Answer: If the rate is constant, then the situation is a proportional relationship. If the rate is not constant, then the situation cannot be a proportional relationship.
Zachary recorded the grade-level and instrument of everyone in the middle school
School of Rock below.
Seventh Grade Students
Instrument # of Students
Guitar
Bass
Drums
Keyboard
7
14
15
9
Eighth Grade Students
Instrument # of Students
Guitar
Bass
Drums
Keyboard
2
15
2
11
Based on these results, express the probability that an eighth grader chosen at
random will play the drums as a percent to the nearest whole number.
Percent to the nearest whole number = 7%
What is probability?
Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.
Probability = (Number of possible outcomes)/(Total number of outcomes)
Total number of outcomes = 2 + 15 + 2 + 11 = 30
Number of possible outcomes = 2
Probability = 2/30 = 1/15 = 0.0666
Percent to the nearest whole number = 0.0666 *100 = 7%
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Answer:7
Step-by-step explanation:
(1 point) find the critical point and the interval on which the given function is increasing or decreasing, and apply the first derivative test to the critical point. let f(x)
If f(x) = 7x2 + 5, then 0 is the critical point. As a result, the interval f grows when f is positive.
When does a point become crucial?Although this may appear like a frivolous issue—t = 0 is designated as a key point in each case—it is occasionally crucial to understand why is it that a position is indeed a critical point. In fact, we'll observe a fact which only holds true at crucial sites where the derivative equals zero in a few sections.
Briefing:f is maximal because we replace x = 0 well at derivatives at the crucial point. After calculating the derivative, equating x to zero, and arriving at 0, we arrive at the critical point, which is at this position.
The interval just on left of the crucial moment is - infinity f 0 on the this interval increasing whilst also f is negative on the right of the critical point 0 >= f +infinity on this interval f is rising whilst also f is positive. This indicates that f is maximum since at the critical point people substitute x = 0 at the variant we have 5 > 0.
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△
A
B
C
is similar to
△
X
Y
Z
.
A
B
is 8 feet and
B
C
is 11 feet while
X
Y
is 4 feet. Then what length is
Y
Z
?
The corresponding sides of two triangles are proportionate if they are identical then the length of side ZX exists 10.5 units.
What is meant by right triangles?If one of the triangle's angles is 90 degrees, the triangle is said to be right-angled. 90 degrees is the sum of the other two angles. Perpendicular and the triangle's base make up the sides that the right angle is formed from. The hypotenuse, or third side, is the longest of the three. It is also known as the hypotenuse.
If two triangles are similar, then their corresponding sides are proportional.
Since [tex]$\triangle A B C \sim \triangle X Y Z$[/tex], therefore
AB/X Y = BC/YZ = CA/ZX
substitute the values in the above equation, we get
2/7 = 4/14 = 3/N
2/7 = 2/7 = 3/N
2/7 = 3/N
On cross multiplication, we get
2 × N = 3 × 7
2N = 21
Divide both sides by 2
N = 21/2
N = 10.5
Therefore, the length of side ZX exists 10.5 units.
The complete question is:
In the figure below, ABC is similar to XYZ . What is the length of ZX ? Enter only the number as an integer or decimal. An image shows two similar right triangles, A B C and X Y Z. Triangle A B C is smaller than triangle X Y Z. In triangle A B C, side A B is 2, side B C is 4, and side C A is 3. In triangle X Y Z, side X Y is 7, side Y Z is 14, and side Z X is labeled N.
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explain how to solve the equation 16 + 7/x = 24
Answer:
x=8/7
Step-by-step explanation:
16+7/x=24
Subtract 16 on each side
7/x=8
multiply 1/7 on each side
x=8/7
In the diagram, b || c. Find the value of y
Using the corresponding angle theorem, the value of y is 36 degree.
In the given question, b||c.
We have to find the value of y.
Given: b||c
Find: Value of y
Let x be the value of side angle of (2y+34) degree.
So, using the corresponding angle theorem
x = 74 degree
As we know that the sum of straight line is 180 degree.
So 2y+34+x = 180
Now putting the value of x
2y+34+74=180
After simplifying
2y+108=180
Subtract 108 on both side, we get
2y=72
Divide by 2 on both side, we get
y=36
Hence, the value of y is 36 degree.
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The 9th term of an arithmetic sequence is -5 and the 15th term is 31 find an expression for the nth term explicitly in term of n
The expression for the nth term is aₙ = 37+6n
What is an arithmetic sequence?An arithmetic sequence is a type of sequence in which the difference between the successive and preceding term is constant.
Given that, The 9th term of an arithmetic sequence is -5 and the 15th term is 31
The formula for nth term is given by;
aₙ = a+(n-1)xd
Where, a is the first term
n = number of terms
d = common difference
a₉ = a+(9-1)xd
a+8d = -5.......(i)
And
a₁₅ = a+(15-1)xd
a+14d = 31........(ii)
Solving the equation, we get,
d = 6
Putting, d = 6 in eq(i)
a+8x6 = -5
a = -5+48
a = 43
Now solving for nth term,
aₙ = 43+(n-1)x6
aₙ = 43+6n-6
aₙ = 37+6n
Hence, the nth term is (37+6n)
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decide whether you can use the given information to prove that $\triangle abc\cong\triangle def$ . explain your reasoning. $\angle c\cong\angle f,\ \overline{ab}\cong\overline{de},\ \overline{bc}\cong\overline{ef}$
According to SAS congruent the △abc congruent △def. Thus using the given information, it can be prove.
What is congruent?
In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.
There are four rules to prove congruency. They are SAS, AA, ASA, and SSS.
Given that ∠c ≅ ∠f
ab ≅ de
bc ≅ ef.
According to SAS rule, if two sides and one angle of a triangle is equal to two sides and one angle of another triangle, they the triangle are congruent.
Here two sides and one angle of △abc is congruent of two sides and one angle of △def.
Therefore △abc congruent △def.
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Larissa sold 50 items at the state fair and made $450. She sold compact mittors and small pouches. Each mirror is $7 and each pouch is $12.
Write and solve a system of equations to represent the given scenario.
What does the solution to the system of equations represent in the context of the problem? Explain.
The equations are x+y=50 and 7x + 12y = 450
x = the number of mirrors = 30
y = the number of pouches = 20
What is the solution to an equation?
In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.
Let x be the number of mirrors
Let y be the number of pouches
x+y=50......(1)
Each mirror is $7
cost of x mirrors = 7x
Each pouch is $12.
cost of y pouches = 12y
7x + 12y = 450 .........(2)
(1) => x=50-y ...........(3)
Substitute (3) into (2)
(2) => 7(50-y) + 12y = 450
350 - 7y + 12y = 450
5y = 450 - 350 = 100
y= 100/5 = 20
(1) => x = 50 - 20 = 30
Thus, x = the number of mirrors = 30
y = the number of pouches = 20
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in the figure below measaure of angle 1 is 36. find angle 2,3, and 4
9. A park ranger stands a certain distance from an observation tower. Write an equation and then solve for x
53.6 feet
70.0 feet
58.7 feet
37.8 feet.
Using the trigonometry ration, the value of x is 53.6.
In the given question, a park ranger stands a certain distance from an observation tower.
We have to write an equation and then solve for x and choose the right option.
From the diagram we can see that the height of an observation tower is 45 and angle is 40.
To find the value of x we use the trigonometry ratio.
As we know that tangent is the ratio of perpendicular side and adjacent side.
From the given diagram
tan(40)=45/x
Now simplifying
0.8391 = 45/x
Multiply by x on both side, we get
0.8391x = 45
Divide by 0.8391 on both side, we get
x = 53.6 feet
Hence, the value of x is 53.6.
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Pls someone help I’ll give 100 points pls
Answer:
ST and RQ
Step-by-step explanation:
The 'arrows' on the line segments mean they are parallel
How does the graph of g(x) = −(x + 3)^4 compare to the parent function of f(x) = x^4?
1. Find x Round to the nearest tenths place.
12.2
24.5
11.8
8.4
The value of x is 11.8. So the option c is correct.
In the given question, we have to find the value of x.
The given options are:
(a) 12.2
(b) 24.5
(c) 11.8
(d) 8.4
To find the value of x we use the trigonometry ratio.
As we know that cosine is the ration of adjacent side and hypotenuse.
From the given diagram
Cos(46) = x/17
Now simplifying
0.695=x/17
Multiply by 17 on both side, we get;
x = 11.8
Hence, the value of x is 11.8. So the option c is correct.
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The number of multiple-choice questions on a final exam is 3 less than 4 times the number of essay questions. Which equation represents the situation? Let e represent the number of essay questions and m represent the number of multiple choice questions
O m =4e-3
O m=4e +3
O e=3m +4
O e=3-4m
m =4e-3 is the equation represents the number of multiple-choice questions on a final exam is 3 less than 4 times the number of essay questions.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Let the multiple questions be denoted by m.
The essay questions be denoted by e.
The given sentence is the number of multiple-choice questions on a final exam is 3 less than 4 times the number of essay questions.
In the sentence there is less than which means a value is subtracted and it has times which is meant by product.
m =4e-3 is the required equation of the given sentence.
Hence, m =4e-3 is the equation represents the situation.
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X/5= -2 in one step?
Answer:
To solve the equation X/5 = -2 in one step, we can multiply both sides of the equation by 5 to isolate the variable X. This gives us the equation X = -2 * 5 = -10. Therefore, the value of X that satisfies the equation X/5 = -2 is X = -10.
Step-by-step explanation:
What is the percent error when an exact distance of 15 meters is approximated at 14.75 meters?
Answer:
98.3% or 98% if your doing sig. figs.
Step-by-step explanation:
you take 14.75 (the approximated) and divide it by the actual 15
I have finished half of this problem but i am still unsure on how to finish.
Answer:
Triangle PQR maps onto triangle KLM. This is possible because △PQR ≅ △KLM by ASA, and one congruent figure can be mapped onto another using rigid motions.
Step-by-step explanation:
For the first blank, we are given congruence statements for 1 side on each triangle and their two adjacent angles. This means we can use the Angle-Side-Angle theorem to declare △PQR and △KLM congruent.
For the second blank, we know that rigid transformations do not change the figure, they simply move its position on a plane, so this is the correct answer; had the △PQR and △KLM not been congruent, a non-rigid transformation would have to have occured, but this is not the case here.
Answer:
ASArigidStep-by-step explanation:
Given triangles PQR and KLM with QR ≅ LM, ∠Q ≅ ∠L, and ∠R ≅ ∠M, you want to know the applicable congruence postulate and whether the triangles are mapped to each other by rigid or non-rigid motion.
Sides and anglesThe segment QR has angle Q at one end and angle R at the other end. That means the side lies between the two angles. Likewise, segment LM lies between angles L and M.
When claiming congruence of these triangles, the appropriate postulate is the one that refers to the geometry with the congruent side between the congruent angles: ASA.
Motion"Rigid" motion is motion that preserves angle and length measures. By contrast, "non-rigid" motion may involve stretching or compression in one or more directions. It may or may not preserve angles or lengths.
Congruence is about showing that angles and lengths are the same from one figure to another. If you want to map congruent figures to each other, you must do so using rigid motion.
__
Additional comment
The rigid motions include ...
translationrotationreflection.<95141404393>
2)
Earings (in dollars)
SALESPERSON'S EARNINGS
500
400
300
200
100
y
0 1 2 3 4 5 6 7 8
Sales (Thousands of dollars)
2a) Explain what x represents. Sales
2 b) Explain what y represents earnings
2 c) Find the slope of the line. Make sure to include units
2 d) Explain what the slope represents for this example.
Use the numbers in your explanation.
The solution is
a) The x represents the number of sales
b) The y represents the total earnings in dollars
c) The slope of the line m = 50 earnings (in dollars) per sale
d ) The slope represents the total earnings per sales and it is $ 50 per sale
What is an Equation of a line?
