Based on the given graphs and their equations, the solutions will be located at points (-2, 7) and (0, 1).
Where are solutions located?To find the solution to y = -2x+ 3, assume that x is a certain number then solve for y.
Given the options, we can assume that x = -2. Solution is:
= -2(-2) + 3
= 4 + 3
y = 7
Solution point is (-2, 7)
The second equation can be solved by equating x to 0:
y = 0² - 0 + 1
y = 1
Solution point is:
= (0, 1)
In conclusion, the solution points are (-2, 7) and (0,1).
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The line y= mx + c is parrallel to the line y=2x + 8
The distance AB is 9 units
Find the value of m and the value of c.
Answer: 2 and -10 respectively
Step-by-step explanation:
m in the equation is 2 as it is parallel to a line with a slope of 2
Both point A and B are on the x-axis so both of them have a y value of 0
To find the x value of A, we have to substitute y = 0 into the equation
2x + 8 = 0
x = -4, so the coordinate for A is A(-4,0)
As AB is 9 units, we can figure out that B(5,0)
Substitute x = 5 and y = 0 into the equation y = 2x + c to find c
0 = 2(5) + c
c = -10
So m = 2 and c = -10
Jane has 8 toy cats and 4 baskets. If she wants to arrange 2 toy cats in each basket, how many different ways can she arrange the toy cats?
Step-by-step explanation:
In mathematics, a combination is a selection of items from a set that has distinct members, such that the order of selection does not matter.
The number of combinations of n objects taken r at a time is determined by the following formula:.
nCr = n! / (n-r)! r!
n = total number of objects in the set
r = number of choosing objects from the set
so here , Jane has 8 toys and first she wants to take 2 toys ....
so , 8C2 = 8! / 6! 2! = 28 ways
so , she selected 2 toys ,,, After she wants to take 2 toys among 6 toys ....
so , 6C2 = 6! / 4! 2! = 15
next , picking 2 toys out of 4
So , 4C2 = 4! / 2! 2! = 6
next , 2C2 = 2! / 0! 2! = 1
total ways to pick toys = 28 × 15 × 6 × 1
= 2520 different ways ..
request :- Sorry if there are some mistakes in my English.
In the diagram below, EF || HG, EF = 5, HG = 12, FI = 1 4x + 3
and HI= 6.1x - 6.5.
What is the length of HI?
The length of HI in the similar triangles is: (4) 24.
What are Similar Triangles?The corresponding sides of triangles that are similar to each other have ratios that are equal to each other, thus, they are proportional.
Triangle EFI and triangle GHI are similar to each other. Therefore, their corresponding sides have ratios that are equal. Thus, we will have the following:
HI/FI = HG/EF
Given:
EF = 5,
HG = 12,
FI = 1.4x + 3
HI = 6.1x - 6.5
Plug in the values
6.1x - 6.5/1.4x + 3 = 12/5
Cross multiply
5(6.1x - 6.5) = 12(1.4x + 3)
Open the bracket
30.5x - 32.5 = 16.8x + 36
30.5x - 16.8x = 32.5 + 36
13.7x = 68.5
Divide both sides by 13/7
13.7x/13.7 = 68.5/13.7
x = 5
HI = 6.1x - 6.5
Plug in the value of x
HI = 6.1(5) - 6.5
HI = 30.5 - 6.5
HI = 24
The length of HI in the similar triangles is: (4) 24.
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Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
In the given diagram, ∆ABC is a right triangle with . Segment AB is divided into four equal parts.
A right triangle A C B with A at (negative 3, negative 1), C at (negative 3, negative 3), and B at (6, negative 3). Side A B has 3 points D, E, and F, from the top to the bottom in equal increments. A line runs down from D to G on side C B.
The coordinates of point F are (
,
), and the coordinates of point G are (
,
).
The coordinates of point F are (15/4 , -5/2)
The coordinates of point G = (-3/4 , -3)What is the coordinates about?From the image attached:
AB divided into 4 similar parts, hence
E is the mid-point of AB D is the mid-point of AE F is the mid-point of EBNote that the rule of the mid-point states that:
When M (x , y) is the mid-point of the segment of AB, where A (x1 , y1) and B (x2 , y2), Then x = (x1 + x2)/2 and that of y = (y1 + y2)/2
Then lets solve for points E, F, D
Since A (-3 , -1) and B (6 , -3),
E is the mid-point of AB
Then E =[(-3 + 6)/2, (-1 + -3)/2]
= (3/2 , -2)
Since F is the mid-point of EB,
E (3/2 , -2) , B (6 , -3)
Then F = [(3/2 + 6)/2 , (-2 + -3)/2]
= (15/4 , -5/2)
Since D is the mid-point of AE, A (-3 , -1), E (3/2 , -2)
Then D = [(-3 + 3/2)/2 , (-1 + -2)/2]
= (-3/4 , -3/2)
Note also that:
BC is said to be an horizontal segment due to the fact that B and C have similar y - coordinate and G can be found on BC.
Since the y-coordinate of G is similar to y-coordinate of B and C
Then y-coordinate of G is = -3
Since DG ⊥ BC
Then DG = vertical segment
So G has similar x-coordinate of D
Then The x-coordinate of G = -3/4
The G = (-3/4 , -3)
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please answer my question
Answer:
[tex]\frac{8}{3}[/tex]
Step-by-step explanation:
mean: (22+12+14+14+13+9)=14
|22-14| + |12-14| + ... + |9-14| =16
MAD = 16/6 = [tex]\frac{8}{3}[/tex]
The table shown below gives the estimated number of text messages sent in the U.S. by year. Approximately how many times as many text messages were sent in the U.S. in 201120112011 as in 200520052005?
The approximate number of text messages sent in 2011 is 2 x 10^1.
What is the approximate number of text messages sent in 2011 ?Scientific notation is used in expressing large numbers in smaller numbers. To write a number in scientific notation, the number is written as a decimal number, between 1 and 10 and multiplied by a power of 10.
118, 000, 000, 000 in scientific notation is 1,18 x 10^11
2,357, 000, 000, 000 in scientific notation is 2.357 x 10^12
Difference in messages sent in 2011 compared to 2005 : (2.357 / 1.18) x 10^(12 - 11)
2 x 10^1
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An urn contains balls numbered 1 through 15. a ball is chosen, returned to the urn, and a second ball is chosen. what is the probability that the first and second balls will be a 6?
Can someone help me with this?
20 points for the Answer to this
Thank You for leaving your answer here!
Answer:
182000
Step-by-step explanation:
4.82 x 10^5
1.
10^5 is equal to 10 being multiplied 5 times. So this can be expressed as:
10 x 10 x 10 x 10 x 10.
When you multiply 10s, you just add the number of zeros next to one.
==> 100000 (5 zeros total)
2.
We multiply 100000 to 4.82.
100000 x 4.82 = 182000
So our final answer will be 182000.
Answer:
482,000.
Step-by-step explanation:
The 5 tells us this number is 6 digits long.
The answer is
482,000
help if u can ty! pls do not answer if u cannot help
Based on the logarithms given, the requirement to use one digit, and the figures to be produced, the right numbers are:
log₈2 · 4log₇ 6/5log₉3¹What log produces an integer?The log of a number gives 1 which is an integer so we can find numbers that when multiplied, produce a number that can be taken a log of. Those numbers are 2 and 4:
= 2 x 4
= 8
Log₈ = 1
What log produces an irrational number?Taking the log of a number to a decimal form leads to an irrational number. So, find numbers that when divided, will give a decimal:
= 6/5
= 1.2
Take a log of 7:
log₇ (1.2) will give an irrational number.
The remaining numbers ae 9, 3, and 1.
What log produces a rational number?With the numbers 9,3 and 1, the log to produce a rational number is:
log₉3¹ = log₉9¹/² = 1/2
1/2 is a rational number.
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Pls answer both the question its urgent
Answer:
not sure but I think it is this
Use the recursive formula to find the first five terms in the arithmetic sequence.
Answer:
is 54, 45, 36, 27, 18
Step-by-step explanation:
Recursive formulas give us two pieces of information:
1. The first term of the sequence
2. The pattern rule to get any term from the term that comes before it
In the formula given,
n is any term number
f(n) is the nth term
This means
f(1) is the first term
f(f-1) is the term before the nth term
To find the first five numbers in this arithmetic sequence, we know the formula has given us these two pieces of information:
1. The first term is 54
2. The rule to get any term from its previous term is -9
So, we know the sequence for this formula is 54, 45, 36, 27, 18 because starting off with 54, then minus 9 from every sum gives us the following equations
54-9=45
45-9=36
36-9=27
27-9=18
HELP ME ASAP
20 points !!!
How to factorise completely please help this is algebra
(a) (x-12)(x+11)
(b) x³-4x=x(x²-4)=x(x-2)(x+2)
A spirit shop outside the hockey stadium sells merchandise representing the three school districts that built the arena. the entrances to the arena, the spirit shop, and the parking lot form the vertices of a triangle. the planning committee has decided to erect a memorial statue and would like it to be equidistant from the entrances to the arena, the spirit shop, and the parking lot. at what point should the statue be located? explain your answer.
Point E is where the statue should be placed.
What is called a triangle?A triangle in geometry is a three-sided polygon with three edges and three vertices. The fact that a triangle's internal angles add up to 180 degrees is its most crucial characteristic. This characteristic is known as the triangle's angle sum property.Triangles are three-sided shapes. The various kinds of triangles go by various names. The angles' size and the sides' length determine the type of triangle (corners). Equilateral, isosceles, and scalene triangles are the three varieties of triangles based on the length of the sides.The triangle is most frequently seen in our daily lives on traffic signs. The signs are triangular in shape and equilateral, which means that all three of their sides are the same length and have the same angle.At what point should the statue be:
The intersection of the doors to the arena, the spirit store, and the parking lot forms a triangle, with Point E in its center. The radius of the circumscribed circle will therefore equal the distance from the statue to each vertex, placing it at the same distance from all three landmarks.
Point E is where the statue should be placed.
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Consider the following set of equations:
Equation A: y = -x + 5
Equation B: y = 6x - 2
Which of the following is a step that can be used to find the solution to the set of equations?
O-x=6x + 2
O-x-2= 6x + 5
O-x+5= 6x-2
dations:
O-x+ 5 = 5x
The correct option is the thrid one, the first step is
-x+5= 6x-2
Which of the following is a step that can be used to find the solution to the set of equations?Here we have the system of equations:
y = -x + 5
y = 6x - 2
Now, the variable "y" should represent the same thing in both equations, then we can write:
-x + 5 = y = 6x - 2
If we remove the middle part, we get the equation that only depends on x:
-x + 5 = 6x - 2
This is the first step that we should use to solve the system of equations, which is the one in option 3.
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Please help with 54 :(
Answer:
A is the answer
[tex]x = \frac{1}{48} [/tex]
find the value of n:
[tex]\frac{n}{11} = \frac{3.5}{7}[/tex]
The value of n from the given expression is 5.5
Solution to linear equation and fractionsFractions are expression written as a ratio of two integers. The linear equation on the other hand has a leading degree of 1.
Given the equation below;
n/11 = 3.5/7
Simplify to have
n/11 = 1/2
Cross multiply the given result to have:
11 = 2n
Swap
2n = 11
Divide both sides by 2 to have;
2n/2 = 11/2
n = 5.5
Hence the value of n from the given expression is 5.5
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HELP ASAP!!
ABC is similar to QRS. If AB=3 when QR=1,
what is the measure of BC if RS=1.5?
A: 1.5
B: 3
C: 4.5
D: 5
Answer:
C
Step-by-step explanation:
Im going to be quick on this since your in a hurry, is AB is 3 and QR = 1 and their similar then BC would be 3 times the amount of RS which is 1.5 so the Answer is 4.5
Answer:
C
Step-by-step explanation:
___ AA
*~/■ ■ ⊂ P
| ■ ■.(_)
U U ̄ ̄U U
4. Which of the following can be used
to support the idea that the set of
polynomials is closed under
multiplication?
A (5x-1)(3x² +4x)
B
(9x³-5)(2x-17)
(10x0.5-8)(5x0.5 +4)
D(2x¹5x¹)(7x-2x5)
The option that can be used to support the idea that the set of polynomials is closed under multiplication is; Option C: (10x^(0.5) - 8)(5x^(0.5) + 4)
What is the Closure property under multiplication?When multiplying polynomials, the variables' exponents are added, according to the rules of exponents. It is pertinent to note that the exponents in polynomials are whole numbers. The whole numbers are closed under addition, which guarantees that the new exponents will be whole numbers. Thus, we can also say that the polynomials are closed under multiplication.
Now, looking at the options, we can say that option C is the only polynomial that is closed under multiplication because its' variables and exponents will not change;
(10x^(0.5) - 8)(5x^(0.5) + 4)
The output will retain the same thing.
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G= -x^2 - 2xy - y^2
K= x^2 + 4y^2 + 4xy
H= 4x^2 - 12xy + 9y^2
L= 25 - 10 + y^2
M= 10y^4 + 25x^6 +y^8
Answer:
Step-by-step explanation:
I am assuming you want to factor these functions
G= -x^2 - 2xy - y^2
= -(x^2 + 2xy + y^2)
We need 2 terms whose product is y^2 and whose sum is +2xy
- they are + x and + y
= - (x + y)(x + y)
= -(x + y)^2
The other functions are worked out in the same way:
K = x^2 + 4y^2 + 4xy
= (x + 2y)(x + 2y)
= (x + 2y)^2
H = 4x^2 - 12xy + 9y^2
= (2x - 3y)^2
L= 25 - 10 + y^2
= (5 - y)^2
M = 10y^4 + 25x^6 +y^8
- this is prime (no factors)
Find the area of quadrilateral abcd. [hint: the diagonal divides the quadrilateral into two triangles.]
The area of quadrilateral ABCD exists equivalent to the area of triangle ABD plus the area of triangle ADC
Heron's Formula exists a technique for estimating the area of a triangle when you know the lengths of all three sides.
Therefore, the total area of quadrilateral abcd exists 28.53 [tex]$$units^2[/tex].
How to find the area of quadrilateral abcd?Let a, b, and c be the lengths of the sides of a triangle.
The area is given by:
[tex]$$A = \sqrt{p(p-a)(p-b)(p-c)}[/tex]
where p exists half the perimeter
[tex]$p = \frac{a+b+c}{2}[/tex]
To estimate the area of triangle ABD
we have
a = AB = 2.89 units
b = BD = 8.59 units
c = DA = 8.6 units
To estimate the perimeter
[tex]$p = \frac{2.89+8.59+8.6}{2}[/tex]
= 10.4 units
To estimate the area
[tex]$A = \sqrt{10.04(10.04-2.89)(10.04-8.59)(10.04-8.6)}[/tex]
[tex]$A = \sqrt{10.04(7.15)(1.45)(1.44)}[/tex]
[tex]$A = \sqrt{149.89}[/tex]
A = 12.24 [tex]$$units^2[/tex]
To estimate the area of the triangle ADC
we have
a = AC = 4.3 units
b = AD = 8.6 units
c = DC = 7.58 units
To estimate the half perimeter p
[tex]$p = \frac{4.3+8.6+7.58}{2}[/tex]
= 10.24 units
To estimate the area
[tex]$A = \sqrt{10.24(10.24-4.3)(10.24-8.6)(10.24-7.58)}[/tex]
[tex]$A = \sqrt{10.24(5.94)(1.64)(2.66)}[/tex]
[tex]$A = \sqrt{265.35}[/tex]
A = 16.29 [tex]$$units^2[/tex]
To estimate the total area
A = 12.24+16.29 = 28.53 [tex]$$units^2[/tex].
Therefore, the total area of quadrilateral abcd exists 28.53 [tex]$$units^2[/tex].
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What must be true in order to find a sum for an infinite geometric series?
Answer:
0 < r < 1
Step-by-step explanation:
That every sequence gets multiplied by a number less than 1 but more than 0
The law is
Common ratio or r must lies in between 0 and 1
It means
r is in (0,1)
r is greater than 0 but less than 1The formula is
[tex]\boxed{\sf S_{\infty}=\dfrac{a}{1-r}}[/tex]
x = 2, y = 7
x = 5, y = 2
x = 3, y = 5
x = 7, y = 3
f(x) = 4x² - 7x - 15
Part A: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)
Part B: Is the vertex of the graph of f(x) going to be a maximum or minimum? What are the
coordinates of the vertex? Justify your answers and show your work. (3 points)
Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers
obtained in Part A and Part B to draw the graph. (5 points)
(10 points)
Look at the attached image above ☝️for explanation
Hope it helps! and if it's not pls tell me on the comment.
How many ways are there to select five unordered elements from a set with three elements when repetition is allowed?
The number of ways or permutations to select five unordered elements from a set with three elements when repetition is allowed is 243.
According to the given question.
The total number of elements, n = 3
The number of elements to be selected at a time when repetition is allowed, r = 5
Since, we know that " the number of ways or permutations of n things taken r all at a time, when repetition of things are allowed, is [tex]n^{r}[/tex].
Therefore,
The number of ways or permutations to select five unordered elements from a set with three elements when repetition is allowed
= [tex]3^{5}[/tex]
= 243
Hence, the number of ways or permutations to select five unordered elements from a set with three elements when repetition is allowed is 243.
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Zhang is constructing a loading ramp (BA) that is 4-feet high (AC). The back of the base (BC) must be 12.8 ft. How long must the entire base (BD) be?
Proportion : __________________
Front of base: __________
Total base: __________
The front of the base is 1.25 ft and the total base is 14.05 ft.
How to find the side of a right triangle?A right triangle has one of its angles as 90 degrees. The side of a right angle triangle can be found using trigonometric ratios.
The sides CD and BD can be found using similar triangle principle.
In similar triangles, corresponding sides are always in the same ratio.
Therefore, the following proportion can be established as follows;
[tex]\frac{BC}{AC}=\frac{AC}{CD}[/tex]
Hence,
[tex]\frac{12.8}{4}=\frac{4}{CD}[/tex]
cross multiply
4 × 4 = 12.8 CD
16 = 12.8CD
divide both sides by 12.8
CD = 16 / 12.8
CD = 1.25 ft
BD = 1.25 + 12.8 = 14.05 ft
Therefore, the front of the base is 1.25 ft and the total base is 14.05 ft.
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What is the domain of the function graphed below? x<7 x less than or equal to 7 -2 less than or equal to x less than or equal to 3 all real numbers
The domain of the function shown in the graph is x < 7
How to determine the domain of the function shown in the graph?The complete question is added as an attachment
The domain is the set of x values the function can take
From the graph, we have the following x values
Minimum x value = Negative infinityMaximum x value = 7 (with an open circle)This means that the domain of x in the graph is x < 7
Hence, the domain of the function shown in the graph is x < 7
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Sariah has just begun training for a half-marathon, which is latex: 13.1 13 . 1 miles. since she was on vacation, she started the training program later than the rest of her running club. there are latex: 6 6 weeks of training runs remaining before the race. in her first week of training, sariah ran latex: 3 3 miles. she ran latex: 4.5 4 . 5 miles the second week and latex: 6 6 miles the third week. if she continues to increase the length of her runs the same way, will there be enough time left in the training program for her to get up to half-marathon distance? describe how you would solve this problem using polya's four-step problem-solving method. complete each task as part of your response. be sure to number your answers task 1–task 4 so that your instructor can tell which part you are answering. otherwise, you may not receive credit.
Sariah has just begun training for a half-marathon, which is latex: 13.1 13 . 1 miles. since she was on vacation, she started the training program later than the rest of her running club. there are latex: 6 6 weeks of training runs remaining before the race. in her first week of training, sariah ran latex: 3 3 miles. she ran latex: 4.5 4 . 5 miles the second week and latex: 6 6 miles the third week. if she continues to increase the length of her runs the same way, will there be enough time left in the training program for her to get up to half-marathon distance? describe how you would solve this problem using polya's four-step problem-solving method. complete each task as part of your response. be sure to number your answers task 1–task 4 so that your instructor can tell which part you are answering. otherwise, you may not receive credit. Understand the problem.
Task 1: Read the problem and restate in y0ur own words what the question asks.
2. Formulat3 a plan.
Task 2: Identify the model y0u would use to represent the problem and explain why y0u chose that model.
3. Implement th3 plan.
Task 3: Solve the problem and state y0ur answer.
4. Review th3 results.
Task 4: Explain the problem-solving process and how y0u know y0ur answer is correct.
What is half-marathon?Half of a marathon's distance, or 21.0975 kilometers (13 miles 192.5 yards), is covered during a half marathon. Using nearly the same course with a later start, an earlier finish, or shortcuts, a half marathon event is sometimes held alongside a marathon or a 5K race. If finisher medals are given out, they might not look exactly like the ones given out for the full marathon. Although these measurements are rounded and not officially correct, the half marathon is frequently referred to as a 21K, 21.1K, or 13.1 miles.
The International Association of Athletics Federations recognizes a half marathon world record.
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Arrange the Fractions in Descending order
Step-by-step explanation:
How can these fractions be arranged in descending order?Arranging fractions in descending order means arranging the fractions starting from the highest to the lowest.
Finding the LCM of 3, 16, 12, 24,
[tex] \frac{2}{3} \: \frac{5}{16} \frac{7}{12} \frac{11}{24} \\ \\ \frac{32 + 15 + 28 + 22}{48} \\ \\ Arranging \: the \: fractions \: in \: descending \: order \\ \frac{2}{3} \frac{7}{12} \frac{11} {24} \frac{5}{16} [/tex]
PLS IM SO STUCK ITS MATH
Answer:
y-intecept: (0,14), x-intercept: (-8,0)
Step-by-step explanation:
Let us first solve for the y-intercept, solve the equation for y to set it to slope-intercept form.
[tex]-7x+4y=56\\4y=56+7x\\y=14+\frac{7}{4}x\\y=\frac{7}{4}x+14\\[/tex]
Now we have our y-intercept, 14
To solve for the x-intercept, all we have to do is set y to 0 and solve for x:
[tex]0=\frac{7}{4}x+14\\-14=\frac{7}{4}x\\-56=7x\\-8=x[/tex]
Therefore our x-intercept is -8.
To find the vector (x and y value) of the x intercept, we set the y value equal to 0, such as the vector of the x-intercept is equal to (-8,0).
For the y-intercept we follow a similar approach setting the x-value equal to 0, making it (0,14)