Answer:
sqrt of (m-7) = n+3
m = (n+3)^2 + 7 or m= n^2 + 6n + 16
sqrt of (m)-7 = n+3
m = (n+10)^2 or m =n^2 + 20n + 100
Step-by-step explanation:
(2) move the constants to the other side, and square
or (1) square and move constants
then you can solve for m
Answer:
[tex]n^2+6n+16[/tex]
Step-by-step explanation:
I'm going to assume you meant [tex]\sqrt{m-7} = n+3[/tex], not [tex]\sqrt{m} - 7 = n+3[/tex].
[tex](\sqrt{m-7}) ^2 = (n+3)^2\\\\(\sqrt{m-7}^2) = (n+3)^2\\\\(m-7)^{\frac{2}{2} } = (n+3)^2\\\\m - 7 = (n+3)^2\\\\m - 7 = n^2 + 2n\cdot3 + 3^2\\\\m - 7 = n^2 + 6n + 9\\\\m - 7 + 7 = n^2 + 6n + 9 + 7\\\\m = n^2 + 6n + 16[/tex]
Hope this helped!
Figure B is a scaled copy of Figure A.
9
3.6
3.6
9
Figure A
1.2
3
1.2
3
Figure B
What is the scale factor from Figure A to Figure B?
Answer:
1/3
Step-by-step explanation:
We are going to a small shape from a big shape, so the scale factor must be less than 1.
3 (which is a side on the blue figure) and 9 (a side on the green figure)
3 and 9 are easy numbers (for me...) so 3:9 is smaller than 1.
3:9 simplified is 1:3 = 1/3
so 1/3 is the scale factor.
Let's make sure it's right....
9 * 1/3 (green figure to blue figure) is = 3.
3.6 * 1/3 = 1.2
you can check it yourself on a calculator if you don't believe me
I hope this helps have a great day!!!!
Lara is x years old and her two best friends are (x-2) and (x+2). Write an expression for the square of Lara’s age and the product of ages of Lara’s best friends.
Please help with a detailed step by step thanks
Answer: x^2 + (x+2)(x-2)
Step-by-step explanation:
The caret ^ before the 2 indicates that the 2 is an exponent. It means "x squared"
If the keyboard doesn't allow exponents the caret is the thing to use.
The expression for the square of Lara’s age and the product of ages of Lara’s best friends is x² + (x-2)(x+2)
The first thing to do is to calculate the square of Lara's age and this will be:
= x × x = x²
The product of the ages of Lara’s best friends will be (x-2)(x+2).
Therefore, the expression that can be used to calculate the square of Lara’s age and the product of ages of Lara’s best friends is x² + (x-2)(x+2)
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Which side of the quadrilateral ABCD has a length equal to 10? Question 5 options: Which side of the quadrilateral ABCD has a length equal to 10? Question 5 options: A. BC B. DA C. BA D. CD
Answer:
Side DA
Step-by-step explanation:
The point A has coordinates of (-2,6) and the point D has coordinates of (-2,-4). Since both points have the same x-coordinate, we can subtract point A's y-coordinate from point D's y-coordinate.
6 - ( -4) = 10 (Basically adding 4 to six since the 2 minus signs make a plus sign)
That's your answer!
Hope that helps and maybe earns a brainliest!
Have a great day! :)
The side of the quadrilateral ABCD has a length equal to 10 is AD.
What is distance?Distance is the amount of space between two points. The distance between two points A(x₁, y₁) and B(x₂, y₂) on the coordinate plane is given by:
[tex]AB=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]
The coordinate of vertex A = (-2, 6) while for D is D(-2, -4). Hence:
[tex]AD=\sqrt{(-4-6)^2+(-2-(-2))^2}=10\ units[/tex]
The side of the quadrilateral ABCD has a length equal to 10 is AD.
