Answers and Step-by-step explanations
13. Square both sides: x^2 + 4x + 4 = 16(x - 2) = 16x - 32
Move all the terms to one side: x^2 - 12x + 36 = 0
Factorize: (x - 6)^2 = 0 ⇒ x = 6
14. Move one of the roots to one side: [tex]-\sqrt{2x-1} =\sqrt{3x-12}[/tex]
Square both sides: 2x - 1 = 3x - 12
Solve for x: x = 11
15. Subtract 4 from both sides: x - 4 = [tex]2\sqrt{x-4}[/tex]
Square both sides: x^2 - 8x + 16 = 4(x - 4) = 4x - 16
Move all the terms to one side: x^2 - 12x + 32 = 0
Factorize: (x - 4)(x - 8) = 0 ⇒ x = 4 or x = 8
16. Square both sides: x^2 - 4x + 4 = 9x - 36
Move all the terms to one side: x^2 - 13x + 40 = 0
Factorize: (x - 5)(x - 8) = 0 ⇒ x = 5 or x = 8
Hope this helps!
Answer:
13. x = 6
14. No real solutions
15. x = 4, 8
16. x = 5, 8
Step-by-step explanation:
13. Square both sides
(x + 2)² = 4²(x - 2)
x² + 4x + 4 = 16x - 32
x² - 12x + 36 = 0
x² - 6x - 6x + 36 = 0
x(x - 6) - 6(x - 6) = 0
(x - 6)(x - 6) = 0
x = 6
14. sqrt(2x - 1) = -sqrt(3x - 12)
No real solutions because a positive square root can not be equal to a negative square root
15. x - 4 = 2sqrt(x - 4)
(x - 4)² = 4(x - 4)
(x - 4)² - 4(x - 4) = 0
(x - 4)(x - 4 - 4) = 0
(x - 4)(x - 8) = 0
x = 4, 8
16. x - 2 = sqrt(9x - 36)
(x - 2)² = (9x - 36)
x² - 4x + 4 - 9x + 36 = 0
x² - 13x + 40 = 0
x² - 5x - 8x + 40 = 0
x(x - 5) - 8(x - 5) = 0
(x - 8)(x - 5) = 0
x = 5, 8
Note: Figure is not drawn to scale.
If r = 10 units and x = 13 units, then what is the volume of the cylinder shown above?
V cylinder =
2h
O A.
460 T cubic units
OB. 130 cubic units
oc. 1,300 cubic units
OD. 5,200 cubic units
Final answer:
To find the volume of the cylinder with a given radius of 10 units and height of 13 units, we use the formula V = πr²h, which yields an approximate volume of 4085.48 cubic units using π as 3.1416. The nearest given option is C (1300 cubic units), although the calculated volume does not exactly match any of the provided choices.
Explanation:
To calculate the volume of a cylinder, we use the formula V = πr²h, where V represents the volume, r is the radius, and h is the height of the cylinder. Given the radius r as 10 units and the height x (which likely represents the height h in this context) as 13 units, we plug these values into the formula:
V = π(10²)(13) = π(100)(13) = 1300π cubic units.
Since π is approximately 3.1416, the volume is approximately:
V ≈ 1300(3.1416) ≈ 4085.48 cubic units.
As none of the multiple-choice options provided exactly match this calculated volume, this could indicate a typo or error in the question or options. However, if we use a rounded value of π as 3.14, then:
V ≈ 1300(3.14) ≈ 4082 cubic units.
The closest match to this calculated volume is option C (1300 cubic units). However, the student should verify the precision of π used in their classroom or the context of the question to ensure this match is consistent with their requirements.
Dave determines the meal he ordered at the restaurant contains 22% of his daily sodium intake. If the meal contains 260 mg of sodium, how many mg of sodium are in Dave's daily diet? Round your answer to the nearest whole mg
Answer:
1182 mg to the nearest mg.
