By calculating the cost per shrub at both the nursery and the garden store, then multiplying by 21 shrubs, we find that Kevin saves $21.00 by purchasing from the garden store instead of the nursery.
Explanation:Kevin is trying to decide between two stores to purchase a total of 21 shrubs for his yard. In order to calculate how much money Kevin can save by choosing the garden store over the nursery, we will need to determine the cost per shrub at each location and then multiply by the total number of shrubs Kevin wants to purchase.
At the nursery, six shrubs cost $72.00, which means each shrub costs $72.00 ÷ 6 = $12.00.
For 21 shrubs, the cost at the nursery would be 21 × $12.00 = $252.00.
At the garden store, six shrubs cost $66.00, which gives us a cost of $66.00 ÷ 6 = $11.00 per shrub.
Therefore, for 21 shrubs, the total cost would be 21 × $11.00 = $231.00.
Now, let's find out the savings if Kevin buys from the garden store instead of the nursery: $252.00 - $231.00 = $21.00.
Thus, Kevin will save $21.00 by purchasing the shrubs from the garden store.
solve by substitution or elimination 5x+3y=-15 -8x-2y=10
Answer:
x=0, y=-5
Step-by-step explanation:
The system is
(1) 5x+3y=-15
(2) -8x-2y=10
Let's solve it by elimination. In order to do it, you have to multiply the equations by suitable numbers in such a way that when you add the 2 equations, one of the unknowns is eliminated
Multiply (1) by 2 and (2) by 3
(1) 10x+6y=-30
(2) -24x-6y=30
Add the two equations
10x-24x+6y-6y=-30+30 ----> -14x=0---->x=0
Now replace this value in any equation, for example in (1)
6y=-30 ----> y=-30/6----> y=-5
Answer: The required solution is (x, y) = (0, -5).
Step-by-step explanation: We are given to solve the following system of equations by the method of substitution or elimination :
[tex]5x+3y=-15~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\-8x-2y=10~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
We will be solving the given system by substitution method.
From equation (ii), we have
[tex]-8x-2y=10\\\\\Rightarrow -4x-y=5\\\\\Rightarrow y=-4x-5~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)[/tex]
Substituting the value of y from equation (iii) in equation (i), we get
[tex]5x+3(-4x-5)=-15\\\\\Rightarrow 5x-12x-15=-15\\\\\Rightarrow -7x=0\\\\\Rightarrow x=0.[/tex]
From equation (iii), we get
[tex]y=-4\times0-5=-5.[/tex]
Thus, the required solution is (x, y) = (0, -5).
Hakeem subtracted 8 from a number then multiply the difference by 5 the result was 20 write and solve an equation to find the number X
Answer:
(×-8)5=20
(5×-40)=20
5×(-40+40)=(20+40)
5×=60
5×÷5=60÷5
×=12
Based on the equation given, the value of the number is 12.
Let the number be represented by x.
Based on the information given, the equation to solve the question will be:
(x - 8) × 5 = 20
5x - 40 = 20
Collect like terms
5x = 20 + 40
5x = 60
Divide both side by 5
5x/5 = 60/5
x = 12
Therefore, the number is 12.
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Subtract 2 1/6- 1 7/8
Answer:
The answer is 7/24
Step-by-step explanation:
Rewriting our equation with parts separated
=2+16−1−78
Solving the whole number parts
2−1=1
Solving the fraction parts
16−78=?
Find the LCD of 1/6 and 7/8 and rewrite to solve with the equivalent fractions.
LCD = 24
424−2124=−1724
Combining the whole and fraction parts
1−1724=724
Solution by Formulas
converting mixed numbers to fractions, our initial equation becomes,
136−158
Applying the fractions formula for subtraction,
=(13×8)−(15×6)6×8
=104−9048
=1448
Simplifying 14/48, the answer is
=724
Hope I helped :)
What is 33+12f=51 please help
Answer:
f=3/2
Step-by-step explanation:
33+12f=51
1) subtract 33 on both sides:
12f=18
2) Divide both sides by 12:
f=18/12
3) Simplify the fraction:
f=3/2
Figure 1 is congruent to Figure 2.
Figure 1
K 3.5 cm L
Figure 2
5 cm
T
4.5 cm
3 cm
2 cm
What is the length of NP?
