Answer:
-13 + j*2
Step-by-step explanation:
The additive inverse of a complex number x = a +j*b
is a number y, such that
x + y = 0
This means that
y = -x = - a - j*b
Therefore
The additive inverse of 13 - j*2 is equal to
-(13 - j*2) = -13 +j*2
The form he builds is 40 1/2 in. long, 10 in. deep, and 8 in. high. How much cement is needed to fill the form
This question clearly states that it is a 'find the volume' question.
Given dimensions of the object are :
Length of the object = [tex]40\frac{1}{2}[/tex] inches or 40.5 inches
Depth of the object = 10 inches
Height of the object is = 8 inches
So, the volume becomes = [tex]40.5\times10\times8[/tex] = 3240 cubic inch
Hence, the amount of cement needed is 3240 cubic inches.
To fill the form, you use the formula for the volume of a rectangular prism (length x width x height) to find that 3240 cubic inches of cement is needed.
The student is asking about the volume of cement needed to fill a form with specified dimensions. To calculate the volume, we need to use the formula for the volume of a rectangular prism, which is length x width x height. In this case, we need to convert the mixed number into an improper fraction before multiplying, or we could convert it to a decimal.
First, convert the length from 40 1/2 inches to 40.5 inches. Then, use the formula:
Volume = length x width x height
Volume = 40.5 in x 10 in x 8 in
Volume = 405 in x 8 in
Volume = 3240 cubic inches
Therefore, to fill the form, 3240 cubic inches of cement is needed.
Find the unknown angle measures.
Answer:
43°
Step-by-step explanation:
From the diagram
∠xwy=∠xyw = isosceles triangle where base angles are equal
∠y= ∠w = (180-86)÷2 = 47°
if ∠xzy=90° and ∠xyz =47° then ∠d=?
∠d= 180°-(90°+47°)
∠d=180°-137° =43°
what is measure of angle R?
The measure of the angle R in the right-angle triangle will be 22.62°.
What is a right-angle triangle?It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.
Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.
The measure of the angle R is given by the sine rule. The sine of angle R is the ratio of the perpendicular to the hypotenuse. Then we have
sin R = 5 / 13
R = sin⁻¹(5/13)
R = 22.62°
The measure of the angle R in the right-angle triangle will be 22.62°.
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The measure of angle R is 30 degrees.
To determine the measure of angle R, we can use the properties of special right triangles, specifically the 30-60-90 right triangle. In such a triangle, the angles are 30 degrees, 60 degrees, and 90 degrees, and the lengths of the sides opposite these angles are in the ratio 1:√3:2, respectively.
Given that side PR is the hypotenuse of the right triangle PQR and it is 2 units long, we can deduce that triangle PQR is a 30-60-90 triangle. The side QR, which is opposite the 30-degree angle at Q, is half the length of the hypotenuse. Since PR is 2 units, QR must be 1 unit.
The side PQ is opposite the 60-degree angle at P and is 3 times the length of QR. Since QR is 1 unit, PQ must be 3 units.
The angle R is opposite the side PQ, and since we have established that PQR is a 30-60-90 triangle, angle R must be the smallest angle, which is 30 degrees.
Therefore, the measure of angle R is 30 degrees.
How to solve for x in math
Answer:
x = 15; m<(3x) = 45; m<(2x + 15) = 45
Step-by-step explanation:
The measures of the angles measuring 3x and 2x + 15 add up to 90 degrees.
3x + 2x + 15 = 90
5x + 15 = 90
5x = 75
x = 15
m<(3x) = 3 * 15 = 45
m<(2x + 15) = 2 * 15 + 15 = 30 + 15 = 45
Is 6(4x-5) equivalent to 3+22x-33-2x?
YES or NO?????
Show your work!
6(4x-5) 3+22x-33-2x
Answer:
NO
Step-by-step explanation:
To find if they are equivalent, we need to simplify them first.
Using the distributive property we get:
6(4x-5) = 24x - 30
In this case we need to combine like terms.
3 + 22x - 33 - 2x = 20x - 30
So now we can compare.
24x - 30 ≠ 20x - 30
So we can conclude that the two expressions are not equal because 24x - 30 and 20x - 30 are obviously not equal.
Answer:
Not equivalent
Step-by-step explanation:
We are given an expression [tex] 6 ( 4 x - 5 ) [/tex] and we are to check if it is equal to [tex] 3 + 22 x - 33 - 2 x [/tex] or not.
Evaluation the given expression first:
[tex] 6 ( 4 x - 5 ) = 24 x - 30 [/tex]
While adding the terms in [tex] 3 + 22 x - 33 - 2 x [/tex], we get:
[tex] 22 x - 2 x - 33 + 3 = 20 x - 30 [/tex]
[tex] 24 x - 30 \neq 20 x - 30 [/tex]
Therefore, [tex] 6 ( 4 x - 5 ) [/tex] is not equivalent to [tex] 3 + 22 x - 33 - 2 x [/tex].
What is the value of x and y in degrees? Please show steps!
Check the picture below.
The manager of a store that specializes in selling tea decides to experiment with a new blend.She will mix some Earl Grey tea that sells for $6 per pound with some Orange Pekoe tea that sells for $4 per pound to get 600 pounds of the new blend. the selling price of the new blend is $4.50 per pound and there was something to be no difference in revenue from selling the new blend versus selling the other types. how many pounds of the Earl Grey tea and orange Pekoe tea are required?
Answer:
Earl Grey: 150 poundsOrange Pekoe: 450 poundsStep-by-step explanation:
Let "e" represent the number of pounds of Earl Grey tea required for the mix. Then (600-e) is the number of pounds of Orange Pekoe tea required. The total cost of the mix is ...
6·e + 4·(600 -e) = 4.50·600
2e = 600·(4.50 -4.00) . . . . . simplify, subtract 4·600
e = 300/2 = 150 . . . . . . . . . . divide by the coefficient of x
Required are 150 pounds of Earl Grey and 450 pounds of Orange Pekoe.
The amount of Earl Grey and Pekoe tea required for the new blend is :
150 pounds of Earl450 pounds of PekoePrice of new blend per pound = $4.50
Price per pound of Earl tea = $6
Price per pound of Pekoe tea = $4
Let :
Pound of Earl tea = a
Pound of Pekoe tea = b
Converting the information to Mathematical expressions :
a + b = 600 - - - (1)6a + 4b = 600(4.50)6a + 4b = 2700 - - - (2)From (1):
a = 600 - b
Put a = 600 in (2)
6(600 - b) + 4b = 2700
3600 - 6b + 4b = 2700
Collect like terms :
-6b + 4b = 2700 - 3600
-2b = -900
b = 900 ÷ 2
b = 450
Recall :
a = 600 - b
a = 600 - 450
a = 150
Therefore,
Pound of Earl tea required = 150Pound of Pekoe tea required = 450Learn more : https://brainly.com/question/11335251
What is the measure of angle E?
Answer: 55
Step-by-step explanation: The inside measure of a triangle should be 180 so knowing this subtract 43 and 82 and you get 55.
In the given triangle ∠E = 55° and side EF = 12.49 unit
As we know the sum of all three angles in a triangle is 180°
so ∠E = 180-43-82 = 55°
What is a sine rule?In a triangle ABC if BC = a, AC = b, AB = c
then [tex]\frac{Sin A}{a} = \frac{sin B}{b} = \frac{SinC}{c}[/tex]
From sine rule,
[tex]\frac{sin 43}{EF} = \frac{Sin 55}{15}[/tex]
[tex]EF = 15* \frac{Sin43}{Sin55}[/tex]
EF = 12.49
Therefore, in the given triangle ∠E = 55° and side EF = 12.49 unit
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What’s the standard form of the following polynomial?
(3x-2)(x-1)+2(x-5)^2-25
Answer
x^2 + 4x - 49
Step-by-step explanation:
you have to do PEMDAS first then add all the like-terms
hope this helps
p.s. you're pretty
Ellie read 30 pages of her social studies book in 1.5 hours at a constant rate. She then switched to reading a novel and read 150 pages in 2 hours at a constant rate. Wh at percent of Ellie’s social studies reading rate is her Novel reading rate?
Social Studies rate, S = 30/ 1.5 = 20pages/hr
Novel rate, N = 150/2 = 75pages/hr
Novel rate as a % of Social Studies rate...
N/S × 100% = 75/20 × 100% = 375%
percent of Ellie’s social studies reading rate is her Novel reading rate is 375%.
What are mathematics operations?
A mathematical operation is a function that converts a set of zero or more input values (also called "b" or "arguments") into a defined output value. The number of operands determines the operation's arity. Most commonly studied operations are binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive and multiplicative inverses.
• Zero-arity operations, or nullary operations, are constants, and mixed products are arity three operations, or ternary operations.
Here, it is given that :
Ellie read 30 pages of her social studies book in 1.5 hours at a constant rate, let first find Ellie's social studies reading rate :
rate = 30 pages/1.5 hours = 20 pages/ hr.
Now, to find out the unit rate, divide the total number of pages reading novel by the total time spent.
rate = 150 pages/ 2 hours = 75 pages/ hr.
To find out the percentage divide Ellie's novel reading rate by Ellie's social studies reading rate and multiply by 100
percent of Ellie’s social studies reading rate is her Novel reading rate = 75/20 x 100 = 375%.
Therefore, percent of Ellie’s social studies reading rate is her Novel reading rate is 375%.
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If m EAB = 195 degrees and m EC = 75 degrees what is the measure of angle EDC
Answer:
The measure of angle EDC is [tex]60\°[/tex]
Step-by-step explanation:
we know that
The measurement of the external angle is the semi-difference of the arcs which comprises
so
[tex]m<EDC=\frac{1}{2}(arc\ EAB-arc\ EC )[/tex]
substitute the values
[tex]m<EDC=\frac{1}{2}(195\°-75\°)=60\°[/tex]
It is 9 kilometers from Maria's house to the nearest mailbox. How far is it in meters
Answer: 9,000 meters
Step-by-step explanation: There are 1,000 meters in one kilometer. 9 times 1,00p is 9,000.
Answer:
9000 Meters
Step-by-step explanation:
What is the solution set to this inequality, where x is a real number: -4x
Answer:
x ≥ 9
Step-by-step explanation:
Considering the equation is;
-4x (less than or equal to ) 36 , as provided by the questioner;
-4x ≤ 36
Dividing both sides by -4
-4x/-4≤ 36/-4
We get;
x ≥ -9 , the sign ≤ changes to ≥ since we have divided by a negative.
x ≥ 9what is the median for 83 73 76 72 75 85 79 76?
Answer:
The answer is 76
HOPE THIS HELPS!
Step-by-step explanation:
Darren filled boxes with tins of Orange juice and numbered the boxes in the order in which they were filled. He packed the 496th tin in box 21 then stopped for lunch. Box 21 was not completely filled. How many tins were in box 21?
Answer:
16
Step-by-step explanation:
Darren completely filled each box before the 21st box. This means he completely filled 20 boxes. To find out how many tins fit in each box, divide:
496/20 = 24.8
This means each of the 20 preceding boxes held 24 tins. To get these filled, Darren used 20(24) = 480 tins of juice.
This left Darren with 496-480 = 16 tins of juice to put in box 21 before lunch.
Final answer:
To find out how many tins are in box 21, we subtracted the number of tins contained in the first 20 fully packed boxes from the total number of tins Darren packed. We found that each of the first 20 boxes must contain 24 tins, hence, there are 16 tins in the partially filled box 21.
Explanation:
The student's question is about finding how many tins were in box 21 before Darren stopped for lunch. To determine this, we need to figure out the pattern of how the tins were packed into the boxes. Since Darren packed the 496th tin in box 21, and since box 21 is not completely full, we can start by assuming that each box before box 21 was filled completely. If we can find the number of tins each box can hold, we will know the number of tins in box 21.
Let's assume the number of tins each box can hold is x. Since 20 boxes are completely full, they would contain a total of 20x tins. Box 21 contains fewer than x tins. The total number of tins, including those in box 21, is 496. Thus, we have the equation 20x + (496 - 20x) = 496. Simplifying, we get 20x = 496 - (496 - 20x), leading to 20x = 20x, which means each of the first 20 boxes contains the same number of tins. To find x, we need to divide the total number of tins not including box 21 by 20. Now we subtract that product from 496 to find the number of tins in box 21.
Since 496 is not evenly divisible by 20, we find that x is a decimal, which is not possible since we cannot have a fraction of a tin. Therefore, we subtract 1 from 496 to make it divisible by 20, giving us 495 tins to be divided evenly among the 20 full boxes. So, 495 ÷ 20 = 24.75, which means each full box holds 24 tins (since we can't have a fraction of a tin). Therefore, the number of tins in box 21 is 496 - 20*24 = 496 - 480 = 16 tins.
Robert is in charge of a community swimming pool. Each sprig he drains it in order to clean it. Then he refills the pool, which holds 120,000 gallons of water. Robert fills the pool at a rate of 10 gallons each minute. What is the rate at which Robert will fill the pool? Is it constant? Write an equation for the direct variation.
Answer:
It is constant (10 gallons a minute)
120,000/10 = 12,000
12,000 minutes to fill the pool
120,000 - 10x
Step-by-step explanation:
Answer:
The pool holds 120,000 gallons of water.
Robert fills the pool at a rate of 10 gallons each minute.
That means for filling 120000 gallons, he will need = [tex]\frac{120000}{10}[/tex] = 12000 minutes
If we convert this to hour, then in 1 hour, [tex]10\times60[/tex] = 600 gallons can be filled.
So, the rate in gallons per hour = [tex]\frac{120000}{600}[/tex] = 200 gallons per hour.
Therefore, the rate at which Robert will fill the pool is 200 gallons per hour.
Yes the rate is constant.
Add -5+2/8 PLEASE HELP MEEE
[tex]\bold{Hey\ there!} \\ \bold{-5+\frac{2}{8}} \\ \bold{-5=-\frac{5}{1}}\\ \bold{Problem\ becomes\rightarrow -\frac{5}{1}+\frac{2}{8}} \\ \bold{\frac{2\div2}{8\div2}=\frac{1}{4}}\\ \bold{-\frac{5}{1}+\frac{1}{4}} \\ \bold{-5\times4=-20}\\ \bold{1\times4=4} \\ \bold{Problem\ becomes:\frac{-20+1}{4}} \\ \bold{-20+1=-19} \\ \bold{4=4} \\ \boxed{\boxed{\bold{Answer:\frac{-19}{4}}}}\checkmark[/tex]
[tex]\bold{Good\ luck\ on\ your\ assignment\ \& \ enjoy\ your\ day!} \\ \\ \\ \frak{LoveYourselfFirst:)}[/tex]
Evan mixed 2,2/3 pounds of nuts with 1,5/6 pounds of raisins and 1,7/8 pounds of chocolate chips how many pounds did this mixture weigh?
Answer:
6.375 or 6 3/8
Step-by-step explanation:
Just add 2 2/3+1 5/6+1 7/8 and that= 6.375 or 6 3/8
The following expression represents the density of an object that has a mass of m and a volume of V.
M/V
If a laptop has a volume of 2,850 cubic centimeters and a mass of 2,300 grams, what is the density of the laptop in G/cm3
A. 1 5/23
B.15/19
C. 1 11/46
D. 46/57
Final answer:
The density of the laptop is calculated by dividing the mass (2,300 grams) by the volume (2,850 cubic centimeters), resulting in a density of 0.807 g/cm³, which is approximately 46/57.
Explanation:
To find the density of the laptop in grams per cubic centimeter (g/cm³), we use the formula density = mass/volume. The mass of the laptop is given as 2,300 grams and the volume is given as 2,850 cubic centimeters. By substituting into the formula:
Density = Mass / Volume = 2,300g / 2,850cm³ = 0.807 g/cm³.
When expressed as a fraction in simplest form, this is approximately 46/57 (since 0.807 ≈ 46/57). Hence, the answer is D. 46/57.
Which word has a horizontal line of symmetry?
A. LIT
B. HAD
C. HIP
D. BED
D.Bed because if you were to split the word BED in half horizontally you would be able to put them together and it match up.
Who is correct and why?
Nadine is incorrect because she should have applied the quotient of powers rule first.
Nadine is correct because she correctly applied the power of a product rule.
Calvin is incorrect because he should have applied the power of a product rule first.
Calvin is correct because he correctly applied the quotient of powers rule.
Answer:
answer D
Step-by-step explanation:
The person that is correct is; Calvin is correct because he correctly applied the quotient of powers rule.
How to apply the rule of exponents?The expression that Nadine and Calvin were trying to simplify is;
r⁻⁵s⁻³/(r⁸s⁻²)
Now, we are told that Nadine claims the first step is to simplify the expression is to raise the numerator and denominator to the given power.
Meanwhile, Calvin claims the first step to simplify the expression is to apply the quotient of powers.
We can conclude that Calvin is correct because he correctly applied the quotient of powers rule.
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The coordinates of points M,N, and P are ....
Answer:
(-1, -1) Let me know if the explanation didn't make sense.
Step-by-step explanation:
If we graph the three points we can see what looks like a quadrilateral's upper right portion, so we need a point in the lower left. This means M is only connected to N here and P is only connected to N. So we want to find the slope of these two lines.
MN is easy since their y values are the same, the slope is 0.
NP we just use the slope formula so (y2-y1)/(x2-x1) = (-1-3)/(5-4) = -4.
So now we want a line from point M with a slope of -4 to intersect with a line from point P with a slope of 0. To find these lines weuse point slope form for those two points. The formula for point slope form is y - y1 = m(x-x1)
y-3 = -4(x+2) -> y = -4x-5
y+1 = 0(x-5) -> y = -1
So now we want these two to intersect. We just set them equal to each other.
