Step 1) Solve the second equation for
x
:
x
+
3
y
=
−
5
x
+
3
y
−
3
y
=
−
5
−
3
y
x
+
0
=
−
5
−
3
y
x
=
−
5
−
3
y
Step 2) Substitute
−
5
−
3
y
for
x
in the first equation and solve for
y
:
3
(
−
5
−
3
y
)
−
2
y
=
7
−
15
−
9
y
−
2
y
=
7
−
15
−
11
y
=
7
15
−
15
−
11
y
=
15
+
7
0
−
11
y
=
22
−
11
y
=
22
−
11
y
−
11
=
22
−
11
−
11
y
−
11
=
−
2
y
=
−
2
Step 3) Substitute
−
2
for
y
in the solution to the second equation at the end of Step 1 and calculate x:
x=−5−(3×−2)
x=−5−(−6)
x=−5+6
x=1
The solution is x=1 and y=−2
Answer:
Step-by-step explanation:
After takeoff, a plane flies in a straight line for a distance of 4000 feet in order to gain an altitude of 800 feet. Find the angle of elevation from the ground to the plane.
Need help please, thank you!
Answer:
The angle of elevation from the ground to the plane is 11.5 degrees
Step-by-step explanation:
Given -
Horizontal distance from the point of takeoff to which the plane flies in a straight line = 4000 feet
The vertical distance travelled from the ground to the plane is 800 feet
Angle of Elevation
[tex]Sin X= \frac{800}{4000} \\X = Sin^{-1}\frac{800}{4000}\\X = 11.5[/tex]
The angle of elevation from the ground to the plane is 11.5 degrees
help me answer the last question
could somebody answer both?
1. Our new computer is 3 times faster than our old one. How fast is the new computer?
2.A geology kit costs $85. Sophia has $25 and plans to save $5 a week until she can pay for the kit. How many weeks will it take before she can buy the geology kit?
Answer:
1. 3x faster
2. 12 weeks
Step-by-step explanation:
(85-25)/5=12
If the discriminant of an equation is positive, which of the following is true of the equation
A it has one complex solution
B it has one real solution
C it had two real solutions
D it has two complex solutions
Answer:
C it has two real solutions
Step-by-step explanation:
If the discriminant of a quadratic equation is positive, it means that the graph intersects the x-axis, and hence produces two real solutions.
If the discriminant is zero, then the graph is tangential to the x-axis, and there will be two real coincident solutions.
If the discriminant is negative, then there are two complex solutions.
Answer:
C
Step-by-step explanation:
What is (1/2+i √3/2)^5?
Answer:
Hello! I know I am late but here is the answer for anyone else who might need it.
D. 1/2-i√3/2
Step-by-step explanation:
I got it right on edge. Hope this helps!
The value of given expression is [tex]\frac{1}{2}-\frac{\sqrt{3} i}{2}[/tex].
What is binomial theorem?
The expression of the form (a+b)^n is expand by binomial theorem.
The expansion is [tex](a+b)^{n}=\sum_{r=0}^{n}{ }^{n} C_{r} a^{n-r} b^{r}[/tex].
What is the value of given expression?Use a=1/2 and b=[tex]b=\frac{i\sqrt{3} }{2}[/tex] into the expansion of binomial.
