Every radical can be rewritten has an exponent .
Extraneous Solutions occur because squaring both sides of a square root equation results in 2 solutions (the positive and negative number).
1. Exponents that are written as fractions are referred to as rational exponents.
The top of the rational exponent is the new exponent on the radical, and the bottom of the rational exponent is the root, therefore a rational power can be reinterpreted as a radical in this fashion.
2. Separate the radical expression from the equal sign on one side. Put every every clause over there on the other side. Square both sides of the equation if the radical is a square root. Raise both sides of the equation to the third power if it is a cube root. Write an expression as a radical if the expression has a logical exponent. By examining the exponent's numerator, you may determine the power. By examining the exponent's denominator, you can get the root. Raise the radicand to the power while using the base as the radicand, and use the root as the index.
3. Extraneous Solutions appear because there are two solutions when you square the two sides of a square root equation (the positive and negative number). As a result, one of those figures will represent an extra solution, or a solution that is added but does not satisfy the initial equation.
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Sally is 10 years older than her brother mark . Who is x years old. How old is sally?
Answer:
Mark is x years old.
Sally is 10+x years old
Question 23 (1 point)
What is the equation of the circle if the radius is 9 and the center is (2,7)
The equation of a circle that has a radius of 9 and a center at (-2, 7) is the option;
(x + 2)² + (y - 7)² = 81What is the definition of a circle?A circle is a set that comprises all points that are equidistant from a point on a plane
The general form of the equation of a circle is; x² + y² + 2•g•x + 2•f•y + c = 0
The equation of a circle can also be presented in standard form as follows;
(x - h)² + (y - k)² = r²Where;
(h, k) = The coordinates of the center of the circle
r = The measure of the length of the radius of the circle
The given parameters are;
The radius of the circle, r = 9
Taking the coordinates of the center of the circle, (h, k) = (-2, 7)
The equation of the circle in standard form is therefore obtained by plugging in the values of h, k, and r as follows;
(x - h)² + (y - k)² = r²
Which gives;
(x - (-2))² + (y - 7)² = 9²
Which gives;
(x + 2)² + (y - 7)² = 9² = 81
The equation of the circle is therefore the option;
(x + 2)² + (y - 7)² = 9² = 81Learn more about the equation of a circle given the center and radius here:
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which expression has a value of 3/4?
Answer:
6/8
Step-by-step explanation:
3/4 if we further multiply we get 6/8
Flora is buying dog food for her dog. She wants to buy enough to last five weeks (35 days). Her dog eats 2 cups in a day, and there are 24 cups in each bag. How many bags of dog food should flora buy?
Answer:
3 bags
Step-by-step explanation:
For all 35 days, the dog will need 35 * 2 = 70 cups
She will need at least 3 bags (72 cups) to sustain 5 weeks
Write a two-column proof to prove that vertical angles are congruent.
The manipulatives and paragraph forms are the two-column proof to prove that vertical angles are congruent.
Using manipulatives: Draw the same two intersecting lines on the paper. Then, fold the paper along the line via the joint. The fold bisects the other two borders, but only the lines of the folded border which are on top of each other are required. The edges check and lie straight on top of each separately. This folding procedure can be utilized with two vertical corners. As a result, the vertical angles are the same.
Paragraph Form: When ∠1 and ∠3 are connected to ∠2, they form a linear pair. This indicates that whether added dimension ∠2 to dimension ∠1 or dimension ∠2 to dimension ∠3, the total is 180°. That is, the measures of 1 and 3 are equal to the sum left before adding ∠2. As a result, the angles are the same. This argument applies to all pairs of vertical angles.
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round -125 over 4
-125/4
Answer:
Step-by-step explanation:
-125/4
-124/4=-31
-31 1/4
(x −8, y + 5) y(5-5)
Answer:
brainliest pls
Step-by-step explanation:
The lowest point in California is Death Valley, at 282 ft
below sea level. The highest point in Texas is Guadaloupe
Mountain, at 8,749 ft above sea level. What is the
difference in elevation between these two points?
Which is larger, 3.3 x 105 or 3.1 x 105? who ever answers get 50 points :)
Answer:
3.3*10^5 is the largest one.
Step-by-step explanation:
Comment
The threes out in front are the same. The next digit, (the tenths) are 3 and 1 since 3 is greater than 1, the answer is
3.3*10^5 > 3.1*10^5
Think of it this way. Take away the 10^5 and just look at 3.1 and 3.3. Which is bigger. 3.3 is the larger one.
Answer:
A
Step-by-step explanation:
What are the first two common multiples of the number 3 and 5?
Answer:
D
Step-by-step explanation:
3x5=15
3x10=30
5x6=30
Given ^PRS = ^CFH, find the values of x, y, and z.
