Answer:
It's an acute angled triangle.
Step-by-step explanation:
15^2 = 225
12^2 = 144
10^2 = 100
Adding:
10^2 + 12^2 = 244.
So as 15^2 < 12^2 + 10^2 this is an acute angled triangle.
The triangle with given sides of 10 inch , 12 inch and 15 inch is an acute angled triangle.
The length of three sides of a triangle are given
Length of first side = 10 inch
Length of second side = 12 inch
Length of third side = 15 inch
here we can observe that the third side is the longest side for the given triangle
Let us check whether the given triangle satisfies the Pythagorean theorem
For a right angled Pythagorean theorem is given by equation (1)
[tex]\rm H^2 = P^2 + B^2 .........(1)\\where \\H = Hypotenuse\\P = Perpendicular\\B = Base\\[/tex]
From the given data we can conclude that
[tex]\rm 15 ^2 = 225 \\10^2 = 100\\12^2 = 144 \\15^2 \neq 10^2 +12^2 \\\\Since\; 225\neq 244[/tex]
The given triangle does not satisfies the Pythagorean theorem and hence it is not a right angled triangle
also [tex]225< 244[/tex]
So we can conclude that it is an acute angled triangle.
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The domain of a function is representative of which one of the following
characteristics of the function?
A. all possible outputs of the function
B. all possible F(x) values of the function
c. all possible (x, y) coordinates
D. all possible inputs of the function
Answer:
D. all possible inputs of the function
Step-by-step explanation:
Lets look at the options one by one
A. all possible outputs of the function
This is not the correct option because the possible outputs are range of the function
B. all possible F(x) values of the function
Not correct because the f(x) values are the output of the function.
c. all possible (x, y) coordinates
This is also not correct because domain only consists of all the values of independent variable that make the function produce some output
D. all possible inputs of the function
This is the correct answer because domain is the set of all values of independent variable for which the function is not undefined ..
Find the missing factor.
4b2 + 17b + 15 = (b + 3)(
)
Answer:
(4b + 5)
Step-by-step explanation:
To get 4b^2 you already have b^2 if you put b inside the second set of brackets. But that would mean you don't have 4 anywhere to get 4b^2.
So the first step has to be
(b + 3)(4b
Now look at the 15 for a moment. It is plus 15. The only way you can get a plus 15 is if both signs are plus (after the b terms) or both terms are minus.
The middle term (17b) is plus so both terms after b are plus.
(b + 3)(4b +
Now we need something that multiplies to 15. 3*5 = 15. So the term you want is 5.
(b + 3)(4b + 5)
Does the middle term work?
5*b + 3*4b = 5b + 12b = 17b
Everything looks fine.
The second factor is 17b.
The difference of 2 numbers is 21 and the quotient of the equation is 4 then what are the two numbers?
Answer:
The two numbers are 28 and 7.
Step-by-step explanation:
Let the first number be x
Let the second number be y
The difference of x and y is x-y=21
The quotient of two numbers is x/y = 4
x-y =21 (This is equation 1)
x/y=4 (This is equation 2)
By solving equation 2 we will get the value of x.
x/y=4
x=4y (Lets call it equation 3)
Now, put the value of x(equation 3) in (equation 1)
x-y=21
4y-y=21
3y=21
y=21/3
y=7
Now put the value of y in equation 3 to get the value of x
x=4y
x=4(7)
x=28
Solution Set {(x,y)(28,7)}
Answer:
28 and 7
Step-by-step explanation:
Choose the correct description of the graph of the compound inequality (1 point)
x − 3 < −11 or x + 5 greater than or equal to 14.
A)A number line with a closed circle on −8, shading to the left, and an open circle on 9, shading to the right
B)A number line with an open circle on −8, a closed circle on 9, and shading in between
C)A number line with an open circle on −8, shading to the left, and a closed circle on 9, shading to the right
D)A number line with a closed circle on −8, an open circle on 9, and shading in between
Heyyyyyyy
C is the answer
I had the same ques
L m a o
Answer:
C) A number line with an open circle on −8, shading to the left, and a closed circle on 9, shading to the right
Step-by-step explanation:
Given compound inequality,
x − 3 < −11 or x + 5 greater than or equal to 14.
⇒ x − 3 < −11 or x + 5 ≥ 14.
⇒ x < - 11 + 3 or x ≥ 14 - 5
⇒ x < -8 or x ≥ 9
Thus, the possible values of x are all real numbers less than -8 excluding -8 and all real numbers greater than 9 including 9,
That is, x ∈ (-∞, -8 ) ∪ [ 9, ∞ )
In the number line the numbers are arranged in ascending order from left to right also in the interval the excluded number is represented by open circle and included number is represented by closed circle.
Hence, correct option is,
A number line with an open circle on −8, shading to the left, and a closed circle on 9, shading to the right
Which equation can be used to solve for b?
b = (8)tan(30o)
b = 8/tan(30o)
b = (8)sin(30o)
b = 8/sin(30o)
Answer:
b=(8) tan (30°)
Step-by-step explanation:
We can use trigonometric ratios to solve a right triangle if the length of one side and an acute angle is known.
In the provided figure the side b is opposite the acute angle BCA while a is adjacent.
Therefore we can use the tangent to find the value of b.
Tan 30 =b/a
Tan 30 =b/8ft
b=(8) tan 30°
Answer:
A. (8)tan(30)
Step-by-step explanation:
Factoring Trinomials (
Factor each completely.
1) 3p² – 2p - 5
Answer:
factors (3p - 5) and (p + 1)
Step-by-step explanation:
The quadratic formula always "works" when you're looking to factor a quadratic expression or equation. Here, the coefficients are a = 3, b = -2 and c = -5. The discriminant is thus b²-4ac, which here is (-2)²-4(3)(-5), or 4+60, or 64. Because this discriminant is positive, we know that the quadratic has two real, unequal roots. These roots are:
-(-2)±√64 2 ± 8
p = ------------------- = --------------- = 10/6 and -1, or 5/3 and -1.
2(3) 6
These roots correspond to the factors (3p - 5) and (p + 1).
A roller coaster can take 162 passengers around the track in 9
minutes. The roller coaster operates at a constant rate.
How many passengers can the roller coaster take around the track per minute?
Answer: 18 people per minute
Step-by-step explanation: 162 divide by 9 equals 18
To find the answer, divide 162 by 9, since you divide 9 by 9 to get 1 minute.
162/9=18
The roller coaster takes 18 passengers around the track per minute.
Hope this helps!
Ms. Cole has 4 yards of string. She cuts the string into pieces that are each 1/2 yard long. How many pieces of string does Ms. Cole have?
Answer:
8
Step-by-step explanation:
got it right
Answer:
8
Step-by-step explanation:
got it right in Ed
Sienna has $8 and is saving $3 per week. Jacob has $6 and is saving $4 per week. Which model represents the equatio
that can determine when Sienna will have the same amount of money as Jacob?
Let the amount saving by Sienna and Jacob be x
Sienna has $8 and is saving $3 per week
So the equation will be 3x + 8
Jacob has $6 and is saving $4 per week
So the equation will be 4x + 6
Sienna will have same amount as Jacob, so
3x + 8 = 4x + 6
So the model two will represents the equation that Sienna will have same amount as Jacob.
Answer:
Model B
Step-by-step explanation:
Model B correctly displays sienna's and jacob's equations.
For sienna, the $8 can be represented as 8 unit blocks, which is displayed in model 2. The $3 per week can be represented as 3 x tiles, as shown in the picture, because it represents how many weeks.
For jacob, the model shows 6 unit blocks which represents his 6 dollars. The $4 per week is represented with the 4 x tiles, and we use x tiles because we are calculating how many weeks.
If you apply the below transformations to the square root parent function,
F(x) = VX, what is the equation of the new function?
• Shift 12 units right.
• Shift seven units down.
Answer:
We have the following function: [tex]f(x) =\sqrt{x}[/tex]
We know that given a function f(x), the function g(x) = f(x+m) is exactly the same function f(x) but shifted m units to the left.
Therefore, to shift the function 12 units right we should:
[tex]f(x) =\sqrt{x}[/tex] ⇒ [tex]f(x-12) =\sqrt{x-12}[/tex]
We know that given a function f(x), the function g(x) = f(x)+m is exactly the same function f(x) but shifted m units up.
Therefore, to shift seven units down we should:
[tex]f(x) =\sqrt{x}[/tex] ⇒ [tex]f(x) =\sqrt{x}-7[/tex]
Let f(x)=x2+4x+12 . What is the vertex form of f(x)? What is the minimum value of f(x)?
