Answer:
The equation is y = -x + 2.5
Step-by-step explanation:
* Lets explain how to solve the problem
- The form of the equation of a line is y = mx + c , where m is the slope
of the line and c is the y-intercept
- The y-intercept means the line intersect the y-axis at point (0 , c)
- The slope of the line which passes through points (x1 , y1) , (x2 , y2)
is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
* Lets solve the problem
∵ The line passes through the points (-8.5 , 11) and (5 , -2.5)
- Let point(x1 , y1) = (-8.5 , 11) and point (x2 , y2) = (5 , -2.5)
∴ x1 = -8.5 , x2 = 5 and y1 = 11 , y2 = -2.5
∴ [tex]m=\frac{-2.5-11}{5-(-8.5)}=\frac{-13.5}{5+8.5}=\frac{-13.5}{13.5}=-1[/tex]
∴ The slope of the line is -1
∵ y = mx + c
∴ y = -x + c
- To find c substitute x and y in the equation by the coordinates of
one of the two points
∵ Point (5 , -2.5) lies on the line
∴ x = 5 at y = -2.5
∵ y = -x + c
∴ -2.5 = -(5) + c
∴ -2.5 = -5 + c
- Add 5 to both sides
∴ c = 2.5
∴ y = -x + 2.5
* The equation is y = -x + 2.5
The slope and y-intercept to get y = -x + 2.5.
The slope is calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the given points. Substituting the given points into the formula, we get m = (-2.5 - 11) / (5 - (-8.5)) = -13.5 / 13.5 = -1.
Next, we use the slope-intercept form of a line, y = mx + b, to find the y-intercept (b). Substituting one of the points and the slope into this equation, for example, (-8.5, 11), gives us 11 = (-1)(-8.5) + b, which simplifies to b = 2.5.
Therefore, the equation of the line is y = -x + 2.5.
Louise measured the perimeter of her rectangular scrapbook to be 152 cm. If the scrapbook is 42 cm wide, how long is the scrapbook?
A.
76 cm
B.
34 cm
C.
32 cm
D.
68 cm
Answer:
B. 34
Step-by-step explanation:
Perimeter= 42+42+x+x
First add the 42 together
42+42 = 84
Then subtract the number away because this was added to the total
152 - 84 = 68
68 is not your missing number
Dividing 68 by 2 which gives you 34
So,
Perimeter = 42+42+34+34 = 152
Does the point (-10,3) lie on the circle that passes through the point (-2,9) with center (-3,2)? Explain
Answer:
yes
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
here (h, k) = (- 3, 2), so
(x + 3)² + (y - 2)² = r²
r is the distance from the centre to a point on the circle
Calculate r using the distance formula
r = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (- 3, 2) and (x₂, y₂ ) = (- 2, 9)
r = [tex]\sqrt{(-2+3)^2+(9-2)^2}[/tex] = [tex]\sqrt{1^2+7^2}[/tex] = [tex]\sqrt{50}[/tex], hence
(x + 3)² + (y - 2)² = 50 ← equation of circle
Substitute (- 10, 3) into the left side of the equation and if equal to the right side then the point lies on the circle
(- 10, 3) : (- 10 + 3)² + (3 - 2)² = (- 7)² + 1² = 49 + 1 = 50
Hence (- 10, 3) lies on the circle
Amy collected data to determine how many minutes it takes each member of her freshman track team to run five miles. Identify the striking deviation in her data.