-1 = -4x -5 -> -1 = x
So this gives us our x value. Now we can plug that into either function to find the y value. This is super easy of we use y = -1 because all y values in this are -1, so the point Q is (-1, -1)
A parallelogram has sides of length 30 centimeters and 18 centimeters. One of its angles measure 58 degrees. Which is the best estimate for the parallelogram
A 274.8 cm squared
B 286.2 cm squared
C 457.9 cm squared
D 540.0 cm squared
Answer:
D
Step-by-step explanation:
I'm assuming you're looking for area here.
The formula is b * h = A
So all you're doing is multiplying 30 by 18 to get 540.
The pitch of a roof is found the same way as the slope of a line. What is the pitch of a roof that has a height of 9 ft and a horizontal run of 7
Answer:
9/7
Step-by-step explanation:
Since the pitch is found the same way as the slope of a line
Tangent= slope = pitch
But; Tangent = Opposite/Adjacent
Therefore;
Tan x = 9/7
Thus;
The pitch of the roof is 9/7
Tell whether the angles are adjacent or vertical. Then find the value of x
Answer:
Vertical angles
x =37
Step-by-step explanation:
Adjacent angles are next to each other and share one side
Vertical angles are across from each other and only share a vertex.
These angles are vertical angles. Vertical angles are equal
3x-4 = 107
Add 4 to each side
3x-4 +4 =107+4
3x = 111
Divide by 3
3x/3 = 111/3
x=37
what does trace of matrix mean explain with examples
Trace of a matrix is defined only for a square matrix . It is the sum of the elements on the main diagonal, from the upper left to the lower right, of the matrix
Kelsey is hiking from the woods to the lodge. She hikes past tree A (3 Miles) and B (4 Miles) in order to get to the lodge. How much distance should she have saved by going straight to the lodge from tree A ?
Answer:
1 mile
Step-by-step explanation:
Y=f(x) = -1x find f(x) when x= 0
f(0) equals 0. When x is 0 in the given function, the result of f(x) is also 0.
To find the value of f(x) when x=0 for the function f(x) = -1x, substitute 0 for x:
f(0) = -1(0) = 0.
Therefore, f(0) equals 0. When x is 0 in the given function, the result of f(x) is also 0.
Gina has 400 records. If Johnny were to double the number of records that he now owns, he would still have fewer than Gina has.
Johnny currently owns fewer than 200 records.
Let's denote:
- \( x \) as the number of records Johnny currently owns.
Given:
- Gina has 400 records.
- Johnny would still have fewer than Gina has if he were to double the number of records he owns.
We can set up the following inequality:
[tex]\[ 2x < 400 \][/tex]
To find the maximum value of \( x \), we solve for it:
[tex]\[ x < \frac{400}{2} \]\[ x < 200 \][/tex]
So, Johnny currently owns fewer than 200 records.
In the figure, KT and KY are tangent segments to circle O. Find KT and OY. You must show your work. Someone please help me out !!!
Answer:
KT = 60
OY = 11
Step-by-step explanation:
Remember that the tangent to a circle theorem states that if a line is tangent to a circle, it is perpendicular to the radius at the point of tangency. Which means angles OTK and OYK are right angles.
If OTK and OYK are right angles, triangles KOT and KYO are right triangles. Since KOT is a right triangle, we can use the Pythagorean theorem to find KT:
[tex]hypotenuse^2=leg^2+leg^2[/tex]
[tex]KO^2=KT^2+OT^2[/tex]
[tex]61^2=KT^2+11^2[/tex]
[tex]KT^2=61^2-11^2[/tex]
[tex]KT=\sqrt{3600}[/tex]
[tex]KT=60[/tex]
Now, remember that the "hat" theorem states that tangents to a circle from the same external point are congruent, so KT and KY are congruent.
The Hypotenuse-Leg theorem states that if the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg another right triangle, then the triangles are congruent. The hypotenuse, KO, of both right triangles are the same (therefore congruent) and legs KT and KY are congruent by the hat theorem, therefore triangles KOT and KYO are congruent. Since corresponding parts of congruent triangles are congruent, OY ≅ OT.
OY = OT = 10
OY = 10
Let's summary the above in a short proof:
1. ∠OTK and ∠OYK are ∟ angles Tangent to a circle theorem
2. ΔOTK and ΔOYK are ∟ triangles Definition of right triangles
3. KT ≅ KY Hat theorem
4. KT = 60 Pythagorean theorem
5. OY ≅ OT CPCTC
6. OY = 10 Definition of congruency