Answer:
7
Step-by-step explanation:
You can convert the fourth square roots to [tex]7^{\frac{1}{4}}} * 7^{\frac{1}{4}}} * 7^{\frac{1}{4}}} * 7^{\frac{1}{4}}}[/tex]. Using the product of powers rule, we can add the four terms' exponents, resulting in [tex]7^1[/tex], which is 7.
5.
A number is squared, then multiplied by 6. The result is 54. What was the number?
Answer:
Answer:
± 3
Step-by-step explanation:
let n be the number then the number squared is n² , so
6n² = 54 ( divide both sides by 6 )
n² = 9 ( take the square root of both sides )
n = ± [tex]\sqrt{9}[/tex] = ± 3
That is the number is 3 or - 3
Solve 5 (2x + 1 ) + 4 = 6 ( 3x + 2) - 7
5(2x+1)+4=6(3x+2)-7
10x+5+4=18x+12-7
10x-18x=12-7-5-4
-8x=-4 (-1)
8x=4
x=4/8 (/4)
x=1/2
Answer:
x = 1/2
Step-by-step explanation:
5(2x + 1) + 4 = 6 (3x + 2) - 7
~Simplify both sides
10x + 9 = 18x + 5
~Subtract 9 from both sides
10x = 18x - 4
~Subtract 18x to both sides
-8x = -4
~Divide -8 to both sides
x = 1/2
Best of Luck!
A farmer wishes to construct a fence around his rectangular field. The farmer has 150 feet of fence and
wishes to have the length be three more than the width. What is the width of the field. Make sure and
include feet in your answer.
Help
Answer:
The width is 36 feet
Step-by-step explanation:
If the width of the fence is x then its length is x+3.
The perimeter is 150 feet, so we have the equation:
2(x + x + 3) = 150
4x + 6 = 150
x = 144/4 = 36 feet
Factor this polynomial expression.
3x^2 - 12x+ 12
A. (3x - 2)(x-6)
B. 3(x-2)(x + 2)
C. 3(x-2)(x-2)
D. 3(x + 2)(x + 2)
look at the image below
Answer:
201.1 km²
Step-by-step explanation:
Surface area of the figure,
4πr²
= 4×π×4²
= 64π
= 201.1 km² (rounded to the nearest tenth)
HELPPPP PLZ
Witch statement is true about the value of |6|?
Answer:
The third choice is the correct one.
Step-by-step explanation:
The absolute value of six means that it's the distance from 0 to six, and that distance will be positive regardless of the number being negative or not.
Answer: The third answer is correct
Step-by-step explanation:
Since |6| is the absolute value of positive six, the value of an absolute value of any number is always positive.
Primo car rental agency charges $21 per day plus $0.20 por milo. Ultimo car rental agency charges $24 per day plus $1.00 per milo. Find the daily mileage for which the Ultimo charge is four times the Primo charge.
The mileage is
Answer:
300 miles
Step-by-step explanation:
Let us consider the miles they travelled is 'm'
Mileage for Primo= 21 + (m × 0.20) = 21+0.2m
Mileage for Ultimo= 24+ ( m× 1.00) = 24 + m
Question says The mileage is equal when Ultimo's charge is 4× Primo
Thus,
4 × (21+0.2m) = 24+ m
84 + 0.8m = 24 + m
60 = 0.2m
m = 300
Salaries of entry-level computer engineers have Normal distribution with unknown mean and variance. Three randomly selected computer engineers have following salaries (in $1000s): 70, 80, 90. The average and the standard deviation of the data in the sample are 80 and 10. Using hypothesis testing, determine if this sample provides a sufficient evidence, at a 10% level of significance, that the average salary of all entry-level computer engineers is different from $60,000.
a. Null hypothesis.
b. alternative hypothesis.
c. test statistic.
d. acceptance region.
