Answer:
[tex] {(4x + 3y)}^{2} \\ = {(4x)}^{2} + 2 \times 4x + 3y + {(3y)}^{2} \\ 16 {x}^{2} + 24xy + 9 {y}^{2} \\ thank \: you[/tex]
How would you simplify and rationalize this expression? [tex]\frac{5\sqrt[4]{2}}{4\sqrt[4]{162} }[/tex]
Answer:
5/12
Step-by-step explanation:
(5 * 2^1/4)/4 * 162^1/4) = (5 * 2^1/4)/4 * 3 *2^1/4)
multiply top and bottom by 2^3/4
(5 * 2)/4 * 3 * 2) = 10/24 = 5/12
if x = -5
x2 + 3
x - 2
Answer:
Step-by-step explanation:
Evaluate this |-2+3|
[tex]\displaystyle \Large \boldsymbol{} |-2+3| =|1|=1[/tex]
The perimeter of a rectangular field is 368 yards. If the length of the field is 98 yards, what is its width?
Answer:
86 = w
Step-by-step explanation:
The perimeter of a triangle is
P = 2(l+w)
368 = 2(98+w)
Divide each side by 2
368/2 = 2/2(98+w)
184 = 98+w
Subtract 98 from each side
184-98 = 98+w-98
86 = w
Find the length of the leg of a right triangle with leg length b= 21.5 inches and the hypotenuse c= 31.9 inches. Use a calculator to estimate the square root to one decimal place.
Answer:
23.6 (approximate value)
Step-by-step explanation:
a*a+b*b=c*c Pythagorean thereom(21.5)^2 + b*b = (31.9)^2b*b= 1017.61 - 462.25√b*b= √555.36b=23.6(approximate value)Answer:
Step-by-step explanation:
23.6
Can someone help??????????
Answer:
(C) 1 and 3
Step-by-step explanation:
Corresponding angles are angles that are at the same corner at the different intersections.
We can see that 1 is on the bottom right corner of the bottom line, now we need to see what angle is at the bottom right corner of the top line?
That's 3.
So 1 and 3 are congruent because they are corresponding.
Hope this helped!
On a map’s coordinate grid, Panthersville is located at (−3, 2), and Heel City is located at (4, 8). Falconton is the midpoint between Panthersville and Heel City. What is the approximate distance from Panthersville to Falconton? (Each unit on the grid represents 1 mile.) A. 3.25 miles B. 4.61 miles C. 5.00 miles D. 9.22 miles
Answer:
B. 4.61 miles
Step-by-step explanation:
midpoint is (-3+4)/2, (2+8)/2 = (1/2, 5)
distance = √(-3-1/2)² + (2 - 5)² = 4.609772299
Susan's haircut was $18 if she gave a 20% tip what will her total cost be
Answer:
21.60
Step-by-step explanation:
First find the tip
18 * 20%
18 *.2
3.60
Then add it to the cost of the haircut
18 + 3.60
21.60
10 cows, 26 horses and 4 goats are in a paddock. What is the percentage of animals that are horses?
Answer:
10+26+4=40
in total there is 40 animals
because there is in total for 40 animals then that mean 40 animals is 100%
now we see that there are 26 horses we only need to divid ( but remember you have to divid the percent and the number of animals together)
40 ÷ 20 = 2. 2 x 13 = 26
100% ÷ 20 = 5%. 5% x 13 = 65%
the answer for this question:
the percentage of animals that are horses is 65%
A hypothesis test is to be performed to test the equality of two population means. The sample sizes are large and the samples are independent. A 95% confidence interval for the difference between the population means is (1.4, 8.7). If the hypothesis test is based on the same samples, which of the following do you know for sure:
A: The hypothesis µ1 = µ2 would be rejected at the 5% level of significance.
B: The hypothesis µ1 = µ2 would be rejected at the 10% level of significance.
C: The hypothesis µ1 = µ2 would be rejected at the 1% level of significance.
A) A and B
B) A and C
C) A only
D) A, B, and C
Answer:
C) A only
Step-by-step explanation:
In statistics, the null hypothesis is the default hypothesis and the alternative hypothesis is the research hypothesis. The alternative hypothesis usually comes in place to challenge the null hypothesis in order to determine if the test is statistically significant or not.
Similarly,
In hypothesis testing, the confidence interval consist of all reasonable value of the population mean. Values for which the null hypothesis will be rejected [tex]H_o[/tex] .
Given that:
At 95% confidence interval for the difference between the population means is (1.4, 8.7).
The level of significance = 1 - 0.95 = 0.05 = 5%
So , If the hypothesis test is based on the same samples, The hypothesis µ1 = µ2 would be rejected at the 5% level of significance.
Use inductive reasoning to predict the most probable next number in each list.
9, 13, 21, 33, 49, 69, ?
Answer:
93
Step-by-step explanation:
First differences increase by 4 each time. The given numbers are a quadratic sequence that can be described by 2n² -2n +9. The 7th term would be 93.
_____
First differences are ...
13-9 = 4, 21-13 = 8, 33-21 = 12, 49-33 = 16, 69-49 = 20
Second differences are ...
8-4 = 4, 12-8 = 4, 16-12 = 4, 20-16 = 4
When second differences are constant, the sequence can be represented by a second-degree polynomial function. The leading coefficient is half the value of the second differences.
on the same graph draw line 2y-x=10 and y=3x
Answer:
Step-by-step explanation:
Help Please. I will Give Brainliest.
Answer:
1/2
Step-by-step explanation:
● 1/4 + 4(1/2 - 3/4 )^2
To make it easier convert the fractions to decimal numbers.
● 1/4 = 0.25
● 1/2 = 0.5
● 3/4 = 0.75
So the expression will be:
● 0.25 + 4(0.5 - 0.75)^2
Calculte first 0.5-0.75 (0.5-0.75= -0.25)
● 0.25 + 4 × (-0.25)^2
-0.25^2 is the same as 0.25^2
● 0.25 + 4 × (0.25)^2
0.25^2 is 0.0625
● 0.25 + 4×0.0625
Multiplication has the priority (4 ×0.0625) wich is 0.25
● 0.25 + 0.25
● 0.5
0.5 is 1/2
So the answer 1/2
Answer:
[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
[tex]\frac{1}{4}+4(\frac{1}{2}-\frac{3}{4})^2\\\frac{1}{4}+4(\frac{2-3}{4})^2\\\frac{1}{4}+4(\frac{-1}{4})^2\\\frac{1}{4}+4(\frac{1}{16})\\\frac{1}{4}+\frac{1}{4}=\frac{2}{4}=\frac{1}{2}[/tex]
I'm not sure about this one please I need someone to help me.
Answer:
The corresponding graph is Graph A.
Step-by-step explanation:
Part 1: Rewriting the inequality and solving for d
To start, the inequality will need simplified.
[tex]9-4d\geq -3\\\\-4d\geq -12\\\\\frac{-4d}{-4} \geq \frac{-12}{-4} \\\\d \leq 3[/tex]
Because simplifying the inequality involved dividing by a negative number, the sign must be flipped.
Part 2: Determining the graph for the inequality
Now, refer to the rules for graphing inequalities.
If the sign is simply < or >, the graph will start at the number that it begins at and the circle will be open.If the sign is ≤ or ≥, the graph will start at the number that it begins at and the circle will be closed.Therefore, because [tex]d \leq 3[/tex], the graph will start at 3 as a closed dot. Then, it will go left because values must be equal to 3 or less than 3.
Therefore, the graph that represents this is Graph A.
Answer:
Graph A
I hope this helps!
Complete the square to evaluate the definite integral
∫dx/x^2-2x+5
Bounds:1-3
[tex]\displaystyle \int_1^3 \frac{\mathrm dx}{x^2-2x+5}[/tex]
Follow the instruction and complete the square in the denominator:
x ² - 2x + 5 = (x ² - 2x + 1) + 4 = (x - 1)² + 4
Then the integral is
[tex]\displaystyle \int_{x=1}^{x=3} \frac{\mathrm dx}{(x-1)^2+4}[/tex]
Substitute y = x - 1 and dy = dx :
[tex]\displaystyle \int_{y+1=1}^{y+1=3} \frac{\mathrm dy}{y^2+4} = \int_{y=0}^{y=2}\frac{\mathrm dy}{y^2+4}[/tex]
Substitute y = 2 tan(z) and dy = 2 sec²(z) dz :
[tex]\displaystyle \int_{2\tan(z)=0}^{2\tan(z)=2}\frac{2\sec^2(z)}{(2\tan(z))^2+4}\,\mathrm dz = \frac12 \int_{z=0}^{z=\pi/4} \frac{\sec^2(z)}{\tan^2(z)+1}\,\mathrm dz \\\\ = \frac12 \int_{z=0}^{z=\pi/4} \frac{\sec^2(z)}{\sec^2(z)}\,\mathrm dz \\\\ = \frac12 \int_{z=0}^{z=\pi/4} \mathrm dz = \frac12 z\bigg|_{z=0}^{z=\pi/4} = \frac12 \left(\frac\pi4-0\right) = \boxed{\frac\pi8}[/tex]
y - 4= -2(x + 3)
Complete the missing value in
the solution to the equation.
(-3, _ )
Answer:
4
Step-by-step explanation:
i distributed the -2 to what's in the parentheses. that equal 0. I then moved the 4 to the zero so that it becomes positive. I just assumed that you were ask for Y
Step-by-step explanation:
y-4=-2(x+3)....eq(1)
y- 4= -2x-6
y=-2x-2...eq(2)
subtituting equation 2 in equation 1
(-2x-2)-4=-2x-6
-2x-6=-2x-6
=0
Frances has 4 square baking dishes. Each pan is 7 inches × 7 inches × 2 inches. Which expression will give her the total volume of all the pans? A. 7^2 × 2 B. 7 × 2^4 C. (7 × 2 × 2) × 4 D. (7^2 × 2) × 4
Answer:
D. (7^2 X2) x 4
The equation inside the parenthesis finds the volume of one pan and then that is multiplied by 4 which is the total number of pans. This will find the volume of all 4 pans.
Answer: (7^2 × 2) × 4
Step-by-step explanation:
In politics, marketing, etc. we often want to estimate a percentage or proportion p. One calculation in statistical polling is the margin of error - the largest (reasonble) error that the poll could have. For example, a poll result of 72% with a margin of error of 4% indicates that p is most likely to be between 68% and 76% (72% minus 4% to 72% plus 4%). In a (made-up) poll, the proportion of people who like dark chocolate more than milk chocolate was 35% with a margin of error of 2.5%. Describe the conclusion about p using an absolute value inequality.
Answer:
The conclusion about p using an absolute value inequality is
[tex]0.325 < p < 0.375[/tex]
Step-by-step explanation:
From the question we are told that
The sample proportion is [tex]\r p = 0.35[/tex]
The margin of error is [tex]E = 0.025[/tex]
The confidence interval is mathematically represented as
[tex]\r p -E < p < \r p +E[/tex]
=> [tex]0.35 - 0.025 < p < 0.35 + 0.025[/tex]
=> [tex]0.325 < p < 0.375[/tex]
Which table represents the same linear relationship as the equation y=2x•6? (answers are in the image) Please include ALL work!
Answer:
Table in option C represents the linear relationship as the equation, [tex] y = 2x + 6 [/tex]
Step-by-step explanation:
The equation given seems to be wrong. The equation should be [tex] y = 2x + 6 [/tex], because, taking a look at the tables given, the table in option C is the only table that has values that conforms to the equation, [tex] y = 2x + 6 [/tex].
In table C, when x = 2 using the equation, [tex] y = 2x + 6 [/tex], thus,
[tex] y = 2(2) + 6 = 4 + 6 = 10 [/tex].
When x = 3,
[tex] y = 2(3) + 6 = 6 + 6 = 12. [/tex]
Theredore, the equation, [tex] y = 2x + 6 [/tex], represents the relationship between the X and y variables in the table in option C.
Is speed the rate of change in the velocity of a moving body?
I need help with the questions that are blank
9514 1404 393
Answer:
TRIANGLES
Possible
4) Yes
Unique
1) No
2) No
3) Yes
3D SHAPES
Step 2: triangle area 8.75 ft²; total area 52.5 ft²
Step 3: TOTAL AREA = 52.5 ft² + 31.5 ft² = 84 ft²
Step-by-step explanation:
TRIANGLESPossible Triangles
The requirement on side lengths is that the sum of the short two exceed the longest.
4) 5 + 6 = 11 > 7 . . . . Yes, can form a triangle
__
Unique Triangles
The available congruence theorems are a good starting point for determining if a triangle is unique. If you have side and angle definitions that correspond to AAS, ASA, SAS, SSS, or HL, then the triangle is uniquely determined.
You will notice that SSA is not on this list. However, there are special cases where SSA can be used. If the given angle is opposite the longest given side, then the triangle is uniquely determined. (You will notice that this is the case in an HL triangle, where the given H side is opposite the right angle.)
1) SSA; angle is opposite the short side — triangle is not unique
2) AAA; no side is given — triangle is not unique
3) SAS; — triangle is unique
__
3D SHAPESStep 2: The area is 1/2bh = 1/2(3.5 ft)(5 ft) = 8.75 ft². The area of all triangles together is 6×8.75 ft² = 52.5 ft².
Step 3: TOTAL AREA = 52.5 ft² + 31.5 ft² = 84 ft².
Marco purchased a large box of comic books for $300. He gave 15 of the comic books to his brother and then sold the rest on an internet website for $330 making a profit , making a profit of $1.50 on each one.how many comic books were in the box? what was the original price of each comic book (assuming they all cost the same amount)?
Answer: There are 75 books.
Price of each book = $4.
Step-by-step explanation:
Let x = Number of books in the box.
Then as per given,
Cost of x books = $300
Cost of one book = [tex]\$(\dfrac{300}x)[/tex]
Books left after giving 15 of them = x-15
Selling price of (x-15) books= $330
Selling price of one book = [tex]\$(\dfrac{330}{x-15})[/tex]
Profit on each book= $1.50
Profit = selling price - cost price
[tex]\Rightarrow 1.50=\dfrac{330}{x-15}-\dfrac{300}{x}\\\\\Rightarrow\ 1.50=\dfrac{330(x)-300(x-15)}{x(x-15)}\\\\\Rightarrow\ 1.50=\dfrac{330x-300x+4500}{x^2-15x}\\\\\Rightarrow\ 1.50(x^2-15x)=30x+4500\\\\\Rightarrow\ 1.50x^2-22.5x=30x+4500\\\\\Rightarrow\ 1.50x^2-52.5x-4500=0\\\\\Rightarrow\ 1.50x^2-52.5x-4500=0\\\\\Rightarrow\ x^2-25x-3000=0\ \ [\text{divide by 1.5}][/tex]
[tex]\Rightarrow (x+40)(x-75)=0\\\\\Rightarrow\ x=-40,75[/tex]
Number of books cannot be negative.
So, there are 75 books.
Price of each book = [tex]\dfrac{300}{75}=\$4[/tex]
So price of each book = $4.
Payton took a friend for a birthday dinner. The total bill for dinner was $44.85 (including tax and a tip). If Payton paid a 19.5% tip, what was his bill before adding the tip?
(Round your answer to the nearest cent.)
$
Number
Answer:
The answer closest to 36.10425. So 36.10 or 36.1
Step-by-step explanation:
x = 44.85 ( 1 - 0.195) = 36.10425
If this helps, it would be nice if 5 stars are given, and a brainliest :)
The amount of the bill before adding the amount of tip is evaluated being of $37.53 approx.
How to find the percentage from the total value?Suppose the value of which a thing is expressed in percentage is "a'
Suppose the percent that considered thing is of "a" is b%
Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).
Thus, that thing in number is
[tex]\dfrac{a}{100} \times b[/tex]
For this case, we can assume the amount of bill without tip being A.
Then, as given, Payton gave 19.5% tip (tip is given assumingly on A), then:
Total price of the bill = Bill amount before tip + Tip
44.85 = A + (19.5 % of A)
(we don't write symbols like of currency generally in equations, and understand it from context(which is dollars here))
44.85 = A + (19.5 % of A)
or
[tex]44.85 = A + \dfrac{A}{100} \times 19.5\\\\\text{Multiplying 100 on both the sides}\\\\4485 = 100A + 19.5A\\4485 = 119.5A\\\\\text{Dividing both the sides by 119.5}\\\\\dfrac{4485}{119.5} = A\\\\37.53 \approx A\\\\A \approx 37.53 \: \rm \text{(in dollars)}[/tex]
Thus, the amount of the bill before adding the amount of tip is evaluated being of $37.53 approx.
Learn more about percent here:
https://brainly.com/question/11549320
I need help on this question
Answer:
Figure G.
Step-by-step explanation:
Let's check through the values and calculate the radius and area for all the circle.
For circle R
Diameter = 2 feet
Radius= 1 feet
Area= πr²
Area= 3.14*1
Area= 3.14 feet²
CircleS
Diameter= 4 feet
Radius= 2 feet
Area= πr²
Area= 3.14*2²
Area= 12.56 feet²
Circle T
Diameter= 8 feet
Radius= 4 feet
Area = π r²
area= 3.14*4²
Area=50.24 feet²
Circle U
Diameter= 12 feet
Radius= 6 feet
Area = π r²
area= 3.14*6²
Area=113.04 feet²
The values of the radius and Area all match the graph in figure G
What is the length of the line?
A triangle has sides with lengths of 5x - 7, 3x -4 and 2x - 6. What is the perimeter of the triangle?
Answer:
Step-by-step explanation:
perimeter of triangle=sum of lengths of sides=5x-7+3x-4+2x-6=10x-17
Answer:
10x - 17
Step-by-step explanation:
To find the perimeter of a triangle, add up all three sides
( 5x-7) + ( 3x-4) + ( 2x-6)
Combine like terms
10x - 17
if a gallon of milk costs $2.49 how much will 3 1/2 gallons cost
average of 2721 2557 2999 2278 4339
Answer:
Step-by-step explanation:
So we know that the average of numbers is all of the numbers added up and divided by the total amount of numbers.
2721
+ 2557
-------------------
5278
.... AND SO ON.........
=14,894 is all of the number added together!!!
Then we count up the numbers= 5
14,894/5
=2978.8
I hope this helps!!!
please help me!
find x
Answer:
√13 miles
Step-by-step explanation:
Using Pythagorean Theorem,
h^2=p^2+b^2
Here,
h=x
p=2miles( taking the angle opposite to 2miles as reference)
b=3miles
Now,
x^2=2^2+3^2
x=√(4+9)
x=√13 miles
Following are the outcomes that are possible when a couple has three children. Refer to that list, and find the probability of each event.
1st 2nd 3rd
Boy Boy Boy
Boy Boy Girl
Boy Girl Boy
Boy Girl Girl
Girl Boy Boy
Girl Boy Girl
Girl Girl Boy
Girl Girl Girl
a. Among three children, there are exactly 2 boys.
b. Among three children, there are exactly o girls.
c. Among three children, there is exactly 1 girl.
1. What is the probability of exactly 2 boys out of three children?
2. What is the probability of exactly 0 girls out of three children?
3. What is the probability of exactly 1 girl out of three children?
Answer:
a.0.375
b.0.125
c.0.375
1.0.375
2.0.125
3.0.375
Step-by-step explanation:
a.
The total events in a sample space are n(S)=8
The events that contains exactly two boys
Boy Boy Girl,Boy Girl Boy,Girl Boy Boy.
Let A be the event that there are exactly two boys. Thus, n(A)=3.
So, probability of exactly 2 boys is P(A)=n(A)/n(S)=3/8=0.375.
b.
The event that contains exactly 0 girls.
Boy Boy Boy
Let B be the event that contains exactly 0 girls. Thus, n(B)=1.
So, probability of exactly 0 girls is
P(B)=n(B)/n(S)=1/8=0.125.
c.
The events that contains exactly 1 girl.
Boy Boy Girl,Boy Girl Boy,Girl Boy Boy
Let C be the event that contains exactly 1 girl. Thus, n(C)=3.
So, probability of exactly 1 girl is
P(C)=n(C)/n(S)=3/8=0.375.
Q1 is same as part a.
Q2 is same as part b.
Q3. is same as part c