[tex]\left(\frac{1}{2}+\frac{\sqrt{3} i}{2}\right)^{5}=\sum_{k=0}^{5}\left(\begin{array}{l}5 \\k\end{array}\right)\left(\frac{1}{2}\right)^{5-k}\left(\frac{\sqrt{3} i}{2}\right)^{k}[/tex]
When k=0 then, [tex]\left(\begin{array}{l}5 \\0\end{array}\right)\left(\frac{1}{2}\right)^{5-0}\left(\frac{\sqrt{3} i}{2}\right)^{0}=\frac{5 !}{(5-0) ! 0 !}\left(\frac{1}{2}\right)^{5-0}\left(\frac{\sqrt{3} i}{2}\right)^{0}=\frac{1}{32}[/tex]
When k=1 then, [tex]\left(\begin{array}{l}5 \\1\end{array}\right)\left(\frac{1}{2}\right)^{5-1}\left(\frac{\sqrt{3} i}{2}\right)^{1}=\frac{5 !}{(5-1) ! 1 !}\left(\frac{1}{2}\right)^{5-1}\left(\frac{\sqrt{3} i}{2}\right)^{1}=\frac{5 \sqrt{3} i}{32}[/tex]
When k=2 then, [tex]\left(\begin{array}{l}5 \\2\end{array}\right)\left(\frac{1}{2}\right)^{5-2}\left(\frac{\sqrt{3} i}{2}\right)^{2}=\frac{5 !}{(5-2) ! 2 !}\left(\frac{1}{2}\right)^{5-2}\left(\frac{\sqrt{3} i}{2}\right)^{2}=-\frac{15}{16}[/tex]
When k=3 then, [tex]\left(\begin{array}{l}5 \\3\end{array}\right)\left(\frac{1}{2}\right)^{5-3}\left(\frac{\sqrt{3} i}{2}\right)^{3}=\frac{5 !}{(5-3) ! 3 !}\left(\frac{1}{2}\right)^{5-3}\left(\frac{\sqrt{3} i}{2}\right)^{3}=-\frac{15 \sqrt{3} i}{16}[/tex]
When k=4 then, [tex]\left(\begin{array}{l}5 \\4\end{array}\right)\left(\frac{1}{2}\right)^{5-4}\left(\frac{\sqrt{3} i}{2}\right)^{4}=\frac{5 !}{(5-4) ! 4 !}\left(\frac{1}{2}\right)^{5-4}\left(\frac{\sqrt{3} i}{2}\right)^{4}=\frac{45}{32}[/tex]
When k=5 then, [tex]\left(\begin{array}{l}5 \\5\end{array}\right)\left(\frac{1}{2}\right)^{5-5}\left(\frac{\sqrt{3} i}{2}\right)^{5}=\frac{5 !}{(5-5) ! 5 !}\left(\frac{1}{2}\right)^{5-5}\left(\frac{\sqrt{3} i}{2}\right)^{5}=\frac{9 \sqrt{3} i}{32}[/tex],
Now we will add all the results to get the expansion of given expression,
[tex]\left(\frac{1}{2}+\frac{\sqrt{3} i}{2}\right)^{5}=\frac{1}{32}+\frac{5 \sqrt{3} i}{32}-\frac{15}{16}-\frac{15 \sqrt{3} i}{16}+\frac{45}{32}+\frac{9 \sqrt{3} i}{32}[/tex]
On simplifying,
[tex]\left(\frac{1}{2}+\frac{\sqrt{3} i}{2}\right)^{5}=\frac{1}{2}-\frac{\sqrt{3} i}{2}[/tex]
Therefore, the value of given expression is [tex]\frac{1}{2}-\frac{\sqrt{3} i}{2}[/tex].
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A 16 oz package of brown rice costs 79 cents and a 32 oz package of
brown rice costs $2.09. Which package is a better deal?
I have to get this done by tonight please help me!!
Answer:
The 16oz is a better deal
Step-by-step explanation:
32 = 2 * 16
buying 2 packages of 16 oz cost
0.79 * 2 = 1.58
1.58 < 2.09
The 16oz is a better deal
Answer:
The 16 oz package.
Step-by-step explanation:
Make the 16 oz a 32 oz so we can compare the prices
Mutiply 0.79 X 2 = 1.58
The 16 oz is because you can buy it twice making it a 32 oz for less than the orginal 32 oz.
(Compared side by side)
2.09 > 1.58
hope this helped!
A ladder is leaning against a building. Find the height at which the ladder is touching the building
Answer:
13.9 ft
Step-by-step explanation:
Since the triangle is a right triangle we can use pythagoreom theorm.
16^2=8^2+a^2 (a is the unknown side)
256= 64+a^2
192= a^2
Square root both sides and you get around 13.9 ft
26. If you know the lengths of two sides and the measure of _____ angle(s) of a right triangle, you can find the measure of the other two angles and the length of the other side.