Step-by-step explanation:
22% is equivalent to 260 mg sodium, so
100% is equivalent to 260 * (100/22)
= 1181.82 mg.
what is percentage?
A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.
Examples of percentages are:
10% is equal to 1/10 fraction
20% is equivalent to ⅕ fraction
25% is equivalent to ¼ fraction
50% is equivalent to ½ fraction
75% is equivalent to ¾ fraction
90% is equivalent to 9/10 fraction
Given,
Dave determines the meal he ordered at the restaurant contains 22% of his daily sodium intake
Meal contains 260 mg of sodium
22% is equivalent to 260 mg sodium, so
100% is equivalent to 260 x ([tex]\frac{100}{22}[/tex])
= 1181.82 mg.
22% is equivalent to 260 mg sodium, so
100% is equivalent to 260 * (100/22)
= 1181.82 mg.
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Can you help me with this please
Step-by-step explanation:
This is a cube
Formula surface area of a cube = s2 × 6
Where s is one side
Square of 8 = 64
64 × 6 = 384
If half of the pie below is eaten, what fraction remains?
Answer:
u have the answer tho right
Step-by-step explanation:
In mathematical terms, a whole pie is considered as 1 (or 1/1). If half (1/2) of it is eaten, what remains is the other half (1/2). So, the fraction that remains of the pie is 1/2.
Explanation:When we talk about a pie in mathematics, we usually refer to it as a whole. If you've eaten half of the pie, essentially, you've consumed 1/2 of the pie. If that amount is subtracted from the whole pie (which is always considered as 1 or 1/1), what remains is the other half of the pie. Meaning, if you subtract 1/2 from 1 (or 1/1), you're left with 1/2 of the pie. Hence, if half of the pie is eaten, the fraction that remains is 1/2.
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f(x) = 4x2 + 7x - 18
Find f(-9)
Answer:
f(-9)= 243
Step-by-step explanation:
f(x) = 4x²+7x -18
f(-9) = 4(-9)²+7(-9)-18
= 4(81) -63-18
= 324- 81
= 243
Answer:279
Step-by-step explanation:
Bc
Which value of x makes the equation true?
x + 7 = -9
Answer:
x = -16
Step-by-step explanation:
x + 7 = -9
x = -9 - 7
x = -16
Answer:
X=-16
Step-by-step explanation:
If you add -16 Then add a positive 7 you will end up with a -9
Have a great day
For the given maximization problem, (a) determine the number of slack variables needed, (b) name them, and (c) use slack variables to convert each constraint into a linear equation. a. How many slack variables are needed? 3 b. Which slack variables should be used? A. s 1, s 2, s 3 B. s 1, s 2 C. x 1, x 2, x 3 D. x 1, x 2 c. What is the equation using a slack variable that corresponds to the first constraint, 5 x 1 plus 8 x 2 plus 10 x 3 less than or equals 173? A. 5 x 1 plus 8 x 2 plus 10 x 3 less than or equals 173 B. 5 x 1 plus 8 x 2 plus 10 x 3 plus s 1 less than or equals 173 C. 5 x 1 plus 8 x 2 plus 10 x 3 plus x 1 equals 173 D. 5 x 1 plus 8 x 2 plus 10 x 3 plus s 1 equals 173 What is the equation using a slack variable that corresponds to the second constraint, 5 x 1 plus 4 x 2 plus 17 x 3 less than or equals 245? A. 5 x 1 plus 4 x 2 plus 17 x 3 plus s 2 equals 245 B. 5 x 1 plus 4 x 2 plus 17 x 3 less than or equals 245 C. 5 x 1 plus 4 x 2 plus 17 x 3 plus x 2 equals 245 D. 5 x 1 plus 4 x 2 plus 17 x 3 plus s 2 less than or equals 245 Maximize zequals5x 1plus3x 2plusx 3 subject to: 5 x 1 plus 8 x 2 plus 10 x 3 less than or equals 173 5 x 1 plus 4 x 2 plus 17 x 3 less than or equals 245 with x 1greater than or equals0, x 2greater than or equals0, x 3greater than or equals0
Answer:
a) 2
b) s₁ and s₂
c) First linear equation: 5*x₁ + 8*x₂ + 10*x₃ + s₁ = 173
Second linear equation: 5*x₁ + 4*x₂ + 17*x₃ + s₂ = 254
Step-by-step explanation:
The problem statement, establishes two constraints, each one of them will need a slack variable to become a linear equation, so the answer for question
a) 2.
