On solving the given equation the value of y=7/10 so this value the given equation will be true as the definition of solution of equation says ,"A solution to an equation is a number that can be plugged in for the variable to make a true number statement. "
What is solution to equation?A number that can be entered for the variable to produce a true number statement is the solution to an equation. One-step equations can be solved in four different ways: by adding, subtracting, multiplying, and dividing. In an equation, both sides will remain equal if we add the same amount to each side. Systems of equations can be solved using one of three techniques: graphing, substitution, or elimination. Simply plot the given equations on a graph and locate the point(s) where they all intersect to solve a system by graphing. You can find the values of the variables you are solving for by finding the coordinate of this point.
Here,
12y - 1/2 = 9y +8/5
3y=8/5+1/2
3y=(16+5)/10
3y=21/10
y=7/10
According to the definition of an equation's solution, "A solution to an equation is a number that can be plugged in for the variable to make a true number statement," the value of y will be 7/10 when the given equation is solved.
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Given the equations and the table below, what is the first x-value when the y-value of equation 2 is greater than the y-value of equation 1 after the functions first intersect?Equation 1: f(x)=5x^3Equation 2: f(x)=2x+3A: x=14B: x=7C: x=17D: x=12
From what I explained in the session before, the x value must be between 10 and 15, so only 2 options are viable, 14 and 12. Let's evaluate each of them
[tex]\begin{gathered} f(x)=5x^3 \\ f(12)=5(12)^3 \\ f(12)=5(1728) \\ f(12)=8640 \\ \\ f(x)=2^x+3 \\ f(12)=2^{(12)}+3 \\ f(12)=4096\text{ +3 = 4099} \end{gathered}[/tex]So, 12 is not the answer. Let's evaluate 14
[tex]\begin{gathered} f(x)=5x^3 \\ f(14)=5(14)^3 \\ f(14)=5(2744) \\ f(14)=13720 \\ \\ f(x)=2^x+3 \\ f(14)=2^{14}+3 \\ f(14)=16384+3 \\ f(14)=16387 \end{gathered}[/tex]So, x = 14 is the correct answer
(21. Little to big ratio:22. Litt5712кGх2PJHProportion to solve for x:ProportX =FH =X=MNIII
Using the properties of similar triangles and ratio and proportion we get the vale of x as 2.8 units.
In the given figure the triangle ΔKFG and ΔFJH
KG is parallel to JH
Hence ΔKFG is similar to ΔFJH
Now using the property of similarity and proportion we can say that:
FG/FH = KF/JF
putting the values in the above proportion we get:
7 /(7+x) = 5/ 7
or, 49 = 35 +5 x
or, 14 = 5x
or, x =14/5
or, x = 2.8
The majority of ratio and percentage explanations involve using fractions.
A proportion states that two variables are equal, whereas a ratio is a fraction that is written as a:b. The two ratios given are equal to one another, as demonstrated by the proportional equation.
Hence the value of x is 2.8 units.
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Suppose that 45% of all babies born in a particular hospital are girls. If 7 babies born in the hospital are randomly selected, what is the probability that at most 2 of them are girls?Carry your intermediate computations to at least four decimal places, and round your answer to two decimal places.
Solution:
Since the sample size is fixed;
[tex]n=7[/tex]And the probability of picking a girl is constant for each trial, the binomial distribution is appropriate;
[tex]\begin{gathered} P(X=r)=^nC_rP^r(1-P)^{n-r} \\ \\ P(X\leq2) \end{gathered}[/tex]Thus;
[tex]\Rightarrow^7C_0(0.45)^0(0.55)^7+^7C_1(0.45)^1(0.55)^6+^7C_2(0.45)^2(0.55)^5[/tex][tex]\Rightarrow0.0152+0.0872+0.2140=0.3164[/tex]ANSWER: 0.32
The mean of a data set can be greater than any of the data sets
True or false and explain your reason.
The mean of a data set can be greater than any of the data sets is True.
The average is basically a model of the dataset. The most frequently occurring value. However, the mean value is often not one of the actual values observed in the dataset. The median can be larger or smaller than the mean of the distribution. So the given statement is wrong.
The mean is affected by outliers that do not influence the mean. Therefore, when the average distribution of data is skewed to the left, the mean is often less than the median. When the distribution is skewed to the right, the mean is often greater than the median. No matter what value we add to the set, the mean, median, and mode will shift by that amount but the range and the IQR will remain the same. The same will be true if we subtract an amount from every data point in the set.
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HELP!!!! I NEED THIS ASAP PLEASE!!!
