The simplified expression is √10 - √14 + √15 - √21.
To simplify the expression (√2 + √3)(√5 - √7), we can use the distributive property of multiplication.
Expanding the expression, we get:
(√2 + √3)(√5 - √7) = √2 x √5 + √2 x (-√7) + √3 x √5 + √3 x (-√7)
Now, simplifying each term with FOIL method we have:
√2 * √5 = √(2 x 5) = √10
√2 * (-√7) = -√(2 x 7) = -√14
√3 * √5 = √(3 x 5) = √15
√3 * (-√7) = -√(3 x 7) = -√21
Combining the simplified terms, we get:
√10 - √14 + √15 - √21
Therefore, the simplified expression is √10 - √14 + √15 - √21.
In this process, we applied the distributive property to expand the expression and then simplified each term by multiplying the square roots together. Finally, we combined the like terms to obtain the simplified expression.
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Answer:
√10 + √15 - √14 - √21
Step-by-step explanation:
(√2 + √3)(√5 - √7)
= √2(√5 - √7) + √3(√5 - √7)
= √10 - √14 + √15 - √21
= √10 + √15 - √14 - √21
Please help me it's homework.
You are preparing to tile the floor of a rectangular room that is 15.5 feet by 18 feet in size. The tiles you plan to use are squares, measure 12 inches on each side, and are sold in boxes that contain enough tiles to cover 25 square feet. Each box costs $30.
To determine the cost of materials you multiply 15.5 by 18, divide by 25, round up to the next whole number, and multiply by 30. Is this correct?
A) Yes.
B) No, you need to round down and then multiply by 30.
C) No, you need to round down and then multiply by 144.
D) No, you need to divide by 144, round up, and then multiply by 30.
E) No, you need to divide by 144, round down, and then multiply by 30.
To find the cost of tiling the room, you have to calculate the area in square feet, convert tile size to the same units, calculate how many boxes needed and round up, then multiply by the cost per box. The correct answer is D).
Explanation:The correct answer is D). The process to determine the cost of the tiles needed to cover the room starts with calculating the area of the room in square feet. This is done by multiplying the room's length and width, so 15.5 feet * 18 feet which equals 279 square feet.
The tiles are 12 inches in size on each side, but the dimensions of the room are in feet. Therefore, we need to convert the tile size to square feet. Since 1 foot = 12 inches, 1 square foot = 144 square inches. Our tile is 12 inches * 12 inches = 144 square inches, which equals 1 square foot.
However, the tiles are sold in boxes that cover 25 square feet. So, we will divide the total room area by the area covered by one box of tiles. 279 square feet / 25 = 11.16 boxes needed, approximately.
It's important to round up at this stage, as you can't buy a fraction of a box. So, you'd need 12 boxes.
The last step is to calculate the total cost, which is done by multiplying the number of boxes by the cost of each box. So, 12 * $30 equals $360.
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.can you please help me thank you you will be given brainley
Given that ∆MTW ≅ ∆CAD, which angles are corresponding parts of the congruent triangles?
∠M ≅ ∠A
∠M ≅ ∠D
∠M ≅ ∠C
Answer:
It is M = C
Step-by-step explanation:
The measure of the angle ∠WMT is congruent to the measure of the angle ∠DCA. Then the correct option is C.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
The ratio of the matching sides will remain constant if two triangles are comparable to one another.
The triangle ∆MTW is congruent to the triangle ∆CAD. Then we have
∠MTW ≅ ∠CAD
∠TWM ≅ ∠ADC
∠WMT ≅ ∠DCA
The proportion of the point ∠WMT is harmonious with the proportion of the point ∠DCA. Then, at that point, the right choice is C.
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Ava bought a rectangular rug for her hallway. The rug is 2\3 yards wide and 2 3\4 yards long. What is the area of the rug as a mixed number in simplest form?
Answer:
1 5/6
Step-by-step explanation:
Find the exact value of sin ( 2
a. if cos a = 3 /5 . assume a is a quadrant i angle in standard position.