Answer:
H0 : μ = 60000
H1 : μ ≠ 60000
Test statistic = 3.464
Step-by-step explanation:
Given :
Sample mean salary, xbar = 80000
Sample standard deviation, s = 10000
Population mean salary , μ = 60000
Sample size, n = 3
Hypothesis :
H0 : μ = 60000
H1 : μ ≠ 60000
The test statistic :
T = (xbar - μ) ÷ (s/√(n))
T = (80000 - 60000) ÷ (10000/√(3))
T = 20000 / 5773.5026
T = 3.464
The Decison region :
If Tstatistic >Tcritical
Tcritical at 10%, df = 2 ; two - tailed = 2.9199
Tstatistic > Tcritical ; He
A bicyclist is at point A on a paved road and must ride to point C on another paved road. The two roads meet at
an angle of 38° at point B. The distance from A to B is 18 mi, and the distance from B to C is 12 mi (see
the figure). If the bicyclist can ride 22 mph on the paved roads and 6.8 mph off-road, would it be faster for the bicyclist to ride from A to C on the paved roads or to ride a direct line from A to C off-road? Explain.
Answer:
Step-by-step explanation:
The diagrammatic expression to understand this question very well is attached in the image below.
By applying the law of cosine rule; we have:
a² = b² + c² - 2bc Cos A --- (1)b² = a² + c² - 2ac Cos B --- (2)c² = a² + b² - 2ab Cos C --- (3)From the diagram attached below, we need to determine the side "b" by using equation (2) from above:
b² = a² + c² - 2ac Cos B
From the information given:
a = 12 miles; c = 18 miles; ∠B = 38°
∴
replacing the values into the above equation:
b² = 12² + 18² - 2(12)(18) Cos (38°)
b² = 144 + 324 - 432 × (0.7880)
b² = 468 - 340.416
b² = 127.584
[tex]b = \sqrt{127.584}[/tex]
b = 11.30 miles
However, we are also being told that the speed from A → C = 6.8 mph
Thus, the time required to go from A → C can be determined by using the relation:
[tex]\mathbf{speed = \dfrac{distance}{time}}[/tex]
making time the subject of the formula, we have:
[tex]\mathbf{time= \dfrac{distance}{speed }}[/tex]
[tex]\mathbf{time= \dfrac{11.30}{6.8}}[/tex]
time = 1.66 hours
By using the paved roads, the speed is given as = 22 mph
thus, the total distance covered = |AB| + |BC|
= (18+12) miles
= 30 miles
∴
[tex]\mathbf{time= \dfrac{distance}{speed }}[/tex]
[tex]\mathbf{time= \dfrac{30}{22}}[/tex]
time = 1.36 hours
Therefore, the time used off-road = 1.661 hours while the time used on the paved road is 1.36 hours.
Since we are considering the shortest time possible;
We can conclude that it would be faster for the bicyclist to ride from A to C on the paved roads since it takes a shorter time to reach its destination compared to the time used off-road.
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It would be faster for the bicyclist to ride from A to C on the paved roads since the time to go from A to C on the paved roads is 1.4 h and the time to go from A to C off-road is 1.7 h.
To calculate which way would be faster we need to find the distance from point A to C with the law of cosines:
[tex] \overline{AC}^{2} = \overline{AB}^{2} + \overline{BC}^{2} - 2\overline{AB}\overline{BC}cos(38) [/tex]
Where:
[tex]\overline{AB}[/tex]: is the distance between the point A and B = 18 mi
[tex]\overline{BC}[/tex]: is the distance between the point B and C = 12 mi
[tex] \overline{AC} = \sqrt{(18 mi)^{2} + (12 mi)^{2} - 2*18 mi*12 mi*cos(38)} = 11.3 mi [/tex]
Now, let's find the time for the two following cases.
1. From point A to C on the paved roads (t₁)
[tex] t_{1} = t_{AB} + t_{BC} [/tex]
The time can be calculated with the following equation:
[tex] t = \frac{d}{v} [/tex] (1)
Where:
d: is the distance
v: is the velocity
Then, the total time that it takes the bicyclist to go from point A to C on the paved roads is:
[tex] t_{1} = t_{AB} + t_{BC} = \frac{18 mi}{22 mph} + \frac{12 mi}{22 mph} = 1.4 h = 84 min [/tex]
2. From point A to C off-road (t₂)
With equation (1) we can calculate the time to go from point A to C off-road:
[tex] t_{2} = \frac{\overline{AC}}{v_{2}} = \frac{11.3 mi}{6.8 mph} = 1.7 h = 102 min [/tex]
Therefore, it would be faster for the bicyclist to ride from A to C on the paved roads.
To find more about the law of cosines, go here: https://brainly.com/question/15740431?referrer=searchResults
I hope it helps you!
