Answer:
Step-by-step explanation:
If the sides exist in a ratio to one another, then when you multiply some number x by both the length and the width, they still remain as a ratio. The length will be 3x and the width will be 1x. The perimeter formula is
P = 2L + 2W and since our perimeter is 72 and we have both the length and the width, we can fill in the formula and solve for x:
72 = 2(3x) + 2(1x) and
72 = 6x + 2x and
72 = 8x so
9 = x.
If x = 9, then 1x = 9 and 3x = 27. Let's check the perimeter against those side lengths.
P = 2(3x) + 2(1x) and
P = 2(27) + 2(9) and
P = 54 + 18 so
P = 72
and you're done! (The bold numbers above are the width and length, respectively.)
Jonathan's parents told him that for every 2 hours of homework or reading he completes, he would be able to play 30 minutes of video games. His friend Lucas's
parents told their son that he could play 1.5 hours for 5 hours of homework or reading time he completes. What is the unit rate for each boy? You must label both unit rates.
Answer:
Jonathan's Unit rate = 4 hr (reading/homework)/(1 hour for video games)
Lucas' Unit rate = 3 hr (reading/homework)/(1 hour for video games)
Step-by-step explanation:
The unit rate is the rate per unit of a quantity, that is the rate at which the denominator has been made a unit or one
The given parameters are;
The number of hours of homework or reading Jonathan needs to do for his parents to allow him to play video games for 30 minutes = 2 hours
The number of hours of homework or reading Lucas needs to do for his parents to allow him to play video games for 30 minutes = 1.5 hours
We note that 30 minutes = 0.5 hours
For Jonathan we have
Unit rate = (Number of hours of reading or homework)/(Number of hours playing video games)
Unit rate = (2 hours)/(0.5 hours) = 4 hours of reading or homework per hour of paying video games
Jonathan's Unit rate = 4 hr (reading/homework)/(1 hour for video games)
For Lucas we have
Unit rate = (Number of hours of reading or homework)/(Number of hours playing video games)
Unit rate = (1.5 hours)/(0.5 hours) = 3 hours of reading or homework per hour of paying video games
Lucas' Unit rate = 3 hr (reading/homework)/(1 hour for video games).
If a polygon has an area of 10 cm² and is dilated by a factor of 2, what will be the area of the dilated polygon?
Area depends on the product of sides,
so if the sides are shortened by a factor of 2, area will reduce by a factor of 4. (2×2)
new area = 10/4=2.5 cm²
1. (a) Find the greatest common divisor of the term 144x3y2and 81xy4
(b) Hence factorise completely this expression 144x3y2-81xy4
Answer:
Step-by-step explanation:
a) 144x³y² = 2 *2*2*2* 3* 3* x³ * y² = 2⁴ * 3² * x³ * y²
81xy⁴ = 3 * 3 * 3 * 3 * x * y⁴ = 3⁴ * x * y³
GCD is that are in both term
Greatest common divisor = 3² * x * y² = 9xy²
b) 144x³y² - 81xy⁴ = 9xy² * 16x²y - 9xy²*9y²
= 9xy²(16x²y - 9y²)
Find the values of a and b so that the following
system of linear equations have infinitely solutions:
(1) (2a - 15x + 3y - 5 = 0, 3x + (6 - 1)y - 2 = 0
plz answer step by step
Answer:
a = 15/2, b = 2/5
Step-by-step explanation:
For a system of two linear equations to have infinitely many solutions, the equations must be equivalent to one another.
Assuming a and b to be constants, and since b is absent from equations, there must be a typo where b was mistaken for a 6.
Modified equations:
2a - 15x + 3y - 5 = 0 ...................(1)
3x + (b - 1)y - 2 = 0 .....................(2)
rearrange equations to standard form:
-15x + 3y + 2a-5 = 0 .................(1a)
3x + (b-1)y -2 = 0 ........................(2)
To equalize the coefficient of x, multiply (2) by -5
-15x - 5(b-1) y +10 = 0 ................(2a)
Subtract (2a) from (1a)
3y + 5(b-1)y + 2a-5 -10 = 0 ..............(3)
For the two equations (1a) and (2a) to be identical, coeffients of y and constant term of (3) must equal zero.
3+5(b-1) = 0 .................(4)
3+5b-5 = 0
5b = 2
b = 2/5
2a-5-10 = 0 .....................(5)
a = 15/2
z3+(y2-4x) x is 6 y is 8 z is 3
Answer:
9
Step-by-step explanation:
x = 6
y = 8
z = 3
3z + (2y - 4x)
= (3)3 + (2[8] - 4[6])
= 9 + (16 - 16)
= 9 + 0
= 9
Hope this helps! Tell me if am wrong about the answer, please!
URGENTT PLEASE ANSWER
Answer:
Step 2
Step-by-step explanation:
9 was added to both sided so the equation would remain equal and the 9 would be cancelled out on the left side.
En la figura adjunta se muestra un estuche de brocas de acero que sirven para perforar paredes de cemento. Las brocas están numeradas de menor a mayor tamaño y las dimensiones están dadas en pulgadas.
En la figura, por falta de espacio, se dan solo las dimensiones de las brocas 1 y 12. Se sabe que las demás brocas son de 9/16 de pulgadas, 3/16 de pulgada, 7/16 de pulgada, 5/16 pulgada, 11/16 pulgada, 1/4 pulgada, 3/8 pulgada, 1/2 pulgada, 5/8 pulgada y 1/8 de pulgada.
Identifica la medida de las brocas 2 a la 11 en pulgadas y ordénalas de menor a mayor tamaño.
Answer:
1/16 2/16 3/16 4/16 5/16 6/16 7/16 8/16 9/16 10/16 11/16 12/16
Step-by-step explanation:
Para la identificación de las brocas tenemos dos consideraciones:
1.- Fracciones de igual denominador son mas grandes en orden creciente según vayan creciendo los numeradores, de tal forma que entre
9/16 3/16 7/16 5/16 11/16 el orden es como sigue ( de menor a mayor)
3/16 5/16 7/16 9/16 11/16
2.- Las fracciones con denominadores distintos pueden llevarse a denominador común /16 amplificando la fracción es decir por ejemplo
1/4 = 1*4/4*4 = 4/16
Con ese procedimiento las convertimos todas al caso señalado en el punto anterior y ordenamos
1/4 = 4/16
3/8 = 6/16
1/2 = 8/16
5/8 = 10/16
1/8 = 2/16
Entonces hay diez brocas la primera será 1/16 y la número 12 12/16
Y finalmente el orden es:
1/16 2/16 3/16 4/16 5/16 6/16 7/16 8/16 9/16 10/16 11/16 12/16
The graphs below have the same shape. What is the equation of the blue
graph?
Answer:
B
Step-by-step explanation:
Given f(x) then f(x + k) represents a horizontal translation of f(x)
• If k > 0 then shift left by k units
• If k < 0 then shift right by k units
Here g( x) is f(x) moved 5 units right, thus
g(x) = (x - 5)² → B
please i really need help The line plot below displays the fraction of incoming calls answered before the second ring by a group of employees. What fraction of employees answered less than of their incoming calls before the second ring?
Answer:
B
Step-by-step explanation:
If we count the number of points we find out that there are 36 employees
so the fraction must go like x/36
x is the numbers of dots that are less than a 1/2 which are 1/8, 1/4 and 3/8
so x=6
6/36
1/6
so option B
Plz help with this question! What is 1/3 * 3/5 * 5/7 ... * 97/99
Answer:
Step-by-step explanation:
(1/3)*(3/5)*(5/7)*.......*(93/95) * (95/97) * (97/99)
The denominator of each fraction will cancel out the numerator of the next fraction.
Take a close look
Therefore the result is 1/99
HOPE IT HELPS!!
The product of the geometric series is 1/99.
The product is a geometric series with first term 1/3 and common ratio 2/3. The number of terms is 49. The sum of the series is 1/99.
Here's the explanation:
A geometric series is a series where each term is multiplied by a constant value to get the next term. The constant value is called the common ratio.
In this case, the first term is 1/3 and the common ratio is 2/3. This means that each term is multiplied by 2/3 to get the next term.
The number of terms in the series is 49. This means that there are 49 terms in the series, starting with 1/3 and ending with 97/99.
The sum of the series is 1/99. This can be found using the formula for the sum of a geometric series:
S = a × (1 - [tex]r^{n}[/tex]) / 1 - r
where a is the first term, r is the common ratio, and n is the number of terms.
In this case, a = 1/3, r = 2/3, and n = 49. Substituting these values into the formula, we get:
S = (1/3) × (1 - (2/3)49) / 1 - (2/3) = 1/99
Therefore, the product is 1/99.
Learn more about geometric series here: brainly.com/question/30264021
#SPJ2
3. Solve 2log4y - log4 (5y - 12) = 1/2
Answer:
y = 4 or y = 6
Step-by-step explanation:
2log4y - log4 (5y - 12) = 1/2
2log_4(y) - log_4(5y-12) = log_4(2) apply law of logarithms
log_4(y^2) + log_4(1/(5y-12)) = log_4(/2) apply law of logarithms
log_4(y^2/(5y-12)) = log_4(2) remove logarithm
y^2/(5y-12) = 2 cross multiply
y^2 = 10y-24 rearrange and factor
y^2 - 10y + 24 = 0
(y-4)(y-6) = 0
y= 4 or y=6
I need help with this please.
Answer:
the slope is 60
Step-by-step explanation:
the slope is the number multiplying the x value, or t in this case.
Answer:
The slope is 60, and create the graph by dragging one point to (0,0) and one point to (1,60).
Step-by-step explanation:
If we have the proportional relationship [tex]d=60t[/tex], then the slope will be what we multiply t by to get d, therefore the slope is 60.
Since there is no y-intercept, the line WILL pass through the origin (0,0), so a point goes there.
If we make t 1, then d will be at point (1,60) because [tex]60\cdot1=60[/tex].
Hope this helped!
What adds to be the bottom numbers but also multiplies to be the top?
39 at the bottom and 25 on the right above 39
Answer:
well i cant answr it if i oont have more inforomartion
Step-by-step explanation:
Answer:
Step-by-step explanation:
if we add 11,36,61,... to the bottom we get bottom as a multiple of numerator.
please help!!!! Use the graph to complete the statement. O is the origin. Ry−axis ο Ry=x: (-1,2)
A. (1, -2) B. (-1, -2) C. (2, -1) D. (-2, -1)
Answer: D. (-2, -1)
Step-by-step explanation:
Here we do two reflections to the point (-1, 2).
First, we do a reflection over the line x = y. Remember that a reflection over a line keeps constant the distance between our point and the given line, so we have that for a pint (x, y), the reflection over the line y = x is:
Ry=x (x, y) = (y, x)
so for our point, we have:
Ry=x (-1, 2) = (2, -1)
Now we do a reflection over the y-axis, again, a reflection over a line keeps constant the distance between our point and the given line, so if we have a point (x,y) and we do a reflection over the y-axis, our new point will be:
Ry-axis (x,y) = (-x, y)
Then in our case:
Ry-axis (2, -1) = (-2, -1)
The correct option is D.
What are the solutions of x2 + 20 = 12x.
Answer:
x₁ = 2
x₂ = 10
Step-by-step explanation:
x² + 20 = 12x
x² - 12x + 20 = 0
(x-2)(x-10) = 0
then:
x₁ = 2
x₂ = 10
Check:
x₁
2² + 20 = 12*2
3 + 20 = 24
x₂
10² + 20 = 12*10
100 + 20 = 120
what is mean absolute deviation (MAD) and how do I find it?
Steps to find MAD:
Step 1. Calculate mean([tex]\overline{x}[/tex]) of the data using formula: [tex]\overline{x}=\dfrac{\sum x}{n}[/tex] , where x denotes data points and n is the number of data points.
Step 2. Calculate distance of each data point from mean :
Distance = [tex]|x-\overline{x}|[/tex]
Step 3. Divide distance of each data point from mean by n:
MAD = [tex]\dfrac{\sum |x-\overline{x}|}{n}[/tex] , which is the final computation to find MAD.
Solve y+1=-3/4 (x+2) and y-3= 2/3 (x-4) please show how you solve it
Answer:
y = -3/4x-5/2 and y = 2/3x-1/3
Step-by-step explanation:
y+1 = -3/4(x+2)
y+1 = -3/4x-3/2
y = -3/4x-3/2-1
y = -3/4x-5/2
-----
y-3 = 2/3(x-4)
y-3 = 2/3x-8/3
y = 2/3x-8/3+3
y = 2/3x-1/3
find a rational number that is between 5.2 and 5.5. explain why it is rational.
