Answer:
D
Step-by-step explanation:
The minimum value is the value of the y- coordinate of the vertex.
Given a parabola in standard form, y = ax² + bx + c ( a ≠ 0 )
Then the x- coordinate of the vertex is
[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]
y = [tex]\frac{3}{4}[/tex] x² + 6x + 6 ← is in standard form
with a = [tex]\frac{3}{4}[/tex] , b = 6, thus
[tex]x_{vertex}[/tex] = - [tex]\frac{6}{\frac{3}{2} }[/tex] = - 4
Substitute x = - 4 into y and evaluate
y = [tex]\frac{3}{4}[/tex] (- 4)² + 6(- 4) + 6 = 12 - 24 + 6 = - 6
Thus minimum value = - 6 → D
a man bought a lot for 1200 and sold it for 1500. his percent of gain based on his purchase was
Answer: The percent gain was 25%.
Step-by-step explanation:
Given, Cost price of lot = $1,200
Selling price of lot = $1,500
The percent gain = [tex]\dfrac{\text{selling price- cost price}}{\text{cost price}}\times100[/tex]
⇒ Percent gain =[tex]\dfrac{1500-1200}{1200}\times100\%[/tex]
[tex]\Rightarrow\text{ Percent gain}=\dfrac{300}{1200}\times100\%\\\\\Rightarrow\text{ Percent gain}=\dfrac{1}{4}\times100\%\\\\\Rightarrow\text{ Percent gain}=25\%[/tex]
Hence, the percent gain was 25% based on his purchase.
Nina and Ryan each ran at a constant speed for a 100-meter race. Each runner’s distance for the same section of the race is displayed on the left. Who had a head start, and how big was the head start? ________had a head start of _________ meter
Answer:
ryan had a head start of 10 meters.
Step-by-step explanation:
Answer:
A) Ryan
B) 10
Step-by-step explanation:
How do I find the value of x? Can someone please explain
Answer:
4solution,
[tex] {x}^{3} = 64 \\ or \: x = \sqrt[3]{64} \\ or \: x = \sqrt[3]{4 \times 4 \times 4} \\ x = 4[/tex]
Hope this helps...
Good luck on your assignment...
Answer:
x=4
Step-by-step explanation:
x^3=64
it means same number multiply by it self three times to get 64
to find x you need to use cubic root because it is to the power 3
∛x^3=∛64
∛x*x*x=∛4*4*4 or ∛4^3
x= 4
What is the y-intercept of the function f(x)= -2/9x+1/3?
Answer:
1/3
Step-by-step explanation:
y=MX+b
y=-2/9x+1/3
b=y-intercept
Pls help with the solution of the question.
Answer:
[tex]\frac{17}{13}[/tex]
Step-by-step explanation:
Given
tan x = [tex]\frac{5}{12}[/tex] = [tex]\frac{opposite}{adjacent}[/tex]
5 and 12 are the legs of a 5- 12- 13 right triangle with hypotenuse 13, thus
sin x = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{5}{13}[/tex]
cos x = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{12}{13}[/tex]
Thus
sin x + cos x = [tex]\frac{5}{13}[/tex] + [tex]\frac{12}{13}[/tex] = [tex]\frac{17}{13}[/tex]
The value of the digit 2 in 425.3 is
The place value of 2 in 425.3 is tens of 20.
What is place value?The value a digit in a number represents based on where it is in the number is known as place value. The place value of 7, for instance, is 700 or 7 hundred.
Given digit:
425.3
Write the number as shown below,
425.3 = 400 + 20 + 5 + 0.3
As you can see, the 2 is attached to the tens place,
Therefore, the place value of 2 in 425.3 is tens of 20.
To know more about place value:
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Which expression is equivalent to -4 * 4 * 4 * 4 * 4 * 4 * 4 * 4
Answer:
-65536
Step-by-step explanation:
-1*4^8
Answer:
-65536
Step-by-step explanation:
In rectangle ABCD what are the values of y and z?
