[tex]5\sqrt{3x+1} = 10\\\\\implies \sqrt{3x+1} = \dfrac{10}5 \\\\\implies \sqrt{3x+1} = 2 \\\\\implies 3x +1 = 4\\\\\implies 3x = 4-1 \\\\\implies 3x = 3\\\\\implies x =1[/tex]
Answer:
x = 1
Step-by-step explanation:
Given equation:
[tex]\dfrac{5(3x+1)^1}{2} =10[/tex]
If a term has "1" as it's exponent, it means that it's the number itself. Therefore, we can remove the "exponent".
[tex]:\implies\dfrac{5(3x+1)}{2} =10[/tex]
Simplify the distributive property:
[tex]:\implies\dfrac{15x+5}{2} =10[/tex]
Using cross multiplication:
[tex]:\implies15x+5} =10 \times 2[/tex]
Simplify the R.H.S:
[tex]:\implies15x+5} =20[/tex]
Subtract 5 both sides:
[tex]:\implies15x+5 - 5} =20 - 5[/tex]
Simplify both sides:
[tex]:\implies15x} =15[/tex]
Divide 15 both sides:
[tex]:\implies\dfrac{15x}{15} } =\dfrac{15}{15}[/tex]
Simplify both sides:
[tex]:\implies x= 1[/tex]
The solid below is dilated by a scale factor of 5. Find the surface area of the solid
created upon
dilation.
W = 3
L = 6
H= 3
Considering the dilation, the surface area of the rectangular prism is of 0.432 units².
What is the surface area of a rectangular prism?The surface area of a rectangular prism of dimensions l, w and h is given by:
Sa = lwh.
In this problem, the dilation means that all dimensions are divided by 5, hence they will be considered as:
w = h = 0.6, l = 1.2.
Hence the surface area of the prism will be of:
Sa = lwh = 1.2 x 0.6 x 0.6 = 0.432 units².
More can be learned about the surface area of a rectangular prism https://brainly.com/question/21208177
The surface area of the solid created upon dilation by a factor of 5 is 2250 unit²
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The solid below is dilated by a scale factor of 5. Hence:
New length = 6 * 5 = 30, new width = 3 * 5 = 15, new height = 3 * 5 = 15
Surface area = 2(30 * 15 + 30 * 15 + 15 * 15) = 2250 unit²
The surface area of the solid created upon dilation by a factor of 5 is 2250 unit²
Find out more on equation at: https://brainly.com/question/2972832
3a(6a 2– 4ab 2 ) + 8a 2 b 2– 2b 3
Answer: ...
Ok done. Thank to me :3
Make sure to Show your math steps to arrive at your answers and Explain each step in complete sentence please
Answer:
Min is 51 and max is 75 and the the mediem is 63 and the q1 is 54 and q2 is 55 and 57 and q3 is 65 and 69
Step-by-step explanation:
the least is 51 and the most is 75 and the mean is 63 if u list them in order and than u find the quartiles that are between the median and 51 and q3 is between the median and the max.
Segment bc is parallel to De. Use the proportion from a B to BD to find the missing length of CE
Answer:
CE = 6
Step-by-step explanation:
we use the proportion relationship:
[tex]\frac{AB}{BD} = \frac{AC}{CE\\}\\then[/tex]
[tex]\frac{2}{3} = \frac{4}{CE}\\\\then[/tex]
2×CE = 3 ×4 (cross multiply)
then
2×CE = 12
then
CE = 12/2 = 6
What graph represents -14x -7y <4
Answer:
-14x-7y < 4
There is no equals sign so we know that is must be a dotted line
Add 14x to each side
-7y < 14x+4
Divide by -7, remembering to flip the inequality
-7y/-7 > 14/-7 x+4/-7
y > -2x -4/7
Y is greater so we shade above.
To sew a pair of jeans, 630 feet of thread is needed. Unfortunately the fabric store only sells thread in yards. How many yards of fabric would you need to buy from the store to make a pair of jeans?
Answer:
210
Step-by-step explanation
One yard is equal to 3 feet so the simplest way is to divide the number of feet by 3 and that will give you your answer.
Answer:
210
Step-by-step explanation:
this is writing linear equations
Answer:
[tex]y = 3x +1[/tex]
Step-by-step explanation:
We can verify it by substituting the [tex]x[/tex] with the numbers in the [tex]x[/tex] column to get the same [tex]y[/tex] in the [tex]y[/tex] column.
Check:
[tex]y = 3(-2) +1\\y = -6 +1\\y= 5[/tex]
It matches; therefore, the answer is [tex]y = 3x +1[/tex]. You can try with the other equations given and take the same steps, but it will not match.
