Answer:
x = 3 , x = 7
Step-by-step explanation:
3(x - 5)² - 17 = - 5 ( add 17 to both sides )
3(x - 5)² = 12 ( divide both sides by 3 )
(x - 5)² = 4 ( take square root of both sides )
x - 5 = ± [tex]\sqrt{4}[/tex] = ± 2 ( add 5 to both sides )
x = 5 ± 2
then
x = 5 - 2 = 3
x = 5 + 2 = 7
A factory makes light fixtures with right regular hexagonal prisms where the edge of a hexagonal base measures 4 cm and the lengths of the prisms vary. It cost $0.04 per square centimeter to fabricate the prisms and the factory owner has set a limit of $11 per prism. What is the maximum length of each prism?
The maximum length of the prism is highest length of the hexagonal prism
The maximum length of each prism is 8.0 cm
How to determine the maximum length of each prism?The surface area of the hexagonal prism is calculated using:
A = 6al + 3[tex]\sqrt[/tex]3 a^2
Where:
a represents the edge length; a = 4 cm
l represents the length (or height) of the prism
The surface area costs $0.04 per square centimeter.
So, we have:
C = 0.04 * [6al + 3[tex]\sqrt[/tex]3 a^2]
The maximum cost is $11.
So, the equation becomes
11 = 0.04 * [6al + 3[tex]\sqrt[/tex]3 a^2]
Substitute 4 for a
11 = 0.04 * [6 * 4l + 3[tex]\sqrt[/tex]3 * 4^2]
Evaluate the products and exponents
11 = 0.04 * [24l + 48[tex]\sqrt[/tex]3]
Divide both sides by 0.04
275 = 24l + 48[tex]\sqrt[/tex]3
Subtract 48[tex]\sqrt[/tex]3 from both sides
24l = 275 - 48[tex]\sqrt[/tex]3
Evaluate the difference
24l = 191.9
Divide both sides by 24
l = 8.0
Hence, the maximum length of each prism is 8.0 cm
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Answer:
275, 7.99
Step-by-step explanation:
i got it right
and please get me too branliest
Which expressions are aquivalent to j + j + 2k ?
Choose all answers that apply:
A 2jk
B 2(j+j+k0
C None of the above
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Let's see ~
[tex]\qquad \sf \dashrightarrow \:j + j + 2k[/tex]
[tex]\qquad \sf \dashrightarrow \:2j + 2k[/tex]
[tex]\qquad \sf \dashrightarrow \:2(j + k)[/tex]
・．━━━━━━━━━━†━━━━━━━━━━━━．・
Part B.
Directions: Solve for the area of the triangle in each of the following problems.
10) 22 cm 21 cm
11) 16 m 15 m
Answer:
#10=462
#11=240
Step-by-step explanation:
22x21=462
16x15=240
Given m \| nm∥n, find the value of x.
Answer:
x=140(corresponding angle)
Corresponding angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.
Corresponding angles are equal
The 140° angle on line m and the x° angle on line n are corresponding angles.
The value of x is 140°
What are corresponding angles?The angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.
Corresponding angles are equal.
We have,
The figure is given,
Line m and Line n are parallel.
t line is the transversal line on the two parallel lines, line m and line n.
We see that,
140° angle on line m is corresponding to the x° angle on line n.
Corresponding angles are equal.
So,
140° = x°
x° = 140°
Thus,
The 140° angle on line m and the x° angle on line n are corresponding angles.
The value of x is 140°
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Find area of the circle. Use 3.14 as (pie symbol) the diameter is 104. Please help will mark brainliest!!
Answer:
8490.56 yd^2
Step-by-step explanation:
find radius by dividing 104 by 2
we get 52 yd
now the area of circle is [tex]\pi r^{2}[/tex]
we use 3.14 for pi
so 3.14 times 52*52
3.14 times 2704
8490.56
what the geometric mean of 18 and 30 as a square root?
The geometric mean of 18 and 30 is the product of 18 and 30 square rooted, so:
[tex]\sqrt{18*30} =\sqrt{540} =\sqrt{9*4*15} =\sqrt{36*15} =6\sqrt{15}[/tex]
Hope that helps!
