The simplified expression of (7 + 9i)(8 - 10i) is 146 + 2i
How to simplify the expression?The expression is given as:
(7 + 9i)(8 - 10i)
Expand the bracket
7 * 8 + 9i * 8 -7 * 10i - 9i * 10i
Evaluate the products
56 + 72i -70i - 90(i²)
Evaluate the difference
56 + 2i - 90(i²)
In complex numbers;
i² = -1
So, we have:
56 + 2i - 90(-1)
Evaluate
56 + 2i + 90
Add the like terms
146 + 2i
Hence, the simplified expression of (7 + 9i)(8 - 10i) is 146 + 2i
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b) 9 11 13 15 17
Terms of
n, an expression for the nth term
Answer:
Tn= a+( n-1) 3
Tn= 9+(n-1)3
Two adjacent rooms are rectangles, both of length 13 feet by 10 feet. Jerry wants to change the carpets in both rooms. How many square feet should he order?
Answer:
260 square feet
Step-by-step explanation:
The area of a rectangle is given by the formula ...
A = LW
The area of two same-size rectangular rooms will be double the area of one of them.
__
room areaEach room has an area of ...
A = LW = (13 ft)(10 ft) = 130 ft²
carpet orderThe order for carpet must be for 2 times the area of one room:
carpet order = 2 × 130 ft² = 260 ft²
Jerry should order 260 square feet of carpet.
In the diagram, points D and E are marked by drawing arcs of equal size centered at B such that the arcs intersect and . Then, intersecting arcs of equal size are drawn centered at points D and E. Point P is located at the intersection of these arcs.
Based on this construction, m∠ABP is
°, and m∠ABC is
°.
The measure of ∠ABP and ∠ABC are 32° and 64° respectively.
what is a bisector of an angle?Any line which divides an angle into two equal halves is a bisector of that angle.
Analysis:
Since the arcs at D and E are drawn with the same radius and arc using center D and E are intersected by line PB( which is the bisector of the full arc with center B) then ∠ABP = ∠PBC = 32°.
∠ABC = ∠ABP + ∠PBC
∠ABC = 32 + 32 = 64°
In conclusion, ∠ABP and ∠ABC are 32° and 64°
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Answer:ABP is 32 degrees, and ABC is 64 degrees
Step-by-step explanation: bi hope this helped if not sorry:)
Let H be the set of real numbers less than or equal to eleven
Answer:
The answer would be Set: "S" = the set of natural numbers greater than 11.
Hope this helps!
Help me please it’ll be a big help
ow many decimals numbers are there whose value equals the average of their digits?
For example, 2.3 has the digits 2 and 3. Their average is 2.5 -- so that doesn’t work. But there are some that do!
There are a few rules:
Answer:
Step-by-step explanation:
there are infinite numbers between 2 and 3 having average=2.5
2.49,2.51
2.48,2.52
2.47,2.53
2.46,2.54
.................
2.491,2.509
2.492,2.508
2.493,2.507
......................
one side of a square is represented
Answer:
therees nothing here to help you with?
Step-by-step explanation:
srry abt that but add the square number
What additional information is needed to prove the triangles are congruent by the SAS postulate
Answer: [tex]\angle XWY \cong \angle ZWY[/tex]
Step-by-step explanation:
We know that [tex]\overline{WY} \cong \overline{WY}[/tex] by the reflexive property, so we need the included angles to be congruent (meaning [tex]\angle XWY \cong \angle ZWY[/tex]
Need one person help for math Plato class
Answer:
The answer is B. 13.7 inches
i hope this can help you! :)
Show that tanø+Cotø = Secø Cosecø
Answer:
True.
Keys:
Manipulate left/right sidesStep-by-step explanation:
[tex]\tan \left(\theta\right)+\cot \left(\theta\right)=\sec \left(\theta\right)\csc \left(\theta\right)\\\tan \left(\theta\right)+\cot \left(\theta\right)\\=\frac{\cos ^2\left(\theta\right)+\sin ^2\left(\theta\right)}{\cos \left(\theta\right)\sin \left(\theta\right)}\\=\frac{1}{\cos \left(\theta\right)\sin \left(\theta\right)}\\\\\sec \left(\theta\right)\csc \left(\theta\right)\\=\frac{1}{\cos \left(\theta\right)\sin \left(\theta\right)}[/tex]
What was shown throughout this problem?
