Answer:
d. 36 sq. ft
Step-by-step explanation:
The area of a triangle is given by
A = 1/2 bh where b is the base and h is the height
A = 1/2 (12) * 6
A = 36 ft^2
A rectangle is 9 ft long and 40 in. wide. What is its perimeter in inches?
Answer:
296 inches
Step-by-step explanation:
The perimeter is the sum of sides of a rectangle
As the length is in feet while the width is in inches, a unit conversion must take place
As 1 feet equals to 12 inches
9 feet would be equal to 12*9=108 inches
The perimeter of a rectangle= 2(width)(length)
= 2(108)(40)
=296 inches
WILL MARK BRAINLIEST
The surface area of a sphere is 900pi square inches. What is the radius of the sphere?
Recall the formula SA= 4 pi r^2.
15 inches
18 inches
30 inches
60 inches
Answer:
15 inches
Step-by-step explanation:
The formula for the circumference of a circle of radius R is 2*Pi*R. Similarly, the volume of a ball enclosed by a sphere of radius R is (4/3)*Pi*R3. And the formula for the surface area of a sphere of radius R is 4*Pi*R2. And, you can check that the latter is the derivative of the former with respect to R.
Answer:
15 inches
Step-by-step explanation:
SA=4PIR^
900PI=4PIR^2
R^2=900PI/4PI
R^2=225
R=SQRT225
R=15 IN.
PROOF:
900PI=4PI^15^2
900PI=4PI*225
900PI=900PI
Which similarity statement expresses the relationship between the two triangles ?
AXYZ-AQRS
AXYZ AROS
AZXY-AQSR
AZXY-AQRS
Answer: [tex]\triangle{ZXY}\sim\triangle{QRS}[/tex]
Step-by-step explanation:
in the given picture , we have two triangles ΔXYZ and ΔRSQ, in which
[tex]\overline{XY}=14=4\times3.5=4\times\overline{RS}[/tex]
[tex]\overline{YZ}=16=4\times4=4\times\overline{SQ}[/tex]
[tex]\overline{ZX}=12=4\times3=4\times\overline{SR}[/tex]
i.e. [tex]\dfrac{XY}{RS}=\dfrac{YZ}{SQ}=\dfrac{ZX}{QR}=\dfrac{4}{1}[/tex]
By SSS-similarity postulate, we get
[tex]\triangle{ZXY}\sim\triangle{QRS}[/tex]
SSS-similarity postulate says that if the lengths of the corresponding sides of two triangles are proportional, then the triangles must be similar
The graph of f ′ (x), the derivative of f of x, is continuous for all x and consists of five line segments as shown below. Given f (0) = 7, find the absolute minimum value of f (x) over the interval [–3, 0].
A. 0
B. 2.5
C. 4.5
D. 11.5
Answer:
B
Step-by-step explanation:
f(0) - f(-3) = area under f'(x) from x=0 to x=3.
We can find the area under f'(x) in this interval by finding the area of the triangle formed by the line.
A = 1/2 b h
A = 1/2 (3) (3)
A = 4.5
f(0) - f(-3) = 4.5
Since f(0) = 7:
7 - f(-3) = 4.5
f(-3) = 7 - 4.5
f(-3) = 2.5
if a customer receives 15% off a shirt that cost $20 and has to pay 6% sales tax. How much did the customer pay?
Answer:
$20(.85)(1.06) = $18.02
f(x) = 3x+2
What is f(5)?