Your mom is building a garden around a fountain she has a space marked out but decides she wants to enlarge it without altering the center of it what type of transformation is this
Answer:
u didnt give out the choses but it might be a chance to be dilation
Step-by-step explanation:
"the action or condition of becoming or being made wider, larger, or more open."
since she enlarge it without altering the center of it
In the figure below, S is between Q and T, R is the midpoint of QS. If QT=10 and RS=2 find ST
Answer:
ST = 6
Step-by-step explanation:
The segment sum is ...
QR +RS +ST = QT
QR +2 +ST = 10 . . . . use given values
Since R is the midpoint of QS, we know QR = RS = 2. Now, we have ...
ST = 10 -2 -QR = 10 -2 -2 = 6
The length of ST is 6.
please solve the Magic Square I will mark you as brainliast please
[tex]\begin{bmatrix}\frac{1}{6} & \frac{1}{2} & \frac{1}{3} \\ \\ \frac{3}{6}& \frac{2}{6} & \frac{1}{6} \\ \\ \frac{1}{3} & \frac{4}{24} & \frac{1}{2} \\ \end{bmatrix} [/tex]
Explanation:
The magic square is a n×n square which contains different number and sum of all the number of any row or column gives same value.
in any magic square the sum values of all row or column is three time of the number in centre of the square.
in above magic square the middle number is 2/6
so we can calculate the final value by multiplying with 3,
[tex] \frac{2}{6} \times 3 = \frac{2}{ \cancel6}_2 \times \cancel3 = \cancel{\frac{2}{2}} = 1[/tex]
The magic number or sum of any row or column is 1,
using this we can find the missing,
in column first,
1/6 and 1/3 are given and middle term is missing
let the middle term be x now,
[tex]x + \frac{1}{6} + \frac{1}{3} = 1 \\ x = 1 - \frac{1}{6} - \frac{1}{3} \\ x = 1 - ( \frac{3 + 6}{18}) \\ x = 1 - \frac{9}{18} \\ x = \frac{18 - 9}{18} \\ x = \cancel \frac{9}{18} = \frac{1}{2} [/tex]
similarly we can solve for the 3rd fraction of second column,
let the third number be y,
[tex] \frac{3}{ 6} + \frac{2}{6} + y = 1 \\ y = 1 - \frac{3}{ 6} - \frac{2}{6} \\ y = 1 - \frac{5}{6} = \frac{1}{6} [/tex]
Now in first and third row, the third number is missing which can be calculated in same way.
The rough work and final calculation is attached!
Thanks for joining brainly community!
What is the lateral area of the cone?
Answer:
54.96
Step-by-step explanation:
Using the formulas
AL=πrl
l=r2+h2
Solving for AL
AL=πrh2+r2=π·3·52+32≈54.95543
(21x⁵· y⁸)² divided by 3x²
show ur work
[tex]\cfrac{(21x^5y^8)^2}{3x^2}\implies \cfrac{((3)(7)x^5y^8)^2}{3x^2}\implies \cfrac{3^2\cdot 7^2x^{5\cdot 2}y^{8\cdot 2}}{3x^2}\implies \cfrac{3^2}{3}\cdot \cfrac{7^2 x^{10} y^{16}}{x^2} \\\\\\ 3\cdot 7^2 x^{10}\cdot x^{-2} y^{16}\implies 3\cdot 49x^{10-2}y^{16}\implies 147x^8y^{16}[/tex]
Graph: f(x) = 1/2 (2)x
Answer:
11
Step-by-step explanation:
Cancel out 22 and 22.
\frac{\mathrm{d}}{\mathrm{d}x}(x)
dx
d
(x)
The derivative of ax^{n}ax
n
is nax^{n-1}nax
n−1
.
x^{1-1}x
1−1Subtract 11 from 11For any term tt except 00, t^{0}=1t
0
=1.
HELP! WILL GIVE BRAINLEST!
Answer:
A
Step-by-step explanation:
tan theta will equal zero if theta = n × pi where n is an integer
A 25-foot tree casts a 6 1/4-foot shadow. At the same time, a fence casts a 2-
foot shadow. How tall is the fence?
Answer: 16.666666 feet
Explanation: 25/9=x/6 (25*2)/3 =50/3 I hoped this helped you solve your problem. Have a good day love!
The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. The Height of the fence is 8 feet.
What is Tangent (Tanθ)?The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. it is given as,
tan(θ) = Perpendicular/Base
where,
θ is the angle,
Perpendicular is the side of the triangle opposite to the angle θ,
Base is the adjacent smaller side of the angle θ.
Given that a 25-foot tree casts a 6 1/4-foot shadow. Also, At the same time, a fence casts a 2-foot shadow.
