Answers
Area of a Triangle
Given a triangle of base length B and height length H, the area can be calculated by the formula:
[tex]A=\frac{B\cdot H}{2}[/tex]The base and the height must be perpendicular.
The height of the given triangle is H=7 in. We need to calculate the length of the base.
We are providing a new image where a variable x is introduced to help us calculate the base length:
The triangle formed by the sides 9-7-x is right, so we can calculate the value of x by applying the Pythagora's Theorem:
[tex]7^2+x^2=9^2[/tex][tex]49+x^2=81[/tex]Solving for x:
[tex]\begin{gathered} x^2=81-49=32 \\ x=\sqrt[]{32} \end{gathered}[/tex]The length of the base is:
[tex]B=9+\sqrt[]{32}[/tex]Thus, the area of the triangle is:
[tex]A=\frac{7\cdot(9+\sqrt[]{32})}{2}[/tex]Calculating:
A = 51.3 square inches
Related Questions
Question 15 ptsIf Martha puts $181 in the bank today at 2%, how much will she have have in 8 years? (Round to the 2decimal places)Question 25 ptsHow much will Bill and Mary need to put in the bank today at 5% to have $103,897 in 9 years? (Roundto 2 decimal places)
Answers
Question 1
Interest in 1 year at 2% per annum = 2/100 x $181 = $3.62
Total Interst after 8 years = 8 x $3.62 = $28.96
Total amount she has after 8 years = initial amount + Total Interst after 8 years
=$181 + $28.96 = $209.96 (2 decimal places)
Question 2
rate per annum, r = 5%
Time = 9years
Total amount = $103,897
Let the initial amount invested be p
interst after 1 year = 5% of p =$5p/100
Total interest after 9 years = 9 x 5p/100 = $45p/100
Total amount = p + 45p/100
That is,
103,897= p + 45p/100
[tex]undefined[/tex]A _____ is a line that best approximates the linearrelationship between two variables in a data set. *
Answers
We have the following:
A line of best fit is a straight line that is the best approximation of the given data set. It is used to study the nature of the relationship between two variables.
Therefore, the answer is line of best fit.
A line of best fit is a line that best approximates the linear
relationship between two variables in a data set.
Line AB is parallel to line CD. What is the measure of Z1?1/2BA3/45 80°7/8→D
Answers
From the image above,
measured angle 2 is 80degrees because the corresponding angles are equal.
Also meansured angle 1 + measured angle 2 is 180 degrees;
because the sum of angles on a straight line is 180 degrees
Write 2.78 x 10-4in standard form.
Answers
Given ,
The scientific notation of the equation is,
[tex]2.78\times10^{-4}[/tex]The standard notation of the scientific notation is,
[tex]\begin{gathered} 2.78\times\frac{1}{10^4} \\ =\frac{2.78}{10000} \\ =0.000278 \end{gathered}[/tex]Hence, the standard form is 0.000278.
Solve and graph the following inequality. 6c-12>42
Answers
We have the next inequality
[tex]6c-12>42[/tex]And we must solve and graph it.
First, we need to solve the inequality
To solve the inequality we must:
1. Add 12 to both sides
[tex]\begin{gathered} 6c-12+12>42+12 \\ \text{ Simplifying,} \\ 6c>54 \end{gathered}[/tex]2. Divide both sides by 6
[tex]\begin{gathered} \frac{6c}{6}>\frac{54}{6} \\ \text{ Simplifying,} \\ c>9 \end{gathered}[/tex]So, the solution of the inequality is c > 9
Finally, we must graph it
We can see that the solution are all values greater than 9, so the graph would be
What is the quotient and the remainder of 26÷3
Answers
Answer:
Quotient: 8
Remainder: 2
Explanation:
If we divide 26 by 3, we get:
So, the quotient is 8 and the remainder is 2.
Answer: Quotient: 8 Remainder: 2
Step-by-step explanation: 26/3 = 8 r2
An expression is shown. 14.1-(2.24*5); what is the value of the expression?
