Solution:
We know that:
Interior angles of a triangle sum up to 180°.[tex]3a + 7u + 9 = 180\°[/tex]This means that:
[tex](7u + 9) + (2a - 3) + 32 = 3a + 7u + 9[/tex]Let's simplify the equation to find a.
Step-by step calculations:
Open the brackets:
[tex](7u + 9) + (2a - 3) + 32 = 3a + 7u + 9[/tex][tex]7u + 9 + 2a - 3 + 32 = 3a + 7u + 9[/tex]Cancel same terms on both sides:
[tex]7u + 9 + 2a - 3 + 32 = 3a + 7u + 9[/tex][tex]2a - 3 + 32 = 3a[/tex]Simplify the LHS:
[tex]2a + 29 = 3a[/tex]Subtract 2a both sides:
[tex]2a - 2a + 29 = 3a - 2a[/tex]=> [tex]29 = 3a - 2a[/tex]Simplify the RHS and change the sides:
=> [tex]\bold{a = 29}[/tex]Let's substitute the value of a in 3a + 7u + 9 = 180° to find u.
[tex]3a + 7u + 9 = 180\°[/tex]=> [tex]3(29) + 7u + 9 = 180\°[/tex]Simplify the LHS:
=> [tex]87 + 9 + 7u = 180[/tex]=> [tex]96 + 7u = 180[/tex]Subtract 96 both sides:
=> [tex]96 - 96 + 7u = 180 - 96[/tex]=> [tex]7u = 84[/tex]Divide 7 both sides:
=> [tex]\frac{7u}{7} = \frac{84}{7}[/tex]=> [tex]\bold{u = 12}[/tex]what is a slope of a line mean?
What is the slope of the line that cuts through the points (1, 2) and (5, 4)?
What is the slope of the line that cuts through the points (1, -5) and (3, 5)?
Is the function that cuts through the points (2, 3) and (-1, 6) increasing or decreasing?
What is the slope of the line that cuts through the points (4, 2) and (-2, 2)?
Answer:
1/2, 5, decreasing, 0Step-by-step explanation:
Use slope formula:
m = (y2 - y1)/(x2 - x1)1) Points (1, 2) and (5, 4)
m = (4 - 2)/(5 - 1) = 2/4 = 1/22) Points (1, -5) and (3, 5)
m = (5 - (-5))/(3 - 1) = 10/2 = 53) Points (2, 3) and (-1, 6)
m = (6 - 3)/(-1 - 2) = 3/-3 = -1Slope is negative, so function is decreasing4) Points (4, 2) and (-2, 2)
m = (2 - 2)/(-2-4) = 0/-6 = 0Answer:
1/5, 1, decreasing, 0
Step-by-step explanation:
Find each value
10/9 of 72
Question 4 of 5
What shape is this cross-section?
A. Rectangle
B. Triangle
C. Pyramid
D. Trapezoid
Answer:
It is a trapezoid! because you can tell that that is the shape of the entire model
Which of the following sets does the number 49 belong to?
Answer:
please give the complete question. cannot find answer with only half of the question
Fill in the blank to complete the sentence.
Jessie has 2 containers.
The first container has a capacity of 2 gallons.
The second container has a capacity of 9 quarts.
What is the difference in the capacity of the two containers? Give your answer in cups.
a. The difference in the capacity of the two containers is___cups
HELP ASAP
Answer:
they have a difference of 4 cups.
Step-by-step explanation:
container one: 1 gallon = 16 cups. 2 gallons = 32 cups.
container Two: 1 quart = 4 cups. 9 quarts = 36 cups.
36 cups - 32 cups = 4 cups
ABC and ADE are similar. Find the length of size CA
Answer:
since ABC and ADE are similar,they have equal areas.
(AC)^2/(AE)^2=area ABC/ADE
areaABC=ACE=1
so substitute it in the afformentioned equation
u will get,AC=AE
The length of side CA in triangle ABC is c * (a² + ab + ac) / (a * (a + b + c)).
To find the length of side CA in triangle ABC, we need to use the concept of similarity and corresponding sides. Let's denote the lengths of sides in each triangle:
Triangle ABC:
Length of side AB: a
Length of side BC: b
Length of side CA: c
Triangle ADE:
Length of side AD: x (corresponding to side AB in ABC)
Length of side DE: y (corresponding to side BC in ABC)
Length of side EA: z (corresponding to side CA in ABC)
Since triangles ABC and ADE are similar, their corresponding sides are in proportion:
AD/AB = DE/BC = EA/CA
We know that AD corresponds to AB, and DE corresponds to BC, so we can set up the following proportions:
x/a = y/b
Solving for y, we get:
y = (b * x) / a
Next, we can set up the proportion for EA/CA:
z/c = x/a
Solving for z, we get:
z = (c * x) / a
Now, we have expressions for y and z in terms of x, a, and b. Since the sum of the lengths of the sides of a triangle is always constant, we can write the equation:
x + y + z = a + b + c
Substituting the expressions for y and z:
x + (b * x) / a + (c * x) / a = a + b + c
To find the value of x, we can multiply the entire equation by a to eliminate the denominator:
a * x + b * x + c * x = a² + ab + ac
Combining the x terms:
x * (a + b + c) = a² + ab + ac
Dividing both sides by (a + b + c):
x = (a² + ab + ac) / (a + b + c)
Now that we have found the value of x, we can substitute it back into the expression for z:
z = (c * x) / a
z = (c * (a² + ab + ac) / (a + b + c)) / a
Simplifying:
z = c * (a² + ab + ac) / (a * (a + b + c))
Thus, we have found the length of side CA in triangle ABC:
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Question 1
An investment of $42 earns 12.5% simple interest for 4 years. How much is to worth?
O $85.50
O $77.76
O $63
O $9.83
Total amount after 4 years will be $63. If he invest principle amount of $42 for rate of interest of 12.5%.
How to calculate total amount ?Simply multiply the principal amount by the interest rate and the time to calculate simple interest. "Simple Interest = Principal x Interest Rate x Time," the formula says. You must multiply the borrowed principal amount by 1 plus the interest rate.
The simple interest rate is the rate at which you borrow or lend money. When a borrower borrows money from a lender, the lender receives an additional sum of money. The principal is the borrowed money that is given for a specific period of time. The interest is the extra amount paid back to the lender for using the money.
First, converting R percent to r a decimal
r = R/100 = 12.5%/100 = 0.125 per year.
To find the total amount A = P (1+rt).
= 42(1 + 0.125 *6)
= $63
The total amount is $63
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Jayla buys and sells vintage clothing. She bought two blouses for $25.00 each and later sold them for $38.00 each. She bought three skirts for $15.00 each and later sold them for $26.00 each. She bought five pairs of pants for $30.00 each and later sold them for $65.00 each.
Jayla’s expenses for purchasing the items were
Jayla’s revenue from the sale of the items was
Jayla’s total profit was
Answer:
Jayla's expenses are: $245.00
Jayla's revenue from the sales are: $479.00
Total profit: $234.00
------------------------------------------
Hope this helps! This should be correct !
Answer:
- $245
+ $479
+ $234
Step-by-step explanation:
expenses : (25 x 2) + (15 x 3) + (30 x 5) = 50 + 45 + 150 = 95 + 150 = $245
revenue : (38 x 2) + (26 x 3) + (65 x 5) = 76 + 78 + 325 = 154 + 325 = $479
total profit : 479 - 245 = $234
Suppose you deposit $1,000 in a savings account that pays interest at an annual rate of 5%. If no money is added or withdrawn from the account, answer the
following questions
a. How much will be in the account after 4 years?
b. How much will be in the account after 16 years?
c. How many years will it take for the account to contain $1,500?
d. How many years will take for the account to contain $2,000?
Answer:
3 dollars 3 years
Step-by-step explanation:
don't ask
don't ask
Function or not?please heeeeeelp
Answer:
not a function
Step-by-step explanation:
the vertical line test. if you can put a vertical line on the graph that goes through two points on the parrabola it is not a function
40 is what percent of 20
Answer:
200%
Step-by-step ex
Answer:
200%
Step-by-step explanation:
x% of 20 = 40
x/100 × 20 = 40
x/10 × 2 = 40
x/5 = 40
x = 40×5
x = 200
Find 30% of 279.
A. 83.7
B. 84.69
C. 85.50
D. 86.49
Answer:
B - 84.69
Step-by-step explanation:
The answer is b because you have to multiply 7 by 12 then you'll get 84
Answer:
A
Step-by-step explanation:
because you have to multiple 7 by 12 then you will get 84.70
(23 – 4x2 + 6x – 4) = (x - 2)
Answer:
is it 150?
