Answers
Answer:
Leg 1: 4
Leg 2: 3
Hypotenuse: 5
Step-by-step explanation:
Pythagorean Theorem
a^2+b^2=c^2
4^2+3^2=c^2
16+9=c^2
25=c^2
5=c
Hope this helps :)
Answer: side c =5
Step-by-step explanation:
We can use Pythagorean Theorem.
a squared + b squared = c squared
We know leg a is 4 units and leg b is 3 units.
4^2+3^2=16+9=25
We square root both c and 25 to get our answer.
sqr 25= sqr c squared
5=c
Related Questions
4Solve for x given that det5 31det2-4Tха
Answers
ANSWER:
The value of x is 2
STEP-BY-STEP EXPLANATION:
We have the following equation:
[tex]\det \begin{pmatrix}4 & -1 \\ -4 & x\end{pmatrix}=\det \: \begin{pmatrix}5 & 3x \\ 1 & 2\end{pmatrix}[/tex]We solve as follows:
[tex]\begin{gathered} \det \begin{pmatrix}4 & -1 \\ -4 & x\end{pmatrix}=4\cdot x-(-4)\cdot(-1)=4x-4 \\ \det \: \begin{pmatrix}5 & 3x \\ \: 1 & 2\end{pmatrix}=5\cdot2-1\cdot3x=10-3x \\ \text{therefore:} \\ 4x-4=10-3x \\ 4x+3x=10+4 \\ 7x=14 \\ x=\frac{14}{7} \\ x=2 \end{gathered}[/tex]set M below consist of the positive even integer less than or equal to 20. M = 2,4,6,8,10,12,14,16,18,20 . if a number from set M is selected at a 4random, what is the probability that the number selected will be A factor of 12
Answers
the set consist totally 10 numbers,p(s)=numbers divided by 12/total number
[tex]\text{total number of factors os 12 is 4}[/tex][tex]so,\frac{4}{20}=0.2[/tex]for a circle with a diameter of 4 centimeters, what is its exact area?
Answers
Solution
The area of a circle with diameter d is
[tex]\begin{gathered} A=\pi(\frac{d}{2})^2 \\ \\ A=\pi(\frac{4}{2})^2 \\ \\ A=4\pi \end{gathered}[/tex]Therefore, the exact area is 4π centimeters square.
These triangles are scaled copies of each other. Triangle G has area of 6. Triangle B has area of 1.5. How many times larger if the area of Triangle B than Triangle G
Answers
The area of triangle G is 4 times the area of triangle B.
The region that an object's shape defines as its area. The area of a figure or any other two-dimensional geometric shape in a plane is how much space it occupies.
Triangles G and B are scaled copies of each other.
The area of Triangle G is 6 and the area of triangle B is 1.5.
Let x be the number by which the area of triangle G is greater than the area of triangle B.
So,
area of triangle G = x times Triangle B
6 = 1.5x
x = 6/1.5
x = 4
The area of triangle G is 4 times greater than the area of triangle B.
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At a sale, a suit is being sold for 66% of the regular price. The sale price is $429. What is the regular price?
Answers
Let x be the regular price, then we can set the following equation:
[tex]x\cdot0.66=429[/tex]Solving for x we get:
[tex]\begin{gathered} x=\frac{429}{0.66}=650 \\ x=650 \end{gathered}[/tex]Determine the check digit (d) for the UPC bar code number 2-91273-05213-d. Show your work?
Answers
the given UPC bar code digit is
2- 91273 - 05213 - d
for determining d we will follow the rule
first, we sum up all the odd place numbers
like
2 + 1 + 7 + 0 +2 + 3 = 15
then multiply with 3
15 * 3 = 45
then
we sum up all the even place numbers,
9 + 2 + 9 +5 + 1 = 26
now we will add these two results
26 + 45 = 71
now we can see that 71 is 9 less than the next multiple of 10 that is 80 in this case'
80 - 71 = 9
so the answer is
d = 9 .
2
9
m
8
4
3
5 6
7
If l is parallel m and r parallel s explain how you know Angele 1 and Angle 6 are supplementary
Answers
Angle 4 and angle 6 are supplementary to each other.
Given : the two line r and s are parallel to each other and there are two transversals
And thus angle 6 and angle 4 are equal because angles corresponding angles are equal. This is because of a theorem which states that angles on the same side of the two parallel lines are equal .
And this further implies that the angle adjacent to angle 4 and angle form will form an angle whose sum would be equal to 180 degree. That is they will form a supplementary angle .
And this angle and angle 1 are equal because these two angles are corresponding angles and as mentioned above because of that theorem they are equal.
Thus from these two above mentioned arguments it is clear that angle 4 and angle 6 are supplementary angles .
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There are 96 new houses being built in a neighborhood. Last month, 1/3 of them were sold. This month, 1/8 of the remaining houses were sold. How many houses are left to be sold?
Answers
Using the given fractions we can say that there are 56 houses left to be sold.
A fraction, which also denotes a component of a whole, or a ratio is any number divided into equal parts. When expressed in common English, a fraction, such as one-half, eight-fifths, or three-quarters, specifies the number of components of a specific size.
1/3 of 96 were sold...
number of houses sold = 1/3 × 96 = 96/3 = 32
So the first month 32 houses were sold.
Number of houses left = 96 - 32 = 64 houses.
number of houses sold next month = 1/8 × 64 = 64/8 = 8
8 houses were sold the second month
number of houses left 64 - 8 = 56
Therefore using the fractions 56 houses were left to be sold.
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d what is 38 divided by 7? Round to the nearest hundredth if necessary
Answers
Choose the right graph: A,B,C Or DX < -5Then write the solution interval notation
Answers
x ≤ -5
This can be written in interval notation as :
( - ∞ , -5]
The correct option is option A
could someone please help me with math I'm lost <3
Answers
D is not the midpoint of line BG (false)
E is the midpoint of line AI (True)
M coordinates = (-1, 4)
M coordinates = (7, -3.5)
Explanation:
1) Distance or length of line BG = 5
The mid point is the point between them. The midpoint is the #rd number between line BG.
And the 3rd number is E not D.
Hence, D is not the midpoint of line BG (false)
2) Distance or length of line AI = 8
The mid point is the point between them. The midpoint is the 4th number between line AI.
And the 3rd number is E.
Hence, E is the midpoint of line AI (True)
3) A(1,2) and B(-3, 6)
Mid point formula:
[tex]\begin{gathered} M\text{ = }\frac{\mleft(x_1+x_2\mright)}{,2},\frac{y1_{}+y_2}{2} \\ M\text{ = }\frac{1-3}{2},\frac{6+2}{2} \\ M\text{ = -2/2, 8/2} \\ M\text{ = -1, 4} \end{gathered}[/tex]4) A(6, -5) and B (8, -2)
[tex]\begin{gathered} M\text{ = }\frac{(x_1+x_2)}{,2},\frac{y1_{}+y_2}{2} \\ M\text{ = }\frac{6+8}{2},\frac{-5-2}{2} \\ M\text{ = 14/2, -7/2} \\ M\text{ = 7, -3.5} \end{gathered}[/tex]If the point (3,-2) is on the graph of y = f(x), which point is on the graph of y = f-¹(x)
Answers
[tex]f^{ - 1} (x)[/tex]
IS THE INVERSE OF f(x) .TO OBTAIN THE INVERSE OF A GRAPH WE SWAP POINTS. MEANING WHAT WAS THE X COORDINATE BECOMES THE Y COORDINATE AND WHAT WAS THE Y COORDINATE BECOME THE X COORDINATE.
DOING WHAT I EXPLAINED (-2,3)IS THE POINT OF THE INVERSE GRAPH .
GOODLUCK
angle ABC is a circumscribed about point H with points of tangency D,E, F what is the perimeter of a b and c? but i know AB =7 and ac+ad+dc=6+4=10 but i dont know BC and on
Answers
Answer
Perimeter = 22 units
Explanation
To answer this, we need to note that two tangents to a circle that start from the same point usually have the same lengths.
So,
AD = AE = 6
CD = CF = 4
Since,
AB = 7 and AB = AE + EB
AE = 6
So,
AB = AE + EB
7 = 6 + EB
EB = 7 - 6
EB = 1
FB = EB = 1
So,
AC = AD + DC = 6 + 4 = 10
AB = 7
CB = CF + FB = 4 + 1 = 5
So, the perimeter of the triangle is given as the sum of all its exterior sides
Perimeter = AB + AC + CB
Perimeter = 7 + 10 + 5 = 22 units
Hope this Helps!!!
If there are 28 apples and 42 bananas for a fruit basket, fill out all of the possible ratios of apples to bananas that could be made.