b) The constraints are: s₁ and s₂
c) First constraint
5*x₁ + 8*x₂ + 10*x₃ ≤ 173
We add slack variable s₁ and the inequality becomes
5*x₁ + 8*x₂ + 10*x₃ + s₁ = 173
The second constraint is:
5*x₁ + 4*x₂ + 17*x₃ ≤ 254
We add slack variable s₂ and the inequality becomes
5*x₁ + 4*x₂ + 17*x₃ + s₂ = 254
Answer:
A. Two slack variables are needed
B. S1 and s2 (option b)
C. Option d (5X1 + 8X2 + 10X3 + s1 = 173)
D. Option a (5X1 + 4X2 + 17X3 + s2 = 245)
E. Z is maximized at 173 when (X1, X2, X3) = (34.6, 0, 0)
Step-by-step explanation:
In a linear maximization problem like this, if we want to convert the inequality (constraint) into a linear equation, we add slack variables to the left hand side of each inequality.
Therefore we add s1 and s2 to the first and second inequality respectively.
[tex]5X1 + 8X2 + 10X3 \leq 173\\5X1 + 4X2 + 17X3 \leq 245[/tex]
Imputing the slack variables, we obtain as follows:
[tex]5X1 + 8X2 + 10X3 + s1 = 173\\5X1 + 4X2 + 17X3 + s2 = 245[/tex]
[tex]Maximize :\\Z = 5X1 + 3X2 + X3[/tex]
Subject to
[tex]5X1 + 8X2 + 10X3 \leq 173\\5X1 + 4X2 + 17X3 \leq 245\\With \\X1 \geq 0\\X2 \geq 0\\X3 > 0[/tex]
Solution :
[tex]5X1 + 8X2 + 10X3 + s1 = 173\\5X1 + 4X2 + 17X3 + s2 = 245\\-5X1 - 3X2 - X3 + Z = 0[/tex]
5X1 on the first equation is the pivot because the negative value of -5 is the highest and 173/5 is less than 245/5
We perform eq1 - eq2 on the first row and eq1 + eq3 on the third row to get X1 and clear the rest.
We
X1 = 173/5 = 34.6
X2 = 0 (inactive)
X3 = 0 (inactive)
s1 = 0 , s2 = -72/-1 = 72,
Z = 173/1 =173
Therefore the minimum value of Z is 173 when (X1, X2, X3) = (34.6, 0, 0)
In a lab, 180 cells are present at the beginning of an experiment. During the first 9 hours, the number of cells increased by 8% each hour. Write an exponential model giving the number of cells y present t hours after starting the experiment. Estimate the time when the number of cells is 360.
Answer:
The answer is 9 hours
Step-by-step explanation:
From the initial population of 180 cells, the number grows by 8% every hour for the first 9 hours.
This represents a increased population of 108% the previous population.
108% = 108/100 = 1.08
So the new population after n hours is
180 x 1.08^n
When population is 360
360 = 180 x 1.08^n
1.08^n = 2
Take log of both sides
n x Log1.08 = Log 2
n = Log 2/Log 1.08
n = 9
I need help please?!!!
Answer: (3)/(4)(3x+8), x^(2)-4, 3^(2+)x, -5(x-3)
Step-by-step explanation: Those are the right answers, trust me, this took a while.
Have a good day, brainliest wouldn't be bad :)
A 12 sided die with sides labeled 1 through 12 will be rolled once each number greater than 10?