What is value of x?
https://static.k12.com/nextgen_media/assets/8093716-NG_GMT_SemB_08_UT_12.png
The calculated measure of the angle x is 76 degrees
How to determine the measure of the angle xFrom the question, we have the following parameters that can be used in our computation:
The figure
Also, we have
Angle with a measure of 76 degrees
By the theorem of corresponding angles, we have
x = 76
Hence, the measure of the angle x is 76 degrees
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Can someone please help me with 4?? I’m really struggling.
what do all similar circles have in common
a) congruent circumference value
b) congruent diameters
c) π
All the similar circles have π in common.
Thus, option (c) is correct.
When two circles are similar, it means they have the same shape but possibly different sizes.
However, the ratio of their corresponding lengths, including the circumference, remains constant.
Second, the ratio of the diameter will be constant but not congruent.
Third, the value of π is the universal constant whose value is 22/7 or 3.14.....
which is the same for every similar circle.
Thus, π has a common value.
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A 10-foot ladder is leaning against a tree. The bottom of the ladder is 4 feet away from the bottom of the tree. Approximately how high up the tree does the top of the ladder reach?
A.2.4
B.6.0
C. 9.2
D. 10.8
Why would someone choose to use a graphing calculator to solve a system of linear equations instead of graphing by hand? Explain your reasoning.
Sample Response: A graphing calculator is more accurate than graphing by hand. If the slope and/or y-intercept is a fraction or decimal, it is more difficult to accurately graph by hand. Using a calculator might also be more time efficient because it might accept a line in any form. A calculator’s window can be adjusted quickly instead of having to redraw a graph by hand when adjusting the scale.
Mr Savage used 3 gallons of paint to cover 1,350 square feet of wall space. At this rate, how much paint will be needed to cover 1,800 square feet
Which equivalent expression would you set up to verify the associative property of addition for (3x + 4) + ((5x2 – 1) + (2x + 6))
(3x + 4) + (5x2 – 1)
(5x2 – 1) + ((3x + 4) + (2x + 6))
((3x + 4) + (5x2 – 1)) + (2x + 6)
(3x + 4) + (5x2 – 1) + (2x + 6)
It's C.
Trust me, I had trouble figuring out this answer...
The image of a figure is shown. What are the coordinates of X in the pre-image of the figure if the rule that created the image was T–5.2, 1.4(x, y)? PLEASE ANSWER
X =
a. (-7.2, 3.4)
b. (1.2, 6.6)
c. (3.2, 0.6)
b. (9.2,-0.4)
Question 11 options: you take a ride on a ferris wheel which has a diameter of 300 feet. if you ride for four revolutions, what linear distance did you travel? use 3.14 for pi when completing your calculations. round your answer to the nearest whole number, if necessary. the distance traveled is
Select the correct factor from the presentation and calculate how many calories used. (Round to the hundredths.) A person weighing 165 lbs. jogs 1 mile in 8 minutes. How many calories used?
A. 102.30
B. 107.25
C. 253.85
D. 266.13
Answer:
the answer is 107.25
Step-by-step explanation:
Answer:
B. 107.25
Step-by-step explanation:
Let x be the calories burnt by the man,
Since, when a person runs 1 miles in 8 minutes,
Then,
[tex]\frac{\text{Calories used by him}}{\text{His weight in lb}}=65\%[/tex],
Given,
Weight of the person = 165 lb,
Thus,
[tex]\frac{x}{165}=\frac{65}{100}[/tex],
[tex]x = \frac{165\times 65}{100}[/tex]
[tex]x=\frac{10725}{100}[/tex]
[tex]\implies x=107.25[/tex]
Hence, 107.25 calories will be used.
Which linear function has the greatest y-intercept?