Answer:
1
Step-by-step explanation:
For any triangle, you only need to know 3 pieces of information out of the 6 angles and sides to solve for the rest of the triangle.
Please solve 6 - 3x = 14
Answer:
Step-by-step explanation:
Answer:
X= -8/3
Step-by-step explanation:
Please help FIND DB.....
How many milliliters equal to 8.25 liters 
Answer: 8,500
Step-by-step explanation:
Answer:
8250 mL
Step-by-step explanation:
Multiply the volume value by 1000
What us the y-intercept of the function described in the table
Answer:
10
Step-by-step explanation:
Find the missing length. The triangles in each pair are similar.
A. 17
B. 16
C. 11
D. 13
The scale factor of a model car is the actual car is 300. If the model car is 2 in tall, how all is the car
Answer:
600
Step-by-step explanation:
The length of the actual car is 600.
What is a scale factor?Scale factor is that it is a number that multiplies times a given quantity to produce a smaller or larger version of the original number. The ratio of any two corresponding lengths in two similar geometric figures.
For the given situation,
The scale factor of a model car = 2
The length of the model car = 300
The length of the actual car = [tex]300(2)[/tex]
⇒ [tex]600[/tex]
Hence we can conclude that the length of the actual car is 600.
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A manufacturer makes decorative globes out of silver in the shape of a solid sphere. Suppose each sphere has a radius of 3 cm. If silver is priced at $7.00 per cm", how much will the silver cost to make one solid sphere?
Use 3.14 for , and do not round your answer.
Answer: [tex]\$791.28[/tex]
Step-by-step explanation:
Given
The radius of the sphere is 3 cm
Silver cost [tex]\$7[/tex] per [tex]cm^3[/tex]
The volume of a sphere is [tex]\frac{4\pi}{3}r^3[/tex]
Put the values
[tex]\Rightarrow \dfrac{4\pi}{3}\times 3^3\\\\\Rightarrow \dfrac{4\times 3.14}{3}\times 3\times 3^2\\\\\Rightarrow 113.04\ cm^3[/tex]
The price of this sphere is
[tex]\Rightarrow 113.04\times 7=\$791.28[/tex]
The Monument in Santiago measures 175 meters. A child measures 87.5 centimeters. How much is the Monument taller than the child?
Answer:
The Monument is taller than the child by 174.125 meters
Step-by-step explanation:
The Monument in Santiago measures 175 meters. A child measures 87.5 centimeters.
Step 1
Convert child's height to meters
100cm = 1 m
87.5 cm = x
Cross Multiply
100cm × x = 87.5 cm × 1m
x = 87.5 cm × 1m/100cm
x = 0.875m
Step 2
How much is the Monument taller than the child?
This is calculated by subtracting Child's height from Monument height
= 175 m - 0.875m
= 174.125 m
Therefore, the Monument is taller than the child by 174.125 m
Margaret and Bethany have a lemonade stand for one week each summer.
Each day they spend $1.50 on the ingredients necessary to make 20 cups
of lemonade. They sell each cup of lemonade for $0.25. How much do the
girls, after expenses, earn on a day that they sell 18 cups of lemonade? *
$6.00
$4.50
$3.50
$3.00
Answer:
6.00
Step-by-step explanation:
In the diagram below of triangle GHIGHI, JJ is the midpoint of \overline{GI} GI and KK is the midpoint of \overline{HI} HI . If JK=-21+9xJK=−21+9x, and GH=-2x+18GH=−2x+18, what is the measure of \overline{GH} GH ? G H
Answer:
25.5
Step-by-step explanation:
2( -21+9x)=2x+18
-42+18x=2x+18
+42 +42
18x=2x+60
-2x -2x
16x=60
60/16=3.75
x=3.75
GH=2x+18
2(3.75)+18
7.5+18=25.5
GH=25.5
1. Put the following numbers in order from least to greatest. 0.8, 1/10, 3/100, 0.91
2. Put the following numbers in order from least to greatest. 0.9, 0.35, 11/100, 7/10, 0.6, 0.21
3 Put the following numbers in order from least to greatest. 36/100, 0.2, 1/10, 8/100, 0.5, 0.44
PLEASE HELP ITS DUE IN 10 MINUTES
Answer:
0.8,0.91,1/10,3/100
0.6,0.9,0.21,0.35,7/10,11/100
0.2,0.5,1/10,0.44,8/100
Step-by-step explanation:
Answer:
0.8,0.91,1/10,3/100
0.6,0.9,0.21,0.35,7/10,11/100
0.2,0.5,1/10,0.44,8/100Step-by-step explanation: IVE DONE THIS BEFORE TOO
URGENT!!!!!!
