Answer:
[tex]\large\boxed{\dfrac{4}{\sqrt{10}-\sqrt6}=\sqrt{10}+\sqrt6}[/tex]
Step-by-step explanation:
[tex]\dfrac{4}{\sqrt{10}-\sqrt6}\\\\\text{use}\ (a-b)(a+b)=a^2-b^2\ \text{and}\ (\sqrt{a})^2=a\\\\=\dfrac{4}{\sqrt{10}-\sqrt6}\cdot\dfrac{\sqrt{10}+\sqrt6}{\sqrt{10}+\sqrt6}=\dfrac{4(\sqrt{10}+\sqrt6)}{(\sqrt{10})^2-(\sqrt6)^2}=\dfrac{4(\sqrt{10}+\sqrt6)}{10-6}\\\\=\dfrac{4(\sqrt{10}+\sqrt6)}{4}=\sqrt{10}+\sqrt6[/tex]
The rationalization of the given expression will be equal to
[tex]\dfrac{4}{\sqrt{10}-\sqrt{6}}=\sqrt{10}+\sqrt{6}[/tex]
What is rationalization?Rationalization is a procedure used in elementary mathematics to remove the irrational number from the denominator.
The rationalization of the given fraction will be :-
[tex]=\dfrac{4}{\sqrt{10}-\sqrt{6}}\times \dfrac{\sqrt{10}+\sqrt{6}}{\sqrt{10}+\sqrt{6}}[/tex]
[tex]\dfrac{4\sqrt{10}+\sqrt{6}}{\sqrt{10}^2-\sqrt{6}^2}=\dfrac{4\sqrt{10}+\sqrt{6}}{10-6}[/tex]
[tex]\dfrac{4\sqrt{10}+\sqrt{6}}{\sqrt{10}^2-\sqrt{6}^2} =\dfrac{4\sqrt{10}+\sqrt{6}}{4}=\sqrt{10}+\sqrt{6}[/tex]
Hence rationalization of the given expression will be equal to
[tex]\dfrac{4}{\sqrt{10}-\sqrt{6}}=\sqrt{10}+\sqrt{6}[/tex]
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Please Help! :C A bathroom is located at (-9, 0) on the map. How far would someone have to walk to get from the checkout desk to the bathroom. Explain or show how you got your answer.
Answer:
you would have to walk 9 to the left.
Step-by-step explanation:
I'm assuming that the checkout desk is at (0,0) You would have to walk 9 to the left because on a coordinate plane negative is either left or down. since the -9 is on the x axis it is 9 to the left. Can I get brainliest
Answer:
walk 9 to the left
Step-by-step explanation:
Plz help me with this
Only the last two options are true.
The first one is false, because 4.5 is the value of the maximum of f(x), not the point where it is reached.
The second one is false, because g(x) has a maximum of 9, so it is a downward-facing parabola (just like f(x)), so it doesn't have a minimum.
The third one is true, because the maximum value of f(x) is 4.5, and the maximum value of g(x) is 9, which is twice the maximum of f(x)
The last one is false (see point 2).
Answer:
The third and last one.
Step-by-step explanation:
First, by looking at the graph you can tell that the parabola peaks where x = 0.5, not 4.5, so this one is incorrect.
The second one is incorrect, because the value of the g(x) at 0 is 9, but he function is less at other values such as when x is -3 and the g(x) is 0.
The maximum value of the g(x) is 9. We can tell this because points with an equal difference of x values away from x = 0 (where g(x) = 9), also have the same y values. Because 9 is twice of 4.5, and 4.5 is the maximum value of the f(x), the third one is correct.
Lastly, The last one is true, because quadratic functions only have a minimum or a maximum value and we already know that both of these functions have a maximum value.
In the drawer, there are 9 knives, 9 spoons, and 4 forks. What is the probability of randomly drawing a knife or spoon?
Answer:
Hello! Your answer is 36%
Step-by-step explanation:
9+9=18.
18/5 = 18÷5
18÷5 = 3.6 = 36%
HOPE THIS HELPS!
Answer:
Your answer is 36%
Step-by-step explanation:
9+9=18÷5=3.6=36%
Which expression is represented by the model?
A. X-3
B. X+3
C. -X-3
D.-X+3
first we know that the X is negative so we can ignore number A and B because they are positive.
Then we are left with two solutions and if you referred to the picture we know that whatever comes after has to be positive
So the correct answer is D
Answer:
D. -X + 3.
Step-by-step explanation:
There are 3 plus signs and a -x.