Answer:
f(5) = 17
Step-by-step explanation:
f(x) = 3x+2
Let x =5
f(5) = 3(5) +2
f(5) = 15+2
f(5) = 17
Factor completely 3x4 − 30x3 + 75x2. 3(x − 5)2 3x2(x − 5)2 3x2(x2 − 10x + 25) 3x2(x + 5)(x − 5)
Answer:
The complete factorization is 3x² (x - 5)² ⇒ 2nd answer
Step-by-step explanation:
* Lets revise how to factorize a trinomial
- Find the greatest common factor of the coefficients of the three terms
∵ The trinomial is 3x^4 - 30x³ + 75x²
- The greatest common factor of 3 , 30 , 75 is 3
∵ 3 ÷ 3 = 1
∵ 30 ÷ 3 = 10
∵ 75 ÷ 3 = 25
∴ 3x^4 - 30x³ + 75x² = 3(x^4 - 10x³ + 25x²)
- Now lets find the greatest common factor of the variable x
∵ x² is the greatest common factor of the three terms
∵ x^4 ÷ x² = x²
∵ 10x³ ÷ x² = 10x
∵ 25x² ÷ x² = 25
∴ 3(x^4 - 10x³ + 25x²) = 3x² (x² - 10x + 25)
- Lets factorize (x² - 10x + 25)
∵ √x² = x
∵ √25 = 5
∵ 2 × 5 × x = 10x
∴ x² - 10x + 25 is a completing square
∴ (x² - 10x + 25) = (x - 5)²
∴ 3x² (x² - 10x + 25) = 3x² (x - 5)²
* The complete factorization is 3x² (x - 5)²
Answer:
3x^2 (x-5)^2
Step-by-step explanation:
3x^4 − 30x^3 + 75x^2
We can factor out a 3x^2 from each term
3x^2 (x^2 -10x +25)
The term inside the parentheses can be factored
What 2 numbers multiply to 25 and add to -10
-5*-5 = 25
-5+-5 = -10
3x^2 (x-5) (x-5)
3x^2 (x-5)^2
Simplify.
3√7/25−√28/25+√63/25
Answer:
4√7/5
Step-by-step explanation:
to take a root of a fraction, take the root of the numerator and denominator separately3×√7/5-√28/5+√63/5
calculate the product3√7/5-2√7/5+3√7/5
calculate the sum or difference4√7/5
The simplified value of [tex]\frac{3\sqrt{7} }{25} -\frac{\sqrt{28} }{25} +\frac{\sqrt{63} }{25}[/tex] will be [tex]\frac{4\sqrt{7}}{25}[/tex].
What is system of equations?System of equations is a finite set of equations for which common solutions are sought.
We have,
[tex]\frac{3\sqrt{7} }{25} -\frac{\sqrt{28} }{25} +\frac{\sqrt{63} }{25}[/tex]
Now,
Take LCM, of the given fraction,
We get,
[tex]\frac{3\sqrt{7} -\sqrt{28}+\sqrt{63}}{25}[/tex]
Now,
Simplify by rewriting every number in numerator in form of [tex]\sqrt{7}[/tex],
i.e.
[tex]\frac{3\sqrt{7} -\sqrt{4*7}+\sqrt{9*7}}{25}[/tex]
Now,
[tex]\frac{3\sqrt{7} -2\sqrt{7}+3\sqrt{7}}{25}[/tex]
Now,
Every digit is in the form of [tex]\sqrt{7}[/tex],
So,
Simplify,
We get,
[tex]=\frac{4\sqrt{7}}{25}[/tex]
So,
This is the simplified form of the given equation.
Hence, we can say that the simplified value of [tex]\frac{3\sqrt{7} }{25} -\frac{\sqrt{28} }{25} +\frac{\sqrt{63} }{25}[/tex] will be [tex]\frac{4\sqrt{7}}{25}[/tex].
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The system shown is _____.
consistent
equivalent
inconsistent
Answer:
consistent
Solution at (3,2)
Step-by-step explanation:
A consistent and independent solution to a system of linear equations is one point
A consistent and dependent solution to a system of linear equations is where they are the same line ( they could also be called equivalent)
An inconsistent solution is where there is no solution, the lines do not cross
Since the lines cross at exactly one point, this is a consistent and dependent solution
The solution is at x = 3 ( 3 units to the right of the origin)
and y = 2 ( 2 units up from the origin)
(3,2)
Answer:
Consistent :)
Step-by-step explanation:
3(b+4)+8=-3 as a linear equation.
For this case we have the following equation:
[tex]3 (b + 4) + 8 = -3[/tex]
If we apply distributive property to the terms within the parenthesis we have:
[tex]3b + 12 + 8 = -3[/tex]
We add similar terms to the left side of the equation:
[tex]3b + 20 = -3[/tex]
Subtracting 20 from both sides of the equation:
[tex]3b = -3-20\\3b = -23[/tex]
Dividing between 3 on both sides of the equation:
[tex]b = - \frac {23} {3}[/tex]
In mixed number we have:
[tex]b = -7 \frac {2} {3}[/tex]
Answer:
[tex]b = -7 \frac {2} {3}[/tex]
What is the product -9x(5x-2x)
Answer:
−27x2
Step-by-step explanation:
It's -27x to the second power so the small 2 at the end
What is the total surface area of the cone? 147π cm2 224π cm2 175π cm2 273π cm2
Answer:
Step-by-step explanation: I believe you would just take 147 + 224 + 175 + 273 = 819pi cm2
So your answer would be 819pi cm2
The answer is 224 pi
.....................................
what is −7−4p−(−5) ??
