we must find b one of the parallel sides before proceeding to find h
from the diagram b = 7cm
[tex]\begin{gathered} \text{Area = }\frac{10\text{ +7}}{2}\times h \\ 51\text{ = }\frac{17}{2}\times h \end{gathered}[/tex][tex]\begin{gathered} 51\text{ x 2 = 17h} \\ h\text{ =}\frac{51\times2}{17} \\ h\text{ =6cm} \end{gathered}[/tex]Given the following five-number summary, find the IQR.
2.9, 5.7, 10.0, 13.2, 21.1.
The IQR of the given series 2.9, 5.7, 10.0, 13.2, 21.1 is 15.4
In the given question, a five number summary is given as follows
2.9, 5.7, 10.0, 13.2, 21.1
We need to find the IQR
So, first we'll find the median of the given series
The middle value in a sorted, ascending or descending list of numbers is known as the median, and it has the potential to describe a data collection more accurately than the average does.
So, the given series is already in ascending order. And the middle value is 10.0. So the median is 10.0
Now to find the IQR the given formula will be used,
IQR = Q3 - Q1
Where Q3 is the last term in lower series and Q1 is the last term in upper series
Lower series - 2.9, 5.7
Upper series - 3.2, 21.1
Q3 = 5.7 , Q1 = 21.1
IQR = Q3 - Q1 = 21.1 - 5.7 = 15.4 ( IQR is always positive)
Hence, the IQR of the given series 2.9, 5.7, 10.0, 13.2, 21.1 is 15.4
To learn more about, IQR here
https://brainly.com/question/15191516
#SPJ1
Rewrite y + 1 = -2x – 3 in standard form
The algebraic expressions can be written as
[tex]a+b+c=0[/tex]The given expression is,
[tex]\begin{gathered} y+1=-2x-3 \\ -2x-y=1+3 \\ -2x-y=4 \\ -2x-y-4=0 \\ 2x+y+4=0 \end{gathered}[/tex]CorrectBob's Golf Palace had a set of 10 golf clubs that were marked on sale for $840. This was a discount of 10% off the original selling price.Step 3 of 4: What was the store's percent of profit based on cost ($390)? Follow the problem-solving process and round your answer tothe nearest hundredth of a percent, if necessary.
The percent change is given by:
[tex]Percent_{\text{ }}change=\frac{New_{\text{ }}value-old_{\text{ }}value}{old_{\text{ }}value}\times100[/tex]The old value is $390
A basic cellular package costs $20/month for 60 minutes of calling with an additional charge of $0.20/minute beyond that time. The cost function C(x) for using x minutes would beIf you used 60 minutes or less, i.e. if if x≤60, then C(x)=20 (the base charge). If you used more than 60 minutes, i.e. (x−60) minutes more than the plan came with, you would pay an additional $0.20 for each of those (x−60) minutes. Your total bill would be C(x)=20+0.20(x−60). If you want to keep your bill at $50 or lower for the month, what is the maximum number of calling minutes you can use?
The maximum number of calling minutes you can use for $50 is 210 minutes.
To solve this, we have the function cost C(x) that depends on the amount of acalling munutes (x)
We want this cost to be $50 or lower. This means:
[tex]\begin{gathered} CostFunction\colon C(x)=20+0.2(x-60) \\ Maximum\text{ value of 50:}C(x)\le50 \end{gathered}[/tex]Then we can create an inequality:
[tex]50\ge20+0.2(x-60)[/tex]And now we can solve for x:
[tex]\begin{gathered} 50\ge20+0.2(x-60) \\ \frac{50-20}{0.2}\ge x-60 \\ 150+60\ge x \\ x\le210\text{ minutes} \end{gathered}[/tex]Thus, with $50 we can talk up to 210 minutes.
To be sure of the result, let's plug x = 210 in the function and it should give us a cost of C(210) = 50:
[tex]\begin{gathered} x=210\Rightarrow C(210)=20+0.2(210-60) \\ C(210)=20+0.2\cdot150 \\ C(210)=20+30=50 \end{gathered}[/tex]This confirms the result.
6. The graph shows how much money Priya has in her savings account weeksafter she started saving on a regular basis.
Given:
Graph is given.
6a.
[tex]\text{Money in the account after 10 weeks= \$320}[/tex]6b.
[tex]\text{Number of weeks take to save \$200= 5 weeks}[/tex]6c.
[tex]\text{Priya have \$80 in her account when she started the savings regularly}[/tex]Use the quadratic function fly)=-22 +53411 to answer the following questions,a) Use the vertex formula to determine the vertes.The verteris(Type an ordered pair Simplify your answer.)
The vertex of a quadratic function can be found by using the following expression:
[tex]x=\frac{-b}{2a}[/tex]Where "a" is the number multiplying x² and b is the number multiplying x. For this function a = -2 and b = 5. Applying these on the problem we have:
[tex]x=\frac{-5}{2\cdot(-2)}=\frac{-5}{-4}=\frac{5}{4}=1.25[/tex]To find the y coordinate of the vertex we need to use the value for x that we found above. We have:
[tex]\begin{gathered} f(x)=-2x^2+5x+11 \\ f(\frac{5}{4})=-2\cdot(\frac{5}{4})^2+5\cdot(\frac{5}{4})+11 \\ f(\frac{5}{4})=-2\frac{25}{16}+\frac{25}{4}+11 \\ f(\frac{5}{4})=\frac{-50}{16}+\frac{25}{4}+11 \\ f(\frac{5}{4})=-3.125+6.25+11=14.125 \end{gathered}[/tex]The ordered pair for this function's vertex is (1.25, 14.125)
A circular pool measures 12 feet across. One cubic yard of concrete is to be used to create a circular border of uniform width around the pool. If the border is to have a depth of 6 inches, how wide will the border be?
SOLUTION:
Step 1:
In this question, we are given the following:
A circular pool measures 12 feet across.
One cubic yard of concrete is to be used to create a circular border of uniform width around the pool.
If the border is to have a depth of 6 inches, how wide will the border be?
Step 2:
From the question, we can see that:
[tex]6\text{ inches = 0. 5 feet}[/tex][tex]1\text{ cubic yard = 3 ft x 3ft x 3ft = }27ft^3[/tex][tex]\begin{gathered} \text{Let the radius of the pool = ( 6+x ) feet} \\ \text{Let the width of the concrete that is used to } \\ \text{create the circular border = 6 feet} \end{gathered}[/tex][tex]\text{Let the depth of the border = 6 inches = }\frac{6}{12}=\text{ 0. 5 inches}[/tex]Step 3:
[tex]\begin{gathered} U\sin g\text{ } \\ \pi R^2h\text{ - }\pi r^2\text{ h = 27} \\ \pi(6+x)^2\text{ 0. 5 - }\pi(6)^2\text{ 0. 5 = 27} \\ \text{0. 5}\pi(x^2\text{ + 12x + 36 - 36 ) = 27} \\ 0.\text{ 5 }\pi(x^2\text{ + 12 x) = 27} \\ \text{Divide both sides by 0. 5 }\pi\text{ , we have that:} \end{gathered}[/tex][tex]x^2\text{ + 12 x - (}\frac{27}{0.\text{ 5}\pi})=\text{ 0}[/tex]Solving this, we have that:
CONCLUSION:
From the calculations above, we can see that the value of the x:
( which is the width of the border ) = 1. 293 feet
(correct to 3 decimal places)
I don't get any of this help me please
Using scientific notation, we have that:
a) As an ordinary number, the number is written as 0.51.
b) The value of the product is of 1445.
