SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Represent the sides of the rectangle
Let the length be represented by l
Let the width be represented by w
STEP 2: Interpret the statements in the question.
[tex]\begin{gathered} length\text{ is 1m more than the double of the width:} \\ double\text{ of the width}\Rightarrow2w \\ 1m\text{ more than the double}\Rightarrow2w+1 \\ \therefore l=2w+1 \end{gathered}[/tex]STEP 3: Equate the area of the rectangle to given measure
[tex]\begin{gathered} Area=length\times width \\ length=2w+1,width=w \\ Area=(2w+1)\cdot w=28 \\ By\text{ simplification,} \\ w(2w+1)=28 \end{gathered}[/tex]STEP 4: Solve for the width
[tex]\begin{gathered} w(2w+1)=28 \\ By\text{ expansion,} \\ 2w^2+w=28 \\ Subtract\text{ 28 from both sides} \\ 2w^2+w-28=28-28 \\ 2w^2+w-8=0 \end{gathered}[/tex]STEP 5: Solve the equation using quadratic formula
[tex]quadratic\text{ formula}\Rightarrow\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]From the equation,
[tex]a=2,b=1,c=-28[/tex]By substitution,
[tex]\begin{gathered} w_{1,\:2}=\frac{-1\pm\sqrt{1^2-4\cdot\:2\left(-28\right)}}{2\cdot\:2} \\ \sqrt{1^2-4\times2(-28)}=15 \\ By\text{ substitution,} \\ w_{1,\:2}=\frac{-1\pm \:15}{2\cdot \:2} \\ \mathrm{Separate\:the\:solutions} \\ w_1=\frac{-1+15}{2\cdot \:2},\:w_2=\frac{-1-15}{2\cdot \:2} \\ w=\frac{-1+15}{2\times2}=\frac{14}{4}=\frac{7}{2}=3.5 \\ w=\frac{-1-15}{2\cdot\:2}=\frac{-16}{4}=-4 \end{gathered}[/tex]Since the width cannot be negative, this means that the value of the width is 3.5m
STEP 6: Solve for the length
By substitution into the formula in step 2, we have:
[tex]\begin{gathered} l=2w+1 \\ l=2(3.5)+1=8 \\ l=8 \end{gathered}[/tex]Hence,
length = 8m
width = 3.5m
WILL MARK BRAINLIEST Rectangle PQRS is shown above. Point C is the center of the rectangle.Maggle claims that there are transformations that preserve the length of the rectangle's sides. Which of the following transformations could be used to support Maggie's claim? select all that apply1.) a translation of 10 units to the right2.) a rotation of 90' clockwise about vortex Q3.) a reflection over the side RS4.) a diation of scale factor 1 through contor5.) a vertical stretch of scale factor 2 through contor C
With the given options;
(1) A translation of 10 units to the right will only map the rectangle onto a different location, but the lengths would remain as it were
(3) A reflection over the side RS will turn the rectangle into a mirror reflection of itself, and this means the sides remain the same measurement but is now being observed from the opposite side (but top now bwcomes bottom and vice versa).
(4) A dilation of scale factor 1 through center
Classify the following triangle as acute, obtuse, or rightO A. AcuteO B. ObtuseOc. RightOD. None of theseSUBMIT
Given:
Triangle is given with the angles.
Given triangle is Acute
A rocket is launched by Team Flash from the ground on Earth-73. The rocket passes a sensor at a height of5760 feet after 8 seconds and lands back on Earth-73 after 53 seconds.Write an equation for the height of the rocket, h, in feet as a function of the number of seconds, t, since therocket was launched.Round to 3 decimal places as needed.After how many seconds will the rocket reach its maximum height?Round to 3 decimal places as needed.What is the maximum height in feet that the rocket reaches?Round to 3 decimal places as needed.
We know two points of the trajectory of the rocket:
1) A height of 5760 ft at time t=8 seconds after launch.
2) A height of 0 ft (landing) at time t=53 seconds after launch.
We also know that the initial position was a height of 0 ft at t=0 seconds.
So we have 3 points to write the equation, that will be a quadratic equation for this kind of trayectory.
As we know we have roots at t=0 and t=53, we can start writing it as:
[tex]h(t)=a(t-0)(t-53)=at(t-53)[/tex]We have one point left, (t,h) = (8, 5760), to find the parameter "a". We can replace t and y in the equation and solve as:
[tex]\begin{gathered} h(t)=at(t-53) \\ 5760=a\cdot8\cdot(8-53) \\ 5760=a\cdot8\cdot(-45) \\ 5760=a\cdot(-360) \\ a=\frac{5760}{-360} \\ a=-16 \end{gathered}[/tex]Then we can write the equation as:
[tex]h=-16t(t-53)=-16t^2+848t[/tex]We can graph it as:
In this kind of trajectories, the maximum height is reached halfway between the launch and the landing.
For any function, we can find the maximum of minimums deriving the function and equal it to 0. We will do it for this function:
[tex]\begin{gathered} \frac{dh}{dt}=-16(2t)+848=0 \\ -32t+848=0 \\ 32t=848 \\ t=\frac{848}{32} \\ t=26.5 \end{gathered}[/tex]The maximum height is reached at time t=26.5 seconds.
Now we can calculate the height at t=26.5 seconds, the maximum height, as:
[tex]\begin{gathered} h(26.5)=-16(26.5)^2+848(26.5) \\ h(26.5)=-16\cdot702.25+22472 \\ h(26.5)=-11236+22472 \\ h(26.5)=11236 \end{gathered}[/tex]Answer:
a) The equation is h(t) = -16t²+848t
b) The maximum height is reached at time t=26.5 seconds.
c) The maximum height is 11236 ft.
hello can u help me please5.Admission to the Basketball Hall of Fame in Springfield is $5.00 per student. A group of students bought admission tickets. One student spent an extra $9.00 for a poster. The total amount they spent was $34.00. How many students were in the group?a.4b.5c.6d.7
Given:
The price per student for the admission, m=$5.
Extra amount spent by a student, c=$ 9.
Total amount spent, T=$34.
Let x be the number of students. Then, the expression for the total amount is,
[tex]T=mx+c[/tex]Substitute values and solve for x.
[tex]\begin{gathered} 34=5x+9 \\ 34-9=5x \\ 25=5x \\ x=\frac{25}{5} \\ x=5 \end{gathered}[/tex]Therefore, the number of students is 5.
Option (b) is correct.
what is the slope of the line described by 5x+7y=19
Answer:
-5/7
Explanation:
Given the equation 5x+7y = 19
The standard form of an equation is y = mx+c
m is the slope
c is the intercept of a line
Make y the subject of the formula from the given equation
5x+7y = 19
7y = -5x + 19
Divide through by 7
7y/7 = -5x/7 + 19/7
y = -5/7 x + 19/7
Comparing with general formula;
mx = -5/7 x
m = -5/7
Hence the slope of the line is -5/7
determine whether the equation below has a one solutions, no solutions, or an infinite number of solutions. afterwards, determine two values of x that support your conclusion. 4(x+4) = 4x+16the equation has ____ solutions.a value of x that makes the equation true is __,which when simplified makes the equation turn into____=_____.a value of x that makes the equation false is____, which when simplified makes the equation turn into ___=___.
4(x+4) = 4x+16
Apply distributive property:
4(x)+4(4)= 4x+16
4x+16=4x+16
Add and subtract alike terms
4x-4x= 16-16
0=0
Since x can have many values, it has an infinite number of solutions.
we can replace x by 1, by 3, by 2 and the equality will remain.
the equation has an infinite number of solutions.
find the slope of the line through the points (-6,5) and (3, -2)
We have to find the slope of the line that pass through points P1=(-6,5) and P2=(3,-2).
We can calculate it as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{-2-5}{3-(-6)}=\frac{-7}{9}=-\frac{7}{9}[/tex]Answer: the slope of the line is m = -7/9
Last year, Emma went bowling several times and earned an average score of 130 points. This
year, after taking a class at school, she improved her score to an average of 234 points. What
is the percent of increase in Emma's average score?
Answer:
80%
Step-by-step explanation:
234-130
=104
(n×p)×100=answer
(130×p)÷100= 10
(130 × p) ÷ 100=104
(130 × p) ÷ 100) × 100 = 104 × 100
130p = 10400
130p ÷ 130 = 10400 ÷ 130
p = 80%
My dog got hurt and needed surgery,so I had to use my credit card to pay the vet bill. His surgery costed me $5,323.21. If my monthly interest rate is 1.42%, how much is my finance charge for the first billing cycle?
Answer:
$75.59.
Explanation:
• Cost of the surgery = $5,323.21
,• Monthly interest rate = 1.42%
A finance charge is a fee charged for the use of a credit card. A billing cycle is usually between 28 to 31 days, i.e. a month.
To find the finance charge, multiply the interest rate by the cost of surgery.
[tex]\begin{gathered} \text{Fnance Charge}=1.42\%\text{ of \$}5,323.21 \\ =\frac{1.42}{100}\times5,323.21 \\ =\$75.59 \end{gathered}[/tex]The finance charge for the first billing cycle is $75.59.
Yovanni went on a hike. He climbed 4/5 of mile in 1/4 of an hour. What was his hiking speed in miles per hour
We have the following information
Distance
[tex]d=\frac{4}{5}\text{miles}[/tex]Time
[tex]t=\frac{1}{4}\text{hours}[/tex]To find his hiking speed we need to use the formula for speed:
[tex]s=\frac{d}{t}[/tex]where d is the distance and t is the time.
We substitute our values into the formula:
[tex]s=\frac{\frac{4}{5}\text{miles}}{\frac{1}{4}\text{hours}}[/tex]In this type of divisions, we multiply the extremes of the expression (4 by 4) and this will be our numerator. Also, we multiply the numbers in the middle (5 by 1) and this will be our denominator:
[tex]s=\frac{4\times4}{5\times1}=\frac{16}{5}=3.2\text{ mi/h}[/tex]Answer: 3.2 mi/h
what is the graph of x= 1 ?
The given equation x = 1 represents a horizontal lines that passes thourgh (1, 0).
Hence, the graph isThe answer is D.Find the equation of the line through the given points. (-8, 6) and (-8, 0)
The equation of a line is typically written as y=mx+b, where m is the slope and b the y-intercept.
The slope can be calculated like this:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]In this case you have x1=-8, y1=6, x2=-8 and y2=0. Replace this values on the slope formula
[tex]m=\frac{0-6}{-8-(-8)}=\frac{-6}{-8+8}=\frac{-6}{0}\text{ the slope is undefined}[/tex]An undefined slope indicates that you have a vertical line parallel to the y-axis.
This line will pass through all points in the plane with an x-coordinate=constant (c). In this case this constant will be -8
The equation is written in the form x = c, then the equation of this line will be
[tex]x=-8[/tex]Calculate the maximum number of cylindrical paint cans that carvers auto custom can stock if the paint comes in a 2-pack hazmat box that mesures 15 inches by 7 inches by 6 inches
The volume of Hazmat box is,
[tex]v=15\times7\times6[/tex][tex]v=630in^3[/tex]Convert inches to feet ,
[tex]undefined[/tex]The volume of the warehouse when half of the warehouse is painted with cams and rims is.
[tex]V=\frac{8000}{2}\times20ft^3[/tex][tex]V=80,000ft^3[/tex]V11, -14 and w -19, 15 are the influence of the line segment what is the midpoint M of that line segment right the coordinates as decimals are integers
Step 1: Problem
Mid-point of V ( 11, -14 ) and W ( -19, 15 )
Step 2: Concept
[tex]\begin{gathered} coordinatesofthe\text{mid}-po\text{ int = ( x , y )} \\ x\text{ = }\frac{x_1+x_2}{2} \\ y\text{ = }\frac{y_1+y_2}{2} \end{gathered}[/tex]Step 3: Method
Substitute the given data to find the coordinates of the mid-point
Given data
x1 = 11
y1 = -14
x2 = -19
y2 = 15
[tex]\begin{gathered} x\text{ = }\frac{-\text{ 19 + 11}}{2}\text{ = }\frac{\text{ -}8}{2}\text{ = -}4 \\ y\text{ = }\frac{15\text{ +(-14)}}{2}\text{ = }\frac{1}{2}\text{ = }0.5 \end{gathered}[/tex]Step 4: Final answer
The coordinates of the mid-point = ( -4 , 0.5 )
Why is x² + 36 NOT factorable? In other words, why is it prime? What are twodetails that draw you to this conclusion?
SOLUTION:
Step 1:
In this question, we are given the following:
a) Why is x² + 36 NOT factorable?
b) In other words, why is it prime?
c) What are two details that draw you to this conclusion?
Step 2:
The details of the solution are as follows:
[tex]\begin{gathered} a)\text{ x}^2\text{ + 36 is not factorizable under of field of integers Z,} \\ since\text{ it cannot be expressed as product of two squares} \end{gathered}[/tex]b) In other words, why is it prime?
It is a prime polynomial because a prime polynomial is one that cannot be factored into the product of two polynomials, using integer values.
-
c) What are two details that draw you to this conclusion?
1) You can factor a difference of squares, but not a sum of squares.
2) A prime polynomial is one that cannot be factored into the product of two polynomials, using integer values.
-
2. Which answer of
the following is an
example of a SUM?
A 12-3=9
B 12+3=15
C 12×3=36
D 12÷3=4
Answer: B : 12+3=15
Step-by-step explanation:
A sum is the answer of an addition problem
Solve 431 ÷ 3 on paper. You'll see that there is a remainder.
What digit in the ones place would give us no remainder?
Answer:
2 in the ones place.
Step-by-step explanation:
431/3 won't work because 4+3+1=NOT multiple of 3.
The closest number in the ones place that will make it an integer is 2, because 4+3+2=multiple of 3
Answer:
2, 5, or 8.
Step-by-step explanation:
There is actually a trick to this one.
---
If the digits in a number add up to a multiple of 3, then the whole number is divisible by 3.
For example:
843
Add the digits:
8+4+3=15
You could add the digits again:
1+5=6
Six is a multiple of 3, so 843 is a multiple of 3.
---
Now your number was 431.
4+3+1=8
8 is not divisible by 3, so 431 is not divisible by 3.
432, 435, and 438 would work in this situation.
PLEASE MARK AS BRANLIEST!!A total of $54,000 is invested at an annual interest rate of 5.25%. Find the balance after 6 years if it is compounded monthly.
Using the compound interest formula:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where:
A = Amount
P = Principal = 54000
r = Interest rate = 5.25% = 0.0525
n = Number of times the interest is compounded per year = 12
t = Number of years = 6
So:
[tex]\begin{gathered} A=54000(1+\frac{0.0525}{12})^{12\cdot6} \\ A\approx73943.18 \end{gathered}[/tex]Answer:
The balance is $73943.18
There are a total of 37800 members at club A and the ratio of club A to club B is 20:13. The ratio of 40 and older group is 70% of club B the ratio of under 40members in club A to club B is 176:39
I NEED HELP QUICKLY ITS DUE 8PM AND I HAVE OTHER HOMEWORK TO DO.
Answer:
$5625
Explanation:
The equation for your earning y = 150x - x² is the equation of a parabola, so the maximum point of the parabola has a coordinate x equal to -b/2a
Where b is the number beside the x and a is the number beside the x²
In this case, a is -1 and b is 150, so the x-coordinate of the maximum is:
[tex]x=\frac{-b}{2a}=\frac{-150}{2(-1)}=\frac{-150}{-2}=75[/tex]With the value of x, we can calculate the value of y, so:
y = 150x - x²
y = 150(75) - (75)²
y = 11250 - 5625
y = 5625
Therefore, the maximum amount that you can earn is $5625.
Its says for pi do 3.14 and round to tje nearest hundredth.
EXPLANATION
Measure of the rectangular window:
length = 24 inches
width = 18 1/4 inches = 73/4 inches = 18.25 inches
The area is given by the following relationship:
[tex]\text{Area}_{wi\text{ndow}}=\text{length}\cdot\text{width}=24\cdot18.25=438in^2[/tex]The picture is as follows:
Find the 5and term of the arithmetic sequence 5, 9, 13,
Notice that:
[tex]\begin{gathered} 9-5=4, \\ 13-9=4. \end{gathered}[/tex]Since the sequence is arithmetic then, the nth term has the following form:
[tex]a_n=5+4\cdot(n-1)\text{.}[/tex]Therefore:
[tex]a_{52}=5+4(51)=5+204=209.[/tex]Answer: 209.
Find the perimeter of the shaded region of this composite figure .You can use 3.14 for pi.llAlso round the answer to the nearest hundreth.
ANSWER
18.58 m
EXPLANATION
We need to find the perimeter of the shaded region of the figure.
The figure is made up of a rectangle with the cut out of a semi-circle, so, to find the perimeter, we will subtract the perimeter of the semi-circle (without the diameter) from that of the rectangle.
The perimeter of the rectangle is:
P = 2(L + B)
where L = length = 8 m
B = breadth = 6 m
So, the perimeter of the rectangle is:
P = 2(8 + 6) = 2 * 14
P = 28 m
The perimeter (circumference) of the semi-circle (without the diameter) is:
C = π * R
where R = radius of the semicircle
The diameter is 6 m, so the radius is:
R = D / 2 = 6 / 2 = 3 m
So, the circumference of the semicircle is:
C = 3.14 * 3
C = 9.42 m
So, the perimeter of the composite figure is:
P = 28 - 9.42
P = 18.58 m
That is the answer.
SHOW THE PROPORTION YOU ARE SETTING UP.Four out of 10 adults in a certain city buy their drugs at large drug stores. If this city has 34,000 adults, how many of these adults would you expectto buy their drugs at large drug stores?
You know that 4 out of 10 adults buy their drugs at large drug stores. To calculate the value of the proportion you have to divide 4 by 10
[tex]\begin{gathered} p=\frac{4}{10} \\ p=0.4 \end{gathered}[/tex]The city has n=34,000 adults, to determine the expected number of adults that buy at large drugstores, you have to multiply the total number of adults by the proportion:
[tex]E(X)=np[/tex]n=34,000 and p=0.4
[tex]\begin{gathered} E(X)=34000\cdot0.4 \\ E(X)=13600 \end{gathered}[/tex]Out of the 34,000 you could expect 13,600 adults to buy at large drug stores.
List the potential rational zeros of the polynomial function. Do not find the zeros.f(x) = -4x^4 + 2x^2 - 3x + 6A± , ± , ± , ± , ± 1, ± 2, ± 3, ± 4, ± 6B± , ± , ± , ± , ± 1, ± 2, ± 3, ± 6C± , ± , ± , ± , ± , ± 1, ± 2, ± 4D± , ± , ± , ± , ± , ± 1, ± 2, ± 3, ± 6
Answer:
±1,±2,±3 and ±6
Explanation:
We make use of the Rational Zero theorem below:
If a polynomial has integer coefficients, then every rational zero of f(x) has the form p/q where p is a factor of the constant term and q is a factor of the leading coefficient.
Given the function:
[tex]f\mleft(x\mright)=-4x^4+2x^2-3x+6[/tex]The steps to follow are given below.
Step 1: Determine all factors of the constant term and all factors of the leading coefficient.
The constant term is 6: Factors are ±1,±2,±3 and ±6
The leading coefficient is -4: Factors are ±1,±2, and ±4.
Step 2: Determine all possible values of p/q.
[tex]\begin{gathered} \frac{p}{q}=\pm\frac{1}{1},\pm\frac{2}{1},\pm\frac{2}{2},\pm\frac{3}{1},\pm\frac{6}{1},\pm\frac{6}{2} \\ =\pm1,\pm2,\pm1,\pm3,\pm6,\pm3 \\ =\pm1,\pm2,\pm3,\pm6 \end{gathered}[/tex]Therefore, the potential zeros are: ±1,±2,±3 and ±6.
i inserted a picture of the question can you make it very shorta -4 b 8c 4d -8
a. -4
Explanation
the average rate of change is given by:
[tex]\begin{gathered} rateofch=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1} \\ where \\ P1(x_1,y_1)\text{ is the start point} \\ P2(x_2,y_2)\text{ is the end point} \end{gathered}[/tex]then
Let
[tex]\begin{gathered} x_1=1 \\ f(x_1)=0 \end{gathered}[/tex]and
[tex]\begin{gathered} x_2=3 \\ f(x_2)=-8 \end{gathered}[/tex]hence
P1(1,0)
P2(3,-8)
now, replace in the formula
[tex]\begin{gathered} rateofch=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1} \\ \text{rate of change=}\frac{-8-0}{3-1}=\frac{-8}{2}=-4 \\ \text{rate of change=-}4 \end{gathered}[/tex]therefore, the answer is
a. -4
I hope th
A student finished 45 of her homework problems in class. If the ratio of problems shefinished to problems she still had left was 9:4, how many homework problems did shehave total?
The ratio between the amount of problems she finished and the problems she still had left is given by the division between those amount. Since this ratio is 9:4, if we call the amount of homework she still has left as x, we have the following relation
[tex]\frac{45}{x}=\frac{9}{4}[/tex]Solving for x, we have
[tex]\begin{gathered} \frac{45}{x}=\frac{9}{4} \\ \frac{x}{45}=\frac{4}{9} \\ x=\frac{4}{9}\cdot45 \\ x=\frac{4\cdot45}{9} \\ x=\frac{180}{9} \\ x=20 \end{gathered}[/tex]She still has 20 problems left to solve. The total amount of problems is given by the sum between the problems she already finished and the problems left to solve, then, the total amount of problems is
[tex]45+20=65[/tex]65 problems.
HELP. i am so confused. the question is in the picture
1) If we consider that y=f(2x) is a transformed version of y=f(x) then we can set a t-table and plug for the given point (16,8) the x-coordinate x=16
[tex]\begin{gathered} (16,8)-\longrightarrow f(x)-->y=\frac{1}{2}x \\ \end{gathered}[/tex]Since the new function, f(2x) requires us to divide the input by 2 to compensate
1. Consider the following functions. f(x) = 3x2 + x + 2 g(x) = 4x2 + 2(3x – 4) h(x) = 5(x2 - 1) a. Find f (x) - g(x). b. Find g(x) - h(x).
a.
Let's write function g(x) better:
[tex]g(x)=4x^2+2(3x-4)=4x^2+6x-8[/tex]Now we can do the substraction easier
[tex]f(x)-g(x)=(3x^2+x+2)-(4x^2+6x-8)_{}[/tex][tex]f(x)-g(x)=3x^2+x+2-4x^2-6x+8[/tex][tex]f(x)-g(x)=(3-4)x^2+(1-6)x+2^{}+8[/tex][tex]f\mleft(x\mright)-g\mleft(x\mright)=-x^2-5x+10[/tex]That's answer a
b.
We write h(x) better too:
[tex]h(x)=5(x^2-1)=5x^2-5[/tex]And do the same as before:
[tex]g(x)-h(x)=(4x^2+6x-8)-(5x^2-5)[/tex][tex]g(x)-h(x)=4x^2+6x-8-5x^2+5[/tex][tex]g(x)-h(x)=(4-5)x^2+6x-8+5[/tex][tex]g(x)-h(x)=-x^2+6x-3[/tex]That's answer b
What percentage of 371 is 120?
This question is about percentages.
To know which percentage of 371 is 120, we just have to divide
[tex]\frac{120}{371}=0.32[/tex]Then, we multiply by 100 to express it in percentage
[tex]\text{0}.32\cdot100=32[/tex]Therefore, 120 represents 32% of 370, approximately.