The system of linear equations that best represents the situation are:
z+y=18
3z +2y=44
What are the linear equations?In order to determine the values of the two types of cheese, two set of linear equations can be formed from the question. The equations have to be solved together using either the elimination , substitution or graphical methods.
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Q
7/0
The mean weight of 8 girls in a group is 35 kg. The individual weights of seven of then
are 35kg, 28kg, 43kg, 25kg, 33kg, 51kg, and 22kg. Find the weight of the 8th girl.
The weight of the 8th girl in the class is 43 kg
How to determine the weight of the 8th girl?The given parameters are:
Mean weight = 35 kg
Weight of 7 girls = 35kg, 28kg, 43kg, 25kg, 33kg, 51kg, and 22kg
Let the weight of the 8th girl be x.
Mean is calculated using:
Mean = Sum/Count
So, we have:
(35+ 28+43+25+33+51+22 + x)/8 = 35
Evaluate the sum
(237 + x)/8 = 35
Multiply both sides by 8
237 + x = 280
Subtract 237 from both sides
x = 43
Hence, the weight of the 8th girl is 43 kg
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Select the correct answer.
One leg of a right triangle is 10 units, and its hypotenuse is 12 units. What is the length of the other leg?
A.
about 7 units
B.
about 15 units
C.
about 25 units
D.
about 122 units
E.
about 224 units
Given that XW bisects AXZ, what theorem or theorems could be used to justify that W is equidistant from the two outside rays?
Answer:
HA congruence postulate
Step-by-step explanation:
In order to show W is equidistant from A and Z, we must demonstrate that WA ≅ WZ. The HA congruence postulate can be used for that purpose.
__
proofWX bisects AXZ, so ∠WXA≅∠WXZ by the definition of an angle bisector. By the reflexive property of congruence, WX≅WX. The angles at A and Z are given as right angles.
So, we have triangles WAX and WZX that are right triangles with congruent hypotenuse and corresponding angle. These are the preconditions for the application of the HA congruence postulate. That postulate says the triangles WAX and WZX are congruent, so ...
WA ≅ WZ by CPCTC. Hence W is equidistant from the outside rays.
__
Additional comment
The definition of distance from a point to a line is the perpendicular distance from the point to the line. In this geometry, the perpendicular distances from W to the outside rays are the lengths of segments WA and WZ. That is why we need to show those lengths are the same.
Which polynomial function could be represented by the graph below?
A. [tex]f(x) = x^2 - 4x[/tex]
B. [tex]f(x) = x^2 + 4x[/tex]
C. [tex]f(x) = -x^2 - 4x[/tex]
D. [tex]f(x) = -x^2 + 4x[/tex]
Answer:
[tex]f(x) = {x}^{2} + 4x[/tex]
Step-by-step explanation:
The graph is concave up, this means that the leading term x^2 is positive.
[tex]f(x) = {x}^{2} + 4x[/tex]
[tex]y = {x}^{2} + 4x[/tex]
For the x intercept, let y = 0[tex] {x}^{2} + 4x = 0[/tex]
[tex]x(x + 4) = 0[/tex]
[tex]x = 0 \: \: \: or \: \: \: \: x = - 4[/tex]
The x intercepts are:
(0 , 0) and (-4 , 0)
For the y intercept, let x = 0
[tex]y = {0}^{2} + 4(0) = 0[/tex]
y intercept :(0, 0)
For the turning point:[tex]t.p = \frac{x1 + x2}{2} [/tex]
[tex]t.p = \frac{0 + ( - 4)}{2} = - 2[/tex]
[tex]f( - 2) = {( - 2)}^{2} + 4( - 2) = - 4[/tex]
Turning point:(-2 , -4)
If you connect all these coordinates you will get the parabola shown in the picture.
please answer this !!
uhm i dont know sorry but i can't help you
Multiply the following
(a) 2.7x4
(b) 0.79x32.4
(c)1.07 x 0.02
(d) 2.3x4.35
(e) 2.5x100
(f) 0.0008x100
g) 0.25x 10000
h)3x0.55
i)0.08x5
j)351.06x4
k)0.3x0.03
l) 21.7x0.1
m) 200.02 x 2.2
Kindly look into this and try to answer all of them this contains 30 points
Find the value of y in 4y + 2x = 8 and 2x + 5y = 14.
