If the square sum of the perpendicular and base is less than the square of hypotenuse then the angle will be an obtuse angle. Then the correct option is C.
What is a Pythagoras theorem?The Pythagoras is the sum of the square of two sides is equal to the square of the longest side. And it is given as
P² + B² = H²
A triangle with side lengths of 6 cm, 10 cm, and 12 cm.
We know that if the square sum of the perpendicular and base is greater than the square of hypotenuse then the angle will be an acute angle.
Ans if the square sum of the perpendicular and base is less than the square of hypotenuse then the angle will be an obtuse angle.
Then we have
6² + 10² < 12²
Then the angle will be an obtuse angle.
More about the Pythagoras theorem link is given below.
https://brainly.com/question/343682
Answer: C
Explanation: Obtuse, because 6^2+10^2<12^2
WILL GIVE BRAINLIEST!!!
Solve 3(2x - 3) = 15. Explain ALL steps.
Answer:
x=4
Step-by-step explanation:
distributive property goes first.
you get 6x-9=15
add 9 on both sides so 9 cancells out on the left side.
you get 6x=24
divide by 6 and you get x=4
A right triangle has leg lengths of 9 units and 12 units. Write an equation that can be
used to determine the length of the hypotenuse, c .
The Pythagorean Theorem: [tex]a^2+b^2=c^2[/tex]
a and b are the two legs in a right trianglec is the hypotenuse (the longest side of a right triangle; opposite the 90° angle*keep in mind that this theorem applies only to right trianglesSolving the QuestionWe're given:
Legs = 9 units and 12 unitsHypotenuse = cPlug these measurements into the Pythagorean theorem:
[tex]a^2+b^2=c^2\\9^2+12^2=c^2[/tex]
⇒ Combine like terms:
[tex]81+144=c^2\\c^2=225[/tex]
Answer[tex]c^2=225[/tex]
Please help! Easy for everyone but me for some reason.
What's the value of x? Show your work.
Answer:
x = 9
Step-by-step explanation:
using Pythagoras' identity in the right triangle
the square on the hypotenuse is equal to the sum of the squares on the other 2 sides , that is
x² + 6² = ([tex]\sqrt{117}[/tex] )²
x² + 36 = 117 ( subtract 36 from both sides )
x² = 81 ( take square root of both sides )
x = [tex]\sqrt{81}[/tex] = 9
What’s the area of the circle?
r= 4m
Answer:
50.3
Set A to the value of pi times the radius squared.
[tex]4^2 = 4 * 4 = 16\\\\A = \pi *r^2(4^2) = 50.26548245...[/tex]
PLS I really need this a have 40 questions due tomorrow :( (please help anyone) 16 points
what is x if 1/4x = 9?
Answer:
x is 36
Step-by-step explanation:
the way to find out is 1/4 multiplied by what gives you 9. 9 divided by 1/4 is 36. 36 1/4's gives you 9.
Answer: 2
Step-by-step explanation:first u subtract 1-9=8then u divide 4/8=2 tell me if wrong
From first principle, find the derivative of y=2x^3+x²+4x with respect to X
Answer:
[tex]derivative \: of \: y = 6 {x}^{2} + 2x + 4[/tex]
Step-by-step explanation:
we know that
[tex] \frac{d}{dx} {x}^{n} = n {x}^{n - 1} [/tex]
Now the derivative of y=2x³+x²+4x
[tex] \frac{dy}{dx} = \frac{d}{dx} (2 {x}^{3} + {x}^{2} + 4x)[/tex]
[tex] \frac{dy}{dx} = \frac{d}{dx} (2 {x}^{3} ) + \frac{d}{dx}( {x}^{2} ) + \frac{d}{dx} (4x)[/tex]
[tex]\frac{dy}{dx} = 2(\frac{d}{dx} {x}^{3} ) + \frac{d}{dx} {x}^{2} + 4(\frac{d}{dx} x)[/tex]
here
[tex]\frac{d}{dx} {x}^{3} = 3 {x}^{2} [/tex]
[tex]\frac{d}{dx} {x}^{2} = 2x[/tex]
[tex]\frac{d}{dx} x = 1[/tex]
Now
[tex]\frac{dy}{dx} = 2(3 {x}^{2} ) + 2x + 4(1)[/tex]
[tex]\frac{dy}{dx} = 6 {x}^{2} + 2x + 4[/tex]
I hope it helped you
The mean of 4, 10, 3, 6, a, 9 and 10 is 7, find the value
of a
Answer:
The value of a is 7.
Step-by-step explanation:
To calculate mean, add all of the numbers in the set and divide by the number of terms in said set. There are 7 numbers in this set, so the equation can be set up as follows.
(4 + 10 + 3 + 6 + a + 9 + 10)/7 = 7
Simplify the terms on the top.
(42 + a)/7 = 7
Multiply both sides by 7.
42 + a = 49
Subtract both sides by 42.
a = 7.
Proof:
(4 + 10 + 3 + 6 + a + 9 + 10)/7 = 7
Substitute variable.
(4 + 10 + 3 + 6 + 7 + 9 + 10)/7 = 7
Add in the parenthesis.
49/7 = 7
Divide.
7 = 7.
How to solve 3x - 1/2 = 8 1/2 please no links and do it step by step
Answer:
[tex]x=\frac{3}{2}[/tex]
Step-by-step explanation:
Step 1. Put each term in [tex]3x-\frac{1}{2}[/tex] over the common denominator 2.
[tex]\frac{6x}{2}-\frac{1}{2}[/tex]
Therefore we have [tex](\frac{6x}{2}-\frac{1}{2})=4[/tex]
Step 2.
Combine [tex]\frac{6x}{2}-\frac{1}{2}[/tex] into a single fraction.
[tex]\frac{6x-1}{2}[/tex]
Therefore we have [tex](\frac{1}{2}(6x-1))=4[/tex] or [tex]\frac{6x-1}{2}=4[/tex]
Step 3.
Multiply both sides by a constant to simplify the equation.
Multiply both sides of [tex]\frac{6x-1}{2}=4[/tex] by 2:
[tex]\frac{2*(6x-1)}{2}=4*2[/tex]
Step 4.
Cancel the common terms in the numerator and denominator of [tex]\frac{2*(6x-1)}{2}[/tex]
Then we get [tex]\frac{2}{2}*(6x-1)[/tex] which simplifies to [tex](6x-1)[/tex]
So all together we have [tex](6x-1)=2*4[/tex]
Step 5.
Multiply 2 and 4 together and remove the parenthesis.
[tex]6x-1=8[/tex]
Step 6.
Isolate terms with the variable x to the left hand side.
So add 1 to both sides:
[tex]6x+(1-1)=8+1[/tex]
Evaluate [tex]1-1=0[/tex] which cancels out
Step 7.
Add the like terms on the right side:
[tex]6x=9[/tex]
Step 8.
Divide both sides by a constant to simplify the equation.
Divide both sides of [tex]6x=9[/tex] by 6.
[tex]\frac{6x}{6} =\frac{9}{6}[/tex]
Any non-zero number divided by itself is 1.
[tex]x=\frac{9}{6}[/tex] which simplifies to [tex]x=\frac{3}{2}[/tex]
Find the solution to the system of equations.
You can use the interactive graph below to find the solution.
y= 22 + 3
y = -3.2 + 3
2=
y =
y
Answer:
Step-by-step explanation:
y=2x+3
y=-3x+3
**This is what's on the image.**
You need to aline the two together.
2x+3 = -3x+3
Add 3x both sides
3x+2x+3=3
5x+3=3
Now subtract 3 from both sides
5x=3-3
x= 0
This should be a vertical line from (0,0) to above since there is no slope you should have a straight line that is vertical.
(WILL MARK BRAINLIST)
Write an inequality to represent the graph.
у
-5
4
3
(0, 2)
2 1
x
x
-5 -4 -3 -2 -1 0
-1
2
4 5 6 7 8 9 10
(4,-1)
-2
-3
-4
-51
-6
-7
-8
-9
-Previous Question
Question 1 (Answered)
x2 +9 x- 22,
Which graph shows the solution set of
20?
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8
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Answer...
Ok done. Thank to me >:3
The sum of 5 times a number and 7 equals 8
Answer:
0.2
Step-by-step explanation:
the sum of 5 times 0.2 and 7 equals 8
Jean estimates that her friend completes a new level of a video game on the first try 20% of the time. She conducts a simulation to predict how many times out of 80 her friend would complete a new level on the first try. Jean uses a random number generator. Every digit that is 8 or 9 represents completing the level. Examine the table.
The probability of the friend completing the new level in her first try is 22.5%
What is probability?This is a concept that is used to talk about the likelihood or the chances of an event occuring.
For the digit 8, the frequency is 7
For the digit 9, the frequency is 11
The total number of frequencies is given as
10 + 9 + 6+ 7 + 8 + 12 + 4 + 6 + 7 + 11 = 80
7 + 11 = 18
Probability = 18/80
= 0.225 x 100
= 22.5%
Read more on probability here: https://brainly.com/question/251701
The shorter leg of a right triangle has a measure of x + 5. The longer leg is one less than three times the length of the shorter leg. The hypotenuse is thirteen more than two times the shorter leg. The area of the triangle, A, is 2.5 times the magnitude of the perimeter.
Create a system of equations to model the situation above. Determine if there are any solutions, and, if possible, whether or not they are viable.
How many total possible solutions of the form (x, A) are there for this situation?
How many total viable solutions of the form (x, A) are there for this situation?
Answer:
Given:
[tex]\textsf{Shorter leg}=(x+5)[/tex][tex]\textsf{Longer leg}=3(x+5)-1[/tex][tex]\textsf{Hypotenuse}=2(x+5)+13[/tex][tex]\sf A=2.5P\quad \textsf{(where A is area and P is perimeter)}[/tex][tex]\begin{aligned} \textsf{Perimeter} & =\textsf{shorter leg + longer leg + hypotenuse}\\ & = (x+5)+[3(x+5)-1]+[2(x+5)+13]\\ & = x+5+3x+15-1+2x+10+13\\ & = 6x+42\end{aligned}[/tex]
[tex]\begin{aligned} \textsf{Area} & =\dfrac12\textsf{(shorter leg)(longer leg)}\\ & =\dfrac12(x+5)[3(x+5)-1]}\\ & =\dfrac12(x+5)(3x+14)\\ & = \dfrac12(3x^2+29x+70)\\ & = \dfrac32x^2+\dfrac{29}{2}x+35 \end{aligned}[/tex]
[tex]\begin{aligned} \textsf{Area} & =2.5 \sf (Perimeter)\\ \implies \dfrac32x^2+\dfrac{29}{2}x+35 & =\dfrac52(6x+42)\\ 3x^2+29x+70 & =5(6x+42)\\ 3x^2+29x+70 & =30x+210\\ 3x^2 -x-140 & =0\\ 3x^2-21x+20x-140 & =0\\ 3x(x-7)+20(x-7) &=0\\ (x-7)(3x+20)& =0\end{aligned}[/tex]
Therefore:
[tex](x-7)=0 \implies x=7[/tex]
[tex](3x+20)=0 \implies x=-\dfrac{20}{3}[/tex]
[tex]x=-\dfrac{20}{3}[/tex] is not a viable solution as when inputting this into the formula for the shorter leg, it gives a negative value:
[tex]\textsf{Shorter leg}=-\dfrac{20}{3}+5=-\dfrac53[/tex]
As distance cannot be negative, this is not a viable solution.
When x = 7:
[tex]\textsf{Shorter leg}=7+5=12[/tex]
[tex]\textsf{Longer leg}=3(7+5)-1=35[/tex]
[tex]\textsf{Hypotenuse}=2(x+5)+13=37[/tex]
[tex]\textsf{Perimeter}=6(7)+42=84[/tex]
[tex]\textsf{Area} & =\dfrac32(7)^2+\dfrac{29}{2}(7)+35=210[/tex]
Therefore, there is one viable solution. This solution in the form (x, A) is (7, 210)
Twelve identical cylindrical pop cans are placed in a box. If sand fills the space between the pop cans and the cans and the sides of the box, what volume of sand is needed?
Answer:
Step-by-step explanation:
I don't see any information on dimensions of the cans or box, so I'll assume the question wants a general solution.
Three steps will result in the volume of sand required to fill the remaining space in the box.
1. Calculate the volume of a can using the equation for the volume of a cylinder: Vol = πr²h
2. Multiply the can volume by 12. This will give the total volume of the 12 cans in the box.
3. Calculate the volume of the box: Volume = (Base)(Width)(Height)
[Make sure the units are the same as those used in calculating the can volume. E.g., if the can is calculated with cm as the measue, the box dimensions must also be cm]
4. Subtract the volume of the12 cans (from step 2) from the volume of the box.
The result from 4 will be the volume of sand required to fill the box containing 12 cans.
I'm not clear why filling the box with sand is important, but perhaps it will absorb any soda released from cans broken when the heavy box is dropped by the person shocked that 12 cans of pop could be so heavy.
What is the percent of increase from 26 to 91?
Answer:
250
Step-by-step explanation:
The equation y = 8x 12, where x is the number of hours and y is the total cost, represents what the surf instructor charges for lessons. use this information to describe how to draw the line on a graph.
Answer:
Use points (0,12) and (1,20) on graphing paper or a program to find final answer.
Step-by-step explanation:
In the problem, I was unable to understand the equation so I am presuming the equation actually means y=8x+12
Whenever you graph a Linear Function you always need two points. The first point is always easy to acquire.
You can plug in any value for x, which will be your x cordinate and the output (solution) of the equation will be you y cordinate.
I'm plugging in 0 for X first.
y=8x+12
y=8(0) +12
y=12
We have our first point as (0,12)
Now you can plug in any other number for X other then Zero.
I choose 1 this time for X.
y=8x+12
y=8(1)+12
y=8+12
y=20
We now have our second point (1,20). Two points will be enough to graph this graph, you can graph these two points and then draw a line if on paper or use an application and get the line that way.
Answer:
Use the rise/run strategy to draw the line. Start at the y-intercept (0, 12), and count 8 up and 1 to the right to the point (1, 20). Then, draw a line through the points. Test the point (3,36) in the equation y = 8x + 12 to verify that the line is correct.