Brainliest + Points! I need help please explain
Answer:
D
Step-by-step explanation:
AB is in the first quadrant
Coordinate points in the first quadrant are (x, y)
Under a reflection in the x- axis
a point (x, y ) → (x, - y) ← a point in quadrant 4 → D
Jeffrey surveys the 13 girls and 13 boys in his class to find out how many pairs of shoes they have in their closets. Which statement is true
Answer:
the answer is c
Step-by-step explanation:
The median number of shoes for the girls is greater than the median number of shoes for the boys. To find the medians, order the data sets and find the middle value.
The statement which is true about Jeffery's survey of the 13 girls and 13 boys is;
Mean and Median as a measure of Central TendencyAlthough, the mean and median are statistical measures of central tendency.
It follows from the data obtained from the survey that:
The mean and median for the girls are greater than the mean and median of the boys respectively.Additionally, the value of Q1 and Q3 for the girls is greater than that of the boys respectively.On this note, it follows from the Inferences above that, the statement which is true about the survey is; The value of Q1 for the girls is greater than the value of Q1 for the boys.
Remarks:
A)The value of Q1 for the girls is greater than the value of Q1 for the boys.
B) The value of Q3 for the boys is greater than the value of Q3 for the girls.
C)The mean number of shoes for the boys is greater than the mean number of shoes for the girls.
D)The median number of shoes for the boys is greater than the median number of shoes for the girls.
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nicole worked for 6 hours and 15 minutes. how should she write that on her time card
A. 7.0
B. 6.25
C. 6.15
D. 6.75
Answer:
B since 6 is a whole number for hours it would be 6 and 15 is 1/4 of 60 it would be 0.25 meaning, 6.25
Step-by-step explanation:
The time card will have 6.25 hours.
What are the steps in converting measurement of time?To convert units of measurement for time, here are the steps.
Step #1: Identify the units used.
Step #2: Determine the relationship between the units.
Step #3: Determine the conversion factor (in fraction form).
Step #4: Multiply the original measurement by the conversion factor.
Given:
6 hours and 15 minutes
= 6 + 15/60
=6 + 1/4
=6+0.25
=6.25 hours
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Reynaldo is a landlord who owns several rental homes one all wood home in the suburbs is worth 95,000 because the renters insure their own belongings what is the premium Reynaldo pays for property insurance per year?
Answer:B
95,000÷100 then multiply by $0.83 since it's a wood home in the suburbs.
Step-by-step explanation:
Answer:
788.5
Step-by-step explanation:
Suppose that we wish to assess whether more than 60 percent of all U.S. households in a particular income class bought life insurance last year. That is, we wish to assess whether p, the proportion of all U.S. households in the income class that bought life insurance last year, exceeds .60. Assume that an insurance survey is based on 1,000 randomly selected U.S. households in the income class and that 640 of these households bought life insurance last year
Answer:
dont know
Step-by-step explanation:
Answer:
Step-by-step explanation:
Set up hypotheses as:
[tex]H-0: p=0.60\\H_a: p >0.60[/tex]
(Right tailed test)
Sample proportion p = favourable/total = [tex]\frac{640}{1000} =0.64[/tex]
p difference [tex]=0.64-0.60 =0.04[/tex]
Sample std error = [tex]\sqrt{\frac{pq}{n} } =\sqrt{\frac{0.64(0.36)}{1000} } \\=0.0152[/tex]
Critical value for95% = 1.96
Margin of error = [tex]1.96(0.0152)\\= 0.0298[/tex]
Confidence interval for proportions
=[tex](0.64-0.0298, 0.64+0.0298)\\=(0.6102,0.6698)[/tex]
Since confidence interval does not contain 0.60 we reject null hypothesis.
At 5% significance level we can accept thta proportion >0.60
Pls does anyone know the answer??
Answer:
The on the bottom is right.
Step-by-step explanation:
Answer:
A is the correct answer
Step-by-step explanation:
whats 4 ways to make 23 cents using dimes,nickels, and pennies
23 pennies
4 nickels, 3 pennies
2 dimes, 3 pennies
1 dime, 2 nickles, 3 pennies
What’s 92508253 in words
92,508,253
Ninety-two million, five hundred eight thousand, two hundred fifty-three
Answer:
ninety-two million, five hundred eight thousand, two hundred fifty-three
Find the values for c and d that would make the following equation true. (cy^2)(4y^d)=-20y^3
Answer:
c = -5 and d = 1
Step-by-step explanation:
First, multiply out (cy^2)(4y^d). We get: 4cy^(2+d).
