Answer:
[tex]\large\boxed{(2g+4h)(x)=8x^3+20x^2}[/tex]
Step-by-step explanation:
[tex]g(x)=-4x\\\\h(x)=2x^3+5x^2+2x\\\\(2g+4h)(x)=2g(x)+4h(x)\\\\2g(x)=(2)(-4x)=-8x\\\\4h(x)=(4)(2x^3+5x^2+2x)\qquad\text{use the distributive property}\\\\4h(x)=(4)(2x^3)+(4)(5x^2)+(4)(2x)=8x^3+20x^2+8x\\\\(2g+4h)(x)=-8x+8x^3+20x^2+8x\qquad\text{cancel}\ 8x\\\\(2g+4h)(x)=8x^3+20x^2[/tex]
Solve for all missing posts of triangles with the given information. B =53 degrees, a =10, b=17
Answer:
Therefore,
[tex]m\angle A =28\°\\\\m\angle C =99\°\\\\c=21\ units[/tex]
Step-by-step explanation:
Consider a Δ ABC with
m∠ B = 53°
BC = a = 10
AC = b = 17
To Find:
AC = c = ?
m∠ A = ?
m∠ C = ?
Solution:
We know in a Triangle Sine Rule Says that,
In Δ ABC,
[tex]\dfrac{a}{\sin A}= \dfrac{b}{\sin B}= \dfrac{c}{\sin C}[/tex]
substituting the given values we get
[tex]\dfrac{a}{\sin A}= \dfrac{b}{\sin B}[/tex]
[tex]\dfrac{10}{\sin A}= \dfrac{17}{\sin 53}\\\\\sin A=0.469\\A=\sin^{-1}(0.469)=28.02\approx 28\°[/tex]
Therefore m∠A = 28°
Triangle sum property:
In a Triangle sum of the measures of all the angles of a triangle is 180°.
[tex]\angle A+\angle B+\angle C=180\\\\28+53+\angle C=180\\\therefore m\angle C =180-81=99\°[/tex]
Therefore m∠C = 99°
Now From Sine rule we have
[tex]\dfrac{b}{\sin B}= \dfrac{c}{\sin C}[/tex]
Substituting the values we get
[tex]\dfrac{17}{\sin 53}= \dfrac{c}{\sin 99}\\\\c=21.02\approx 21\ unit[/tex]
Therefore,
[tex]m\angle A =28\°\\\\m\angle C =99\°\\\\c=21\ units[/tex]
Identify the slope and y-intercept of the
equation:
2x + 2y = -10
Answer:
Step-by-step explanation:
2x + 2y = -10
Making y as subject
2y = -2x - 10
Dividing by 2
y = -2x/2 - 10/2
y = -x - 5
Comparing with y = mx + c
Slope m = -1, y intercept c = -5
The equation is first rewritten in slope-intercept form as y = -x - 5, revealing that the slope is -1 and the y-intercept is -5.
To find the slope and y-intercept of the given equation 2x + 2y = -10, you need to rewrite it in the slope-intercept form, which is y = mx + b, where m represents the slope, and b represents the y-intercept. First, let's separate the y-term on one side by subtracting 2x from both sides of the equation:
2y = -2x - 10
Now divide the entire equation by 2 to solve for y:
y = (-2x/2) - (10/2)
y = -x - 5
Comparing this with the slope-intercept form y = mx + b, we can see that the slope (m) is -1, and the y-intercept (b) is -5.
The students of a bayside middle school are going on a field trip . 15 students fit in a van and 3 students will be traveling in a car. write an algebraic expression for this problem and what is the meaning of the variable in your expression
Answer:
[tex]v = 15 \\ c = v \div 5[/tex]
Step-by-step explanation:
It could be this
Evaluate the expression -9 W + 9 when w equals 15
Answer:
The value of the given expression -9w+9 when w=15 is -126
Step-by-step explanation:
Given expression is -9w+9
To find the given expression when w=15:
That is put w=15 in the given expression we get
-9w+9=-9(15)+9
=-135+9 ( adding the like terms )
=-126
Therefore the value of the given expression -9w+9 when w=15 is -126
N 4n3 2m 6m 5n 2n
Identify like terms
Final answer:
In the given algebraic expression, 4n³ and 2n³, 2m and 6m, and 5n and 2n are identified as like terms.
Explanation:
The question asks to identify like terms in a given algebraic expression. Like terms in algebra are terms that have the exact same variables raised to the same powers, although they can have different coefficients.
For example, 4n³ and 2n³are like terms because they both contain the variable n to the third power.
On the other hand, 2m and 6m are like terms because they both contain the variable m to the first power.
Lastly, 5n and 2n are like terms because they contain the variable n to the first power.
Theodore needs to mix a 10% fungicide solution with a 50% fungicide solution to create 100 milliliters of a 26% solution. How many milliliters of each solution must Theodore use?
Answer:
Therefore 40 milliliter of 50% fungicide solution is required
Therfore 60 milliliter of 10% fungicide solution is required
Step-by-step explanation:
i) Let the 10% fungicide solution have x milliliter and the 50% fungicide solution have y milliliter.
ii) Therefore 10x + 50y = 26(x + y)
x + y = 100
iii) form the first equation in ii) we get
16 x = 24 y Therefore [tex]x = \frac{24}{16} y = \frac{3}{2} y[/tex]
iv) substituting the value obtained in iii) in the second equation in ii) we get
[tex]\frac{3}{2} y + y = \frac{5}{2} y = 100[/tex]
Therefore y = 100 ÷ 2.5 = 40 milliliter
Therfore x = 100 - 40 = 60 milliliter
200 points What are the classifications of each system?
Drag the answer into the box to match each system.
Answer:
Part 1)Is a inconsistent system
Part 2) Is a consistent independent system
Part 3) Is a consistent dependent system
see the attached figure
Step-by-step explanation:
we know that
If a system has at least one solution, it is said to be consistent .
If a consistent system has exactly one solution, it is independent .
If a consistent system has an infinite number of solutions, it is dependent
If a system not have solution, it is said to be inconsistent
Part 1) we have
[tex]x+5y=-2[/tex]
[tex]x+5y=4[/tex]
This system of linear equations has two parallel lines (their slopes are equal) with different y-intercept
so
The lines don't intersect
The system has no solution
therefore
Is a inconsistent system
Part 2) we have
[tex]y=3x+4[/tex]
[tex]-2x+y=4[/tex]
we know that
If two lines have different slopes, then the lines intersect at one point and the system of equations has one solution
In this problem, the lines have different slopes )m=3 and m=2)
so
The system has one solution
therefore
Is a consistent independent system
Part 3) we have
[tex]3x+y=4[/tex] ----> equation A
[tex]-6x-2y=-8[/tex] ----> equation B
Multiply equation A by -2 both sides
[tex]-2(3x+y)=-2(4)[/tex]
[tex]-6x-2y=-8[/tex] ----> equation C
Compare equation B and equation C
Are identical lines
so
The system has infinity solutions
therefore
Is a consistent dependent system
A can company makes a cylindrical can that has a radius of 6 cm and a height of 10 cm. One of the company's
clients needs a cylindrical can that has the same volume but is 15 cm tall. What must the new radius be to meet the
client's need? Round to the nearest tenth of a centimeter.
2.7 cm
4.9 cm
O 7.3 cm
24.0 cm
Answer:
Step-by-step explanation:
V=πr²h
=3.14*6*6*10
=1130.4 cm³
New cylinder:
h = 15cm
V= 1130.4 cm³
πr²h = 1130.4
3.14*r²*15=1130.4
r²=1130.4/15*3.14
r²=24
r=√24
r=4.898 = 4.9 cm
The radius be to meet the client's need is 4.9 cm.
What is Volume?Volume is a mathematical term used to describe how much three-dimensional space an item or closed surface occupies.
Volume is sometimes referred to as capacity.
We have,
Radius of cylinder (r)= 6 cm
Height of cylinder (h) = 10 cm
and, Height of new cylinder (H) = 15 cm
Radius of new cylinder = R cm
Now, Volume of cylinder can be compared as
πr²h = πR²H
6 x 6 x 10 = R² x 15
360 / 15 = R²
R² = 24
R= 4.9 cm
Thys, the radius is 4.9 cm.
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Jean practices for 19 quarter hour periods each month how many hours does she practice
Angela worked on a straight 12% commission. Her friend worked on a salary of $750 plus a 5% commission
The question is about comparing Angela's 12% commission structure against her friend's $750 fixed salary plus 5% commission. The answer examines how the volume of sales would affect their respective incomes.
Explanation:This problem is about comparing commission rates and overall income. If Angela worked on a straight 12% commission, it means that she earns 12% of the total sales she makes. Her friend, however, has a fixed salary of $750, in addition to earning 5% of his total sales as commission. To compare their incomes, we would need to know the total sales each of them makes. Generally, the more sales they make, the more beneficial the commission system becomes.
