Answers
Answer:
Step-by-step explanation:
( g ° f )(x) = ( x + 7 )² = x² + 14x + 49
20 + 3(x² + 14x + 49) = - 34
20 + 3x² + 42x + 147 = - 34
3x² + 42x + 201 = 0 ⇔ x² + 14x + 67 = 0
D = 196 - 268 = - 72 < 0
There is no any roots in set of real numbers.
The values of x in set of complex numbers are:
[tex]x_{12}[/tex] = [tex]\frac{- 14 }{2}[/tex] ± [tex]\frac{6\sqrt{2}i }{2}[/tex]
[tex]x_{12}[/tex] = - 7 ± 3√2 i
Related Questions
Please help
Write the equation of the line shown
Answers
Answer:
Equation of line is y = 8 as it is horizontal
4xº
(3x + 8)°
B
Find m
Answers
If angle BAD=4x° and angle DAC=(3x+8)° then the equation showing angle BAC is equal to (7x+8)°.
Given that angle BAD=4x° and angle DAC=(3x+8)°.
We are required to find the equation showing the angle BAC.
Angle is basically the figure formed by two rays which is called the sides of the angle and sharing a common endpoint called the vertex of the angle.
∠BAD=4x° and ∠DAC=(3x+8)°
To find the equation showing angle BAC we have to just add the two expressions given in the equation.
∠BAC=∠BAD+∠DAC
∠BAC=4x+3x+8
∠BAC=(7x+8)°
Hence if angle BAD=4x° and angle DAC=(3x+8)° then the equation showing angle BAC is equal to (7x+8)°.
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i will give brianliest to however gets it right
Answers
Let [tex] \rm|M|[/tex] denote the determinant of a square matrix M. Let [tex] \rm g : \bigg[0, \dfrac{\pi}{2} \bigg] \to \mathbb{R}[/tex] be the function defined by [tex] \rm g( \theta) = \sqrt{f( \theta) - 1} + \sqrt{f \bigg( \dfrac{\pi}{2} - \theta\bigg) - 1} [/tex] where
[tex] \rm f( \theta) = \dfrac{1}{2} \left| \begin{matrix} 1& \sin( \theta) &1 \\ - \sin( \theta) &1& \sin( \theta) \\ - 1& - \sin( \theta)&1 \end{matrix} \right | + \left| \begin{matrix} \sin(\pi) & \cos( \theta + \frac{\pi}{4} ) & \tan( \theta - \frac{\pi}{4} ) \\ \sin( \theta - \frac{\pi}{4} ) & - \cos( \frac{\pi}2 ) & \log_{e} ( \frac{4}\pi ) \\ \cot( \theta + \frac{\pi}{4} ) & \log_{e} ( \frac{\pi}4 )& \tan(\pi) \end{matrix} \right | [/tex]
Let p(x) be a quadratic polynomial whose roots are the maximum and minimum values of the function g([tex]\theta [/tex]) , and p(2)=2-[tex]\sqrt{2}[/tex]. Then which of the following is True?
[tex] \rm(1) \: p \bigg( \frac{3 + \sqrt{2} }{4} \bigg) < 0 \\ \rm(2) \: p \bigg( \frac{1 + 3 \sqrt{2} }{4} \bigg) > 0 \\ \rm(3) \: p \bigg( \frac{5\sqrt{2} - 1 }{4} \bigg) > 0 \\ \rm(4) \: p \bigg( \frac{5 - \sqrt{2} }{4} \bigg) < 0[/tex]
Answers
The second matrix in the definition of [tex]f[/tex] is singular, since
[tex]\sin(\pi) = -\cos\left(\dfrac\pi2\right) = \tan(\pi) = 0[/tex]
[tex]\cos\left(\theta+\dfrac\pi4\right) = \sin\left(\dfrac\pi2 - \left(\theta+\dfrac\pi4\right)\right) = \sin\left(\dfrac\pi4-\theta\right)=-\sin\left(\theta-\dfrac\pi4\right)[/tex]
[tex]\cot\left(\theta+\dfrac\pi4\right) = \tan\left(\dfrac\pi2 - \left(\theta+\dfrac\pi4\right)\right) = \tan\left(\dfrac\pi4 - \theta\right) = -\tan\left(\theta-\dfrac\pi4\right)[/tex]
[tex]\ln\left(\dfrac4\pi\right) = -\ln\left(\dfrac\pi4\right)[/tex]
In other words, it's antisymmetric; [tex]A^\top=-A[/tex]. It's easy to show that [tex]\det(A)=0[/tex] if [tex]A[/tex] is 3x3 and antisymmetric.