Dan's car depreciates at a rate of 17% per year.
By what percentage has Dan's car depreciated after 4 years?
Give your answer to the nearest percent.
Answer:
an=yearn−year−0.17n+0.34
Step-by-step explanation:
Answer:
68%
Step-by-step explanation:
17% × 4
68%
Help please?
.........................
Find the volume of the solid. Round your answer to the nearest tenth.
Answer:
31.71 mm
Step-by-step explanation:
#1: Find V of cube
(L)(W)(H) = V
(3)(3)(3) = V
27= V
#2: Find V of the half sphere.
3 (diameter) × π = 9.42 (rounded)
9.42/2 (since 9.42 is the volume for a whole sphere)
=4.71
#3: 4.71+27= 31.71
:)
Which line is parallel to the line y= x + 7 ?
Answer: y=x+
Step-by-step explanation:
In order for two lines to be paralell, their slopes must be the same but their y intercepts must be different. Therefore, any line that looks like y=x+ (anything but 7) will be paralell.
what is equivalent to 3(x+6)
Answer:
3x + 18
Step-by-step explanation:
Given
3(x + 6) ← multiply each term in the parenthesis by 3
= 3x + 18
Scores of an IQ test have a bell-shaped distribution with a mean of 100 and a standard deviation of 14. What percentage of people has an IQ score greater than 114?
Answer:
15.87%
Step-by-step explanation:
We start with getting the z score
Mathematically , we have this as;
z-score = (x-mean)/SD
where x = 114
z-score = (114-100)/14 = 14/14 = 1
So we want to calculate the probability values that are greater than 1
We can use the standard normal distribution table
so we have P(z> 1) = 0.15866
in percentage, we multiply by 100 and that gives 15.866 which is 15.87 people
Connor makes 3 batches of muffins . Each batch has 12 muffins . Connor eats 2 muffins . What is m, the number of muffins Connor has left
Lesson 6 Homework Practice Select an Appropriate Display
4. What is the value of x in the equation 512x3 = 8?
A 3/4
B 3 1/4
C 4
D 1/4
Answer1/4 hope this help
Step-by-step explanation:
Geometry questionnn!
Answer:
88 units
Step-by-step explanation:
[tex] In\: \triangle OBR \:\&\: \triangle OWN[/tex]
BR || WN (Given)
Therefore,
[tex] \angle OBR \cong \angle OWN[/tex] (Alternate angles)
[tex] \angle BOR \cong \angle WON[/tex] (Vertical angles)
[tex] \therefore \triangle OBR \sim \triangle OWN[/tex] (AA postulate)
[tex] \therefore \frac{OR}{ON} =\frac{BR}{WN} [/tex] (csst)
[tex] \therefore \frac{OR}{56} =\frac{24}{42} [/tex]
[tex] \therefore \frac{OR}{56} =\frac{4}{7} [/tex]
[tex] \therefore OR =\frac{4\times 56}{7} [/tex]
[tex] \therefore OR ={4\times 8} [/tex]
[tex] \therefore OR =32 [/tex]
RN = OR + ON
RN = 32 + 56
RN = 88 units
1 ÷ 1/4 what does that equal
Answer:
4
Step-by-step explanation:
Answer:
4
Step-by-step explanation: