The value of the function is, y = 3.61
What is the value of the function?
The objective function's value at a solution is given by the value function of an optimization problem, which only depends on the problem's parameters.
Consider the given function,
[tex]y = \sqrt{x+10}[/tex]
We have to find the value of y at x = 3.
So, plug x = 3 in the above equation.
We get,
[tex]y = \sqrt{3 + 10} = \sqrt{13} = 3.61[/tex]
When we plug x = 3 then we get y = 3.61.
Therefore, the value of the given function is, y = 3.61
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help meeeeeeeeee pleasee
Answer: 9.7 seconds
Step-by-step explanation:
[tex]16t^2=1503\\\\t^2 =\frac{1503}{16}\\\\t=\sqrt{1503/16} \text{ } (t > 0)\\\\t \approx 9.7[/tex]
The vertices of a rectangle are R(-5, -5), S(-1, -5), T(-1, 1), and U(-5, 1). After translation, R' is the point (-9, 1). Find the translation rule and
coordinates of U'.
2 of 27
Answer:
Transformation rule: (x, y) → (x - 4, y + 6),Coordinates of U' = ( - 9, 7).==============
Compare the coordinates of R and R' to find the transformation rule:
R(- 5, - 5) → R'(- 9, 1)Change in x:
-9 - (-5) = - 4Change in y:
1 - (-5) = 6The rule is:
(x, y) → (x - 4, y + 6)Apply this rule to U to find the coordinates of U':
U(-5, 1) → U'(-5 - 4, 1 + 6) = U'(-9, 7)12x(4+16)-78×3 =
O A) 6
O B) 54
O C) 159
OD) 486
Answer:
The answer for 12x(4+16)-78×3= is 6
The exact Value of the sine, cosine, and tangent about of the angle
Answer:
Below are the exact values of sine, cosine, and tangent of the given angle -11π/12.
[tex]sin(-\frac{11\pi}{12})=\frac{-\sqrt{6}+\sqrt{2}}{4}[/tex][tex]cos(-\frac{11\pi}{12})=\frac{-\sqrt{6}-\sqrt{2}}{4}[/tex][tex]tan(-\frac{11\pi}{12})=\frac{sin(-\frac{11\pi}{12})}{cos(-\frac{11\pi}{12})}=2-\sqrt{3}[/tex]Explanation:
We can use the following trigonometric identities to solve the exact value of the given angle.
[tex]\begin{gathered} sin(x+y)=sin\text{ }x\text{ }cos\text{ }y+cos\text{ }x\text{ }sin\text{ }y \\ cos(x+y)=cos\text{ }x\text{ }cos\text{ }y-sin\text{ }x\text{ }sin\text{ }y \end{gathered}[/tex]For sine function, we have:
[tex]\begin{gathered} sin(-\frac{11\pi}{12})=sin(\frac{\pi}{4}-\frac{7\pi}{6}) \\ sin(\frac{\pi}{4}-\frac{7\pi}{6})=sin\text{ }\frac{\pi}{4}cos(-\frac{7\pi}{6})+cos\text{ }\frac{\pi}{4}sin(-\frac{7\pi}{6}) \end{gathered}[/tex]Simplify.
[tex]\begin{gathered} sin(\frac{\pi}{4}-\frac{7\pi}{6})=\frac{\sqrt{2}}{2}(-\frac{\sqrt{3}}{2})+\frac{\sqrt{2}}{2}(\frac{1}{2}) \\ sin(\frac{\pi}{4}-\frac{7\pi}{6})=\frac{-\sqrt{6}}{4}+\frac{\sqrt{2}}{4} \\ sin(\frac{\pi}{4}-\frac{7\pi}{6})=\frac{-\sqrt{6}+\sqrt{2}}{4} \\ sin(-\frac{11\pi}{12})=\frac{-\sqrt{6}+\sqrt{2}}{4} \end{gathered}[/tex]For cosine function, we have:
[tex]\begin{gathered} cos(-\frac{11\pi}{12})=cos(\frac{\pi}{4}-\frac{7\pi}{6}) \\ cos(\frac{\pi}{4}-\frac{7\pi}{6})=cos\frac{\pi}{4}cos(-\frac{7\pi}{6})-sin\frac{\pi}{4}sin(-\frac{7\pi}{6}) \end{gathered}[/tex]Simplify.
