Answers
Since the trapezoid is isosceles, U = T, V = S.
a) T = 109°
b) U = 109°
C) V = 71°
Related Questions
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
3/4 of what number is 8?
Answers
The sum of two complementary angles is 90°. For one pair of complementary angles, the measure of the first angle is 15 less than twice the measure of the second angle. Write a system of equations that can be used to determine the measure of the first angle, a, and the measure of the second angle, b.
•a+b=90
a-2b=15
•a+b=90
2b-15=a
•a+b=90
2b+15=a
•a+b=90
2a-15=b
Answers
a---------------> first angle
b---------------> second angle
we know that
a+b=90
and
the measure of the first angle is 15 less than twice the measure of the second angle
a=(2b)-15
A system of equations that can be used to determine the measure of the first angle, a, and the measure of the second angle, b is
a+b=90
a=(2b)-15
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:
Nadia needs half of a dollar for bus fare. Which amount is equivalent to her bus fare?
Answers
help me please asap!!!!!!!
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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
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.
Anybody know the answer to this?
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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%.
Each leg of a 45°-45°-90° triangle measures 14 cm. What is the length of the hypotenuse? 7 cm cm 14 cm cm
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This one helps too.
Ur welcome.
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?
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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
Find an angle between 0° and 360° that is coterminal with 538°.
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Find the slope and the y-intercept of the equation y − 3(x − 1) = 0.
slope = -3 and y-intercept = -3
slope = 3 and y-intercept = 3
slope = -3 and y-intercept = 3
slope = 3 and y-intercept = -3
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The slope and the y-intercept of the equation y − 3(x − 1) = 0 are: slope = 3 and y-intercept = -3. The correct option is the fourth option (slope = 3 and y-intercept = -3)
To determine the slope and y-intercept of the equation, we will rewrite the equation in the form of the slope-intercept form of the equation of a straight line.
The slope-intercept form equation of a straight line is
y = mx + c
Where m is the gradient
and c is the y-intercept
From the question, the given equation is y − 3(x − 1) = 0
This can be rewritten in form of the equation of a straight line as
y -3x +3 = 0
Then,
y = 3x - 3
Now, compare this to y = mx + c (the slope-intercept form of the equation of a straight line)
Then,
m = 3 and c = -3
That is,
slope = 3 and y-intercept = -3
Hence, the slope and the y-intercept of the equation y − 3(x − 1) = 0 are: slope = 3 and y-intercept = -3. The correct option is the fourth option (slope = 3 and y-intercept = -3)
Learn more here: https://brainly.com/question/20341753
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.
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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 the system of equations is consistent, consistent and coincident, or inconsistent?
y=−12x+3y=4x+2
Select the correct answer from the drop-down menu.
Drop-down Menu: consistent, consistent and coincident, or inconsistent
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You can eliminate an inconsistent system. That would happen when the lines are parallel.
! Hope this helps!
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
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Ryanne is 14. her brother's age is three more than half her age. how old is her brother?
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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
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?
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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.
Which number completes the square? x2 + 18x + _____?
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Thus x^2 + 2(9)(x) + (9)^2 = x^2 + 18x + 81
How many odd integers from 1000 through 9999 have distinct digits?
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step 1
the number of elements in a list from n to m is (m-n)+1
therefore
from 1000 to 9999 there are
(9999-1000)+1 = 9000 elements
step 2
Since even and odd numbers alternate, half of our list is composed of odd numbers. Therefore, there are 4500 of them
step 3
To construct a 4 digit odd number, we have 5 choices for the last digit.
(1-3-5-7-9)
then
we have
8 choices for the first (not 0 or same as last digit),
8 choices for the second
7 choices for the third.
there are (8)(8)(7)(5) = 2240
the answer is 2240 odd numbers with distinct digits in the list
A cube has a length of 9.3 cm. what is the surface area of the cube?
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Explanation:
The surface area of the cube is given by
Surface Area = 6*(edge)²
Since the edge of the cube in this problem is its length, the egde is 9.3 cm. Hence, the surface area of the cube is calculated as
Surface Area = 6*(edge)²
= 6*(9.3 cm)²
Surface Area = 518.94 square centimeters
Write the equation of the circle with center (−1, −3) and (−7, −5) a point on the circle.
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well, the radius will be the distance from the center to any point on the circle, it just so happen that we know -7, -5 is on it, thus
[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\\\ \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~ -1 &,& -3~) % (c,d) &&(~ -7 &,& -5~) \end{array} \\\\\\ d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ r=\sqrt{[-7-(-1)]^2+[-5-(-3)]^2}\implies r=\sqrt{(-7+1)^2+(-5+3)^2} \\\\\\ r=\sqrt{36+4}\implies r=\sqrt{40}\\\\ -------------------------------[/tex]
[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{-1}{ h},\stackrel{-3}{ k})\qquad \qquad radius=\stackrel{\sqrt{40}}{ r} \\\\\\\ [x-(-1)]^2+[y-(-3)]^2=(\sqrt{40})^2\implies (x+1)^2+(y+3)^2=40[/tex]
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.
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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
is -4 real, complex, pure imaginary, or nonreal complex. (More than one of these descriptions may apply.)
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Hope this helps!
Twenty-seven minus of a number (x) is not more than 36. What is the number? x > 42 x ≥ -6 x < 3 x ≤ -6
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54 - 3x ≤ 72
-3x ≤ 72 - 54
-3x ≤ 18
x ≥ 18/(-3)
x ≥ -6
..........................................................
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?
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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
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Answer:
It is one.
Step-by-step explanation:
If you didn't get 1 re read the problem
express the perimeter of the rectangle as a polynomial. help please.
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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.
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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.
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Factor and find all the zeros of 2x^3+3x^2-8x+3 if -3 is a zero
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.. 2x^2 -3x +1
That, in turn, factors as
.. (2x -1)(x -1)
So the complete factorization is
.. (2x -1)(x -1)(x +3)
and the zeros are confirmed by a graphing calculator to be
.. x = 1/2, 1, -3
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?
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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!