We showed that two different sides are capable of taking the same form.
Inaaya has a jar of coins containing only nickels, dimes, and quarters. A nickel is worth 5 cents, a dime is worth 10 cents, a quarter is worth 25 cents, and a dollar is worth 100 cents.
The ratio of the number of quarters to the number of dimes to the number of nickels in the jar is 9:3:1. The total value of all the coins in the jar is $18.20. How many coins does Inaaya have in her jar?
Answer: 91 coins
9 x 25 = 2.25 dollars
3 x 10 = 30 cents
1 x 5 = 5 cents
Determine the true statements about trend lines in scatterplots. Check all that apply.
A trend line can be used to make predictions in real-world situations.
A scatterplot that shows no correlation between the variables does not have a trend line.
A line of best fit must contain at least two of the original points.
A regression line and trend line are equivalent terms.
Answer:
give that 13.3cm is 15% of a certain length, what is the complete length
Answer: A,B and D ARE THE CORRECT ANSWERS
Step-by-step explanation:
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
The quotient of is
.
The value of the quotient of 0.378 ÷ 0.3 is 1.26
Missing information in the questionThe quotient of 0.378 ÷ 0.3 is
How to determine the quotient?The expression is given as:
0.378 ÷ 0.3
Rewrite as a fraction
0.378/0.3
Multiply the fraction by 1
Express 1 as 1000/1000
0.378/0.3 * 1000/1000
Evaluate the product
378/300
Divide 378 by 300
1.26
Hence, the quotient of 0.378 ÷ 0.3 is 1.26
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Triangle \triangle ABC△ABCtriangle, A, B, C is reflected across line nnn to create \triangle A'B'C'△A
′
B
′
C
′
triangle, A, prime, B, prime, C, prime.
A triangle A B C. The length of side CA is sixty one units. The angle B is sixty seven degrees. The line n is to the right of triangle A B C. Triangle A prime B prime C prime is the image of triangle A B C after being reflected across line n. The length of side C prime B prime is fifty seven units. Angle A prime is fifty nine degrees.
A triangle A B C. The length of side CA is sixty one units. The angle B is sixty seven degrees. The line n is to the right of triangle A B C. Triangle A prime B prime C prime is the image of triangle A B C after being reflected across line n. The length of side C prime B prime is fifty seven units. Angle A prime is fifty nine degrees.
What is the measure of \angle C∠Cangle, C?
Answer: [tex]54^{\circ}[/tex]
Step-by-step explanation:
Because reflections are rigid motions, we know that [tex]\triangle ABC \cong \triangle A'B'C'[/tex], and thus [tex]\angle B \cong \angle B'[/tex].
It follows that since angles in a triangle add to 180 degrees, [tex]m\angle C'=180^{\circ}-59^{\circ}-67^{\circ}=\boxed{54^{\circ}}[/tex]
if g(X)=3x-5,then find g^-1(5),where g is one to one onto function
Answer:
g^-1(5)=10/3
Step-by-step explanation:
g(x)=3x-5
g(x)= y
g^-1( y)=x
3x-5=y
3x=y+5
x=y+5/3
g^-1(y)=y+5/3
g^-1(5)=5+5/3
g^-1(5)=10/3
A bicycle wheel travels exactly 26/pi inches in I full rotation, what is the area, to the nearst square inch, of a circle the same size az the bicycle wheel?
The area, to the nearst square inch, of a circle the same size az the bicycle wheel is 531 inches².
What is the area of the circle?A circle is a bounded figure which points from its center to its circumference is equidistant.
Area of a circle = πr²
Where :
π = pi = 22/7
R = radius
The full rotation of the wheel is equal to the circumference of the wheel.
circumference of the wheel = 2 πr
26π = 2 πr
r = 13 inches
Area = 22/7 x 13³ = 531 inches²
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Translate then Solve for the variable:
The sum of two times a number and 10 is five times the difference of a number and six.
Solve for the variable then type the answer after rounding your answer to the nearest hundredths
The linear equation will be 2x + 10 = 5(x - 6). Then the value of the variable x will be 23.33.
