Area of Triangles What is the area of this triangle? bh A 0 24 in? 8 in O 30 in 48 in 96 in
Answers
Given the triangle:
We're going to find its area.
To do this, we just multiply the base of the triangle by its height and then divide this result by 2:
[tex]A=\frac{6in\cdot8in}{2}=24in^2[/tex]Therefore, the area equals 24 in2.
Related Questions
A rectangular room is 2 times as long as it is wide, and its perimeter is 48 meters. Find the dimension of the room.
Answers
Answer:
=16cm
Step-by-step explanation:
Let's read the problem carefully:
it says that one side of the rectangular room (let's call it b) is twice as long as the other (let's call it a), which in mathematical terms would be b = 2*a
It also says that the perimeter of the room is 48 meters, which means that (a + b)*2 = 48 => a + 2*a = 48/2 =>
3*a = 24 => a = 8, b = 16
Suppose you invested $4,500 and it grew by 4% every year for 30 years. How much would this investment be worth after 30 years?
Answers
Answer:
a) 14,595.29
Explanation:
We'll use the below compound interest formula to solve the given problem;
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where A = future amount
P = initial amount = $4500
r = interest rate in decimal = 4/100 = 0.04
n = number of compounding periods = 1
t = time period = 30 years
Let's go ahead and substitute the above values into our formula and solve for A;
[tex]\begin{gathered} A=4500(1+\frac{0.04}{1})^{1\times30} \\ A=4500(3.24339751003) \\ A=14,595.29 \end{gathered}[/tex]We can see from the above that the investment would be worth $14,595.29 after 30 years.
The recommended daily allowance of niacin for adults is 20 mg. One serving of a certain breakfast cereal provides 8 mg of niacin, What percent of the recommendeddaily allowance of niacin does one serving of this cereal provide?
Answers
Given:
Total allowance = 20mg.
Used = 8 mg
Percentage of daily allowance is:
[tex]\begin{gathered} =\frac{8}{20}\times100 \\ =\frac{8}{2}\times10 \\ =8\times5 \\ =40 \end{gathered}[/tex]So 40% daily allowance .
Acellus Find the area of the shaded region. 60° 5 cm A = [?] cm2 Enter a decimal rounded to the nearest tenth.
Answers
hello
to solve this question, we simply need to apply the formula of area of a segment
the formula is given as
[tex]A_{\text{segment}}=\frac{1}{2}\times(\theta-\sin \theta)\times r^2[/tex]let's write out the variables given in the question
[tex]\begin{gathered} \theta=60^0 \\ r=5\operatorname{cm} \end{gathered}[/tex]we can now input those values into the equation
[tex]\begin{gathered} A_{\text{segment}}=\frac{1}{2}\times(\theta-\sin \theta)\times r^2 \\ A_{\text{segment}}=\frac{1}{2}\times(60-\sin 60)\times5^2 \\ A_{\text{segment}}=\frac{1}{2}\times(60-0.8660)\times25 \\ A_{\text{segment}}=\frac{1}{2}\times1478.35 \\ A_{\text{segement}}=739.175\operatorname{cm}^2 \end{gathered}[/tex]to get the value of the area of the shaded region,
[tex]\text{area of shaded region=area of circle - area of segment}[/tex]let's calculate the area of the circle
[tex]undefined[/tex]Which system type is a linear system with infinitely many solutions?InconsistentConsistent dependentInconsistent dependentConsistent independent
Answers
We are asked which system type is a linear system with infinitely many solutions.
Inconsistent = No solution
Consistent independent = One solution
Consistent dependent = infinitely many solutions.
In a consistent dependent system, the lines are merged and they basically become the same line. Hence, every coordinate pair on the line is a solution to both lines.
Therefore, the correct answer is Consistent dependent.
A consistent dependent system is a linear system with infinitely many solutions.
Find the solution set of the quadratic inequalities3x^2 - 15x - 18 > 0
Answers
Given -
3x²- 15x - 18 > 0
To Find -
The solution set of the quadratic inequalities =?
Step-by-Step Explanation -
Firstly, We will find the solution to the quadratic equation.
3x²- 15x - 18 = 0
[tex][/tex]Sebastian used difference of squares to factor the expression x^4– 16. His work is shown below. His teacher says that he did not "factor completely."How would you explain to Sebastianwhat he needs to do to completely factorthis expression?
Answers
To factor properly this expression, we need to use the next expression for the product of the difference of two squares as follows:
[tex]a^2-b^2=(a+b)\cdot(a-b)[/tex]Since the squares are:
[tex](x^2)^2-(4)^2=(x^2+4)(x^2-4)[/tex]We can also see that we have another difference of two squares in the last part of the expression:
[tex]undefined[/tex]if a plane can travel 480 miles per hour with the wind and 380 miles per hour against the wind,find the speed of the wind and the speed of the plane in still air . what is the speed of the plane in still air .
Answers
Let x be the speed of the plane while still in the air and let y be the speed of the wind
so
x + y = 480mph ......(1)
x - y = 380mph ...... (2)
add both equations and solve for x
2x = 860 mph
x = 860/2=430mph = speed of the plane while stil in air
using equation .....(1)
430 + y =480 mph
y = 480 - 430 = 50 mph =speed of the wind
Use angle relationships (complementary, supplementary, vertical, or adjacent) to find the measure of angle b.
Answers
Answer:
vertical, b = 46
Explanation:
Two angles are vertical if they are formed by intersection of two lines.
For examole, the follwing angles are vertical.
The angles b and 46 are vertical, and therefore, their measures are the same.
Therefore,
[tex]b=46^o[/tex]surface area for 3ft length 3ft width and 3ft height
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We are given a cube of side 3 ft and we are asked to determine its surface area. The surface area of a cube is 6 times the area of one of its faces. The area of its faces is the side squared, therefore, the total surface area is:
[tex]S=6l^2[/tex]Where:
[tex]l=\text{ length of the side }[/tex]Now, we plug in the value of the side:
[tex]S=6(3ft)^2[/tex]Solving the operations:
[tex]S=54ft^2[/tex]Therefore, the surface area is 54 square feet.
In the past year, the number of frogs living in a pond had increased by 10% to 528, and the number of newts living there too had increased by 15% to 621. How many frogs and newts lived in the pond a year ago
Answers
Answer:
480 frogs, 540 newts
Step-by-step explanation:
528 ÷ 1.10 = 480 frogs
621 ÷ 1.15 = 540 newts
find the grade-point average. assume A=4,B=3,C=2,D=1 and F=0
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Average is define as the ratio of sum of all the data to the total number of data
[tex]\text{Average=}\frac{Sum\text{ of all the data}}{Total\text{ number of data}}[/tex]In the given question , we hvae five grades
[tex]\begin{gathered} A=4 \\ B=3 \\ C=2 \\ D=1 \\ F=0 \end{gathered}[/tex]Total number of data=5
Use the expression of average to find the average of grade point
[tex]\begin{gathered} \text{Average}=\frac{4+3+2+1+0}{5} \\ \text{Average}=\frac{10}{5} \\ \text{Average}=2 \end{gathered}[/tex]The average of the grade-point is 2.
you are machinist setting up a part that requires a5/8 inch diameter finished hole.stardart practice is to drill an initial g hole with a diameter that is undersided by 1/32 inch before finishing What should be the diameter inches of the initial hole?
Answers
We will have that the initial size of the hole should be:
[tex]\frac{5}{8}-\frac{1}{32}=\frac{19}{32}[/tex]So, the diameter of the initial hole should be 19/32 inches.
which choice represents the best rational approximation for 15 ?es)A)2B)2.2C)2.5D)2.7
Answers
ANSWER:
STEP-BY-STEP EXPLANATION:
[tex]undefined[/tex]Lloyd is working a problem on the board in his math class. He needs to simplifythe expression below.(2x-3) + (2x*- 3x) – (3x*- 5).What should he write as his answer?
Answers
Answer:
-x² - x + 2
Step-by-step explanation:
We are given the following expression:
(2x-3) + (2x²- 3x) – (3x²- 5).
