State the number of possible triangles that can be formed using the given measurements.
Answers
Answer: 39) 1 40) 2
41) 1 42) 0
Step-by-step explanation:
39) ∠A = ? ∠B = ? ∠C = 129°
a = ? b = 15 c = 45
Use Law of Sines to find ∠B:
[tex]\dfrac{\sin B}{b}=\dfrac{\sin C}{c} \rightarrow\quad \dfrac{\sin B}{15}=\dfrac{\sin 129}{45}\rightarrow \quad \angle B=15^o\quad or \quad \angle B=165^o[/tex]
If ∠B = 15°, then ∠A = 180° - (15° + 129°) = 36°
If ∠B = 165°, then ∠A = 180° - (165° + 129°) = -114°
Since ∠A cannot be negative then ∠B ≠ 165°
∠A = 36° ∠B = 15° ∠C = 129° is the only valid solution.
40) ∠A = 16° ∠B = ? ∠C = ?
a = 15 b = ? c = 19
Use Law of Sines to find ∠C:
[tex]\dfrac{\sin A}{a}=\dfrac{\sin C}{c} \rightarrow\quad \dfrac{\sin 16}{15}=\dfrac{\sin C}{19}\rightarrow \quad \angle C=20^o\quad or \quad \angle C=160^o[/tex]
If ∠C = 20°, then ∠B = 180° - (16° + 20°) = 144°
If ∠C = 160°, then ∠B = 180° - (16° + 160°) = 4°
Both result with ∠B as a positive number so both are valid solutions.
Solution 1: ∠A = 16° ∠B = 144° ∠C = 20°
Solution 2: ∠A = 16° ∠B = 4° ∠C = 160°
41) ∠A = ? ∠B = 75° ∠C = ?
a = 7 b = 30 c = ?
Use Law of Sines to find ∠A:
[tex]\dfrac{\sin A}{a}=\dfrac{\sin B}{b} \rightarrow\quad \dfrac{\sin A}{7}=\dfrac{\sin 75}{30}\rightarrow \quad \angle A=13^o\quad or \quad \angle A=167^o[/tex]
If ∠A = 13°, then ∠C = 180° - (13° + 75°) = 92°
If ∠A = 167°, then ∠C = 180° - (167° + 75°) = -62°
Since ∠C cannot be negative then ∠A ≠ 167°
∠A = 13° ∠B = 75° ∠C = 92° is the only valid solution.
42) ∠A = ? ∠B = 119° ∠C = ?
a = 34 b = 34 c = ?
Use Law of Sines to find ∠A:
[tex]\dfrac{\sin A}{a}=\dfrac{\sin B}{b} \rightarrow\quad \dfrac{\sin A}{34}=\dfrac{\sin 119}{34}\rightarrow \quad \angle A=61^o\quad or \quad \angle A=119^o[/tex]
If ∠A = 61°, then ∠C = 180° - (61° + 119°) = 0°
If ∠A = 119°, then ∠C = 180° - (119° + 119°) = -58°
Since ∠C cannot be zero or negative then ∠A ≠ 61° and ∠A ≠ 119°
There are no valid solutions.
Related Questions
Translate into an algebraic expression: How much 50% sugar syrup can you make if you have x grams of sugar ?
Answers
Answer:
The algebraic expression is v = 2x
v is the volume of the sugar syrup and
x is the mass of sugar in grams.
Step-by-step explanation:
Let x be the mass of sugar in grams and v be the volume of sugar syrup.
So, mass of sugar in grams/volume of sugar syrup × 100 % = 50 %
x/v × 100 % = 50 %
x/v = 50/100
x/v = 1/2
v = 2x
So, the algebraic expression required is v = 2x where v is the volume of the sugar syrup and x is the mass of sugar in grams.
