged 12 times its original size.
To find the new coordinates of the point after the dilation, we multiply the original coordinates by the scale factor. Let the original coordinates of the point be (x, y). Then, the new coordinates of the point after the dilation are:
New x-coordinate = 12 × x
New y-coordinate = 12 × y
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A rectangle has a width of (4g) and a length of (28 - 3). The perimeter of the rectangle is 54 units. What is the
value of g?
Answer:
Step-by-step explanation:
sorry do not .know
To find the value of g, we need to use the formula for the perimeter of a rectangle, which is:
P = 2(l + w)
where P is the perimeter, l is the length, and w is the width.
We are given that the width is 4g and the length is 28 - 3 = 25, so we can substitute these values into the formula:
54 = 2(25 + 4g)
Next, we can simplify the equation by first distributing the 2:
54 = 50 + 8g
Then, we can isolate g on one side of the equation by subtracting 50 from both sides:
4 = 8g
Finally, we can solve for g by dividing both sides by 8:
g = 4/8
Simplifying this expression gives us:
g = 1/2
Therefore, the value of g is 1/2.
Hope this helps <3
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There are 4 red, 8 yellow, and 6 blue socks in a drawer. Once a sock is selected, it is not replaced. Find the probability of reaching into the drawer without looking and drawing out 2 blue socks.
Answer:
11/306
Step-by-step explanation:
Probability is the ratio of the number of possible outcome to the number of total outcome.
Given that there are 4 red, 8 yellow, and 6 blue socks in a drawer where the probability of picking a red, yellow and blue socks be p(r), p(y), and p(b) respectively.
The probability of reaching into the drawer without looking and drawing out 2 blue socks
= 6/(4 + 8 + 6) * 5/(4 + 8 + 5)
= 6/18 + 5/17
= 11/306
The area of a rectangle is 30 m². If the length is V75 m, what is the width?
Answer:
Divide both sides by sqrt(75) and you get 30/sqrt(75) = Width. You can simplify sqrt(75). It equals 5sqrt(3). So it is 30/(5sqrt(3))= Width.
Step-by-step explanation:
Mr. Morris is going to save money and replace his sailboat's mainsail himself. He must determine the area of the mainsail in order to buy the correct amount of material. Calculate the area of the parallelogram to determine how much material should be purchased. Be sure to explain how to decompose this shape into rectangles and triangles. Describe their dimensions and show your work. Parallelogram with base of 20 feet, height of 15 feet, and triangular base of 4 feet.
According to the given information the area of the parallelogram is 300ft².
How do parallelograms function?A geometric shape having parallel sides in two dimensions is called a parallelogram. It is a type of four-sided polygon where each parallel set of sides is the same length (commonly referred to as a quadrilateral). The adjacent angles of such a parallelogram add up approximately 180 degrees.
Width of parallelogram = 20 feet.
Base of triangle = 4 feet.
Height of triangle = 15 feet.
To figure out the parallelogram's surface area:
To begin with, we would calculate the triangles' surface areas.
Note: The parallelogram supplied can be divided into two (2) triangles.
the triangle's surface area formula.
The formula: yields the triangle's area mathematically.
\(\begin{matrix}\mathrm{\ Area\ }=\frac{1}{2}\times\mathrm{\ base\ } \times\mathrm{\ height\ } \\\mathrm{\ Area\ }=\frac{1}{2}\times4\times15\\\mathrm{\ Area\ }=2\times15\\\mathrm{\ Area\ }=\mathbf{30}f^2\\\end{matrix}\)
For the two (2) triangles:
\(Area =2\times30\\Area =\mathbf{60}ft^2\)
For the rectangle left:
\(Length =15ft.\\Width =20-4=16ft.\\Area = length \times width\\Area =15\times16\\Area =\mathbf{240}ft^2\)
Now, the area of the parallelogram:
Area of parallelogram =60+240
Area of parallelogram \(=\mathbf{300}{\rm ft}^2\)
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PLEASE I NEED HELPNSMKSJSBW
Check the picture below.
\(\stackrel{\measuredangle U}{(3x-4)}~~ + ~~\stackrel{\measuredangle V}{(x+20)}~~ + ~~\stackrel{\measuredangle W}{(6x+6)}~~ = ~~180 \\\\\\ 10x+22=180\implies 10x=158\implies x=\cfrac{158}{10}\implies {\Large \begin{array}{llll} x=\cfrac{79}{5} \end{array}}\)
Find the measure of the exterior angle.
Answer:
108°
Step-by-step explanation:
the measure of an exterior angle of a triangle is equal to the sum of the two interior angles opposite it, so:
2a = a+10 + 44
2a = a + 54
a = 54
exterior angle is 2a or 2(54) = 108°
Which statement correctly describes the expression (–12)7
Answer:
answer #n
Step-by-step explanation:
we cant see the options
Answer:
One factor is positive and one factor is negative, so the product will be negative.
Step-by-step explanation: