Answer:
Part A)
Our system of equation is:
[tex]\displaystyle \begin{aligned} 2x+y&=25\\x+y&=20\end{aligned}[/tex]
Where x represent the amount of cheese wafers bought and y represent the amount of chocolate wafers bought.
Part B)
Mike and his friends bought five cheese wafers and 15 chocolate wafers.
Step-by-step explanation:
Let cheese wafers be represented by x and let chocolate wafers be represented by y.
Part A)
They spent a total of $25. Since each cheese wafer cost $2 and each chocolate wafer cost $1, we can write that:
[tex]2x+1y=25[/tex]
Or, simply:
[tex]2x+y=25[/tex]
They also purchased a total of 20 packets of wafers. Hence:
[tex]x+y=20[/tex]
Our system of equation is:
[tex]\displaystyle \begin{aligned} 2x+y&=25\\x+y&=20\end{aligned}[/tex]
Where x represent the amount of cheese wafers bought and y represent the amount of chocolate wafers bought.
Part B)
Since both equations have the same coefficient for y, we can use elimination. First, multiply the second equation by negative one:
[tex]-x-y=-20[/tex]
Add it to the first equation:
[tex](2x+y)+(-x-y)=(25)+(-20)[/tex]
Simplify:
[tex]x=5[/tex]
So, five cheese wafers were bought.
Using the second equation again, we can see that:
[tex](5)+y=20\Rightarrow y=15[/tex]
So, 15 chocolate wafers were bought.
Notes:
If we wanted to solve this using substitution, we can subtract x (or y, doesn't really matter) from both sides from either equation. Using the second equation, this yields:
[tex]y=20-x[/tex]
Substitute this into the first:
[tex]2x+(20-x)=25[/tex]
Simplify:
[tex]x=5[/tex]
And we will acquire the same answer:
[tex]y=20-(5)=15[/tex]
Solve the equation. Round to the nearest thousandth.
[tex] - 5 + 2ln(3x) = 5[/tex]
Answer:
[tex] x \approx \: \boxed{49.471}[/tex]
Step-by-step explanation:
[tex] - 5 + 2In(3x) = 5 \\ 2In(3x) = 5 + 5 \\ 2In(3x) = 10 \\ In(3x) = \frac{10}{2} \\ In(3x) = 5 \\ \implies \: 3x = {e}^{5} \\ \implies \: x = \frac{ {e}^{5} }{3} \\ x = \frac{148.41316}{3} \\ x = 49.4710533 \\ x \approx \: \boxed{49.471}[/tex]
Answer:
x= e^ 5 / 3 OR 49.471
Step-by-step explanation:
-5=2In (3x)=5
determine the defined range
-5+2In (3x) = 5, x>0
move the constant to the right- move the five to the right and change the sign
2In (3x)= 5+5
calculate- add them together
2In (3x)=10
divide both sides by 2
In (3x)=5
covert into exponential form ( x=e^5)
3x= e^5
divide both sides by 3
x=e^5/3 , x> 0
(check if the solution is in the defined range) which is the answer
Use the number line to find the measure of SV
Answer:
8
Step-by-step explanation:
S = -7 to V= 1 you count from -7 to 1
A stationer fixes an equal rate of profit in his each item . If he sells a calculator costing Rs 700 for Rs 756 , how much should a customer pay for a novel book costing Rs 450 ?
Answer:
The customer should pay RS 506 for a novel book costing RS 450.
Step-by-step explanation:
We are given that
Selling price of calculator, S.P=RS 756
Cost of calculator, C.P=RS 700
We have to find S.P of novel book when the cost of novel book RS 450.
Profit=S.P-C.P
Profit=756-700
Profit=RS 56
Profit of each item is equal.
Therefore, profit for novel book=RS 56
C.P of novel book=RS 450
S.P=C.P+ Profit
Using the formula
S.P=450+56
S.P=RS 506
Hence, the customer should pay RS 506 for a novel book costing RS 450.
When a = 1 and b = 5, what is the value of c?
Answer:
5.1
Step-by-step explanation:
a² + b² = c²
1² + 5² = c²
1 + 25 = c²
26 = c²
c = 5.1
Answer:
The constant of variation is k =
3/8
When a = 1 and b = 5, what is the value of c?