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Are x and y inversely proportional in the table below?
x: 0.1 0.3 25 100
y: 200 40 0.8 0.2
Mr. Jackson took the 8th grade class on
field trip. While taking attendance, he
noticed there were 51 boy and 21 girls on
the trip. Write the ratio of boys to girls, as a
fraction in simplest terms
Answer:
17/7
Step-by-step explanation:
the ratio would be 51/21 then to simplify divide both numbers by 3 to get 17/7
Hi there! :)
Answer:
[tex]\huge\boxed{\frac{17}{7} }[/tex]
Given ratio of 51 boys to 21 girls:
Write as a ratio:
[tex]51 : 21[/tex]
Divide both terms by GCF, or 3:
[tex]\frac{51}{3} : \frac{21}{3}[/tex]
[tex]17 : 7[/tex] or [tex]\frac{17}{7}[/tex]
Therefore, the ratio is 17 boys to 7 girls, or [tex]\boxed {\frac{17}{7}}[/tex]
Use a number line to approximate the value of root 33
Let's think about the square root of 33 here for a second.
What two perfect squares surround 33?
The answer is 25 and 36.
Then, let's take the square root of both 25 and 36, which are 5 and 6. Therefore, since the square root of 25 and 36 are both nearest to the square root of 33, then the square root of 3 must be between 5 and 6.
The correct answer is A (or option 1): 5 < root 33 < 6
Hope this helps! :)
Answer:
a (the first choice)
Step-by-step explanation:
To start, you should think of square root values near 33 that you know the answer to. For example, the square root of 25 is 5, and the square root of 36 is 6. Therefore, you know that the square root of 33 is 5.something because it is in between 25 and 36.
A doctor asks a nurse to give a
patient 250 mg (milligrams) of the
drug Simethicone. The drug is
available only in a solution whose
concentration is 40 mg Simethicone
per 0.6 ml (milliliter) of solution.
How many milliliters of solution
should the nurse give the patient?
Answer:
Hey there!
For this question, we write a proportion.
[tex]\frac{40}{0.6}=\frac{250}{x}[/tex]
[tex]40x=150[/tex]
[tex]x=3.75[/tex]
Thus, the nurse to give the patient exactly 3.75 ml of the solution.
Let me know if this helps :)
The volume of the simethicone solution given by a nurse is 3.75 milliliters.
Given:
Doctor asks a nurse to give a patient 250 milligrams of the drug Simethicone.The concentration of a drug is 40 mg of Simethicone per 0.6 mL.To find:
The milliliters of a solution to be given to the patient by a nurse.
Solution:
Mass of simethicone drug to be given = 250 mg
Let the volume of the solution with 250 mg of simethicone be x.
The concentration of simethicone in solution = 40 mg/0.6 mL
Mass of simethicone in 1 mL of solution:
[tex]40 mg/0.6 mL=\frac{40 mg}{0.6 mL}\\\\=\frac{400 mg}{6 mL}[/tex]
The mass of simethicone in 'x' mL of solution:
[tex]250 mg=x\times \frac{400 mg}{6 mL}\\\\x=\frac{250 mg\times 6 mL}{400 mg}\\\\x=3.75 mL[/tex]
The volume of the simethicone solution given by a nurse is 3.75 milliliters.
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Please answer my question
Answer:
its
1/7
step by step
Answer:
The answer is H because there are 7 balls in total and two of which is red so the possiblity of getting the red ball is 2/7
Question: 4 x 1 2/5 Answer with a mixed number in simplest form!
