Answer:
1) [tex]x^{2/3}[/tex]
[tex]3[/tex] → index
[tex]\sqrt[3]{x^{2} }[/tex]
[tex]Index: 3[/tex]
----------------
2) [tex]7^{5/4}[/tex]
[tex]=\sqrt[4]{7^{5} }[/tex]
[tex]=(\sqrt[4]{7})^{5}[/tex]
----------------
3) [tex]\sqrt[7]{2^{3} }[/tex]
[tex]=(2^{3} )^{1/7}[/tex] [tex][\sqrt[x]{n} =n^{1/n} ][/tex]
[tex]=2^{3/7}[/tex]
----------------
3) [tex]\sqrt[12]{8^{4} }[/tex]
[tex]y=(8^{4} )^{1/12}[/tex]
[tex]y=(8)^{1/3}[/tex]
[tex]y=(2)^{3\times 1/3}[/tex]
[tex]y=2[/tex]
------------------
4) [tex]128^{3/7}[/tex]
[tex]=\sqrt[7]{2\times 2\times2\times 2\times 2\times2\times 2}[/tex]
[tex]=(2)^{3}[/tex]
[tex]=8[/tex]
----------------------
OAmalOHopeO
If paul puts 300 dollars in a saving account that earns 3% interest how much interest will he earn after 2 years?
Answer:
[tex] \boxed{18 \: dollars}[/tex]Step-by-step explanation:
Principal ( P ) = $ 300
Rate ( R ) = 3%
Time ( T ) = 2 years
Now, let's find the simple Interest:
I = [tex] \mathsf {\frac{PTR}{100} }[/tex]
[tex] \mathsf{ = \frac{300 \times 2 \times 3}{100} }[/tex]
[tex] \mathsf{ = \frac{1800}{100} }[/tex]
[tex] \mathsf{ = 18}[/tex]
Extra information:
Simple Interest
In our daily life when we borrow a sum of money either from a moneylender or from any financial company, we have to pay the money back by adding with extra sum of money. This borrowed money is called principal. The extra money to be paid for the borrowing money is called interest , which is paid after certain duration in certain rate. At last, the borrowed money should be paid back along with interest which is called amount.
Interest is based on three factors : Principal ( P ) , Rate of interest ( R ) and Time ( T ). While computing the interest, the rate must be in percent and time in years.
[tex] \mathsf{ \: simple \: interest \: = \frac{PTR}{100} }[/tex]
On simplifying
[tex] \mathsf{p = \frac{I \times 100}{T \times R} }[/tex]
[tex] \mathsf{t = \frac{I \times 100}{P \times R} }[/tex]
[tex] \mathsf{r = \frac{I \times 100}{P \times T}} [/tex]
And from the definition,
Amount ( A ) = Principal ( P ) + Interest ( I )
Principal ( P ) = Amount ( A ) - Interest ( I )
Interest ( I ) = Amount ( A ) - Principal ( P )
Hope I helped!
Best regards!
Answer:$18
Step-by-step explanation:3% of $300 is $9.$9 is the interest of 1 year so the interest of 2 years is 2 multiplied by 9 which is $18.
What is the value of x?
26°
xº
O
x
= [?]
Answer: x = 154°
Step-by-step explanation:
In this tangents are formed
So the two unknown opposite angles at the curves will be 90° each.
So using angle sum property of a quadilateral in which all angles adds upto 360°
We get x as
90+90+26+x = 360
206+x = 360
x = 360 - 206
x = 154
please click thanks and mark brainliest if you like :)
Help anyone can help me do the question,I will mark brainlest.
Answer:
<ADC=90
therefore AC= 20 using Pytagoras
BAC is a right angle triangle because it belongs to the Pytagoras theorem:25,20,15 i.e 25²=15²+20²
3) I DON'T THINK PQR IS A RIGHT ANGLE TRIANGLE because it doesn't belong to the Pytagoras triple.
Find the value of x.
Answer:
48
Step-by-step explanation:
(204-x)/2=78
or, 204-x=156
or, x=204-156
or, x=48
If d-1/d=6 evaluate d+1/d
[tex]{ \boxed{\boxed{\begin{array}{cc} \maltese \bf \: given \: \\ \\ \rm \: d - \frac{1}{d} = 6 \\ \\ \bf \: now \\ \\ \rm {(d + \frac{1}{d} })^{2} = ( {d - \frac{1}{d} })^{2} + 4 \times d \times \frac{1}{d} \\ \\ = {6}^{2} + 4 \\ \\ = 36 + 4 \\ \\ = 40 \\ \\ \rm \: d + \frac{1}{d} = \pm \sqrt{40} \end{array}}}}[/tex]
Solve five and six eighths plus four and four fifths.
