Answer:
w = 3; w = 4
Step-by-step explanation:
We can start by expanding the equation on the left hand side:
[tex](w+5)^2=2w^2+3w+37\\(w+5)(w+5)=2w^2+3w+37\\w^2+5w+5w+25=2w^2+3w+37\\w^2+10w+25=2w^2+3w+37[/tex]
We can first simplify the equation subtracting all the terms on the right hand side and having the equation equal 0:
[tex]w^2+10w+25=2w^2+3w+37\\(w^2-2w^2)+(10w-3w)+(25-37)=0\\-w^2+7w-12=0[/tex]
Now, we have one equation in standard form (ax^2 + bx + c = 0).
We can solve this equation using the quadratic equation which is
[tex]x = \frac{-b+\sqrt{b^2-4ac} }{2a} \\\\x=\frac{-b-\sqrt{b^2-4ac} }{2a}[/tex]
Since -1 is our a value, 7 is our b, and -12 is c, we simply plug in our values and solve for x:
First x:
[tex]x=\frac{-7+\sqrt{7^2-4(-1)(-12)} }{2(-1)}\\ \\x=\frac{-7+\sqrt{1} }{-2}\\ \\x=\frac{-7+1}{-2}\\ \\x=\frac{-6}{-2}\\ \\x=3[/tex]
Second x:
[tex]x=\frac{-7-\sqrt{7^2-4(-1)(-12)} }{2(-1)}\\ \\x=\frac{-7-\sqrt{1} }{-2}\\ \\x=\frac{-7-1}{-2}\\ \\x=\frac{-8}{-2}\\ \\x=4[/tex]
Finally, we must check for extraneous solutions, which (if present) will make the equations not true. We simply plug in 3 for w and 4 for w to check for such solutions:
Checking 3:
[tex](3+5)^2=2(3)^2+3(3)+37\\8^2=2(9)+9+37\\64=18+9+37\\64=64[/tex]
Checking 4:
[tex](4+5)^2=2(4)^2+3(4)+37\\9^2=2(16)+12+37\\81=32+12+37\\81=81[/tex]
Since the equations are true for both 3 and 4, both values work for w.
a/(a−b)(a−c)+b/(b+c)(b−a)b+c/(a−c)(b−c)
Answer:
a^2-ac/a-b + b^3-b^2*a/b+c + bc-c^2/a-c
Step-by-step explanation:
l-80-20l – 100 + l-100l = ???
Step-by-step explanation:
We can simplify the given expression using the rules of absolute values:
l-80-20l – 100 + l-100l
= -(20l + 80) - 100 + 100 (since |x| = -x when x is negative)
= -20l - 80
= -20(l + 4)
Therefore, the simplified expression is -20(l + 4).
Answer:
100
Step-by-step explanation:
[tex] | - 80 - 20| - 100 + | - 100| \\ = | - 100| - 100 + | - 100| \\ = 100 - 100 + | - 100| \\ = | - 100| \\ = \boxed{100}[/tex]
____________
hope it helps!
simplify the expression, 23.5 - 2.4 (3.9 - 8.6 ) + 4.4
Two brothers drove home together from a trip. Kevin drove for 12 hours at a average speed of 65 per hour. Jeffery drove 24 hours at an average speed of 60 miles per hour. What is the total number of miles driven by the two brothers?
The total number of miles driven by the two brothers is 2,220 miles.
What is the total number of miles driven?Average speed is the ratio of total distance and time. It measures how fast an object is moving with respect to time.
Average speed = distance / time
In order to determine the formula for distance from the formula of average speed, multiply both sides of the equation by time.
Distance = time x average speed.
The distance that Kevin covered = 65 x 12 = 780 miles
The distance that Jeffery covered = 60 x 24 = 1440 miles
The total distance is the sum of the distance covered by Kevin and the distance covered by Jeffery.
Total distance = 1440 + 780 = 2,220 miles
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(1x10⁶) - (8x10⁴) I'm scientific notation
Answer: 9.2 x 105
Step-by-step explanation:
Which of the following is the same as 8(9+2)?
8*9+8
8*9+2
8*9+8*2
9(8+2)
2(8+9)
Answer:
The third one
Step-by-step explanation:
if you look at it, and actually solve it its 88.
The following table represents measurement of the height of a bean sprout:
Days after sprout
was planted 7 9 11 13
Height of sprout
in inches 3 4.5 6 7.5
Create a linear equation to represent this situation. According to your equation, how tall will the sprout
be after 14 days?
The linear equation representing the situation is y = 0.75x - 2.25, and according to this equation, the height of the sprout after 14 days would be 8.25 inches.