Answer:
[tex]5\frac{3}{5}[/tex]
Step-by-step explanation:
[tex]4*1\frac{2}{5} = 4 * \frac{7}{5} = \frac{28}{5} = 5\frac{3}{5}[/tex]
Answer:
[tex]\boxed{ 5\frac{3}{5}}[/tex]
Step-by-step explanation:
[tex]\displaystyle 4 \times 1\frac{2}{5}[/tex]
[tex]\sf Convert \ mixed \ fraction \ into \ improper \ fraction.[/tex]
[tex]\displaystyle 4 \times \frac{7}{5}[/tex]
[tex]\sf Multiply.[/tex]
[tex]\displaystyle \frac{28}{5}[/tex]
[tex]\sf Convert \ improper \ fraction \ into \ mixed \ fraction.[/tex]
[tex]\displaystyle 5\frac{3}{5}[/tex]
18 silly bands are equally shared by 6 children. 2 children put their silly bands in the same drawer. How many silly bands are in the drawer?
Answer:
6
Step-by-step explanation:
18 silly bands / 6 children = 3 silly bands per child.
2 children * 3 bands each = 6 bands total
Answer:
6 silly bands
Step-by-step explanation:
18 divided by 6 = 3 , so each child gets 3 so 3 + 3 is 6 which means 6 silly bands are in the drawer
Select all sets in which the number - 1/7
is an element.
A.
integers
B.
rational numbers
C.
whole numbers
D.
natural numbers
E.
irrational numbers
F.
real numbers
-1/7 belongs to B. Rational numbers and F. Real numbers.
What is a set ?A set is a collecting of well defined objects one form of writing a set is in roaster method where we write the elements with commas and close them with second brackets.
According to the given question we have to select all the sets in which the number - 1/7 is an element.
-1/7 is a rational number as it can be written in p/q form where q ≠ 0.
This also contain in the set of real numbers as in -1/7 there is no imaginary part.
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Help Resource
Find the total surface area of the
following square pyramid:
4 cm
6 cm
SA = [?] cm2
Answer:
64 cm^2
Step-by-step explanation:
I assume the side of the base measures 4 cm, and the height of each triangular side (the slant height) is 6 cm.
SA = s^2 + 4 * bh/2
SA = (4 cm)^2 + 2(4 cm)(6 cm)
SA = 16 cm^2 + 48 cm^2
SA = 64 cm^2
The width of a rectangle is 14 feet less than 3 times the length. If the area is 24 fta,
find the width and length.
Width = 4 and Length = 6
Width = 2 and Length = 4
Width = 10 and Length = 12
Width = 6 and Length = 8
Answer:
Width: 4
Length: 6
Step-by-step explanation:
We can create a systems of equations for this problem, assuming W is width and L is length.
W = 3L-14
WL = 24
We can substitute W into the equation.
(3L-14)L = 24
3L²-14L = 24
3L² - 14L - 24 = 0
(3L+4)(L-6)=0
L = 6
Now we can find W by substituting L into the equation.
[tex]6\cdotw=24\\w = 4[/tex]
Hope this helped!
Find the area diagram below: Round to the nearest tenth.
30°
18m
1403
70.1
187
12
Answer:
The answer is option 2.
Step-by-step explanation:
First, you have to find the height of the triangle using Cosine Rule, cosθ = adjacent/hypotenuse :
[tex]cos(θ) = \frac{adj.}{hypo.} [/tex]
[tex]θ = 30,adj. = h,hypo = 18[/tex]
[tex] \cos(30) = \frac{h}{18} [/tex]
[tex]18 \cos(30) = h[/tex]
[tex]h = 9 \sqrt{3} \: m[/tex]
Next, you have to find the area of triangle using Sin Rule, Area = 1/2×a×b×sinC where a, b represent the side length of the angle and C is the angle :
[tex]area = \frac{1}{2} \times a \times b \times sin(C)[/tex]
[tex]let \: a = 9 \sqrt{3} ,b = 18,C = 30[/tex]
[tex]area = \frac{1}{2} \times 9 \sqrt{3} \times 18 \times \sin(30) [/tex]
[tex]area = 70.1 \: {m}^{2} \: (near.tenth)[/tex]
Answer:
70.1
Step-by-step explanation:
This is a 30-60-90 right triangle.
The ratio of side lengths is as follows:
short leg : long leg : hypotenuse
1 : sqrt(3) : 2
The short leg is 1/2 the hypotenuse.
The long leg is sqrt(3) times the short leg.
A = bh/2
A = (18/2)(18/2 * sqrt(3))/2
A = 70.1
Among the licensed drivers in the same age group, what is the probability that
a 57-year-old was involved in an accident? Use the table below.
Drivers in
Age group accidents
(thousands)
19 and under 2150
20-24
2620
25-34 3740
35-44 3220
45-54 3030
55-64
1990
65-74
790
75 and over 560
Drivers in
fatal
accidents
5,400
8.700
10.700
9600
9400
6500
3800
4300
Licensed
Drivers
(thousands)
10,034
17.173
35,712
40,322
40,937
30,355
17,246
13,321
Answer:
The probability that a 57-year-old was involved in an accident is 0.0656.
Step-by-step explanation:
We are given the data for the drivers involved in an accident of different age groups.
And we have to find the probability that a 57-year-old was involved in an accident.
From the table given to us, it clear that a 57-year-old driver will lie in the age group of 55 - 64.
Now, the number of licensed drivers in the age group of 55 - 64 are 30,355 (in thousands).
The point to be noted here is that the data given of drivers in accidents (thousands) will include the data of drivers in fatal accidents.
So, the number of 57-year-old drivers involved in accidents are 1990 (in thousands).
The probability that a 57-year-old was involved in an accident is given by;
= [tex]\frac{1990}{30,355}[/tex]
= [tex]\frac{398}{6071}[/tex] = 0.0656 or 6.56%
How would you describe the difference between the graphs of f(x) = 2x2 and
g(x) = -2x2 ?
A. g(x) is a reflection of f(x) over the line y=-1.
B. g(x) is a reflection of f(x) over the line y = x.
C. g(x) is a reflection of f(x) over the yaxis.
D. g(x) is a reflection of f(x) over the x-axis.
Answer:
D. g(x) is a reflection of f(x) over the x-axis.
Step-by-step explanation:
Given
f(x) = 2x²
g(x) = -2x²
Required
Determine the difference between f(x) and g(x)
Start by expanding g(x)
g(x) = -2x²
g(x) = -1 * 2x²
Substitute 2x² for f(x)
g(x) = -1 * f(x)
g(x) = -f(x)
Using the format (x,y):
Take for instance x = 2
f(x) = 2x² = 2 * 2² = 2 * 4 = 8
This means (x,y) = (2,8)
g(x) = -f(x)= -8
This means that (2,-8)
Notice that only the y value changed in both cases from 8 to -8
From the above expression, g(x) = -f(x) and illustration of when x = 2
This implies that g(x) is a reflection of f(x) along the x axis..
From the list of given options, the correct answer is D.
A vending machine accepted any combination of nickels, dimes, and quarters that added to $0.40. How many different combinations of coins were possible?
Answer: 1 quarter, 1 dime and 1 nickel.
Step-by-step explanation:
Quarter: 25 cents.
Dime: 10 cents
Nickel: 5 cents
25 + 10 = 35
35 + 5 = 40
Answer: 25 (1 quarter), 10 (1 dime), 5 (1 nickel) is 0.40 cents when all three numbers are summed up.
HELPPP
The diagram below represents a tower. Given the tower resembles a cone on top of a cylinder, which of
the measures below is the closest to the volume of the tower.
T
10 m
0
100
30 m
10 m
o
2600
2200
9400
10500
Previous
Answer:
the answer must be A as it is the closest, i think its a computer error
Answer:
if the answer wasn't A i would try B since its the next closest answer
Step-by-step explanation:
write the slope- intercept form of the equation for the line
y=-8/7x-3/2
y=7/8x-3/2
y=-7/8x-3/2
y=-3/2x+7/8
Answer: All options are in slope-intercept form
i hope this helps .
Step-by-step explanation:
1.
[tex]\mathrm{For\:a\:line\:in\:the\:form\:of\:}\mathbf{y=mx+b}\mathrm{,\:the\:slope\:is}\:\\\mathbf{m}\:\mathrm{and}\:\mathbf{y}\:\mathrm{intercept\:is}\:\mathbf{b}\\y=-\frac{8}{7}x-\frac{3}{2}\\[/tex]
2.
[tex]\mathrm{For\:a\:line\:in\:the\:form\:of\:}\mathbf{y=mx+b}\mathrm{,\:the\:slope\:is}\:\\\mathbf{m}\:\mathrm{and}\:\mathbf{y}\:\mathrm{intercept\:is}\:\mathbf{b}\\\\y=\frac{7}{8}x-\frac{3}{2}[/tex]
3.
[tex]\mathrm{For\:a\:line\:in\:the\:form\:of\:}\mathbf{y=mx+b}\mathrm{,\:the\:slope\:is}\:\\\mathbf{m}\:\mathrm{and}\:\mathbf{y}\:\mathrm{intercept\:is}\:\mathbf{b}\\\\y=-\frac{7}{8}x-\frac{3}{2}[/tex]
4.
[tex]\mathrm{For\:a\:line\:in\:the\:form\:of\:}\mathbf{y=mx+b}\mathrm{,\:the\:slope\:is}\:\\\mathbf{m}\:\mathrm{and}\:\mathbf{y}\:\mathrm{intercept\:is}\:\mathbf{b}\\\\y=-\frac{3}{2}x+\frac{7}{8}\\[/tex]
Write a equation representing the area Bruce covered, y, in terms of the number of tiles he used,x.
A equation representing the area Bruce covered, y, in terms of the number of tiles he used x is y = 4x
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. For example, 3x – 5 = 16 is an equation
According to the question
The area Bruce covered shows by y axis
The number of tiles he used is x axis .
The tiles Bruce used is 1/4 of a square foot in area .
Therefore,
Area of tiles in square foot = 4 number of titles
= 4x
now,
Equation will be :
y = 4x
Hence, A equation representing the area Bruce covered, y, in terms of the number of tiles he used x is y = 4x
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What type of number is −7? There may be more than one correct answer. Select all that apply. If only one answer is correct, select "only" and the answer that applies. integer only whole rational natural
Answer:
-7 is a Negative Number, which is also an integer.
Step-by-step explanation:
Negative numbers are any number less than 0. The greater a negative number is, is the smaller its value.
Which point below is not on the graph of h(x) ^3√x+64 = ? (65, 5) (-37, 3) (-72, -2) (-64, 0)
Answer:
(-37, 3)
Step-by-step explanation:
Vertex Form y=a(x-h)^2+k what does each variable represent if they were in a problem.
There are four points on a line: A, B, C and D, so that AB=1, BC=2, CD=4. Find the length of segment AD .Consider all possibilities and draw a picture for each one of them.
Answer:
The answer is 7
Length of all the the three segments is equal to the length of the line segment AD
A line plot has a range of 4, from 1 to 5, with 5 modes. How would you describe the graph?
The graph has an outlier.
The data is clustered around 3.
Each column will be the same height.
There is not enough information.
will give brainliest
Answer:
Each column will be the same height.
Step-by-step explanation:
Mode refers to the most occurring number, and there are five within a data set that is 4 wide, so there will be 5 columns of equal length.
What is the value of f(1)?
Answer:
A function normally tells you what y is if you know what x is.
Cathy is paid at a rate of $7 20 per hour for a basic hour-week of 70 hours. She is paid time-and-a-half for over-time during the week and double-time on weekends. In a fortnight she worked 160 hours, and 4 hours on Saturday and 2 hours on Sunday. What is Cathy's hours in a fortnight
Cathy worked a total of 160 + 4 + 2 = 166 hours in a fortnight.
So the answer is 166
Here is the calculation:
Cathy's basic pay for the fortnight is 7.2 × 70 = $504.
Her overtime pay for the week is (1.5 × 7.2) × 9 = $97.2.
Her weekend pay is (2 × 7.2) × 6 = $86.4.
Her total pay for the fortnight is 504 + 97.2 + 86.4 = $687.6.
Therefore, Cathy worked a total of 160 + 4 + 2 = 166 hours in a fortnight.
So the answer is 166
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Find the average rate of change of g(x)= – x2 over the interval [ – 8, – 2]. Write your answer as an integer, fraction, or decimal rounded to the nearest tenth. Simplify any fractions.
Answer:
[tex]Average\ Rate = 10[/tex]
Step-by-step explanation:
Given
[tex]g(x) = -x^2[/tex]
[tex](-8,-2)[/tex]
Required
Determine the average rate of change;
Average rate of change is calculated as thus;
[tex]Average\ Rate = \frac{g(b) - g(a)}{b - a}[/tex]
Where
[tex](a,b) = (-8,-2)[/tex]
i.e. a = -8 and b = -2
[tex]Average\ Rate = \frac{g(b) - g(a)}{b - a}[/tex] becomes
[tex]Average\ Rate = \frac{g(-2) - g(-8)}{-2 - (-8)}[/tex]
[tex]Average\ Rate = \frac{g(-2) - g(-8)}{-2 + 8}[/tex]
[tex]Average\ Rate = \frac{g(-2) - g(-8)}{6}[/tex]
Calculating g(-2)
Substitute -2 for x in [tex]g(x) = -x^2[/tex]
[tex]g(-2) = -(-2)^2[/tex]
[tex]g(-2) = -4[/tex]
Calculating g(-8)
Substitute -8 for x in [tex]g(x) = -x^2[/tex]
[tex]g(-8) = -(-8)^2[/tex]
[tex]g(-8) = -64[/tex]
Substitute values for g(-2) and g(-8)
[tex]Average\ Rate = \frac{g(-2) - g(-8)}{6}[/tex]
[tex]Average\ Rate = \frac{-4 - (-64)}{6}[/tex]
[tex]Average\ Rate = \frac{-4 + 64}{6}[/tex]
[tex]Average\ Rate = \frac{60}{6}[/tex]
[tex]Average\ Rate = 10[/tex]
Hence, the average rate of change is 10
Min read 1/8 of his book before lunch and 1/4 of his book after lunch. He says he has read 2/12of his book.
Which statement is most accurate?
2/12 is a reasonable answer for the fraction of his book Min has read.
2/12 is not a reasonable answer for the fraction of his book Min has read. The fraction should be closer to 1/2.
2/12 is not a reasonable answer for the fraction of his book Min has read. The fraction should be closer to 1.
Answer:
2/12 is not a reasonable answer for the fraction of his book Min has read. The fraction should be closer to 1/2.
Step-by-step explanation:
First, find common denominators. Note that what you do to the denominator, you must do to the numerator:
1/8
1/4 x (2/2) = 2/8
1/8 + 2/8 = 3/8
Find common denominators between the amount he read as well as the amount he thinks he read:
(3/8)(3/3) = 9/24
(2/12)(2/2) = 4/24
Min has read 9/24 of his book, while he states that he read 4/24 of his book.
2/12 is not a reasonable answer for the fraction of his book Min has read. The fraction should be closer to 1/2.
Note: 9 is only 3 parts away from 12 (12/24), while 9 is 5 parts away from 4 (4/24).
~
Answer: i think its b
Step-by-step explanation:
Help me please I guess
Root 16=4 and root 49=7
Therefore,4 and 7 are rational as they have terminating decimal expansion.
Therefore,4+7=11 (rational)
[tex] \sqrt{16} + \sqrt{49} = \boxed{11}[/tex]