Answer:
The value of x and y are x = 15 and y = 63
Step-by-step explanation:
If two adjacent angle formed a straight line, then the two angles formed a pair of linear anglesThe sum of the measures of the linear angles is 180°From the given figure
∵ The angles of measures (9x - 7)° and (4x - 8)° are adjacent angles
∵ The angles of measures (9x - 7)° and (4x - 8)° formed a line
∴ They formed a pair of linear angles
∵ The sum of the measures of the linear angles is 180°
→ That means add them and equate the sum by 180
∴ (9x - 7) + (4x - 8) = 180
→ Add the like terms
∵ (9x + 4x) + (-7 + -8) = 180
∴ 13x + (-15) = 180
→ Remember (+)(-) = (-)
∴ 13x - 15 = 180
→ Add 15 to both sides
∴ 13x - 15 + 15 = 180 + 15
∴ 13x = 195
→ Divide both sides by 13
∵ [tex]\frac{13x}{13}[/tex] = [tex]\frac{195}{13}[/tex]
∴ x = 15
∵ Lines m and n are parallels
∵ A line intersected them
∵ The angles of measures (2y + 2), (9x - 7) are interior alternate angles
∵ The interior alternate angles are equal in measures
∴ 2y + 2 = 9x - 7
∵ x = 15
→ Substitute the value of x
∴ 2y + 2 = 9(15) - 7
∴ 2y + 2 = 135 - 7
∴ 2y + 2 = 128
→ Subtract 2 from both sides
∴ 2y + 2 - 2 = 128 - 2
∴ 2y = 126
→ Divide both sides by 2
∴ [tex]\frac{2y}{2}[/tex] = [tex]\frac{126}{2}[/tex]
∴ y = 63
The values of x and y are 15 and 63, respectively
The angles in the figure are: (9x - 7)° and (4x - 8)°
These angles are adjacent angles.
So, we have:
[tex]\mathbf{9x - 7 + 4x - 8 = 180}[/tex]
Collect like terms
[tex]\mathbf{9x + 4x = 180 + 8 + 7}[/tex]
[tex]\mathbf{13x = 195}[/tex]
Divide both sides by 13
[tex]\mathbf{x = \frac{195}{13}}[/tex]
[tex]\mathbf{x = 15}[/tex]
Also, we have:
[tex]\mathbf{2y + 2 = 9x - 7}[/tex] -- interior angles
Subtract 2 from both sides
[tex]\mathbf{2y = 9x - 9}[/tex]
Substitute 15 for x
[tex]\mathbf{2y = 9\times 15 - 9}[/tex]
[tex]\mathbf{2y = 126}[/tex]
Divide both sides by 2
[tex]\mathbf{y = 63}[/tex]
Hence, the values of x and y are 15 and 63, respectively
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The ratio of boys to girls is 1:1.
If there are 250 boys, how many
girls are there?
twice a number k plus the quantity s minus 2
Answer:
2k+s-2
im assuming
Simplify.
7√10+2√10-√10
7√10+2√10-√10
Every square root has the same radicand, which is 10. So, simply combine terms.
7 + 2 - 1 = 9 - 1 = 8
Answer: 8√10
Tthe area of a circle increases at a rate of 5 cm^2/s.
Required:
a. How fast is the radius changing when the radius is 4 cm?
b. How fast is the radius changing when the circumference is 5 cm?
Answer:
(a) 0.198 cm/s (b) 1 cm/s
Step-by-step explanation:
It is given that,
The rate of change of area of a cicle, [tex]\dfrac{dA}{dt}=5\ cm^2/s[/tex]
(a) The area of a circle is given by :
[tex]A=\pi r^2[/tex]
Differentiate both sides,
[tex]\dfrac{dA}{dt}=2\pi r\dfrac{dr}{dt}\\\\\text{Put the value of dA/dt and r = 4 cm}\\\\\dfrac{dr}{dt}=\dfrac{dA/dt}{2\pi r}\\\\\dfrac{dr}{dt}=\dfrac{5}{2\pi \times 4}\\\\\dfrac{dr}{dt}=0.198\ cm/s[/tex]
(b) Circumference, [tex]C=2\pi r[/tex] = 5 cm
[tex]\dfrac{dA}{dt}=2\pi r\dfrac{dr}{dt}\\\\\dfrac{dr}{dt}=\dfrac{dA/dt}{2\pi r}\\\\\dfrac{dr}{dt}=\dfrac{5}{5}\\\\\dfrac{dr}{dt}=1\ cm/s[/tex]
Hence,
(a) 0.198 cm/s (b) 1 cm/s
Will mark as brainless if you answer correctly
Answer:
ans=10
Step-by-step explanation:
Answer:
10
Step-by-step explanation:
10(4-7) / -(4 - 1)
10(-3) / -(3)
-30 / -3 =
10
3z2 - 2z + 8
-
(10z2 +7z - 12)
Answer: 7z²-9z+20
Step-by-step explanation:
PEMDAS - Please Excuse My Dear Aunt Sally - Parentheses, Exponents, Multiplication, Division, Addition, Subtraction
A car covered a certain distance at a speed of 24 mph. While returning, the car covered the same distance at a speed of 16 mph. What was the average speed of the car for the entire journey? \
Answer:
19.2 mph
Step-by-step explanation:
just trust me
Find -48a divided by 8 when a =1 . Write the answer in simplest form.
The solution is
Answer: -6
if a=1 then -48a=-48
so when we divide by 8 we ger -48/8 which is -6
The solution to -48a divided by 8 when a =1 is -6.
what is expression?A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation.
Let's examine the writing of expressions. The other number is x, and a number is 6 greater than half of it. In a mathematical expression, this proposition is denoted by the expression x/2 + 6. Complex riddles are solved using mathematical expressions.
Given:
-48a divided by 8 when a =1 .
Now, put a=1 in -48a
=-48 x 1
=48
Now, -48 is divided by 8
=-48/8
= -6
Hence, the solution is -6.
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a plane takes off from an airport and travels at a steady speed of 350 miles per hour. which of these graphs best represents the distance the plane is from the airport, y, after traveling for x hours?
Answer:
what do the graphs look like, it would have a slope of 350
Step-by-step explanation:
when a pendulum swings, at which point is potential energy highest?
Simplify the fraction 36/8
Answer:
4 4/8
Step-by-step explanation:
36 can go into 8, 4 times. With 4 left over so the answer is 4 4/8.
Answer:
[tex]4\frac{1}{2}[/tex]
Step-by-step explanation:
Find all whole numbers m such that m and 5m+1 are prime numbers.
Answer:
2 only
Step-by-step explanation:
Only even PRIME number is 2.
Why do we need EVEN PRIME numbers?
Say we do 11*5 we get 55 but when we add one we get 56
Meaning: An odd number multiplied by an odd number plus an odd number equals EVEN number which isn't PRIME. 2 being the ONLY even prime is therefore the only number we can choose.
Forty-seven thousand people ride the city bus every day. On
average, about how many people ride the bus each hour?
Use these methods to normalize the following group of data:
200, 300, 400, 600, 1000
a) min-max normalization by setting min = 0 and max = 1
b) z-score normalization
c) normalization by decimal scaling
Step-by-step explanation:
b is the answer , z-score normalization
Normalization is applied to data values in other to ensure that the data scales well, such that data values conforms to a certain range. The output of the various normalization techniques are given below ;
Given the data:
200, 300, 400, 600, 10001.)
Min - Max normalization :
[tex]\frac{value - min}{max - min} [/tex] Min = minimum = 200Max = maximum = 1000Value = 200 :
[tex]\frac{200 - 200}{1000 - 200} = 0[/tex]
Value = 300 :
[tex]\frac{300 - 200}{1000 - 200} = 0.125[/tex]
Value = 400 :
[tex]\frac{400 - 200}{1000 - 200} = 0.25[/tex]
Value = 600 :
[tex]\frac{600 - 200}{1000 - 200} = 0.5[/tex]
Value = 1000 :
[tex]\frac{1000 - 200}{1000 - 200} = 1[/tex]
Normalized values = (0, 0.125, 0.25, 0.5, 1)
2.)
Zscore normalization :
[tex]\frac{value - μ}{σ} [/tex]Using a calculator :
Mean, μ = 500Standard deviation = 316.227Value = 200 :
[tex]\frac{200 - 500}{316.227} = -0.949[/tex]
Value = 300 :
[tex]\frac{300 - 500}{316.227} = -0.632[/tex]
Value = 400 :
[tex]\frac{400 - 500}{316.227} = -0.316[/tex]
Value = 600 :
[tex]\frac{600 - 500}{316.227} = 0.316[/tex]
Value = 1000 :
[tex]\frac{1000 - 500}{316.227} = 1.581[/tex]
Normalized values = (-0.949, -0.632, -0.316, 0.316, 1.581)
3.)
Decimal Scaling :
Maximum value = 1000Hence, we can divide our values by 10000200 / 10000 = 0.02
300/1000 = 0.03
400/1000 = 0.04
600/1000 = 0.06
1000/1000 = 0.1
Hence, the Normalized values (0.02, 0.03, 0.04, 0.06, 0.1)
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Store A sells 3 candy bars for $3.45.
Store B charges $5.45 for 5 candy bars.
Store C sells 7 candy bars for $7.56.
Which store offers the best value?
Answer:
store C
Step-by-step explanation:
if you divide 7.56 by 7 it'll be $1.08 per candy bar.
Multiply and simplify. (12 2/3)(3 1/4)
A) 36 1/12
B) 36 1/6
C) 41 1/12
D) 41 1/6
Answer:
41 1/6 is the answer lets do it step by step
Step-by-step explanation:
You are usually taught to multiply the improper fractions and simplify the result.
.. (38/3)*(13/4) = (38/4)*(13/3)
.. = (19/2)*(13/3)
.. = (19*13)/6
.. = 247/6
.. = 41 1/6
You can also multiply the parts.
.. (12 2/3)*(3 1/4) = 12*3 + 12*(1/4) +(2/3)*3 +(2/3)*(1/4)
.. = 36 +3 +2 +1/6
.. = 41 1/6
hope this helps:D
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation:}[/tex]
[tex]\mathsf{12 \dfrac{2}{3}\times 3\dfrac{1}{4}}[/tex]
[tex]\huge\textbf{Simplifying:}[/tex]
[tex]\mathsf{12 \dfrac{2}{3}\times 3\dfrac{1}{4}}[/tex]
[tex]\mathsf{= \dfrac{12\times3+2}{3}\times \dfrac{3\times4+1}{4}}[/tex]
[tex]\mathsf{= \dfrac{36 + 2}{3} \times \dfrac{12 + 1}{4}}[/tex]
[tex]\mathsf{= \dfrac{38}{3}\times\dfrac{13}{4}}[/tex]
[tex]\mathsf{= \dfrac{38\times13}{3\times4}}[/tex]
[tex]\mathsf{= \dfrac{494}{12}}[/tex]
[tex]\mathsf{= \dfrac{494\div2}{12\div2}}[/tex]
[tex]\mathsf{= \dfrac{247}{6}}[/tex]
[tex]\mathsf{\approx 41 \dfrac{1}{6}}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\boxed{\mathsf{Option\ D.)\ 41 \dfrac{1}{6}}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
What percent is:
45 of 36
Answer:
45 is 125% of 36, and 36 is 80% of 45.
Step-by-step explanation:
rationalise the denominator 1/√20
Answer:
1/10
Step-by-step explanation:
uf no me dij hi g go be h in go i
Step-by-step explanation:
Given:1/√20
The denominator = 20
We know that
The rationalising factor of √a is √a. To rationalise the denominator of 1/√20, we multiply this by √20/√20.
1/√20
→ (1/√20) * (√20/√20)
→ [1(√20)]/[(√20)(√20)]
→ (√20)/√(20×20)
→ √20/20 Ans.
Determine whether the Mean Value Theorem can be applied to f on the closed interval [a, b]. If the Mean Value Theorem can be applied, find all values of c in the open interval (a, b) such that f '(c) = f (b) − f (a) b − a . If the Mean Value Theorem cannot be applied, explain why not.
f(x) = x^3 + 2x, [-1,1]
Answer:
There is a value of [tex]c[/tex] in (-1, 1), [tex]c = 0.577[/tex].
Step-by-step explanation:
Let [tex]f(x) = x^{3}+2\cdot x[/tex] for [tex]x \in[-1,1][/tex], we need to prove that [tex]f(x)[/tex] is continuous and differentiable to apply the Mean Value Theorem. Given that [tex]f(x)[/tex] is a polynomical function, its domain comprises all real numbers and therefore, function is continuous.
If [tex]f(x)[/tex] is differentiable, then [tex]f'(x)[/tex] exists for all value of [tex]x[/tex]. By definition of derivative, we obtain the following expression:
[tex]f'(x) = \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}[/tex]
[tex]f'(x) = \lim_{h \to 0} \frac{(x+h)^{3}+2\cdot (x+h)-x^{3}-2\cdot x}{h}[/tex]
[tex]f'(x) = \lim_{h \to 0} \frac{x^{3}+3\cdot x^{2}\cdot h+3\cdot x\cdot h^{2}+h^{3}+2\cdot x+2\cdot h-x^{3}-2\cdot x}{h}[/tex]
[tex]f'(x) = \lim_{h \to 0} \frac{3\cdot x^{2}\cdot h+3\cdot x\cdot h^{2}+h^{3}+2\cdot h}{h}[/tex]
[tex]f'(x) = \lim_{h \to 0} 3\cdot x^{2}+ \lim_{h \to 0} 3\cdot x \cdot h+ \lim_{h \to 0} h^{2}+ \lim_{h \to 0} 2[/tex]
[tex]f'(x) = 3\cdot x^{2}+2[/tex] (Eq. 2)
The derivative of a cubic function is quadratic function, which is also a polynomic function. Hence, the function is differentiable at the given interval.
According to the Mean Value Theorem, the following relationship is fulfilled:
[tex]f'(c) = \frac{f(1)-f(-1)}{1-(-1)}[/tex] (Eq. 3)
If we know that [tex]f(-1) = -3[/tex], [tex]f(1) = 3[/tex] and [tex]f'(c) = 3\cdot c^{2}+2[/tex], then we expand the definition as follows:
[tex]3\cdot c^{2}+2 = 3[/tex]
[tex]3\cdot c^{2} = 1[/tex]
[tex]c = \sqrt{\frac{1}{3} }[/tex]
[tex]c \approx 0.577[/tex]
There is a value of [tex]c[/tex] in the interval (-1, 1), [tex]c = 0.577[/tex].
18. Which product is greater. (-4)-(-6) or
(-7).(-8)? Explain.
Answer:
So when u do (-4)-(-6) it equals 2.
But when u do (-7)*(-8) it equals 56
Therefore saying that (-7)*(-8)=56 is the greatest product.
Step-by-step explanation:
What is the measure of angles DEC and GAH?
Answer:
DEC is 30°
because 180° - 50° would be 40°
In the figure shown, What is the value of x? a. 57° b. 123° c. 33° d. 147°
A local hamburger shop sold a combined total of 721 hamburgers and cheeseburgers on Thursday. There were 71 more cheeseburgers sold than hamburgers. How many hamburgers were sold on Thursday?
Answer:771-71/2= 350 hamburgers and 350 +71 cheeseburgers
Step-by-step explanation:
Can someone Help me ASAP plss!!
PLS ANSWER I WILL MARK YOU AS BRAINLIEST IF YOU ANSWER CORRECTLYYY! PLS AND TY! :D
Answer: Kell would be making more money in 19 hours.
Step-by-step explanation:
If you add it up, Kell makes 136$ in only 16 hours but mariko makes 133 in the full 19 hours. Which means that Kell would make more in 19 hours. The total Kell makes in 19 hours is 161.5 and $161.5 > $133. Let me know if you need any more help!
An exam has two probability problems, 1 and 2. If 37% of the students solved problem 1 and 12% of the students solved both problems 1 and 2, what is the percent of students who solved problem 2 given that they solved problem 1
Answer:
63%
Step-by-step explanation:
37% did not solve problem 2
100% - 37% = 63%
A builder is designing a rectangular patio that has a length of 12 units. Find the total number of square units the patio will cover if the width is 4
Answer:
48 square units
Step-by-step explanation:
Use the area formula, A = lw, where l is the length and w is the width
Plug in the length and width:
A = lw
A = (12)(4)
A = 48
So, the patio will cover 48 units²
6^3x=14 Show your work
Answer:
Is 3x supposed to be an exponent?
Step-by-step explanation:
Both possible answer are provided
3x as an exponent and as 6 times 3x
determine the slope of the line that passes through each pair of points (3,8) and (1,5)
Answer:
3/2
Step-by-step explanation:
-413.4=-15.9n please help
Answer:
[tex]\boxed {n = 26}[/tex]
Step-by-step explanation:
Solve for [tex]n[/tex]:
[tex]-413.4 = -15.9n[/tex]
-Switch sides:
[tex]-15.9n = -413.4[/tex]
-Divide both sides by [tex]15.9[/tex] and expand by multiplying both numerator and denominator by [tex]10[/tex]:
[tex]\frac{-15.9n}{-15.9} = \frac{-413.4}{-15.9}[/tex]
[tex]n = \frac{-4134}{-159}[/tex]
-Divide [tex]-4134[/tex] and [tex]-159[/tex]:
[tex]n = \frac{-4134}{-159}[/tex]
[tex]\boxed {n = 26}[/tex]
Therefore, the value of [tex]n[/tex] is [tex]26[/tex].