Answer:
Step-by-step explanation:
−7−4p+5
−4p+(−7+5)
Ans
−4p−2
your answer is: -4p - 2
Explanation:
first, ignore the -4p for now. do the small equation without the variable. SO, we would do 7 - 5 = 2.
there aren't any addition symbols being used in the equation and there aren't any other numbers with the p variable. this means that the -4p will stay the same. so we would end up with -4p - 2
(this isn't the normal way of solving this, but I did my own way and got the same answer)
the graph shows the relationship between the volume of a rectangular prism and the volume of a square pyramid with an identical base and height what is the slope of the line
Answer:
The difference in volume is that the prism's volume is 3 times greater than the pyramid's volume.
Without seeing the graph, I can't tell what the slope is, but depending on the way the graph is drawn, the slope should be 1/3 or 3.
Answer:
The answer is 1/3
I NEED HELP PLS!!!!
Out of fifty students, twenty five are taking Math Competition classes and 29 are taking Geometry. Given that 12 are taking History and no math classes and nineteen students are in both math classes.
a. How many students are in neither class?
IF YOU HELP, I'LL MARK YOU THE BRAINLIEST ANSWER!!!!!!!
By applying the principle of inclusion-exclusion and considering students in History, we find that 3 students are in neither Math Competition classes nor Geometry.
Explanation:To determine how many students are in neither Math Competition classes nor Geometry, we can use the principle of inclusion-exclusion. We have 50 students in total, with 25 in Math Competition classes and 29 in Geometry. However, since 19 students are in both classes, they were counted twice when we added the students in Math Competition classes and Geometry together. Thus, we subtract the number of students in both to avoid double-counting:
(25 + 29 - 19) = 35 students are in at least one of the math classes. Additionally, 12 students are in a History class and no math classes. Therefore, the number of students in at least one class (math or history) is 35 + 12 = 47.
Finally, to find the number of students in neither class, we subtract the number of students in at least one class from the total number of students:
50 - 47 = 3 students are in neither Math Competition classes nor Geometry.
Simplify the expression. 8P3
Answer:
336
Step-by-step explanation:
Using the definition of n[tex]P_{r}[/tex] = n ! / (n- r) !
where n ! = n(n - 1)(n - 2).... × 3 × 2 × 1
8[tex]P_{3}[/tex]
= 8 ! / (8 - 3) !
= 8 ! / 5 !
= [tex]\frac{8(7)(6)(5)(4)(3)(2)(1)}{5(4)(3)(2)(1)}[/tex]
[ cancel 5(4)(3)(2)(1) on numerator/denominator
= 8 × 7 × 6 = 336
ANSWER
[tex]^8P_3 = 336[/tex]
EXPLANATION
Recall that;
[tex]^nP_r = \frac{n!}{(n - r)!} [/tex]
The given expression is:
[tex]^8P_3[/tex]
We substitute n=8 and r=3
[tex]^8P_3 =\frac{8!}{(8- 3)!} [/tex]
[tex]^8P_3 =\frac{8!}{(5)!} [/tex]
This simplifies to :
[tex]^8P_3 =\frac{8 \times 7 \times 6 \times 5!}{5!} [/tex]
We cancel out the common factors to get:
[tex]^8P_3 = 8 \times 7 \times 6[/tex]
[tex]^8P_3 = 336[/tex]
log; (3x+2) = log,(4x-6)
Answer:
x = 8
Step-by-step explanation:
Using the rule of logarithms
log x = log y ⇔ x = y
Given
log(3x + 2) = log(4x - 6), then
4x - 6 = 3x + 2 ( subtract 3x from both sides )
x - 6 = 2 ( add 6 to both sides )
x = 8
Angle f and angle G are complementary. The measure angle f is four times the measure of angle G. What is the measure of each angle?
Complementary means they add to 90°
f=90-g
f=4g
4g =90-g
5g=90
g=18
f=4g=4(18)=72
Answer: f=72°, g=18°
Please help question in picture please
Answer:
-1,3,5,9,13
Step-by-step explanation:
2(-3)+5=-6+5=-1
2(-1)+5=-2+5=3
2(0)+5=0+5=5
2(2)+5=4+5=9
2(4)+5=8+5=13
Based on the table below, evaluate f(1).
