Answer:
cos C
Step-by-step explanation:
Using the cosine ratio in the right triangle
cos C = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{12}{13}[/tex]
Use Descartes' Rule of Signs to find the number of possible positive real roots and the number of possible negative real roots for the function f(x) = x^4+ 2x^3-3x^2- 8x - 4.
a positive 1; negative 3 or 1
b. positive 1; negative 3 or 5
C. positive 3; negative 3 or 1
d. positive 3; negative 3 or 5
Answer:
a positive 1; negative 3 or 1
Step-by-step explanation:
To determine the number of positive roots, we have to determine the number of sign changes for f(x) = x⁴ + 2x³ - 3x² - 8x - 4.
The coefficients in f(x) are +1, +2, -3, -8, -4.
Since there is only one sign change from +2 to -3, we have 1 positive root.
To determine the number of negative roots, we have to determine the number of sign changes for f(-x) = (-x)⁴ + 2(-x)³ - 3(-x)² - 8(-x) - 4 = x⁴ - 2x³ - 3x² + 8x - 4
The coefficients in f(-x) are +1, -2, -3, +8, -4.
Since there is three sign change from +1 to -2, from -3 to +8, and from +8 to -4. So,we have 3 or 1 negative root, since the number of negative roots is equal to the number of sign changes or an even number less than the number of sign changes. So, 3 -2 = 1
So, the number roots are of positive 1; negative 3 or 1
Answer:
a.positive 1; negative 3 or 1
Step-by-step explanation:
EDGE 2020
What is an equivalent equation for 3 x = 12 minus 4 y when solved for x? X = 4 minus four-thirds y x = 4 + four-thirds y x = negative 4 + four-thirds y x = negative 4 minus four-thirds y
Answer:
[tex]x = 4 - \frac{4}{3}y[/tex]
Step-by-step explanation:
If we have the equation [tex]3x = 12-4y[/tex], we can simplify this equation down.
Divide both sides by 3:
[tex]x = 4 - \frac{4}{3}y[/tex] .
Hope this helped!
Answer:
X = 4 minus four-thirds y
Step-by-step explanation:
Well to solve for x we single it out.
3x = 12 - 4y
Divide 3 by everything,
x = 4 - 4/3y
Thus,
X = 4 minus four-thirds y.
I do hope this helps :)
Is (0, 3) a solution to the following system?
Y=-x+3
Y=2x-3
A No, because it does not check in either equation.
B. No, because it does not check in the first equation.
C. No, because it does not check in the second equation.
D. Yes, because it checks in both equations.
Solve each equation with (0, 3)
y = -x + 3
3 = -0 + 3
y = 3 (correct since y = 3 in (0, 3))
y = 2x - 3
3 = 2(0) - 3
3 = 0 - 3
3 = -3 (incorrect since it isn't equal)
So... No, because it does not check in the second equation.
Best of Luck!
Find the sum of two consecutive odd numbers is 56 find the numbers
Answer:
[tex]\boxed{\sf 27 \ and \ 29}[/tex]
Step-by-step explanation:
Let the first consecutive odd integer be [tex]\sf x[/tex].
Let the second consecutive odd integer be [tex]\sf x+2[/tex].
The sum of the two numbers is 56.
[tex]\sf x+x+2=56[/tex]
[tex]\sf 2x+2=56[/tex]
[tex]\sf 2x=54[/tex]
[tex]\sf x=27[/tex]
Put x as 27 for the second consecutive odd integer.
[tex]\sf 27+2=29[/tex]
The two numbers are 27 and 29.
Please help, ty if you do
Answer:
C
Step-by-step explanation:
4,800 times 7% is 336, and 1200 times 14% is 168, and 168 is half as much as 336, so the correct answer is c
Answer:
C
Step-by-step explanation:
Multiply .7 to 6000 and solve
PLEASE HELP! I WILL GIVE BRAINIEST! Look at the figure below: A triangle ABC is drawn. D is a point on BC such that BD is equal to DC. A straight line joins points A and D. This line extend Based on the figure, which pair of triangles is congruent by the Side Angle Side Postulate? a Triangle ABD and triangle ECD b Triangle ABC and triangle ECD c Triangle ABD and triangle ADC d Triangle ADC and triangle ABC
Answer:
ADB and ADC
Step-by-step explanation:
SAS is side angle side. so, which 2 triangles have same side, then angle, then side. We have to have it in that specific order.
Answer:
ABD and ECD
Step-by-step explanation:
EDC and ADB are vertical angles, so that is the angle we need for the SAS postulate. The markings on each of the corresponding sides is the same, which means we have 2 congruent sides, as well as an angle.
The formula for finding the kinetic energy, E, of an object is given below, where m represents the mass and v represents the speed of the object.
Answer:
v=√E/m or v=√E /√m
Step-by-step explanation:
Complete question below:
The formula for finding the kinetic energy, E, of an object is given below, where m represents the mass and v represents the speed of
the object.
E = mv^2
Solve the formula for v.
Solution
E=mv^2
Where,
E=kinetic energy
m=mass
v=speed of the object
E=mv^2
Divide both sides by m
E/m=mv^2/m
E/m=v^2
It can be rewritten as
v^2=E/m
Square root both sides
√(v^2)=√E/m
v=√E/m
Or
v=√E/√m
This is to say speed (v)=square root of kinetic energy (E) Over masa(m)
Please factorise the equations in the doc bellow ASAP. please show full working
Answer:
b. x² + 8x + 12 =
1. use the factoring X (see attachment)
2. 6 x 2 = 12; 6 + 2 = 12
3. (x + 6)(x + 2) = 0
4. x = -6, -2
c. x² + 13x + 12 =
1. 12 x 1 = 12; 12 + 1 = 13
2. (x + 12)(x + 1) = 0
3. x = -12, -1
c. x² + x - 12 =
1. 4 · (-3) = -12; 4 - 3 = 1
2. (x +4)(x - 3) = 0
3. x = -4, 3
f. x² + 15x + 36 =
1. 12 x 3 = 36; 12 + 3 = 15
2. (x + 12)(x + 3) = 0
3. x = -12, -3
hope this helps :)
Answer:
b) - (x + 2)(x + 6)
c) - (x + 12)(x + 1)
c) - (x - 3)(x + 4)
f) - (x + 12)(x + 3)
Step-by-step explanation:
Well to factor the given info we need to find the factors.
b)
[tex]x^2 + 8x + 12[/tex]
So 6*2 = 12
6x + 2x = 8x
x*x = x^2
Factored - (x + 2)(x + 6)
c)
[tex]x^2 + 13x + 12[/tex]
Well x*x = x^2
and 12*1 = 12
12x + x = 13x
Factored - (x + 12)(x + 1)
The second c)
[tex]x^2 + x - 12[/tex]
Well x*x = x^2
-3*4 = -12
-3x + 4x = x
Factored - (x - 3)(x + 4)
f)
[tex]x^2 + 15x + 36[/tex]
So x*x = x^2
12*3 = 36
12x + 3x = 15x
Factored - (x + 12)(x + 3)
Thus,
everything factored is (x + 2)(x + 6) , (x + 12)(x + 1) , (x - 3)(x + 4) ,
(x + 12)(x + 3).
Hope this helps :)
Robert buys $3 shirts at $16.90 each, and a pair of jeans for $20.50. The shop has a sale on, and so he receives a $7.12 discount.
Write and solve a numerical expression for how much he spends in total.
Answer:
64.08
Step-by-step explanation:
3^16.90+1*20.50-7.12
Find the equation of the line.
Answer:
y = 2x + 4
Step-by-step explanation:
y = mx + b
b = y-intercept = 4
m = slope = rise/run = 4/2 = 2
y = 2x + 4
which expression is equal to 5/ square root 11 ?
Answer:
5√11 ÷ 11 (The very last choice)
Step-by-step explanation:
I first found out what 5/√11 was and got 1.507556723 and checked all the other options and found that 5√11 ÷ 11 was the only option that had the exact same quotient as 5/√11.
Which of the following is a like radical to 3x sqrt 5
Answer:
The last option
Step-by-step explanation:
Source: Trust bro
Answer:
d) y sqrt 5
Step-by-step explanation:
radicals are like if they have the same index and radicand, here they are both square roots and have a radicand of five
Mrs johnson grows herbs in square plots Her basil plot measures. 5. 9 yd on each side. A. Find the total area of the basil plot. B. Mrs. Johnson puts a fence around the basil. If the fence was 2 ft from the edge of the garden on each side, whats the perimeter
Answer:
Area = 34. 81 yd^2
Perimeter = 86.6 feets
Step-by-step explanation:
Given the following :
Shape of Mrs. Johnson's plot = square
All sides of a square are of equal length
Measure of each side = 5.9 yd
A.) Area of plot
Area of plot = Area of a square
Area of a square(A) = a^2
Where a = side length
A = 5.9^2
A = 34.81 yd^2
B) Perimeter of Basil plot = Perimeter of a square
Converting yard to feet
1 yard = 3feets
Therefore,
5.9 yards = (3 * 5.9) = 17.7 feets
Fence is 2ft from the garden on each side,
Length of fence on each side = (2 + 17.7 + 2) Feets = 21.7 Feets
Perimeter of a square (P) = 4a
Where a = side length
P = 4 × 21.7
P = 86.6 feets
Answer:
86.6 feet
Step-by-step explanation:
What is the equation of the circle shown below?
Answer:
( x+2)^2 + ( y+2) ^2 = 9
Step-by-step explanation:
The center is at (-2,-2)
The radius is 3 which is the number of units from the center to the circles edge
The equation of a circle can be written as
( x-h) ^2 + (y-k) ^2 = r^2 where ( h,k) is the center and r is the radius
( x--2) ^2 + (y--2) ^2 = 3^2
( x+2)^2 + ( y+2) ^2 = 9
Which equation describes the line graphed above? A. -4x-5 B. -1/5x-4 C. -5x-4 C. -4x-1/5
The equation is -1/5x-4 represented by the graph. The correct option is B.
What is an equation?The equation in mathematics is the relationship between the variables and the number and establishes the relationship between the two or more variables.
Let us check the equation -1/5x-4. The line goes down one and turns right 5. The Slope is -1/5x and the y-intercept is at -4. The graph of the equation is attached with the answer below.
Hence, option B is correct.
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find the center of the circle (x-2)^2+(y-8)^2=33
Answer:
The center is (2,8)
Step-by-step explanation:
The equation of a circle is written as
(x-h)^2+ (y-k)^2 = r^2
where ( h,k) is the center and r is the radius
(x-2)^2+(y-8)^2=33
The center is (2,8) and the radius is sqrt(33)
ASAP!! Please help me. I will not accept nonsense answers, but will mark as BRAINLIEST if you answer is correctly with solutions.
Answer:
The third option is correct.
The domain of the function is given by
[tex]Domain = 0 \leq t \leq 40[/tex]
The range of the function is given by
[tex]Range = 0 \leq V(t) \leq 200[/tex]
Step-by-step explanation:
Sara bought a cell phone for $200 and its value has decreased at rate of $5 per month.
V(t) is the value of the phone and t is the number of months.
The domain of the function is the possible values of the number of months t.
The domain of the function is given by
[tex]Domain = 0 \leq t \leq 40[/tex]
The range of the function is the values of V(t) that we get after substituting the possible values of the number of months t.
The range of the function is given by
[tex]Range = 0 \leq V(t) \leq 200[/tex]
When the number of months is t = 0 then the value of the function is maximum V(t) = 200
When the number of months is t = 40 then the value of the function is minimum V(t) = 0
Therefore, the third option is correct.
A circle has a radius of sqrt 45 units and is centered at -2.4, -4.8 write the equation of the circle
Answer:
(x+2.4)^2+(y+4.8)^2=2025
If you'd like additional help with math or another subject, check out growthinyouth.org!