Answer:
Two and three fourtieths.
Step-by-step explanation:
5 6/8 + 4 4/5
= 46/8 + 24/5
= 83/40
= 2 3/40
Two and three fourtieths(2 3/40) is the answer.
Answer: 9 22/40
Step-by-step explanation:
Solve for x. 7x+38=45
Answer:
x=1
Step-by-step explanation:
subtract 38 from both sides:
7x=7
divide both sides by 7 to isolate x:
x=1
HOPE THIS HELPS!!!! :)
I NEED HELP!! which expression is the radical form of x - 9/8
Answer:
Step-by-step explanation:
Please use " ^ " to indicate exponentiation.
Your "x - 9/8" should be x ^(-9/8).
The 8 represents "the eighth root" of x, and the -9 represents the power to which x is to be raised. Finally, the " - " sign shows that this 9th power is in the denominator.
x ^(-9/8) in radical form is ----------------
[tex]1 divided by \sqrt[8]{x^9\\} \\[/tex]
A 2 inch by 2 inch square has its area increased by 21 square inches producing a new square. How many inches long is a side of the new square?
Answer:
A 2 by 2 inch square has an area of 4 square inches.
If its area is increased by 21 inches, then its area equals 25 square inches.
To find the length of the side we take the square root of 25 square inches which is 5 inches.
Step-by-step explanation:
Points C and D are on a number line (not shown).
The coordinate of point C is -16 and the coordi-
nate of point D is 14. Point E is a point on line
segment CD. If the distance from point E to point C
is 1
4
the distance from point E to point D, what is
the coordinate of point E?
Answer:
17
Step-by-step explanation:
what is (a x b) x c, if a = 11, b = 9, and c = 1? PLEASE HELP!!!
Answer:99
Step-by-step explanation:(11×9)×1=99
Answer:
The answer is 99Step-by-step explanation:
(a x b) x c
a = 11, b = 9, and c = 1
In order to solve substitute the values of a , b and c into the above expression
That's
( 11 × 9) × 1
Solve the terms in the bracket first
99 × 1
We have the final answer as
99Hope this helps you
List in increasing order.
22. 807; 780; 870
3103
Please answer for 70 points! :)
Answer:
This is already listed in increasing order:
22. 807; 780; 870; 3103Given order .
807;780;870We have to arrange it in increasing means lowest to highest
[tex]\\ \sf\longmapsto 780<807<870[/tex]
The listing will be
[tex]\\ \sf\longmapsto 780;807;870[/tex]
Solve for x in the equation x squared + 11 x + StartFraction 121 Over 4 EndFraction = StartFraction 125 Over 4 EndFraction.
Answer:
Below
Step-by-step explanation:
● x^2 + 11x + 121/4 = 125/4
Substract 125/4 from both sides:
● x^2 + 11x + 121/4-125/4= 125/4 -125/4
● x^2 + 11x - (-4/4) = 0
● x^2 +11x -(-1) = 0
● x^2 + 11 x + 1 = 0
This is a quadratic equation so we will use the determinanant (b^2-4ac)
● a = 1
● b = 11
● c = 1
● b^2-4ac = 11^2-4*1*1 = 117
So this equation has two solutions:
● x = (-b -/+ √(b^2-4ac) ) / 2a
● x = (-11 -/+ √(117) ) / 2
● x = (-11 -/+ 3√(13))/ 2
● x = -0.91 or x = -10.9
Round to the nearest unit
● x = -1 or x = -11
The solutions are { -1,-11}
The solution of the equation x² + 11x + (121/4) = 125/4 will be 0.09 and negative 11.09.
What is the solution to the equation?The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.
