Answer:
(-3,1)
y= 1
x= -3
Step-by-step explanation:
4x-9y=-21
-4x-3y=9
solve the equation
4x=-21+9y
-4x-3y=9
substitute the value of 4x onto an equation
-1(-21+9y)-3y=9
multiply -1 to the numbers in parenthesis
-21+-9-3y=9
add -9 to 9 and put the negative on nine as a positive.
-21-3y=18
add -21 to 18 but since 21 is a negative the equation is subtraction.
-3y=-3
divide Both sides by -3
y=1
substitute the value of y into an equation
-4x-3•1=9
multiply 3 to 1
-4x-3=9
put -3 as a positive and add 3 to 9
-4x=12
divide both sides by -4
x= -3
(-3,1)
The solution for x and y in the given equations is x = 27 and y = 11.
Let's consider the second equation, -x + 3y = 6, and rewrite it in the form ax + by = c.
To get the equation in the required form, we'll rearrange the terms:
-x + 3y = 6
Add x to both sides:
3y = x + 6
Now, subtract 6 from both sides:
3y - 6 = x
This equation can be rewritten in the form ax + by = c by swapping sides:
x = 3y - 6
Now, let's substitute this expression for x into the first equation: 4x - 9y = 9.
4x - 9y = 9 becomes 4(3y - 6) - 9y = 9.
Simplify the equation: 12y - 24 - 9y = 9.
Combine like terms: 3y - 24 = 9.
Add 24 to both sides: 3y = 33.
Divide both sides by 3: y = 11.
Substitute y = 11 into x = 3y - 6: x = 3 × 11 - 6.
Calculate: x = 33 - 6 = 27.
Therefore, the solution for x and y in the given equations is x = 27 and y = 11.
Complete Question:
4x-9y=9; -x+3y=6 Rewrite one of the two equations above in the form ax + by = c, where a, b, and c are constants, so that the sum of the new equation and the unchanged equation from the original system results in an equation in one variable.
Given f(x) = 3x – 2, find f(-5).
Answer:
f(-5)= -17
Step-by-step explanation:
We want to find at what value of f(x), or y, does x=-5
So, to find when x=-5, or f(-5), substitute -5 in for x
f(x)=3x-2
f(-5)=3(-5)-2
Multiply first (PEMDAS)
f(-5)=-15-2
Subtract
f(-5)= -17
Hope this helps! :)
Answer:
f(-5) = -17
Step-by-step explanation:
f(x) = 3x – 2 Substitute -5 for x
f(-5) = 3(-5) - 2 Multiply
f(-5) = -15 - 2 Subtract
f(-5) = -17
Ivan wants to ship a box that is 6 in. Tall, 4 in. Wide, and 5 in. Long to his cousin, and used the calculation below. What was his error, and what is the correct volume? V = lwh V = 5 x 4 x 6 = 20 x 6 = 26 in.3
Answer:
the correct volume is 120in.3
Step-by-step explanation:
he did his math wrong, 20 x 6 is not 26.
V = 5 x 4 x 6 = 20 x 6 = 120
Answer:
He added instead of multiplying 20 and 6. The correct answer is 120 cubic inches.
Step-by-step explanation:
on edg2020
How many solutions does this system have?
2x-4y=8
x+y=7
The system has ______
solution(s)
Answer:
The solution for the system is the pair (6,1).
Step-by-step explanation:
The system has two equations and two variables, therefore i has only one solution. To solve it we will multiply the second equation by "-2". So we have:
2x-4y = 8
x + y = 7 *(-2)
2x - 4y = 8
-2x -2y = -14
We now sum boh equations:
2x -2x -4y -2y = 8 -14
-6y = -6
y = -6/-6 = 1
2x - 4(1) = 8
2x - 4 = 8
2x = 8 + 4
2x = 12
x = 12/2 = 6
The solution is the pair (6,1).
Answer:
The system has 2 solution .
