Given:
Two intergers have a sum of 47 and a difference of 23.
Let's find the product of the two numbers.
Let x and y represent the numbers.
We have:
Two integers have a sum of 47: x + y = 47
Two integers have a difference of 23: x - y = 23
We gave the system of equations:
x + y = 47.......................equation 1
x - y = 23.......................equation 2
Let's solve the system simultaneously using substitution method.
Rewrite equation 1 for x:
x = 47 - y
Substitute (47 - y) for x in equation 2:
(47 - y) - y = 23
47 - y - y = 23
47 - 2y = 23
Subtract 47 from both sides:
47 - 47 - 2y = 23 - 47
-2y = -24
Divide both sides of the equation by -2:
[tex]\begin{gathered} \frac{-2y}{-2}=\frac{-24}{-2} \\ \\ y=12 \end{gathered}[/tex]Now, substitute 12 for y in either of the equations.
Let's take equation 1.
x + y = 47
x + 12 = 47
Subtract 12 from both sides:
x + 12 - 12 = 47 - 12
x = 35
Therefore, we have:
x = 35, y = 12
The numbers are 35 and 12.
To find the product of the numbers, let's multiply the numbers:
35 x 12 = 420
Therefore, the product of the numbers is 420.
ANSWER:
420
Michael is constructing a boat ramp. He knows that the angle of elevation of the ramp is 30°. If the distance from the bottom of the boat ramp to the top of the boat ramp is 40 feet, what is the height of the boat ramp?
Let's draw a rough figure:
Here, h is the distance we are solving for.
Now,
With respect to the given angle 30 degrees, we have the hypotenuse and want to find the opposite side.
The trig ratio relating opposite side and hypotenuse is SINE.
Thus, we can write:
[tex]\sin (30)=\frac{opposite}{\text{hypotenuse}}=\frac{h}{40}[/tex]Cross multiiplying, we solve for h [remember, value of sin(30) is 1/2]:
[tex]\begin{gathered} \sin (30)=\frac{h}{40} \\ h=40\times\sin (30) \\ h=40\times\frac{1}{2} \\ h=20 \end{gathered}[/tex]The height of the boat ramp is 20 feet.
Thomas is buying football jerseys for his high school football team. Thecost of each jersey is $80. The company also charges a processing fee of$100.Write an equation that represents Thomas' total cost for purchasing xnumber of jerseys.What is Thomas' total cost, if he buys 55 jerseys?
Thomas is buying football jerseys for his high school football team.
The cost of each jersey is $80.
The company also charges a processing fee of $100.
We could write an equation that models Thomas's total cost for purchasing x
number of jerseys.
Since for every x jerseys Thomas buys, he pays
[tex]80x\text{ dollars}[/tex]But he also has to pay the company's processing fee, this is independent of the quantity bought.
So, the total cost for buying x number of jerseys is;
[tex]y=80x+100\text{ dollars}[/tex]ii. What is Thomas's total cost, if he buys 55 jerseys?
We can use our formula,
[tex]\begin{gathered} y=80x+100\text{ , when x =55, we have;} \\ y=80(55)+100 \\ y=4400+100 \\ y=4500\text{ dollars} \end{gathered}[/tex]Therefore, Thomas's total cost for 55 jerseys is $4500
Write a general formula to describe the variation. M varies directly with the square of d and inversely with the square root of x; M=12 when d=3 and x=4
Given that 'M' varies directly with the square of 'd',
[tex]M\propto d^2[/tex]Given that 'M' varies inversely with the square root of 'x',
[tex]M\propto\frac{1}{\sqrt[]{x}}[/tex]Combining the relationships,
[tex]M\propto\frac{d^2}{\sqrt[]{x}}[/tex]Let 'k' be the constant of proportionality. Then,
[tex]M=k\cdot\frac{d^2}{\sqrt[]{x}}[/tex]Given that M=12 when d=3 and x=4,
[tex]\begin{gathered} 12=k\cdot\frac{(3)^2}{\sqrt[]{4}} \\ 12=k\cdot\frac{9}{2} \\ k=\frac{12\cdot2}{9} \\ k=\frac{8}{3} \end{gathered}[/tex]Substitute the value of this constant in the general expression,
[tex]M=\frac{8}{3}\cdot\frac{d^2}{\sqrt[]{x}}[/tex]Thus, the required general formula to describe the relation is obtained as,
[tex]M=\frac{8}{3}\cdot\frac{d^2}{\sqrt[]{x}}[/tex]There are 45 students in the 4th grade at Akili Academy. If Ms. Lause found out that 68% of them attended the football game over the weekend, how many students attended the game? You may have to round to the closest whole student.
There are 45 students in the 4th grade at Akili Academy. If Ms. Lause found out that 68% of them attended the football game over the weekend, how many students attended the game? You may have to round to the closest whole student.
we have that
45 students represents -------> 100%
so
Applying proportion
Find out how much students represents 68%
45/100=x/68
solve for x
x=(45/100)*68
x=30.6
therefore
the answer is 31 studentssolve for tangent x= -1 in radians without a calculator
Answer:
[tex]x\text{ = }\frac{3}{4}\pi\text{ or }\frac{7}{4}\pi[/tex]Explanation:
Here, we want to calculate the value of x without using a calculator
We have to look for the quadrants where the tan is negative
These are the second and the fourth quadrant
On the second quadrant, we have the reference angles as:
[tex]180-x[/tex]Mathematically in degrees:
[tex]\begin{gathered} \text{if tan x = 1} \\ x\text{ = 45 deg} \end{gathered}[/tex]Now, on the second quadrant, we have it that:
[tex]180-45\text{ = 135 deg}[/tex]On the fourth quadrant, we have the reference angle calculated as:
[tex]\begin{gathered} 360-\theta \\ \theta\text{ = 360-45} \\ \theta\text{ = 315 deg} \end{gathered}[/tex]Lastly, we have to convert these angles to radians
Mathematically, 1 pi is 180 degrees:
[tex]\begin{gathered} 1\text{ }\pi=\text{ 180 deg} \\ x\text{ = 135 deg} \\ x\text{ = }\frac{135\pi}{180}\text{ = }\frac{3}{4}\pi \\ \\ \text{Lastly:} \\ 1\pi\text{ = 180 deg} \\ x\text{ = 315 deg } \\ \\ x\text{ = }\frac{315}{180}\pi\text{ = }\frac{7}{4}\pi \end{gathered}[/tex]1. How is the orientation of the triangie affected by the translation?
Solution: The orientation is inverted
Explanation:
Given a triangle ABC if we reflect if along a straight line L we get the triangle A'C'B' and now we are going to draw it
Exercises 11.3- omplete the following: Find the slope of a line parallel to the line through the points. (a) (2, 5) and (4, -6)
If the lines are parallel then the slopes will be equal
The slope is the ratio of the rate of change in y coodinate with respect to rate of change in x coordinate
[tex]\text{ Slope=}\frac{y_2-y_1}{x_2-x_1}_{}[/tex]The given pair of coordinates : (2,5) and (4,-6)
[tex]\begin{gathered} \text{ Slope = }\frac{-6-5}{4-2} \\ \text{ Slope=}\frac{-11}{2} \end{gathered}[/tex]The slope of the line is -11/2
The slope of the line parallel to line whose coordinates are (2,5) and (4,-6) is -11/2
it says use the table to rewrite the expression you wrote for problem 2. rewrite that expression so that both terms are written with the same exponent number 4. says use the distributive property simplify the expression you wrote for problem 3.number 5. says write your expression as the product of a decimal times a power of 10.number 6 says write your solution in scientific notation and number 7. says Evaluate (7.4 x 10^15 -- (9.9 x 10^13number 8 says Evaluate (8.9 x 10^5) + (6.5) x 10^6
7)
Given data:
The given expresson is a=7.7x10^15-(9.9x10^13)
The given expression can be written as,
a=770x10^13-9.9x10^13
=(770-9.9)x10^13
=760.1x10^13.
8)
Given data:
The given expresson is b=8.9x10^5-(6.5)x10^6
The given expression can be written as,
b=8.9x10^5-65x10^5
=(8.9-65)x10^5
=-56.1x10^5
Write the function below in slope intercepts form. Show all the steps
we need to find the equation in the form y=mx+b, so:
4x+y=5
y=-4x+5
the "4x" go subtracting to the other side
and we have m=-4 and b=5
so the answer is: y=-4x+5
Find the image of (1,2) after a reflection about x=3 followed by a reflection about x=7.
EXPLANATION
Given the point (1,2), if we reflect the point the new image must be at the same distance from the reflective line just at the original image.
Therefore when (1,2) is reflected over x= 3 the image becomes
[tex](5,2)[/tex]As the distance between line x=3 is 2 units on both sides.
When we then reflect (5,2) over x =7, using the same idea above the image becomes
Answer:
[tex](9,2)[/tex]ABC High School is debating whether or not to write a policywhere all students musthave uniforms and wear them during school hours. In a survey,45% of the studentswanted uniforms, and 55% did not.Calculate the probability that a person selected at random fromABC High School will want the school to have uniforms or willnot want the school to have uniforms.
If 45% don't want uniforms, it means that 45 out of 100 students don't want them, so the probability is 45/100 = 9/20
And 55% want unifrms, so the probability = 55/100 = 11/20
Harold and Harry both rented cars from Hurry Up Motors. Harold rented his car for 6 days andwas charged $194. Harry rented his car for 3 days and was charged $122. Choose theequation that represents y, the rental cost, in terms of x, the days of the rental.
Step 1:
Write the coordinates in terms of cost and number of days.
( cost , days )
Step 2
( 3 , 122 ) and ( 6, 194)
Step 3:
Find the slope
[tex]\begin{gathered} \text{Slope m = }\frac{y_2-y_1}{x_2-x_1} \\ x_1\text{ = 3} \\ y_1\text{ = 122} \\ x_2\text{ = 6} \\ y_2\text{ = 194} \\ m\text{ = }\frac{194\text{ - 122}}{6\text{ - 3}} \\ m\text{ = }\frac{72}{3} \\ m\text{ = 24} \end{gathered}[/tex]Step 4
Find the equation using the slope m and point 1
[tex]\begin{gathered} m\text{ = }\frac{y-y_1}{x-x_1} \\ 24\text{ = }\frac{y\text{ - 122}}{x\text{ - 3}} \\ \text{y - 122 = 24(x - 3)} \\ \text{y - 122 = 24x - 72} \\ y\text{ = 24x - 72 + 122} \\ y\text{ = 24x + 50} \end{gathered}[/tex]Final answer
The equation is y = 24x + 50
simplify the expression so there is only one positive power for the base -5
When we are dividing, exponents are subtracted!
The rule is shown below:
[tex]a^b\div a^c=a^{b-c}[/tex]We can apply this rule to this problem as shown:
[tex]\begin{gathered} -5^7\div-5^2 \\ =-5^{7-2} \\ =-5^5 \end{gathered}[/tex]Solve the quadratic equations in questions 1 – 5 by factoring.1. x2 – 49 = 02. 3x3 – 12x = 03. 12x2 + 14x + 12 = 184. –x3 + 22x2 – 121x = 05. x2 – 4x = 5
Given:
There are given the equation:
[tex]-x^3+22x^2-121x=0[/tex]Explanation:
According to the question:
We need to find the value of x by using the factoring:
S0,
From the equation:
[tex]-x^{3}+22x^{2}-121x=0[/tex]Tthen,
[tex]\begin{gathered} -x^{3}+22x^{2}-121x=0 \\ -x(x^2-22x+121)=0 \end{gathered}[/tex]Then,
[tex]\begin{gathered} -x(x^2-22x+121)=0 \\ x(x-11)^2=0 \\ x=0; \\ x-11=0 \\ x=11 \end{gathered}[/tex]Final answer:
Hence, the value of x by using factor method is shown below:
[tex]x=0,11[/tex]During a lab Jill made a solution that was 3% water. Rewrite this percent as a fraction in simplest form.
Hello, I need some assistance with this homework question please for precalculusHW Q17
Solution:
Given the image;
Thus, there is a local maximum at;
[tex]x=-2[/tex]CORRECT OPTION: Yes
The local maximum is;
[tex]y=4[/tex]you rent a moving van you have to pay a flat fee of $99 plus $0.50 per mile you drive 120 miles how much does it cost to drive the van also I NEED work
It cost $159 to drive the van for 120 miles
Explanation:
The flat fee of the van = $99
The charge per mile = $0.50
Let m represent the number of miles
T = total cost
The total cost becomes:
T = 0.5m + 99
When you drive 120 miles, m = 120 miles
T = 0.5(120) + 99
T = 60 + 99
T = $159
Hence, it cost $159 to drive the van for 120 miles
DONT IGNORE! PLEASE HELP ME! 50 POINTS!
Answer: The answer is C (or the third option)
Step-by-step explanation: The formula for finding the measure of interior hexagon angles is ( n − 2) × 180 °. This means that C is the correct answer
Hi, can you help me to solve this exercise, please!!
Given the Right Triangle BCD, you know that:
[tex]\begin{gathered} BD=8 \\ m\angle BCD=63\degree \end{gathered}[/tex]Then, you can use the following Trigonometric Function in order to find the length of the side CD:
[tex]\sin \beta=\frac{opposite}{hypotenuse}[/tex]In this case:
[tex]\begin{gathered} \beta=63\degree \\ opposite=BD=8 \\ hypotenuse=CD \end{gathered}[/tex]Therefore, substituting values and solving for CD, you get:
[tex]\begin{gathered} \sin (63\degree)=\frac{8}{CD} \\ \\ CD\cdot\sin (63\degree)=8 \end{gathered}[/tex][tex]\begin{gathered} CD=\frac{8}{\sin(63\degree)} \\ \\ CD\approx9.0 \end{gathered}[/tex]Hence, the answer is:
[tex]CD=9.0[/tex]Calculate the population variance and population standard deviation for the following data said if necessary round to one more decimal place than the largest decimal
Given the dataset
2, 3, 4, 5, 6, 7, 8, 9, 10, 11
range is given by
[tex]range=maxValue-MinValue[/tex][tex]range=11-2[/tex][tex]range=9[/tex]Range=9
population variance is given by
[tex]s^2=\frac{SumSquares}{n}[/tex][tex]s^2=\frac{82.5}{10}[/tex][tex]s^2=8.25[/tex]rounded
population variance = 8.3
population standar deviation is given by
[tex]std=\sqrt{\frac{SumSquares}{n}}[/tex][tex]std=\sqrt{8.25}[/tex][tex]std=2.872[/tex]rounded
population standar deviation= 2.9
What should you multiply the first equation (top equation) by in order to eliminate the variable y when the two equations are added together? {x+2y=5{3x-4y=8
2
Explanationgiven
[tex]\begin{gathered} x+2y\rightarrow equation(1) \\ 3x-4y=8\rightarrow equation(2) \end{gathered}[/tex]Step 1
a) to eliminate the y variable we have
[tex]\begin{gathered} 2y \\ -4y \end{gathered}[/tex]in order to be eliminated both terms must have the same value and different sign,in other words the addition must equla zero, so weed a number (a) that makes the term from teh first equation equals (4y)
so
[tex]\begin{gathered} (2y*a)-4y=0 \\ 2ay=4y \\ so \\ 2a=4 \\ divide\text{ both sides by 2} \\ \frac{2a}{2}=\frac{4}{2} \\ a=2 \end{gathered}[/tex]therefore, the first equation should be multiplied by 2
I hope this helps you
change this standard form equation into slope intercept form 6x - 2y=-8
we have the equation
6x-2y=-8
Convert to slope-intercept form
y=mx+b
so
Isolate the variable y
step 1
Adds 2y both sides
6x-2y+2y=-8+2y
6x=-8+2y
step 2
Adds 8 both sides
6x+8=-8+2y+8
6x+8=2y
step 3
Divide by 2 both sides
3x+4=y
rewrite
y=3x+4What are the known solution to you can see the solution in the picture
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
The known solutions to:
[tex]f(x)\text{ = g(x) are:}[/tex][tex]\begin{gathered} \text{when x= 1,} \\ f(1)\text{ = 14,} \\ g(1)\text{ = 14} \\ \text{and } \\ \text{when x = 9 ,} \\ f(1)\text{ = 6} \\ g(1)\text{ = 6} \end{gathered}[/tex]CONCLUSION:
The correct answers are:
[tex]\begin{gathered} \text{ x = 1 -- OPTION A} \\ \text{and } \\ \text{x = 9 }--\text{OPTION D} \end{gathered}[/tex]Define the domain of the following:A. -3,-2,-1,0,1,2,3,4,5,6,7,8,B. 3,-1,2,0,-2C. -3,-1,1,3,6D. All real numbers
The domain is the values of x in the given graph
Since the graph is some points
(-3, 3), (-1, -1), (1, 2), (3, 0), (6, -2)
Then the domain is the x-coordinates of all point
D = {-3, -1, 1, 3, 6}
The answer is C
)Mr. Nacarrato and his family are going on a road trip that is
2457 miles long. They have already driven 128 53/100 miles
How much further do they have to drive?
They need to go further 2328.47 miles distance.
What is improper fraction and mixed fraction?
A mixed fraction is one that has both a correct fraction and a whole number portion, and whose value is consistently greater than 1. When the numerator is always higher than or equal to the denominator, the fraction is said to be inappropriate. 4/3, 7/3, 11/5, and other incorrect fractions are a few instances.
Here the road trip is 2457 miles long .
They already drive 128 [tex]\frac{53}{100}[/tex] miles.
That is in mixed fraction , we need to convert them in improper fraction , then,
=> 128 [tex]\frac{53}{100}[/tex] = [tex]\frac{128*100+53}{100}= \frac{12853}{100}[/tex]
Now we need to subtract them from total distance then ,
=> 2457 - [tex]\frac{12853}{100}[/tex]
=> [tex]\frac{2457*100-12853}{100}[/tex]
=> [tex]\frac{245700-12853}{100}[/tex]
=> 2328.47 miles.
They need to go further 2328.47 miles.
To learn more about improper fraction and mixed fraction
https://brainly.com/question/1055953
#SPJ1
Did you turn the volume of the cylinder given. Calculate using pi on calculator and grounded to the nearest tenth. Is the correct option A, B, or C?
V= 14726 ft^3
2 points Bob flips a coin. He also spins the pointer on the spinner shown below. What is the probability that Bob flips the coin so that it lands tails up and spins the pointer so it stops on the letter R? * N E Your answer
Answer: 1/16 = 0.0625
Step by step solution:
The probability (P) of an event happening is
[tex]P=\frac{Numbe\text{r of ways it can happen}}{Total\text{ number of outcomes}}[/tex]When Bob flips the coin he has two options, head or tail. The probability that it lands tails up is:
[tex]P=\frac{1}{2}[/tex]The probability that the pointer stops on the letter R is:
[tex]P=\frac{1}{8}[/tex]Now, the probability of both events happening (tails up and pointer on R) is:
[tex]P=\frac{1}{2}\times\frac{1}{8}=\frac{1}{16}=0.0625[/tex]A man is approaching a pole 75 feet high and walking at the rate of
3 miles/hour. At what rate is he approaching the top of the pole
when he is 100 feet away from the pole?
Answer:
375!
Step-by-step explanation:
3 x 100 = 300
Now he is at the pole. Now he has to get to the top of it
which your basically doing
3 x 100 = 300 + 75 = 375
( 375 - 75 = 300 300 ÷ 100 = 3 )
I have to find the length of x but I need guidance
Since we are dealing with a right triangle, we can use trigonometric identity below
[tex]\begin{gathered} sin\theta=\frac{O}{H} \\ \theta\rightarrow\text{ interior angle} \\ O\rightarrow\text{ opposite side to}\theta \\ H\rightarrow\text{ hypotenuse} \end{gathered}[/tex]Therefore, in our case,
[tex]\begin{gathered} sin(45\degree)=\frac{5}{x} \\ \Rightarrow x=\frac{5}{sin(45\degree)}=\frac{5}{\frac{1}{\sqrt{2}}}=5\sqrt{2} \end{gathered}[/tex]Thus, the answer is x=5sqrt(2), the second optionWhat is the Effective Annual Yield in percent when the annual nominal interest rate is 7.042% compounded quarterly?EAY = ___%
Answer:
Given that,
Annual nominal interest rate is 7.042% compounded quarterly
To find the effective annual yield.
Explanation:
The formula for calculating effective annual yield (E) is,
[tex]E=(1+\frac{r}{n})^n-1[/tex]where r is the interest rate, n is the number of compounds per year.
Here, r=7.042 % and n=4
Substitute the values we get,
[tex]E=(1+\frac{7.042}{100\times4})^4-1[/tex][tex]E=(1+0.017605)^4-1[/tex][tex]E=1.07230154-1[/tex][tex]E=0.07230154[/tex][tex]E=0.07230154\approx7.23\%[/tex]Effective annual yield is 7.23%