We know that the height of the rectangular shape is BC=AD= 4 feet and the the area is A=29.2 ft^2. Since the area of our rectangle is given by
[tex]A=(DC)\times(BC)[/tex]we get
[tex]29.2=DC\times4[/tex]By moving the number 4 to the left hand side, we have
[tex]\begin{gathered} \frac{29.2}{4}=DC \\ \text{then} \\ DC=7.3 \end{gathered}[/tex]which also is the lenght of one side of our parallelogram.
Now, the area of our parallelogram is given by
[tex]A_P=\text{base}\times height[/tex]where the base is given by segment DC=7.3 ft and the height FG=2 BC. Then, we get
[tex]\begin{gathered} A_P=DC\times FG \\ A_P=DC\times2BC \end{gathered}[/tex]by substituting our previous result and BC=4 ft, we obtain
[tex]\begin{gathered} A_P=7.3\times2(4) \\ A_P=7.3\times8 \\ A_P=58.4ft^2 \end{gathered}[/tex]Then, the answer is 58.4 ft^2
In the diagram, what is the relationship between segments AC and BC? Explain your answer.
In the diagram the relationship between AC and BC is that they are the hypotenuse if the right angle triangles ADC and BDC and they are equal
What is a hypotenuse?The longest side in a right triangle is called the hypotenuse. In a right triangle, it is the side opposite the right angle.
The right triangle's hypotenuse is longer than its other two sides
When a perpendicular bisector (CD) bisects a line (in this case AB) the hypotenuse formed in the process are equal
The base and the perpendicular side, are related in accordance with the Pythagoras theorem. The square of the hypotenuse of a right triangle is the sum of the squares of its base and perpendicular side.
Learn more about Pythagoras theorem:
https://brainly.com/question/231802
#SPJ1
What is the solution to the equation below? Round your answer to twodecimal places.eX = 7.9
Solution
For this case we have the following equation:
[tex]e^x=7.9[/tex]For this case we can apply natural log in both sides and we got:
[tex]\ln (x)=\ln (7.9)=2.07[/tex]and then the solution would be:
D. x =2.07
if a/ b+1 = 2, what does 2b equal?
Number 9, Im not quite sure on how to do these
Solution:
Given:
[tex]f(x)=2(x-3)^2+1[/tex]The equation of a parabola in vertex form is given by:
[tex]y=a(x-h)^2+k[/tex]The coordinates of the vertex is given by (h,k).
Hence, comparing both equations,
[tex]\begin{gathered} f(x)=2(x-3)^2+1 \\ y=a(x-h)^2+k \\ a=2 \\ h=3 \\ k=1 \end{gathered}[/tex]Therefore, the coordinates of the vertex is;
[tex](h,k)=(3,1)[/tex]Jordyn and Anya left a 30% tip after having lunch at a restaurant. The amount of the tip was $14.10. Jordyn's lunch cost $22. Write and solve an equation you can use to find x, the cost of Anya's lunch.
The cost of Anya's lunch would be = $25
What is lunch?Lunch is the type of meal that is taken after the noon day or in the afternoon.
The percentage of tip left by Jordyn and Anya = 30%
The amount of the tip = $14.10
If 30% = 14.10
100% = $x
$x = 100 × 14.10/30
$x = 1,410/30
$x = 1,410/30
$x = $47
This is the total amount for the cost of lunch.
To find Anya's cost for lunch would be;
Total cost - Jordyn lunch cost = Anya lunch cost
Anya lunch cost = 47 - 22
= $25
Learn more about lunch here:
https://brainly.com/question/28699961
#SPJ1
Help me in these equation9^2 + b^2 = 15.81^2
ANSWER
b = 13
EXPLANATION
We want to solve the equation:
[tex]9^2+b^2=15.81^2[/tex]To do this, simplify the equation:
[tex]81+b^2=249.96[/tex]Isolate b:
[tex]\begin{gathered} b^2=249.96-81 \\ b^2=168.96 \\ Find\text{ the square root of boths side:} \\ b=\sqrt[]{168.96} \\ b=13 \end{gathered}[/tex]That is the answer.
It is Nadine’s birthday, and she is making walnut brownies for her sleepover. She invited eight of her friends to her party. The recipe that she is using makes twenty-four brownies, but she only wants to make eight. The recipe for twenty-four calls for \large 4\frac{1}{2} cups of walnuts. How many cups of walnuts will she need for eight people?
1 1/2 cups of walnuts she will need for eight people.
In the given question,
It is Nadine’s birthday, and she is making walnut brownies for her sleepover.
She invited eight of her friends to her party.
The recipe that she is using makes twenty-four brownies, but she only wants to make eight.
The recipe for twenty-four calls for [tex]4\frac{1}{2}[/tex] cups of walnuts.
We have to find how many cups of walnuts she needs for eight people.
From the question we know that the recipe that she is using makes twenty-four brownies.
For making twenty-four brownies she needs [tex]4\frac{1}{2}[/tex] cups of walnuts.
We can write [tex]4\frac{1}{2}[/tex] in simplified form by multiplying the 4 by 2 then add the result of multiplying 4 by 2 to 1.
So [tex]4\frac{1}{2}[/tex] = 9/2
24 brownies = 9/2 cups of walnuts
So 1 brownies = (9/2)/24 cups of walnuts
We can write it as
1 brownies = 9/2×1/24 cups of walnuts
Simplifying
1 brownies = 9/48 cups of walnuts
Since she have to make eight brownies.
So 8 brownies = 9/48×8 cups of walnuts
Simplifying
8 brownies = 9/6 cups of walnuts
8 brownies = 3/2 cups of walnuts
8 brownies =1 1/2 cups of walnuts
Hence, 1 1/2 cups of walnuts she will need for eight people.
To learn more about division method link is here
https://brainly.com/question/24269538
#SPJ1
“One subtracted
from the
product of 4 and
a number is 1 1”
how would i write it??
Beginning with the equation x=-27 write the new equation produced by dividing both sides by 3
Answer:
[tex]\frac{x}{3}=-9[/tex]
i need to know how to solve this question please
ANSWER
w = 6.71 or -6.71
EXPLANATION
Working together, two secretaries can stuff the envelopes for a political fund-raising letter in 4 hours. Working alone, it takes the slower worker 15 hours longer to do the job than the faster worker. How long does it take each to do the job alone?.
The slower worker takes 20 hours and faster worker takes 5 hours to complete the job .
In the question,
it is given that ,
two secretaries stuff the envelopes for a political fund-raising letter in 4 hours .
let the time taken by fast worker to complete the job be x hours .
the slower worker takes 15 hours longer to do the job than faster worker
So , the time taken by slow workers to complete the job will be (x+15) hours .
the amount of work done by faster worker in 1 day = 1/x
the amount of work done by slower worker in 1 day = 1/(x+15)
total work done by both in 1 day = 1/x + 1/(x+15)
their combined 1 day work will be equal to 1/4 .
The equation representing is
1/x + 1/(x+15) = 1/4
(x+15+x)/(x²+15x) = 1/4
(2x+15)/(x²+15x) = 1/4
4(2x+15) = x²+15x
8x + 60 = x²+15x
x² + 15x - 8x - 60 = 0
x² + 15x - 8x - 60 = 0
x² + 7x - 60 = 0
x² + 12x - 5x - 60 = 0
x(x+12) -5(x+12) = 0
(x-5)(x+12)=0
we get x -5 = 0 or x+12=0
x = 5 or x = -12 .
the time cannot be in negative ,
So , fast worker to complete the job in = 5 hours
slow worker to complete the job in = 20 hours
Therefore , The slower worker takes 20 hours and faster worker takes 5 hours to complete the job .
Learn more about Equation here
https://brainly.com/question/12944940
#SPJ4
What is the point slope form of the line with slope -1/4 that passes through the
point (9, 2)?