A) 25-30 mins
B) 35-40 mins
C) 45-50 mins
D) 50-60 mins
Consider a striking deviation as an outlier (Something that stands out in a pattern, EX: 2, 3, 4, 4, 4, 5, 5, 10 where the outlier would be 10.) Because there is a piece of data at 25-30 minutes that deviates (Or, separates, in a way), it would be considered an outlier (Or, a Striking deviation). Using this information, we can conclude that the answer would be A: 25-30 minutes.
find the quotient. simplify if possible q7÷q26q7÷q26
[tex]\bf q^7\div q^{26}q^7\div q^{26}\implies \cfrac{q^7}{1}\div \cfrac{q^{26}q^7}{1}\div \cfrac{q^{26}}{1}\implies \cfrac{\begin{matrix} q^7 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix} }{1}\cdot \cfrac{1}{q^{26}~~\begin{matrix} q^7 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix} }\cdot \cfrac{1}{q^{26}} \\\\\\ \cfrac{1}{q^{26}q^{26}}\implies \cfrac{1}{q^{26+26}}\implies \cfrac{1}{q^{52}}\implies q^{-52}[/tex]
Find the missing factor.
5y2 + 4y - 1 = (5y - 1)(
)
Answer:
(y + 1)
Step-by-step explanation:
Given
5y² + 4y - 1
To factorise the quadratic
Consider the factors of the product of the coefficient of the y² term and the constant term which sum to give the coefficient of the y- term
product = 5 × - 1 = - 5 and sum = + 4
The factors are + 5 and - 1
Use the factors to split the y- term
5y² + 5y - y - 1 ( factor the first/second and third/fourth terms )
= 5y(y + 1) - 1(y + 1) ← factor out (y + 1) from each term
= (y + 1)(5y - 1)
Miguel has a ladder with legs of equal length. He opened the ladder and placed it on the floor. What type of triangle is formed by the ladder and the floor?
Answer:
(B) isosceles
Step-by-step explanation:
An isosceles triangle is one that has two sides of equal length.
___
If the distance between the legs were the same as the leg length, then the triangle would be equilateral. There is nothing in the problem statement suggesting this is the case.
What is the sample space for the event of flipping a coin and then spinning a four-part spinner, numbered 1, 2, 3, 4?
1. H-1 H-2 H-3 H-4
2. H-1 H-2 H-3 H-4, T-1 T-2 T-3 T-4
3. H-1 T-2 H-3 T-4
.4 1-H 2-H 3-H, 1-T 2-T 3-T
Answer:it is 2 since it include3s all possible answers for both heads & tails.
Step-by-step explanation:
you can get a H1-4 & a T1-4 since you have 4 parts one the spinner & 2 things on a coin (Heads & tails) you can just times 4*2 & know that you have 8 possible answers.
Answer:
H-1 H-2 H-3 H-4, T-1 T-2 T-3 T-4
Harriet calculated 27 divided 4 = 6.75 how can you find 270 divided 4 without dividing
ANSWER
Rewrite and make substitution.
EXPLANATION
Since Harriet calculated 27 divided 4 and had 6.75.
This means that:
[tex] \frac{27}{4} = 6.75[/tex]
Now we want to find
[tex] \frac{270}{4} [/tex]
without divide.
Therefore we need to rewrite the expression so in terms of
[tex] \frac{27}{4} [/tex]
so that we can substitute.
This will give us;
[tex] \frac{270}{4} = \frac{27}{4} \times 10[/tex]
This implies that,
[tex]\frac{270}{4} = 6.75 \times 10[/tex]
[tex]\frac{270}{4} = 67.5[/tex]
If ON= 5x - 7, LM = 4x+ 4, NM = x -7, and OL =3y-4, find the values of c and y for which LMNO MUST BE a parallelogram.
Answer:
x=11, y=8/3
Step-by-step explanation:
Consider quadrilateral LMNO. If this quadrilateral MUST BE a parallelogram, then
LM=NO
and
LO=MN
Thus,
[tex]\left\{\begin{array}{l}4x+4=5x-7\\ \\x-7=3y-4\end{array}\right.[/tex]
Solve this system of two equations. From the first equation:
[tex]4x-5x=-7-4\\ \\-x=-11\\ \\x=11[/tex]
Substitute it into the second equation:
[tex]11-7=3y-4\\ \\3y-4=4\\ \\3y=4+4\\ \\3y=8\\ \\y=\dfrac{8}{3}[/tex]
Let D = {xlx is a state in the United States} be the domain, and let f(x) - "the state capital" be the possible function. Determine if the relation is an example of a function.
Yes, f is a function.
ANSWER
Yes, f is a function.
EXPLANATION
The domain of the relation is D = {xlx is a state in the United States}
The rule is that f(x) ="the state capital"
The relation will be a function if and only if no two elements in the first set have the same image in the second set.
Since no two states will have the same capital, the relation is a function.
A number cube is rolled 360 times, and the results are recorded as follows: 41 ones, 54 twos, 62 threes, 75 fours, 33 fives, and 95 sixes. What is the experimental probability of rolling a 2 or a 3?
A : 0.32
B: 0.18
C: 0.07
D: 0.68
They had 54 twos and 62 threes.
54 + 62 = 116 outcomes of either 2 or 3
The probability is the number of outcomes divided by the total number of rolls.
116 / 360 = 0.32
The answer is A.
Answer:
0.32.
Step-by-step explanation:
Prob(Rolling a 2) = number of 2's rolled / total number of rolls
= 54/360 = 0.15
Similarly Prob(rolling a 3) = 62/360 = 0.17.
So the probability of a 2 or a 3 = 0.15 + 0.17 = 0.32.
What are the solutions to the equation 4b^2-45=-9
Answer:
b = ±3
Step-by-step explanation:
4b^2-45=-9
Add 45 to each side
4b^2-45+45=-9+45
4b^2 = 36
Divide by 4
4b^2 = 36/4
b^2 =9
Take the square root of each side
sqrt(b^2) = sqrt(9)
b = ±3
Please help anyone please
To solve the problem, we need to find the area of the triangle, and then find 2/3 of that triangle.
The equation to find the area of a triangle is bh1/2 or base*height*1/2.
Now substitute the known values.
24*16*1/2
Solve
24*8
192.
Now, the easiest way to find 2/3 of a number is to divide that number by 3 and multiply the answer by 2.
192/3=64
64*2=128
Omar kept 128 square centimeters of the flag.
Hope this helps!
[tex] \frac{16 \times 24}{2} = \frac{384}{2} = 192[/tex]
192 is the total area of the triangle; since he kept 2/3 of the flag divide the area by three and times it by two:
[tex]192 \div 3 = 64 \times 2 = 128[/tex]
answer is 128cm^2
What is the sum of the geometric sequence −4, 24, −144, ... if there are 6 terms?
Answer:
-6718464
Step-by-step explanation:
-4x-6=24
24x-6=-144
and keep on doing times -6 6 more times
Answer: The sum is 25220
Step-by-step explanation:
1) -4
2) -4*-6 =24
3) 24*6 = 144
4) 114*-6 = -864
5) -864*6 = -5184
6) -5184*-6= 31104
The sum is: 25220
The graph below represents the average monthly rainfall (y), in inches, in
Miami, FL during 2012 plotted against the time (x), in months. Which of the
following descriptions is representative of the data presented in the graph?
Answer:
The amount of rainfall increases as an exponential function of time.
Step-by-step explanation:
Answer:
C ;
Here is the picture if the letter changes! Sorry, it was hard to screenshot proof!
☆
EDGE2023; Good Luck :3!!
Evaluate 13 - 0.75w + 8x when w = 12 and x = 1/2
Answer:
8
Step-by-step explanation:
13 - 0.75 (12) + 8 (0.5)
13 - 0.75 (12) + 4
13 - 9 + 4
4 + 4
8
Answer:
8
Step-by-step explanation:
The ratio of dogs to cats at the pet stores 1:3. If there are 6 more cats than Dogs, how many dogs are the pet store?
Answer:
3
Step-by-step explanation:
The number of dogs are 3 if the ratio of dogs to cats at the pet store's 1:3. If there are 6 more cats than Dogs.
