Answer:
Length = 22 inches, Width = 5 inches
Step-by-step explanation:
Let P represent the Perimeter, L , the length and W, the width
Perimeter of a rectangle, P = 2 (L + W) ....eq 1
from the question;
L = 2 + 4W .....eq 2
Slotting in the respective values of P and L in eq 1
54 = 2{(2 + 4W) + W}
Expanding the bracket
54 = 2(2 + 5W)
54 = 4 + 10W
Subtracting 4 from both sides of the equation
54 - 4 = 10 W
50 = 10W
Dividing both sides by the coefficient of W which is 10
5 = W
Therefore, W = 5 inches
Slotting in the value of W in eq 2
L = 2 + 4(5)
L = 2 + 20
L = 22 inches
Now lets check our answers by slotting in the values of P, L and W in eq 1
54 = 2 (22 + 5)
54 = 2 (27)
54 = 54
Since both sides of the equation are equal, the values of L and W are correct
Hence Length = 22 inches, Width = 5 inches
300,000+900+4
write this number in standard form
Answer:
300,904
Step-by-step explanation:
what is (4x + 3) + (-2x + 4)
Answer:
(4x + 3) + (-2x + 4) = 2x + 7
Step-by-step explanation:
(4x + 3) + (-2x + 4) = you then collect like terms
(4x + -2x) + (3 + 4)= like this, and you add what's inside perenthesis
= 2x + (3 + 4). step-by-step
= 2x + 7. then that is how you get =2x+7
Answer:
The answer to your equation would be 2x + 7.
Step-by-step explanation:
4x + 3 + -2x + 4
= (4x + -2x) + (3 + 4)
= 2x + (3 + 4)
= 2x + 7
Therefor, your answer would be 2x + 7.
Which of these statements are correct about a line segment with a length of 12 units in a coordinate plane? Select all that apply.
Correct statements are:
If it is reflected across the y-axis, its length still will be 12 units.
If it is rotated 270° about the origin, its length still will be 12 units.
If it is translated 15 units up, its length still will be 12 units.
Step-by-step explanation:
Whatever it may be rotation, reflection or translation, the size of the line will never change. So length of the line is same as 12 units in the image.
So the wrong statements are
If its reflected across y = -x then the length will no longer be 12 units.
If it is rotated 90° about the origin, then the length will no longer be 12 units.
If it is translated 18 units to the right, then the length will no longer be 12 units.
You can use the fact that reflection, rotation or translation, all three are not modifying the line itself and only its position can change. Whatever be the position, if the line segment itself isn't modified, the length will be same.
Thus, the correct choices are:
Option A: If it is reflected across the y-axis, the length will still be 12 units.Option B: If it is rotated 270° about the origin, its length still will be 12 units.Option E: If it is translated 15 units up, its length still will be 12 units.Rest of the choices are wrong since they blame reflection or rotation or translation to modify the length of that line segment.
Why is the length of a line segment not modified when it is reflected along an axis, rotated or translated by some units in some direction?Suppose you've got a baseball stick. Will it's length change when you take it somewhere else like from your home to playground? No. Will its length change if you hold it upside down? No.
This is the same case with line segment being rotated, reflected, or translated. All these processes do not change the line segment's length and can just move that line segment from one position to other.
Using above conclusion to find the correct options in the given contextSince reflection, rotation, or translation won't affect the length of the line segment,.
Thus, the correct choices are:
Option A: If it is reflected across the y-axis, the length will still be 12 units.Option B: If it is rotated 270° about the origin, its length still will be 12 units.Option E: If it is translated 15 units up, its length still will be 12 units.Rest of the choices are wrong since they blame reflection or rotation or translation to modify the length of that line segment.
Learn more about reflection, rotation and translation of line segment here:
https://brainly.com/question/17201260
The pet store has 20 mice: 11 are white, five are
grey, and four are brown. If the pet storeowner
randomly chooses a mouse for the window
display, what is the probability that the mouse
will be grey?
Answer:
The answer is: 5/20 or a 25% chance
The probability that the pet store owner randomly selects a grey mouse for the window display is 0.25 or 25%.
Explanation:The question asks for the probability of selecting a grey mouse from a pet store that has a total of 20 mice consisting of 11 white, 5 grey, and 4 brown mice. To find the probability, we use the ratio of the number of grey mice to the total number of mice.
The formula for probability is:
Probability (P) = Number of favorable outcomes / Total number of outcomes
We apply the formula as follows:
P(grey mouse) = Number of grey mice / Total number of mice = 5 / 20 = 0.25 or 25%
Therefore, the probability that the pet store owner selects a grey mouse for the window display is 25%.
Solve for x: 14-14x^1/3 =2
Answer: 216/343 or 0.6297
Step-by-step explanation:
[tex]14-14x^{1/3} = 2\\14 -2 = 14x^{1/3}\\12 = 14x^{1/3}\\\frac{12}{14} =x^{1/3}\\\frac{6}{7} =x^{1/3}\\(\frac{6}{7})^3 =(x^{1/3})^3\\\frac{6^3}{7^3} =x\\\\\frac{216}{343} = 0.629737609 = x[/tex]
Answer ........................
(1)
Section 3
Mr. Lenny paid $1480.00 for 4 cricket balls and 2 cricket bats. The cost of 1 cricket bat is twice as
much as a ball. What is the cost of 1 cricket ball and 1 cricket bat?
Answer.
.
.
.
.
....(
4) (answer with explanation)
Answer:
The cost of one cricket bat is $370, while the cost of one cricket ball is $185.
Step-by-step explanation:
Let's identify what we already know:
1) Mr. Lenny paid a TOTAL of $1480.00 for 4 cricket balls, and two cricket bats.
2) The cost of one cricket bat is twice as much as a cricket ball.
We can create an initial equation:
(4 times x) + (2 times y) = $1480.00
x is the price of one cricket ball, while y is the price of one cricket bat. Considering how the problem is set up, I know the 4 balls should add up to the same price as two bats.
So, the four balls should equal half of $1480, which is $740, and the two bats should also equal $740.
Calculate it out, and you'll find that one cricket bat equals $370, while one ball equals $185.
The question can be solved by representing the cost of a ball as x and bat as 2x, forming the equation 4x + 2(2x) = 1480. Solving this equation finds the cost of the individual cricket ball and bat.
Explanation:In this question, we know that the cost of one cricket bat is twice the cost of a cricket ball, and that Mr. Lenny bought 4 cricket balls and 2 cricket bats for $1480.00. To solve for the individual price of each item, we can use the method of substitution in algebra.
Let's represent the cost of a ball as x and a bat as 2x. This becomes an equation of 4x (cost of 4 balls) + 2(2x) (cost of 2 bats) = 1480.
Solving for x will give us the cost of one cricket ball, and multiplying the value of x by 2 will offer the cost of a single cricket bat.
Learn more about Algebra here:https://brainly.com/question/24875240
#SPJ12
a student earns 42 points out of 60 points on a test what percent of the points did the student answer
Answer:
It would be a 70%
Step-by-step explanation:
Convert fraction (ratio) 42 / 60 Answer: 70%
Answer:
I think 24% percent?????
Gilberto’s grandfather gives him $5 for his birthday and then $.50 for each math question he answers correctly on his math exams for the year. Write an equation that represents the amount of money that Gilberto receives during the school year. Explain what the variables and numbers mean.
Answer:
Therefore total amount of money that he got is = $(5+0.50x) [ x = number of correct math]Step-by-step explanation:
Given, Gilberto's grandfather gives him $5 for his birthday and then$0.50 for each math he answers correctly on his math exam for the year.
Let , the number of math that he answers correctly on his his math exam for the year is x
Therefore he got = $(0.50× x) =$ 0.50x for doing correct math.
Therefore total amount of money that he got is = $(5+0.50x) [ x = number of correct math]
the length of the top of a rectangular-shaped deck is 6 meters longer than its width. if the area of the top of the deck is 72 square meters, what is it’s length in meters?
Answer:
6 meters
Step-by-step explanation:
length= 6+x
width= x
x (x+6)= 72⇔ [tex]x^{2}[/tex] + 6x - 72= 0⇔ x= (-6 ±[tex]\sqrt{6^{2} -4 *1*(-72) }[/tex]) / 2*1⇔
⇔ x= (-6±√324)/2 ⇔ x= (-6±18)/2 ⇔ x= 6 ∨ x= -12
Since the width of a rectangle can't be negative, the answer will be 6 meters.
Solve 3(x - 2) < 18.
{x | x < 8}
{x | x > 8}
{x | x < -8}
{x | x > -8}
Answer:
3x - 6 < 18
3x < 24
x < 8
answer is a
1/3(z+4)-6=2/3(5-z)
Find the answer
Step-by-step explanation:
[tex] \frac{1}{3} (z + 4) - 6 = \frac{2}{3} (5 - z) \\ \\ \therefore \: \frac{ (z + 4) - 6 \times 3}{3} = \frac{2(5 - z) }{3} \\ \\ \therefore \: \frac{ z + 4 -18}{3} = \frac{10 - 2z }{3} \\ \\ \therefore \: \frac{ z - 14}{3} = \frac{10 - 2z}{3} \\ \\ \therefore \: z - 14 = 10 - 2z \\ \\ \therefore \: z + 2z = 10 + 14\\ \\ \therefore \: 3z =24 \\ \\ \therefore \: z = \frac{24}{3} \\ \\ \: \: \: \: \: \: \: \: \huge \orange{ \boxed{ \therefore \: z = 8}}[/tex]
Julia bought 12 bags of cucumber seeds. each bag contains 42 seeds. if she plant one half of the seeds how many seeds does she have left
Answer:
She will have 252 seeds left.
Step-by-step explanation:
12 x 42 = 504
504 ÷ 2 = 252
So, she will have planted 252 seeds and she will have 252 seeds left to plant.
Final answer:
Julia has 252 seeds left after planting half of the seeds.
Explanation:
To find out how many seeds Julia has left, we first need to determine the total number of seeds she has. Julia bought 12 bags of cucumber seeds, and each bag contains 42 seeds. So the total number of seeds she has is 12 bags × 42 seeds per bag = 504 seeds.
If Julia plants one-half of the seeds, she would be planting 504 seeds × 1/2 = 252 seeds.
To find out how many seeds she has left, we subtract the number of seeds she planted from the total number of seeds she initially had. 504 seeds - 252 seeds = 252 seeds left.
Write 2.14 in word form
Answer:
two dollars and fourteen cents
Step-by-step explanation:
Answer:two point fourteen
Step-by-step explanation:
The first term of a geometric sequence is 32, and the 5th term of the sequence is 818 .
What are the geometric means between these terms?
Enter your answer by filling in the boxes to correctly complete the geometric sequence. Enter any fractions as simplified fractions.
Answer:
[tex]32,24,18,\frac{27}{2} ,\frac{81}{8}[/tex]
Step-by-step explanation:
Let x, y , and z be the numbers.
Then the geometric sequence is [tex]32,x,y,z,\frac{81}{8}[/tex]
Recall that term of a geometric sequence are generally in the form:
[tex]a,ar,ar^2,ar^3,ar^4[/tex]
This implies that:
a=32 and [tex]ar^4=\frac{81}{8}[/tex]
Substitute a=32 and solve for r.
[tex]32r^3=\frac{81}{8}[/tex]
[tex]r^4=\frac{81}{256}[/tex]
Take the fourth root to get:
[tex]r=\sqrt[4]{\frac{81}{256} }[/tex]
[tex]r=\frac{3}{4}[/tex]
Therefore [tex]x=32*\frac{3}{4} =24[/tex]
[tex]y=24*\frac{3}{4} =18[/tex]
[tex]z=18*\frac{3}{4} =\frac{27}{2}[/tex]
Answer:
Step-by-step explanation:
LULUI VIEW
If f(x) = 4x and g(x)= x4 - 2, what is go f(x)?
Answer:
256[tex]x^{4}[/tex] - 2
Step-by-step explanation:
To evaluate (g ￮ f )(x), substitute x = f(x) into g(x)
g(4x) = [tex](4x)^{4}[/tex] - 2 = 256[tex]x^{4}[/tex] - 2
In September, Jerry read for 2/5 of an hour every day for 20 days. How many
hours did he read in September?
Show your work.
Answer:
Step-by-step explanation:
- 2/5 of an hour is equal to 24 min
- 24 times 20 is 480 minuets during September
- 480 minuets is 8 hours
Solutions to -8x + 5 less than or equal to 11
Answer:
[tex]x\geq -\frac{3}{4}[/tex]
Step-by-step explanation:
[tex]-8x+5\leq 11\\\\1. -8x\leq 11-5\\ -8x\leq 6[/tex]
Isolate the parts of the equation with the x variable
[tex]2. \frac{-8}{-8} x\geq\frac{6}{-8} \\x\geq -\frac{3}{4}[/tex]
When you divide or multiply by a negative number in inequalities, you must flip the sign of the inequality.
Hello there!
Im assuming you're solving for X!
Answer:
Your answer in Inequality Form comes to:
x > -3/4
Explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Micah is preparing for a piano recital. He practices for 50 minutes on Monday and 90 minutes on Wensday
Answer:
She increased 80% the practise time
Step-by-step explanation:
The question is incomplete, the following is missing:
by how much did she increase the time she practised each day?
From Monday to Wednesday she increased 90 - 50 = 40 minutes the practise time.
To compute the increment as a percentage use: increment/reference *100
In this case, that is: 40/50*100 = 80%, where 50 minutes is taken as a reference.
Answer: increased by 40
she increased by 80%
Step-by-step explanation:
5+15x=5( ) I'm not writing 20 characters
Answer:
(1 + 3x).
Step-by-step explanation:
We have to evaluate the missing term within the brackets in the following equation.
The equation is, 5 + 15x = 5(?)
Now, 5 + 15x
= 5 × 1 + 5 × 3x {We have to factorize the term where 5 is a factor}
= 5(1 + 3x) {This is reverse of the distributive property of multiplication}
Therefore, the missing term within the brackets is (1 + 3x). (Answer)
3/3 as a whole number
Answer:1
Step-by-step explanation:
3 full parts out of 3 is 1
Answer:
1
Step-by-step explanation:
Any number over itself always simplifies to 1
which value of x is in the solution set of the following inequality?
The right answer is Option 2.
Step-by-step explanation:
Given inequality is;
-3x+5>17
Solving the inequality
Subtracting 5 from both sides of the inequality;
[tex]-3x+5-5>17-5\\-3x>12[/tex]
Dividing both sides of inequality by -3;
[tex]\frac{-3x}{-3}>\frac{12}{-3}\\\\x>-4[/tex]
The solution to the inequality is -4.
The right answer is Option 2.
Keywords: subtraction, division
Learn more about subtraction at:
brainly.com/question/12884373brainly.com/question/12896802#LearnwithBrainly
The area of a rectangle is 54x^9y^8 square yards. If the length of the rectangle is 6x^3y^4 yards, which expression represents the width of the rectangle in yards?
60x^12y^12
9x^3y^2
9x^6y^4
48x^6y^4
Answer:
9 x⁶y⁴
Step-by-step explanation:
for a rectangle
area = length x width, (rearranging)
width = area / length
given area = 54x⁹y⁸ and length = 6x³y⁴
width = 54x⁹y⁸ / 6x³y⁴
= (54/6) ( x⁹y⁸ / x³y⁴)
= 9 ( x⁹y⁸ / x³y⁴)
= 9 ( x⁹⁻³y⁸⁻⁴ )
= 9 ( x⁶y⁴ )
= 9 x⁶y⁴
The expression represents the width of the rectangle in yards is 9 x⁶y⁴.
What is the area of the rectangle?The area of the rectangle is the product of the length and width of a given rectangle.
The area of the rectangle = length × Width
For a rectangle
width = area / length
The given area = 54x⁹y⁸ and length = 6x³y⁴
width = 54x⁹y⁸ / 6x³y⁴
= (54/6) ( x⁹y⁸ / x³y⁴)
= 9 ( x⁹y⁸ / x³y⁴)
= 9 ( x⁹⁻³y⁸⁻⁴ )
= 9 ( x⁶y⁴ )
= 9 x⁶y⁴
Hence, the expression represents the width of the rectangle in yards is 9 x⁶y⁴.
Learn more about the area;
https://brainly.com/question/1658516
#SPJ6
twenty is 150% of what number
13.33.
We have, 150% × x = 20
or,
150
100
× x = 20
Multiplying both sides by 100 and dividing both sides by 150,
we have x = 20 ×
100
150
x = 13.33
If you are using a calculator, simply enter 20×100÷150, which will give you the answer.
Oi, give flamenco brainliest.
pls help!
Multiply the following polynomials. 3x3(5x2+4x)
8x6+7x3
15x6+12x4
15x6+12x3
15x5+12x4
8x5+7x4
15x5+12x3
Answer:
78
Step-by-step explanation:
you multiply
Answer:
15x^9+12x^4
b is the answer
If 130 is invested in a savings account that earns 4% interest per year, which of the following is closest to the amount in the account at the end of 10 years
Which of the following best describes the situation below?
The number of miles a car can run depends on the gallons of gasoline in the
tank.
O
O
O
A. A relation that is not a function
B. A relation that is a function
C. The range of a function
D. The domain of a function
Answer:
c
Step-by-step explanation:
The situation described where the number of miles a car can run depends on the gallons of gasoline in the tank is a relation that is a function. Because for each amount of gas, there is one corresponding maximum distance the car can travel.
Explanation:The situation described illustrates a relation that is a function. In this case, the amount of gasoline (in gallons) in the car's tank is the input or the independent variable (the domain), and the distance the vehicle can travel (the output or dependent variable) is a function of this input. For each amount of gasoline, there is only one corresponding maximum distance the car can travel, so this is a function. Thus, the best answer is B. A relation that is a function.
Learn more about Function here:https://brainly.com/question/30721594
#SPJ2
suppose you are performing an experiment in science class in which you start with 70 bacteria and the amount of bacteria triples every hour write a function to represent the growth of the bacteria overtime in your science experiment
The function to represent the growth of the bacteria overtime in your science experiment is:
[tex]y = 70(3^x)[/tex]
Solution:
Given that,
Suppose you are performing an experiment in science class in which you start with 70 bacteria and the amount of bacteria triples every hour
Let,
y is the number of bacteria at time x
x is the number of hour(time)
As per the given information,
You start your experiment with 70 bacteria,and the bacteria triples in every hour
Therefore,
At end of 1 hour,
y = 70 x 3 = 210
At the end of 2 hours,
[tex]y = 210 \times 3 = 630\\\\Which\ can\ also\ be\ written\ as\\\\y = 70 \times 3^2 = 70 \times 9 = 630[/tex]
At the end of 3 hours,
[tex]y = 630 \times 3 =1890 \\\\Which\ can\ also\ be\ written\ as\\\\y = 70 \times 3^3 = 70 \times 27 = 1890[/tex]
Thus at end of "x" hours we will have,
[tex]y = 70 \times 3^x\\\\y = 70(3^x)[/tex]
Thus the function to represent the growth of the bacteria overtime in your science experiment
If an intercepted arc measures 124°, what is the measure of its inscribed angle? the same, 124° twice the measure, 248° half the measure, 62°
Answer:
The correct option is C.) half the measure 62°
Step-by-step explanation:
i) Intercepted arc measures 124°
ii) The measure of the inscribed angle will be half of the intercepted arc
therefore inscribed angle = 124° / 2 = 62°
iii) Therefore the correct option is C.) half the measure 62°
The measure of an angle inscribed in a circle is half the measure of its intercepted arc. Therefore, if the intercepted arc is 124°, the inscribed angle would be 62°.
Explanation:This problem is related to the relationship between arcs and inscribed angles in circles. In geometry, there's a specific rule that states: the measure of an angle inscribed in a circle is half the measure of its intercepted arc.
Therefore, if the intercepted arc measures 124°, its inscribed angle would have half the measure, or 62°. If the inscribed angle were to have the same measure, it would imply that the arc measure was double the angle, which is not the case here.
Learn more about Arcs and Inscribed Angles here:https://brainly.com/question/16044660
#SPJ3
What is the equation of the following line? Be sure to scroll down first to see
all answer options.
Answer: y=- 1/3x
Step-by-step explanation:
Expression equivalent to (0.28t-0.3)-(0.7t-0.28)?
A. 0.42t+0.58
B. -0.42t-0.02
C. 0.42t-0.02
D. -0.42t+0.58
Please help!