Answer:
Vertex =(5,7)
Latus rectum = 2
Step-by-step explanation:
The general equation of a parabola can be expressed as x = a(y-h)²+k where 'a' is a constant and (h,k) is the vertex of the parabola.
Comparing the general equation with the given equation x= 1/2(y - 5)² + 7, it can be seen that a = 1/2, h = 5 and k = 7. Hence the vertex of the equation is (5,7) on comparison.
The length of the latus rectum of a parabola is 4a
On comparing the equation with the general equation, a = 1/2
Length of the latus rectum = 4(1/2)
Length of the latus rectum = 4/2 = 2
Hence the vertex is (5,7) and the length of latus rectum is 2
rational number 3 by 40 is equals to
Answer:
6/80, 9/120, 12/160 etc
Answer:
3/40 = 6/80 = 9/120 = 12/160 etc......
Hope it helps
Mark it as Brainliest pls!!!!! ( the crown icon)
If QR = 3x; LM - 8x -17; and ST = 31 calculate LM.
Answer:
5
Step-by-step explanation:
The midsegment of a trapezoid is equal to one half the sum of the bases.
1. Set up the equation using the midsegment formula: 1/2 (QR + ST)
1/2 (3x + 31) = 8x - 17
2. Solve
1.5x + 15.5 = 8x - 17
32.5 = 6.5x
x = 5
Answer:
[tex]\huge \boxed{23}[/tex]
Step-by-step explanation:
QR < LM < ST
LM is the middle segment, it is in between the length of QR and ST.
LM is also the average or mean of QR and ST.
(QR+ST)/2 = LM
(3x+31)/2 = 8x-17
Multiply both sides by 2.
(2)(3x+31)/2 = (2)8x-17
3x + 31 = 16x - 34
Subtract 16x and 31 from both sides.
3x + 31 - 16x - 31 = 16x - 34 - 16x - 31
-13x = -65
Divide both sides by -13.
(-13x)/-13 = -65/-13
x = 5
Substitute x = 5 for LM.
8(5) - 17
40 - 17
= 23
What are the lower quartile, upper quartile, and median for this box and
whisker plot?
A) LQ = 22 UQ = 10 Median = 18.5
B) LQ = 10 UQ = 22 Median = 18
C) LQ = 10 UQ = 22 Median = 18.5
D) LQ = 10 UQ = 22 Median = 19
Answer:
C
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
The lower quartile range is shown by the bottom of the box which is at 10.
The median is shown in the middle line, which is closer to 18 than 18.5.
The upper quartile range in the end of the box, which is at 22!
(You can also look at the picture attached if that helps.)
factories each of the following −2x2 −20x −18
Answer:
2(x + 9)(x + 1)
Step-by-step explanation:
First, take out a GCF if possible. Each coefficient is dividable by 2, so 2 is the GCF.-2(x^2 + 10x + 9)
→ The main quadratic equation is equal to ax^2 + bx + c.
Then, use a factoring pattern to factor the expression in parentheses. The factors of C that add up to equal B are the two factors.2(x + 9)(x + 1)
The expression cannot be factored any further.
4x +16 x+4
Simplify your answer as much as possible.
Answer:
20x+4
Step-by-step explanation:
Keith's height and his nephews height was at a ratio of 15:7 then, keith's Height increased by 16% and his nephews height doubled. If Keith is now 34cm taller than his nephew, what is their total current height?
Answer:
314 cm
Step-by-step explanation:
If Keith's height is 15x and his nephew's height is 7x, we can write the following equation:
1.16 * 15x = 34 + 7x * 2 -- (We get the 1.16 from the 16% increase)
17.4x = 34 + 14x
3.4x = 34
x = 10 so Keith's current height is 1.16 * 15 * 10 = 174 cm and his nephew's height is 174 - 34 = 140 cm for a total current height of 174 + 140 = 314 cm.
in a group of 240 game lovers, 135 like cricket and 120 like football.
find:How many people like both the game?
Answer:
15
Step-by-step explanation:
120+135= 255
255 is 15 more than 240.
15 people enjoy both games.
1. Draw the graph of f(x) = cos x for 0 I know how to construct the graph but I don’t know how to get the figures. Please help
Answer:
Please refer to the attached figure.
Step-by-step explanation:
Given the function:
[tex]f(x) =cosx \ where\ \{0^\circ\leq x\leq 360^\circ\}[/tex]
OR, the given function can also be written as:
[tex]y = f(x) = cosx[/tex]
We know that graph of cosine is a wave.
and the range of cosine function is [-1, 1]
First of all, let us have a table of values at major values of x.