Answers
Answer:
28:42
12:21
4:7
Step-by-step explanation:
To get 12:21, divide both numbers by two
To get 4:7, divide 12:21 by 3
Answer:
28:42, 21:14, 7:10.5, 56:84
There are a lot more, but for the basics of ratios you only need to know this:
- The order is very important in the ratio, whatever number came first stays in that order.
- You can only multiply or divide the same numbers. For instance, if the ratio was 1:2, you would multiply or divide the numbers by the same number.
- When you multiply or divide the ratio/numbers, you cannot not only do whole numbers, but also decimals like 0.25 or mixed decimals like 1.5.
- Remember numbers are infinite, so you can multiply or divide your ratio/numbers by any decimal or number.
Hope this helps! :D
if f(x)=x^2+4x-3 then what is the remainder when f(x) is divided by x-3?
Answers
The remainder, R(3) = 18
Explanations:The given function is:
[tex]f(x)=x^2\text{ + 4x - 3}[/tex]According to the remainder theorem, the remainder when the function f(x) is divided x-3 is gotten by substituting x = 3 into f(x)
[tex]\begin{gathered} f(3)=R(3)=3^2+4(3)-3 \\ f(3)\text{ = R(3) = 9 + 12 - 3} \\ f(3)\text{ = R(3) = 18} \end{gathered}[/tex]The remainder = 18
Given the graph of y= f (x) find the value f (1)
Answers
SOLUTION:
The graph presented is a quadratic graph with the expression f(x)
It forms a n-curve indicating a negative quadratic curve.
the vertical axis is the y-axis or f(x)-axis AND
the horizontal axis is the x-axis
f(1)
We are required to find by tracing the value of y when x=1
Final answer:
The value of y when x=1 is -3
f(1) OR y= -3
Geometry help please
Question 13 to 15
Answers
The angle relationship of the diagram is as follows:
13. ∠AGH and ∠DHG are alternate interior angles
14. ∠FGB and ∠CHE are alternate exterior angles.
15. ∠CHG and ∠DHE are vertically opposite angles.
How to find angles?When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate angles, vertically opposite angles, linear angles etc.
The parallel lines are line AB and CD.
The transversal line is FE.
Therefore,
∠AGH is congruent to ∠DHG because they are alternate interior angles.
Alternate interior angles are congruent.
∠FGB is congruent to ∠CHE because they are alternate exterior angles.
Alternate exterior angles are congruent.
∠CHG is congruent to ∠DHE because they are vertically opposite angles.
Vertically opposite angles are congruent.
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Write a simplified expression for the area of a rectangle with a length of (-3x - 4) and a width of (-9). Remember, Area = length x width
Answers
Area = length x width
Lenght: -3x-4
Width : -9
Replace the values of length and width in the area formula:
Area: (-3x-4) (-9)
Apply distributive property:
A = -3x(-9)+ (-4)(-9)
A = 27x+36
Use the distributive property to simplify the expression:
1/2{-6b+18}
PLEASE HELP ASAP I'LL GIVE 64 POINTS AND THE BRAINIEST IF YOU CAN HELP ME!!!!!!!!!!!!
Answers
The triangle is rotated 180° about the origin. Give the coordinates of the points in the image:B-5-4-3-210N45-2-3-4-5ACBCC'(Blank 1:Blank 2:Blank 3:Blank 4:Blank 5:Blank 6:
Answers
Generally when a coordinate (x , y) is rotated 180 degrees about the origin, it becomes (-x , -y).
Now, the coordinates of the vertices of the triangle will follow a similar transformation when the triangle is rotated 180 degrees about the origin, as follows:
[tex]A(0,4)\text{ will become : A1 (0, -4)}[/tex][tex]B(2,3)\text{ will become : B1(-2, -3)}[/tex][tex]C(-1,-1)\text{ will become : C1(1, 1)}[/tex]See the figure below which shows the transformation
For each relation decide whether or not it’s a function(this is one problem I do an online math program with this is considered one problem)
Answers
Answer: According to the definition, the function is a relationship between two sets of numbers that matches numbers from one set to another:
Diagram for the Illustration:
Do note! That the single input can not have two outputs.
