Answers
Answer:
[tex]x=9.5[/tex]
[tex]y=8.8[/tex]
Step-by-step explanation:
We have been given a diagram of triangles. We are asked to find the value of x and y.
We can see that triangle JKL and JMN share same vertex that is angle J. Since line KL is parallel to line MN, therefore, there corresponding angles will be equal.
Therefore, Angle-angle-angle similarity [tex]\Delta JKL\sim \Delta JMN[/tex].
Since corresponding sides of similar triangles are always proportional, so we can set a proportion for the sides of our given triangles as:
[tex]\frac{x-2}{5}=\frac{12}{8}[/tex]
Upon cross multiplying our equation we will get,
[tex]8(x-2)=12*5[/tex]
[tex]8x-16=60[/tex]
Let us add 16 to both sides of our equation.
[tex]8x-16+16=60+16[/tex]
[tex]8x=76[/tex]
Let us divide both sides of our equation by 8.
[tex]\frac{8x}{8}=\frac{76}{8}[/tex]
[tex]x=9.5[/tex]
Therefore, x equals 9.5.
We can also set a proportion to solve for y as:
[tex]\frac{y}{22}=\frac{8}{12+8}[/tex]
[tex]\frac{y}{22}=\frac{8}{20}[/tex]
Upon cross multiplying our equation we will get,
[tex]20y=22*8[/tex]
[tex]20y=176[/tex]
Let us divide both sides of our equation by 20.
[tex]\frac{20y}{20}=\frac{176}{20}[/tex]
[tex]y=8.8[/tex]
Therefore, y equals 8.8.
Related Questions
The length of a rectangular garden is 8 feet longer than the width. The garden is surrounded by a 4-foot sidewalk. The sidewalk has an area of 320 square feet. Find the dimensions of the garden.
Answers
The width of the garden is 12 feet and the length of the garden is 20 feet.
Explanation:Let's denote the width of the garden as 'w'. The length will then be 'w + 8'. Measurements are in feet. The garden is surrounded by a 4-foot sidewalk. Therefore, the total length of the garden including the sidewalk is 'w + 8 + 4 + 4 = w + 16', and the total width is 'w + 4 + 4 = w + 8'.
The area of the sidewalk surrounding the garden is the area of the large rectangle minus the area of the garden. So, we set up the following equation:
(w + 16)(w + 8) - (w)(w + 8) = 320.
After simplifying, we can get a quadratic equation: w² + 8w - 320 = 0 and then solve this equation, which gives us w = 12 or w = -28. We ignore the negative solution as the width cannot be negative. So, the dimensions of the garden are:
Width: 12 feet
Length: 20 feet.
https://brainly.com/question/12509806
#SPJ12
Kim solved the equation below by graphing a system of equations. log2(3x-1)= log4(x+8) What is the approximate solution to the equation?
Answers
The approximate solution of the equation log₂(3·x - 1) = log₄(x + 8), obtained algebraically is about x = 1.353. The solution cain be verified using the attached graph created with MS Excel
The steps used to find the solution of the logarithm equation can be presented as follows;
The logarithm equation is; [tex]\log_2(3\cdot x - 1) = \log_4(x + 8)[/tex]
Converting the logarithm to the same base, we get;
[tex]\log_4(x + 8) = \frac{\log_2(x + 8)}{\log_2 4}[/tex]
[tex]\log_4(x + 8) = \frac{\log_2(x + 8)}{2}[/tex]
[tex]\log_2(3\cdot x - 1) = \frac{\log_2(x + 8)}{2}[/tex]
2 × log₂(3·x - 1) = log₂(x + 8)
log₂(3·x - 1)² = log₂(x + 8)
(3·x - 1)² = (x + 8)
(3·x - 1)² - (x + 8) = 0
9·x² - 7·x - 7 = 0
Solving using technology, we get; x ≈ 1.353 and x ≈ -0.575
Plugging in the value of x = 1.353, we get;
log₂(3 × 1.353 - 1) ≈ 1.613
log₄(1.353 + 8) ≈ 1.613
The value of the logarithm are much different when x ≈ -0.575, the expression log₂(3·x - 1) have no solution. The solution is therefore; x ≈ 1.353
Please find the attached the graph of the equation log₂(3·x - 1) = log₄(x + 8), showing the solution as x ≈ 1.353
Final answer:
To solve the equation log2(3x-1) = log4(x+8), we can rewrite the equation and simplify it to calculate the approximate solution as x = 4.5.
Explanation:
To solve the equation log2(3x-1) = log4(x+8), we can start by using the property of logarithms that states log(a) = log(b) if and only if a = b. Based on this property, we can rewrite the equation as 3x - 1 = x + 8. Simplifying this equation, we get 2x = 9. Finally, by dividing both sides by 2, we find that x = 4.5. Therefore, the approximate solution to the equation is x = 4.5.
An investment of $750 will be worth $1500 after 12 years of continuous compounding at a fixed interest rate. What percent is the interest rate?
Answers
Final answer:
The interest rate is 100%, or 1 as a decimal, for continuously compounded interest.
Explanation:
To find the interest rate, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the final amount ($1500)P is the principal amount ($750)r is the interest rate (unknown)n is the number of times interest is compounded per year (continuously compounded)t is the time in years (12)Using the given information, we can plug in the values and solve for r:
$1500 = $750(1 + r/1)^(1*12)$2 = 1 + rr = $2 - 1 = $1The interest rate is 100%, or 1 as a decimal, for continuously compounded interest.
The interest rate, for continuous compounding, is approximately 5.775%.
To find the interest rate for continuous compounding, we can use the formula for compound interest:
[tex]\[ A = P \times e^{rt} \][/tex]
Where:
- [tex]\( A \)[/tex] is the final amount of money,
- [tex]\( P \)[/tex] is the principal amount (initial investment),
- [tex]\( r \)[/tex] is the interest rate (annual rate in decimal),
- [tex]\( t \)[/tex] is the time the money is invested for (in years),
- [tex]\( e \)[/tex] is the base of the natural logarithm, approximately equal to 2.71828.
Given:
- [tex]\( P = $750 \)[/tex],
- [tex]\( A = $1500 \)[/tex],
- [tex]\( t = 12 \)[/tex] years.
We need to solve for [tex]\( r \)[/tex], the interest rate.
Step 1 :**Substitute the Given Values into the Formulaa :
[tex]\[ 1500 = 750 \times e^{12r} \][/tex]
Step 2 :**Divide Both Sides by 750**:
[tex]\[ \frac{1500}{750} = e^{12r} \][/tex]
[tex]\[ 2 = e^{12r} \][/tex]
Step 3 :**Take the Natural Logarithm of Both Sides**:
[tex]\[ \ln(2) = \ln(e^{12r}) \][/tex]
[tex]\[ \ln(2) = 12r \ln(e) \][/tex]
[tex]\[ \ln(2) = 12r \][/tex]
Step 4 :**Solve for [tex]\( r \)[/tex]**:
[tex]\[ r = \frac{\ln(2)}{12} \][/tex]
[tex]\[ r = \frac{0.693}{12} \][/tex]
[tex]\[ r = 0.05775 \][/tex]
Step 5 :**Convert the Interest Rate to a Percentage**:
[tex]\[ r_{\text{percentage}} = 0.05775 \times 100\% \][/tex]
[tex]\[ r_{\text{percentage}} = 5.775\% \][/tex]
So, the interest rate is approximately 5.775%.
The perimeter of a rectangle is 42 inches. If the length of the rectangle is 14 inches, which equation could be used to find the width, x? A. 2(x + 14) = 42 B. x + 2(14) = 42 C. 14(x + 2) = 42 D. x + 14 = 42
Answers
(2x = 14
x = 7
2(7) + 2(14) = 14 + 28 = 42)
Answer:
Option A is correct
equation [tex]2(x+14)=42[/tex] could be used.
Step-by-step explanation:
Given: The length of a rectangle [tex](l)[/tex] is 14 inches and perimeter of rectangle is 42 inches.
Perimeter(P)of a rectangle in inches is given by:
[tex]P= (2l+w)[/tex] ; where [tex]l[/tex] is the length of the rectangle and w is the width of the rectangle.
Substitute the value of P=42 inches , w =x inches and [tex]l = 14[/tex] inches in the above formula we get;
[tex]42 = 2 \cdot (14+x)[/tex]
Divide by 2 on both sides we get;
[tex]21 = 14+x[/tex]
On simplify, we get;
x = 21-14 = 7 inches
therefore, the width of the rectangle is, x = 7 inches
Check :
Substitute the value of x =7 in option A.
[tex]2(x+14) =42[/tex]
[tex]2(7+14)=42[/tex]
[tex]2\cdot 21 =42[/tex]
42 = 42
Hence, the only equation that could be used to find the width, x is, [tex]2(x + 14) = 42[/tex]
At how many points does the graph of the function below intersect the x-axis?
y = 25x2 - 10x + 1
A. 0
B. 1
C. 2
Answers
Answer:
It is one.
Step-by-step explanation:
If you didn't get 1 re read the problem
3/4 of what number is 8?
Answers
what is a possible value for the missing term of the geometric sequence ?
50, blank, 450, ..
a. 1,350
b. 150
c. 3
d. 53
Answers
So the answer is b 150
What is the approximate area of the circle shown below 60cm
Answers
This is the answer your welcome
Answer:
[tex]\text{Hence, the approx. area of circle }2827 cm^2[/tex]
Step-by-step explanation:
Given the diameter of circle 60 cm
we have to find the area of circle
Diameter=60 cm
Radius=30 cm
[tex]\text{Area of circle=}\pi r^2[/tex]
[tex]=\frac{22}{7}\times (30)^2=2828.57143\sim 2827(approx)[/tex]
[tex]\text{Hence, the approx. area of circle }2827 cm^2[/tex]
Option A is correct
Twenty-seven minus of a number (x) is not more than 36. What is the number? x > 42 x ≥ -6 x < 3 x ≤ -6
Answers
54 - 3x ≤ 72
-3x ≤ 72 - 54
-3x ≤ 18
x ≥ 18/(-3)
x ≥ -6
..........................................................
which or the following will happen if you miss a monthly credit card payment?
A)You will be charged a late fee.
B)You loose reward points
C)Your APR will increase the next month
D)Both A & B
Answers
Nadia needs half of a dollar for bus fare. Which amount is equivalent to her bus fare?
Answers
What is the first error he made in computing the standard deviation?
A.Yuri failed to find the difference between each data point and the mean.
B.Yuri divided by n instead of n -1.
C.Yuri did not subtract 9 - 14 correctly.
D.Yuri failed to square -2 correctly.
Answers
Answer:
Step-by-step explanation:
Given is a sample with 4 items as
12,9,14,21
Mean = average of 4 = 14
s is the square root of sample variance
Sample variance is the sum of squares divided by n-1
But Yuri divided by 4 = n instead of 3 = n-1
That is the only mistake he did and all other steps are right.
is -4 real, complex, pure imaginary, or nonreal complex. (More than one of these descriptions may apply.)
Answers
Hope this helps!
Ryanne is 14. her brother's age is three more than half her age. how old is her brother?
Answers
half her age : 14 ÷ 2 = 7
three more : 7 + 3 = 10
Her brother is 10 years old.
Answer:
10 years old
Step-by-step explanation:
I will use the letter r to denote Ryanne's age:
r = 14
And according to the problem, her brother's age is THREE MORE THAN HALF HER AGE
so, we start by finding how much is half of Ryanne's age:
r/2 = 14/2 = 7
and next, we find that three more than half her age is:
7 + 3 = 10
Her brother is 10 years old
express the perimeter of the rectangle as a polynomial. help please.
Answers
Anybody know the answer to this?
Answers
If the radius of the circle is 1, the side length of the square is √2 and its area is (√2)^2 = 2.
The ratio of square area to circle area is 2/π ≈ 63.7%.
The profits of mr cash’s company is represented by the equation p(t)=-3t^2+18t-4, where p(t) is the amount of profit in hundreds of thousands of dollars and t is the number of years of operation. he realizes his company is on the down turn and wishes to sell before he ends up in debt. in what year of operation does mr cash’s business show the maximum profit?
Answers
Explanation:
Note that p(t) is a quadratic function and so its graph is a parabola. Since the coefficient of t² in p(t) is negative, the maximum point in p(t) exist at its vertex. Moreover, the maximum value of p(t) is the y-coordinate of its vertex.
Note that p(t) can be expressed as:
[tex]p(t) = a(t-h)^2 + k [/tex] (1)
Where (h, k) are the coordinates of the vertex of p(t).
To manipulate p(t) in the form expressed in equation (1), we factor out the coefficient of t² in p(t) so that
[tex]p(t) = -3t^2+18t-4 \\ \boxed{p(t) = -3 \left( t^2 - 6t + \frac{4}{3} \right)}[/tex]
Then, we let
[tex]q(t) = t^2 - 6t + \frac{4}{3}[/tex]
So that
[tex]p(t) = -3q(t)[/tex] (2)
We need q(t) to be expressed as the sum of a perfect square trinomial and a constant. To form the perfect square trinomial in q(t), we can find a constant k such that [tex]t^2 - 6t + k [/tex] is a perfect square.
To find the value of k, we divide the coefficient of t by 2 and get the square of the result. Since the coefficient of t in q(t) is -6,
[tex]k = \left( \frac{-6}{2} \right)^2 = 9[/tex]
To avoid changing the value of q(t), if we add the constant k = 9, we need to subtract it by the same number. Since k = 9,
[tex]q(t) = t^2 - 6t + \frac{4}{3} + k - k \\ = t^2 - 6t + \frac{4}{3} + 9 - 9 \\ = (t^2 - 6t + 9) + \frac{4}{3} - 9 \\ \boxed{q(t) = (t - 3)^2 - \frac{23}{3}} [/tex]
From equation (2),
[tex]p(t) = -3q(t) \\ p(t) = -3\left( (t - 3)^2 - \frac{23}{3} \right) \\ \boxed{p(t) = -3 (t - 3)^2 + 23}[/tex]
Hence the vertex of p(t) is (3, 23) and maximum value is attained at t = 3. Therefore, the Mr. Cash's business has maximum profit at the 3rd year of operation.
The square of the sum of two consecutive natural numbers is greater than the sum of the squares of these two numbers by 112. find the two numbers.
Answers
Then, ( 2a + 1 )^2 = 112 + a^2 + a^2 + 2a +1;
4a^2 + 4a + 1 = 113 + 2a^2 + 2a;
Finally, 2a^2 + 2a - 112 = 0;
a^2 + a - 56 = 0;
We use Quadratic Formula for this Quadratic Equation;
The solutions are a1 = 7 and a2 = -8;
But a is a natural number; so, a = 7;
The natural consecutive numbers are 7 and 8.
The two consecutive numbers are 7 and 8.
Consecutive numbers are numbers that follow each other. For example, 1,2,3,4 are consecutive numbers.
Let:
x = first number
(x + 1) = second number
From the question, this expression can be derived:
[(x) + (x + 1)] ²
This can be simplified to (2x +1)²
The second expression is : x² + (x +1)²
(2x +1)² - [x² + (x +1)²] = 112
expanding the bracket gives:
(4x² + 4x + 1) - [x² + (x² + 2x +1) = 112
4x² + 4x + 1 - 2x² - 2x - 1 = 112
Add like terms
2x² + 2x = 112
Divide both sides by 2
x² + x = 56
x² + x - 56 = 0
Factorise the equation
The factors of -56x² that add up to x are : 8x and -7x
(x² - 7x) (8x - 56) = 0
x(x - 7) 8(x -7) = 0
x = 7
or
x = -8
Since x cannot be a negative number, x is 7 and (x + 1) = 8
A similar question was solved here: https://brainly.com/question/14024870?referrer=searchResults
Each leg of a 45°-45°-90° triangle measures 14 cm. What is the length of the hypotenuse? 7 cm cm 14 cm cm
Answers
This one helps too.
Ur welcome.
Match each whole number with a rational exponential expression. HELPP ME PLEEASE FASTTT
Answers
3rdrt[(343(343)]
49
2. [2,197^(1/3)]^2
[3rdrt(2,197)]^2
169
3. 729^(2/3)
3rdrt[729(729)]
81
4. (1,000^2)^(1/3)
3rdrt(1,000^2)
100
5. [3rdrt(9261)]^2
441
6. [3rdrt(216^2)]
36
Hope this helps!
