Answers
Related Questions
An angle measures 72° less than the measure of a complementary angle. What is the measure of each angle?
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Angle a: 90 degrees - 72 degrees = 18 degrees
Angle b: 72 degrees
Answer: [tex]81^{\circ}\ \text{ and }\ 9^{\circ}[/tex]
Step-by-step explanation:
We know that the sum of two complementary angles is [tex]90^{\circ}[/tex].
Given : An angle measures 72° less than the measure of a complementary angle.
Let x be the angle , then the measure of other angle will be x-72.
Since they area complementary , then we have
[tex]x+x-72=90\\\\\Rightarrow\ 2x=90+72\\\\\Rightarrow\ 2x=162\\\\\Rightarrow\ x=\dfrac{162}{2}=81[/tex]
Therefore, the measure of angles are :
[tex]81^{\circ}\ \text{ and }\ (81-72)^{\circ}=9^{\circ}[/tex]
Calculus HELP PLEASE? A highway runs due north. A car traveling at 50 mph exits the highway at a 30° angle. After driving another 1.5 hours at the same speed and direction, how far away is the car from the highway?
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notice that the car exits the northbound highway, and whilst going at 50mph for 1.5 hours, that simply means going for 75 miles.
make sure your calculator is in Degree mode.
Answer:
37.5 miles is the answer.
Step-by-step explanation:
Since car is travelling with a speed = 50 mph
Angle between the highway and the track on which the car is travelling = 30°
Now we know sin∅ = distance between highway and the car/Distance traveled by the car on the new track
Distance traveled by the car in 1.5 hours = speed × time
= 50 × 1.5 = 75 mi.
Therefore sin 30° = x/75
x = 75×sin30° = 75 × 1/2 = 37.5 mi.
Therefore the answer is 37.5 mi away.
Use the quadratic formula to determine the exact solutions to the equation.
x^2−2x−4=0
Enter your answers in the boxes.
x=__ or x=___
Answers
______________________________________________________
Given:
______________________________________________________
" x² − 2x − 4 = 0 " ;
______________________________________________
Solve for "x" by using the "quadratic formula" :
Note: This equation is already written in "quadratic format" ; that is:
" ax² + bx + c = 0 " ; { "a [tex] \neq [/tex] 0" } ;
in which: "a = 1" {the implied coefficient of "1" ;
since "1", multiplied by any value, equals that same value};
"b = -2 " ;
"c = -4 " ;
_______________________________________________________
The quadratic equation formula:
x = { - b ± √(b² − 4 ac) } / 2a ; {"a[tex] \neq [/tex]0"} ;
______________________________________________________
Substitute our known values:
______________________________________________________
→ x = { - (-2) ± √[(-2)² − 4(1)(-4)] } / 2(1) ;
→ x = { 2 ± √(4 − 4(-4) } / 2 ;
→ x = { 2 ± √(4 − (-16) } / 2 ;
→ x = { 2 ± √(4 + 16) } / 2 ;
→ x = { 2 ± √(20) } / 2 ;
→ x = { 2 ± √4 √5} / 2 ;
→ x = { 2 ± 2√5} / 2 ;
→ x = 1 ± √5 ;
_______________________________________________________
→ "x = 1 + √5" or "x = 1 − √5" .
_______________________________________________________
Mr. Berger assigned the following system of equations to be solved for homework. 2x-3y = -12
4x+ y= -10
Which is the x-coordinate of the correct solution?
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Answer:
A: x= -3
Step-by-step explanation:
The x- coordinate is of solution is -3.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
2x-3y = -12...........(1)
4x+ y= -10..............(2)
Now, multiply Equation (1) by 2 we get
4x - 6y = -24
4x + y = -10
________
-7y = -14
y= 2
and, 4x+ y= -10
4x + 2 = -10
4x = -12
x= -12/4
x= -3.
Hence, the x- coordinate is -3.
Learn more about Equation here:
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Complete the statement If x/7 = 5/3, then x+7/7 =?
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[tex] \frac{x}{7} = \frac{5}{3} [/tex]
We can cross multiply, to find the value of x
3x = 7 x 5
3x = 35
We have to divide by 3 on either sides to isolate x
[tex] \frac{3x}{3} = \frac{35}{3} [/tex]
3 and 3 cancels out
x = [tex] \frac{35}{3} [/tex]
Then, x + [tex] \frac{7}{7} [/tex] ( 7 divided by 7 is 1)
[tex] \frac{35}{3} [/tex] + 1 = [tex] \frac{38}{3} [/tex]
Consider the quadratic equation. x^2=4x-5. How many solutions does the equation have? a.) one real solution b.) two real solutions c.)no real solutions d.)cannot be determined
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. (02.02 HC) Dominic earns $18 an hour plus $25 an hour for every hour of overtime. Overtime hours are any hours more than 35 hours for the week. Part A: Create an equation that shows the amount of money earned, E, for working x hours in a week when there is no overtime. (3 points) Part B: Create an equation that shows the amount of wages earned, T, for working y hours of overtime. Hint: Remember to include in the equation the amount earned from working 35 hours. (3 points) Part C: Dominic earned $730 in 1 week. How many hours (regular plus overtime) did he work? Show your work. (4 points) (10 points)
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Let
E-----------> the amount of money earned
x----------> hours working in a week-----> $18 an hour
we know that
E=18x ---------> equation that shows the amount of money earned for working x hours in a week
conditioned to x<= 35 hours--------> is no overtime
Part B)
Let
T----------------> the amount of money earned
y -------------- > hours of overtime-------> $25 an hour
for x=35 hour----------> E=18*35=$630
T=630+25y------> equation that shows the amount of wages earned for working y hours of overtime and 35 hour in a week
Part C)
if Dominic earned $730 in 1 week
$630------------> earned for working 35 hours in a regular week
[hours of overtime]=(730-630)/25=100/25=4 hours
[total hours worked]=35+4=39 hours
the answer is 39 hours (35 hours regular +4 hours overtime)
Answers anybody?????
Answers
.. (1/2)*20*12 = (1/2)*30*h
.. h = (2/3)*12 = 8 . . . . . feet
Use the chart above to determine the premium for 10-year term insurance. $10,000 policy for a 35-year-old male. Premium = _____?
6.11
61.10
611.00
6,110.00
Answers
Answer:
Option B 61.10
Step-by-step explanation:
Given is a chart giving the premium to be paid for 10 year term insurance for different age groups for an amount of 1000 policy.
We have to calculate the premium for a 35 year old man for 10 year term insurance for 10000 policy.
From the chart we find that for a 35 year old man premium = 6.11
This premium is for 1000 dollars.
Since here sum assured is 10000 dollars, we get the premium
=6.11(10) = 61.10 dollars
Option B is correct
Premium = 61.10 dollars
what is the approximate distance between the points (-5 1) and (-2 3) on a coordinate grid
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This figure shows circle Z with chords AB and RS . mAR=55° mRB=66° AB=8 m RS=8 m What is mRS?
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m RB = 66°
Like AB=8 m =RS →m RS = m AB
m AB = m AR + m RB
m AB = 55° + 66°
m AB = 121°
m RS = m AB
M RS = 121°
Answer: m RS is 121°
Answer:
The correct answer is, mRs = 121°
Step-by-step explanation:
From figure we get ,
mAR=55° mRB=66° AB=8 m RS=8 m
To find mRS
Using given information we can write,
mAB = mAR + mRB = 55 + 66 = 121°
Since AB=8 m RS=8 m,
AB = RS
⇒ mAB = mRS
mAB = 121°
Therefore mRS = 121°
The correct answer is given by,
mRS = 121°
Explain why the function f(x)=x^2 is not invertible
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When you reflect the curve across the line y=x, it becomes multiple-valued, hence its inverse is not a function.
Are the two triangles are congruent ?
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Johnny is five years older than his brother. the sum of their ages is 37. how old is Johnny
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If you take 21 and add 16, you get 37.
21+16= 37
21-16= 5
What number is 22 spaces to the right of negative 7?
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Final answer:
By adding 22 to -7, we find that the number 22 spaces to the right of -7 on the number line is 15.
Explanation:
The question asks for the number that is 22 spaces to the right of negative 7 on a number line. To find this, you can simply add 22 to negative 7. Here's the calculation: -7 + 22 = 15. Therefore, the number that is 22 spaces to the right of negative 7 is 15. To determine the number that is 22 spaces to the right of -7 on the number line, we need to add 22 to -7. Moving 22 spaces to the right indicates an increase in value by 22. Therefore, when we add 22 to -7, we get the final answer of 15. This calculation reflects the concept that moving to the right on the number line corresponds to increasing the numerical value, while moving to the left corresponds to decreasing it. In this case, starting from -7 and moving 22 spaces to the right results in a value of 15. Hence, 15 is the number that is 22 spaces to the right of -7.
Given cos A = 0.25 find angle A in degrees. Round your answer to the nearest hundredth.
34.12°
123.98°
56.78°
75.52°
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cos A=0.25
so
A=arc cos (0.25)-------> using a calculator----> A=75.5225°
Round to the nearest hundredth-----> A=75.52²
the answer is
the option 75.52°
describe the vertical asymptotes) and holes) for the graph of y=(x+2)(x+4)/(x+4)(x+1)
A. asymtotes: x=-1 and hole: x=4
B. asymtotes: x=2 and hole: x=-1
C. asymtotes: x= -1 and hole: x=-4
D. asymtotes: x=1 and hole: x=4
Can someone plzzzz help me!??
Answers
The function is not defined for those values where the denominator is equal to zero.
We have then:
y = (x + 2) (x + 4) / (x + 4) (x + 1)
Studying the denominator:
(x + 4) (x + 1) = 0
x = -4
x = -1
Answer:
C. asymtotes: x = -1 and hole: x = -4
The measure of dispersion which is not measured in the same units as the original data is the
a. variance
b. standard deviation
c. median
d. coefficient determination
Answers
Variance is not expressed in the same units as the original data.
Variance is measured by:
Finding the difference between the mean of a data set and the variables in the data set Squaring this difference Summing up the squaresBecause variance is squared, it is no longer the same units as the rest of the data set. For instance, if the data set is in centimeters, the variance will be in centimeters².
In conclusion, the variance of a data set is not measured in the same unit as the data set.
Find out more at https://brainly.com/question/20317994.
Final answer:
The measure of dispersion which is not measured in the same units as the original data is the variance.
Explanation:
The measure of dispersion which is not measured in the same units as the original data is the variance. The variance is a squared measure and does not have the same units as the data. On the other hand, the standard deviation is derived from the variance and it measures the spread in the same units as the data.
Then again, the standard deviation, which is the square foundation of the fluctuation, is estimated in similar units as the first information. It gives a proportion of the spread of the information that is all the more effectively interpretable. The middle is a proportion of focal inclination and doesn't give data about the scattering or spread of the information.
The coefficient of assurance, otherwise called R-squared, is a proportion of how well the relapse line fits the information and isn't straightforwardly connected with scattering.
The formula represents the surface area S of a cube with side lengths x.
S=6x^2
Solve for x.
Answers
The solution of x is √(S/6).
The formula to find the surface area of a cube with side lengths x is:
S = 6x2
To solve for x:
Divide both sides by 6: S/6 = x2
Take the square root of both sides to isolate x: x = √(S/6)
look at the pictures below
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How do you do x ^4-4? What is the x values?
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A difference of two perfect squares (A² - B²) can be factored into (A+B) • (A-B)
then
x ^4-4--------> (x²-2)*(x²+2)
(x²-2)--------> (x-√2)*(x+√2)
x1=+√2
x2=-√2
the other term
(x²+2)=0-> x²=-2-------------- x=(+-)√-2
i is called the imaginary unit. It satisfies i² =-1
Both i and -i are the square roots of -1
√ -2 =√ -1• 2 = √ -1 •√ 2 =i • √ 2
The equation has no real solutions. It has 2 imaginary, or complex solutions.
x3= 0 + √2 i
x4= 0 - √2 i
the answer is
the values of x are
x1=+√2
x2=-√2
x3= 0 + √2 i
x4= 0 - √2 i
Algebraically prove that X^3+10/x^3+9=1+ 1/x^3+9 where x is not equal to -3
Answers
[tex] \dfrac{x^3+10}{x^3+9}=1+\dfrac{1}{x^3+9} \\ \\ \\ \dfrac{x^3+10}{x^3+9}=\dfrac{(x^3+9)+1}{x^3+9}\\ \\ \\ \dfrac{x^3+10}{x^3+9}=\dfrac{x^3+10}{x^3+9} \\ \\ \\x\in R \qquad x\in (-\infty, +\infty) [/tex]
A circle has an arc of length 24pi that is intercepted by a central angle of 80 degrees. what is the radius of the circle?
Answers
80/360 x 2pi x r = 24pi
r = 54
Suppose the time it takes a data collection operator to fill out an electronic form for a database is uniformly distributed between 1.0 and 2.1 minutes. (a) determine the mean of x. (round your answer to 2 decimal places.)
Answers
= (1.0+2.1) / 2
=1.55
The ratio of zoya's age to nelya's age is 1:4. twenty years from now, nelya will be twice as old as zoya will be then. find their present ages.
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B) 2 * (z + 20) = nelya + 20
Inputting equation A into B)
2z + 40 = 4z + 20
2z = 20
zoya's age is 10 and nelya's age is 40
Answer:
Zoya is 10 years old. Nelya is 40 years old.
Does the function model exponential growth or decay? g(t)=1.7 * 0.8^t
Answers
Answer:
decay
just answered this question.
Step-by-step explanation:
Answer:
decaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecay
Step-by-step explanation:
Kevin is 4 times as old as Daniel and is also 6 years older than Daniel.
Answers
Here's what you know:
· Kevin's age is 4 times Daniel's age.
· Kevin's age is 6 more than Daniel's age.
In numbers:
· 4d
· d + 6
where d is Daniel's age. Kevin's age is constant, and both expressions represent his age, so you can set them equal to each other to solve for d.
4d = d + 6
4d - 6 = d
-6 = -3d
2 = d
Daniel is 2 and Kevin is 8.
I hope this helps you!
A rectangular prism has a volume of 360 in3. If the height measures 4 in., which base measurements could the prism have? 4 in. by 20 in. 45 in. by 45 in. 6 in. by 15 in. 5 in. by 19 in.
Answers
Let Ab = area of the base
h = 4 in
V = Ab × h
360 = Ab × 4
Ab = 360 ÷ 4
Ab = 90 in²
Ab = l × w
The product of the base measurements must be 90.
90 = l × w
⇒ 6 in × 15 in = 90 in² ⇒ The base measurements could be: 6 in by 15 in
Solve x + y + z = 12
2x – y – z = -6
x + 3y + 5z = 44
(4, 3, 5)
no solutions
(2, 4, -6)
(2, 4, 6)
Answers
Proof:
Solve the following system:{x + y + z = 12 | (equation 1){2 x - y - z = -6 | (equation 2){x + 3 y + 5 z = 44 | (equation 3)
Swap equation 1 with equation 2:{2 x - y - z = -6 | (equation 1){x + y + z = 12 | (equation 2){x + 3 y + 5 z = 44 | (equation 3)
Subtract 1/2 × (equation 1) from equation 2:{2 x - y - z = -6 | (equation 1){0 x+(3 y)/2 + (3 z)/2 = 15 | (equation 2){x + 3 y + 5 z = 44 | (equation 3)
Multiply equation 2 by 2/3:{2 x - y - z = -6 | (equation 1){0 x+y + z = 10 | (equation 2){x + 3 y + 5 z = 44 | (equation 3)
Subtract 1/2 × (equation 1) from equation 3:{2 x - y - z = -6 | (equation 1){0 x+y + z = 10 | (equation 2){0 x+(7 y)/2 + (11 z)/2 = 47 | (equation 3)
Multiply equation 3 by 2:{2 x - y - z = -6 | (equation 1){0 x+y + z = 10 | (equation 2)v0 x+7 y + 11 z = 94 | (equation 3)
Swap equation 2 with equation 3:{2 x - y - z = -6 | (equation 1){0 x+7 y + 11 z = 94 | (equation 2){0 x+y + z = 10 | (equation 3)
Subtract 1/7 × (equation 2) from equation 3:{2 x - y - z = -6 | (equation 1){0 x+7 y + 11 z = 94 | (equation 2){0 x+0 y - (4 z)/7 = (-24)/7 | (equation 3)Multiply equation 3 by -7/4:{2 x - y - z = -6 | (equation 1){0 x+7 y + 11 z = 94 | (equation 2){0 x+0 y+z = 6 | (equation 3)
Subtract 11 × (equation 3) from equation 2:{2 x - y - z = -6 | (equation 1){0 x+7 y+0 z = 28 | (equation 2){0 x+0 y+z = 6 | (equation 3)
Divide equation 2 by 7:{2 x - y - z = -6 | (equation 1){0 x+y+0 z = 4 | (equation 2){0 x+0 y+z = 6 | (equation 3)
Add equation 2 to equation 1:{2 x + 0 y - z = -2 | (equation 1){0 x+y+0 z = 4 | (equation 2){0 x+0 y+z = 6 | (equation 3)Add equation 3 to equation 1:{2 x+0 y+0 z = 4 | (equation 1){0 x+y+0 z = 4 | (equation 2){0 x+0 y+z = 6 | (equation 3)
Divide equation 1 by 2:{x+0 y+0 z = 2 | (equation 1){0 x+y+0 z = 4 | (equation 2){0 x+0 y+z = 6 | (equation 3)
Collect results:
Answer: {x = 2, y = 4 , z = 6
The volume, V, of a soap bubble is related to its surface area, A. In cubic centimeters, this relationship is shown by the formula V = 0.094A 3/2. What is the surface area of a bubble with a volume of 5 cm3 ?
Answers
V = 0.094 * (A) ^ (3/2)
Now we clear the area:
(A) ^ (3/2) = V / 0.094
A = (V / 0.094) ^ (2/3)
We now replace the volume:
A = (5 / 0.094) ^ (2/3)
A = 14.14364782 cm ^ 2
Answer:
The surface area of a bubble with a volume of 5 cm3 is:
A = 14.14364782 cm ^ 2
The surface area of a soap bubble with a volume of 5 cm³, given the relationship V = 0.094 [tex]A^{3/2[/tex], can be calculated by rearranging and solving the formula, resulting in an approximate surface area of 36.3 cm².
To find the surface area of a soap bubble with a volume of 5 cm³, using the given relationship V = 0.094 [tex]A^{3/2[/tex], we need to rearrange the formula to solve for A (the surface area). We will take the following steps to find A:
First, divide both sides of the equation by 0.094 to isolate [tex]A^{3/2[/tex] on one side:
[tex]A^{3/2[/tex] = V / 0.094
Next, substitute V = 5 cm³ into the equation:
[tex]A^{3/2[/tex] = 5 / 0.094
Calculate the right-hand side:
[tex]A^{3/2[/tex] ≈ 53.19
Finally, raise both sides of the equation to the power of 2/3 to solve for A:
A = [tex](53.19)^{2/3[/tex]
Calculating the right-hand side gives us the surface area A. After performing these calculations, we find that the surface area of a bubble with a volume of 5 cm³ is approximately 36.3 cm².