[tex]\bf \textit{vertex of a vertical parabola, using coefficients} \\\\ f(x)=\stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{+4}x\stackrel{\stackrel{c}{\downarrow }}{+12} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{4}{2(1)}~~,~~12-\cfrac{4^2}{4(1)} \right)\implies (-2~~,~~12-4)\implies (-2~,~8)[/tex]
well, the quadratic has a leading term with a positive coefficient, meaning is a parabola opening upwards, like a "bowl", comes from above down down down, reaches a U-turn, namely the vertex, and goes back up up up.
so the minimum value is at the vertex of course, and the minumum is well, just the y-coordinate of the vertex, 8.
Martha is training for a duathlon, which includes biking and running. She knows that yesterday she covered a total distance of over 55.5 miles in more than than 4.5 hours of training. Martha runs at a speed of 6 mph and bikes at a rate of 15.5 mph.
Answer:
Distance: 6x + 15.5y > 55.5
Time: x + y > 4.5
Step-by-step explanation:
We are given that Martha is training for a duathlon and she covered a total distance of over 55.5 miles in more than than 4.5 hours of training.
Also, she runs at a speed of 6 mph and bikes at a rate of 15.5 mph.
We are to write inequalities representing the distance she traveled and the total time she spent training.
Distance: 6x + 15.5y > 55.5
(formula for distance = speed x time so speeds for running and biking are multiplied by their number of hours)
Time: x + y > 4.5
(she trained for more than 4.5 hours, x hours for running and y hours for biking.
The formula V = πr2h gives the volume of a cylinder with radius r and height h. Solve the formula for r. Show your work.
Answer:
[tex]r = \sqrt{\frac{V}{\pi h}}[/tex]
Step-by-step explanation:
The formula to calculate the volume is:
[tex]V = \pi r^{2} h[/tex]
Where r is the radius and h the height of the cylinder.
We need to isolate r. First step is to move pi and h, they can go to the other side dividing.
[tex]V = \pi r^{2} h\\ \pi r^{2} h = V\\ \pi r^{2} =\frac{V}{h}\\r^{2} =\frac{V}{\pi h}[/tex]
Second step, as radius is with an exponent of two, we can use square root.
[tex]r^{2} =\frac{V}{\pi h}\\\sqrt{r^{2}} = \sqrt{\frac{V}{\pi h}}[/tex]
Finally, we can isolate radius - r
[tex]r = \sqrt{\frac{V}{\pi h}}[/tex]
(25 points) Can someone please solve this I just need to see how its solved to understand
x = total amount of students in 8th Grade.
we know only one-thrid of the class went, so (1/3)x or x/3 went.
we also know 5 coaches went too, and that the total amount of that is 41.
[tex]\bf \stackrel{\textit{one third of all students}}{\cfrac{1}{3}x}+\stackrel{\textit{coaches}}{5}=\stackrel{\textit{total}}{41}\implies \cfrac{x}{3}+5=41\implies \cfrac{x}{3}=41-5 \\\\\\ \cfrac{x}{3}=36\implies x=3(36)\implies x=108[/tex]
now, to verify, well, what do you get for (108/3) + 5?
Mrs. Culland is finding the center of a circle whose equation
is x2 + y2 + 6x + 4y - 3 = 0 by completing the square. Her
work is shown.
x2 + y2 + 6x + 4y – 3 = 0
x2 + 6x + y2 + 4y - 3 = 0
(x2 + 6x) + (y2 + 4y) = 3
(x2 + 6x + 9) + (x2 + 4y + 4) = 3 + 9 + 4
Answer:
The center of the circle is (-3,-2)
Step-by-step explanation:
we know that
The equation of a circle in standard form is equal to
[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]
where
(h,k) is the center
r is the radius
In this problem we have
[tex]x^{2} +y^{2}+6x+4y-3=0[/tex]
Completing the square
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex](x^{2}+6x) +(y^{2}+4y)=3[/tex]
Complete the square twice. Remember to balance the equation by adding the same constants to each side.
[tex](x^{2}+6x+9) +(y^{2}+4y+4)=3+9+4[/tex]
[tex](x^{2}+6x+9) +(y^{2}+4y+4)=16[/tex]
Rewrite as perfect squares
[tex](x+3)^{2} +(y+2)^{2}=16[/tex]
therefore
The center of the circle is (-3,-2)
Answer: ITS D !! ON EDGE
Step-by-step explanation:
What is the other solution?
