Answers
Answer:
Domain: (-infinity, infinity) Range: (-infinity, infinity)
Step-by-step explanation:
They are parabolas, therefore you can assume that they go on infinitely. To find range, you must look at your y values. Look for your lowest point. Because the line goes done forever, your beginning mark would be (-infinity.
To find the other part, you look at your positive y values. Look for the highest value. Because this goes on infinitely, the completed version of your notation would be (-infinity, infinity). Be sure to use the infinity symbol though, which looks like an 8 rotated 90 degrees.
To find domain, look at your x values. To begin, look at your left-most values, which would be the negative numbers. Because the line goes on forever to the left, your notation would be (-infinity. To find the other part of domain, look at your positive x values. Because this line goes on infinitely as well, the completed version of your notation would be (-infinity, infinity). Infinity is never bracketed, it is always in parenthesis.
Related Questions
Can anyone HELP with my HOMEWORK for GRADE‼️
Answers
Answer:
The coordinates of point C are (a,0).
Step-by-step explanation:
Given information: ABC is right isosceles triangle.
From the given figure it is noticed that the side BC is hypotenuse of the triangle ABC.
By pythagoras theorem,
[tex]hypotenuse^2=leg^2+leg^2[/tex]
[tex]hypotenuse^2=2leg^2[/tex]
[tex]hypotenuse=leg\sqrt{2}[/tex]
Therefore hypotenuse cannot be equal to leg. So, we can say that in triangle ABC,
[tex]AB=AC[/tex]
Length of AB is
[tex]AB=\sqrt{(a-0)^2+(0-0)^2}=a[/tex]
From the figure it is noticed that the point C lies on the x-axis, therefore the y-coordinates of C is 0.
Let the coordinates of C be (x,0) and length of AC must be a.
[tex]AC=\sqrt{(x-0)^2+(0-0)^2}[/tex]
[tex]a=x[/tex]
Therefore coordinates of point C are (a,0).
PLEASE HELP ASAP WILL GIVE BRAINLIEST
Answers
Answer:
(25/54)x⁻⁶y⁻⁹
Step-by-step explanation:
[4(5x³y³)²]/(6x⁴y⁵)³ Do the outside exponents first
= [4(25x⁶y⁶)]/(216x¹²y¹⁵) Group like terms
= [(4×25)/216] × x⁶/x¹² × y⁶/y¹⁵ Reduce fractions to lowest terms
= 25/54 × x⁻⁶ × y⁻⁹ Recombine the terms
= (25/54)x⁻⁶y⁻⁹
Kelly reads x hours a week. Tim reads two times more than Kelly and Jim reads five hours more than Tim. Which expression represents the amount of time Jim reads? A) 2(5x) B) 2x - 5 C) 2x + 5 D) 2(x - 5)
Answers
Tim reads 2 more times than Kelly(2x) and then you add 5 because Jim reads 5 more hours than Tim.
Solve the problems below. Please answer with completely simplified exact value(s) or expression(s). Given: ΔАВС, m∠ACB = 90° CD ⊥ AB , m∠ACD = 60°,BC = 6 cm Find CD, Area of ΔABC
PICTIURE:https://homework.russianschool.com/resource?key=00j42
Answers
Answer:
[tex]CD=3\sqrt{3}\ cm,\\ \\A_{ABC}=18\sqrt{3}\ cm^2[/tex]
Step-by-step explanation:
Triangle ABC is right triangle. Since m∠ACB = 90° and m∠ACD = 60°, you get m∠BCD = 90°-60°=30°.
Triangle BCD is rigth triangle, then the leg that is opposite to the angle of 30° is half of the hypotenuse. Thus,
[tex]BD=\dfrac{1}{2}BC=\dfrac{1}{2}\cdot 6=6\ cm.[/tex]
By the Pythagorean theorem,
[tex]CD^2=BC^2-BD^2=6^2-3^2=36-9=27,\\ \\CD=3\sqrt{3}\ cm.[/tex]
Then
[tex]CD^2=AD\cdot BD,\\ \\27=3\cdot AD,\\ \\AD=9\cm.[/tex]
Hypotenuse AB of the triangle ABC is equal to
[tex]AB=AD+BD=9+3=12\ cm.[/tex]
The area of the triangle ABC is
[tex]A_{ABC}=\dfrac{1}{2}\cdot AB\cdot CD=\dfrac{1}{2}\cdot 12\cdot 3\sqrt{3}=18\sqrt{3}\ cm^2.[/tex]
CD is √3 cm, and the area of right-angled triangle ABC, with ∠ACB = 90° and ∠ACD = 60°, is 9 cm², obtained by applying the Pythagorean Theorem and area formula.
