Answer:
x = -2
Step-by-step explanation:
What is the variable equal to?
x 7 = 14
Answer:
Varible x equals 2
Step-by-step explanation:
7x = 14
Dividing both sides by 7, we will have
x = 14/7
x = 2
Right Triangle Trig.
The values are vx = [tex]\frac{14\sqrt{3} }{\sqrt{2} }[/tex], vw = [tex]\frac{14\sqrt{3} }{\sqrt{2} }[/tex] and m∠x = 45°, for the given right angle diagram.
Step-by-step explanation:
The given is,
Right angled triangle XVW,
XW = 14[tex]\sqrt{3}[/tex]
m∠V = 90°
m∠W = 45°
Step:1
Given diagram is right angle triangle,
Trigonometric ratios for right angle is,
[tex]sin[/tex] ∅ [tex]=\frac{Opp}{Hyp}[/tex]............................(1)
[tex]cos[/tex] ∅ [tex]= \frac{Adj}{Hyp}[/tex] .........................(2)
[tex]tan[/tex] ∅ [tex]= \frac{Opp}{Hyp}[/tex]..........................(3)
Step:2
For the value of VX,
[tex]sin[/tex] ∅ [tex]=\frac{VX}{XW}[/tex]
From given,
∅ = 45°
XW = 14[tex]\sqrt{3}[/tex]
Above equation becomes,
[tex]sin[/tex] 45 [tex]=\frac{VX}{14\sqrt{3} }[/tex]
Where, Sin 45 = [tex]\frac{1}{\sqrt{2} }[/tex],
[tex]\frac{1}{\sqrt{2} } = \frac{VX}{14\sqrt{3} }[/tex]
[tex]VX = \frac{14\sqrt{3} }{\sqrt{2} }[/tex]
Step:3
For the value of VW,
[tex]cos[/tex] ∅ [tex]=\frac{VW}{XW}[/tex]
From given,
∅ = 45°
XW = 14[tex]\sqrt{3}[/tex]
Above equation becomes,
[tex]cos[/tex] 45 [tex]=\frac{VW}{14\sqrt{3} }[/tex]
Where, cos 45 = [tex]\frac{1}{\sqrt{2} }[/tex],
[tex]\frac{1}{\sqrt{2} } = \frac{VW}{14\sqrt{3} }[/tex]
[tex]VW = \frac{14\sqrt{3} }{\sqrt{2} }[/tex]
Step:4
For the value m∠x = a,
[tex]tan[/tex] a [tex]=\frac{VX}{VW}[/tex]
From given,
VX = [tex]\frac{14\sqrt{3} }{\sqrt{2} }[/tex]
VW = [tex]\frac{14\sqrt{3} }{\sqrt{2} }[/tex]
Above equation becomes,
[tex]tan[/tex] a [tex]=\frac{\frac{14\sqrt{3} }{\sqrt{2} } } {\frac{14\sqrt{3} }{\sqrt{2} } }[/tex]
[tex]tan[/tex] a = 1
a = [tex]tan^{-1}[/tex] (1)
a = 45°
m∠x = a = 45°
Step:5
Check for solution,
m∠v = m∠w + m∠x
= 45° + 45°
90° = 90°
Result:
The values are vx = [tex]\frac{14\sqrt{3} }{\sqrt{2} }[/tex], vw = [tex]\frac{14\sqrt{3} }{\sqrt{2} }[/tex] and m∠x = 45°, for the given right angle diagram.
Solve each equation. Check your solution. 4x - 8= 5x
Answer:
x= -8
Step-by-step explanation:
Answer:
x= -8
Step-by-step explanation:
After a 25% increase this year, the population of Boom Town is now 6,600 people. What WAS the population last year?
Answer:
4,950
Step-by-step explanation:
Answer:
According to my calculations, my answer is $4,950.
Step-by-step explanation:
Alex has trained his puppy, Popper, to jump through a ring. According to Alex's measurements and calculations, the ring has a diameter of 3.5 feet. What is the ring's circumference (use 3.14 for pi)?
Answer:
11 ft
Step-by-step explanation:
The ring takes circular shape and for a circle, circumference is given by
[tex]C=\pi d[/tex]
Where C represent circumference and d is the diameter.
