Answers
The gradient of the line y = x/3 - 4 is; 1/3
What is the gradient of the given line?
Slope is defined as the gradient of a graph at any point
We are given the equation of the line as;
y = x/3 - 4
Now, the formula for equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
Thus, from the given equation, we can tell that the gradient which is the slope is 1/3.
Thus, we conclude that the gradient of the line y = x/3 - 4 is; 1/3
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Related Questions
8 A geometric sequence has all
positive terms. The sum of the
first two terms is 15 and the sum
to infinity is 27.
a
Find the value of the common
ratio.
b Hence, find the first term.
Answers
Let the terms be a, ar, ar², ...
The sum to infinity being 27 means that:
[tex]\frac{a}{1-r}=27 \implies a=27(1-r)[/tex]
The sum of the first two terms being 15 means:
[tex]a+ar=15 \\ \\ (27-27r)+r(27-27r)=15 \\ \\ 27-27r+27r-27r^2 =15 \\ \\ 27r^2 -12=0 \\ \\ 27r^2 =12 \\ \\ r^2=\frac{12}{27}[/tex]
Since all the terms are positive, r>0.
[tex]\boxed{r=\frac{2}{3}} \\ \\ \implies a=27\left(1-\frac{2}{3} \right)=\boxed{9}[/tex]
Biking Tri
Maureen went on a 3 day, 59 mile biking trip. The first day she biked 15.5 miles. The second day she
biked 21.9 miles. How many miles did she bike on the 3rd day ?
Answers
Answer:
21.6 miles
Step-by-step explanation:
59-15.5-21.9= 21.6
or
21.6+15.5+21.9= 59
The heights of all the newborns in a certain country are normally distributed,
with a mean of 18 inches and a standard deviation of 1 inch. A mother just
delivered a baby that is 16 inches long. Which of the following represents the
z-score of the baby's height? (Round your answer to two decimal places.)
Answers
The z-score of the baby's height is -2.0.
The baby's height (x) is 16 inches.A determined "center" value of a group of numbers, the arithmetic mean, is the average of the values.The mean of the heights of all the newborns in the country (µ) is 18 inches.The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.The standard deviation of the heights of all the newborns in the country (σ) is 18 inches.The z-score in statistics is the number of standard deviations that a raw score deviates from or exceeds the mean of the phenomenon being observed or assessed.Let the z-score be denoted by "z".z = (x-µ)/σz = (16-18)/1z = -2To learn more about standard deviation, visit :
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3.What is the official language of cape verd
Answers
Answer:
Portuguese
Step-by-step explanation:
My brother-in-law lived in Cape Verde for 2 years, and he is fluent in Portuguese as a result.
Answer:
Portuguese is the official language of Cape Verde
Translate to an equation, but do not simplify or solve.
Eight more than x is equal to 53.
Solve the equation.
X =
+
Answers
Answer:
x + 8 = 53
Step-by-step explanation:
x + 8 = 53
8 more than x is x + 8 because ur adding 8 more to x. And that is equal to 53 because it literally says IS EQUAL to 53. therefore.
to solve isolate x by subtracting 8 from both side so:
x = 53-8
x = 45
Question 3 (1 point)
Solve the following equation for x
X=
Blank 1:
Next Page
Back
4 (x5)-8 (8 + x) = -64 Pls answer quick
Answers
Answer: -72 I think
Step-by-step explanation:
Solve for g.
G+1/ 2=2
Answers
Answe
G=1.5
Step-by-step explanation:
Simplify to create an equivalent expression.
−
5
(
1
−
5
k
)
−
4
(
2
k
+
5
)
Answers
Answer:
Step-by-step explanation:
1) Distribute the numbers outside of the parenthesis to the numbers inside the parenthesis. This means multiple the outside number to all the numbers that are inside the parenthesis:
-5+25k-8k-20
2) Combine the like terms. The number with k get combined together since they both have a k. The numbers without a k get combined together. When you combine, you ADD the numbers together.
-13k+5
That should be right!
f(x) = 7_4z
20
What is the value of f (6).?
0-0
10
10
5
O
O
15
Answers
Answer:
f(6) = [tex]\frac{3}{5}[/tex]
Step-by-step explanation:
substitute x = 6 into f(x)
f(6) = [tex]\frac{6^2-4(6)}{20}[/tex] = [tex]\frac{36-24}{20}[/tex] = [tex]\frac{12}{20}[/tex] = [tex]\frac{3}{5}[/tex]
the scale from a square park to a drawing is 5 m to 1 cm .the actual park has an area of 1600 m2 .what is the area of the drawing of the park
Answers
The area of the drawing of the park is 64 cm²;
Scale: Square park to Drawing = 5m:1cm
= 5m:0.01m;
Therefore; Square Park Area = 1600m²;
Drawing Area = 1600 ×(0.01/5)²
= 0.0064m² = 64 cm²
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n=.1515
You need to multiply n by a power of 10 to help you find the fraction. Decide on the power of 10 to multiply by, and tell how you identified that number.
