The prime factorizations of the numbers are
[tex]110 = 2\times 5 \times 11,\quad 40= 2^3\times 5,\quad 120=2^3\times 3\times 5[/tex]
The greatest common factor is composed by all common primes, taken with the lowest exponent possible. In this case, it will be
[tex]2\times 5 = 10[/tex]
Select the correct answer
Which table shows a proportional relationship between x and y?
A
Answer:
C
Step-by-step explanation:
You are looking for when y divided by x is the same number per each row.
Choice A.. 4/2 doesn't equal 9/4 so not choice A
Choice B.. 4/3 doesn't equal 16/9 so not choice B
Choice C works because 12/4 = 15/5 = 18/ 6 ... all of these equal 3 so choice C is an answer
Choice D.. 4/1 doesn't equal 15/3 so not choice D
Choice C is the only one where you have y/x is the same per each row
If the parabola of the form y = a(x – h)2 + k is always shifted horizontally h units and vertically k units, then its vertex is always
Answer:
(h,k)
Step-by-step explanation:
because of how the h is horizontal that is the x value and the k is vertical making it the y value.
(pls mark brainliest)
The vertex gets shifted by h units horizontally and k units vertically.
The parabola is defined by
y = a(x - h)² + k
has its vertex at (h,k).
After a shift by h units right, followed by a shift of k units vertically, the parabola is defined by
y = a(x - 2h)² + 2k
which has its vertex at (2h, 2k).
∴ (h,k).
Vertex Form of the Equation of a Parabola: The equation y=a(x−h)2+k y = a ( x − h ) 2 + k of a parabola is said to be in vertex form because the vertex can be determined by examining the equation: (h,k) is the vertex.
What is the formula of parabola?The equation of a parabola can be written in two basic forms: Form 1: y = a( x – h) 2 + k. Form 2: x = a( y – k) 2 + h.
What is parabola and examples?A parabola is nothing but a U-shaped plane curve. Any point on the parabola is equidistant from a fixed point called the focus and a fixed straight line known as the directrix. Terms related to Parabola.
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Find the measure of the reference angle for an angle of 152º.
Answer:
28 deg
Step-by-step explanation:
Reference angle is the smallest angle formed by the terminal ray, x-axis, and origin. So at 180 you are on the x-axis so just for this question you have to do 180-152=28.
The reference angle should be a positive between 0 and 90 degrees.
What is the average rate of change for this function for the interval from x 3 to x 5?
Answer:
49
Step-by-step explanation:
The average rate of change is the ratio of the CHANGE IN Y COORDINATE and CHANGE IN X COORDINATE
In this table we are asked to determine the change in rate from x= 3 to x=5
at x =3 , y = 27
at x=5 , y=125
Hence
Change in y = 125-27 = 98
Change in x = 5-3 = 2
Hence Average Rate of Change = 98/2 = 49
Answer = 49
Which quadratic equation is equal to (x+2)^2+5(x+2)-6=0
Answer:
(x+2)^{2} +5(x+2)-6=0
Let
u=(x+2)
Substitute in the expression
(u)^{2} +5(u)-6=0
therefore
the answer is
(u)^{2} +5(u)-6=0 is equivalent to (x+2)^{2} +5(x+2)-6=0
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Math help, I'm stuck with my homework and I want to get it done.
if the gragh of y=-4x+7 is perpendicular to the gragh of y=mx+3 then what does m equal
Answer:
m = [tex]\frac{1}{4}[/tex]
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - 4x + 7 is in this form with slope m = - 4
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-4}[/tex] = [tex]\frac{1}{4}[/tex]
Hence the value of m = [tex]\frac{1}{4}[/tex]
What is the volume of the cylinder shown? (Use 3.14 for pi.)