Answer:
y = 6
Step-by-step explanation:
4y + 2x = 8 → (1)
5y + 2x = 14 → (2)
subtracting (1) from (2) term by term will eliminate x
y + 0 = 6
y = 6
Decide whether quadrilateral ABCD with vertices 4(-3,0), B(-4,1), C(-1.4), and D(0,3) is a rectangle, rhombus, square, or parallelogram.
Answer: rectangle
Step-by-step explanation:
The options imply the figure is a parallelogram. Furthermore, we can tell that not all the sides are congruent, so we can rule out the possibility that it is a rhombus or a square.
To determine if it is a rectangle, we can use the slope formula to determine if there is a pair of perpendicular sides. If this is the case, then this will be a parallelogram with a right angle, making it a rectangle.
[tex]m_{\overline{AB}}=\frac{1-0}{-4-(-3)}=-1\\m_{\overline{BC}}=\frac{4-1}{-1-(-4)}=1\\\therefore \overline{AB} \perp \overline{BC}[/tex]
So, the most specific classification is a rectangle
HELP ME PLEASE ON MATHEMATICS!!
Answer:
1)526 kw
2)1943 m³
3) 33
4) 43 m³
5) 5010 kw
Step-by-step explanation:
1) 7675-7149= 526
2) 462+ 1481= 1943
3) 168-135 = 33
4) 1499 -l456= 43
5) 4945+65= 5010
Please help asap 25 points
Answer:
[tex]y = - 2 |x - 2| + 4[/tex]
Step-by-step explanation:
as the function moved to the right 2 steps, and up 4 steps
tìm số hữu tỉ
(x-5/6)^2=1/36
Answer:
x = [tex]\frac{2}{3}[/tex] , x = 1
Step-by-step explanation:
(x - [tex]\frac{5}{6}[/tex] )² = [tex]\frac{1}{36}[/tex] ( take square root of both sides )
x - [tex]\frac{5}{6}[/tex] = ± [tex]\sqrt{\frac{1}{36} }[/tex] = ± [tex]\frac{1}{6}[/tex] ( add [tex]\frac{5}{6}[/tex] to both sides )
x = [tex]\frac{5}{6}[/tex] ± [tex]\frac{1}{6}[/tex] , then
x = [tex]\frac{5}{6}[/tex] - [tex]\frac{1}{6}[/tex] = [tex]\frac{4}{6}[/tex] = [tex]\frac{2}{3}[/tex]
x = [tex]\frac{5}{6}[/tex] + [tex]\frac{1}{6}[/tex] = [tex]\frac{6}{6}[/tex] = 1
A cylinder has a radius of 12 m and a height of 9 m.
What is the exact volume of the cylinder?
108π m³
216π m³
972π m³
1296π m³
[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=12\\ h=9 \end{cases}\implies V=\pi (12)^2(9)\implies V=1296\pi ~m^3[/tex]
What does the word progressive mean in the sentence below
What is the sentence and what are the questions. Until I know I can't help. But I should be able to answer if you can tell me
Bella can rake the leaves in 3 hours and Jordan can complete the same task in 4 hours. If they work together, how long will it take Bella and Jordan to rake the leaves? Round your answer to the nearest hundredth of an hour.
Using the together rate, it is found that it will take 1.71 hours for Bella and Jordan to rake the leaves.
What is the together rate?It is the sum of each separate rate.
In this problem, the rates are given as follows:
Together: 1/x.Bella's: 1/3.Jordan's: 1/4.Hence:
[tex]\frac{1}{x} = \frac{1}{3} + \frac{1}{4}[/tex]
[tex]\frac{1}{x} = \frac{4 + 3}{12}[/tex]
[tex]x = \frac{12}{7}[/tex]
x = 1.71.
It will take 1.71 hours for Bella and Jordan to rake the leaves.
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Which lists all of the x-intercepts of the graphed
function?
O (0, 6)
O (1, 0) and (2, 0)
O (1, 0), (2, 0), and (-3, 0)
O (1, 0), (2, 0), (-3, 0), and (0, 6)
Answer:
(1, 0), (2, 0), and (-3, 0)
Step-by-step explanation:
The x intercepts are where it crosses the x axis. It crosses at (-3,0), (1,0) and (2,0)
which of the following is the equation of a line in sloep intercept form for a line with slope = 1/3 and y intercept at 0,-4
Answer:
Step-by-step explanation:
y + 4 = 1/3(x - 0)
y + 4 = 1/3x - 0
y = 1/3x - 4
Expand and simplify
4(2x + 3) + 4(3x + 2)
Answer: 20x + 20
Step-by-step explanation:
We will distribute the four into the expressions to expand, then we will simplify.