Answer:
-6
Step-by-step explanation:
m^2 - 36 = 0
Add 36 to each side
m^2 -36+36 = 0+36
m^2 = 36
Take the square root of each side
sqrt( m^2) = ± sqrt(36)
m = ±6
We know one root is 6
The other root is -6
Reflection Lines
A reflection line is equidistant from a pre-image point and its image.
Therefore, in segment AA’, point M is the
Answer:
Midpoint
Step-by-step explanation:
Equidistant from the pre = image AA would be the middle
Answer:
Mid Point, thats all there is, its the answer, just that
Step-by-step explanation:
Please answer this question in the picture!
Ignore the writing over it and the answer! It’s probably wrong.
Answer:
c [tex]113\:m[/tex]
Step-by-step explanation:
[tex]113,391 = 4\frac{9}{10}[2\frac{1}{10}]^{2} + 135 \\ \\ 113 ≈ h[/tex]
I am joyous to assist you anytime.
what is the sum of 12x^2+3x+6 and -7x^2-4x-2
Answer: [tex]5x^2-x+4[/tex]
Step-by-step explanation:
In addition of polynomials, you only have to add the like terms.
Remember the multiplication of signs:
[tex](+)(+)=+\\(-)(-)=+\\(-)(+)=-[/tex]
Then, given the polynomial [tex]12x^2+3x+6[/tex] and the polynomial [tex]-7x^2-4x-2[/tex], you can find the sum of them by adding the like terms.
Observe the procedure below:
[tex](12x^2+3x+6)+(-7x^2-4x-2)=12x^2+3x+6-7x^2-4x-2=5x^2-x+4[/tex]
Therefore, the sum is:
[tex]5x^2-x+4[/tex]
Based on the graph below, how would you describe the curve?
A. The curve is a 'one-to-one' function
B. The curve is a linear function
c. The curve is not a function
D. The curve is a 'many-to-one" function
D. is the correct answer
Hopes this helps
5x+3=23 what’s is x?
Answer:
x=4
Step-by-step explanation:
First of all subtract 3 from both sides.
5x+3−3=23−3
5x=20
Then divide both sides by 5.
5x/5=20/5
x=4
The solution to the equation 5x + 3 = 23 is x = 4.
Given is an equation 5x + 3 = 23, we need to solve the equation for the value of x,
To solve the equation 5x + 3 = 23 for the value of x, we'll go through the following steps:
Step 1: Subtract 3 from both sides of the equation to isolate the term with x on the left side:
5x + 3 - 3 = 23 - 3
5x = 20
Step 2: Divide both sides of the equation by 5 to solve for x:
(5x)/5 = 20/5
x = 4
Therefore, the solution to the equation 5x + 3 = 23 is x = 4.
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45+45-6+122/5+92-35*9+12-10/2+19-25?
Answer:-568/5
Step-by-step explanation:
Answer:
-568/5 is the answer
The given graph represents the function f(x) = 2(5)
How will the appearance of the graph change if the a
value in the function is decreased, but rerrains greater
than 0?
The graph will increase at a slower rate.
The graph will show a decreasing, rather than
increasing, function.
The graph will show an initial value that is lower on
the y-axis
The graph will increase at a constant additive rate,
rather than a multiplicative rate.
What’s the awnser
Answer:
It's C on e2020
Step-by-step explanation:
which equation is in quadratic form?
a)4(x-2)^2+3x-2+1=0
b)8x^5+4x^3+1=0
c)10x^8+7x^4+1=0
d)9x^16+6x^4+1=0
Solve the right triangle shown in the figure
Answer:
Option B
Step-by-step explanation:
step 1
Find the measure of angle A
Remember that the sum of the interior angles of a triangle must be equal to 180 degrees
∠A+∠B+∠C=180°
substitute the given values
∠A+23.4°+90°=180°
∠A+23.4°+90°=180°-113.4°=66.6°
step 2
Find the length of side BC (a)
Applying the law of sines
c/sin(C)=a/sin(A)
3.3/sin(90)=a/sin(66.6)
a=3.3*sin(66.6)/sin(90)
a=3.0 mm
step 3
Find the length side AC (b)
Applying the law of sines
c/sin(C)=b/sin(B)
3.3/sin(90)=b/sin(23.4)
b=3.3*sin(23.4)/sin(90)
b=1.3 mm
Yesterday, a factory used 2/3 of a tub of peanut butter. They use 1/6 of a tub of peanut butter for each batch of peanut butter cookies. How many batches of peanut butter cookies did the factory make yesterday?