Length of the shadow = 6 1/4 feet = 6 + 1/4 = 6.25 feet
Now, since the sun is at the same angle, therefore, the angle between the top of the object and the top of the its shadow will be the same for all the objects. Therefore,
tan(θ) = Height of the tree/Shadow of the tree = Height of the fence/Shadow of the fence
tan(θ) = 25 feet / 6.25 feet = Height of the fence / 2 feet
Height of the fence = (2feet × 25 feet) / 6.25 feet
Height of the fence = 8 feet
Hence, the Height of the fence is 8 feet.
Learn more about Tangent (Tanθ) here:
https://brainly.com/question/10623976
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Find the measure bog and interior angle of the regular nonagon x=
Answer:
140 degrees
Step-by-step explanation:
The formula of the hint is the sum of the angles in a nonagon (9 sided polygon). If we divide the sum of the angles in a nonagon by nine we should be able to get the angle of each nonagon.
(9-2) * 180 = 7 * 180 = 1260
1260/9 = 140 degrees
How much did David earn if he earns $5.60 per hour and works 36 hours?
Answer:
$201.6
Step-by-step explanation:
5.60 multiplied by 36 is 201.6
Answer:
$201.60
Step-by-step explanation:
5.6 times 36 = 201.6
What is the value of x in (7x + 2)
Answer:
x = 9
Step-by-step explanation:
(7x + 2)
7x can't be added with 2 because 2 has no x
therefor ,
we take x out
X ( 7 + 2 )
so
X = 9
warning :
sory if the answer is wrong
The first number in a pattern is 84. The pattern follows the rule divide by 2 then add 10. Find the next three terms and then describe the pattern.
Answer: 52 , 36 , 28
I goygot these numbers by following the rule . Each time you divide by 2 so u get the half and then add 10 . I see the numbers are even and they are decreasing so they are getting smaller . Hope it helps
7.2
8.3
152 in^3
What is the correct answer
Answer:
1094.4
Step-by-step explanation:
assuming you want volume
Please solve this and only answer with image
[tex]\cot^4 A - \cot^2 A = 1\\\\\cot^4 A = 1 + \cot^2 A\\\\\frac{\cos^4 A}{\sin^4 A} = 1 + \frac{\cos^2 A}{\sin^2 A}\\\\\frac{\cos^4 A}{\sin^4 A} = \frac{\sin^2 A}{\sin^2 A}+\frac{\cos^2 A}{\sin^2 A}\\\\\frac{\cos^4 A}{\sin^4 A} = \frac{\sin^2 A+\cos^2 A}{\sin^2 A}\\\\\frac{\cos^4 A}{\sin^4 A} = \frac{1}{\sin^2 A}\\\\\cos^4 A = \frac{\sin^4 A}{\sin^2 A}\\\\\cos^4 A = \sin^2 A\\\\[/tex]
This then means,
[tex]\cos^4 A + \cos^2 A = 1\\\\\sin^2 A + \cos^2 A = 1\\\\[/tex]
which is the pythagorean trig identity. This concludes the proof.
Therefore, if [tex]\cot^4 A - \cot^2 A = 1[/tex], then [tex]\cos^4 A + \cos^2 A = 1[/tex]
6a-4(2a+3)
what is the answer
HELP Thank you
Answer:
[tex]\huge\boxed{\bf\:2 (-a - 6)}[/tex]
Step-by-step explanation:
[tex]6a - 4(2a + 3)\\6a - (4*2a + 4*3)\\6a - (8a + 12)\\6a - 8a - 12\\- 2a - 12\\\boxed{\bf\:2 (-a - 6)}[/tex]
Steps:
Factorise the second term as the first is already in its simplified form.Solve the first term and the second term by doing the required arithmetic operations.Take the common factor out.The result will be : 2 (- a - 6).[tex]\rule{150pt}{2pt}[/tex]
Answer:
[tex]\Longrightarrow: \boxed{\sf{-2a-12}}[/tex]
Step-by-step explanation:
Use the distributive property.
[tex]\underline{\text{DISTRIBUTIVE PROPERTY:}}\\\\\Longrightarrow: \sf{A(B+C)=AB+AC}[/tex]
6a-4(2a+3)First, multiply by expand.
⇒ -4(2a+3)
⇒ -4*2a=-8a
⇒ -4*3=-12
⇒ -8a-12
→ 6a-8a-12
Solve.
Add or subtract the numbers from left to right.
⇒ 6a-8a=-2a
= -2a-12
[tex]\Longrightarrow: \boxed{\sf{-2a-12}}[/tex]
Therefore, the correct answer is -2a-12.I hope this helps! Let me know if you have any questions.