What is the ratio?It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.
The ratio of dogs to cats at the pet stores is:
1:3
Let's suppose there are x dogs, then cats are 3x
3x = x + 6
2x = 6
x = 3
Thus, the number of dogs are 3 if the ratio of dogs to cats at the pet store's 1:3. If there are 6 more cats than Dogs.
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Which pair of functions is not a pair of inverse functions?
A. f(x)= x+1/6 and g(x)= 6x-1
B. f(x)= x-4/19 and g(x)= 19x+4
C. f(x)= x5 and g(x)= 5√x
D. f(x)= x/x + 20 and g(x)= 20x/x-1
ANSWER
A,B, and C
EXPLANATION
If
[tex]f(g(x))=g(f(x))=x[/tex]
then f and g are inverse functions.
A.
[tex]f(x) = \frac{x + 1}{6} [/tex]
[tex]g(x) = 6x - 1[/tex]
[tex]f(g(x)) = \frac{6x - 1 + 1}{6} = \frac{6x}{6} = x[/tex]
B.
[tex]f(x) = \frac{x - 4}{19} [/tex]
[tex]g(x) = 19x + 4[/tex]
[tex]f(g(x)) = \frac{19x + 4 - 4}{19} = \frac{19x}{19} = x[/tex]
C.
[tex]f(x) = {x}^{5} [/tex]
[tex]g(x) = \sqrt[5]{x} [/tex]
[tex]f(g(x)) = (\sqrt[5]{x})^{5} = x[/tex]
D.
[tex]f(x) = \frac{x}{x + 20 } [/tex]
[tex]g(x) = \frac{20x}{x - 1} [/tex]
[tex]f(g(x)) = \frac{ \frac{20x}{x - 1} }{ \frac{20x}{x - 1} + 20} = \frac{20x}{40x - 20} = \frac{x}{2x - 1} [/tex]
The correct answers are A, B , C
State if the triangles in each pair are similar.
If so, state how you know they are similar and complete the similarity statement.
A) similar; SAS similarity; ΔBAC
B) not similar
C) similar; SSS similarity; ΔABC
D) similar; SAS similarity; ΔABC
Answer:
Option C) similar; SSS similarity; ΔABC
Step-by-step explanation:
we know that
The SSS similarity state : If the corresponding sides of two triangles are proportional, then the two triangles are similar
In this problem
80/30=56/21=72/27
2.67=2.67=2.67 -----> is true
therefore
The triangles STU and ABC are similar by SSS similarity
Answer: The correct option is
(C) similar; SSS similarity; ΔABC.
Step-by-step explanation: We are given to check whether the pair of triangles in the figure are similar to each other or not.
If so, we are to complete the similarity statement.
From the figure, we note that
the lengths of the sides of triangle STU are
ST = 72, TU = 80 and SU = 56.
And, the lengths of the sides of triangle ABC are
AB = 27, BC = 30 and AC = 21.
So, we get
[tex]\dfrac{ST}{AB}=\dfrac{72}{27}=\dfrac{8}{3},\\\\\\\dfrac{TU}{BC}=\dfrac{80}{30}=\dfrac{8}{3},\\\\\\\dfrac{SU}{AC}=\dfrac{56}{21}=\dfrac{8}{3}.[/tex]
That is,
[tex]\dfrac{ST}{AB}=\dfrac{TU}{BC}=\dfrac{SU}{AC}=\dfrac{8}{3}.[/tex]
Therefore, the corresponding sides of the two triangles are proportional.
Hence, triangle ABC and STU are similar by SSS similarity.
Option (C) is CORRECT.
What is the mode for the data set? 59, 57, 56, 50, 58, 51, 54, 59, 55, 52, 53.
Mode means the number that appears most often in the data. Below I provided a tally of how many each of the numbers appear
59: twice
57: once
56: once
50: once
58: once
51: once
54: once
59: once
55: once
52; once
53: once
As you can see 59 appears the most often, being listed twice in the data set, and is therefore the mode
Hope this helped!
Answer:
your answer would be 59 scenice it goes twice i hope this helps have a great day
Step-by-step explanation:
What would be the appropriate units and intervals to use along the x- and y-axes
X axes are supposed to be positive and the y is negative.
A cylinder has a volume of 140pi
cubic meters and a height of 14 meters. What is the area of the base?
Answer:
The area of the base is [tex]10\pi m^2[/tex]
Step-by-step explanation:
The volume of a cylinder is calculated using the formula:
[tex]Volume=\pi r^2h[/tex]
The volume is given to be:
[tex]V=140\pi m^3[/tex]
The height of the cylinder is h=14 meters.
We substitute these values into the formula to obtain;
[tex]140\pi=\pi r^2\times 14[/tex]
Divide both sides by 14.
[tex]\frac{140\pi}{14}=\pi r^2[/tex]
[tex]10\pi=\pi r^2[/tex]
The area of the base is a circle which is [tex]\pi r^2=10\pi m^2[/tex]
In a child's bank are 11 coins that have a value of S1.85. The coins are either
quarters or dimes. How many coins each does child have?
a. Define your variables:
b. Write the equations:
d. Check:
c. Solve:
Answer:
The child has 6 dimes and 5 quarters.
Step-by-step explanation:
Let q and d represent the number of quarters and of dimes respectively.
Then q + d = 11 (Equation A), and ($0.25/quarter)q + ($0.10/dime)d = $1.85 (Equation B).
Multiply the 2nd equation by 100 to remove the decimal fractions:
25q + 10d = 185 (Equation C)
Now multiply the 1st equation by -10 to obtain -10q - 10d = -110 (Equation D), and combine this result with Equation C:
-10q - 10d = -110
25q + 10d = 185
--------------------------
15q = 75, and so q = 75/15 = 5.
According to Equation A, q + d = 11. Replacing q with 5, we get:
5 + d = 11, and so d = 6.
The child has 6 dimes and 5 quarters.
The surface area of a plastic ball is 196 pi. A sponge ball has a radius twice that of the plastic ball. What is the surface area of the sponge ball?
A. 9,604 pi
B. 993 pi
C. 784 pi
D. 546 pi
Explain your answer and please show all work.
Answer:
Option C. [tex]784\pi\ units^{2}[/tex]
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared
Let
z-----> the scale factor
x----> surface area of the sponge ball
y----> surface area of a plastic ball
[tex]z^{2}=\frac{x}{y}[/tex]
we have
[tex]z=2[/tex]
[tex]y=196\pi\ units^{2}[/tex]
substitute and solve for x
[tex]2^{2}=\frac{x}{196\pi}[/tex]
[tex]x=4*(196\pi)=784\pi\ units^{2}[/tex]
Please help I’m very confused I will mark brainliest
Answer:
$3.52 or $3.53
Step-by-step explanation:
We know that he is paying $2.35 per pound, and that he is buying 1.5 pounds worth of pears. Simply multiply 2.35 times 1.5 to get your answer, depending on how far you round, which is 3.52 or 3.53.
1 pound = $2.35
Leo bought 1 pound and 0.5 of a pound (half of a pound). To find how much 0.5 of a pound costs divide 2.35 (the cost of one full pound) by two
2.35 ÷ 2 = 1.18
so...
1 + 0.5 = 1.5
and
2.35 + 1.18 = 3.53
Leo spent $3.53 on 1.5 pounds of pears
Hope this helped!
~Just a girl in love with Shawn Mendes
if 3x+1 has a value of 17 for some value of x then the expression 6x+1 will have which of the following?
1)22
2)33
3)35
4)42
Answer:
2) 33
Explanation:
First, identify x.
3x+1=17
3x=16
X=16/3
Then substitute x in the expression.
6x+1=?
6(16/3)+1=?
32+1=?
33=?
So, the answer is #2.
When the equation 3x + 1 equals 17, the value of x is 16/3. Substituting this value of x into the expression 6x + 1 results in an answer of 33.
Explanation:The subject of the question is Mathematics and it appears to be at a High School level. Given the equation 3x + 1 = 17, we can first solve for x by subtracting 1 from both sides resulting in 3x = 16 and then dividing both sides by 3 which gives x = 16/3. Then we can substitute this value of x in the expression 6x + 1 giving us 6*(16/3) + 1 which simplifies to 32 + 1 = 33. So, the value of the expression 6x + 1 is 33 when the value of the expression 3x + 1 is 17.
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Find the equation of the line specified.
The slope is 6, and it passes through ( -4, 4).
a.
y = 6x + 4
c.
y = 12x + 28
b.
y = 6x - 20
d.
y = 6x + 28
Answer:
y = 6x + 28
Step-by-step explanation:
We are to determine the equation of a line whose slope or gradient is 6 and passes through the point (-4, 4)
The slope-intercept form of the equation of the straight line would be given by;
y = mx + c
y = 6x + c
We proceed to use the given point to determine c;'
when x = -4, y = 4
4 = 6(-4) + c
4 = -24 + c
c = 28
The slope-intercept form of the equation of the straight line is thus;
y = 6x + 28
For this case we have that by definicon, the equation of a line of the slope-intersection form is given by:
[tex]y = mx + b[/tex]
Where:
m: It's the slope
b: It is the cut point with the y axis.
They tell us that the slope is 6, then:
[tex]y = 6x + b[/tex]
We substitute the given point, to find the cut point:
[tex]4 = 6 (-4) + b\\4 = -24 + b\\b = 4 + 24\\b = 28[/tex]
Finally:
[tex]y = 6x + 28[/tex]
Answer:
Option D
This year, when Latifa and Jameel add their ages, the sum is 29. Latifa’s age is 10 less than twice Jameel’s age. The system of equations that represents this situation is { L+J=29 { L=2J-10. (L is Latifa’s age and J is Jameel’s age). How old is Latifa?
Answer:
Jameel is 13 and Laitfa is 13 x 2 - 10 = 16
16 + 13 = 29
Step-by-step explanation:
The equation has already been given to us, so we just have to solve it.
According to the question,
L + J = 29
L = 2J - 10
L
2J - 10 + J = 29
add 10 both sides
2J + J = 29 + 10 = 39
3J = 39
J = 39/3 = 13
Done!
A bicycle tire makes 40 full revolutions while traveling from where Scott is standing to where Steve is standing.
If the tire has a diameter of 20 inches, what is the approximate distance between Scott and Steve
Answer:approximatly 800 inches is the distance between Scott and Steve
Step-by-step explanation: 40 revolutions * 20 inches
The approximate distance between Scott and Steve is 2513.27 inches.
What is an expression?In mathematics, expression is defined as the relationship of numbers, variables, and functions using mathematical signs such as addition, subtraction, multiplication, and division.
Each revolution of the bicycle tire covers a distance equal to the circumference of the tire, which is equal to pi times the diameter of the tire.
The distance travelled by the bicycle tire for 40 full revolutions is:
Distance = 40 x π x 20 inches
Distance ≈ 2513.27 inches
Therefore, the approximate distance between Scott and Steve is 2513.27 inches.
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4m = ? dm please help me
Answer:
40
Step-by-step explanation:
Just look up the conversion factor and set up the proportion.
1 dm = 1/10 th of a meter
x dm = 4 meters. Cross multiply.
1 dm * 4m = x * 1/10 of a meter. Change 1/10 to a decimal.
1 dm * 4 m = x * 0.1 m Divide by 0.1
1 dm * 4 m /0.1 m = x
x = 40 dm