3/40
which expression is equivalent to 5^3√6c+7^3√6c, if c ≠ 0
Answer:
Option C
Step-by-step explanation:
complete question
A. 35[3]6cB. 12[3]12cC. 12[3]6cD.72c
The given equation can be written as
5^3√6c+7^3√6c
5 * [tex]\sqrt{3 *3*2c}[/tex] + 7 * [tex]\sqrt{3 *3*2c}[/tex]
5 * 3 *[tex]\sqrt{2c}[/tex] + 7 * 3 *[tex]\sqrt{2c}[/tex]
15 *[tex]\sqrt{2c}[/tex] + 21 *[tex]\sqrt{2c}[/tex]
36 *[tex]\sqrt{2c}[/tex]
12 [3]*[tex]\sqrt{2c}[/tex]
Option C is correct
Dianna made several loaves of bread yesterday. Each loaf required 2 and two-thirds cups of flour. All together, she used 13 and one-third cups of flour. How many loaves did Dianna make?
Answer:
5 loaves
Step-by-step explanation:
13 1/3 divided by 2 2/3 is 5 so the answer is 5 loaves.
Rewrite the fractions as improper fractions then divide the total amount used by the amount per loaf:
13 1/3 = 40/3
2 2/3 = 8/3
40/3 / 8/3
When dividing by a fraction flip the fraction over and multiply
40/3 x 3/8 = (40 x3) /( 3 x 8) = 120/24 = 5
She made 5 loaves of bread.
Help help help help
Answer:
its the second option
Step-by-step explanation:
Answer:
y = 3x - 4
Step-by-step explanation:
x = 2:
3(2) - 4 = 2
x = 3:
3(3) - 4 = 5
x = 4:
3(4) - 4 = 8
x = 5:
3(5) - 4 = 11
How do you solve x^2+5x-14=0
Answer:
x = -7 , x = 2
Step-by-step explanation:
[tex]x^2 + 5x -1 4= 0\\\\x^2 + 7x -2x - 14 = 0\\\\x(x + 7) -2(x + 7) = 0\\\\(x+7)(x-2) = 0\\\\x+ 7 = 0 , \ x - 2 = 0 \\\\x = - 7 , \ x = 2[/tex]
Answer:
x = - 7, x = 2
Step-by-step explanation:
Solve by factoring , that is
x² + 5x - 14 = 0
Consider the factors of the constant term (- 14) which sum to give the coefficient of the x- term (+ 5)
The factors are + 7 and - 2 , since
7 × - 2 = - 14 and 7 - 2 = + 5 , then
(x + 7)(x - 2) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 7 = 0 ⇒ x = - 7
x - 2 = 0 ⇒ x = 2
WILL GIVE U BRAINLIEST ♡ Rationalize the denominator of fraction with numerator square root of -36 divided by (2-3i)+(3+2i)
Answer:
[tex] - \frac{3}{13} + \frac{15i}{13} [/tex]
Step-by-step explanation:
[tex] \frac{ \sqrt{ - 36} }{(2 - 3i) + (3 + 2i)} [/tex]
Set up equation
Step 1: Simplify
[tex] \frac{6i}{5 - i} [/tex]
Step 2:Multiply by conjugate
[tex] \frac{6i}{5 - i} \times \frac{5 + i}{5 + i} [/tex]
Step 3:Simplify
[tex] \frac{30i + 6 {i}^{2} }{ {i}^{2} - 5 {}^{2} } [/tex]
We can reduce this and we must make the imaginary number and real number serpate equations.
[tex] - \frac{6}{26} + \frac{30i}{26} [/tex]
Reduce each by 2
[tex] - \frac{3}{13} + \frac{15i}{13} [/tex]
Which expression is equivalent to 24x2 – 22x + 5?
Answer:
C: (12x - 5) ( 2x - 1)
Step-by-step explanation:
12 x ( 2x- 1 ) -5 (2x - 1 )
= (12x - 5 ) ( 2x -1)
Hope it helps !
Answer:
12x-5 2x-1
Step-by-step explanation:
This is the correct answer. Answer C
write the solution as a coordinate pair. SHOW YOUR WORK!!!!!
GIVING BRAINIEST TO WHOEVER HELPS ME AND GETS IT RIGHT!!!
Answer:
(-4,8)
Step-by-step explanation:
x + 4y = 28
+ -x + y = 12
5y = 40
y = 8
-x + (8) = 12
-x + 8 = 12
-x = 4
x = -4
Which expression is equivalent to 96?
Answer:
[tex]4\sqrt{6}[/tex]
Step-by-step explanation:
[tex]\sqrt{96}[/tex]
[tex]\sqrt{2*2*2*2*2*3}[/tex]
[tex]2*2\sqrt{2*3}[/tex]
[tex]4\sqrt{6}[/tex]
Increase 14187.13 by 14.5
Answer:
14201.63
Step-by-step explanation:
14187.63
+ 14.50
=14201.63
Can some one pls help get the answers
Answer:
[tex] \frac{1}{5} [/tex]
n(S) = 5
n(6) =1
So, P(6)= n(6)/n(S)
=1/5
The area of a rectangle is 99 square units. Its width measures 11 units. Find the length of its diagonal. Round to the nearest tenth of a unit.
Answer:
14.21267
Step-by-step explanation:
pls say fast wrong answers = report
Answer:
[tex]a = - \frac{179}{171} \ , \ b = - \frac{20 \sqrt7}{171}\\\\[/tex]
Step-by-step explanation:
[tex]\frac{2 + 5 \sqrt7}{2 - 5 \sqrt7} = \frac{2 + 5 \sqrt7}{2 - 5 \sqrt7} \times \frac{2 + 5 \sqrt7}{2 + 5 \sqrt7}[/tex] [tex][ \ rationalize \ the \ denominator \ ][/tex]
[tex]=\frac{(2 + 5 \sqrt7)^2}{(2)^2 -( 5 \sqrt7)^2}[/tex] [tex][ \ (a - b)(a+b) = a^2 - b^2 \ ][/tex]
[tex]=\frac{4 + 25(7) + 20 \sqrt7}{4 - 25(7)}\\\\= \frac{4 + 175 + 20 \sqrt7}{4 - 175} \\\\= \frac{179 + 20 \sqrt7}{- 171} \\\\= \frac{179}{ -171} + \frac{20 \sqrt7}{-171}\\\\= - \frac{179}{ 171} - \frac{20 \sqrt7}{171}\\\\[/tex]
It takes the staff 7.2 hours to clean 27 rooms in hotel many hours would it take them to clean 15 room? srep by step
Answer:
4
Step-by-step explanation:
The staffs takes 7.2 hours to clean 27 rooms
Therefore in one hour, the number of rooms cleaned is
= 7.2/27
= 0.2666
The number of hours required to 15 rooms is
= 0.2666×15
= 4 hours
Drag an answer to each box to complete this paragraph proof.
Given:
Prove:
M
Complete question is;
Drag an answer to each box to complete this paragraph proof.
Given:
<ABC and <CBD are complementary angles and M<ABC = 35°
Prove:
M<CBD = 55°
It's given that <ABC and <CBD are ________.
So, m<ABC + m<CBD = 90° using the _______.
It is also given that m<ABC = 35°
Using substitution property of equality, you have ___ + m<CBD = 90°.
Therefore, using the subtraction property of equality, m<CBD = ___
Attached is an image of both angles.
Options to drag are;
Complementary angles, supplementary angles, definition of supplementary angles, definition of complementary angles, 35°, 55°, 90°
Answer:
It's given that <ABC and <CBD are __complementary angles___.
So, m<ABC + m<CBD = 90° using the __definition of complementary angles___.
It is also given that m<ABC = 35°
Using substitution property of equality, you have _35°_ + m<CBD = 90°.
Therefore, using the subtraction property of equality, m<CBD = _55°_
Step-by-step explanation:
Now, from angle properties, we know that the Sum of 2 Complementary angles is equal to 90°.
Thus, <ABC and <CBD are complementary angles.
Then;
m<ABC + m<CBD = 90° (using the definition of complementary angles as seen above).
It is also given that m<ABC = 35°
Now, Using substitution property of equality, we will have;
35°+ m<CBD = 90°
Subtract 35° from both sides to get;
35 - 35 + m<CBD = 90 -35
m<CBD = 55°
The plastic straws were placed under the wooden block to
Answer:
What? Your not even done.
Step-by-step explanation:
The figure below shows three quadrilaterals on a coordinate grid: A coordinate grid is shown from positive 8 to negative 8 on the x axis and from positive 8 to negative 8 on the y axis. An image of a rectangle labeled E is shown on ordered pair negative 1, negative 1 and negative 3, negative 1 and negative 3, negative 2 and negative 1, negative 2. Another image of a rectangle labeled G is shown on ordered pair negative 2, negative 2 and negative 6, negative 2 and negative 6, negative 4 and negative 2, negative 4. Another image of a rectangle labeled F is shown on ordered pair negative 1, 1 and negative 1, 2, and negative 3, 2 and negative 3, 1. Which of the following statements is true about the three quadrilaterals? E and F are similar but not congruent. E and G are similar but not congruent. G and F are similar and also congruent. E and G are similar and also congruent.
Answer:
lot of words for a simple question about which rectangle is the same!
E and F are similar but not congruent.
Step-by-step explanation:
What is the equation of the line that passes through the point (3,-5)(3,−5) and has a slope of \frac{2}{3}
Answer:
y = 2/3x - 7.
Step-by-step explanation:
Using the point-slope form of a straight line:
y - y1 = m (x - x1) so we have
y -(-5) ) = 2/3 (x - 3)
y + 5 = 2/3x - 2
y = 2/3x - 7.
