A circular table top has a radius of 24 inches.
What is the area of the table top, to the nearest square inch? Use 3.14 for n.
75 in.2
151 in.
1809 in.2
7235 in.2
Answer:
(C) 1809 in.2
Step-by-step explanation:
Took the test on edg :3
How much will Bob need to save each month if he wants to buy a $30,000 car with cash in 5 years? He can earn a nominal interest rate of 10% compounded monthly.
a) $2.50
b) $250.00
c) $25.00
d) $1,862.76
Answer:
B
Step-by-step explanation:
C is too little and D is too much
Solve the system of equations algebraically.
{Y=(x-2)^2+2
{Y+4=3x
Answer:
(5, 11) and (2, 2)
Step-by-step explanation:
y = (x-2)² + 2
y + 4 = 3x
(x-2)² + 2 + 4 = 3x
x² - 4x + 4 + 6 = 3x
x² - 7x + 10 = 0
(x - 5)(x - 2) = 0
x - 5 = 0, x = 5
x - 2 = 0, x = 2
y = (5-2)² + 2 = 11
(5, 11)
y = (2-2)² + 2 = 2
(2, 2)
Answer:
[tex]\large \boxed{\sf \bf \ \text{ The solutions are } x=2, y=2 \text{ and } x=5, y=11.} \ \ }[/tex]
Step-by-step explanation:
Hello, please consider the following.
We want to solve this system of equations.
[tex]\begin{cases}&y=(x-2)^2+2\\&y+4=3x\end{cases}[/tex]
This is equivalent to (subtract 4 from the second equation).
[tex]\begin{cases}&y=(x-2)^2+2\\&y=3x-4\end{cases}[/tex]
Then, we can write y = y, meaning:
[tex](x-2)^2+2=3x-4\\\\\text{*** We develop the left side. ***}\\\\x^2-4x+4+2=3x-4 \\\\\text{*** We simplify. *** }\\\\x^2-4x+6=3x-4\\\\\text{*** We subtract 3x-4 from both sides. ***}\\\\x^2-4x+6-3x+4=0\\\\\text{*** We simplify. *** }\\\\x^2-7x+10=0[/tex]
[tex]\text{*** The sum of the zeroes is 7 and the product 10 = 5 x 2 ***}\\\\\text{*** We can factorise. ***}\\\\x^2-5x-2x+10=x(x-5)-2(x-5)=(x-2)(x-5)=0\\\\x-2 = 0 \ \ or \ \ x-5 = 0\\\\x= 2 \ \ or \ \ x=5[/tex]
For x = 2, y =0+2=2 (from the first equation) and for x = 5 y=3*5-4=15-4=11 (from the second equation)
So the solutions are (2,2) and (5,11)
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
evaluate sine squared theta for theta equals 45 degrees
pleaz!!! some body help with number #4 at the bottom
Answer:
See my explanation
Step-by-step explanation:
-2x + (x - 4) = 18
-x - 4 = 18
-x = 22 <- this is wrong in question writing as x = 22
so, x = -22
Instructions: Find the measure of the indicated angle to the
nearest degree
Answer:
? = 33
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan ? = opp / adj
tan ? = 13/20
Take the inverse tan of each side
tan ^-1 tan ? = tan ^-1 ( 13/20)
? = 33.02386756
To the nearest degree
? = 33
Answer:
33.
Step-by-step explanation:
inverse tan (13/20) = 33.023867579302
The quotient of two rational numbers is positive. What can you conclude about the signs of the dividend and the divisor? That’s us my question it’s confusing please someone help meee I’m in grade 7
Answer:
The divisor and dividend have the same signs.
Step-by-step explanation:
Let's look at all of the possible outcomes of dividing with different signs.
Positive / positive = positive
Positive / negative = negative
Negative / positive = negative
Negative / negative = positive
We can see that whenever the signs are the same, the quotient is positive.
Find the value.
X3-4 when x=3
PLEASE HELP!!! ASAP!!!