The number of batches is 4.
What is the unitary method?When a problem arises if 4 is required for 2 of these things then how many things does 20 require?
We use the unitary method to solve the problem where we find how much is required for one thing and then multiply it by the required.
Solving the given problem.1/6 tub of peanut butter is used for one batch of cookies.
2/3 of it was used for the whole day.
So to find the total number of batches we divide the total tub used by the amount of tub used for one batch of cookies hence = 2/3/(1/6) = 4
Hence the answer to the given problem is 4.
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If its 10/16 what is answer as a decimal
Answer:
0.625 is a decimal and 62.5/100 or 62.5% is the percentage for 10/16.
Step-by-step explanation:
Please mark brainliest and have a great day!
[tex]\text{Hey there!}[/tex]
[tex]\frac{10}{16}=10\div16= 0.625[/tex]
[tex]\boxed{\boxed{\text{Answer: 0.625}}}\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
Take 4a - 3b + 2c from 2a - 3b + 4c.
-2a + 2c
-2a - 2c
2a + 2c
2a - 2c
Answer:
Option 1 [tex]-2a+2c[/tex]
Step-by-step explanation:
To find : Take [tex]4a - 3b + 2c[/tex] from [tex]2a - 3b + 4c[/tex].
Solution :
The equation [tex]4a - 3b + 2c[/tex] ....(1)
[tex]2a - 3b + 4c[/tex] ....(2)
Taking (1) from (2) means subtracting equitation (2) from (1),
i.e [tex]=(2a - 3b + 4c)-(4a - 3b + 2c)[/tex]
[tex]=2a - 3b + 4c-4a+3b-2c[/tex]
[tex]=-2a+2c[/tex]
So, Taking [tex]4a - 3b + 2c[/tex] from [tex]2a - 3b + 4c[/tex] is [tex]-2a+2c[/tex]
Therefore, Option 1 is correct.
Find the greatest possible error for each measurement 10 1/8 oz
The greatest possible error for a measurement of 10 1/8 oz is ± 1/16 oz, considering that 1/8 oz is the smallest visible increment on the measuring scale.
Explanation:The greatest possible error in a measurement refers to the smallest unit that the measuring instrument can discern. In the case of the measurement 10 1/8 oz, we consider the precision of the measuring tool used.
If the smallest division the scale can measure to is 1/8 oz, then the greatest possible error in this case would be ± 1/16 oz. This is because 1/8 oz is the smallest increment visible on the scale, and the actual measurement could be halfway between two increments.
The concept of greatest possible error is critical in determining the accuracy and precision of a measurement. It helps to understand how reliable a given measurement is.
For example, when taking several measurements of the same quantity, like the weight of grocery items, there is often a small variation. This variation is a normal part of measuring and can be due to the limitations of the measuring tool or the person taking the measurement.
Final answer:
The greatest possible error for the measurement of 10 1/8 oz is +/- 1/16 oz, which accounts for the uncertainty of the least precise digit in the measurement.
Explanation:
When considering the greatest possible error for a measurement, it's important to understand that this refers to the uncertainty associated with the least precise digit of the measurement. For a measurement like 10 1/8 ounces, if we are using a standard measuring device that has graduations for every 1/8 of an ounce, then the greatest possible error is half of the smallest unit measured, which in this case is 1/16 of an ounce.
The reason for this is because when a measurement falls between two lines or markings, the measurer must estimate the value to the nearest possible marking. If the measurement is exactly on a line, or marking, there is no need to estimate, but if it is not, then the convention is to record the number to the nearest marking and recognize that there's a potential error up to half the distance to the next marking. So, for the given measurement of 10 1/8 ounces, the greatest possible error would be +/- 1/16 of an ounce.
Paula Pruitt invested $4,334 in the stock market. The investment has declined 7% in value. Determine the worth of the investment now
Answer:
(4334/100)*93 = $ 4,030.62
Step-by-step explanation:
N/A