The solution for the given equation is x = -5 and x = 3.
How to solve a quadratic equation by substitution?
The equation is first transformed into a more familiar form. Replace the substitutions with the original variables after factoring the problem. The difference of squares equation is used to finish the factorization and locate the answers for x.
Given, the equation for solving is: (x + 2)² - 2(x + 2) - 15 = 0 --(i)
Let in the equation, y = x + 2 --(ii)
Equating (i) and (ii), we get:
y² - 2y - 15 = 0 ⇒ y² - 5y + 3y - 15 = 0 ⇒ y(y - 5) + 3(y - 5) = 0
⇒ (y + 3)(y - 5) = 0 ⇒ y = -3, 5 (by solving the equations)
Thus, from (ii) and value of y obtained above, we get,
x + 2 = -3 ⇒ x = -3 -2 = -5 and x + 2 = 5 ⇒ x = 5 - 2 = 3
Thus, (b) x = -5 and x = 3 is the correct answer.
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suppse that you buy and exerice ball with diameter of 85 cm and your brother buys and exercise ball with 65 cm what is the diffrence bewtween the volume and surface are of both balls? round to the nearest 100
Given:
• Diameter of my ball = 85 cm
• Diameter of my brother's ball = 65 cm
Let's find the difference between the volume of the both balls and also let's find the difference between the surface area of both balls.
A ball has the shape of a sphere.
Therefore, we have the following formulas:
• Volume of a sphere formula:
[tex]V=\frac{\pi d^3}{6}[/tex]• Surface area of a sphere formula:
[tex]A=\pi d^2[/tex]Where d is the diameter.
• Now, to find the difference between the volume of both balls, we have:
[tex]V_1=\frac{\pi d^3}{6}=\frac{\pi85^3}{6}=321555.09\approx321555\text{ cm}^3[/tex]The volume of my ball is 321555 cubic cm.
[tex]V_2=\frac{\pi *65^3}{6}=143793.3\approx143793\text{ cm}^3[/tex]Volume of my brother's ball is 143793 cubic cm.
Therefore, to find the difference between the volume of both balls, we have:
V = V1 - V2 = 321555 - 143793 = 177762 cm³ = 177800 cm³
The difference between the volume of both balls is 177800 cm³
• Now for the surface area, we have:
[tex]A_1=\pi d^2=\pi *85^2=22698.01=22698\text{ cm}^2[/tex]The surface area of my ball is 22698 cm²
For surface area of my brother's ball:
[tex]A_2=\pi d^2=\pi *65^2=13273.23\approx13273\text{ cm}^2[/tex]The surface area of my brother's ball is 13273 cm².
Difference of surface areas:
A = A1 - A2 = 22698 - 13273 = 9425 cm² = 9400 cm²
Therefore, the difference between the surface area of both balls is 940O cm².
ANSWER:
• Difference between volume of both balls= 177800 cm³
• Difference between the surface area of both balls = 9400 cm²
The area of each square in the image below is 25 square units.
1) What is the perimeter of the figure?
2) How can you rearrange the squares (so that sides of the squares line up) to create a figure...
(a) with the same perimeter?
Answer:
1) 120 units
2) see attachment
Step-by-step explanation:
Given a figure composed of 21 squares that each have an area of 25 square units, you want to know (1) the perimeter of the figure, and (2) how to rearrange it to have the same perimeter, but with sides that line up.
(1) PerimeterThe perimeter is the sum of the lengths of the sides that form the boundary of the figure. The boundary consists of ...
6 top-side horizontal edges6 bottom-side horizontal edges6 left-side vertical edges6 right-side vertical edgesfor a total of 6·4 = 24 edges of the squares shown.
Each of the squares shown has an area of A = s² = 25 units², so a side length of s = √(25 units²) = 5 units.
The perimeter is the length of 24 of these edges, so is ...
perimeter = 24 × 5 units = 120 units
(2) RearrangementThe 21 squares shown in the figure can only be rearranged into rectangles that are 21 × 1 squares or 7 × 3 squares. These will have perimeters of 44 or 20 edges, respectively. Hence, it is not possible to have "sides of the squares line up" in a rectangle with the same perimeter.