Answer:
23
Step-by-step explanation:
Raise 3 to the power of 3
27 - 4
Subtract 4 from 27
23
Hope this was correct
Answer:
23
Explanation:
step 1 - rewrite the expression with the value of x
[tex]x^3 - 4[/tex]
[tex](3)^3 - 4[/tex]
step 2 - solve the exponent
[tex](3)^3 - 4[/tex]
[tex]27 - 4[/tex]
step 3 - subtract
[tex]27 - 4[/tex]
[tex]23[/tex]
therefore, the value of the expression is 23.
Pleaseeeeeee HELP❤️❤️❤️
Answer:
1) [tex]\boxed{Option \ 3}[/tex]
2) [tex]\boxed{Option \ 2}[/tex]
Step-by-step explanation:
A) [tex]x^2-5x+6[/tex]
Using mid term break formula
[tex]x^2-6x+x-6\\x(x-6)+1(x-6)\\Taking \ (x+6) \ as \ common\\(x-6)(x+1)[/tex]
B) [tex]\frac{-20p^{-5}qr^6}{16p^{-2}q^{-3}r^4}[/tex]
Solving it using the two rules: => [tex]\frac{a^m}{a^n} = a^{m-n} \ and \ a^m * a^n = a^{m+n}[/tex]
=> [tex]\frac{-5p^{-3}q^4r^2}{4}[/tex]
We need to put p in the denominator to cancel its negative sign
=> [tex]\frac{-5q^4r^2}{4p^3}[/tex]
Answer:
C and b
Step-by-step explanation:
First question:
The polynomial expression we want to factor is x^2-5x-6
Let's calculate the discriminant to find the roots. The discrminant is b^2-4ac
● b= -5
● a = 1
● c = -6
b^2-4ac= (-5)^2-4*1*(-6) = 25+24 = 49>0
So this polynomial expression has two roots since the discriminant is positive
Let x" and x' be the roots:
● x'= (-b-7)/2a = (5-7)/2= -1
● x"= (-b+7)/2a = (5+7)/2 =6
7 is the root square of the discrminant
The factorization of this pulynomial is:
● a(x - x') (x-x")
● 1*(x-(-1)) (x-6)
● (x+1)(x-6)
So the right answer is c
■■■■■■■■■■■■■■■■■■■■■■■■
Second question:
The expression is: (-20*p^(-5)*q*r^(6))/(16*p^(-2)*q^(-3)*r^3)
To make it easier we will simplify the similar terms one by one.
● Constant terms
-20/16 = (-5*4)/(4*4) = -5/4
● terms containing p
-p^(-5)/p^(-2) = p^(-5-(-2)) = p^(-3) =1/p^3
● terms containg q
q/q^(-3)= q(1-(-3)) = q^4
● terms containg r
r^6/r^4 = r^(6-4) = r^2
Multiply all terms together:
● -5/4 *1/p^3 *q^4 *r^2
● (-5*q^4*r^2)/(4p^3)
The right answer is b
Devi’s mother is three times as old as Devi. Five years ago, Devi’s mother was four times as old as Devi was then. Find their present ages
Answer:
Devi's present age = 15 years
Devi's Mother's present age = 45 years
Step-by-step explanation:
Let the present age of Devi be x years.
Therefore, mother's present age = 3x
Five years ago:
Devi's age = (x - 5) years
Mother's age =( 3x - 5) years
According to the given condition:
Five years ago:
Devi's mother's age = 4 times Devi's age
3x - 5 = 4( x - 5)
3x - 5 = 4x - 20
20 - 5 = 4x - 3x
15 = x
x = 15 years
3x = 3* 15 = 45 years
Hence,
Devi's present age = 15 years
Devi's Mother's present age = 45 years
Callie has a new kitten. The kitten weighs 3 pounds less than half the weight of Callie’s cat. Together, the cat and the kitten weigh 18 pounds. Which system of equations could be used to find the weight of each animal?
Answer:
y = [tex]\frac{1}{2} x - 3[/tex]
x + y = 18
Step-by-step explanation:
Let the kitten's weight be y and the cat's weight be x
Condition # 1:
y = [tex]\frac{1}{2} x - 3[/tex]
Condition # 2:
x + y = 18
PLSSSS HELPPP. The price of a tennis racquet is inversely proportional to its weight. If a 20 oz. racquet cost $30.00, what would a 25 oz. racquet cost?
Answer:
$24 will be the cost of tennis racquet with weight 25 oz.
