Answer:
$200 at 2%.
$2200 at 3.5%.
Step-by-step explanation:
Let the two amounts be x and y.
x earns 2% interest, and y earns 3.5% interest.
Since the total is $2400, then
x + y = 2400
Now we can solve for y and express the second amount in terms of x.
y = 2400 - y
The two amounts are x and 2400 - x.
In one interest period, the amount of interest earned is the amount of money in the account multiplied by the interest.
2% = 0.02; 3.5% = 0.035
The x amount earns 0.02x interest.
The y amount earns 0.035y interest.
The total interest earned is the sum of the interest amounts of the two accounts.
0.02x + 0.035y
We now replace y with 2400 - x, and we set the sum of the interest amounts equal to the total interest earned, $81.
0.02x + 0.035(2400 - x) = 81
The equation above is the linear equation.
Now we solve it. Distribute on the left side.
0.02x + 84 - 0.035x = 81
Combine like terms on the left side.
-0.015x + 84 = 81
Subtract 84 from both sides.
-0.015x = -3
Divide both side by -0.015.
x = 200
$200 was deposited in the account earning 2%.
y = 2400 - x
y = 2400 - 200
y = 2200
$2200 was deposited in the account earning 3.5%.
There are 25 students in Mr. Jones’ art class. Mr. Jones is planning a project where each student needs 0.3 jar of paint. Exactly how much paint does Mr. Jones need for the art project?
Answer:
7.5 jars
Step-by-step explanation:
There are 25 students in the art class.
Mr Jones is planning that for the project, each of the 25 students will need 0.3 jar of paint.
The amount of paint Mr Jones needs for this project is therefore the product of the number of students in the class by the amount of paint each student needs.
That is:
25 * 0.3 = 7.5 jars of paint
Mr Jones needs 7.5 jars of paint for the art project.
HELPPPP I need help finding x a and b pleaseeee
Answer:
5x-18 this angle is equal to 92
3x+22 this angle is equal to 88
angle a=88
angle b=92
Step-by-step explanation:
set 5x-18 and 3x+22 equal to 180 and solve to get x=22. Now look for ways to fill in a and b. A is an alternate interior angle that will be equal to 3x+22
angle b will be equal to the angle 5x-18
Answer:
The value of x is22°, a is 88° and b is 92°.
Hope it helps..
Help please!!! Thanksss
Answer:
6:00 p.m.
hope this helps :)
a sector with a radius of 12cm has an area of 60pi cm what is the central angle in radians
Answer:
5/6π.
Step-by-step explanation:
The following data were obtained from the question:
Radius (r) = 12 cm
Area (A) = 60π cm²
Centre angle in radian (∅) =...?
Since we are to look for the centre angle in radian, the area of the sector will be given by:
A = ½r²∅
Inputting the values of the area, A and radius, r, the centre angle, ∅ can be obtained as follow:
A = ½r²∅
60π = ½ × 12² × ∅
60π = ½ × 144 × ∅
60π = 72 × ∅
Divide both side by 72
∅ = 60π/72
∅ = 5/6π
Therefore, the centre angle measured in radian is 5/6π.
Determine the parent function.
Answer:
y= [tex]\sqrt{x}[/tex]
Step-by-step explanation:
Find the midline for f(x)=2cos(3x−5π6)−2
Answer: y = -2
Step-by-step explanation:
f(x) = A cos (Bx - C) + D
↓
center line (aka midline)
f(x) = 2 cos (3x - 5π/6) - 2
↓
midline = -2
The midline of the cos function f(x) = 2cos(3x − 5π/6) − 2 is y = -2 after comparing with standard cos function f(x) = Acos(Bx - C) + D
What is cos function?It is defined as a function that is sin-cos wave in nature, and it has a domain of all real numbers and lies between the [a, a] where is the amplitude of the function.
It is given that the cos function is:
f(x) = 2cos(3x - 5π/6) - 2
As we know, the standard form of the cos function is:
f(x) = Acos(Bx - C) + D
Here, A is the amplitude
B is the period of the cos function
C is the phase shift of the cos function
D is the vertical shift of the cos function/midline
On comparing:
D = -2
The midline:
y = -2
Thus, the midline of the cos function f(x) = 2cos(3x − 5π/6) − 2 is y = -2 after comparing with standard cos function f(x) = Acos(Bx - C) + D
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Find f o g and g o f to determine if f and g are inverse functions. If they are not inverses, pick the function that would be the inverse with f(x). F(x) = -4x + 1; g(x) = (x+1)/4 Choices: a. G(x) has to be: (1-x)/4 b. Inverses c. G(x) has to be: 1/(4 - x) d. G(x) has to be: x/4
Answer:
G(x) = (1 - x)/4
is the inverse function required.
Step-by-step explanation:
Given F(x) = -4x + 1
Let y = F(x)
Then y = -4x + 1
=> y - 1 = -4x
4x = 1 - y
x = (1 - y)/4
That is, the inverse is (1 - x)/4
Therefore, G(x) has to be (1 - x)/4
two regular polygons are such that the ratio of the measures of their interior angles is 4:3 and the ratio between their number of sides is 2:1 find the number of sides of each polygon
hey mate, here is ur answer in the attachment!
Mark the absolute maximum point of the graph.
is the absolute maximum point (-3,5)?
graph itttt plssssss
━━━━━━━☆☆━━━━━━━
▹ Answer
You can use a graphing calculator. Attached is a picture of it graphed.
Hope this helps!
CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
Given the coordinate points of the preimage, use the transformation given to provide the points of the image. E(−5,−1) D(−5,1) C(−1,0) B(−2,−3) Rotation: 180∘ about the origin
Answer:
The points of the image are;
E'(5, 1), D'(5, -1), C'(1, 0), E'(-2, -3)
Step-by-step explanation:
The coordinates of the preimage are E(-5, -1) D(-5, 1) C(-1, 0) B(-2, -3)
Rotation of a point 180° about the origin gives;
Coordinates of the point of the preimage before rotation = (x, y)
The coordinates of the image after rotation = (-x, -y)
Therefore, the coordinates of the points EDCB after 180° rotation about the origin are;
E(-5, -1) rotated 180° becomes E'(5, 1)
D(-5, 1) rotated 180° becomes D'(5, -1)
C(-1, 0) rotated 180° becomes C'(1, 0)
B(-2, -3) rotated 180° becomes E'(-2, -3).
30% of a number is 45 what is the number ?
Hey there! I'm happy to help!
When talking about percents, the word "is" usually means equals. Let's use this to solve an equation! We will call our number n. Note that 30% is equal to 0.3 in decimal form because 0.3 is 30% of one! :D
0.3n=45
To solve, we need to isolate the n. To do this, we divide both sides by 0.3 because this cancels out the 0.3 that is being multiplied by n and it shows us what n will then equal.
0.3n÷0.3=45÷0.3
n=150
Therefore, 30% of 150 is 45. Try multiplying 0.3 by 150 and you will get 45!
Have a wonderful day! :D
Given that Arccos (√3/2)=β, what are all the angle measurements for right triangle ABC?
Answer:
30°, 60° and 90°
Step-by-step explanation:
Given the expression Arccos (√3/2)=β, we can use the expression to calculate one of the acute angles in a right angled triangle.
Note that a right angled triangle is made up of two acute angles and a right angled (90°)
Let's get one of the acute angles first
If Arccos (√3/2)=β
β = cos^-1 √3/2
β = 30°
This shows that one of the acute angles is 30°
To get the third angle, we know that sum of angles in a triangle is 180° and since we already know two of the angles, i.e 90° and 30°, we can get the third angle.
90+30+x = 180
120+x = 180
x = 180-120
x = 60°
All the angle measurement for the right angled triangle are 30°, 60° and 90°
the shape of a piece is pallelogram whose adjacent side are 12m and 9 m and the corresponding diagonal is 15 .find the area of land
Answer: The area of land =108 m²
Step-by-step explanation:
In the given piece of land is in the shape of a parallelogram.