A y = 5; z = 55
B y = 5; Z = 5
C y = 35; z = 55
D y = 55; z = 5
Answer:
The answer is option A.
∆BDC is a right angled triangle
Angles in a triangle add up to 180°
That's
z + 35 + 90 = 180°
z = 180 - 35 - 90
z = 55°
Alternate angles are equal
Angle DBC = Angle BDA
That's
35 = 7y
Divide both sides by 7
y = 5
y = 5 z = 55
Hope this helps you
Henry earns a base salary plus commission. At the end of March he was paid \$2,427 based on his monthly sales of \$15,800. At the end of April he earned \$2,771.50 based on \$21,100 in sales. What was his base salary?
You don't have to show your work
Answer:
The base salary is $1,400
Step-by-step explanation:
Here, we are interested in calculating the base salary.
Now let’s picture his earnings as this, a base salary of let’s say $x and a percentage of y% of total sales as commission.
So let’s move!
For the month of march, his earnings is calculated as follows;
x + (y/100 * 15,800) = 2427
so we have;
x + 158y = 2427 •••••••(i)
For the month of April, we have
x + (y/100 * 21,100) = 2771.5
x + 211y = 2771.5 ••••••(ii)
So we have two equations to solve simultaneously.
We can easily get y by subtracting equation i from ii
That would be ;
(211y-158y) = 2771.5-2427
53y = 344.5
y = 344.5/53
y = 6.5%
So we can now get the base salary by substituting the value of y in any of the equations. Let’s use the first
x + 158(6.5) = 2427
x + 1027 = 2427
x = 2427-1027
x = $1,400
Please answer this question now in two minutes
Answer:
130
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
130.4
can someone please help?
Which number line represents the solutions to –2|x| = –6?
Answer:
D. the last one with dots on -3 and 3
Step-by-step explanation:
-2|x| = -6
divide each side by -2
|x| = 3
x = -3 or 3
The explicit formula for the geometric sequence Negative one-ninth, one-third, negative 1, 3, negative 9, ellipsis is f (x) = negative one-ninth (negative 3) Superscript x minus 1. What is the common ratio and recursive formula for this sequence?
Answer:
Common ratio, r=-3
Recursive Formula
[tex]f(n)=-3f(n-1),$ $n\geq 2\\f(1)=-\dfrac{1}{9},[/tex]
Step-by-step explanation:
The formula for the geometric sequence: [tex]-\dfrac{1}{9} ,\dfrac{1}{3}, -1,3,-9,\cdots[/tex] is given as:
[tex]f(x)=-\dfrac{1}{9}(-3)^{x-1}[/tex]
Common Ratio
Dividing the next terms by the previous terms, we obtain:
[tex]\dfrac{1}{3} \div -\dfrac{1}{9} = \dfrac{1}{3} \times -9 =-3\\3 \div -1 =-3\\-9 \div 3 =-3[/tex]
Therefore, the common ratio of the sequence, r=-3
Recursive Formula
We observe that the next term, [tex]f(n)[/tex] is obtained by the multiplication of the previous term. f(n-1) by -3.
Therefore, a recursive formula for the sequence is:
[tex]f(n)=-3f(n-1),$ $n\geq 2\\f(1)=-\dfrac{1}{9},[/tex]
Answer:
It is in fact B. −3; f(x + 1) = −3(f(x))
Step-by-step explanation:
If you have this question on Edge, go with this.
A linear function has an x-intercept of 12 and a slope of StartFraction 3 Over 8 EndFraction. How does this function compare to the linear function that is represented by the table? x y Negative two-thirds Negative three-fourths Negative one-sixth Negative StartFraction 9 Over 16 EndFraction One-third Negative StartFraction 3 Over 8 EndFraction StartFraction 5 Over 6 EndFraction Negative StartFraction 3 Over 16 EndFraction It has the same slope and the same y-intercept. It has the same slope and a different y-intercept. It has the same y-intercept and a different slope. It has a different slope and a different y-intercept.
Answer:
(B) It has the same slope and a different y-intercept
Step-by-step explanation:
The table is presented below:
[tex]\left|\begin{array}{c|c}x&y\\----&---\\-\frac{2}{3} &-\frac{3}{4}\\\\-\frac{1}{6}&-\frac{9}{16}\\\\\frac{1}{3}&-\frac{3}{8}\\\\\frac{5}{6}&-\frac{3}{16}\end{array}\right|[/tex]
Gradient
[tex]m=\dfrac{-\frac{3}{8}-(-\frac{3}{4})}{\frac{1}{3}-(-\frac{2}{3})}\\=\dfrac{-\frac{3}{8}+\frac{3}{4}}{\frac{1}{3}+\frac{2}{3}}\\=\frac{3}{8}\div \frac{3}{3}\\m=\frac{3}{8}[/tex]
Next, we determine its y-intercept
Using the pair [tex](-\frac{2}{3},-\frac{3}{4})[/tex] in y=mx+b
[tex]-\frac{3}{4}=(\frac{3}{8})(-\frac{2}{3})+b\\-\frac{3}{4}+\frac{1}{4}=b\\b=-\frac{1}{2}[/tex]
Comparing with the linear function has an x-intercept of 12 and a slope of [tex]\frac{3}{8}[/tex], we find out that It has the same slope and a different y-intercept.
Option B is the correct option.
Answer:
B
It has the same slope and a different y-intercept
Step-by-step explanation:
please rate and ❤️❤️❤️
could someone help?
Answer:
Step-by-step explanation:
subtract 3 from each
8-3≤3-5z-3<12-3
or 5≤-5z<9
divide by 5
5/5 ≤ -5z/5<9/5
or 1≤-z<1.8
multiply by -1
-1 ≥z>-1.8
or -1.8≤z<-1
Answer:
-1 ≥ z > -1.8
Step-by-step explanation:
Maybe you want to find the solution set.
__
Subtract 3 from the inequality:
5 ≤ -5z < 9
Divide by -5:
-1 ≥ z > -1.8
_____
Personally, I like to write these with the inequality symbols pointing to the left. That way, the elements of the expression are in number-line order.
-1.8 < z ≤ -1
What type of function is represented in the table?
quadratic
exponential
logarithmic
linear
Answer:
Option (4)
Step-by-step explanation:
Given table in the picture is,
x y 1st difference
0 -7 -
1 -2 -2 - (-7) = 5
2 3 3 - (-2) = 5
3 8 8 - (3) = 5
4 13 13 - 8 = 5
5 18 18 - 13 = 5
There is a common difference of 5 between every consecutive numbers.
Therefore, this table represents a linear function.
Option (4) will be the answer.
The type of function represented in the table is linear.
Given the table in the picture is,
x y 1st difference
0 -7 -
1 -2 -2 - (-7) = 5
2 3 3 - (-2) = 5
3 8 8 - (3) = 5
4 13 13 - 8 = 5
5 18 18 - 13 = 5
There is a common difference of 5 between every consecutive number.
What is the linear function?The term linear function refers to two distinct but related notions: In calculus and related areas, a linear function is a function whose graph is a straight line, that is, a polynomial function of degree zero or one.
Therefore, this table represents a linear function.
Option (4) will be the answer.
To learn more about the linear function visit:
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Hi, I’m really confused if anyone could help me out that would mean a lot?:)
Hey there! :)
Answer:
a) 32 sticks.
b) 5n + 2 sticks.
Step-by-step explanation:
Solve this by finding the pattern.
Pattern # 1 = 7 sticks.
Pattern #2 = 12 sticks
Pattern #3 = 17 sticks.
We can see an increase of 5 sticks within each. We can use this to write an equation:
f(n) = 7 + 5(n-1)
***Where n is the term number
You can simplify the equation to become:
f(n) = 7 + 5n - 5
f(n) = 5n + 2.