Step-by-step explanation:
Given that Price of racquet is inversely proportional to its weight.
i.e.
[tex]Price \propto \dfrac{1}{Weight}[/tex]
We can replace the proportional sign with a constant of proportionality.
[tex]Price = \dfrac{C}{Weight}[/tex]
Where C is a constant named as constant of proportionality.
Given that cost of 20 oz. racquet is $30.00
Putting both the values :
[tex]30 = \dfrac{C}{20}\\\Rightarrow C = 600[/tex]
So, the equation becomes:
[tex]Price = \dfrac{600}{Weight}[/tex]
Now, we have to find the price of 25 oz. racquet.
Putting Weight = 25 oz and finding Price:
[tex]Price = \dfrac{600}{25}\\\Rightarrow Price = \$24[/tex]
So, $24 will be the cost of tennis racquet with weight 25 oz.
please help Evaluate 5 - (3/2) to the 3 power A.) 13/8 B.) 9.5 C.) 18.5 D.) 2197/8
Answer: THE ANSWER IS A
Step-by-step explanation:
5-(3/2)^3
=13/8
im a math god
Solve =14+3 l = 14 j + 3 k for k. Select one: a. =+143 k = l + 14 j 3 b. =−143 k = l − 14 j 3 c. =3+14 k = l 3 + 14 j d. =3−14
Answer:
k= l/3 - 14/3j
Step-by-step explanation:
l = 14j + 3k
Solve for k
l = 14j + 3k
Subtract 14j from both sides
l - 14j =14j + 3k - 14j
l - 14j = 3k
Divide both sides by 3
l - 14j / 3=3k / 3
k= l/3 - 14/3j
Or
1/3(l - 14j) = k
Answer:
Which expression is equivalent to ‐10
k
‐
10
?
Step-by-step explanation:
Find the area in square centimeters of the composite shape shown
below. Enter only a number as your answer.
A
E
13 cm
D
11 cm
7 cm
B
18 cm
C
Answer:
73cm²
Step-by-step explanation:
Area of rectangle=½ length×width
=½×18×7
=63cm²
Area of triangle=½b×h
base=18-13= 5cm
height=11-7 =4cm
½×b×h
½×5×4
=10cm²
Area of total=63+10
73cm²
Answer: 73c2
Step-by-step explanation:
please help me. I will love u forever if u do <333
Answer:
61% is a reasonable choice
Step-by-step explanation:
The probability of a strike is 79% or 0.79
=> Independently, the probability of 2 consecutive strikes:
P = 0.79 x 0.79 = 0.6241 ~ 61%
Clark collected 200 fruits from his orchard. 56 of the fruits were durians and the rest were mangoes. What percentage of the fruits were mangoes?
Answer:
72%
Step-by-step explanation:
First find the number of mangoes
200 -56 = 144
Take the number of mangoes over the total
144/200
.72
Change to percent by multiplying by 100
72%
Answer:
72%
Step-by-step explanation:
If 56 of the 200 fruits were durians, then [tex]200-56[/tex] of the fruits were mangoes. Therefore, 144 of the fruits were mangoes.
Now we can set up a percentage proportion to find what percent of 200 144 is.
[tex]\frac{144}{200} = \frac{x}{100}[/tex]
Multiply the cross values and divide by the value thats diagonal to the variable.
[tex]144\cdot100=14400\\14400\div200=72[/tex]
So, the answer is 72%
Hope this helped!
Convert the following to Slope-Intercept Form: 4x – 3y = 24.
The equation 4x – 3y = 24 can be represented in the slope-intercept form will be y = (4/3)x - 8.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The linear equation is given below.
4x – 3y = 24
Convert the equation from standard form to slope-intercept form. Then we have
4x – 3y = 24
3y = 4x - 24
y = (4/3)x - 24 / 3
y = (4/3)x - 8
The equation 4x – 3y = 24 can be represented in the slope-intercept form will be y = (4/3)x - 8.
