Answer:
The answer is 13.
Step-by-step explanation:
(b) Find the value of 2a + b: Remember that 2a means 2 × a. Replacing a by 4 and b by 7 gives 2×4 + 7.
Two possible values for 2a - b are 4i√2 and -4i√2, where 'i' is the imaginary unit.
To find the value of 2a - b, we need to eliminate 'b' from the two equations given.
Given equations:
1. 2a + b = 4
2. ab = -3
Let's solve for 'a' and 'b' using these equations.
Step 1: Solve for 'b' in terms of 'a' from equation (1).
2a + b = 4
b = 4 - 2a
Step 2: Substitute the value of 'b' from step 1 into equation (2).
a(4 - 2a) = -3
[tex]4a - 2a^2 = -3[/tex]
Step 3: Rearrange the equation to a quadratic form:
[tex]2a^2 - 4a + 3 = 0[/tex]
Step 4: Solve the quadratic equation for 'a'. You can use the quadratic formula:
a = [ -(-4) ± √([tex](-4)^2[/tex] - 4*2*3) ] / (2*2)
a = [ 4 ± √(16 - 24) ] / 4
a = [ 4 ± √(-8) ] / 4
a = [ 4 ± 2i√2 ] / 4
a = 1 ± i√2
Now we have two possible values for 'a': a = 1 + i√2 and a = 1 - i√2, where 'i' is the imaginary unit (√(-1)).
Step 5: Find the corresponding values of 'b' using the equation b = 4 - 2a.
For a = 1 + i√2:
b = 4 - 2(1 + i√2) = 4 - 2 - 2i√2 = 2 - 2i√2
For a = 1 - i√2:
b = 4 - 2(1 - i√2) = 4 - 2 + 2i√2 = 2 + 2i√2
Now we have two sets of values for 'a' and 'b':
1. a = 1 + i√2, b = 2 - 2i√2
2. a = 1 - i√2, b = 2 + 2i√2
Step 6: Calculate the value of 2a - b for each set of values:
For a = 1 + i√2, b = 2 - 2i√2:
2a - b = 2(1 + i√2) - (2 - 2i√2)
= 2 + 2i√2 - 2 + 2i√2
= 4i√2
For a = 1 - i√2, b = 2 + 2i√2:
2a - b = 2(1 - i√2) - (2 + 2i√2)
= 2 - 2i√2 - 2 - 2i√2
= -4i√2
So, the two possible values for 2a - b are 4i√2 and -4i√2, where 'i' is the imaginary unit.
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Complete Question:
If 2a + b = 4 and ab = -3, what is the value of 2a - b
unit 10: circles Homework 4: Inscribed angles. please complete the following questions and explain how it is done.
Answer:
Step-by-step explanation:
5. angle FDE = 180-90-63 = 27°
arc FE = 2×27 = 54°
6. arc GJ = 360-68-31-115 = 146°
angle GHJ = 146/2 = 73°
7. angle GIJ = 146/2 = 73°
8. arc DAB = 2×101 = 202°
arc BCD = 360°-202 = 158°
angle A = 158/2 = 79°
angle B = 360-79-110-68 = 112°
10. see picture
5) The sum of angle in the triangle DEF is 180 degrees
mFE = <D
Recall that <D+<E+<F = 180⁰
<D+63+90 = 180
<D = 180-153
<D = 27 degrees
Hence the measure of arc FE is 27degrees
6) For this circle geometry, we will use the theorem
The sum of Opposite side of a cyclic quadrilateral is 180 degrees.
A + C = 180
m<A + 101 = 180
m<A = 180-101
m<A = 79degrees
Similarly
B + D = 180
m<B + 68 = 180
m<B = 180-68
m<B = 112degrees
7) The sum of angle in a circle is 360, hence;
arcGJ+68+31+115 = 36p
arcGJ = 360 - 214
arcGJ = 146⁰
Since the angle at the centre is twice angle at the circumference, then;
<GHJ = 1/2 arcGJ
<GHJ = 1/2(146)
<GHJ = 73⁰
<GHJ = <GIJ = 73⁰ (angle in the same segment of the circle are equal)
8) Recall that the sum of Opposite side of a cyclic quadrilateral is 180 degrees.
P + R = 180
57 + <R = 180
m<R = 180-57
m<R = 123degrees
Similarly, m<Q+m<S = 180⁰
Since the triangle in a semi circle is a right angled triangle, hence m<Q = 90 degrees (triangle PQR is a right angled triangle)
m<S = 180 - 90
m<S = 90 degrees
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simply the ratio of 650ml to 2litre
Answer:
13: 40
Step-by-step explanation:
as 650 ml is given
so 2l = 2000 ml
ratio = 650 / 2000
13/40
13:40
Frisco ISD had a student enrollment of approximately 46,000 students in 2013 and is growing at an average rate of about 6% annually. If this rate continues the enrollment growth can be modeled using the equation 46000(1.06)t = y where t represents time in years and y represents number students. How many years will pass until the population of Frisco ISD is at 100,000 students? ≈ 13.33 years ≈ 85.91 years ≈ 5.62 years ≈ 2.05 years
Answer:
≈ 13.33 years
Step-by-step explanation:
The population of Frisco ISD after t years is given by the following equation:
[tex]y(t) = 46000(1.06)^{t}[/tex]
How many years will pass until the population of Frisco ISD is at 100,000 students?
This is t for which [tex]y(t) = 100000[/tex]. So
[tex]y(t) = 46000(1.06)^{t}[/tex]
[tex]46000(1.06)^{t} = 100000[/tex]
[tex](1.06)^{t} = \frac{100000}{46000}[/tex]
[tex]\log{(1.06)^{t}} = \log{\frac{100000}{46000}}[/tex]
[tex]t\log{1.06} = \log{\frac{100000}{46000}}[/tex]
[tex]t = \frac{\log{\frac{100000}{46000}}}{\log{1.06}}[/tex]
[tex]t = 13.33[/tex]
So the answer is ≈ 13.33 years
The question is in the picture down below!
25 degrees
35 degrees
45 degrees
55 degrees
Answer:
35°
Step-by-step explanation:
Complementary angles has a sum of 90°
m<A + m<B = 90°
2x + 23 + 4x -29 = 90° add like terms
6x - 6 = 90° add 6 to both sides
6x = 96 divide both sides by 6
x = 16 now replace the x in m<B = 4x - 29 with 16
4×16 - 29 = 35
Whats the relationship between a and b
they are supplemen angles
Distribute and Combine Like Terms. 2(x + 7) - 2x
Answer:
14
Step-by-step explanation:
You just multiply 2 to (x + 7) which gets you 2x + 14 and then subtract 2x from 2x seeing as they are like terms and you end up with 14.
Can someone help me? I'll reward points and brainalist
Answer:
135 degrees
Step-by-step explanation:
45 is for half of the square so u would add 45+45+45 or 45x3. there is a half and 1 whole square.
Step-by-step explanation:
135 is the I g
forgot how to spell it but yeah
Which expression is equivalent to this polynomial expression? (2x^2 – 3y^2)(4x^4 + 6x^2y^2 +9y^4)
Answer:
[tex]26 {x}^{6} - 18 {x}^{2} {y}^{4} - 27 {x}^{4} {y}^{2} [/tex]
Step-by-step explanation:
click the link for alot more explanation, I'm tried typing
https://photomath.net/s/l5LVxj
Answer:
B
Step-by-step explanation:
Which resource is a renewable resource?
coal
O gemstones
metal
trees
Answer:
trees
Step-by-step explanation:
Trees are renewable resources. Trees can be planted, grown up, and harvested for timber. Forests are a different thing, however. A forest is a mature ecosystem.
Trees are renewable resource.
Option D is correct.
What is Renewable Resource?A renewable resource is one that can replace itself spontaneously over time. As a result, despite human usage, it is sustainable.
Renewable resources are particularly important because of their potential to replace non-renewable, or finite, resources in energy production. Furthermore, renewable resources can provide cleaner energy solutions than nonrenewable resources such as coal and fossil fuels.
Coal, gemstones, and metals are considered as non-renewable resources since they can be exhausted and are not available for lengthy periods of time. They are used as time goes on.
Thus, Trees are Renewable resources.
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PLEASE HELP ME!!!!!!!!!!!!!!!!!!!!!
Nancy has a lot of things in her locker. There are 14 items in her locker, including 6 pencils. What is the probability that a randomly selected item from Nancy's locker will be a pencil?
A. 8/14
B 7/14
C 3/7
Answer: B 7/14
Step-by-step explanation:
Pls HELP THANKS
A smaller number is 3 less than half a larger number. The larger number is 10 times 1 less than the smaller number.
Let x represent the smaller number, and let y represent the larger number. Which equations can be used to model the
situation? Check all that apply.
X equals 1/2 Y -3
2X minus Y equals -6
2X minus Y equals -3
X equals 1/2 ( Y -3)
Y equals 10 (X -1)
Answer:
Step-by-step explanation:
Solve x2 + 18x – 19 = 0 by completing the square.
Answer:
x = 1, x = -19
Step-by-step explanation:
1) factorise
(x−1)(x+19)=0
2) equal to 0
x−1=0 or x+19=0
x=1 or x=−19
Answer:
[tex]x = 1[/tex]
[tex]x = 19[/tex]
Step-by-step explanation:
Set up equation
[tex] {x}^{2} + 18x - 19 = 0[/tex]
Add 19 on both sides
[tex] {x}^{2} + 18x = 19[/tex]
Divide 18 by 2 and sqr it.
[tex]( \frac{18}{2}) {}^{2} [/tex]
[tex] {9}^{2} = 81[/tex]
Add 81 on both sides
[tex] {x}^{2} + 18x + 81 = 100[/tex]
Using the AC method, isolate the left side into a binomial.
[tex](x + a)(x + b)[/tex]
that a and b can be added to equal 18 and be multiplied to equal 81.
Only number that does that is 9. 9+9=18, 9×9=81
[tex](x + 9)(x + 9)[/tex]
[tex](x + 9) {}^{2} [/tex]
Set up equation
[tex](x + 9) {}^{2} = 100[/tex]
Take sqr root of both sides
[tex]x + 9 = 10[/tex]
Since sqr root of a positve number can be negative, set up this equation also
[tex]x - 9 = 10[/tex]
[tex]x = 1[/tex]
OR
[tex]x = 19[/tex]
Pls help with these math questions. Don't just do it for points pls I really need help . 3 questions Multiple choice
Answer:
6,7,7 is your answer
6.
3x+2=2x+8
x=6
Step-by-step explanation:
7.14x+12+10x=180
24x=180-12
x=168/24=7
8.9x-3=7x+11
9x-7x=11+3
2x=14
x=14/2=7
Riley invested $8,500 in an account paying an interest rate of 3.8% compounded
daily. Assuming no deposits or withdrawals are made, how long would it take, to the
nearest year, for the value of the account to reach $18,040?
Answer:20
Step-by-step explanation:
GIVING BRAINIEST!!!!!!!!!!!! 3 times the difference of 4g and 4 is less than -6 times the sum of -3g and 4!
Answer:
3(4g-4)<-6(-3g+4)
HELP MEEE!!!
Use the drawing below to answer the questions that follow.
What is the scale factor going from smaller to larger?
(reference photo please)
Step-by-step explanation:
Part A: Let see what number we can multiply by 3 to get 13.5
[tex]3x = 13.5[/tex]
[tex]x = 4.5[/tex]
so our answer is 4.5
Part B : Set up the proportion
3 and 13.5 correspond with each other and the question mark side corresponds with the 9 cm side.
let x = the side we are trying to find
[tex] \frac{3}{x} = \frac{13.5}{9} [/tex]
Cross multiply
[tex]27 = 13.5x[/tex]
[tex]x = 2[/tex]
so our answer is 2.
ill mark brainlist plss help
Answer:
Milligram
Step-by-step explanation:
milligram b/c kilogram and gram are too big of a mass measurement for a strand of hair and meter does not measure the mass of the strand of hair it could measure the length
For this question, if the answer is not a whole number, enter it as a fraction using / as the fraction bar.
Rajek, a truck driver, hauls containers for his customers. One customer wants to know the total amount of cardboard that can fit in a container at one time. The truck Rajek uses is shown below.
The base of the container has an area of 50 1/4 square feet.
Answer:
226 1/8
Step-by-step explanation:
Substitute the measurements of the container into the formula.
The amount of cardboard Rajek can fit in the container at one time is cubic feet.
The total surface area of the container is 9L + 9W + 50 1/4
What is a rectangle?A rectangle is a 2-D shape with length and width.
The length and width are different.
If the length and width are not different then it is a square.
The area of a rectangle is given as:
Area = Length x width
We have,
To find the total amount of cardboard that can fit in the container at one time, we need to find the surface area of the container.
The container has a rectangular base with an area of 50 1/4 square feet.
Let's assume the length of the base is L and the width is W.
We know that:
L x W = 50 1/4
We also know that the height of the container is 4(1/2) feet, which is equivalent to 9/2 feet.
The container has two identical sides, which are rectangles with a length of L and a height of 9/2 feet.
The surface area of one side is:
L x (9/2) = (9/2)L
The container also has two identical ends, which are rectangles with a width of W and a height of 9/2 feet.
The surface area of one end is:
W x (9/2) = (9/2)W
Finally, the container has a top, which is a rectangle with a length of L and a width of W.
The surface area of the top is:
L x W
To find the total surface area of the container, we add up the surface area of each of these parts:
Total surface area = 2(L x (9/2)) + 2(W x (9/2)) + (L x W)
Simplifying this expression, we get:
Total surface area = 9L + 9W + LW
We know that L x W = 50 1/4, so we can substitute this into the equation:
Thus,
The total surface area of the container is 9L + 9W + 50 1/4
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10 POINTS PLS ANSWER PLSS ASAP THANKS
Answer: C
Step-by-step explanation:
Niko has 3 friends he gives his friends 1/4 pieces of candy each. How much does each person get?
Answer:
12
Step-by-step explanation:
Please help!
Thanks!
Answer:
i think it's -2, -14 quardrant 2
Step-by-step explanation:
What is the area of the shaded region?
16 cm
A. 25.16 cm
B. 27.52 cm
C. 50.24 cm
D. 55.04 cm
you roll two 6-sided number cubes
where is the question I dont see it
NEED HELP QUICK
Jenny placed three bets on the football game over the weekend she lost the total amount of $27 how much money did she bet each time and what is X
Answer:
9
Step-by-step explanation:
She bet 9 each time, you can find this by doing 27 ÷ 3 :)
Answer:
she bet $9 each time and x is the number of bets
Step-by-step explanation:
27/3=9
$9 per bet
9x
x=number of bets
On a recent holiday evening, a sample of 500 drivers was stopped by the police. Three hundred seventy-five were under 30 years of age. A total of 275 were under the influence of alcohol. Of the drivers under 30 years of age, 225 were under the influence of alcohol.
Let A be the event that a driver is under the influence of alcohol.
Let Y be the event that a driver is less than 30 years old.
1. Show the joint probability table.
2. Are A and Y mutually exclusive events? Explain.
3. Are A and Y independent events? Explain.
Answer:
Joint probability table :
_____ A _____ A'
_ Y_ 0.45 ___ 0.30
_ Y'_ 0.05___ 0.20
No
No
Step-by-step explanation:
Given :
Sample, size n = 500
A = driver is under the influence of alcohol :
Y = driver is less than 30 years old
P(A) = 275 / 500 = 0.55
P(Y) = 375 / 500 = 0.75
P(AnY) = 225 / 500 = 0.45
P(YnA') = (1 - 225/375)*0.75 = 0.4 * 0.75 = 0.30
Joint probability table :
_____ A _____ A'
_ Y_ 0.45 ___ 0.30
_ Y'_ 0.05___ 0.20
To determine if it is mutually exclusive : P(AnY) = 0
P(AnY) = 0.45 ; hence, it is not mutually exclusive
For A and Y to be independent ; P(A|Y) = P(A) ;
P(A|Y) = P(AnY) / P(Y)
P(A|Y) = 0.45 / 0.75 = 0.6
Hence, A and Y are not independent.
I need help fast! The measures of the angles of a triangle are shown in the figure below. Solve for x.
Answer:
60
Step-by-step explanation: will from the other two degrees added together then subtract from 180 and boom there's your answer
Answer:
x=8
Step-by-step explanation:
The sum of angles of any triangle=18076+44=120
so to get the value of the remained angle subtract that from 180
180-120=60
so
8x-4=60 add 4 to both sides
8x=64 divide both sides by 8
x=8
In ΔEFG, the measure of ∠G=90°, the measure of ∠E=6°, and GE = 3.3 feet. Find the length of EF to the nearest tenth of a foot.
Answer:
EF = 3.3 ft
Step-by-step explanation:
cos 6 = 3.3/EF
0.9945 = 3.3/EF
EF = 3.32 ft
a grocery store receives a shipment of 700 oranges the manager randomly selects 25 oranges to weigh. in that sample 2 oranges weigh 5 ounces. How many oranges in the shipment can the manager predict weigh 5 ounces
The number of oranges in the shipment can the manager predict weighing 5 ounces would be; 56.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The relations between variables, either direct or inversely proportional, can be built to find the desired measures in the problem.
Given that a grocery store receives a shipment of 700 oranges the manager randomly selects 25 oranges to weigh in that sample 2 oranges weigh 5 ounces.
Now set up a proportion;
2/25 = (x)700
Cross multiplication;
700(2)= 25(x)
1400/25=x
x=56
Therefore, the number of oranges in the shipment can the manager predicts weighing 5 ounces would be; 56.
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So far, Hans has burned 112.4 calories. He wants to burn a total of 300 calories. How many more calories must Hans burn?
Answer:
You have to 300-112.4 which equals 187.6
and that is your answer!
Step-by-step explanation:
Look at the chart showing a clothing stores daily stock data for the past month . Which statement is a fair conclusion based on the chart
Answer: c
Step-by-step explanation:
