Answers
#6 is using using ratios:
7/2x+4 = 4/x+3 =
8x+16 =7x+21 =
8x=7x+5 =
x=5
AC = 2(5)+4= 14 + 5+3=8, 14+8 =22
#7
ratio of known sides 9/4 =2.25 now multiply other 2 sides by 2.25
7*2.25 = 15.75
9*2.25=20.25
perimeter = 9 +15.75+20.25 = 45
Related Questions
find the area of the kite
Answers
The diagonals are 3 cms long each. The area of the kite in the given figure is 9 [tex]cm^2[/tex].
Mathematically, a quadrilateral with two pairs of adjacent sides that are congruent (have equal length) is termed a "kite". Note that not all quadrilaterals with congruent adjacent sides are kites. Kites have numerous applications in geometry, including the study of polygons, symmetry, and angles. They can be used to solve geometric problems and to analyze relationships between sides, angles, and diagonals within the quadrilateral.
Given that the length of the diagonals = 3 cm.
It is known that
Area of a quadrilateral with equal diagonals = product of the diagonals.
Area = 3 [tex]\times[/tex] 3.
Area = 9 [tex]cm^2[/tex].
The area of the kite is 9 [tex]cm^2[/tex].
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what three consecutive integers equal 81
Answers
so middle number = 27
the other 2 are 26 and 28
answer
26, 27, 28 are three consecutive integers equal 81
That sum to 81:
n+n+1+n+2=81 combine like terms on left side
3n+3=81 subtract 3 from both sides
3n=78 divide both sides by 3
n=26
So the three numbers are 26, 27, and 28.
Mr. Smith brings home 7 animals for his 7 children. Each child will adopt a pet to be her or his own. There are 4 different cats (a Siamese, a Persian, a Calico, and a Minx), 2 different dogs (a Poodle and a Golden Retriever), and a goldfish. Anna and Betty refuse to take care of the goldfish, and Charlie and Danny insist on having cats. The other 3 kids are easier to please -- they'll take anything. In how many ways can Mr. Smith give the children pets?
Answers
Given the constraints, the total number of ways Mr. Smith can distribute pets to his children is calculated as 216 ways. This involves the concept of combinations and permutations from combinatorics in mathematics.
Explanation:The problem posed is a typical combinatorics or probability question found in mathematics. Given the constraints, the number of ways Mr. Smith can distribute pets is calculated as follows:
Let's first assign pets to Charlie and Danny. They insist on having cats, but are not particular about which one. As there are 4 cats, there are *4 choose 2* ways to select two cats for them, which is 6. Anna and Betty refuse to take care of the goldfish, so they can either get the remaining two cats or one of the two dogs. This can be done in *4 choose 2* ways, or 6 ways. The remaining three children can accept any of the three remaining pets. Therefore, there are *3!* (3-factorial) ways to distribute the remaining pets. The factorial function (represented by !) means multiply all positive integers from the number to 1. Therefore, 3! = 3x2x1 = 6.
Since these scenarios are independent, we multiply these results. Hence, the total number of ways Mr. Smith can distribute pets to his children is 6 x 6 x 6 = 216.
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Considering the preferences of each child, there are 2160 different possible ways Mr. Smith can distribute the 7 pets to his 7 children.
Explanation:The question posed is a classic problem of combinatorics. We have Anna, Betty, Charlie, Danny, and three other unnamed children who will be receiving pets. Anna and Betty do not want the goldfish, and Charlie and Danny want only cats. Therefore, options for Anna and Betty include the 4 cats and 2 dogs (6 choices total). For each choice Anna makes, Betty has one less choice (5). We can multiply these together, which will give us 30 possible assignments for Anna and Betty. For Charlie and Danny, who just want cats, there are 4 available. Charlie can have one of 4, then Danny can have one of the remaining 3, yielding 12 possibilities.
With Anna, Betty, Charlie, and Danny assigned pets, there are 3 children and 3 pets (2 dogs and 1 goldfish) remaining. Three children can be given 3 pets in 3! = 3*2*1 = 6 ways.
Finally, multiplying these together gives us 30 * 12 * 6 = 2160 possible ways Mr. Smith can distribute the pets among his children.
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Find all complex solutions of x^2+5x-5=0.
(If there is more than one solution, separate them with commas.)