Answer:
f(1) = 24
Step-by-step explanation:
f(1) is the value of f(x) when x = 1, that is from the table
f(1) = 24
Identify an equation in point-slope form for the line perpendicular to
y=-4x - 1 that passes through (-2,7).
O A. y-7 - -4(x +2)
O B. y+2- (x-7)
O C. y+7 -- (x-2)
O D. y-7 - 3(x+2)
SUBMIT
Answer:
A. y - 7 = -4(x + 2)
Step-by-step explanation:
Insert the coordinates into the formula with their CORRECT signs. Remember, in the Point-Slope Formula, y - y₁ = m(x - x₁), all the negative symbols give the OPPOSITE term of what they really are. In addition, I recall that perpendicular lines have OPPOSITE MULTIPLICATIVE INVERSE [RECIPROCAL] rate of changes [slopes], so -4 really should be replaced with ¼, but if your assignment says otherwise, then this is the answer.
To find the equation of a line perpendicular to y=-4x -1 that passes through (-2, 7), we take the negative reciprocal of -4 to find the slope of the perpendicular line. Plugging in the values (-2, 7) and 1/4 for the slope, we get the equation y - 7 = 1/4(x + 2). Therefore, the correct answer is A. y - 7 = -4(x + 2).
Explanation:To find the equation of a line perpendicular to a given line, we need to determine the slope of the perpendicular line. The given equation is in the form y = mx + b, where m represents the slope. The slope of the given line is -4. To find the slope of the perpendicular line, we take the negative reciprocal of -4, which is 1/4. Now that we have the slope, we can use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line. Plugging in the values (-2, 7) for (x1, y1) and 1/4 for the slope, we get the equation y - 7 = 1/4(x + 2). Therefore, the correct answer is A. y - 7 = -4(x + 2).
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A student skipped a step when she tried to convert 26 hours into seconds,
and she got the following incorrect result:
26 hours
60 seconds
1 minute
- 1560 seconds
What conversion ratio did she skip in this multiple-step conversion?
60 minutes
O
A.
1 hour
60 seconds
1 minute
1 hour
60 minutes
1 minute
60 seconds
Help ASAP
Final answer:
The student missed the conversion from minutes to hours. The correct conversion is 26 hours × 60 minutes/hour × 60 seconds/minute, which equals 93,600 seconds.
Explanation:
Identifying the Missed Conversion Step
The student was attempting to convert 26 hours into seconds but arrived at an incorrect result of 1560 seconds. The error occurred because the student skipped the correct conversion ratio between minutes and hours. For such conversions, it is essential to use the correct conversion factors: 60 minutes per hour and 60 seconds per minute.
Correct Conversion Process
To convert 26 hours to seconds:
First, convert hours to minutes: 26 hours × 60 minutes/hour = 1560 minutes.
Then, convert minutes to seconds: 1560 minutes × 60 seconds/minute = 93,600 seconds.
Therefore, the correct number of seconds in 26 hours is 93,600 seconds.
Solve the two-step equation.
-0.45х + 0.33 = -0.66
What is the solution?
Ox = -2.2
Ox = -1.4
Ox = 1.4
Ox= 2.2
Answer:
x= 2.2
Step-by-step explanation:
-0.45х + 0.33 = -0.66
Subtract .33 from each side
-0.45х + 0.33-.33 = -0.66-.33
-.45x = -.99
Divide each side by -.45
-.45x/.-45 = -.99/.-45
x =2.2
A 52-inch pipe is cut into two pieces. One piece is three times the length of the other. Find the length of the shorter piece.
Answer:
The length of the shorter piece is 13 inches
Step-by-step explanation:
Let's represent the longer piece of pipe with the variable L and the shorter piece of pipe with variable S.
Since the pipe is going to be the length of L and S together, we can make this equation:
L+S=52
Also we know that the longer piece is three times the shorter piece or
L=3S
Substitute the second equation into the first equation.
L+S=52
3S+S=52
4S=52
Divide both sides by 4
4S/4=52/4
S=13 inches
The length of the shorter piece is 13 inches....
To find the length of longer piece, put the value S=13 in L=3S
L=3S
L=3(13)
L=39 inches
The length of the longer piece is 39 inches....