Use multiplication or division to find the missing number
2/5 = ?/15
HELP IVE BEEN ON THIS QUESTION FOR HOURS!!
god bless you and your family if your reading this .
What is 2/5 of 15?
Want to quickly learn or show students how to convert 2/5 of 15? Play this very quick and fun video now!
How to Calculate the Fraction of a Whole Number
How to Calculate the Fraction of a Whole Number
You probably know that the number above the fraction line is called the numerator and the number below it is called the denominator. To work out the fraction of any number, we first need to convert that whole number into a fraction as well.
Here's a little tip for you. Any number can be converted to fraction if you use 1 as the denominator:
15
1
So now that we've converted 15 into a fraction, to work out the answer, we put the fraction 2/5 side by side with our new fraction, 15/1 so that we can multiply those two fractions.
That's right, all you need to do is convert the whole number to a fraction and then multiply the numerators and denominators. Let's take a look:
2 x 15
5 x 1
=
30
5
In this case, our new fraction can actually be simplified down further. To do that, we need to find the greatest common factor of both numbers.
You can use our handy GCF calculator to work this out yourself if you want to. We already did that, and the GCF of 30 and 5 is 5.
We can now divide both the new numerator and the denominator by 5 to simplify this fraction down to its lowest terms.
30/5 = 6
5/5 = 1
When we put that together, we can see that our complete answer is:
6
1
The complete and simplified answer to the question what is 2/5 of 15 is:
6
hope this helps
Missing number is 6
Set up the proportion
[tex] \frac{2}{5} = \frac{x}{15} [/tex]
Cross multiply to get 5x=30.
Divide both sides by 30 to get the answer
5x÷5=30÷5
x=6
Question 9 of 14 V
Question 9
Levi was designing a kite. He needs to determine the measure of A before cutting the fabric.
(1100
(6x + 4)º
A А
(4x + 26)
What is the measure of angle A?
The measure of angle A in the kite before cutting the fabric is 42 degrees.
What is a kite?A kite is a quadrilateral with four sides and four angles. Adjacent sides are equal, and the diagonals bisect each other at 90 degrees.
Also, there is a pair of equal opposite angles.
From the diagram:
110 + (6x + 4) + (4x + 26) = 180 (sum of angles in a straight line)
10x + 30 = 70
x = 4
∠A = 4(4) + 26 = 42°
The measure of angle A in the kite before cutting the fabric is 42 degrees.
Find out more on kite at: https://brainly.com/question/386327
Please help with this question thanks! :`D Also please give me simple explanations thank you.
Answer:
Step-by-step explanation:
The last one.
A would be a quadratic if the leading coefficient was anything but 0. 0 eleminates the x^2. Not A
B has no x^2 term to begin with. B is not the answer.
C is in exponential form. C is not the answer
D has an x^2 term. There is nothing using x that is higher. D is the answer.
If you have
[tex]3^{n-1} *\frac{n(n+1)}{2} = 20412[/tex]
whats the process for solving n?
Answer:
Step-by-step explanation:
3^(n-1) * (n(n+1)/2 = 20412
The n(n +1)/2 is a factorial which is defined for integers so we are looking for a whole number solution.
We could draw a graph manually or using software and get the solution where the graph cuts the x axis.
Also we could find the prime factors of 20412:
20412 = 2^2 * 3^6 * 7
and try substituting 2, 3 and 7 into the equation
Using this method we see that one solution is n = 7.
I could have tried n = 7 first because 3^n-1 = 3^6!!
4) What is the slope of the line joining (7, 8) and (17, 13)
slope is = (13 - 8) / (17 - 7) = 5/10 = 1/2 or 0,5
slope for A (xa ; ya) and B (xb ; yb) = (yb - ya) / (xb - xa)
I need help but I need the correct answer everyone is giving me the wrong answer !!