Use this equation to solve for pattern # 6:
f(6) = 7 + 5(n-1)
f(6) = 7 + 5(5)
f(6) = 7 + 25
f(6) = 32.
Rachel reads 36 chapters of a book in 6 hours. What is her rate in chapters per hour?
Answer:
6 chapters per hour
Step-by-step explanation:
36 chapters divided by 6 hours equals 6 chapters per hour.
Answer:
6
Step-by-step explanation:
36 devide by 6=6
An airline charges an extra fee if a carry-on bag weighs more than 30 pounds. After packing, Lorrie’s carry-on weighs 21.2 pounds. The inequality represents the amount of weight Lorrie can add to the carry-on without going over the 30-pound limit. 21.2 + w less-than-or-equal-to 30 How much weight can Lorrie add to the carry-on without going over the 30-pound limit? less than 8.8 pounds more than 8.8 pounds no less than 8.8 pounds no more than 8.8 pounds
Answer:
No more than 8.8 lb
Step-by-step explanation:
21.2 + w ≤ 30
Subtract 21.2 from each side
w ≤ 8.8
Lorrie can add no more than 8.8 lb.
Answer:
no more then 8.8
Step-by-step explanation:
tell me if i am right or wrong plz
AC and DB are chords that intersect at point H. A circle is shown. Chords A C and D B intersect at point H. The length of A H is 20 minus x, the length of H B is 12 minus x, the length of D H is x + 4, and the length of H C is x. What is the length of line segment DB?
Answer:
16 units
Step-by-step explanation:
Chords AC and DB intersect at H and:
AH =20-x
HB=12-x
DH=x + 4
HC=x.
Using the theorem of intersecting chords
AH X HC = DH X HB
[tex]x(20-x)=(x+4)(12-x)\\20x-x^2=12x-x^2+48-4x\\20x=8x+48\\20x-8x=48\\12x=48\\x=4[/tex]
Therefore:
DB = DH +HB
=x+4+12-x
=4+4+12-4
=16 Units
Answer:
The answer is C on Edge 2020
Step-by-step explanation:
I did the Exam
Just ignore the language that you not understand, just read in English... Pls help me...
Answer:
Step-by-step explanation:
LX ^2=30^2+16^2=900+256=1156
LX=✓1156=34m
LZ=40-14=26m
ZY=2pi*14/4=22/7*7=22m
YN=30-14=16m
NX=24m
P=34+26+22+16+24=122 m
solve simple maths question...
Answer:
1) (-1,4)
2) (3,-2)
3) (4,1)
4) (3,0)
Step-by-step explanation:
Half the distance between the different coordinates, ignoring the coordinates that are the same between both points. (1,0) and (5,0) become (3,0) because 5-1=4 and 4/2 = 2 and 1+2=3.
Hope this helps <3
Answer:
Step-by-step explanation:
ABCD is a parallelogram. m∠x = ° m∠y = ° m∠z = °
Answer:
m∠x = 63
m∠y = 45
m∠z = 72
Answer:
m∠x = 63
m∠y = 45
m∠z = 72
Step-by-step explanation:
plato
Simple question
please help me solve this
Answer:
290 m³
Step-by-step explanation:
Volume of the composite figure can be calculated by using the formula for volume of a rectangular prism to calculate, separately, the volume of the top prism, then volume of the prism beneath, before summing both volumes together.
Volume of rectangular prism = width (w) × height (h) × length (l)
==>The prism on top has:
l = 3m
w = 8-3 = 5m
h = 6m
Volume (V1) = 3*5*6 = 90m³
==>The prism beneath has:
l = 8m
w = 5m
h = 5m
Volume (V2) = 8*5*5 = 200m³
Volume of the composite figure = V1 + V2 = 90+200 = 290 m³
Find the cost per ounce of a gold alloy made from 10 oz of pure gold that costs $1288 per ounce and 55 oz of an alloy that costs $900 per ounce. (Round your answer to the nearest cent.)
Answer:
$959.69 per oz
Step-by-step explanation:
A gold alloy is produced from pure gold and alloy.
10 oz of pure gold costs $1,288 per ounce
55 oz of alloy costs $900 per ounce
The first step is to add the cost of both the pure gold and alloy together
= (10 oz × $1288)+(55 oz × $900)
= $12,880+$49,500
= $62,380
Therefore the cost per ounce can be calculated as follows
= $62,380/10 oz + 55 oz
= $62,380/65 oz
= $959.69 per oz.
Hence the cost per ounce of the gold alloy is $959.69 per ounce
the diagram shows a 5cm x 5cm x 5cm cube calculate the length of the diagonal AB give your answer correct to 1 decimal place
Answer:
√3 * 5 = 5√3 cm
Step-by-step explanation:
→ ABCDEFGH is a cube.
→ CF = Diagonal of cube.
→ CH = Diagonal of Base Face BCDH.
→ Let the side of Each cube = a.
Than,
in Right ∆CFH, By Pythagoras Theoram, we have,
→ CH² + FH² = CF² --------- Equation (1)
and, Similarly, in Right ∆CDH ,
→ CD² + DH² = CH² ------- Equation (2).
Putting Value of Equation (2) in Equation (1), we get,
→ (CD² + DH²) + FH² = CF²
→ a² + a² + a² = CF²
→ CF² = 3a²
→ CF = √3a .
Hence, we can say That Diagonal of a cube is √3 times of its sides.
__________________
Given:-
Side of cube = 5cm.
So,
→ Diagonal of cube = √3 * 5 = 5√3 cm. (Ans.)
A 6 sided die numbered 1 to 6 is rolled . Find the probability that in the roll of the results is an odd number or less than 4
Answer:
4/6 or 66%
Step-by-step explanation:
Odd numbers from 1 to 6 are: 1, 3, 5
Numbers less than 4 are: 1, 2, 3
So there are 4/ 6 possible outcomes.
So the probability is 4/6 or 66%.
Find the midpoint of the line segment with end coordinates of: ( 2 , 4 ) and ( 4 , 4 )
Answer:
(3, 4)
Step-by-step explanation:
Midpoint Formula: [tex](\frac{x1 + x2}{2} , \frac{y1 + y2}{2} )[/tex]
Just plug in the coordinates as variables to find your answer:
(2 + 4)/2 = 3
(4 + 4)/2 = 4
Can any kind soul help me
Step-by-step explanation:
2.(a) uniform speed = distance/ time
= ( 9×16) / 9
= 16 m/s
(b) 19-10 = 9s
(c) 16×9 = 144m
(d) rate of change of speed
= (v-u)/ t
= ( 7-16)/ 6
= -3/2 m/s²
3.(a) uniform speed = distance/ time
= ( 12×20 ) / 12
= 20 m/s
(b) 22-10 = 12s
(c) (12×20) + 1/2(20+60)(18)
= 240+720
= 960m
(d) acceleration
= (v-u)/ t
= ( 60-20 ) / 18
= 20/9 m/² or 2.22 m/s²
A bag contains 5 red marbles, 2 blue marbles, and 3 green marbles what is the probability of drawing a green marble
Answer:
Hey there!
Total marbles= 5+2+3=10
Green marbles= 3
3/10=30%
Hope this helps :)
Find the angle of one interior angle in this regular polygon, round your answer to the nearest tenth if possible.
Answer:
147.3°
Step-by-step explanation:
Step 1: Find the sum of all interior angles
180(n - 2)
n = 11
180(11 - 2)
180(9)
1620°
Step 2: Find 1 angle
1620/11 = 147.273°
Answer:
144 or 140
Step-by-step explanation:
If you meant round to the nearest ten it would be 140