Please help me with this
Answers
Answer:
3, 8, 12, 12, 14, 20, 21, 23, 26, 34
stem leaf
0 3 8
1 2 2 4 (you have 12,12,14)
2 0 1 3 6 ( numbers 20,21,23,26)
3 4 ( number 34)
calcula la diagonal de un cuadrado cuyo lado tiene cada una de las siguientes medidas en centímetros. a.4 b.7 c.13
Answers
Answer:
[tex]4\sqrt{2}\\\\7\sqrt{2} \\\\13\sqrt{2}[/tex]
Step-by-step explanation:
Well the diagonal using pythagora's theorem:
[tex]x\sqrt{2}[/tex] where x is the lenght is the side of the square
so when x=4
[tex]4\sqrt{2}[/tex]
when x=7
[tex]7\sqrt{2\\}[/tex]
when x=13
[tex]13\sqrt{2}[/tex]
The length of diagonal is for (a=4) is [tex]4\sqrt{2}[/tex], for(a=7) is [tex]7\sqrt{2}[/tex] and for (a=13) is[tex]13\sqrt{2}[/tex].
Given side of squares.
We have to calculate the length of diagonal.
We know that in square shape,
length of diagonal [tex]=\sqrt{2} a[/tex], here a is the side of square.
So when square has a side of 4 then its diagonal becomes [tex]4\sqrt{2}[/tex].
when square has a side of 7 then its diagonal becomes [tex]7\sqrt{2}[/tex].
when square has a side of 13 then its diagonal becomes [tex]13\sqrt{2}[/tex].
Hence the length of diagonal is for (a=4) is [tex]4\sqrt{2}[/tex], for(a=7) is [tex]7\sqrt{2}[/tex] and for (a=13) is[tex]13\sqrt{2}[/tex].
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What is the solution set of x for the given equation? x^2/3-x^1/3+4=6 A. -2, -1 B. 2, -1 C. -8, -1 D. 8, -1 E. 2, 8
Answers
Answer: The answer is D.
Step-by-step explanation: Ok, we start by simplifing the equation to 3√x^2 - 3√x=2. Now, by plugging the possible options in, we can find the answer. You find that -1 is a possible answer for x, so that eliminates E. Since there is no cube root for 2, we elimate A and B. By plugging in C and D, you find that C=6, not C=2. So D must be the answer.
What are the coordinates of the image of L for a dilation with center (0, 0) and scale factor 4?
Answers
Answer:
A. (-8, 20)
Step-by-step explanation:
The formula for dilations is
[tex]\left(x_{1}\cdot t_{1},\ y_{1}\cdot t_{1}\right)[/tex] Where t is the scale factor
The first step is to plug in the numbers appropriately
[tex](-2*4,5*4)[/tex]
Then, multiply -2 by 4 and 5 by 4 to get
[tex](-8, 20)[/tex]
So your answer is (-8, 20)
Hope this helps
Have a great day! :)
Allen and Stephan went shopping for Mother's day. Stephan spent $30 for 4 roses and 2 CDs. Allen bought 2 roses and 3 CDs for $40. What was the cost of a rose and a CD?
Answers
Answer:
work is shown and pictured
a) A and B are the subsets of a universal set U in which there are n (U) = 54,
n (A) = 32, n (B) = 22 and n (
AB) = 9.
(i) Draw a Venn-diagram to illustrate the above information.
(ii) Find the value of n (AUB).
Answers
Step-by-step explanation:
I DON'T KNOW WHICH ANSWER IS CORRECT .
BUT MY ANSWER CAME THIS .
I HOPE IT WILL HELP YOU.
HAVE A NICE DAY.....
Molly is doing her math homework. To receive full credit, she must answer this question: What key features are necessary-and how are the features used-to create the sketch of a polynomial function? What is Molly's correct answer, so she receives full credit for the question? Explain in complete sentences. (10 points)
Answers
Answer:
The axis of symmetry, vertex, degree of polynomial and x and y intercepts
Step-by-step explanation:
When we talk of a polynomial function, we refer to a function that involves only non-negative integer(whole number) powers of the independent variable (x in most cases). Thus, popular examples of polynomial functions include quadratic, cubic and triatic functions.
Kindly note that once a function includes a non negative power, it is not a polynomial any longer. That is why although x^2 + 2x is a polynomial function, x^2 + 2x^-1 is not a polynomial function.
Now, there are some key features that are necessary in sketching a polynomial function.
These are the vertex, axis of symmetry, x and y intercepts and the degree of the polynomial
These properties are needed to successfully make a sketch of a polynomial function.
