Answer:
b. t < 10
Step-by-step explanation:
[tex]-3t + 9>-21[/tex]
divide both sides by -3
[tex]t - 3 < 7[/tex]
(you have to flip the sign because you are dividing by a negative)
add 3 to both sides
[tex]t<10[/tex]
A farmer finds there is a linear relationship between the number of bean stalks, n , she plants and the yield, y , each plant produces. When she plants 30 stalks, each plant yields 30 oz of beans. When she plants 33 stalks, each plant produces 29 oz of beans. Find a linear relationship in the form y=mn+b that gives the yield when n stalks are planted.
The equation y = -0.5x +45 represent the linear relationship.
According to the statement
We have given that the When she plants 30 stalks, each plant yields 30 oz of beans and When she plants 33 stalks, each plant produces 29 oz of beans.
And we have to find the linear relationship between the plants which are stalks.
So, For this purpose,
When we consider this graph as a straight line, the two points lying on the line would be
(30, 30) and (34, 28) taking n as horizontal and y vertical
Using two point equation we find that
the equation of the line is
y-y1 / y2-y1 = x-x1 / x2-x1
Substitute the points as x =n and put the other values in it then
y-30 / 28-30 = x-30 / 34-30
Then
y = -0.5x +45
This represent the relationship.
So, The equation y = -0.5x +45 represent the linear relationship.
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Use the chart to find the constant of variation
As k₁ = k₂ = k₃, the table represents a linear relation whose constant of variation is - 4.
Does the table represent a linear relation?
A table between two variables represents a linear relation if and only if every pair of values (x, y) have the same constant:
k = y/x (1)
Now we proceed to check the existence of the constant of variation:
k₁ = 8/(- 2) = - 4
k₂ = (- 16)/4 = - 4
k₃ = (- 36)/9 = - 4
As k₁ = k₂ = k₃, the table represents a linear relation whose constant of variation is - 4.
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When given -5(x + 4) = 90 and trying to prove that x = -18, what should be placed in line A of the two-column proof? Statement Reason 1. -5(x + 4) = 90 1. Given 2. -5x − 20 = 90 2. _____A______ 3. _______B________ 3. Addition Property of Equality 4. x = -22 4. ____C_______ Subtraction Property of Equality Distributive Property
The 4 reasons for the Algebra proof are respectively;
Given; Distributive property; Addition Property; Division Property
How to use algebra properties?We want to use algebra properties to find the value of x in the expression; -5(x + 4) = 90
Statement 1; -5(x + 4) = 90
Reason 1; Given
Statement 2; -5x - 20 = 90
Reason 2; Distributive property of Algebra because we distributed -5 into the bracket terms.
Statement 3; -5x = 110
Reason 3; Addition property of equality because we added 20 to both sides to achieve that.
Statement 4; x = -22
Reason 4; Division property of equality because we divided both sides by -5 to obtain x = -22.
Thus, the 4 reasons are respectively;
Given; Distributive property; Addition Property; Division Property
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A grove of redwood tree has an estimated 3,400,000 board feet of lumber at the
start of 2022. If redwoods grow at an exponential rate of 9% each year, then what
would be the growth formula? Within which year will the grove reach one billion board
feet of lumber?
The exponential growth formula is 3,400,000 x (1.09^t).
The year in which the grove would reach one billion board feet is 63.16 years.
What is the exponential growth formula?The exponential growth formula usually has this form:
FV = P (1 + r)^n
FV = Future growth P = Present growth R = rate of growthN = number of years3,400,000 x (1.09^t).
The year in which the grove would reach one billion board feet = (In 1,000,000,000 / 3,400,000) / 0.09 = 63.16 years
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A person draws a card from a hat. Each card is one color, with the following
probabilities of being drawn: 1/25 for blue, 1/15 for yellow, 1/10 for green, and
1/20 for white. What is the probability of pulling a green or yellow card, written
as a reduced fraction?
FU
Answer:
1/6
Step-by-step explanation:
1/15 yellow, 1/10 green, and 1/20 white
1/15 + 1/10 is the probability for yellow or green.
2/30 + 3/30 = 5/30 = 1/6
Brainliest, please :)
pls help giving all my points!! Find the probability of “landing” in the shaded region of the figures below. Round your answer to the nearest hundredth.
Big circle r = 25 cm
Small circle r = 8 cm
The probability of landing on the shaded region of the figure is 0.10
How to find the probability of landing on the shaded region?The probability of landing on the shaded region can be calculated as follows;
area of the bigger circle = πr² = 3.14 × 25² = 1962.5 cm²
area of the smaller region = πr² = 3.14 × 8² = 200.96 cm²
Therefore,
the probability of landing on the shaded region of the figure = 200.96 / 1962.5
the probability of landing on the shaded region of the figure = 0.10
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Find QR.
A).12
B).-8
C).9
D).6
Answer:
D. 6
Step-by-step explanation:
Let's first find x :-
[tex]\sf 3 + 2x + 22 = x + 17[/tex]
[tex]\sf 2x + 25 = x + 17[/tex][tex]\sf 2x - x = 17 - 25[/tex][tex]\sf x = - 8[/tex]Now that we found x, let's find QR :-
QR = 2x + 22
[tex]\sf QR = 2( - 8) + 22[/tex][tex] \sf - 16 + 22[/tex][tex]\sf 6[/tex]Therefore, QR = 6 !!!
Create a line that is parallel to and passes through point C. You can use the tools available in GeoGebra to create parallel lines for this construction. Take a screenshot of your results, and paste it below.
reate a line that is parallel to and passes through point C. You can use the tools available in GeoGebra to create parallel lines for this construction. Take a screenshot of your results, and paste it below.
Create a line that is parallel to AB and passes through point C. You can use the tools available in GeoGebra to create parallel lines for this construction. Take a screenshot of your results, and paste it below.
The attached line is a parallel line that goes through C and parallel to AB
What are parallel lines?Parallel lines are lines on the same plane that have the same slope, they do not intersect even when they are extended indefinitely
How to create the parallel lines?From the question, we have the following points and line:
Line ABPoint CThe following steps would create the parallel line that goes through C and parallel to AB
Draw a line from point C to touch the line segment AB at anywhereMark a point anywhere on the line drawn from point C such that the line is short. Call this point KCreate a circle that has a radius F KMark the intersection of the circle and the initial lineCreate another circleMark the intersection of the circle and the line ABCreate another circleConnect the endpoints of the linesSee attachment for the parallel line that goes through C and parallel to AB
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Find the difference: -2-6
Grace and Jack are playing a game with a gigantic bucket of markers. Jack took a random sample of markers from the bucket and counted 12 yellow markers, 37 blue markers, and 1 red marker. Use the observed frequencies to create a probability model for the color of the next randomly selected marker from the gigantic bucket of markers. Input your answers as fractions or as decimals rounded to the nearest hundredth.
Using the given frequencies, the probabilities for the next color chosen is:
P(yellow) = 0.24.P(blue) = 0.74.P(red) = 0.02What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
There were 50 markers, of which 12 were yellow, 37 blue and 1 red, hence the probabilities for each are given as follows:
P(yellow) = 12/50 = 0.24.P(blue) = 37/50 = 0.74.P(red) = 1/50 = 0.02More can be learned about probabilities at https://brainly.com/question/14398287
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Bruce pitches for his little brother's baseball team. He has observed that the number of pitches a batter hits varies and is given by the function f(x) = x – 11, where x is the number of pitches and f(x) is the number of hits. If batters get {4, 12, 14, 27, 42} hits, how many pitches did Bruce throw? A. {13, 21, 24, 26, 44} B. {17, 24, 27, 28, 35} C. {20, 27, 32, 33, 45} D. {15, 23, 25, 38, 53}
Answer:
D.{15,23,25,38,53}
Step-by-step explanation:
Replace f(x) with any other variables of your choice.
Substitute the value of the variable for the given set of hits
that is {4,12,14,27,42}
Solve for x for each value of the variable from the above set
Put all the solution for x in a set that is inside {,} brackets.
The correct option should be D
What is the question of the translated function, g(x), if f(x)=x^2
-Dear lord help
The graph of the parabola g(x) is (x+2)^2 + 3
Translation of functionGiven the following parent function of the parabola expressed as;
f(x) = x^2
The function g(x) shows a horizontal translation to the left by 2 units and vertical translation up by 3 units to have the equation;
g(x) = (x+2)^2 + 3
Hence the graph of the parabola g(x) is (x+2)^2 + 3
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Part 2 - Find the error(s) and solve the problem correctly. Explain your corrections. Solve: 2cos x = 4 cos x sin 2 x Answer: 2cos x = 4 cos x sin 2 x 2cos x = 4 cos x sin ( 2 x 2 cos x in common onboth sides) 1 = sin 2 x The only place sin x = 1 is where the angle is . π 2 x = π
Answer:
l dont know l am not studying it sorry
Answer:
hey what was the answer?
Step-by-step explanation:
I need help im going to failllll!!!!!!
Find the domain of the function. Express the exact answer using interval notation.
f(x) = 2/3x+8
Answer:
(-oo, -8/3) U (-8/3, oo)
Step-by-step explanation:
Hope this helps.
The domain of the equation f(x) = 2/(3x + 1) is (-∝, -8/3) U (-8/3, ∝)
How to calculate the domain of the equation?From the question, we have the following parameters that can be used in our computation:
f(x) = 2/(3x + 1)
The above equation is a rational function
The rule of a function is that
The domain is the set of all input numbers
For the domain, we set the denominator not equal to 0
So, we have
3x + 8 ≠ 0
Evaluate
x ≠ -8/3
When represented as interval notation, we have
Domain = (-∝, -8/3) U (-8/3, ∝)
Hence, the domain is (-∝, -8/3) U (-8/3, ∝)
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Can someone answer this for me
The equation of the line in standard form is 6x - 7y = - 11
How to represent linear equation in standard form?The standard form for linear equations in two variables is Ax + By = C.
Therefore, using (-3, -1)(1 / 2, 2)
y = mx + b
where
m = slopeb = y-interceptHence,
m = 2 + 1 / 1 /2 + 3 = 6 / 7
Hence,
-1 = 6 / 7(-3) + b
- 1 = - 18 / 7 + b
-1 + 18 / 7 = b
b = -7 + 18/ 7
b = 11 / 7
Therefore,
y = 6 / 7 x + 11 / 7
Using the standard form,
6 / 7 x - y = - 11 / 7
6x - 7y = - 11
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The linear equation in standard form is:
6x - 7y = -11
Which is the last option.
How to get the equation of the line?
The line in slope-intercept form is written as:
y = a*x + b
We can see that the line passes through the points (-3, -1) and (1/2, 2), then the slope is:
[tex]a = \frac{2 - (-1)}{1/2 - (-3)} = \frac{3}{3.5} = \frac{6}{7}[/tex]
Then we can write:
y = (6/7)*x + b
To find the value of b, we use the first point. It means that when x = -3, the value of y is -1, then we get:
-1 = (6/7)*-3 + b
-1 + 18/7 = b
-7/7 + 18/7 = b
11/7 = b
Then the equation is:
y = (6/7)*x + 11/7
If we multiply both sides by 7 we get:
7y = 6x + 11
Now we move the term with "x" to the left:
7y - 6x = 11
That is the line in standard form.
If we multiply both sides by -1, we get the last option:
6x - 7y = -11
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The function h(x) = 2|x] is a transformation of the absolute value parent
function, f(x) = |xl. Which graph shows h(x)?
The graph is shown in the attached image.
100 POINTS
Construct a horizontal line that passes through the intersection of lines AC and BC at point C. Add a vertical line segment connecting the horizontal line to line AC called FG and another vertical line connecting the horizontal line to line BC called DE.
Complete the proof.
LOOK AT IMAGE PLEASE
The blanks are as follows:
Angle addition postulateSubtraction property of equalityCorresponding sides of similar triangles are proportionalMultiplication property of equalityWhich of the following graphs represents a function?
The third graph represents a function.
In a function, every input (x value) has exactly one output (y value). If even a single input has zero or two outputs, the graph does not represent a function.
A good way of testing this is using a vertical line. As you move a vertical line from left to right across a graph, it should always be touching exactly one point on the graphed line.
In this case, every graph fails this vertical line test except for the third graph, so the third graph represents a function.
An equestrian club orders magazine subscriptions for new members.
Last year they had 32 new members and spent $624 on subscriptions.
Use the equation 32m = 624 to find the cost of each subscription.
Enter your answer in the box.
Answer:
$19.50
Step-by-step explanation:
Dividing both sides by 32, we get $19.50.
What is the equation of the line that passes through the point (6,-3) and has an undefined slope?
Answer:
x=6
Step-by-step explanation:
This is a vertical line going through (6,0). If you take this point and the point given and calculate the slope you find the change in y over the change in x.
0-(-3)/6-6 The slope is undefined because the denominator of the slope would be zero.
"You helped 3.6 customers per half hour yesterday."
Employee: "So I helped __________ customers in 7.5 hours yesterday."
Answer: 54
Step-by-step explanation:
So I helped 54 customers in 7.5 hours yesterday.
What is multiplication?Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.
Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.
Given:
You helped 3.6 customers per half hour yesterday.
That means,
for one hour:
Using multiplication
(3.6) x 2 per 1/2 x 2 hours
7.2 per hour.
Therefore,
if n hours so,
(7.2) per n hours
Here, n = 7.5
(7.2) x (7.5) per 7.5 hours
54 customers per 7.5 hours.
Therefore, I helped 54 people in 7.5 hours.
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Find the value of x.
B
A
2
30°
5
30°
5
x = [?]
X
C
D
Translate the following phrase into algebraic expression , the number of dollars Paul owes minus 32
Using a system of equations, the translated expression is:
P - 32.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variable is the number of dollars Paul owes, which is P. That amount minus 32 is represented by:
P - 32.
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m(t)=120e−0.018t
How much mass remains after 50 years? Round to 2 decimal places.
The mass that would remain after 50 years is 48. 79 kilograms
How to determine the amountIt is important to note that half - life is the time it takes for amount of a substance to reduce to half of its initial value.
Given the equation
m(t)=120e−0.018t
Where
m(t) is the amount = unknown
t = time = 50 years
[tex]m(t) = 120e^0^.^0^1^8^t[/tex]
Substitute the value into the equation
[tex]m(t) = 120e^0^.^0^1^8^(^5^0^)[/tex]
[tex]m(t) = 120e^-^0^.^9[/tex]
Find the exponential value
[tex]m(t) = 48.788399[/tex]
m(t) = 48. 79 kilograms in 2 decimal places
Thus, the mass that would remain after 50 years is 48. 79 kilograms
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Zoya asked the students of her class their baseball scores and recorded the scores in the table shown below:
Baseball Scores
Score Number of Students
0 1
1 2
2 5
3 3
4 6
5 7
6 9
Based on the table, what is the mean baseball score?
2.5
2.9
3.5
4.1
Option D, 4.1 is the correct answer. The mean baseball score is 4.1 given the table of values of baseball scores and score number of students. This can be obtained by using the formula for mean.
Calculate mean for the data:Mean can be obtained by the formula,
Mean = [tex]\frac{sum\ of\ observations}{total\ number\ of\ observations}[/tex]
Sum of basketball scores = 0×1 + 1×2 + 2×5 + 3×3 + 4×6 + 5×7 + 6×9
= 0 + 2 + 10 + 9 + 24 + 35 + 54
total number of basketball scores = 1 + 2 + 5 + 3 + 6 + 7 + 9 = 33
Mean = [tex]\frac{0+2+10+9+24+35+54}{33}[/tex] = 4.06 ≈ 4.1
Hence the mean baseball score is 4.1 given the table of values of baseball scores and score number of students. Option D, 4.1 is the correct answer.
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The diagram is supposed to be used for both question 7 and 8. WORTH 30 POINTS.
7. D. Arc JK = 124°
8. Applying the angle of intersecting chords theorem, m∠1 = 115°.
What is the Angle of Intersecting Chords Theorem?The angle of intersecting chords theorem states that the angle (∠1) formed by two chords in a circle, equals half of the sum of the intercepted arcs (arcs ML and JK).
Arc JMK = 2(118) = 236° [inscribed angle theorem]
Arc JK = 360 - arc JMK = 360 - 236
Arc JK = 124°
Arc ML = 236 - 70 - 60 = 106°.
m∠1 = 1/2(arc JK + arc ML)
m∠1 = 1/2(124 + 106)
m∠1 = 115°.
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solve and graph 2cos(2x) = x radians
The solutions of the equation 2cos(2x) = x are (0.626, 0.626), (-1.607,-1.607) and (-1.798,-1.798)
How to solve the equation?The equation is given as:
2cos(2x) = x
Split the equation as follows:
y = 2cos(2x)
y = x
Next, we plot the graph of y = 2cos(2x) and y = x (see attachment)
From the attached graph, y = 2cos(2x) and y = x intersect at the following points
(x, y) = (0.626, 0.626), (-1.607,-1.607) and (-1.798,-1.798)
Hence, the solutions of the equation 2cos(2x) = x are (0.626, 0.626), (-1.607,-1.607) and (-1.798,-1.798)
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-102/119 in standard form
Answer:-8.5714285714 × 10-1
Step-by-step explanation:
-101/119=-0.85714285714
remember Any number that we can write as a decimal number, between 1.0 and 10.0, multiplied by a power of 10, is said to be in standard form.
so -0.85714285714 in standard form is -8.5714285714 × 10-1
Measure the angle in degrees.
Answer:
Angle is measured in degrees (°) and radians. It is formed between the two adjacent sides of a polygon. Every polygon has different sides and different numbers of angles. The formula to find the angles in degrees is useful in geometry and trigonometry. It is essential to understand other concepts of mathematics, such as arc, a central angle of the circle, etc.
A full circle = 360°
A straight line = 180°
A semicircle= 180°
A Quarter circle = 90°
exampleGiven: Hypotenuse = 12
Perpendicular = 6
The trigonometry function to calculate the angle is given by:
sinA = 6/12
A = 30°
i need help with number 70
The volume of the rectangular prism is of 28.6875 mm³.
What is the volume of a rectangular prism?
The volume of rectangular prism of length l, width w and height h is given by:
V = lwh.
For this problem, the dimensions are:
2(1/8)mm = 2 + 1/8 = 2.125 mm.6(3/4)mm = 6 + 3/4 = 6.75 mm.2 mm.Hence the volume is:
V = 2.125 x 6.75 x 2 = 28.6875 mm³.
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