For example, if Angela made $1000 in sales, she would earn $120 (12% of $1000). If her friend made the same amount in sales, he would earn $800 ($750 salary + $50 from 5% of $1000). However, if they only made $100 in sales, Angela would earn $12, and her friend would earn, $755. So, the best system depends on the volume of sales.
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Pls help meeee!!! I have benchmarks monday
Answer:
therefore the correct options are:
B. the equation is an exponential decay equation.
F. $28000 represents the initial cost of an automobile that depreciates 27% per year over the course of t years.
Step-by-step explanation:
i) the cost of an automobile is given by the equation is
C(t) = [tex]28000\times(0.73)^{t}[/tex], where C(t) represents the cost and t represents the time in years
ii) the above equation is an exponential decay equation. It is a decay equation because growth rate is 0.73 which is less than 1 and greater than zero.
ii) when t = 0 then the cost is C(0) = 28000 represents the initial cost.
iii) from the equation in i) we can understand that the cost depreciates 27% per year over the course of t years.
therefore the correct options are:
B. the equation is an exponential decay equation.
F. $28000 represents the initial cost of an automobile that depreciates 27% per year over the course of t years.
Using 6 as a denominator, what fraction completes the following equation: 1 − 2/12 = ? a.4/6 c. 3/6 b.5/6 d. 2/6
Answer:
5/6
Step-by-step explanation:
[tex]1-\frac{2}{12}=1-\frac{1}{6}=\frac{1*6}{1*6}-\frac{1}{6}\\\\=\frac{6}{6}-\frac{1}{6}=\frac{6-1}{6}=\frac{5}{6}[/tex]
In which model are 60% of the squares shaded? A grid model with 100 squares. 6 squares are shaded. A grid model with 100 squares. 36 squares are shaded. A bar diagram has 6 shaded squares and 4 unshaded squares. A bar diagram has 4 shaded squares and 6 unshaded squares.
Answer:
6 shaded squares and 4 unshaded....shaded = 60%
Step-by-step explanation:
a grid with 100 squares, 6 are shaded....6/100 = 0.06 = 6%
a grid with 100 squares, 36 are shaded....36/100 = 0.36 = 36%
6 shaded squares and 4 unshaded...6:4...added = 10
shaded = 6/10 = 0.6 = 60% <====
4 shaded squares and 6 unshaded...4:6...added = 10
shaded = 4/10 = 0.4 = 40%
Answer: The answer is C
An item is on sale for 15% off its original cost. If the original cost of the item is represented by p, and the sale price is represented by s, which equation can be used to find the sale price of an item?
A) s= 0.75p
B)s= 0.85p
C)s=1.15p
D)s=0.015p
I need this ASAP
30 points if it’s right!
Answer:
B
Step-by-step explanation:
15% = 0.15
1 - 0.15 = 0.85
[Plug in the p and s]
4.4% of what number is 66
Answer:
1,500
Step-by-step explanation:
Find x in proportional form.
Answer: 1,500
Step-by-step explanation:
use the is/of = %/100 proportion
Jake and Mary are both members of a population and a simple random sample is being conducted if the chance of jake being selected is 1/800, what is the chance of Mary being selected
The relation Q is described as a list of ordered pairs, shown below.
Q = { (-2, 4), (0, 2), (-1, 3), (4, -2) }
Domain:
Range:
Answer:
Domain : {-2, -1, 0, 4}
Range: {-2, 2, 3, 4}
Answer:
b,c
Step-by-step explanation:
Bees bill for dinner was $98. She left a 15% tip. What was the total cost including the tip?
Answer:
$112.7
Step-by-step explanation:
15%=0.15
0.15*98=14.7
98+14.7=112.7
Phoebe bought a pencil and a ruler. She paid £1.45.loeh bought a ruler and two pencils.she paid£1.80. How much does the ruler cost?
Answer:
$ 1.10
Step-by-step explanation:
p + r = 1.45....p = 1.45 - r
2p + r = 1.80
2(1.45 - r) + r = 1.80
2.90 - 2r + r = 1.80
-2r + r = 1.80 - 2.90
-r = - 1.10
r = 1.10 <=== a ruler costs $ 1.10
p + r = 1.45
p + 1.10 = 1.45
p = 1.45 - 1.10
p = 0.35 .......a pencil will cost $ 0.35
By setting up simultaneous equations based on the purchases of Phoebe and Ioeh and solving them, we find that the cost of the ruler is £1.10.