The other determinant reduces to
[tex]\begin{vmatrix}1 & \sin(\theta) & 1 \\ - \sin(\theta) & 1 & \sin(\theta) \\ -1 & -\sin(\theta) & 1 \end{vmatrix} = 2 + 2\sin^2(\theta)[/tex]
Hence
[tex]f(\theta) = 1 + \sin^2(\theta) \implies f\left(\dfrac\pi2\right) = 1 + \cos^2(\theta)[/tex]
With [tex]g[/tex] defined on [tex]\left[0,\frac\pi2\right][/tex], both [tex]\sin(\theta)[/tex] and [tex]\cos(\theta)[/tex] are non-negative. So
[tex]g(\theta) = \sqrt{f(\theta)-1} + \sqrt{f\left(\dfrac\pi2-\theta\right)-1} \\\\ ~~~~ = \sqrt{\sin^2(\theta)} + \sqrt{\cos^2(\theta)} \\\\ ~~~~ = |\sin(\theta)| + |\cos(\theta)| \\\\ ~~~~ = \sin(\theta) + \cos(\theta) \\\\ ~~~~ = \sqrt2\,\sin\left(\theta + \dfrac\pi4\right)[/tex]
which is maximized at [tex]t=\frac\pi4[/tex] with a value of [tex]\sqrt2\,\sin\left(\frac\pi2\right)=\sqrt2[/tex], and minimized at [tex]t=0[/tex] and [tex]t=\frac\pi2[/tex] with a value of [tex]\sqrt2\,\sin\left(\frac{3\pi}4\right)=1[/tex].
Edit: The rest of my answer wouldn't fit. Continued in attachment.
A car rental agency advertised renting a car for $27.95 per day and $0.25 per mile. If Greg rents this car for 3 days, how many whole miles can he drive on a $150 budget?
Answers
Answer: 264.6 miles
Step-by-step explanation: Let's put the info we got from the problem into an equation. If the car is rented for three days, we need to multiply 27.95 by 3, which will give us 83.85. Now let's use the equation 150=83.85 + 0.25x, where x represents miles. Subtract 83.85 from both sides and we get 66.15 = 0.25x. Now divide both sides by 0.25 and we get x = 264.6.
Answer:
264 miles
Step-by-step explanation:
y = 27.95x + 0.25n where:
y = budget
x = days rented
n = miles driven
150 = 27.95(3) + 0.25n
150 = 83.85 + 0.25n
150 - 83. 85 = 0.25n
66.15 = 0.25n
66.15 / 0.25 = n
n = 264.6 miles
27.95(3) + 0.25(246.6) = $150
For each value of 1 ≤ n ≤ 100, the highest common factor of 8n + 3 and 5n + 4 is written down. What is the sum of these values
Answers
Highest common factor of 8n + 3 and 5n + 4 is either 1 or 17 for all n and its sum is 18
what is greatest integer divisor ?
The greatest common divisor (GCD) of two nonzero integers a and b is the greatest positive integer d such that d is a divisor of both a and b; that is, there are integers e and f such that a = de and b = df, and d is the largest such integer. The GCD of a and b is generally denoted gcd(a, b).
For each value of 1 ≤ n ≤ 100, the highest common factor of 8n + 3 and 5n + 4 is written down. What is the sum of these values
Let gcd(8n + 3, 5n + 4) = d
⟹d|8n+3∧d|5n+4
⟹d|8(5n+4)−5(8n+3)
⟹d|17
Therefore highest common factor of 8n + 3 and 5n + 4 is either 1 or 17 for all n and its sum is 18
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Is the slope of a linear demand curve positive or nega-
tive?