The vertex of a polynomial function refers to that point on the curve of the function where it changes direction. For example, quadratic polynomial functions are known to have a parabolic sketch. That point in which there is a change in direction of the parabolic curve is known as the vertex of the polynomial function. A knowledge of this would ensure a proper sketch of the polynomial function curve. It helps in showcasing the concavity of the function.
The axis of symmetry applies to polynomials with even degrees. A polynomial function with an axis of symmetry will have mirror images on each side of a line that directly cuts through the polynomial.
The x and y intercepts talks about the points at which the function touches the axes of the plot
The degree of the polynomial helps to find the end behavior of the polynomial. The degree of a polynomial refers to the highest power to which the independent variable is raised. It is an important factor in determining if a polynomial function sketch will possess an axis of symmetry.
Which of the following equations have infinitely many solutions? Choose All that apply. A: 37x-37=37x-37 B: 74x-37=74-37 C: 73x-37=73x-37 D: x-37=x-37
Answers
Answer:
(A), (C) and (D).
Step-by-step explanation:
An equation will have infinite solutions if both sides of the equal sign are the exact same thing, for instance [tex]4x+4=4x+4[/tex]. (You can test this with any value of x and find that they all work!)
So to find the equations that have infinite solutions, we need to see which have the same exact sides.
[tex]37x-37 = 37x-37[/tex] have the same thing on each side: [tex]37x-37\\[/tex], so this has infinite solutions.
[tex]74x-37 = 74-37[/tex] does not have the same thing on each side, so it doesn’t have infinite solutions (it has 1)
[tex]73x-37 = 73x-37[/tex] has the same thing on each side: [tex]73x-37[/tex], so this has infinite solutions.
And finally, [tex]x-37=x-37[/tex] has the same thing on each side: [tex]x-37[/tex], so it has infinite solutions.
Hope this helped!
Answer:
question is not clear please send clear question
The speed at which a ball bits the ground is proportional to the
height to which the ball rebounds. If the ball hits the ground at
a speed of 20 miles per hour and rebounds to a height of 10 feet,
then how fast must it be traveling (in miles per hour) to rebound
to a height of 15 feet?
Answers
Answer:
30 mph
Step-by-step explanation:
let s represent speed and h represent rebound.
Given that s is proportional to h then the equation relating them is
s = kh ← k is the constant of proportion
To find k use the condition s = 20, h = 10, then
20 = 10k ( divide both sides by 10 )
2 = k
s = 2h ← equation of proportionality
When h = 15 , then
s = 2 × 15 = 30 mph
the figure is cut into 8 equal pieces shade 3/4 of the figure
Answers
Answer:
You have to shade 6 pieces.
Step-by-step explanation:
Hope it helps!
Can someone help me find the surface area
Answers
Answer:
144 m²
Step-by-step explanation:
top triangle area: (8 x 6) / 2 = 24
bottom triangle area: (8 x 6) / 2 = 24
back rectangle area: 8 x 4 = 32
left rectangle area: 6 x 4 = 24
right rectangle area: 10 x 4 = 40
add all: 144 m²
Answer:
There are 5 surfaces for which you will have to calculate area.
the back is 4 by 8 = 32 mi^2
The bottom is 4 by 6 = 24 mi^2
the tilted ramp 4 by 10 = 40 mi^2
There are 2 side triangles 8 by 6 area of 1 triangle = 8*6/2 = 24 mi^2
area of BOTH triangles = 2 * 24 = 48 mi^2
Total area = 32 + 24 + 40 + 48 = 144 mi^2
Step-by-step explanation:
Price elasticity of demand for tomatoes is 1.30. If hail storm adversely affects the nation’s production of tomatoes what will be the impact on total revenue from tomatoes and why?
Answers
Answer:
The total revenue will decrease.
Step-by-step explanation:
The price elasticity of demand is 1.30 that shows that change in the quantity of tomatoes is greater than the change in the price of tomatoes. The hail storm will decrease the quantity (supply) of tomatoes. However, this decrease in supply will increase the price but the ratio of change in quantity will be more than the ratio of change in price. Thus, total revenue from tomatoes will also fall.