Diagonals divide it into 2 equal parts.
So, area of parallelogram = 2 x (Area of triangle with sides 12m and 9 m and 15 m)
Heron's formula :
Area of triangle = [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex], where [tex]s=\dfrac{a+b+c}{2}[/tex]
Let a= 12 , b= 9 and c = 15
[tex]s=\dfrac{12+9+15}{2}=18[/tex]
Area of triangle = [tex]\sqrt{18(18-12)(18-9)(18-15)}[/tex]
[tex]=\sqrt{18\times6\times9\times3}=\sqrt{2916}=54\ m^2[/tex]
Then, area of parallelogram= 2 x 54 = 108 m²
Hence, the area of land =108 m²
Check all that apply. If tan theta = 15/8 then:
Answer:
B, C, D
Step-by-step explanation:
if tan theta = 15/8 then the hypotenuse is 17
therefore the correct answers are B, C, D
This is Algebra 1 functions and I'm struggling with this one function-
-1•f(-9)+7•g(6)=_____
Answer:
38
Step-by-step explanation:
f(-9) is the value of f(x) when x = -9. Therefore, f(-9) = 4 from the graph. Doing the same with g(6), we can see that g(6) = 6. Our expression becomes:
-1 * 4 + 7 * 6
= -4 + 42
= 38
14
Select the correct answer
Which equation describes the line graphed above?
OA y = -41 - 5
OB. y = -x - 4
oc y = -51 - 4
Answer:
Option B
Step-by-step explanation:
Hope it is right
The value of equation describes the line graphed is,
⇒ y = -1/5x - 4
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
Two points on the line are (0, -4) and (5, -5).
Now,
Since, The equation of line passes through the points (0, -4) and (5, -5).
So, We need to find the slope of the line.
Hence, Slope of the line is,
m = (y₂ - y₁) / (x₂ - x₁)
m = (- 5 - (-4)) / (5 - 0)
m = - 1 / 5
Thus, The equation of line with slope - 1/5 is,
⇒ y - (-4) = -1/5 (x - 0)
⇒ y + 4 = -1/5x
⇒ y = -1/5x - 4
Therefore, The equation of line passes through the points (0, -4) and
(5, -5). will be;
⇒ y = -1/5x - 4
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Figure G is rotated 90Degrees clockwise about the origin and then reflected over the x-axis, forming figure H. On a coordinate plane, triangle G has points (negative 3, 1), (negative 1, 2), (negative 2, 5). Triangle H has points (2, negative 1), (1, negative 3), (5, negative 2). Which sequence of transformations will produce the same results?
Answer:
The 1st selection is appropriate.
_____
2nd: the rotation would need to be 90° CCW
3rd, 4th: rotation or double reflection will give the original orientation. This figure is reflected an odd number of times, so has its orientation reversed.
Hope it helps.. Mark brainliest
The sequence of transformations are reflection over the y-axis and then a rotation 90 clockwise about the origin.
What is rotation rule of 90°?Here are the rotation rules: 90° clockwise rotation: (x, y) becomes (y, -x) 90° counterclockwise rotation: (x, y) becomes (-y, x) 180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y).
Given that, figure G is rotated 90° clockwise about the origin and then reflected over the x-axis, forming figure H.
Vertices of triangle G are (-3, 1), (-1, 2) and (-2, 5).
The reflection of point (x, y) across the y-axis is (-x, y).
On reflection over x-axis, we get coordinates as (3, 1), (1, 2) and (2, 5)
90° clockwise rotation: (x, y) becomes (y, -x)
On 90° clockwise rotation, we get coordinates as (1, -3), (2, -1) and (5, -2)
Triangle H has points (2, -1), (1, -3), (5, -2).
Hence, the sequence of transformations are reflection over the y-axis and then a rotation 90° clockwise about the origin.
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What is 1/9 of 63% of 6000?
Answer:
420
Step-by-step explanation:
To find 63% of 6000, we can do 0.63 * 6000 = 3780 because 63% = 0.63.
1/9th of that is 1/9 * 3780 = 420.
Answer:
420
Step-by-step explanation:
Let's first start by finding 63% of 6000 so we can later find 1/9 of that number.
We can set up a percentage proportion.
[tex]\frac{x}{6000} = \frac{63}{100}[/tex]
[tex]6000\cdot63=378000\\378000\div100 = 3780[/tex]
Now to find 1/9 of 3780.
[tex]\frac{1}{9} \cdot \frac{3780}{1}\\\\\frac{3780}{9} = 420[/tex]
So, the answer is 420.
Hope this helped!
Solve the inequality.
9p+23<41
Answer:
p < 2
Step-by-step explanation:
9p + 23 < 41
p < 2
Answer:
p < 2
Step-by-step explanation:
9p + 23 < 41
9p < 18
p < 2
Graph [tex]y=\frac{2}{3} x[/tex] Which of the following statements are true?
Answer:
A,C,D
Step-by-step explanation:
When b=0, there is a proportional relationship.
The slope in y=mx+b is the value next to x.
Using RISE/RUN when there is a change of 3 units in x, there is a change of 2 units in y.
need HELP ON THIS A S AP !!!!!
Answer:
803.84yd²
Step-by-step explanation:
Surface Area of A Sphere: [tex]A=4\pi r^2[/tex]
We are given the radius of 8 yards.
Using 3.14 for pi:
[tex]A=4*3.14*8^2\\\\A=4*3.14*64\\\\A=12.56*64\\\\\boxed{A=803.84}[/tex]
The correct answer should be 803.84yd².
Brainilest Appreciated.
Answer:
803.84 yd^2
Step-by-step explanation:
4*3.14*8^2
12.56*64
803.84
brainliest pls
hope i helped
-ZYLYNN
y=8-2x. What is the value of y when x = 8?
Answer:
y = -8
Step-by-step explanation:
Start by filling 8 in place of x
y = 8 - 2(8)
Multiply -2(8)
y = 8 - 16
Subtract 16 from 8
y = -8
Write an equation of the line that passes through the point (–4, 6) with slope –4.
Answer:
y = - 4x - 10
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = - 4 , thus
y = - 4x + c ← is the partial equation
To find c substitute (- 4, 6) into the partial equation
6 = 16 + c ⇒ c = 6 - 16 = - 10
y = - 4x - 10 ← equation of line
Answer:
y = -4x+10
Step-by-step explanation:
Using the slope intercept form of a line
y = mx+b where m is the slope and b is the y intercept
y = -4x +b
Substituting the point in
6 = -4(-4) + b
6 = 16+b
Subtract 16 from each side
-10 =b
The equation is
y = -4x+10
Sophia‘s favorite homemade cookie recipe requires one cup of chocolate chips for 10 servings if the number of cups required for multiple batches is proportional to the number of servings being made how many cups of chocolate chips will she need to make enough cookies for 30 servings
Answer:
3 cups
Step-by-step explanation:
We can use a proportion to find how many cups of chocolate chips she needs for 30 servings. Assuming c = cups of chocolate chips and b = batches
[tex]\frac{c}{b}[/tex]
[tex]\frac{1}{10} = \frac{c}{30}[/tex]
We can now multiply the diagonal values that don't include the missing variable (30 and 1) and then divide it by the value that is diagonal to the variable (10)
[tex]30 \cdot 1 = 30\\30 \div 10 = 3[/tex]
Therefore, she needs 3 cups of chocolate chips to make 30 servings.
Answer:
3 cups
Step-by-step explanation:
We can use ratios to solve
1 cup x cups
---------------- = ----------------
10 servings 30 servings
Using cross products
1*30 = 10x
Divide by 10
30/10 = x
3 =x
3 cups
The first three steps in determining the solution set of the system of equations algebraically are shown.
y = x2 − x − 3
y = −3x + 5
What are the solutions of this system of equations?
(−2, −1) and (4, 17)
(−2, 11) and (4, −7)
(2, −1) and (−4, 17)
(2, 11) and (−4, −7)
Answer:
(2, −1) and (−4, 17)
Step-by-step explanation:
I used a graphing tool to graph the systems of equations. The parabola and line pass at points (2, -1) and (-4, 17).
Answer:(2, −1) and (−4, 17) Its C on Edge 2023
Step-by-step explanation: Its (C) after an extensive research
which line segment could be a midsegment of ∆abc
Answer:
[tex]\overline{DF}[/tex] could be a midsegment of ∠ABC.
Step-by-step explanation:
A midsegment of a triangle must be two things:
1. Parallel to the 3rd side, in this case, [tex]\overline{AD}[/tex].
2. Half the length of the 3rd side, in this case, [tex]\overline{AD}[/tex].
Since we don't know the lengths, we can only go off of 1. There is only one line that is parallel to [tex]\overline{AD}[/tex] and it is [tex]\overline{DF}[/tex].
Hope this helped!
Campus rentals rent 2 and 3 bedroom apartments for 700$ and 900$ a month respectively. Last month they had six vacant apartments and reported $4600 in lost rent. How many of each type of apartment were vacant?
Answer:
2 - bedroom apartment = 4
3 - bedroom apartment = 2
Step-by-step explanation:
Given the following :
2 - bedroom apartment = $700 / month
3 - bedroom apartment = $900 / month
Last month:
Number of vacant apartment = 6
Amount of Lost rent = $4600
Let a = 2 - bedroom apartment and b = 3 - bedroom apartment
Vacant apartment :
a + b = 6 - - - (1)
Lost rent :
700a + 900b = 4600 - - - (2)
From (1),, a = 6 - b
Substitute a = 6 - b into (2)
700(6 - b) + 900b = 4600
4200 - 700b + 900b = 4600
4200 + 200b = 4600
200b = 4600 - 4200
200b = 400
b = 400/200
b = 2
From (1) ;
a + b = 6
a + 2 = 6
a = 6 - 2
a = 4
a = 2 - bedroom apartment = 4
b = 3 - bedroom apartment = 2
Samuel is solving the equation 3 (x minus 1) + 4 = 2 minus (x + 3). Which equivalent equations might Samuel use? Check all that apply.
3 x minus 3 + 4 = 2 minus x minus 3
3 x minus 1 + 4 = 2 minus x + 3
3 x minus 3 + 4 = 2 minus x + 3
3 x + 1 = negative x minus 1
3 x + 3 = negative x + 5
3 x + 1 = negative x + 5
Answer: 3 x minus 3 + 4 = 2 minus x minus 3
3 x + 1 = negative x minus 1
Step-by-step explanation:
A and D. Edge 2020
The required equation that Samuel used is 3x -3 + 4 =2- x -3. option A is correct.
Samuel is solving the equation 3 (x minus 1) + 4 = 2 minus (x + 3). Which equivalent equations might Samuel use, is to be determined.
The equation is the relationship between variables and represented as[tex]y = ax +b[/tex] is an example of a polynomial equation.
Given equation is [tex]3(x-1) +4 =2 -(x+3)[/tex]
Simplification of the above equation,
opening the parenthesis on both sides
step 1⇒ 3x - 3 + 4 = 2 - x - 3
step 2⇒ 3x + 1 = -x - 1
Transposition of -x to the left side and +1 to the right side
step 4 ⇒ 3x +x = -1 -1
4x = -2
Transposition of 4 to the denominator of -2.
step 5⇒ x = -2/4
x = -1/2
Thus , Step 1 3x -3 + 4 =2- x -3 is the equivalent equation used by the samuel.
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Find the value of x in the
following parallelogram:
2x - 10
2x + 50
Answer:
The value of x is 35
Step-by-step explanation:
In order to calculate the value of x in the following parallelogram: 2x - 10
2x + 50, we would have to calculate the following formula:
m<QPS+m<PQR=180°
According to the given data we have the following:
m<QPS=2x - 10
m<PQR=2x + 50
Therefore, 2x - 10+2x + 50=180
4x+40=180
x=140/4
x=35