Step-by-step explanation:
got it right
Point P is located at (4, 6) on a coordinate plane. Point P will be reflected over the x-
axis. What will be the coordinates of the image of point P? What transformation was
performed on the given figure
1. (8,4)
2. (4-6)
3. (4,28)
4. (24,4)
Answer:
2.
Step-by-step explanation:
it's the reciprocal
so it's gonna reflect
pls help what is the circumstance of a circle with a diameter of 8 feet? Use 3.14 for n
Answer:
D. 25.12 feet
Step-by-step explanation: C= r(pi)^2
Using the tree diagram below, what is the probability of getting tails and an even number?
hi the awnser us defiantly going to be that I 56
Step-by-step explanation:
edge
A square pyramid is 6.3 in by 4 in by 4 in what is the surface area of the pyramid
Answer:
32.2 square feet
What is the area of a square enclosure that uses 320 meters of fencing?
Answer:
A = 6400 m²
Step-by-step explanation:
the sides s of a square are congruent , then
s = 320 ÷ 4 = 80 m
tahe area (A) of a square is calculated as
A = s² = 80² = 6400 m²
The required area of square, having side 80 meters, is 6400 square meters.
What is square ?A square is a quadrilateral with four equal sides and four equal angles that is a regular quadrilateral. The square's angles are at a straight angle or 90 degrees.
Given that,
The length of fencing enclosure a square = 320 meters,
Let the side of the square is a meter,
According to given condition, perimeter of square,
4a = 320
a = 80
Since, the area of square having side a, is a²
Area = a²
Area = (80²)
Area = 6400 square meters.
The area of square, having side 80, is 6400 square meters.
To learn more about Square on:
https://brainly.com/question/28776767
#SPJ2
What is the circumference of the following circle? or r=5
Answer: [tex]C=31.4[/tex]
Step-by-step explanation: When you are finding the circumference of a circle you use the formula
[tex]C=2\pi r[/tex]
[tex]C=2*3.14 *5[/tex]
[tex]C=31.4[/tex]
If the percent of discount of an item is 25 percent and the sale price is $40 what is the original price
Answer:
$53.33
Step-by-step explanation:
40/1 - .25
40/.75 = $53.33
Helpppp I will mark brainliest
Problem 25
Point P has the x coordinate x = -5, while point Z has the x coordinate x = 5. This is a distance of 10 units on the number line. Segment PZ is 10 units long which is the base of the triangle.
The height of the triangle is 8 units because it's the vertical distance from R to segment PZ. Notice we go from x = 4 to x = -4. The base and height are always perpendicular to one another.
Area = (base*height)/2
Area = (10*8)/2
Area = 80/2
Area = 40
Answer: 40 square units==========================================================
Problem 26
I'm not sure about this one because the instructions mention a grid, but I don't see any grid lines here. I'm not sure if the grid lines are just really faint or if your teacher forgot to put them in.
Two angles are supplementary. The larger angle is 15 more than 10 times the smaller angle. FInd the measure of each angle.
[tex]\text{Larger angle} =x\\\\\text{Smaller angle} =y\\ \\\text{According to the condition,}\\\\x=10y+15\\\\\text{The two angles are supplementary, so their sum is}~ 180^{\circ} \\\\x+y=180\\\\\implies 10y+15 +y = 180\\\\\implies 11y = 180-15\\\\\implies 11y=165\\\\\implies y = \dfrac{165}{11}\\\\\implies y = 15\\\\\text{So,} ~x =180-15 = 165\\\\\text{Hence the larger angle is}~ 165^{\circ}~ \text{and the smaller angle is }15^{\circ}[/tex]
15. Which three lengths could be the lengths of the sides of a triangle?
Step-by-step explanation:
11 cm, 6 cm, 17 cm
Answer::
11cm, 6cm, 17cm
step by step explanation:
the correct answer is 11cm 6cm and 17cm
because in a right angled triangle, the square of the hypothenus is equal to the square of the sum of the other two sides
hypothenus= 17cm other two sides=11cm and 6cm
Need help with khan geometry no link pls just answer
Angles ABC and CBD are complementary - they add up to 90°. This means
(4x + 52°) + (8x - 10°) = 90°
Solve for x :
12x + 42° = 90°
12x = 48°
x = 4°
It follows that angle CBD has measure
4 • 4° + 52° = 16° + 52° = 68°
a fishing tackle box is 13 inches long 6 inches wide and 2 1/2 inches high. what is the volume of the tackle box
Answer:
195 cubic inches
Step-by-step explanation:
A fishing tackle box is 13 inches long, 6 inches wide, and inches high. What is the volume of the tackle box? SOLUTION: The volume of the tackle box is 195 cubic inches.