The attached figure is the next best thing. It shows a 6 × 4 rectangle with three squares removed (to keep the total at 21). The number of horizontal and vertical edges total 24, as required to keep the same perimeter.
consider the function h(x)=(1/64)(x^5+16x^3). It can be seen from the graph that h(x) is one-to-one and so has an inverse function h^-1(x). Compute the slope of each respective graph at this point.
(h^-1)'(-32)=
The numeric value of the slope of the inverse function at x = -32 is given by:
(h^-1)'(-32) = 0.03.
How to find the inverse of a function?To find the inverse of a function, we exchange x and y in the original function, then isolate y.
This means that if the original function has a point (x,y) graphed, the inverse will have point (y,x) graphed.
From it's graph, the function h(x) has these two following points:
(-4.552, -32) and (-4.555, -32.1)
Hence the inverse will have these two following points:
(-32, -4.552) and (-32.1, -4.555).
The slope is given by change in y divided by change in x, hence:
(h^-1)'(-32) = (-4.552 - (-4.555))/(-32 - (-32.1)) = 0.03.
Which is also equivalent to the derivative of the inverse function at x = -32.
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16, 12, 20,35,21,17,19,20,13,12,15
What is the
O A. 7 OC. 20
OB. 13 OD. 12
interquartile range of the scores?
Interquartile range of the scores is 7.
What is interquartile range?When values are ranked from lowest to highest, the IQR designates the middle 50% of those values. Find the median (middle value) of the bottom half and upper half of the data before calculating the interquartile range (IQR). Quartile 1 (Q1) and Quartile 3 are these values (Q3). The IQR represents the variation between Q3 and Q1. The strongest indicator of variability in data sets with outliers or skewed distributions is the interquartile range. It's unlikely to be impacted by outliers because it's based on numbers that come from the center half of the distribution.
Given Set
16, 12, 20,35,21,17,19,20,13,12,15
12, 12, 13, 15, 16, 17, 19, 20, 20, 21, 35
25 percentile(Q₁) = 13
50 percentile(Q₂) = 17
75 percentile(Q₃) = 20
Interquartile range = Q₃ - Q₁
Interquartile range = 20-13
Interquartile range = 7
Interquartile range of the scores is 7.
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Question 3
Write an addition problem that has a sum of -3/ 2/3
The answer is -3 2/3 + 1 = -2 3/5
It's a linear equation form -3/ 2/3
What is linear equation?
An equation between two variables that, when plotted on a graph, produces a straight line or say first degree equation is known as linear equation.
An addition problem that has a sum of -3 2/3 may take different forms one of which is the answer supplied where; -3 2/3 is added to 1 and the result is -2 3/5
Therefore, the answer of -3 2/3 is -2 3/5
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Solve the inequality.x² + 3x - 28 < 0
We need to solve the inequality:
[tex]x^{2}+3x-28<0[/tex]We can start by sketching the graph of the parabola:
[tex]x^{2}+3x-28=0[/tex]Then, we need to find the points of the parabola below the x-axis.
The zeros of that parabola are given by:
[tex]\begin{gathered} x=\frac{-3\pm\sqrt[]{3^{2}-4(1)(-28)}}{2(1)} \\ \\ x=\frac{-3\pm\sqrt[]{9+112}}{2} \\ \\ x=\frac{-3\pm\sqrt[]{121}}{2} \\ \\ x=\frac{-3\pm11}{2} \\ \\ x_1=-7 \\ \\ x_2=4 \end{gathered}[/tex]And since the coefficient of x² is positive, the parabola opens upwards. So, its graph looks like this:
Thus, the points on the parabola below the x-axis are those for which:
[tex]-7Therefore, in interval notation, the solution to the inequality is:[tex](-7,4)[/tex]Use congruent triangles to find side lengths.If you were asked to draw the two congruent triangles described below, what would be each side length? ABC≈ EFGAB = 6, GF = 8, AC = 10.
ANSWER
• AB and EF
,• BC and FG
,• AC and EG
EXPLANATION
The order in which the vertices of the triangles are named gives us which sides are congruent. If ΔABC ≅ ΔEFG, then the pairs of corresponding congruent sides are,
[tex]\begin{gathered} AB\cong EF \\ BC\cong FG \\ AC\cong EG \end{gathered}[/tex]11. Richard's resting heart rate is 54 beats per minute (bpm). a. How many times will his heart beat in 4 minutes? b. How long will it take to beat 855 times?
Answer: a) 216 beats b) almost 16 minutes
Step-by-step explanation:
54 beats/minute x 4 minutes = 216 beats
855 beats / 54 beats/minutes = 15.83333 minutes
Hope this helps!
The following data shows the number of contacts that a sample of high school students had in their cell phones. 154,109,137,115,152,140,154,178,80,103,126,126,137,165,165,129,200,148A.) Identify any outliers in the dataB.) Draw a box plot to represent the dataC.) Analyze your data
Given set :
154,109,137,115,152,140,154,178,80,103,126,126,137,165,165,129,200,148.
Rewrite the given data set from least to highest values.
80, 103, 109, 115, 126, 126, 129, 137, 137, 140, 148, 152, 154, 154, 165, 165, 178, 200.
Recall that a data point is an outlier if it is over 1.5 times the IQR below the first quartile or 1.5 times the IQR above the third quartile.
We know that
[tex]\text{IQR}=Q_3-Q_1[/tex][tex]Q_3=The\text{ third quartile = The median of the upper half of the data set.}[/tex][tex]Q_1=The\text{ first quartile = The median of the lower half of the data set.}[/tex]The upper half of the data set is
{137, 140, 148, 152, 154, 154, 165, 165, 178, 200}
The number of data in the set is even.
There are two middle terms in this upper half of the given set. That are 154 and 154.
[tex]Q_3=\frac{154+154}{2}=154[/tex]The lower half of the data set is
{80, 103, 109, 115, 126, 126, 129, 137, 137, 140}
The number of data in the set is even.
There are two middle terms in this lower half of the given set. Which are 126 and 126.
[tex]Q_1=\frac{126+126}{2}=126[/tex]Substitute known values in the IQR formula.
[tex]\text{IQR}=154-126=28[/tex]We get IQR=28.
[tex]\text{HIgher outlier }\ge Q_3+(1.5\times IQR)[/tex][tex]undefined[/tex]Find the quotient and remainder for the following expression using the division algorithm.
33402
The quotient of 33/402 is 0 and the remainder is 369
How to determine the quotient?
The division expression is given as
33/402
From the above expression, we have
Numerator = 33
Denominator = 402
As a general rule of quotient, when the denominator is greater than the numeration, then the quotient is 0
How to determine the remainder?The division expression is given as
33/402
From the above expression, we have
Numerator = 33
Denominator = 402
As a general rule of quotient, when the denominator is greater than the numeration, then the remainder is 0
Remainder = Denominator - Numerator
This gives
Remainder = 402 - 33
Evaluate
Remainder = 369
This means that the remainder of 33/402 is 369
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Possible question
Find the quotient and remainder for the following expression using the division algorithm.
33/402
3/5 3) Find the equation of the line passing through the points (1, -2) and (-2, 7). Write the equation in slop-intercept from. Oy = 3x - 5 Oy= 3x + 13 Oy=-3x + 1 Oy=-3x - 2 Previous Next Submit arch O
hello
to solve this question we would first of all find the slope of the line
[tex]\begin{gathered} slope(m)=\frac{y_2-y_1}{x_2-x_1} \\ \end{gathered}[/tex][tex]\begin{gathered} y_1=-2 \\ x_1=1 \\ y_2=7 \\ x_2=-2 \end{gathered}[/tex]we can now substitute this into the equation
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{7-(-2)}{-2-1} \\ m=\frac{7+2}{-3}=\frac{9}{-3}=-3 \end{gathered}[/tex]the slope of the line is -3
we can write out how the equation looks
[tex]\begin{gathered} y=mx+b \\ y=-3x+b \\ b=\text{intercept} \end{gathered}[/tex]we can use one of the points to solve for b
[tex]\begin{gathered} y=-3x+b \\ u\sin g\text{ the first point} \\ (1,-2) \\ -2=-3(1)+b \\ -2=-3+b \\ b=3-2 \\ b=1 \end{gathered}[/tex]we can now rewrite our equation with slope and intercept
[tex]\begin{gathered} y=mx+b \\ y=-3x+1 \end{gathered}[/tex]from the calculation above, the equation of the line is given as y = -3x + 1
what is the answer to 7 3/16 + 4 5/48
Answer:
[tex]11\frac{14}{48}[/tex]
Step-by-step explanation:
[tex]7\frac{3}{16}+4\frac{5}{48}[/tex]
First, make these improper fractions.