Answer:
y - 2 = 6 (x - 1)
Step-by-step explanation:
Slope intercept form equations look like this:
y - y1 = m (x - x1)
***m = [tex]\frac{y2-y1}{x2-x1}[/tex]
Using the point (1,2), we know that x1 = 1 and y1 = 2. Let's sub these values into the slope intercept equation:
y - 2 = m (x - 1)
To complete this equation, we need to find slope. Pick out another point on the graph and plug into the slope equation. We can use point (2,8), where (1,2) = Point 1 and (2,8) = Point 2.
[tex]\frac{y2-y1}{x2-x1}=\frac{8-2}{2-1} =\frac{6}{1} =6[/tex]
Now that we know m = 6, let's plug that back into the original equation to get our final answer:
y - 2 = 6 (x - 1)
I hope this helps!
fill in the table using this function rule. y= 3x + 4
x- 3,6,7,8
y- blank
Answer:
y: 13, 22, 25, 28
ordered pairs: (3, 13) (6, 22) (7, 25) (8, 28)
Step-by-step explanation:
Given:
function: y = 3x + 4values of x: -3, 6, 7, 8To find the y-values, substitute the x-values into the function and solve.
when x = 3
y = 3(3) + 4
= 9 + 4
= 13
when x = 6
y = 3(6) + 4
= 18 + 4
= 22
when x = 7
y = 3(7) + 4
= 21 + 4
= 25
when x = 8
y = 3(8) + 4
= 24 + 4
= 28
Therefore, the ordered pairs are; (3, 13) (6, 22) (7, 25) (8, 28)
melanie and patrick have different phone services. the relationship of the monthly cost, y dollars, to send or receive x text messages, is a linear function. the cost of patricks texting is described by y = 0.03x + 5. the cost of melanies texting is shown in the table
Answer:
Melanie: y = 0.25x
Patrick: y = 0.03x + 5
Patrick's service is cheaper when 50 texts are sent or received in one month.
Step-by-step explanation:
Let's find out Melanie's monthly texting cost function using the table. We are given multiple points that the line describing her monthly text costs passes through, so we can use the slope formula to calculate the slope of this line first.
m = (y2 - y1) / (x2 - x1)Substitute (5, 1.25) and (10, 2.50) into this formula.
m = (2.5 - 1.25) / (10 - 5)m = 1.25 / 5 m = 0.25Now we can use the point-slope equation to determine the line that describes Melanie's monthly texting cost.
I'm going to use the point (5, 1.25) and the slope m = 0.25.
y - y1 = m(x - x1)y - 1.25 = 0.25(x - 5)y - 1.25 = 0.25x - 1.25 y = 0.25xWe have Melanie's function:
y = 0.25xWe have Patrick's function:
y = 0.03x + 5
We want to determine which service is cheaper when 50 texts are sent/received in one month.
The number of texts sent and received is represented with the variable "x", and the cost of this service is represented with the variable "y".
All we need to do is substitute 50 for x in both equations to see if Melanie or Patrick's service is cheaper.
Starting with Melanie:
y = 0.25x y = 0.25(50)y = 12.50Now with Patrick:
y = 0.03x + 5 y = 0.03(50) + 5y = 1.5 + 5 y = 6.5Patrick's service is substantially cheaper than Melanie's service when 50 texts are sent or received in one month.
The area of a room is 26.025 m sqaure. If its length is 12.5m . find the breadth of the room
Answer:
2.082.
Step-by-step explanation:
Solution,
Given,
Area ( A ) = 26.025 m².
Length ( L ) = 12.5 m.
Now,
Breadth ( B ) = Area ÷ Length.
= 26.025 ÷ 12.5
= 2.082.
Thus, The breadth of the room is 2.082 m.
