Answer:
Rachel has to drive for 5.789 seconds
Step-by-step explanation:
The equation that represents Rachel's remaining distance is:
[tex]D=-38t+220[/tex]
When Rachel completely escaped from the explosion, she has no distance to cover.
Hence D=0.
[tex] - 38t + 220 = 0[/tex]
[tex] - 38t = - 220[/tex]
Divide both sides by -38 to get:
[tex]t = \frac{ - 220}{ - 38} [/tex]
[tex]t = 5.789[/tex]
Rachel will cover 220m in approximately 6 seconds.
The total distance she has to drive is 220m
Rachel has to drive for approximately 6 seconds to reach her destination before the building explodes.
The given equation represents the relationship between Rachel's remaining distance (D) in meters and the time elapsed (t) in seconds.
The equation is:
D = -38t + 220
To find how long the distance Rachel has to drive, we need to find the value of D when she reaches her destination, which means D = 0 (since the distance remaining will be zero when she reaches the destination).
0 = -38t + 220
Now, solve for t:
38t = 220
t = 220 / 38
t ≈ 5.79 seconds
So, Rachel has to drive for approximately 6 seconds to reach her destination before the building explodes.
The total distance she has to drive is 220m.
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Which expression is an equivalent expression of 12x + 10 + 4y?
A. 2(6x+2y+6)
B. 3(4x + y + 10)
OC. 2(6x + 4y+8)
D.
2(6x + 5+ 2y)
Answer:
D. 2(6x + 5+ 2y)
Step-by-step explanation:
12x + 10 + 4y
Factor out a 2
2(6x+5+2y)
CAN SOMEONE PLEASE SOLVE THIS?????????? NEED HELP!!!!!!!!!!!!!!!!!!!
Answer:
x = 9, GH = 21, CD = 17
Step-by-step explanation:
Quadrilateral CDEF is a trapezoid in which G and H are mid points of the sides CF and DE respectively.
In a trapezoid, segment joining the mid points is equal to the half of the sum of the parallel sides.
[tex] \therefore \: GH = \frac{1}{2} (CD + FE) \\ \\ \therefore \:3x - 6 =\frac{1}{2} (2x - 1 + 25) \\ \\ \therefore \:3x - 6 =\frac{1}{2} (2x + 24) \\ \\ \therefore \:3x - 6 =\frac{1}{2} \times 2 (x + 12) \\ \\ \therefore \:3x - 6 = x + 12 \\ \\ \therefore \:3x - x = 12 + 6 \\ \\ \therefore \:2x = 18 \\ \\ \therefore \:x = \frac{18}{2} \\ \\ \huge\red{ \boxed{\therefore \:x = 9}} \\\\ \because \overline{GH} = 3x - 6 \\ \\\therefore \:\overline{GH} =3 \times 9 - 6 \\ \\ \therefore \:\overline{GH} =27 - 6 \\ \\ \huge\purple{ \boxed{\therefore \:\overline{GH} =21}} \\ \\ \because\overline{CD} = 2x - 1 \\\\ \therefore \:\overline{CD} =2 \times 9 - 1 \\ \\ \therefore \:\overline{CD} =18 - 1 \\ \\ \huge\pink{ \boxed{\therefore \:\overline{CD} =17}} \\ \\ [/tex]
Add 5 to me.Then divide by 7.If you add 12 and the subtract 7,you get 10
Answer: 30
Step-by-step explanation:
Let the number be y
Add 5 to me
Y+5............equ1
Divide by 7
Y+5/7
Add 12
Y+5/7+12
Subtract 7
(Y+5)/7+(12-7)=10
12-7=5
Substitute
(Y+5)/7+5=10
Find the lowest common multiple
((Y+5)+7(5))/7=10
(Y+5)+35)/7=10
Cross multiply
Y+5+35=70
Y+40=70
Y=70-40
Y=30
The unknown number is 30
- Rick has only 2 hour and 44 minutes until he needs to leave. He wants to watch a movie that goes
for 158 minutes. Does he have enough time to watch the whole movie before he has to leave?
Answer:
No he does not
Step-by-step explanation:
158 / 60 = 2.63
which is about a 3 hour long movie.
A rectangular restaurant kitchen has a perimeter of 34 meters and an area of 70 square meters. What are the dimensions of the kitchen?
Answer:
The kitchen has a length of 10 meters and a width of 7 meters.