Step-by-step explanation:
The equation is a simultaneous equation
2x - 4y=8 ............(i)
x + y=7................(ii)
make x the subject of the formula in equation (ii)
x = 7 - y
Substitute the value of x in equation(i)
2(7 - y) - 4y = 8
14 - 2y - 4y = 8
14 - 6y = 8
-6y = 8 - 14
-6y = -6
divide both sides by -6
y = 1
insert the value of in equation (ii)
x + y = 7
x + 1 = 7
x = 7 - 1
x = 6
The system has 2 solution .
A yearbook company was investigating whether there is a significant difference between two states in the percents of high school students who order yearbooks. From a random sample of 150 students selected from one state, 70 had ordered a yearbook. From a random sample of 100 students selected from the other state, 65 had ordered a yearbook. Which of the following is the most appropriate method for analyzing the results?
A. A one-sample zz-test for a sample proportion
B. A one-sample zz-test for a population proportion
C. A two-sample zz-test for a difference in sample proportions
D. A two-sample zz-test for a difference in population proportions
E. A two-sample zz-test for a population proportion
Answer:
Null hypothesis: [tex] p_1 = p_2[/tex]
Alternative hypothesis: [tex] p_1 \neq p_2 [/tex]
So we need to conduct a:
D. A two-sample z-test for a difference in population proportions
Because the idea is to check if the population proportions in the states are similar or not.
Step-by-step explanation:
For this case they are trying two proof if there is a significant difference between two states in the percents of high school students who order yearbooks, and we chan check this with the difference of proportions.
Lets say that [tex]p_1,p_2[/tex] are the two proportions of interest and we want to check the following hypothesis:
We have the following info given:
[tex]\hat p_1 = \frac{70}{150}= 0.47[/tex] proportion of students that had ordered a yearbook from one state
[tex]\hat p_2= \frac{65}{100}= 0.65[/tex] proportion of students that had ordered a yearbook from another state
[tex]n_1 = 150[/tex] sample size from one state
[tex]n_2=100[/tex] sample size from another state
Null hypothesis: [tex] p_1 = p_2[/tex]
Alternative hypothesis: [tex] p_1 \neq p_2 [/tex]
So we need to conduct a:
D. A two-sample z-test for a difference in population proportions
Because the idea is to check if the population proportions in the states are similar or not.
Donna paints ornaments for a school play.Each ornament is made up of two identical cones,as shown. How many bottles of paint does she need to paint 70 ornaments?
12 bottles of paint does she need to paint 70 ornaments. Hence 12 is correct answer.
1. Calculate the surface area of one cone:
The surface area of a cone is the sum of the area of the base (a circle) and the lateral surface area. Since the cone is cut in half vertically, we only need to consider half of the base and lateral surface area.
Base area: The base is a circle with radius r. The area of a circle is πr². Since the cone is cut in half, the base area is πr² / 2.
Lateral surface area: The lateral surface area is a sector of a circle with radius r and arc length equal to the circumference of the base. The circumference of the base is 2πr. The area of a sector is (arc length × radius) / 2. In this case, area of sector is (2πr×r) / 2 = πr^2.
Therefore, total surface area of one cone is (πr²/ 2) + πr² = 3πr² / 2.
2. Calculate the surface area of one ornament:
Since each ornament is made up of two identical cones, the surface area of one ornament is twice the surface area of one cone. Therefore, the surface area of one ornament is 2×(3πr² / 2) = 3πr^2.
3. Calculate the total surface area of all ornaments:
If Donna needs to paint 70 ornaments, the total surface area she needs to cover is 70×3πr² = 210πr².
4. Convert the surface area to square meters:
However, if you provide the radius in meters, you can multiply the surface area you calculated in 3 by 1 to convert it to square meters.
5. Estimate the number of bottles of paint needed:
The total surface area in square meters, you can estimate the number of bottles of paint Donna needs by dividing the surface area by the coverage area of one bottle of paint. This information is typically available on the paint bottle itself. For example, if one bottle of paint covers 10 square meters, and the total surface area of the ornaments is 210 square meters, Donna would need approximately 210 square meters / 10 square meters/bottle = 21 bottles of paint.
The dot plot below represents the number of dollars in allowance that students receive each week in mrs.jimenez’s class.what is the median amount of allowance?