The given triangle is right-angled at C (as per the given condition m∠ACB = 90°), and ∠ACD is 60°.
Thus, we know that ΔACD is a 30-60-90 triangle because the remaining angle of the triangle (∠ADC) would have to be 30° (since all angles in any triangle sum up to 180°).
In a 30-60-90 triangle, the ratio of the sides opposite to these angles respectively is 1 : √3 : 2. This tells us AC is 2 times the length of CD and AC is √3 times the length of AD.
We don't have the lengths of AC, AD, or CD yet, but we can solve for CD using the Pythagorean Theorem in triangle ABC. Since it's a right triangle, the square of the hypotenuse (AC in our case) is equal to the sum of the squares of the other two sides. We can express this as:
AC² = BC² - CD²
Substituting AC = 2CD into this equation, we get:
(2CD)² = 6² - CD²
Solving this equation yields CD = BC / (2 √3) = 6 / (2 √3) = √3 cm
So the length of CD is √3 cm.
Now let's find the area of triangle ΔABC. The area is typically given by the formula 0.5 * base * height.
In this case, BC is the base of triangle ABC, and CD is the height due to its perpendicular nature to side AB by the given condition (CD ⊥ AB). So, the calculation would go as follows:
Area = 0.5 * BC * CD = 0.5 * 6 cm * √3 cm = 3 √3 cm².
But by rationalizing the denominator, which is a common practice especially when having square roots in the denominator, we get Area = 3√3 * √3 * √3 cm² = 3 * 3 cm² = 9 cm².
Therefore, CD = √3 cm and the area of ΔABC is 9 cm².
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identify an equation in point-slope form for the line parallel to y=-2/3x+8 that passes through (4,-5)
Answers
Answer:
y +5 = (-2/3)(x -4)
Step-by-step explanation:
The point-slope form of an equation of a line with slope m through point (h, k) is ...
... y -k = m(x -h)
You have (h, k) = (4, -5) and a slope the same as that of the parallel line, m = -2/3. Then the equation is ...
... y -(-5) = (-2/3)(x -4)
... y +5 = (-2/3)(x -4)
Which ordered pair describes a point that should be removed from the graph so that the graph represents a function.
Answers
Answer:
A
Step-by-step explanation:
Function cannot have at least two points on same vertical line.
Vertical test fails at x = 1. So we need to eliminate either point (1, 1) or (1, 3).
There is option (1, 1), so A.
To represent a function, we must have unique y-values for each x-value. Thus, the point (1,1) should be removed. The correct answer is A).
To determine which ordered pair should be removed from the graph to represent a function, we need to check for uniqueness in the x-values. In a function, each x-value can only be associated with one y-value.
Let's examine the given points:
(1,1)
(3,2)
(5,2)
(7,4)
(1,3)
The x-values are: 1, 3, 5, 7, and 1.
Notice that the x-value 1 is associated with both (1,1) and (1,3). In a function, an x-value should have a unique y-value. Therefore, the point (1,1) should be removed from the graph to represent a function.
So, the correct option is A) (1,1).
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Solve: 2(x - 5) < -6(1 - x)
A.
x < -1
B.
x > -1
C.
x < 1
D.
x > 1
Answers
Answer:
B. x > -1
Step-by-step explanation:
Subtract the left side:
... 0 < -6(1 -x) -2(x-5)
... 0 < -6 +6x -2x +10 . . . . eliminate parentheses
... 0 < 4 +4x . . . . . . . . . . . collect terms
... 0 < 1 +x . . . . . . . . . . . . . divide by 4
... -1 < x . . . . . . . . . . . . . . . add -1. Matches selection B.
who's better Messi or Ronaldo when messi has scored 700 goals in his carrer and ronaldo has scored 600 what is the ratio please for a bunch of points
Answers
Answer:
The ratio of Messi : Ronaldo
7:6
Step-by-step explanation:
The ratio of Messi : Ronaldo
700 :600
Divide each side by 100
7:6
You cannot tell who is better because we do not know how many shots they took.
