a) The variables are:
x = number of cookies bought.y = number of brownies bought.b)
x + y ≥ 12
x*$0.75 + y*$1.25 ≤ $15
How to write the system of inequalities?a) First we need to define the variables, in this case we have:
x = number of cookies bought.y = number of brownies bought.b) Now we want to write the system, we know that he must buy at least 12 items, then:
x + y ≥ 12
And he can spend, at most, $15, then:
x*$0.75 + y*$1.25 ≤ $15
These two inequalities conform the system of inequalities:
x + y ≥ 12
x*$0.75 + y*$1.25 ≤ $15
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A surveyor found the angle of elevation from the ground to the top of the building at two locations 20 feet apart as shown below.
2 lines are drawn from the ground to the top of a building, forming 2 triangles with the ground. The angle of elevation of the first line is 48 degrees. The second line is 20 feet away from line 1. The angle of elevation of the second line is 33 degrees. c is the length of the first line and h is the height of the building. Angle A is the angle to the left of angle 48 degrees, and angle B is the angle at the convergence of the 2 lines with the top of the building.
Which measurements are correct? Round side lengths to the nearest hundredth. Check all that apply.
m∠A = 57°
m∠B = 15°
c ≈ 10.89 ft
h ≈ 8.09 ft
h ≈ 31.28 ft
Applying the sine ratio and law of sines, the correct measurements are:
B. m∠B = 15°
E. h ≈ 31.28 ft.
What is the Sine Ratio?Sine ratio that can be used to determine the side length of a right triangle is, sin ∅ = opposite side/hypotenuse.
Find c using the law of sines:
C = 33°
A = 180 - 48 = 132 [linear pair]
B = 180 - 33 - 132 = 15° [triangle sum theorem]
b = 20 ft
c = ?
Using the law of sines, b/sin B = c/sin C, we have:
20/sin 15 = c/sin 33
(c)(sin 15) = (20)(sin 33)
c = (20 × sin 33)/sin 15
c ≈ 42.09
Use the sine ratio to find h:
∅ = 48°
Hypotenuse = c = 42.09
Opposite = h = ?
sin 48 = h/42.09
h = (sin 48)(42.09)
h ≈ 31.28
The correct measurements are:
B. m∠B = 15°
E. h ≈ 31.28 ft
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Answer:
B. and E.
Step-by-step explanation:
The figure shows secants LH and and tangent J intersecting at point L. AHIL is a right triangle. Find m/HLJ, which is
the value for x, and m I, which is the value for y.
A. x = 274
y = 86
B. x = 137
y = 43
C. x = 47
y = 86
D. x = 317
y = 43
The values of x and y from the given diagram are 47 ad 86 degrees respectively
Circle theoremFrom the given circle, the triangle HJL is a right triangle.
Determine the value of y
43 = 1/2 <y
<y = 43 * 2
<y = 86 degrees
Since the sum of angle on a straight line is 180 degrees, such that;
x+90+43 = 180
x + 133 = 180
x = 47 degrees
Hence the values of x and y from the given diagram are 47 ad 86 degrees respectively
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Consider the volume of the region shown below, which shows a right circular cone with a top radius of 3 cm and height 9cm
Answer:
84.82 cm
Step-by-step explanation:
Volume of a cone: [tex]\frac{1}{3} \pi r^2h[/tex]
[tex]\frac{1}{3} \pi r^2h\\\\\\\\= \frac{1}{3}\pi (3)^2(9)\\\\= \frac{1}{3}\pi(9)(9)\\\\\\\= \frac{1}{3} \pi (81)\\\\= 27\pi \\[/tex]
≈ 84.82 cm
Can some solve for x please?
Answer:
x = 19
Step-by-step explanation:
You would use vertical angles to move the 8x - 14 so that we could use the Consecutive Interior angles theorem. Which says that consecutive angles equal 180. So, you would set up your equation: 8x-14+2x+4 = 180. Add the 8 and 2 = 10. Add the -14 and 4 = -10. You get 10x-10 = 180. 180+10 = 190. 190/10 = 19. X = 19
Five possibilities are equally likely and have payoffs of $2, $4, $6, $8, and $10. the expected value is:____.
a. $4
b.$5
c. $6
d. $7
The expected value for the given Five possibilities is $6.
We have,
Payoffs of $2, $4, $6, $8, and $10.
Now,
We know that,
The expected value [tex]=\Sigma (x*P(x))[/tex]
i.e. The sum of product of possible outcome and each outcome.
Here, x = Each outcome
And
P(x) = Possible outcomes
So,
Probability of x (Px) [tex]=\frac{1}{5}[/tex],
Now,
According to the above mentioned formula,
i.e.
The expected value [tex]=\Sigma (x*P(x))[/tex]
We get,
[tex]=\Sigma\ (\frac{1}{5} * 2) + (\frac{1}{5} * 4) + (\frac{1}{5} * 6) +(\frac{1}{5} * 8) +(\frac{1}{5} * 10)[/tex]
On solving we get,
[tex]=\Sigma\ (0.4 + 0.8 + 1.2 + 1.6 + 2)[/tex]
i.e.
The expected value = $6
So,
The expected value for given possibilities is $6.
Hence we can say that the expected value for the given Five possibilities is $6.
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Read each question carefully and show work. Put your answer in the provided space.
Compare the measures of the different angles of elevation and depression that are labeled in the diagram. Which statements are true? Check all that apply.
x > y
v > x
w = y
y < v
v = w
x < w
The statements that are true about the angle include:
x > y
w = y
y < v
How to illustrate the information?From the information, the first has legs 529m and 229m. Then tan x = 529/229. Also tan y = 529/347.
It can be seen that tan x is greater than tan y. Angles x, v, y, and w are alternate angles. Therefore, the correct options are A, C, avd D.
A weather balloon is 529 meters above the ground. Two weather stations, A and B, monitor the balloon’s progress. Compare the measures of the different angles of elevation and depression that are labeled in the diagram. Which statements are true
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Complete the equation describing how x and y are related.
X | Y
0 | -1
1 | -1.5
2 | -2
3 | -2.5
4 | -3
5 | -3.5
Y= [?]x + [?]
A triangle has two sides of lengths 6 and 9
the third side be?
Check all that
What value
apply.
could the length of
Answer:
A, C, E, F
Step-by-step explanation:
since nothing else was said, it is a general triangle. nothing special about it.
so, the only rules are that the sum of any pair of sides must be longer than the 3rd side (otherwise, if the 3rd side is longer, the sides could not connect).
A. 10.
so, we have
6 + 9 > 10 true
6 + 10 > 9 true
9 + 10 > 6 true
therefore this is a possible 3rd side.
B. 2.
so, we have
6 + 9 > 2 true
6 + 2 > 9 false
9 + 2 > 6 true
therefore this is NOT a possible 3rd side.
C. 4.
so, we have
6 + 9 > 4 true
6 + 4 > 9 true
9 + 4 > 6 true
therefore this is a possible 3rd side.
D. 15.
so, we have
6 + 9 > 15 false
6 + 15 > 9 true
9 + 15 > 6 true
therefore this is NOT a possible 3rd side (this triangle is a special case as 6+9 = 15 : it can only exist as a completely flat line and is therefore not a triangle).
E. 12.
so, we have
6 + 9 > 12 true
6 + 12 > 9 true
9 + 12 > 6 true
therefore this is a possible 3rd side.
F. 7.
so, we have
6 + 9 > 7 true
6 + 7 > 9 true
9 + 7 > 6 true
therefore this is a possible 3rd side.
TIME REMAINING
43:25
Triangles X Y Z and X prime Y prime Z prime are shown.
ΔXYZ was reflected over a vertical line, then dilated by a scale factor of One-half, resulting in ΔX'Y'Z'. Which must be true of the two triangles? Select three options.
△XYZ ~ △X'Y'Z'
AngleXZY ≅ AngleY'Z'X'
YX ≅ Y'X'
XZ = 2X'Z'
mAngleYXZ = 2mAngleY'X'Z'
Answer:
△XYZ ~ △X'Y'Z'AngleXZY ≅ AngleY'Z'X'XZ = 2X'Z'Step-by-step explanation:
Reflection over any line is a rigid transformation that does not change angles or lengths. Dilation is a transformation that changes lengths by the same scale factor, but has no effect on angles. Dilated figures are similar to the original.
ApplicationWhen ΔXYZ is reflected over a vertical line, no lengths or angles are changed. When the reflected triangle is dilated by half, we get ...
Y'X' = (1/2)YX . . . . . . . makes option 3 false
X'Z' = (1/2)XZ . . . . . . . makes option 4 true
Since no angles are changed, we have ...
Angle XZY ≅ Angle Y'Z'X' (another name for angle X'Z'Y')
... makes option 2 true
Of course, the resulting triangle is similar to the original, so ...
△XYZ ~ △X'Y'Z' . . . . . option 1 is true
ANSWER ASAP!
Tim is playing table tennis with a friend. the ball accidentally falls off the table and each bounce reaches a third of the height of the previous bounce. The ball starts bouncing with a height of 3 feet. Which sequence describes the balls bounce height?
A. 3, 6, 9, 12,...
B. 1, 3, 9, 27,...
C. 1/9, 1/3, 1, 3,...
D. 3, 1, 1/3, 1/9,...
The sequence of the ball is 3, 1, 1/3, 1/9,...
How to find terms of a sequence?The ball starts bouncing with a height of 3 feet.
Each bounce reaches a third of the height of the previous bounce.
Therefore,
a = first term = 3
r = common ratio = 1 / 3
Therefore,
nth term = arⁿ⁻¹
where
a = first termr = common ration = number of termsFirst term = 3
2nd term = 3 × (1 / 3) = 1
Third term = 3 × (1 / 3)² = 1 / 3
Fourth term = 3 × (1 / 3)³ = 1 / 9
Therefore, the sequence of the ball is 3, 1, 1/3, 1/9,...
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which of the following would be a good name for the function that takes the length of a race and returns the time needed to complete it?
A. time(length)
B.length(time)
C.cost(time)
D. time(race)
The answer choice which best fits the function described in the task content is; Choice A; time(length).
Which would be a good name for the function?It follows from the task content that the function takes the length of a race and returns the time needed to complete it.
On this note, it follows that the time taken is a function of the length of the race.
Hence, the appropriate name of the function is; Choice A.
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If the growth rate of bacteria at any time t is proportional to the number present at t and triples in 1 week
If the growth rate of bacteria at any time is proportional to the number of bacteria present at t then the population after 20 weeks will be 403.42[tex]x_{0}[/tex] in which [tex]x_{0}[/tex] is the initial population.
Given that the growth rate of bacteria at any time t is proportional to the number present at t and triples in 1 week.
We are required to find the number of bacteria present after 10 weeks.
let the number of bacteria present at t is x.
So,
dx/dt∝x
dx/dt=kx
1/x dx=k dt
Now integrate both sides.
[tex]\int\limits {1/x} \, dx[/tex]=[tex]\int\limits{k} \, dt[/tex]
log x=kt+log c----------1
Put t=0
log [tex]x_{0}[/tex]=0 +log c ([tex]x_{0}[/tex] shows the population in beginning)
Cancelling log from both sides.
c=[tex]x_{0}[/tex]
So put c=[tex]x_{0}[/tex] in 1
log x=kt+log [tex]x_{0}[/tex]
log x=log [tex]e^{kt}[/tex]+log [tex]x_{0}[/tex]
log x=log [tex]e^{kt}x_{0}[/tex]
x=[tex]e^{kt}x_{0}[/tex]
We have been given that the population triples in a week so we have to put the value of x=2[tex]x_{0}[/tex] and t=1 to get the value of k.
2[tex]x_{0}[/tex]=[tex]e^{k} x_{0}[/tex]
2=[tex]e^{k}[/tex]
log 2=k
We have to now put the value of t=20 and k=log 2 ,to get the population after 20 weeks.
x=[tex]e^{20log 2}[/tex][tex]x_{0}[/tex]
x=[tex]e^{0.30*2}[/tex][tex]x_{0}[/tex]
x=[tex]e^{6}x_{0}[/tex]
x=403.42[tex]x_{0}[/tex]
If the growth rate of bacteria at any time is proportional to the number of bacteria present at t then the population after 20 weeks will be 403.42[tex]x_{0}[/tex] in which [tex]x_{0}[/tex] is the initial population.
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The given question is incomplete as the question incudes the following:
Calculate the population after 20 weeks.
What is the missing reason in the proof?
Given: ∠ABC is a right angle, ∠DBC is a straight angle
Prove: ∠ABC ≅ ∠ABD
A horizontal line has points D, B, C. A line extends vertically from point B to point A. Angle A B C is a right angle.
definition of angle bisector
segment addition property
definition of congruent angles
transitive property
Mark this and return
We can identify that the missing reason in the proof is: Definition of Congruent angles.
How to give proof of a congruent triangle?We know that an angle measure of 90° of ∠ABC in the triangle means that it is a right angle triangle.
We also see that ∠ADB is also a right angle and is equal to 90°.
Now, since they have exactly the same measure, these angles are congruent. Then we can say that the angles are congruent and as such:
∠ABC ≅ ∠ABD
Thus, we can identify that the missing reason is: Definition of Congruent angles.
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i’ll give brainliest!!
(last choice is d^2sqrt7e)
Answer:
D (the last choice)
Step-by-step explanation:
Taking the fourth root of each element individually:
49^(1/4) = sqrt(7)
(d^8)^(1/4) = d^2
(e^2)^(1/4) = sqrt(e)
Multiplying them back together:
sqrt(7) * d^2 * sqrt(e) = d^2 * sqrt(7e)
Answer:
The last bubble (that of which is cut from the screen) is simplified.
Step-by-step explanation:
The provided equation is simplified by following these steps:
[tex](49d^{8}e^2)^\frac{1}{4}[/tex]
= [tex](49)^\frac{1}{4}(d)^\frac{8}{4}(e)^\frac{2}{4}[/tex]
[tex](7)^\frac{2}{4}(d)^\frac{8}{4}(e)^\frac{2}{4}[/tex]
=[tex]\sqrt{7} (d^2)(\sqrt{e})[/tex]
Lukas paid for a pair of shoes with a $50 bill. After the clerk added 9% tax to the purchase, Lukas received $17.30 in change. What was the price of the shoes, not including the tax?
Answer:
$29.75
Step-by-step explanation:
If Lukas paid for the shoes with $50, and got $17.30 back, the total price of the shoes with the tax was $32.70. Because we are trying to find the price of the shoes without the 9% tax, we calculate what 91% of 32.70 is, which is $29.757
A triangular metal plate has base measuring 18 cm. Its height is unknown.
What equation models the area of this plate?
Let A represent the area, b represent the base, and h represent the height of the plate.
The model is based on the formula for the area of a triangle.
The area as a function of the height H is:
[tex]A= 9cm*H[/tex]
Which equation models the area of the metal plate?
We know that for a triangle of base B and height H, the area is given by:
[tex]A = \frac{B*H}{2}[/tex]
In this case, we already know that the base measures 18cm, then the formula for the area as a function of the height H is:
[tex]A= \frac{18cm*H}{2} = 9cm*H[/tex]
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If f(x) = –x2 + 3x + 5 and g(x) = x2 + 2x, which graph shows the graph of (f + g)(x)? On a coordinate plane, a straight line with a negative slope crosses the y-axis at (0, 5) and crosses the x-axis at (1, 0). On a coordinate plane, a parabola opens down. It goes through (negative 2, negative 4), has a vertex at (0, 5), and goes through (2, negative 2) On a coordinate plane, a parabola opens up. It goes through (negative 3, 7), has a vertex at (negative 1, 2), and goes through (0, 5). On a coordinate plane, a straight line with a positive slope crosses the x-axis at (negative 1, 0) and crosses the y-axis at (0, 5) - edge21
Answer:
Can i have the graph? THis doesn't make sense
Step-by-step explanation:
The graph of (f+g)(x) is on the coordinate plane, a straight line with a positive slope crosses the x-axis at (negative 1, 0) and crosses the y-axis at (0, 5).
What is the graph of a parabolic equation?The graph of a parabolic equation is a curved U-shape graph from where the domain, the range, x-intercept(s), and the y-intercept(s) can be determined.
Given that:
f(x) = -x² + 3x + 5
g(x) = x² + 2x
To find (f + g)(x), we have:
(f + g)(x) = (-x² + 3x + 5)+(x² + 2x)
(f + g)(x) = -x² + 3x + 5 +x² + 2x
(f + g)(x) = 3x + 2x + 5
(f + g)(x) = 5x + 5
Use the Slope-intercept form: We are to find the graph of y = 5x + 5
y = 5x + 5
Here:
Slope = 5 x-intercept = (-1, 0)y-intercept = (0,5)Therefore, we can conclude that on the coordinate plane, a straight line with a positive slope crosses the x-axis at (negative 1, 0) and crosses the y-axis at (0, 5)
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For 3, 5, Are the triangles similar? If so, state the similarity and the postulate or theorem that justifies your answer.
Which choice is equivalent to the quotient below? √16 OA. A OB. N/హ / OC. 2 D. √√2
Answer:
C
Step-by-step explanation:
Please refer to the attached photo for step by step solutions.
Note: Square roots and squares will always cancel out each other.
WILL MAKE BRAINLIEST!! Solve for x
Answer:
x=17
Step-by-step explanation:
Since they are intersecting lines, 3x=51
x=17
Answer:
x = 17
Step-by-step explanation:
When two lines intersect each other, the opposite angles are identical. Therefore, you can set both angles equal to each other to find the value of "x".
3x = 51
x = 17
ANSWER BOTH QUESTIONS PLEASE REALLY IMPORTANT AND URGENT! WILL GIVE BRAINLIEST! THANK YOU!!!
Answer:
10. Area: ((6+4) * 8)/2 = 40 ft^2
Perimeter: 6 + 4 + 8 + 12.8 = 30.8 ft
8. 22 + 22 + 22 + 38 + 27.2 = 131.2 ft
please help em
A (1,2), B(3,8) and C(7,4) are the corners of a triangle. Draw this triangle on a grid.
The triangle drawn on a grid is in the image attached and the complete procedure for the construction of the triangle is summarized in the explanation.
How to draw a triangle on a Cartesian plane
In this question we are asked to draw a triangle on a Cartesian plane. The procedure is summarized below:
Mark the points of the vertex on the plane with respect to the origin.Connect each pair of points by drawing straight line segments.Lastly, we present the result of this method in the image attached below.
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how to solve for problem 14
m∠ AEM = 20°
How to determine the angle
From the given figure, we can see that m∠ AEM is alternate to m∠ ACE
Note that m∠ ACE = 20°
Alternate angles are equal.
If m∠ ACE is alternate to m∠ AEM
Then, m∠ AEM = 20°
Hence, m∠ AEM = 20°
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WILL GIVE BRAINLIEST! I’m desperate for help! This assignment is due today I’m stuck! Pls help!
Which expression represents the following statement? Multiply 6 by 3, and then subtract the quotient of 18 and 9.
6 x (3 ÷ 18) + 9
6 + 3 + (18 ÷ 9)
(6 x 3) − 18 ÷ 9
6 x (3 + 18) + 9
Answer:
Step-by-step explanation:
the third one is correct
[tex]6 \times 3 - \frac{18}{9} \\ (6 \times 3) - (18 \div 9)[/tex]
A college's basketball team will play 33 games next winter. Each game can result in one of 2 outcomes: a win or a loss. Find the total possible number of outcomes for the season record.
The total possible number of outcomes for the season record is [tex]2^{33}[/tex].
What is an outcome?An event that may be given a mathematical probability is known as an outcome in mathematics (an outcome of an experiment). The amount of potential outcomes for a particular experiment determines the probability assigned to each result.The result of an experiment is a number of outcomes.
According to the question,
The basketball team at a college will play 33 games next winter. There are only two possible outcomes for each game: a win or a loss.
So, the total number of possible outcomes for the season record=[tex]2^{33}[/tex].
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What type of function is represented by the table of values below?
A. cubic
B. exponential
C. quadratic
D. linear
The table represents an exponential function:
[tex]f(x) = 3^x[/tex]
Then the correct option is B.
What type of function is represented by the table?
Here we have the table:
x y
1 3
2 9
3 27
4 81
5 243
You can see that each time that x increases by one unit, the value of is multiplied by 3. This is clearly an exponential function.
The function actually is:
[tex]f(x) = 3^x[/tex]
Evaluating it we get:
[tex]f(1) = 3^1 = 3\\\\f(2) = 3^2 = 9\\\\f(3) = 3^3 = 27\\...[/tex]
So the correct option is B, exponential.
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HELP !! Which of the following points lies on the graph of this equation? y =2x -2
Answer:
A.
Step-by-step explanation:
i'm 99% sure!
Answer:
B
Step-by-step explanation:
Plug in the coordinates.
The volume, in cubic centimeters, of a fish
tank is represented by the polynomial
model
The polynomial's maximum value is relative.
Is the maximum relative or absolute?Here we have the polynomial:
[tex]V(x) = 36x^2 - 3.75x^3[/tex]
Notice that the leading coefficient is negative, so, as x tends to negative infinite, V(x) will tend to positive infinite.
So we only have a relative maximum, because is local maximum (at x = 6.4), but the function can take larger values than that.
You can also check that on the graph of V(x), which you can see below:
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This system of equations has been placed in a matrix:
y = 700x + 200
y = 5,000 − 75x
Complete the matrix by filling in the missing numbers.
Answer:
Hello,
Step-by-step explanation:
here is the answer in a picture.