Answer:
7x-7 ;x=4
we will just substitute for the values
=7(4)-7
=28-7
=21
Step-by-step explanation:
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3i (2i-4)
Show steps and answer
Answer:
6i^2-12i
Step-by-step explanation:
3i×2i =6i^2
3i×4 =12i
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:
Can you rewrite a sum as a product!!!??? QUICK ANSWER PLEASE
yes of course it can surely be
Answer:
Yes, you can factor out common factors to write equivalent algebraic expressions.
[from edge's summary video script]
A school paid $248 for new basketballs and soccer balls. The number of basketballs purchased was 6 less than 3 times the number of soccer balls purchased. Basketballs cost $28 each and soccer balls cost $20 each. If b represents the number of basketballs and s represents the number of soccer balls, which system of equations best describes this situation?
Answer: D
Step-by-step explanation:
248 = 28x + 20y
x = 3y - 6
x = 28
y = 20
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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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 =
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
A shoe store was having a back to school sale where you could buy 6 pairs of shoes for $52.62. If a large family decided to buy 3 pairs of shoes, how much would it cost them?
Answer: The family would buy the three pairs of shoes for $26.31 because you have to divide $52.62 in half since they bought half the amount of pairs of shoes that are given in the sale.
Answer:
$26.31
Step-by-step explanation:
3 × [tex]\frac{52.62}{6}[/tex]
3 × [tex]\frac{5262}{600}[/tex]
3 × [tex]\frac{877}{100}[/tex]
[tex]\frac{3 *877}{100}[/tex]
[tex]\frac{2631}{100}[/tex]
= 26.31
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]What is the y intercept of the line?
A: 0
B: 1
C: 1/2
D: -2
Check the picture below.
Find the trigonometric form of the complex number. Hint: Graph the complex number first to give yourself a visual representation.
First, let's graph the complex number:
The trigonometric form will be given by:
[tex]-2-2i=r(\cos \theta+i\sin \theta)[/tex]The angle θ here is 225° (5π/4), the r-value will be
[tex]\begin{gathered} r=\sqrt[]{(-2)^2+(-2)^2} \\ \\ r=\sqrt[]{4+4} \\ \\ r=\sqrt[]{8}=2\, \sqrt[]{2} \end{gathered}[/tex]Now we have the trigonometric representation:
[tex]-2-2i=2\, \sqrt{2}\mleft(\cos \mleft(\frac{5\pi}{4}\mright)+i\sin \mleft(\frac{5\pi}{4}\mright)\mright)[/tex]Therefore the correct answer is the letter D.
the prime factorization is 3 to the power of 2 times 5 to the power of 2 what is the number
Answer:
225
Step-by-step explanation:
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 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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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 √
Use the appropriate identity to rewrite the expression 8x^6 +64.
Answer:
The answer is B
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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(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
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.
Kayla has $10 in a savings account. The interest rate is 5% per year and is not compounded. How much will she have in 2 years? Use formula i=p*r*t, where i is the interest earned, p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years
This is a question of Simple Interest. The simple interest is given by the formula:
[tex]I=P\cdot R\cdot T[/tex]That is:
Interest = Principal * Rate * Time
From the question, we have:
P = $10
R = 5% ---> 5/100 = 0.05
T = 2 years
Then, we have that the interest is (without units):
[tex]I=10\cdot0.05\cdot2\Rightarrow I=1[/tex]Therefore, the interest is $1.
However, Kayla will have in two years this interest plus the starting amount, that is:
$10 + $1 = $11.
Hence, Kayla will have $11 in two years in her savings account.
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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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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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]
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°
Find an equation for the line that passes through the points (5, 2) and (1, 4).
The equation of the line that passes through the points (5,2) and (1,4) is given by [tex]y=-\frac{x}{2} +\frac{9}{2}[/tex].
Let the points [tex](5,2) = (x_{1} , y_{1} )[/tex] and [tex](1,4) = (x_{2} , y_{2} ).[/tex]
The two-point form of the equation of a line is given by,
[tex]y-y_{1} =\frac{y_{2} -y_{1} }{x_{2}- x_{1} } (x-x_{1} )[/tex]
Substituting the values of [tex]x_{1} , x_{2}, y_{1}[/tex] and [tex]y_{2}[/tex] in the above equation, we get,
[tex]y-2=\frac{4-2 }{1-5 } (x-5 )\\\\ y-2 = \frac{2 }{-4 } (x-5 )\\\\ y-2=-\frac{1}{2} (x-5)\\ \\y-2=-\frac{x}{2} +\frac{5}{2} \\ \\y=-\frac{x}{2} +\frac{5}{2} +2\\ \\y=-\frac{x}{2} +\frac{9}{2}[/tex]
Thus the equation of the line is [tex]y=-\frac{x}{2} +\frac{9}{2}[/tex].
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When we multiply or divide both sides of an inequality by a negative number, what happens to the inequality symbol?
Step-by-step explanation:
When we multiply or divide both sides of an inequality by a negative number, what happens to the inequality symbol?
Answer:
The sign flips.
≤ becomes ≥
and ≥ becomes ≤
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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Which equations are true equations? Select ALL correct answers.
Responses:
1.) 8^2−5^2=. 4^2−7
2.)24/2^2= 50−6^2−8
3.)39−3⋅6=. 6⋅10/4+4
4.)56÷8+3^2= 2⋅2^3
The system of equations which are correct are mentioned below:
2 ) [tex]24/2^2= 50- 6^2 - 8[/tex]
and 4 ) 56÷8+3^2= 2⋅2^3
The solution of all the system of equations are given below;
1 ) [tex]8^2 - 5^2= 4^2 - 7[/tex]
LHS = 64 - 25 = 39
RHS = 16 - 7 = 9
Since LHS is not equal to RHS the given equation is not correct.
2) [tex]24/2^2= 50- 6^2 - 8[/tex]
LHS = 24 / 4 = 6
RHS = 50 - 36 - 8 = 6
Since LHS = RHS the above system of equation is correct.
3 ) [tex]39 - 3 X 6=6 X 10/4+4[/tex]
LHS = 39- 18 = 21
RHS = 60 / 8 = 7.5
Since LHS is not equal to RHS the given system of equations is wrong
4 ) 56÷8+3^2= 2⋅2^3
LHS = 12
RHS = 12
Since LHS = RHS the above system of equations is correct.
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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.