Answers
The slope of a linear demand curve is negative
The demand curve's negative slope indicates that there is an inverse link between price and demand.
It is true that the demand curve's negative slope indicates an inverse link between price and quantity desired. According to the demand curve, demand declines as prices increase and rises as prices decrease.
This statement is false since it only applies to Giffen products, where the demand curve has a positive slope and a direct correlation between price and quantity desired.
Because unit requests rise when prices decrease and decline when prices rise, the demand curve often slopes downward (i.e., is negative). Demand increases when prices are low, but demand decreases when prices are high.
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The number of counties in state A and the number of counties in state B are consecutive even integers whose sum is 106. If state A has more counties
than state B, how many counties does each state have?
Answers
Answer: State A has 54 counties and B has 52 counties
Step-by-step explanation: Since the number of counties are even integers, I did a guess and check. Divided 106 by two to get 53. Then realized that if you take away 1 from on of the 53's and add it to the other, they become consecutive even integers 52 and 54
Kent Fuller is in the 26 percent tax bracket. A nontaxable employee benefit with a value of $2,400 would have a tax-equivalent value of: (Round your
answer to the nearest whole number.)
Answers
The tax equivalent value will be $3243. The third option is correct
Tax bracket Kent Fuller is currently in is 26 percent
Nontaxable employee benefits value: $2400
The return that a taxable benefit would need to provide in order to match the yield on a comparable tax-exempt benefit is known as the tax-equivalent value. This is very useful for investors to compare the return between a tax-free and a taxable alternative.
Finding out the tax equivalent value using the formula:
Tax equivalent value = Tax exempt value/(1 - Tax Rate)
Tax equivalent value = 2400/(1 - 0.26)
= 2400/0.74
Tax equivalent value = 3243.24 or 3243
Therefore, the tax equivalent value will be $3243. Hence, the third option is correct
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125 tickets at $6 and $10 were sold for $1,022. How many $6 tickets and how many $10 tickets were sold?
Answers
Answer:
This is the answer :20 5/6 and 102.2
:1022/10
:102.2
So the answer to the second question is 102.2 or 102 (rounded).
Help with my geometry problem (included as image)
Answers
Answer:
40°
Step-by-step explanation:
We know that
[tex]m\angle 2=28^{\circ}+m\angle 1[/tex]
Thus, by the angle addition postulate,
[tex]28+m\angle 1+m\angle 1=108^{\circ} \\ \\ 2m\angle 1=80^{\circ} \\ \\ m\angle 1=40^{\circ}[/tex]
Huai take out a 2$2600 to be on at 6.8% to help him with a two-year community college after finishing the two years he transferred to State University and Brows another $12,300 to defray expenses for the five semesters he needs to graduate. He graduates for years and four months after acquiring the first song and payments are deferred for three months after graduation the second long was acquired two years after the first and had an interest rate of 7.6% find the total amount of interest that we are acquire until payments begin
Answers
If the amount of loan taken in community college is $2900 and the rate of interest is 6.8% then the amount of interest that will accrue for loan 1 is $364.
Given that the amount of loan in community college is $2900 and the rate of interest is 6.8%.
We are required to find the amount of interest that will accrue for
loan 1.
Compound interest is the amount of interest that is calculated on the aggregate of principal and interest of previous years.
Compounded amount=P[tex](1+r)^{n}[/tex]
To find out the amount of interest for the loan 1,we have to find the compounded amount after 2 years.
Compounded amount=2600([tex](1+0.068)^{2}[/tex]
=2600*[tex](1.068)^{2}[/tex]
=2600*1.14
=$2964
Interest=2964-2600=$364
Hence if the amount of loan in community college is $2900 and the rate of interest is 6.8% then the amount of interest that will accrue for loan 1 is $364.
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Use the graph to determine which statement describes f(x).
-5
y = f(x)
5.