The equation is given below.
x² + 11x + (121/4) = 125/4
Simplify the equation, then the equation will be
4x² + 44x + 121 = 125
4x² + 44x + 121 - 125 = 0
4x² + 44x - 4 = 0
x² + 11x - 1 = 0
We know that the formula, then we have
[tex]\rm x = \dfrac{-b \pm \sqrt {b^2 - 4ac}}{2a}[/tex]
The value of a = 1, b = 11, and c = -1. Then we have
[tex]\rm x = \dfrac{-11 \pm \sqrt {11^2 - 4 \times 1 \times (-1)}}{2 \times 1}\\\rm x = \dfrac{-11 \pm \sqrt {121 +4}}{2 }\\x = \dfrac{-11 \pm \sqrt {125}}{2 }[/tex]
Simplify the equation, then we have
x = (- 11 ± 11.18) / 2
x = (-11 - 11.18) / 2, (-11 + 11.18) / 2
x = -11.09, 0.09
The solution of the equation will be 0.09 and negative 11.09.
More about the solution of the equation link is given below.
https://brainly.com/question/545403
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Acellus, Inscribed Angles
Find the value of y.
x
120°
Answer:
[tex]y=60\textdegree[/tex]
Step-by-step explanation:
The Tangent-Secant Interior Angle Measure Theorem states that the measure of an angle formed by a tangent and a secant of a circle at the point of tangency is equal to half of the measure of its intercepted arc.
Therefore, [tex]y=\frac{1}{2} *120\textdegree = \bf 60\textdegree[/tex]. Hope this helps!
Using the conversion 1 mile equals 1.6093 km to convert 4.9 kilometers to miles, round o the nearest tenth of a mile
Answer:
3.0 miles
Step-by-step explanation:
Using the conversion 1 mile equals 1.6093 km to convert 4.9 kilometers to miles, round to the nearest tenth of a mile.
1 mile = 1.6093 km
Convert 4.9km to mile
We can use cross multiplication :
Let the number of miles = m
1 mile = 1.6093 km
'm' miles = 4.9 km
Cross multiply :
m × 1.6093 = 4.9 × 1
m = 4.9 / 1.6093
m = 3.0448020 miles
Rounding 3.0448020 to the nearest tenth :
3.0 miles
The point (-3,-1) is the midpoint of (x,y) and (5,4). Find the point (x,y).
Answer:
(-11, -6)
Step-by-step explanation:
Find the distance between the midpoint, (-3, -1) and (5, 4). This can be calculated by finding the difference between the x coordinates and y coordinates.
-3 - 5 = -8 (distance between x coordinates)
-1 - 4 = -5 (distance between y coordinates)
Find the point (x, y) by subtracting 8 from the midpoint's x value, and then subtracting 5 from the midpoint's y value.
-3 - 8 = -11
-1 - 5 = -6
So, the point (x, y) is (-11, -6)
When writting a equation how do you know where to put the equal sign?
Event A: Flipping heads on a coin #1. Event B: Flipping heads on a coin #2. What is P(A and B)?
Answer:
coin 1
Step-by-step explanation: i think this is it
Answer:
Heads is a 50, 50 situation. so 1/2 plus 1/2 is 1/4
You have this information about ΔABC, ΔFDE, and ΔGIH:
AB = DF
AB = GI
BC = HI
DE = HI
m∠B = m∠D = m∠I
Which triangles must be congruent?
The triangle ABC, triangle FDE, and triangle GIH are congruent with each other.
What is a triangle?Three sides and three internal angles define a triangle, a basic shape. The symbol is used to represent one of the geometric shapes in which the three corners are connected to one another. Triangles are categorized according to their sides into numerous different forms.
As per the given data in the question,
Sides AB = DF, AB = GI, BC = HI, and DE = HI are equal to each other.
Also, the angles, m∠B = m∠D = m∠I are equal.
Then by the property of the side angle side all the triangles are congruent with each other.
To know more about Triangle:
https://brainly.com/question/2773823
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Answer:
A. ΔABC, ΔFDE, and ΔGIH
Find the coordinates for the function,
1.) f(x)=-2(2.5)
2.) f(x)= 4(1.5)
Answer: 1: Slope 0 Y- Intercept -5
2: Slope 0 Y- Intercept 6
Step-by-step explanation:
5. Eight adults and six children travel in a cable car.
Estimate the total mass of the people in the cable car.
Answer: 1880 pounds
Step-by-step explanation: when you take the average adult weight, around 160 lbs. you multiply that by eight. you get 1280. then you estimate that each of the children weigh around 100 lbs, then you add 600 to 1280 and get 1,880 lbs
Pete earns graduated commission on his sales each month. He earns 7% commission on the first $35,000 in sales and 9% on anything over that. If Pete had $43,000 in sales this month, how much commission did he earn?
a. $2,610
b. $3,170
c. $3,870
d. $6,880
Please select the best answer from the choices provided A B C D
Answer:
b.$3170
Step-by-step explanation:
43,000-35,000=8,000
SO you would find 9% commission on 8,000
8,000x.09=720
then, you would find his normal commission if he only made 35,000
so you would do 35,000x.07=2450
you would, then, add the two together to get his entire commission, which is $3170
Answer:
b
Step-by-step explanation:
In Art Class, you designed a rectangle stained glass window. The
length is (2x+2) inches, and the height is 6x. What is the perimeter of
the window? (Hint: draw a diagram and label the sides)
Answer:
Step-by-step explanation:
Draw a triangle and label the sides (picture below):
● the length is 2x+2
● and the width or the height is 6x
The perimeter of a rectangle is the sum of the sides
● P = 2x+2 + 6x + 2x+2 + 6x
Isolate the similar terms
● P = (2x+2x+6x+6x) + (2+2)
● P = 16x + 4
The perimeter of the window of lengths 2x+2 and 6x is 16x + 4
The formula for calculating the perimeter of a rectangle is expressed as:
[tex]P=2(L+W)[/tex] where:
L is the length of the rectangular stained glass window.
W is the width of the rectangle stained glass window
Given the following
L = (2x +2) inches
W = 6x inches
Substitute the given values into the formula as shown:
[tex]P = 2(2x+2+6x)\\P=2(2x+6x+2)\\P=2(8x+2)\\P=2(8x)+2(2)\\P=16x+4[/tex]
Hence the perimeter of the window is 16x + 4
Learn more here: https://brainly.com/question/10452031
Find n. A. 5 B. 5√3 C. 10 D. 10√3/3
Answer:
Option A
Step-by-step explanation:
Using trigonometry ratios
tan∅= opp/adj
tan 30°=n/(5√3)
1/√3 = n/(5√3)
n = (5√3)/√3
n = 5
Factorise the following
Answer:
4ny²+4n²-4n-8+y⁴-2y²
To the nearest whole percent, what is the probability that a randomly chosen member of the JV swim team does not wear glasses and is in the 10th grade? 14% 17% 55% 67%
Answer: 14%
Step-by-step explanation:
Complete question is provided in the attachment below:
Probability that members of the junior varsity swim team wear glasses = 55%=0.55
Given: P(wear glasses) = 0.55
P(not wear glasses) = 1-0.55 = 0.45
P(member in 10th grade | not wear glasses) = 30%
Using conditional probability formula:
[tex]P(B|A)=\dfrac{P(A\text{ and } B)}{P(A)}[/tex]
[tex]\Rightarrow\ 0.30=\dfrac{P(\text{not wear glasses and in 10th grade})}{0.45}\\\\\Rightarrow\ P(\text{not wear glasses and in 10th grade})=0.45\times0.30\\\\0.135=13.5\%\approx14\%[/tex]
Hence, the probability that a randomly chosen member of the JV swim team does not wear glasses and is in the 10th grade = 14%.
So, the correct option is "14%".
what is twelve less than a variable
Answer:
x - 12
Step-by-step explanation:
"twelve" - number
"less than" - switches the entire expression
"a variable" - a unknown number shown as a letter. can be x.
Now we have cut the entire word expression into smaller peices, we can combine it into a actual expression.
12 - x will turn into:
x - 12
Hope this helped.
Answer:
x-12
Step-by-step explanation:
Let the variable be x
12 less than x
x-12
find the slope and y intercept
Answer:
slope = -1
y intercept (0,-2)
Step-by-step explanation:
We can use the two points to find the slope
(-4,2) and (1,-3)
m = ( y2-y1)/(x2-x1)
= (-3 -2)/(1 - -4)
= -5 /(1+4)
= -5/5
- 1
The y intercept is where it crosses the y axis
y intercept is (0,-2)
K = 3x + 8 and m M = x + 12, find the m K. How do I solve?
Answer:
Step-by-step explanation:
3(m-12)+8
x=m-12
Hunter assumed he would only get 64
problems correct on his test, but he
actually got 78 correct. What was his
percent error
Round to the nearest percent.
Answer:
22%
Brainliest, please!
Step-by-step explanation:
78 - 64 = 14
14 / 64 = 0.21875
= 22% (when rounded)