12 to 20 is 60 percent
12 is 60% of 20
To find the percent you must divide to two numbers 12 and 20. You then get 0.6 which is 60 percent because 6 is in the tenths place which also determines how many zeros there are.
Write the given equation in exponential form.
log7 = 3
For this case we have that by definition of logarithmic properties that, the expression
[tex]log_ {b} (a) = c[/tex] is equivalent to:
[tex]b ^ c = a[/tex]
Then, we have the following expression:
[tex]log_ {7} () = - 3[/tex]
It can be equivalent to:
[tex]7 ^ {- 3} =[/tex]
Answer:
The correct option is option A
[tex]7 ^ {-3}[/tex]
The sum of the interior angles of a triangle is_____.
The sum of the measures of the interior angles of a triangle is 180˚. Example 3: In NMQ. ∆.
For this case, we have given an ABC triangle with internal angles α,β,γ. By definition, the sum of the internal angles must be 180 degrees.
That is to say:
α+β+γ=180
This can be demonstrated according to the fifth postulate of Euclid. From there we have to draw a parallel to one of the sides, by the vertex opposite him, the interior angles of the left side add two right angles.
Answer:
180 degrees
Points are plotted at (-2, 2), (-2, -4), and (2, -4). A fourth point is drawn such that the four points can be connected to form a rectangle. What is the area of this rectangle?
8 square units
12 square units
16 square units
24 square units
Answer:
24
Step-by-step explanation:
4x6 = 24
-2 and 2 are 4 apart
2 and -4 are 6 apart
Answer:
24 square units
Step-by-step explanation:
The sales tax in your city is 8.8\%8.8%8, point, 8, percent, and an item costs \$63$63dollar sign, 63 before tax.
How much tax would you pay on that item?
Round to the nearest hundredth or cent.
\$\
Convert the tax rate from a percent to a decimal number by moving the decimal point 2 places to the left.
8.8% = 0.088
Now multiply the price of the item by the tax rate:
63 x 0.088 = 5.544
Now round that to the nearest cent = $5.54
Answer:
$5.54
Step-by-step explanation:
Please help me (~_~;) (~_~;) (~_~;) (~_~;) (~_~;) (~_~;) (~_~;) (~_~;) (~_~;) (~_~;)
Answer:
Frequency is the number of times that roll occurred.
Ex: 7 occurred 5 times...... 5 goes in the frequency column.
Solving equations (algebra). Thank you!
Answer:
[tex]\large\boxed{\dfrac{1}{x^2}+x^2=23}[/tex]
Step-by-step explanation:
[tex]\left(\dfrac{1}{x}+x\right)^2=25\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\\left(\dfrac{1}{x}\right)^2+2(x\!\!\!\!\diagup)\left(\dfrac{1}{x\!\!\!\!\diagup}\right)+x^2=25\\\\\dfrac{1}{x^2}+2+x^2=25\qquad\text{subtract 2 from both sides}\\\\\dfrac{1}{x^2}+x^2=23[/tex]
The value of [tex]\frac{1}{x^{2} } +x^{2}[/tex] is equal to 23 by using the algebraic identity which has the relationship between [tex](\frac{1}{x } +x)^2[/tex] and [tex]\frac{1}{x^{2} } +x^{2}[/tex] is [tex](a+b)^2 = a^2 +b^2 +2ab[/tex].
Given that if [tex](\frac{1}{x } +x)^2[/tex] = 25 then find the value of [tex]\frac{1}{x^{2} } +x^{2}[/tex] .
To find the value of [tex]\frac{1}{x^{2} } +x^{2}[/tex] by using the algebraic identity and follow the steps:
Apply the algebraic identity to the given equation, that is :
[tex](a+b)^2 = a^2 +b^2 +2ab[/tex]
Given that :
[tex](\frac{1}{x } +x)^2=25[/tex]
Expand the LHS by using mentioned algebraic identity:
[tex]\frac{1}{x^2 } +x^2+2x\times\frac{1}{x} =25[/tex]
On cancelation of the variable x in third term of the LHS gives:
[tex]\frac{1}{x^2 } +x^2+2=25[/tex]
Subtract by 2 on both sides, gives:
[tex]\frac{1}{x^2 } +x^2=23[/tex]
Therefore, the value of [tex]\frac{1}{x^{2} } +x^{2}[/tex] is equal to 23 by using the algebraic identity which has the relationship between [tex](\frac{1}{x } +x)^2[/tex] and [tex]\frac{1}{x^{2} } +x^{2}[/tex] is
[tex](a+b)^2 = a^2 +b^2 +2ab[/tex]
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Problem:
Emilia bought 8 t-bone steaks for $55.92. Each steak was the same price. How much did Emilia pay for a
steak?