What’s the distance between -50 and 30
Answer:
80
Step-by-step explanation:
-50+x=30
x=80
Answer:
im pretty sure its 80
Step-by-step explanation:
Can somone please help me before tomorrow? I will give brainlist! Question: Timothy went to a baseball game. After the game, he wanted to do the bus tom The red line and the blue line buses both stop at the sam • A red line and a blue line bus both left the stadium at 400 m • Red line buses were scheduled to leave the stadium every • Blue line buses were should to leave the stadium every minutes of the buses our on schedule, when is the next time red line and a blue line bus will leave together?
Answer:
4:24 pm
Step-by-step explanation: I first drew it out on a time line and both buses came back together at 4:24 pm. I also looked at the common denominator was for both numbers, 6 and 8: 24.
To check my answer, I substituted other numbers and found that they came back together again at the LCD. Hope this helps.
uhh lol help?
'' The Jurassic period (199.6 million to 145.5 million years ago) was characterized by a warm, wet climate that gave rise to lush vegetation and abundant life. Many new dinosaurs emerged—in great numbers. Among them were stegosaurs, brachiosaurs, allosaurs, and many others. Combined these three dinosaurs measured over 749 feet tall. The brachiosaurs was four times larger than the allosaurs, the stegosaurs was twice the size of the allosaurs. How tall was the brachiosaurs? "
A. 107 feet
B. 214 feet
C. 321 feet
D. 428 feet
(1) State 3 side lengths that would create a triangle.
(2) State 3 angle measures that would create a right isoscele
triangle.
Answer:
1) 1, 1, [tex]\sqrt{2}[/tex]
2) 45°, 45°, 90°
Step-by-step explanation:
side lengths need to be proportional like 1, 1, [tex]\sqrt{2}[/tex], which is proportional for isoscele triangle.
isosceles is the one that has 90° angle and 2 equal angles so two 45° angles.
Given the equation : 5 + x - 14 = x - 7
Part A. Solve the equation . 5 + x - 14 = x - 7 In your final answer, be sure to state the solution and include all of your work.
Part B. Use the values x = -2, 0, 3 to verify your solution to the equation .5 + x - 14 = x - 7 In your final answer, include all of your calculations.
Well, at first consider the given equation, then will be solving for Part A) and B),
[tex]{:\implies \quad \sf 5+x-14=x-7}[/tex]
Subtracting x from both sides will yield ;
[tex]{:\implies \quad \sf 5-14=-7}[/tex]
[tex]{:\implies \quad \sf -9=-7}[/tex]
But, -9 ≠ -7, so their is no solution for values of x, as -9 can't be equal to -7 , so from definition of algebra, we can say that, their are no solutions for x, as there are no solutions for x, so nothing can be concluded from Part A and Part B
Answer:
Part A: -9 ≠ -7
no solution
Part B: below for the answers
Step-by-step explanation:
Part A: 5 + x - 14 = x - 7
subtract x on both sides
x - 5 + x - 14 = x - 7 - x
then, we take away the x's
5 - 14 = -7
-9 ≠ -7
there is no solution
Part B: 5 + -2 - 14 = -2 - 7
-11 ≠ -9
5 + 0 - 14 = 0 - 7
-9 ≠ -7
5 + 3 - 14 = 3 - 7
-6 ≠ -4
A triangle has one side that measures 9 units, another side that measures x, and a third side that measures 2 units more than x. The perimeter is 29 units.
Which equation would we use to find the value of x?
Answer:
9 + x + x + 2 = 29
Step-by-step explanation:
all of the sides added together is 29
so
9 + x + x + 2 = 29
that is your equation
Which agency is responsible for promoting the welfare and opportunities of wage earners? a. fda b. hud c. dol d. cpsc please select the best answer from the choices provided a b c d
Answer:
the answer is (C) DOL
Step-by-step explanation:
!!!!40 POINTS AND BRAINLIEST!!!!
If you are trying to calculate a company's initial profit, you can graph the profit function
and find:
A)the highest point of the graph.
B)the point where the graph crosses the x-axis.
C)the lowest point of the graph.
D)the point where the graph crosses the y-axis.
(Make sure to explain)
Answer:
D) the point where the graph crosses the y-axis
Step-by-step explanation:
The "initial" value of a function is generally taken to mean the function value when the independent variable is zero.
On a graph of the profit function, that will be the y-intercept: the point where the graph crosses the y-axis.
__
The highest point on the graph will be the maximum profit.
The points where the graph crosses the x-axis will be where profit is zero, referred to as "break-even" points.
The lowest point on the graph will be where the profit is a minimum. That point may actually indicate a loss (negative profit).