[tex]\frac{115}{16} +\frac{197}{48}[/tex]
And now to add these fractions, make the denominators the same.
For that, multiply both the numerator and denominator of the fraction 115/16 by 3.
[tex]\frac{115*3}{16*3} +\frac{197}{48}\\\\\frac{345}{48} +\frac{197}{48}\\\\\frac{542}{48} \\\\=11\frac{14}{48}[/tex]
Nancy is buying a new pair of boots. The store is having a sale and all boots are 20% off. Part A Choose an expression that can represent the sale price of the boots where x is the original price of the boots (0.2x, 0.8x, 1.2x) Part B Thus means that the sale price of the boots is (20%, 80%, 120%) of the original. cost
Answer:
Part A: 0.8x
Part B: 80% of the original price.
Explanation:
Part A:
The store sells the boots at a sale price of 20% off, meaning the price of the shoes is 100% - 20 % = 80% of the original price. If we call x the original price, then the sale price would be
[tex]\frac{80}{100}\times x[/tex][tex]=0.8x[/tex]Part B:
The sale price of the boots is 100% - 20% = 80% of the original price.
Lynn Golding is employed as a payroll supervisor and earns $18 per hour. This pay period she worked 40 hours. She is married and claims 6 allowances. The state tax is 3.0% of gross earnings, and the local tax is 1.5% of gross earnings. Lynn pays $35 for medical insurance and $17 in union dues. Calculate Gross pay, net pay, federal income tax, social security, Medicare, State, Local, Medical and Union Dues.
The earnings and deductions, are given as follows:
Gross pay: $720.Net pay: $498.07.Federal income tax: $82.45.Social security tax: $44.64.Medicare tax: $10.44.State tax: $21.60.Local tax: $10.80.Medical due: $35.Union due: $17.What are her earnings and deductions?First we find her gross earning, which is given by the hourly wage multiplied by the number of hours worked, hence:
Gross pay = 40 x 18 = $720.
Hence her yearly income is given by:
Yearly income = 52 x 720 = $37440.
Meaning that her federal tax rate is of $19.76 a week plus 12% of the excess over $197.60, then:
Federal tax = 19.76 + 0.12 x (720 - 197.60) = $82.45.
The social security tax rate is of 6.2% of her gross weekly earnings, hence it is given by:
Social Security = 0.062 x 720 = $44.64.
The medicare tax rate is of 1.45% for Lynn(employee), hence:
Medicare = 0.0145 x 720 = $10.44.
The state tax is 3% of her gross earnings, hence:
State tax = 0.03 x 720 = $21.60.
The local tax is 1.5% of her gross earnings, hence:
State tax = 0.015 x 720 = $10.80.
The medical and union dues are stated in the problem, hence the sum of all discounts is given by:
82.45 + 44.64 + 10.44 + 21.60 + 10.80 + 35 + 17 = $221.93.
The net pay is the gross pay subtracted by the discounts, hence:
Net pay = 720 - 221.93 = $498.07.
Missing informationThe value of an allowance is not stated, hence they are not considered for the calculations.
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The figure below represents of a full circle. Find the measure of the marked centralangle.10Answer: Central Angle=Submit Answerattempt 1 out of 2
ANSWER
36°
EXPLANATION
A full circle has a central angle of 360°. If this figure represents 1/10 of a full circle, then its central angle is 1/10 of the central angle of the full circle:
[tex]360\degree\cdot\frac{1}{10}=36\degree[/tex]Hence, the measure of the central angle in this figure is 36°.
Can some on help me on these please and thank you!