I will make u brainliest n give u five stars if u answer this right Pls find the area oh H in mm squared
Answers
Answer:
[tex]24200 mm^{2}[/tex]
Step-by-step explanation:
200*50+200*50+70*60
=24200 mm^{2}
can someone help me please
Answers
Answer:
-3x
Step-by-step explanation:
-3 is the coefficient and x is the variable.
What are the independent and dependent variables in the relationship?
Answers
w is the width and it is the independent variable. You can pick any positive whole number you want (within reason of course; you can't go to infinity or go beyond some set boundary). Whatever you picked for w, the expression 2w-5 will be dependent on it. So the length is dependent on the width.
For instance, if the width is w = 10 feet, then 2w-5 = 2*10-5 = 20-5 = 15 feet is the length. The choice of 10 feet for the width directly affects the length being 15 feet.
HELP!!! A plumber charges a fee of $25 plus $30 per hour on the job. Make a table of values for the total charge depending on the number of hours the plumber works. Determine if this can be defined by a linear or an exponential function. What is the function? Linear: t=25+30h Linear:T=30+25h Exponential:T=30(25)^h Exponential: T=25(30)^h HELP I HAVE 10 MINS LEFT
Answers
Answer:
Yes, this function can be defined by linear model.
Step-by-step explanation:
[tex]\mathrm{Total\:=\:Fixed\:Fee\:+\:Hourly\:Rate\:\times Number\:of\:hours}[/tex]
[tex]\mathrm{Linear:}\:\:T=\:$25+30h[/tex]
Best Regards!
What is the range of the function?
Answers
***HOPE This Help You***
En el mercado del satisfactor X hay 10,000 individuos idénticos, cada uno con una función de demanda definida por Qdx = 12 – Px y 1,000 productores idénticos del satisfactor X, cada uno con una función de oferta dada por Qsx = 20 Px
Answers
Answer:
Px = $4
Step-by-step explanation:
Given that:
En el mercado de satisfacción X hay 10,000 individuos idénticos, cada uno con una función de demanda definida por Qdx = 12 - Px y 1,000 productores idénticos de X satisfactorio, cada uno con una función de oferta dada por Qsx = 20 Px
El precio de equilibrio y la cantidad de equilibrio se pueden determinar de la siguiente manera;
Qdx = 10000(12-Px)
Qdx = 120000 - 10000Px
Qsx = 1000(20 Px)
Qsx = 20000 Px
El punto de equilibrio para completar el enunciado, cuando Qdx = Qsx es:
Qdx = Qsx
120000 - 10000 Px = 20000 Px
120000 = 20000 Px + 10000 Px
120000 = 30000 Px
Px = [tex]\mathbf{ \dfrac{120000}{30000}}[/tex]
Px = $4
{b(1)=-2 {b(n)=b(n-1)-7 What’s the 3rd term?
Answers
Answer: the answer is b(5)
Step-by-step explanation:
To find the third term work backwards and plug it in. That was when you plug the solution of b(n-1) everything fits.
Answer:
b(3)=-16
Step-by-step explanation:
We have to figure out the second term
b(2)=b(1)-7
b(2)=-2-7
b(2)=-9
and now the third one
b(3)=b(2)-7
b(3)=-9-7
b(3)=-16
How many pairs of points are reflections across the x-axis?
A)1
B)2
C)3
D)4
Answers
Answer:
C. 3
Step-by-step explanation:
C&D, A&F, K&J
The pairs of points are reflections across the x-axis will be 3. The correct option is C.
What is coordinate geometry?A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis.
A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.
In the given graph number of points is given in all four quadrants. The reflections of the points across the x-axis will be of the points C and D, A and F, K and J.
Therefore, the pairs of points that are reflections across the x-axis will be 3.
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Which equation represents a line that has a slope of −2/3 and a y-intercept of 4?
Answers
Answer:
y = -2/3x + 4
Step-by-step explanation:
In an equation that represents a line, the number with which no variable is multiplied is the y-intercept.
The number with which "x" is multiplied is the slope.
So in this case, the slope is -2/3; so the equation should be like -2/3x.