A. 2 cm
B, 3 cm
C: 3.5 cm
D, 4.5 cm
E, 5 cm
Answer:
E.) 5 cm
Step-by-step explanation:
The shapes are congruent and are the same size, side TU is the same as NP. If TU is 5, then NP is 5.
Answer:
E. 5 cm.
Step-by-step explanation:
As the 2 figures are congruent then corresponding sides are congruent.
NP corresponds to UT = 5 cm.
So NP is 5cm long.
(If we rotate Figure 2 through 180 degrees anticlockwise we see that it fits exactly on to figure 1.)
What is the distance between 178 and 313 on a number line some one help me
The distance between 178 and 313 on a number line is: 135
Step-by-step explanation:We know that the distance between two points a and b on a number line is equal to the absolute difference between the two numbers.
i.e. Distance between two numbers = |a-b|
Here we have:
a= 178
and b=313
This means that:
|a-b|=|178-313|=|-135|=135
Please help me idk this
Answer:
The anwser is 2.8000
Step-by-step explanation:
You look at the tenth place its 8 :
2.8151
Then you look to the right which is 1
is 1 more than 5 or less
1 < 5
8 stays the same but 1, 5, and 1 turn into zeros
Answer:
2.8151 rounded to the nearest tenth is 2.8, because tenths lie right after the decimal
I hope i helped :)
Which angle is in standard position?
Answer:
RIght
Step-by-step explanation:
RIght is an equal angle so, therefore it would be right
The angle in the standard position is the graph given below.
We have,
An angle in standard position refers to an angle that is formed by the initial side and terminal side in the Cartesian coordinate system.
The initial side is the positive x-axis, and the terminal side is a ray that starts from the origin (0, 0) and extends in a specific direction.
Now,
The graph given below starts from the origin (0, 0).
The initial side is in the positive x-axis.
The terminal is a ray parallel to the positive x-axis.
Thus,
The angle in the standard position is the graph given below.
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A bag contains the following marbles: 4 black marbles, 14 blue marbles, 8 brown marbles, and 20 green marbles. What is the ratio of blue marbles to green marbles? Express your ratio as a fraction or with a colon
Answer:
14 to 20 or 7 to 10 is the ratio
Final answer:
The ratio of blue marbles to green marbles is 14:20, which simplifies to 7:10 or as a fraction, 7/10.
Explanation:
The ratio of blue marbles to green marbles from a bag containing 4 black marbles, 14 blue marbles, 8 brown marbles, and 20 green marbles is simply the number of blue marbles divided by the number of green marbles. To express this ratio, we would do the following:
Count the blue marbles: There are 14 blue marbles.
Count the green marbles: There are 20 green marbles.
Write the ratio: The ratio of blue marbles to green marbles would be 14 blue marbles to 20 green marbles.
Express as a fraction or with a colon: As a fraction, this is 14/20, which simplifies to 7/10. Or, using a colon, it is represented as 14:20, which also simplifies to 7:10.
What is 42% of 75?
A.
315
B.
105
C.
31.5
D.
10.5
Answer:
31.5
Step-by-step explanation:
42% of 75 is 31.5. The working is as follows :
42 ÷ 100 × 75 = 31.5
You can also use the picture ^^
Answer:
[tex]C.[/tex] [tex]31.5[/tex]
Step-by-step explanation:
When trying to find a percent of a number, you must always do the following steps:
Multiply the number by the percent number.
[tex]42 * 75 = 3150[/tex]
Dividing you answer by 100.
[tex]3150 / 100 = 31.5[/tex]
Add percent sign.
31.5%
A model for my number has
6 ones blocks, 2 hundreds blocks, and 3 tens
blocks. What number am I
Answer:
A model for my number has 6 ones blocks, 2 hundreds blocks, and 3 tens blocks. The model number is 236.
Solution:
Given that the model has 6 ones blocks, 2 hundreds blocks, and 3 tens blocks. The model number can be found out by,
[tex]\bold{\begin{array}{l}{=\text { (number of hundreds block } \times 100)+(\text { number of tens block } \times 10)+} \\ {\text { (number of ones block } \times 1)}\end{array}}[/tex]
Given that number of one blocks = 6 blocks. Hence we get [tex]6 \times 1=6[/tex]
Number of ten blocks = 3.Hence we get [tex]3 \times 10 = 30[/tex]
Number of hundred blocks = 2 .Hence we get [tex]2 \times 100=200[/tex]
So the model number = 6 + 30 + 200
=236
Hence the model number is 236.
Which expression is equivalent to (f g) (5)?
f (5) times g (5)
f (5) + g (5)
5 f (5)
5 g (5)
Answer:
Option A.
Step-by-step explanation:
Expression given in the question is (f g)(5).
We know when two functions are f(x) and g(x) then (f g)(x) represents the multiplication of two functions.
(f g)(x) = f(x).[g(x)]
For x = 5
(f g)(5) = f(5).g(x)
It may be represented by the operation as
(f g)(5) = f(5) × g(x)
Therefore, option A. will be the answer.
The function (f g)(5) can be expressed as f(5) × g(5) as an equivalent expression.
Equivalent expression to (f g)(5)The equivalent expression is determined as follows;
Two given functions such as (f(5) and g (5), can be represented by the multiplication of the two functions as shown below.
(f g) (5) = (f (5) x g (5)
(f g) (5) = (f (5) x g (5)
Thus, the function (f g)(5) can be expressed as f(5) × g(5) as an equivalent expression.
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Jillian owns 60% of the stock
in a private catering
corporation. There are 1,200
shares in the entire
corporation. How many
shares does Jillian own?
Answer:
720
Step-by-step explanation:
Percentage share owned by Jillian = 60%
Total shares in corporation = 1200
Number of shares owned by Jillian = [tex]\frac{60*1200}{100} = 720[/tex]
A storeowner orders 25 calculators that cost $32 each.The storeowner can sell each calculator for 40$ .the storeowner sold 22 calculators to cudtomers.He had to return 3 calculators that were never sold and pay a $2 charge for each returned calculator(although the initial cost is refunded)What is the storeowners profit
Answer:
$74
Step-by-step explanation:
25*32 will be the total amount he spent at first. ($800)
He sells 22 calculators at 40$, 22*40 = 880.
He was unable to sell 3, and he had to pay 2$ per (2*3 = 6)
He had an 80 dollar profit before he returned them, (880-800).
Then he returned three for 6$ (80-6)
His end profit was 74.
You deposit $750 in an account that earns 7.5% simple interest. How much will be in the account after 5 years?
Answer:
$1,031.25 will be in the account
Answer:
$1031.25.
Step-by-step explanation:
The formula for simple interest is
I = PRT/100 so substituting:
I = 750 * 7.5 * 5 / 100
Interest I = $281.25.
Amount in account = 750 + 281.25
= $1031.25.
4|w − 5| = 4
Write your answers as integers or as proper or improper fractions in simplest form.
w = or w =
Answer:
w = 9 or w = 1
Step-by-step explanation:
4|w − 5| = 4
Divide both sides by 4
w - 5 = 4 w - 5 = -4
+ 5 + 5 + 5 + 5
w = 9 w = 1
complete 2x+21= using only the communtative property of addition
Answer:
-9.5
Step-by-step explanation:
2x + 21 =
2x + 20 = 1 (C.P)
2x = 1-20
2x = - 19
x= - 19/2
x = - 9. 5
Which quadratic function only has one x-intercept?
A f ( x ) = x 2 − 12 x + 36
B f ( x ) = x 2 − 13 x + 36
C f ( x ) = x 2 + 13 x + 36
D f ( x ) = x 2 + 20 x + 36
Answer:
f(x) = x² - 12x + 36 = (x - 6)²
The correct answer is A.
The quadratic function that has only one \(x\)-intercept is A. [tex]\( f(x) = x^2 - 12x + 36 \)[/tex]
A quadratic function has only one [tex]\(x\)[/tex]-intercept if it touches the [tex]\(x\)[/tex]-axis at exactly one point, which happens when the discriminant [tex](\(\Delta\))[/tex] of the quadratic equation is zero. The discriminant of a quadratic function [tex]\(ax^2 + bx + c = 0\)[/tex] is given by:
[tex]\[ \Delta = b^2 - 4ac \][/tex]
Let's calculate the discriminant for each given function to determine which one has only one [tex]\(x\)[/tex]-intercept.
Option A: [tex]\( f(x) = x^2 - 12x + 36 \)[/tex]
[tex]\[ a = 1, \, b = -12, \, c = 36 \][/tex]
[tex]\[ \Delta = (-12)^2 - 4 \cdot 1 \cdot 36 \][/tex]
[tex]\[ \Delta = 144 - 144 \][/tex]
[tex]\[ \Delta = 0 \][/tex]
Option B: [tex]\( f(x) = x^2 - 13x + 36 \)[/tex]
[tex]\[ a = 1, \, b = -13, \, c = 36 \][/tex]
[tex]\[ \Delta = (-13)^2 - 4 \cdot 1 \cdot 36 \][/tex]
[tex]\[ \Delta = 169 - 144 \][/tex]
[tex]\[ \Delta = 25 \][/tex]
Option C: [tex]\( f(x) = x^2 + 13x + 36 \)[/tex]
[tex]\[ a = 1, \, b = 13, \, c = 36 \][/tex]
[tex]\[ \Delta = 13^2 - 4 \cdot 1 \cdot 36 \][/tex]
[tex]\[ \Delta = 169 - 144 \][/tex]
[tex]\[ \Delta = 25 \][/tex]
Option D: [tex]\( f(x) = x^2 + 20x + 36 \)[/tex]
[tex]\[ a = 1, \, b = 20, \, c = 36 \][/tex]
[tex]\[ \Delta = 20^2 - 4 \cdot 1 \cdot 36 \][/tex]
[tex]\[ \Delta = 400 - 144 \][/tex]
[tex]\[ \Delta = 256 \][/tex]
Only option A has a discriminant of 0, which means it has exactly one \(x\)-intercept.
use the digits 0-7 to create two 4 digit numbers whose sum is greater than 9999.
Answer:
7,045 and 6,123. The sum is 13,168
Answer:
The numbers 7654 and 5463 meets the given conditions.
Step-by-step explanation:
We are given the following information in the question:
We have to create two four digits number from the digits between 0 and 7 such that there sum is greater than 9999.
Let x and y be the four digits number, then x and y must satisfy the equation:
[tex]x + y > 9999[/tex]
We choose the number 7654 and 5463. These are randomly fenerated from digits between 0 and 7.
Adding the two numbers:
[tex]x + y = 7654 + 5463 = 13117 > 9999[/tex]
Hence, the numbers 7654 and 5463 meets the given conditions.
Simplify: (sin x)/(1+cot^2 x)
Answer:
sin³x
Step-by-step explanation:
Using the trigonometric identities
1 + cot²x = csc²x
cscx = [tex]\frac{1}{sinx}[/tex]
Given
[tex]\frac{sinx}{1+cot^2x}[/tex]
= [tex]\frac{sinx}{csc^2x}[/tex]
= [tex]\frac{sinx}{\frac{1}{sin^2x} }[/tex]
= sinx × sin²x
= sin³x
d) Calculate the area of a circle with a circumference of 31.4 in.
Answer:
A ≈ 78.54
Step-by-step explanation:
Area of a circle is A=πr^2
Since you do not know r (radius) you take the formula for the circumference of a circle (C=2πr), plug in 31.4 for C, and solve for r
Now that you have the radius of 4.99746521, you round it up to 5 and solve the area formula with 5 in as r.
answer:78.5
for explanation see the picture
An art exhibition contains paintings, sculptures, and drawings. 1/4 of the works on display are sculptures, 2/5 are paintings, and the remainder are drawings. What fraction of the work on display are drawings?
Answer:
The fraction of the work that are drawings is [tex]\frac{7}{20}[/tex]
Step-by-step explanation:
we have that
100%=100/100=1
we know that
The sum of the fractions of the works must be equal to 1
Let
x -----> the fraction of the work that are drawings
so
[tex]1=\frac{1}{4}+\frac{2}{5}+x[/tex]
Solve for x
[tex]1=\frac{13}{20}+x[/tex]
Subtract 13/30 both sides
[tex]x=1-\frac{13}{20}[/tex]
[tex]x=\frac{7}{20}[/tex]
Which of the following transformations will make parallel lines p and q coincide with parallel lines p' and q'?
A.Counterclockwise rotation 90 about the origin
B.Counterclockwise rotation 90 about the origin, followed by translation 4 units to the left
C.Reflection across the x-axis, followed by a counterclockwise 90 rotation about the origin
D.Reflection across the line y-axis, followed by a counterclockwise 90 rotation about the origin
Answer:
A. Counterclockwise rotation 90 about the origin
Step-by-step explanation:
All we have to do is make the 270°-clockwise [90°-counterclockwise] rotation to map it exactly on q' and p'.
I am joyous to assist you anytime.
Option (A) counterclockwise rotation 90° about the origin makes the the parallel lines p and q will coincide with parallel lines p' and q' is the correct answer.
What is transformation of rotation?A rotation is a transformation that turns the figure in either a clockwise or counterclockwise direction on the coordinate plane. In both transformations the size and shape of the figure stays exactly the same.
For the given situation,
The graph shows the parallel lines p, q and p', q' in the plane.
The parallel lines p and q coincide with parallel lines p' and q' when we transformed the parallel lines by counterclockwise rotation 90° about the origin.
After this transformation of rotation, the parallel lines p and q will coincide with parallel lines p' and q'.
Hence we can conclude that option (A) counterclockwise rotation 90° about the origin makes the the parallel lines p and q will coincide with parallel lines p' and q' is the correct answer.
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-3(y+3)=2y+3
what’s the answerrr is there even a solution???
Answer:
y = -2 2/5
Step-by-step explanation:
-3(y+3)=2y+3
-3y - 9 = 2y + 3
-3y - 2y = 3 + 9
-5y = 12
y = 12/-5 = -12/5 = - 2 2/5
-3(y+3)=2y+3
Mutiply the bracket by -3
(-3)(y)= -3y
(-3)(3)= -9
-3y-9= 2y+3
Move -9 to the other side
Sign changes from -9 to +9
-3y-9+9= 2y+3+9
-3y= 2y+3+9
-3y= 2y+12
Move 2y to the other side
Sign changes from +2y to -2y
-3y-2y= 2y-2y+12
-3y-2y=12
-5y= 12
Divide both sides by -5
-5y/-5= 12/-5
Answer:
y= -12/5 or y=- 2 2/5
A regular polygon has 24 sides. What's the measure of each exterior angle?
A. 18°
B. 15°
C. 20°
D. 16°
Hey!
----------------------------------------
Explanation and Solution:
A polygon has to at least have 360° total to form a polygon.
Since there are 24 sides you divide 360 by 24.
360 / 24 = 15
----------------------------------------
Answer:
The measure of each exterior angle has to be at least 15° to form a complete polygon of 24 sides.
----------------------------------------
Hope This Helped! Good Luck!
beth and her brother went to the arcade. it cost 75 cents to play 3 games. they played 21 games in all. how much money did they spend?
Answer:
$5.25
Step-by-step explanation:
if it cost 75 cents to play 3 games, that means it cost 25 cents per game. Multiply 21 games by 25 cents per game and you get 525, or $5.25.
Below is a graph of the Murphys' annual expenses. If the Murphys' gross annual household income is $85,420, how much will they pay in federal taxes?
a. $3,559.17
b. $8,542.00
c. $20,500.80
d. $29,897.00
[tex]\text{Hello there!}\\\\\text{We know that Murphy makes \$85,420}\\\\\text{However, we need to find how much he needs to pay in federal taxes}\\\\\text{Looking at the chart, you'll see that federal taxes is 24\%}\\\\\text{This means we have to multiply 85,420 by .24 to see how much he needs}\\\text{to pay}\\\\85420*.24=20500.8\\\\\boxed{\text{Answer: C). \$20500.8}}[/tex]
The amount paid as Federal tax by the Murphys' is $20,500.80.
What is a pie chart?A pie chart is a kind of graph that is plotted in circular form. It is often used to present information succinctly and for easy digestion by the target audience.
In order to obtain the amount of money that the Murphys' pay as federal tax;
Total or gross income of the Murphys' = $85,420Percentage paid as federal tax = 24%Hence;
Amount paid as federal tax = 24/100 × $85,420 = $20,500.80
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17x=13x solve for x
I’m not sure but I got this with the same side interior angles theorem. I have to find the measure of angle EFG
It takes 2 and a 1/2 poster boards to display half of your project. How many poster boards will you need for your entire project?
Answer:
5 poster boards
Step-by-step explanation:
Sara is cutting bows out of ribbon which
will be used to wrap gifts. If Sara needs 1/4 of
a foot of ribbon to make a bow, and she has
5 feet of ribbon, then how many bows can
Sara make?