Answer:
See the explaination
Step-by-step explanation:
Total No. of rolling each side of the 12-sided die= 12 x 12= 144 outcomes
No. of outcomes equals 10 are: (1, 9), (9, 1), (2, 8), (8, 2), (3, 7), (7, 3), (4, 6), (6, 4), (5, 5) = 9 outcomes.
No. of outcomes of rolling a No. >10: 144–9 = 135 outcomes.
Probability, Pr, of rolling a No. >10= 135/144
Pr (No. >10) = 0.9375 (to 4 dec. pl.)
Answer: I think you’re missing something on your question. But I think what your asking is how many numbers greater than 10. It should 2/12 or
Step-by-step explanation:
Calculate the simple interest on
N650.00 for 2 years at 6% per
annum.
Answer:
N78
Step-by-step explanation:
The explanation is in the picture
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Answer:
(x+3)(2x+7)
Step-by-step explanation:
Step 1 :
Equation at the end of step 1 :
(2x2 + 13x) + 21
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 2x2+13x+21
The first term is, 2x2 its coefficient is 2 .
The middle term is, +13x its coefficient is 13 .
The last term, "the constant", is +21
Step-1 : Multiply the coefficient of the first term by the constant 2 • 21 = 42
Step-2 : Find two factors of 42 whose sum equals the coefficient of the middle term, which is 13 .
-42 + -1 = -43
-21 + -2 = -23
-14 + -3 = -17
-7 + -6 = -13
-6 + -7 = -13
-3 + -14 = -17
-2 + -21 = -23
-1 + -42 = -43
1 + 42 = 43
2 + 21 = 23
3 + 14 = 17
6 + 7 = 13 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 6 and 7
2x2 + 6x + 7x + 21
Step-4 : Add up the first 2 terms, pulling out like factors :
2x • (x+3)
Add up the last 2 terms, pulling out common factors :
7 • (x+3)
Step-5 : Add up the four terms of step 4 :
(2x+7) • (x+3)
Which is the desired factorization
Final result :
(x + 3) • (2x + 7)
- If you want this explained differently please let me know. Hope this helps!
Which of the following are in the correct order from least to greatest? StartFraction 3 pi Over 10 EndFraction, 60°, StartFraction pi Over 2 EndFraction, StartFraction 2 pi Over 3 EndFraction, 255° 255°, StartFraction 2 pi Over 3 EndFraction, StartFraction pi Over 2 EndFraction, 60°, StartFraction 3 pi Over 10 EndFraction StartFraction 3 pi Over 10 EndFraction, StartFraction pi Over 2 EndFraction,StartFraction 2 pi Over 3 EndFraction 60°, 255° 255°, 60°, StartFraction 2 pi Over 3 EndFraction, StartFraction pi Over 2 EndFraction, StartFraction 3 pi Over 10 EndFraction
Answer:
D) 69.1 ft
Step-by-step explanation:
Answer: a
Step-by-step explanation:
Solve the equation 2x2 + 13x + 15 = 0 by factoring. Show all steps.
Answer:
(2x + 3)(x + 5)
Step-by-step explanation:
2x² + 3x + 15 = 0
(2x + 3)(x + 5)
2x + 3 = 0
2x = -3
x = -3/2
x + 5 = 0
x = -5
Yolanda reads 24 chapters of a book in 6 hours. What is her rate in chapters per hour?
Answer:
4 chapters an hour
Step-by-step explanation:
24 / 6 = average of 4 chapters an hour
Answer:
4 chapters per hour
Step-by-step explanation:
[tex]rate \: of \: reading \\ = \frac{total \: chapters}{total \: time} \\ \\ = \frac{24}{6} \\ \\ = 4 \: chapters \: per \: hour[/tex]
i need the steps for 28
Find the solutions of the quadratic equation Choose 1 answer:
Answer:
B
Step-by-step explanation:
What is the area of a triangle that has a base of 15 yards and a height of 11yards
Answer:
6
Step-by-step explanation:
you have to multiply it by joe mama
The cost of an entry ticket to an amusement park is $5 for a child and $8 for an
adult. During a given 15 minute period, 120 people entered the park, and the total
revenue from ticket sales was $810. During that 15 minute period, how many adults
entered the amusement park?