To create a linear equation that represents the relationship between the height of the bean sprout and the number of days after planting.
Therefore, the slope of the line is:
slope = change in height / change in days = (7.5 - 3) / (13 - 7) = 1.5
The intercept of the line can be found by substituting one of the data points into the point-slope form of a line:
y - y1 = m(x - x1)
where m is the slope, x1 and y1 are the coordinates of one of the data points. We choose the first data point (7, 3):
y - 3 = 1.5(x - 7)
y - 3 = 1.5x - 10.5
y = 1.5x - 7.5
Therefore, the linear equation that represents the relationship between the height of the bean sprout (y) and the number of days after planting (x) is:
y = 1.5x - 7.5
To find the height of the sprout after 14 days, we substitute x = 14 into the equation:
y = 1.5(14) - 7.5
y = 10.5
Therefore, the height of the sprout after 14 days is predicted to be 10.5 inches.
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Ivan bought a desk on sale for $179.20. This price was 32% of the original price.
Answer:
Below
Step-by-step explanation:
I suppose you are looking for the ORIGINAL price
x = original
32% is .32 in decimal
so .32 * x = $ 179.20
x = 179.20/.32 = $ 560.
please answer the question
a.) The area covered by algae for 10 days after it was spotted would be = 35.7 m²
How to calculate the area covered by the algae after 10 days?The area covered by the algae when it was first spotted = 12.5 m²
For every week(7 days) = 2(12.5)
But 10 days = x
Make X the subject of formula;
X = 10× 2(12.5)/7
X = 250/7
X = 35.7 m²
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Need help on multiple choice question
Need help asap!
Solve the following system of equations and show all work. y = −x2 + 4 y = 2x + 1
Answer:
The solutions to the given system of equations are:
x = 1, y = 3x = -3, y = -5Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}y=-x^2+4\\y=2x+1\end{cases}[/tex]
To solve the given system of equations, substitute the second equation into the first equation:
[tex]\implies 2x+1=-x^2+4[/tex]
Add x² to both sides:
[tex]\implies x^2+2x+1=4[/tex]
Subtract 4 from both sides:
[tex]\implies x^2+2x-3=0[/tex]
Factor the quadratic equation:
[tex]\implies x^2+3x-x-3=0[/tex]
[tex]\implies x(x+3)-1(x+3)=0[/tex]
[tex]\implies (x-1)(x+3)=0[/tex]
Apply the zero product property:
[tex](x-1)=0 \implies x=1[/tex]
[tex](x+3)=0 \implies x=-3[/tex]
Substitute the found values of x into the second equation and solve for y:
[tex]x=1 \implies y=2(1)+1=3[/tex]
[tex]x=-3 \implies y=2(-3)+1=-5[/tex]
Therefore, the solutions to the given system of equations are:
x = 1, y = 3x = -3, y = -5I'LL MARK THE BRAINLIEST
What is the exact circumference of the circle?
Answer: c=2πr
Step-by-step explanation:
because im just that guy
Answer:
c=62.8
Step-by-step explanation:
diameter=20
radius=10
c=2πr
c=2×22/7×10
c=62.8
There are 3 teaspoons in a tablespoon. There are 10 16 times more teaspoons in a cup. How many teaspoons are in a cup?
Work 1.1.8 The president of South Africa, Mr Cyril Ramaphosa, announced that there will be an inflow of R10 billion investment in South Africa in the following year. Use the multiplier formula to calculate the eventual change in aggregate expenditure due to this R10 billion injection. The marginal propensity to save (mps) is 0,4. Remember to show all formulas and calculations!
Using the multiplier formula, the eventual change in aggregate expenditure due to the inflow of R10 billion into South Africa and using the marginal propensity to consume (MPC) is R6 billion.
What is the multiplier formula?The multiplier formula is used to compute the amount of new income generated from the flow of extra income.
The multiplier formula uses the MPS (marginal propensity to save) to compute the multiplier as follows:
M = 1 / MPS
The marginal propensity to save gives the proportion of income that will be saved.
The marginal propensity to save (MPS) = 0.4
M = 1 / MPS
M = 1/0.4)
= 2.5
Change in aggregate expenditure = R25 billion (2.5 x R10 billion)
Thus, we expect the aggregate expenditure in South Africa to increase by R25 billion following the inflow of R10 billion investment.
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which of the following statements are not true? check all that apply.
Answer:
A
b
D
Step-by-step explanation:
The sun revolves around the Earth." Statements 1 and 4 are true.
As the question asks for statements that are not true, I will go through each statement and determine if it is true or false. Statement 1: "Water boils at 100 degrees Celsius."
This statement is true. Water boils at 100 degrees Celsius at sea level under normal atmospheric conditions.
Statement 2: "The moon is made of cheese." This statement is not true. The moon is not made of cheese. It is primarily composed of rock and does not contain any dairy products.
Statement 3: "The sun revolves around the Earth." This statement is not true.
The Earth revolves around the sun in an elliptical orbit. The concept that the Earth is at the center of the solar system and the sun revolves around it was disproven by the heliocentric model proposed by Nicolaus Copernicus in the 16th century.
Statement 4: "Gravity only exists on Earth." This statement is not true. Gravity exists everywhere in the universe. It is a fundamental force that attracts objects with mass towards each other.
While the strength of gravity may vary depending on the mass of the objects and their distance apart, it is present throughout the universe.
To summarize, the statements that are not true are: 2. "The moon is made of cheese." 3. "The sun revolves around the Earth." Statements 1 and 4 are true.
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)) The players on Matthew's soccer team each bring a water bottle with them to practice.
For a statistics project, Matthew asked each player how much water his bottle held. This box
plot shows the results.
12
Water bottle volume (oz.)
Submit
20
16
4) What fraction of the water bottles held at least 24 ounces?
24
28
32
Please help rn
The fraction of the water bottles that has at least 24 ounces is 1/4.
What fraction of the water bottles held at least 24 ounces?A box plot is a graph that is used to show the distribution and level of a set of scores. The scores are distributed into 4 groups. Each group has a value of 25%
24 represents the third quartile of the dataset. The third quartile represents 75% of the dataset. A third quartile value of 24 means that at most 3/4 (75%) of the dataset has a value that is at most 24 and 1/4 or 25% of the dataset has a value that is at least 24.
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Jason wants to buy a new HD television but he thinks that if he waits, the quality of HD televisions will improve. The television he wants to buy costs $2500 now, and based on pricing trends, Jason thinks that the price will increase by 4% each year. (SHOW ALL WORK)
a. Write an exponential growth equation to represent the price y of a new HD television t years from now.
b. Use the equation to predict when a new HD television will cost $3000.
c. Jason decides to wait to buy a new television and saves his money. He puts $2200 in a savings account with 4.7% annual interest compounded continuously. Determine when the amount in his savings will exceed the cost of a new television.
the amount in Jason's savings will exceed the cost of a new television approximately 7.22 years from now.
a. The exponential growth equation to represent the price y of a new HD television t years from now is:
y = $2500[tex](1 + 0.04)^t[/tex]
where t is the number of years from now.
b. To predict when a new HD television will cost $3000, we can set y = $3000 and solve for t:
$3000 = $2500[tex](1 + 0.04)^t[/tex]
1.2 = [tex]1.04^t[/tex]
ln(1.2) = t ln(1.04)
t = ln(1.2) / ln(1.04)
t ≈ 3.97
Therefore, a new HD television will cost $3000 approximately 4 years from now.
c. To determine when the amount in Jason's savings will exceed the cost of a new television, we can use the formula for continuous compound interest:
A = [tex]Pe^(rt)[/tex]
where A is the amount in savings after t years, P is the principal amount, e is the mathematical constant approximately equal to 2.71828, r is the annual interest rate expressed as a decimal, and t is the time in years.
In this case, P = $2200, r = 0.047 (since the annual interest rate is 4.7%), and we want to find the time t when A = $2500. Plugging these values into the formula, we get:
$2500 = $2200[tex]e^(0.047t)1.13636 = e^(0.047t)[/tex]
ln(1.13636) = 0.047t
t = ln(1.13636) / 0.047
t ≈ 7.22
Therefore, the amount in Jason's savings will exceed the cost of a new television approximately 7.22 years from now.
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a six sided cube with the letters s,o,l,v,e,d is rolled twice. what is the probability of rolling two consonants? express as a fraction in simplest form.
There are 6 possible outcomes for each roll of the cube, since there are 6 letters on the cube. Out of the 6 letters, there are 3 consonants (S, L, V) and 3 vowels (O, E, D).
To find the probability of rolling two consonants, we need to multiply the probability of rolling a consonant on the first roll (3/6) by the probability of rolling a consonant on the second roll (also 3/6), since the rolls are independent events.
(3/6) * (3/6) = 9/36 = 1/4
Therefore, the probability of rolling two consonants is 1/4, which can also be expressed as 25%.
An interior angle of a regular polygon measures 140 degrees how many sides does the polygon have
1. Write the equation of the circle, (x-2)²+(y-5)²=7² in general form.
Answer:
The equation in general form is x² + y² - 4x - 10y - 20 = 0
Answer:
x² + y² - 4x - 10y - 20 = 0
Step-by-step explanation:
The general equation of circle is
x² + y² + ax + by + c = 0
where a, b and c are constants
To convert the standard form of the equation (x - 2)² + (y - 5)² = 7² into general form, expand the squares and the constant on the right side and adjust the terms to have 0 on the right side
(x - 2)² = x² - 4x + 4
(y - 5)² = y² - 10y + 25
7² = 49
(x - 2)² + (y - 5)² = 7²
= x² - 4x + 4 + y² - 10y + 25 = 49
Subtract 49 from each side to get 0 on the right:
x² - 4x + 4 + y² - 10y + 25 - 49 = 0
Simplify the constant terms
4 + 25 - 49 = 29 - 49 = -20
Required equation is
x² + y² - 4x - 10y - 20 = 0
You participate in a 5K competitive race. Which Z-score would you prefer to have compared to your competitors for the time it took you to complete the race?
The z-scοre is prefer tο have cοmpared tο yοur cοmpetitοrs fοr the time it tοοk yοu tο cοmplete the race is -2.50.
What is z-scοre?When a value is given a Z-scοre, it shοws hοw far οff frοm the standard deviatiοn it is. The amοunt οf standard deviatiοns a given data pοint is abοve οr belοw the mean is represented by the Z-scοre, alsο knοwn as the standard scοre. The level οf variability within a particular data cοllectiοn is effectively reflected in the standard deviatiοn.
We knοw that ,
=> z=(x-µ)/σ
If we have z scοre less it means we cοmplete the race in less time as cοmpare tο οthers.
Sο, z scοre -2.50 is least as per given all the οptiοns. sο ,we wοuld yοu prefer -2.50 cοmpared tο οur cοmpetitοrs fοr the time it tοοk yοu tο cοmplete the race.
Hence the z-scοre is -2.50.
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the foot m and n of two vertical poles MT and NK are in line with a point D on the same horizontal level ground.Mt and NK are 8cm and 12cm respectively, M lies between D and N is 30m from d.the angle of elevation of k from t is 40: calculate 1.distance KT,2.distance dn correct to two significant figures 3.angles of elevation of k from d correct to two decimal places
The distance KT and angle of elevation of the pole's top, K, with respect to the ground, D, are;
KT is about 6.2 cm
DN = 30 m
The angle of elevation of K from D is 0.23°
What is an angle of elevation?The angle created between a horizontal line and the line of sight of a viewer gazing up at an object is known as the angle of elevation.
The two vertical poles are MT and NK
The height of MT = 8 cm
The height of NK = 12 cm
From the top of the pole MT, point T, to the top of the pole NK, point K, there is a 40-degree elevation difference.
The poles' height differences are 12 cm - 8 cm, or 4 cm.
The distance KT can be found as follows;
Therefore;
sin(40°) = 4/KT
KT = 4/(sin(40°)) ≈ 6.2
The distance KT is approximately 6.2 cm
According to the information in the question, the distance is DN = 30 m.
The base of the poles MT and NK is on the same level ground as point D.
ND=30m
Hence, the trigonometric ratio for tangent may be used to get the angle of elevation,, of the top of the pole NK, (point K), from D as follows;
tan(θ) = NK/ND
tan(θ) = (12 cm)/(30 m) = 0.12/30 = 0.004
θ = arctan(0.004) ≈ 0.23°
K is elevated from d at an angle of roughly 0.23°.
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How do I correctly simplify the expression and where did the student go wrong?
Part A: The student that simplified the give trigonometrical identity expression incorrectly is student B.
Part B: The correct complete solution is shown below
Simplifying Trigonometrical identities expressionsFrom the question, we are to determine the student that simplified the expression incorrectly.
Part A:
The student that simplified the expression incorrectly is student B.
The student is went wrong in step 3.
From step 2, the student divided (1 + tan²θ) by (tanθ/cotθ). The student is supposed to divide [(1 + tan²θ)/tanθ] by cotθ
Part B:
The correct solution is shown below
[(1 + tan²θ)/tanθ] ÷ cotθ
(sec²θ/tanθ) ÷ cotθ
Which can be written as:
(sec²θ/tanθ) ÷ 1/tanθ
Then,
(sec²θ/tanθ) × tanθ/1
= sec²θ/1
= sec²θ
Hence, the correct simplified expression is sec²θ
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I will give brainliest to whoever answers this correctly, Answer is not x=0.1
The value of x in the infinite geometric series, x = (7 ± i√107) / 26.
What is the value of xWe can start by simplifying the left-hand side of the equation:
-1 + 1/x + x + x² + ...+ xⁿ + ...