What is scientific notation?An ordinary number written in scientific notation is given as follows:
[tex]a \times 10^b[/tex]
With the base being [tex]a \in [1, 10)[/tex], meaning that it can assume values from 1 to 10, with an open interval at 10 meaning that for 10 the number is written as 10 = 1 x 10¹, meaning that the base is 1.
For item a, to add one to the exponent, making it zero, we need to divide the base by 10, hence the ordinary number is given as follows:
5.1 x 10^(-1) = 5.1/10 = 0.51.
For item b, to multiply two numbers, we multiply the bases and add the exponents, hence:
(1.7 x 10^4) x (8.5 x 10^-2) = 1.7 x 8.5 x 10^(4 - 2) = 14.45 x 10².
To subtract two from the exponent, making it zero, we need to multiply the base by 2, hence the base number is given as follows:
14.45 x 100 = 1445.
More can be learned about scientific notation at https://brainly.com/question/16394306
#SPJ1
Solve each system of the equation by elimination method. x+3y=-204x+5y=-38
Given the equation system:
[tex]\begin{gathered} x+3y=-20 \\ 4x+5y=-38 \end{gathered}[/tex]To solve this system using the elimination method, the first step is to multiply the first equation by 4 so that the leading coefficient is the same, i.e., both equations start with "4x"
[tex]\begin{gathered} 4(x+3y=-20) \\ 4\cdot x+4\cdot3y=4\cdot(-20) \\ 4x+12y=-80 \end{gathered}[/tex]Then subtract the second equation from the first one
From the resulting expression, you can calculate the value of y
[tex]\begin{gathered} 7y=-42 \\ \frac{7y}{7}=-\frac{42}{7} \\ y=-6 \end{gathered}[/tex]Next, you have to substitute the value of y in either the first or second equation to find the value of x:
[tex]\begin{gathered} x+3y=-20 \\ x+3\cdot(-6)=-20 \\ x-18=-20 \\ x=-20+18 \\ x=-2 \end{gathered}[/tex]The solution of the system is (-2,-6)
A 35-foot wire is secured from the top of a flagpole to a stake in the ground. If the stake is 1 feet from the base of the flagpole, how tall is the flagpole?
The figure for the height of flagpole, wire and ground is,
Determine height of the pole by using the pythagoras theorem in triangle.
[tex]\begin{gathered} l^2=b^2+h^2 \\ (35)^2=(14)^2+h^2 \\ 1225-196=h^2 \\ h=\sqrt[]{1029} \\ =32.078 \\ \approx32.08 \end{gathered}[/tex]Thus, height of the flagpole is 32.08 feet.
In Mr. Peter's class, 75% of the students have a pet. There are 15 students with pets in the class. How many total students are in the class?
Answer:
20 Students
Explanation:
Let the total number of students in the class = x
Number of students that have pets = 15
Percentage of students that have pets = 75%
Therefore:
[tex]75\%\text{ of x=15}[/tex]We then solve for x.
[tex]\begin{gathered} \frac{75}{100}\times x=15 \\ 0.75x=15 \\ x=\frac{15}{0.75} \\ x=20 \end{gathered}[/tex]We have 20 students in total in the class.
helpppppp!!!!!!!!!!!!!!!!!!!!
Answer
D. Observations of constellations show that stars have moved over time.
Explanation:
A scientific claim is basically an observation in science.
Constellation changes there position over time because of earth's rotation around sun. So, observation of constellations shows that stars have moved over time is a scietific claim. If stars would not move then constellation will not form.
A cat is stuck in the tree and the fire department needs a ladder to rescue the cat. The fire truck available has a 95-foot ladder, which starts 8 feet above ground. Unfortunately, the fire truck must park 75 feet away from the tree. If the cat is 60 feet up the tree, does the cat get rescued? If not, what ladder length is need to allow the cat to be rescued?
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Draw the given scenario
STEP 2: Describe how to answer the question
The question forms a right angle triangle. where the height of the cat on the tree is the opposite side of the triangle. The distance between the cat and the tree is the adjacent side of the triangle .
Recall the 95 foot ladder can only start 8 feet above the ground .The diagram is represented above:
The ladder height should be the hypotenuse of the triangle.
using Pythagoras's theorem,
[tex]hypotenuse^2=opposite^2+adjacent^2[/tex]STEP 3: Write the given sides
[tex]\begin{gathered} adjacent=75fto \\ opposite=52ft \\ hypotenuse=x\text{ ft} \end{gathered}[/tex]STEP 4: find x
[tex]\begin{gathered} x^2=75^2+52^2 \\ x^2=5625+2704 \\ x^2=8329 \\ x=\sqrt{8329}=91.26335519 \\ x\approx91.26ft \end{gathered}[/tex]The expected length of the ladder should be approximately 91.26ft. Since the ladder is 95 foot, therefore the cat will be rescued with the given ladder.
Use Polya's four-step problem-solving strategy and the problem-solving procedures presented in this section to solve the following exercise.The number of ducks and pigs in a field totals 37. The total number of legs among them is 98. Assuming each duck has exactly two legs and each plg has exactly fourlegs, determine how many ducks and how many pigs are in the field.ducks?pigs?
Lets call x to the number of ducks
and y the number of pigs.
Then:
[tex]2x+4y=98[/tex]Because there are 2 legs per duck and 4 legs per pig.
If the total of animals is 37, then:
[tex]x+y=37[/tex]Then:
[tex]x=37-y[/tex]And replacing on the first equation we get:
[tex]2(37-y)+4y=98[/tex][tex]74-2y+4y=98[/tex][tex]2y=98-74[/tex][tex]2y=24[/tex][tex]y=\frac{24}{2}[/tex][tex]y=12[/tex]There are 12 pigs and therefore 25 ducks.
Which statement is true for all real values of θ? sin2θ − cos2θ = 1 cos2θ − sin2θ = 1 cos2θ = sin2θ − 1 cos2θ = 1 − sin2θ
The statement holds true for all true values of is cos²θ = 1 − sin²θ
What is meant by trigonometric identities?Trigonometric Identities are equalities that involve trigonometry functions and hold true for all variables in the equation. There are numerous trigonometric identities involving the side length and angle of a triangle. Trigonometry identities are trigonometry equations that are always true, and they are frequently used to solve trigonometry and geometry problems as well as understand various mathematical properties. Knowing key trig identities aids in the retention and comprehension of important mathematical principles as well as the solution of numerous math problems. Convert everything to sine and cosine terms. When possible, use the identities. Begin by simplifying the left side of the equation, then move on to the right side if you get stuck.To learn more about trigonometric identities, refer to:
https://brainly.com/question/24496175
#SPJ1
What is the name of the decimal number?7.1seventy-one seven and one hundredthsseven and one tenth seventeen
Answer:
seven and one-tenth.
Explanation:
To name decimal number, we first name the values before the decimal point, in this case, seven
Then, we add an and that corresponds to the decimal point
Finally, we say the number after the decimal point and the place of this number, in this case, one-tenth.
Therefore, the name of the decimal number 7.1 is:
seven and one-tenth.
The function h (t) = -4.9t² + 19t + 1.5 describes the height in meters of a basketball t secondsafter it has been thrown vertically into the air. What is the maximum height of the basketball?Round your answer to the nearest tenth.1.9 metersO 19.9 meters16.9 metersO 1.5 meters
Since the function describing the height is a quadratic function with negative leading coefficient this means that this is a parabola that opens down. This also means that the maximum height will be given as the y component of the vertex of the parabola, then if we want to find the maximum height, we need to write the function in vertex form so let's do that:
[tex]\begin{gathered} h(t)=-4.9t^2+19t+1.5 \\ =-4.9(t^2+\frac{19}{4.9}t)+1.5 \\ =-4.9(t^2+\frac{19}{4.9}t+(\frac{19}{9.8})^2)+1.5+4.9(\frac{19}{9.8})^2 \\ =-4.9(t+\frac{19}{9.8})^2+19.9 \end{gathered}[/tex]Hence the function can be written as:
[tex]h(t)=-4.9(t+1.9)^2+19.9[/tex]and its vertex is at (1.9,19.9) which means that the maximum height of the ball is 19.9 m
I need help, I don’t know which one would have factors of 5x-8
In this case, we'll have to carry out several steps to find the solution.
Step 01:
data:
factor:
5x - 8
Step 02:
difference of squares:
(5x - 8)(5x + 8) = 25x² - 64
The answer is:
25x² - 64
Solve the system of inequalities by graphing.y\ge-3
cuántos cifras tiene el cociente de 900÷25
Given the expression
help meeeee pleaseeeee!!!
thank you
Step-by-step explanation:
what is the problem ?
first you need to put "1" in place of the x and calculate, and then you need to put "2" in place of the x and calculate.
just simple calculation !
(a)
R(1) = 1000×1² / (1² + 4) = 1000 / 5 = 200
$200 million
(b)
R(2) = 1000×2² / (2² + 4) = 4000 / 8 = 500
$500 million
there ! that's all that was needed.
Can u help me with my math I’m confused and don’t know
We want to find the area of the rectangle.
The area of a rectangle is given by;
[tex]\text{Area}=\text{Length x Breadth}[/tex]The length is x + 7 and the breadth is given by x + 5.
Thus the area is;
[tex]\begin{gathered} A=(x+7)(x+5) \\ A=x^2+7x+5x+35 \\ A=x^2+12x+35 \end{gathered}[/tex]Therefore, the area is;
[tex]A=x^2+12x+35[/tex]I’m not firmiliar with the sun or difference of cubes (HW assignment)
Given:
[tex]125r^3-216[/tex]Find-: Factor using the formula of the sum or difference of cube.
Sol:
Factoring sum and differences of cubs is:
[tex]\begin{gathered} x^3-y^3=(x-y)(x^2+y^2+xy) \\ \\ x^3+y^3=(x+y)(x^2+y^2-xy) \end{gathered}[/tex]Apply for the given information.
[tex]\begin{gathered} =125r^3-216 \\ \\ =(5r)^3-(6)^3 \end{gathered}[/tex][tex]\begin{gathered} x^3-y^3=(x-y)(x^2+y^2+xy) \\ \\ (5r)^3-(6)^3=(5r-6)((5r)^2+(6)^2+(5r)(6)) \\ \\ =(5r-6)(25r^2+36+30r) \end{gathered}[/tex]In triangle ABC, if AC = 17 cm, CB = 10 cm, AD = x cm, DB = y cm and AB = 21 cm, find the value of (x − y).
The value of (x-y) is 9 cm for the given triangle ABC.
According to the question,
We have the following information:
In triangle ABC, if AC = 17 cm, CB = 10 cm, AD = x cm, DB = y cm and AB = 21 cm.
So, we have:
x+y = 21 cm
y = (21-x) cm
Using Pythagoras theorem in right-angled triangle ADC and CDB:
[tex]AC^{2} = AD^{2} +CD^{2}[/tex] and [tex]BC^{2} = BD^{2}+CD^{2}[/tex]
Now, we have the equal values of [tex]CD^{2}[/tex]:
[tex]17^{2} -x^{2} = 10^{2} -y^{2}[/tex]
289 -[tex]x^{2}[/tex] = 100 - [tex](21-x)^{2}[/tex]
289 - [tex]x^{2}[/tex] = 100 - (441+[tex]x^{2}[/tex]-42x)
289-[tex]x^{2}[/tex] = 100 - 441-[tex]x^{2}[/tex] + 42x
289 = 100 -441+42x
42x-331 = 289
42x = 289+331
42x = 630
x = 630/42
x = 15 cm
y = 21-x
y = 21-15
y = 6 cm
Now, x-y = 15-6
x-y = 9 cm
Hence, the value of (x-y) is 9 cm.
To know more about triangle here
https://brainly.com/question/2773823
#SPJ1
the sign shown below is posted in front of a roller coaster ride at the Wadsworth country fairgrounds.if h represents the height of a rider in inches,what is the correct translation of the statement on this sign?h<48h>58h≤48h≥48
Answer:
h≥48
Explanation:
If all riders must be at least 48 inches tall, it can mean the following.
0. The height of the riders can be ,exactly 48 inches, tall (h=48)
,1. The height of the riders can be, greater than 48 inches,, (h>48).
Combining the two, we have:
h≥48
Write the equation of the line through the given point. Use slope-intercept form. (-5,2); perpendicular to y = - 2/3x +5
Explanation
Step 1
we have a perpendicular line, its slope is
[tex]\begin{gathered} y=\frac{-2}{3}x+5 \\ \text{slope}=\frac{-2}{3} \end{gathered}[/tex]two lines are perpendicular if
[tex]\begin{gathered} \text{slope}1\cdot\text{ slope2 =-1} \\ \text{then} \\ \text{slope}1=\frac{-1}{\text{slope 2}} \end{gathered}[/tex]replace
[tex]\text{slope1}=\frac{\frac{-1}{1}}{\frac{-2}{3}}=\frac{-3}{-2}=\frac{3}{2}[/tex]so, our slope is 3/2
Step 2
using slope=3/2 and P(-5,2) find the equation of the line
[tex]\begin{gathered} y-y_0=m(x-x_0) \\ y-2=\frac{3}{2}(x-(-5)) \\ y-2=\frac{3}{2}(x+5) \\ y-2=\frac{3}{2}x+\frac{15}{2} \\ y=\frac{3}{2}x+\frac{15}{2}+2 \\ y=\frac{3}{2}x+\frac{19}{2} \end{gathered}[/tex]Solve the system of equations.y= x2 - 3x + 6y = 2x + 6
We have the following:
[tex]\begin{gathered} y=x^2-3x+6 \\ y=2x+6 \end{gathered}[/tex]We subtract the equations:
[tex]\begin{gathered} y-y=x^2-3x+6-2x-6 \\ 0=x^2-5x \\ 0=x(x-5) \\ x=0;x=5 \end{gathered}[/tex]for y:
[tex]\begin{gathered} y=2\cdot0+6 \\ y=6 \\ y=2\cdot5+6 \\ y=16 \end{gathered}[/tex]therefore, the answer is:
(0,6) and (5,16), the option D.
In 2005 there were 744 radio stations, by 2015 that number had increased by 13.8%. How many radio stations in 2015?
Answer: We have to find the radio stations in 2015, which is 13.8% more than the radio stations in 2005 which were 744:
[tex]\begin{gathered} x=\text{ Radio stations in 2015} \\ \\ x=(1.138)\times(744) \\ \\ x=846.672 \\ \\ x\approx847 \end{gathered}[/tex]Find the area of each figure. Round to the nearest 10th if necessary.
1.
First, divide the figure into 3 different figures.
Find the area of each figure, and then add them:
A1 is a rectangle:
Area of a rectangle: Lenght x width
A1 = 8 x 5.3 = 42.4 in2
A2 is also a rectangle:
Lenght = 4
width = 8 - 5.3 = 2.7
A2 = 4 x 2.7 = 10.8 in2
A3 is a triangle:
Area of a triangle = (base x height) / 2
base = 2.7
Height = 8-4 = 4
A3= ( 2.7 x 4 ) / 2 = 5.4 in2
Total area = A1 + A2 + A3 = 42.4 + 10.8 + 5.4 = 58.6 in2
Answer = 58.6 in2
In the triangle below, suppose that mZW=(x+4)º, mZX=(5x-4)°, and mLY= (4x)".Find the degree measure of each angle in the triangle.