[tex]x = 0, f(x) = 1\\x = 90, f(x) = 0\\x = 180, f(x) = -1\\x = 270, f(x) = 0\\x = 360, f(x) = 1[/tex]
So, the table of values for f(x) is:
[tex]\begin{center}\begin{tabular}{ c c }x & cosx \\0 & 1 \\90 & 0\\180 & -1\\270 & 0\\360 & 1\\\end{tabular}\end{center}[/tex]
Let us mark these points on the xy coordinate axis where x axis represents value of x and y axis represents value of [tex]f(x) = cosx[/tex] and then join the points using a wave.
Please refer to the attached graph for the answer image.
The sum of 3 consecutive even numbers is 132
pleaase help!!!
Answer:
42,44,46
Step-by-step explanation:
we first divide the 132 by the 3 which gives 44
since the numbers involved are even numbers and we know even numbers are numbers divisible by 2 we subtract 2 from the 44 and also add 2 to the 44 the get the rest of the two numbers which is from the above explanation
(44-2),44,(44+2)
42,44,46
we can check whether the above numbers are correct by adding to see whether we get 132
42+44+46=132 which are consecutive even numbers
Answer: 42, 44, and 46
Explanation: Make sure you read through the problem carefully so that you recognize that we are dealing with consecutive even numbers here.
So we can represent our numbers as follows.
X ⇒ first even integer
X + 2 ⇒ second even integer
X + 4 ⇒ third even integer
Since their sum is 132, our equation reads x + (x + 2) + (x + 4) = 132.
Solving from here, we find that x = 42.
So x + 2 is 44 and x + 4 is 46.
What am I supposed to do when parentheses are side by side like this?
Answer:
Evaluate each expression inside both grouping symbols, then multiply the result.
Step-by-step explanation:
[tex]\displaystyle (3 - 1)(4 + 2) = (2)(6) = 12[/tex]
G - Grouping Symbols
E - Exponents
M\D - Division & Multiplication [left to right]
S\A - Subtraction & Addition [right to left OR vice versa]
I am joyous to assist you at any time.
The sum of two consecutive odd integers is at least 36, find the integers
Answer:
The two integers are greater than or equal to 17 and 19
Step-by-step explanation:
Consecutive odd integers means 1, 3, 5, 7, 9 and so on
That means there is a always a gap of 2 in between each of them. Knowing this, we can set up an equation. Let x represent the first of the consecutive integers.
x+(x+2)=36
x+2 represents the second consecutive interger
x+x=34
2x=34
x=17
The two integers are 17 and 19
Two co-interior angles
formed between the
two parallel lines are in the ratio of 11.7.
Find the measures
of angles
Answer:
110° and 70°
Step-by-step explanation:
The angles are supplementary, thus sum to 180°
sum the parts of the ratio, 11 + 7 = 18
divide 180° by 18 to find the value of one part of the ratio
180° ÷ 18 = 10° ← value of 1 part of the ratio
Thus
11 parts = 11× 10° = 110°
7 parts = 7 × 10° = 70°
The angles are 110° and 70°
The table shows the number of balls, by sport, in the gym. Select the true statements about the information in the table.
Answer:
Soccer you use the lease amount of balls and in tennis you use the most
In a mathematics class, half of the students scored 89 on an achievement test. With the exception of a few students who scored 48, the remaining students scored 79. Which of the following statements is true about the distribution of scores?
A. The mean is less than the median.
B. The mean and the median are the same.
C. The mean is greater than the mode.
D. The mean is greater than the median.
Answer:
A. The mean is less than the median.
Step-by-step explanation:
Half the students scored 89. The next highest score is 79. So the median is (79 + 89) / 2 = 84.
A few students scored 48, so the mean is slightly lower than the mean of 79 and 89.
Therefore, the mean is less than the median.
Answer:
A. The mean is less than the median.
Step-by-step explanation:
Say that half the students answered 79, and the rest 89.
We'd have a distribution something like this:
79 79 79 89 89 89
The median is in the smack middle. Since we have an even number of scores, the median would be the number between the 2 middle numbers. Here, that's 79 and 89. Thus, the median is 84.
The mean is the "average" of all values. Since we have an equal number of 79s to 89s, the mean would also be in the middle of those values (balancing an equal number on both sides). So, the mean would also be 84.
HOWEVER, we have an unspecified number of 48's.
The distribution looks something like
48 79 79 89 89 89
The median is still the same, smack middle between the 2 values in the middle. 84.
But the mean has changed. We have smaller values on the left. The mean is brought down by these 48 values. It doesn't matter how many, the fact that we have at least 1 will bring the mean, the average, down.
Help fast please!! Which expression is equivalent to..
Answer:
1/8 = 2³ * 2⁻⁶
Step-by-step explanation:
2³ * 2⁻⁶ = 2³⁻⁶ = 2⁻³ = 1/2³ = 1/(2*2*2) = 1/8
HELP ME PLZZzzzzzzzz
Answer:
5 cm
Step-by-step explanation:
The volume (V) of milk in the container is calculated as
V = 8 × 15 × 12 = 480 cm³
After change of position with depth d then
8 × 15 × d = 480
120d = 480 ( divide both sides by 120 )
d = 4 cm
Find the circumference and the area of a circle with diameter 2 cm.
Use the value 3.14 for pie, and do not round your answers. Be sure to include the correct units in your answers.
Answer:
Hey There!! The question to this is: The circumference and the area of the circle are 6.28 yards and 3.14 yd² respectively. The Circumference: This is defined as the distance around a circle.
The circumference of a circle is
P = πd............................. Equation 1
Where p = circumference of the circle, d = diameter of the circle
Area: This is the region bounded by a plane surface.
The area of a circle is
A = πd²/4 .................................. Equation 2
Where A = area of the circle, π = pie = constant.
Given: d = 2 yd.
Constant: π = 3.14
Substituting these values into equation 1 and 2 respectively.
P = 3.14(2)
P = 6.28 yard.
P = 6.28 yd
and
A = 3.14(2)²/4
A = 3.14×4/4
A = 3.14 yd²
Thus the circumference and the area of the circle are 6.28 yards and 3.14 yd² respectively.
Hope This Helped!~ ♡
ItsNobody~ ☆
what is the no solution, the one solution, and the infinitely many solution of 2x+5+2x+3x
Answer:
This problem shows an expression, not an equation.
It cannot be solved.
An equation needs an equal sign.
Which operation involving complex numbers requires the use of a conjugate to be carried out?
Answer:
The correct answer will be "Division".
Step-by-step explanation:
The procedure represents numerous values requiring something like a conjugate to have been done becomes division, since the denominator conjugate multiplies the numeric values including its quotient to represent the quotient of several complex numbers throughout the standard language.It is indeed a method used to separate a set of items across equal proportions.Consider these three numbers written in scientific notation: 6.5 × 103, 5.5 × 105, and 1.1 × 103. Which number is the greatest, and by how many times is it greater than the smallest number?
Answer:
6.5×10'3=6,500.
5.5×10'5=550,000
1.1×10'3=1,100
so as u can see the second number is greater
by 548,900
Answer:C
Step-by-step explanation: 5.5 is 500 times better than 1.1 I did the math.
5.5 x 10^5 = 550,000
1.1 x 10^3 = 1,100
500 times greater
Convert each number to scientific notation or standard notation.
1.0395 × 10^9
4 × 10^2
Answer:
1)1,0395x10^9
2)its already in scientific notation?
If you write it in standard notation, which is actually just regular notations it's 400.
Step-by-step explanation:
Scientific notation can be used to represent very large or small numbers. A number written in scientific notation will have one non-zero digit to the left of the decimal point, multiplied by a power of 10 , with the power corresponding to the amount of places the decimal should move.
Somebody helpppp meeee ???
Answer:
Step-by-step explanation:
plane parallel to the vertical axis :a rectangle
plane parallel to the circular base: a circle
plane making an angle with the vertical axis without passing though the base or top surface :an oval
plane making an angle with the vertical axis and passing through the base and top surface :a pair of curved lines connected by straight lines at each of their endpoints
plane making an angle with the vertical axis and passing through either the base or the top surface, but not both: a cut-off section of an oval whose boundary has two endpoints connected by a straight line
Set A={XIX is an even whole number between 0 and 2) = 0
True? or false?
false
Step-by-step explanation:
false
jacob received $500 for christmas from his parents, he wants to put it into an account that will pay him 7.75% interest each year. if he wants to withdraw all his funds at the end of the year. how much will he withdraw
Answer:
He will have $538.75 after one year.
Step-by-step explanation:
First we need to find how much is 7.75% of 500. We can find it by multiplying 500 x .0775
This equals 38.75
That means after one year, he has $38.75 more.
500+38.75=538.75
He will have $538.75 after one year.
A new brand of gym shoe claims to add up to 2 inches to an athlete’s vertical leaps. Design an experiment to test this claim.
Describe a sample procedure.
A) Find the average vertical leap of all the athletes in their regular shoes. Give the control group the new shoes and the experimental group a different pair of shoes. Find the average vertical leap of the athletes in both groups. Compare the increases in vertical leap for each group.
B) Find the average vertical leap of all the athletes in their regular shoes. Give the experimental group the new shoes and the control group a different pair of shoes. Find the average vertical leap of the athletes in both groups. Compare the increases in vertical leap for each group.
C) Find the average vertical leap of a group of athletes in their regular shoes. Then give them each the new shoes and find their average vertical leap. Compare the before and after results.
Answer:
The correct option is (B).
Step-by-step explanation:
In this case, we need to test whether the claim made by the new brand of gym shoe is correct or not.
Claim: A new brand of gym shoe claims to add up to 2 inches to an athlete’s vertical leaps.
So, we need to test whether the average vertical leap of all the athletes increased by 2 inches or not after using the new brand of gym shoe.
The sample procedure would be to compute the average vertical leap of a group of athletes in their regular shoes (or a different pair) and the average vertical leap of a group of athletes in their new shoes.
Compare the two averages to see whether the difference is 2 inches or not.
The experimental group would be the one with the new shoes and the control group would be the one with the different pair of shoes.
Thus, the correct option is (B).
Answer:
B) Find the average vertical leap of all the athletes in their regular shoes. Give the experimental group the new shoes and the control group a different pair of shoes. Find the average vertical leap of the athletes in both groups. Compare the increases in vertical leap for each group.
Step-by-step explanation:
Write an equation for a line on the graph that passes through the points (0.4) and (12,16)
Answer:
[tex] y = x + 4 [/tex]
Step-by-step explanation:
Use the two-point form of the equation of a line.
[tex] y - y_1 = \dfrac{y_2 - y_1}{x_2 - x_1}(x - x_1) [/tex]
[tex] y - 4 = \dfrac{16 - 4}{12 - 0}(x - 0) [/tex]
[tex] y - 4 = \dfrac{12}{12}x [/tex]
[tex] y - 4 = x [/tex]
[tex] y = x + 4 [/tex]
Answer:
y = x + 4
Step-by-step explanation:
An equation for a line looks like:
=> y = mx +b
=> In this equation "m" is the slope.
=> "b" is the y-intercept.
To find the slope:
=> y/x - y1/x1
=> 16/12 - 4/0
=> 16 -4 / 12 - 0
=> 12 / 12
=> 1
So, the slope is 1.
Now our equation looks like:
y = 1x + b
=> y = x + b
Let's take some the values of "x" and "y" of (0,4)
So, our now look like:
=> 4 = 1 (0) + b
=> 4 = b
So, b (y-intercept) = 4
Now, our final equation is:
=> y = x + 4
Compute
3/10 + 3/5 - 1/5
Answer:
7/10
Step-by-step explanation:
3/10 + 3/5 - 1/5
Combine like terms
3/10 + 2/5
Get a common denominator of 10
3/10 + 2/5 * 2/2
3/10 +4/10
7/10
Answer:
7/10
Step-by-step explanation:
You want to first get all common denominators, in this case that will be 10.
It is now (3/10)+(6/10)-(2/10)
3+6-2=7
7/10
what is the reciprical of 4/7?
Answer:
7/4
Step-by-step explanation:
To find the reciprocal of 4/7, flip the fraction.
The numerator goes in the denominator and the denominator goes in the numerator
7/4
Answer:
7/4
Step-by-step explanation:
Keep it, change it, flip it.
What’s the difference between rational and irrational numbers?
Answer:
rational numbers are perfect squares irrational numbers are non terminating/go on forever
Step-by-step explanation:
A baker has three banana muffin recipes. Recipe AAA uses 333 bananas to make 121212 muffins. Recipe BBB uses 555 bananas to make 242424 muffins. Recipe CCC uses 111111 bananas to make 484848 muffins. Order the recipes by number of bananas per muffin from least to greatest.
Answer:
The order from least to greatest is B, A, C
Step-by-step explanation:
Given
Recipe A = 3 bananas to 12 Muffins
Recipe B = 5 bananas to 24 Muffins
Recipe C = 11 bananas to 48 Muffins
Required
Order the recipe from least to greatest
To solve this, we have to divide the number of bananas by number of muffins; this will give the unit banana per muffin
Recipe A: 3 bananas to 12 Muffins
[tex]A = \frac{3}{12}[/tex]
[tex]A = 0.25[/tex]
Recipe B: 5 bananas to 24 Muffins
[tex]B = \frac{5}{24}[/tex]
[tex]B = 0.2083[/tex]
Recipe C: 11 bananas to 48 Muffins
[tex]C = \frac{11}{48}[/tex]
[tex]C = 0.229167[/tex]
By comparison;
Recipe B (0.2083) is the smallest; followed by Recipe C (0.229167) then Recipe A (0.25)
Hence; the order from least to greatest is B, A, C
Answer:
its BCA
Step-by-step explanation:
