Given:
Base of triangle = b
Height of triangle, h, is 3 feet less than twice its base. This is expressed as:
h = 2b - 3
Area of triangle = 52 ft²
To find the height of the triangle, use the Area of a triangle formula below:
[tex]A=\frac{1}{2}bh[/tex]Thus, we have:
[tex]\begin{gathered} 52=\frac{1}{2}\times b\times(2b-3) \\ \\ 52=\frac{b(2b-3)}{2} \end{gathered}[/tex]Let's solve for the base, b:
[tex]\begin{gathered} 52=\frac{2b^2-3b}{2} \\ \\ Multiply\text{ both sides by 2:} \\ 52\times2=\frac{2b^2-3b}{2}\times2 \\ \\ 104=2b^2-3b \end{gathered}[/tex]Subtract 104 from both sides to equate to zero:
[tex]\begin{gathered} 2b^2-3b-104=104-104 \\ \\ 2b^2-3b-104=0 \end{gathered}[/tex]Factor the quadratic equation:
[tex](2b+13)(b-8)[/tex]Thus, we have:
[tex]\begin{gathered} (2b+13)\text{ = 0} \\ 2b\text{ + 13 = 0} \\ 2b=-13 \\ b=-\frac{13}{2} \\ \\ \\ (b-8)=0 \\ b=8 \end{gathered}[/tex]We have the possible values for b as:
b = - 13/2 and 8
Since the base can't be a negative value, let's take the positive value.
Therefore, the base of the triangle, b = 8 feet
To find the height, substitute b for 8 from the height equation, h=2b-3
Thus,
h = 2b - 3
h = 2(8) - 3
h = 16 - 3
h = 13 feet.
Therefore, the height of the triangle, h = 13 feet
ANSWER:
13 feet
the coordinates of the point shown in fig 23.16 are (3,5)
Answer:
False
Explanation:
In the coordinate notation (x, y), the left entry represents the x-coordinate and the right entry the y-coordinate. Therefore, if we want to represent the point x = 5, y = 3, we would write
[tex](5,3)[/tex]Hence, the representation (3, 5) does not represent the point x =5, y = 3, rather, it represents x = 3, y = 5, and therefore, the statement given is false.
810 А 30° E Given: Circle C. What is the value of angle x? B 99° 69° 132 30°
In this problem you can reflect the small triangle and you will see that the angle D is equal to the angle x, and the angle E is equal to the angle B so we can sum tyhe internal angles of the big triangle to find x so:
[tex]x+81+30=180[/tex]And we solve for x so:
[tex]\begin{gathered} x=180-81-30 \\ x=69 \end{gathered}[/tex]the angles x is equal to 69º
Use the sum and difference identities to rewrite the following expression as a trigonometric function of a single number.tan(80°) – tan (20)1 + tan(80°)tan (20
Okay, here we have this:
Considering the provided expression, we are going to use the tangent formula of a subtraction, and is the following:
[tex]\tan (A-B)=\frac{tan\mleft(A\mright)-tan\mleft(B\mright)}{1+tan\mleft(A\mright)tan\mleft(B\mright)}[/tex]We can see that the expression they provide us has the same form as that of the tangent of a subtraction, where A is equal to 80° and B is equal to 20°, so we obtain:
[tex]\begin{gathered} \frac{tan\left(80°\right)-tan\left(20°\right)}{1+tan\left(80°\right)tan\left(20°\right)} \\ =\tan (80\degree-20\degree) \\ =\tan (60\degree) \end{gathered}[/tex]Finally we obtain that the original expression is equal to tan(60°).
Evaluate ( (dx-4) dx 16 S (WX - 4) dx = ( (Type an exact answer in simplified form) 9
Identifies which property it belongs to1) 15^8/5^32) (8^2)^1
Given the calculation
[tex]\frac{15^8}{5^3}[/tex]Second calculation
[tex](8^2)^1[/tex]29. How long will it take to double an investment at 3.7% compounded continuously? Round your answer to the nearest tenth of a year. years
The formula for compounding continuously is :
[tex]A=Pe^{rt}[/tex]where A is the future amount
P is the principal amount
e is a constant
r is the rate of interest
and
t is the time in years.
The question stated that the investment will be doubled, so the future amount will be twice the principal amount.
A = 2P
The rate of interest is 3.7%
e is a constant approximately equal to 2.71828..
Subsitute the values to the formula and solve the value of t :
[tex]\begin{gathered} A=Pe^{rt} \\ 2P=Pe^{0.037t} \\ 2=e^{0.037t} \end{gathered}[/tex]Take the natural logarithm of both sides,
note that ln e = 1
[tex]\begin{gathered} \ln 2=\ln e^{0.037t} \\ \ln 2=0.037t\ln e \\ \ln 2=0.037t(1) \\ t=\frac{\ln 2}{0.037}=18.73 \end{gathered}[/tex]The answer is 18.73 years
Mailk earns 10 dollars per hour at his job. He wants to change to a job that will play 12 dollars per hour. What will be the porcent increase in Mailk's hourty pay if he makes this jobs change.:))))))))))))))))))))))))))))))))))))))
Given the following exponential function, identify whether the change representsgrowth or decay, and determine the percentage rate of increase er decrease.y = 2500(1.04)
The equation of a exponential function is of the form
[tex]y=a(b)^x[/tex]where
b is the base of the exponential function
If the value of b>1 -----> is a growth function
If the value of b<1 ----> is a decay function
In this problem
b=1.04
1.04 > 1
therefore
Is a growth functionPart b
Determine the percentage rate of increase
we have that
b=1+r
r=b-1
r=1.04-1
r=0.04
convert to percentage
r=0.04*100
r=4%what is the value of the expression when m=2 and n=-3. (4m^-3n^2)^2
Giving the funtion
[tex](4m^{-3}n^2)^2[/tex]m=2
n=-3
[tex](4(2)^{-3}(-3)^2)^2[/tex][tex](\frac{4}{2^3}(9))^2[/tex][tex](\frac{36}{2^3})^2[/tex][tex](\frac{36^2}{2^6})[/tex][tex](\frac{2^49^2}{2^2*2^4})=\frac{9^2}{2^2}[/tex][tex]\frac{81}{4}[/tex]then the evaluated function in m=2 n=-3
has a value of 81/4
48, -24, 12, -6,... 50th term
For the next series we will calculate its expression
[tex]a_n=(-1)^{n+1}3\cdot2^{^{5-n}}[/tex]For n = 1
an = 48
For n = 2
an = -24
For n = 50
an = 8.5265128e-14
How are these functions related? How are their graphs related
Notice that the difference between the two equations is the +5 on the right side of the second equation.
The graph of the following equations are as folllows:
For y=x:
For y=x+5:
Thus, the graph of y = x was shifted 5 units upward to obtain the graph of y=x+5.
Therefore, each value or output of y=x+5 is 5 more than the corresponding output of y=x. Consequently, the graph of y=x+5 is the graph of y=x translated up by 5 units.
Thus, the correct answer is option C.
A researcher randomly purchases several different kits of a popular building toy. The following table shows the number of pieces in each kit in the sample. Find the standard deviation of the data. Round your answer to the nearest hundredth, if necessary.
The Solution:
Given:
We are required to find the standard deviation of the given data.
Find the sample mean of the given data.
Find the standard deviation of the data.
Therefore, the correct answer is 68.07
whats the rate of change in the equation 0.860(17) + 3.302.
Given:
Let y= 0.860(17) + 3.302
The rate of change is the same as the slope of the equation
Comparing the given equation with the standard for of the equation y =mx + b
Determine if the following equations are parallel, perpendicular, or neither. 7(x – 1) = 3y + 21 and 3.5x + 1.5y = 4.5
Given the two equations
7(x - 1) = 3y + 21
3.5x + 1.5y = 4.5
To determine if the lines are visible or perpendicular
Step 1: Expand the equations and make y the subject of the formula
7(x - 1) = 3y + 21
=> 7x - 7 = 3y + 21
=> 3y = 7x - 7 - 21
=> 3y = 7x -28
Divide both sides by 3
y = 7/3x - 28/3 ------equation 1
3.5x + 1.5y = 4.5
1.5y = -3.5x + 4.5
Divide both sides by 1.5
y = -3.5/1.5 x + 4.5/1.5
y = -7/3x + 3--------equation 2
Step 2: compare the two equations to the equation of a line, y = mx + c
For equation 1
m = 7/3
For equation 2
m= -7/3
The slopes are not the same
Also, the product of the gradients did not give -1
It can be seen that the lines are neither perpendicular nor parallel
can you please help me
The slope intercept form is y = m x + b
We need to put the equation -x + 4y = -8 in this form
At first, add both sides by x
[tex]\begin{gathered} -x+x+4y=-8+x \\ 4y=-8+x \end{gathered}[/tex]Then divide both sides by 4 to make the coefficient of y = 1
[tex]\frac{4y}{4}=\frac{-8}{4}+\frac{x}{4}[/tex]-8/4 = -2
x/4 = 1/4 x
[tex]y=-2+\frac{1}{4}x[/tex]Now switch -2 and 1/4 x
[tex]y=\frac{1}{4}x-2[/tex]Let us find which choice is?
It is the first one for the equation
Let us choose the graph
For the graph, the line intersects the y-axis at (0, -2)
The slope is positive, then its direction to the right
The x-intercept is (8, 0)
Then it is the last graph you post with equation y = 1/4 x - 2
Do you see it
-What is the product of (a - 1) and (2a + 2)?A 2(a2 - 2)B 2(a2 - 1)C a2 + 4a - 2D2a2 - 4a - 2-
The product of the sum and difference binomials is
[tex](x-y)(x+y)=x^2-y^2[/tex]We will use this rule to solve the question
We need to find the product of (a - 1) and (2a + 2)
At first, we will take 2 as a common factor from the second bracket
[tex]\begin{gathered} 2a+2=2(\frac{2a}{2}+\frac{2}{2}) \\ 2a+2=2(a+1) \end{gathered}[/tex]Now, we will multiply (a - 1) by 2(a + 1)
[tex](a-1)(2a-2)=2(a-1)(a+1)[/tex]By using the rule of the product of the sum and difference above, then
[tex]\begin{gathered} 2(a-1)(a+1)=2(a^2-1^2) \\ 2(a-1)(a+1)=2(a^2-1) \end{gathered}[/tex]The answer is B
The dot plot shows how many customers purchased different numbers of shirts at a sale last weekend.
The interquartile range IQR of a dataset is the difference between the upper and lower quartiles, Q3 and Q1
The median of the whole dataset is Q2 and corresponds to the value x=3.5
The value of Q1 is the median of the lower 3 values: Q1=2
The value of Q3 is the median of the upper 3 values: Q3=5
The IQR is: 5 - 2 = 3
Convert from Point-Slope Form into Slope-Intercept Form. Show your work!1. y + 1 = 7(x + 2) 2. y – 1 = –2(x – 1) 3. y – 2 = 1/4(x – 1) 4. y – 4 = 3(x – 3)
1. y+10=7(x+2) (applying the distributive law to the right side of the equation)
y= 7x+14-10 (substracting 10 in both sides of the equality)
y=7x+4
2. y-1=-2(x-1) (applying the distributive law to the right side of the equation)
y-1=-2x+2 (adding 1 in both sides of the equality)
y=-2x+2+1 (simplifying)
y=-2x+3
3. y-2=1/4(x-1) (applying the distributive law to the right side of the equation)
y-2=x/4 -1/4 (adding 2 in both sides of the equality)
y=1/4(x) -1/4+2 (simplifying)
y=1/4(x) +7/4
4. y-4=3(x-3) (applying the distributive law to the right side of the equation)
y-4=3x-9 (adding 4 in both sides of the equality)
y=3x-9+4 (simplifying)
y=3x-5
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Select the correct anawer Which of the following represents a function?
A function relates input to output. Functions can be one to one or many to one. The x values represent the input while the y values represent the output. In the case of one to one, it means that the output has only one corresponding input. Many to one means that there are many input values for one output value. An input value cannot have more than 1 output value. If this happens, then it is not a function. Looking at the options given,
Option A is a function since no input value has more than one output value
Option B is not a function since the output values of 7 and 1 has the same input value of - 1
For option C, the values are (- 3, - 2)' (- 1, 1), (- 1, - 5), (1, 4). It is not a function since the output values of 1 and - 5 has the same input value of - 1
Option D is not a function since the output values of 7 and 1 has the same input value of - 1
The correct option is A
Cuanto es 123 x 200?
Answer:
[tex]123\times200=24600[/tex]Explanation:
We want to find the product of 123 and 200;
Therefore, the product of 123 and 200 is;
El producto de 123 y 200 es;
[tex]123\times200=24600[/tex]The mean per capita income is 24,653 dollars per annum with the standard deviation of 778 dollars per annum. What is the probability that the sample mean would be less than $24,745 if a sample of 441 persons is randomly selected? Round your answer to four decimal places
Remember that
[tex]z=\frac{x-μ}{\frac{σ}{\sqrt{n}}}[/tex]where
μ=24,653
σ=778
n=441
X=24,745
substitute
[tex]\begin{gathered} z=\frac{24,745-24,653}{\frac{778}{\sqrt{441}}} \\ \\ z=2.4833 \end{gathered}[/tex]using the values of the z-score table
we have that
P(x>2.4833) = 0.0065086
therefore
The answer is 0.0065Points S and T are midpoints of the sides of triangle FGH.Triangle G H F is cut by line segment S T. Point S is the midpoint of side H G and point T is the midpoint of H F. The lengths of H T and T F are 6 centimeters. The lengths of H S and S G are 4 centimeters. The length of S T is 8 centimeters.What is GF?
The measure of length of GF is 16 cm.
Given that point S is the midpoint of side HG and point T is the midpoint of HF of triangle FGH, the line segment ST is parallel to the side GF, and the triangles FGH and TSH are similar with proportional sides, then:
[tex]\frac{GF}{ST}=\frac{FH}{TH}=\frac{GH}{SH}[/tex]
We are given the following;
FH = HT + FT = 6 + 6 = 12 cm [HT = FT = 6 cm]
GH = HS + GS = 4 + 4 = 8 cm [HS = GS = 4 cm]
ST = 8 cm
Substitute the given values, we will get the following;
[tex]\frac{GF}{8} =\frac {12}{6} = \frac{8}{4}\\\frac{GF}{8} =\frac {12}{6}\\\frac{GF}{8} = 2[/tex]
GF = 2 * 8 = 16 cm
Thus, the measure of the length of GF is 16 cm.
To learn more about the midpoint theorem visit:
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The volume of an iceberg that is below the water line is 2^5 cubic meters. the volume that is above the water line is 2^2 cubic meters. how many times greater is the volume below the water line than above it?
Let:
[tex]\begin{gathered} V_1\colon\text{ volume of iceberg below the water line} \\ V_2\colon\text{ volume of iceberg above the waterline} \end{gathered}[/tex]We want to finde some number k such that we can express the volume of the iceberg below the water line as the product of k and the volume of the iceberg above the waterline, this is:
[tex]V_1=k\cdot V_2[/tex]then, solving for k we have the following:
[tex]\begin{gathered} V_1=2^5m^3 \\ V_2=2^2m^3 \\ V_1=k\cdot V_2 \\ \Rightarrow k=\frac{V_1}{V_2}=\frac{2^5}{2^2}=2^{5-2}=2^3^{} \\ k=2^3 \end{gathered}[/tex]we have that k=2^3. This means that the volume of the iceberg above the water line is 2^3 times the volume of the iceberg below the water line
Work each problem according to the instructions given.a. Solve:2r +3=8=Previewb. Find r when y = 0:2x + 3y = - 8T =Previewc. Find y when I = 0;21 + 3y =- 8y =Previewd. Solve for y:2x + 3y8y =Preview
a)
The given equationis expressed as
2x + 3 = - 8
To solve for x, the first step is to subtract 3 from both sides of the equation. We have
2x + 3 - 3 = - 8 - 3
2x = - 11
Finally, we would divide both sides of the equation by 2. We have
2x/2 = - 11/2
x = - 11/2
which of the following expressions could be used to determine?
We have the following:
They tell us that the capacity is 350, therefore that is the maximum value, it means that we must subtract the exchange rate from this value, that is, the number od tickets per hour that are sold, 23
thus
[tex]350-23h[/tex]The answer is the option B.
Watch help videoKevin has a bag that contains orange chews, strawberry chews, and peach chews. Heperforms an experiment. Kevin randomly removes a chew from the bag, records theresult, and returns the chew to the bag. Kevin performs the experiment 32 times. Theresults are shown below:An orange chew was selected 5 times.A strawberry chew was selected 17 times.A peach chew was selected 10 times.Based on these results, express the probability that the next chew Kevin removesfrom the bag will be peach chew as a percent to the nearest whole number.Answer:Submit Answer
Divide the amount of times that a peach chew was selected over the total number of times that the experiment was performed to find the probability that the next chew will also be a peach chew:
[tex]\frac{10}{32}=0.3125=31.25\text{ \%}[/tex]Then, as a percent to the nearest whole number, the probability that the next chew Kevin removes from the bag will be a peach chew, is:
[tex]31\text{ \%}[/tex]Determine whether the equation x + y2 = 5 is linear. If so, graph the function. If not, explain why.
Which points are on the graph of a linear function? Select all that apply
We will determine the points that belong to a linear function as follows:
*First set: We calculate the slope of the three points:
[tex]m_1=\frac{5-7}{0-(-1)}\Rightarrow m_1=-2[/tex][tex]m_2=\frac{3-7}{1-(-1)}\Rightarrow m_2=-2[/tex]So, the first set belongs to a linear function.
*second set:
[tex]m_1=\frac{0-1}{0-(-1)}\Rightarrow m_1=-1[/tex][tex]m_2=\frac{1-1}{1-(-1)}\Rightarrow m_2=0[/tex]So, the second set does not belong to a linear function.
*Third set:
[tex]m_1=\frac{5-5}{2-0}\Rightarrow m_1=0[/tex][tex]m_2=\frac{14-5}{3-0}\Rightarrow m_2=3[/tex]So, the third set does not belong to a linear function.
*Fourth set:
[tex]m_1=\frac{5-(-3)}{2-0}\Rightarrow m_1=4[/tex][tex]m_2=\frac{13-(-3)}{4-0}\Rightarrow m_2=4[/tex]So, the fourth set belongs to a linear function.
Explain why this is true.6x1/9=3x2/9
prove that
[tex]6\cdot(\frac{1}{9})=3\cdot(\frac{2}{9})[/tex]start on the left side
[tex]\frac{6}{1}\cdot\frac{1}{9}=\frac{6}{9}=\frac{2}{3}[/tex]continue with the right side
[tex]\frac{3}{1}\cdot\frac{2}{9}=\frac{6}{9}=\frac{2}{3}[/tex]we can conclude that both expressions are equal to 2/3.
.27 = as a percentage
.27 = as a percentage
To find out the number as percentage , multiply by 100
so
0.27*100=27%