The property tax on a $160,000 home is $3,840. At this rate, what is the property tax on a home appraised at $260,000? $
Answer:
$6240
Step-by-step explanation:
Find the rate by dividing property tax by the appraisal value.
[tex]\frac{3840}{160000}=0.024[/tex]
Now multiply the appraised value by this rate to find the property tax.
[tex]260000*0.024=6240[/tex]
The property tax on a home appraised at $260,000 is $6,240.
Explanation:To find the property tax on a home appraised at $260,000, we can set up a proportion using the given information. The property tax on a $160,000 home is $3,840, so we have:
$160,000 : $3,840 = $260,000 : x
Using cross-multiplication, we can solve for x:
x = ($260,000 * $3,840) / $160,000
Calculating this, we find that the property tax on a home appraised at $260,000 is $6,240.
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please answer and thank you!!!
Answer:
In the photos
Step-by-step explanation:
First, create your trees (following instructions on the photo you attached). Then, circle the prime numbers in each tree you made. If the prime number shows up once put that number once on your prime factorization. If the prime number appears multiple times, put the number down and have an exponent (the exponent is determined by how many times that number appears).
Hope this helps a bit,
Flips
3x^2-x-2=0
Show all work please
Answer:
[tex]\large\boxed{x=-\dfrac{2}{3}\ or\ x=1}[/tex]
Step-by-step explanation:
[tex]3x^2-x-2=0\\\\3x^2+2x-3x-2=0\\\\x(3x+2)-1(3x+2)=0\\\\(3x+2)(x-1)=0\iff3x+2=0\ \vee\ x-1=0\\\\3x+2=0\qquad\text{subtract 2 from both sides}\\3x=-2\qquad\text{divide both sides by 3}\\x=-\dfrac{2}{3}\\\\x-1=0\qquad\text{add 1 to both sides}\\x=1[/tex]
Kasey has a job that pays $865 per week. How much is withheld from each paycheck for Social Security?
Kasey has $53.63 withheld from her weekly paycheck of $865 for Social Security, which is calculated by multiplying her weekly pay by the Social Security tax rate of 6.2%.
Explanation:The question asks us to calculate how much is withheld from Kasey's paycheck for Social Security.
With a weekly pay of $865, we need to find 6.2% of that amount since that is the percentage deducted for Social Security taxes.
To find this amount, we multiply $865 by 0.062.
Calculation: $865 × 0.062 = $53.63
Therefore, $53.63 is withheld from Kasey's paycheck each week for Social Security.
what is the distance between the points (2 -3) and (-6 4) on the coordinate plane
Answer:
√113
or
10.6301458127
Step-by-step explanation:
Plug the coordinated into this equation and make sure you match up the corrdinates in the correct order
d = √(x2 - x1)^2 + (y2 - y1)^2
The number next to the number does NOT mean multiply it mean like this
(x2, y2) and (x1, y1) so you would plug them in like this:
d = √(-6 - 2)^2 + (4 - (-3))^2
d = √(-8)^2 + (7)^2
d = √(64 + 49
d = √113
or 10.6301458127
Answer with Step-by-step explanation:
The distance(d) between the points (a,b) and (c,d) is given by:
[tex]d=\sqrt{(c-a)^2+(d-b)^2}[/tex]
Here, we have to find distance between (2,-3) and (-6,4)
(a,b)=(2,-3) and (c,d)=(-6,4)
[tex]d=\sqrt{(-6-2)^2+(4-(-3))^2}[/tex]
[tex]d=\sqrt{8^2+7^2}[/tex]
[tex]d=\sqrt{64+49}[/tex]
[tex]d=\sqrt{113}[/tex]
Hence, the distance between the points (2 -3) and (-6 4) on the coordinate plane is:
[tex]\sqrt{113}[/tex]
The input-output diagram represents F(x) - X+4.
What is the missing output value?
Answer:
9
Step-by-step explanation:
(5)+4=9
The missing output value is:
9
Step-by-step explanation:The function in terms of the variable x, where x represents the input value is given by the formula:
[tex]F(x)=x+4[/tex]
where F(x) is the output value corresponding to the input value x.
We are asked to find the missing output value i.e. we are asked to find the value of F(x) at x=5.
i.e. we have:
[tex]F(5)=5+4\\\\i.e.\\\\F(5)=9[/tex]
Hence, the missing output value is: 9