The ratios 4/6 and 8/12 are equivalent ratio of 2/3 which we obtain by multiplying or dividing both numerator and denominator by same number.
To find a ratio that is the same as 2/3, we can multiply or divide both the numerator and the denominator by the same non-zero number.
This will result in an equivalent ratio.
If we multiply both the numerator and denominator of 2/3 by 2, we get:
(2 × 2) / (3 × 2)
= 4/6
Therefore, the ratio 4/6 is the same as 2/3.
Similarly, if we multiply both the numerator and denominator of 2/3 by 2, we get:
8/12
So, the ratio 8/12 is also the same as 2/3.
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put the steps for rewriting the equation of a circle below in standard form completing the square in order
Answer:
a) 1.
f)6.
d)5.
c)7.
g)3.
e)4.
b)2.
Step-by-step explanation:
putting the steps for rewriting the equation of a circle below in standard form completing the square in order:
Step 1)
a. where 36 is added on both sides of the equation
as it is square of half of 12.
x^2 +12x+36 +y^2 +30y=24+36 ..........(1)
Step 2)
f. where 225 is added on both sides of equation as it is square of half of 30
x^2 +12x+36 +y^2 +30y+225=24+36+225 ............(6)
Step3)
d. adding numbers on r.h.s
x^2 +12x+36 +y^2 +30y+225=285 ............(5)
Step4)
c) Factoring the x values into binomial factors
(x+6)(x+6) +36 +y^2 +30y+225=285 .............(7)
Step5)
g) re-writing x factors as squares
(x+6)^2 +36 +y^2 +30y+225=285 ...............(3)
Step6)
e)Factoring the y values into binomial factors
(x+6)^2 +36 +(y+15)(y+15)=285 ...............(4)
Step7)
b)re-writing x factors as squares
(x+6)^2 +36 +(y+15)^2=285 ...........(2)!
HELP ME PLEASE! I really need help on this question
Answer:
given
Step-by-step explanation:
The vertically opposite angles, ∠4 and ∠2 are equals.
What is vertically opposite angles?Vertical angles are angles opposite each other where two lines cross.
What is linear pair?A linear pair can be defined as two adjacent angles that add up to 180° or two angles which when combined together form a line or a straight angle.
According to the given question.
On line m, we have
∠4 + ∠1 = 180 degrees ...(i) (by linear pair)
On line n, we have
∠1 + ∠2 = 180 degrees ...(ii) (by linear pair)
from equation (i) and (ii)
∠4 + ∠1 = ∠1 + ∠2
⇒ ∠4 = ∠2
Hence, we proved that the vertically opposite angles ∠4 and ∠2 are equals.
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Kalon has $175 and needs to save at least $700 for a new computer. If he can save $35 per week, what is the minimum number of weeks Kalon will need to save to reach his goal?
700-175=525. 525/35=15
Each of the 12 cards shown has a number and a color or pattern. Each card is equally likely to be drawn. Find each probability.
Please check linked image ^^
Answer:
A) P(stars) = 1/3
B) P(odd)= 4/7
C)P(solid grays or stars or striped)= 1
D)P(1,4 or 7)= 3/7
E)P(not striped)= 2/3
Step-by-step explanation:
Given:
sample set contains 1-7 solid gray, 1-7 stars and 1-7 striped cards
Let solid gray be x
stars be y
striped be z
then sample set be
1x,2x,3x,4x,5x,6x,7x,
1y,2y,3y,4y,5y,6y,7y,
1z,2z,3z,4z,5z,6z,7z
total number of cards in sample set =21
Now
a)Finding probability of stars
Number of star cards in above sample set = 7
P(stars)= 7/21
P(y)=1/3
b)Finding probability of odd
Number of odd cards in above sample set = 12
P(odd)= 12/21
=4/7
c)Finding probability of solid grays or stars or striped
P(solid grays or stars or striped) = P(x or y or z)
=P(x U y U z)
As the events are mutually exclusive
P(x U y U z)= P(x)+P(y)+P(z)
now P(x)= 1/3
P(y)=1/3
P(z)=1/3
P(x U y U z) = 1/3 + 1/3 + 1/3
= 3/3
=1
d)Finding probability of 1,4 or 7
Number of 1,4 or 7 cards in above sample set = 9
P(1,4 or 7) = P(1 U 4 U 7)
As the events are mutually exclusive
P(1,4 or 7) = P(1) + P(4) + P(7)
P(1)= 3/21
=1/7
P(4)= 3/21
=1/7
P(7)= 3/21
=1/7
P(1,4 or 7)= 1/7 + 1/7 + 1/7
=3/7
e)Finding probability of not striped
Number of not striped cards in above sample set = 14
P(not striped)= 14/21
= 2/3 !
Write two and thirty-one hundredths as a decimal number.
A) 0.231
B) 2.031
C) 2.31
D) 231.00
Answer:
c
Step-by-step explanation:
A polynomial function can be written as (x + 2)(x + 3)(x − 5). What are the x-intercepts of the graph of this function? (1 point) (2, 0), (3, 0), (−5, 0) (−2, 0), (−3, 0), (5, 0) (2, 0), (3, 0), (5, 0) (−2, 0), (−3, 0), (−5, 0)
Answer:
(-2, 0), (-3, 0), and (5, 0)
Step-by-step explanation:
The x-intercept is found when y = 0.
So, we have to find x when (x + 2)(x + 3)(x - 5) = 0
We can do that by pulling apart all parts, because if one part = 0, the whole thing will have to be too (multiplication property of identity).
1. When x + 2 = 0, x = -2
2. When x + 3 = 0, x = -3
3. When x - 5 = 0, x = 5
That gives us (-2, 0), (-3, 0), and (5, 0)
Answer:
(-2, 0), (-3, 0) and (5, 0)Step-by-step explanation:
x-intercepts are for
(x + 2)(x + 3)(x - 5) = 0
The product is equal to 0 if one of the factors is equal to 0.
Therefore
x + 2 = 0 or x + 3 = 0 or x - 5 = 9
x + 2 = 0 subtract 2 from both sides
x = -2
x + 3 = 0 subtract 3 from both sides
x = -3
x - 5 = 0 add 5 to both sides
x = 5
Find the missing angle of a triangle if the first two values are 91* and 87 degrees
Answer:
The missing angle has a measure of 2 degrees.
Step-by-step explanation:
Every triangle's inner angles can be added and will always equal 180. Therefore, use subtraction to find any missing angle. In this case,
180 - 91 = 89
89 - 87 = 2
So, your answer is 2.
If the two angles of the triangle are 91° and 87°. Then the measure of the third angle of the triangle will be 2°.
What is the triangle?A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
The two angles of the triangle are 91° and 87°.
Then the measure of the third angle of the triangle will be
Let x be the third angle. Then we have
91° + 87° + x = 180
x = 180° - 87° - 91°
x = 2°
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To find the slope, Jackie makes right triangle P by using the graph of the line as the hypotenuse of the triangle as shown in the figure. To check her work, she repeats the process and makes a right triangle Q as shown. Which statement explains why the slope of the line should be the same when calculated with either triangle?
A
The two triangles are similar.
B
The two triangles are congruent.
C
One triangle is a translation of the other triangle.
D
The lengths of the hypotenuse of each triangle are equal.
Answer:
A
Step-by-step explanation:
Answer: A
Step-by-step explanation:
A mason is building a rectangular foundation wall that is to be 75 feet by 40 feet.what is the total distance around the wall?
Answer: 230ft
Step-by-step explanation:
The perimeter is just all 4 sides added together, so,
75+75+40+40=230
The total distance around the wall is 230ft.
What percent of 72 is 27?
if we take 72 as the 100%, what is 27 off of it in percentage?
[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 72&100\\ 27&x \end{array}\implies \cfrac{72}{27}=\cfrac{100}{x}\implies \cfrac{8}{3}=\cfrac{100}{x}\implies 8x=300 \\\\\\ x=\cfrac{300}{8}\implies x=\cfrac{75}{2}\implies x=37.5[/tex]
To calculate the percentage, divide the part (27) by the whole (72) and multiply by 100, resulting in 37.5%.
Percentage is a way of expressing a portion or fraction of a whole as a value out of 100. It is commonly used to compare relative quantities, represents proportions, or express the relationship between a part and a whole.
The term "percent" comes from the Latin phrase "per centum," which means "per hundred." It signifies that percentages are calculated on a scale of 100.
In practical terms, a percentage represents a fraction of a whole, where the whole is equal to 100%. It allows us to easily compare different quantities and understand their relative sizes or proportions.
To calculate a percentage, you typically divide the part (the specific quantity you want to express as a percentage) by the whole (the total or reference quantity) and then multiply by 100 to obtain the value as a percentage.
To calculate the percentage, you can divide the given number (27) by the total number (72) and then multiply the result by 100. So, to find out what percent 27 is of 72:
(27 ÷ 72) × 100 ≈ 37.5%
Therefore, 27 is approximately 37.5% of 72.
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Find 100,000 more than 3,489,234.
Answer:
The answer is 3,589,234
Step-by-step explanation:
Because it basically means addition meaning you just have to add it 3,489,234 + 100,000 gives you the answer
What are all the possible values of x?
X3=216
[tex]\bf x^3=216\implies x=\sqrt[3]{216}\implies x=6[/tex]
Divide 216 by 3 to get your x-value
consider the following precise wise-defined function
Answer:
11
Step-by-step explanation:
The x-value -4 is less than 3, so use the first formula for f: x^2 - 5.
Then f(-4) = (-4)^2 - 5 = 11
A sum of $4200 was invested, part at 8% and the remainder at 11%. If $426.00 was earned in interest after one year, how much was invested at 11%?
Answer:
$3000 was invested at 11%.
Step-by-step explanation:
The total interest was $426. This was comprised of interest earned at 8% (represented by e) and (separately) interest earned at 11% (represented by v).
Then e + v = $4200 total investment, and
i = $426 = e(0.08)(1 year) + v(0.11)(1 year)
We eliminate the variable e as follows: since e + v = $4200, e = $4200 - v. Thus,
i = $426 = e(0.08)(1 year) + v(0.11)(1 year) becomes:
i = $426 = ($4200 - v)(0.08)(1 year) + v(0.11)(1 year)
This is one equation in one unknown, the amount of $ invested at 11%.
Performing the indicated multiplications:
426 = 4200(0.08) - 0.08v + 0.11v. Simplifying this further, we get:
426 = 336 + 0.03v.
Then 90 = 0.03v, and v = 90 / 0.03 = $3000.
$3000 was invested at 11%.
A ski resort has 18 inches of snow on the ground. The snow is falling at a rate of 4 inches per hour. which type of functions best model this situation?
Answer:
Linear Function
[tex]y=4x+18[/tex]
Step-by-step explanation:
Let
x----> the time in hours
y----> the total inches of snow on the ground
we know that
The function that best model this situation is the linear function
so
[tex]y=mx+b[/tex]
In this problem
[tex]m=4\frac{in}{h}[/tex]
[tex]b=18\ in[/tex] ----> the y-intercept
substitute
[tex]y=4x+18[/tex]
Answer:
Linear decreasing function best model this situation and the required function is
f(x)=4x+18
Step-by-step explanation:
It is given that a ski resort has 18 inches of snow on the ground. The snow is falling at a rate of 4 inches per hour.
If a function has constant rate of change, then the it is a linear function.
It the given case the rate of change is constant so linear function best model this situation.
The slope intercept form of linear function is
[tex]f(x)=mx+b[/tex] ... (1)
where, m is slope and b is y-intercept or initial value.
Ski resort has 18 inches of snow on the ground it means initial value is 18.
The snow is falling at a rate of 4 inches per hour. So, m=4.
Substitute m=4 and b=18 in equation (1).
[tex]f(x)=4x+18[/tex]
Therefore the required function is f(x)=4x+18.
What is the maximum number of relative extremes contained in the graph of this function f(x)=3x^4-x^2+4x-2
Answer:
Final answer is 3.
Step-by-step explanation:
Given function is [tex]f\left(x\right)=3x^4-x^2+4x-2[/tex].
Now we need to find about what is the maximum number of relative extremes contained in the graph of the given function [tex]f\left(x\right)=3x^4-x^2+4x-2[/tex].
Degree of the given function = 4.
Because degree is the highest power of variable.
Then relative number of extremas = degree - 1 = 4 - 1 = 3
Hence final answer is 3.
21. In your day-to-day routines, you likely use measurement to cook or do home renovations, such as adding new tile flooring. How do you imagine that you will use measurement in your healthcare career?
Answer:
Depending of the exact career but measurements are plentiful in the healthcare business.
First, you'll most likely deal with weight and height... since that's part of most health care consultations.
Then, if you deal with medication, you'll use grams, milligrams, milliliters, liters all the time. depending if the medication is in solid or liquid form.
Even as a nutritionist, you'll deal with grams and such for portion sizes.
There are countless of ways you'll use maths and measurements in the healthcare sector.
Answer:
Measurement can be used in healthcare career also. Like - the doctors and nurses are well trained to give medicines accurately as per measurement of milligrams or nano-gram. High doses can prove fatal with some medicines, so the correct measurement is very necessary.
Similarly, measurement is used in syrups. Like a child can be given upto 5 mg of syrup twice daily.
Prove ABC~EDC ?
AA similarity theorem
ASA similarity theorem
AAS similarity theorem
SAS similarity theorem
Answer:
AA similarity theorem
Step-by-step explanation:
we know that
AA (Angle-Angle) Similarity states that In two triangles, if two pairs of corresponding angles are congruent, then the triangles are similar
In this problem we have that
∠BCA=∠ECD ----> by vertical angles
∠BAC=∠DEC ---> because AB is parallel to ED (alternate interior angles)
therefore
Triangles ABC and EDC are similar by AA similarity theorem
find the magnitude and direction angle for the vector v = 5 cos 144°j
Answer:
5, 144°
Step-by-step explanation:
A vector with magnitude v and angle θ can be split into x and y components as:
vx = v cos θ
vy = v sin θ
Here, we're given the components and asked to find the magnitude and direction. By matching, we can see the magnitude is 5 and the angle is 144°.
So the answer is 5, 144°.
If the mean of four numbers 2, 4, x and 6 is 5, then x is ?
Answer:
x = 8
Step-by-step explanation:
Step 1: Create an equation
(2+4+x+6) ÷ 4 = 5
Step 2: Solve the equation
(12+x) ÷ 4 = 5
(12+x) = 20
x = 8
The value of the unknown number x is 8.
The given numbers include:
2, 4, x, 6mean = 5The sum of the given numbers is calculated as follows;
2 + 4 + x + 6 = 12 + x
The mean of the given 4 numbers is calculated as follows;
[tex]\frac{12 + x}{4} = 5\\\\12 + x = 20\\\\x = 20 -12\\\\x = 8[/tex]
Thus, the value of the unknown number x is 8.
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What is the missimg term in this aeithmetic sequence 9,14,19,_29,34,
ANSWER
The missing term is 24
EXPLANATION
The given arithmetic sequence is 9,14,19,_29,34
We can observe that:
[tex]14 = 9 + 5[/tex]
[tex]19 = 14 + 5[/tex]
Let the missing term be x, then
[tex]x = 19 + 5[/tex]
[tex]x = 24[/tex]
Therefore the missing term is 24.
What is the scale factor?
AFGH - AMNO
G
9
The scale factor [tex]\( k \)[/tex] is [tex]\( \frac{x}{6} = \frac{10}{6} = \frac{5}{3} \)[/tex].
The scale factor between two similar triangles is the ratio of the corresponding side lengths. In this case, we can find the scale factor by comparing the corresponding sides of triangles FGH and MNO.
Let's denote the scale factor as [tex]\( k \)[/tex]:
[tex]\[ k = \frac{MN}{FG} \][/tex]
Given that NO = 15 units and FG = 6 units, and MN is denoted as [tex]\( x \)[/tex], we can substitute these values into the formula and solve for [tex]\( x \)[/tex]:
[tex]\[ k = \frac{x}{6} \][/tex]
Since [tex]\( k = \frac{NO}{FG} \)[/tex] we can set up the equation:
[tex]\[ \frac{x}{6} = \frac{15}{9} \][/tex]
Now, solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{15}{9} \times 6 \][/tex]
[tex]\[ x = 10 \][/tex]
So, the scale factor [tex]\( k \)[/tex] is [tex]\( \frac{x}{6} = \frac{10}{6} = \frac{5}{3} \)[/tex].
The scale factor of the given figures is 5 : 3.
The value of x is 10
What is the scale factor?
Scale factor is calculated by finding the ratio of the dimensions of the new shape to the dimensions of the original shape.
15 : 9 = x : 6
15/9 = x/6
Cross product
15 × 6 = 9 × x
90 = 9x
Divide both sides by 9
x = 90/9
x = 10
Therefore, the scale factor 15 : 9
= 15/9
= 5/3
= 5 : 3
I need help with this question
Answer: First option.
Step-by-step explanation:
Given the function f(x):
[tex]f(x)=2x-7[/tex]
And the function g(x):
[tex]g(x)=-6x-3[/tex]
You need to add them to get [tex]f(x)+g(x)[/tex]. Then:
[tex]f(x)+g(x)=(2x-7)+(-6x-3)[/tex]
Therefore, when you add the like terms you get that [tex]f(x)+g(x)[/tex] is:
[tex]f(x)+g(x)=2x-7-6x-3[/tex]
[tex]f(x)+g(x)=-4x-10[/tex]
Since it is a linear function, the Domain is: All real numbers.
You can observe that the result obtained matches witht the first option.
Ryder shot a model rocket over an area that consists of two grassy areas, shown in green, and an area with no grass, shown in white. What is the probability that the rocket has landed in the grassy area, 0.2 0.3 0.4 0.6
Answer:
its 0.4
Step-by-step explanation:
Answer:
The answer is C) 0.4
Instead of using the values {1,2,3,4,5,6}
on dice, suppose a pair of dice have the
following: {1,2,2,3,3,4} on one die and
{1,3,4,5,6,8} on the other. Find the
probability of rolling a sum of 9 with
hy these dice. Be sure to reduce.
Answer:
1/9
Step-by-step explanation:
Of the 36 possible sums, 4 of them are 9. The probability is 4/36 = 1/9.
_____
Comment on these dice
Interestingly, the probability of any given sum is the same as it is with "normal" dice.
Let f (x) = 1/x
and g(x) = x² – 3x. What
two numbers are not in the domain of fºg?
For this case we have the following equations:
[tex]f (x) = \frac {1} {x}\\g (x) = x ^ 2-3x[/tex]
We must find [tex](f_ {o} g) (x):[/tex]
By definition of composition of functions we have to:
[tex](f_ {o} g) (x) = f (g (x))[/tex]
So:
[tex](f_ {o} g) (x) = \frac {1} {x ^ 2-3x}[/tex]
We must find the domain of f (g (x)). The domain will be given by the values for which the function is defined, that is, when the denominator is nonzero.
[tex]x ^ 2-3x = 0\\x (x-3) = 0[/tex]
So, the roots are:
[tex]x_ {1} = 0\\x_ {2} = 3[/tex]
The domain is given by all real numbers except 0 and 3.
Answer:
x other than 0 and 3
ANSWER
0 and 3
EXPLANATION
The given functions are
[tex]f(x) = \frac{1}{x} [/tex]
and
[tex]g(x) = {x}^{2} - 3x[/tex]
[tex]( f \circ g)(x) = f(g(x))[/tex]
[tex]( f \circ g)(x) = f( {x}^{2} -x )[/tex]
[tex]( f \circ g)(x) = \frac{1}{ {x}^{2} - 3x} [/tex]
Factor the numerator:
[tex]( f \circ g)(x) = \frac{1}{ x(x - 3)} [/tex]
The function will be undefined if the denominator is zero.
[tex]x(x - 3) \ne0[/tex]
[tex]x \ne0 \: and \: x \ne3[/tex]
Therefore 0 and not in the domain of the composed function.
Central Park in New York City is rectangular in shape, 4km in length and 0.8 km wide. How far would a run in central be?
Answer:
basically you have to calculate the perimeter-
Step-by-step explanation:
4+4+0.8+0.8=8+1.6=9.6
First you need to find the parameter
P= (L x 2)+(W x 2)
P=(4km x 2)+(0.8km x 2)
P=8km+1.6km
P=9.6km
A restaurant offers a "Create Your Own Pizza" menu option. There are 33 types of meat, 66 types of vegetables, and 33 kinds of cheese. Customers may choose one meat, one vegetable, and one cheese. Enter values to answer the questions below.
Enter values to answer the questions below.
1) How many different possible pizzas can be made by choosing one meat, one vegetable, and one cheese? (WHOLE NUMBER)
2) You decide to have the chef choose the toppings randomly. What is the probability that the chef will make a pizza with chicken, banana peppers, and ricotta cheese? (FRACTION)
Process would be helpful!
Answer:
54
Step-by-step explanation:
You have to do the number of options in each category by itsself
Point O is the center of the circle. What is the value of x?
Answer:
66°
Step-by-step explanation:
Since segments MN and MP are tangent to the circle, then
[tex]\angle MPO=\angle MNO=90^{\circ}[/tex]
The sum of the measures of all interior angles of the quadrilateral is equal to 360°, so
[tex]\angle NOP+\angle MPO+\angle MNO+\angle NMP=360^{\circ}\\ \\114^{\circ}+90^{\circ}+90^{\circ}+x^{\circ}=360^{\circ}\\ \\x^{\circ}=360^{\circ}-114^{\circ}-90^{\circ}-90^{\circ}\\ \\x^{\circ}=66^{\circ}[/tex]
Answer:
The value of x = 66°
Step-by-step explanation:
From the figure we can see that,
PM and MN are the tangent from the point M to the circle with center O
m<PON = 114°
To find the value of x
From the figure we can write,
m<PON + m<PMN = 180°
114 + x = 180
x = 180 - 114 = 66°
Therefore the value of x = 66°
Find the missing number.
a. 3 : 24 = ___ : 72
b. ___ : 18 = 5 : 9
c. 6: ___ = 36 : 36
A 9
B 10
C 6
Hope this helps;$
Answer:
a. 3:24 = 9:72.
b. 10:18 = 5:9.
c. 6:6 = 36:36.
Step-by-step explanation:
a. 72 / 24 = 3 so we multiply 3 by 3 to give 9.
b. 18/9 = 2 so we multiply 5 by 2 = 10.
c. The answer is 6.