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
Translate then Solve for the variable:
The sum of two times a number and 10 is five times the difference between a number and six.
Let the number be x.
Then the equation will be
2x + 10 = 5(x - 6)
Then the value of x will be
2x + 10 = 5x - 60
5x - 2x = 60 + 10
3x = 70
x = 23.33
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PLEASE HELP ME!!! I WILL GIVE BRAINLEST
PLEASE
Answer:
7
Step-by-step explanation:
you just multiply from the least and once you get to the greatest, it should be 7
NEED HELP ASAP!!! PLEASE
The linear function that has a different rate of change from y = -3x+4 is A, a function with a y-intercept of -4 that passes through the point (-3,-13)
What is an intercept?An intercept is the point where a straight line or a curve meets with the x or y axes.
Analysis:
The rate of change is the same as slope. The slope of y = -3x + 4 is -3,
All other functions Except A have a slope of -3.
for linear function A,
if y = mx + c, c = -4, x = -3, y = -13
-13= -3m - 4
-3m = -9
m = 3
In conclusion, linear function A with a y-intercept of -4 passing through the point (-3,-13) has a different rate of change from y = -3x + 4
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Which function is shown in the graph below?
O y = logo 4x
O y = log₁x
O y = log3x
O y = log10x
The correct function shown in the graph is,
⇒ log₁₀ (ax) = 1
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
It has been given that the point (3,1) is on the graph. For the point (3,1) to be on the graph, the following must hold true:
⇒ log₁₀ (ax) = 1
or , ax = 10¹ = 10
Thus, x = 10/a
So, in order for the point (3,1) to lie on the graph, of all the given options the closest we can get is when we have Option D, that is, when a = 3. That will make x = 3.33 and thus, .
⇒ log (3 × 3.33) = 0.99 ≈ 1
Thus, out of the given options only Option D seems to be the most probable answer.
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OMG SUPER HARD QUESTION I DONT KNOW
bob has 2 apples then he eats 1 apple how many apples does he have left
Answer:
1 apple
Step-by-step explanation:
unless you are a psycho who counts the one he ate as still in his possession,
therefore 2 - 1 = 1
hope this helps:)
Which criterion, if any, could prove the triangles are congruent?
Answer: None
Step-by-step explanation:
There is only one pair of angles and one pair of sides, which is not sufficient to prove triangle congruence.
Help pleaseeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
PROBLEMS
1) Add the following: 30 mg, 2.5 kg and 7.0 g. Express the answer in g.
2) Express the amount of 1.243 g as:
mg ________
kg ________
mcg _______
3) How many grams of the active ingredient "aspirin" would be needed to make 500 aspirin tablets if each tablet must contain 325 mg?
Answer:
1. 2507.034 g
2. 1243mg
0.001243kg
1,243,000 mcg
3. 162.5g
Step-by-step explanation:
1. First of all we need to convert 30mg and 2.5kg to gram.
⇒ 1 gram = 1000 milligrams
x = 35mg
⇒ 1000mg(x) = 35mg
⇒ x = 35mg = 35 = 0.035g
1000mg 1000
Next we convert 2.5kg to gm.
⇒ 1 kilogram = 1000g
2.5kg = x
(We then criss cross)
⇒ x = 2.5kg × 1000g = 2500g = 2500g
1kg 1
Now that we converted them all to gram, we will add them.
⇒ 30mg + 2.5kg + 7g = 0.035g + 2500g + 7g = 2507.035 ≈ 2507g
2. We convert 1.234g into
a. mg
⇒ 1 gram = 1000 milligram
1.243g = x
⇒ x = 1.243g × 1000mg = 1243mg = 1243mg
1g 1
b. kg
⇒ 1 kilogram = 1000gram
x = 1.243 gram
⇒ x = 1.243g × 1kg = 1.243kg = 0.001243kg = 1.243 × 10⁻³ kg
1000g 1000
c. mcg
⇒ 1 gram = 1000000mcg
1.243g = x
⇒ x = 1.243g × 1,000,000mcg = 1,243,000mcg = 1,243,000mcg
1 g 1
3. We need 500 aspirin, the amount of grams needed and we know that one tablet contains 325mg.
So now we can derive the formula such that:
⇒ 1 tablet = 325mg
500 tablet = x
But first we need to convert 325mg to grams.