The measure of central tendency most influenced by outliers is the ______. A. Mode b. Median c. Mean d. Variance
PLS HELP ME 50 POINTS AND I WILL MARK THE BRAINLIEST
Answer:
1. 392 in², 2. 94.99 cm², 3. 145.2 ft², 4. 161.5 m², 5. 17 ft and 81 cm
Step-by-step explanation:
1. A = 16 x 19
A = 304
A = 1/2(11x16)
A = 1/2(176)
A = 88
304 + 88 = 392 in²
2. A = πr²
A = 3.14*5.5²
A = 3.14*30.25
A = 94.985
A = 94.99 cm²
3. A = 1/2(bh)
A = 1/2(11x26.4)
A = 1/2(290.4)
A = 145.2 ft²
4. A = bh
A = 9.5*17
A = 161.5 m²
5. part 1
A = (1/2) · (p + q) · h
112 = (1/2)(11+q)(8)
112 = 4(11+q)
112 = 44 + 4q
68 = 4q
17 = q
17 ft
5. part 2
A = lw
364.5 = 27w
13.5 = w
P = 2l + 2w
P = 2(27) + 2(13.5)
P = 54 + 27
P = 81
81 cm
Hope this helps :)
A cylinder has a height of 9 millimeters and a radius of 11 millimeters. What is its volume? Use ≈ 3.14 and round your answer to the nearest hundredth.
Answer:
3419.46 mm3
Step-by-step explanation:
volume of cylinder = area of circle x heoight
A of circle = pie r sqy = 3.14 x 11 x 11 = 379.94
379.94 x 9 = 3419.46
Rhonda has 12 marbles more than douglas . Doughlas has 6 marbles more than bertha . Rhonda has twice as many marbles as bertha has . How many marbles does douglas have
24
Explanation:
R = D + 12 (1)
D = B + 6 (2)
R = 2*B (3)
Put (3) into (1): 2*B = D + 12 (4)
Rewrite (2) as B = D - 6 and put this into (4): 2*(D - 6) = D + 12
So: 2D - 12 = D + 12
Subtract D from both sides and add 12 to both sides to get: D = 24
(not suree)
If 2 fair dice are tossed what is the probability that the sum of the number of dots on the top faces will be 7
Answer:
⅙
Step-by-step explanation:
it could be 6 and 1, 5 and 2, 4 and 3, 3 and 4, 2 and 5 or 1 and 6.
It is 2 fair dice, so all together, the probability is 36.
6/36 can be simplified to ⅙
Workers in an office of 60 staff were asked their favourite type of take-away.
The results are summarised in the table.
Pizza=8
Curry=8
Fish & chips=5
Kebab=9
Other=30
Work out the size of each angle to draw a pie chart.
Pine Bluff, Ark has been continuously declining in population at a rate of 12.5 percent due to unemployment. If
the city's current population is 100,258 then in how long before the population drops to 87,751 at this current rate?
(Round your answer to the nearest year)
a. l
b. 3
C. 4
d. 2
y=- 8x - 20
How do I graph this
Answer: Here, this should help ya out :
With graphing lines and slopes use desmos graphing calulator dont worry, its safe ;)
Answer:
See below ↓
Step-by-step explanation:
Step 1 : Mark the y-intercept.
b = -20Therefore, the y-intercept's coordinates are : (0, b)⇒ (0, -20)Step 2 : Draw the slope.
m = -8Therefore after marking the y-intercept you can either mark a point 8 spaces up, 1 to the left or mark a point 8 spaces down, 1 to the rightAfter doing this, join the two points using a ruler and draw a line Your graph is ready!It should look like this :What are the zeros of the function y=6x^2-11x+3
Combine like terms
4x+3(2x+5b)-4b-2x+6
Answer:
[tex]\boxed{\sf{8x+11b+6}}[/tex]Step-by-step explanation:
To solve this problem, you have to combine like terms of x and b from one side of the equation.
4x+3(2x+5b)-4b-2x+6Combine like terms.
3(2x+5b)+4x-2x-4b+6
Solve.
4x-2x=2x
Rewrite the problem down.
3(2x+5b)+2x-4b+6
Expand the form.
Use a distributive property.
Distributive property:
A(B+C)=AB+AC
3(2x+5b)
Multiply.
3*2x=6x
3*5b=15b
Rewrite the problem.
6x+15b
6x+15b+2x-4b+6
Combine like terms.
6x+2x+15b-4b+6
Add the numbers from left to right.
6x+2x=8x
8x+15b-4b+6
Then, you add again.