The y-intercept is 4, so it is the number with which no variable is multiplied.
So the equation is:
=> y = -2/3x + 4
.
Look at the table. Is ƒ(x) an exponential function? If so, identify the base. If not, why not?
No, there is no base common to any two successive terms.
yes, the base is 4
Answers
Answer:
yes, the base is 4
Step-by-step explanation:
which equation represents the line that is perpendicular yo y=3/2x+1 and passes through (-12,6)
Answers
Answer:
y = -2/3x - 2
Step-by-step explanation:
Step 1: Find slope m of perpendicular line
Simply take the negative reciprocal of the given line
m = -2/3
y = -2/3x + b
Step 2: Find b
6 = -2/3(-12) + b
6 = 8 + b
b = -2
Step 3: Rewrite perpendicular equation
y = -2/3x - 2
Which expression can be used to determine the slope of the linear function represented in the table?
х
0
у
5
9
4
9-5
4-0
O
4-0
9-5
o
5-0
9-4
O
9-4
5-0
Answers
Answer:
to find the slope of a linear function, there is only one formula
this formula requires two points, which are stated in tables and graphs alike
these points do not need to be one after the other as it is slope and slope predicts what the next point graphed will be.
Formula for Slope:
y2 - y1______x2 - x1this should help. take any two points and substitute for each; y values in the correct spots and x values in their correct spots
make sure to put the values of second point where it is labelled y2 and x2 And make sure to substitute first point values in those labelled y1 and x1
It is important to remember that if this becomes a fraction, SIMPLIFY
We can write the slope of the function as -
{m} = (9 - 5)/(4 - 0).
What is function?A function is a relation between a dependent and independent variable. We can write the examples of function as -
y = f(x) = ax + b
y = f(x, y, z) = ax + by + cz
Given is a table for the function as -
{x} 0 4
{y} 5 9
We can write the slope of the function as -
{m} = (9 - 5)/(4 - 0)
Therefore, we can write the slope of the function as -
{m} = (9 - 5)/(4 - 0).
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I need help!
- 7(x + 2) = 21
Answers
Answer:
x = -5
Step-by-step explanation:
-7(x + 2) = 21
Divide each side by -7
-7/-7(x + 2) = 21/-7
x+2 = -3
Subtract 2 from each side
x+2-2 = -3-2
x = -5
Answer:
x = -5
Step-by-step explanation:
distribute: -7x-14 = 21
add 14 to both sides
divide by -7
x = -5
what is the ratio of the volumes of two similar spheres, given that the ratio of their radii is 5:9?
PLEASE NEED ANSWERS
Answers
Answer:
125 : 729
Step-by-step explanation:
Given the ratio of the radii of 2 similar spheres = a : b , then
ratio of volumes = a³ : b³
Here the ratio of radii = 5 : 9 , thus
ratio of volumes = 5³ : 9³ = 125 : 729
If you wrote the numbers from 1-8, and it equals to three, how do you make the statement true if you can't change the 3 but you could connect two or more numbers to make the statement true if you also can only do subtraction?
Answers
Answer:
Just add 6 to the right side of 3 which will make as 36
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 36
Hope it helps u...pls mark as brainliest
To decrease a number by 40%, what do we multiply by???
Answers
Answer:
Step-by-step explanation:
to decrease a number by 40% i would do
100% = number you got
50% divide by 2
10%= dived 100% number by 10 then take the 10% away from the 50% to get 40%
then take the 40% away from the 100%
hope this helps :)
An electrician earns $110 after his first hour of working for a client. His total pay based on the number of hours worked can be represented using the sequence shown. 110, 130, 150, 170, ...
Answers
Answer:
f(n + 1) = f(n) + 20
Step-by-step explanation:
Let f(x) equals their pay at every hour of X
Where x is the number of hours, then if we go with the trend where f(1)=110, f(2)=130 f(3)=150 f(4)=170 then would see that as they are working every hour they have their pay increased by $20, from f(1)=110+ $20 gives us f(2)=130 and that is after an hour then we can say
1 hour work=$20
Then additional 1hour+ n= $20 + n
Hence,f(n+1)=f(n)+20