Answer:
[tex]y - 2 = - \frac{1}{4} (x - 9)[/tex]
Nate's age is six years more than twice Connor's age. If the sum of their ages is 24 find each age
Answer:
12
Step-by-step explanation:
nate's age=6
connor's age =6+6=12
Nate's age +connor's age =24
Nate's age=24÷3=8
connor's age=8+8=16
the sum of thier ages =24
Evaluate inverse functions The graph of y= h(x) is a line segment joining the points (-7,-5) and (-1,-2) Drag the endpoints of the segment below to graph y=h^-1(x)
When we have an inverse function, the domain and range are switched.
All x-coordinates become y-coordinates and vice-versa.
So, if the point (-7, -5) is a solution of h(x), the point (-5, -7) is a solution of h^-1(x)
If the point (-1, -2) is a solution of h(x), the point (-2, -1) is a solution of h^-1(x).
Therefore, the endpoints of the segment that represents the inverse function are the points (-5, -7) and (-2, -1).
4. A rectangular garage has a volume of 480 m, a length of 12 m and a width of 8 m. What isthe height of the garage?
Answer:
5 m
Explanation:
The volume of the rectangular garage can be calculated as:
[tex]\text{Volume }=\text{Length }\times\text{ Width }\times\text{ Height}[/tex]If we replace Volume by 480, Lenght by 12, and Width by 8, we get:
[tex]480=12\times8\times\text{ Height}[/tex]Now, we can solve the equation for the Height as:
[tex]\begin{gathered} 480=96\times\text{ Height } \\ \frac{480}{96}=\frac{96\text{ }\times Height}{96} \\ 5=\text{Height} \end{gathered}[/tex]Therefore, the height of the garage is 5 m
You deposited $3,000 in the bank in 2019. It is compounded annually at 4%. How much money will you have in 9 years (in 2028)?
ANSWER
[tex]\begin{equation*} \$4,269.94 \end{equation*}[/tex]EXPLANATION
To find the amount of money that you will have in 9 years, apply the formula for annually compounded amount:
[tex]A=P(1+r)^t[/tex]where P = principal
r = interest rate
t = number of years
Hence, the amount after 9 years is:
[tex]\begin{gathered} A=3000(1+\frac{4}{100})^9 \\ A=3000(1+0.04)^9=3000(1.04)^9 \\ A=\$4,269.94 \end{gathered}[/tex]That is the answer.
Help the question is attached
The correct option will be A that is t=(A-P)/Pr by the simplification of equation, "an equation is a mathematical statement that shows that two mathematical expressions are equal ".
What is equation?In its most basic form, an equation is a mathematical statement that shows that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. In mathematics, an equation is a relationship of equality between two expressions written on both sides of the equal to sign. 3y = 16 is an example of an equation. Some examples of important equations are:
Linear equationsQuadratic equationsCubic equationQuadratic equationsDifferential equationsParametric equationsHere,
A=P+Prt
A-P=Prt
t=(A-P)/Pr
The answer is A, which is t=(A-P)/Pr using the equation's simplified form. An equation is a mathematical statement that demonstrates the equality of two mathematical expressions.
To know more about equation,
https://brainly.com/question/25845758?referrer=searchResults
#SPJ1
By half-time at a basketball game, Tracy had already made 18 points. He makes only 3-point baskets in the second half of a game and made a total of 33 points the entire game.
Discrete or Continuous?
A recipe calls for 5 teaspoons of orange juice. A can of orange juice is 21 fluid ounces. How many teaspoons of juice is in the can?
Answer:
21 fluid ounces = 126 teaspoons
Step-by-step explanation:
1 teaspoons is 0.166667 fluid ounces
Now we just have to think 0.166667 * x = 21
21 ounces = 126 teaspoons
Hope this helped :)
Answer: the can contains 126 teaspoons in the can of range juice.
Step-by-step explanation:
given,
no. of teaspoons of orange juice is the call= 5 teaspoons
ounces in the orange juice can= 21 fluid ounces
if 1 ounce = 6 teaspoons
then, 21 ounces= 126 teaspoons.
to know more about conversions,
brainly.com/question/10499702
What would be the height of a building the cast a shadow 50 feet long at the same time
Given:
The height of the girl is 5 ft and the length of the shadow is 2 ft., at the same time the shadow of the building is 50 ft .
Required:
To find the height of the building.
Explanation:
Let the height of the building is h ft.