What is the equation in standard form of a parabola that models the values in the table
X -2. 0. 4
F(x) 2.5 1.5 -60.5
A
B
C
D
Answers
9514 1404 393
Answer:
(b) y = -2.5x² -5.5x +1.5
Step-by-step explanation:
The table entry (0, 1.5) tells you that the y-intercept is 1.5. That eliminates choices C and D.
Substituting x=4 into the first equation (choice A) shows you it is incorrect:
y = -5.5(4²) -2.5(4) +1.5 = -88 -10 +1.5 = -96.5 . . . not -60.5
This only leaves choice B, a choice confirmed by a quadratic regression using a graphing calculator (or spreadsheet).
y = -2.5x² -5.5x +1.5
Final answer:
The equation in standard form of the parabola that models the values in the table is y = -2.3x^2 + 2.6x + 1.5
Explanation:
The equation in standard form of a parabola that models the values in the table is y = ax^2 + bx + c. To find the values of a, b, and c, we can use the given table:
XF(x)-22.501.54-60.5
Plugging in the values from the table into the equation, we get a system of three equations:
4a - 2b + c = 2.5
c = 1.5
16a + 4b + c = -60.5
Solving this system of equations, we find that a = -2.3, b = 2.6, and c = 1.5.
Therefore, the equation in standard form of the parabola that models the values in the table is y = -2.3x^2 + 2.6x + 1.5.
In a trapezoid the lengths of bases are 11 and 18. The lengths of legs are 3 and 7. The extensions of the legs meet at some point. Find the length of segments between this point and the vertices of the greater base.
Answers
The values of x and y are 5/7 and 11 respectively.
Similar triangles are triangles with equal corresponding angles and equal side ratios.
We use similarity theorem to solve for x and y
x/3+x = 11/18
18x = 33 + 11x
collect like terms
18x - 11x = 33
7x = 33
x = 33/7
x = 4 5/7
y/7+y = 11/18
18y = 77 + 11y
7y = 77
y = 11
Therefore, the values of x and y are 4 5/7 and 11 respectively.
Find the area of the shaded regions. Give your answer as a completely simplified exact value in terms of π (no approximations). PLEASE HELP ME ASAP!!!
Answers
Answer:
The area of the entire yellow region is 48 cm^2.
Step-by-step explanation:
See the attached image :)
PLssss answer
Which expression below gives the average rate of change of k on -3 ≤ x ≤ 5 ?
Answers
Answer:
ave rate of change = k(5) - k(-3)
----------------
5+3
Step-by-step explanation:
To find the average rate of change
ave rate of change = f(x2) - f(x1)
----------------
x2-x1
We know that x2 = 5 and x1 = -3
ave rate of change = k(5) - k(-3)
----------------
5--3
ave rate of change = k(5) - k(-3)
----------------
5+3
Sully is driving a race car in a race. The table gives the speeds recorded by the speedometer on Sully's car with respect to time.
x
(seconds)
y
(mph)
x y
2 60
8 120
16 170
What type of function is the function representing Sully's speed?
It is a constant function.
It is a linear function.
It is a nonlinear function.
It is a decreasing function.
Answers
It is a nonlinear function.
Step-by-step explanation:When the points are graphed, they do not all lie on the same line. The lines connecting the points have positive slope, so the function is neither constant nor decreasing.
Answer: It is a nonlinear function.
Step-by-step explanation:
A function is said to be linear if the rate of change of dependent varaible (y) with respect to independent variable (x) is constant.
Rate of change in function [tex]=\dfrac{\text{Change in y}}{\text{Change in x}}[/tex]
The table gives the speeds recorded by the speedometer on Sully's car with respect to time. :
x y
(seconds) (mph)
2 60
8 120
16 170
For x= 2 and x= 8 , the rate of change in function will be
[tex]\dfrac{\text{Change in y}}{\text{Change in x}}\\\\=\dfrac{120-60}{8-2}=\dfrac{60}{6}=10[/tex]
For x= 8 and x= 16 , the rate of change in function will be
[tex]=\dfrac{170-120}{16-8}=\dfrac{50}{8}=6.25[/tex]
But 10 ≠ 6.25.
⇒ Rate of change is not constant.
It means the function non- linear.
Also , it is not a constant function because values of y is not constant w.r.t to x.
It is not a decreasing function because values of y increase with increase in x.
Point w id located at (-2,3) on a coordinate plane. Point W is reflected over the x-axis to create point W" is then reflected over the Y- axis to create point W". What ordered pair describes the location of point W" ?
