Final answer:
In an isosceles triangle with a perimeter of 22 cm and one side of 6 cm, the other two sides must be equal in length and must be 8 cm each to satisfy the perimeter condition.
Explanation:
The question asks for the possible lengths of the other two sides of an isosceles triangle with a perimeter of 22 cm, where one side is already known to be 6 cm. In an isosceles triangle, the two other sides must be of equal length because an isosceles triangle has two sides that are the same.
Let's denote the length of these two equal sides as 'x'. The perimeter of a triangle is the sum of the lengths of all three sides:
6 cm + x + x = 22 cm
2x + 6 cm = 22 cm
2x = 22 cm - 6 cm
2x = 16 cm
x = 8 cm
Therefore, the other two sides of the triangle must each be 8 cm long.
It's important to note that all three sides of a triangle must satisfy the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In this case, the other two sides cannot both be less than 6 cm, otherwise, they will not form a triangle with the third side of 6 cm. The solution provided meets this requirement.
The equation of a circle is (x + 3)2 + (y – 5)2 = 81. Determine the coordinates of the center of the circle and the length of the radius.
Answer:
The center of the circle is (-3 , 5) and the length of the radius is 9 units
Step-by-step explanation:
* Lets revise the standard form of the equation of the circle
- The center-radius form of the circle equation is in the format
(x – h)² + (y – k)² = r², where the center is the point (h, k) and
the radius is r.
- This form of the equation is helpful, because you can easily find
the center and the radius.
* Now lets solve the problem
- The equation is (x + 3)² + (y - 5)² = 81
- By comparing the two equations
∵ (x – h)² + (y – k)² = r² and (x + 3)² + (y - 5)² = 81
# x - h = x + 3
∴ -h = 3 ⇒ divide both sides by -1
∴ h = -3
# y - k = y - 5
∴ k = 5
# h and k are the coordinates of the center of the circle
∴ The center of the circle is (-3 , 5)
# r² = 81 ⇒ take √ for both sides
∴ r = 9
∴ The length of the radius = 9 units
* The center of the circle is (-3 , 5) and the length of the radius is 9 units
The center of the circle is at (-3, 5), and the radius of the circle is 9, determined by the given equation (x + 3)^2 + (y – 5)^2 = 81.
Explanation:The student is asking about the equation of a circle and how to determine the coordinates of the center and the length of the radius. The given equation is (x + 3)2 + (y – 5)2 = 81. The general form of a circle's equation is (x - h)2 + (y - k)2 = r2, where (h, k) is the center and r is the radius.
To find the center of the circle, we look at the values h and k in the equation, which are the opposites of the constants added to x and y, respectively. Therefore, the center is at (-3, 5). To find the radius of the circle, we take the square root of the number on the right side of the equation. The square root of 81 is 9, so the radius is 9.
Please help. Brainliest to first answer.
I think they are complementary angles but i am not sure
Answer:
They form a linear pair.
Step-by-step explanation:
Because both are not 180 so that marks out the last checkbox and the second. Plus, they both don't add up to 90 so it checks off the first.
Write an equation with integer solutions of:
x = ±6, y = 0
and
x = 0, y = ±12
A)x2 + y2 + 6 = 0
B)4x2 + y2 + 144 = 0
C)x2 + y2 − 6 = 0
D)4x2 + y2 − 1
The correct answer is:
D. 4x2 + y2 − 1
[tex]|Huntrw6|[/tex]
Answer: Option 'D' is correct.
Step-by-step explanation:
Since we have given that
x = ±6, y = 0
and x = 0 and y = ±12
And we need an equation which has above as an integer solutions.
So, it becomes,
Consider [tex]4x^2+y^2-144=0[/tex]
Put x = 0, we get
[tex]0+y^2=144\\\\y^2=144\\\\y=\sqrt{144}\\\\y=\pm 12[/tex]
Similarly,
Put y = 0,
[tex]4x^2+0=144\\\\4x^2=144\\\\x^2=\dfrac{144}{4}\\\\x^2=36\\\\\x=\pm 6[/tex]
Hence, Option 'D' is correct.