Answer:
6
Step-by-step explanation:
search up on quizizz
Shane is measuring a shelf. It is 24 inches long. He measures again to find the number of feet. Will the length of the shelf be less than, greater than, or the same length in feet?
Answer:
Same length
24 ÷ 2=12
There is 12 inches in a foot
1 + 1= 2 ft
24 inches = 2 feet
Answer:
The length of the shelf will be less than 24 in feet. It will be 2 feet long.
Step-by-step explanation:
Inches are a smaller unit than feet, meaning that when something is measured in inches, the numerical amount of inches will be higher than the numerical amount of feet. The ratio is 12 inches to 1 foot, meaning that even though the length may be the exact same, inches represents the length with a higher numerical value and feet represent the length with a lower numerical value.
Ariel and her family are going to order one large circular pizza that has a diameter of 20 inches and one small circular pizza that has a diameter of 12 inches. Which measurement is closest to the difference between the area of the large pizza and the area of the small pizza in square inches? *
5 points
804 in. squared
427 in. squared
314 in. squared
201 in. squared
To calculate the difference in area between two circular pizzas, first compute the area of each using the formula A = πr². After finding the areas, subtract the smaller area from the larger one to find the difference. The result is approximately 201 square inches.
Explanation:The question involves calculating the area of two circles and finding the difference between the two. First, we need to find the radius of each pizza. Since the diameter is twice the radius, the large pizza has a radius of 10 inches (20 inches divided by 2), and the small pizza has a radius of 6 inches (12 inches divided by 2). The area of a circle is calculated using the formula A = πr², where π is approximately 3.14159, and r is the radius.
The area of the large pizza is A = π(10 inches)² = π * 100 inches² = 314.16 inches² (rounded to two decimal places). The area of the small pizza is A = π(6 inches)² = π * 36 inches² = 113.10 inches² (rounded to two decimal places). To find the difference, we subtract the area of the small pizza from the area of the large pizza, which gives us 314.16 inches² - 113.10 inches² = 201.06 inches², which is closest to 201 inches².
Water leaks from a vertical cylindrical tank through a small hole in its base at a rate proportional to the square root of the volume of water remaining. The tank initially contains 350 liters and 20 liters leak out during the first day. When will the tank be half empty? How much water will there be after 4 days?
To solve the problem, use the concept of differential equations and solve for the rate of water leakage. Then, find the time at which the tank will be half empty and the volume of water after 4 days.
Explanation:To solve this problem, we can use the concept of differential equations. Let's denote the volume of water in the tank at any time t as V(t). We are given that the rate at which water leaks is proportional to the square root of the remaining volume, so we can write the differential equation:
dV/dt = k * sqrt(V)
Where k is the proportionality constant. We also know that during the first day, 20 liters leak out, so we can find k:
dV/dt = k * sqrt(350) = -20
Now, we can solve this differential equation to find the time at which the tank will be half empty, and the volume of water after 4 days.
Learn more about differential equations here:https://brainly.com/question/33814182
#SPJ3
The tank will be half empty (175 liters remaining) after approximately 3.6 days, and there will be about 135 liters of water remaining after 4 days. The problem involves solving differential equations relating to the leak rate being proportional to the square root of the remaining volume.
This problem involves solving a differential equation based on the rate at which water leaks out of a cylindrical tank. The leak rate is proportional to the square root of the volume of water remaining in the tank.
Differential Equation and Initial Conditions
Given:
Initial volume: 350 liters (V0)20 liters leak out in the first dayRate of leakage, dV/dt = -k√VWhere k is a constant. To find k, we use the initial conditions:
At t = 1 day,
V = 350 - 20
= 330 liters.
We integrate the differential equation:∫dV/√V = [tex]-k\int_{V_0(350)}^{V(330)} dt \quad \text{from} \quad t=0 \quad \text{to} \quad t=1[/tex]
Solving, we get:[tex]2\sqrt{V}\Bigg|_{350}^{330} = -kt\Bigg|_{0}^{1}[/tex]
2(√330 - √350) = -k(1)
Solving for k, we get:k ≈ 2(√350 - √330)
Finding When the Tank is Half Empty
Half of the initial volume is 350/2 = 175 liters.