Step-by-step explanation:
10x7=70 meters squared
10+10+7+7=34 meters
I need tynessa's coloring plzzz
Answer:
4 +2n
Step-by-step explanation:
Tynessa has colored 4 red blocks in each figure. The number of blue blocks in each figure is the same as the figure number in both the top and bottom rows. That is, the total number of blue blocks is 2 times the figure number.
If the figure number is n, Tynessa might write the pattern rule as ...
number of blocks = 4 + 2n
How many different ways can 9 trumpet players in the marching band line up?
Answer:
362880 ways
Step-by-step explanation:
In this case, the order does matter therefore to know how many ways it can be aligned, we must resort to permutations.
The formula for permutations is:
P = n!
we know that there are 9 trumpet players, therefore:
P = 9!
P = 362880
So there are 362,880 ways to line up
Use a calculator to solve for xin the equation 2e^3x = 400. Round your answer to
three decimals.
To solve the equation 2e^3x = 400, we isolate e^3x and then use the natural logarithm to solve for x, which gives x ≈ 2.995 when rounded to three decimals.
Explanation:The question asks us to solve the equation 2e^3x = 400 for the variable x. First, we isolate e^3x by dividing both sides of the equation by 2. We get: e^3x = 400/2 which is e^3x = 200. Finding x means solving for 'x' in an exponential equation, which involves using the natural logarithm.
So, our equation becomes: x = ln(200)/3. Using a calculator, x ≈ 2.995 when rounded to three decimals.
Learn more about Solving Exponential Equations#SPJ2What is x rounded to the nearest tenth please help
Answer:
8.9
Step-by-step explanation:
how do I simplify this? -4k - 13 + 6k +23
-4k + 6k -13 +23
2k +10
you can even write it like this:
2 ( k+ 5)
Solve the inequality.
−4>−4/3s
The solution is ___
Answer:
3 < s
Step-by-step explanation:
−4>−4/3s
Multiply each side by -3/4 to isolate s. Remember to flip the inequality since we are multiplying by a negative
-4 * -3/4 < -4/3s * -3/4
3 < s
If r is an integer greater than 1, what is the value of (−1)r +1 if: a r is an odd integer
Answer:
The value of the given expresion is zero.
Step-by-step explanation:
I am assuming that, your exprssion is
[tex] {( - 1)}^{r} + 1[/tex]
where r is an integer greater than 1.
Let us see what a negative base 1 to an off exponent give us:
[tex] {( - 1)}^{1} =-1[/tex]
[tex] {( - 1)}^{3} =-1[/tex]
[tex] {( - 1)}^{5} =-1[/tex]
[tex] {( - 1)}^{7} =-1[/tex]
If r is odd, then
[tex] {( - 1)}^{r} = - 1[/tex]
This implies that:
[tex] {( - 1)}^{r} + 1 = - 1 + 1 = 0[/tex]
The value of the given expresion is 0.
Does anyone knows how to solve this question??
Answer:
24
Step-by-step explanation:
cos(x) is just a trigonometric function. To find it on a right triangle, you take the "adjacent" side, which should be the side next to the angle x, and divide it by the hypotenuse.
In this case, the adjacent side is 12. We don't know the hypotenuse, but we can figure it out using the Pythagorean Theorem: [tex]\sqrt{9^{2}+12^{2}}[/tex] = [tex]\sqrt{225}[/tex] = 15. So, the hypotenuse is 15.
Thus, cos(x) = 12/15 = 4/5. We want 30 * cos(x), so we get: 30 * (4/5) = 24, and that is our answer.
Answer:
24
Step-by-step explanation:
From the mnemonic SOHCAHTOA you would know that cos x = adjacent/hypotenuse.
Adjacent side is given as 12, but we must calculate the hypotenuse.
For that we use Pythagoras.
hypotenuse = √(9²+12²) = 15
Now you can calculate
30×cos(x) = 30×12/15 = 24
In a survey of 105 people, there were half as many adults as children. How many children were there?
Answer:
70
Step-by-step explanation:
Set up a system:
C + A = 105
C = 2A
Substitute:
3A = 105
A = 35
C = 70
Answer:
70 children 35 adults
Step-by-step explanation:
X= children
Y=Adults
x+y=105
1/2x=y
x+y=105
1/2x-y+0
x+y+105
x-2y=0
3y=105
y=35
x+35=105
x=70
The triangle on the grid will be translated two units down.
Which shows the triangle when it is translated two units down?
Answer:
c
Step-by-step explanation:
The points that show the triangle when it is translated two units down are (2, 3) (0, 1), and (2, 1).
What are transformations?A function, f, that maps to itself are known as a transformation, or f: X- X. The pre-image X becomes the picture X following the transformation. This transformation can use any operation, or a combination of operations, including translation, rotation, reflection, and dilation. Translation, rotation, reflection, and dilation can all be used to move a function in one direction or another.
Given that the initial coordinate of triangles ABC are at points
(2, 1), (0, -1), (2, -1).
The coordinate base of the triangle must be (2, 1) and (2, -1)
When the triangle is translated two units down.
2 will be added to all its y coordinates. While the x coordinate remains the same
The new coordinate will be
(2, 2+1), (0, 2-1), (2, 2-1)
(2, 3) (0, 1) and (2, 1)
Hence the new coordinates are (2, 3) (0, 1), and (2, 1).
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The complete question is,
The triangle on the grid will be translated two units down. On a coordinate plane, triangle A B C has points (2, 1), (0, negative 1), (2, negative 1). Which shows the triangle when it is translated two units down
Find the area of the semicircle.
Either enter an exact answer in terms of
or use 3.14 for and enter your answer as a decimal.
units
Answer:
8 pie
Step-by-step explanation:
area of a circle is pie(radius squared)
radius is 4
4 squared is 16
divide by two because its a semi circle
Answer:
8pi
Step-by-step explanation:
A=pi*r^2
A=pi(4^2)
A=16pi
16pi would be the area if the circle was complete, but since this is a semicircle you just have to divide by two which would give us:
A=8pi
!!!!!HURRY!!!!!!
Bethany used the steps below in an attempt to solve for angle B in triangle ABC.
Where is bethanys error?
The measure of angle B in triangle ABC is 63.9°. Hence, Bethany has done a mistake in step 2.
Given that, in the triangle ABC, AC=4.1 cm, AB=4.5 cm and BC=2.7 cm.
We need to find the measure of angle B.
What is the trigonometric function to find the angle in the triangle?The trigonometric function to find the angle in the triangle is b²=a²+c²-2ac cosB.
Now, (4.1)²=(4.5)²+(2.7)²-2×4.5×2.7 cosB.
⇒16.81=20.25+7.29-24.3 cosB
⇒16.81-27.54=-24.3 cos B
⇒cos B=0.44
⇒B=63.9°
The measure of angle B in triangle ABC is 63.9°. Hence, Bethany has done a mistake in step 2.
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Answer:
B. Bethany took the square root of each squared term before isolating cosB and solving for B.
Step-by-step explanation:
took the quiz
Find the area of each trapezoid.
The hypotenuse of a right triangle is 10m and the length of one of the legs is 8m , find the length of the other leg of the triangle
Answer:
6 m
Step-by-step explanation:
a squared + b squared = c squared
8 squared plus ? squared = 10 squared
64 + ? = 100
100 - 64 = 36
the square root of 36 is 6
Final answer:
Using the Pythagorean theorem, the length of the other leg of the right triangle is found to be 6 meters.
Explanation:
The student is asking to find the length of the other leg of a right triangle, given the lengths of the hypotenuse (10m) and one leg (8m). To solve this problem, we use the Pythagorean theorem, which relates the lengths of the sides of a right triangle: a² + b² = c², where c is the hypotenuse and a and b are the legs of the triangle. Since the hypotenuse length (c) is 10m and one leg (a) is 8m, we can solve for the length of the other leg (b) using the equation 8² + b² = 10².
First, square the known length of one leg: 8² = 64.
Next, square the hypotenuse: 10² = 100.
Now, subtract the squared length of the known leg from the squared hypotenuse to find b²: 100 - 64 = 36.
Finally, take the square root of 36 to find b: √36 = 6m. So, the length of the other leg is 6 meters.
Consider the original complex figure and the reduction.
Figures not drawn to scale.
What is the scale factor of the reduction?
1/8
1/5
5
9
Answer:
1/8
Step-by-step explanation:
I'm going to try to explain this as easy as possible. What I did was take the original shape and divide it by the new shape. For this question, I solved it by dividing 32(the original base) by 4(the new base) and got 8. So the scale factor of the reduction was 1/8.
Answer:
1/8
Step-by-step explanation:
The only one that makes sense
In a bag of 18
18
oranges, 12
12
have gone bad.
What is the ratio of good oranges to bad oranges?
Answer:
1 :2
Step-by-step explanation:
18 oranges
12 bad
-------
6 good
good: bad
6 :12
Divide each by 6
6/6 : 12/6
1 :2
The ratio of good oranges to bad oranges is 1:2.
To find the ratio of good oranges to bad oranges in a bag containing 18 oranges, where 12 oranges have gone bad, follow these steps:
Determine the number of good oranges:
Total oranges in the bag: 18Bad oranges: 12Good oranges: 18 - 12 = 6Find the ratio of good oranges to bad oranges:
Good oranges: 6Bad oranges: 12Simplify the ratio:
The ratio of good oranges to bad oranges can be written as 6:12.Simplify this by dividing both numbers by their greatest common divisor (GCD), which is 6.Simplified ratio: 6 ÷ 6 : 12 ÷ 6 = 1:2
Question 2 and 3, if u just feel like answering one that’s okay
Answer:
[tex]w^{20}[/tex]; [tex]y^7[/tex]
Step-by-step explanation:
[tex](w^4)^5=\\w^{4*5}=\\w^{20}\\\\\frac{y^9}{y^2}=\\ y^{9-2}=\\y^7[/tex]
Answer:
1) =W20
2=Y7
Both 20 and 7 are exponents but i cannot type them in that format since I am on a computer. Hope this helps!
Step-by-step explanation:
May You Please Help Me? :(
In triangle ABC, the length of side AB is 11 inches and the length of side BC is 18 inches. Which of the following could be the length of side AC?
1. 5 inches
2. 31 Inches
3. 34 inches
4. 19 inches
calculate the area of this figure
Answer:
78.
Step-by-step explanation:
13/2=6.5
6.5X12=78.
78/2=39
39X2=39. You times it by 2 because there are two equivalent sides.
A number is selected at random from the set (2, 3, 4, ... 10). Which eventby definition, covers the entire sample space of this experiment?
A.
The number is greater than 2.
OB.
The number is not divisible by 5.
C.
The number is even or less than 12.
OD. The number is neither prime nor composite.
E.
The square root of the number is less than 3.
Answer:
C
Step-by-step explanation:
A doesn't include the term "2"
B doesn't include "5" or "10"
D doesn't include "10"
SO... it's C
A sphere has a radius of 3.5 inches.
What is the volume of the sphere rounded to the nearest tenth?
Use 3.14 for pi.
Answer:
volume = 179.59
please give this the brainliest!!
Step-by-step explanation:
formula = V=4/3πr3
4/3·π·3.5^3
≈179.59438
In a class of 150 students, 95 are taking Math, 75 are taking Science and 55 are taking both.What is the probability that a student is taking neither Math or science?
Answer:
[tex] \frac{7}{30} [/tex]
Step-by-step explanation:
In a class of 150 students, 95 are taking Math, 75 are taking Science and 55 are taking both.
We want to determine the probability that a student is taking neither Math or science.
The number taking only Math is
[tex] = 95 - 55 = 40[/tex]
The number taking only Science
[tex] = 75 - 55 = 20[/tex]
The number of students taking Math, Science, or both
[tex] = 40 + 55 + 20 = 115[/tex]
The number taking neither Mathematics or Science
[tex] = 150 - 115 = 35[/tex]
The probability that a student is taking neither Math or science
[tex] = \frac{35}{150} [/tex]
[tex] = \frac{7}{30} [/tex]
PLS help meee i have posted this 3 othe times
Answer:
help with what
Step-by-step explanation:
Answer:
What do you want help with?
Step-by-step explanation:
A traveler is driving across the country and spots Gateway Arch in St. Louis, Missouri. She has read that the arch is 630 feet tall. Her angle of elevation to the top of the arch is 3º. How far away is Gateway Arch, to the nearest tenth of a mile?
Answer:
d = 12,021.1 ft
The Gateway Arch is 12,021.1 ft away
Step-by-step explanation:
Given;
Angle of elevation = 3°
Height of arch = 630 ft
Tanθ = opposite/adjacent
Opposite = 630 ft
Adjacent = d
Substituting the values;
Tan3 = 630/d
d = 630/tan3
d = 12,021.1 ft
The Gateway Arch is 12,021.1 ft away
Answer:
[tex]x = 12021.1\,ft\,(2.3\,mi)[/tex]
Step-by-step explanation:
The distance is given by the following trigonometric equation:
[tex]x = \frac{y}{\tan \alpha}[/tex]
[tex]x = \frac{630\,ft}{\tan 3^{\textdegree}}[/tex]
[tex]x = 12021.1\,ft\,(2.3\,mi)[/tex]
what is one third of three sevenths equals
Answer:
0.14285714285
Hope this helps :)
Step-by-step explanation:
Answer:
.1428
Step-by-step explanation:
1/3 times 3/7= .1428