[tex]\begin{gathered} cos(\frac{\pi}{4}-\frac{7\pi}{6})=\frac{\sqrt{2}}{2}(-\frac{\sqrt{3}}{2})-(\frac{\sqrt{2}}{2})(\frac{1}{2}) \\ cos(\frac{\pi}{4}-\frac{7\pi}{6})=\frac{-\sqrt{6}}{4}-\frac{\sqrt{2}}{4} \\ cos(\frac{\pi}{4}-\frac{7\pi}{6})=\frac{-\sqrt{6}-\sqrt{2}}{4} \\ cos(-\frac{11\pi}{12})=\frac{-\sqrt{6}-\sqrt{2}}{4} \end{gathered}[/tex]Lastly, for tangent function, it is the ratio between sine and cosine function.
[tex]tan(-\frac{11\pi}{12})=\frac{sin(-\frac{11\pi}{12})}{cos(-\frac{11\pi}{12})}[/tex]Applying the division rule, we get the reciprocal of the denominator and multiply it to the numerator. The equation becomes:
[tex]tan(-\frac{11\pi}{12})=sin(-\frac{11\pi}{12})\times\frac{1}{cos(-\frac{11\pi}{12})}[/tex]Now, let's replace the sine and cosine value that we have calculated above.
[tex]tan(-\frac{11\pi}{12})=\frac{-\sqrt{6}+\sqrt{2}}{4}\times\frac{4}{-\sqrt{6}-\sqrt{2}}[/tex]Since 4 is a common factor on both numerator and denominator, we can cancel it out. The equation then becomes,
[tex]tan(-\frac{11\pi}{12})=\frac{-\sqrt{6}+\sqrt{2}}{-\sqrt{6}-\sqrt{2}}[/tex]To further simplify the function, let's remove the radicals in the denominator by rationalization.
[tex]\begin{gathered} tan(-\frac{11\pi}{12})=\frac{-\sqrt{6}+\sqrt{2}}{-\sqrt{6}-\sqrt{2}}\times\frac{-\sqrt{6}+\sqrt{2}}{-\sqrt{6}+\sqrt{2}} \\ tan(-\frac{11\pi}{12})=\frac{6-\sqrt{12}-\sqrt{12}+2}{6-\sqrt{12}+\sqrt{12}-2} \end{gathered}[/tex][tex]\begin{gathered} tan(-\frac{11\pi}{12})=\frac{8-2\sqrt{12}}{4} \\ tan(-\frac{11\pi}{12})=\frac{8-2\sqrt{4\times3}}{4} \\ tan(-\frac{11\pi}{12})=\frac{8-(2\times2\sqrt{3})}{4} \\ tan(-\frac{11\pi}{12})=\frac{8-4\sqrt{3}}{4} \\ Factor\text{ }4\text{ }in\text{ }the\text{ }numerator. \\ tan(-\frac{11\pi}{12})=\frac{4(2-\sqrt{3})}{4} \\ Cancel\text{ }4. \\ tan(-\frac{11\pi}{12})=2-\sqrt{3} \end{gathered}[/tex] PLS HELP Which of the following quantities are directly proportional?
the number of pumps used to fill a tank and the time needed to fill that tank
Number of pipes to fill a tank and the time required to fill the same tank is directly proportional.
Given,
Direct proportion;
When the ratio x:y is constant, two values, x and y, are said to be directly proportional to one another. If we spend $50 on two pens, as an example. For four pens, it will cost us 100 $When the ratio x:y1 is
Here
Option d Number of pipes to fill a tank and the time required to fill the same tank is directly proportional. Because in a fixed time interval, as the speed of a vehicle increases, the distance travelled by it also increases in the same ratio.
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The given question is incomplete. Completed question is given below;
Which of the following is in direct proportion?
(a) One side of a cuboid and its volume.
(b) Speed of a vehicle and the distance travelled in a
fixed time interval.
(c) Change in weight and height among individuals.
(d) Number of pipes to fill a tank and the time required
to fill the same tank.
First try was incorrect
Latasha earns a 14.8% commission as a salesperson. She sold a
kitchen play set for $160.87.
What is the amount of Latasha's commission? Round your answer to
the nearest hundredth.
