Answer:
The approximate difference between m∠C and m∠A is 45° to the nearest degree
Step-by-step explanation:
* Lets talk about the right triangle
- It has one right angle and two acute angles
- The side opposite the the right angle is called hypotenuse
- The other sides are called the legs of the right angle
- In ΔABC
∵ AC is the hypotenuse
∴ ∠B is the right angle
∴ AB and BC are the legs of the right angle
∴ Angles A and C are the acute angles
∵ m∠B = 90°
- The sum of the measures of the interior angles of a Δ is 180°
∴ m∠A + m∠C = 180° - 90° = 90°
- We will use trigonometry to find the measures of angles A and C
- sin A is the ratio between the opposite side to angle ∠A and the
hypotenuse
∵ BC is the opposite side of angle A
∴ sin A = BC/AC
∵ BC = 5 cm
∵ AC = 13 cm
∴ sin A = 5/13
- Lets find m∠∠A by using sin ^-1
∴ m∠A = [tex]sin^{-1}\frac{5}{13}=22.62[/tex]
- Lets use the rule of the sum of angles A and C to find the measure
of the angle C
∵ m∠A + m∠C = 90°
∴ 22.62° + m∠C = 90 ⇒ subtract 22.62 from both sides
∴ m∠C = 67.38°
- Lets find the difference between m∠C and m∠A
∴ The approximate difference between m∠C and m∠A is:
67.38° - 22.62° = 44.78° ≅ 45° to the nearest degree
What is linear equation?
What is quadratic equation?
Final answer:
A linear equation represents a straight line and is written in the form y = mx + b. A quadratic equation represents a parabolic curve and is written in the form y = ax² + bx + c.
Explanation:
A linear equation is an equation that represents a straight line when graphed. It is typically written in the form y = mx + b, where m is the slope of the line and b is the y-intercept. The slope describes the rate of change between the independent and dependent variables, while the y-intercept is the point where the graph crosses the y-axis.
On the other hand, a quadratic equation is an equation that represents a parabolic curve when graphed. It is typically written in the form y = ax² + bx + c, where a, b, and c are constants. The graph of a quadratic equation is symmetric around a vertical line called the axis of symmetry, and it has either a maximum point or a minimum point.
Which polynomial function has a leading coefficient of 3 and roots -4,1, and 2, all with multiplicity 1?
Of(x) = 3(x + 4)(x - 1)(x - 2)
Of(x) = (x - 3)(x + 4)(x-7)(x-2)
Of(x) = (x − 3)(x + 4)(x - 1)(x + 1)(x - 2)
Of(x) = 3(x + 4)(x - 1)(x + 1)(x - 2)
For this case, we can discard options B and C because they do not have coefficients. Also, we discard option D because it has 4 roots given by -4.1, -1,2 each with multiplicity "1".
The multiplicity indicates the number of times a root is repeated.
Then, we have that the correct option is option A, we have a coefficient of "3", in addition to three roots (-4,1,2) with multiplicity "1", because they only repeat once.
Answer:
Option A
Answer: A
Step-by-step explanation:
PLEASE I NEED HELP AGAIN ATTACHMENT BELOW
Answer:
A.) 1/81
Step-by-step explanation:
This is your equation:
f(x) = 9^x
They want you to solve for x = -2, so substitute -2 in for x.
f(-2) = 9^-2
When you solve this, you get, 1/81.
So, the answer is A.)
I hope this helps! :)
Help pls !! A survey asked students wether they have any siblings and pets
Answer:
The correct answer option is B. 60%.
Step-by-step explanation:
We are given the results of a survey which asked the students whether they have any siblings and pets.
We are to determine the likelihood that student has a pet, given that he or she does not have a sibling.
Assuming A to be the event showing that a student does not have a sibling and B to be the event that a students has a pet.
Then P(B|A) is:
[tex]P(B|A)=\dfrac{P(A\bigcap B)}{P(A)}[/tex]
Substituting the given values, P(A)=0.25 and P(A∩B)=0.15:
[tex]P(B|A)=\dfrac{0.15}{0.25}\\\\P(B|A)=\dfrac{3}{5}\\\\P(B|A)=0.6[/tex]
So the percentage will be:
[tex]0.6\times 100 = [/tex] 60%
what is the quotient 2y^-6y-20/4y+12 ÷ y+5y+6/3y^2+28y+27
Answer with explanation:
[tex]\rightarrow \frac{\frac{2y^2-6 y-20}{4 y+12}}{\frac{y^2+5 y+6}{3 y^2+28 y+27}}\\\\\rightarrow \frac{\frac{y^2-3y-10}{2 y+6}}{\frac{(y+2)(y+3)}{3 y^2+28 y+27}}\\\\\rightarrow \frac{\frac{(y-5)(y+2)}{2 (y+3)}}{\frac{(y+2)(y+3)}{3 y^2+28 y+27}}\\\\\rightarrow \frac{(y-5)(y+2)}{2 (y+3)}} \times {\frac{3 y^2+28 y+27}{(y+2)(y+3)}}\\\\ \rightarrow\frac{(y-5)\times(3 y^2+28 y+27)}{2 (y+3)^2}}[/tex]
→y²+5y+6
=y²+3 y+2 y+6
=y×(y+3)+2×(y+3)
=(y+2)(y+3)
→y² -3 y-10
=y² -5 y+2 y -10
=y×(y-5)+2×(y-5)
=(y+2)(y-5)
Answer:
B. 3(y-5)/2 on edge
Step-by-step explanation:
There are 162 people waiting in line to ride a roller coaster when the line closes for the day. Each roller coaster car holds 12 people. After loading c cars on the roller coaster, there are 6 people still in line. Write an equation to represent the number of cars, c, that have been loaded on the roller coaster. Solve the equation to find the number of cars on the roller coaster.
Answer:
13 Cars Have Been Loaded, Equation: 12x + 6 = 162
Step-by-step explanation:
If a car holds 12 people, and there are 162 people waiting divide 162 by 12. This gives you 13.5, which means that 13 total cars have been loaded, while .5 or 6 are left waiting on the line. So 13!
Answer:
162
Step-by-step explanation:
ADD EMMM UPPP GIRLLLLLGET IT TOGETHER
In which direction would you progress in order to find the terminal quadrant of a -400 degree angle?
Clockwise
Counterclockwise
Both
Neither
Answer:
negative angles are clockwise
Step-by-step explanation:
negative angel: An angle whose generating line is rotated clockwise.
hope this helps!!
Clockwise and counterclockwise are used to indicate the direction of an angle.
The terminal quadrant of -400 degrees is in the clockwise direction
The angle is given as:
[tex]\mathbf{\theta = -400^o}[/tex]
The condition for clockwise direction is: [tex]\mathbf{\theta < 0}[/tex]
While the condition for counterclockwise direction is:[tex]\mathbf{\theta > 0}[/tex]
By comparison:
[tex]\mathbf{-400 < 0}[/tex]
Hence, the terminal quadrant of -400 degrees is in a clockwise direction
Read more about terminal quadrants at:
https://brainly.com/question/15533872
Find the solution of this system of equations.
Separate the x- and y-values with a comma.
x - 4y = -22
x- y=-10
Enter the correct answer.
DONE
Answer:
{-6,4}
Step-by-step explanation:
Given
x-4y=-22 Eqn 1
x-y=-10 Eqn 2
Subtracting both equations:
The left hand side of equation 2 will be subtracted from left hand side of eqn 1 and the right side of equation 2 will be subtracted from right hand side of eqn 1.
[tex](x-4y)-(x-y)=-22-(-10)\\x-4y-x+y=-22+10\\-4y+y=-12\\-3y=-12\\\frac{-3y}{-3}=\frac{-12}{-3}\\ y=4[/tex]
Putting y=4 in eqn 2
[tex]x-4=-10\\x=-10+4\\x=-6\\So,\\Solution Set = \{-6,4\}[/tex]
Answer:
{x, y} = {-6, 4}
Step-by-step explanation:
It is given that,
x - 4y = -22 ------(1)
x - y= -10 -------(2)
To ind the value of x and y
subtract eq(2) from eq(1)
x - 4y = -22 ------(1)
x - y= -10 -------(2)
0 -3y = -12
3y = 12
y = 12/3 = 4
Substitute the value of y in eq (1)
x - 4y = -22 ------(1)
x - (4*4) = -22
x - 16 = -22
x = -22 +16 = -6
Therefore {x, y} = {-6, 4}
The quotient of two numbers is negative. What must be true about the two numbers?
If the quotient of two numbers is negative, it means that the result of dividing one number by the other is negative.
This situation can only occur if the two numbers have opposite signs. In other words, one number must be positive, and the other must be negative.
When we divide a positive number by a negative number or a negative number by a positive number, the resulting quotient will always be negative. So, to satisfy the given condition, the two numbers must have opposite signs—one positive and one negative.
Therefore, If the quotient of two numbers is negative, it means that the result of dividing one number by the other is negative.
Learn more about quotient here
https://brainly.com/question/13489082
#SPJ6
Final answer:
For the quotient of two numbers to be negative, one of the numbers must be positive and the other must be negative. This principle follows the general rules for multiplication and division involving signed numbers.
Explanation:
For a quotient of two numbers to be negative, one number must be positive and the other negative. This rule aligns with the multiplication and division rules for signs, whereby the product or quotient of two numbers with opposite signs results in a negative outcome.
Essentially, this can be understood by considering examples of multiplication, such as (-3) x 2 = -6 and 4 x (-4) = -16, which similarly apply to division. The same principle holds when dividing two numbers; if their signs are opposite, the result is negative.
This mathematical rule is fundamental and applies universally across mathematics, ensuring consistency in the calculation and understanding of operations involving signed numbers.
If x + y = 12 and xy = -5, calculate the value of 1/x + 1/y.
[tex]\dfrac{1}{x}+\dfrac{1}{y}=\dfrac{y}{xy}+\dfrac{x}{xy}=\dfrac{x+y}{xy}=\dfrac{12}{-5}=-\dfrac{12}{5}=-2,4[/tex]
(08.03)
Given the geometric sequence where a1 = 4 and the common ratio is 3, what is the domain for n?
Answer:
Domain of a geometric or arithmetic sequence is the counting numbers unless otherwise noted.
Answer: Set of Natural numbers.
Step-by-step explanation:
We know that the domain of a function is the set of all values for x for which the function must be defined.
The domain of the geometric sequence is always the set of natural numbers , since each term has a particular position in the sequence according to an order which can only represent by natural numbers.
Hence, the domain for the given geometric sequence = Set of natural numbers.
What is the prime factorization of 440?
2 3 · 5 · 9
2 3 · 3 2 · 5
2 · 4 · 5 · 11
2 3 · 5 · 11
Answer:
I would say the correct answer is 2^3 • 5 • 11
Step-by-step explanation:
To find the prime factors, you start by dividing the number by the first prime number, which is 2. If there is not a remainder, meaning you can divide evenly, then 2 is a factor of the number. Continue dividing by 2 until you cannot divide evenly anymore. Write down how many 2's you were able to divide by evenly. Now try dividing by the next prime factor, which is 3. The goal is to get to a quotient of 1.Here are the first several prime factors: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29...
Let's start by dividing 440 by 2
440 ÷ 2 = 220 - No remainder! 2 is one of the factors!
220 ÷ 2 = 110 - No remainder! 2 is one of the factors!
110 ÷ 2 = 55 - No remainder! 2 is one of the factors!
55 ÷ 2 = 27.5 - There is a remainder. We can't divide by 2 even anymore. Let's try the next prime number
55 ÷ 3 = 18.3333 - This has a remainder. 3 is not a factor.
55 ÷ 5 = 11 - No remainder! 5 is one of the factors!
11 ÷ 5 = 2.2 -There is a remainder. We can't divide by 5 evenly anymore. Let's try the next prime number
11 ÷ 7 = 1.5714 - This has a remainder. 7 is not a factor.
11 ÷ 11 = 1 - No remainder! 11 is one of the factors!
If we put all of it together we have the factors 2 x 2 x 2 x 5 x 11 = 440. It can also be written in exponential form as 2^3 x 5^1 x 11^1.
here is also the factor tree method : -
Which is the value of this expression when a=5 and k=-2
Answer:
Option C is correct.
Step-by-step explanation:
We are given the expression:
[tex](\frac{3^2a^{-2}}{3a^{-1}})^k[/tex]
The value of a =5 and k = -2
Putting the values and solving
[tex]=(\frac{3^2*5^{-2}}{3*5^{-1}})^-2\\=(\frac{3^{2-1}}{5^{-1+2}})^-2\\=(\frac{3^{1}}{5^{1}})^-2\\\\=(\frac{3}{5})^-2\\if \,\,a^{-1} \,\,then\,\, 1/a\\=\frac{(3)^{-2}}{(5)^{-2}}\\ Can\,\,be\,\,written\,\,as\\\\=\frac{(5)^{2}}{(3)^{2}} \\=\frac{25}{9}[/tex]
Option C is correct.
The graph shown here is the graph of which of the following rational functions?
Answer:
there is no graph
Step-by-step explanation:
Simplify. x-2/x^2+4x-12
a. 1/x+6; where x= -6
b. 1/x+6; where x= -6, 3
c. 1/x+2; where x= -2
d. x+2
[tex]\bf \cfrac{x-2}{x^2+4x-12}\implies \cfrac{\begin{matrix} x-2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix} }{(x+6)~~\begin{matrix} (x-2) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}\implies \cfrac{1}{x+6}\qquad \{x|x\in \mathbb{R};x\ne 2,x\ne -6\}[/tex]
2x+5y=20 select the ordered pair that is a solution to the equation
Answer:
The ordered pair that is a solution to the equation (5, 2)
Step-by-step explanation:
It is given that,
2x + 5y = 20
To find the ordered pairs
Multiples of 2 are,
2, 4, 6, 8, 10, 12....
Multiples of 5 are,
5, 10, 15, 20,...
20 can be written as,
20 = 2x + 5y
2x is the multiple of 2 and 5y is the multiple of 5
From the above data we get, 20 = 10 + 10
2x = 10 then x = 5
5y = 10 then y = 2
Therefore the ordered pair that is a solution to the equation (5, 2)
Final answer:
To determine if an ordered pair is a solution to the equation 2x + 5y = 20, substitute the values into the equation and check if the simplified result equals 20.
Explanation:
To find an ordered pair that is a solution to the equation 2x + 5y = 20, we need to check which pair (x, y) satisfies the equation when we substitute the values of x and y into it. This involves basic algebraic skills, including substitution and simplification.
Step-by-Step Explanation
Select a potential ordered pair solution.Substitute the x-value and the y-value into the equation.Simplify to see if the values satisfy the equation and make it true.If the left side of the equation equals the right side after substitution, then the ordered pair is a solution to the equation. For example, if we substitute x = 2 and y = 4, we get 2(2) + 5(4) = 20 which simplifies to 4 + 20 = 24, not equal to 20. Thus, (2,4) is not a solution. Find an ordered pair where, after the substitution and simplification, the equation is satisfied.
How do I solve for x ?
Answer:
x=30
Step-by-step explanation:
The two angles form a straight line
4x+2x = 180
6x= 180
Divide each side by 6
6x/6 = 180/6
x = 30
Answer:
X=30
Step-by-step explanation:
the degree of a straight line is 180
Add 2x and 4x together = 6x
Then divide 6x = 180 by 6 to get the x value.
The answer is 30
What is this answer ?
Answer:
Step-by-step explanation:
A isn't. You have that right. A sinusoidal wave is one that creates a sine curve.
Absolute value curves look sort of like a spear head.
20p!!!ill mark you as brain please help!!! hurry
Answer:
[tex]\boxed{\text{1172 in}^{2}}[/tex]
Step-by-step explanation:
SA = SA(prism) + SA(cylinder) – 2SA(cylinder base)
1. Surface area of rectangular prism
The formula for the surface area of a rectangular prism is
S = 2(lw + lh + wh)
Data:
l = 16 in
w = 11 in
h = 11 in
Calculations:
2(Top + Bottom) = 2lw = 2 × 16 × 11 = 352 in²
2(Front + Back) = 2lh = 2 × 16 × 11 = 352 in²
2(Left + Right) = 2wh = 2 × 11 × 11 = 242 in²
Total area = 946 in²
2. Surface area of cylinder
A = A(top) + A (base) + A(side) = 2A(base) + A(side)
Data:
d = 8 in
h = 9 in
Calculations:
r = ½d = ½ × 8 = 4 in
[tex]\begin{array}{rcl}SA & = & 2\pi r^{2}+ 2\pi rh \\& = & 2 \times 3. 14\times 4^{2} +2\times 3. 14 \times 4\times 9\\& = & 6.28\times 16 + 226.08\\& = & 100.48 + 226.08\\& = & 326.56 \text{ in}^{2}\\\end{array}[/tex]
3. Excluded area
Excluded area = 2A(base) = 100.48 in²
4. Total area
[tex]A = 946 + 326.56 - 100.48 \approx \boxed{\textbf{1172 in}^{2}}[/tex]
What is the following quotient?
sqr root 6 + sqr root 11/ sqr root 5+ sqr root 3
Answer:
[tex]\frac{\sqrt{30}-3\sqrt{2}+\sqrt{55}-\sqrt{33} }{2}[/tex]
Step-by-step explanation:
The given expression is
[tex]\frac{\sqrt{6}+\sqrt{11}}{\sqrt{5}+\sqrt{3} }[/tex]
To solve this quotient, we just have to apply a rationalization, which consists in eliminating every root in the denominator. To do so, we multiply and divide the expression by the opposite binomial of the denominator, as follows
[tex]\frac{\sqrt{6}+\sqrt{11}}{\sqrt{5}+\sqrt{3} }=\frac{\sqrt{5}-\sqrt{3} }{\sqrt{5}-\sqrt{3} }\\\\\frac{(\sqrt{6}+\sqrt{11})(\sqrt{5}-\sqrt{3})}{(\sqrt{5}+\sqrt{3})(\sqrt{5}-\sqrt{3})}\\\\\frac{\sqrt{30}-\sqrt{18}+\sqrt{55}-\sqrt{33} }{5-3}\\ \\\frac{\sqrt{30}-3\sqrt{2}+\sqrt{55}-\sqrt{33} }{2}[/tex]
Therefore, the right answer is the second option.
A triangle has an area of 38.4 cm2. The
height of the triangle is 12.8 centimeters.
What is the length of the base of the
triangle?
Answer:
6cm
Step-by-step explanation:
[tex]A = \frac{h_b b}{2}[/tex]
[tex]38.4 = \frac{12.8_b b}{2}[/tex]
[tex]b = 2\frac{A}{h_b}[/tex]
[tex]b = 2\frac{38.4}{12.8}[/tex] = 6
The total space enclosed by the three boundaries of the triangle is called the area of the triangle.
The length of the base of the triangle is 6 cm.
GivenA triangle has an area of 38.4 cm2.
The height of the triangle is 12.8 centimeters.
What is the area of the triangle?The total surface or space enclosed by the three boundaries of the triangle is called the area of the triangle.
The formula to calculate the area of the triangle is given by;
[tex]\rm Area \ of \ the \ rectangle = \dfrac{1}{2} \times Base \times Height\\\\[/tex]
Substitute all the values in the formula;
[tex]\rm Area \ of \ the \ triangle= \dfrac{1}{2} \times Base \times Height\\\\\rm 38.4 = \dfrac{1}{2} \times Base \times 12.8\\\\ Base = \dfrac{38.4 \times 2}{12.8}\\\\Base = 3 \times 2\\\\Base = 6 \ cm[/tex]
Hence, the length of the base of the triangle is 6 cm.
To know more about the Area of the Triangle click the link given below.
https://brainly.com/question/21812978
Find the coordinates of point B that lies along the directed line segment from A(-5, 2) to C(11, 0) and partitions the segment in the ratio of 5:3.
A. (3, 1)
B. (5,3/4)
C. (10, 5)
D. (6, 2)
ANSWER
The correct answer is B.
EXPLANATION
If the point B(x,y) partitions
[tex]A(x_1,y_1)[/tex]
and
[tex]C(x_2,y_2)[/tex]
in the ratio m:n then, then we have
[tex]x = \frac{mx_2+nx_1}{m + n} [/tex]
and
[tex]y= \frac{my_2+ny_1}{m + n} [/tex]
We want to find the coordinates of the point B(x,y) that lies along the directed line segment from A(-5, 2) to C(11, 0) and partitions the segment in the ratio of 5:3.
This implies that:
[tex]x = \frac{5 \times 11+3 \times - 5}{5 + 3} [/tex]
[tex] \implies \: x = \frac{55 - 15}{8} [/tex]
[tex] \implies \: x = \frac{40}{8} = 5[/tex]
[tex]y = \frac{5 \times 0 + 3 \times 2}{5 + 3} [/tex]
[tex]y = \frac{0 + 6}{8} [/tex]
[tex]y = \frac{6}{8} = \frac{3}{4} [/tex]
Therefore the coordinates of B are
[tex](5, \frac{3}{4} )[/tex]
Answer:
B. (5,3/4)
Step-by-step explanation:
Since, when a segment having end points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is divided by or partitioned by a point, that lies on the segment, in the ratio of m : n,
Then the coordinates of that points are,
[tex](\frac{mx_2+nx_1}{m+n}, \frac{my_2+my_1}{m+n})[/tex]
Here, point B that lies along the directed line segment from A(-5, 2) to C(11, 0) and partitions the segment in the ratio of 5:3,
Thus, the coordinates of B are,
[tex](\frac{5\times 11+3\times -5}{5+3}, \frac{5\times 0+3\times 2}{5+3})[/tex]
[tex](\frac{55-15}{8}, \frac{0+6}{8})[/tex]
[tex](\frac{40}{8}, \frac{6}{8})[/tex]
[tex](5, \frac{3}{4})[/tex]
Option 'B' is correct.
The perimeter of a quadrilateral is 38 yards. If three of the sides measure 5.8 yards, 7 yards, and 11.2 yards, what is the length of the fourth side?
Answer:
14 yds
Step-by-step explanation:
To find the perimeter, we add up all the sides
P = s1 + s2+ s3 + s4
38 = 5.8+7+11.2 + s4
Combine like terms
38 = 24+s4
Subtract 24 from each side
38-24 = 24-24 +s4
14 = s4
The 4th side is 14 yds
Answer:
14yd
Step-by-step explanation:
Which functions C(x) represents the monthly cost in dollars in terms of x, the number of gigabytes used in a month
Answer:
The answer in the procedure
Step-by-step explanation:
Let
x ----> the number of gigabytes used in a month
C(x)------> the monthly cost in dollars
step 1
For the interval ----> [0,2]
[tex]0\leq x\leq 2[/tex]
[tex]C(x)=15[/tex]
step 2
For the interval ---->(2,6]
[tex]2< x\leq 6[/tex]
Find the equation of the line
Find the slope
we have
[tex](2,20),(6,40)[/tex]
[tex]m=(40-20)/(6-2)=5[/tex]
The equation of the line in to point slope form is equal to
[tex]y-20=5(x-2)\\ y=5x-10+20\\ y=5x+10[/tex]
therefore
[tex]C(x)=5x+10[/tex]
step 3
For the interval ----> (6,∞]
[tex]x> 6[/tex]
[tex]C(x)=50[/tex]
Answer:
C(x)=[tex]15, 0\leq x\leq 2[/tex]
[tex]5x+10, 2<x\leq 6[/tex]
[tex]50, [/tex] 6<x≤∞
Step-by-step explanation:
C(x) represents the monthly cost in dollars in terms of x, the number of gigabytes used in a month
Lets find C(x) on each interval (for every line graph)
first interval 0 to 2
the value of y is 15 on the interval 0 to 2
Its horizontal line . So equation is c(x)=the constant y value
[tex]C(x)= 15, 0\leq x\leq 2[/tex]
Second interval 2 to 6
Pick two points to get the equation of that line
(3,25) and (6,40)
[tex]slope = \frac{y_2-y_1}{x_2-x_1} =\frac{40-25}{6-3} =5[/tex]
Equation of the line is using m=5 and (3,25)
[tex]y-y1=m(x-x1)[/tex]
[tex]y-25=5(x-3)[/tex]
[tex]y-25=5x-15[/tex]
[tex]y=5x+10[/tex]
[tex]C(x)= 5x+10, 2<x\leq 6[/tex]
Now we look at the third interval
6 to infinity
For the third graph , the value of y is 50 (constant)
It is a horizontal line
So [tex]C(x)= 50, [/tex] 6<x≤∞
We got three equations for C(x)
C(x) is a piecewise function
C(x)=[tex]15, 0\leq x\leq 2[/tex]
[tex]5x+10, 2<x\leq 6[/tex]
[tex]50, [/tex] 6<x≤∞
Two bikers leave the same shopping center at the same time traveling in
opposite directions. If the first biker travels 2 mph faster than the second,
how fast is each riding if after 3 hours they are 78 miles apart?
The faster biker travels
mph
The slower biker travels
mph
Answer:
fast bike speed = 41/3= 17mph
slower bike speed = 37/3 =12.33 mph
Final answer:
The slower biker's speed is 12 mph and the faster biker's speed is 14 mph, determined by setting up an equation with their combined distances equating to 78 miles after 3 hours.
Explanation:
To resolve the puzzle of the two bikers departing from the same location and traveling in opposite directions, we can apply concepts of rate, time, and distance. We are given that the two bikers are 78 miles apart after 3 hours and that one biker is traveling at a speed that is 2 mph faster than the other.
Let's denote the speed of the slower biker as $x$ mph. Consequently, the speed of the faster biker would be $x + 2$ mph. Considering that they have been traveling for 3 hours, the slower biker would have covered 3$x$ miles and the faster biker 3($x + 2$) miles. The sum of these distances is the total distance between the bikers after 3 hours, which is 78 miles.
Mathematically, we can represent the situation as:
3$x$ + 3($x + 2$) = 78
Simplifying the equation:
3$x$ + 3$x$ + 6 = 78
6$x$ + 6 = 78
6$x$ = 72
$x$ = 12
Thus, the slower biker's speed is 12 mph and the faster biker's speed is 12 mph + 2 mph = 14 mph.
Answer: The faster biker travels at 14 mph and the slower biker travels at 12 mph
When 30% of a number is added to the number, the result is 130.
Answer:
100
Step-by-step explanation:
100% of a number + 30% of a number is 130% of a number.
This means 130 = 1.3x.
Now we simplify:
130=1.3x
/1.3 /1.3
100=x
x=100
Therefore, the number is 100.
The unknown number is 100.
Given that, 30% of a number is added to the number, the result is 130.
What is a percentage?The term "percentage" was adapted from the Latin word "per centum", which means "by the hundred". Percentages are fractions with 100 as the denominator. In other words, it is the relation between part and whole where the value of the whole is always taken as 100.
Let the unknown number be x.
30% of x+x=130
⇒0.3x+x=130
⇒1.3x=130
⇒x=100
Therefore, the unknown number is 100.
To learn more about the percentage visit:
https://brainly.com/question/24159063.
#SPJ2
HELP ASAP PLEASE!!!!!!!!!!!!!!!
What is the third quartile of {6, 9, 16, 11, 12, 16, 5, 14, 5}
The answer is 9.5
You tube is awesome for explaining this
Round the following decimal to the nearest tenth.
543.67
Answer:
543.7
Step-by-step explanation:
.67 is closer to .7 than to .6
Answer:
543.7
Step-by-step explanation:
The 7 rounds up to a 6 in the tenth place.
Someone plz help me
Answer:
Step-by-step explanation:
Write the explanation x-4
If it’s Wrong then please send an invitation of me to be a friend so that I can help you with update updated answers on brainly