Answers
remember that √-1=i
so
for
ax^2+bx+c=0
[tex]x=\frac{-b+/-\sqrt{b^2-4ac}}{2a}[/tex]
so
given
1x^2+5x-5=0
a=1
b=5
c=-5
[tex]x=\frac{-5+/-\sqrt{5^2-4(1)(-5)}}{2(1)}[/tex]
[tex]x=\frac{-5+/-\sqrt{25+20}}{2}[/tex]
[tex]x=\frac{-5+/-\sqrt{45}}{2}[/tex]
[tex]x=\frac{-5+/-3\sqrt{5}}{2}[/tex]
solutions:
[tex]x=\frac{-5+3\sqrt{5}}{2}, \frac{-5-3\sqrt{5}}{2}[/tex]
The complex solutions of x^2+5x-5=0 are (-5 + √45)/(2) and (-5 - √45)/(2).
Explanation:To find the complex solutions of x2+5x-5=0, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac))/(2a)
Substituting the values a=1, b=5, and c=-5 into the formula, we get:
x = (-5 ± √(5^2 - 4(1)(-5)))/(2(1))
Simplifying further,
x = (-5 ± √(25 + 20))/(2)
x = (-5 ± √(45))/(2)
Since the square root of 45 cannot be simplified, we can write the solutions as:
x = (-5 ± √45)/(2)
Therefore, the complex solutions to the equation x2+5x-5=0 are:
x = (-5 + √45)/(2), (-5 - √45)/(2)
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Find the slope and y-intercept of the line. y = 7/4x – 10
Answers
y-int: (0,-10)
y-intercept = -10
(02.01 LC)
Line segment AB has a length of 3 units. It is translated 2 units to the right on a coordinate plane to obtain line segment A prime B prime. What is the length of A prime B prime?
A. 1 unit
B.2 units
C. 3 units
D. 5 units
Answers
Answer:
The correct option is C.
Step-by-step explanation:
It is given that line segment AB has a length of 3 units. It is translated 2 units to the right on a coordinate plane to obtain line segment A'B'.
Translation is a rigid transformation. It means the shape and size of preimage and image are same. In other words we can say that the preimage and image are congruent.
Corresponding sides of congruent figures are congruent.
[tex]AB\cong A'B'[/tex]
[tex]AB=A'B'[/tex] (Definition of concurrent segment)
[tex]3=A'B'[/tex] (AB=3 units)
The length of A'B' is 3 units. Therefore the correct option is C.
I need help with number 17
Answers
(3x-21)-(3x+21)
Flip the signs in the second binomial
(3x-21)-3x-21
Combine like terms
3x-3x-21-21
-21-21
-42
The final answer is -42. X is irrelevant because whatever you plug in will always equal -42.
A test consists of 20 problems and students are told to answer any 15 of these questions. In how many different ways can they choose the 15 questions?
Answers
2 - 17
3 - 18
4 - 19
5 - 20
n!/(k!(n-k)!), where n=total amount of choices, k=number of choices made.
In this case:
20!/(15!(20-15)!)
20!/(15!*5!)
15504
Write an equation in point-slope form for the line through the given point with the given slope. (8, –3); m = -1/4
Answers
To write the equation in point-slope form, plug in the given values of the point and slope into the formula and simplify.
Explanation:To write an equation in point-slope form for a line, we use the formula: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line. In this case, the given point is (8, -3) and the slope is -1/4. Plugging in these values into the formula, we get:
y - (-3) = (-1/4)(x - 8)
Simplifying the equation, we have:
y + 3 = (-1/4)x + 2
Therefore, the equation in point-slope form for the line through the point (8, -3) with slope -1/4 is y + 3 = (-1/4)x + 2.
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Probability help please? In a certain instant lottery game, the chances of a win are stated as "1 in 19." Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive. (round to three decimal places) I am confused and need a step by step instructions. Please help
Answers
1/19 (One divided by 19)=0.0526
0.0526 rounded is about 0.053 (to three decimal places).
Answer: About 0.053
Final answer:
To convert the chances of a '1 in 19' win into a probability value, you divide 1 by 19 to get 0.05263 and then round to 0.053. Therefore, the lottery win probability is 0.053.
Explanation:
To express the likelihood of a win in a lottery game as a probability value between 0 and 1, when the chances of a win are stated as "1 in 19", you follow these steps:
Understand that "1 in 19" means there is one chance to win for every 19 trials, so the total number of possible outcomes is 19 (18 losses + 1 win).
Express the chance to win as a fraction with the number of wins (1) over the total number of potential outcomes (19).