Since triangle ABC is similar to the triangle DEF.
Thus by using the similarity condition.
[tex]\begin{gathered} \frac{AC}{DF}=\frac{AB}{DE} \\ \frac{5}{h}=\frac{2}{50} \\ h=\frac{50\times5}{2} \\ h=125\text{ ft} \end{gathered}[/tex]Final Answer:
Thus the third option is the correct answer.
Solve for n: 2n = n + 3 O A. 1 O O c. 3 3 OD. 5 E 6
Step 1: Problem
2n = n + 3
Step 2: Concept
Collect like terms and find the value of x.
2n = n + 3
2n - n = 3
n = 3
Step 3: Final answer
n = 3
A new bank customer with $4,500 wants to open a money market account. The bank is offering a simple interest rate of 1.6%.
a. How much interest will the customer earn in 20 years?
b. What will the account balance be after 20 years?
a. The customer will earn
in interest.
a. The customer will earn $1440 as a interest after 20 years.
b. The account balance will be $5,940 after 20 years.
What is the simple interest?
Simple interest is, by definition, the amount of interest paid on a specific principal sum of money when an interest rate is applied.
The formula of simple interest is I = Prt.
P = principal
r = rate of interest per year.
t = time.
Given that, a customer deposits $4,500 for 20 years.
According to question, P = $4,500, r =1.6% = 0.016, t = 20 year
Putting the value of P, r, and t in I = Prt:
I =4,500 × 0.016 ×20
I =4,500 × 0.016 ×20
I = 1440
The interest is $ 1440.
The account balance will be $(1440 + 4,500) = $5,940.
To learn more about simple interest, you can visit below link:
https://brainly.com/question/29439608
#SPJ1
PLEASE HELP!! ILL GIVE YOU BRAINLIEST
Using your equation from step 2d, estimate the GPA of a student who studies for 15 hours a week. Justify your answer.
hours on left side (x) , gpa on right side (y)
The GPA of a student who studies for 15 hours a week is 2.935.
What is a GPA?
Grade point average, or GPA, is a conventional method of evaluating academic performance in the United States on a scale of 0 to 4.
How to calculate GPA?
To calculate your GPA, divide the total number of grade points earned by the total number of letter-graded units undertaken.
Here,
We have an equation y = 0.164x + 0.475
put x= 15
we get,
y = 0.164* 15 + 0.475
y = 2.935
Hence, The GPA of a student who studies for 15 hours a week is 2.935
To learn more about the GPA from the given link
https://brainly.com/question/14626093
#SPJ13
The ratio of adults to children is 400 to 150
SOLUTION
In mathematics, a ratio indicates how many times one number contains another.
And when we write quantities in ratio form, we represent ratio with the symbol :
For example: The ratio of A to B is written mathematically as A:B
Another important thing we must note when writing ratios is to always express both quantities in their simplest form.
With the above explanation, we can proceed in answering the question.
The ratio of adults to children which is 400 to 150, can be written mathematically in ratio form as:
[tex]\begin{gathered} =\frac{400}{150} \\ \text{Divide both the numerator and denominator by 10} \\ =\frac{40}{15} \\ \text{Divide both the numerator and denominator by 5} \\ =\frac{8}{3} \end{gathered}[/tex]Final answer: The ratio of adults to children is:
[tex]8\colon3[/tex]Mr. March sells popcorn at his theater. He uses 3 3/4 cups of unpopped corn to make 15 bags of popped corn. Write an equation for the number of bags of popcorn b that can be made with c cups of unpopped corn.
The equation for the number of bags of popcorn 'b' that can be made with 'c' cups of unpopped corn is
b = 4c.
Given, Mr. March sells popcorn at his theater.
He uses 3(3/4) cups of unpopped corn to make 15 bags of popped corn. We have to write an equation for the number of bags of popcorn 'b' that can be made with 'c' cups of unpopped corn.
Now, according to the question
3(3/4) cups = 15 bags
15/4 cups = 15 bags
1 cup = 4 bags
So, in 'c' cups he will make, 4c bags
therefore, 4c = b
Hence, the equation for the number of bags of popcorn 'b' that can be made with 'c' cups of unpopped corn is
b = 4c.