Emma is 9 and one fourths Year’s old. How many months old is Emma?
She is 4 years an d3 months old
Answer:
111 months
Step-by-step explanation:
First, look at how many whole years old Emma is. Emma is 9 whole years old. 1 year consists of 12 months. So, multiply 9 [years] by 12 [months] to get 108. The number 108 is how many months are in 9 years. However, Emma is 9 months and 1/4 years old.
To find out how many months 1/4 of a year is, multiply 1/4 [year] by 12 [months] . 12 is the same as 12/1, so multiply the numerators and denominators of 1/4 and 12/1
1 x 12 = 12
4 x 1 = 4
12/4 = 3
Therefore, 1/4 year is 3 months. Now, add 108 months and 3 months to get 111 months. Therefore, Emma is 111 months old.
I hope this helps! :)
I don't know how to do this practice problem :/
Could someone explain? I was told in class that the answer is yes but don't quite understand why
First of all, we know that Emily travels 3/4 of a mile in 4 minutes and 30 seconds (i.e. 9/2 of a minute). So, her current velocity is
[tex]v = \dfrac{\frac{3}{4}}{\frac{9}{2}} =\dfrac{3}{4}\cdot\dfrac{2}{9} = \dfrac{1}{6}[/tex] of a mile per minute.
At this speed, it takes
[tex]t = \dfrac{s}{v} = \dfrac{3.42}{\frac{1}{6}} = 3.42\cdot 6 = 20.52[/tex]
minutes to travel 3.42 miles.
Since she left at 8.25, she will arrive at about 8.46, so she's on time for school.
Pablo's is running a special for Cinco de Mayo (fifth of May). All entree's are $5.55. You and your family, a total of six people, eat. The tax is 7%. It was extremely busy that night and the service wasn't good. Mom leaves a 12% tip. How much money did she spend in all? *
Please HELP!
Answer:
$39.91
Step-by-step explanation:
6*5.55=33.30
33.30*1.07=35.63
35.63*1.12=39.91
Don't know how to delete the incorrect answer that my sister put but I can edit it, so this is what I'm editing it to.
Find the missing term. The roots of x2 − ( ) + 34 are 5 ± 3i.
Answer:
the required equation is:
[tex]x^2 -10 +34[/tex]
Step-by-step explanation:
The equation given is:
[tex]x^2 -()+34[/tex]
Comparing it with standard quadratic equation
[tex]a^2 +bx+c[/tex]
a= 1,
b=?
C= 34
We can find the value of b using Vieta's formulas :
That states that if roots x₁ and x₂ are given then,
x₁ + x₂ = -b/a
We are given roots: 5 ± 3i i.e, x₁= 5 + 3i and x₂= 5 - 3i
solving
5 + 3i + 5 - 3i = -b/1
10 = -b
Since the given equation already gives b as -b so, -b= 10 => b=10
Putting value of b in the missing place the required equation will be:
[tex]x^2 -10 +34[/tex]
To find the missing term in a quadratic equation given complex roots, use the properties of conjugate roots to determine the term.
Since the roots are in the form of a complex number, they are conjugates of each other, which helps in finding the missing term.
Given roots: 5 ± 3i
Using the sum and product of roots formula
Sum: (5 + 3i) + (5 - 3i) = 10. Product: (5 + 3i)*(5 - 3i) = 34
Construct the equation: x2 - (10x) + 34 = 0
Find the value of the expression given below. 2/3-1/7
Answer:
the answer is 11/21 or 0.523809524
hope this helped
Step-by-step explanation:
Find the arc length of a partial circle
Answer is...
23.55
See attached photo
In 2011, it was estimated that the number of U.S households which had dogs as pets was 4.33 x 10^7 and the average number of dogs per household was 1.6 based on the infomation, approximately how many dogs were household pets in the US in 2011 in Scientific notation
A. 2.71 x 10^7
B. 3.70 x 10^8
C. 5.33 x 10^8
D. 6.93 X 10^7
The right answer is
D. 6.93 X 10^7
the graph shows the amount of money Hachi earns at his job in relation to the number of hours he works.
what is Hachi's pay rent in dollars per hour? record your answer and fill in the bubbles on your answer form. Be sure to use the correct place value.