Answers
Answer:
W'' = (2, -3)
Step-by-step explanation:
Reflection over the x-axis negates the y-coordinate and leaves the x-coordinate alone. The W becomes ...
... W' = (-2, -3)
Reflection over the y-axis negates the x-coordinate and leaves the y-coordinate alone. The W' becomes ...
... W'' = (2, -3)
Answer:
The coordinates of point W'' are (2,-3).
Step-by-step explanation:
The coordinates of given point are W(-2,3).
If point W is reflected over the x-axis, then
[tex](x,y)\rightarrow (x,-y)[/tex]
[tex]W(-2,3)\rightarrow W'(-2,-3)[/tex]
If point W' is reflected over the y-axis, then
[tex](x,y)\rightarrow (-x,y)[/tex]
[tex]W'(-2,-3)\rightarrow W''(2,-3)[/tex]
Therefore the coordinates of point W'' are (2,-3).
Shenelle has
1
0
0
100 meters of fencing to build a rectangular garden.
The garden's area (in square meters) as a function of the garden's width
w
w (in meters) is modeled by:
A
(
w
)
=
−
(
w
−
2
5
)
+
6
2
5
A(w)=−(w−25)
2
+625
What side width will produce the maximum garden area?
Answers
Answer:
w = 25
Step-by-step explanation:
The function A(w) = -(w-25)² +625 is in vertex form. The vertex (maximum) is at (w, A) = (25, 625). A width of 25 meters will maximize the area.
Find the domain of the inverse function, q−1(x). Express your answer as an inequality.
Answers
Hello from MrBillDoesMath!
Answer:
x >=4
Discussion:
The inverse of q is
-1 +\- (x-4)^(1/4) (the fourth root of x-4)
(Inverse found by solving x= (y+1)^4 +4 for y)
The domain of the inverse is therefore x such that x -4 >=0 , i.e. x >=4
Regards,
MrB
P.S. I'll be on vacation from Friday, Dec 22 to Jan 2, 2019. Have a Great New Year!
Two circles have the same center but different radii. Which of the following is true about the circles? A. They are not similar because they have different radii. B. They are congruent because they have the same center. C. They are congruent because they have the same shape and size. D. They are similar because they are of the same shape but different size.
Answers
Final answer:
Two circles that have the same center but different radii are similar because they share the same shape but differ in size. The answer, therefore, is D. They are similar because they are of the same shape but different sizes.
Explanation:
The question involves two circles that share the same center but have different radii. According to geometric principles, similar figures have the same shape but not necessarily the same size, while congruent figures have both the same shape and the same size. Since the two circles share the same center (co-centric circles) and therefore the same shape (both are circular) yet differ in size, due to their different radii, the correct answer is that they are similar. Hence, the correct option is:
D. They are similar because they are of the same shape but different sizes.
This addresses the concept that similarity in geometry is about shape, rather than size. If the circles were both identical in size and shape, they would be congruent; however, because their sizes vary, they cannot be congruent.
Solve the system of linear equations. −x+2y=4 and −2x−2y=14
Answers
Answer:
x=-6, y=-1
Step-by-step explanation:
−x+2y=4 and −2x−2y=14
I will solve by elimination. We can eliminate the y variable by adding these together.
−x+2y=4
−2x−2y=14
-----------------
-3x = 18
Divide each side by -3
-3x/-3 = 18/-3
x = -6
But we still need to solve for y
-x + 2y =y
Substitute x in
- -6 +2y =4
6 +2y = 4
Subtract 6 from each side
6-6 + 2y = 4-6
2y = -2
2y/2 = -2/2
y= -1
To solve the system, we added the two equations, resulting in -3x = 18. Solving for x, we found x = -6 and then substituted this value into one of the original equations to solve for y, yielding y = -1. The final solution is (x, y) = (-6, -1).
To solve the system of linear equations -u+2y=4 and -2x-2y=14, we can utilize the elimination method. This involves adding the two equations together in order to eliminate one of the variables, resulting in an equation with a single variable which can be easily solved.
We begin by adding the two equations:
-(-x+2y)+(-2x-2y)=4+14
x - 2y - 2x - 2y = 18
-3x = 18
Divide both sides by -3 to find the value of x:
x = -6
With the value of x known, we substitute it back into one of the original equations to solve for y. Let's use the first equation:
-(-6) + 2y = 4
6 + 2y = 4
2y = -2
Divide both sides by 2 to find the value of y:
y = -1
The solution to the system of equations is (x, y) = (-6, -1).