-5.
5
Answers
Option a is correct. f(x) has an inverse function because its graph passes the horizontal line test.
An inverse function is a function that serves to undo another function. That is, if f(x) produces y, then putting y into the inverse of f produces the output x.
From the graph we can see that the horizontal lines intersect less than 2 points, this shows that the f(x) has an inverse.
From the graph, it gets to know.
Hence from the given graph we get to know that f(x) is the inverse function.
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The angles in a triangle are in the ratio 1 : 2 : 3.
a) Show that the triangle is a right-angled triangle.
b) The hypotenuse of the triangle is 19 cm long.
Calculate the length of the shortest side in the triangle.
Answers
Answer:
a) the largest angle is 90°, making it a right triangle
b) the shortest side is 9.5 cm long
Step-by-step explanation:
You want the largest angle and the shortest side in a triangle whose angles are in the ratio 1 : 2 : 3.
AnglesLet x represent the smallest angle. Then the other two angles are 2x and 3x. Their sum is ...
x +2x +3x = 180°
x = 30° . . . . . divide by 6
3x = 90° . . . . find the largest angle
The largest angle is 90°, a right angle. So, the triangle is a right-angled triangle.
SidesA triangle with angles of 30°, 60°, and 90° is a "special" right triangle. Its sides are in the ratio 1 : √3 : 2. That is, the shortest side is 1/2 the length of the longest side.
shortest side = 1/2(19 cm) = 9.5 cm
The length of the shortest side in the triangle is 9.5 cm.
__
Additional comment
In case you're not familiar with the side length ratios of the 30-60-90 special triangle, you can figure the side length from the Law of Sines. That tells you ...
a/sin(A) = b/sin(B) = c/sin(C)
where A, B, C are the angles; and a, b, c are their opposite sides.
The shortest side is opposite the smallest angle, so we have ...
a/sin(30°) = (19 cm)/sin(90°)
a = sin(30°)×(19 cm) = 1/2(19 cm) = 9.5 cm
The length of the shortest side is 9.5 cm.
A whole salmon, weighing 7 # 6 oz, costs $2.74/#. The fillets are removed, boned, and trimmed. The head, bones, and all trim is thrown into the trash. What is the total value of the remaining fillets, which now weigh only 4 # 15 oz? What is their price per pound? What is the salmon’s yield percentage? If the next salmon weighs 6 # 14 oz, how much boneless salmon fillet would you expect to yield from it after fabrication?
Answers
Using proportions, it is found that:
The total value of the remaining fillets is of $13.53.The price per pound is of $2.54.The salmon’s yield percentage is of 66.95%.You would expect to yield 4.6 pounds of boneless salmon fillet from the next salmon weighing 6 # 14 oz.What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
Before beginning the problem, we have that the symbol # represents a pound, which has 16 ounces.
The remaining fillets weight 4 # 15 oz = 4 pounds + 15/16 of a pound. Hence, considering the cost of $2.74 per pound:
4 x 2.74 + 15/16 x 2.74 = $13.53.
The total value of the remaining fillets is of $13.53.
The price per pound is still the same, of $2.54.
The yield is of 4 pounds + 15/16 of a pound = 4.9375 pounds out of 7 + 6/16 = 7.375 pounds, hence the percentage is:
4.9375/7.375 x 100% = 66.95%.
The salmon’s yield percentage is of 66.95%.
Hence, for 6 + 14/16 = 6.875 pounds, the yield would be of:
0.6695 x 6.875 = 4.6 pounds.
You would expect to yield 4.6 pounds of boneless salmon fillet from the next salmon weighing 6 # 14 oz.
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two cars travel the same distance car one travels at 50 mph and car 2 at 65 mph if it takes car 1 one more hour to travel than car two how far did the cars travel
Answers
50(t+1)=65t
50t+50=65t
15t=50
t=10/3=3:20
65 * 10/3 = 216 2/3 mi. Distance they traveled.