A) x + 6y = 36
B) y = 15x + 5
C) 3x + 8y = 24
D) y = 4x + 7
Answer:
the answer is y=4x+7
Step-by-step explanation:
X divides into the line PQ in the ratio 2:3 P is (2,1) and Q is (12.5,7.5) work out the coordinates of point X
Answer: (6.2, 3.6)
Step-by-step explanation:
We know that if a point M (x,y) divide a line segment having endpoints [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] in ratio m:n , then the coordiantes of M is given by :-
[tex]x=\dfrac{mx_2+nx_1}{m+n}\ ;\ y=\dfrac{my_2+ny_1}{m+n}[/tex]
Given : X divides into the line PQ in the ratio 2:3 P is (2,1) and Q is (12.5,7.5).
Then, coordinate of X is given by :-
[tex]x=\dfrac{2(12.5)+3(2)}{2+3}\ ;\ y=\dfrac{2(7.5)+3(1)}{2+3}\\\\\Rightarrow\ x=\dfrac{31}{5}\ ;\ y=\dfrac{18}{5}\\\\\Rightarrow\ x=6.2\ ;\ y=3.6[/tex]
Hence, the coordinate of X = (6.2, 3.6)
A employer, who started a new business, has promised his employees a minimum starting wage of $3, with an increase of $2 every 4 years. Sketch a graph of wage as a function of time for 16 years. Assume the wages take effect at the beginning of the year where the change is made. (HINT: use a step function to represent the function.)
To sketch the graph, use a step function to represent the wage as a function of time over 16 years. The minimum starting wage is $3, and it increases by $2 every 4 years.
Explanation:
To sketch a graph of wage as a function of time for 16 years, we can use a step function to represent the function.
The minimum starting wage is $3 and it increases by $2 every 4 years. For the first 4 years, the wage will be $3. At the start of the 5th year, the wage will increase to $5. This pattern continues, with the wage increasing by $2 every 4 years.So, the graph will have flat lines representing each 4-year interval, with a step up at the start of each interval.
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Find all real values of $v$ that satisfy the equation $(v+6)^2 = 324$. If you find more than one, then list your values in increasing order, separated by commas.
Answer:
The values of v in increasing order are, -24, 12
Step-by-step explanation:
Given equation is,
[tex](v+6)^2=324[/tex]
[tex]v+6=\pm 18[/tex]
[tex]v=-6\pm 18[/tex]
[tex]\implies v=-6-18\text{ or }v=-6+18[/tex]
[tex]\implies v = -24\text{ or }v=12[/tex]
Since, -24 < 12
Thus, the values of v in increasing order are,
-24, 12
What is the denominator of the fraction 1/9?
HELP! ASAP!
What is the measure of ∠A?
What is the measure of ∠B?
Answer:
What is the measure of ∠A?
72°
What is the measure of ∠B?
108°
Step-by-step explanation:
I literally copied and pasted from edge
How could the relationship of the data be classified? (1 point)
scatter plot with points loosely scattered going down to the right
Match the corresponding function formula with each function when h(x) = 3x + 2 and g(x) = 2 x .
1. k(x) = 2x + 3x + 2 k(x) = g(x) ∘ h(x)
2. k(x) = 2x - 3x - 2 k(x) = g(x) + h(x)
3. k(x) = (3x)2-x + 2-x + 1 k(x) = h(x) ÷ g(x)
4. k(x) = 23x + 2 k(x) = g(x) - h(x)
5. k(x) = 2x(3x + 2) k(x) = g(x) × h(x)
6. k(x) = 3(2x) + 2 k(x) = h(x) ∘ g(x)
To simplify the other user's answer (which is correct):
1 = B
2 = D
3 = C
4 = A
5 = E
6 = F
Alternatively, your right boxes should look like:
4
1
3
2
5
6
Solve the following system of equations using matrices.
4x – 2y = -6
3x – 6y = -18
(40, 90)
(3, 0)
(0, 3)
(-6, 18)
Debra is on the swim team. Each week she swims a total of 7000 meters. How many kilometers does she swim each week?
How do you solve this inequality: 7 ≤ x+11
Number of security staff = a over 100 if a audience, is 10500, how many security staff are needed for the event
Find the smallest value of k if 264k is a perfect square
Which graph shows the equation y = x + 2?