Step 1) Set up a proportion to find how much Peter spent
45 cards / x dollars = 3 cards / 2 dollars
Step 2) Cross-multiply to solve the proportion
3x = 90
x = $30
Step 3) Set up a proportion to find how much Peter made
45 cards / x dollars = 5 cards / 4 dollars
5x = 180
x = $36
Step 4) Subtract the amount Peter made by the amount he spent
36 - 30 = $6
Answer: Peter made $6
($2/3) * 45 = $30
($4/5) * 45 = $36
$36 - $30 = $6
Solve a = 2x + 6xz for X
Answer:
See Below.
Step-by-step explanation:
We are given the equation:
[tex]a=2x+6xz[/tex]
And we want to solve for x.
On the right-hand side, we can factor:
[tex]a=x(2+6z)[/tex]
And divide both sides by the factored expression. Hence:
[tex]\displaystyle x=\frac{a}{6z + 2}[/tex]
And we're done!
Answer:
x=a/2(1+3z)
Step-by-step explanation:
The spinner below shows 10 equally sized slices. Rachel spun the dial 500 times and got the following results.
Answer:
most likely got 50 of each slice since they were the same size
Step-by-step explanation:
500/10=50
Answer:
50
Step-by-step explanation:
A person on the top of a tall building looks through his binoculars at his friend that is 300 ft away from the building on the ground. If the angle of depression from the person on the building is 30°, how far are the two people away from one another? Round your answer to the nearest foot.
Answer:
520 feet
Step-by-step explanation:
The easiest way to visualize this problem is to sketch a quick diagram.
For this problem, you are given an angle and the length of the side of a triangle. If you look at the diagram, you'll see that the length given is the opposite side of the angle given. For this situation, that means you will use the sine function (refer to SOH-CAH-TOA acronym). Then you plug in the given values and solve for x.
Hope this helps!
Let u = 2i + j, v = i + j, and w = i - j. Find scalars a and b such that u= av + bw.
Answer:
1/2 and 3/2Step-by-step explanation:
Given the expression u= av + bw where u = 2i + j, v = i + j, and w = i - j, to find the scalars a and b, we will first substitute the vectors into the expression given as shown;
u= av + bw
2i + j = a( i + j)+b(i-j)
open the parenthesis
2i + j = ai+aj+bi-bj
collect like terms at the right hand side of the equation
2i + j = ai+bi+aj-bj
2i + j = (a+b)i+(a-b)j
compare the coefficient of complex value i and j on both sides
a+b = 2 ............... 1
a-b = 1................. 2
solve the resulting equation simultaneously using elimination method
Subtract both equation from each other.
(a-a) +(b-(-b))= 2-1
0+2b = 1
b = 1/2
Substitue b = 1/2 into equation 2 to get a
From equation 2, a = 1+b
a = 1 + 1/2
b = 3/2
Hence the scalars a and b are 1/2 and 3/2 respectively
[tex]a=\frac{3}{2},b=\frac{1}{2}[/tex]
A complex number is of the form [tex]\boldsymbol{a+ib}[/tex] where [tex]a,b[/tex] are real numbers.
[tex]u=2i+j[/tex]
[tex]v=i+j[/tex]
[tex]w=i-j[/tex]
[tex]u=av+bw[/tex]
So,
[tex]2i+j=a(i+j)+b(i-j)[/tex]
[tex]2i+j=(a+b)i+(a-b)j[/tex]
Therefore,
[tex]2=a+b\\1=a-b[/tex]
Add these equations.
[tex]3=2a\\\frac{3}{2}=a[/tex]
So,
[tex]1=\frac{3}{2}-b\\\\b=\frac{3}{2}-1\\[/tex]
[tex]=\frac{1}{2}[/tex]
For more information:
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The perimeter of a rectangle is 36 feet. If the length is 13, find the width
Answer: 5 feet
Step-by-step explanation: To find the width of the rectangle,
start with the formula for the perimeter, shown below.
Perimeter = 2l + 2w
Since we know the perimeter is 36 and the
length is 13, we have 36 = 2(13) + 2w.
Simplifying on the right, we have 36 = 26 + 2w.
Not subtract 26 from both sides to get 10 = 2w.
Now divide both sides by 2 and 5 = w.
So the with is 5 feet.
x-(-6)=4
please help me SASP
Hey there! I think the answer is x=(-2)
Answer:
-2
Step-by-step explanation:
The constant rate of change of a line is also called what
Answer:
The slope of the line.
Step-by-step explanation:
In other words, SLOPE is the VERTICAL change between any two points divided by the HORIZONTAL change in any two points.
Answer
The constant rate of change of a line is also called what
...SLOPE...
Janice works part-time in a pizza restaurant. She makes a monthly salary of $240. She spends 3/5 of her salary on gas for her car. How much does Janice have left at the end of the month for her other expenses
Answer: 144
Step by step: In order to solve this easily, you should convert 3/5 into a decimal. In order to do that, you have to divide the numerator by the denominator. 3 divided by 5 = 0.6. Then you multiply 240 by 0.6 to get your answer, 144.
Find the sum 32 +33 +34 + 35 + ... + 112 + 113.
Answer:
5945
Step-by-step explanation:
The sum for an arithmetic series is given by the formula:
[tex]S=(x_1+x_k)\cdot\frac{k}{2}[/tex]
Where x₁ is the initial term, x_k is the last term, and k is the number of elements in the series.
From the sequence, we can see that the first term is 32. The last term is 113.
To determine how many elements we have, subtract 113 and 32:
[tex]113-32=81[/tex]
However, we must add 1 to this number since this doesn't include the first term. Thus:
[tex]81+1=82[/tex]
So, there are 82 terms in total.
Therefore, our sum is:
[tex]S=(32+113)\cdot\frac{82}{2}[/tex]
[tex]S=(145)\cdot 41=5945[/tex]
Answer:
5945
Step-by-step explanation:
an = a1 + ( n - 1) 1
a1 = first term
n = number of terms
an = last term
113 = 32 + ( n - 1 ) 1
113 = 32 + n -1
113 = 31 + n
n = 113 - 31
n = 82.
Sn = n/2(a1 + an)
S82 = 82/2 (32 + 113)
S82 = 41 (145)
S82 = 5945.
2x+2=-59 I need help I don’t know the answer
Answer:
x= -30.5
Step-by-step explanation:
In order to solve equations like this, we need to have all the x terms on one side, and all the other terms on the other side. For this equation so far, the x term (2x) is not alone (there is a +2) so we need to move the +2 to the other side to have x by itself. Whatever you do to one side of equation, you must also do to the other side to keep the equation equal. Therefore we can subtract 2 from both sides which moves the two to the other side while keeping the equation equal. In order to move a term to the other side, we must do the operation opposite to what the term has. E.g. +2 is adding 2, so to move it to the other side, we need to subtract 2.
2x +2 -2 = -59 -2
Which cancels out the 2 on the left side and gives us:
2x = -59-2
2x = -61
Then we just need to remove the 2.
In this case, this 2 is being multiplied to the x, so to move it, we will need to divide both sides by 2.
2x/2 = -61/2
which finally gives us:
x = -30.5
Hope this helped!
Solve -x/4 < 7
A. x < -28
B. x < 28
C. x > -28
D. x > 28
Answer: [tex]x>-28[/tex]
Simplify both sides of the inequality
[tex]1/4x<7[/tex]
Multiply both sides by 4/-1
[tex](4/-1)*(-1/4x)<(4/-1)*(7)\\x<-28[/tex]
Area of triangle=42, the width is x+3 and the length is 2x+8, find the value of x
Step-by-step explanation:
Area of triangle = 1/2 × the width × the length
42 = 1/2(x+3)(2x+8)
42 = 1/2×2×(x+3)(x+4)
42 = (x+3)(x+4)
(x+3)(x+4) = 42
x² + 7x + 12 = 42
x² + 7x + 12 - 42 = 0
x² + 7x - 30 = 0
(x-3)(x+10) = 0
x = 3, -10
x can't be -10 because the width and the length should be only + values
x = 3
The value of x found by using the area of triangle concept is 3
What is the Area of a Triangle?
The entire area filled by a triangle's three sides on a two-dimensional plane is referred to as the triangle's area. The fundamental equation for a triangle's area is A = 1/2 b × h, where b and h are the product of the triangle's base and height. All triangle shapes, including scalene, isosceles, and equilateral triangles, may be calculated using this formula. It is important to keep in mind that a triangle's base and height are perpendicular to one another.
In the question, It is given that:
Area of triangle = 42.
Width of the triangle = x+3
Length of the triangle = 2x+8;
And, we know that:
Area of triangle = [tex]\frac{1}{2}[/tex]×[tex]lw[/tex]
⇒[tex]42[/tex] = [tex]\frac{1}{2}[/tex]×[tex](x+3)(2x+8)[/tex]
⇒42 = (x+3)(x+4)
⇒(x+3)(x+4) = 42
⇒x² + 7x + 12 = 42
⇒x² + 7x + 12 - 42 = 0
⇒x² + 7x - 30 = 0
⇒(x-3)(x+10) = 0
⇒x = 3, -10
x can't be -10 because the width and the length should be only + values
⇒x = 3
Hence, The value of x is 3.
To learn more about the area of the triangle visit the given link:
https://brainly.com/question/17335144
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3. Which point is coplanar with E, F, and H in the diagram below?
Answer: G
Step-by-step explanation: Points are coplanar if they lie on the same plane.
So, G would be a coplanar point with E, F, and H.
Answer:
G
Step-by-step explanation:
i just took the test and got it right! (:
All of the following are equivalent, except
3x
2x^2
x(2 + 1)
2x + x
Answer:
2x^2 is not equivalent
Step-by-step explanation:
3x = 3x
2x^2 = 2x^2
X(2+1) = 3x
2x + x = 3x
the odd one out is 2x^2
Water flows through a pipe at a rate of 91 fluid ounces every 2.5 weeks. Express this rate of flow in cups per hour.
Answer:
[tex]Rate = 0.2167\ fl\ oz/hour[/tex]
Step-by-step explanation:
Given
[tex]Rate = \frac{91\ fl\ oz}{2.5\ weeks}[/tex]
Required
Express the rate as per hour
[tex]Rate = \frac{91\ fl\ oz}{2.5\ weeks}[/tex]
There are 168 hours in a week;
So, the rate becomes
[tex]Rate = \frac{91\ fl\ oz}{2.5 * 168\ hours}[/tex]
[tex]Rate = \frac{91\ fl\ oz}{420\ hours}[/tex]
[tex]Rate = 0.2167\ fl\ oz/hour[/tex]
Hence;
The equivalent of the given rate is [tex]0.2167\ fl\ oz/hour[/tex]
how to estimate 72,931+18,563
Answer:
Your answer is 91, 494
Step-by-step explanation:
I will tell how is your answer is 91,494
72,931
+18,563
=91,494
Just add the question then you have your answer
16 squared with explanation.
Answer:
256
Step-by-step explanation:
Multiply 16 by 16.
You bet 256, right?
The answer is 256 now.
Hope it helps!
Formula: multiply number you have x number you have.
Noah drew 22 hearts and 76 circles. What is the ratio of circle to all shapes
Answer:3 to 10
Step-by-step explanation:
Suppose that Cand D are points on the number line. If CD=11 and D lies at 6, where could C be located?separate them with commas.
what
help
Answer:
Step-by-step explanation:
There can only be 2 location which is to the right and to the left, this is because it means the difference between is 17. Add them together. So the two answers are…
17
and
-17
15 POINTS Can someone help me solve this PLEASE
Answer:
should have dded like variables first
Step-by-step explanation:
Answer:
X=6
Step-by-step explanation:
3x+2x-6=24
add 3x and 2x this gives 5x
5x-6=24
then add the 6 to 24
5x=30
then divide both sides by 5
then X=6
Please hurry i cant wait for too long ;-;.
Answer:
the answer is 1/6.......
Will records the wins and losses for his high school basketball team each year. He notices that the ratio of wins to
losses has been consistent each year.
Wins
18
45
36
27
Losses
2.
5
4
Х
Using the information in the table, how many losses should he predict for next year if the number of games won is 27?
1
3
Answer:
3
Step-by-step explanation:
Suppose the average yearly salary of an individual whose final degree is a master's is $41 thousand less than twice that of an individual whose final degree is a bachelor's. Combined, two people with each of these educational attainments earn $115 thousand. Find the average yearly salary of an individual with each of these final degrees.
Answer:N/B The amount is in thousands
The total amount earned by a Bachelor's person be $x:
amount earned by a masters person will be $(2x-38)
Total amount earned by the two individuals will be:
x+(2x-38)=115
solving for x we get:
x+2x-38=115
3x=115+38
3x=153
x=153/3
x=51
also:
2x-38=2*51-38=64
therefore we conclude that master's individual earns average of $ 64,000 while the Bachelor's individual earns $51,000.
Step-by-step explanation:plzzzzz give brainleyest
3/4 and 1/6 find the least common denominator
Answer: 12 is the least common denominator
Step-by-step explanation:
The least common denominator is the greatest multiple that the two denominators share.
So find the multiples of 4 and 6.
LCM of 4. is 4 ,8 ,12,16,20,24, 28,32,
LCM of 6 is 6,12,18,24,30,36, 42,48
The first multiple that they share is 12
What is the value of the expression below when z = 4?
10z - 3
━━━━━━━☆☆━━━━━━━
▹ Answer
37
▹ Step-by-Step Explanation
Plug in 4 for z:
10(4) = 40
Subtract:
40 - 3 = 37
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
what is 3⁴×3⁵ can anyone help me
Let's look at the multiplication exponent rule.
[tex]x^a*x^b=x^{a+b}[/tex]
Meaning that the exponents will add together when the same base is multiplied.
[tex]3^4*3^5=3^{4+5}=3^9[/tex]
Hope this helps.
頑張って!
Answer:
19683
Step-by-step explanation:
3x3x3x3= 81
3x3x3x3x3=243
81x243=19683
PlusExplain no solution 3(xplus4)equals 3(x-5)
Answer 7
Step-by-step explanation
do theis prdcjkfbiubnvckdnsgjibjkdsvhbrhvbbghbvhvbhbgfndjsnjdnsndj
What is the rate of 3.5 hours:$10
Answer:
$2.85 per hour
Step-by-step explanation:
Answer:
I think the answer is 35 or are trying to find how much is in and hour
Find out the unknown length. Please i really need help on this one really bad...
Answer:
6
Step-by-step explanation:
using similar triangles
x/(x+8) =15/35
x/(x+8) =3/7
cross multiply the two sides which will give u
3(x+8) =x*7
3x +24 =7x
24=7x-3x
24=4x
using 4 to divide both sides
24/4=4x/4
6=x
x=6
Evaluate 6•(4+)^2-3^2
Answer:
87
Step by step explanation:
(6)(16) - [tex]3^{2}[/tex]
96 - [tex]3^{2}[/tex]
96 - 9
87