Answer:
Step-by-step explanation:
Define number of videos purchased as "n" and number of CD's purchased as "c" then we can equation the total purchases and the costs by:
8 nephews:
n + c = 8
Spent $121.53
14.95*n + 16.88*c = 121.53
Substitute one variable as a function of the other. Preference the simpler equation (n + c = 8)
n = 8 - c
=>
14.95*(8-c) + 16.88c = 121.53
119.60 + 1.93c = 121.53
1.93c = 1.93
c = 1
=>
n = 7
*Check:
14.95*(7) + 16.88*(1) = 121.53
im so sorry if this is wrong :/
A square dullhouse has an area of 361 square inches. How long is each side of the dullhouse
Answer:
19 inches
Step-by-step explanation:
Area of a square = s^2
s^2 = 361
s = 19
The Bionic Woman gives Batman a 12 second
start in a 2 kilometre race. If the Bionic Woman
runs at 5 km/min, and Batman runs at 3 km/
min, who will win the race and by how many
seconds?
Answer:
The Bionic Woman will win the race by 4 sStep-by-step explanation:
[tex]v=\dfrac st\quad\implies\quad t=\dfrac sv[/tex]
s = 2 km
t - time of run
v - speed of running
Batman:
v = 3km/min
[tex]t = \dfrac{2\,min}{3\,\frac{km}{min}}=2\,km\cdot\dfrac{min}{3\,km}=\dfrac23\,min = \dfrac23\cdot 60\,s=40\, s[/tex]
The Bionic Woman:
v = 5 km/min
[tex]t = \dfrac{2\,min}{5\,\frac{km}{min}}=2\,km\cdot\dfrac{min}{5\,km}=\dfrac25\,min = \dfrac25\cdot 60\,s=24\, s[/tex]
time from Batman's start: 24 s + 12 s = 36 s
40 - 36 = 4
Help!!!!!!!!!!!!!!!!!!!!!
x < -3 or x > 1
=====================================================
Work Shown:
Solve the first inequality for x
3x+2 < -7
3x < -7-2 .... subtract 2 from both sides
3x < -9
x < -9/3 .... divide both sides by 3
x < -3
Do the same for the second inequality
-4x+5 < 1
-4x < 1-5
-4x < -4
x > -4/(-4) .... note the inequality sign flips
x > 1
So either x < -3 or x > 1. This points to choice A as the answer.
jimmy cn run 3.5 miles in 20 minutes. How far can he run in one hour and ten minutes?
Answer: 12.25miles.
Step-by-step explanation:
This is a simple proportion.
20 miles = 3.5miles
∴ 1 mile = 3.5/20
∴ 1hour 10minutes which is equivalent to 70minutes will be
= (3.5/20 x ⁷⁰/₁ ) miles
= 12.25miles
Write an equation in slope intercept form for the graph (-3,3) (3,-1)
Answer:
y = (-3/2)x + 7/2
Step-by-step explanation:
Find the slope of this line first.
As you move from the first point to the second, x (the 'run') increases by 6 and y (the 'rise') decreases by 4 (from 3 to -1). Thus the slope is
m = rise/run = -6/4 or -3/2.
Find b for this situation, using y = mx + b, m = -3/2, y = -1 and x = 3:
-1 = (-3/2)(3) + b. Multiply all three terms by 2:
2(-1) = -9 + 2b, or 7 = 2b. Then b = 7/2, and the desired equation is
y = (-3/2)x + 7/2
Find the product. 2√3•√15 A)5√5 B)√45 C)6√5 D)18√5
First multiply the numbers inside the radicals together.
So √3 · √15 is √45.
So we have 2√45.
Note that the 2 can't be multiplied by anything since
√15 has nothing outside of the radical.
So we have 2√45.
Now, break down your square root.
√45 breaks down as 9 · 5 and 9 breaks down as 3 · 3.
Since we have a pair of 3's, a 3 comes outside of the radical
multiplying by the 2 that was previously outside to get 6.
The 5 doesn't pair up so it stays inside.
So our final answer is 6√5.
Answer:
C) [tex]6\sqrt{5}[/tex]
Arithmetic without explanation:
[tex]2\sqrt{3}* \sqrt{15}\\ = 2\sqrt{3}* \sqrt{3*5} \\ = 2\sqrt{3^2} *\sqrt{5} \\ = 2 * 3\sqrt{5} \\= 6\sqrt{5}[/tex]
Example of radical multiplication:
Take [tex]y\sqrt{x} * a\sqrt{b}[/tex] as an example:
1. Multiple the numbers inside the roots
[tex]\sqrt{x} * \sqrt{b} = \sqrt{x*b} = \sqrt{xb}[/tex]
2. Multiple the numbers outside the roots
[tex]y*a = ya[/tex]
3. Combine them and simplify
[tex]ya\sqrt{xb}[/tex]
Step-by-step explanation:
We are given the expression [tex]2\sqrt{3}*\sqrt{15}[/tex]
1. Identify the roots and multiply them
The roots are [tex]\sqrt{3}[/tex] and [tex]\sqrt{15}[/tex]
[tex]\sqrt{3} *\sqrt{15} \\= \sqrt{45}[/tex]
2. Multiply the numbers outside the root
For [tex]2\sqrt{3}[/tex] it is [tex]2[/tex] and for [tex]\sqrt{15}[/tex] it is [tex]1[/tex]
[tex]2*1 = 2[/tex]
3. Combine and simplify
Combine:
[tex]2* \sqrt{45}\\= 2\sqrt{45}[/tex]
Simplify:
*Note: [tex]\sqrt{n^2} = n[/tex]
1. Find the Prime factorization of 45
[tex]45 = 3^2 * 5[/tex]
2. Simplify the Root
[tex]2\sqrt{45} \\ = 2\sqrt{3^2 * 5} \\= 2\sqrt{3^2} * \sqrt{5} \\= 2 * 3\sqrt{5}\\ =6\sqrt{5}[/tex]
We end up with [tex]6\sqrt{5}[/tex]
On a number line, suppose the coordinate of A is 0 and AR=21. What are the possible coordinates of the midpoint of AR?
Answer:
The possible coordinates of the midpoint are -10.5 and 10.5
Step-by-step explanation:
The given parameters are;
The coordinate of A = 0
The distance from A to R which is the same as AR = 21
Given that R is on the number line, we have;
When R is on the left side of A, which is = 0 - 21 = -21, we have;
The coordinates of the midpoint, M from -21 to 0 is given as follows;
M = (A + R)/2 = (0 - 21)/2 = -10.5
When R is on the right side of A, which is = 21 - 0 = 21, we have;
The coordinates of the midpoint, M from 21 to 0 is given as follows;
M = (A + R)/2 = (0 + 21)/2 = 10.5
Therefore, the possible coordinates of the midpoint are -10.5 and 10.5.
Write the equation of the line in slope intercept form that passes through (-2, -8) and (-9, 4)
Please provide steps to solve if possible
Answer:
[tex]y=-\frac{12}{7}x-\frac{80}{7}[/tex]
Step-by-step explanation:
In order to find the slope-intercept form of a line when given two points, we need to first put it into point-slope form. The point-slope form is given by the equation:
[tex]y-y_1=m(x-x_1)[/tex]
Where m is the slope and x₁ and y₁ is one of the two points.
Anyways, let's first find the slope. Let's designate (-2,-8) as x₁ and y₁ and (-9,4) as x₂ and y₂ (it doesn't really matter). The formula for slope is:
[tex]m=\frac{y_2-y_1}{x_2-x_1} =\frac{(4)-(-8)}{(-9)-(-2)}=12/-7=-12/7[/tex]
So, the slope is -12/7.
Now, pick a point for the point-slope form. To keep things consistent, I'm going to use the point (-2,-8) as x₁ and y₁. Plug in -12/7 for m. Therefore:
[tex]y-(-8)=-\frac{12}{7}(x-(-2))\\[/tex]
Now, simplify, distribute, and isolate the y:
[tex]y+8=-\frac{12}{7}(x+2)\\y+8=-\frac{12}{7}x-\frac{24}{7}\\y=-\frac{12}{7}x-\frac{24}{7}-8\\y=-\frac{12}{7}x-\frac{24}{7}-\frac{56}{7} \\y=-\frac{12}{7}x-\frac{80}{7}\\y=-\frac{12}{7}x-\frac{80}{7}[/tex]
Solve for n
3n-2=2n
N=
Step-by-step explanation:
3n-2=2n
-2=2n-3n
-2=-n
-2=-n
divide by - to get 2
Write in point-slope form an equation of the line that passes through the point (8, 9) with slope 7.
Answer:
y = 7x -47Step-by-step explanation:
[tex]m = 7\\(8,9)=(x_1 , y_1)\\\\y-y_1=m(x-x_1)\\\\y - 9=7(x -8)\\y-9=7x-56\\\\Collect\:like\:terms\\\\y = 7x-56+9\\\\y = 7x-47[/tex]
$150 in prize money is going to be split among 6 contestants in a competition at a charity event. The person in first place receives the most money, the person in second place receives the second most, the person in third place receives the third most, and so on. Did the person in second place receive at least $40 of the prize money? (1) The person in first place won $50 (2) No individual prize was within $10 of another prize
Answer: yes
Step-by-step explanation:
adding 50 40 30 20 10 and 0 gets you 150 so 2nd place gets 40
f(13) = -3x+ 7
What’s the answer?
Answer:
3.3
Step-by-step explanation:
7-7=0
-3+-7=-10
10 divided by 3 is 3.3
preform the indicated multiplication below. reduce the terms and simplify (2+i)(3-i)(1+2i)(1-i)(3+i)
Answer:
Hey there!
Expand (2+i)(3-i). You should get 7+i
Expand (7+i)(1+2i). You should get 5+15i
Expand (5+15i)(1-i). You should get 20+10i
Expand (20+10i)(3+i). You should get 50+50i as your final answer.
Let me know if this helps :)
Sumi
Cal's go cart has a gas tank with the dimensions shown below.
He uses a gas can that holds 1 liter of gas, to fill the go cart tank.
1 liter = 1000 cm
and d
cm
and d
ems
25 cm
40 cm
How many full gas cans will it take to fill the go cart's gas tank?
Answer: 8 liters can.
Step-by-step explanation:
First we need to find the volume of the cart tank . Since it is in the shape of a rectangular prism we have to multiply the length by the width by the height to find the volume.
V= 40 * 25 * 8
V = 8000
Which means that the volume is 8000 cubic centimeters.
Now convert 8000 cubic centimeters to liter.
It gives us a hint that 1 liter is equal to 1000 cm^3
So to convert 8000 cubic centimeters to liters we will have to divide it by 1000.
8000/1000 = 8 liters.
The arc length theta shown below is 15 feet
Answer:
Part I: 2πr*X/360
Part II: 2.5 radians
Part III: 143.24°
Step-by-step explanation:
Part II: and Part III: 2π(6)*x/360 = 15, x = 143.24°
143/360 = x/2π, x = 2.5 radians
The function h(x)=12x^8+49 is an even function. Which transformation of h(x) would result in a function that is neither even nor odd?
A) reflection over the x-axis
B) vertical stretch by a factor of 7
C) translation 8 units to the right
D) horizontal compression
Explanation of the correct answer would be nice so that I understand it better.
Answer:
The correct option is;
C) Translation 8 units to the right
Step-by-step explanation:
The function h(x) = 12·x⁸ + 49 is an even function
However a translation 8 units to the right would yield the following function;
h(x) = 12 × (x+ 8)⁸ + 49 = 12x⁸ + 768x⁷ + 21504x⁶ + 344064x⁵ + 3440640x⁴ + 22020096x³ + 88080384x² + 201326592x + 201326641
For h(1) = 516560701
Also h(-x) = 12 × (-x+ 8)⁸ + 49 = 12x⁸ - 768x⁷ + 21504x⁶ - 344064x⁵ + 3440640x⁴ - 22020096x³ + 88080384x² - 201326592x + 201326641
For h(-1) = 69177661
Therefore h(x) ≠ h(-x) after the translation 8 units to the right and the function is neither even nor odd.
Kelly likes to fish at the lake near her house. She caught 8 fish last week, measured them, and put them back in the lake. The
lengths of the fish, in inches, are shown.
9, 12, 10, 8, 11, 12, 13,6
Assuming this data is representative of the fish in the lake, what is the mean length of the fish in the lake?
OA. 1.875 inches
OB
10.5 inches
Ос.
3.5 inches
OD
10.125 inches
Answer:The answer is OD 10.125
Step-by-step explanation:
Add all the lengths of the fish (6+8+9+10+11+12+12+13) = 81
Divide by 8
81/8
=10.125
-4 = 2t - 2
What’s da answer
Answer: the answer is -1.
the inverse operation of subtraction is addition so you would add 2 on both sides. now you have -4 + 2= -2. now the opposite of multiplication is division. so -2 divided by 2 is -1. hope this helps. Brainliest please!
Answer:
−1=t
Step-by-step explanation:
−4=2t−2
Simplify
First, add the same terms to both of the sides of this equation.
−4=2t−2
−4 + 2 =2t - 2 + 2
Secondly, simplify.
add the numbers
−4 + 2 =2t - 2 + 2
-2 = 2t - 2 + 2
Then,
-2 = 2t - 2+2
-2 = 2t
v
It's simplified to -2 = 2t
Thirdly, Divide both sides of the equation by the same term.
−2=2t
2 over −2
=
2 over 2t
Simplify
(divide the numbers)
2 over −2
=
2 over 2t
which also equals to
(simplify fraction)
−1 = 2 over 2t
-1 = t
Therefore, the solution is −1=t
Refrer to the attached picture on which question is written. This question will be done according to Pathagoras theorem. This question answer is √a2-25 . I want step to step explanation.
i got something different
On the number line, graph the solution to the inequality -5(x+1) > 7x + 31? Can you tell me how to go about doing this problem I have tried a few methods but can't figure it out.
Answer:
x < -3
Step-by-step explanation:
First we simplify:
-5x - 5 > 7x + 31
-12x > 36
x < -3.
We reverse the sign because we divided by a negative number on both sides.
That should be easy to graph.
The sum of a number and two equal to negative seven. Translate this sentence to an equation and then find the number
Answer:
-9
Step-by-step explanation:
x+2=-7
x+2-2=-7-2
x=-9
Answer:
-9
Step-by-step explanation:
i took this assignment
Write the inequality for the graph below. In two or three sentences, explain how you generated the inequality. Make sure to explain how you got the slope, y-intercept, and inequality.
Please Help, I Really Need The Answer To This Question
Answer: y < (-1/4)*x + 1.
Step-by-step explanation:
The first thing you need to notice is that the line is not solid and that the shaded part is under the line, so our inequality will be strictly smaller than a linear equation.
y < a*x + b.
Now let's find the equation of the line.
A linear relationship can be written as:
y = a*x + b
where a is the slope and b is the y-axis intercept.
For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:
a = (y2 - y1)/(x2 - x1).
In the graph, we can see that the line passes through the points: (0,1) and (4. 0)
Then the slope is:
a = (0 - 1)/(4 -0) = -1/4.
Now we know that the line is:
y = (-1/4)*x + b
To find the value of b, just replace the value of one of the points in the equation.
We know that (0,1) is a solution of the equation (x= 0, y = 1)
1 = (-1/4)*0 + b = b
1 = b
Then our inequality is:
y < (-1/4)*x + 1.
A flat surface made up of points that extends infinitely
in all directions
Answer: Plane
Step-by-step explanation: A plane is a flat surface that has no thickness.
Think of a plane as a wall or a floor of a room.
Another important characteristic of a plane is that it has no edges.
So it extends forever in all directions.
A bag contains 30 pieces of candy. There are 15 grape, 7 cherry, 3 lemon, 5 strawberry. What is the probability of NOT drawing a cherry?
Answer:
The probability is 23/30, .77, or 77 percent.
Step-by-step explanation:
Add up all the non cherry options, then put them over the total, 30. You would get 23/30, or .7666666666..., which is also known as about 77 percent. So the probability is 23/30, .77, or 77 percent.
PLSSSS HELPP: One day at a particular school, 15% of the students were absent and there were 1020 students at school that day. How many students did the school have altogether?
Answer:
1,200
Step-by-step explanation:
1020 divided by 0.85= 1200
7 t-shirt cost $28. Calculate the cost of 1 t-shirt
Answer:
One tshirt is $4
Step-by-step explanation:
28/7= 4
Answer:
$4.
Step-by-step explanation:
If 7 shirts equals 28 in total then just do 28/7 = 4.
4x7 = 28.
Find the measure of GE¯¯¯¯¯¯¯¯. A. 14 B. 20 C. 15 D. 16
Answer:
D. 16
Step-by-step explanation:
[tex] GH^2 = GF \times GE[/tex]
[tex] 12^2 = 9 \times (9+x - 2)[/tex]
[tex] 144= 9 \times (7+x)[/tex]
[tex] \frac{144}{9}= (7+x)[/tex]
[tex] 16= 7+x [/tex]
[tex] 16-7=x [/tex]
[tex] 9=x [/tex]
GE = 9 + x - 2 = 9 + 9 - 2 = 18 - 2
GE = 16
help me pretty plzzzzzzzzzzzzz
Answer:
A) A
Step-by-step explanation:
The square root of 7 is just over two and a half.
Answer:
A. A
Step-by-step explanation:
Step 1: Find closest perfect roots near √7
We know that √4 = 2
We also know that √9 = 3
√7 is between √4 and √9, so √7 is between 2 and 3.
Therefore, our answer is A.
The measures of two angles of a triangle are 49° and 75°. Find the measure of the third angle in degrees.
Answer:
The third angle is 180-(49+75)=56 degrees
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Answer:
56
Step-by-step explanation:
TOTAL ANGLE IN A TRIANGLE =180°180 -(49+75)180 - 124=56°CHECK56+49+75=180°If Q is the midpoint of PR, find the coordinates of R if P(l 1, -2) and Q(4, 3).
Answer:
Step-by-step explanation:
P(1, -2) ;Q(4,3)
Let R(x1,y1)
Midpoint=[tex](\frac{x_{1}+x_{2}}{2},\frac{y_1+y_2}{2})\\[/tex] = (4,3)
[tex](\frac{1+x_1}{2},\frac{-2+y_1}{2})=(4,3)\\[/tex]
Compare x coordinates and y coordinates
[tex]\frac{1+x_1}{2}=4 ; \frac{-2+y_2}{2}=3[/tex]
1+x1 = 4*2 ; -2+y2 = 3*2
1+x1 = 8 ; -2 +y2 = 6
x1= 8-1 ; y2 = 6+2
x1 = 7 ; y2 = 8
R(7 , 8)