Answer:
70 adults
Step-by-step explanation:
because there is 70 adults and 50 kids
the wheels of a bicycle are 0.6 m in diameter. If I go around the bike block, each wheel will perform 346 full turns. What distance, to the tenth of a meter ready, that represents it
Answer:
The distance that represents it is 651.9 m.
Step-by-step explanation:
In order to calculate the distance that the wheel travelled we need to find the length of the circumference of the wheel. This is given by the following formula:
length = 2*pi*r = pi*d
Since the diameter of the wheel is 0.6 m we can find the length of the wheel that is:
length = 3.14*0.6 = 1.884 m
The wheel made 346 full turns, that means that the total distance is the number of turns multiplied by the length of the wheel.
distance = 346*1.884 = 651.9 m
The distance that represents it is 651.9 m.
Robert recently discovered a forgotten student loan bill. The amount due after 10 years is
now $10,819.33. He found some old statements and determined that after 7 years the bill
was $8831.80 and after 5 years he owed $7714.03.
1. How much did Robert borrow initially?
2. Robert is planning to pay the loan in full next year. How much will he owe then?
3. What is the interest rate on Robert’s loan?
Answer:
1.Robert borrowed $ 5,500.00
2.The amount Robert would repay next year is $ 11,576.69
3.The interest rate on the loan is 7%
Step-by-step explanation:
The interest on the loan can be computed using compound annual growth
rate
CAGR=(EB/BB)^1/n-1
EB is ending balance of $8831.80 in year7
BB is the balance of year 5 $7714.03
n=7-5=2
CAGR=(8831.8/7714.03)^(1/2)-1
CAGR==1.070000427-1
CAGR=0.070000427
CAGR=7%
The amount borrowed can be computed using the PV formula
At year 0 year 5 amount of $7714.03 is the future value
rate of interest is 7%
number of years is 5
PV=$7714.03*(1+7%)^-5
PV=$ 5,500.00
The amount Robert would pay next year is :
FV=$10,819.338(1+7%)^1
FV=$ 11,576.69
What is the value of the expression StartAbsoluteValue negative 7 EndAbsoluteValue + StartAbsoluteValue negative 4 EndAbsoluteValue?
Answer:
11
Step-by-step explanation:
|-7|+|-4|
-|-7|-|-4|
Answer 11
Answer:
11
Step-by-step explanation:
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Find four solutions of the equation. Write the solutions as ordered pairs.
y = x+5
Answer:
when x=1, y=6. etc.
Step-by-step explanation:
x y
1 6
2 7
3 8
4 9
There are 2 brown marbles, 3 black marbles, and 4 gold marbles in a bag. What is the probability of drawing 2 brown marbles if the first is replaced after it is drawn?
Answer:
.049 (2sf)
Step-by-step explanation:
[tex] \frac{2}{9} \times \frac{2}{9} = 0.4938[/tex]
Answer & explanation:
The correct answer is 4/81. The probability of each marble drawn being brown is 2/9 because there are two brown marbles in a bag of nine total marbles. So, the probability that both marbles drawn will be brown is 2/9 times 2/9 or 4/81!
What is the value of the soccer ball?
1. baseball + basketball = 240
2. tennisball + soccerball = 500
3. soccerball - basketball + tennisball = 455
4. baseball + tennisball = 215
Subtract 1 from 4
5. tennisball - basketball = -25
Rearrange 3
6. soccerball + tennisball - basketball = 455
Substitute 5 into 6
7. soccerball - 25 = 455
Solve
soccerball = 480
The triangular prism below has a base area of 9 cm and a height of 23 cm. What is the volume of the prism?