Taking use 3.14 for pi as instructed and substituting 3.5 ft for diameter d then
C=3.14*3.5=10.99 ft
Rounding off, this is approximately 11 ft
Answer:
10.99 ft
Step-by-step explanation:
Given: The ring has a diameter of 3.5 feet
To find: The ring's circumference
Formula: [tex]C = 2\pi r[/tex]
Solution: To calculate the circumference of a circle, multiply the diameter of the circle with π (pi). The circumference can also be calculated by multiplying 2 × radius with pi (π = 3.14).
C = pi × 2r
C = pi × diameter (3.5)
C = 3.14 × 3.5 = 10.99
Hence, the ring's circumference is 10.99 ft
Danny brought $43.00 to the state fair. He bought a burger, a souvenir, and a pass. The burger was 1/4 as much as the souvenir, and the souvenir cost 2/3 the cost of the pass. Danny had $4.50 left over after buying these items. What was the cost of each item?
The cost of each item that Danny bought in this case are: Pass of the fair was of $21, the cost of souvenir was $14 and the cost of burger was $3.5
How to form mathematical expression from the given description?You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.
Given that:
The cost of burger is expressed in terms of cost of souvenir and of souvenir in terms of the cost for pass.
So, let we take:
Cost of pass = x dollars,
Then, cost of souvenir = 2/3 of x = 2x/3 dollars
And the cost of burger = 1/4 of cost of souvenir = 1/4 (2x/3) = [tex]\dfrac{2x}{12} = \dfrac{x}{6}[/tex] dollars.
Also, we have:
Total initial amount = Amount spent + Amount remaining
or
43 = Cost of all those 3 items + 4.5
[tex]43 = x + \dfrac{2x}{3} + \dfrac{x}{6} + 4.5\\43 = \dfrac{6x}{6} + \dfrac{4x}{6} + \dfrac{x}{6} + 4.5\\\\43 = \dfrac{11x}{6} + 4.5\\\\\text{Subtracting 4.5 from both the sides}\\\\43-4.5 = \dfrac{1x}{6}\\\\\\dfrac{11x}{6} = 38.5\\\\\text{Multiplying 6/11 on both the sides}\\\\x = \dfrac{6 \times 38.5}{11} = 21[/tex]
Thus, the cost of pass was $21
Now, we get:
Cost of souvenir = 2x/3 = [tex]\dfrac{2(21)}{3} = 2\times7 = 14[/tex] dollars,
and cost of burger = [tex]\dfrac{x}{6} = \dfrac{21}{6} = 3.5[/tex] dollars.
Thus, the cost of each item that Danny bought in this case are: Pass of the fair was of $21, the cost of souvenir was $14 and the cost of burger was $3.5
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Find the area of the figure to the nearest tenth.
The volume of the prism is 90 cubic meters. Find the value of x
.
The value of [tex]\( x \)[/tex] in a prism with volume [tex]\( 90 \)[/tex] cubic meters is approximately [tex]\( 2.466 \)[/tex] meters.
To find the value of [tex]\( x \)[/tex], knowing the volume [tex]\( V \)[/tex] of the prism, use the formula:
[tex]\[ V = l \times w \times h \][/tex]
Given [tex]\( V = 90 \)[/tex] cubic meters, if we assume the length [tex]\( l = 3x \)[/tex], width [tex]\( w = 2x \)[/tex], and height [tex]\( h = x \)[/tex], then:
[tex]\[ 90 = (3x) \times (2x) \times (x) \][/tex]
[tex]\[ 90 = 6x^3 \][/tex]
[tex]\[ x^3 = \frac{90}{6} \][/tex]
[tex]\[ x^3 = 15 \][/tex]
[tex]\[ x = \sqrt[3]{15} \][/tex]
[tex]\[ x \approx 2.466 \] meters.[/tex]
A cylinder-shaped kid's pool has a diameter of 12 feet and a height of 2 feet. If each cubic footholds 7.48 gallons of water, about how many gallons of water can the kid's pool hold?
Answer:
About 1691.886 gallons.
Step-by-step explanation:
The firs step is to find the volume of the pool in cubic feet. The formula for the volume of a cylinder is [tex]\pi r^2 h[/tex], which in this case is [tex]\pi \cdot 6^2 \cdot 2\approx 226.188[/tex] cubic feet. Multiplying this by 7.48, you get a total of about 1691.886 gallons of water. Hope this helps!
All I need is the answer if your right you will be marked brainzileient
Answer:
C; E
Step-by-step explanation:
They are the only 2 equivalent expressions
Answer:
C & E is the correct answer.
Rafael spins the pointers of the two spinners shown at the right. Find the probability of each possible sum
Step-by-step explanation:
P(sum)= 2On the left: possible outcome has the value of 1 (1) = [tex]\frac{1}{2}[/tex]
On the right: 1 possible outcome has the value of 1 (1)= [tex]\frac{1}{3}[/tex]
=> the probability of possible P(sum)= 2
= [tex]\frac{1}{2}[/tex]* [tex]\frac{1}{3}[/tex]
= [tex]\frac{1}{6}[/tex]
P(sum)= 3On the left: possible outcome has the value of 1 = [tex]\frac{1}{2}[/tex]
On the right: 1 possible outcome has the value of 2 = [tex]\frac{1}{3}[/tex]
On the left: possible outcome has the value of 2 = [tex]\frac{1}{2}[/tex]
On the right: 1 possible outcome has the value of 1 = [tex]\frac{1}{3}[/tex]
=> the probability of possible P(sum)= 3
= [tex]\frac{1}{2}[/tex]*[tex]\frac{1}{3}[/tex] + [tex]\frac{1}{2}[/tex]*[tex]\frac{1}{3}[/tex]
= [tex]\frac{1}{3}[/tex]
P(sum)= 4On the left: possible outcome has the value of 1 = [tex]\frac{1}{2}[/tex]
On the right: 1 possible outcome has the value of 3 = [tex]\frac{1}{3}[/tex]
On the left: possible outcome has the value of 2 = [tex]\frac{1}{2}[/tex]
On the right: 1 possible outcome has the value of 2= [tex]\frac{1}{3}[/tex]
=> the probability of possible P(sum)= 4
= [tex]\frac{1}{2}[/tex]*[tex]\frac{1}{3}[/tex] + [tex]\frac{1}{2}[/tex]*[tex]\frac{1}{3}[/tex]
= [tex]\frac{1}{3}[/tex]
P(sum)= 5On the left: possible outcome has the value of 2 = [tex]\frac{1}{2}[/tex]
On the right: 1 possible outcome has the value of 3 = [tex]\frac{1}{3}[/tex]
=> the probability of possible P(sum)= 5
= [tex]\frac{1}{2}[/tex]* [tex]\frac{1}{3}[/tex]
= [tex]\frac{1}{6}[/tex]
The probability of getting sum 2 is [tex]\frac{1}{6}[/tex]
The probability of getting sum 3 is [tex]\frac{1}{3}[/tex]
The probability of getting sum 4 is [tex]\frac{1}{3}[/tex]
The probability of getting sum 5 is [tex]\frac{1}{6}[/tex]
Probability :Two spinners shown in the question.
First spinner is divide into two equal parts.
Second spinner is divided into three equal parts.
The probability of getting sum 2 is,
[tex]P(sum=2)=\frac{1}{2} *\frac{1}{3}\\ \\P(sum=2)=\frac{1}{6}[/tex]
The probability of getting sum 3 is,
[tex]P(sum=3)=(\frac{1}{2}*\frac{1}{3}) +(\frac{1}{2}*\frac{1}{3})\\\\P(sum=3)=\frac{1}{3}[/tex]
The probability of getting sum 4 is,
[tex]P(sum=4)=(\frac{1}{2}*\frac{1}{3}) +(\frac{1}{2}*\frac{1}{3})\\\\P(sum=4)=\frac{1}{3}[/tex]
The probability of getting sum 5 is,
[tex]P(sum=5)=\frac{1}{2} *\frac{1}{3}\\ \\P(sum=5)=\frac{1}{6}[/tex]
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If the point G(–4, 6) was moved horizontally 4 units to the left, which of the following is the correct mapping to define the translation? (x, y) Right-arrow (x, y + 4) (x, y) Right-arrow(x + 4, y) (x, y) Right-arrow (x, y – 4) (x, y) Right-arrow (x – 4, y)
Answer:
(x, y ) → (x - 4, y )
Step-by-step explanation:
A horizontal move of 4 to the left means subtract 4 from the x- coordinate, leaving the y- coordinate unchanged, thus
(x, y ) → (x - 4, y ) ← translation rule
Answer:
(x, y) Right-arrow (x – 4, y)
Step-by-step explanation:
just did it
Rob is a high school student taking both algebra and geometry. Last night he had 27 homework problems combined from the two classes, and he took a total of 90 minutes to do them. If each algebra problem took him 2 minutes and each geometry problem took him 5 minutes, how many algebra problems did he have for homework?
2
5
12
15
Answer:
15
Step-by-step explanation:
Let x represent the number of algebra problems. Then the number of geometry problems was 27-x and the total working time was ...
2x +5(27 -x) = 90
-3x = 90 -135 . . . . subtract 135
x = -45/-3 = 15 . . . divide by -3
Rob had 15 algebra problems for homework.
Answer:
15 problems
Step-by-step explanation:
HELLO? Can anyone answer my question PLS!!! HELP!!!
Write the explicit equation
for the sequence
9, 5, 1, -3, -7…
Answer:
13-4n
Step-by-step explanation:
The generic formula to calculate this is. a+(n-1) d
“a” is the first term and “d” is the difference in our case “a” is 9 and “d” is -4
9+(n-1)(-4)
9-4n+4
13-4n
Answer:
[tex]a_{n}[/tex] = 13 - 4n
Step-by-step explanation:
Note the common difference d between consecutive terms, that is
d = 5 - 9 = 1 - 5 = - 3 - 1 = - 7 - (- 3) = - 4
This indicates the sequence is arithmetic with n th term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = 9 and d = - 4, thus
[tex]a_{n}[/tex] = 9 - 4(n - 1) = 9 - 4n + 4 = 13 - 4n ← explicit equation
Highlight the ordered pair that is a the solution. Show your work to justify your answer.
To determine the ordered pair that is a solution, we need an equation or a system of equations.
Explanation:The question asks to highlight the ordered pair that is a solution. To do this, you would need an equation or a system of equations to solve. Without the equation(s), it is not possible to determine the ordered pair that is a solution. Please provide the equation(s) so we can help you further.
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Which describes a uniform probability model?
A) drawing a red or black card from a deck of cards
B) selecting a ball from 2 red balls and 3 yellow balls
C) selecting a sock from 5 black socks and 10 white socks
D) equally divided five section spinner with three colors
Answer:a
Step-by-step explanation:
David has 56 baseball card I wish he sells three cars per week write an equation representing the number of cards n he has left at the end of any given week W
Answer:
56-3=N
Step-by-step explanation:
David starts with 56 baseball cards and sells 3 per week, so the equation representing the cards remaining after W weeks is n = 56 - 3W.
The equation that represents the number of baseball cards David has left at the end of any given week W is n = 56 - 3W. Here, 'n' stands for the number of cards he has left, '56' is the initial number of cards, '3' is the number of cards he sells each week, and 'W' is the number of weeks that have passed.
For example, at the end of week 1 (when W = 1), David will have:
n = 56 - 3(1) = 56 - 3 = 53 cards left.
At the end of week 2 (when W = 2), it would be:
n = 56 - 3(2) = 56 - 6 = 50 cards remaining.
This pattern continues as more weeks pass.
Which graph shows the solution set for 2 x + 3 greater-than negative 9?
A number line going from negative 8 to positive 2. An open circle is at negative 3. Everything to the left of the circle is shaded.
A number line going from negative 8 to positive 2. An open circle is at negative 3. Everything to the right of the circle is shaded.
A number line going from negative 8 to positive 2. An open circle is at negative 6. Everything to the left of the circle is shaded.
A number line going from negative 8 to positive 2. An open circle is at negative 6. Everything to the right of the circle is shaded.
Correct option is D) A number line going from negative 8 to positive 2. An open circle is at negative 6. Everything to the right of the circle is shaded.
Step-by-step explanation:
We have following inequality :2 x + 3 greater-than negative 9 or ,
⇒ [tex]2x+3>-9[/tex]
Let's solve this :
⇒ [tex]2x+3>-9[/tex]
⇒ [tex](2x+3)+9>-9+9[/tex]
⇒ [tex]2x+12>0[/tex]
⇒ [tex](2x+12)-12>0-12[/tex]
⇒ [tex]2x>-12[/tex]
⇒ [tex]x>-6[/tex]
So , the value of x is greater then -6 . So , Correct option is D) A number line going from negative 8 to positive 2. An open circle is at negative 6. Everything to the right of the circle is shaded.
Answer:
The person in the comments said...
The answer is c. When your dividing by a negative number the arrow is turned around.
Step-by-step explanation:
Hi, have a great day/night whichever one, stay safe and always be kind ^w^
p.s. i'm giving all the credit to the person in the comments
Pythagorean theorem (picture provided)
Answer:
12
Step-by-step explanation:
To solve for a side using pythag:
[tex]\sqrt{37^2-35^2}[/tex]
Justin opened a savings account with $500. He plans to save $50 per week from his paycheck. Which equation would represent his total balance, y, after x weeks of saving?
A . x = 50y + 500
B . y = x
C .y = 500x + 50
D. y = 50x + 500
6-2/3 doubled would be?
Answer:
10.6
Step-by-step explanation:
1. 2(6-2/3)
a. 2(5.33)
b. 10.6
Answer:
32/3, 10 2/3, 10.67
Step-by-step explanation:
First, we can set up the expression.
2(6-2/3)
Use the distributive property.
12-4/3
Get a common denominator.
12*3/3=36/3
36/3-4/3
32/3
or
10 2/3
or
10.66 (repeated)
Round it to 10.67
A region with a 15 mile diameter has a population density of about 5000 people per square mile. Find the number of people who live in the region.
Answer:
55 of people
A bag of marbles has 5 blue marbles, 3 red marbles, and 6 yellow marbles. A marble is drawn from the bag at
random. How many possible outcomes are there?
3
5
6
14
Answer:
14
Step-by-step explanation:
As you are only pulling out one marble, the colors are irrelevant; each marble has exactly one 'chance' at getting pulled out. There are 14 marbles, so there are 14 possible outcomes. [Based on how basic the problem is, I tried to stick to basic mathematical terms].
Answer:14
Step-by-step explanation:
I just did it :)
The surface area of this square prism is
A) 45 ft2.
B) 69 ft2.
C) 78 ft2.
D) 245 ft2.
Answer:
C) 78 ft2
step-by-step explanation:
(1) volume: V = a²h(2) surface area: S = 2a(a+2h)(2) is the one you want to find out.
Volume= 45 ft2
Surface area= 78 ft2
Principal = $800
Interest Rate = 3.5%
Time = 6 months
Find the interest earnedi
The interest earned is $14.
To find the interest earned, we can use the formula for simple interest:
[tex]\[ \text{Simple Interest} = \frac{P \times R \times T}{100} \][/tex]
Where:
- [tex]\( P \)[/tex]is the principal amount (the initial amount of money) [tex]= $800[/tex]
-[tex]\( R \)[/tex]is the interest rate per period (in decimal form) [tex]= 3.5% = 0.035[/tex]
-[tex]\( T \)[/tex] is the time the money is invested for (in years)[tex]= 6 months = 0.5 years[/tex]
Now, plug in the values:
[tex]\[ \text{Simple Interest} = \frac{800 \times 3.5 \times 0.5}{100} \][/tex]
[tex]\[ \text{Simple Interest} = \frac{800 \times 3.5 \times 0.5}{100} \][/tex]
[tex]\[ \text{Simple Interest} = \frac{800 \times 1.75}{100} \][/tex]
[tex]\[ \text{Simple Interest} = \frac{1400}{100} \][/tex]
[tex]\[ \text{Simple Interest} = \[14 \][/tex]
Complete correct question:
Principal = $800
Interest Rate = 3.5%
Time = 6 months
Find the interest earnedi
Find the correct result.
1+4=5
2+5=12
3+6=21
5+8=
Based on the scale drawing, what is the length, in feet, of the actual parking lot? On the drawing they have the width 12.8 cm and the length is 3.2 cm.
Answer:
The width of 48 feet is represented by 12.8cm; the length represented by 1cm is 48/12.8 = 15/4 = 3.75 feet.
The length on the drawing is 3.2cm, which is exactly 1/4 of the width of 12.8cm; therefore the length of the actual parking lot is 48/4 = 12 feet.
To find the actual length of a parking lot based on a scale drawing, you need the scale, which is often given as a ratio like '1 cm : 10 ft'. You would multiply the length on the drawing by the scale value to get the actual length. However, without the scale, a definitive answer cannot be provided.
Explanation:To find the actual length of the parking lot, you need to know the scale of the drawing, which is not provided in the current question. The scale is usually expressed as a ratio, essentially representing a conversion factor. An example could be '1 cm : 10 ft', meaning every one centimeter on the drawing represents ten feet in real life.
Let's say the scale is '1 cm : 10 ft' as an example. You would then multiply the scale value (10 ft) by the length of the parking lot on the drawing (3.2 cm). So: 3.2 cm * 10 ft/cm = 32 ft. Hence, in this example, the actual length of the parking lot would be 32 feet. However, without the scale, we cannot provide a definitive answer.
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Which equation can be used to find the surface area of the cylinder?
Answer:
the first option
Step-by-step explanation:
the formula to find the surface area of a cylinder is
2πrh+2πr²
Answer:
A=2πrh+2πr2=2·π·4·16+2·π·42≈502.65482
Step-by-step explanation:
up there
An oval track is made by erecting semicircles on each end of a 46 m by 92 m rectangle. Find the length of the track and
the area enclosed by the track.
Answer:
[tex]Length\,\, of\,\, the\,\, track=420.44\,m\\\\Area\,\,covered \,\,by\,\, the\,\, track=5893.06\,m^2[/tex]
Step-by-step explanation:
Length of the Track:
Perimeter of the rectangle + Circumference of the two semicircle
Perimeter of the rectangle= [tex]2(Length+Width)[/tex]
[tex]Length=92\,m\\Width=46\,m[/tex]
Perimeter of the rectangle:
[tex]=2(92+46)\\\\=2(138)\\\\=276\,m[/tex]
Circumference of Two Semicircle with same radius:
[tex]r=\dfrac{46}{2} =23\,m[/tex]
[tex]Circumference=2\times \pi \times r\\\\[/tex]
[tex]=2\times 3.14\times 23\\\\=6.28 \times 23\\\\=144.44\,m[/tex]
Total Length of the track is :
[tex]=276+144.44\\\\=420.44\,m[/tex]
Area Covered by the track is :
Area of the two semicircle + Area of the rectangle
[tex]=(\pi \times r^2) + (Length\times Width)\\\\=(3.14\times (23\times 23 ))+(92\times 46)\\\\=1661.06 +4232\\\\=5893.06\,m^2[/tex]
The total length of the oval track is 420.51m and the area enclosed by the track is 5893.90m².
Explanation:The dimensions of the rectangular part of the track are 46m and 92m respectively. Thus, the total distance around the rectangle (perimeter) is 2*(46m + 92m) = 276m. The two semicircles on either end of the rectangle form a complete circle with a diameter of 46m. The circumference of this circle (which equates to the remaining path length of the race track) is given by the formula πd or π*46m ≈ 144.51m. Thus, the total length of the track is 276m + 144.51m = 420.51m.
As for the area enclosed by the track, it consists of two main parts: the area of the rectangle and the area of the circle. The area of the rectangle is given by the formula L*W, or 46m*92m = 4232m². The area of the circle is given by the formula π(r²), where r is the radius of the circle. So, π(23m²) equals approximately 1661.90m². Adding the two results together, the total area enclosed by the track is 4232m² + 1661.90m² = 5893.90m².
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Find the volume of the sphere.
Either enter the exact terms of pi or use 22/7 for pi.
The radius is 1/2 !
Answer: 1/6 pi
Step-by-step explanation:
1. Formula: Volume of a sphere= 4/3pi x 1/2^3
2. Solve: 1/2^3 = 1/8
3. Place 1/8 into problem: 4/3pi x 1/8
4. Solve: 4/3pi x 1/8 = 4/24pi
5. simplify
Answer: 1/6pi