Given a= -3, b= 4 and c= -5, evaluate ab + C.
-4
-17
07
Answer:
a= -3, b= 4 and c= -5
ab + c = (-3)4+(-5) = -12 -5 = -17
Answer:
answer is -17
Step-by-step explanation:
all you have to do for this question is to plug the values for a, b, and c in the question.
ab + c would be
(-3)*4+(-5)
-12+(-5)
= -17
therefore the answer is -17
In triangle ABC, a=7, b=3 and cos C = 1/2. The value of c is
1. Sqrt 8
2. Sqrt 37
3. Sqrt 27
4. 4
Answer:
Correct option: 2 -> sqrt(37)
Step-by-step explanation:
To solve this problem, we just need to use the law of cosines. This law is used to find the third side of a triangle, when we have the two other sides and the angle between them.
The equation of the law of cosines is:
c^2 = a^2 + b^2 - 2 * a * b * cos(C)
So, we have that:
c^2 = 7^2 + 3^2 - 2 * 7 * 3 * (1/2)
c^2 = 49 + 9 - 21
c^2 = 37
c = sqrt(37)
Correct option: 2
How many different pairs of regular polygons can be made with 16 toothpicks? WILL MARK BRAINLIEST 35 POINTS!
Answer:
6
Step-by-step explanation:
We can make:
A 3 sided shape and a 13 sided shape (3 + 13 = 16)
A 4 sided shape and a 12 sided shape (4 + 12 = 16)
A 5 sided shape and an 11 sided shape
A 6 sided shape and a 10 sided shape
A 7 sided shape and a 9 sided shape
2 8 sided shapes
Therefore the answer is 6.
Please help quickly
Answer:
Step-by-step explanation:
-0.75 + 0.4 + 0.4 - 0.75
-1.50 + 0.8
-0.70
what is 9y5−4y3−8y7−5y6+3y4 written in standard form?
Answer:
-8y^7 - 5y^6 + 9y^5 + 3y^4 - 4y^3
Step-by-step explanation:
Please be sure to use " ^ " to indicate exponentiation. Then,
your 9y5−4y3−8y7−5y6+3y4 becomes 9y^5 - 4y^3 - 8y^7 - 5y^6 + 3y^4.
We must now write that in descending order by powers of y:
-8y^7 - 5y^6 + 9y^5 + 3y^4 - 4y^3
Which is the graph of 3x – 4y = 6?
Answer:
D
Step-by-step explanation:
3x-4y=6
-4y=-3x+6
y=(3/4)x-(3/2)
positive slope with y-intercept at -3/2 corresponds to D
Graph includes the points (0,-3/2) and (2,0). Therefore, option D is the correct answer.
What is the graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter.
The given linear equation is 3x-4y=6
Graph the line using the slope and y-intercept, or two points.
Slope: 3/4
y-intercept:
(0,-3/2)
Plot the points (0,-3/2) and (2,0)
Therefore, option D is the correct answer.
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Explain how you can use the inscribed angle theorem to justify its second corollary, that an angle inscribed in a semicircle is a right angle
Step-by-step explanation:
Explanation:
An inscribed angle is an angle formed by two chords in a circle which have a common endpoint. This common endpoint forms the vertex of the inscribed angle. The other two endpoints define what we call an intercepted arc on the circle. The intercepted arc might be thought of as the part of the circle which is "inside" the inscribed angle. (See the pink part of the circle in the picture above.)
A central angle is any angle whose vertex is located at the center of a circle. A central angle necessarily passes through two points on the circle, which in turn divide the circle into two arcs: a major arc and a minor arc. The minor arc is the smaller of the two arcs, while the major arc is the bigger. We define the arc angle to be the measure of the central angle which intercepts it.
The Inscribed Angle Conjecture I gives the relationship between the measures of an inscribed angle and the intercepted arc angle. It says that the measure of the intercepted arc is twice that of the inscribed angle.
The precise statements of the conjectures are given below. Each conjecture has a linked Sketch Pad demonstration to illustrate its truth (proof by Geometer's Sketch Pad!). The linked activities sheet also include directions for further "hands on" investigations involving these conjectures, as well as geometric problems which utilize their results.
The precise statement of the conjectures:
Conjecture (Inscribed Angles Conjecture I ): In a circle, the measure of an inscribed angle is half the measure of the central angle with the same intercepted arc..

Corollary (Inscribed Angles Conjecture II ): In a circle, two inscribed angles with the same intercepted arc are congruent.

Proof: The measure of each inscribed angle is exactly half the measure of its intercepted arc. Since they have the same intercepted arc, they have the same measure.
Corollary (Inscribed Angles Conjecture III ): Any angle inscribed in a semi-circle is a right angle.

Proof: The intercepted arc for an angle inscribed in a semi-circle is 180 degrees. Therefore the measure of the angle must be half of 180, or 90 degrees. In other words, the angle is a right angle.
Can anyone solve this?
Answer:
[tex]x= \frac{20}{3}[/tex]
Step-by-step explanation:
Set up the equation
[tex]\frac{15}{10} =\frac{10}{x}[/tex]
and cross multiply to solve for x.
AB is a diameter of circle C. What is the degree measure of x?
using SOH CAH TOA, solve for x.
Answer:
x=10.93 or 10.9
Step-by-step explanation:
To find x we use sin
sin(40) = 0.6427876097 then * 17
= 10.9273
= 11
We can check and plug in answer as inverse to find other side
11/sin (40degree) x (90 degree) = 17.11
If we plug in the original 10.9273 we actually find 17
So we should show the correct amount 10.9273 and if rounding try 10.93
10.93/sin (40 degree) x sin (90 degree) = 17.00
URGENTTT!!!!! Which of the following graphed relations does not represent a function?
Answer:
D
Step-by-step explanation:
last one.
if a vertical line cuts the curve at more than one points ,then it is not a function.
Answer:
I agree that it is D
Step-by-step explanation:
Can someone help me with this ASAP please and thank you
Answer:
C
Step-by-step explanation:
Triangles will only be right triangles if a² + b² = c² where a and b are legs and c is hypotenuse. Numbers 1 and 2 pass this test so the answer is c.
Answer:
C. I and IV only
Step-by-step explanation:
Apply the Pythagorean theorem to all triangles, and see which ones make the equation true.
I.
8^2 + 15^2 = 64 + 225 = 289
17^2 = 289
289 = 289
Right Triangle
II.
4^2 + 5^2 = 16 + 25 = 41
6^2 = 36
41 is not equal to 36
Not a Right Triangle
III.
2^2 + 2^2 = 4 + 4 = 8
3^2 = 9
8 is not equal to 9
Not a Right Triangle
IV.
9^2 + 12^2 = 81 + 144 = 225
15^2 = 225
225 = 225
Right Triangle
Answer: C. I and IV only
12.
What is the solution of the equation x2 + 2x - 7 = 0?
Answer:
cancel out as much of the equation as possible by doing inverse operations so add the 7 to both sides
x2 + 2x = 7
Divide by 2
x2 = 3.5
divide by 2 again
x = 1.75
now change x with 1.75 to check
1.75 x 2 = 3.5
3.5 + 3.5 - 7 = 0 so 1.75 is correct
Hope this helps
Step-by-step explanation:
If two events. A and B, are independent then which of the following is always true about their probabilities?
1) P(A)=P(B)
2) P(A and B)=P(A) P(B)
3) P(A OR B)=P(A) P(B) - P(A and B)
4) P(A and B) = P(A) +P(B)
Answer:
P(A and B)= p(A) * P(B)
Step-by-step explanation:
The Formula for the probability of A and B (independent events) is
p(A and B) = p(A) * p(B).
The perpendicular line which of the following equations represents the line that passes through the point 1,-1
Answer:
The answer is the letter A
which of the following is not a possible r-value -0.3 -1.6 0.8 0.3
Answer: -1.6 is not a possible r-value.
Step-by-step explanation:
R-values range from -1 to +1. Out of all these numbers, -1.6 does not belong. Hence, -1.6 is not a r-value.
Evaluate \sqrt{-75s}
−75s
square root of, minus, 75, s, end square root where s = -3s=−3s, equals, minus, 3.
Answer:
Step-by-step explanation:
the answer is 15!
The square root of the number -√75 will be -3√5.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
The square root of the number will be calculated as below:-
-√75 = - √( 3 x 3 x 5 )
= -3√5
Therefore, the square root of the number -√75 will be -3√5.
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Which of the following relations is a function? A.{(0,2),(1,2),(2,2),(3,2)} B.{(2,0),(2,1),(2,2),(2,3)} C.{(3,5) ,(4,7),(5,9),(5,11)} D. {(4,5),(6,7),(8,9),(8,11)}
Answer:
the answer is A
Step-by-step explanation:
What is the slope-intercept equation of this line?
Answer:
A. y=-3x+4
Step-by-step explanation:
Since the equation is in y=mx+b form, m represents the slope of a line. To solve for slope-intercept, use the equation m=(y2-x2)/(y1-x1).
[tex]m=\frac{-2-4}{2-0}[/tex]
[tex]m=\frac{-6}{2}[/tex]
[tex]m=-3[/tex]
Make sure to plug in one of the points into the equation to check if the numbers equal to one another or not.
What are the lines in the picture parallel ?
A. They both lie in the same plane
B. They both travel on forever and ever
C. They are both the same size
D. They are equal width apart, travel in the same direction, and never meet.
Please help me with this
The lines in the picture parallel because they are equal width apart , option (D) is correct.
What are parallel lines?Two straight lines in a plane such that even on getting extend till infinity they do not intersect each other and always at same distance from each other .
In the given picture the red line and black lines appears to have same distance between them .They are parallel not only because they are coplanar as coplanar lines can intersect each other.
Two lines travelling to infinity need not to be parallel always as they can intersect at some point and still travel to infinity.
If two lines of same size are there still they can have different perpendicular distance between them at diff points, they can be slightly tilted towards each other . Therefore they need not be parallel when they are of same size. And given lines are infinite therefore we cannot say that they are of same size also.
If two lines are equal width apart and never meet then it means the distance between them is always same therefore they are parallel,
Therefore, the lines in the picture are parallel because they are equal width apart option (d) is correct.
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The graph below shows the distance in miles, m, hiked from a camp in h hours.
Which hourly interval had the greatest rate of change?
1) hour 0 to hour 1
3) hour 2 to hour 3
2) hour 1 to hour 2
4) hour 3 to hour 4
Answer:
Option 1) is correct
Step-by-step explanation:
Given: The graph shows the distance in miles, m, hiked from a camp in h hours.
To find: hourly interval that had the greatest rate of change
Solution:
Rate of change between two points refers to the vertical change divided by the horizontal change.
For hour 0 to hour 1:
rate of change = [tex]\frac{2-0}{1-0}=2[/tex]
For hour 2 to hour 3:
rate of change = [tex]\frac{4.5-3.5}{3-2}=1[/tex]
For hour 1 to hour 2:
rate of change = [tex]\frac{3.5-2}{2-1}=1.5[/tex]
For hour 3 to hour 4:
rate of change = [tex]\frac{5-4.5}{4-3}=0.5[/tex]
So, rate of change is greatest in interval: hour 0 to hour 1
The greatest rate of change between the interval 0 to 1 hour.
Given that,
The graph below shows the distance in miles, m, hiked from a camp in h hours.
We have to determine,
Which hourly interval had the greatest rate of change?
According to the question,
The greatest rate of change between the interval is determined by the rate of change between two points refers to the vertical change divided by the horizontal change.
1. The rate of change between 0 to 1 hours is,
[tex]\rm Rate \ of \ change = \dfrac{2-0}{1-0}\\\\ Rate \ of \ change= \dfrac{2}{1}\\\\ Rate \ of \ change= 2[/tex]
The rate of change between 0 to 1 hour is 2.
2. The rate of change between 2 to 3 hours is,
[tex]\rm Rate \ of \ change = \dfrac{4.5-3.5}{3-2}\\\\ Rate \ of \ change= \dfrac{1}{1}\\\\ Rate \ of \ change= 1[/tex]
The rate of change between 2 to 3 hours is 1.
3. The rate of change between 1 to 2 hours is,
[tex]\rm Rate \ of \ change = \dfrac{3.5-2}{2-1}\\\\ Rate \ of \ change= \dfrac{1.5}{1}\\\\ Rate \ of \ change= 1.5[/tex]
The rate of change between 1 to 2 hours is 1.5.
4. The rate of change between 3 to 4 hours is,
[tex]\rm Rate \ of \ change = \dfrac{5-4.5}{4-3}\\\\ Rate \ of \ change= \dfrac{0.5}{1}\\\\ Rate \ of \ change= 0.5[/tex]
The rate of change between 2 to 3 hours is 1.
Hence, The required greatest rate of change between the interval 0 to 1 hour.
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There are twice as many students in the cooking club as in the drama club. Suppose there are $a$ students in the drama club and $b$ students who are members of both clubs. Find an expression for the total number of students who are in the cooking club or the drama club but not both. Give your answer in simplest form.
Answer:
Total Students = 3a - 2b
Step-by-step explanation:
Given
Students in drama club = a
There are twice as many students in cooking club as in drama club;
So, Students in cooking club = 2a
Members of both clubs = b
Required
Expression for total students in cooking or drama club but not both;
To do this, number of students in individual clubs need to be calculated;
Let Students in drama club only be represented by D and Students in cooking club only be represented by C
So,
D = Students in drama club - Members of both clubs
D = a - b
Similarly,
C = Students in cooking club - Members of both clubs
C = 2a - b
So, total students in cooking or drama club but not both D + C
Total students = a - b + 2a - b
Collect like terms
Total Students = a + 2a - b - b
Total Students = 3a - 2b
Not a test just that. ? Is throwing me off after 25x what does that mean genuinely confused
Answer:
For addition and subtraction, use the standard + and - symbols respectively. For multiplication, use the * symbol. A * symbol is not necessary when multiplying a number by a variable. For instance: 2 * x can also be entered as 2x. Similarly, 2 * (x + 5) can also be entered as 2(x + 5); 2x * (5) can be entered as 2x(5). The * is also optional when multiplying with parentheses, example: (x + 1)(x - 1).
Step-by-step explanation:
Its right?
someone help please, summer school is annoying
Answer:
6
Step-by-step explanation:
2y/3 + 1/3 = y/2 + 1/6
We want to eliminate the fractions
The least common multiple of 3,2 and 6 is 6
Multiply each side by 6 to get rid of the fractions
6(2y/3 + 1/3) = 6(y/2 + 1/6)
4y +2 = 3y +1
Points are plotted at (-2, 2), (-2,4), and (2,-4). A fourth point is drawn such that the four points can be connected to form
a rectangle. What is the area of this rectangle?
8 square units
12 square units
16 square units
24 square units
The area is 24 square units
At the school the ratio of boys to girls is 5:3 if there are 385 boys in the school, how many students are there altogether?
Answer:
There are 616 total students
Step-by-step explanation:
boys : girls: total
5 3 5+3 = 8
There are 385 boys
385/5 = 77
Multiply each term by 77
boys : girls: total
5*77 3*77 8*77
385 539 616
There are 616 total students
Answer:
616 total students
Step-by-step explanation:
5 : 3
385 : x
5 x 77 : 3 x 77
385 : 231
385 + 231 = 616
Exponential function f is represented by the table.
x 0 1 2 3 4
f(x) 15 7 3 1 0
Function g is an exponential function passing through the points (0,9) and (3,0).
Which statement correctly compares the two functions?
A.
Both functions are decreasing on [0, 3], and function g is decreasing at a faster rate.
B.
Only function g is decreasing on [0, 3], and only function f is positive on that interval.
C.
Only function f is decreasing on [0, 3], and both functions are positive on that interval.
D.
Both functions are decreasing on [0, 3], and function f is decreasing at a faster rate.
Considering the given exponential functions, it is found that the correct statement is:
D. Both functions are decreasing on [0, 3], and function f is decreasing at a faster rate.
What is the behavior of each exponential function?For function f, we have that it is decreasing, as it is greater at x = 0 than at x = 4, and it decreases by an average of 3.75 units when the input changes by 1.For function g, we also have that it is decreasing, as as it is greater at x = 0 than at x = 3, and it decreases by an average of 3 units when the input changes by 1.Hence option D is correct.
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Which equations are true?
Choose all answers that apply:
Ⓐ 0 = 0+1-2
Ⓑ 0=(-2)-(-2) +0
Ⓒ None of the above
Answer:
B
Step-by-step explanation:
A is false. 0 + 1 - 2 = -1, not 0.
B is true.
(-2)-(-2) +0
= -2 + 2 + 0
= 0
C is false, since B is true.
Equation B 0=(-2)-(-2) +0 is true, which is simplified by subtraction.
What is the equation?The equation is defined as a mathematical statement that has a minimum of two terms containing variables or numbers that are equal.
For equation A:
0 = 0+1-2
We can simplify the right-hand side of the equation by combining like terms:
0 = -1
This is not true, so we might be tempted to say that equation A is false.
For equation B:
0 = (-2)-(-2) + 0
We can simplify the right-hand side of the equation by performing the subtraction:
0 = 0 + 0 + 0
This simplifies to:
0 = 0
This equation is true.
Therefore, equation B is true.
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A roll of gift-wrapping paper can cover 232.2 sq. in. Jimmy wants to wrap a soccer ball that he is giving as a gift. What is the maximum radius of the ball that Jimmy can wrap? Use 3.14 for π.
a. 3.8
b. 4.3
c. 9.2
d. 18.5
Answer:
Radius, r = 3.8 inch
Step-by-step explanation:
A roll of gift-wrapping paper can cover 232.2 sq. in. Jimmy wants to wrap a soccer ball that he is giving as a gift.
We need to find the maximum radius of the ball that Jimmy can wrap. The volume of a spherical shaped object is given by :
[tex]V=\dfrac{4}{3}\pi r^3[/tex]
r = radius of the ball
[tex]r=(\dfrac{3V}{4\pi})^{1/3}\\\\r=(\dfrac{3\times 232.2}{4\times 3.14})^{1/3}\\\\r=3.8\ \text{inch}[/tex]
So, the maximum radius of the ball that Jimmy can wrap is 3.8 inches. Hence, this is the required solution.
The maximum radius of the ball that Jimmy can wrap is 3.8 inches.
Maximum radius of the ball
The maximum radius of the ball is calculated from volume of a sphere.
V = ⁴/₃πr³
where;
r is radius of the spherical ball232.2 = ⁴/₃πr³
3(232.2) = 4πr³
696.6 = 4πr³
r³ = 696.6/4π
r³ = 55.433
r = (55.433)^¹/₃
r = 3.8 in
Thus, the maximum radius of the ball that Jimmy can wrap is 3.8 inches.
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Can someone please help me with this??
Answer: (x,y)=(-2/3,15)
Negative 2 over three