It takes eva 6 minutes to fill an online order at her clothing boutique. If she has the help of briana, her store manager, it takes four minutes to fill an order. How long does it take Briana to fill an order alone? Use the equation 1/6 + 1/x = 1/4
Answers
Briana will take minutes to fill an order alone at her clothing boutique is 12 minutes.
Eva takes to fill an online order at her clothing boutique. = 6 minutes
If Eva and Briana fill an order together = 4 minutes
Briana will take minutes to fill an order alone at her clothing boutique = X minutes.
then the equation will be :
1/6 + 1/x = 1/4
1/x = 1/4 - 1/6
now solve equation by taking LCM
1/x = (6-4)/4x6
1/x = 2/24
1/x = 1/12
x = 12
so the value of x is 12
Briana will take minutes to fill an order alone at her clothing boutique is 12 minutes.
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A company produces a logic board for computers. The annual fixed cost for the board is $323,902, and the variable
cost is $109 per board. If the logic board sells for $479, write an inequality that gives the number of logic boards that
will give a profit for the product.
Write the linear inequality?
Answers
The inequality that give the number of logic boards that will give a profit for the product is profit = x($479-$109)-$323,902.
Given that, a company produces a logic board for computers. The annual fixed cost for the board is $323,902, and the variable cost is $109 per board. So, we have to write an inequality which will gives the number of logic boards that will give a profit for the product, if the logic board sells for $479.
We simply use the formula that,
profit + annual fixed cost = number of logic board sold x (logic board sales price-variable cost of logic board)
Let the number of logic board sold be x.
profit + $323,902 = x($479-$109)
profit = x($479-$109)-$323,902
Therefore, we can denote the above listed information in profit = x($479-$109)-$323,902 term. This is the required answer.
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what type of number is 16/14
Answers
Answer:
fraction..............................
or improper fraction.
Hercules and Gretta are hiking on the same trail. Hercules's elevation
5
is-26 feet whereas Gretta's elevation is -4-feet. How much
8
greater is Gretta's elevation than Hercules's?
Answers
Answer:
-22
Step-by-step explanation:
put the subtraction sign to the side
26 (Gretta's elevation)
- 4 (Hercules' elevation)
22
then re-add the subtraction sign (-22) then you have an answer
An airline offers discounted flights from Atlanta to five American cities . Below is a frequency distribution of the number of tickets purchased for each location based on a random sample of purchased tickets. Complete parts (a) through (f)
-(a) construct a relative frequency distribution of the data. (round to three decimal places as needed)
Answers
According to the given statement The relative frequency distribution of the data is = 964.400
What is the data's relative frequency distribution?A relative frequency distribution, which is connected to a probability distribution and is widely used in statistics, illustrates the percentage of the total number of observations associated with each value or class of values.
What is the purpose of using relative frequency distribution?Relative frequency distributions are particularly valuable because they show how common a value is in a dataset in comparison to all other values.
According to the given information:The relative frequency distribution of the data:
= the frequency/ total number of data.
So,
the frequency of the data is:
1227 + 884 + 1160 + 634 + 917
= 4,822
The total number of data: = 5
Now applying the formula we get:
= 4822/5
= 964.400
According to the given statement the frequency of the data is = 964.400
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Samera is asked to find the multiples of 24. Her work is shown below.
Answers
Pls answer this question
Answers
Answer: 1/4
Step-by-step explanation:
The easiest way to solve this is to make them all common denominators.
The common denominator for this problem is 24.
Change the denominators:
1/4 = 6/24
4/12 = 8/24
3/8 = 9/24
2/6 = 8/24
This way it is easier to see which one is smaller and closest to 0. In this case, it is 6/24 or 1/4 because 6/24 is the smallest out of all of them.
Suppose the spinner shown to the right is spun once, to determine a single-digit number, and we
are interested in the event E that the resulting number is even. Give each of the following.
(a) the sample space
(b) the number of favorable outcomes
(c) the number of unfavorable outcomes
(d) the total number of possible outcomes
(e) the probability of an even number
(f) the odds in favor of an even number
Answers
The sample space for the event is given by {2,3,4}
The sample space is a collection of all possible outcomes of an experiment. The sample space is used in probability where the it represents all possible outcomes.
a) In the spinner there are only three possibilities.