2. Solve the following system of equations. y = 5 + x 2x + 2y = 30
Sydney has finished all his work on time, but many of his teammates are still struggling to complete their assignments. What should he do? a) Not distract them; they may get farther behind. O b) Listen to them complain about their workloads O c) Help them complete their work d) Share his thoughts on how they could get their work done faster
Answer:
I think the correct option is c
Answer:
I think the correct answer is (d)
Step-by-step explanation:
if he shares his thoughts on how they could get their work done faster like using an app like this, then it would be of great help to them
if the value of a any quadratic function f (x)=ax^2 + BX + C is -8, the function will
Answer:
The parabola will open downward
Step-by-step explanation:
f (x)=ax^2 + BX + C
Since a = -8
The parabola will open downward
When a< 0 the graph opens downwards
a>0 the graph opens upwards
Convert the degree measurement to radians. Express answer as multiple of π: - 60°
A. π/3
B. −π/4
C. −π/5
D. −π/3
Answer:
-pi/3
Step-by-step explanation:
To convert from degree to radians, multiply by pi/180
-60 * pi/180 = -60/180 *pi = -pi/3
Answer:
D. -pi/3
Step-by-step explanation:
degree to radians formula: x=degree, x*pi/180
x=-60
-60*pi/180=-pi/3
8x + 2 = = 7 + 5x + 15
Answer:
2.5
Step-by-step explanation:
8x + 2 = 7 + 5x + 15
Combine like terms:
8x + 2 = 7 + 5x + 15
8x + 2 = 22
-2 -2
-----------------
8x = 20
---- ----
8 8
x = 2.5
Hope this helped.
A 40-foot tree casts a shadow 60 feet long. How long would the shadow of a 6-foot man be at that time?
Answer:
26 ft
Step-by-step explanation:
I'm guessing this is how it's done
60-40= 20
there for at this time any shadow would be 20x it's original height/length
so 6+20=26 ft
lmk if I'm correct
Taking ratios
Let the shadow length=x ft
[tex]\\ \sf\longmapsto 40:60=6:x[/tex]
[tex]\\ \sf\longmapsto \dfrac{40}{60}=\dfrac{6}{x}[/tex]
[tex]\\ \sf\longmapsto \dfrac{4}{6}=\dfrac{6}{x}[/tex]
[tex]\\ \sf\longmapsto 4x=6(6)[/tex]
[tex]\\ \sf\longmapsto 4x=36[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{36}{4}[/tex]
[tex]\\ \sf\longmapsto x=9[/tex]
The graph shows the solution of the following system of equations. y=-5/3x+3 y=1/3x-3 What is the solution? A. (-3,2) B. (3,2) C. (-3,-2) D. (3,-2)
Answer:
(3,-2)
Step-by-step explanation:
-5/3x + 3 = 1/3x - 3
-5/3x = 1/3x - 6
-2x = -6
x = 3
y = -5/3(3) + 3
y = -5 + 3
y = -2
Can someone help me with this?
Answer:
183.3 in^3
Step-by-step explanation:
Find the volume of the rectangular bottom
V = l*w*h
V = 5*5*6 =150 in^3
Find the volume of the triangular pyramid
V = 1/3 Bh where B is the area of the base and h is the height
V = 1/3 ( 5*5) * 4 = 100/3
Add the two volumes together
150 + 100/3
150 +33.3
183.3 in^3
For the function F defined by F(x) = x2 – 2x + 4, find F(b+3).
Answer:
[tex]\displaystyle F(b + 3) = b^2 + 4b + 7[/tex]
Step-by-step explanation:
We are given the function:
[tex]\displaystlye F(x) = x^2 - 2x + 4[/tex]
And we want to find F(b + 3).
We can substitute:
[tex]\displaystyle F(b + 3) = (b + 3)^2 - 2(b+3) + 4[/tex]
Expand:
[tex]\displaystyle = (b^2 + 6b + 9) + (-2b -6) + 4[/tex]
Rearrange:
[tex]\displaystyle = (b^2) + (6b-2b) + (9 - 6 + 4)[/tex]
Combine like terms. Hence:
[tex]\displaystyle = b^2 +4b + 7[/tex]
In conclusion:
[tex]\displaystyle F(b + 3) = b^2 + 4b + 7[/tex]
what is the answer I need help?
Answer:
8 1/8 units^3
Step-by-step explanation:
This figure is a rectangular prism, and the volume of a rectangular prism is given by the formula:
lwh
But since we have the area of the base snd the height of the figure, there is also one formula that we can use to find the volume:
bh
Which means area of base times the height.