Answer:
y = 2/3x -7
Step-by-step explanation:
We know the equation of a line is
y = mx+b where m is the slope and b is the y intercept
y = 2/3 x +b
Substitute the point into the equation
-5 = 2/3 (3)+b
-5 = 2+b
Subtract 2 from each side
-7 = b
The equation of the line
y = 2/3x -7
Uhh.. Hello can you please answer this? I am actually having hard time answer this activity.. Please!! Im not from Us im from Philippines and no one answeering my question correctly they're all useless!! HELP ME!! T^T
Mean=all added together divide by total amount
median order them all and the middle number
mode the most common number
hope this helps you find out the answer
I need help with these questions please answer :(
Answer:
1. Electrons
2. amphere
3. closed
4. positive to negative
5.open
What is 5 7/8 - 1 1/8
Answer to this equation:
4 3/4
Answer:
4.75
Step-by-step explanation:
This is what I got. have a nice day:)
Which of the following are solutions to the quadratic equation? Check all that
apply.
x2 + 8x + 16 = 7
Answer:
x=-9/10
Step-by-step explanation:
2x+8x+16=7
Step 1: Simplify both sides of the equation.
2x+8x+16=7
(2x+8x)+(16)=7(Combine Like Terms)
10x+16=7
10x+16=7
Step 2: Subtract 16 from both sides.
10x+16−16=7−16
10x=−9
Step 3: Divide both sides by 10.
10x/10
=
−9/10
x=-9/10
Answer:
x = - 4 ± [tex]\sqrt{7}[/tex]
Step-by-step explanation:
Given
x² + 8x + 16 = 7 ( subtract 16 from both sides )
x² + 8x = - 9
Using the method of completing the square
add ( half the coefficient of the x- term)² to both sides
x² + 2(4)x + 16 = - 9 + 16
(x + 4)² = 7 ( take the square root of both sides )
x + 4 = ± [tex]\sqrt{7}[/tex] ( subtract 4 from both sides )
x = - 4 ± [tex]\sqrt{7}[/tex]
Then
solutions are x = - 4 - [tex]\sqrt{7}[/tex] , x = - 4 + [tex]\sqrt{7}[/tex]
The volume of aright circular cone is 12 litres calculate the volume of the two parts into which the cone is divided by a plane parallel to the base a quarter of the way down from the vertex to the base
Answer:
the New Cone Volume is 0.1875 litres & the Volume of frustum is 11.8125 litres.
Step-by-step explanation:
According To Question,
We have Given A Right Circular Cone, Volume = 12 Litres .
Now, Let The Radius Of the base be r & the height be h .
Volume of Cone = 1/3×π×r²×h
thus, 1/3×π×r²×h=12
π×r²×h=36 → Equation. 1
Now, The new Cone is cut from the Plane Parallel to a base a quarter the way down from the vertex of the base. then the cone is cut at 1/4 from the base . So the Height of new Cone is h/r and the radius is r/4 .
Then, Volume Of new Cone=1/3×π×(r²/16)×(h/4) ⇔ (Put Value From Equ. 1)
V= 12/64 ⇔ 0.1875 litres of new cone volume .
Then, the volume of Frustum = 12-0.1875 = 11.8125 litres
Help me plsssssssss
[tex]y \: \alpha \: x[/tex]
Let c be the constant
[tex]y = cx \\ 16 = c4 \\ c = \frac{16}{4} \\ c = 4[/tex]
SO:-[tex]y = cx \\ y = 4 \times ( - 2) \\ y = ( - 8)[/tex]
Answer:
y = 4x
Step-by-step explanation:
Given y varies directly with x then the equation relating them is
y = kx ← k is the constant of variation
To find k use the condition y = 16 when x = 4 , then
16 = 4k ( divide both sides by 4 )
4 = k
y = 4x ← equation of variation
When x = - 2 , then
y = 4 × - 2 = - 8
Name a geometric figure that could be the height of a tree
Answer:
Triangle
Step-by-step explanation:
h = Tan A x d, where h is the tree height, d is the distance from tree, and A is the angle to the top of the tree.
Basically you want to solve for the hypotenuse by using basic trig
Pls I beg someone to finish ALL of this :(. I’ve stayed up all night to do this but I couldn’t figure all of them out. Pls pls pls!!! ill mark you brainliest n I can give you a thank you such as 5 Stars in return. Please take your time and I hope you all have a amazing day!
Answer:
9. 1:53
10. 4:17
11. 2:52
12. 3:35
This should be it have a great day buddy!
Hi can someone answer this question for me I would really appreciate it.