Answer: 4th Quadrant
Step-by-step explanation:
When plotted, the point (2, -4) lies in the 4th quadrant.
how to find two consecutive whole numbers that square root 40 lies between
First, we need to identify the square root of the fisrt squared numbers:
[tex]\begin{gathered} \sqrt{1}=\text{ 1} \\ \sqrt{4}=2 \\ \sqrt{9}=3 \\ \sqrt{16}=4 \\ \sqrt{25}=5 \\ \sqrt{36}=6 \\ \sqrt{49}=7 \\ \sqrt{64}=8 \end{gathered}[/tex]Since 40 is a number between 36 and 49, we can say that the square root of 40 is between 6 and 7. So:
[tex]6<\sqrt{40\text{ }}<7[/tex]The height of the Empire State Building is 1250 feet tall. Your friend, who is 75 inches tall, is standing nearby and casts a shadow that is 33 inches long. What is the length of the shadow of the Empire State Building? Please help me draw triangles
The length of the building's shadow = 550.66 ft
Explanations:The height of the Empie State Building = 1250 feet
The friend's height = 75 inches
The length of the friend's shadow = 33 inches
[tex]\frac{Actual\text{ height of the friend}}{\text{Length of the friend's shadow}}=\text{ }\frac{Height\text{ of the building}}{\text{Length of the building's shadow}}[/tex][tex]\begin{gathered} \frac{75}{33}=\text{ }\frac{1250}{\text{Length of the building's shadow}} \\ 2.27\text{ = }\frac{1250}{\text{Length of the building's shadow}} \\ \text{Length of the building's shadow = }\frac{1250}{2.27} \\ \text{Length of the building's shadow = }550.66\text{ f}et \end{gathered}[/tex]Trying to solve this problem kind of having a hard time
Future Value of an Investment
The formula to calculate the future value (FV) of an investment P for t years at a rate r is:
[tex]FV=P\mleft(1+\frac{r}{m}\mright)^{m\cdot t}[/tex]Where m is the number of compounding periods per year.
Leyla needs FV = $7000 for a future project. She can invest P = $5000 now at an annual rate of r = 10.5% = 0.105 compunded monthly. This means m = 12.
It's required to find the time required for her to have enough money for her project.
Substituting:
[tex]\begin{gathered} 7000=5000(1+\frac{0.105}{12})^{12t} \\ \text{Calculating:} \\ 7000=5000(1.00875)^{12t} \end{gathered}[/tex]Dividing by 5000:
[tex]\frac{7000}{5000}=(1.00875)^{12t}=1.4[/tex]Taking natural logarithms:
[tex]\begin{gathered} \ln (1.00875)^{12t}=\ln 1.4 \\ \text{Operating:} \\ 12t\ln (1.00875)^{}=\ln 1.4 \\ \text{Solving for t:} \\ t=\frac{\ln 1.4}{12\ln (1.00875)^{}} \\ t=3.22 \end{gathered}[/tex]It will take 3.22 years for Leila to have $7000
Write the rate as fraction in simplest form 22 gallons of pest rifles for 8 acres of crops
Since the given rate is 22 gallons of pest for 8 acres of crops, then
We need to find how many acres per gallon
Then we will divide 22 acres by 8 gallons to find the rate
[tex]rate=\frac{22}{8}[/tex]Divide up and down by 2 to simplify
[tex]\begin{gathered} rate=\frac{\frac{22}{2}}{\frac{8}{2}} \\ \\ rate=\frac{11}{4} \end{gathered}[/tex]The answer is:
The rate is 11/4 gallon per acre (2 3/4)
Approximate the measure in degrees of angle in a right triangle given that the side adjacent to angle is 5 and the hypotenuse of the triangle is 9 units. (Round your answer to one decimal place.)
Measure of perpendicular side for the given right triangle with adjacent side 5units and hypotenuse 9 unit is equal to 7.5 units(Upto one decimal place).
As given in the question,
In a right triangle,
Measure of a adjacent side = 5units
Measure of a hypotenuse = 9units
Let x be the measure of the perpendicular side
Using Pythagoras theorem we get,
(Hypotenuse)² = (Adjacent side)² +(perpendicular side)²
⇒ (9)² = (5)² + (x)²
⇒ (x)² = (9)² - (5)²
⇒x² = 81 -25
⇒ x = √56
⇒ x= 7.4833..
⇒x = 7.5 units(round upto one decimal)
Therefore, measure of perpendicular side for the given right triangle with adjacent side 5units and hypotenuse 9 unit is equal to 7.5 units(Upto one decimal place).