Answer:
(A) - Hachi does not earn any money if he does not work
Step-by-step explanation:
THE FIRST GUY IS WRONG TRUST ME.If you think about it the graphed point is (0,0), so it is self explanatory that he works 0 hours and OBVIOUSLY he wont earn any money if he doesnt work.
The graph shows the amount of money Hachi earns at his job in relation to the number of hours he works. Hachi does not earn any money if he does not work.
What is a function?A function is defined as a relation between the set of inputs having exactly one output each.
We can see that the graph linearly increases as the hour he worked and the money he earned will increase.
we know that the graphed point is (0,0),
He earned 10 money per hour of work.
so it is self-explanatory that he works 0 hours and obviously, he won't earn any money if he doesn't work.
Thus, Hachi does not earn any money if he does not work.
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Charles owed 390$ to his friend. On the first day Charles paid his friend 12$. Each following week the amount Charles paid his friend increased by the same amount. After 10 payments, Charles had paid back the full amount. By how much did each payment increase?
Simplify 5x/(-3+2x+x^2)
Answer:5x/(x-1)(x+3)
Step-by-step explanation:Factor -3+2x+x^2 by using the AC method hope this helps. Branliest plz
What is the answer?
Answer:
x ≤ - 4
Step-by-step explanation:
Given
3 - x ≥ 2x + 15 ( add x to both sides )
3 ≥ 3x + 15 ( subtract 15 from both sides )
- 12 ≥ 3x ( divide both sides by 3 )
- 4 ≥ x, hence
x ≤ - 4
3 - x is greater than equal to 2 X + 15
3 is greater than equal to 3X + 15
- 12 is greater than equal to 3 x
- 4 is greater than equal to x
hence x b - 4 - 4 is greater than x
All equilateral triangles are ________ triangles.
10pts this on is easy
Answer:
isosceles
Step-by-step explanation:
chester wanted to find the product of 3840 and 5.he was going to use an area model to help find the product.finish chesters incomplete area model below and find the product
Answer:
fghjk²;.
Step-by-step explanation:
Final answer:
To find the product of 3840 and 5 using an area model, we can draw a rectangle with a length of 3840 units and a width of 5 units. Then, we divide the rectangle into smaller squares or rectangles of equal size. The product of 3840 and 5 is 19,200.
Explanation:
To find the product of 3840 and 5 using an area model, we can draw a rectangle with a length of 3840 units and a width of 5 units. Then, we divide the rectangle into smaller squares or rectangles of equal size. For example, we can divide the rectangle into 384 squares of length 10 and width 5, or into 192 squares of length 20 and width 10. After that, we count the total number of squares to find the product. In this case, the product of 3840 and 5 is 19,200.
how do i factor this trinomial?
[tex]\text{Hey there!}[/tex]
[tex]\text{The answer is: (3g + 2)(g + 2)}[/tex]
[tex]\text{To make sure it comes back to the original problem}\bf{(3g^2+8g+4)}[/tex] [tex]\text{You would have to distribute the answer}[/tex]
[tex]\text{3g(g)=}3g^2\\ \text{3g(2)=6g}\\ \text{2(g)=2g}\\ \text{2(2)=4}[/tex]
[tex]\text{After distributing combine your like terms:}[/tex]
[tex]\text{In this particular answer we have: 1 term with TWO LIKE TERMS}[/tex]
[tex]\text{6g+2g=8g(That's how we got the 8g in the original equation)}[/tex]
[tex]\text{The}\bf{\ 3g^2}\text{ stays the same because there's nothing to go with it}[/tex]
[tex]\text{The 4 also stays the same because nothing goes with it as well}[/tex]
[tex]\boxed{\boxed{\text{Answer:(3x + 2 (x + 2)})}}\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
A 50ft. cable is stretched from the top of an antenna to an anchor point on the ground 15 ft. from the base of the antenna. How tall is the antenna? Round the nearest tenth.
Answer:
h = 47.70 ft
The antenna is 47.70 ft tall.
Step-by-step explanation:
The height of the antenna is approximately 47.4ft when calculated using the Pythagorean theorem: √((50ft)^2 - (15ft)^2).
Explanation:The question is asking for the height of the antenna. We can solve this problem by using the Pythagorean theorem, which states that in a right triangle the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Here, the hypotenuse is the length of the cable (50 ft), one side is the distance from the base of the antenna to the anchor point (15 ft) and the other side (which we are trying to find), is the height of the antenna.
According to the Pythagorean theorem, the height of the antenna can be calculated as follows: Height = √(Hypotenuse^2 - Base^2), which translates into Height = √((50ft)^2 - (15ft)^2). When you calculate that you get the height of the antenna as approximately 47.4 feet, rounded to the nearest tenth.
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confused, so can someone pls help
Answer:
Choice C
Step-by-step explanation:
(f+g)(x) is a composite function which is obtained by adding the two given functions f(x) and g(x)
(f+g)(x) = f(x) + g(x)
= [tex]3^{x} +10x+4x-2[/tex]
= [tex]3^{x} +14x-2[/tex]
if i worked for 7h and 45 min and got paid 93 dollors what is my dollor per hour rate
8 per hour. have a nice day
What is the perimeter of the rectangle shown below?
Answer:
To find perimeter, you must add length plus length plus width plus width.
(L+L+W+W)
the length is 5, and the width is 8. since there are 4 sides, we must add 5+5+8+8, and that equals 26.
So the perimeter of the rectangle is 26 units.As we know the formula for finding the perimeter of a rectangle is:
[tex]Perimeter=2(L+B)[/tex]
here, L is the length of the rectangle and B is the breadth of the rectangle.
As the values of the length and breadth are given, we will put in the formula;
[tex]Perimeter=2(8+5)[/tex]
[tex]Perimeter=2(13)[/tex]
[tex]Perimeter=26[/tex]
Hence, the perimeter of the rectangle is 26 units.
What is the perimeter in math?Perimeter is the distance around the edge of a shape.
What is a perimeter and its formula?The total length of the boundary of a closed shape is called its perimeter. Hence, the perimeter of that shape is measured as the sum of all the sides. Thus, the perimeter formula is Perimeter(P) = Sum of all the sides.
What is parameter formula?Any equation expressed in terms of parameters is a parametric equation. The general equation of a straight line in slope-intercept form, y = mx + b, in which m and b are parameters, is an example of a parametric equation.
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Express 2/5% as a fraction and decimal
fraction=
decimal=
HELP ASAP!
Answer:
Fraction: 1/250
Decimal: 0.004
Step-by-step explanation:
2/5=0.4 0.4%=0.004 0.004=4/1000=2/500=1/250
At your construction job, you're standing on a ladder at ground level. First, you climb down 7 feet to see the basement. Then you climb up 22 feet to see the second floor. Later, you climb down 9 feet. How high above or below the ground are you?
7 feet below the ground
6 feet below the ground
9 feet above the ground
9 feet below the ground
6 feet above the ground
Final answer:
After descending 7 feet, ascending 22 feet, and descending 9 feet, the individual is 6 feet above the ground level.
Explanation:
The question involves a sequence of movements by an individual on a ladder at a construction site. To solve this, let's track each movement relative to the initial position at ground level.
The individual climbs down 7 feet to the basement, so they are now 7 feet below ground.Then they climb up 22 feet which brings them 15 feet above ground level (since they were originally 7 feet below).Finally, climbing down 9 feet from the second floor, they are now 6 feet above the ground level.Therefore, the individual is 6 feet above the ground after these movements.
find a9 in the arithmetic sequence with a1 = -2.75 and d = 0.25
Answer:
The ninth term is -0.75.
Step-by-step explanation:
Let's write the actual formula for this arith. seq.
It will have the general form a(n) = a(1) + (n-1)d, where a(1) is the first term, n is the term counter (1, 2, 3, .... ) and d is the common difference.
Here, a(n) = -2.75 + (n - 1)(0.25)
So the ninth term of this sequence is
a(9) = -2.75 + (9 - 1)(0.25
= -2.75 + 8(0.25)
= -2.75 + 2
= -0.75
The ninth term is -0.75.
Answer:
[tex]a_9=-0.75[/tex]
Step-by-step explanation:
The given sequence has the first term, [tex]a_1=-2.75[/tex] and d=0.25
The general formula for an arithmetic sequence is given by;
[tex]a_n=a_1+d(n-1)[/tex]
Since we want to find [tex]a_9[/tex], it means n=9
We substitute the given values into the formula to obtain;
[tex]a_9=-2.75+0.25(9-1)[/tex]
[tex]a_9=-2.75+0.25(8)=-0.75[/tex]
Hence, the 9th term is
[tex]a_9=-0.75[/tex]
What is the value of x?!
Answer:
5[tex]\sqrt{3}[/tex]
Step-by-step explanation:
Using the sine ratio in the right triangle and the exact value of
sin60° = [tex]\frac{\sqrt{3} }{2}[/tex], then
sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{10}[/tex]
Multiply both sides by 10
10 × sin60° = x
10 ×[tex]\frac{\sqrt{3} }{2}[/tex], hence
x = 5[tex]\sqrt{3}[/tex]
find the value of the trigonometric function sin (t) if sec t = -4/3 and the terminal side of angle t lies in quadrant II
Answer:
[tex]sin(t) =\frac{\sqrt{7}}{4}[/tex]
Step-by-step explanation:
By definition we know that
[tex]sec(t) = \frac{1}{cos(t)}[/tex]
and
[tex]cos ^ 2(t) = 1-sin ^ 2(t)[/tex]
As [tex]sec(t) = -\frac{4}{3}[/tex]
Then
[tex]sec(t) = -\frac{4}{3}\\\\\frac{1}{cos(t)} =-\frac{4}{3}\\\\cos(t) = -\frac{3}{4}[/tex]
Now square both sides of the equation:
[tex]cos^2(t) = (-\frac{3}{4})^2[/tex]
[tex]cos^2(t) = \frac{9}{16}\\\\[/tex]
[tex]1-sin^2(t) =\frac{9}{16}\\\\sin^2(t) =1-\frac{9}{16}\\\\sin^2(t) =\frac{7}{16}\\\\sin(t) =\±\sqrt{\frac{7}{16}}[/tex]
In the second quadrant sin (t) is positive. Then we take the positive root
[tex]sin(t) =\sqrt{\frac{7}{16}}[/tex]
[tex]sin(t) =\frac{\sqrt{7}}{4}[/tex]
The value of sin(t) = √7/4 because sine is positive in Quadrant II.
First, recall that sec(t) is the reciprocal of cos(t):
sec(t) = 1/cos(t)
Given: sec(t) = -4/3, so:
cos(t) = -3/4
Since angle t lies in Quadrant II, cosine is negative, and sine is positive. Use the Pythagorean identity:
sin²(t) + cos²(t) = 1
Substitute cos(t):
sin²(t) + (-3/4)² = 1
sin²(t) + 9/16 = 1
Solve for sin²(t):
sin²(t) = 1 - 9/16
sin²(t) = 16/16 - 9/16
sin²(t) = 7/16
Take the square root of both sides:
sin(t) = √(7/16) = √7/4
Since we are in Quadrant II, sine is positive:
sin(t) = √7/4
If a sample proportion is 0.26 which of the following is most likely the range of possible values that best describes an estimate for the population parameter
Answer: (0.15,0.37)
Step-by-step explanation:
did the quiz
The range of possible values that best describes the estimate for the population parameter is [0.16, 0.38]. Therefore, the correct answer is option D.
Given that, a sample proportion is 0.26.