USE THE FORMULA bh:
16 1/4 x 1/2
= 65/4 x 1/2
= 65/8
SIMPLIFIED: 8 1/8
Volume is measured in cubic units
SO YOUR ANSWER IS 8 1/8 units^3
any equations that equal three?
Draw the line segment with endpoints (-5, 9) and (-1, -7) and find the value of y if x=-4;-2.5;-2;-1.5;0 plz answer asap
Answer:
5, - 1, - 3, - 5, - 11
Step-by-step explanation:
The equation of the line is y=-4x-11. The y values corresponding to x are 5, - 1, - 3, - 5, - 11
Solve the inequality
Answer:
hope this helps buddy, please mark the brainliest.
Step-by-step explanation:
a team's stadium has a capacity of 86,047. The fan base is notorious for selling out of tickets every game. If every game sells out this year, how many tickets are sold in their 12 game regular season play?
Answer:
1,032,564 tickets
Step-by-step explanation:
Find how many tickets they sell in total by multiplying the capacity of the stadium by the number of games in the season:
86,047(12)
= 1,032,564
So, if every game sells out, 1,032,564 tickets will be sold.
Choose Yes or No to tell if each statement is true.
3
.
072
>
3
.
2
Choose...
728
.
307
>
729
.
07
Choose...
12
.
040
=
12
.
04
Choose...
531
.
135
<
531
.
315
Choose...
Answer:
1. No 2. No 3. Yes 4. Yes
Step-by-step explanation:
Compare the value of each digit from the leftmost digit.
Teddy wants to taste all of the flavors of ice cream at the mall, one by one. Tasting any one flavor will change the way the next flavor taste after it. The flavors are chocolate, vanilla, strawberry, birthday cake, Rocky Road, and butter pecan. In how many ways can he taste the ice cream.
A. 30
B.120
C. 360
D.720
Answer: (d)
Step-by-step explanation:
Given
There are six flavors of ice-cream that is chocolate, vanilla, strawberry, birthday cake, rocky road, and butter pecan
First ice-cream can be tasted in 6 different ways
Second can be in 5 ways
similarly, remaining in 4, 3, 2 and 1 ways
Total no of ways are [tex]6\times5\times 4\times 3\times 2\times 1=720\ \text{ways}[/tex]
Option (d) is correct.
Explain how you would solve the following system of equations using substitution. math step in your explanation, too!! This is the system that you should use: y= 4x -5 y = 3x -3
Answer:
[tex]x=2\\y=3[/tex]
Step-by-step explanation:
Solve by substitution method
[tex]y=4x-5\\y=3x-3[/tex]
First, solve [tex]y=4x-5[/tex] for [tex]y[/tex]:
Substitute [tex]4x-5[/tex] for [tex]y[/tex] in [tex]y=3x-3[/tex]
[tex]y=3x-3[/tex]
[tex]4x-5=3x-3[/tex]
[tex]4x-3x=5-3[/tex]
[tex]x=2[/tex]
Now that we have the value of x
substitute [tex]2[/tex] for [tex]x[/tex] in [tex]y=4x-5[/tex]
[tex]y=4x-5[/tex]
[tex]y=4(2)-5[/tex]
[tex]y=8-5[/tex]
[tex]y=3[/tex]
∴ The value of [tex]x[/tex] is [tex]2[/tex] and the value of [tex]y[/tex] is [tex]3[/tex]
find the surface area of the triangular prism below.
Step-by-step explanation:
At first you need to take its lateral surface area by using the perimeter of base of the triangle and the height of prism.
Then after calculating it you need to find out its total surface area which is asked in the question and that is calculated by adding the area of both triangles of the prism in the lateral surface area.
Then that's your answer.
9514 1404 393
Answer:
544 square units
Step-by-step explanation:
The surface area is the sum of the area of the two triangular bases and the three rectangular faces. The relevant area formulas are ...
A = 1/2bh . . . . area of a triangle with base b and height h
A = LW . . . . . are of a rectangle of length L and width W
__
SA = 2(1/2)(12)(8) + (10 +10 +12)(14)
SA = 96 +448 = 544 . . . square units
Line JK passes through points J(–3, 11) and K(1, –3). What is the equation of line JK in standard form?