Which ordered pair is a solution to the system of equations?
[tex]\left \{ {{y=5x} \atop {y=4x+1}} \right.[/tex]
answer is option 2 : (1, 5) because:
when x = 1 , y should = 5:
[tex]\left \{ {{y=5x} \atop {y=4x+1}} \right.\\\\\left \{ {{y=5(1)} \atop {y=4(1)+1}} \right.\\\\\left \{ {{y=5} \atop {y=5}} \right.[/tex]
Graph h(x) = 38(0.51)x. What is the constant percent rate of change of f(x) with respect to x? Does the graph show growth or decay?
49% growth
49% decay
51% growth
51% decay
Answer:
Step-by-step explanation:
This is decay, the rate of change is 49%
hope this helps!
The correct rate of change is B)49% decay.
What constant rate of change ?
A rate of change is constant when, at any given point along the function, the ratio of the output to the input remains constant. The slope is another name for the rate of change that is constant. A linear function's rate of change will be constant.
Here the given function is ,
=> h(x)=38(0.51)x.
For any exponential function in which the base is less than 1, it will be an exponential decay situation.
In this problem, the base is 0.51.
Then,The amount that the base is less than 1 ( i.e. 1 - base) . It represents the rate of change in decimal ,
=> 1-0.51 = 0.49
Converting into percentage => 0.49 *100 = 49%
Therefore the correct option is B) 49% decay.
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What is the y intercept of the line?
A: 0
B: 1
C: 1/2
D: -2
Check the picture below.
Solve the system by substitution. y= y= \,\,-2x+1 −2x+1 -9x-2y= −9x−2y= \,\,3 3
Using substitution method of simultaneous linear equation the results are x = -1 and y = 3
What is simultaneous linear equation?
At first it is important to know about linear equation
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A one degree equation is known as linear equation.
Two or more linear equations, which can be solved together to obtain common solution are known as simultaneous linear equation.
Here,
Substitution method of simultaneous linear equation is used
y = -2x + 1
-9x - 2y =3
Putting the value of y in the second equation
-9x - 2(-2x + 1) = 3
-9x +4x -2 = 3
-5x = 3 + 2
-5x = 5
[tex]x = -\frac{5}{5}\\x = -1[/tex]
Putting the value of x in the first equation,
[tex]y = -2 \times -1+1\\y = 3[/tex]
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help meeeeeeeeeeeeeeeeeeee pleaseee rnnnn rn!!!!
Answer:
length:12m width: 6m
Step-by-step explanation:
w=l-6, lw=72. l*l-6=72, l^2-6l=72. l^2-6l-72=0, l=12 or -6, length cant be negative. L=12. W=L-6, w=6.
Zavier and Maria shared 70 books, Zavier had 2 more books than Maria, how many did Maria have?
Answer:
Zavier had 37 books, and Maria had 33 books
Step-by-step explanation:
You take 70 and divide it by 2 (cause you are only dividing the books up to maria and Zaviar); this will give you 35 books to each person EXCEPT Zavier has two more books to his pile, so you subtract two books from Marie and add it to Zaviers!
Find the area of the figure below
Answer:
Step-by-step explanation:
b/c we can fairly say, that the parallelgram is also a rectangle of size 24 x 11, we can just solve that area
24*11= 264
We can see, this is a parallelogram.
The formula to calculate the area of a parallelogram is b x h, where b is base and h is height.
Given that base = 24 in, height = 11 in, we can calculate the area as : 24 x 11 = 264 in2.
Which of the following numbers is the greatest? 16.007; 15.999; 15.99; 16.01
16.01 is the greatest number.
Numbers:
In everyday life, we use numbers. They are frequently known as numbers. We are unable to count things, dates, hours, money, etc. without numbers. These numerals are utilised for labelling and measurement purposes at various periods. The characteristics of numbers enable them to be used in arithmetic operations. Both verbal and quantitative representations are used to express these numbers.
Math teaches us about the various kinds of numbers there are. The types of numbers include natural and whole numbers, odd and even, rational and irrational, etc. In addition to this, the numbers are employed in numerous other contexts, including the creation of number series and arithmetic tables.
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Which bot clicked more in one second
Answer:
Bot 4
Step-by-step explanation:
Here is one way
rate of bot 3 36 /5 in ten seconds 36/5 *10 = 72 clks
rate of bot4 26/3 in ten seconds 26/3 * 10 = ~ 87 clks
Which property is illustrated by the statement? explain
Associative Property of Addition
Commutative Property of Multiplication
Inverse Property of Multiplication
Commutative Property of Addition
The statement represents the commutative property of Multiplication.
What is the Commutative Property of Multiplication?Commutative is derived from "commute," which means to move about or travel. The commutative property of multiplication states that the result is unaffected by the order in which the numbers are multiplied.
According to the commutative property, the result of addition or multiplication remains the same regardless of the sequence in which the numbers are added or multiplied. It should be noted that the commutative feature only applies to addition and multiplication, not to division or subtraction. As an illustration, the sum of 6 + 7 and 7 + 6 equals 13. Like 6 x 7 = 42, so does 7 x 6.
A statement is given as follows:
[tex]2\left(-\frac{3}{9}\right)=\left(-\frac{3}{9}\right) 2[/tex]
Observe that terms are exchanged on the left side and right side of the given equation.
It stands on the definition of the commutative property of Multiplication.
So, the statement represents the commutative property of Multiplication.
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I have no idea how to solve this problem, could someone help me?△ABC∼△XYZ. Find the values of x and b (side lengths).
The symbol ∼ denotes similarity, that is, the triangles ABC and XYZ are similar. When two triangles are similar, they have the same shape but not necessarily the same size and their corresponding angles are the same. In turn, the corresponding sides of two corresponding triangles are in the same ratio. Graphically,
[tex]\frac{a}{a^{\prime}}=\frac{b}{b^{\prime}}=\frac{c}{c^{\prime}}[/tex]So to find x in the small triangle, you have
[tex]\begin{gathered} \frac{15}{10}=\frac{9}{x} \\ \text{ Multiply by x on both sides of the equation} \\ \frac{15}{10}\cdot x=\frac{9}{x}\cdot x \\ \frac{15}{10}x=9 \\ \text{ Multiply by }\frac{10}{15}\text{ on both sides of the equation} \\ \frac{10}{15}\cdot\frac{15}{10}x=9\cdot\frac{10}{15} \\ x=6 \end{gathered}[/tex]Finally, to find b in the large triangle, you have
[tex]\begin{gathered} \frac{15}{10}=\frac{b}{8} \\ \text{ Multiply by 8 on both sides of the equation} \\ \frac{15}{10}\cdot8=\frac{b}{8}\cdot8 \\ 12=b \end{gathered}[/tex]Therefore, the lengths of the sides x and b are
[tex]\begin{gathered} x=6 \\ b=12 \end{gathered}[/tex]3i (2i-4)
Show steps and answer
Answer:
6i^2-12i
Step-by-step explanation:
3i×2i =6i^2
3i×4 =12i
Write the coordinates of the verticals after a rotation 270 counter clockwise around the origin
D=
E=
F=
G=
Check the picture below.
Complete the two-way frequency table below, which shows the relationship between students who enroll in advanced algebra and physics in
particular high school. From a sample of 40 students, it is found that 29 are taking algebra, 14 are taking physics, and 5 are enrolled in both. How
many students are enrolled in either algebra physics?
By making use of Set Theory, we calculate that a total of 38 students are enrolled in either physics or algebra.
Number of students taking algebra n(A)= 29
Number of students taking physics n(B)= 14
Number of students taking both subjects n(A∩B)= 5
So, the number of students taking either physics or algebra will be the union of sets i.e. n(A∪B)
The union of two sets is a set containing all elements that are in A or in B (possibly both).
As we know,
n(A∪B) = n(A) + n(B) - n(A∩B)
n(A∪B) = 29 + 14 - 5
n(A∪B) = 38
Therefore, A total of 38 students are enrolled in either physics or algebra.
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Use the appropriate identity to rewrite the expression 8x^6 +64.
Answer:
The answer is B
Pleaseeeeee helpppppp!
I will mark brainliest, but pls only if you know the answer
Its Geometry A
Answer:
see explanation
Step-by-step explanation:
A base angle
B leg
C vertex angle
D leg
E base angle
F base
in any isosceles triangle there are 2 congruent legs and 2 congruent base angles.
the base angles are opposite the congruent legs
the remaining side, the base is the 3rd side of the triangle
the vertex angle is formed by the 2 congruent legs
Write –9.575 as a mixed number.
which property is demonstrated in the equation 7*(8*9)=(7*8)*9
Explanation:
Associative properties for multiplication is stated as follows:
(a * b) * c =
6) Calculate the volume and surface area of the cuboid below:
Volume =
Surface area =
Answer:
what's that bottom number???
Answer:
Answer: 54
Step-by-step explanation:
3x2=6 6x9=54
Step 1:
3x2=6
Step 2:
get the 6 from last step and multiply it by 9
6x9=54 √
can anyone help??????