2
#x²
label required
X M
The commission earned by Latasha is $23.81
Given:
Latasha earns 14.8% commission as a salesperson.
She sold a kitchen play for $160.87
we are asked to determine the amount of Latasha's commission = ?
we should take out the percentage of the item she sold:
= 14.8% of $160.87
= 14.8/100 × 160.87
= 2380.876/100
= 23.808
Hence Latasha earns a commission of $23.808 for selling a kitchen play set.
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One year, the population of a city was 253,000. Several years later it was 288,420. Find the percent increase.
The percentage increase is 14%
Given,
In the question;
The population of a city was 253,000.
and, Several years later it was 288,420.
To find the percent increase.
Now, According to the question;
Based on the given conditions,
Formulate:
The population of a city was 253,000.
Several years later = 288,420
(288420 - 253000) ÷ 253000
[tex]\frac{288420 - 253000}{253000}[/tex]
Calculate
= 35420/ 253000
= 7/50
Convert to percentage
7/50
Multiply a number to both the numerator and the denominator
7/50 x 2/2
= 14/100
= 14%
Hence, The percentage increase is 14%
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Use the quadratic formula to find both solutions to the quadratic equation
given below.
2x^2+ 3x-5 =0
Answer:
X would be -5/2 and 1
Step-by-step explanation:
The quadratic formula is (-b±√(b^2-4ac))/2a. By substituting the values in, we get the expression (-3±√(3^2-4(2)(-5))/2(2). By Simplifying, we get (-3±√(9+40))/4. More simplification: (-3±√(49))/4. Even more simplification: (-3±7)/4. The expression now splits into two parts, (-3-7)/4, and (-3+7)/4. The first expression becomes -10/4, which simplified is -5/2. The second expression becomes 4/4, which simplifies to 1. Therefore, your answers are x=1, -5/2.
Hope this helps!
The robotics team needs new uniforms. The students plan to sell plush toy lions(The school mascot) for 5$ each. The students find three companies on-line that sell stuffed mascots. Company a sell 18 lions for $51.84. company B sells 12 lions for 34.32. company c charges 42.75 for 15 lions. which company has the best buy
Answer:
Company B would be the best place to get their supply from. First, I multiplied all of the quantities by 5 (33.72*5)(44.48*5)(42.6*5) and got my sums. Then, I subtracted the price to be earned from selling the plush toys by the price of the bundle. Lastly, I compared the amounts earned by using each.
A. $26.28 B. $35.52 C. $32.4
Company B is the best place to buy from.
Answer quick! Due today!Please help with explanation each graph shown is a translation of the graph of f(x)=x^2 write the function in vertex form
For a graph with f(x)=x^2, the vertex of the parabola is at the origin.
In the given graph, the parabola is shifted 3 units to the left and 1 unit down.
The general vertex form of a parabola is,
[tex]f(x)=a(x-h)^2+k[/tex]Here, h is the horizontal shift and k is the vertical shift.
Since the graph is only translated and not shrinked or expanded , a=1.
Since the graph is shifted horizonatlly to the left, h is negative.
So, h=-3.
Since the graph is shifted vertically down, k is negative.
So, k=-1.
So, the equation for the given graph becomes,
[tex]\begin{gathered} f(x)=(x-(-3)^2-1 \\ f(x)=(x+3)^2-1_{} \end{gathered}[/tex]Therefore, the function in vertex form is,
[tex]f(x)=(x+3)^2-1[/tex]3. Sharon is using a calculator to find out
how many hours she has spent on a
certain job. She divides, and her display
reads:
4.666666666
Assuming her calculations are correct,
how many hours did she spend on the
job?
A. 4 1/6
B. 4 2/3
C. 4 6/7
D. 46
Answer:
4 6/7
Step-by-step explanation:
(Not really sure you should go with whatever answer you're sure of)
or 4 1/6
Answer:
B. 4 2/3
it's right, I took this last year.
Assume that a researcher randomly selects 14 newborn babies and counts the number of girls, x. The probabilities corresponding to the 14 possible values of x are summarized in the given table. Answer the questions using the table.
Find the probability of selecting 5 or fewer girls.
A probability distribution is one that lists all of the outcomes of an experiment or a variable together with their respective probabilities. The total probability must equal 0.0424 because it includes all of the possible outcomes.
How do you calculate probability?probability distribution for 5 fewer girls is
(0.001+0.006+0.022+0.061+0.122) divided by 5
is equal to 0.0424
The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event could occur. Probability and odds are two distinct ideas. Odds are calculated by dividing the likelihood of an event by the likelihood that it won't.In everyday speech, the term "probability" refers to the likelihood that a specific event (or group of events) will take place, represented as a number between 0 and 100% or as a linear scale from 0 (impossibility) to 1 (certainty). Statistics is the study of events that follow a probability distribution.Theoretical Probability is one of three main categories of probability. Scientific Probability. Probability axiomatically.To learn more about probability refer to:
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Trying to pass math class
Answer:
55
Step-by-step explanation:
All the triangles are right angled triangles.
So, one of the angle is 90°.
There is a property of angle of triangles.
Exterior angle = Sum of opposite interior angles
145 = m∠1 + 90
m∠1 = 145 - 90
m∠1 = 55
What is the approximate surface area of an AA battery?
a. 5,583 mm^2
b. 1,242 mm^2
c. 2,176 mm^2
d. 2,485 mm^2
The approximate surface area of an AA battery would be = 5,583 mm^2. That is option A.
What is an AA battery?An AA battery is defined as the type of battery that is used to supply chemical energy to electronic gadgets.
The AA battery has the shape of a cylinder and the formula for the surface area of cylinder:
h = 49.5mm
r = 14mm
π = 3.14
A=2πrh+2πr²
A = (2×3.14 ×14×49.5)+ (2× 3.14×14²)
A = 4,352.04 + 1,230.88
A = 5582.92
Therefore the surface area of the AA battery is approximately 5,583 mm^2.
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Answer: D. 2,485 mm²
Step-by-step explanation: Right on Plato
Which of the following equations has the same graph as 2x + 3y = 12?
Select all that apply.
A. y-2=-2/3(x-3)
B. x+3/2y=6
c. -2x-3y = - 12
D. y-2=-2/3x+4
E. y=-2/3x+4
Answer:
A, B, C, E
Step-by-step explanation:
You want to know the equations on the list that have the same graph as 2x+3y=12.
Comparing equationsEquations are most easily compared when they are written in the same form. Here, there is a mix of "standard form", "slope-intercept form", and "point-slope form." We can convert all of these to slope-intercept form to make the comparison.
EquationsReference equation
2x +3y = 12 ⇒ 3y = -2x +12 ⇒ y = -2/3x +4
A.y -2 = -2/3(x -3) ⇒ y = -2/3x +2 +2 ⇒ y = -2/3x +4 . . . equivalent
B.x +3/2y = 6 ⇒ 3/2y = -x +6 ⇒ y = -2/3x +4 . . . equivalent
This is the original equation divided by 2.
C.-2x -3y = -12 ⇒ -2x +12 = 3y ⇒ y = 2/3x +4 . . . equivalent
This is the original equation multiplied by -1.
D.y -2 = -2/3x +4 ⇒ y = -2/3x +6 . . . not equivalent
E.y = -2/3x +4 . . . equivalent
Jodi buys nine pens at $1.10 per pen. Which of the following represents the change she would receive if she purchased the pens using a $20 bill?
A $20 – (9)($1.10)
B ($20 – 9)($1.10)
C $20 + (9)($1.10)
D ($20 – $1.10)(9)
E $20 – 9 – $1.10
The expression (A) $20 – (9)($1.10) will correctly represents the given situation.
What are expressions?An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.You must substitute a number for each variable and carry out the arithmetic operations in order to evaluate an algebraic expression. Since 6 + 6 equals 12, the variable x in the example above is equal to 6. If we are aware of the values of our variables, we can substitute those values for the original variables before evaluating the expression.So, the expression that represents the given situation will be:
The total bill is 20$.The number of pens purchased is 9.Each pen cost $1.10.Then, the expression will be:
20 - 9(1.10)Therefore, the expression (A) $20 – (9)($1.10) will correctly represents the given situation.
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A child pushes a toy car with a force of
5.25 N a distance of 6.5 m. The car rolls
for a total distance of 32 m. How much
work is done on the toy car?
The work is done on the toy car is 164.4 J .
How to calculate work done?We are aware that the definition of work is the multiplication of the magnitude of the displacement (d) and the component of the force acting in the displacement direction.
When an object moves over a distance while being applied with force, the work is considered to have been completed.
Three categories can be used to classify the type of labor performed. Positive work, negative work, and zero work are the three types. The angle between force and displacement determines the kind of work that is done. Positive work is defined as any work that causes an object to move in the direction of the applied force.
Given ,
Work = force * distance
Force = 5.2 N
Distance = 32 m
So ,
Work = 5.2 * 32
= 166. 4 J
Therefore the work is done is 164.4 J
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pounds. To be able to ride in a car together, how muchcan you weigh? Write and solve an inequality.(1 point)Ox-60221; at most 60 pounds
Let x represent your weight, then we can set the following inequality:
[tex]x+60\leq221.[/tex]Solving the inequality for x, we get:
[tex]\begin{gathered} x+60-60\leq221-60, \\ x=161. \end{gathered}[/tex]Therefore, at most, you can weigh 161 pounds.
Answer: [tex]x+60\leq221,\text{ at most 161 pounds.}[/tex]Which inequality below is represented by the following graph: A. y < -2x² + 10z - 8 B. y 2x² + 10x – 8
Explanation
We are required to determine the inequality that satisfies the given graph.
This is achieved thus:
We can deduce from the graph that the curve drawn is not a broken line. Therefore, it cannot be strictly greater than or strictly less than.
We know that only "true" region is shaded. By testing the origin, we can deduce that the correct inequality is:
[tex]y\geqslant-2x^2+10x-8[/tex]Hence, the answer is:
Option D
Find number if 5/3 of it is 15
Answer:
25
Step-by-step explanation:
15/3 = 5
5*5 = 25
Easy as pie
HELP PLSSS CAN SOMEONE SOLVE THIS
Step-by-step explanation:
we use the law of sine :
a/sin(A) = b/sin(B) = c/sin(C)
a, b, c being the sides, A, B, C being the opposing angles of the sides.
and remember, the sum of all angles in a triangle is 180°.
so,
JL/sin(90) = KL/sin(72)
JL/1 = KL/sin(72)
KL = JL × sin(72) = 10 × 0.951056516... =
= 9.51056516... ≈ 10
JK/sin(L) = JL/sin(90) = JL
JK = JL × sin(L)
angle L = 180 - 90 - 72 = 18°
JK = JL × sin(18) = 10 × 0.309016994... =
= 3.09016994... ≈ 3
Let f= {(5,5),(8,-8),(-8,5)}. Find (a) f(5) and (b) f(-8).
The given function f(x) is
[tex]f(x)=\lbrace(5,5),(8,-8),(-8,5)\rbrace[/tex]We need to find
a) f(5)
It means finding the value of the y-coordinate in the ordered pair that has x-coordinate = 5
Look at the function
At x = 5, y = 5 (1st orderd pair), then
f(5) = 5
b) f(-8)
It means finding the value of the y-coordinate in the ordered pair that has x-coordinate = -8
Look at the function
At x = -8, y = 5, (last ordered pair), then
f(-8) = 5
Employee at an antique store are hired at a wedge of $15 per hours, and they got a $9.75 raise each year. naomi make $20.25 per hours working at the store. how long has she worked there
Number of years she worked at the store is 0.5385 years ( 0.6 years approx. ).
What is rate of change ?A rate of change is a measurement of the ratio of one quantity to another. Rate of Change: 1608042=802=401; Change in Y = Change in X; Change in Distance; Change in Time. It develops either at a 40 or 401 rpm rate. This shows that an automobile is traveling at a 40 mph speed.
CalculationRate of early age of employee = $15 per hour
raise price per year = $9.75
Naomi wage per hour = $20.25
then gain extra wage = 20.25 - 15
= $5.25
number of years she worked = 5.25 / 9.75
= 0.5385 years ( 0.6 years approx)
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0Over ten years, the population of fish in a lake increases by 3%. After the increase, there are 10,094 fish. Whichexpressions are equivalent to the number of fish ten years before? Select all that apply.9,80010,39710,094 : 1.0310,094 (100+310010,094 - 3%Brun
The fish population has been increasing over 10 years giving a total of 10094 as a result. We are asked to find the initial population of fish.
