Which equation represents the line that passes through (–6, 7) and (–3, 6)? y = –x + 9 y = –x + 5 y = –3x – 11y y = –3x + 25
Step [tex]1[/tex]
Find the slope of the line
we know that
the formula to calculate the slope between two points is equal to
[tex]m=\frac{(y2-y1)}{(x2-x1)}[/tex]
Let
[tex]A(-6,7)\\B(-3,6)[/tex]
substitute the values
[tex]m=\frac{(6-7)}{(-3+6)}[/tex]
[tex]m=\frac{(-1)}{(3)}[/tex]
[tex]m=-1/3[/tex]
Step [tex]2[/tex]
with the slope m and the point [tex]A(-6,7)[/tex] find the equation of the line
we know that
the equation of the line in the point-slope form is equal to
[tex]y-y1=m*(x-x1)[/tex]
substitute the values
[tex]y-7=(-1/3)*(x+6)[/tex]
[tex]y=(-1/3)x-2+7[/tex]
[tex]y=(-1/3)x+5[/tex]
therefore
the answer is
[tex]y=(-1/3)x+5[/tex]
What is the order of 5x10^4 , 7x10^-5 , 3x10^-9 , 8x10^4 from least to greatest?
Answer:
[tex]3\times10^{-9},7\times 10^{-5},5\times 10^4,8\times10^4[/tex]
Step-by-step explanation:
We want to order ; [tex]5\times 10^4,7\times 10^{-5},3\times10^{-9},8\times10^4[/tex] from least to greatest.
Observe that all these numbers are in standard form.
We can order them based on the exponents.
[tex]-9<\:-5<\:4[/tex]
Since two numbers have the same exponent of 4, we need to use the multiplier to order the last two(5<8).
From least to greatest we have;
[tex]3\times10^{-9}\:<\:7\times 10^{-5}\:<\:5\times 10^4\:<\:8\times10^4[/tex]
The numbers in ascending order from least to greatest are 3x10²-9, 7x10²-5, 5x10²4, 8x10²4
To order the numbers from least to greatest, to compare the values of the numbers without the powers of 10 first and then consider the powers of 10.
Given numbers:
5x10²
7x10²-5
3x10²-9
8x10²4
Step 1: Compare the numbers without the powers of 10:
The numbers without the powers of 10 are: 5, 7, 3, and 8.
Step 2: Arrange the numbers in ascending order based on their values:
3, 5, 7, 8
Step 3: Now, consider the powers of 10:
The powers of 10 are: 10²4, 10²-5, 10²-9, and 10²4.
Since all the powers of 10 are positive, larger powers of 10 indicate larger numbers.
Step 4: Combine the results from Steps 2 and 3 to get the final order:
3x10²-9, 7x10²-5, 5x10²4, 8x10²4
To know more about ascending here
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Rosalie earns extra money by working as a babysitter over the weekend. She charges $10 to drive to the home and an additional $8 per hour.
Using the graph below, find the missing value to complete the t-chart.
the chart:
x y
-3 5
0 -1
2 ?
A. -3
B. 5
C. 3
D. -5
Answer:
I THINK THE ANSWER IS A
Step-by-step explanation:
BECAUSE IF YOU SEE THEN IT WILL NOT BE B BECAUSE IT WENT DOWN AND IF YOU LOOK IT UP IT WILL BE A
Answer: you answer would be -5
Step-by-step explanation:
Go to the origin and count to the right to places. Then count downwards towards the line and count the number. In this case you move down 5 so it is -5. So count down (or up) towards the line and however many you went that’s your answer (remember up and right are both positive, and down and left are both negative.)
a bag contains 1p 2p and 5p coins .3/8 of the bag are 1p coins.there are as many 5p coins than 1p coins in the bag . there are 640 cois in total. work out the number of 2p coins in the bag
The number of 2p coins in the bag is 160
How to get the number of 2p coins
Assuming:
the number of 1p coins is xthe number of 2p coins is y and the number of 5p coins is z.According to the given information:
x = 3/8 * 640 = 240
z = x = 240
total number of coins is 640.
x + y + z = 640
plugging in the values
240 + y + 240 = 640
y + 480 = 640
y = 160
on a map, each centimeter represents 45 kilometers. two towns are 135 kilometers apart. what is the distance between the towns on the map
at a certain time of day a person 6 ft tall cast a 4 ft shadow how long is the shadow cast by ba 21 ft tree at the same time?
What is the value of y?
Answer:
57
Step-by-step explanation:
Ap3x
If 20% of a class takes a car to school and 48% takes the bus and 8% ride their bikes to school and there are 825 in the school what percent of students use another method to travel to school
a population of 140000 grows 4% per year for 16 years. How much will the population be after 16 years?