The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is given by the equation
Let the number of sales be = x
Let the total earnings be = y
Now , let the two points on the graph be A and B
where the value of A = A ( 3 , 200 )
And , the value of B = B ( 5 , 300 )
Now , the slope of the line between the points A and B is given by
Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 300 - 200 ) / ( 5 - 3 )
Slope m = 100 / 2
Slope m = 50
So , the slope of the line is given by m = 50 earnings per sales
And , Slope m = $ 50 per sales
The equation of line is y - y₁ = m ( x - x₁ )
Substituting the values in the equation , we get
y - 200 = 50 ( x - 3 )
y - 200 = 50x - 150
Adding 200 on both sides of the equation , we get
y = 50x + 50
Therefore , the equation of line is y = 50x + 50
Hence ,
a) The x represents the number of sales
b) The y represents the total earnings in dollars
c) The slope of the line m = 50 earnings (in dollars) per sale
d ) The slope represents the total earnings per sales and it is $ 50 per sale
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A shirt normally costs £42. If you receive a 15%
discount, how much change will you get from £50?
A-£35.70
B-£23.00
C-£8.00
D- £14.30
to search
1
OE
Answer:
If you receive a 15% discount on a shirt that normally costs £42, the discounted price of the shirt will be £42 - (15/100) * £42 = £35.70. If you pay £50 for the shirt, you will receive £50 - £35.70 = £14.30 in change. Therefore, the correct answer is D- £14.30.
Step-by-step explanation:
Can someone please help me with this basic geometry?
The value of side MN is 18.2
What is a Trapezoid?
A quadrilateral is a polygon with four sides.
There are many special types of quadrilateral.
The Trapezoid is a 4 sided polygon. Two sides of the shape are parallel to each other and they are termed as the bases of the trapezoid. The non-parallel sides are known as the legs or lateral sides of a trapezoid.
Given data ,
Let the side to be calculated be = MN
Now , the two quadrilaterals are GHIJ and KLMN
And , quadrilaterals GHIJ and KLMN are congruent
So ,
The sides are in the ratio
MN / IJ = NK / JG
On simplifying the equation , we get
Substituting the values in the equation , we get
MN / 47 = 12 / 31
Multiply by 47 on both sides of the equation , we get
MN = ( 12 x 47 ) / 31
On simplifying the equation , we get the value of side MN
MN = 564 / 31
MN = 18.19
On rounding to the nearest tenth , we get
MN = 18.2
Therefore , the value of side MN is 18.2
Hence , The value of side MN is 18.2
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HELP PLS ASAPPP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
I need this answer asap
Answer:
x=-8
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Answer:
x= -8
Step-by-step explanation:
-------------------------
PLEASE HELP WITH THE QUESTION IN THE PICTURE
Answer:
[tex]\sqrt[3]{3375}=15[/tex]
Step-by-step explanation:
[tex]3375=15^2 \implies \sqrt[3]{3375}=15[/tex]
Two systems of equations are given below.
For each system, choose the best description of its solution.
If applicable, give the solution.
System A
x+3y=9
-x-3y=9
System B
-x-3y=-3
x+3y=3
O The system has no solution.
O The system has a unique solution:
(x, y) = (
O The system has infinitely many solutions.
They must satisfy the following equation:
y = 0
O The system has no solution.
O The system has a unique solution:
(x, y) = (D)
O The system has infinitely many solutions.
They must satisfy the following equation:
y=0
The system A has no solution.
The system B has the solution y=( 3-x )/3
What is the solution to an equation?
In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.
System A:
x+3y=9..........(1)
-x-3y=9 ..........(2)
(1) => x=9-3y........(3)
Substitute (3) into (2)
(2) = > - ( 9-3y ) - 3y = 9
-9 + 3y - 3y = 9
-9 =9
This is false.
So, the system has no solution.