So we write the expression for popukation increase:
[tex]N(t)=N_{0\, }(1+0.03)^t[/tex]where No is the initial population, and what we want to find, while N(t) is the current population (10094) and the exponent (t) is the equivalent to ten year units (so we use "1"). The rate is 3% per ten years, and this in decimal form is 0.03.
We solve for No in the equation by dividing bby 1.03, which gives us:
No= 10094 / 1.03 = 9800
Therefore, one has to select the option 10094 divided by 1.03, (typed as 10094 : 1.03), and also the numerical answer 9800 (first option)
Simplify
[tex]( \sqrt{3}) \: ( {}^{5} \sqrt{3} )[/tex]
a :
[tex]3 \frac{1}{10} [/tex]
B:
[tex]3 \frac{3}{5} [/tex]
C:
[tex]3 \frac{9}{10} [/tex]
D:
[tex]3 \frac{7}{10} [/tex]
Also Due Today
2. Which point is located on the line represented by the equation y + 4 = - 5(x - 3)
(- 4, - 5)
(- 5, - 4)
(3, - 4)
(- 3, 4)
3. Which equation represents the line that passes through the points (6, - 3) and (- 4, - 9) ^ prime
y + 4 = 3/5 * (x + 9)
y + 3 = 3/5 * (x - 6)
y - 3 = 3/5 * (x + 6)
y + 4 = 5/3 * (x + 9)
2) (3, -4)
3) y + 3 + 3/5 (x - 6)
How to graph using this info and create a function ?
The instantaneous rate of change at x = 2 is 0
at x = 3 is negative
0 <= x <= 4 is 0
a function has an instantaneous rate of change of 0 at a maximum or minimum
the instantaneous rate of change at x = 3 being negative means it goes down after the maximum or minimum meaning it is a maximum
the average rate of change on the interval is 0, so the function goes up and then down
these all sound like a parabola
y = -2(x - 2)^2 + 10 is a parabola that fits the requirements
Write an equation in slope-intercept form of the lineO24+2+4161O A y=-7xBy=2x + 7OCy=2x - 7D. Y:-7x + 2
From the graph provided, we will need to find the slope and also coordinates in other to find the equation of the graph.
For the slope,
[tex]m=\frac{y_2-y_1}{x_2-x_{1_{}}_{}}_{}[/tex]From the graph,
Where x=0, y=0 which can be written in coordinates of (x2, y2) as (0, 0)
Where x=3.5, y=-7 which can be written in coordinates of (x1, y1) as (3.5, -7)
To find the slope,
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{0-(-7)}{0-3.5}=\frac{7}{-3.5}=-2_{}[/tex]The slope of the graph m is -2
The formula for the equation of a graph is,
[tex]\frac{y-y_1}{x-x_1}=m[/tex]Where (x1, y1) is (3.5, -7),
[tex]\begin{gathered} \frac{y-y_1}{x-x_1}=m \\ \frac{y-(-7)_{}}{x-(3.5)}=-2 \\ \frac{y+7}{x-3.5}=-2 \\ \text{Crossmultiply} \\ y+7=-2(x-3.5) \\ y+7=-2x+7 \\ y=-2x+7-7 \\ y=-2x \end{gathered}[/tex]Hence, the equation of the graph is deduced above.
15. A scale model of the Shanghai Tower is 3 inches tall. The actual tower is 2,073 feet tall. What is the scale?
en español porfis
The scale is of 8,292 ft. 1 ft in the scale is equal to 8292 ft of the actual.
Given, a scale model of the Shanghai Tower is 3 inches tall.
The actual tower is 2,073 feet tall.
We have to find the scale.
Now, as 1 ft = 12 inch
1 inch = 1/12 ft
3 inches = 3/12 ft
3 inches = 1/4 ft
So, 1/4 ft of scale = 2,073 ft of actual
1 ft of scale = 8,292 ft of actual
So, 1 ft in the scale is equal to 8,292 ft of the actual.
Hence, 1 ft in the scale is equal to 8,292 ft of the actual.
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If you have a 77.2% and you got 34% on a test and it’s worth 60% of your grade, what would you grade be now?
Answer:
If you have a 77.2% and you got 34% on a test and it’s worth 60% of your grade, your percentage grade would be 63.2%.