Answer:
140
Step-by-step explanation:
triangles equal to 180
64+76+x=180
x=40
180-40=140
Answer:
140°
Step-by-step explanation:
We know that,
the exterior angle of a triangle is equal to the sum of the interior opposite angles of a triangle.
Accordingly,
k = 64 + 76
k = 140°
Part I: Domain and Range-identify the domain and range of each graph Problem/Work A
The domain refers to all the values of x (inputs) for the function
The range refers to all the values of y (outputs) for the function
[tex]\begin{gathered} domain=-2\le x\le1;\mleft\lbrace-2,-1,0,1\mright\rbrace \\ range=0\le x\le3;\mleft\lbrace0,1,2,3\mright\rbrace \end{gathered}[/tex]We have the domain & range thus:
[tex]\begin{gathered} (domain,range)=(-2,0),(-1,3),(0,0),(1,3) \\ domain=-2,-1,0,1 \\ range=0,3,0,3 \end{gathered}[/tex]The local furniture store pays $60 for a sofa andsells it with a 30% markup. What is the sellingprice of the sofa?
Question:
The local furniture store pays $ 60 for a sofa and sells it with a 30% markup. What is the selling price of the sofa?.
Solution:
Let the following data:
Base price = $60
30% of base price = $60 x 0.3 = $18
Then:
Selling price = $60 + $18 = $78.
Then, we can conclude that the correct answer is:
The selling price of the sofa is $78.
The diagram shows a right-angled triangle.
14 cm
8 cm
Find the size of angle x.
Give your answer correct to 1 decimal place.
The size of angle x is 34.84°
What is right angled triangle ?
A right triangle, also known as a right-angled triangle, an orthogonal triangle, or formerly a rectangled triangle, is a triangle with one right angle, meaning that its two sides are perpendicular. Trigonometry's foundation is the relationship between the right triangle's sides and other angles.
To find the value of x we will use the trigonometric formula
sin x = [tex]\frac{opposite}{hypotenuse}[/tex]
cos x = [tex]\frac{adjacent}{hypotenuse}[/tex]
tan x = [tex]\frac{opposite}{adjacent}[/tex]
cosec x = [tex]\frac{1}{sin x}[/tex]
sec x = [tex]\frac{1}{cos x}[/tex]
cot x = [tex]\frac{1}{tan x}[/tex]
As we know the value
hypotenuse = 14cm
opposite side = 8cm
∴ sin x = [tex]\frac{8}{14}[/tex]
= [tex]\frac{4}{7}[/tex]
x = 34.84°
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Answer:
angle x =34.8°
Step-by-step explanation:
sinX=opposite/hypotenuse this means sin(θ) is the ratio of the opposite side to the hypotenuse
so, to solve this problem we have to find the value of sin X then we can get the value of X.
Let sin X = 8/14
=0.571
SO, X =sin-1(0.571) =34.8°
PLEASE PLEASE HELP
write an equation for the parabola that has the given vertex and passes through the given point
vertex (-1,-3) point (1,5)
f(x) = [?] (x + [?]) ^2 + [?]
Answer:
f(x)=x2 f ( x ) = x 2
Step-by-step explanation:
Question 1 (1 point)
What is the mode of: 3.7, 5, 9.2, 4, 6.1, 5, 2.6, 4, 5.2, 5?
O a
Ob
Oc
Od 5
4.88
6.6
4.5
the mode is 5 i don't understand what the the other part is
(2)/(3)x-1=9-(1)/(6)x
For the given equation the value of x is, x = 12.
What is solving an equation?
Finding an equation's solutions, which are values (numbers, functions, sets, etc.) that satisfy the equation's condition and often consist of two expressions connected by an equals sign, is known as solving an equation in mathematics. One or more variables are identified as unknowns when looking for a solution.
Consider, the given equation[tex]\frac{2}{3}x - 1=9-\frac{1}{6}x[/tex]
Add 1 on both sides,
[tex]\frac{2}{3}x -1+1 = 9-\frac{1}{6}x+1\\ \frac{2}{3}x=10-\frac{1}{6}x[/tex]
Add 1/6(x) to both sides,
[tex]\frac{2}{3}x + \frac{1}{6}x = 10 - \frac{1}{6}x+\frac{1}{6}x\\ \frac{5}{6}x = 10[/tex]
Multiply both sides by 6/5
[tex]\frac{5}{6}x (\frac{6}{5}) = 10(\frac{6}{5}) \\ x = 12[/tex]
Hence, the value of x is, x = 12.
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