Answer:
1. 49
2. 169
3. 81
4. 100
5. 441
6. 36
Step-by-step explanation:
1. [tex](343)^{\frac{2}{3}}=\sqrt[3]{(343)^{2} }[/tex]
= [tex]\sqrt[3]{(343)(343)}=\sqrt[3]{(7^{3})(7)^{3}}[/tex]
= 7×7 = 49
2. [tex](2197^{\frac{1}{3}})^{2}=(\sqrt[3]{2197})^{2}[/tex]
= [tex](\sqrt[3]{13^{3}})^{2}=13^{2}[/tex]
= 169
3. [tex]729^{\frac{2}{3} }=(\sqrt[3]{729})^{2}[/tex]
= [tex](\sqrt[3]{9^{3}})^{2} = 9^{2}[/tex]
= 81
4. [tex](1000^{2})^{\frac{1}{3}}=(\sqrt[3]{1000})^{2}[/tex]
= 10²
= 100
5. [tex](\sqrt[3]{9261})^{2}=(\sqrt[3]{(21)^{3} })^{2}[/tex]
= 21²
= 441
6. [tex](\sqrt[3]{216})^{2}=(\sqrt[3]{6^{3} })^{2}[/tex]
= 6²
= 36
Find the value of the missing side of a triangle practice
Answers
Be sure to understand the differences between a right-angled triangle and an irregular-shaped triangle.
Right-angled triangle
Two sides must be known.
[tex] {a}^{2} = {b}^{2} + {c}^{2} [/tex]
where 'a' squared is the hypotenuse of the triangle.
To find the non-hypotenuse side, the formula can be rearranged to
[tex] {b}^{2} = {a}^{2} - {c}^{2} [/tex]
'b' can be any non-hypotenuse side.
Non-right angled triangle.
Cosine rule
Two sides and an angle must be know.
[tex]a = {b}^{2} + {c }^{2} - 2ab \cos(angle \: facing \: a) [/tex]
That is just a few of the formulas I have listed.
table Mary used Delicious (d) and Golden Delicious (g) apples to make homemade applesauce. Delicious apples are $0.75 each and Golden Delicious apples are $1.25 each. Mary spent $21.00 on 22 apples. How many Golden Delicious apples did Mary buy?
Answers
2. The equations are:
d+g=22 (i)
0.75d+1.25g=21 (ii)
3. If you clear "d" from the equation (i), you have:
d+g=22
d=22-g
4. Now, you must substitute d=22-g into the equation (ii):
0.75d+1.25g=21
0.75(22-g)+1.25g=21
5. When you clear "g", you obtain its value:
16.5-0.75+1.25g=21
16.5+0.5g=21
0.5g=21-16.5
g=4.5/0.5
g=9 Golden Delicious apples
6. If you also want to know the value of "d", you can substitute g=9 into the equation (i) and clear "d":
d+g=22
d+9=22
d=22-9
d=13 Delicious apples
How many Golden Delicious apples did Mary buy?
The answer is: Mary bought 9 Golden Delicious apples.
Tldr: The answer is 9
How many pieces of pie will you have if 4 banana caramel cream pies are sliced into 1 8 servings? A) 12 B) 18 C) 24 D) 32
Answers
When 4 banana caramel cream pies are sliced into 1/8 servings, the number of pieces of pie obtained is 32.
Explanation:To determine the number of pieces of pie obtained when 4 banana caramel cream pies are sliced into 1/8 servings, we need to find the total number of pie servings. Each pie is sliced into 1/8 servings, so if we have 4 pies, we can calculate the total number of servings by multiplying 4 by 1/8.
4 x 1/8 = 4/8 = 1/2Therefore, we will have 1/2 pie when 4 banana caramel cream pies are sliced into 1/8 servings. Since 1/2 pie is equivalent to 4/8 pie, the answer is D) 32 pieces.
WILL GIVE BRAINLIEST
WILL GIVE BRAINLIEST AND 50 points
out of a port departed a steam boat with a speed of 36.8km/h. In 1.75 hours out of the same port and going the Sam direction departed a speed boat. In 1.8 hours after the the department of the speed boat, the distance between the speed boat and the steam boat was 86.9km. What was the speed boats speed in km/h?