⇒ 1 gram = 1000mg
x = 325mg
⇒ x = 325mg × 1 g = 325g = 0.325g
1000mg 1000
So now instead of using 325mg we can use 0.325g.
⇒ 1 tablet = 0.325g
500 tablets = x
⇒ x = 500 tablets × 0.325g = 162.5g = 162.5g
1 tablet 1
3. The circumference of a circle is 607 cm. What is the diameter of the circle?
120 cm
30 cm
60 cm
90 cm
Answer:
the circumference is 30 cm,
Step-by-step explanation:
Hope it helps
Use the given right triangle to find ratios, in reduced form, for sin A, cos A, and tan A. 6 10
Answer:
1.0452
Step-by-step explanation:
10*sin6
10*0.1045
the answer is 1.0452
A motor boat can travel 45 km downstream in 2 h and 30 min; and 39 km upstream in 3 h and 15 min. What is the speed of the boat in still water? What is the speed of the current?
Answer:
c = speed of current = 3 km/hr
r = speed of boat in still water = 15 km/hr
Step-by-step explanation:
Use the formula distance = time x rate to set up these equations
45 = 2.5 (r+c)
39 = 3.25 (r-c)
(r + c) is the speed of the boat added to the speed of the current, downstream
(r - c) is the speed of the boat minus the speed of the current, upstream
Use one equation to isolate a variable then substitute it into the other equation to solve the system.
39/3.25 = r - c
12 + c = r
45 = 2.5 ( 12 + c + c )
18 = 12 + 2c
6 = 2c
c = 3
Then use the equation 12 + c = r from above
12 + c = r
12 + 3 = 15
r = 15 km/hr
triangle.
A,
angle CAB = 90°, angle ABC = 52° and AC = 9.2.
Calculate the length of BC rounded to 3 SF.
[tex]\\ \rm\Rrightarrow sin\theta=\dfrac{Perpendicular}{Hypotenuse}[/tex]
[tex]\\ \rm\Rrightarrow sin52=\dfrac{AC}{BC}[/tex]
[tex]\\ \rm\Rrightarrow sin52=\dfrac{9.2}{B C}[/tex]
[tex]\\ \rm\Rrightarrow B C=\dfrac{9.2}{sin52}[/tex]
[tex]\\ \rm\Rrightarrow B C=9.3[/tex]
Answer:
11.7 (3 s.f.)
Step-by-step explanation:
Given information:
∠CAB = 90°∠ABC = 52°AC = 9.2As one of the given angles is 90°, the triangle is a right triangle.
Draw the triangle using the given information (see attached) to help visualize the problem.
To calculate the length of BC, use the sine trigonometric ratio:
[tex]\sf \sin(\theta)=\dfrac{O}{H}[/tex]
where:
[tex]\theta[/tex] is the angleO is the side opposite the angleH is the hypotenuse (the side opposite the right angle)From inspection of the attached triangle:
[tex]\theta[/tex] = 52°O = AC = 9.2H = BCSubstitute the values into the formula and solve for BC:
[tex]\implies \sf \sin(52^{\circ})=\dfrac{9.2}{BC}[/tex]
[tex]\implies \sf BC=\dfrac{9.2}{\sin(52^{\circ})}[/tex]
[tex]\implies \sf BC=11.67496758...[/tex]
[tex]\implies \sf BC=11.7\:\:(3 \:s.f.)[/tex]
Therefore, the length of BC is 11.7 (3 s.f.).
Photo is attached, please help! Will give brainliest.
Answer:0.124402866242
Step-by-step explanation:here’s my attempt: dv/dt=d/dt(4pi/3r^3). 100=d/dt((4pi/3)*(8+X*t)^3) at t=0. 100/(4(pi)*8^2)=x where x is the rate of change of the radius. Not 100% sure though
Write the standard number.
3.6 * 10^-6
Answer:
The answer is 0.0000036.
Step-by-step explanation:
Move the decimal place 6 spaces to the left. I hope this helps! :)
what is the quotient of 1/5 divide by (-5/7) =
Answer:
-7/25
Step-by-step explanation:
=(1/5) ÷ (-5/7)
Copy dot flip
=(1/5) * (-7/5)
=-7/25