$447.36
B
$6.99
C
$6300
$63.92
$47.92
End
Session
Answer:
The answer would be B $6.99. With this problem you would need to divide the total cost by 8 to get the price for a single steak.
Step-by-step explanation:
Use the function rule. Find y for x = 1, 2, 3, and 4. y = x – 5
-y = 4, 3, 2, 1
-y = 6, 7, 8, 9
-y = –5, –4, –3, –2
-y = –4, –3, –2, –1
Answer:
is the fourth one
Step-by-step explanation:
just replace x with the numbers given
and then work it out.
y=x-5
y=1-5=-4
y=2-5=-3
and so on
hope this helps
For this case we have a function of the form [tex]y = f (x)[/tex]where:
[tex]f (x) = x-5[/tex]
We must find the values of "y" when [tex]x = 1,2,3,4[/tex]
Then, keeping in mind that different signs are subtracted and the sign of the major is placed:
[tex]x = 1\\f (1) = 1-5 = -4\\So, y = -4[/tex][tex]x = 2\\f (2) = 2-5 = -3\\So, y = -3[/tex][tex]x = 3\\f (3) = 3-5 = -2\\Thus, y = -2[/tex][tex]x = 4\\f (4) = 4-5\\f (4) = - 1\\Thus, y = -1[/tex]Answer:
Option D
a cylinder with a diameter of 24 inches and a height of 8 inches has the same volume as a cone with a diameter of 12 inches. what is the height of the cone?
Answer:
The height of the cone is 97 in
Step-by-step explanation:
Equate the formulas for the volume of a cylinder and that of a cone:
Vol-Cyl Vol-Cone
πr²h = (1/3)πr²h
Now cancel out items that are the same on both sides (π):
r²h = (1/3)r²h
Now substitute the given values for both solids:
(12 in)²(8 in) = (1/3)(6 in)²(h-cone)
1152 in³
Then (h-cone) = -------------------- = 97 in
12 in²
The height of the cone is 97 in
Answer:
96 in
Step-by-step explanation:
What are the zeros of the function? F(x) = x^2+2x-35
Answer:
x = - 7, x = 5
Step-by-step explanation:
To find the zeros equate f(x) to zero, that is
x² + 2x - 35 = 0
To factorise the quadratic
Consider the factors of the constant term (- 35) which sum to give the coefficient of the x- term (+ 2)
The factors are + 7 and - 5, since
7 × - 5 = 35 and 7 - 5 = + 2, hence
(x + 7)(x - 5) = 0
Equate each factor to zero and solve for x
x + 7 = 0 ⇒ x = - 7
x - 5 = 0 ⇒ x = 5
ANSWER
[tex]x = - 7 \: or \: x = 5[/tex]
EXPLANATION
The given function is
[tex]f(x) = {x}^{2} + 2x - 35[/tex]
To find the zeros, we equate the function to zero.
[tex] {x}^{2} + 2x - 35 = 0[/tex]
Split the middle term to obtain,
[tex]{x}^{2} + 7x - 5x- 35 = 0[/tex]
Factor by grouping:
[tex]{x}(x + 7) - 5(x + 7)= 0[/tex]
[tex](x + 7)(x - 5) = 0[/tex]
[tex](x + 7) = 0 \: or \: (x - 5) = 0[/tex]
.
[tex]x = - 7 \: or \: x = 5[/tex]
Draw a line with a negative slope
What you did in the graph was correct. Essentially, all you have to do to achieve a negative slope is either make the rise negative or the run negative (make sure not to do both, as the negatives would cancel out and make a normal line)
PLZ HURRY WILL MARK BRAINLIEST
Jerry solved the system of equations.
x - 3y = 1
7x + 2y = 7
As the first step, he decided to solve for y in the second equation because it had the smallest number as a coefficient. Max told him that there was a more efficient way. What reason can Max give for his statement?