1,978.2 in^3
20,771.1 in^3
14,836.5 in^3
1,413 in^3
Answer:
14,836.5 in^3
Step-by-step explanation:
The volume of a cylinder is given by the equation (πr^2)h where r stands for radius and h stands for height
The radius of the cylinder is 15 in
The height of the cylinder is 21 in
Volume=15×15×21×π
=14836.5 in^3
what is 10 divided by 05
[tex]10 \div .05[/tex]
let's convert the 0.05 to a fraction first, so we have two decimals, so our fraction will have two zeros then.
[tex]\bf 0.\underline{05}\implies \cfrac{005}{1\underline{00}}\implies \cfrac{1}{20} \\\\[-0.35em] ~\dotfill\\\\ 10\div 0.05\implies \cfrac{10}{1}\div \cfrac{1}{20}\implies \cfrac{10}{1}\cdot \cfrac{20}{1}\implies 200[/tex]
Solve the system of equations.
y= 2x
y= x^2 - 15
Answer:
Since both equations are equal to each other given that they are both equal to y, you can say that . . .
2x = x^2 - 15
x^2 - 2x - 15 = 0
(x-5) (x+3) = 0
Zero Product Property
x = 5 ; x = -3
Solve for y:
y = 2(5) ; y = 2(3)
y = 10 ; y = 6
Please mark for Brainliest!! :D Thanks!!
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Solve |5-8x| -7 < 8
Answer:8
Step-by-step explanation:
Solving the given equation we get [tex]\[ -\frac{5}{4} < x < \frac{5}{2} \][/tex]
1. We start by isolating the absolute value expression by adding 7 to both sides of the inequality.
2. Then, we split the inequality into two cases based on the inner expression of the absolute value: when [tex]\( 5 - 8x \)[/tex] is non-negative and when it is negative.
3. Solving each case separately, we find the range of values for [tex]\( x \).[/tex]
4. Finally, we combine the solutions from both cases to get the final solution: [tex]\( -\frac{5}{4} < x < \frac{5}{2} \).[/tex]This means that[tex]\( x \)[/tex]lies between -5/4 and 5/2.
To solve the inequality[tex]\( |5 - 8x| - 7 < 8 \)[/tex], we'll first isolate the absolute value expression and then solve for [tex]\( x \).[/tex]
1. Add 7 to both sides:
[tex]\[ |5 - 8x| < 15 \][/tex]
2. Now, we'll split the inequality into two cases based on the inner expression of the absolute value:
Case 1: [tex]\( 5 - 8x \geq 0 \)[/tex]
[tex]\[ 5 - 8x < 15 \][/tex]
[tex]\[ -8x < 10 \][/tex]
[tex]\[ x > \frac{10}{-8} \][/tex]
[tex]\[ x > -\frac{5}{4} \][/tex]
Case 2:[tex]\( 5 - 8x < 0 \)[/tex]
[tex]\[ -(5 - 8x) < 15 \][/tex]
[tex]\[ -5 + 8x < 15 \][/tex]
[tex]\[ 8x < 20 \][/tex]
[tex]\[ x < \frac{20}{8} \][/tex]
[tex]\[ x < \frac{5}{2} \][/tex]
So, we have two sets of solutions:
Case 1: [tex]\( x > -\frac{5}{4} \)[/tex]
Case 2:[tex]\( x < \frac{5}{2} \)[/tex]
Combining these two cases, we get:
[tex]\[ -\frac{5}{4} < x < \frac{5}{2} \][/tex]
1. We start by isolating the absolute value expression by adding 7 to both sides of the inequality.
2. Then, we split the inequality into two cases based on the inner expression of the absolute value: when \( 5 - 8x \) is non-negative and when it is negative.
3. Solving each case separately, we find the range of values for \( x \).
4. Finally, we combine the solutions from both cases to get the final solution: [tex]\( -\frac{5}{4} < x < \frac{5}{2} \).[/tex] This means that [tex]\( x \)[/tex] lies between -5/4 and 5/2.
Complete question
Solve |5-8x| -7 < 8
The following dot plot summarizes the number of vitamins Omur's mom took each day since she started her new diet. Each dot represents one day.
