Answer:
The length of the hypotenuse is [tex]h = 6.71\ units[/tex]
Step-by-step explanation:
For a straight triangle it is true that
[tex]h = \sqrt{a ^ 2 + b ^ 2}[/tex]
Where has is the hypotenuse of the right triangle and a and b are the lengths of the other two sides.
In this case we know that:[tex]a = 3\\b = 6[/tex]
So the hypotenuse is:
[tex]h = \sqrt{3 ^ 2 + 6 ^ 2}[/tex]
[tex]h = \sqrt{3 ^ 2 + 6 ^ 2}[/tex]
[tex]h = 3*\sqrt{5}[/tex]
[tex]h = 3*\sqrt{5}[/tex]
[tex]h = 6.71[/tex]
ANSWER
The hypotenuse is 3√5 units.
EXPLANATION
We use the Pythagoras Theorem.
Let h be the hypotenuse.
The Pythagoras Theorem says that, the hypotenuse square is equal to the sum of the squares of the two shorter legs.
[tex] {h}^{2} = {3}^{2} + {6}^{2} [/tex]
[tex]{h}^{2} = 9+ 36[/tex]
[tex]{h}^{2} = 45[/tex]
Take positive square root.
[tex]h = \sqrt{45} [/tex]
[tex]h = 3 \sqrt{5} units[/tex]
Sixty-five percent of what number is 32.5?
21.125
140
30
50
Final answer:
To find 65% of a number, use the equation 0.65x = 32.5 and solve for x by dividing both sides by 0.65 to get x = 50.
Explanation:
Sixty-five percent of what number is 32.5?
Let's denote the unknown number as x.
Translate the given information into an equation: 0.65x = 32.5
To solve for x, divide both sides by 0.65 giving x = 32.5 / 0.65 = 50.
What is in extraneous solution to the equation b/b-7 - 2/b = 7/ b-7 ?
Answer:
b = 2 or b = 7
Step-by-step explanation:
b/(b-7) - 2/b = 7/ (b-7)
b * b - 2(b - 7) = 7 * b
b^2 - 2b + 14 = 7b
b^2 - 9b + 14 = 0
(b - 2)(b - 7) = 0
b - 2 = 0; b = 2
b - 7 = 0; b = 7
Answer
b = 2 or b = 7
James bought two T-shirts and one pair of jeans at an online store and paid $40, not including taxes, for his purchase. A month later, the same store
sold the T-shirts and jeans at a 50% discount from their original prices. James bought two T-shirts and five pairs of jeans for $60, not including taxes.
and
Assuming the base prices of the T-shirts and the jeans are the same on both occasions, and ignoring the taxes, the price of a T-shirt is $
the price of a pair of jeans is $
Answer:
[tex]\boxed{\text{\$10; \$20}}[/tex]
Step-by-step explanation:
Let t = the price of a T-shirt
and j = the price of a pair of jeans
You have a system of two equations:
[tex]\begin{cases}(1)& 2t + j = 40\\(2) & 2(0.5t) + 5(0.5j) = 60\end{cases}\\[/tex]
[tex]\begin{array}{lrcll}(3) & t+ 2.5j & = & 60 &\text{Removed parentheses in (2)}\\(4)& 2t + 5j & = & 120 &\text{Multiplied (3) by 2}\\& 4j & = & 80 &\text{Subtracted (4) from (1)}\\(5)& j & = & 20 &\text{Divided each side by 4} \\& 2t + 20& = & 40 & \text{Substituted (5) into (1)} \\&2t & = & 20 & \text{Subtracted 20 from each side}\\& t & = & 20 & \text{Divided each side by 2}\\\end{array}[/tex]
[tex]\text{The price of a T-shirt is \boxed{\textbf{\$10}}}\\\\\text{and the price of a pair of jeans is \boxed{\textbf{\$20}}}\\[/tex]
Check:
[tex]\begin{array}{rclcrcl}2\times10\ + 20 & = & 40 & \qquad &2(0.5\times10) + 5(0.5\times20)&=&60\\20 + 20 & = & 40 & \qquad &2\times5 + 5\times 10& = &60\\40& = & 40 &\qquad &10 + 50 & = & 60\\& & &\qquad &60 & = & 60\\\end{array}[/tex]
OK.
Alicia receives 2/5 of a $120 gift, and Jason receives 1/3 of the gift. What is the ratio of Jason's share to Alicia's share? Express your answer as a common fraction. Plzzz help this is urgent
Answer:
5/6
Step-by-step explanation:
Step 1: Find Alicia's share of the gift. To do this, all you have to do is multiply 120 by 2/5, which is 40%. 120 * 40% (0.4) is 48. Alicia's share is $48.
Step 2: Find Jason's share of the gift. In this case, divide 120 by 3. 120/3 is 40. Jason's share is $40.
Step 3: Express the numbers as a fraction and simplify it. 40/48 is the common fraction. Find the GCF of 40 and 48. When you solve for it, the GCF is 8. Divide both the numerator and the denominator by 8. 40/8 is 5/ 48/8 is 6. There. 5/6 is our simplified fraction, which is the ratio.
Which equation does the graph represent?
Answer:
B.
Step-by-step explanation:
I plugged it into a graphing calculator which got me this.
what is the most important thibg one must do when solving an algerbraic equation
Answer:
using the foil
Step-by-step explanation:
you always have to get rid of the x for example if it is +3x you add it on to get rid of it and you carry on until you have solved x.
Answer:
getting the correct answer
Step-by-step explanation:
a bag contains six red balls, six greens balls, five yellow balls and three black balls. A ball is picked at random from the bag. Find the following probabilities.
Answer:
the 6 greens
At the zoo, for every 6 adult camels, there are 5 baby camels. There are a total of 44 adult and baby camels at the zoos.
How many baby camels are at the zoo?
Find the common ratio, by adding the adults and babies together: 6+5 = 11
Divide the total by that:
44/11 = 4
the common ratio is 4.
Now multiply the given ratios by the common ratio:
Adults = 6 x 4 = 24
Babies = 5 x 4 = 20
There are 20 babies.
Carl worked six and one-half hours on Monday. He worked eight and two-third hours on Tuesday. How many hours did Carl work in all?
Answer:
15 hours and 10 min
Step-by-step explanation:
6 1/2 hours on Monday
8 2/3 hours on Tuesday
You have to make the fractions equal to each other so you would have
1/2 x 3 = 3/6
2/3 x 2 = 4/6
Then add them together to get
7/6 or 1 1/6
6+8 = 14
Then add the 1 to 14 to get 15
1/6 of an hour is 10 minutes
Therefore your answer would be 15 hours and 10 minutes
What is 63.14 X 2.08
Answer:
131.3312
Step-by-step explanation:
Answer:
131.3312
Step-by-step explanation:
63.14
x 2.08
50512
0000
12628
131.3312
Which inequality is true for x = 2? A) 6x + 20 < 29 B) 7x − 10 < 11 C) 14x + 10 < 37 D) 15x − 18 < 12
For this case we substitute the value of "[tex]x = 2[/tex]" in each of the inequalities and evaluate:
Option A:
[tex]6x + 20 <29\\6 (2) +20 <29\\12 + 20 <29\\32 <29[/tex]
It is not fulfilled!
Option B:
[tex]7x-10 <11\\7 (2) -10 <11\\14-10 <11\\4 <11[/tex]
Is fulfilled!
Option C:
[tex]14x + 10 <37\\14 (2) +10 <37\\28 + 10 <37\\38 <37[/tex]
It is not fulfilled!
Option D:
[tex]15x-18 <12\\15 (2) -18 <12\\30-18 <12\\12 <12[/tex]
It is not fulfilled!
ANswer:
Option B
Terrence is folding paper cranes at a constant rate. The table below shows the amount of time he needs to fold cranes.
Write an equation to describe the relationship between c, the number of cranes, and t, the total time in minutes.
Look at attachment for table details! UwU
Answer:
Its 3.5c
Step-by-step explanation:
Let's find the constant of proportionality.
In the proportional relationship between c, the number of cranes, and t, the total time in minutes, one constant of proportionality is the amount of time per crane. It is the number we multiply by the number of cranes to get the total time.
c times ? =t
The constant of proportionality is 3.5 This means we can multiply 3.5 by the number of cranes to get the total time.
Now, let's represent that as an equation.
total time= time per crane X number of cranes
total time
t
time per crane×number of cranes
3.5c
One correct equation is:
t= 3.5c
Answer:
t = 3.5c
Step-by-step explanation:
This represents a proportional relationship because it is linear (he is folding at a constant rate) and passes through the origin (it would take him 0 minutes to fold 0 cranes). The formula for a proportional relationship is y = kx, where k is the constant of proportionality.
To find k, divide the dependent variable by its corresponding indepent variable. In this example, the amount of minutes is the dependent variable and the amount of cranes is the independent variable.
Using the first row of the table, we get [tex]k = \frac{17.5}{5} = 3.5[/tex].
Just to confirm our answer, let's try the other values given in the table:
[tex]k = \frac{28}{8} = 3.5\\k = \frac{42}{12} = 3.5[/tex]
So, we get that it takes Terrence 3.5 minutes to make one crane, so t = 3.5c
Cramer's rule:
What is [Ax] in the system below?
Answer:
Ax = [tex]\left[\begin{array}{cc}-3&-1\\5&1\end{array}\right][/tex] ⇒ 3rd answer
Step-by-step explanation:
Lets revise the Cramer's rule
- If the system of equation is ax + by = c and dx + ey = f
- A is the matrix represent this system of equation
- The first column has the coefficients of x, and
the second column has the coefficients of y
∴ A = [tex]\left[\begin{array}{cc}a&b\\d&e\end{array}\right][/tex]
- Ax means replace the column of x by the answers of the equation
∴ Ax = [tex]\left[\begin{array}{cc}c&b\\f&e\end{array}\right][/tex]
- Ay means replace the column of y by the answers of the equation
∴ Ay = [tex]\left[\begin{array}{cc}a&c\\d&f\end{array}\right][/tex]
* Now lets solve the problem
∵ 4x - y = -3 and -2x + y = 5
∴ A = [tex]\left[\begin{array}{cc}4&-1\\-2&1\end{array}\right][/tex]
- Replace the column of x by the answer to get Ax
∴ Ax = [tex]\left[\begin{array}{cc}-3&-1\\5&1\end{array}\right][/tex]
* Ax in the system of equation is [tex]\left[\begin{array}{cc}-3&-1\\5&1\end{array}\right][/tex]
Answer:
C
Step-by-step explanation:
Edge2021
Drew has completed 18 of his last 30 passes in football practice. If he attempts 120 passes this week, how many is he likely to complete?
Answer:
72
Step-by-step explanation:
He makes 18/30 passes. We need to see how many passes he can make out 120, so we need to see how many times 30 goes into 120.
120/30=4
So 120 is equivalent to 4 30s. Now to find out how many passes he'd make we multiply 18 by 4.
18*4=72
What is the area of the rectangle?
_________ft2
Answer: 180 ft2
Step-by-step explanation:
The formula for the area of a rectangle is Area = length X width. Since the length is 20 feet and the width is 9 feet , you multiply 20 X 9, which gives you 180 square feet. Hope this helps!
Which largest geometric shape can we get from a rope?
Answer:
A circle.
Step-by-step explanation:
This is it the correct answer to this question.
Hope this helps!!!
Kyle.
The Venn diagram shows the results of two events resulting from rolling a number cube.
Find P(A | B).
P(A) × P(B)
P(B)
P(A)
Answer:
P(A) x P(B)
Step-by-step explanation:
If im wrong, im so sorry
P(A | B) is found using the formula P(A AND B) / P(B), which in the context of rolling a dice and looking at events such as rolling a prime number (A) given rolling an odd number (B) would imply looking at the shared outcomes of both events and then calculating the probability.
Explanation:The Venn diagram question is asking for P(A | B), which is the probability of event A happening given that event B has happened.
The multiplication rule is an important tool to solve this problem, stating that if A and B are independent events, then P(A AND B) = P(A) × P(B).
However, the calculation of P(A | B) is different.
To find P(A | B), which is read as "the probability of A given B," you use the formula P(A AND B) / P(B).
If we consider that A is the event of rolling a prime number (e.g., numbers 2, 3, 5 in a dice) and B is the event of rolling an odd number (e.g., numbers 1, 3, 5), then the outcomes that are both prime and odd (A AND B) would be {3, 5}.
If event B has already occurred (rolling an odd number), we adjust the sample space accordingly and calculate the probability of A within this new space.
Which complex number has a distance of the root of 17 from the origin on the complex plane?
2 + 15i
17 + i
20 – 3i
4 – i
Answer:
4 -i
Step-by-step explanation:
For your condition to be met, neither the real part nor the imaginary part can exceed √17 in magnitude. That excludes the first three answer choices.
The magnitude of 4-i is ...
√(4^2 +(-1)^2) = √17.
Answer:
4 – iStep-by-step explanation:
First, we need to know that a complex number, which has a real part and an imaginary part, it's like a vector, where the horizontal coordinate is the real part, and the vertical coordinate is the imaginary part.
So, to find the distances we applied the conventional definition:
[tex]d=\sqrt{r^{2}+i^{2} }[/tex]
Where [tex]r[/tex] refers to the real part and [tex]i[/tex] refers to the imaginary part.
So, we test each answer and see which one gives us the root of 17.
Option 1.[tex]d=\sqrt{2^{2}+15^{2} }=\sqrt{4+225}=\sqrt{229}[/tex]
Option 2.[tex]d=\sqrt{17^{2}+1^{2} }=\sqrt{290}[/tex]
Option 3.[tex]d=\sqrt{20^{2}+(-3)^{2} }=\sqrt{409}[/tex]
Option 4.[tex]d=\sqrt{4^{2}+(-1)^{2} }=\sqrt{17}[/tex]
Therefore, the right answer is the last one, because the distance is the squared root of 17.
What is the input value for which g(x) = -2?
x = ?
g(x)=-2
Simplfy: y=-2
x=-9
*Look at where the points intersect
Answer:
x=-9
Step-by-step explanation:
Find the sum of the first 15 terms of 2 + 6 + 18 + 54 + ...
S_n = n(first term + a_n)/2
n = 15
S_15 = 15(2 + a_n)/2
We need a_n.
a_n = first term + d(n - 1)
a_n = 2 + d(15 - 1)
1. Find d.
2. Plug d into expression to find a_n.
3. After finding a_n, plug back into
S_15 = 15(2 + a_n)/2 to find the sum of the first 15 terms.
Take it from here.
What’s is 13.75 of 2/5
Answer:
5.5
Step-by-step explanation:
Of means multiply
13.75 * 2/5
27.5/5
5.5
[tex]\text{Hey there!}[/tex]
[tex]\text{When you come across the word of in mathematics (high learning math at that)}[/tex][tex]\text{, it means to multiply.}[/tex]
[tex]\text{So, your new equation becomes: 13.75}\times\frac{2}{5}\text{multiply those two}[/tex] [tex]\text{numbers.}[/tex]
[tex]\text{The formula to solving for these times of equation is:\ }\frac{b\times c}{d}[/tex]
[tex]\text{So,}\frac{2 \times13.5}{5}[/tex]
[tex]2\times 13.75=27.5[/tex]
[tex]\frac{27.5}{5}=27.5\div5=5.5[/tex]
[tex]\boxed{\boxed{\text{Answer: 5.5}}}\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
can anyone answer like trigonometry question or geometry
Yes, what do you need help with?
a line segment has endpoints at (-4,-6) and (-6,4) which reflection will produce and image with endpoints at (4,-6) and (6,4)
The reflection that will produce that image would be a reflection across the y-axis
The line segment should be reflected across the y-axis to obtain the desired image with endpoints at (4, -6) and (6, 4).
Explanation:To find the reflection of the line segment with endpoints (-4,-6) and (-6,4) that will produce an image with endpoints at (4,-6) and (6,4), we can use the formula for reflecting a point in the x-axis or y-axis. The reflection of a point (x, y) in the x-axis is (x, -y) and the reflection of a point (x, y) in the y-axis is (-x, y). Applying these formulas to the given endpoints, we can determine that the reflection in the y-axis will produce the desired image. So, the line segment will be reflected across the y-axis to obtain the image with endpoints at (4, -6) and (6, 4).
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The formula V=Bh, where B represents the area of the base, can be used to find the volume of a cylinder. Which formula is equivalent to V=Bh when finding the cylinders volume?
Answer:
C
Explanation:
B=Base Area
In a cylinder, the base area is a circle.
Area Circle=pi r^2
Replace base area with area of circle:
V=pi r^2 H
Answer:
Volume of Cylinder = (pi)(radius^2)(height)
John, Rick, and Molli can paint a room working together in 6 hours. Alone, John can paint the room in 12 hours. If Rick works alone, he can paint the room in 15 hours. Write an equation comparing the group rate to the sum of the individual rates. Then find how long it will take Molli to paint the room if working alone.
