The equation of a circle if the ends of the diameter are (18,-13) and (4,-3) is [tex](x-11)^{2}+(y+8)^{2}=74[/tex]
Solution:Given that ends of diameter are (18, -13) and (4, -3)
To find the equation of circle, let us first find the center (h, k) of the circle
We know that the center of the circle lies in the center of the diameter also. In order to find the center, get the average of both x and y
[tex]\mathrm{c}=\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)[/tex]
[tex]\begin{array}{l}{c=\frac{18+4}{2}, \frac{-13-3}{2}} \\\\ {c=\frac{22}{2}, \frac{-16}{2}} \\\\ {\mathrm{c}=(11,-8)}\end{array}[/tex]
These are the coordinates of the center of the circle
Now we need to find the radius, we need the center (h, k) and one of the given points (4, -3):
The equation of circle is given as:
[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]
[tex]\begin{array}{l}{(4-11)^{2}+(-3-(-8))^{2}=r^{2}} \\\\ {(-7)^{2}+(-3+8)^{2}=r^{2}} \\\\ {(-7)^{2}+(5)^{2}=r^{2}} \\\\ {49+25=r^{2}} \\\\ {r=\sqrt{74}}\end{array}[/tex]
So the equation of the circle is:
[tex]\begin{array}{l}{(x-11)^{2}+(y-(-8))^{2}=(\sqrt{74})^{2}} \\\\ {(x-11)^{2}+(y+8)^{2}=74}\end{array}[/tex]
Please explain answer to the math question in the picture thanks so much!
Answer:
[tex]m = -6 \ or \ m = -\frac{1}{4}[/tex]
Step-by-step explanation:
Given
[tex]\frac{1}{m^2+7m+6}+\frac{m+3}{m^2+7m+6}= \frac{5}{m+6}\\[/tex]
Simplifying the above equation we get:
Step 1: Solving for common denominator term we get;
[tex]\frac{1+m+3}{m^2+7m+6}= \frac{5}{m+6}\\\\\frac{m+4}{m^2+7m+6}= \frac{5}{m+6}[/tex]
Step 2: Multiplying denominators on both side we get;
[tex](m+4)(m+6)=5(m^2+7m+6)\\m^2+6m+4m+24 = 5m^2+35m+30\\m^2+10m+24 = 5m^2+35m+30\\5m^2+35m+30-m^2-10m-24=0\\4m^2+25m+6=0[/tex]
Step 3: Now we need to find the factors of m.
[tex]4m^2+25m+6=0\\4m^2+m +24m+6=0\\m(4m+1)+6(4m+1)=0\\(4m+1)(m+6)=0[/tex]
Step 4: Solving for both terms we get;
[tex]4m+1=0\\4m =-1\\m= - \frac{1}{4}[/tex]
Also,
[tex]m+6=0\\m=-6[/tex]
Hence [tex]m = -6 \ or \ m = -\frac{1}{4}[/tex]
What is the slope of a line
Answer:
y=mx+b form; m is the slope
Step-by-step explanation:
So the slope would be the m
Answer: -a/b
Step-by-step explanation:
ax+by=c right?
then slope = -a/b
Jim currently has 1,250 in his bank account and Sally has 1,400 her bank account. Jim deposits 27,50 per week and Sally deposits 20 per week into her account. After how many weeks will they have the same amount of money?
Answer:
In 20 weeks they will have the same amount of money.
Step-by-step explanation:
A direct variation function contains the points (–9, –3) and (–12, –4). Which equation represents the function?
Answer: y = x/3
Have a nice day!
Answer:
[tex]\displaystyle y = \frac{1}{3}x[/tex]
Step-by-step explanation:
First, find the rate of change [slope]:
[tex]\displaystyle \frac{-y_1 + y_2}{-x_1 + x_2} = m \\ \\ \frac{3 - 4}{9 - 12} = \frac{1}{3}[/tex]
Then plug these coordinates into the Slope-Intercept Formula instead of the Point-Slope Formula since you get it done much swiftly that way. It does not matter which ordered pair you choose:
−4 = ⅓[−12] + b
−4
[tex]\displaystyle ±0 = b \\ \\ y = \frac{1}{3}x[/tex]
_______________________________________________
−3 = ⅓[−9] + b
−3
[tex]\displaystyle ±0 = b \\ \\ y = \frac{1}{3}x[/tex]
**You see? I told you it did not matter which ordered pair you choose because you will ALWAYS get the exact same result.
I am joyous to assist you anytime.
