Answer:
2/5
Step-by-step explanation:
4ounces of coffee in cup 1
4 ounces of cream in cup 2
In the first step pour 4/2=2 ounces of coffee from cup 1 to cup 2, getting:
2 ounces of coffee in cup 1
2 ounces of coffee and 4 ounces of cream in cup 2
In the second step we pour 2/2=1 ounce of coffee and 4/2=2 ounces of cream from cup 2 to cup 1, getting:
2+1=3 ounces of coffee and 0+2=2ounces of cream in cup 1
so the answer is 2/5
The table below gives input and output values for the function h(x) = a^x.
Answer:
It's the first one.
hope it helps :)
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
1. A point on the ground is 50 feet from my house. The angle of elevation to the top of the house is 48 Find the height of the house to the nearest tenth
2. A bird is flying at a height of 2 meters above the sea level. The angle of depression from the bird to the fish it sees on the surface of the ocean is 15^c irc. Find the distance the bird must fly to be directly above the fish. Round to the nearest tenth
Please help me as soon as possible! I have to get this done before tomorrow! Please helpppp
Answer:
(1)55.5 feet
(2)7.5 feet
Step-by-step explanation:
Question 1
The diagram is attached below.
Using Trigonometric ratio
[tex]\tan 48^\circ = \dfrac{h}{50} \\h=50 \times \tan 48^\circ\\h=55.5$ feet (to the nearest tenth)[/tex]
The height of the house is 55.5 feet to the nearest tenth.
Question 2
In the diagram, we are required to find the distance the bird must fly to be directly above the fish. This has been represented by x.
Using Trigonometric ratio
[tex]\tan 15^\circ = \dfrac{2}{x} \\x \tan 15^\circ=2\\x=2 \div \tan 15^\circ\\x=7.5 $ feet (to the nearest tenth)[/tex]
The distance the bird must fly to be directly above the fish is 7.5 feet.
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:
I NEED HELP PLEASE, THANKS! :)
Answer: A
Step-by-step explanation:
The standard form of a cosine equation is: y = A cos (Bx - C) + D where
Amplitude (A) is the distance from the center to the maxPeriod (P) is the length of the function = 2π/B Phase Shift is the distance the max is moved from the y-axis = C/BCenter (D) is the imaginary line between the max and minPlot the points (see graph below).
A = 28
[tex]\dfrac{1}{2}P=6\quad \rightarrow \quad P=12\\\\\\P=\dfrac{2\pi}{B}\qquad \rightarrow \qquad 12=\dfrac{2\pi}{B}\qquad \rightarrow \qquad \large\bold{B=\dfrac{\pi}{6}}[/tex]
Phase Shift = 7 = C/B
[tex]7=\dfrac{C}{\frac{\pi}{6}}\qquad \rightarrow \qquad \large\bold{C=\dfrac{7\pi}{6}}[/tex]
D = 49
Input the values of A, B, C, and D into the standard form of a cosine equation to get:
[tex]\large\boxed{y=28\cos \bigg(\dfrac{\pi}{6}x-\dfrac{7\pi}{6}\bigg)+49}[/tex]
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
A 4cm ladder rest against a vertival wall with it's foot 2 m from the wall. How far up the wall does the ladder reach?
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
A pilot wants to arrive at her destination as soon as possible. Air traffic is busy, so she can take off 10 minutes later than expected and will be able to travel three times faster than expected if she waits. Create an equation to represent her total travel time, including wait time, where x is the number of minutes the flight was expected to take.
Answer:
y = x/3 + 10
Step-by-step explanation:
Let y be the number of minutes the flight takes
She can take off 10 minutes later than expected. She will be able to travel at a speed three times than expected.
Let her expected speed be s, therefore, she can travel at 3s.
x = number of minutes the flight was expected to take.
In terms of distance and speed:
x = d / s ______(1)
where d = total distance traveled
The time for the flight (minus waiting time) is now the division of the distance she traveled and her speed, i.e.:
t = d / 3s
From (1):
=> t = x / 3
The time she spent waiting is 10 minutes.
Therefore, the total time that the flight takes (plus waiting time) is:
y = t + 10
=> y = x/3 + 10
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 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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ADDISON RAE mixed L of water with 1 L vegetable oil. Which fluid will be floating? Why? The total volume is 2 L. If water’s density is 1 g/cm^3 and the oil’s density is 0.9 1 g/cm^3, what is the density of the mixture? How about 1.9L of water and 0.1 L of the same oil?
Answer:
The FitnessGram Pacer Test is a multistage aerobic capacity test that progressively gets more difficult as it continues. The 20 meter pacer test will begin in 30 seconds. Line up at the start. The running speed starts slowly but gets faster each minute after you hear this signal bodeboop. A sing lap should be completed every time you hear this sound. ding Remember to run in a straight line and run as long as possible. The second time you fail to complete a lap before the sound, your test is over. The test will begin on the word start. On your mark. Get ready!… Start
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
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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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]
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
Stevie and Michael share their profit in a ratio 3:5. Stevie gets £120 more than Michael. How much profit did they make altogether?
Answer:
£480
Step-by-step explanation:
we can multiply both terms of ratio with same number without changing the ratio.
Example
a:b = ax: bx (here we have multiplied both terms with x)\
Given
Stevie and Michael share their profit in a ratio 3:5
Let the profit for Stevie and Michael be 3x and 5x
Given Stevie gets £120 more than Michael
Profit for Steve = 120 + profit for Michael
3x = 120 + 5x
3x-5x = 120
=> -2x = 120
=> x= -120/2 = -60
As we see profit is negative , hence it cannot be solution.
It can be solved if Stevie and Michael share their profit in a ratio 5:3
(note: in ratio , bigger number should have bigger term in ratio)
Let the profit for Stevie and Michael be 3x and 5x
Given Stevie gets £120 more than Michael
Profit for Steve = 120 + profit for Michael
5x = 120 + 3x
5x-xx = 120
=> 2x = 120
=> x= x120/2 = 60
Profit for stevei = 5x =5*60 = 300
Profit for Michael = 3x = 3*60 = 180
Total profit for them together = 300 + 180 = 480 Answer.
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.)
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
Just divide and check,
(x^2 + 7x + 10) ÷ (x + 2)
Answer:
x+5
Step-by-step explanation:
so first you would divide by x (which means you would multiply x+2 by -x)
x^2 + 7x + 10
-x^2 - 2x
5x + 10
then you would divide by 5 (which means you would multiply x+2 by -5)
5x + 10
5x +10
0
So then to check it you would multiply x+5 by x+2
(x+5)(x+2)
x^2 + 2x + 5x + 10
then simplify to get
x^2 + 7x + 10
PLEASE HELP ME IS FOR TOMMOROW
Answer:
65°
Step-by-step explanation:
The missing angle is x°
tan x° = [tex]\frac{opposite }{adjacent}[/tex]
tan x° = [tex]\frac{850}{400\\}[/tex]
tan x° = 2.125
Using a calculator insert
tan^(-1)(2.125) ≈ 65° (after rouding the the nearest unit)
Of a certain road 7.264km are down hill, 3.873km are up hill and 6.89 are level.what is the length of the road pls urgent tnx
Answer:
18.027
Step-by-step explanation:
7.264+3.873+6.89
18.027
Please help me asapppppp
Answer:
3x+4
Step-by-step explanation:
The perimeter is given by
P = 2 ( l+w)
We know the perimeter is 8x+8
8x+8 = 2 ( l+w)
Divide each side by 2
4x+4 = l+w
The width is x
4x+4 = l+x
Subtract x from each side
4x+4-x = l+x-x
3x+4 = l
The length is 3x+4
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
Work out the mean for the data set below: 2.2, 2, 8.9, 4.1, 8.2
Which word best compleates the statement below look at the diagram to help
Answer:
The answer is option B.
RectanglesHope this helps you
Answer:
trapezoids
Step-by-step explanation:
i know i can delete rectangles and square, but rhombuses and parallelogram don't really have in common so the answer is trapezoids.
is quite easy 4th grade math
hope this helped :)
PLEASE ANSWER ASAP!! THANKS!!
Answer:
40
Step-by-step explanation:
The angles stay the same but, the position of the triangle changes.
Hope this helps,
kavitha
Answer: A’ = 40ᴼ
Step-by-step explanation:
The angles are congruent and add to equal 180ᴼ
A = 40ᴼ
The measure of A stays the same when the angles are rotated
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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Can you please help me I really need help please help me thank you
Answer:
a) x = 17/8
b) x = 23
c) x = -8/11.
Step-by-step explanation:
a)
-3x + 5 = 5x - 12
Add 3x to both sides:
5 = 8x - 12
Add 12 to both sides:
17 = 8x
Divide both sides by 8:
17/8 = 8x/8
x = 17/8.
---------------------
b)
6(x-3)-4(x+2) = 20
Distribute:
6x - 18 - 4x - 8 = 20
Combine like terms:
2x - 26 = 20
Add 26 to both sides:
2x = 46
Divide both sides by 2:
x = 23.
---------------------
c)
-2/5(x + 3) = 1/3(x - 2)
Distribute:
-2/5x - 6/5 = 1/3x - 2/3
Add 2/5x to both sides by creating a common denominator:
-6/15x - 6/5 = 5/15x - 2/3
-6/5 = 11/15x - 2/3
Add 2/3 to both sides. Create common denominator:
-18/15 = 11/15x - 10/15
-8/15 = 11/15x.
Divide both sides by 11/15:
[tex]\frac{-8}{15}* \frac{15}{11} = \frac{-8}{11} = x[/tex]
x = -8/11.