= -1 + (1/x) * (1/(1 - x))
Using the formula for the sum of an infinite geometric series:
1 + r + r² + ... = 1/(1 - r) for |r| < 1
We can simplify the left-hand side further:
= -1 + (1/x) * (1/(1 - x))
= -1 + (1/(x - x²))
Now we have:
-1 + (1/(x - x²)) = 10/3
Multiplying both sides by 3(x - x²), we get:
-3(x - x²) + 3 = 10(x - x²)
Simplifying, we get:
13x² - 7x + 3 = 0
Using the quadratic formula, we can solve for x:
x = (7 ± √(7² - 4133)) / (2*13)
x = (7 ± i√(107)) / 26
Since the expression is defined only for |x| < 1, we can discard the solution with the plus sign, leaving:
x = (7 - √(-143)) / 26
x = (7 - 3i√13) / 26
Therefore, the solution for x is x = (7 ± i√107) / 26.
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Question 9 Explain work
The condition that proves congruent of two given triangles ΔDEF ∼ ΔJKL would be option (a) DE : JK = 3:1 but ratio value in option is given wrong.
What is the congruent triangle?In this case triangle in congruent when two sides and one angle of first triangle is equal to two sides and one angle of second triangle.
we have given proof two triangles congruent by the postulate of SAS.
Since two corresponding sides of these triangles are congruent and one angle is also congruent. So to prove both the triangles congruent.
∠EDF ≅ ∠KJL will complete the SAS property to prove both the triangles are congruent.
DE : JK
= 21 : 7
= 3 : 1
So, DE: JK = 3:1 is answer.
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4. A certain radioactive material is known to decay at a rate proportional to the amount present. A block of this material originally having a mass of Qograms is observed, after 24hrs, to have experienced a reduction in mass of 10%. Find an expression for the mass of the block at any time.
Therefore , the solution of the given problem of expressions comes out to be Q = Q0 e(ln(0.9)/24)t this is the formula for the block's mass at any moment t.
Explain expression.Calculations such as joining, random subdivision, variable multiplier, and elimination are required. They would accomplish the following if they were united: An algorithm, some information, and a mathematical equation. Numerical information, formulas, elements, and arithmetic operations like additions, erasures, errors, and categories are all included in a declaration of truth. Words and phrases can be evaluated and analysed.
Here,
Let's write Q for the radioactive material's mass at any moment t. (t). We can write: Because the substance decays at a rate proportional to its mass.
=> -kQ = dQ/dt
where k is a measure of ratio. This first-order differential equation can be solved by separating the variables, and it is separable:
=>-k dt Equals dQ/Q
By combining both parts, we obtain:
=>Q = -kt + C, where
where C is the integration constant. We can use the original assumption that the material has a mass of Q grammes at time t = 0 to determine C:
=> ln(Q) = C
When we add this to the prior solution, we obtain:
=> Q = -kt + ln, where (Q0)
where Q0 is the starting mass of the material.
=> 0.9Q0 = Q(24) = Q0 e^(-k*24)
After finding k, we obtain:
=> k = ln(0.9)/(-24) (-24)
Using this value of k as a substitute in the preceding equation, we obtain:
=> (ln(0.9)/24)t - ln(Q) + ln (Q0)
If we simplify, we get:
=> Q = Q0 e(ln(0.9)/24)t
This is the formula for the block's mass at any moment t.
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Which trinomials are prime?
Choose all answers that are correct.
x² + 4x-21
x²-5x-2
x² + 3x + 7
x²-x-1
Answer:
Step-by-step explanation:
x² + 4x-21
x²-5x-2
x² + 3x + 7
x² + 4x-21
x²-5x-2
x² + 3x + 7
x²-x-1
x²-x-1
W(4y-4)
Z
52°
Y
14
3y
X
Check the picture below.
[tex]52=(4y-4)+(3y)\implies 52=76-4\implies 56=7y \\\\\\ \cfrac{56}{7}=y\implies \boxed{8=y} \\\\\\ \stackrel{\measuredangle W}{4y-4}\implies 4(8)-4\implies \text{\LARGE 28}[/tex]
Asher is interviewing for a job as an elementary school teaching assistant. The interviewer notices that he is very friendly, kind, and calm. In terms of context, what might the interviewer think about Asher?
a
Asher comes off as though he is hiding something.
b
Asher has personality traits that are a great fit for this type of job.
c
Asher should be hired as a principal instead of a teaching assistant.
d
Asher would be a better fit as a maintenance worker at the school.
someone please help :,)) (picture attached) click question to see photo
Answer:180 square inches
Step-by-step explanation:
18*6+9*8=180