The complete question is :
Approximate the measure in degrees of angle in a right triangle given that the side adjacent to angle is 5 and the hypotenuse of the triangle is 9 units. Find the measure of perpendicular side.(Round your answer to one decimal place.)
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Find the volume of the figure. 6 cm. 6 cm. 1 8 cm. 10 cm. Volume of the prism cm3
The volume of the pyramid is 144 cm³
Explanations:The volume of a prism is given by the formula:
V = BH
where B is the base area
and H is the height
The base of the the pyramid is the lateral triangle, and the area is given by the formula:
B = 0.5 x b x h
b = 8 cm
h = 6 cm
B = 0.5 x 8 x 6
B = 24 cm²
The volume is then:
V = BH, where H = 6 cm
V = 24 x 6
V = 144 cm³
what is the equation of the line with x-intercept (6,0) and y-intercept (0, 2)
Answer:
3y=6-x
Explanation:
The slope-intercept form of a line is y=mx+b.
First, we determine the slope(m) of the line.
[tex]\begin{gathered} m=\frac{2-0}{0-6} \\ =-\frac{2}{6} \\ m=-\frac{1}{3} \end{gathered}[/tex]Since the y-intercept, b=2
The equation of the line is:
[tex]\begin{gathered} y=-\frac{1}{3}x+2 \\ y=\frac{-x+6}{3} \\ 3y=6-x \end{gathered}[/tex]Home Liquidators marks up its merchandise 35% on cost. What is the company’s equivalent markup on selling price?
Home Liquidators marks up its merchandise 35% on cost, the company's equivalent markup on the selling price is 25.9%.
What is an equivalent value?An equivalent value represents equality.
Equivalent values show that two paired mathematical expressions are equal.
How is the markup on the selling price determined?The markup on the selling price can be derived by equating the markup on cost with the markup on the selling price as follows:
Markup on cost = 35%
Cost = 100%
Selling price = 135%
Markup on selling price = 25.9% (0.35/1.35 x 100)
Thus, we can describe Home Liquidators' markup on the selling price as equivalent to 25.9% or simply 26%.
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Fill in the missing number to complete the linear equation that gives the rule for this tablex: 4, 5, 6, 7y: 32, 40, 48, 56y = ?x
according to the equation and information given we can see that the equation is in the form
[tex]y=kx[/tex]in which k is the constant of proportionality
use one of the points to find the constant
[tex]\begin{gathered} 32=k(4) \\ k=\frac{32}{8} \\ k=8 \end{gathered}[/tex]replace withone of the points to see if its true in all the points
[tex]\begin{gathered} 40=8\cdot5 \\ 40=40 \end{gathered}[/tex]according to this the equation for the table will be
[tex]y=8x[/tex]Evaluate the following expression.
1-4x (-3) +8 x (-3)
Answer:
-11
Step-by-step explanation:
1-4x(-3)+8x(-3)=
first you multiple
-4x(-3)=12
8x(-3)= -24
bring down the 1
1+12-24=
now we add
13-24=
then subtract and we get
-11
write an equation in slope -intercept form for the line with y- intercept -1 and slope -3/2
The line equation in the slope -intercept form can be written as,
[tex]y=mx+b[/tex]Here, m is the slope and b is the y intercept.
Given,
m = -3/2 and b = -1, therefore we can write the equation as,
[tex]y=-\frac{3}{2}x-1[/tex]The equation is, y =(-3/2)x-1.
The marching band director is standing on a platformoverlooking the band practice. The pit section is located 8feet from the base of the platform. If the angle ofdepression from the band director to the pit section is 67°find the height of the platform.
Through trigonometry, we calculated that the height of the platform is 18.8 feet.
The director of the marching band is observing the band practice from a platform. 8 feet separate the base of the platform from the pit area. If the pit section's angle of depression is 67 degrees from the band director,
The angle formed by the horizontal line and the item as seen from the horizontal line is known as the angle of depression. When the angles and the separation of an object from the ground are known, it is mostly used to calculate the distance between the two objects.
We have,
So, the Angle of Depression = [tex]\alpha[/tex] = 67
Let x be the height of the platform,
Tan [tex]\alpha = \frac{x}{8}[/tex]
[tex]Tan 67 = \frac{x}{8} \\\\2.35 =\frac{x}{8} \\x = 2.35 *8 = 18.8[/tex]
Hence, The height of the platform is 18.8 feet.
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An actor invests some money at 7%, and $24000 more than three times the amount at 11%. The total annual interest earned from the investment is $27040. How much did he invest at each amount? Use the six-step method.
0.07x+0.11(3x+24000)=27040
we will solve for x
x=61,000 [ investment at 7%]
Investment at 11% = 3x + 24000
= 3(61000)+24000
= 207000 [ investment at 11%]
What is the area of a rectangle with vertices
(-1, -4), (-1, 6), (3, 6), and (3, -4)?
* 16 square units
24 square units
O 36 square units
40 square units
The most appropriate choice for distance formula will be given by Area of rectangle is 40 sq units
What is distance formula?
Distance formula is used to find the distance between two points.
Let A and B be two points with coordinate [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] respectively
Distance between A and B = [tex]\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex]
Here,
Let A = (-1 , -4), B = (-1, 6), C = (3, 6) and D = (3, -4)
Length of AB =
[tex]\sqrt{((-1)-(-1))^2 + (-4-6)^2}\\\sqrt{100}\\10 units[/tex]
Length of BC =
[tex]\sqrt{((-1)-3)^2 + (6-6)^2}\\\sqrt{16}\\4 units[/tex]
Length of rectangle = 10 units
Breadth of rectangle = 4 units
Area of rectangle = [tex]10 \times 4[/tex] = 40 sq units
Fourth option is correct
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In the accompanying regular pentagonal prism, suppose that each base edge measures 7 in. and that the apothem of the base measures 4.8 in. The altitude of the prism measures 10 in.A regular pentagonal prism and a pentagon are shown side by side. The pentagon contains a labeled segment and angle.The prism contains a horizontal top and bottom and vertical sides. The front left face and front right face meet the bottom base at right angles.The pentagon is labeled "Base".A line segment starts in the center of the pentagon, travels down vertically, and ends at the edge. The segment is labeled a.The vertical segment forms a right angle with the edge.(a)Find the lateral area (in square inches) of the prism.in2(b)Find the total area (in square inches) of the prism.in2(c)Find the volume (in cubic inches) of the prism.in3
To determine the lateral area of the prism;
[tex]Lateral\text{ area=perimeter of the base}\times height[/tex][tex]Lateral\text{ area=5\lparen7\rparen }\times10=350in^2[/tex]To determine total area of the prism;
[tex]Total\text{ area=2\lparen area of base\rparen+Lateral area}[/tex][tex]\begin{gathered} Total\text{ area of the prism=2\lparen}\frac{1}{2}\times perimeter\text{ of the base}\times apotherm\text{\rparen+350} \\ \end{gathered}[/tex][tex]\begin{gathered} Total\text{ area of the prism=2\lparen}\frac{1}{2}\times5(7)\times4.8\text{\rparen+380=168+350=518in}^2 \\ \end{gathered}[/tex]To determine the volume of the prism;
[tex]Volume\text{ = base area }\times height[/tex][tex]Volume=\frac{1}{2}\times5(7)\times4.8\times10=840in^3[/tex]Hence
If the trend shown in the graph above continued into the next year, approximately how many sport utility vehicles were sold in 1999?
ANSWER :
EXPLANATION :
Geometry ? What is the coordinate of G if triangle E’F’G’ is created by dilating EFG with a scale factor of 4 about the origin
In order to dilate the figure around the origin by a scale of 4, we need to multiply the coordinates of each point by 4. This is done below:
[tex]\begin{gathered} F^{\prime}=(4\cdot-1,4\cdot2)=(-4,8) \\ G^{\prime}=(4\cdot2,4\cdot-2)=(8,-8) \\ E^{\prime}^{}=(4\cdot-2,,4\cdot0)=(-8,0) \end{gathered}[/tex]The coordinates are: F'(-4, 8), G'(8,-8) and E'(-8,0).
50 points.
Daisy is a botanist who works for a garden that many tourists visit. The function f(s) = 3s + 30 represents the number of flowers that bloomed, where s is the number of seeds she planted. The function s(w) = 12w represents the number of seeds she plants per week, where w represents the number of weeks.
Part A: Write a composite function that represents how many flowers Daisy can expect to bloom over a certain number of weeks.
Part B: What are the units of measurement for the composite function in Part A?
Part C: Evaluate the composite function in Part A for 36 weeks.
From the situation described in this problem, it is found that:
A. The composite function is: f(s(w)) = 36w + 30.
B. The unit of measurement of the composite function is: flowers.
C. After 36 weeks, Daisy can expect to bloom 1326 flowers.
Composite functionFor a composite function, the output of the inner function serves as the input of the outer function.
In the context of this problem, the functions are given as follows:
f(s) = 3s + 30.s(w) = 12w.Hence the composite function that represents how many flowers Daisy can expect to bloom over a certain number of weeks is:
f(s(w)) = f(12w) = 3(12w) + 30 = 36w + 30.
The unit of measurement of the composite function is the unit of the outer function, which is flowers.
After 36 weeks, the number of flowers that Daisy can expect to bloom is given as follows:
f(s(36)) = 36(36) + 30 = 1326 flowers.
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I believe the answer to be c but I'm not the best at word problems this is a practice study guide.
In order to find the interval of values where 95% of the shoe sizes lie, let's find the values of z-score that represents 2.5% to the left and 2.5% to the right of the standard distribution curve:
Looking at the z-table for the probabilities of 0.025 and 0.975, we have z1 = -1.96 and z2 = 1.96.
Now, we can calculate the values that define the interval using the formula below:
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ -1.96=\frac{x-8.1}{1.47} \\ x-8.1=-2.88 \\ x=-2.88+8.1 \\ x=5.22 \\ \\ 1.96=\frac{x-8.1}{1.47} \\ x-8.1=2.88 \\ x=2.88+8.1 \\ x=10.98 \end{gathered}[/tex]Therefore the correct option is the second one. (It's the only option with very close values to the ones calculated)
What does the y-intercept mean? What does the x-intercept mean? Explain what each intercept means and then Identify the x-intercept and y-intercept from each equation.A. y=7/2x -2B. x=-3
x intercept = where the function crosses the x axis (x,0)
y intercept = where the function crosses the y-axis (0,y)
A. y=7/2x-2
x intercept , replace y by 0 and solve for x:
0 =7/2x-2
2= 7/2 x
2 / (7/2) = x
x= 4/7
y-intercept, replace x by 0 and solve for y
y= 7/2x-2
y= 7/2 (0) -2
y=-2
B.
x-intercept:
x=-3
y-intercept
0=-3
It doesn't have a y-intercept.
For a standard normal distribution,Find P(-1.21 < Z< 2.26)
Answer:
The range of z-score is given below as
[tex]P(-1.21Using a graphing calculator, we will have the image be[tex]\begin{gathered} P(z<-1.21)=0.11314 \\ P(z<2.26)=0.9881 \\ P(-1.21Hence,The final answer is
[tex]P(-1.21\lt z\lt2.26)=0.8750[/tex]whats the simplest term of 9m-2(3m-1)
Answer:
[tex]3m+2[/tex]
Step-by-step explanation:
I'm assuming you mean: [tex]9m-2(3m-1)[/tex] and not: [tex](9m-2)(3m-1)[/tex]
So you simply need to know the Distributive Property, which allows you to expand out values being multiplied within parenthesis without adding the values first as such: [tex]A(B+C)=AB+AC[/tex]
Applying this to distribute the -2, we get: [tex]9m-6m+2[/tex]
Adding like terms we get: [tex]3m+2[/tex]
gabriella bought two hoodies that were $15 each. The store was having a sale, everything in the store 15% off. If the sales tax on the purchase was 8%, what was the final cost of the hoodie?
Given:
The cost of each hoodie is, C = $15.
The discount percentage is, d = 15%.
The tax percentage on purchase is t = 8%.
The objective is to find the final cost of the hoodie.
The selling price of one hooie can be calculated as,
[tex]\begin{gathered} SP=c-d \\ =15-(\frac{15}{100}\times15) \\ =15-2.25 \\ =12.75 \end{gathered}[/tex]Now, by adding sales tax to the selling price the final cost will be,
[tex]\begin{gathered} FC=SP+t \\ =12.75+(\frac{8}{100}\times12.75) \\ =12.75+1.02 \\ =13.77 \end{gathered}[/tex]Cost of two hoodie can be calculated as,
[tex]\begin{gathered} C(\text{two)}=2\times13.77 \\ =27.54 \end{gathered}[/tex]Hence, the final cost of one hoodie is $13.77 and final cost of two hoodie is $27.54.
Which transformations can be used to carry ABCD onto itself? The point ofrotation is (3,2). Check all that apply.у5DС321АВ012345
The point of rotation is (3, 2). We would subtract this origin from each vertex. Let us consider vertex D(1, 3). Subtracting, we have (1 - 3, 3 - 2) = (- 2, 1).
if we rotate it 180 degrees, we have (- - 2, - 1) = (2, - 1). If we add the vertex again, it becomes (- 2 + 3, 1 + 2) = (1, 3). If we reflect it over the line, y = 2, we have (3, 2)
The correct options are
B. Rotate 180 degrees
D) reflection over the line, y = 2
Wouldnt 8-4 be 8? because if u think about it your taking away the 4 so its not there anymore so then 8 is left ?
The subtraction of 4 from 8 is equal to 4 and not 8
What is subtraction of numbers?
In math, subtracting means to take away from a group or a number of things. When we subtract, the number of things in the group reduces or becomes less. The minuend, subtrahend, and difference are parts of a subtraction problem.
Now in this question, let's assume you have 8 apples in your bag. During lunchtime, you gave 4 out to your friends to share with you. If you check your bag again, you would notice that you no longer have 8 apples again in your bag because you have given 4 out and you would be left with 4 apples.
So, whenever we subtract 4 from 8 i.e. 8 - 4, the answer is and must always be equal to 4 and not 8.
Mathematically, this is written as 8 - 4 = 4.
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The given pair of triangles are similar. Find X and Y.
Given that the pair of triangles are similar, then their corresponding sides are in proportion, this means that:
[tex]\frac{\text{longer leg of the triangle on the left}}{\text{shorter leg of the triangle on the left}}=\frac{\text{longer leg of the triangle on the right}}{\text{shorter leg of the triangle on the right}}[/tex]Substituting with the information of the diagram:
[tex]\frac{27}{x}=\frac{x}{9}[/tex]Cross multiplying:
[tex]\begin{gathered} 27\cdot9=x\cdot x \\ 243=x^2 \\ \sqrt[]{243}=x \\ 15.58\approx x \end{gathered}[/tex]Considering the triangle on the left, and applying the Pythagorean theorem with c = y (the hypotenuse), a = 27, and b = x (the legs), we get:
[tex]\begin{gathered} c^2=a^2+b^2 \\ y^2=27^2+x^2 \\ y^2=729+243 \\ y^2=972 \\ y=\sqrt[]{972} \\ y\approx31.18 \end{gathered}[/tex]
64, 57, 50, 43, ... 50th term
For the next series, we will calculate its expression
[tex]v(n)=64-7(n-1)[/tex]For n = 1
v = 64
For n = 2
v = 57
For n = 3
v = 50
For n = 50
v = -279
Solve the following quadratic equation by factoring. If needed, write your answer as a fraction reduced to lowest terms
The given equation is
[tex]y^2-5y-36=0[/tex]For solving it we will factorize the number 36 as 9 x 4 which on subtraction gives 5 and on multiplication gives 36.
Then, we have
[tex]\begin{gathered} y^2-(9-4)y-36=0 \\ y^2-9y+4y-36=0 \\ y(y-9)+4(y-9)=0 \\ (y-9)(y+4)=0 \\ y-9=0\text{ and y+4=0} \\ y=p\text{ and y=-4} \end{gathered}[/tex]Hence, the values of y are 9 and -4.
A family is traveling from their home to avacation resort hotel. The table below showstheir distance from home as a function of time.Time (hrs)0257Distance(mi)0140375480Determine the average rate of change betweenhour 2 and 7, including the units.
Let
x -------> the time in hours
y -------> the distance in miles
we know that
To find the average rate of change, we divide the change in the output (y) value by the change in the input value (x)
so
For x=2 h ------> y=140 mi
For x=7 h ------> y=480 mi
rate of change=(480-140)/(7-2)
rate of change=340/5=68 mi/h
The average rate of change is equal to the speed in this problem
You deposit $5000 in an account earning 6% interest compounded continuously. How much will you have in the account in 5 years?
For us to determine how much the account will be in 5 years at compounded continuously, we will be using the following formula:
[tex]\text{ A = P}_0e^{rt}[/tex]Where,
P = Principal amount (Initial Value)
A = Final amount (Future Value)
r = interest rate (in decimal)
t = time (in years)
e = mathematical constant approximately 2.7183
Given:
P = $5,000
r = 6% = 6/100 = 0.06
t = 5 years
We get,
[tex]\text{ A = P}_0e^{rt}[/tex][tex]\text{ A = (5,000)(2.7183)}^{(0.06)(5)}[/tex][tex]\text{ A = (5,000)(2.7183)}^{0.3}[/tex][tex]\text{ A = (5,000)(}1.34986151469)[/tex][tex]\text{ A = }6,749.30757343\text{ }\approx\text{ \$6,749.30}[/tex]Therefore, in 5 years, at 6% compounded continuously, your account will be $6,749.30