Based on this data, what is a reasonable estimate of the probability that Omur's mom takes exactly 6 vitamins tomorrow?
CHOOSE 1 ANSWER:
A.) 18%
B.) 23%
C.) 27%
D.) 38%
Please help me on this question and answer too.C
Answer: C) 27%
Step-by-step explanation:
There are 3 dots (vitamins) on six and 11 dots (vitamins) total.
The probability is [tex]\dfrac{successes(vitamins\ on\ six)}{total\ possible\ outcomes(all\ vitamins)}=\dfrac{3}{11}=\large\boxed{27\%}[/tex]
Option: C is the correct answer.
C. 27%
Step-by-step explanation:The dot plot can be reoresented in tabular form as follows:
Number of vitamins Number of days
1 2
3 1
4 2
5 1
6 3
7 1
9 1
Hence, the total number of days= 2+1+2+1+3+1+1=11
Also, the number of days in which Omur's mother took 6 vitamins= 3
( Since there are 3 dots over 6)
Hence, the estimated probability that Omur's mom take exactly 6 vitamins tomorrow is:
[tex]=\dfrac{3}{11}\times 100\\\\=27.27\%\\\\\text{which\ is\ approximately}\\\\=27\%[/tex]
One number is 4 less than 3 times a second number. If 3 more than two times the first number is decreased by 2 times the second number, the result is 11. Use the substitution method. What is the first number?
Answer:
The first number is 8
Step-by-step explanation:
Let
x -----> the first number
y ----> the second number
x=3y-4 ----> equation A
3+2x-2y=11 ----> equation B
Substitute equation A in equation B and solve for y
3+2(3y-4)-2y=11
3+6y-8-2y=11
4y=11+5
y=16/4=4
Find the value of x
x=3(4)-4=8
The Constitution gives Congress the power to create federal courts
lower than the Supreme Court
higher than the Supreme Court
equal to the Supreme Court,
unaffected by the Supreme Court.
The federal courts that the Constitution gives the Congress the power to create are federal courts: lower than the Supreme Court.
What are Federal Courts?Federal courts can be described as lower courts having limited jurisdiction. This implies that they are only authorized to hear cases that arise under the federal statues in the United States.
The Supreme Court is the highest court. District courts are the lowest federal courts.
Therefore, the federal courts that the Constitution gives the Congress the power to create are federal courts: lower than the Supreme Court.
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The U.S. Constitution allows Congress to establish federal courts lower than the Supreme Court, but not higher, equal to, or unaffected by it. The Supreme Court is the highest court in the U.S. judiciary.
Explanation:The Constitution gives Congress the power to create federal courts that are lower than the Supreme Court. According to Article III, Section 1 of the Constitution, 'The judicial Power of the United States, shall be vested in one supreme Court, and in such inferior Courts as the Congress may from time to time ordain and establish.'
The Constitution does not give Congress the power to create courts that are higher than, equal to, or unaffected by the Supreme Court. The Supreme Court is the highest court in the U.S. judicial system, and all lower courts must follow the legal precedents set by it.
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What is the solution to the inequality below?
2- 2x>-20
Answer:
x<11
Step-by-step explanation:
Subtract by 2 both sides of equation.
2-2x-2>-20-2
Simplify.
-2x>-22
Multiply -1 from both sides of equation.
(-2x)(-1)<(-22)(-1)
Simplify.
2x<22
Divide by 2 from both sides of equation.
2x/2<22/2
Simplify, to find the answer.
22/2=11
x<11 is the correct answer.
To solve the inequality 2 - 2x > -20, we isolate the variable term by adding 2x to both sides, subtracting 2, and then dividing by 2 to find that the solution is x < 11.
To solve the inequality 2 - 2x > -20, we can follow these steps:
Add 2x to both sides of the inequality to isolate the constants: 2 > -20 + 2x.Then subtract 2 from both sides to isolate the variable term on one side: 0 > -22 + 2x or -22 + 2x < 0.Divide both sides by 2, noting that division by a positive number does not change the direction of the inequality: -11 + x < 0 or x < 11.The solution to the inequality is x < 11.