We equate this result to the right side of the equation: - 20y^3.
Then, equating the exponents and solving for d, we get: 2 + d = 3, or d = 1.
Equating the coefficients, we get 4c = -20, or c = -5.
72 subtract 3 equals 36
That is not true. 72-3=69
Which graph matches the equation y = -(x-2)2
The equation y = -(x-2)² represents a parabola opening downwards with a vertex at (2, 0). To find the matching graph, plot several points by calculating y for chosen x values and then connect the points to reveal the parabola's shape.
Explanation:The student is asking for the graph that matches the equation y = -(x-2)². This equation represents a parabola that opens downwards due to the negative sign in front of the parenthesis. To plot this, we'll need to create a table of values by choosing different x values, inserting them into the equation, and calculating the corresponding y values. After plotting these points, we'll see the shape of the parabola. Its vertex, the highest point on the graph due to the downward opening, will be at (2, 0) since the equation is in the form y = -a(x - h)², where (h, k) is the vertex of the parabola.
Steps for Plotting:Choose x values around the vertex (2, 0).Calculate y for each x.Plot the points on the coordinate plane.Connect the points to form a parabola.72/10 is equal to which number
It is equal to 7.2
Hope this helps.
Answer:
7.2
Step-by-step explanation:
Imagine math 2021
ΔABC with vertices A(-3, 0), B(-2, 3), C(-1, 1) is rotated 180° clockwise about the origin. It is then reflected across the line y = -x. What are the coordinates of the vertices of the image?
Answer: The answer would be C. Please give me a thanks :) bye!
Step-by-step explanation:
Simplify the expression. X^2-x/2x-2x^2
Answer:
[tex]\large\boxed{\dfrac{x^2-x}{2x-2x^2}=-\dfrac{1}{2}}[/tex]
Step-by-step explanation:
[tex]\dfrac{x^2-x}{2x-2x^2}=\dfrac{x^2-x}{-2(x^2-x)}\\\\\text{cancel}\ (x^2-x)\\\\=-\dfrac{1}{2}[/tex]
Mr. Jones is getting a 6% raise. If he made $720 a week, how much more will he make with the raise?
$720 * .06 = 43.2
He will make $43.20 more each week.
Tickets numbered 1 to 20 are mixed up and drawn at random. What is the probability that the ticket drawn has a number which is a multiple of three or five.
8/15
2/5
9/20
1/2
Answer:
B. 2/5
Step-by-step explanation:
First we write down the numbers.
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20.
Multiplies of three or five above are: 6,9,10,12,15,16,19,20 (there are 8)
So 8/20.
8/20 simplified is 2/5
So, it's B.
Which expression represents the area of the rectangle
(2x+7)(4x+5)?
So we'll do FOIL (first, outer, inner, last)
The equation is (4x+5)(2x+7)
First, 4x·2x=8x²
Outer, 4x·7=28x
Inner, 5·2x=10x
Last, 5·7=35
Add like terms and you get:
8x²+38x+35
The area of the rectangle represented by the expression (2x+7)(4x+5) is calculated by distributing and combining like terms, yielding the answer 8x^2 + 38x + 35.
Explanation:The expression (2x+7)(4x+5) represents the area of rectangle in Algebra. The area of a rectangle is calculated as length times width, and in this case, the length is 2x+7 and the width is 4x+5.
To calculate the area, we will need to multiply these two expressions, also known as using the distribution property of multiplication over addition.
Apply the distributive property:
2x * 4x = 8x^22x * 5 = 10x7 * 4x = 28x7 * 5 = 35Combine like terms:
8x^2 + 10x + 28x + 35 = 8x^2 + 38x + 35.So, the area of the rectangle is represented by the expression 8x^2 + 38x + 35.
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Please Help Asap, Thank You!
Given :△ABC (to the right), AB = 15, BD = 9,
AD ⊥BC m∠C = 30°. Find the perimeter of triangle.
Answer:
48 + 12√3 units
Step-by-step explanation:
ALL LENGTHS MUST BE POSITIVE (I did this to avoid writing ± and showing that only + works)
1. Find AD (you'll find why later): 15² = 9² + AD² --> AD² = 144 --> AD = 12
2. 30-60-90: 12-DC-AC --> AC = 24, DC = 12√3 (side opposite of 90 is double side opposite of 30, side opposite of 60 is √3 times the opposite of 30)
P = AB + BD + DC + AC = 15 + 9 + 12√3 + 24 = 48 + 12√3 units
The perimeter of triangle △ABC is found by summing all sides of the triangle, resulting in 51.