We need to find t when V = 175.
Integrating the differential equation again:[tex]2\left(\sqrt{V}\Bigg|_{350}^{175}\right)[/tex] = -kt
2(√350 - √175) = kt
Substituting k, we get t ≈ 3.6 days.
Volume After 4 Days
We use our k value and solve for V when t = 4:[tex]2\left(\sqrt{V}\Bigg|_{350}^{V}\right)[/tex] = -k(4)
2√V = 2√350 - 4k
Solving for V, we find V ≈ 135 liters.PJ11
HELP!!!!for the given situation identify the independent and dependent variables and then find a reasonable domain and range of values. Listed below will be four statements that relate to the given situation. She’s the statement that would have to be false given the situation and it’s parameters.
Jimmy earns eight dollars an hour at his job. He can work up to 40 hours per week
here are the statements
1)The range will be from zero to $400
2) there a dependent variable will be the amount of money he earns
3) The independent variable will be the number of hours he works
4) The domain will be from 0 to 40 hours
Answer:
1
Step-by-step explanation:
he cant earn 400 dollars because 8*40 is 320. if he cant work more than eight hours, theres no possible way he can earn 400 dollars ('least in a math equation).
The city limits of Las Pythagoras form a perfect shape of an isosceles right triangle whose legs are both 25 kilometers long. The population in Las Pythagoras is 100,000,000 people. What is the population density of Las Pythagoras?
Answer:
320,000 people / km²
Step-by-step explanation:
We need to find the area of the city first.
The area of a triangle is: [tex]A=\frac{1}{2} bh[/tex], where b is the base and h is the height.
Here, both b and h are the legs of the right triangle and they're equal to 25 km. So:
[tex]A=\frac{1}{2} bh[/tex]
[tex]A=\frac{1}{2} *25*25=312.5[/tex] km²
Population density is simply (population) ÷ (area). Here, the population is 100,000,000 people and the area is 312.5 km², so:
100,000,000 ÷ 312.5 = 320,000 people / km²
Answer:
320,000 people per km²
Step-by-step explanation:
Since two angles are equal, their opposite lengths are also equal
Assuming it's a right ankle triangle,
Area = ½ × 25 × 25 = 312.5 km²
Population density:
100,000,000/312.5
320,000
Which graph represents this system? y = 2 x + 1. y = negative 4 x + 7. On a coordinate plane, a line goes through (0, 7) and (1, 3) and another goes through (1, 3) and (2, 5). On a coordinate plane, a line goes through (negative 4, 0) and (0, 7) and another line goes through (negative 4, 3) and (0, 1). On a coordinate plane, a line goes through (0, negative 4) and (1, 3) and another goes through (0, 2) and (1, 3). On a coordinate plane, a line goes through (0, 7) and (8, 5) and another line goes through (0, 1) and (8, 5).
Answer:
It is the first choice. (A)
Step-by-step explanation:
Red line: y = 2x + 1
Blue line: y = -4x + 7
What is the solution to -5m = -40?
Answer:
m=8
Step-by-step explanation:
-40 divided by -5
Your answer is 8
Answer:
8m would be the answer
Step-by-step explanation:
-5m/-5 = -40/5 = positive 8
Dayle and his two brothers each eat 5/12 (five-twelfths) of a chocolate bar. How much chocolate bar did they eat altogether? Solve, show your work, and record your answer on a piece of scratch paper. *
Answer:
N = 5/4 = 1.25
Altogether they eat 1.25 chocolate bar
Step-by-step explanation:
Dayle and his two brothers each eat 5/12 (five-twelfths) of a chocolate bar;
Three of them ate = 5/12 chocolate bar each
Total for the 3 of them N;
N = 3 × 5/12 = 15/12
N = 5/4 = 1.25
Altogether they eat 1.25 chocolate bar
Find the area of the rectangle below.
(3x + 4) feet
(x + 3) feet
Answer:
Area= (3x+4)×(x+3)
Step-by-step explanation:
(3x^2+10x+12)feet
Answer:
3x² + 13x + 12 ft²
Step-by-step explanation:
To work out the area of a rectangle you have to multiply the length and width together. In this case the length is 3x + 4 and the width is x + 3
So
( 3x + 4 ) × ( x + 3 )
Remember FOIL when expanding brackets
F = First two so 3x × x = 3x²
O = Outer two so 3x × 3 = 9x
I = Inner two so 4 × x = 4x
L = Last two so 4 × 3 = 12
but we aren't finished
3x² + 9x + 4x + 12 = 3x² + 13x + 12
Don't forget unit! ft²
For what value of X is expression
2x-1/x
[tex]2x - 1 \div x[/tex]
Steps to simplify:
2x - 1 / x
~Convert to fraction
2xx/x - 1/x
~Combine the fractions
2xx-1/x
~Simplify
2x²-1/x
Best of Luck!
At the city museum, child admission is $5.70 and adult admission is $9.50. on Friday, 155 tickets were sold for a total sales of $1255.90. how many child tickets were sold that day?
i love brainless tttree
Answer: 57 child tickets were sold that day.
Step-by-step explanation:
Let x represent the number of child tickets that were sold.
Let y represent the number of adult tickets that were sold.
on Friday, 155 tickets were sold. It means that
x + y = 155
At the city museum, child admission is $5.70 and adult admission is $9.50. The ticket sales totaled $1255.90 on that day. It means that
5.7x + 9.5y = 1255.9- - - - - - - - - 1
Substituting x = 155 - y into equation 1, it becomes
5.7(155 - y) + 9.5y = 1255.9
883.5 - 5.7y + 9.5y = 1255.9
- 5.7y + 9.5y = 1255.9 - 883.5
3.8y = 372.4
y = 372.4/3.8
y = 98
x = 155 - y = 155 - 98
x = 57
A cylinder has a radius of 5 cm and a height of 16 cm. Another cylinder is four times as tall but has the same radius. How does the volume of the second cylinder compare to that of the first?
Answer:
The answer to your question is 4 times bigger.
Step-by-step explanation:
Data
radius = 5 cm
height = 16 cm
Cylinder 2, 4 times taller the radius is the same
Process
1.- Calculate the volume of the first cylinder
Volume 1 = πr²h
-Substitution
Volume = π(5)²(16)
-Simplification
Volume = 400π cm³
2.- Calculate the volume of the second cylinder
height = 4(16)
= 64
-Substitution
Volume = π(5)²(64)
-Simplification
Volume 2 = 1600π cm³
3.- Find the relationship between the volume
Volume 2 / volume 1 = 1600π / 400π
= 4
4.- The second cylinder is 4 times bigger than the first cylinder
The total cost of attending a state university is $19,700 for the first year. • A student's grandparents will pay half of this cost. • An athletic scholarship will pay another $5,000. Which amount is closest to the minimum that the student will need to save every month in order to pay off the remaining cost at the end of 12 months?
Answer:
The student will have to save $404.2 minimum monthly
Step-by-step explanation:
Given that the total cost for the first year= $19,700
The grandparents paid half the amount = 1/2(19700)= $9850
The remaining balance to be paid is
19,700 - 9850=$9850
If an athlete paid $5000
The the remaining balance to be paid = 9850-5000=$4850
For the student to clear this amount in 12 months he must save
monthly 4850/12= $404.166
Hence the minimum amount to be saved per month is $404.2
Answer:
The student will have to save a minimum of $404.17 every month.
Step-by-step explanation:
The total cost of attending the sate university is $19, 700 for the first year alone.
Total cost for a year = $19700
A student's grandparent will pay half of the cost . This means the grand parents will pay
1/2 of the total cost for a year
1/2 × 19700 = $9850
The grand parent will pay $9850
An athletic scholarship will pay $5000 . It will be 9850 - 5000 = 4850 . The remaining amount to pay is $4850 .
At the end of 12 months the minimum amount the student will save every month to be able to pay the remaining amount will be the amount payable divided by 12 month.
minimum amount to save every month = 4850/12
minimum amount to save every month = 404.16666667
minimum amount to save every month ≈ 404.17
find the diameter of a circle with an area of 90.25 pi square meters
Answer:
19 meters
Step-by-step explanation:
The area of a circle is given as [tex]90.25\pi[/tex]
-A circle's area is calculated using the formula:
[tex]A=\pi r^2, r=0.5D, D=Diameter[/tex]
#We substitute for area in the equation and solve for D;
[tex]A=\pi (0.5D)^2\\\\90.25\pi=\pi (0.5D)^2\\\\\sqrt{90.25}=0.5D\\\\D=19[/tex]
Hence, the circle's diameter is 19 meters
Diameter of a circle = 19 meters
Circle :
Circle is a rounded figure that consists of points that are equidistance from the center
Area of a circle :Area of a circle is the area enclosed by the circle . The distance between the center to the circumference of circle is the radius.
Diameter is a straight line from one end of circle to the other end and it passes through the center of the circle
Given that area of the circle is 90.25 pi square meters
Area of the circle formula is
[tex]Area = \pi r^2\\90.25\pi =\pi r^2\\divide \; both \; sides \; by \; pi\\90.25=r^2\\take \; square \; root \; on \; both \; sides\\r=\sqrt{90.25}\\ r=9.5[/tex]
diameter of the circle = 2 times of the radius
Diameter = 2 times 9.5=19 meters
Diameter of a circle = 19 meters
Learn more information about 'Circle' here :
brainly.com/question/23984227
Plz help ->
Find the arithmetic and the geometric means of
5 and 125
1 and 9
4 and 9
Answer: ok so for 5 and 125 it is 65 and 25
for 1 and 9 it is 5 and 3 and for 4 and 9 it is 13/2 and 6
Which ratio is also equal to StartFraction R T Over R X EndFraction and StartFraction R S Over R Y EndFraction? StartFraction X Y Over T S EndFraction StartFraction S Y Over R Y EndFraction StartFraction R X Over X T EndFraction StartFraction S T Over Y X EndFraction
Answer:
△RST ~ △RYX by the SSS similarity theorem. Which ratio is also equal to RT/RX and RS/RY ?
A.XY/TS
B.SY/RY
C.RX/XT
D.ST/YX
Step-by-step explanation:
Check attachment for solution
Answer:
D
Step-by-step explanation:
Zachary is making a scale model of the sydney oprera house fir a report on sydney.Tge sydney opera house is 213 feet tall measuring from the ground to thr tip of thevjighest roof shell.If thevmodel is 1/100 the actual size of the sydney operahouse,how tall is the model?
Answer:
The height of Sydney opera house in the model is 2.13 feet.
Step-by-step explanation:
We are given the following in the question:
Height of Sydney opera house = 213 feet
Height in model =
[tex]\dfrac{1}{100}\text{ of the actual height}[/tex]
We have to evaluate the height of Sydney opera house in model.
Height in model =
[tex]=\dfrac{1}{100}\times 213\\\\=2.13\text{ feet}[/tex]
Thus, the height of Sydney opera house in the model is 2.13 feet.
PLZ HELP ME
I appreciate any help, especially if you can show me how you got the answer
Answer:
C
Step-by-step explanation:
Since this is an indererminate form, use L'Hopital
d(sint)/dt = cos(t)
d[ln(2e^t) - 1] = (2e^t)/[2e^t - 1]
As t --> 0,
cos(0) = 1
(2e^t)/[2e^t - 1] = 2
1/2 is the limit
Hello so I need help with my math since that's not my best subject and I'm also squarely brained so can I get some help
Answer:
212
Step-by-step explanation:
47 goes into 99 2 times
Bring down the 5
47 goes into 56 1 time
Bring the 9
47 goes into 94 2 times
The Captain has probability \dfrac{1}{2} 2 1 start fraction, 1, divided by, 2, end fraction of hitting the pirate ship. The pirate only has one good eye, so he hits the Captain's ship with probability \dfrac{1}{6} 6 1 start fraction, 1, divided by, 6, end fraction. If both fire their cannons at the same time, what is the probability that both the pirate and the Captain hit each other's ships?
Answer:
0.083 is the required probability.