Convert the fraction into a decimal by dividing the numerator (1) by the denominator (19), which gives you approximately 0.05263.
Round the result to three decimal places, as requested, which gives you a probability value of 0.053.
Therefore, the probability of winning the lottery game is 0.053.
What is the solution to the system of linear equations graphed below?
A. (0,3)
B. (0,-2)
C. (-2,-2 1/2)
D. (-2 1/2, -2)
Answers
The solution to the system of linear equations graphed is (-2.5, -2). So, the correct answer is option D.
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
The ordered pair that is a solution to both equations is the system's solution. We graph both equations in the same coordinate system in order to visually solve a system of linear equations. The intersection of the two lines is where the system's answer will be found.
In the given graph, the intersection point is (-2.5, -2).
Therefore, option D is the correct answer.
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The population of a local species of flies can be found using an infinite geometric series where a1 = 940 and the common ratio is one fifth. write the sum in sigma notation, and calculate the sum (if possible) that will be the upper limit of this population.
Answers
A. Sigma notation
The formula for finding the nth value of the geometric series is given as:
an = a1 * r^n
Where,
an = nth value of the series
a1 = 1st value in the geometric series = 940
r = common ratio = 1/5
n = nth order
The sigma notation for the sum of this infinite geometric series is therefore,
(see attached photo)
B. Sum of the infinite geometric series
The formula for calculating the sum of an infinite geometric series is given as:
S = a1 / (1 – r)
Substituting the given values:
S = 940 / (1 – 1/5)
S = 1,175
Tammy wants to raise $175 for a school fundraiser. She has raised $120 so far. How much does she need to reach her goal?
Answers
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Using the completing-the-square method, rewrite f(x) = x2 − 8x + 3 in vertex form.
Answers
To complete the square of a quadratic expression in standard form, we write the coefficient of x as 2*b, then add and subtract [tex] b^{2} [/tex].
[tex]f(x)= x^{2} -8x+3[/tex]
[tex]f(x)= x^{2} -2*4x+3[/tex]
so b=4, now add and subtract [tex] 4^{2} [/tex].
[tex]f(x)= x^{2} -2*4x+ 4^{2}- 4^{2}+3[/tex]
[tex]f(x)=( x^{2} -2*4x+ 4^{2})- 16+3[/tex]
[tex] f(x)=(x-4)^{2}-13 [/tex]
Solve x2 + 8x − 3 = 0 using the completing-the-square method
Answers
x²+8x-3=0
(x² +2(4)x +4²) -4² -3 = 0
(x+4)²-19 = 0
(x+4)² = 19
x+4 = √19 or x+4 = - √19
x = √19 - 4 or x = -√19 - 4
Find the slope of the line that contains the points named c (3,8),d (-2,5)
Answers
[tex]\bf c(\stackrel{x_1}{3}~,~\stackrel{y_1}{8})\qquad d(\stackrel{x_2}{-2}~,~\stackrel{y_2}{5}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{5-8}{-2-3}\implies \cfrac{-3}{-5}\implies \cfrac{3}{5}[/tex]
Answer:
3/5
Step-by-step explanation:
To find the slope, we use the formula
m = (y2-y1)/(x2-x1)
= (5-8)/(-2-3)
= -3/-5
=3/5
The slope is 3/5
represent each of the fractions below both with a diagram and with words. A.2/3. B.1 1/8. C.6/9.
Answers
2/3 in words is 'two third'
11/8 in words is 'eleven-eighth'
6/9 in words is 'six-ninth'
The number of chips of different colors in vicky's bag is shown below: 5 blue chips 11 pink chips 9 white chips vicky takes out a chip from the bag randomly without looking. she replaces the chip and then takes out another chip from the bag. what is the probability that vicky takes out a blue chip in both draws? 5 over 25 multiplied by 5 over 25 equals 25 over 625 5 over 25 plus 5 over 25 equals 10 over 25 5 over 25 multiplied by 4 over 24 equals 20 over 600 5 over 25 plus 4 over 24 equals 220 over 600
Answers
P( blue on second draw) = 5/25
These events are independent so the probabilities are multiplied
answer is 5/25 * 5/25 = 25/625 = 1/25
The first choice is correct
The probability that Vicky takes out a blue chip in both draws is 5/25 x 5/25 = 25/625.
What is the probability that vicky takes out a blue chip in both draws?
Probability determines how likely it is that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
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the quadratic formula gives which roots for the equation 3x^2+3x=2
Answers
The correct answer is X=-3+or-rad33/6
The roots of the quadratic equation 3x^2+3x-2=0 as provided by the quadratic formula are x1 = (3 + sqrt(33))/6 and x2 = (3 - sqrt(33))/6.
Explanation:
The quadratic equation in question is 3x^2+3x-2=0. Here, a=3, b=3, and c=-2. We can solve this equation using the quadratic formula, which, in general terms, is given as: x = [-b ± sqrt(b² - 4ac)] / 2a.
Plugging the coefficients into the quadratic formula, we get:
x = [-3 ± sqrt((3)² - 4*3*(-2))] / 2*3
= [-3 ± sqrt(9 + 24)] / 6
= [-3 ± sqrt(33)] / 6
That gives us two roots: x1 = (3 + sqrt(33))/6 and x2 = (3 - sqrt(33))/6. These are the solutions for the quadratic equation given.
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(02.05 MC)
Two similar triangles are shown on the coordinate grid:
Which set of transformations has been performed on triangle ABC to form triangle A'B'C'?
Dilation by a scale factor of 4 followed by reflection about the x-axis
Dilation by a scale factor of 2 followed by reflection about the x-axis
Dilation by a scale factor of 4 followed by reflection about the y-axis
Dilation by a scale factor of 2 followed by reflection about the y-axis
Answers
Answer:
Dilation by a scale factor of 2 followed by reflection about the x-axis
Step-by-step explanation:
To answer it and view it properly let's do it by parts.
1) A closer look at the Triangle ABC shows us the coordinate points A(-2,-1) B(0,0) and C(1,-3).
2) Reflection across the x-axis gives us this triangle: A'(-2,1) B'(0,0) and C'(1,3). Notice that all y-coordinates have an opposite sign. This is a natural characteristic of a Reflection: an opposed sign of one Coordinate.
3) Finally, To Dilate a Triangle is to transform it so that it gets bigger than its original size.
If we compare the triangle with points A''(-4,2) B"(0,0) and C"(2,6) to A'(-2,1) B'(0,0) C'(1,3). Each coordinate is multiplied by 2.
Dilation by a scale factor of 2 followed by reflection about the x-axis
Need some help on geometry practice problems!
Answers
[tex]x_m= \cfrac{x_a+x_b}{2}= \cfrac{-1+7}{2}= \cfrac{6}{2}=3 \\ \\ y_m= \cfrac{y_a+y_b}{2}= \cfrac{2+3}{2}= \cfrac{5}{2} \\ \\ \text{midpoint is} \ (3, \frac{5}{2} )[/tex]
What is the solution of x=2+\sqrt(x-2)
x = 2
x = 3
x = 2 or x = 3
no solution
Answers
Answer:
The solution is x = 2 or x = 3
Step-by-step explanation:
we have to find the solution of the equation
[tex] x=2+\sqrt{(x-2)}[/tex]
[tex]x=2+\sqrt{(x-2)}\\ \\x-2=\sqrt{x-2}\\\\\text{Squaring on both sides }\\\\(x-2)^2=x-2\\\\x^2+4-4x=x-2\\\\x^2-5x+6=0\\\\x^2-2x-3x+6=0\\\\x(x-2)-3(x-2)=0\\\\(x-2)(x-3)=0\\\\x=2\text{ or }x=3[/tex]
Hence, correct option is x = 2 or x = 3
Answer:
C) x = 2 or x = 3
Step-by-step explanation:
Edge 2021
Solve x2 + 2 = 6 by graphing the related function.
Answers
Answer:
[tex]x=-2,x=2[/tex]
Step-by-step explanation:
we have
[tex]x^{2}+2=6[/tex]
we know that
The solution of the function is equivalent to solve the following system of equations
[tex]y=x^{2}+2[/tex] ------> equation A
[tex]y=6[/tex] ------> equation B
The x-coordinate of the intersection point both graphs is the solution of the given function
Using a graphing tool
see the attached figure
The intersection points are [tex](-2,6)[/tex] and [tex](2,6)[/tex]
therefore
The solution of the given function are
[tex]x=-2,x=2[/tex]
Traveling at 55 miles per hour how many minutes rounded to the nearest whole number does it take to drive 310 miles
Answers
[tex]\bf \begin{array}{ccll} miles&minutes\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 55&60\\ 310&m \end{array}\implies \cfrac{55}{310}=\cfrac{60}{m}\implies m=\cfrac{310\cdot 60}{55}[/tex]
Janet weighs 20 pounds more than Anna. If the sum of their weights is 250 pounds, how much does each girl weigh?
Answers
Anna = A
J = A + 20
J + A = 250
Considering that Janet and Anna are relatively close to eachother in weight, let's divide the sum by 2 to give us a general idea of where their weight lies.
250 / 2 = 125
Janet's and Anna's weights are around 125.
Let's try 140 for Janet and 120 for Anna
140 = 120 + 20 (J = A + 20), this works!
140 + 120 = 260 (J + A = 250), this unfortunately doesn't work.
Let's try 135 for Janet and 115 for Anna.
135 = 115 + 20 (J = A + 20), this works!
135 + 115 (J + A = 250), this also works!
Janet weighs 135 pounds, and Anna weighs 115 pounds.
I hope this helps!
The weight of Anna is: 115 pounds
and the weight of Janet is: 135 pounds.
Step-by-step explanation:It is given that:
Janet weighs 20 pounds more than Anna.
This means if the weight of Anna is: x pounds
Then the age of Janet is: (x+20) pounds.
Also,
The sum of their weights is 250 pounds.
i.e.
x+x+20=250
i.e.
2x+20=250
On subtracting both side by 20 we have:
2x=250-20
i.e.
2x=230
On dividing both side by 2 we have:
x=115
Hence, the weight of Anna is:115 pounds.
and the weight of Janet is: 115+20=135 pounds.
Segment JG is the same as segment GJ
Answers
WILL GIVE BRAINLIEST!! PPLEASE HELP!!
The graph of which function does not contain the point (0, 1)?
A.
y=(3/4)^x
B.
y=-2^x
C.
y=3^x
D.
y=(1/2)^x
Answers
Since they are all exponential functions, so all of them should pass through (0,1)
However, B has the minus sign, which flips the function vertically, so it passes through (0,-1)
Answer is B
What is the mean salary of a salesperson at the company
Answers
The following data show the height, in inches, of 11 different plants in a garden: 9 4 10 9 5 2 22 10 3 3 5 After removing the outlier, what does the mean absolute deviation of this data set represent?
Answers
Mean = (9+4+10+9+5+2+10+3+3+5)/10 = 6
Then, the mean absolute deviation is
∑(x-mean)^2/n, where x is every single data point and n is the number of data points which is equal to 10
|9-6|+|4-6|+|10-6|+|9-6|+|5-6|+|2-6|+|10-6|+|3-6|+|3-6|+|5-6| = 28
Then,
Mean Absolute Deviation (MAD) = 28/10 = 2.8
This is the average distance of the data from the mean.
Write the sum using summation notation, assuming the suggested pattern continues. -8 - 3 + 2 + 7 + ... + 67
Answers
The correct answer is [tex]\sum_{n=1}^{20} (-8 + 5(n-1))[/tex]
The sum using summation notation, assuming the suggested pattern continues, can be written as:
[tex]\sum_{n=1}^{20} (-8 + 5(n-1))[/tex]
[tex]-8 - 3 + 2 + 7 + \ldots + 67 = \sum_{n=1}^{20} (-8 + 5(n-1))[/tex]
Explanation:
- The pattern appears to be an arithmetic progression with a common difference of 5.
- The first term is -8, and the common difference is 5.
- The nth term of an arithmetic progression can be expressed as [tex]a_n = a_1 + (n-1)d[/tex], where [tex]a_1[/tex] is the first term, and [tex]d[/tex] is the common difference.
- Substituting [tex]a_1 = -8[/tex] and [tex]d = 5[/tex], we get [tex]a_n = -8 + 5(n-1)[/tex].
- The sum of the first 20 terms of this arithmetic progression can be represented using the summation notation, with the index [tex]n[/tex] ranging from 1 to 20.
Therefore, the sum using summation notation is [tex]\sum_{n=1}^{20} (-8 + 5(n-1))[/tex].
Complete question:
Write the sum using summation notation, assuming the suggested pattern continues.
-8 - 3 + 2 + 7 + ... + 67
summation of the quantity negative eight plus five n from n equals zero to fifteen
summation of negative forty times n from n equals zero to infinity
summation of negative forty times n from n equals zero to fifteen
summation of the quantity negative eight plus five n from n equals zero to infinity