More about the linear equation link is given below.
https://brainly.com/question/11897796
#SPJ2
ASAP!!! Please help me with this question!!!!!
r = radius
h = r+12 = height, 12 more than the radius
[tex]V = \text{Volume of cone (oblique or not)}\\\\V = \frac{1}{3}\pi*r^2*h\\\\V = \frac{1}{3}\pi*r^2*(r+12)\\\\V = \frac{1}{3}\pi*r^2*r+\frac{1}{3}\pi*r^2*12\\\\V = \frac{1}{3}\pi*r^3+\frac{1}{3}*12\pi*r^2\\\\V = \frac{1}{3}\pi r^3+4\pi r^2\\\\[/tex]
Answer: Choice BANSWER: SECOND OPTION
Zero product property
x(2x+4)(x+5)=0
A) x=0, x=-2, X=-5
B) x=0, x=2, x=5
C) x greater than or equal to 0
D) x=-2, x=5
Answer:
A
Step-by-step explanation:
Using ZPP we get x = 0, 2x + 4 = 0, x + 5 = 0. Solving these, we get x = 0, x = -2, x = -5.
Solve the equation by completing the square.
3x^2-12x=96
Answer:
x = 8
or
x = -4
Step-by-step explanation:
3x² - 12x = 96
Divide both sides by 3
x² - 4x = 32
Add 4 to both sides
x² - 4x + 4 = 32 + 4
(x - 2)² = 6²
Find the square root of both sides
√(x - 2)² = √6²
x - 2 = +/- 6
x - 2 = +6 or -6
x - 2=+6
x=6+2
x=8
x - 2=-6
x=-6+2
x=-4
x = 8
or
x = -4
i attached the question in the image below
Answer:
45°
Step-by-step explanation:
[tex]tan^{-1}(1)[/tex] = 45°
Answer:
[tex]\huge\boxed{\theta=45^o\ \vee\ \theta=225^o}[/tex]
Step-by-step explanation:
[tex]\tan\theta=1[/tex]
[tex]\bold{METHOD\ 1}\\\\\text{Use the table in the attachment}\\\\\tan45^o=1\to\theta=45^o\ \vee\ \theta=45^o+180^o=225^o\\\\\bold{METHOD\ 2}\\\\\tan\theta=1\to\tan^{-1}1=\theta\to\theta=45^o\ \vee\ \theta=225^o[/tex]
the product of two rational number is -10/9. If one of the number is -5/27 ,find the other.
Answer:
Step-by-step explanation:
Let the unknown number = x
[tex]x *\frac{-5}{27}=\frac{-10}{9}[/tex]
x = [tex]\frac{-10}{9}[/tex] ÷ [tex]\frac{-5}{27}[/tex]
[tex]x=\frac{-10}{9}*\frac{-27}{5}\\\\\\x=-2* - 3\\x = 6[/tex]
Please answer this in two minutes
Answer:
60°
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you of the relation between sides of a right triangle and angles.
Tan = Opposite/Adjacent
tan(T) = SU/ST
tan(T) = (5√51)/(5√17) = √3
Now, the arctangent function is used to find the angle whose tangent is √3.
T = arctan(√3) = 60°
I need help answer quickly please this is timed! What is the product? Assume x greater-than-or-equal-to 0 (StartRoot 3 x EndRoot + StartRoot 5 EndRoot) (StartRoot 15 x EndRoot + 2 StartRoot 30 EndRoot)
Answer:
3x√5 + 6√10x + 5√3x + 10√6
Step-by-step explanation:
(√3x + √5)(√15x + 2√30)
The above expression can be evaluated as follow:
(√3x + √5)(√15x + 2√30)
Expand
√3x (√15x + 2√30) + √5(√15x + 2√30)
x√45 + 2√90x + √75x + 2√150
Express in the best possible surd form.
x•3√5 + 2•3√10x + 5√3x + 2•5√6
3x√5 + 6√10x + 5√3x + 10√6
We can not simplify further.
Therefore,
(√3x + √5)(√15x + 2√30) =
3x√5 + 6√10x + 5√3x + 10√6
Here is the histogram of a data distribution. All class widths are 1.
Which of the following numbers is closest to the mean of this distribution?
A.6
B.7
C.3
D.4
E.5
=======================================================
Explanation:
The distribution is perfectly symmetrical about the center 6. Notice how the left side is a mirror copy of the right side, due to the heights being the same. Because of this, the mean, median and mode are all the same value and that is 6. The mode is equal to 6 as this is the most frequent value.