Answers
Answer:
the answer is two because ur multiplying hope this helps
According to a survey conducted by a city’s chamber of commerce, approximately 41.5% of city residents prefer local businesses over national chains. The survey had a margin of error of ±3.8%. Round to the nearest tenth, if necessary.
Answers
The values in percentages will be 37.7% and the maximum will be: 45.3%
How to illustrate the information?From the information, the approximately 41.5% of city residents prefer local businesses over national chains and the survey had a margin of error of ±3.8%.
Therefore, the minimum number will be:
= 41.5% - 3.8%
= 37.7%
The maximum will be:
= 41.5% + 3.8%
= 45.3%
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The length of a bacterial cell is about 5 x 10 ^−6 m, and the length of an amoeba cell is about 3.5 x 10 ^−4 m. How many times smaller is the bacterial cell than the amoeba cell? Write the final answer in scientific notation with the correct number of significant digits.
1.4 x 10 ^1
7 x 10 ^1
143 x 10 ^1
7 x 10 ^3
Answers
Answer:7 x 10 ^1 is the right answer
Step-by-step explanation:
Hope this helps :)
There is the bacterial cell 7 × 10¹ times smaller than the amoeba cell which is the correct answer would be an option (B).
What is the Scientific Notation?Scientific Notation is a way of writing down in the easy form of very large or very small numbers.
We have been given that a bacterial cell is around 5 × 10⁻⁶ m long, while an amoeba cell is about 3.5 × 10⁻⁴ m long.
To determine the number of times smaller is the bacterial cell than the amoeba cell.
⇒ amoeba cell / bacterial cell
⇒ 3.5 × 10⁻⁴ m / 5 × 10⁻⁶ m
Apply the division operation, and we get
⇒ 0.7 × 10⁻⁴ × 10⁶
Adding the exponents of the above terms
⇒ 0.7 × 10⁻⁴⁺⁶
⇒ 0.7 × 10²
⇒ 7 × 10¹
Hence, there is the bacterial cell 7 × 10¹ times smaller than the amoeba cell.
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HELP!!
What is the limit of the function in the graph at x=4
Answers
Greetings from Brasil...
Checking the side limits of the function f(x), we find that they are equal, so there is a limit of f(x) as x approaches 4
check the attachment
Sam's parents gave him a map to reach his house. He is 1.5cm from his home. If each 3 cm on scale drawing equals 5 km, how far is he from the house?
Answers
Answer: Sam was 2.5 Km far from his house
Step-by-step explanation:
Sam's parents gave him a map to reach his house.
As per Map Sam was =1.5cm from his home.
To find actual distance from house
If we consider actual distance of sam house =X
We have,
If each 3 cm on scale drawing equals 5 km
We know on map 3cm = 5Km
If 1.5 cm = X Km
We need to cross multiple
3X =1.5 × 5
3X = 7.5
X= 7.5÷3
X= 2.5 Km
Sam was 2.5 Km far from his house.
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Sandra bought 4 bars of chocolate and a packet of nuts for $11.50. If a bar of chocolate costs $0.50 less than a packet of nuts, find the cost of a packet of nuts
Answers
Answer:
A packet of nuts costs $2.70
Step-by-step explanation:
Let C represent the cost of a bar of chocolate and P represent the cost of a packet of nuts
4 bars of chocolate will cost $4C
1 packet of nuts costs $P
Total price Sandra paid is $11.50
This can be represented using
4C + P = 11.50 (1)
A bar of chocolate costs $0.50 less than a packet of nuts. So
P - C =0.50
-C + P = 0.50 (2)
Multiply eq (2) by 4 to get
-4C + 4P = 4 x 0.50
-4C + 4P = 2 (3)
Add equations (1) and (3) to eliminate the 4C term
4C + P - 4C + 4P = 11.50 + 2
P+4P = 13.50
5P = 13.50
Dividing by 5 on both sides
5P/5 = 13.50/5
P = 2.70
So a packet of nuts costs $2.70 (Answer)
To verify this is correct,
Use equation (2) to get
-C + P = 0.50
-C + 2.70 = 0.50
Add C to both sides
-C + 2.70 + C = 0.50 + C
2.70 = 0.50 + C
Subtract 0.50 from both sides
2.70-0.50 = 0.50 + C - 0.50
2.20 = C which is C= 2.20
Plug this value into equation (1)
4(2.20) + 2.70 = 8.80 + 2.70 = 11.50
So verified that answers are correct
a car rent is $250 per week plus $0.1 per mile. Find the rental cost for a three week trip of 800 miles.
Answers
Answer:
$258
Step-by-step explanation:
y = mx + b
m is the miles and y is the total cost
y = .1(800) + 250
y = 8 + 250
y = 258
7. Kiara baked 12 oatmeal cookies and 16 chocolate chip cookies to package in plastic containers for her
friends at school. She wants to divide the cookies into identical containers so that each container has the same
number of each kind of cookie. If she wants to have the greatest number of containers possible, how many
containers does she need? How many oatmeal and chocolate chip cookies will be in each container?
Answers
The greatest possible containers required by Kiara is 4.
The number of oatmeal and chocolate chip cookies in each container is 3 and 4 respectively.
What is defined as the highest common factor?The highest common factor, or HCF, is the greatest number that divides each of two or more numbers.HCF is also recognised as the Greatest Common Measure (GCM) and the Greatest Common Divisor (GCD) .For the given question;
The total number of oatmeal cookies = 12.
The total number of chocolate chip cookies = 16.
Taking the HCF of 12 and 16 (the largest multiple pf 12 and 16).
HCF = 4.
Thus, the number of boxes requires is 4.
The oat place in one box is 3. In 4 boxes it will be 12.
Similarly, the chocolate chip cookies placed in one box is 4. In 4 boxes it will be 16.
Thus, the oat placed in each box is 3 and the chocolate chip cookies placed is 4.
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Ride tickets at the fair can be bought in
packs of 5 tickets for $8.75 or 3 tickets for
$6.25. Simone wants to buy 15 tickets. At
these rates, how much more will she spend
if she only buys packs of 3 tickets?
Answers
She will spend 5 dollars extra if she only buys packs of 3 tickets.
What is a numerical expression?A numerical expression is written in form of numbers and their operations.
According to the given question we can buy 15 tickets in two ways either buying 5 packs which contain 3 tickets and cost 6.25 dollars each pack or we can buy 3 packs which contain 5 tickets which costs 8.75 dollars.
For the first case if we buy 5 packs of tickets that contain 3 tickets it will cost (5×6.25) dollars = 31.25 dollars.
In the second case buying 3 packs of tickets that contain 5 tickets that will cost us (3×8.75) = 26.25 dollars.
∴ She will spend (31.25 - 26.25) = 5 dollars she will spend extra if she only buys packs of 3 tickets.
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Kayla has a red number cube and a blue number cube. Each number cube has faces labeled 1 through 6.
What is the probability Kayla rolls an even number on the red cube and a multiple of 3 on the blue cube?
Answers
So probability that kayla rolls an even number on the red cube and a multiple of 3 on the blue cube is 16.66 ≈ 16%
Given that we have red number cube and blue number cube so as we all know that Probability is the ratio of the favourable number of outcomes to the total number of outcomes is known as Probability.
First, find the possible outcomes.
Kalya has a red number cube and a blue number cube. Each number cube has faces labeled 1 through 6
So, possible outcomes =6×6 =36
Let, S be the sample space.
Then, ⁿ(s) =36
Let, E = the event of getting an even number on the red cube and a multiple of on the blue cube.
E = (2,3),(2,6),(4,3),(6,3),(6,6)
Then, ⁿ(E)=6
Let, P is the probability of the event .
So, P(E)= [tex]\frac{n(E)}{n(S)}[/tex] = [tex]\frac{6}{36}[/tex] = [tex]\frac{1}{6}[/tex] = 16.67 percent or 16[tex]\frac{2}{3}[/tex] %
Thus, the probability Kayla rolls an even number on the red cube and a multiple of on the blue cube is 16.66 percent.
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Answer:
16%
Step-by-step explanation:
find the midpoint of a line segment with endpoints A(-5,5) and B(2,-5)
Answers
Answer:
(-1.5,0)
Step-by-step explanation:
Find the average for the x and y values.
x = [tex]\frac{(-5+ 2)}{2}[/tex] = [tex]\frac{-3}{2}[/tex] or -1.5
y = [tex]\frac{(5- 5)}{2}[/tex] = [tex]\frac{0}{2}[/tex] = 0
Help please im stuck
Answers
Answer: 7.2 hours
Step-by-step explanation:
the interval for each number on the number line is 2.4 because 12 divide by 5 intervals = 2.4
and 2.4 x 3 = 7.2
First you need to find out how long it takes to cook a single kilogram of meat, by doing 12/5 you get 2.4 for one kilo of meat. Now you need to multiply 2.4 by 3 and you will get 7.2, so you can either put 7.2 hours or that converts to 7 hours and 12 minutes.
The Formula A = 1/2BH can be used to find the area of a triangle. Solve the formula for H, and use your equation to find the height of a triangle with an 90 Cm2 and a base of 15 cm.
can someone help me solve it and figure out how to solve it
Answers
Answer: H=2A/B
H=12 cm
Step-by-step explanation:
A = 1/2BH
2A=BH
H=2A/B
H=2(90)/15
H=180/15
H=12 cm
The height of the triangle is 12 cm.
To solve the formula A = (1/2)BH for H, we need to isolate the variable H.
A = (1/2)BH
Multiply both sides of the equation by 2 to eliminate the fraction:
2A = BH
To solve for H, divide both sides of the equation by B:
H = 2A / B
Now we have the formula for H in terms of A and B.
To find the height of a triangle with an area of 90 cm² and a base of 15 cm, we can substitute these values into the formula:
H = 2(90) / 15
H = 180 / 15
H = 12 cm
Therefore, the height of the triangle is 12 cm.
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IV. Are these ratios equivalent? 12 birds to 60 animals 17 birds to 85 animals Yes No
Answers
Answer:
True
Step-by-step explanation:
Both fractions simplify to 1/5 and thus are equivalent
Andrew can paint the neighbor's house 5 times as fast as Bailey. The year Andrew and Bailey worked together, it took them 2 days. How long would it take each to paint the house?
Answers
Answer:
12 days for Bailey
2.4 days for Andrew
Step-by-step explanation:
If Andrew is 5 times as fast, then Andrew + Bailey are 6 times as fast as Bailey alone.
That means Bailey would take 2*6 = 12 days to paint alone.
Since Andrew is 5 times faster, he'd only take 12/5 = 2.4 days.
find the value of x
Answers
Answer:
102°
Step-by-step explanation:
540° ÷ 5 = 108° (sum of angles in a 5-sided figure = 540°)
360° ÷ 4 = 90° (sum of angles in a square = 360°)
180° ÷ 3 = 60° (sun of angles in a triangle = 180°)
360° - 108° - 90° - 60° = 102° (angles at a point add up to 360°)
x = 102°
(Do note that dividing the sum of angles by the number of sides is only applicable if all sides are equal.)
Hope this helps! ^^
Help me pls I'm dying rn
Answers
a) The greatest common factor is 3. And the result is 3 × (6 + 7).
b) The greatest common factor is 7. And the result is 7 × (8 + 5).
What is the factor form of the sum of two integers?In this question we must find the greatest common factor, that is, the maximum integer with which can be divided the two number, and take advantage of this result to simplify the sum of the same two numbers, if possible.
First, we proceed to determine the required results for each of the two cases:
18 = 2 × 3 × 3
21 = 3 × 7
Then, the greatest common factor is 3. The complete procedure is:
18 + 21 = 2 × 3 × 3 + 3 × 7 = 3 × (6 + 7)
56 = 2³ × 7
35 = 5 × 7
Then, the greatest common factor is 7. The complete procedure is:
56 + 35 = 2³ × 7 + 5 × 7 = 7 × (8 + 5)
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Graph the image of △RST after a reflection over the line y=x.
Answers
Answer:
Put S=(1,-10) R(-10,-8) T(-8,-9) Make sure to put a ´ after these letters when you put them down
Step-by-step explanation:
let f(x)= |x-4| +1. write a function g whose graph is a vertical shrink of the graph of f by a factor of 1/3
Answers
The function g(x) is (|x-4| +1)/3.
In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way.The relationships between two or more items are frequently represented by the points on a graph.The graph is compressed vertically, or shrunk, in the direction of the x-axis. If k > 1, the graph of y = k*f (x) is the graph of f (x) that has had each of its y-coordinates extended vertically by the factor k.The function f(x) is defined as |x-4| +1. To vertically shrink the graph of f(x) by a factor of 3, divide the function by 3.g(x) = f(x)/3g(x) is equal to (|x-4| +1)/3.To learn more about functions, visit :
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Q. You work for a food wholesaler that provides ingredients for restaurants and other food
producers. A large-scale bakery needs 72 pounds of raisins. The raisins come in 12-ounce
boxes. A total of 24 boxes will fit in a case. How many cases of raisins should you ship to
them?
Answers
The cases that would be shipped is 4.
How many cases would be shipped?The first step is to convert pounds to ounce
1 pound = 16 ounce
16 x 72 = 1152 ounces
The next step is to determine how many boxes would be needed.
Boxes needed = 1152 / 12 = 96 boxes
The third step is to determine the number of cases that would be shipped.
Cases that would be shipped = 96 /24 = 4
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