Answer:
5.3
Step-by-step explanation:
A rational number is a number that can be written as the quotient of two integers.
5.2 and 5.5 are both rational since they can be written as quotients of integers as shown below.
5.2 = 52/10
5.5 = 55/10
5.3 is a number between 5.2 and 5.5, and since 5.3 can be written as 53/10, it is rational.
Answer: 5.3
Answer:
Step-by-step explanation:
rational numbers can be written in form a/b where b≠0
5.2 and 5.5
52/10 and 55/10
so some rational numbers could be
53/10, 54/10
irrational numbers most likely the square root numbers
square them
5.2^2=27.04
5.5^2=30.25
5.2<?<5.5
square everybody
27.04<?²<30.25
so pick a number between 27.04 and 30.25
29 or 30 are 2 numbers
I'll pick 29
?²= 29
square root
?=√29
the irrational number can be √29
it is 5.39 to the hundredth
Question 12
1 pts
Whitney recently created a new smartphone app. As a result of the initial costs and
fees of producing the app, she did not make any money, or profit, selling the app during
the first two months of the app's release. For the first month, Whitney had a loss of
$324. During the second month of sales, she had a loss of $97. She hopes that in the
third month, she will sell enough apps to break even-that is, she hopes to earn enough
money to cover her losses. What is the amount of money Whitney needs to make in the
third month in order to break even with app sales so far?
Answer:
The amount (revenue) she makes in the third month to break even is $97
Step-by-step explanation:
The given parameters are;
The cost of the app = Initial cost + fees for producing the app
The amount she loss in the first month = Cost of the app - revenue = $324
The amount she loss in the second month = Loss from first month - revenue in second month = $324 - revenue in second month = $97
The amount Whitney has to make in the third month to break even is therefore;
The amount she makes in the third month to break even is given by the equation;
Revenue from third month - Loss from second month = 0
Which gives;
The amount she makes in the third month to break even is given by Revenue from third month - $97 = 0
∴ Revenue from third month = $97
The amount (revenue) she makes in the third month to break even = $97
Consider the plot created from the residuals of a line of best fit for a set of data.
Does the residual plot show that the line of best fit is appropriate for the data?
Yes, the points have no pattern.
No, the points are evenly distributed about the x-axis.
No, the points are in a linear pattern.
Yes, the points are in a curved pattern.
Answer:
No, the points are in a linear pattern.
Step-by-step explanation:
Residual plot is a graph that shows the residuals on the vertices. The y-axis has residual values and x-axis has independent variables. The horizontal axis shows the independent variables to determine the best fit for a set. The graph given is in a linear pattern. The random pattern shows that linear model is good fit.
Answer:
C: No, the points are in a linear pattern
Step-by-step explanation:
edg2021
I have been seeing this question with multiple different answers, and no one is sure about anything! All I can say for sure is that IT IS NOT A! So C makes the most sense. B is simply not true, and neither is D, its not curved or evenly distribute.
Simplify the following expression 5(y + 3) + 7(y − 5) + 6
Answer:
12y-14
Step-by-step explanation:
we expand first and doing that we get
5y+15+7y-35+6
12y-14
2(6y-7)
Step-by-step explanation:
5(y+3) + 7(y-5) +6
5y+15+7y-35+6
5y+7y+15-35+6
12y-14
y= -14-12
y= +26
If the coefficient of determination for a data set containing 24 points is 0.5,
12 of the data points must lie on the regression line for the data set.
A. True
O B. False
SUBMIT
Answer:
False
Step-by-step explanation:
False - one has nothing to do with the other. None of the data points can lie on the regression line,
and you can have the coeff. of determination be 0.5.
Two trains leave New York at the same time heading in opposite directions. Train A travels at 4 5 the speed of train one. After seven hours they are 693 miles apart. What was the speed of train A?
Answer:
Speed of train A is 44 miles/hr.
Step-by-step explanation:
Let the speed of train A = [tex]u\ miles/hr[/tex]
Let the speed of train one = [tex]v\ miles/hr[/tex]
Train A travels at [tex]\frac{4}{5}^{th}[/tex] the speed of train one.
i.e.
[tex]u = \dfrac{4}{5}v \\\Rightarrow v =\dfrac{5}{4}u.... (1)[/tex]
Distance traveled = 693 miles
Time taken = 7 hours
They are travelling in opposite directions so the resultant speed will appear to be faster.
Relative speed = [tex]u+v\ miles/hr[/tex]
The trains are 693 miles apart in 7 hours that means they have traveled a total distance of 693 miles in 7 hours with a speed of ([tex]u+v[/tex]) miles/hr.
Using the formula:
[tex]Speed = \dfrac{Distance}{Time}[/tex]
[tex]u+v = \dfrac{693}{7}\\\Rightarrow u+v=99 ...... (2)[/tex]
Putting the value of v using equation (1):
[tex]\dfrac{5}4u+u=99\\\Rightarrow 5u+4u = 99 \times 4\\\Rightarrow 9 u = 99 \times 4\\\Rightarrow u = 11 \times 4 = \bold{44\ miles/hr}[/tex]
Speed of train A is 44 miles/hr.
Patrick deposited $6,875 into a savings account 17 years ago. The account has an interest rate of 4.9% and the balance is currently $15,734.11. How often does the interest compound
Answer:
Quaterly
Step-by-step explanation:
6x-1=11 solve equation
Answer:
x = 2
Step-by-step explanation:
6x-1=11
Add 1 to each side
6x-1+1=11+1
6x = 12
Divide by 6
6x/6 = 12/6
x = 2
Answer:
x = 2Step-by-step explanation:
[tex]6x-1=11 \\\\Collect \: like \:terms\\\\6x = 11+1\\\\Simplify\\\\6x =12\\\\Divide\:both\:sides\:by\:6\\\\\frac{6x}{6} = \frac{12}{6}\\ x = 2[/tex]
The net of a rectangular prism is shown below. What is the total surface area of this prism
Answer:
142 cm^2
Step-by-step explanation:
Okay, we can first break this down into 3 different rectangles.
3 x 5 rectangle
16 x 7 rectangle
3 x 5 rectangle.
From here, we just multiply these out and add them. 15 + 15 + 112 = 142. So our answer is 142 cm^2
Answer:
142 cm²
Explanation:
to find the surface area, you need to find the area of all of the boxes within the image above add them all together.
Starting in the middle row and working from left to right it is,
7×3+7×5+7×3+7×5
21+35+21+35=112
Than the bottom and top box is
3×5+5×3
15+15=30
Than you add both of them together,
112+30=142
what is the greatest common factor of 48,24,and 32
Answer:
8
Step-by-step explanation:
gcf
7 less than the quotient of a number 5 and w in a algebraic expression.
Answer:
5/w -7
Step-by-step explanation:
quotient means division
5/w
less than means it comes after
5/w -7
Answer:
5/w-7
Step-by-step explanation:
First, let's write out "the quotient of a number 5 and w"
The quotient is the result from dividing two numbers. Therefore, we must divide 5 and w.
5/w
Now, let's add on "7 less than". Since it is "less than" it will come after the division. "Less" means subtract. So, subtract 7 from 5/w.
5/w-7
7 less than the quotient of a number 5 and w as an expression is: 5/w-7
Find the value of v in the equation below(in picture)
Answer:
v =3Step-by-step explanation:
[tex]v=\log _7\left(343\right)\\\\\mathrm{Rewrite\:}343\mathrm{\:in\:power-base\:form:}\quad 343=7^3\\\\\log _7\left(7^3\right)=3\log _7\left(7\right)\\\\v=3\log _7\left(7\right)\\\\\mathrm{Apply\:log\:rule}:\quad \log _a\left(a\right)=1\\\\\log _7\left(7\right)=1\\\\v=3\times \:1\\\\=3[/tex]
Question 10(Multiple Choice Worth 1 points) (06.01 LC) Choose the polynomial that is written in standard form.
2x2 + 3x4 + 10x6
4x4 + 6x3 + 10x4
−3x8 + 9x2 + 10x
−7x6 + x3 + 10x8
Answer:
−3x^8 + 9x^2 + 10x
Step-by-step explanation:
A polynomial is in standard form when the exponents of the variable decrease left to right. The only given expression in that form is ...
−3x^8 + 9x^2 + 10x