7x + 2y = –1
7x + 2y = 1
14x + 4y = –1
14x + 4y = 1
9514 1404 393
Answer:
(b) 7x + 2y = 1
Step-by-step explanation:
You don't need to know how to find the equation. You just need to know how to determine if a point satisfies the equation. Try one of the points and see which equation fits. (The numbers are smaller for point K, so we prefer to use that one.)
7(1) +2(-3) = 1 ≠ -1 . . . . . tells you choice A doesn't work, and choice B does
The equation is ...
7x +2y = 1
__
Additional comment
The equations of choices C and D have coefficients with a common factor of 2. If the constant also had a factor of 2, we could say these equations are not in standard form, and we could reject them right away. Since the two points have integer values for x and y, we can reject these equations anyway: the sum of even numbers cannot be odd.
Answer:
b
Step-by-step explanation:
A rectangle with the dimensions of 2 feet
by 8 feet is similar to a rectangle with the
dimensions of
А 4 feet by 16 feet
B. 6 feet by 12 feet
C 12 feet by 32 feet
D 22 feet by 28 feet
Given rectangle: 2 feet by 8 feet. Similar rectangle: Option A (4 feet by 16 feet).
Use the concept of the rectangle defined as:
Rectangles are four-sided polygons with all internal angles equal to 90 degrees. At each corner or vertex, two sides meet at right angles. The rectangle differs from a square in that its opposite sides are equal in length.
Given that,
Rectangle dimensions: 2 feet by 8 feet
And here are the options provided:
A) 4 feet by 16 feet
B) 6 feet by 12 feet
C) 12 feet by 32 feet
D) 22 feet by 28 feet
To determine if two rectangles are similar,
Compare their corresponding side lengths.
In this case,
A rectangle with dimensions 2 feet by 8 feet.
After simplifying it we can write 1:4
Let's check each option to see if it matches the similarity:
A) 4 feet by 16 feet:
The ratio of the corresponding side lengths is 2:8, which simplifies to 1:4. However, the given rectangle has side lengths of 4:16,
Which simplifies to 1:4 as well.
So, option A is similar to the given rectangle.
B) 6 feet by 12 feet:
The given rectangle has side lengths of 6:12,
Which simplifies to 1:2.
So, option B is not similar to the given rectangle.
C) 12 feet by 32 feet:
The given rectangle has side lengths of 12:32,
Which simplifies to 3:8.
So, option C is not similar to the given rectangle.
D) 22 feet by 28 feet:
The given rectangle has side lengths of 22:28,
Which simplifies to 11:14.
So, option D is not similar to the given rectangle.
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∫[tex]\frac{x+2019}{x^{2}+9 }[/tex]
Split up the integral:
[tex]\displaystyle\int\frac{x+2019}{x^2+9}\,\mathrm dx = \int\frac{x}{x^2+9}\,\mathrm dx + \int\frac{2019}{x^2+9}\,\mathrm dx[/tex]
For the first integral, substitute y = x ² + 9 and dy = 2x dx. For the second integral, take x = 3 tan(z) and dx = 3 sec²(z) dz. Then you get
[tex]\displaystyle \int\frac x{x^2+9}\,\mathrm dx = \frac12\int{2x}{x^2+9}\,\mathrm dx \\\\ = \frac12\int\frac{\mathrm du}u \\\\ = \frac12\ln|u| + C \\\\ =\frac12\ln\left(x^2+9\right)[/tex]
and
[tex]\displaystyle \int\frac{2019}{x^2+9}\,\mathrm dx = 2019\int\frac{3\sec^2(z)}{(3\tan(z))^2+9}\,\mathrm dz \\\\ = 2019\int\frac{3\sec^2(z)}{9\tan^2(z)+9}\,\mathrm dz \\\\ = 673\int\frac{\sec^2(z)}{\tan^2(z)+1}\,\mathrm dz \\\\ = 673\int\frac{\sec^2(z)}{\sec^2(z)}\,\mathrm dz \\\\ = 673\int\mathrm dz \\\\ = 673z+C \\\\ = 673\arctan\left(\frac x3\right)+C[/tex]
Then
[tex]\displaystyle\int\frac{x+2019}{x^2+9}\,\mathrm dx = \boxed{\frac12\ln\left(x^2+9\right) + 673\arctan\left(\frac x3\right) + C}[/tex]