Therefore the answer is:
[tex]\begin{gathered} \text{ Relation \lparen1\rparen}\rightarrow\text{ Not a Function} \\ \\ \text{Relat}\imaginaryI\text{on}\operatorname{\lparen}\text{2}\operatorname{\rparen}\operatorname{\rightarrow}\text{Funct}\imaginaryI\text{on} \\ \\ \text{Relat}\imaginaryI\text{on}\operatorname{\lparen}\text{2}\operatorname{\rparen}\operatorname{\rightarrow}\text{ Not a Funct}\imaginaryI\text{on} \\ \\ \text{Relat}\imaginaryI\text{on}\operatorname{\lparen}\text{2}\operatorname{\rparen}\operatorname{\rightarrow}\text{ Not a Funct}\imaginaryI\text{on} \end{gathered}[/tex][tex]\begin{gathered} \text{ Relation \lparen1\rparen}\rightarrow\text{ Not a Function} \\ \\ \text{Relat}\imaginaryI\text{on}\operatorname{\lparen}\text{2}\operatorname{\rparen}\operatorname{\rightarrow}\text{Funct}\imaginaryI\text{on} \\ \\ \text{Relat}\imaginaryI\text{on3}\operatorname{\rparen}\operatorname{\rightarrow}\text{ Funct}\imaginaryI\text{on} \\ \\ \text{Relat}\imaginaryI\text{on\lparen4}\operatorname{\rparen}\operatorname{\rightarrow}\text{ Not a Funct}\imaginaryI\text{on} \end{gathered}[/tex]Or the relation(2) and (3) are functions, and the rest are not functions.
The difference between two numbers is 22. The sum of twice the smaller number and 3 times the greater number is 246.
Answers
Given:
The difference between two numbers is 22.
The sum of twice the smaller number and 3 times the greater number is 246.
Required:
To find the two numbers.
Explanation:
Let the two numbers be x and y.
Let y be the smaller number.
The difference between two numbers is 22.
[tex]x-y=22[/tex]The sum of twice the smaller number and 3 times the greater number is 246.
[tex]2y+3x=246[/tex]Now
[tex]\begin{gathered} 2y+3(22+y)=246 \\ 2y+66+3y=246 \\ 5y=246-66 \\ 5y=180 \\ y=\frac{180}{5} \\ y=36 \end{gathered}[/tex]Now x is,
[tex]\begin{gathered} x-36=22 \\ x=22+36 \\ x=58 \end{gathered}[/tex]Final Answer:
The two numbers are 58 and 36.
f(x) = 2-4
Find f(2)
Answers
Answer:
-8
Step-by-step explanation:
So first off, x is 2-4. So that's the default. It would be -2. If you multiply -2 by 2, it is -4.
If f(x) = 8 - 10x and g(x) = 5x + 4, what is the value of (fg)(-2)?
O-196
O -168
022
O 78
Answers
Answer:
-168
Step-by-step explanation:
f(-2) = 8-10(-2)
f(-2) = 28
g(-2) = 5(-2)+4
g(-2) = -6
28(-6) = -168
Five more than the product of a number and 8 equals 3 Use y for the unknown variable
Answers
Answer
y = -1/4
Step-by-step explanation:
Let the unknown variable be y
5 more than the product of a number and 8 equals to 3 can be expressed mathematically as
Recall, that the unknown variable is y
5 + (8 * y) = 3
Open the parenthesis
5 + 8y = 3
Substract 5 from both sides
5 - 5 + 8y = 3 - 5
8y = -2
y = -2/8
y = -1/4
Find (y + 3)(y2 + 8y – 2). (y + 3)(y2 + 8y – 2) =
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
(y + 3)(y² + 8y – 2). (y + 3)(y² + 8y – 2)
simplify
Step 02:
We must apply the algebraic rules to find the solution.
(y + 3)(y² + 8y – 2). (y + 3)(y² + 8y – 2)
Part 1:
(y + 3)(y² + 8y – 2) = y³ + 8y² - 2y + 3y² + 24y - 6
= y³ + 11y² + 22y - 6
Part 2:
(y³ + 11y² + 22y - 6) * (y³ + 11y² + 22y - 6) =
[tex]y^6+11y^5+22y^4-6y^3+11y^5+121y^4+242y^3-66y^2+22y^4+242y^3+484y^2-132y-6y^3-66y^2-132y+36[/tex][tex]y^6+22y^5+165y^4+472y^3+352y^2-264y\text{ }+36[/tex]That is the full solution.