In statistics, the sample proportion is an estimate for the population parameter. When given a sample proportion, the range of possible values that best describes the estimate for the population parameter is typically the 95% confidence interval for the sample proportion. The 95% confidence interval states that if the same sampling procedure is repeated on many samples, then 95% of the confidence intervals constructed this way will contain the true population parameter.
The 95% confidence interval for a sample proportion is given by [p-1.96√(pq/n), p+ 1.96√(pq/n)], where p is the sample proportion, q is the complement of the sample proportion (q = 1 − p), and n is the sample size.
In this case, the sample proportion given is 0.26, and so p = 0.26, q = 0.74, and the sample size can be assumed to be large (n ≥ 30). Substituting these values into the 95% confidence interval equation yields the range of possible values that best describes the estimate for the population parameter: [0.16, 0.38].
Therefore, the correct answer is option D.
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"Your question is incomplete, probably the complete question/missing part is:"
If a sample proportion is 0.26 which of the following is most likely the range of possible values that best describes an estimate for the population parameter?
A. (0.14, 0.36)
B. (0.17, 0.39)
C. (0.15, 0.37)
D. (0.16, 0.38)
Estimate the sum 7 1/4 + 2 5/8.
Answer:
10
Step-by-step explanation:
What is the probability of getting a vowel (a successes) for the spinner? Compute P(3 successes) for 5 spins of the spinner
Answer:
What is the probability of getting a vowel (a success) for the spinner shown?
✔ 1/3
Suppose you spin the spinner 5 times.
✔ P(3 successes) means “the probability of getting a vowel on exactly 3 of the spins.”
Step-by-step explanation:
edg 2020
Using the binomial distribution, it is found that:
The probability of a success is of 1/3.P(X = 3) = 0.1646.For each spin, there are only two possible outcomes, either it is a vowel, or it is not. The result of a spin is independent of any other spin, hence the binomial distribution is used to solve this question.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.In this problem:
The spinner has 3 regions, A, B and C, one of which is a vowel, hence p = 1/3 = 0.3333.There will be 5 spins, hence n = 5.The probability of 3 successes is given by:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{5,3}.(0.3333)^{3}.(0.6667)^{2} = 0.1646[/tex]
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Calculating area and perimeter worksheet works.com answer #4-9
Step-by-step explanation:
dude i have no idea sorry
The Calculating area and perimeter worksheet from works.com
#4
Area: [tex]360 yd^2[/tex]
Perimeter: 30 yd
#5
Area: [tex]45 yd^2[/tex]
Perimeter: 22 yd
#6
Area: 87 yd^2
Perimeter: 30 yd
#7
Area: 72 ft^2
Perimeter: 24 ft
#8
Area: 150 ft^2
Perimeter: 30 ft
#9
Area: 2128 ft^2
Perimeter: 70 ft.
Area is the amount of space that a two-dimensional shape takes up. It is measured in square units, such as square feet (ft^2), square yards (yd^2), or square meters (m^2).
To calculate the area of a rectangle, multiply the length by the width.
Area of a rectangle = length * width
To calculate the area of a square, multiply the side length by itself.
Area of a square = side length * side length
To calculate the area of a triangle, multiply the base by the height and divide by 2.
Area of a triangle = base * height / 2
Perimeter is the total length of all the sides of a two-dimensional shape. It is measured in linear units, such as feet (ft), yards (yd), or meters (m).
To calculate the perimeter of a shape, add up the lengths of all the sides.
Perimeter of a shape = sum of the lengths of all the sides
Example:
To calculate the area and perimeter of the rectangle in question #4, we would use the following formulas:
Area = length * width = 5 yd * 72 yd = 360 yd^2
Perimeter = sum of the lengths of all the sides = 5 yd + 72 yd + 5 yd + 72 yd = 30 yd
Answers to the remaining questions:
#5:
Area = 45 yd^2
Perimeter = 22 yd
#6:
Area = 87 yd^2
Perimeter = 30 yd
#7:
Area = 72 ft^2
Perimeter = 24 ft
#8:
Area = 150 ft^2
Perimeter = 30 ft
#9:
Area = 2128 ft^2
Perimeter = 70 ft.
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