15b-4b=11b
= 8x+11b+6
Therefore, the final answer is 8x+11b+6.I hope this helps you! Let me know if my answer is wrong or not.
Answer:
8x+11b+6
Step-by-step explanation:
PLEASE HELP!!! Sari stood at a point measured 20 meters away from the base of building A. Turning 40° to building B, she determined that the base
of that building was 25 meters away. How far apart were the buildings? Use a calculator if needed.
Answer:
x = 16.71m
Step-by-step explanation:
KL² = KX² + LX² - 2KX × LX × cos(KXL)
x² = 26² + 20² - 2 × 26 × 20 × cos(40°)
x = 16.713m ≈ 16.71m
PLEASE MARK ME AS BRAINLIEST AND HAVE A NICE DAY :)
A card is drawn from a well-shuffled deck of 52 cards. What is the probability of drawing an ace or a 6?
A. 13/2
B. 7/26
C. 2/13
D. 6/52
Answer:
C
Step-by-step explanation:
There are 4 aces and 4 sixes. 4 + 4 is 8 (since it says or) so the chance is 8 / 52. 8 / 52 simplified, divide both sides by 4 and you get 2 / 13.
Answer:
C
Step-by-step explanation:
there are 4 aces and 4 sixes in a deck of 52 cards.
"And" means a probability * another probability
"Or" means a probability + another probability.
In this case, it is (probability of picking an ace) + (probability of picking an six).
[tex]\frac{4}{54} + \frac{4}{54} = \frac{8}{54} = \frac{2}{13}[/tex]
Please pick as brainliest!
Please help! WILL GIVE BRAINLIEST! George and Sarah were building a cone-shaped sand castle. After some time, the diameter of the sand shaped cone was 12 in. and the height was 14 in. What is the approximate volume of the sand cone rounded to the nearest hundreth? (Show your work. Remember you can draw a picture to help you solve the problem). Label your answers with the correct units.
Use 3.14 to approximate pi
Answer:
They kept adding sand, and ten minutes later the volume of the sand cone had increased by 30%. What is the approximate volume of the sand cone now? Label your answers with the correct units. (Show your work) Use 3.14 to approximate pi
Answer:
volume = 527.52 in³
volume increased by 30% = 685.776 in³
Step-by-step explanation:
Volume of a cone
[tex]V=\dfrac13\pi r^2h[/tex]
(where r is the radius and h is the height)
Given:
diameter = 12 in ⇒ radius = 6 inheight = 14 in[tex]\pi =3.14[/tex][tex]\implies V=\dfrac13 \cdot 3.14 \cdot 6^2 \cdot 14[/tex]
[tex]\implies V=527.52 \ \sf in^3[/tex]
---------------------------------------------------------------------------
If the volume increases by 30% then it will now be 130% of the original volume.
130% as a decimal = 130/100 = 1.3
Therefore, to find the new volume, multiply the original volume by 1.3.
[tex]\implies V=527.52 \cdot 1.3[/tex]
[tex]\implies V=685.776 \ \sf in^3[/tex]
If the probability that a person lives in an industrialized country of the world is 1/5 find
the probability that a person does not live in an industrialized country
Answer:
4/5
Step-by-step explanation:
5/5 - 1/5 = 4/5 is the probability that a person does not live in an industrialized country
The P( person does not lives in an industrialized country ) = 4/5
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
Given:
P( person lives in an industrialized country ) = 1/5
Now, using the Completement probability
P ( person lives in an industrialized country ) + P( person does not lives in an industrialized country ) = 1
P( person does not lives in an industrialized country )
= 1- P ( person lives in an industrialized country )
P( person does not lives in an industrialized country )
= 1- 1/5
= 4/5
Hence, P( person does not lives in an industrialized country ) = 4/5.
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Nancy spends 1/3 of her monthly salary on rent, 0.1 on her car payment, 1/12 on food, and 20% on the bills. She has $680 left for other expenses. What is Nancy's monthly salary?
Answer:
have a good day
Step-by-step explanation:
rump 2020