Step-by-step explanation:
What is 2/z+3\z^2
If z= -1/4
Answer:
40
Step-by-step explanation:
Given :-
z = -1/4
Inputting the values :-
2/z + 3/z²
2/(-1/4) + 3/(-1/4)²
(2 x -4) + (3 x 16)
-8 + 48
= 40
Solution :-
40
Answer:
40
Step-by-step explanation:
[tex]\dfrac{2}{z}+\dfrac{3}{z^2}[/tex]
[tex]\textsf{if} \ z=-\dfrac14[/tex]
[tex]\implies \dfrac{2}{-\frac14}+\dfrac{3}{(-\frac14)^2}[/tex]
[tex]\implies -\dfrac{2}{\frac14}+\dfrac{3}{\frac{1}{16}}[/tex]
[tex]\implies -2 \times 4+3 \times 16[/tex]
[tex]\implies -8+48[/tex]
[tex]\implies 40[/tex]
Describe the transformations necessary to transform the graph of f(x) into that of g(x)
Choose an option
SHOW YOUR WORK
Answer:
C)
Step-by-step explanation:
[tex]\sqrt{x}[/tex] : original function
[tex]\sqrt{-x}[/tex] : reflect across the y-axis
[tex]\sqrt{-\dfrac13x}[/tex] : horizontal stretch by a scale factor of 3
[tex]\sqrt{-\dfrac13(x-3)}[/tex]: translate right 3 units
f(x) : original function
f(-x) : reflection over y-axis
f(ax) : horizontal stretch of the graph by a scale factor of 1/a
f(x - a) : horizontal translation right a units
At 3% annual interest compounded monthly, how long will it take to double your money?
Answer:
If your money is in a savings account earning 3% a year, it will take around 24 years.
Which are the partial products for 72x4? Select all that apply.
Answer:
288
this 8s because 72 x 4 is 288 2x4 is 8 and 4x72 is 28 so the answer is 288
Workout the area and perimeter of the shape below
Step-by-step explanation:
area : 180+130 cm2 = 310cm2
perimeter = 76cm
hope this helps you.
Answer:
P=76 cm / A=310 cm²
Step-by-step explanation:
The perimeter is the sum of all sides in a polygon;
P=20+18+10+5+10+13= 76 cm
The area which i will divide into 2 parts and add them;
The rectangle of length 20 cm and width 13 cm;
A=lw=20×13=260 cm²
The rectangle of length 5 cm and width 10 cm;
A=lw=5×10=50 cm²
A(Total)=260+50= 310 cm²
Question 8 of 10
Write the following equation in standard form: x^5+2x^3+6x+1/5
Answer:
x^5+2x^3+6x+1/5
Step-by-step explanation:
our given equation is already written in standard form.
Answer:
It is already in standard form
Step-by-step explanation:
The standard equation should be arranged from high order to low order
So x^5+2x^3+6x+1/5 = x^5+2x^3+6x+1/5
It is already in standard form
help me guys fast as
[tex]\\ \rm\Rrightarrow tan^2135-cosec^260=-xcos45.sin45.cot60[/tex]
[tex]\\ \rm\Rrightarrow (-1)^2-(\dfrac{2}{\sqrt{3}})^2=-\dfrac{x}{\sqrt{2}}\times \dfrac{1}{\sqrt{2}}\times \dfrac{1}{\sqrt{3}}[/tex]
[tex]\\ \rm\Rrightarrow 1-\dfrac{4}{3}=\dfrac{-x}{2\sqrt{3}}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{3-4}{3}=\dfrac{-x}{2\sqrt{3}}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{-1}{3}=\dfrac{-x}{2\sqrt{3}}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{1}{\sqrt{3}}=\dfrac{x}{2}[/tex]
[tex]\\ \rm\Rrightarrow x=\dfrac{2}{\sqrt{3}}[/tex]
hey guy can you help me with this
Answer:
C. y = 1/8x
D. y = x - 133
Step-by-step explanation:
In order to find the answer, you have to think about the answer choices
A. is saying that if you multiply 152 by 8, you will get 19 which is definitely not true
B. is saying that y is equal to 152/133 which is not true since 152/133= 8/7 which is some wacky decimal
C. would make sense because if you divide 152 and 8, you will get 19
Which makes the equation true because if you multiply 1/8 by 152/1, you get 152/8 which simplifies to 19 which satisfies the equation
D. This would also make sense since 152-133=19
So at the end, we can come to a conclusion that:
C. and D. are the equations that satisfy the relation
What is the measure of x in triangle ABC? A. 35o B. 34o C. 33o D. 24o
Answer:
B, 34 degrees
Step-by-step explanation:
Since all triangles equal to 180 degrees, you have to add together the angles you already know and subtract from 180.
123+23=146 180-146=34
Hopefully this helps, have a nice day/night!
3. The area of this trapezoid is 25.5 ft.
3.2 ft
7 ft
What is the height of the trapezoid? Show your work.
Answer:
Answer:
5 ft
Step-by-step explanation:
You can find the missing dimension by using the area formula and solving it for the missing dimension.
__
A = 1/2(b1 +b2)h . . . . . . . . . . . . formula for the area of a trapezoid
25.5 ft² = 1/2(7 ft +3.2 ft)h . . . . with the given numbers filled in
(25.5/5.1) ft = h = 5 ft . . . . . . . . . divide by the coefficient of h
The height of the trapezoid is 5 ft.
Help me please I will mark BRAINLIEST
Answer:
a) most students got a better grade on the second page than the first. which makes it positive
b) the pupil could've gotten a 61% score
Step-by-step explanation:
Find the total surface area of the pyramid. 4 in. Bx X3.140 10 in.
Answer:
Step-by-step explanation: height h =
slant height s =
side length a =
perimeter of base P =
lateral edge length e =
1/2 side length r =
volume V =
lateral surface area L =
base surface area B =
total surface area A =
Get a Widget for this Calculator
Square Pyramid Shape
Pyramid Diagram with h = height, l = length and w = width and s = slant height
h = height
s = slant height
a = side length
P = perimeter of base
e = lateral edge length
r = a/2
V = volume
L = lateral surface area
B = base surface area
A = total surface area
Calculator Use
This online calculator will calculate the various properties of a square pyramid given 2 known variables. The square pyramid is a special case of a pyramid where the base is square. It is a regular pyramid with a square base.
Units: Note that units are shown for convenience but do not affect the calculations. The units are in place to give an indication of the order of the results such as ft, ft2 or ft3. For example, if you are starting with mm and you know r and h in mm, your calculations will result with s in mm, V in mm3, L in mm2, B in mm2 and A in mm2.
NAN: means not a number. This will show as a result if you are using
Democrat F39 M27 Republican F57 M36 What percentage of the total sample are female Democrats?
Answer: Approximately 24.53%
Explanation:
I could be misreading what you posted, but it appears there are 39 female Democrats out of 39+27+57+36 = 159 total people surveyed.
This leads to the percentage 39/159 = 0.2453 = 24.53% which is approximate.
What is the perimeter of a rectangle with a length of 3x-2 width 2x-8
Answer:
P = 5x - 10
Step-by-step explanation:
The perimeter is:
P = L + w
L = 3x - 2
w = 2x - 8
P = 3x -2 + 2x - 8
P = 5x - 10
To know the exact value we need to know the value of x or the solve of one of the expressions above.
6/9x45 in simplest form?
Answer:
Step-by-step explanation:
6/9 x 45 = 2/3 x 45 = 30
[tex] \frac{2}{3} \times 45 = 30[/tex]
2i-3n=8
i+2n=-3
find i and n
Answer: n = -2; i = 1
Step-by-step explanation:
i + 2n = -3
i = -3 - 2n
Plug in i in 2i - 3n = 8, we get:
2i - 3n = 8
2(-3 - 2n) - 3n = 8
-6 - 4n - 3n = 8
-6 - 7n = 8
-7n = 14
n = -2
substitute n = -2 into i = -3 - 2n
i = -3 - 2n
i = -3 - 2(-2)
i = -3 + 4
i = 1
Please help! In the figure below, what is the length of EG
Answer:
Step-by-step explanation:
The triangles are similar because they have two sides and the angle between them (EFG) respectively equals, and it’s evident the factor between the two triangles is 2. So EG=2CB=2*8=16
Answer:
the value of EG is 20.
Step-by-step explanation:
3×4 = 12, AB and EF is similar but the value of AB is multiplied by 4 to become 12 for EF.
similarly, 4×4 = 16, BC and FG is similar but the value of BC is multiplied by 4 to become 16 for FG..
In this way, AC and EG are also similar so 5×4 = 20.
All the values are multiplied by 4 ...