Answers
Given the expression:
[tex]14.1-(2.24\ast5)[/tex]Let's find the value of the expression.
To find the value of the expression, first evaluate the values in the parentheses:
[tex]\begin{gathered} 14.1-(2.24\ast5) \\ \\ =14.1-(11.2) \\ \\ \end{gathered}[/tex]Solving further:
[tex]\begin{gathered} 14.1-11.2 \\ \\ =2.9 \end{gathered}[/tex][tex]\begin{gathered} 14.1-(2.24\ast5) \\ \\ =14.1-(11.2) \\ \\ \end{gathered}[/tex]Solving further:
[tex]\begin{gathered} 14.1-11.2 \\ \\ =2.9 \end{gathered}[/tex][tex]undefined[/tex]Given b(x) = [X+41, what is b(-10)?O-10O -614
Answers
Given : b(x) = | x + 4 |
So, to find b(-10) , substitute with x = -10 at the function b(x)
So, b(-10) = | -10 + 4 | = | -6 | = 6
The amount of metal needed to be installed spring the workbench is
Answers
To answer this question we will use the following formula to compute the perimeter of a rectangle:
[tex]Perimeter=2(length+width)[/tex]Therefore the perimeter of the workbench is:
[tex]Perimeter=2(5ft+3ft).[/tex]Simplfying the above result we get:
[tex]Perimeter=2(8ft)=16ft.[/tex]Therefore we will need 16ft of metal stripping.
Answer: 16ft.
The stock market opens on Monday morning, a stock was valued at 42.50. The value of that stock increase by the same amount each day for the next three days. After three days, the value of stock was 50.00. Which equation is used to find x, the amount the stock rose in value each day.
Answers
The stock market opens on Monday morning, a stock was valued at 42.50.
The intial value of stock = 42.50
The value of that stock increase by the same amount each day for the next three days.
Let the increase amount in each day is x
then, increase amount in three day = 3x
After three days, the value of stock was 50.00.
Net amount after three day = 50.00
Net amount after three day = Initial value of stock + Incease amount in three day
50 = 42.50 + 3x
3x + 42.50 = 50
Answer: 3x + 42.50 = 50
A Statistics exam has mean m=78 in standard deviation of g=8 estimate the portion of Grades between 66 and 90
Answers
In order to estimate the portion of grades between 66 and 90, first let's find the z-score for these two values, using the formula:
[tex]z=\frac{x-m}{g}[/tex]So we have:
[tex]\begin{gathered} z_1=\frac{66-78}{8}=-1.5 \\ z_2_{}=\frac{90-78}{8}=1.5 \end{gathered}[/tex]Looking at the z-table, a z-score of 1.5 corresponds to a z-value of 0.0668.
Since we have this z-value from the left and right, the percentage we want is:
[tex]\begin{gathered} P=1-0.0668-0.0668 \\ P=0.8664=86.64\text{\%} \end{gathered}[/tex]The proportion of passengers who miss a flight for which they have a reservation is0.0995. Suppose a flight 290 reservations. Find the standard deviation of the sampleproportion, ºf, rounded to the nearest ten-thousandth (4 decimal places).
Answers
Answer
Standard deviation of the sample proportion = 0.0176
Explanation
For a distribution with proportion, p, the standard deviation of the sample proportion is given as
[tex]\sigma_x=\sqrt[]{\frac{p(1-p)}{n}}[/tex]where
p = sample proportion = 0.0995
n = sample size = 290
[tex]\begin{gathered} \sigma_x=\sqrt[]{\frac{p(1-p)}{n}} \\ \sigma_x=\sqrt[]{\frac{0.0995(1-0.0995)}{290}} \\ \sigma_x=\sqrt[]{\frac{0.0995(0.9005)}{290}} \\ \sigma_x=\sqrt[]{\frac{0.08959975}{290}} \\ \sigma_x=\sqrt[]{0.0003089647} \\ \sigma_x=0.0176 \end{gathered}[/tex]Hope this Helps!!!
please help me and also l will send you the pic
Answers
The estimate is 5 while the difference is 4.3
Here, we want to find the estimate the difference and also get the real difference between the two numbers
To get the estimate, we round up each of the numbers to the closest integer
When we talk of an integer, we mean the nearest whole number
Thus, 8.5 becomes 9
while 4.2 becomes 4
The estimated difference is thus 9-4 = 5
However, the actual difference is what we have when we actually make a direct subtraction
Thus, mathematically, we have this as 8.5 - 4.2 = 4.3
Use the figure below to complete the following problem.Given:FLAG isGXYZ isGхYZY=
Answers
∠Y = ∠L (option C)
Explanation:FLAG is similar to XYZG.
This means the corresponding angles are congruent (equal).
∠F = ∠X
∠L = ∠Y
∠A = ∠Z
∠G =∠G
Hence, ∠Y = ∠L (option C)
"A pump can fill a tank in 3 hours. A more powerful pump can fill the same tank in 2 hours. How long would it take to fill the tank with both pumps working?" Is my answer correct or incorrect? 1/3+1/2=3+2/3*2 5/15=15/515/5=3hrs
Answers
A pump can fill a tank in 3 hours. A more powerful pump can fill the same tank in 2 hours. How long would it take to fill the tank with both pumps working?" Is my answer correct or incorrect?
we have that
fisrt pump ------> fill a tank in 3 hours
that means
100% -----> 3 hours
1 hour ------> 33.33%
second pump
fill the same tank in 2 hours
100% -----> 2 hours
1 hour -----> 50 %
therefore
with both pumps working
1 hour ------> (33.33%+50%)=83.33%
applying proportion
1/83.33=x/100
x=100/83.33
x=1.2 hoursyour answer is not correctbecause the total time must be less than 2 hours (time of the second pump)The value of tan(alpha+beta) given sin(alpha)=40/41 and sin(beta)=15/17 and cos(∝ + β)= -528/697 and sin(∝ + β)= 455/679
Answers
Answer
Tan (∝ + β) = -455/528
Explanation
Tan (∝ + β) = ?
Given:
Sin ∝ = 40/41
Sin β = 15/17
Cos (∝ + β) = -528/697
Sin (∝ + β) = 455/697
Note: Tan ∝ = Sin ∝/Cos ∝
⇒ Tan (∝ + β) = (Sin ∝ + β)/(Cos ∝ + β)
Recall Sin (∝ + β) = 455/697 and Cos (∝ + β) = -528/697
∴ Tan (∝ + β) = (455/697)/(-528/697)
Tan (∝ + β) = 455 /697 x (-697/528)
Tan (∝ + β) = -455/528
Question 5 (1 point)A student takes a multiple-choice test with 8 questions on it, each of which have 4 choices. The student randomlyguesses an answer to each question.What is the probability that the student gets exactly 4 questions correct?Round to 3 decimal places.a0.886b0.9730.0870.208d
Answers
We can use Binomial distribution to calculate the probability of exactly 4 success
There are 8 questions which is our trial
Probability of succes (p)
Since in every question, there is 4 options with one right answer, then probability of success (p) = 1/4 = 0.25
probabiliti of failure (q) = 1- p = 1- 0.25 = 0.75
We will now use the formula below
[tex]p(x)^{}=^nC_xP^xq^{n-x}[/tex]substitute the values into the formula
[tex]p(x=4)=^{8\text{ }}C_4(0.25)^4(0.75)^{8-4}[/tex][tex]=\frac{8!}{(8-4)!4!}.(0.25)^4.(0.75)^4[/tex][tex]=\frac{8!}{4!4!}\text{.}(0.25)^4(0.75)^4[/tex][tex]=\frac{8\times7\times6\times5\times4!}{4\times3\times2\times1\times4!}\times(0.25)^4\times(0.75)^4[/tex][tex]=\frac{1680}{24}\times(0.00390625)\times(0.31640625)[/tex][tex]\approx0.087[/tex]According to the data in the table which country has a more population density ?
Answers
The first step to solve the question presented is to calculate the population density for each country, which is defined as the ratio from the population and the area of the country, as follows:
[tex]D=\frac{P}{A}[/tex]Let us to perform the calculation for both countries with data in the table.
[tex]\begin{gathered} D_{\text{America}}=\frac{310,000,000}{3,539,225}\cong87.59\frac{people}{mi^2} \\ D_{\text{Mexico}}=\frac{122,000,000}{742,485}\cong164.31\frac{people}{mi^2}_{} \end{gathered}[/tex]From the solution presented we are able to conclude that the country with the highest population density from those in the table is Mexico
1) Write an equation of the line perpendicular to: y = 3x - 9 with a y-intercept of 4.
Answers
The given equation is
[tex]y=3x-9[/tex]The new line is perpendicular to the given equation, which means we have to use the following formula.
[tex]m\cdot m_1=-1[/tex]Where the slope of the given line is 3 (the coefficient of x).
[tex]m\cdot3=-1[/tex]We solve for m.
[tex]m=-\frac{1}{3}[/tex]So, the slope of the new perpendicular line is -1/3.
According to the problem, the y-intercept of the new perpendicular line is 4. Now, we use the slope-intercept form to write the equation.
[tex]\begin{gathered} y=mx+b \\ y=-\frac{1}{3}x+4 \end{gathered}[/tex]Therefore, the equation of the new line is[tex]y=-\frac{1}{3}x+4[/tex]please try to do the work detailed with answers and work.
Answers
The general sine function is given as
[tex]y=A\sin (B(x-C)+D)[/tex]Where
A=Amplitude; B= Period Factor; Horizontal shift; D= Vertical shift or displacement
From the sine curve, the following can be found
[tex]A=6-3=3[/tex][tex]undefined[/tex]In the right triangle ABC angles B and C are congruent. What is the measure of B and C?
Answers
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
From Triangle ABC, we have that:
[tex]\begin{gathered} A=90^0(Right\text{ angle)} \\ B\text{ = x} \\ C\text{ = x} \\ \text{Because Angles B and C are congruent} \end{gathered}[/tex][tex]\begin{gathered} 90^0+x+x=180^0 \\ 90^{0\text{ }}+2x=180^0 \\ \text{collecting like terms, we have that:} \\ 2x=180^0-90^0 \\ 2x=90^0 \\ \text{Divide both sides by 2, we have that:} \\ \text{x = }\frac{90^0}{2} \\ \text{x = 45}^0 \end{gathered}[/tex]CONCLUSION:
The measure of B and C are: 45 and 45 degrees --- OPTION A
In the diagram from question 15, which statement would prove that line a and b are parallel?
Answers
the answer is D
[tex]m\measuredangle1+m\measuredangle7=180[/tex]How much will a customer spend on a sweater that is $65.00 but discounted 20% and purchased in a state that has an 8% sales tax?
Answers
1) Gathering the data
Sweater $65
Discounted 20%
Tax: 8%
2) We can find this final price using this formula/calculation
Since the price has been discounted by 20% we can multiply $65 x 0.8 to find the discounted price, but the sweater will be sold with a tax of 8% so we can multiply by (1 + 0. 08) to get the final price, i.e. $56.16
A
AGE VS. STATES TRAVELED TO Age States (years) Traveled to 54 46 Linear Regression: y=0.111x+7.668 slope: 12 5 3 1 Y-intercept: 25 17 35 2 Use your equation to predict the age of a person if he/she travelled to 20 states. 68 4 104 12
Answers
The linear regression equation is expressed as
y = 0.
How do you find any unit price?
Answers
The unit price of an item is the cost per unit of the item. We divide the price of certain number of units of an item by the number of units to find the unit price of that item.
what is the solution set of y equals x squared plus 2X + 7 + y equals x + 7
Answers
The given equations are
y = x^2 + 2x + 7
y = x + 7
We would substitute y = x + 7 into the first equation. It becomes
x + 7 = x^2 + 2x + 7
Collecting like terms, it becomes
x^2 + 2x - x + 7 - 7 = 0
x^2 + x = 0
By factorising x, it becomes
x(x + 1) = 0
Thus,
x = 0 or x + 1 = 0
x = 0 or x = - 1
Substituting x = 0 into y = x + 7, it becomes
y = 0 + 7
y = 7
Thus, one solution set is (0, 7)
Substituting x = - 1 into y = x + 7, it becomes
y = - 1 + 7
y = 6
Thus, another solution set is (- 1, 6)
Therefore, the solution sets are
{(0, 7), (- 1, 6)}
Option A is correct
13/50 make as a decimal
Answers
To convert the fraction 13/50 to decimal, we have to divide 13 by 50.
We can also calculate it as:
[tex]\frac{13}{50}=\frac{13}{50}\cdot\frac{2}{2}=\frac{26}{100}=0.26[/tex]In this case, we multiply both the numerator and the denominator by 2. Then, we obtain a denominator of 100, which means that the numerator is in hundredths. Then, we can write is as 0.26.
Answer: the decimal expression of 13/50 is 0.26.
solve following equation6+y=18
Answers
y=12
Explanation
The subtraction property of equality tells us that if we subtract from one side of an equation, we also must subtract from the other side of the equation to keep the equation the same,
in order to know the y value, we have to isolate y, then
Step 1
subtract 6 in both sides
[tex]\begin{gathered} 6+y=18 \\ 6+y-6=18-6 \\ \end{gathered}[/tex]Step 2
add like terms
[tex]\begin{gathered} 6+y-6=18-6 \\ y=12 \end{gathered}[/tex]therefore, the answer is
[tex]y=12[/tex]I hope this helps you
Substitution, SUVAT
Use the correct equation below to work
out the terms required:
v=u + at, or v² = u² + 2as
a) u = 6ms ¹, a = 3ms2, v = 30ms ¹, find t.
b) a = 0.5ms², v = 10.5ms¹, t = 5s, find u.
c) u = 2ms ¹, v = 6ms¹, a = 0.5ms², find s.
Answers
The value of time (t) is equal to 8 seconds.
The value of the initial velocity (u) is equal to 8 meters per seconds.
The value of the distance (s) is equal to 32 meters.
How to find the missing terms?Mathematically, the first and third equation of motion are given by this mathematical expressions:
v = u + at
v² = u² + 2as
Where:
V represents the final velocity.U represents the initial velocity.S represents the distance travelled or covered.t represents the time measured in seconds.For the first part (a), we would find time (t) by using the first equation of motion as follows;
v = u + at
30 = 6 + 3t
3t = 30 - 6
3t = 24
Time, t = 24/3
Time, t = 8 seconds.
For the second part (b), we would find the initial velocity (u) by using the first equation of motion as follows;
v = u + at
10.5 = u + 0.5(5)
10.5 = u + 2.5
Initial velocity (u) = 10.5 - 2.5
Initial velocity (u) = 8 m/s.
For the third part (b), we would find the distance (s) by using the third equation of motion as follows;
v² = u² + 2as
6² = 2² + 2(0.5)s
36 = 4 + s
Distance, s = 36 - 4
Distance, s = 32 meters.
Read more on Initial velocity here: brainly.com/question/13273980
#SPJ1
rita Bob and dale served a total of 83 orders Monday at the school cafeteria. rita served 9 fewer orders than bob. Dale served 2 times as many orders as bob. how many orders did they each serve
Answers
Info given
Bob and dale served a total of 83 orders Monday at the school cafeteria. rita served 9 fewer orders than bob. Dale served 2 times as many orders as bob. how many orders did they each serve
Solution
We can find the number of orders for Rita like this:
[tex]\text{Rita}=83-9=74[/tex]And for Dale we have this:
[tex]\text{Dale}=2\cdot83=166[/tex]