Answer:
The answer is...
Step-by-step explanation:
y = 1/3x
--or--
y = x/3
Both forms of writing are equivalent, so either choice would be correct. I hope this helps!
X divided by X+4 =.6666
Answer:
x = 8
Step-by-step explanation:
x/x+4=2/3
3x = 2x + 8
x = 8
Permutations & Cominations:
Your friend is having a party and has 15 games to choose from. There is enough time to play 4 games. In how many ways can you choose the four games?
Answer:
32760 ways
Step-by-step explanation:
Suppose we all want to play different games, so 4 different games. At the first game there are 15 choices, at the 2nd game there are 14, the 3rd one there are 13 selections, and at the last there are only 12 options to select from. Then the total number of ways you can choose the 4 games is
15*14*13*12 = 32760 ways
There are 1,365 ways to choose four games out of the 15 available games.
Step 1
To find the number of ways you can choose four games out of the 15 available games, we use the combination formula:
[tex]\[ C(n, k) = \frac{n!}{k!(n-k)!} \][/tex]
Where n is the total number of games (15) and k is the number of games to choose (4).
Step 2
Plugging in the values:
[tex]\[ C(15, 4) = \frac{15!}{4!(15-4)!} \][/tex]
[tex]\[ = \frac{15!}{4! \times 11!} \][/tex]
[tex]\[ = \frac{15 \times 14 \times 13 \times 12}{4 \times 3 \times 2 \times 1} \][/tex]
[tex]\[ = \frac{32,760}{24} \][/tex]
[tex]\[ = 1,365 \][/tex]
You can choose the four games out of the 15 available games in 1,365 ways, calculated using the combination formula.
What are the center and vertices of the ellipse given by (x-10)^2/49+(y+4)^2/4=1?
The center of the ellipse is (10 , -4) and its vertices are (17 , -4) , (3 , -4)
Step-by-step explanation:
The standard form of the equation of an ellipse with center (h , k)
and major axis parallel to x-axis is [tex]\frac{(x-h)^{2}}{a^{2}}+\frac{(y-k)^{2}}{b^{2}}=1[/tex]
The coordinates of the vertices are (h ± a , k ) The coordinates of the foci are (h ± c , k), where c² = a² - b²∵ The equation of the ellipse is [tex]\frac{(x-10)^{2}}{49}+\frac{(y+4)^{2}}{4}=1[/tex]
- Compare it by the standard form of the equation of an ellipse
∴ h = 10 and k = -4
∴ a² = 49 and b² = 4
∵ The center of the ellipse is (h , k)
∴ The center of the ellipse is (10 , -4)
∵ Its vertices are (h + a , k) and (h - a , k)
∵ a² = 49
- Take square root for both sides
∴ a = 7
∵ h = 10 and k = -4
- Substitute the values of h , a , k in the vertices above
∴ Its vertices are (10 + 7 , -4) and (10 - 7 , -4)
∴ Its vertices are (17 , -4) and (3 , -4)
The center of the ellipse is (10 , -4) and its vertices are (17 , -4) ,
(3 , -4)
Learn more:
You can learn more about the conics in brainly.com/question/4054269
#LearnwithBrainly
what is the y-intercept of the points (-3, 2) and (-2, -4) ?
Answer: -16
Step-by-step explanation:
slope=rise/run
slope=2-(-4)/-3-(-2)=6/-1=-6
y=mx+b
2=(-6)-3+b
b=-16
Answer:
3_561938 you are your
Step-by-step explanation:
3AM said
The expression 1,000(1.0175)2+ describes the amount of money in a savings account after years. Complete the statements.
each year.
The Interest rate is compounded_____each year
1- 1 time
2-2 times
3- 4 times
4- 12 times
The annual Interest rate on the account is ____
1- 1.75%
2- 3.50%
3- 3.53%
4- 3.56%
Answer:
a) 1 time
b) 1.75%
Step-by-step explanation:
a) The given expression is 1,000(1.0175)^2
Here,
1,000 is the principal (Present Value); (1.0175 = 1 + 0.0175) is the compounding interest rate; and 2 is the number of period (Years).
Since two means 2nd year, therefore, the interest is compounded every year. Hence, it is annual compounding interest.
If the interest rate is compounded annually, the interest will be paid one time each year or period.
b) From part a, if we break the expression,
1,000 is the principal (Present Value); (1.0175 = 1 + 0.0175) is the compounding interest rate; and 2 is the number of period (Years).
Since the interest rate is to be compounded annually, the percentage will not affect.
(1.0175 = 1 + 0.0175) in this expression, one is added to the interest to make the future compounding value.
Therefore, 0.0175 is the interest rate. If we take it to the percentage -
0.0175 x 100 = 1.75%.
Answer:
a) 1 time
b) 1.75%
Step-by-step explanation:
yes
3.
12 gallons of water fill a tank to – capacity.
What is the capacity of the tank?
b. If the tank is then filled to capacity, how many half-gallon bottles can be filled with the water in the tank?
Answer:
a. 16 gallons
b. 32
Step-by-step explanation:
Let the full capacity of the tank is x gallons.
a. It is given that 12 gallons of water fill a tank to [tex]\frac{3}{4}[/tex] capacity.
Hence, we can write [tex]\frac{3x}{4} = 12[/tex]
⇒ [tex]x = \frac{4 \times 12}{3} = 16[/tex] gallons.
b. If the tank is filled to capacity, then there will be 16 gallons of water, with which [tex]\frac{16}{\frac{1}{2} } = 32[/tex] numbers of half-gallon bottles of be filled with water. (Answer)
Bobby believes his video game scores are clustered
closer to his median than Amelia's are to her median.
Explain why you agree or do not agree with Bobby.
Lower Quartile
Upper Quartile
Median
Bobby
472
585
535
Amelia
454
633
535
Answer: Bobby’s interquartile range is 113, while Amelia’s is 179. A lower interquartile range means Bobby’s scores are closer to the median.
Step-by-step explanation:
Answer:
his rang is 113 and amelis is 179
Step-by-step explanation:
What is the slope of this graph?
−3
−13
3
13
Answer:
-3
Step-by-step explanation:
start at the y axis where x= 0, go over one and down till your reach the next intersection of the graph, this is over one down three, or -3 for every x over
The result of which expression will best estimate the actual product
06-1(4)-10-1)
06-1(4)-100
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Submit
Mark this and return
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A
6
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Answer:
The answer is,
[tex](-1) \times \frac {1}{2} \times (-1) \times (1)[/tex]
Step-by-step explanation:
The given product is,
[tex]\frac {-4}{5} \times \frac{3}{5} \times \frac{-6}{7} \times \frac {5}{6}[/tex]
= [tex]\frac {12}{35}[/tex]
[tex]\simeq 0.3429[/tex] ---------------------(1)
Now, the first product to compare is,
[tex](-1) \times \frac {1}{4} \times (-1) \times (-1)[/tex]
= - 0.25 ----------------------------(2)
The second product to compare is,
[tex](-1) \times \frac {1}{2} \times (-1) \times (1)[/tex]
= 0.5 ------------------------(3)
The 3rd product to compare is,
[tex]\frac {-4}{2} \times \frac {3}{2} \times \frac{-2}{5} \times \frac {5}{2}[/tex]
= 3 ----------------------------(4)
The 4th product to compare is,
[tex]\frac {-3}{4} \times \frac {-3}{4} \times \frac {-1}{5} \times \frac {1}{2}[/tex]
= [tex]\frac {-9}{160}[/tex]
= 0.05625 -----------------(5)
Comparing all the values , we get (3) is closest to (1).
Hence, we get, the answer is,
[tex](-1) \times \frac {1}{2} \times (-1) \times (1)[/tex]
In the gym , there is a scale that measures people weight . The needle is 22 cm long , and it roared 124 when Evelyn stepped on it . How far did needle travel as it rotated.