Step-by-step explanation:
Which expression is equal to 5(2x^2-1)+3(7x^2+1)
Answer:
31x² - 2
Step-by-step explanation:
5(2x²-1)+3(7x²+1) = 5*2x² - 5*1 + 3*7x² + 3 = 10x² - 5 + 21x² + 3 = 31x² - 2
how do i wright this as a expression? seven and the quotient of z and eight
8÷7=z and z is the answer you got when you divided,that's how I understand the question
Parallelogram L M N O is shown. Angle L is (x + 40) degrees and angle O is (3 x) degrees. What is the measure of angle O in parallelogram LMNO? 35° 75° 105° 155
Answer:
C, 105 Degrees
Step-by-step explanation:
So the two opposite sides of a parallelogram is equal to each other and the two adjacent angles are supplementary. So if (x+40)+3x=180, this means that 4x+40=180. This gives us 4x=140, so x=35. If we plug it back into the equation it ascertains as such: 3(35)= 105. The answer for this question and angle O is 105 degrees, or C.
The measure of angle O in this parallelogram is 105°.
The properties of a parallelogramThe opposite angles of a parallelogram are equal.The Opposite sides of the parallelogram are equal and parallel.The diagonals of the parallelogram bisect each other.The Sum of the angles = 360°
Solution
Because the properties says that opposite angles are equal.
Angle L = (x + 40)
angle O = (3 x)
Applying the first property
x+40+x+40+3x+3x = 360
collect the like termsx+x+3x+3x+40+40 = 360
8x+80 = 360
8x = 360-80
8x = 280
Divide through the equation by 8
x = 280/8
x = 35
The question wants us to find the value of angle O
O = 3x
O = 3*35
= 105
The value of angle O is equal to 105°
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Bella is going back to school shopping and her favorite store is having a sale. She sees there are 4 packages of 15 tops for $18 and 5 packages of 10 tops for $16 which is the better deal? How do you know
Answer:
The 4 packages of 15 tops for $18 is a better deal
Step-by-step explanation:
We can see which set of tops have the lowest unit price.
4 packages of 15 tops for $18:
4*15=60
There is a total of 60 tops for $18, which means each top costs 18/60 dollars, or $0.30.
5 packages of 10 tops for $16
5*10=50
There is a total of 50 tops for $16, which means that each top costs 16/50 dollars, or $0.32.
0.32>0.3
The 4 packages of 15 tops for $18 is a better deal :)
Have a great day
Factor this polynomial expression, and wrote it in its fully factored form 3x^3 + 3x^2 - 18x
Answer:
3x (x - 2) (x + 3)
Answer 4
Hope this helps :)
A shoe salesperson earns a 5% bonus on weekly sales over $3,000. Consider these functions to answer the following questions. f(x) = x – 3,000 g(x) = 0.05x Part A In your own words, explain what each of the functions represents.
Answer:
g(x)= 0.05x represents the amount of bonus, f(x)=x-3,000 represents weekly sales over $3,000.
Step-by-step explanation:
The function f(x) represents how much money earned by sales person weekly over $3000.
And function g(x) represents the amount of bonus earned by salesperson.
What is function?An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable) is called function.
According to the given question.
The percent of bonus earned by salesperson weekly on sales over $3,000 is 5%.
Also, we have two functions.
[tex]f(x) = x - 3000[/tex]
and [tex]g(x) = 0.05x[/tex]
For the function, f(x) if x is the amount of money earned salesperson in a week, then f(x) will represents how much money salesperson earned apart form $3000.
And the function g(x) represents the amount of bonus earned by the salesperson.
Hence, the function f(x) represents how much money earned by sales person weekly over $3000. And function g(x) represents the amount of bonus earned by salesperson.