Write a polynomial function of least degree with real coefficients in standard form that has the given zeros.–2, –4, –3 + 4i x2 + 6x + 8x4 + 12x3 + 198x + 200x4 + 12x3 + 69x2 + 198x + 200x4 + 69x2 + 198x + 200
Answers
Write the polynomial function of least degree with real coefficients in standard form:
According to the complex conjugate root theorem, if a complex number a+ib is a zero of a polynomial, then its conjugate a-ib is also a zero of than polynomial.
–3 + 4i is zero of the polynomial. So, by complex conjugate root theorem -3-4i is also a zero of required polynomial.
If c is a zero of p(x), then (x-c) is a factor of p(x).
–2, –4, –3 + 4i, -3-4i are zeroes of the polynomials. So, (x+2), (x+4), (x+3-4i), (x+3+4i) are the factors of the required polynomial.
Let the required polynomial be p(x), so
[tex]\begin{gathered} p(x)=(x+2)(x+4)(x-3+4i^2)(x+3+4i^2)_{} \\ P(x)=(x^2+2x+4x+8)(x+3)^2-(4i^2)^2) \\ (a^2-b^2)=(a-b)(a+b) \\ p(x)=x^2+6x+8)(x^2+6x+9-16i^2 \\ i^2\text{=-1} \\ p(x)=(x^2+6x+8)(x^2+6x+9-16(-1) \\ p(x)=(x^2+6x+8)(x^2+6x+9+16^{} \\ p(x)=(x^2+6x+8)(x^2+6x+25) \end{gathered}[/tex][tex]\begin{gathered} p(x)=(x^2+6x+8)(x^2+6x+25) \\ p(x)=x^2(x^2+6x+8)+6(x^2+6x+8)+25(x^2+6x+8) \\ p(x)=x^4+12x^3+69x^2+198x+200 \end{gathered}[/tex]
Combining like terms, we get
Therefore, the required polynomial is x^2 + 12x^3 +69x^2 + 198x + 200
Hence the correct answer is Option C
Please answer urgently.
I will give brainliest to best answer.
All answers given will be appreciated.
3x( 4x +7 ) + 3( 8 + 2 ) = 11( 2x + 3 ) + 11
?
Answers
Answer:
[tex]x=\dfrac{1 +\sqrt{673}}{24}, \quad x=\dfrac{1 -\sqrt{673}}{24}[/tex]
Step-by-step explanation:
Given equation:
[tex]3x( 4x +7 ) + 3( 8 + 2 ) = 11( 2x + 3 ) + 11[/tex]
Distribute the parentheses:
[tex]\implies 12x^2+21x+24+6=22x+33+11[/tex]
[tex]\implies 12x^2+21x+30=22x+44[/tex]
Subtract 22x from both sides:
[tex]\implies 12x^2+21x+30-22x=22x+44-22x[/tex]
[tex]\implies 12x^2-x+30=44[/tex]
Subtract 44 from both sides:
[tex]\implies 12x^2-x+30-44=44-44[/tex]
[tex]\implies 12x^2-x-14=0[/tex]
Use the quadratic formula to solve for x.
Quadratic Formula
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]
[tex]\implies a=12, \quad b=-1, \quad c=-14[/tex]
Therefore:
[tex]\implies x=\dfrac{-(-1) \pm \sqrt{(-1)^2-4(12)(-14)}}{2(12)}[/tex]
[tex]\implies x=\dfrac{1 \pm \sqrt{1+673}}{24}[/tex]
[tex]\implies x=\dfrac{1 \pm \sqrt{673}}{24}[/tex]
Larry needs to change a light bulb in the celling. Larry leans a 16 foot ladder against the wall with its base 5 feet away from the wall. Which is the closest to the distance of the height of the wall to the top of the ladder?
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
ladder = 16 feet
base = 5 feet
height = ?
Step 02:
Pythagoras Theorem Formula
c ² = a² + b²
16 = c
5 = b
height = a
16² = a ² + 5²
16² - 5² = a²
[tex]\sqrt[]{231\text{ }}\text{ = a}[/tex]15.2 = a
The answer is:
The distance to the top of the ladder is 15.2 feet
simplify with like terms; 3(x - 5)
Answers
We are given the following expression:
[tex]3(x-5)[/tex]We can apply the distributive property to get:
[tex]3x-15[/tex]Since there are no like terms this expression can't be simplified any further.
