Answer:
13 units.
Step-by-step explanation:
By Pythagoras:
(x -3)^2 + (x + 4)^2 = (2x - 3)^2
x^2 - 6x + 9 + x^2 + 8x + 16 = 4x^2 -12x + 9
4x^2 - x^2 - x^2 + 6x - 8x - 12x + 9 - 9 - 16 = 0
2x^2 -14x - 16 = 0
2(x^2 - 7x - 8) = 0
2(x -8)(x + 1) =0
x = 8, -1.
As x must be positive we take x = 8
So the hypotenuse is 2(8) - 3 = 13 units long.
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
explain the relationship between the legs and the hypotenuse of a right triangle.
Answer:
According to the pythagorean theorem, a^2 + b^2 =c^2
c signifies the hypotenuse
a and b are the two legs
the sum of the two legs squared measures will equal the measure of the hypotenuse squared.
Step-by-step explanation:
Please help I need it in 5 minutes!
Answer:
[tex]11^{-10}[/tex]
Step-by-step explanation:
When you divide exponents, you subtract their powers:
-5 - 5 = -10
[tex]11^{-10}[/tex]
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:
In a multipack of crisps there are 6 salt and vinegar, 9 ready salted and 6 cheese and onion. Write the ratio of salt & vinegar : ready salted : cheese and onion in its simplest form.
Answer:
salt & vinegar : ready salted : cheese and onion
2 3 2
Step-by-step explanation:
salt & vinegar : ready salted : cheese and onion
6 9 6
Divide each by 3
salt & vinegar : ready salted : cheese and onion
6 /3 9/3 6/3
2 3 2
Answer:
2:3:2
Step-by-step explanation:
Salt and Vinegar: 6
Ready Salted: 9
Cheese and Onion: 6
Put numbers in for the corresponding type:
Salt and Vinegar : Ready Salted : Cheese and Onion
6:9:6
All numbers share a common factor of 3.
Divide all the numbers by 3 to find simplest form.
2:3:2
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:
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.)
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
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
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.
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The length of a rectangle is 5 feet less than 3 times its width. A. Write a rule for the area A as a function of the width w. B. What is the area of the rectangle when its width is 2 feet?
Answer:
A. A = (3w - 5) * w
B. 2 feet squared
Explanation:
A. The length is 5 less than 3 times the width. To write the rule for this, you’d subtract 5 from 3 times the width (3w - 5). The area is the length times the width so the rule would be:
A = (3w - 5) * w
——————————
B. Plug in 2 for w using the given rule.
A = (3[2] - 5) * (2)
Distribute
(6 - 5) * 2
Subtract 5 from 6
1 * 2 = 2
The answer is 2 feet squared since this is area.
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
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
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:
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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
Will give BRANLIEST PLEASE HELP
Answer: n=6
Step-by-step explanation:
To solve this proportion, you solve this as you would any proportion. You would have to first cross multiply.
[tex]\frac{1}{5}(15)=\frac{1}{2}n[/tex]
[tex]3=\frac{1}2}n[/tex] [multiply both sides by 2]
[tex]n=6[/tex]
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]
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:
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 = $1,400
The explicit formula for the geometric sequence Negative one-ninth, one-third, negative 1, 3, negative 9, ellipsis is f (x) = negative one-ninth (negative 3) Superscript x minus 1. What is the common ratio and recursive formula for this sequence?
Answer:
Common ratio, r=-3
Recursive Formula
[tex]f(n)=-3f(n-1),$ $n\geq 2\\f(1)=-\dfrac{1}{9},[/tex]
Step-by-step explanation:
The formula for the geometric sequence: [tex]-\dfrac{1}{9} ,\dfrac{1}{3}, -1,3,-9,\cdots[/tex] is given as:
[tex]f(x)=-\dfrac{1}{9}(-3)^{x-1}[/tex]
Common Ratio
Dividing the next terms by the previous terms, we obtain:
[tex]\dfrac{1}{3} \div -\dfrac{1}{9} = \dfrac{1}{3} \times -9 =-3\\3 \div -1 =-3\\-9 \div 3 =-3[/tex]
Therefore, the common ratio of the sequence, r=-3
Recursive Formula
We observe that the next term, [tex]f(n)[/tex] is obtained by the multiplication of the previous term. f(n-1) by -3.
Therefore, a recursive formula for the sequence is:
[tex]f(n)=-3f(n-1),$ $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 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%.
A factory packed 9600kg of flour in to small bags and large bags. Each small bag contained 3kg of flour and each large bag contained 5kg of flour. 2040 small bags were packed. How many large bags of flour were packed?
Answer:
696 large bags of flour were packed.
Step-by-step explanation:
Let large bags of flour be 'y'
Let small bags of flour be 'x'. That is x=2040 (according to the question)
[tex](3 \times x) + (5 \times y) = 9600[/tex]
[tex](3 \times 2040) + ( 5 \times y) = 9600[/tex]
[tex](6120) + (5 \times x) = 9600[/tex]
[tex](5 \times x) = 9600 - 6120[/tex]
[tex](5 \times x) = 3480[/tex]
[tex]x = 3480 \div 5[/tex]
[tex]x = 696[/tex]
HOPE IT HELPS
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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 :)
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.
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
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
What is the value of
the answer is 2. see attached for step-by-step instructions. hope that helps!
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
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.
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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