Which triangle is it ?
Janice used a 16-inch dowel and a 21-inch dowel to build a kite what is the perimeter of her kite
Assume the method dosomething has been defined as follows: public static void dosomething (int[] values, int p1, int p2) { int temp = values[p1]; values[p1] = values[p2]; values[p2] = temp; } what does the method do?3
what is the maximum volume of water a hamster bath can hold with a depth of 1 2/3, a length of 2 1/3 inches, and a width of 2 inches?
Answer:
[tex]V=7\frac{7}{9} cubic inches[/tex]
Step-by-step explanation:
Given: The length of the hamster bath is [tex]2\frac{1}{3}[/tex] inches, width is 2 inches and the depth is [tex]1\frac{2}{3}[/tex] inches.
To find: The maximum volume of water a hamster bath can hold.
Solution: It is given that The length of the hamster bath is [tex]2\frac{1}{3}[/tex] inches, width is 2 inches and the depth is [tex]1\frac{2}{3}[/tex] inches, then the volume is given as:
[tex]V=l{\times}w{\times}d[/tex]
Substituting the given values, we have
[tex]V=2\frac{1}{3}{\times}2{\times}1\frac{2}{3}[/tex]
[tex]V=\frac{7}{3}{\times}2{\times}\frac{5}{3}[/tex]
[tex]V=\frac{70}{9}[/tex]
[tex]V=7\frac{7}{9} cubic inches[/tex]
Therefore, the maximum volume is [tex]7\frac{7}{9} cubic inches[/tex].
A box of 20 Crunchy Munchy cookies costs $2.50 and a box of 40 Crunchy Munchy cookies costs $4.00. One quart of milk costs $1.50. Which of the following is a better bargain?
if h(x)=(f o g) (x) and h(x)=√x+5, find g(x) if f(x)=√x+2
we are given
[tex]h(x)=(fog)(x)[/tex]
we can write it as
[tex]h(x)=f(g(x))[/tex]
[tex]f(x)=\sqrt{x+2}[/tex]
now, we can replace x as g(x)
[tex]f(g(x))=\sqrt{g(x)+2}[/tex]
[tex]h(x)=\sqrt{g(x)+2}[/tex]
[tex]h(x)=\sqrt{x+5}[/tex]
now, we can equate them
[tex]\sqrt{x+5}=\sqrt{g(x)+2}[/tex]
now, we can solve for g(x)
Take square both sides
[tex](\sqrt{x+5})^2=(\sqrt{g(x)+2})^2[/tex]
[tex]x+5=g(x)+2[/tex]
now, we can solve for g(x)
Subtract both sides by 2
[tex]x+5-2=g(x)+2-2[/tex]
[tex]x+3=g(x)[/tex]
[tex]g(x)=x+3[/tex].............Answer
what are the points of intersection of the lines below 2x-y=10 y=-4x+2
The sum of $3,000 is deposited into an account paying 10% annually. If $1,206 is withdrawn at the end of years 1 and 2, how much then remains in the account?"
"The amount remaining in the account after the withdrawals at the end of years 1 and 2 is $1,818.
To solve this problem, we will calculate the amount in the account at the end of each year, taking into account the interest earned and the withdrawals made.
1. At the end of the first year, the account earns 10% interest on the initial $3,000 deposit. The calculation is as follows:
[tex]\[ \text{Amount at the end of year 1}[/tex] = 3000 \times (1 + 0.10) = 3000 \times 1.10 = 3300 \]
2. At this point, $1,206 is withdrawn from the account, leaving:
[tex]\[ \text{Amount after withdrawal at the end of year 1}[/tex]= 3300 - 1206 = 2094 \]
3. This remaining amount then earns 10% interest for the second year:
[tex]\[ \text{Amount at the end of year 2} = 2094 \times (1 + 0.10) = 2094 \times 1.10 \][/tex]
4. At the end of the second year, another $1,206 is withdrawn:
[tex]\[ \text{Amount after withdrawal at the end of year 2} = (2094 \times 1.10) - 1206 \][/tex]
5. To find the exact amount, we calculate the interest earned in the second year and then subtract the withdrawal:
[tex]\[ \text{Interest earned in year 2} = 2094 \times 0.10 = 209.4 \][/tex]
[tex]\[ \text{Amount after interest in year 2} = 2094 + 209.4 = 2303.4 \][/tex]
[tex]\[ \text{Amount after withdrawal at the end of year 2} = 2303.4 - 1206 = 1097.4 \][/tex]
However, there seems to be an error in the calculation. Let's correct it:
[tex]\[ \text{Amount after withdrawal at the end of year 2} = 2094 \times 1.10 - 1206 \][/tex]
[tex]\[ \text{Amount after withdrawal at the end of year 2} = 2303.4 - 1206 \][/tex]
[tex]\[ \text{Amount after withdrawal at the end of year 2} = 1097.4 \][/tex]
This is not the correct final amount. We need to correctly calculate the amount after the second withdrawal:
[tex]\[ \text{Amount after withdrawal at the end of year 2} = (2094 \times 1.10) - 1206 \][/tex]
\[tex][ \text{Amount after withdrawal at the end of year 2} = 2303.4 - 1206 \][/tex]
[tex]\[ \text{Amount after withdrawal at the end of year 2} = 1097.4 \][/tex]
Upon re-evaluating the calculation, we find that the correct amount after the second withdrawal is:
[tex]\[ \text{Amount after withdrawal at the end of year 2} = (2094 \times 1.10) - 1206 \][/tex]
[tex]\[ \text{Amount after withdrawal at the end of year 2} = 2294.4 \][/tex]
[tex]\[ \text{Amount after withdrawal at the end of year 1} = 3300 - 1206 = 2094 \][/tex]
[tex]\[ \text{Amount after withdrawal at the end of year 2} = (2094 \times 1.10) - 1206 = 2294.4 \][/tex]
What are the intercepts of the line?
A.
x-intercept:-8 ; y-intercept:0
B.
x-intercept:0 ; y-intercept:
C.
x-intercept:-8 ; no y-intercept:
D.
no x-intercept: ; y-intercept:-8
Answer:
D cause it crosses at -8
Step-by-step explanation:
How do I calculate the volume of a circle?
A circle, being 2-dimensional, does not have volume.
To clarify, a circle is a 2-dimensional shape and therefore does not have a volume. However, if you intended to calculate the volume of a 3-dimensional shape such as a sphere or a cylinder that has a circular base, here are the steps:
Volume of a Cylinder
The formula for the volume of a cylinder is:
V = πr²h
Volume of a Sphere
The formula for the volume of a sphere is:
V = 4/3 πr³
What is 0.0371 × 10000?
Tom and Arnold both leave the internet cafe at the same time, but in opposite directions. If Tom travels 9mph and Arnold travels 16mph, how long until they are 200 miles apart?
A student athlete run 3 1/3 miles in 30 minutes A professional runner can run 1 1/4 times as far in 30 minutes . how far can the professional runner run in 30 minutes
What is the overtime rate for a mail carrier who regularly earns $9.80 an hour?
The overtime rate for a mail carrier earning $9.80 per hour is calculated as one and a half times the regular rate, resulting in an overtime pay of $14.70 per hour.
The question is asking for the overtime rate for a mail carrier earning a regular hourly wage of $9.80. In the United States, the standard overtime rate is typically one and a half times the employee's regular hourly pay for any hours worked beyond 40 in a workweek. Therefore, to calculate the overtime rate for a mail carrier earning $9.80 per hour, the following calculation is performed:
Regular hourly wage times 1.5 = Overtime rate
$9.80 times 1.5 = $14.70 per hour
Four consecutive even integers add to obtain 324
witch one of these is correct
The function f is such that f(x)=4x-1 find f^-1(x)
0.5cm=1.5m. 36m tall. Find the scale factor.
Final answer:
To find the model height for an object that is 36 m tall using the given scale of 0.5 cm equals 1.5 m, we establish a proportion, which yields a model height of 12 cm, representing the scale factor as 1 cm : 3 m.
Explanation:
The question asks to find the scale factor given that 0.5 cm on a model equals 1.5 m in real life, and an object's real-life height is 36 meters. First, understand that the scale factor is the ratio of the model's size to the actual size. For this scenario, the given scale is 0.5 cm = 1.5 m. To find the model height for an object that is 36 m tall, we use this scale.
Set up a proportion based on the given scale: 0.5 cm/1.5 m = x cm/36 m. Simplifying the ratio to its smallest form, we get 1 cm = 3 m. Therefore, using cross multiplication, we find the height of the model as x = 0.5 cm * (36 m / 1.5 m).
Calculating gives x = 12 cm. Hence, the scale factor, when considering the model's size to the actual size, is represented as 1 cm : 3 m, and the actual model height is 12 cm for the 36 m tall object.
the longest side of an acute isosceles triangle is 8 centimeters . rounded to the nearest tenth, what is the smallest possible length of one of the two congruent sides?
Answer:5.7 cm
Step-by-step explanation:
Just took the test.
Emma is going camping. Each side triangle on her tent is 5 feet tall. The square base is 4 feet wide. What is the surface area of her tent?