The variable x in the first equation has a coefficient of one so there will be fewer steps to the solution.
The variable x in the second equation has a coefficient of 7 so it will be easy to divide 7 by 7.
The variable y in the second equation has a coefficient of 2 so it will be easy to divide the entire equation by 2.
The variable x in the second equation has the largest coefficient. When dividing by 7, the solution will be a smaller number.
The most efficient way is the 1st option
because all you have to do is add -3y on both sides to isolate x
If you used any other variables, you would have to use division which are extra steps
Answer:
Hence, the correct option is A) The variable x in the first equation has a coefficient of one so there will be fewer steps to the solution.
Step-by-step explanation:
Consider the provided system of equation.
x - 3y = 1 and 7x + 2y = 7
Let first solve the second equation.
[tex]7x + 2y = 7[/tex]
Step 1:
Divide both the sides by 7.
[tex]x + \frac{2y}{7} = 1[/tex]
Step 2:
[tex]x = 1- \frac{2y}{7} [/tex]
It took 2 steps to isolate the the variable x.
Now again consider the system of equation.
But this time we will solve the first equation.
[tex]x - 3y = 1[/tex]
Step 1:
[tex]x = 1 + 3y[/tex]
it took only 1 step to isolate the variable as the variable x in the first equation has a coefficient of one.
Hence, the correct option is A) The variable x in the first equation has a coefficient of one so there will be fewer steps to the solution.
Please Help
Calculate the side lengths a and b to two decimal places.
A. a = 11.40 and b = 13.38
B. a = 11.71 and b = 15.56
C. a = 4.18 and b = 3.15
D. a = 10 and b = 14
The side length of the triangle are as follows:
a = 11.71 and b = 15.56
How to find the side of a triangle?The side of a triangle can be found using sine rule or cosine rule depending on the sides and angles given in a triangle.
Therefore, the sides a and b can be found in the triangle using sine rule as follows:
a / sin A = b / sin B = c / sin C
b / sin 110 = 7 / sin 25°
cross multiply
b sin 25 = 7 sin 110°
b = 7 sin 110° / sin 25
b = 6.5778483455 / 0.42261826174
b = 15.5625174507
b = 15.56 units
Let's find a as follows:
a / sin 45 = 7 / sin 25
a sin 25 = 7 sin 45
a = 7 sin 45 / sin 25
a = 4.94974746831 / 0.42261826174
a = 11.7108376716
a = 11.71 units
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Find the missing value:
__+6=-3
The answer is -9
Answer:
The missing value is -9
Step-by-step explanation:
-9+6 is -3.
Using the quadratic formula to solve 2x^2=4x-7, what's the values of x?
Answer:
1 + 1.58i , 1 - 1.58i
Step-by-step explanation:
2x^2=4x-7
2x^2 - 4x + 7 = 0
x = [-(-4) +/- sqrt((-4)^2 - 4 * 2 * 7 )] / 2*2
= [ 4 +/- sqrt (16 - 56)] / 4
= [4 +/- sqrt (-40) ] / 4
= 1 +/- 6.32i / 4
= 1 + 1.58i and 1 - 1.58i (answer).
Answer:
[tex]\boxed{x = 1 \pm i\sqrt{\frac{5}{ 2}} }\\[/tex]
Step-by-step explanation:
2x² = 4x - 7
2x² - 4x + 7 =0
a = 2; b = -4; c = 7
[tex]y =\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\[/tex]
[tex]=\frac{4\pm\sqrt{(-2)^2-4\times2\times7}}{2\times2}\\[/tex]
[tex]= 1 \pm\frac{\sqrt{16-56}}{4}\\[/tex]
[tex]= 1 \pm\frac{\sqrt{-40}}{4}\\[/tex]
[tex]= 1 \pm\frac{2i\sqrt{10}}{4}\\[/tex]
[tex]= 1 \pm\frac{i\sqrt{10}}{2}\\[/tex]
[tex]= 1 \pm i\sqrt{\frac{10}{4}}\\[/tex]
[tex]\boxed{= 1 \pm i\sqrt{\frac{5}{ 2}} }\\[/tex]
The graph of y = 2x² - 4x + 7 has a minimum at (1, 5). It never touches the x-axis, so both roots are imaginary.