Assume that a 24-month CD purchased for $4000 pays an APY of 4.25% (and of course interest is compounded). How much do you have at maturity?
At the CD's maturity in 2 years' time, the future value that you can collect is $4,347.22.
What is the future value?The future value (FV) of CD is the present value compounded at an interest rate of 4.25% for 2 years in the future.
We can compute the future value using the FV formula or an online finance calculator as below.
N (# of periods) = 2 years (24 months)
I/Y (Interest per year) = 4.25%
PV (Present Value) = $4,000
PMT (Periodic Payment) = $0
Results:
FV = $4,347.22 ($4,000 + $347.22)
Total Interest = $347.22
Thus, the 24-month CD purchased for $4000 will yield a future value of $4,347.22 at maturity.
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Evaluate the expression when c =-2.5 and d= 8.9.4d-c
To solve the exercise, replace in the expression the given values of c and d and then operate:
[tex]\begin{gathered} c=-2.5 \\ d=8.9 \\ 4(8.9)-(-2.5)=35.6+2.5=38.1 \end{gathered}[/tex]Therefore, the value of the evaluated expression is 38.1
Describe the event X<4 in words. What is P(X<4)
X<4 means that the chosen number is less than four and probability if the event X<4, P(X<4) 2/5.
Let us say that we have to select one number between 0-9.
So, the total possible outcomes can be 10.
Let us say that a number x is chosen randomly,
The expression x<4 means that is the chosen number is X, then the number should must be less than 4, not even equal, it should be less than 4.
So, The probability of X<4, we should first find total favorable outcomes,
The total number less than 4 are 0,1,2,3.
So, the total favorable outcomes are 4.
We know,
Probability of event E is,
P(E) = total favorable outcomes/total number of outcomes.
So, P(X<4) = 4/10
P(X<4) = 2/5
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42 divided by (15-2to the power of 3) = Hey y’all it would be great if y’all can help me out!
42 / 15-2^3
First, solve for the exponent:
42 / 15-8
Subtract:
42/7
Divide:
6
If it cost $13 to fill a gas tank in 2000, how much of the same tank
could be filled with $13 in 2010?
Answer:
4.58 gallons
Step-by-step explanation:
13$ in 2000 = 8 1/3 gallons
13$ in 2010 = 4.577 gallons
write the decimal for the given words:forty-one ten-thousandths
1) Since we know the decimal places, then we can write out the following number:
[tex]41.010[/tex]Note the 3 decimal places after the dot is the thousandth's place. Note that we can either write the last digit or omit it.
Dose anyone get this i am confused
Answers:
a) 32500
b) 0.00604
c) 2.4 * 10^6
d) 1.47 * 10^(-3)
===================================================
Explanation:
The exponent over the 10 tells us how many spaces to move right or left. If the exponent is positive, we move right. If negative, we move left. Think of a number line.
For part (a), the exponent is 4. So we move the decimal point 4 spaces to the right.
The 3.25 then becomes 32500
--------------
In part (b), the exponent -3 means we move 3 spots to the left to go from 6.04 to 0.00604
---------------
Part (c)
Place the decimal point between the first two digits and erase the zeros to get 2.4
Then we need to move the decimal point 6 spots to the right to get back to 2,400,000 again
Therefore we can say 2,400,000 = 2.4*10^6
---------------
Part (d)
Place the decimal point just after the first nonzero digit, and erase the zeros to the left to get 1.47
We must move the decimal point 3 spots to the left to go from 1.47 back to 0.00147 again
It means 0.00147 = 1.47*10^(-3)
Answer: he is right
Step-by-step explanation:
complete it for me please urgent
Answer:
8. y=3x+2
9. y=2x-6
10. y=1/2x+3
14. y=-2x
all i know hope this helps
Which would be used to solve this equation? Check all that apply.
StartFraction p Over 3 EndFraction = 12
The steps that would be applied to solve the equation are:
multiplying both sides of the equation by 3
substituting 36 for p to check the solution
What are the steps to take to solve the equation?An equation is a statement in mathematics that consists of two or more expressions that are connected by an equal to sign.
The given equation is:
p / 3 = 12
In order to solve, the equation, p has to be made the subject of the formula.