The sample space is represented by {2,3,4} .
b)The favorable outcomes in this case is 2 and 4.
Hence the number of favorable outcome is 2.
c)There is only 1 unfavorable outcome which is 3.
d)The total number of possible outcomes is 3 , as we see in the sample space there are 3 numbers.
e)The probability is defined as the fraction of favorable outcome to the
total number of outcome. Therefore the probability in this case is given
by [tex]P(even)=\frac{2}{3}[/tex]
f) The ratio of the number of possible outcomes to the number of possible outcomes that do not occur is known as the odds in favor.
Therefore odds in favor = 2:1
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Identify the property that justifies the following
statement. If AB = CD, then CD = AB.
Answers
Answer:
Transitive property for equality
Step-by-step explanation:
=
myLonestar Login
O QUADRATIC, RATIONAL, AND RADICAL EQUATIONS
Solving a word problem using a quadratic equation with irration...
College Al...
initial
height
ground
A ball is thrown from an initial height of 3 feet with an initial upward velocity of 36 ft/s. The ball's height h (in feet) after t seconds is given by the following.
h=3+361-16r²
Find all values off for which the ball's height is 19 feet.
Round your answer(s) to the nearest hundredth.
(If there is more than one answer, use the "or" button.)
[=
alynn senn
seconds
DOD
X
0/5
Ś
A
Answers
The values for which the ball's height is 19 feet are 9.5 sec and 8.5-sec using quadratic equations.
What is a quadratic equation?
In algebra, a quadratic equation is any equation that can be rearranged in standard form as
ax² + b*x + c = 0
The figures a, b, and c are the portions of the equation and may be distinguished by calling them, independently, the quadratic measure, the direct measure, and the constant or free term.
The values of x that satisfy the equation are called results of the equation, and the roots or bottoms of the expression on its left-hand side.
A quadratic equation has at most two solutions.
Given,
Initial height h(0) = 3 ft
Initial upward velocity v(0) = 36 ft/sec
Given ball height after 't' seconds is h(t) = 3 + 36t - 16r²
for h= 19 ft
19 = 3 + 36 t - 16 r²
16 r² - 36 t + 16 = 0
4 r² - 9 t + 4 = 0
Quadratic equation for ax² + b*x + c = 0 is x = -b ±√b² - 4ac / 2a
By using the above formula we get
t = 9 ± √9² - 4*4*4 / 2*4
t = 9 ± √81 - 64 / 8
t = 9 ± √17 / 8
t = 9 + √17 / 8 t = 9 - √17 / 8
t = 9 + 0.5 t = 9 - 0.5
t = 9.5 t = 8.5
The values for which the ball's height is 19 feet are 9.5 sec and 8.5-sec using quadratic equations.
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What value(s) of δ are an appropriate choice when proving the following limit?
limx→−2(x2+8x+17)=5
Enter your answer in terms of ε. You should assume that 0<δ<4.
Answers
Use the given conditions to write an equation for the line in point-slope form and general form.
Passing through (-4,3) and parallel to the line whose equation is 3x - 4y-5-0
The equation of the line in point-slope form is.
(Type an equation. Use integers or fractions for any numbers in the equation.)
Answers
Answer:
I don't know it this question
Step-by-step explanation:
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1. If the length and width of the rectangle are doubled, then what is the value of the new area? 4ft 10ft
O 160
040
80
120
4ft
10ft
Answers
Answer: I think the answer you are looming for is 80 feet.
Step-by-step explanation:
4 x 10 = 40
To double means to multiply by 2 so
40 x 2 = 80
somebody please help me
Answers
Answer:
4
Step-by-step explanation:
[tex] \frac{(2 {)}^{3}(2 {)}^{4} }{(2 {)}^{5} } [/tex]
→[tex] {2}^{3 + 4 + 5} [/tex]
→[tex] {2}^{2} = 4[/tex]
Hope it helps