Learn more about Linear Equations here https://brainly.com/question/24085666
#SPJ9
Two friends drive off in different directions from the same place. One heads North at 40 miles per hour, while the other heads East at 25 miles per hour.
Complete an equation for the distance between the friends after t hours.
The equation for the distance between the friends after t hours is 47.17t.
What is the distance between two points?Let one point be (x, y) and another point be (h, k). Then the distance between the points will be
D² = (x - h)² + (y - k)²
Two companions drive off this way and from a similar spot. One travels North at 40 miles each hour, while different travels East at 25 miles each hour.
The equation for the distance between the friends after t hours is given as,
Let the x-axis as east and the y-axis as north. Then the coordinate after t hours will be (25t, 0) and (0, 40t). Then the distance between them is given as,
D² = (25t - 0)² + (0 - 40t)²
D² = 625t² + 1600t²
D² = 2,225t²
D = 47.17 t
The equation for the distance between the friends after t hours is 47.17t.
Learn more about the distance between two points here:
https://brainly.com/question/18296211
#SPJ1
I need help on the question in the picture attached. i tried posting it but no one is answering it and this was due last week. please help fast
Answer:
Yes
Explanation:
To find our whether Marrissa's budget will be enough for the party, we need to find the linear equation relating the cost and the number of guests. The linear equation is the form
[tex]y=mx+b[/tex]where y is the cost in dollars. m is the cost per guest, and b can be interpreted as additional charges for the party facility.
The cost per guest is given by the slope of cost vs. guest graph.
Let us pick two values (100, 1325) and (50, 725) and compute the slope:
[tex]\frac{\$1325-\$750}{100-50}=\frac{\$12}{\text{guest}}[/tex]With the value of slope m in hand, we now find b by using the values x = 100, y = 1325 (the choice of these values is arbitrary)
[tex]\begin{gathered} 1325=12(100)+b \\ 1325=1200+b \\ \therefore b=125 \end{gathered}[/tex]Hence, the equation relating the cost and the number of guests is
[tex]y=12x+125[/tex]Now, for 75 guests the cost will be
[tex]\begin{gathered} y=12(75)+125 \\ y=\$1025.\text{ } \end{gathered}[/tex]Therefore, Marrissa's budget, which is $1200, is greater than the cost of the party, meaning it will be enough.
Find the area of the figure below
Answer:
Step-by-step explanation:
b/c we can fairly say, that the parallelgram is also a rectangle of size 24 x 11, we can just solve that area
24*11= 264
We can see, this is a parallelogram.
The formula to calculate the area of a parallelogram is b x h, where b is base and h is height.
Given that base = 24 in, height = 11 in, we can calculate the area as : 24 x 11 = 264 in2.
Write an equation of the line in point-slope form that passes through the given points. (-2,8) and (7,-4)
The equation of the line is y-8 = [tex]\frac{-4}{3}[/tex] ( x+2) .
What is equation of the line ?
A line's coordinate plane equation can be expressed in two point form. Depending on the information at hand, a line's equation can be discovered using a variety of techniques. One approach is the two-point form. When two points that are on the line are known, this is used to find the equation of the line. The slope intercept form, intercept form, point slope form, and other crucial forms for representing the line equation.
Here the given two points are ,
[tex](x_1,y_1)=(-2,8)\\(x_2,y_2)=(7,-4)[/tex]
Now using slope formula,
slope m= [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
=> slope m = [tex]\frac{-4-8}{7+2}[/tex]
=> slope m = [tex]\frac{-12}{9}= \frac{-4}{3}[/tex]
Now using equation formula,
=> [tex]y-y_1 = m(x-x_1)\\[/tex]
=> y-8 = [tex]\frac{-4}{3}[/tex] ( x+2)
Hence the point slope form of the equation is y-8 = [tex]\frac{-4}{3}[/tex] ( x+2) .
To learn more about equation of the line ,
https://brainly.com/question/18831322
#SPJ1
Find the value of x in the triangle shown below
The answer is C, the square root of 65 (8.062).