In order to make the subject of the formula, take the following step:
Multiply both sides of the equation by the denominator of p. The denominator of p is 3.
3 x (p/3) = (12 x 3)
p = 36
Substitute for p using 36 to check the accuracy of the answer derived
36 / 3 =12
Here are the options:
subtracting 3 from both sides of the equation
multiplying both sides of the equation by 3
dividing both sides of the equation by 3
substituting 4 for p to check the solution
substituting 36 for p to check the solution
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Write a math problem that this expression could be used to represent. Create a visual fraction model to represent the situation. Record the equation with the product. 9x6
Please, give me some minutes to take over your question
Ben run 6 miles in an hour. How many miles does Ben run in nine hours?
Ratio
6 miles / 1 hour
6 miles/ 1 hour = x miles / 9 hours
x= 6 * 9 = 54 miles
Ben runs 54 miles in 9 hours.
Which is correct for this function pls help
The graph represents a linear function with negative slope.
How does different type of graph and their equations look like?
1. Linear graph: It is of the form y= mx+ c
First-order variables are present in linear functions, and the graph's placement is determined by two constants. These operations graph into a line in every case. The slope of the line is determined by the constant m. The slope of the line will slope up if it is positive and down if it is negative.
2. Quadratic graph: y= ax^2+ bx+ c
These type of graphs have an U shaped curve and their slope can also be obtained by drawing a tangent.
3. Square root graph : F(x)=x is the parent function of all functions with the formula f(x)=a+b. Keep in mind that f(x)=x has an x0 domain and a y0 range. By translating the graph of f(x)=x to a units to the right and then b units up, the graph of f(x)=root x-a+b can be derived.
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Ryan, Darius, and Mason each have $15.75. They each spend the same amount (d), in dollars, at the school fair. The total amount of money they still have can be expressed as 3(15.75 - d). Which expression is equivalent to the total amount, in dollars, they still have?
Use the diagram to answer the question that follows
What is the image of c under the translation described by the translation rule (x,y) (x+11, y-8)
○ D
○ B
○ E
○ A
The image of C under the translation described by this translation rule (x, y) → (x + 11, y - 8) is: (4, -6)
What is a translation?In Geometry, the translation of a geometric figure to the right simply means adding a digit (11) to the value on the x-coordinate (x-axis) of the pre-image while translating a geometric figure down simply means subtracting a digit (8) from the value on the y-coordinate (y-axis) of the pre-image.
Note: Each point on this graph represents 2 units.
Next, we would translate the image of C 11 units to right and 8 units down. Therefore, this transformation can be modeled by this translation rule:
(x, y) → (x + 11, y - 8)
Point at C = (-7, 2) → Point at C' = (-7 + 11, 2 - 8) = (4, -6)
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HELP ASAP WILL GIVE BRAINLEST Write 4,650,000,000 in scientific notation.
4.65 x 10−9
4.65 x 109
465 x 10−7
465 x 107
Answer:
(b) 4.65×10⁹
Step-by-step explanation:
You want 4,650,000,000 written in scientific notation.
Scientific NotationA number is written in scientific notation in the form shown in the second attachment. The coefficient has one digit to the left of the decimal point. The remaining significant digits of the number are to the right of the decimal point.
The exponent is the same as the exponent of the place value of the most significant digit of the number. Some of those exponents are shown in the first attachment.
ApplicationThe given number has its most significant digit (4) in the "billions" place. The corresponding exponent of 10 is 9. Putting 4 to the left of the decimal point, the number is written in scientific notation as ...
4.65×10⁹
__
Additional comment
In the above, we have used the superscript font to indicate the exponent. In plain text, an exponent is indicated with a caret (^), as in 4.65·10^9.
If you use an "x" character for a multiplication symbol, you need to make sure it cannot be confused with a variable named "x".
In spreadsheets and some calculators, the base and exponent are written as "E". Here, the number would be 4.65E9. (This is a carryover from one of the earliest high-level computer programming languages.)
(You will notice that the number in the second attachment is similar to, but not the same as, the one given in this problem statement. We intend that attachment to show the format, not the answer to this question.)