The total income for African American households of a certain country making under $250,000 in 2008 is given in the following table. Use the table to estimate the mean income for
African Americans in 2008.
The mean income for African American households in 2008 was __?
(Round to the nearest dollar as needed.)
Answer:
The mean income for African American households in 2008 was $ 45,613 (Rounded to the nearest dollar)
Step-by-step explanation:
1. Given the information from the table, let's calculate the mean income for African Americans households of a certain country in 2008.
For a successful work, first of all we need to take the data from two columns : Midpoint Salary and Frequency (in thousands):
Mean income = (10,000 * 4,491) + (30,000 * 3.844) + (50,000 * 2,500) + (70,000 * 1,498) + (90,000 * 875) + (125,000 * 994) + (175,000 * 323) + (225,000 * 72)/ Sum of all the frequency (in thousands)
Mean income = (10,000 * 4,491) + (30,000 * 3.844) + (50,000 * 2,500) + (70,000 * 1,498) + (90,000 * 875) + (125,000 * 994) + (175,000 * 323) + (225,000 * 72)/ Sum of all the frequency (in thousands)
Mean income = 665'815,000/ 14,597
Mean income = $ 45,613 (Rounded to the nearest dollar)
To calculate the mean income of African American households in 2008, add up all the income amounts and divide by the number of households. Without specific data, an exact mean cannot be given.
Explanation:In order to estimate the mean income for African American households in 2008, we need to use the given data set. However, without knowing the information in the data set, a concrete answer cannot be provided.
Generally, you would add up all the income amounts for all households included in the study, and then divide by the number of households. This would provide the average, or mean, income.
Here is an example using hypothetical data:
Add together the income of each household: 22050 + 18000 + 25000 = 65050. Count the number of households: in this case, 3. Divide the total income by the number of households to get the mean: 65050 / 3 = 21683.33, rounding to the nearest dollar gives $21683 as the mean income. Learn more about mean income here:
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PLS HELP ASAP I WILL GIVE BRAINERLIST
Answer:
4
Step-by-step explanation:
if x = 32 and y = 2, then you just have to substitute the numbers in:
[tex]\frac{32}{4 * 2}[/tex]
so,
[tex]\frac{32}{8}[/tex]
then you simplify
[tex]\frac{4}{1}[/tex]
so the answer is 4
Answer:
2
Step-by-step explanation:
Replace the variables with the real numbers
32/4 2
Multiply
4 x 3 = 12
Divide
32 / 12 = 2⅔
2⅔ ≈ 2
Answer: 2
Edit: Instead, go with D.) 4
Priya bought two plants for a science experiment. When she brought them home, the first plant was 5cm tall and the second plant was 4cm. Since then, the first plant has grown 0.5 cm a week and the second plant has grown 0.75 cm a week.
a. Which plant is taller at the end of 2 weeks? Explain your reasoning.
b. Which plant is taller at the end of 10 weeks? Explain your reasoning.
c. Priya represents this situation with the equation 5 + 0.5w = 4 + 0.75w, where w represents the end of week w. What does the solution to this equation, w = 4 represent in this situation?
d. what does the solution to the inequality 5 + 0.5w > 4 + 0.75w represent in this situation?
Answer:
a. After 2 weeks the first plant will be taller.
b. After 10 weeks the second plant will be taller.
c. After 4 weeks both the plant will be of the same height.
d. This is the condition for the height of the first plant is greater than that of the second plant.
Step-by-step explanation:
The first plant was 5 cm tall and the second plant was 4 cm.
Again, the first plant has grown 0.5 cm a week and the second plant has grown 0.75 cm a week.
So, the height of the first plant after W weeks will be (5 + 0.5W) cm. and the height of the second plant after W weeks will be (4 + 0.75W) cm.
a. After 2 weeks the first plant will be (5 + 2× 0.5) = 6 cm.
And after 2 weeks the second plant will be (4 + 2 × 0.75) = 5.5 cm
So, after 2 weeks the first plant will be taller.
b. After 10 weeks the first plant will be (5 + 10× 0.5) = 10 cm.
And after 10 weeks the second plant will be (4 + 10 × 0.75) = 11.5 cm
So, after 10 weeks the second plant will be taller.
c. If 5 + 0.5w = 4 + 0.75w, give w = 4 weeks, then this means that after 4 weeks both the plant will be of the same height.
d. If, 5 + 0.5w > 4 + 0.75w, then it means that this condition is for the height of the first plant will be more than the second plant. (Answer)
a. After 2 weeks: First plant: 6 cm (taller), Second plant: 5.5 cm b. After 10 weeks: First plant: 10 cm. Second plant: 11.5 cm (taller) c. Solution to 5+0.5w=4+0.75w is w=4, where both plants are equal in height (5 cm). d. Inequality 5+0.5w>4+0.75w indicates the first plant is taller before w=4 weeks.
a. To determine which plant is taller at the end of 2 weeks, let's calculate their heights:
- First plant after 2 weeks: [tex]\( 5 + 0.5 \cdot 2 = 5 + 1 = 6 \)[/tex] cm
- Second plant after 2 weeks: [tex]\( 4 + 0.75 \cdot 2 = 4 + 1.5 = 5.5 \)[/tex] cm
Since 6 cm (first plant) > 5.5 cm (second plant), the first plant is taller at the end of 2 weeks.
b. Now, let's calculate their heights after 10 weeks:
- First plant after 10 weeks: [tex]\( 5 + 0.5 \cdot 10 = 5 + 5 = 10 \) cm[/tex]
- Second plant after 10 weeks: [tex]\( 4 + 0.75 \cdot 10 = 4 + 7.5 = 11.5 \) cm[/tex]
Since 11.5 cm (second plant) > 10 cm (first plant), the second plant is taller at the end of 10 weeks.
c. The equation given is [tex]\( 5 + 0.5w = 4 + 0.75w \)[/tex]. This equation represents the point in time (number of weeks, w) when both plants will have the same height. Solving for w:
[tex]\[ 5 + 0.5w = 4 + 0.75w \][/tex]
Subtract 0.5w from both sides:
[tex]\[ 5 = 4 + 0.25w \][/tex]
Subtract 4 from both sides:
[tex]\[ 1 = 0.25w \][/tex]
Divide both sides by 0.25:
[tex]\[ w = \frac{1}{0.25} = 4 \][/tex]
Therefore, w = 4 represents the number of weeks after which both plants will have the same height, which is 5 cm.
d. The inequality [tex]\( 5 + 0.5w > 4 + 0.75w \)[/tex] represents the point in time (number of weeks, w) when the first plant's height (5 cm + 0.5w) exceeds the second plant's height (4 cm + 0.75w). Solving for w:
[tex]\[ 5 + 0.5w > 4 + 0.75w \][/tex]
Subtract 4 from both sides:
[tex]\[ 1 + 0.5w > 0.75w \][/tex]
Subtract 0.5w from both sides:
[tex]\[ 1 > 0.25w \][/tex]
Divide both sides by 0.25:
[tex]\[ w < \frac{1}{0.25} = 4 \][/tex]
Therefore, the solution to [tex]\( 5 + 0.5w > 4 + 0.75w \)[/tex] represents the number of weeks w when the first plant is taller than the second plant. This happens for ( w < 4 ) weeks.
Original price of a suit: $250.00
Discount: 25%
Tax: 8%
How much will you pay?
Answer:
207,50
Step-by-step explanation:
1% = 2,5
2,5x25 = 62,5 250 - 62,5 = 187,5
2,5x8 = 20
187,5+20= 207,50
when the polynomial f(x) is divided by (x-2) the remainder is 4, and when it is divided by (x-3) the remainder is 7. Given that f(x) may be written in the form f(x)= (x-2)(x-3)Q(x)+ax+b, find the remainder when f(x) is divided by (x-2)(x-3). If also f(x) is a cubic function in which the coefficient of x^3 is unity and f(1)=1, determine Q(x)
The remainder when a cubic polynomial is divided by (x-2)(x-3) can be found using the given remainders with (x-2) and (x-3) separately, resulting in a = 3 and b = -2. Hence, the remainder is 3x - 2. Then, using the condition that f(1)=1 and f(x) is cubic with a leading coefficient of 1, we can determine the entire function and Q(x).
Explanation:Given that a polynomial f(x) has remainders when divided by (x-2) and (x-3), we can establish that:
f(x) = (x-2)(x-3)Q(x) + ax + b, where a and b are constants that represent the remainder when f(x) is divided by (x-2)(x-3).The condition f(x) divided by (x-2) has remainder 4:f(2) = 4, which gives us (2-2)(2-3)Q(2) + 2a + b = 4.The condition f(x) divided by (x-3) has remainder 7: f(3) = 7, which gives us (3-2)(3-3)Q(3) + 3a + b = 7.From these conditions, we derive two equations:
2a + b = 43a + b = 7Solving these simultaneously gives us a = 3 and b = -2. Thus, the remainder when f(x) is divided by (x-2)(x-3) is 3x - 2.
Considering f(x) is cubic and the coefficient of x^3 is 1, f(x) = x^3 + px^2 + qx + r, and since f(1)=1, we can find out Q(x) by plugging the values a, b, and f(1) into the polynomial f(x) and comparing it with the standard cubic form. This will lead us to determine the function Q(x).
Only 6 pleasee it’s due tomorrow thanks
Answer:
a) The amount of edging needed = 7.54 meters
b) Cost to edge the garden = $32.80
Step-by-step explanation:
a)
the amount of edging needed is basically the circumference (perimeter) of the circle. It has the formula:
[tex]C=2\pi r[/tex]
Where
C is the circumference
r is the radius
Given, diameter = 2.4, radius is HALF of it, so
r = 2.4/2 = 1.2
Now, finding circumference:
[tex]C=2\pi r\\C=2\pi (1.2)\\C=7.54[/tex]
The amount of edging needed = 7.54 meters
b)
$4.35 is needed to edge 1 meter, since we need 7.54 meters, we find the total cost by multiplying 4.35 with 7.54, so we have:
4.35*7.54 = $32.80
Cost to edge the garden = $32.80
ANYONE GOOD AT FINDING RHOMBUS??
Answer:
x = 3
Step-by-step explanation:
The diagonals of a rhombus bisect each other at right angles, thus
BE = ED, that is
4x + 2 = 3x + 5 ( subtract 3x from both sides )
x + 2 = 5 ( subtract 2 from both sides )
x = 3
Since diagonals of rhombus bisect each other,
AC bisects BD into two equal parts
ie,
⇒BE=ED
⇒4x+2=3x+5
⇒4x-3x=5-2
⇒x=3
Which triangles must be congruent?
Answer:
Δ ABC ≅ Δ FDE ≅ Δ GIH
Step-by-step explanation:
Between Δ ABC and Δ FDE, given that
(i) AB = DF
(ii) BC = HI and DE = HI, hence, BC = DE
(iii) ∠ B = ∠ D
Hence, by Side-Angle -Side i.e. SAS criteria Δ ABC ≅ Δ FDE
Again, between Δ ABC and Δ GIH, given that
(i) AB = GI
(ii) BC = HI and
(iii) ∠ B = ∠ I.
Hence, by Side-Angle-Side i.e. SAS criteria Δ ABC ≅ Δ GIH.
Therefore, Δ ABC ≅ Δ FDE ≅ Δ GIH (Answer)
school started at 8:05 a.m and ended at 2:40p.m. the work below shows Erica's calculation of the length of the school day
Which two errors did erica make
A.She subtracted instead of adding the times
B.She subtracted the end time from the start time
C.She did not regroup on hours for 60 minutes to subtract the minutes
D.she did not account for a.m. and p.m. in the start and end times.
E.see switch to hours and minutes in both the start and end times
Plz help▪~▪
Answer:
B. She subtracted the end time from the start time and
D. She did not account for a.m. and p.m. in the start and end times.
Step-by-step explanation:
The school started at 8:05 a.m. and ended at 2:40 p.m.
And the length of the school day is calculated by Erica and it is shown in the attached photo.
See the attached photo.
Erica has done two errors which are
B. She subtracted the end time from the start time and
D. She did not account for a.m. and p.m. in the start and end times. (Answer)
Study the following distribution chart.
Number Frequency
1,400 3
1,450 7
1,500 7
1,550 5
1,600 4
1,650 2
1,700 1
What is the mode?
1,500
1,450 and 1,500
1,550
1,525
Answer:
1,450 & 1,500
Step-by-step explanation:
it occured 7 times each
sorry for my hand writing
Write an equation of the line that passes through the points (2, -1) and (2, 5). Show all work
Answer:
x = 2
Step-by-step explanation:
The 2 coordinate points have the same x- coordinate of 2
This indicates that the line passing through them is vertical with equation
x = c
Where c is the value of the x- coordinates the line passes through, thus
x = 2 ← equation of line
What is the slope of the line depicted in this graph? Answer must be written in simplest form.
Answer:
[tex]\large\boxed{\bold{SLOPE}=\dfrac{1}{3}}[/tex]
Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept (0, b)
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
From the graph we have two points (0, 4) → b = 4, and (3, 5).
Calculate the slope:
[tex]m=\dfrac{5-4}{3-0}=\dfrac{1}{3}[/tex]
If you want the equation of a line, then put the value of m and b to the equation of a line:
[tex]y=\dfrac{1}{3}x+4[/tex]
Kaelyn has some yarn that she wants to use to make hats and scarves. Each hat uses 0.2 kilograms of yarn and each scarf uses 0.1 kilograms of yarn. Kaelyn wants to make 3 times as many scarves as hats and use 5 kilograms of yarn. Let h be the number of hats Kaelyn makes and s be the number of scarves she makes.
Answer:
10 hats and 30 scarves
Step-by-step explanation:
Let h be the number of hats Kaelyn makes and s be the number of scarves she makes.
Kaelyn wants to make 3 times as many scarves as hats, so
s = 3h
Each hat uses 0.2 kilograms of yarn, then h hats use 0.2h kg of yarn.
Each scarf uses 0.1 kilograms of yarn, then s scarves use 0.1s kg of yarn.
Kaelyn wants to use 5 kilograms of yarn, thus
0.2h + 0.1s = 5
You get the system of two equations:
[tex]\left\{\begin{array}{l}s=3h\\ \\0.2h+0.1s=5\end{array}\right.[/tex]
Substitute the first equation into the second
[tex]0.2h+0.1\cdot 3h=5\\ \\0.2h+0.3h=5\\ \\0.5h=5\\ \\5h=50\\ \\h=10\\ \\s=3\cdot 10=30[/tex]
Answer:
s=3h
0.2h+0.1s=15
Step-by-step explanation:
A building is 2 ft from a 7 - ft fence that surrounds the property . A worker wants to wash a window in the building 11 ft from the ground . He plans to place a ladder over the fence so it rests against the building . (See the figure .) He decides he should place the ladder 7 ft from the fence for stability . To the nearest tenth of a foot , how long a ladder will he need ?
Answer:
The ladder is approx 14.21 feet long.
Step-by-step explanation:
The base of the ladder is 7 feet from the fence, which is 2 feet from the building, so it will be 9 feet from the building.
The top of the ladder will reach the window which is 11 feet from the ground.
In this way, we get a right triangle with the ladder as the hypotenuse, that we have to find.
Let the hypotenuse be x.
Using the Pythagorean Theorem, we get;
Hence, the ladder is approx 14.21 feet long.
Write an equation of the line that passes through the
points.
(0, 3), (1, 4)
Answer:
y=x+3
Step-by-step explanation:
y-y1=m(x-x1)
m=(y2-y1)/(x2-x1)
m=(4-3)/(1-0)
m=1/1=1
y-3=1(x-0)
y-3=x
y=x+3
ABCD is a parallelogram. Find the measure of B.
Answer:
∠B = 130°
Step-by-step explanation:
The opposite angles of a parallelogram are congruent, thus
∠D = ∠B, that is
10x - 20 = 9x - 5 ( subtract 9x from both sides )
x - 20 = - 5 ( add 20 to both sides )
x = 15
Hence
∠B = 9x - 5 = (9 × 15) - 5 = 135 - 5 = 130°
Answer:
15
Step-by-step explanation:
9x-5=10x-20
X-20=-5
X=15