The longer way to do this problem is to add up each value shown. We have four copies of '2', six copies of '3', and so on. The total sum you would get is 372. Divide this over 62 because there are 62 smaller green squares. The final result is the mean of 6.
The number closest to the mean of the given distribution is 6. Therefore, option A is the correct answer.
What is mean?In statistics, the mean refers to the average of a set of values. The mean can be computed in a number of ways, including the simple arithmetic mean (add up the numbers and divide the total by the number of observations).
From the given histogram,
Number Frequency
2 4
3 6
4 7
5 9
6 10
7 9
8 7
9 6
10 4
Here, the mean = [2(4)+3(6)+4(7)+5(9)+6(10)+7(9)+8(7)+9(6)+10(4)]/[4+6+7+9+10+9+7+6+4]
= [8+18+28+45+60+63+56+54+40]/62
= 372/62
= 6
Therefore, option A is the correct answer.
To learn more about an arithmetic mean visit:
https://brainly.com/question/15196910.
#SPJ7
Tonia and trinny are twins. Their friends give them identical cakes for their birthday. Tonia eats 1/8 of her cake and trinny eats 1/6 of her cake. How much cake is left? please show working thank youu
Answer:
[tex]\frac{7}{12}[/tex] of the cake
Step-by-step explanation:
add [tex]\frac{1}{8}[/tex] and [tex]\frac{1}{6}[/tex] to see the total amount of cake eaten.
a. find the common denominator: 8 x 3 = 24 and 6 x 4 = 24
b. multiply accordingly to get the correct numerator: [tex]\frac{3}{24}[/tex] + [tex]\frac{4}{24}[/tex]
c. add: [tex]\frac{3}{24}[/tex] + [tex]\frac{4}{24}[/tex] = [tex]\frac{7}{24}[/tex]
subtract found value from total to find left over cake.
a. 24 - 7 = 14
simplify.
a. [tex]\frac{14}{24}[/tex] = [tex]\frac{7}{12}[/tex]
You are left with [tex]\frac{7}{12}[/tex] of the cake.
Pleas answer this question now
Answer:
[tex]x = 17[/tex]
Step-by-step explanation:
According to the two tangent theory, tangent MN and tangent NP, which are both from point N, are congruent.
That is, [tex]x + 4 = 21[/tex]
Solve for x
[tex]x + 4 = 21[/tex]
Subtract 4 from both sides
[tex]x + 4 - 4 = 21 - 4[/tex]
[tex]x = 17[/tex]
HELP ME ASAP! BRAINLIEST UP FOR GRABS
Answer:
-5 ≤ x≤ 3
Step-by-step explanation:
The domain is the values for x
x starts and -5 and includes -5 since the circle is closed
and goes to 3 and includes 3 since the circle is closed
-5 ≤ x≤ 3
Answer:
first option
Step-by-step explanation:
The domain are the values from the x- axis that can be input into the function.
The closed circles at the ends of the graph indicate that x can equal these values.
left side value of x = - 5 and right hand value of x = 3, thus
domain is - 5 ≤ x ≤ 3
A chemist is mixing two solutions, solution A and solution B Solution A is 15% water and solution Bis 20% water. She already has a
beaker with 10mL of solution A in it. How many mL of solution B must be added to the beaker in order to create a mixture that is 18%
water?
Answer:
15 mL of the solution with 20% water will be needed.
Step-by-step explanation:
Use the inverse relationship
10 mL * (18-15)% = x mL * (20-18)%
x = 10 mL * (3/2) = 15 mL
Answer: 15mL
Step-by-step explanation:
Create a table. Multiply across and add down. The bottom row (Mixture) creates the equation.
Qty × % = Total
Solution A 10 15% → 0.15 10(0.15) = 1.5
Solution B x 20% → 0.20 x(0.20) = 0.20x
Mixture 10 + x × 18% → 0.18 = 1.5 + 0.20x
(10 + x)(0.18) = 1.5 + 0.20x
1.8 + 0.18x = 1.5 + 0.20x
1.8 = 1.5 + 0.02x
0.3 = 0.02x
15 = x