Answers
s=d/t
d=st
For the steam boat, the velocity was 36.8, and the time was 1.75 hours before the speedboat left plus the 1.8 hours after the speedboat left. Substitute this information into the equation to find the distance it travels:
d=36.8*(1.75+1.8)
d=130.64 km
According to the question, we know that the distance the speedboat travels is 86.9 km behind the steam boat. So d for the speedboat is 130.64-86.9, or
43.74 km. It is also given that the speedboat travels for 1.8 hours, so t=1.8. Substitute this information into the equation to find the speed.
s=43.74/1.8
s=24.3 km/h
So the speed of the boat is 24.3 km/h
Hi there!
My name is Chris and I'll be helping you today!
So your question states that a boat departed the port at 36.8 km/h.
After 1.75 hours, a second boat emerges from the port.
After 1.8 hours, the second boat is 86.9 km away from the first boat.
Also, remember that speed equals distance over time.
Therefore, your answer will be: The speed boat's speed in km/h was 24.3 km/h. Forgive me if I am incorrect.
Enjoy your day!
help me please asap!!!!!!!
Answers
1. It is where the bisectors meet. This fact creates the next statement.
2. It is the same distance from the incenter to the sides of triangle. Three lines each drawn from the incenter perpendicularly to the sides will create 3 equal lines. These lines will each be equal. Put another way AI = BI = CI which are radii for the incircle.
Any two of AI, BI, and CI and make them equal to each other.
3x + 7 = 5x - 11 Now you can just use algebra to solve. Add 11 to both sides
3x + 7 + 11 = 5x
3x + 18 = 5x. Now subtract 3x from both sides.
18 = 5x - 3x
18 = 2x
x = 9
You should really check this. Do this by equating CI to either AI or BI. I leave it to you to figure out which one I choose.
Check
=====
This will be short so you can fill in the steps for yourself.
3x + 7 = 52 - 2x
5x = 45
x = 45/5
x = 9
Could someone explain this to me?
Answers
[tex]5y^4\frac{dy}{dx}+6y^2x+6x^2y\frac{dy}{dx}+20x^3 = 0[/tex]
Simplify:
[tex] \frac{dy}{dx} (5y^4+6x^2y) + 6y^2x+20x^3 = 0[/tex]
Solve for dy/dx:
[tex] \frac{dy}{dx} = \frac{-6y^2x-20x^3}{5y^4+6x^2y} [/tex]
Now, plug in the given points:
[tex]\frac{dy}{dx} = \frac{-6(2)^2(-1)-20(-1)^3}{5(2)^4+6(-1)^2(2)} = \frac{24+20}{80+12}[/tex]
Further simplification gives:
[tex]\frac{dy}{dx}|_{(2,-1)} =\frac{44}{92} = \frac{11}{23} [/tex]
So, your answer is 11/23 or B.
A FIELD HOCKEY TEAM IS A RECTANGLE 60YARDS BY 100YARDS .WHAT IS THE LENGTH OF THE DIAGONAL FROM ONE CORNER TO THE FIELD TO THE OPPOSITE CORNER ROUND YOUR ANSWER TO THE NEAREST HUNDRETH
Answers
3600 + 10000 = X^2
13600 = x^2
X = Sqrt(13600)
X = 116.619
Diagonal = 116.62 yards
3600 + 10000 = c^2
13600 = c^2
c = 116.62 yd
A pair of shoes that normally costs $75 is on sale for $55. What is the percent decrease in the price, to the nearest whole percent?
Answers
Pablo folds a straw into a triangle with side lengths of 4x -2 inches and 4x -1 inched . The perimeter of the triangle is 12x -6 inched . If x =1.5 what was the length of the straw before it was folded ?
Answers
12(1.5)^2 -6 = length
12(2.25) -6 =
27 -6 =
21
Your answer is: 21 inches
Have an amazing day mate!
Shoutout to: @Apologiabiology
Answer:
21
Step-by-step explanation:
99 POINT QUESTION!!!!!
The prime factorization of a number is 2^3*3^2*5. Which is a true statement about the factors of the number?
Answers
so the number = 8 * 9 * 5 = 360
15 is a factor of 360, so the answer would be the first one: Fifteen is a factor of the number because both 3 and 5 are prime factors
3² = 9
8 x 9 x 5 = 360
15 is a factor of 360, so the answer would be 1. Fifteen is a factor of the number because both 3 and 5 are prime factors