Answer:
[tex]\dfrac{1}{12}+\dfrac{1}{15}+\dfrac{1}{x}=\dfrac{1}{6}[/tex]
60 hours
Step-by-step explanation:
John - 12 hours
Rick - 15 hours
Molli - x hours
Together - 6 hours
Each of them can paint:
John - [tex]\frac{1}{12}[/tex] of a room per hour
Rick - [tex]\frac{1}{15}[/tex] of a room per hour
Molli - [tex]\frac{1}{x}[/tex] of a room per hour
Together - [tex]\frac{1}{6}[/tex] of a room per hour
So the equation is
[tex]\dfrac{1}{12}+\dfrac{1}{15}+\dfrac{1}{x}=\dfrac{1}{6}[/tex]
Solve this equation:
[tex]\dfrac{1}{x}=\dfrac{1}{6}-\dfrac{1}{12}-\dfrac{1}{15}\\ \\\dfrac{1}{x}=\dfrac{10-5-4}{60}=\dfrac{1}{60}\\ \\x=60[/tex]
Molli can paint the room in 60 hours.
Which of the following is the correct factored form of the given equation?
x 2 + 3x - 4 = 0
For this case we must factor the following expression:
[tex]x ^ 2 + 3x-4 = 0[/tex]
We must find two numbers that when multiplied give as result -4 and when summed give as result +3. These numbers are +4 and -1:
[tex]+ 4-1 = + 3\\4 (-1) = - 4[/tex]
Then, the factorization is given by:
[tex](x + 4) (x-1) = 0[/tex]
Answer:
[tex](x + 4) (x-1) = 0[/tex]
I need help with how to solve this problem. It is #14. It already shows the answer (1point) but I need help on how to get there please.
Answer:
Option 4: 0.554
Step-by-step explanation:
As we can see that the intervals and their frequencies are given.
We have to calculate the probability of students' score falling between 70 and 89. It will use the frequency of both intervals 70-79 and 80-89.
So, combined scores of both intervals are:
172+105 = 277
Now to find the probability
= 277/500
=0.554
So option no 4 is the correct answer ..
the expression (5x-15)° represents the measure of one interior angle of a regular triangle. what is the value of x?
The value of x in the expression (5x-15)°, which is the measure of an interior angle of a regular triangle, is 15.
Explanation:The expression (5x-15)° is given as the measure of one interior angle of a regular triangle. This is a bit complex, as regular triangles, also known as equilateral triangles, only have angles that measure 60° each. Thus, we can set up the equation 5x - 15 = 60.
Solving for x, we get:
Add 15 to both sides: 5x = 75.Then divide every term by 5: x = 15.So, the value of x that would result in each angle of an regular triangle measuring (5x-15)° is 15.
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Question 2 of 25
2 Points
For which values of x will the rational expression below be undefined? Check
all that apply.
(x-1)(x + 1)
x+2
If the denominator is 0, and the numerator ≠ 0, your answer will undefined.
If the numerator is 0, and the denominator is a number, it will always = 0.
So you can set the denominator equal to 0
x + 2 = 0 Find x, so subtract 2 on both sides
x = -2
John is 1 8 meter shorter than Paul, and Paul is 0.25 meter taller than Andrew. If John’s height is 1 3 4 meters, what is Andrew’s height?
Answer:
Andrew's height is [tex]1\frac{5}{8}[/tex] meters
Explanation:
We know that John's height is [tex]1\frac{3}{4}[/tex] meters
We are given that:
John is [tex]\frac{1}{8}[/tex] meters shorter than Paul
This means that:
Paul's height = John's height + [tex]\frac{1}{8}[/tex]
Paul's height = [tex]1\frac{3}{4} + \frac{1}{8} = 1\frac{7}{8}[/tex] meter
We are given that:
Paul is 0.25 meters taller than Andrew
This means that:
Andrew's height = Paul's height - 0.25
Andrew's height = [tex]1\frac{7}{8} - 0.25 = 1\frac{5}{8}[/tex] meters
Hope this helps :)
Answer:
1 5/8 meters....
Step-by-step explanation: