The length and width of a rectangle can be expressed as x+3 and x-8 . If the area of the rectangle is 60 square inches , what is the value of x?
Remember that
the area of rectangle is
A=L*W
we have
L=x+3
W=x-8
substitute
A=(x+3)(x-8)
A=60 in2
so
60=(x+3)(x-8)
solve for x
x^2-8x+3x-24=60
x^2-5x-24-60=0
x^2-5x-84=0
solve the quadratic equation using the formula
we have
a=1
b=-5
c=-84
substitute
[tex]x=\frac{-(-5)\pm\sqrt[\square]{-5^2-4(1)(-84)}}{2(1)}[/tex][tex]\begin{gathered} x=\frac{5\pm\sqrt[\square]{361}}{2} \\ \\ x=\frac{5\pm19}{2} \end{gathered}[/tex]the solutions are
x=12 and x=-7 (is not a solution)
therefore
the value of x is 12verifyFor x=12L=12+3=15W=12-8=4Area=15*4=60 in2 -----> is ok55x[78+9]+3 Solve it for me??
first solve for the equation inside the bracket
55×(87)+3
=55×87+3
4785+3
=4788
Simplify 2a x a x 3a + b x 4b
Hello!
We have the following expression:
[tex]2a\cdot a\cdot3a+b\cdot4b[/tex]Let's multiply and simplify it, look:
[tex]6a^3+4b^2[/tex]We multiply a*a*a, so we can rewrite it as a³. The same with b*b as b².
So, the answer in the simplified form is:
6a³ + 4b²
The type and number of fish caught in the Charleston Harbor in March was recorded for a month. The results are recorded in the table below. What is the probability that the next fish caught is a drum or a flounder? Enter a fraction or round your answer to four decimal places
Answer:
0.6275
Explanation:
We were given the following informationL
Flounder = 278
Red Drum = 382
Black Drum = 194
Bluefish = 348
Sea Trout = 159
Total = 278 + 382 +194 + 348 + 159 = 1,361
The probability that the next fish caught is a drum or a flounder is given by:
[tex]\begin{gathered} Probability=\frac{Chances\text{ of event}}{Total\text{ possible outcome}} \\ \\ P(Drum)=P(Red.Drum)+P(Black.Drum) \\ P(Drum)=\frac{382}{1361}+\frac{194}{1361} \\ P(Drum)=\frac{576}{1361} \\ \\ P(Flounder)=\frac{278}{1361} \\ \\ P(Drum\text{ or Flounder})=P(Drum)+P(Flounder) \\ P(Drum\text{ or Flounder})=\frac{576}{1361}+\frac{278}{1361} \\ P(Drum\text{ or Flounder})=\frac{854}{1361} \\ P(Drum\text{ or Flounder})=0.6274797\approx0.6275 \\ P(Drum\text{ or Flounder})=0.6275 \end{gathered}[/tex]Therefore, the probability of the next fish being a Drum or Flounder is: 0.6275
you have an ice cream cone that is 6 in tall with the radius of 2 in the cone is completely filled with ice cream there is a spherical scoop of ice cream on top of the cone with a radius of 3 in how much ice cream do you have in total terms of Pi
Given an ice cream cone,
i.e. the shape is hemispherical top with conical bottom.
So, the volume is given as,
[tex]undefined[/tex]The area of Kamila’s rectangular living room is 2.5 times the area of her square bedroom. The length of the living room is 18 feet and its width is 1.25 times the length of a side of the bedroom.Create a diagram representing Kamila’s living room and her square bedroom. Assign variables to any unknown sides and label the diagram.Find the length of one side of Kamila’s bedroom.In your final answer, include your diagram, and all formulas, equations, and calculations necessary to solve for the length of Kamila’s bedroom.
Answer:
The length of each side of Kamila’s square bedroom is;
[tex]9\text{ feet}[/tex]For the Living room;
[tex]\begin{gathered} A_l=18\times1.25x \\ A_l=22.5x\text{ --------1} \end{gathered}[/tex]For the bedroom;
[tex]\begin{gathered} A_b=x\times x \\ A_b=x^2\text{ -----------2} \end{gathered}[/tex]Recall that the area of Kamila’s rectangular living room is 2.5 times the area of her square bedroom;
[tex]A_l=2.5A_b\text{ ----------3}[/tex]Explanation:
Given that the area of Kamila’s rectangular living room is 2.5 times the area of her square bedroom. The length of the living room is 18 feet and its width is 1.25 times the length of a side of the bedroom.
Recall that the area of a rectangle can be calculated using the formula;
[tex]A=l\times b[/tex]For the Living room;
[tex]\begin{gathered} A_l=18\times1.25x \\ A_l=22.5x\text{ --------1} \end{gathered}[/tex]For the bedroom;
[tex]\begin{gathered} A_b=x\times x \\ A_b=x^2\text{ -----------2} \end{gathered}[/tex]Recall that the area of Kamila’s rectangular living room is 2.5 times the area of her square bedroom;
[tex]A_l=2.5A_b\text{ ----------3}[/tex]substituting equations 1 and 2 into equation 3;
[tex]\begin{gathered} A_l=2.5A_b\text{ ----------3} \\ 22.5x=2.5(x^2) \\ x=\frac{22.5}{2.5} \\ x^{}=9 \\ x=9\text{ feet} \end{gathered}[/tex]Therefore, the length of each side of the square bedroom is;
[tex]9\text{ feet}[/tex]Please help me see solve this problem. This is so confusing
Given that the triangle is right-angled at vertex Q, it follows that,
[tex]m\angle Q=90^{\circ}[/tex]The other two angles' measures are given as,
[tex]\begin{gathered} m\angle R=(5x-39)^{\circ} \\ m\angle S=(2x+31)^{\circ} \end{gathered}[/tex]The Angles Sum Property of a triangle suggests that the sum of the degree measure of the three angles formed by the sides of the triangle at the vertices is always 180.
Applying this in the given triangle QRS,
[tex]m\angle Q+m\angle R+m\angle S=180^{\circ}[/tex]Substitute the values and simplify,
[tex]\begin{gathered} 90^{\circ}+(5x-39)^{\circ}+(2x+31)^{\circ}=180^{\circ} \\ 90+5x-39+2x+31=180 \\ 7x+82=180 \\ 7x=180-82 \\ 7x=98 \\ x=14 \end{gathered}[/tex]Substitute this value to obtain the degree measure of unknown angles as follows,
[tex]\begin{gathered} m\angle R=(5(14)-39)^{\circ}=(70-39)^{\circ}=31^{\circ} \\ m\angle S=(2(14)+31)^{\circ}=(28+31)^{\circ}=59^{\circ} \end{gathered}[/tex]Thus, the measure of angles of the given triangle are,
[tex]\begin{gathered} m\angle Q=90^{\circ} \\ m\angle R=31^{\circ} \\ m\angle S=59^{\circ} \end{gathered}[/tex]Please help I need an answer ASAP!!!!!!!!
The domain is the set of x-values for the points on the graph:
{-5, -3, 1, 2, 3}
a. What is the total amount of food Toby ate over the 10 days? Explain how you got your answer.
SOLUTION
For 10 days, Mario measured the amount of food that his cat Toby ate each day.
The amount he recorded are shown in the table at the right
Graph the results on the line plot
Amount Toby ate each day for 10 days
Amount of food Days
1/ 4 c 2
3/ 8 c 1
1/ 2 c 3
5/ 8 c 3
3/ 4 c 1
TOTAL AMOUNT OF FOOD TOTAL NUMBER OF DAYS
1/ 4 c + 3/ 8 c + 1/2 c + 5/ 8 c + 3/ 4 c = 5/ 2 c = 2 1/2 c 10
What is the total amount of food Toby ate over the 10 days?
Toby ate 2 1/ 2 c over 10 days.
Which of the following best describes the figure with vertices (-8, 2), (4, 14), (16, 2) and(4, -10)? thank
Given:
Vertices (-8, 2), (4, 14), (16, 2) and (4, -10).
Required:
To find the figure that is made by the vertices.
Explanation:
Let A (-8, 2), B(4, 14), C(16, 2) and D(4, -10).
Then find the length of each side by using the distance formula.
[tex]\begin{gathered} AB=\sqrt{(4+8)^2+(14-2)^2} \\ AB=\sqrt{(12)^2+(12)^2} \\ AB=\sqrt{144+144} \\ AB=12\sqrt{2} \end{gathered}[/tex][tex]\begin{gathered} BC=\sqrt{(16-4)^2+(2-14)^2} \\ BC=\sqrt{(12)^2+(-12)^2} \\ BC=\sqrt{144+144} \\ BC=12\sqrt{2} \end{gathered}[/tex][tex]\begin{gathered} CD=\sqrt{(4-16)^2+(-10-2)^2} \\ CD=\sqrt{(-12)^2+(-12)^2}^ \\ CD=\sqrt{144+144} \\ CD=12\sqrt{2} \end{gathered}[/tex][tex]\begin{gathered} AD=\sqrt{(4+8)^2+(-10-2)^2} \\ AD=\sqrt{(12)^2+(-12)^2} \\ AD=\sqrt{144+144} \\ AD=12\sqrt{2} \end{gathered}[/tex]All sides are equal.
AB =BC = CD = AD
We know that the figure in which all sides are equal is called a square.
Final Answer:
Option 2 is the correct answer.
Simplify the expressionSimplify the expression.16(1/2x)4
A bank received 116,714 key chains to give to
customers. Each of the 14 tellers received the same
number of key chains. At most, how many did each
teller receive? How many chains were left over?
Answer:
Each teller would get 8336 keychains, and there would be 10 keychains leftover.
Step-by-step explanation:
[tex]116,714[/tex] ÷ [tex]14 = 8336[/tex] R [tex]10[/tex]
I need help with number ten please and thank you for your help today
We know that there are 3 feet in 1 yard, so:
27 feet < 8 yards.
Express the rule in function notation. (For example, the rule "square, then subtract 5" is expressed as the function f(x) =x^2 - 5.)Add 7, take the square root, then divide by 3.f(x) =
The sentence: add 7 ,take the square root , then divide by 3 is expressed as
[tex]f(x)=\frac{\sqrt{x+7}}{3}[/tex]how to do this problem
Replace x by ( x+ h) , in all x at the equation
So then f(x+h) = (x+h)^2 - 5(x +h) + 2
develope the parenthesis and find
x^2 + 2xh + h^2 -5x -5h + 2
For each of the following statements, say if it is true or if it is false, give acounter-example.1) If 1/4> x then 0.2
1) If 1/4> x then 0.2 It is false. If x=0.19, x would be less than 1/4 (0.25 as a decimal) but 0.19 is not greater than 0.2
2) If x E [0.8; 2] then x E [0.7; 1]
It is false. If x=1.5 it would belong to [0.8; 2] but it does not belong to [0.7; 1].
suppose that $6,200 is invested at 4.9% annual interest rate, compounded monthly. how much money will be in the amount in (A) 11 months? (B) 6 years?
Apply the compound interest formula:
A = P (1 + r/n )^nt
Where:
A = value of investment + interest
P = principal amount = $6,200
r= interest rate ( in decimal form) = 4.9/100 = 0.049
n= number of compounding periods
t= number of years
Replacing:
1 year = 12 months
11 months = 0.92 years
a. 11 months
A = 6,200 (1 + 0.049/12 ) ^ 12 x 0.92
A = 6,200 ( 1.004083333)^ 11
A = $6,484.24
b.For 6 years
A = 6,200 (1 + 0.049/12)^12 x 6
A = $8,314.08
A city's population is currently 189,000. If the population doubles every 55 years, what willthe population be 275 years from now?
ANSWER
[tex]6,048,000[/tex]EXPLANATION
The population doubles every 55 years. This implies that the rate of increase is 200% or 2 times and the time will be measured in terms of 55 years.
We can write an exponential function representing this:
[tex]A=A_0\cdot r^{\frac{t}{55}}[/tex]where t = number of years
r = rate = 2
A0 = initial population of city
We have to solve for A when t = 275.
Therefore:
[tex]\begin{gathered} A=189000\cdot2^{(\frac{275}{55})} \\ A=189000\cdot2^5 \\ A=6,048,000 \end{gathered}[/tex]That will be the population 275 years from now.
Answer two questions about Equations A and B:A. 3(x + 2) = 18B.x+ 2 = 181) How can we get Equation B from Equation A PLEASE HELPPP
we have equation A
3(x+2)=18
Divide both sides by 3
we have
3(x+2)/3=18/3
x+2=6
the answer is the option A
divide both sides by the same non zero constant
PLEASE ANSWERRRRRRRRRRRRR
How many total complex roots does the function have?
Total complex roots the function have is 4
To find the complex roots , we need the check the no.of alternative signs in f(x) and also in f(-x)
Given :
f(x) = x^8 + 2x^5 - 3x + 4
The alternative signs in f(x) is from 2nd term to 4th term
i.e. , 2nd term has '+' , 3rd term has '-' and again 4th term has '+'
So, there are 2 alternative sign changing in f(x) ,
that means it has two positive real roots.
f(-x) = (-x)^8 + 2(-x)^5 - 3(-x) + 4
= x^8 -2x^5 + 3x + 4
The alternative signs in f(-x) is from 1st term to 3rd term
i.e. , 1st term has '+' , 2nd term has '-' and again 3rd term has '+'.
So, there are 2 alternative sign changing in f(-x) ,
that means it has two negative real roots.
The degree of f(x) is 8 , that means it has 8 roots
In that 8 roots , 2 are positive real roots and 2 are negative real roots. Thus remaining 4 roots are complex.
To learn more about complex roots, click the link below
https://brainly.in/question/11187738
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I need help on in the answer to this question
Notice that angle z and the angle with measure 70⁰ is a linear pair. Hence, it follows that they are supplementary (they'll sum up to 180⁰):
[tex]z+70^{\circ}=180^{\circ}[/tex]Solve for z in the equation:
[tex]\begin{gathered} z=180^{\circ}-70^{\circ} \\ \Rightarrow z=110^{\circ} \end{gathered}[/tex]Using the Angles formed by two intersecting chords theorem: If two chords intersect inside a circle, then the measure of the angle formed is one-half the sum of the measure of the arcs intercepted by the angle and its vertical angle , it follows that:
[tex]z=\frac{1}{2}(w+79^{\circ})[/tex]Substitute z=110⁰ into the equation and solve for w:
[tex]\begin{gathered} 110^{\circ}=\frac{1}{2}(w+79^{\circ}) \\ \text{Cross multiply:} \\ \Rightarrow2\times110^{\circ}=w+79^{\circ} \\ \Rightarrow220^{\circ}=w+79^{\circ} \\ \Rightarrow w=220^{\circ}-79^{\circ} \\ \Rightarrow w=141^{\circ} \end{gathered}[/tex]The value of w is 141.
Ms. Mills reported her students' scores on the most recent quiz. Score Number of students 82 2 84 5 99 3 X is the score that a randomly chosen student scored. What is the expected value of X? Write your answer as a decimal.
In order to calculate the expected value of x, we can add the score of all students and divide by the number of students. So we have:
[tex]\begin{gathered} E(x)=\frac{82\cdot2+84\cdot5+99\cdot3}{10} \\ E(x)=88.1 \end{gathered}[/tex]So the expected value of x is 88.1.
A weather researcher compared average monthly temperature data for CapeTown, South Africa, and Luxor, Egypt.Cape TownLuxorMean63.5°F78°FRange21°F29.4°FBased on these data, which statements are true?OA. On average, Cape Town has a higher monthly temperature,However, Luxor's temperatures vary more.O B. On average, Luxor has a higher monthly temperature. However,Cape Town's temperatures vary more.C. On average, Luxor has a higher monthly temperature. Its monthlytemperatures also vary more.D. On average, Cape Town has a higher monthly temperature. Itsmonthly temperatures also vary more.
Given
average monthly temperature data for Cape Town, South Africa, and Luxor, Egypt.
Find
Which statement is true?
Explanation
As we know that mean is given by the sum of the observations divided by the number of observations.
Range is the difference between highest and lowest .
so, considering the mean and range concept , it is found that the correct option is C.
Final Answer
The correct option is C that is On average, Luxor has a higher monthly temperature. Its monthly temperatures also vary more.
y = (x – 3)^2 Vertex? (-3.0) (3.0) (0.3) (0, -3)
*Write an equation to represent the table of values below.
First, we have to find the slope.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Let's replace the points (-10,-11) and (-8,-9).
[tex]m=\frac{-9-(-11)}{-8-(-10)}=\frac{-9+11}{-8+10}=\frac{2}{2}=1[/tex]Then, we use the point-slope formula to find the equation
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \end{gathered}[/tex]Let's replace the point (-8,-9) and the slope 1.
[tex]\begin{gathered} y-(-9)=1(x-(-8)) \\ y+9=x+8 \\ y=x+8-9 \\ y=x-1 \end{gathered}[/tex]Hence, the equation that represents the table is
[tex]y=x-1[/tex]Graph a line trough the given point with the given slope. Point:(4, 4) slope ( -4/3
Given:
point =(4,4) slope(m)=-4/3
x₁=4 y=4
We find the intercept
substitute into y=mx + b
4=4(-4/3)+ b
4 = -16 /3 + b
4+16/3 = b
[tex]\frac{12+16}{3}=b[/tex][tex]b=\frac{28}{3}[/tex]The equation can be form by substituting the value of m and b into y=mx+b
[tex]y=-\frac{4}{3}x+\frac{28}{3}[/tex]To be able to sketch the graph, we need two points, the x and y-intercept.
To find the y-interpet, substitute x=0 into the equation
y = 28/3
Hence, the y-intercept is (0, 9.3)
To find the x-intercept, put y=0 and solve for x
[tex]\begin{gathered} 0=-\frac{4}{3}x+\frac{28}{3} \\ \\ \frac{4}{3}x=\frac{28}{3} \\ \\ x=\frac{28}{3}\times\frac{3}{4} \\ x=\frac{28}{4} \end{gathered}[/tex]The x-intercept is (7,0)
So we can now sketch the graph
Write an equation that could be used to solve for x. 7% – 5 6x + 10 8 See where to Hell
Both angles are alternate exterior angles.
Since both parallel lines are crossed by a transversal, alternate exterior angles are equal:
7x-5=6x+10
Can u help me, click this screenshot pls help me
Using the definition of proportional relationships, it is found that:
1. The number is proportional, and the table is completed at the end of the answer.
2. The number is proportional, and the table is completed at the end of the answer.
3. The left relation is proportional.
Proportional relationshipsA proportional relationship is defined by a function in which the output variable y is given by the multiplication of the input variable x and the constant of proportionality k, by the equation presented as follows:
For item 1, the relationship is given as follows:
y = 225x.
Hence the numeric values are:
x = 1: y = 225.x = 2: y = 450.x = 3: y = 675.x = 4: y = 800.For item 2, the relationship is given as follows:
y = 750x.
Hence the numeric values are:
x = 1: y = 750.x = 2: y = 1500.x = 3: y = 2250.x = 4: y = 3000.In item 3, it is found that:
The left table is a proportional relationship, as 146/2 = 292/4 = 584/8.The right table is not a proportional relationship, as 150/2 is different of 320/4.More can be learned about proportional relationships at https://brainly.com/question/10424180
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Find the slope of the line that passes through (3,11) and (7, 10)
the slope of the line will be:
[tex]m=\frac{11-10}{3-7}=-\frac{1}{4}[/tex]Write each term needed to find the sum and then find the sum.
Given the sum:
[tex]\sum ^5_{i\mathop=0}(i-3)^2[/tex]We will write each term needed to find the sum.
We will substiute with ( i = 1, 2, 3, 4, 5 ) into the given expression.
There are five terms as follows:
[tex]\begin{gathered} a_1=(1-3)^2=(-2)^2=4 \\ a_2=(2-3)^2=(-1)^2=1 \\ a_3=(3-3)^2=(0)^2=0 \\ a_4=(4-3)^2=(1)^2=1 \\ a_5=(5-3)^2=(2)^2=4 \end{gathered}[/tex]The sum will be =
[tex]\sum ^5_{i\mathop=1}(i-3)^2=4+1+0+1+4=10[/tex]Suppose you have 25 socks in a drawer. 10 socks are white, 8 socks are black, and the rest are brown. What is the probability that if you randomly select a sock from the drawer that it will still be black. Round your answer to two decimal places
Given data:
Total number of socks: 25
10 white socks
8 black socks
7 brown socks
Probability select a black sock:
[tex]\begin{gathered} P(B)=\frac{\#\text{black socks}}{\#total\text{ of socks}} \\ \\ P(B)=\frac{8}{25}=0.32 \end{gathered}[/tex]Then, the probability that if you randomly select a sock from the drawer that it will still be black is 0.32