The rule for the number of fish in a home aquarium is 1 gallon of water for each inch of fish length. Marta's aquarium holds 33 gallons of water and Hank's aquarium hold 45 gallons of water. The aquarium holds two types of fish, fish A and fish B. If Marta bought 3 of fish A and 2 of fish B, and Hank bought 3 of fish A and 4 of fish B, how long is fish A and how long is fish B?
Answers
We can let the variables A and B stand for the length in inches of fish A and fish B, respectively.
If we assume each person bought fish having a total length of 1 inch per gallon of aquarium, then we can write equations ...
... 3A +2B = 33 . . . . . total length of Marta's fish
... 3A +4B = 45 . . . . . total length of Hank's fish
Subtracting the first equation from the second, we get ...
... 2B = 12
... B = 6 . . . . . divide by 2
Using this value in the first equation, we have ...
... 3A + 2·6 = 33
... 3A = 21 . . . . . . . . subtract 12
... A = 7 . . . . . . . . . . divide by 3
Fish A is 7 inches long; fish B is 6 inches long.
To determine the lengths of fish A and fish B, two simultaneous equations were formed using the information provided. Solving these equations resulted in finding that fish A is 7 inches long and fish B is 6 inches long.
Explanation:The problem revolves around figuring out the length of fish A and fish B given the rule that each inch of fish requires 1 gallon of water.
Marta's aquarium holds 33 gallons and she bought 3 of fish A and 2 of fish B. Hank's aquarium holds 45 gallons and he bought 3 of fish A and 4 of fish B. Let's denote the length of fish A as 'a' inches and fish B as 'b' inches.
Marta's equation: 3a + 2b = 33 (1)
Hank's equation: 3a + 4b = 45 (2)
To find the length of fish A and B, we solve these simultaneous equations:
Multiply equation (1) by 2: 6a + 4b = 66Subtract equation (2) from this new equation:6a + 4b - (3a + 4b) = 66 - 45
3a = 21
a = 7 inchesNow plug the value of 'a' into equation (1):
3(7) + 2b = 33
21 + 2b = 33
2b = 12
b = 6 inches
Fish A is 7 inches long, and fish B is 6 inches long.
Write a word problem that could be represented and solved by the equation 6S=24.
Answers
Hello, there! :)
Answer:
s=4
*The answer must have a positive sign.*
Step-by-step explanation:
First, you divide by 6 from both sides of an equation.
[tex]\frac{6s}{6}=\frac{24}{6}[/tex]
Then, you divide by the numbers from left to right.
[tex]24/6=4[/tex]
Final answer is s=4
Hope this helps!
Have a nice day! :)
:D
-Charlie
Thank you so much! :)
:D
Cara has driven one-fifth of the total distance, d, to her destination. Which statement explains why both 1/5d and 0.2d can find the distance she has driven?
A Multiplying by 15 is the same as multiplying by 2%.
B The fraction 15 is the same as the decimal 0.8. Therefore, 1/5d can be written as 0.8d.
C Multiplying by 15 is the same as multiplying by 20%.
D
The expressions are not equivalent.
Answers
Answer:
ITS C: Multiplying by 15 is the same as multiplying by 20%
Step-by-step explanation:
The solution is Option C.
The equation of multiplying by 1/5 is the same as multiplying by 20%
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Cara has driven one-fifth of the total distance, d, to her destination
So , the distance traveled by Cara S = ( 1/5 )d
And , the distance traveled by Cara S = 0.2d
On simplifying the equation , we get
The value of ( 1/5 )d = d/5
The value of 0.2d = ( 20/100 )d
The value of 0.2d = 20 % of d
Therefore , the value of ( 1/5 )d = value of 0.2d
Hence , the equations are same
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Cara has driven one-fifth of the total distance, d, to her destination. Which statement explains why both 1/5d and 0.2d can find the distance she has driven?
A Multiplying by 15 is the same as multiplying by 2%.
B The fraction 15 is the same as the decimal 0.8. Therefore, 1/5d can be written as 0.8d.
C Multiplying by 15 is the same as multiplying by 20%.
D
The expressions are not equivalent.
Answers
Answer:
The correct answer is option C, Multiplying by 1/5 is the same as multiplying by 20%.