Step-by-step explanation:
We are given the following in the question:
Probability of captain hitting pirate's ship =
[tex]P(A) = \dfrac{1}{2}[/tex]
Probability of pirate hitting the captain's ship =
[tex]P(B) = \dfrac{1}{6}[/tex]
Probability that both the pirate and the Captain hit each other's ships:
[tex]P(A\cap B) = P(A)\times P(B)[/tex]
Putting values, we get,
[tex]P(A\cap B) =\dfrac{1}{2}\times \dfrac{1}{6} = \dfrac{1}{12} \\\\P(A\cap B) = 0 .083[/tex]
0.083 is the probability that both the pirate and the Captain hit each other's ships.
What is the value of 3/7 times 0.1 divided by 5/21
Answer:
0.18
Step-by-step explanation:
Answer:
9/50
Step-by-step explanation:
0.1 is the equivalent of 1/10
You multiply:
[tex]\frac{3}{7} *\frac{1}{10}[/tex]
= [tex]\frac{3}{70}[/tex]
[tex]\frac{3}{70}[/tex]÷[tex]\frac{5}{21}[/tex] is the equivalent of
[tex]\frac{3}{70}* \frac{21}{5}[/tex]
which equals [tex]\frac{63}{350}[/tex], or [tex]\frac{9}{50}[/tex] simplified (divide both sides by 7)
40 POINTS PLEASE HELP
Explain how solve 4^(x + 3) = 7 using the change of base formula log^ b y= log y/ log b. Include the solution for x in your answer. Round your answer to the nearest thousandth.
Answer:
-1.596
Step-by-step explanation:
4^(x + 3) = 7
log4 both sides
log4[4^(x + 3)] = log4(7)
(x + 3) × log4(4) = lg7/lg4
x + 3 = 1.403677461
x = -1.596322539
There are 10 millimeters in 1 centimeter.Convert 27 centimeters to millimeters.
A. 2.7
B. 27
C. 270
D. 2700
Answer:
C. 270
Step-by-step explanation:
If there are 10 millimeters in 1 centimeter, that means there is 10 times the number of millimeters in a centimeter. So, we would multiply 27 centimeters by 10 to find the number of millimeters.
Mohamed and Li Jing were asked to find an explicit formula for the sequence -5\,,-25\,,-125\,,-625,...−5,−25,−125,−625,...Minus, 5, comma, minus, 25, comma, minus, 125, comma, minus, 625, comma, point, point, point. Mohamed said the formula is g(n)=-5\cdot5^{\large{n}}g(n)=−5⋅5 n g, left parenthesis, n, right parenthesis, equals, minus, 5, dot, 5, start superscript, n, end superscript, and Li Jing said the formula is g(n)=-5\cdot5^{\large{n-1}}g(n)=−5⋅5 n−1 g, left parenthesis, n, right parenthesis, equals, minus, 5, dot, 5, start superscript, n, minus, 1, end superscript. Which one of them is right? Choose 1 answer: Choose 1 answer:
Answer:
Li Jing
Step-by-step explanation:
Given the sequence:
-5,-25,-125,-625,...
Mohamed's Formula is given as: [tex]g(n)=-5\cdot5^{\large{n}}[/tex]
Using Mohamed's formula:
[tex]When\: n=1,g(n)=-5\cdot5^{\large{n}}=-5\cdot5^{1}=-25\\When\: n=2,g(n)=-5\cdot5^{\large{n}}=-5\cdot5^{2}=-125\\[/tex]
Li Jing's Formula is given as: [tex]g(n)=-5\cdot5^{\large{n-1}}[/tex]
Using Mohamed's formula:
[tex]When\: n=1,g(n)=-5\cdot5^{\large{n-1}}=-5\cdot5^{1-1}=-5\\When\: n=2,g(n)=-5\cdot5^{\large{n-1}}=-5\cdot5^{\large{2-1}}=-25\\[/tex]
We can see that Li Jing's Formula produces the gien sequence.
Li Jing is Right.
Answer:
Only Li Jing
Step-by-step explanation:
This is because the formula −5 * 5 is worng as the first term is reapeated again so it is Li Jing