You are choosing 3 of your 8 trophies and arranging them in a row on a shelf.
In how many different ways can you choose and arrange the trophies?
O A. 56
O B. 40,320
O C. 24
O D. 336
[tex]{_8C_3}\cdot 3!=\dfrac{8!}{3!5!}\cdot 6=\dfrac{6\cdot 7\cdot 8}{6}\cdot6=336[/tex]
There are 336 ways we can choose and arrange the trophies.
The answer is option D. 336
What are permutation and combination?A permutation is a mathematical way that determines the number of possible arrangements in a set.In a permutation, the elements are arranged in a specific order.A combination is a method that determines the number of possible arrangements in a set. In a combination, the elements of the set can be arranged in any order.
calculation:-
₃C⁸.3! = 8!/3!5!.6 = (6.7.8)/6.6 = 336
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Foure ABCD is a parallelogram
What is the value of x
please help
Answer:
x = 7
Step-by-step explanation:
The property of a parallelogram is the opposite sides are congruent, hence
AD = BC ← substitute values
5x + 3 = 38 ( subtract 3 from both sides )
5x = 35 ( divide both sides by 5 )
x = 7
Which of the following are true about x? Check all that apply. x ∉ A x ∈ B x ∉ C x ∈ A ⋃ B x ∈ A ⋃ C x ∈ A ⋂ B
Answer:
The true statements are,
x ∈ B
x ∉ C
x ∈ A ⋃ B
x ∈ A ⋂ B
x ∈ A ⋃ C
Step-by-step explanation:
From the figure we can see three sets A, B, C
Check all options
1) x ∉ A
From the figure we get, x is an element of A
x ∉ A is False
2) x ∈ B
From the figure we get, x is an element of B
x ∉ B is True
3) x ∉ C
From the figure we get, x is not an element of C
x ∉ C is True
4). x ∈ A ⋃ B
From the figure we get, x is an element of A ⋃ B
x ∈ A ⋃ B is True
5). x ∈ A ⋃ C
From the figure we get, x is an element of A ⋃ C
x ∈ A ⋃ C is True
6).x ∈ A ⋂ B
From the figure we get, x is an element of A ⋃ B
x ∈ A ⋂ B is True
Answer:
Everything is true expect for the first answer choice .
Step-by-step explanation:
Find the slope the line that contains the points (1,9) and (-5,8). what is the slope formula?
Answer: 1/6
Step-by-step explanation:
Lets say two points are (a,b) and (c,d)
the slope that cross these two points is: (b-d)/(a-c) or (d-b)/(c-a) → either one is fine, but make sure the one you are subtracting is the one from the same point.
Hope it helped!
Answer:
The slope formula is [tex]\frac{y_{2}- y_{1} }{x_{2} -x_{1} }[/tex]
The slope of (1, 9) and (-5, 8) is 1/6
Step-by-step explanation:
(9 - 8)/( 1 - [-5]) = 1/6
X=
A. 115.5
B. 137
C. 180
Answer:
The correct answer option is C. 180
Step-by-step explanation:
We are given a figure of a circle with two known angles measuring 137 degrees and 94 degrees and we are to find the value of x.
Finding x:
[tex]137 = \frac{1}{2} (\angle x + 94)[/tex]
[tex]137 = \frac{1}{2} \angle x + 47[/tex]
[tex]\frac{1}{2} \angle x = 137 - 47[/tex]
[tex]\frac{1}{2} \angle x = 90 [/tex]
[tex] \angle x = 90 \times 2&# 1 0 [/tex]
x = 180
Answer:
the answer is 180
Step-by-step explanation:
Because yes!! Also I hope you have a wonderful wonderful day!! :D
an official playing field (including end zone) for the indoor football league has a length 45 yd longer than its width. the perimeter of the rectangular field is 174 yd. find the length
Given the provided conditions, we set up an equation to determine the width and length of the indoor football field. After simplifying the appropriate mathematical expressions, we find that length of the football field is 66 yards.
Explanation:In this problem, we're solving for the length of an indoor football field. We know that the perimeter of a rectangle is given by [tex]2L + 2W[/tex] (twice the length plus twice the width) and the length is said to be 45 yards longer than the width. Therefore, we would describe the length as 'W + 45'
Let's represent the width as W and thus the length as W + 45. Substituting these into our perimeter equation we get [tex]2(W) + 2(W +45) = 174.[/tex] Simplifying gives [tex]4W + 90 = 174[/tex]
Subtracting 90 from both sides gives 4W = 84. Thus, W = 21. Substituting this value back into our equation for the length gives us L = 21 + 45 which equals 66 yards. Therefore, the length of the indoor football field is 66 yards.
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Given the following: MAB = mBC = mCD.
In circle F, what is the measure of
A. 7.5°
B. 30°
C. 15°
D. 45°
Answer:
The correct answer is option B. 30°
Step-by-step explanation:
Points to remember
The central angle of an arc is double the value of arc subtended on the the other part of the circle
From the figure we can see a circle with center F.
It is given that, mAB = mBC = mCD, means that, central angles of all these three arcs are equal.
To find the m<AFB
Fro the figure we get,m<CED = 15°
Therefore central angle of arc CD = 30°
So m<AFB = 30°
The function g(x) is defined as shown.
x-1, -2
g(x) = 2x+3, -1
6-X, X23
Answer:
B) 3
Step-by-step explanation:
The parts on the right side are to figure out which one to use so since g(3) then you plug in 3 to the equations on the right to see which one is true. The one that it matches into then plug in 3 for x in the equation directly to the left of it:
3 ≥ 3 so 6 - (3) = 3
NEED HELP ASAP 10 POINTS
Answer:
unlikley
Step-by-step explanation:
Solve x2 – 64 = 0.
1. Isolate x2: x2 = 64
2. Apply the square root property of equality: 7x2 = 1/64
3. Isolate the variable:
0
x =
x=
Answer:
x = - 8, x = 8
Step-by-step explanation:
Given
x² - 64 = 0 ( add 64 to both sides )
x² = 64 ( take the square root of both sides )
x = ± [tex]\sqrt{64}[/tex] = ± 8
The length of a rectangle is 3 inches less than twice the width. If the perimeter of the rectangle is 18 inches, find the width of the rectangle
Answer:
y = 4. So this is your width.
Step-by-step explanation:
Use the distributive property to do 2(2y-3) = 2*2y-2*3 = 4y-6. So we have
4y-6+2y = 18. Combine like terms 4y and 2y to get 6y.
6y-6 = 18. Add 6 to both sides to solve for 6y
6y = 24. Divide by 6 to solve for y
y = 4. So this is your width.
length = x
________________
| |
y | | width = y
| |
_________________
x
The width of the rectangle is determined to be 4 inches.
To find the width of the rectangle, we need to set up equations based on the information given. The length (L) is described as being 3 inches less than twice the width (W), so we can express that as L = 2W - 3. The perimeter (P) of a rectangle is calculated as P = 2L + 2W. We are told the perimeter is 18 inches, so we have 18 = 2(2W - 3) + 2W. Simplifying this equation, we get 18 = 4W - 6 + 2W, which combines to 18 = 6W - 6. Adding 6 to both sides gives us 24 = 6W, and dividing both sides by 6 yields W = 4 inches. Therefore, the width of the rectangle is 4 inches.
The process used here is similar to working through proportions and scale factors. For instance, if one is working with scale models, as in the miniature fish pond example, the scale factor is used to determine the dimensions in the model based on actual size dimensions. However, in this case, the given equations allowed us to find the width directly.
Which of the following is a true statement about skew lines?
A. Skew lines are parallel.
B. Skew lines intersect at a single point.
C. Skew lines are perpendicular.
D. Skew lines do not lie in the same plane
The statement which is true about skew lines is:
Option: D
D. Skew lines do not lie in the same plane
Step-by-step explanation:Skew lines-
In mathematics, skew lines are the lines which do not intersect and also they are never parallel.
Also, we know that if two lines are on the same plane i.e. coplanar this means either they will cross i.e. intersect or will be parallel.
This statement imply that skew lines do not lie in the same plane i.e. they are non-coplanar.
Hence, from all of the definition and the property above we get:
D. Skew lines do not lie in the same plane
In f(x) = 2x^2-8x-10 the y intercept is at and the x intercepts are (-1,0) and
Answer:
see explanation
Step-by-step explanation:
To find the y- intercept let x = 0
f(0) = 0² - 8(0) - 10 = 0 - 0 - 10 = - 10
The y- intercept is (0, - 10)
To find the x- intercepts let f(x) = 0, that is
2x² - 8x - 10 = 0 ( divide through by 2 )
x² - 4x - 5 = 0
Consider the factors of the constant term (- 5) which sum to give the coefficient of the x- term (- 4)
The factors are - 5 and + 1, since
- 5 × 1 = - 5 and - 5 + 1 = - 4, hence
(x - 5)(x + 1) = 0
Equate each factor to zero and solve for x
x - 5 = 0 ⇒ x = 5
x + 1 = 0 ⇒ x = - 1
The x- intercepts are (- 1, 0) and (5, 0)
Final answer
The y-intercept of the function f(x) = 2x²8x-10 is at (0, -10), and the x-intercepts are (-1,0) and (5,0).
To determine the y-intercept and the other x-intercept of the quadratic function f(x) = 2x²-8x-10, we can use the standard forms and properties of quadratic equations.
The y-intercept occurs when x=0. Substituting x with 0 in the function, we get f(0) = 2(0)²- 8(0) - 10 = -10. Thus, the y-intercept is at (0, -10).
To find the other x-intercept given one of them as (-1,0), we can factor the quadratic equation, or use the quadratic formula. Factoring gives us:
(2x + 2)(x - 5) = 0
2x + 2 = 0 would give us an x-intercept at x = -1, which we already have. x - 5 = 0 gives us the other x-intercept at x = 5. So, the other x-intercept is at (5,0).
a bicycle tire is 28 inches in diameter. approximately how far does the bicycle move forward each time the wheel goes around? (use 22/7 as an approximation for pi.)
Answer: 88 inches
Step-by-step explanation:
Given : A bicycle tire is 28 inches in diameter. approximately.
To find the distance traveled by the bicycle each time the wheel goes around we need to find the circumference of the tire.
The circumference of a circle : [tex]\pi d[/tex], where d is the diameter of the circle.
Now, the circumference of tire : [tex]\dfrac{22}{7} \times(28)=88[/tex]
Hence, the distance traveled by the bicycle each time the wheel goes around =88 inches.
The wheel moves forward each time, in a single round it will cover distance of 88 inches.
Given information:
The diameter of the tire is 28 inches.
Now, if we need to find the distance covered by the tire in one round, we need to understand that the tire will cover exactly same distance as it's circumference in one round.
So, the distance will be equal to its circumference :
[tex]D=\pi\times d[/tex]
Hence, distance covered (D)
[tex]D=3.14\times 28\\D=88[/tex]
Hence, when the wheel move forward each time the in a single round it will cover 88 inches.
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Sophie sprays 200 fluid ounces of water on the window plants in her house every day. How much water does she spray each day?
A. 1.5625 gal.
B. 1.7500 gal.
C. 2.250 gal.
D. 2.500 gal.
A. 1.5625 gal.
Formula
divide the volume value by 128
I decided 200 by 128 and voila; there is the answer.
What is the slope of the line?
slope = -2
slope = -1
slope = 1
Use the points where the line crosses the x and y axis.
(2,0) and (0,2)
Slope = change in Y over the change in x.
Slope = (2-0) / (0-2)
Slope = 2/-2
Slope = -1