Given:
4(2x + 3) + 4(3x + 2)
Distribute:
8x + 12 + 12x + 8
Combine like terms with addition:
20x + 20
20x + 20
What is the area of an equilateral triangle that has a perimeter of 36 centimeters? Round to the nearest square centimeter.
Answer:
(a is size of side of triangle)
the perimeter of equilateral triangle =3a
or, 36=3a
Thus, a = 13cm
area of equilateral triangle
=√3/4*(a^2 )
=√3/4*(13^2)
=73cm^2
What does x= please help
The value of x is 8
This question is a proportion. To solve it, let's assemble it as follows:5 = 4
10 x
Now, just multiply in the form of a cross. Then, let's split the terms:5 . x = 10 . 4
5x = 40
x = 40 ÷ 5
x = 8
So, the result of x will be 8
The hour and minute hands of a clock form an angle that constantly changes. During each hour of the day, the clock hands will form right, acute, and obtuse angles. Assume the hour hand points directly at the hour.Write a time of day when the two clock hands form each type of angle
The each type of angle are discussed below
What is angle?An angle is formed when two straight lines or rays meet at a common endpoint. The common point of contact is called the vertex of an angle.
If the hours hand point to the hour 1 and minute hand at 12 then
angle will be acute.
If the hours hand point to the hour 2 and minute hand at 12 then
angle will be acute.
If the hours hand point to the hour 3 and minute hand at 12 then
angle will be right angle .
If the hours hand point to the hour 4 and minute hand at 12 then
angle will be obtuse.
If the hours hand point to the hour 5 and minute hand at 12 then
angle will be obtuse.
If the hours hand point to the hour 6 and minute hand at 12 then
angle will be straight angle .
If the hours hand point to the hour 7 and minute hand at 12 then
angle will be reflex.
If the hours hand point to the hour 8 and minute hand at 12 then
angle will be reflex.
If the hours hand point to the hour 9 and minute hand at 12 then
angle will be reflex.
If the hours hand point to the hour 10 and minute hand at 12 then
angle will be reflex.
If the hours hand point to the hour 11 and minute hand at 12 then
angle will be reflex.
If the hours hand point to the hour 12 and minute hand at 12 then
angle will be Complete angle.
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The histogram shows the results of a survey that asked people how many hours of sleep they get each night. Which
statements are true?
The true statements are
The mean is near the median.
The mean is the best measure of center.
The five-number summary is the best measure of variation
What is a histogram?
A histogram is used to represent data graphically. The histogram is made up of rectangles whose area is equal to the frequency of the data and whose width is equal to the class interval.
If the mean is greater than the median, the histogram would be skewed to the right. If the mean is less than the median, the histogram would be skewed to the left.
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A pre-school has 12 four-year old children and 11 three-year old children. What is the ratio of four-year old
children to three-year old children?
Answer:
12:11
Step-by-step explanation
Answer:
I think it would be 12:11
Step-by-step explanation:
This is because you can't down size the 11
The radius of a wheel on a toy truck is 4 inches. To the nearest foot, how far does the wheel
travel when it makes 7 revolutions?
Look at the following sequence.
54, 36, 24, 16, . . .
If it is a geometric sequence, choose the common ratio. If it is not a geometric sequence, choose “not geometric.”
Answer:
[tex]r \: = \: \boxed{ \bold{\frac{2}{3} }}[/tex]
Step-by-step explanation:
Calculate the ratio of the progression by dividing a term of it by the immediately preceding one.[tex]r \: = \: \frac{36}{54} \\ \\ r \: = \: \frac{24}{36} \\ \\ r \: = \: \frac{16}{24} [/tex]
We simplify the fractions:[tex]r \: = \: \frac{2}{3} \\ \\ r \: = \: \frac{2}{3} \\ \\ r \: = \: \frac{2}{3} [/tex]
Since the ratio is the same, that is the common ratio.
MissSpanishwhat type of parent function is f(x) = |x|
Answer: Absolute value function
The type of parent function is f(x)= |x| is Absolute valued function
What is Absolute valued function?
An absolute value function is a function that contains an algebraic expression within absolute value symbols.
Given function:
f(x)= |x|
As, we know the modulus generally give the absolute value of any function and also the modulus always give the positive value.
The above property perfectly resemble the absolute valued function.
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A box contains 50 batteries, of which 10 are dead and 5 are weak. Suppose you select batteries at random from the box and set them aside for recycling if they are dead or weak. If the first battery you select is dead and the second one is weak, what is the probability that the next battery you select will be weak?
You have been given data about gas prices in 15 states. Comparing the two data sets below, what does the larger standard deviation, range, and variance say about gas prices in 2022 compared to gas prices in 2018?
Gas Prices in 2018 Gas Prices in 2022
Max: $2.42
Min: $2.03
Mean: $2.098
Median: $2.06
Mode: $2.04
Variance: 0.0121
Standard Deviation: $0.11
Max: $5.87
Min: $4.48
Mean: $4.83
Median: $4.72
Mode: $4.72
Variance: 0.0142
Standard Deviation: $0.38
Comparing the two data sets shown below
What is standard deviation and variance?Variance is the average squared deviations from the mean, while standard deviation is the square root of this number.
Both the mean and the median can be used to describe where the “center” of a dataset is located.
So, the mean of data in 2022 is more than mean of data in 2018.
It’s best to use the mean when the distribution of the data values is symmetrical and there are no clear outliers.
As the variance of 2022 more than in variance in 2018.
A high variance indicates that the data points are very spread out from the mean, and from one another.
As the standard deviation of 2022 more than in standard deviation in 2018.
The high standard deviation indicates data are more spread out.
The bigger the range, the more spread out the data.
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A function k whose domain is the set of positive integers is defined as k(1) = 4 and k(n) =
k(n - 1) - 2
Function k was evaluated for several numbers. Which of the following are true?
Select each correct answer.
k(2)=
k(1)-24-22Option C is true
k(3)
k(2)-22-20D is true
k(4)
k(3)-2=0-2=-2k(5)
-2-2-4k(6)
-4-2-6E is not true
k(1)
k(0)-2So
k(0)-2=4k(0)=6B is false
Similarly
k(-1)-2=k(0)=6k(-1)=8-1 is not in domain even though
A is false
Only C and D are trueAnswer:
[tex]k(2) = 2[/tex]
[tex]k(3) = 0[/tex]
Step-by-step explanation:
Given:
[tex]\begin{cases}k(1)=4\\k(n)=k(n-1)-2\end{cases}[/tex]
The function [tex]k(n)[/tex] tells us that each term is 2 less than the preceding term.
Therefore:
[tex]\implies k(1)=4[/tex]
[tex]\implies k(2)=k(1)-2=4-2=2[/tex]
[tex]\implies k(3)=k(2)-2=2-2=0[/tex]
[tex]\implies k(4)=k(3)-2=0-2=-2[/tex]
[tex]\implies k(5)=k(4)-2=-2-2=-4[/tex]
[tex]\implies k(6)=k(5)-2=-4-2=-6[/tex]
Rearranging the formula to make the preceding term the subject:
[tex]\begin{aligned} k(n) & = k(n-1) - 2\\\implies k(n)+2 & = k(n-1)\\k(n-1) & =k(n)+2\end{aligned}[/tex]
Therefore:
[tex]\implies k(1)=4[/tex]
[tex]\implies k(0)=k(1)+2=4+2=6[/tex]
[tex]\implies k(-1)=k(0)+2=6+2=8[/tex]
Conclusion
Therefore, the correct answers from the answer options are:
[tex]k(2) = 2[/tex] and [tex]k(3) = 0[/tex]
Don’t know how to solve.
Answer:
$122.88
Step-by-step explanation:
the phone decreases by 20% each year , that is
(100 - 20)% = 80% = [tex]\frac{80}{100}[/tex] = 0.8
the phone reduces by a factor of 0.8 each year , then after 4 years
value = $300 × [tex](0.8)^{4}[/tex] = $122.88
Brainliest if you give correct answer + explanation
Answer:
x = 8
Step-by-step explanation:
Perimeter :
2(Length + Width) = 44 2x + 3 + x - 5 = 22 3x - 2 = 22 3x = 24 x = 8