A) 207 cm3
B) 103.5 cm3
C) 1863 cm3
D) 200 cm3
Answer:
A) 207 cm3
Step-by-step explanation:
9 x 23 = 207
a campground owner had 150 meters of fencing to enclose a rectangualr field adjacent to a river and also bisect that field into two equal halves. No fencing required with river. what are the dimesions of the largest area that can be enclosed
Answer:
Dimension of the Rectangle : 2W - 150 by W
Step-by-step explanation:
Given
Land Size = 150 metres
This land size represents the perimeter of the land
Let P = Perimeter
So, P = 150 m
To bisect the field into two equal halves means to divide length or width of the field into two equal halves
Let L = Length of the field
Let W = Width of the field
Assuming the length of the field is to be bisected., then the campground owner is left with 0.5L (i,e half of the length)
Perimeter of a rectangle is calculated by: 2(Length + Width)
P = 2(L + W) by substitution, becomes
150 = 2(0.5L + W) ----open bracket
150 = L + 2W ---- Male L the subject the formula
L = 2W - 150
The dimension of the largest area that can be enclosed id given by (L,W)
By substitution; the expression becomes
Dimension of the Rectangle : 2W - 150 by W
The model represents the factorization of 2x2+5x+3.
What are the factors of the polynomial?
'O
tx
+X
(2x+3)(x+1)
(2x-3)(x-1)
(3x+2)(x+1)
(3x-2)(x-1)
AX
Answer:
(2x+3)(x+1)
Step-by-step explanation:
Porque si lo factorizas da ese resultado.
The factors of the polynomial are (2x + 3) and (x+1)
Factorizing quadratic expressionsGiven the quadratic equation expressed as:
2x^2+5x+3
We are to find the factors of the given quadratic function as shown:
2x^2+5x+3
2x^2+2x +3x +3
2x(x+1)+ 3(x+ 1)
(2x + 3)(x + 1)
Hence the factors of the polynomial are (2x + 3) and (x+1)
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Use these similar triangles on the coordinate plane to determine the equation of a straight line with a slope of 5/3 that passes through the origin.
y = five-thirds x
y = three-fifths x
y = 3x + 5
y = 5x + 3
Answer:
y = five-thirds x
Step-by-step explanation:
y = mx + b y intercept = 0
y = 5/3 x slope = 5/3
Answer:
The answer is A
Step-by-step explanation:
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A recent study investigated the extent to which hypertension is affected by alcohol consumption. Among other things, the study compared the rate of hypertension in nondrinkers to the rate in people that are moderate beer drinkers (average between 0.5 and 1 glass of beer per day). They found that a 95% confidence interval for the relative risk of hypertension in moderate beer drinkers as compared to nondrinkers was 0.47 to 0.90. A relative risk of 1 means that the two groups have the same risk of hypertension, while a relative risk of less than 1 means that moderate beer drinkers have less risk of hypertension than nondrinkers. If the researchers who ran the study had tested the hypotheses.H0: the relative risk for moderate beer drinkers as compared to nondrinkers = 1
Ha: the relative risk for moderate beer drinkers as compared to nondrinkers ≠ 1
they would have concluded which of the following?
a) reject H0
b) fail to reject H0 at level 0.10
c) Neither choice is correct. We cannot determine what we would do at level a = 0.10 because the interval given is a 95% confidence interval, not a 90% confidence interval.
Answer:
a) reject H0
Step-by-step explanation:
The null and alternative hypotheses:
H0: the relative risk for moderate beer drinkers as compared to nondrinkers = 1
Ha: the relative risk for moderate beer drinkers as compared to nondrinkers ≠ 1
The level of significance, α = 0.1
Since the confidence interval for the relative risk of hypertension in moderate beer drinkers as compared to nondrinkers (0.47 to 0.90) does not contain the relative risk of 1, the null hypothesis will be rejected at the specified level of significance, 0.1. Therefore, the conclusion is to reject H0.