Explanation:In this question, we are dealing with the triangle △ABC. We know that AB = 15, BD = 9, AD is perpendicular to BC, and m∠C = 30°. Remember, the sum of all sides in a triangle constitutes the perimeter.
Given that AB=15 and BD=9, and as BD is the opposite side of m∠C = 30°, we know that the hypotenuse is twice the length of the opposite side in a 30-60-90 triangle. Thus, AD = 2BD = 18. Since AD is also perpendicular to BC, AD divides the triangle into two right triangles.
We know that the side adjacent to ∠C is half the length of the hypotenuse in a 30°-60°-90° triangle. Hence, CD = AD/2 = 18/2 = 9. Now, BC = BD + CD = 9 + 9 = 18. Summing up all sides of the triangle, the perimeter of △ABC = AB + BC + AC = 15 + 18 + 18 = 51.
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Melisa is throwing a birthday party for her son. She ordered 4 pizzas, she realizes that her son invited more people than she thought, so she decides to order 1 more pizza for every 3 people that come to the party. The total number of pizzas, y , can be expressed in terms of the number of people that show up to the party, x . which inequality represents this situation?
y = -one third x + 4
y = one third x + 4
y = 3x - 4
y = 3x + 4
Answer:
y = 3x + 4
Step-by-step explanation:
3x would be the number of people that show up to the party times the number of pizza's needed plus the 4 she already ordered
Which of the following are considered measures of center?
I. mean
II. median
III. mean absolute deviation
Answer:
only 1 and 2
(mean and median)
the mean absolute deviation is the measure of variability
Step-by-step explanation:
Mean and median are the measures of center
The area of the base of a rectangular prism is 18 cm2. The height of the prism is 9 1 2 cm. What is the volume of the prism? A) 27 1 2 cm3 B) 54 1 2 cm3 C) 84 3 4 cm3 D) 171 cm3 please answer quick
Multiply the area of the base by it's height.
18 x 9 1/2 = 171 cm^3
The answer is D.
Answer:
D) 171 cm3
Step-by-step explanation:
Help on number nine please?
im pretty sure true because they do not intersect and are not parallel :)
Answer:
true
Step-by-step explanation:
what is the area of the triangle shown below?
Answer: 18
Step-by-step explanation:
Per a.p.e.x
The area of a triangle can be found using the formula: Area = (base × height) / 2.
Explanation:The area of a triangle can be found using the formula: Area = (base × height) / 2. To find the area of the triangle shown below, you need to know the length of the base and the height. Once you have those values, you can plug them into the formula to calculate the area.
The prism below is made of cubes which measure 1/3 of a centimeter on one side. What is the volume?
A. 20 cubic cm
B. 20/3 cubic cm
C. 20/27 cubic cm
D. 3 cubic cm
Answer:
the answer is C. 20/27 cubic cm.
Step-by-step explanation:
V = LWH
length 5(1/3 cm)
width 2(1/3 cm)
height 2(1/3 cm)
V = (5/3 cm) (2/3 cm) (2/3 cm)
V = 20/27 cubic cm.
Answer:
c
Step-by-step explanation:
If y is 4.5 when x is 3, and y varies directly with x, find y when x is 9. 1.5 7.5 10.5 13.5
ANSWER
13.5
EXPLANATION
It was given that, y varies directly as x.
Therefore, the variation equation is of the form:
[tex]y = kx[/tex]
If y is 4.5 when x is 3, then we can substitute to find the constant of variation.
[tex]4.5 = 3k[/tex]
Divide both sides by 3;
[tex]k = \frac{4.5}{3} [/tex]
[tex]k = \frac{3}{2} [/tex]
Hence the equation becomes:
[tex]y = \frac{3}{2} x[/tex]
When x=9,
[tex]y = \frac{3}{2} \times 9 = 13.5[/tex]
Please hurry!!
The children's section is rectangular and has three of its corners at (-10, 10), (-10, 4), and (-3, 10). What are the coordinates of the remaining corner?
(-3,4)
If its rectangular then parallel lines must be the same size , just draw it and it will make a lot of sense
Answer is (-3,4)
See photo