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Hi, I don't know how to do these, if you could help me answer them, that would be great
Answer:
137°Step-by-step explanation:
From the diagram, mAD lies on the line BDF. Sum of angle on a straight line is 180°. According to the line BDF; mAB + mAD = 180°
From the diagram, mAB = 43°. Substituting this value into the above equation;
mAB + mAD = 180°
43° + mAD = 180°
mAD = 180°-43°
mAD = 137°
Hence, the measure of angle mAD is 137°
Consider the two functions. Which statement is true?
A)Function 1 has a greater rate of change by 13/4
B)Function 2 has a greater rate of change by 13/4
C)Function 1 has a greater rate of change by 13/2
D)Function 2 has a greater rate of change by 13/2
Answer: Function 2 has a greater rate of change by 13/4
Step-by-step explanation:
We must work with linear equations, remember that the general shape is:
y = a*x + b
where a is the slope and b is the y-intercept.
Ok, first we want to find the rate of change (or the slope) of the graphed line:
We know that for a line that passes through the points (x1, y1) and (x2, y2)
The slope is:
a = (y2 - y1)/(x2 - x1)
Then for the graphed function, we can see that it passes through the points:
(0, -2) and (4, 0)
Then the slope is:
a = (0 -(-2))/(4 - 0) = 2/4 = 1/2
Now, the slope of the second line is 15/4.
Let's calculate the difference between the slopes:
15/4 - 1/2 = 15/4 - 2/4 = 13/4
(notice that we are calculating slope2 - slope1)
Then the correct option is:
Function 2 has a greater rate of change by 13/4
Answer:
B) Function 2 has a greater rate of change by 13/4
Step-by-step explanation:
2
What is the solution of the equation 6x - 3 = -51?
A. -9
B. -8
c. 8.
D. 9
Answer:
x = -8
Step-by-step explanation:
6x - 3 = -51
Add 3 to each side
6x - 3+3 = -51+3
6x = -48
Divide each side by 6
6x/6 = -48/6
x = -8
URGENT!!! Please help me with this question!!!
Answer:
Step-by-step explanation:
The inscribed angle intersects an arc that is half the measure of the of the arc intersected by the central angle. The inscribed angle's arc measures 36%, and the central angle's arc measure 72%
Answer:
75
%Step-by-step explanation:
The inscribed angle intersects an arc that is half the measure of the of the arc intersected by the central angle.
Maximize the objective function P = 2x + 1.5y for the feasible region shown. State the maximum value for P and the ordered pair at which the maximum value occurs.
Incomplete question. However, let's assume this are feasible regions to consider:
Points:
- (0, 100)
- (0, 125)
- (0, 325)
- (1, 200)
Answer:
Maximum value occurs at 325 at the point (0, 325)
Step-by-step explanation:
Remember, we substitute the points value for x, y in the objective function P = 2x + 1.5y.
- For point (0, 100): P= 2(0) + 1.5 (100) =150
- For point (0, 125): P= 2(0) + 1.5 (125) =187.5
For point (0, 325): P= 2(0) + 1.5 (325) = 487.5
For point (1, 200): P= 2(1) + 1.5 (200) = 302
Therefore, we could notice from the above solutions that at point (0,325) we attain the maximum value of P.
18. In a recent survey, 75% of the community favored building a police substation in their neighborhood. If 10 citizens are chosen, find the probability that exactly 8 of them favor the building of the police substation.
Answer: 0.28157
Step-by-step explanation:
Given, The proportion of the community favored building a police substation in their neighborhood: p= 0.75
Number of citizens are chosen: n= 10
Let x be the binomial variable that represents the number of citizens favor the building of the police substation.
Then, the probability that exactly 8 of them favor the building of the police substation will be :
[tex]P(x=8)=\ ^{10}C_8(0.75)^8(1-0.75)^2[/tex]
[Using binomial probability function [tex]P(X=x)=^nC_xp^x(1-p)^{n-x}[/tex]]
[tex]=\dfrac{10!}{8!2!}(0.100113)(0.0625)\\\\=0.2815678125\approx0.28157[/tex]
Hence, the probability that exactly 8 of them favor the building of the police substation =0.28157