simplify the expression (x^19 times y^21) divided by (x^2 times y^6)^2
Answer:
[tex]x^{15}.y^{9}[/tex]
Step-by-step explanation:
[tex]\frac{x^{19} . y^{21}}{(x^2. y^6)^2} \\\\Here\,\, exponent\,\, rules\,\, will\,\, be\,\, used.\\First\,\, multiply\,\, power\,\, of \,\,2\,\, with\,\, denominator \,\,exponents\\\\\frac{x^{19} . y^{21}}{x^4. y^{12}}\\If \,\, same\,\, bases\,\, are\,\, divided\,\, then\,\, their\,\, exponents\,\, are \,\,subtracted\,\,\\\\x^{19-4}.y^{21-12}\\\\x^{15}.y^{9}[/tex]
Raj fully simplified the polynomial and then put it in standard form with the last term being 6y3. 2x2y + 8x3 – xy2 – 2x3 + 3xy2 + 6y3 What is the first term of the polynomial Raj ended up with? 6x3 8x3 2xy2 3xy2
Answer: First option.
Step-by-step explanation:
To simplify the polynomial [tex]2x^2y + 8x^3 - xy^2 - 2x^3 + 3xy^2 + 6y^3[/tex] you need to add the like terms, then you get:
[tex]=2x^2y+6x^3+2xy^2+6y^3[/tex]
Now, you know that Raj put this polynomial in standard form with the last term being 6y³, this means that he ordered it in descending order of "x" power and in ascending order of "y" power:
[tex]=6x^3+2x^2y+2xy^2+6y^3[/tex]
You can observe that the first term of the polynomial that Raj ended up with, is:
[tex]6x^3[/tex]
Answer:
The answer would b A
Find the roots of the equation below. 7x^2 + 1 = 0
Answer:
7x2-1 = 0
Step-by-step explanation:
Add 1 to both sides of the equation :
7x2 = 1
Divide both sides of the equation by 7:
x2 = 1/7 = 0.143
When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:
x = ± √ 1/7
Answer:
Step-by-step explanation:
Rewrite 7x^2 + 1 = 0 as 7x^2 = - 1, and then as x^2 = -1/7.
Taking the square root of both sides, and remembering that the square root of a negative number is imaginary, we get:
i√7
x = ±i(1/7) = ± ----------
7
A rectangular prism with a volume of 4 cubic units is filled with cubes with side lengths of 1/3 cubic units
Answer:
108 cubesStep-by-step explanation:
[tex]V_p=4\\\\\text{Calculate the volume of a cube:}\\\\V_{c}=\left(\dfrac{1}{3}\right)^3=\dfrac{1}{27}\\\\\text{Calculate how many times the volume of the prism is greater}\\\text{than the volume of the cube:}\\\\\dfrac{V_p}{V_c}=\dfrac{4}{\frac{1}{27}}=4\cdot27=108[/tex]
Use the Distributive and Commutative properties to determine
whether each pair of expressions is equivalent for all values of x.
a. 3x + 7x and 10x
b. 5x and 5x – 10x c. 4(1 + 2x) - 3x and 5x + 4 d. 5 - 3(2 – 4x) and -1 + 12x
Answer:
a. equivalent
b. not equivalent
c. equivalent
d. equivalent
Step-by-step explanation:
a. 3x +7x = (3+7)x = 10x . . . equivalent to 10x
__
b. 5x -10x = (5 -10)x = -5x . . . not equivalent to 5x
__
c. 4(1 +2x) -3x = 4·1 +4·2x -3x = 4 +(8 -3)x = 4 +5x = 5x +4 . . . equivalent to 5x +4
__
d. 5 -3(2 -4x) = 5 -3·2 -3(-4x) = 5 -6 +12x = -1 +12x . . . equivalent to -1 +12x
you and your best friend are going out for ice cream there are 7 different flavors issues from what is the approximate probability that you both choose chocolate ice cream
The approximate probability that both you and your friend will choose chocolate ice cream from seven different flavors is 1/49, or approximately 0.020408.
We are looking to find the probability that both you and your friend choose chocolate ice cream from a selection of 7 different flavors. Since the choice of ice cream is independent for each person, we can calculate the probability of both events occurring by multiplying the probability of each event occurring individually.
The probability that one person chooses chocolate ice cream is 1 out of 7, or approximately 0.142857. To find the probability that both you and your friend choose chocolate ice cream, we multiply the individual probabilities:
Probability of you choosing chocolate: 1/7
Probability of your friend choosing chocolate: 1/7
Combined probability: 1/7 x 1/7 = 1/49
Therefore, the approximate probability that both you and your friend choose chocolate ice cream is 1/49, or approximately 0.020408.
PLEASE HELP!!! WORTH 100 POINTS !!
What is the value of y and x?? Solve the answer and show a step by step solution!
Answer:
X - 90 degrees
Y - 43 degrees
Step-by-step explanation: When you fold over the triangle to reflect you get 47 degrees as angle C. Then, because X is a perfect right angle it is 90 degrees. Then you add 47 and 90 and get 137, then subtract that from 180 because all the angles within a triangle should eqaul up to 180 degrees.
find the amount at 6% simple interest of rs 1200 due in 9 month
STEP 1: Convert interest rate of 2% per 6 months into rate per year.
rate per year = rate per 6 month⋅2=2%⋅2=4%
STEP 2: Convert 9 months into years.
9 months =
9
12
years=0.75 years
STEP 3: Find principal by using the formula
I=P⋅i⋅t
, where I is interest, P is total principal, i is rate of interest per year, and t is total time in years.
In this example I = $15, i = 4% and t = 0.75 years, so
I
P
P
P
=P⋅i⋅t
=
I
i⋅t
=
15
0.04⋅0.75
=500
Final answer:
To calculate the amount at 6% simple interest on Rs 1200 for 9 months, apply the simple interest formula. Convert time to years, calculate the interest, then add it to the principal to find the total amount due, which is Rs 1254.
Explanation:
To find the amount at 6% simple interest on Rs 1200 due in 9 months, you can use the simple interest formula:
Simple Interest = Principal × Rate × Time
We have the Principal (P) as Rs 1200, the Rate (R) as 6% per annum (or 0.06 when expressed as a decimal), and the Time (T) as 9 months. The rate is given per annum but we have in months so, we need to convert the time to years. There are 12 months in a year, so 9 months is ⅓ or 0.75 years.
Now, let's calculate the simple interest (SI):
SI = 1200 × 0.06 × 0.75 = Rs 54
Total Amount = Principal + Simple Interest
Total Amount = 1200 + 54 = Rs 1254
Therefore, the total amount due at the end of 9 months would be Rs 1254.
The temperature of a chemical reaction ranges between 20 degrees Celsius and 160 degrees Celsius. The temperature is at its lowest point when t = 0, and the reaction completes 1 cycle during an 8-hour period. What is a cosine function that models this reaction?
Answer:
The cosine function that models this reaction is:
[tex]y=-70cos(\frac{1}{4}\pi x) +90[/tex]
Step-by-step explanation:
The general cosine function has the following form
[tex]y = Acos(bx) + k[/tex]
Where A is the amplitude: half the vertical distance between the highest peak and the lowest peak of the wave.
[tex]\frac{2\pi}{b}[/tex] is the period: time it takes the wave to complete a cycle.
k is the vertical displacement.
The maximum temperature is 160 and the minimum is 20. Then the amplitude A is:
[tex]A =\frac{160-20}{2}\\\\A= 70[/tex]
The reaction completes a cycle in 8 hours
Then the period is 8 hours.
Thus:
[tex]\frac{2\pi}{b}=8\\\\ b=\frac{2\pi}{8}\\\\ b=\frac{1}{4}\pi[/tex]
The function is:
[tex]y = 70cos(\frac{1}{4}\pi x)+k[/tex]
when [tex]t=0[/tex] y is minumum therefore [tex]y=-cos(x)[/tex]
So
[tex]y = -70cos(\frac{1}{4}\pi x)+k[/tex]
Now we substitute [tex]t = 0[/tex] in the function and solve for k
[tex]20 = -70cos(0)+k\\\\k=20+70\\\\k=90[/tex]
Finally
[tex]y=-70cos(\frac{1}{4}\pi x) +90[/tex]
mitch bought a total of 13 pizzas and buckets of wings for his big super bowl party. if it costs $11.75 for a pizza and $19.95 for a bucket of wings and he spent $193.75, how many buckets of wings did he buy?
Answer:
Mitch bought 5 buckets of wings
Step-by-step explanation:
y=# of wings
X= # of pizza
X+Y=13
X = 13 - Y
11.75X + 19.95Y = 193.75
11.75(13 - Y) + 19.95Y = 193.75
152.75 - 11.75Y + 19.95Y = 193.75
152.75 + 8.2Y = 193.75
8.2Y = 41
Y = 5
Mitch bought 5 buckets of wings
Mitch bought 5 buckets of wings for his Super Bowl party, which was determined by solving a system of equations using the given information about the total number of items purchased and the total cost.
Explanation:To determine how many buckets of wings Mitch bought for his Super Bowl party, let's define a system of equations based on the information given:
Let's say p represents the number of pizzas, and w represents the number of buckets of wings. We are told that Mitch bought a total of 13 items, which gives us the equation:
p + w = 13.
We are also told that he spent a total of $193.75, with pizzas costing $11.75 each and buckets of wings costing $19.95 each. This gives us the second equation:
11.75p + 19.95w = 193.75.
To solve the system of equations, we can use substitution or elimination. One way is to solve the first equation for p (p = 13 - w) and substitute that into the second equation, leading to:
11.75(13 - w) + 19.95w = 193.75.
Simplifying the equation will allow us to find the value for w. The simplified equation is:
152.75 + 8.2w = 193.75
Subtracting 152.75 from both sides gives us
8.2w = 41,
and dividing both sides by 8.2 yields
w = 5.
Therefore, Mitch bought 5 buckets of wings for the party.
help me you get branliest 100 points and 5-star rating plus a thanks
Answer:
Step-by-step explanation:
Step 1: Additive inverse
Step 2: Additive identity
Step 3: Addition property of equality
22 is D
I need to know a answer
The center-radius form of the circle equation is in the format
(x – h)²+ (y – k)² = r²
with the center being at the point (h, k) and the radius being "r"
So, just plug in the (-5,3) and you get:
(x+5)²+(y-3)²=16
Please help.
Solve 2x - 8 < 7.
ANSWER
The correct answer is C
EXPLANATION
The given inequality is:
[tex]2x - 8 \: < \: 7[/tex]
Group the constant terms on the right hand side to get;
[tex]2x \: < \: 7 + 8[/tex]
Simplify the right hand side
[tex]2x \: < \: 15[/tex]
Divide both sides by 2
[tex]x \: < \: \frac{15}{2} [/tex]
{x|x<15/2}
The correct answer is C
Answer:
[tex]\large\boxed{\left\{x\ |\ x<\dfrac{15}{2}\right\}}[/tex]
Step-by-step explanation:
[tex]2x-8<7\qquad\text{add 8 to both sides}\\\\2x-8+8<7+8\\\\2x<15\qquad\text{divide both sides by 2}\\\\\dfrac{2x}{2}<\dfrac{15}{2}\\\\x<\dfrac{15}{2}[/tex]
What is the area of this triangle?
help pls im failing haha
Answer:
d o the formula Ltimes W divided by 2
Step-by-step explanation:
Answer:
Area of triangle = 44.104 cm²
Step-by-step explanation:
Formula:-
Area of triangle = bh/2
where b - Base and h - Height
To find the height of triangle
Let h be the height of triangle then we can write,
Sin 63 = h/11
h = 11 * sin 63 = 11 * 0.891 = 9.801 cm
To find the area of triangle
Area = bh/2
= (9 * 9.801)/2 = 44.104 cm²
what is the domain of the given function?
{(3,-2), (6,1), (-1,4), (5,9), (-4,0)}
Answer:
-4, -1, 3, 5, 6
Step-by-step explanation:
Answer:
-4, -1, 3, 5, 6
Step-by-step explanation:
The domain is always on the left side. That was the trick I learned to remember. When you plot the numbers you would have them lined as X,Y. X,Y is equal to Domain, Range. I hope this helps!