To simplify, we first need to remove the parenthesis. If there is a negative sign before the parenthesis, we change the signal of everything that is inside(+ goes to -, - goes to +). So
(2x-3) + (2x²- 3x) – (3x²- 5) = 2x - 3 + 2x² - 3x - 3x² + 5
Now we need to combine the like terms:
With x²: 2x² - 3x² = -x²
With x: 2x - 3x = -x
Independent: -3 + 5 = 2
Now adding these terms, we get the simplified expression, which is:
-x² - x + 2
Help me solve this hw problem pls formula for getting g(x)
Answers
Answer:
Explanation:
Given:
A graph of f(x) in red and a graph of g(x) in blue
To find:
the formula for getting g(x)
First, we need to determine the function for f(x) from the graph
The roots of the function for f(x) are -4, 0, 4
The line crosses the x axis at x = -4, x = 0 and x = 4
x + 4 = 0, x - 0 = 0, x - 4 = 0
The factors: (x + 4)(x - 0)(x - 4)
[tex]\begin{gathered} f(x)\text{ = \lparen x + 4\rparen\lparen x\rparen\lparen x - 4\rparen} \\ Expanding\text{ the function:} \\ f(x)\text{ = \lparen x}^2\text{ + 4x\rparen\lparen x - 4\rparen} \\ f(x)\text{ = x}^2(x\text{ - 4\rparen + 4x\lparen x - 4\rparen} \\ f(x)\text{ = x}^3\text{ - 4x}^2\text{ + 4x}^2\text{ - 16x} \\ f(x)\text{ = x}^3\text{ - 16x} \end{gathered}[/tex]Comparing the coordinates of f(x) and g(x):
[tex]\begin{gathered} From\text{ the graph of g\lparen x\rparen in blue} \\ when\text{ x = -4, y = 3, g\lparen x\rparen} \\ \text{ when x = 0, y = 0 f\lparen x\rparen} \\ \\ when\text{ x = 2, y = 2 g\lparen x\rparen} \\ when\text{ x = 2, y = -4 f\lparen x\rparen} \\ \\ when\text{ x = 4, y = 0 f\lparen x\rparen} \\ when\text{ x= 4, y = 3 g\lparen x\rparen} \end{gathered}[/tex]
write an equation for the n th term of the arithmetic sequence 23, 16, 9, 2, ... .Then find a25?
Answers
Given the sequence:
23, 16, 9, 2
Use the arithmetic sequence formula:
[tex]a_n=a_1+(n-1)d[/tex]Where
an = nth term
a1 = first term
n = number of terms
d = common difference
d = a2 - a1 = 16-23 = -7
Since d = -7, let's find the equation for the nth term.
[tex]\begin{gathered} a_n=23+(n-1)-7 \\ a_n=23+n(-7)-1(-7) \\ a_n=23-7n+7 \\ \text{Combine like terms} \\ a_n=-7n\text{ +23}+7 \\ \\ a_n=-7n+30 \end{gathered}[/tex]The equation for the nth term is:
[tex]a_n=-7n+30[/tex]Let's find the 25th term, a25:
Substitute n for 25 and evaluate
[tex]\begin{gathered} a_{25}=-7(25)+20 \\ \\ a_{25}=-175+30 \\ \\ a_{25}=-145 \end{gathered}[/tex]ANSWER:
[tex]\begin{gathered} a_n=-7n+30 \\ \\ \\ a_{25}=-145 \end{gathered}[/tex]What do you notice and /or wonder about the second graph in the image above
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The second graph A'B'C' is the result of a reflection over x axis of the figure ABC; You can see that because the coordinates of the points follow the next rule:
[tex]P(x,y)\rightarrow P^{\prime}(x,-y)[/tex]Point A: (-2,1) becomes A'(-2,-1)
Point B: (1,4) becomes B'(1,-4)
Point C: (3,2) becomes C'(3,-2)
What is the slope of the line shown below?10(-6,3)5(12,5)5101610OAA.6B. -6C. -D. 6
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Consider that the slope (m) of a line passing through two given points is calculated using the formula,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]It is evident from the graph that points (-6,3) and (12,6) lie on the line,
[tex]\begin{gathered} (x_1,y_1)=(-6,3) \\ (x_2,y_2)=(12,6) \end{gathered}[/tex]Then, substitute the values in the formula to obtain the slope of the given line,
[tex]\begin{gathered} m=\frac{6-3}{12-(-6)} \\ m=\frac{3}{12+6} \\ m=\frac{3}{18} \\ m=\frac{3}{6\cdot3} \\ m=\frac{1}{6} \end{gathered}[/tex]Thus, the slope of the given line is,
[tex]\frac{1}{6}[/tex]Therefore, option A is the correct choice.
Find the area 21 m 7 m 21 m O A. 1543.5 m2 O B. 220.5 m2 OC. 294 m2 OD. 588 m2
Answers
EXPLANATION
Given the sides: 21m , 7m and 21 m
The Area is equal to:
Are
Use the long division method to find the result when 2x^3-7x^2+17x-7 is divided by 2x-1.
Answers
Given the expression below
[tex]\frac{2x^3-7x^2+17x-7}{2x-1}[/tex]To divide the above expression using long division, we will follow the steps below:
Step 1: Arrange the indices of the polynomial in descending order. Replace the missing term(s) with 0.
Looking at the expression given, polynomials is already arranged in descending order, from degree 3 to 0, and there are no missing terms of x.
Step 2: Divide the first term of the dividend (the polynomial to be divided) by the first term of the divisor. This gives the first term of the quotient.
Looking at the expression given, it can be seen that
[tex]\begin{gathered} \text{dividend}=2x^3-7x^2+17x-7 \\ \text{divisor}=2x-1 \end{gathered}[/tex][tex]\frac{2x^3}{2x}=x^2[/tex]Step 3: Multiply the divisor by the first term of the quotient.
[tex]x^2(2x-1)=2x^3-x^2[/tex]Step 4: Subtract the product from the dividend then bring down the next term. The difference and the next term will be the new dividend. Note: Remember the rule in subtraction "change the sign of the subtrahend then proceed to addition".
Step 5: Repeat step 2 – 4 to find the second term of the quotient.
[tex]\frac{-6x^2}{2x^2}=-3x[/tex][tex]-3x(2x-1)=-6x^2+3x[/tex]Continue the process until a remainder is obtained. This can be zero or is of lower index than the divisor.
[tex]\frac{14x}{2x}=7[/tex][tex]7(2x-1)=14x-7[/tex]The quotients from the divisions gives
[tex]x^2-3x+7[/tex]Hence, the result of the division is as written below x² - 3x +7
would adam snitch agree that gross domestic product is the best way to measure
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GDP measures our ability to obtain many of the inputs into a worthwhile existence but does not directly measure the things that make life valuable.
What is meant by GDP?GDP accounts for both total income and total expenditure on goods and services in the economy. Thus, GDP per person tells us about the average person's income and expenditure in the economy. Because most people would prefer to have a higher income and spend more money, The average person's GDP per person appears to be a straightforward indicator of their financial security.
People want to know whether an economy's total output of goods and services is increasing or decreasing. However, because GDP is collected at current, or nominal, prices, it is impossible to compare two periods without accounting for inflation.
To calculate "real" GDP, the nominal value must be adjusted to account for price changes, allowing us to see whether the value of output has increased because more is produced or simply because prices have risen.
To learn more about GDP refer :
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I need help I think I’m supposed to multiply straight across
Answers
To find the whole answer, let's look at each multiplication:
[tex]\frac{5280ft}{1\text{ mile}}\cdot\frac{30\text{ miles}}{1\text{ hour}}=\frac{5280ft\cdot30\text{miles}}{miles\cdot hour}=\frac{158400ft}{\text{hour}}[/tex]Now, it changes from hours to minutes:
Use, 1hour = 60 minutes
[tex]\frac{158400\text{ ft}}{1\text{ hour}}\cdot\frac{1\text{ hour}}{60\text{ minutes}}=\frac{158400\text{ ft}\cdot\text{hour}}{\text{hour}\cdot\text{ 60 minutes }}=\frac{158400ft}{60\text{ minutes}}[/tex]Then, it changes from minutes to seconds:
Use, 1 minute = 60 seconds
[tex]\frac{158400\text{ ft}}{60\text{ minutes}}\cdot\frac{1\text{ minute}}{60\text{ seconds}}=\frac{158400\text{ ft}\cdot1\text{ minute}}{60minutes\cdot60\text{seconds}}=\frac{158400\text{ ft}}{3600\text{ seconds}}[/tex]Then:
[tex]\frac{158400\text{ ft}}{3600\text{ second}}=44\text{ f}eet\text{ per second}[/tex]How would I solve Question 1 & 2 to find g(x)-f(x)
Answers
We will have the following:
1)
[tex]g(x)-f(x)=5^x-12-3x[/tex]2)
[tex]\begin{gathered} f(x)-g(x)=log_3(5x-5)-log_3(x-1) \\ \\ \Rightarrow f(x)-g(x)=log_3(\frac{5x-5}{x-1}) \\ \\ \Rightarrow f(x)-g(x)=log_3(5) \end{gathered}[/tex]Kyle has 20 gallons of gasoline to use for his snow plowing business. He uses gasoline in his snow plow at a constant rate. Let a represent the
number of driveways plowed and y represent the amount of gas remaining. Look at the graph of the function. Construct a function for this
scenario. Assume he must complete a driveway once he starts it.
20
10
0
Part A
10
20
30
What is the equation of the line?
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The required equation of the line is y = -(1/2)x + 20 which represents the given function in the shown graph.
Let a represent the number of driveways plowed and y represent the amount of gas remaining.
The graph of the function is given in the question
As per the given function, we take two points (0,20), and (40,0)
The required equation of the line will be as:
y - 20 = [(0 -20)/40-0)](a-0)
y - 20 = -(20/40)a
y - 20 = -(1/2)a
y = -(1/2)a + 20
Therefore, the required equation of the line is y = -(1/2)x + 20.
Learn more about the Lines here:
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Sket the right triangle and find the length of decide not given it necessari approximate the length to the nearest thousand
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Since we are dealing with a right triangle, we can use the Pythagorean theorem, shown below
[tex]\begin{gathered} H^2=L^2_1+L^2_2 \\ H\to\text{ hypotenuse} \\ L_1,L_2\to\text{ legs} \end{gathered}[/tex]In our case,
[tex]\begin{gathered} H=15,L_1=3 \\ \Rightarrow L^2_2=15^2-3^2=216 \\ \Rightarrow L_2=\sqrt[]{216}=14.6969\ldots\approx14.697 \\ \Rightarrow L_2=14.697 \end{gathered}[/tex]The answer is 14.697
Two lines are graphed on the coordinate plane below(INSERT PHOTO)What is the solution to the system represented by the lines?A- (4,6)B- (4, -6)C- (-4,-6)D- (-4, 6)
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Take into account that a system of equations represented by two lines, has a solution that is given by the point where the lines cross each other.
Then, based in the previous explanation and the given graph, you can notice that at the point (4,6) the lines cross each other.
Hence, the point (4,6) is the solution to the system of equations.
Transform 3 tons to pounds
Answers
To transform a ton to pounds we need to remember that each ton is 2000 pounds, then:
[tex]3\text{ T=3(2000) lb=6000 lb}[/tex]Therefore we have 6000 lb
Can anyone help me this please this is my last question to pass
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Lets take 2 pair of points from the table:
[tex]\begin{gathered} (x_1,y_1)=(0,4) \\ (x_2,y_2)=(2,10) \end{gathered}[/tex]The equation of line is y = mx + b
Where
m is slope
b is y-intercept
Let's find the slope (m):
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{10-4}{2-0} \\ m=\frac{6}{2} \\ m=3 \end{gathered}[/tex]So, the equation becomes:
[tex]y=3x+b[/tex]Let's plug in the first point (x, y) = (0,4) to find b:
[tex]\begin{gathered} y=3x+b \\ 4=3(0)+b \\ 4=0+b \\ b=4 \end{gathered}[/tex]Final Equation of the line:
[tex]y=3x+4[/tex]Solve for x in the equation x2+2x+ 1 = 17.X=-1+ /15X=-1+ /17X=-2+2.15X=-1+ /13
Answers
First, write the quadratic equation in standard form. Then, use the quadratic formula to find the solutions for the quadratic equation.
Remember that if a quadratic equation is written in standard form:
[tex]ax^2+bx+c=0[/tex]Where a, b and c are constants, then the solutions for x are given by:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]Starting with the given equation:
[tex]x^2+2x+1=17[/tex]Substract 17 from both members to write the equation in standard form:
[tex]\begin{gathered} \Rightarrow x^2+2x+1-17=17-17 \\ \Rightarrow x^2+2x-16=0 \end{gathered}[/tex]Use the quadratic formula, setting a=1, b=2 and c=-16:
[tex]\begin{gathered} x=\frac{-(2)\pm\sqrt[]{(2)^2-4(1)(-16)}}{2(1)} \\ =\frac{-2\pm\sqrt[]{4+64}}{2} \\ =\frac{-2\pm\sqrt[]{68}}{2} \end{gathered}[/tex]Simplify the expression using the properties of radicals. Since 68 is equal to 4 times 17, then:
[tex]\begin{gathered} x=\frac{-2\pm\sqrt[]{68}}{2} \\ =\frac{-2\pm\sqrt[]{4\cdot17}}{2} \\ =\frac{-2\pm\sqrt[]{4}\cdot\sqrt[]{17}}{2} \\ =\frac{-2\pm2\cdot\sqrt[]{17}}{2} \\ =\frac{2(-1\pm\sqrt[]{17})}{2} \\ =-1\pm\sqrt[]{17} \end{gathered}[/tex]Therefore, the solutions for x in the given equation are:
[tex]\begin{gathered} x_1=-1+\sqrt[]{17} \\ x_2=-1-\sqrt[]{17} \end{gathered}[/tex]