System B:
-x-3y=-3..........(1)
x+3y=3..........(2)
(2) => x=3-3y........(3)
Substitute (3) into (1)
-(3-3y)-3y=-3
-3+3y-3y= -3
-3=-3
This is true,
So, the solution is:
x=3-3y
=> 3y= 3-x
=> y=( 3-x )/3
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How many real solutions are there to 5x^2+6x+4=0?
The given quadratic equation 5x^2+6x+4=0 has no real roots or 0 real roots.
What is a quadratic equation?A quadratic equation is any algebraic expression that can be expressed in a standard form where x represents an unknown number, a, b, and c represent known values, and where a 0 is true.
So, we have the equation:
5x^2+6x+4=0
Discriminant (D): b² - 4ac
Insert values in the given formula as follows:
b² - 4ac is 6² - 4(5)(4).
= 36 - 80
= - 44 and it is less than zero.
No real roots
Therefore, the given quadratic equation 5x^2+6x+4=0 has no real roots or 0 real roots.
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Approximate √/46 to the tenths place.
Answer:
To approximate the square root of 46 to the tenths place, we need to find the two-digit number that is closest to the square root of 46. Since the square root of 46 is between 6 and 7, we can estimate that it is about 6.5. We can check this estimate by finding the square of 6.5, which is 42.25. This is close to 46, but it is still a little bit lower than 46, so we can estimate that the square root of 46 is slightly larger than 6.5. Therefore, an approximation of the square root of 46 to the tenths place is 6.6.
Step-by-step explanation:
Pls help will make brainliest thank you
Which of the following sets of ordered pairs is a function? Pls look at picture and help me out
Answer: C
Step-by-step explanation:
A function cannot have repeated x value in a set, and c is the only one without repeated x value
5. Determine if a triangle with the following measurements is a right triangle. a=14, b=16, c=18
Explain why or why not.
No. 14+16 does not equal 18
Yes. 14²+16^2=18²
Yes. The longest side is c, which is 18.
No. 14²+16² does not equal 18²
The given measurement not forming the right triangle. So the option D is correct.
In the given question, we have to determine if a triangle with the following measurements is a right triangle.
The given measurement is:
a=14, b=16, c=18
We have to explain why or why not the given statement is correct or not.
The given options are:
(a) No. 14+16 does not equal 18
(b) Yes. 14^2+16^2=18^2
(c) Yes. The longest side is c, which is 18.
(d) No. 14^2+16^2 does not equal 18^2
As we know that the given measurement form right triangle we he follows the Pythagorean Theorem.
To prove the right triangle, the square of largest value is equal to the sum of square of other two values. So;
18^2 = 14^2+16^2
324 = 196 + 256
324 = 452(False)
So, the given measurement not forming the right triangle. So the option D is correct.
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valuate each expression for x = -2 and y = 3.
Evaluating each expression with x = -2 and y = 3 gives
3x²y - x = 38
3y - x = 11
x² - y = 7
x + 2xy = 14
4y - 2xy + 2y = 33
2x - y = -7
6 -x = 8
3x - 2y = -12
3x - 2y + xy = -18
How to evaluate the expressionsThe expressions are evaluated by substituting the values of x and y into the equations and solve
solving the expressions
3x²y - x
substituting x = -2 and y = 3
= 3(-2)² * 3 - (-2)
= 38
3y - x =
substituting x = -2 and y = 3
= 3 * 3 - (-2)
= 11
x² + y
substituting x = -2 and y = 3
= (-2)² + 3
= 7
x + 2xy
substituting x = -2 and y = 3
= -2 + 2 * -2 * 3
= -14
4y - 2xy + 3y
7y - 2xy
substituting x = -2 and y = 3
= 7 * 3 - 2 * -2 * 3
= 21 - (-12)
= 33
2x - y =
substituting x = -2 and y = 3
= 2 * -2 - 3
= -7
6 - x
substituting x = -2
= 6 - (-2)
= 8
3x - 2y
substituting x = -2 and y = 3
= 3 * -2 - 2 * 3
= -6 - 6
= -12
3x - 2y + xy
substituting x = -2 and y = 3
= 3 * -2 - 2 * 3 + -2 * 3
= -6 - 6 + (-6)
= -18
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