Answer:
x = 23, y = 7, z = 11
Step-by-step explanation:
Since triangle PRS is congruent to triangle CFH,
PS = CH = 39
2x - 7 = 39
2x = 46
x = 23
Angle PRS = Angle CFH = 90°
13y - 1 = 90
13y = 91
y = 7
Sum of angles in a triangle add up to 180°.
Angle CHF = 180 - 90 - 28 = 62°
6z - 4 = 62
6z = 66
z = 11
simplify this algebraic expression completely 7x-5(x+6)
Step-by-step explanation:
[tex]7x - 5(x + 6) \\ 7x - 5x + 30 \\ 2x + 30[/tex]
I don’t know how to rewrite this in graphing form.
We can write this equation as (x-3)² + (y-2)² =25 in graphing form.
What is graphing form ?The vertex form of a quadratic equation is y = a (x h) 2 + k as opposed to the regular quadratic form, which is an x 2 + b x + c = y. Graphs
f(x) = ax² + bx + c, where a, b, and c are numbers and an is not equal to zero, is a quadratic function. A parabola is the shape of a quadratic function's graph.
Given Data
Equation:
x² +y² -6x +9y - 12 = 0
Writing in graphing form,
(x² - 6x) + (y² + 4y) = 12
(x² - 6x +9-9) + (y² +4y+4-4) = 12
(x² -6x +9) + (y² +4y+4) = 25
(x-3)² + (y-2)² =25
Center (x, y) = (3,-2)
radius r = 5
We can write this equation as (x-3)² + (y-2)² =25 in graphing form.
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Which of the following shows the numbers in order from least to greatest ? -2/3,-3/4,0.7,0
Answer: -3/4; -2/3; 0; 0.7
the nth term of a sequence is givin by 3n2
position of the term that is the first one to have a value over 100
Position of 1083 is 19 in the sequence that is the first one with a value greater than 1000.
What is Sequence?
A list of numbers or objects in a special order is called sequence.
Given that;
The nth term of a sequence = 3n²
Now,
Let [tex]a_{n}[/tex] be the nth term.
Then, [tex]a_{n} = 3n^{2}[/tex]
Let m be the term which is the first term with a value greater than 1000.
Then, [tex]a_{m} > 1000[/tex]
Substituted the value of [tex]a_{m}[/tex] we get;
3m² > 1000
Divide by 3 we get;
m² > 1000/3
m² > 333.333
Take square root both side;
m > √333.33
m > 18.25
Thus, m = 19
So, 19th term is the first one with a value greater than 1000.
Hence, [tex]a_{19} = 3(19)^2 = 3 * 361 = 1083[/tex]
Thus, Position of 1083 is 19 in the sequence that is the first one with a value greater than 1000.
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IUITUI Rauuild Ivoiribers Select the number line that shows that two opposite numbers have a sum of 0. 5 O A. -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 2 OB. + 8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 6 11 C. -8 -7 -6.-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 O D. PREVIOUS
It's important to know that the sum of two opposite numbers is zero because opposite numbers have the same absolute value but opposite sign, for example, 2 and -2 are opposite numbers.
The correct number line must have its final position on zero.
Notice that the number line A shows -5 as the initial number and then goes back 5 units to zero.
Therefore, the answer is A.Jamal hypothesized that when adding two unit fractions together, he can determine the numerator by adding the two denomimators together, thrn could find the new denominator by multiplying the old denominators together. Prove jamal correct. What are some drawbacjs of jamals shortcut?
Jamal is correct ( ½+⅓ =⅚), when he says that when adding two unit fractions, the numerator is found by adding the denominators, and the new denominator can be found by multiplying the previous denominators.
State what is denominator with example?A denominator is the lowest number in a fraction that indicates how many equal parts are divided into a whole. It is a fraction's divisor. In this case, the denominator is 4, thus there are four components overall.
What is an illustration of a numerator?In a fraction, the number above the line is the numerator. For instance, the numerator of the fraction 3/5 is 3. A fraction's numerator displays the number of pieces that make up the whole while the denominator.
Adding 2 unit fractions example ½ and ⅓
By Jamal’s theory, 2+3=5
2*3=6
½+⅓ =⅚
Hence the theory is proved right.
Drawbacks of Jamal’s Shortcut,
It is only for the unit fraction and not for any other type of fractions.
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Determine whether the equation Y=x^2 +13 represents a linear or non linear function and explain
Answer:
yés it is linear because
two variables that gives a straight line when plotted on a graph.
if it was correct tell me good or it was mistake tell me truth
Step-by-step explanation:
hope it was correct
What’s The Value Of X as A Decimal
Step-by-step explanation:
8x + 32 = 12x +19
4x = 13
x = 3.25
How can I find y if x=2?
Answer:
easy put 2 in the place of x and take it's square and subtract 1 that will be the value of y
Step-by-step explanation:
y= x^2-1
y= (2)^2-1
y= 4-1
y= 3
(the arrow head is used for power)
Hellppp
Which describes the graph of y = −(x + 6)2 + 6?
A.Minimum at (6, 6)
B.Maximum at (−6, 6)
C.Maximum at (6, 6)
D.Minimum at (−6, 6)
Find the value of x
(A) x= 135
(B) x= 25
(C) x= 35
(D) x= 90
Answer:
C) 35
Step-by-step explanation:
The sum of the interior angles of a triangle is 180°. We also have a right angle which is 90°.
2x - 8 + 90 + x -7 = 180 Combine like terms
3x + 75 = 180 Subtract 75 from both sides
3x = 165 Divide both sides by 3
x = 35
Pointss!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Step-by-step explanation:
always remember (for your life) : the sum of all angles in a triangle is always 180°.
and the sum of all angles around a single point on one side of a line is also always 180°.
so,
180 = 65 + 51 + angle PSR
angle PSR = 180 - 65 - 51 = 64°
angle PST is the supplementary angle to angle PSR (that means together they have 180°), because of the principle of all angles around a single point (S) on one side of a line (TSR).
so,
180 = angle PST + angle PSR = angle PST + 64
angle PST = 180 - 64 = 116°
Answer:114
Step-by-step explanation:
Please please please Help! I’m tired but have to finish!
A line has a slope of 4 and passes through the point (-1, 10). What is its equation in point-
slope form?
Use the specified point in your equation. Write your answer using integers, proper fractions,
and improper fractions. Simplify all fractions.
Answer: 10=-4+14
Step-by-step explanation:
Find the y-intercept(b) y=Mx+b m=slope.
-1x4
-4
Take -4 to the other side
10+4=b
14=b
10=-4+14
Hope I helped
Mason has a giant oak tree in his front yard. It has 9^3 leaves on the tree. all the leaves fall, and Mason rakes 9 piles of leaves with equal number of leaves in each pile. How many leaves are in each pile?
Please answer the two questions in the photo ( will mark brainliest if correct )
Hector just acquired 200 acres of land for raising animals. He wants to have at least 50 horses and no more than 300 sheep. Horses require at least 2 acres each. A maximum of 6 sheep can share an acre. What are the inequalities for the system
Answer: yes because that is possible
Step-by-step explanation:and i took the quiz it 152
19.7 as a mixed number
19.7 as a mixed number is [tex]19\frac{7}{10}[/tex].
How can a decimal be changed into a mixed number?Discover the place value of the decimal portion to change a decimal into a mixed number. The place value serves as the fraction's denominator, and the decimal portion serves as its numerator. Write the complete number first, then convert the decimal to a fraction by positioning the decimal part over the place value.Given:
Decimal number = 19.7
To convert it to a mixed number,
Remove the decimal point and add 10 in the denominator as it has one number after the decimal point.
19.7 = 197/ 10
Now divide and write it into a mixed fraction form,
= [tex]19\frac{7}{10}[/tex]
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Dan created a map of the state of ohio using a scale factor of 2 centimeters 25 miles The actual distance from cleveland to Columbus is 142 miles. About how far apart are Cleveland and Columbus on Dan's map
On Dan's map the distance between Cleveland and Columbus is 11.36 centimeters .
In the question ,
it is given that ,
the scale factor of Dan's map is 25 miles = 2 cm
So , 1 mile = 2/25 cm
= 0.08 cm
So , on Dan's map 1 mile is represented by 0.08 cm
Given that the actual distance between Cleveland and Columbus is 142 miles .
So , on Dan's map
142 miles = 0.08*142 cm
= 11.36 cm
we get , 142 miles = 11.36 cm
Therefore , On Dan's map the distance between Cleveland and Columbus is 11.36 centimeters .
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Overall, 120 6th grade scholars voted in theclass president election. How many votes did each class president candidate receive?
The number of votes that each class president candidate receive is 48 and 72 votes respectively.
How to calculate the values?Your information is incomplete. Therefore, an overview will be given. Let's say that A received 40% of the vote and B got 60% of the vote.
The number of votes gotten by each person will be:
A = Percentage × Number of votes
= 40% × 120
= 0.4 × 120.
= 48 votes.
B. = Percentage × Number of votes
= 60% × 120
= 0.6 × 120.
= 72 votes.
Therefore, A got 48 votes and B had 72 votes.
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