Step-by-step explanation:
The equation 1/5 = 1 divided by 5 = 0.2
and 0.2 can be expressed as 20%
Thus both the factor 1/5 and 20 % are same
Answer:
c is the answer
Step-by-step explanation:
The distance between city A and B is 600 km. The first train left A and headed towards B at the speed of 60 km/hour. The second train left B heading towards A three hours after the first train left A, and it traveled with a speed of v km/hour. The trains met t hours after the time at which the first train left A. Express v in terms of t. Find the speed v if t=7; t=6.
Answers
Answer:
v(t) = 420/(t-3) -60v(7) = 45 km/hv(6) = 80 km/hStep-by-step explanation:
When the second train leaves, the remaining distance between the trains is ...
... 600 km - (3 h)×(60 km/h) = 420 km
That distance will be covered at the speed of (60 +v) so the time it takes for the second train to cover that distance is ...
... 420/(60 +v)
The variable t represents the time since the first train left, so is 3 hours more than this time value. Hence ...
... t = 3 +420/(60 +v)
Solving for v, we have ...
... t -3 = 420/(60 +v) . . . . subtract 3
... 60 +v = 420/(t -3) . . . . multiply by (60+v)/(t -3)
... v = 420/(t -3) -60 . . . . subtract 60
For t = 7 ...
... v = 420/(7 -3) -60 = 105 -60 = 45
For t = 6 ...
... v = 420/(6 -3) -60 = 140 -60 = 80
x^2+y^2−10=0
Write the values of y, for which the equation has sense.
Answers
Answer: y = 3
Step-by-step explanation:
The objective is to get 0 on the left side to equal the 0 on the right side. I'd like to do this by making the sum of x^2 and y^2 equal to 10. If (x^2+y^2) = 10, the -10 on the left side will cancel it out to equal 0.
1^2 = 1
3^3 = 9
1 + 9 = 10
Therefore, x is 1 and y is 3.
x^2 + y^2 - 10 = 0
1^2 + 3^2 - 10 - 0
1 + 9 - 10 = 0
10 -10 = 0
0 = 0
Charlie's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Charlie $4.85 per pound, and type B coffee costs $5.95 per pound. This month, Charlie made 150 pounds of the blend, for a total cost of $789.10 . How many pounds of type A coffee did he use?
Answers
Answer:
94 pounds
Step-by-step explanation:
Let "a" represent the weight of type A coffee Charlie used. Then 150-a is the weight of the type B coffee. The total cost of the blend is then ...
... 4.85a +5.95(150 -a) = 789.10
... -1.10a +892.50 = 789.10 . . . . . . simplify
... -1.10a = -103.40 . . . . . . . . . . . . . .subtract 892.50
... a = 94 . . . . . . . . . . . . . . . . . . . . . divide by -1.10
Charlie used 94 pounds of type A coffee.
Final answer:
Charlie used 94 pounds of type A coffee for the blend, which was found by setting up a system of equations based on the total weight and cost of the coffee blend and solving for the quantity of type A coffee.
Explanation:
To solve how many pounds of type A coffee Charlie used, we need to set up a system of equations based on the given information.
Let x be the amount of type A coffee and y be the amount of type B coffee. We have two types of coffee totaling 150 pounds, so x + y = 150.
The cost of the two types of coffee leads to the second equation: 4.85x + 5.95y = 789.10.
We solve this system of equations either by substitution or elimination. If we solve for y from the first equation (y = 150 - x) and substitute it into the second equation, it simplifies to 4.85x + 5.95(150 - x) = 789.10, which becomes 4.85x + 892.50 - 5.95x = 789.10. Simplifying further gives -1.10x = -103.40, which when solved for x gives x = 94.
Therefore, Charlie used 94 pounds of type A coffee for his blend.
Find the measure of the acute angle x. Round your answer to the nearest tenth, if necessary.
29.1
0.01
60.9
0.03
Answers
Answer:
29.1°
Step-by-step explanation:
You can use your good sense to select the correct answer.
You know it is not near zero (so, not 0.01 or 0.03—neither of which is rounded to the nearest tenth). Since the adjacent side is longer than the opposite side, you know the angle is less than 45°. (Of the two complementary angles X and T, X is the smaller.) That only leaves one answer choice.
If you really need to figure it out, use SOH CAH TOA to remind you ...
... Tan(X) = Opposite/Adjacent = (5 in)/(9 in)
... X = arctan(5/9) ≈ 29.1° . . . . . make sure your calculator is in degrees mode
In this trigonometric problem, intuitive reasoning and basic principles were used to deduce the angle X as approximately 29.1 degrees, before employing the tangent function for precise calculation.
When faced with a problem involving trigonometry, sometimes you can intuitively deduce the correct answer using logic and a basic understanding of trigonometric principles. Let's break down how to approach the problem step by step:
Eliminate Options: In this case, you are provided with multiple answer choices. You can start by ruling out certain options based on your intuition. You can eliminate answers that are "near zero," such as 0.01 and 0.03, which are not rounded to the nearest tenth.
Analyze the Triangle: By examining the given information, you can infer that the angle you are looking for (angle X) is less than 45°. This deduction is based on the fact that the adjacent side is longer than the opposite side in a right triangle, and X is the smaller of the two complementary angles.
Use SOH CAH TOA: If you want to calculate the angle more precisely, you can apply trigonometric ratios. In this case, you use the tangent function: Tan(X) = Opposite/Adjacent = 5 in / 9 in. Then, you can find the angle using the arctan function, which yields X ≈ 29.1°.
In summary, while you can employ trigonometric functions for precise calculations, sometimes a logical approach and a good understanding of the problem can lead you to the correct answer more efficiently. In this scenario, the angle X is approximately 29.1 degrees, provided your calculator is in degrees mode.
For more such information on: tangent function
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At the movie theatre, child admission is $6.60 and adult admission is $9.80 . On Thursday, 182 tickets were sold for a total sales of $1508.40 . How many adult tickets were sold that day?
Answers
Answer:
96
Step-by-step explanation:
Let x represent the number of adult tickets sold. Then (182-x) is the number of child tickets sold. The total sales is then ...
... 6.60·(182 -x) +9.80·x = 1508.40
... 3.20x = 1508.40 -1201.20 . . . . . simplify, subtract 1201.20
... 307.20/3.20 = x = 96 . . . . . . . . divide by the coefficient of x
96 adult tickets were sold that day.
Final answer:
By setting up and solving a system of equations, it is determined that 96 adult tickets were sold at the movie theatre.
Explanation:
To solve the problem of how many adult tickets were sold at the movie theatre, we need to set up a system of equations based on the given information: child admission is $6.60, adult admission is $9.80, 182 tickets were sold in total, and the sales amounted to $1508.40.
Let's denote the number of child tickets sold as c and the number of adult tickets sold as a. We can then create the following two equations:
c + a = 182 (since the total number of tickets sold was 182)
6.60c + 9.80a = 1508.40 (representing the total sales from the tickets)
We can solve these equations using substitution or elimination methods. Here's the step-by-step solution using the elimination method:
First, we multiply the first equation by -6.60 to set up for elimination:
-6.60c - 6.60a = -1201.20
Now we add this to the second equation:
6.60c + 9.80a = 1508.40
3.20a = 307.20
Dividing both sides by 3.20 gives us a = 96.
Therefore, 96 adult tickets were sold that day.
PLEASE HELP!!!
Find all possible values of m and the corresponding a, b, and c’s for each one. Show your work.
m • a = 196
m • b = 441
m • c = 210
Answers
(m, a, b, c) ∈ {(1, 196, 441, 210), (7, 28, 63, 30)}
Step-by-step explanation:m is a common factor of 196, 210, 441
The prime factors of those numbers are
... 196 = 2²×7²
... 210 = 2×3×5×7
... 441 = 3²×7²
7 is the only prime factor common to all the numbers. Hence the possible values of m are 1 and 7.
For m = 1, (a, b, c) = (196, 441, 210).
For m = 7, (a, b, c) = (196, 441, 210)/7 = (28, 63, 30).
The number k and 1.4 are additive inverses. Drag and drop 1.4 and k to their correct positions on the number line. Drag and drop the label “Sum” to the sum of 1.4 and k.
Answers
The location of the number k is -1.4 and the sum of 1.4 and k is 0
How to determine the positions of the numbers
From the question, we have the following parameters that can be used in our computation:
The number k and 1.4 are additive inverses.
This means that
k + 1.4 = 0
Evaluate the like terms
So, we have
k = -1.4
So, the location of the number k is -1.4 and the sum of 1.4 and k is 0
For 14a through 14d, tell which expressions require you to rename mixed numbers before you can subtract. Find each difference. Write each expression and the difference as an equation in the correct box PLEASE ANSWER