Explanation:To determine the cost of the ruler, we need to set up two equations based on the given information about Phoebe and Ioeh's purchases and use the method of simultaneous equations.
Let's assume 'R' represents the cost of the ruler and 'P' represents the cost of one pencil.
According to the question:
Phoebe bought 1 ruler and 1 pencil, and she paid £1.45. So we get the equation: R + P = £1.45.Ioeh bought 1 ruler and 2 pencils, and she paid £1.80. So we get the equation: R + 2P = £1.80.To find the cost of the ruler, we can solve these equations simultaneously. Subtract the first equation from the second to eliminate R and find P:
1. R + 2P = £1.80
2. R + P = £1.45
Subtract equation 2 from equation 1:
2P - P = £1.80 - £1.45
P = £0.35
Now that we know one pencil costs £0.35, we can substitute P back into either equation to find R. Let's use the first equation:
R + P = £1.45
R + £0.35 = £1.45
R = £1.45 - £0.35
R = £1.10
Thus, the ruler costs £1.10.
A triangle has a perimeter of 50. If 2 of its
sides are equal and the third side is 5 more
than the equal sides, what is the length of
the third side
Answer:
20 units
Step-by-step explanation:
Let the equal sides of the triangle be x.
Then the third side will be (x+5) units
Since the perimeter is 50, we have:
[tex]x + x + (x + 5) = 50[/tex]
We simplify to get:
[tex]3x + 5 = 50[/tex]
This implies that:
[tex]3x = 50 - 5[/tex]
[tex]3x = 45[/tex]
Divide both sides by 3 to get:
[tex]x = \frac{45}{3} = 15 [/tex]
The length of the third side is:
15+5=20
What are the x-intercept and y-intercept of the graph of y=13x−6 ?
Drag and drop your answers into the boxes.
x-intercept:
y-intercept:
-6,-18,-2,2,6,18
Please hurry.
Answer:
x intercept is 6/13
y intercept is -6
Step-by-step explanation:
x intercepted when y is zero.
y intecepted when x is zero...
12 yds
How many square yards of cement are needed to create
the walkway around the rectangular pool?
4 yds
12 yds
w
176 square yards
196 square yards
208 square yards
280 square yards
4 yds
4 yds
6 yds
6 yds
Pool
6 yds
yds
12 yds
4 yds
12 yds
Answer:
176 square yards
Step-by-step explanation:
The picture of the question in the attached figure N 1
we know that
The area of the walkway around the rectangular pool, is equal to the area of two trapezoids (#1 and #2), plus the area of two smaller rectangles (#3 and #4)
see the attached figure N 2 to better understand the problem
step 1
Find the area of the two trapezoids (#1 and #2)
[tex]A=2[\frac{1}{2}(b_1+b_2)h][/tex]
simplify
[tex]A=(b_1+b_2)h[/tex]
we have
[tex]b_1=12\ yd\\b_2=4+12+4=20\ yd\\h=4\ yd[/tex]
substitute
[tex]A=(12+20)(4)=128\ yd^2[/tex]
step 2
Find the area of the two smaller rectangles (#3 and #4)
[tex]A=2[LW][/tex]
we have
[tex]L=4\ yd\\W=6\ yd[/tex]
substitute
[tex]A=2[(4)(6)]=48\ yd^2[/tex]
step 3
Find the area of the walkway around the rectangular pool
[tex]128+48=176\ yd^2[/tex]
Answer:
176 sq yards
Step-by-step explanation:
David rides his bike with a constant
speed of 12 miles per hour. How long
will he take to travel a distance of
12 miles?
Answer: 1 hour
Step-by-step explanation: if he travels 12 mph, it will take 1 hour to travel 12 miles.
What is the sum of the series? 4 ∑k=1 (2k^2−4)
The sum of the series [tex]\sum_{k=1}^{4}\left(2 k^{2}-4\right)[/tex] is 44.
Step-by-step explanation:
The given series is [tex]\sum_{k=1}^{4}\left(2 k^{2}-4\right)=44[/tex]
To find the sum of the series, we need to substitute the values for k in the series.
[tex]\sum_{k=1}^{4}\left(2 k^{2}-4\right)=\left[2(1)^{2}-4\right]+\left[2(2)^{2}-4\right]+\left[2(3)^{2}-4\right]+\left[2(4)^{2}-4\right][/tex]
Now, simplifying the square terms, we get,
[tex][2(1)-4]+[2(4)-4]+[2(9)-4]+[2(16)-4][/tex]
Multiplying the terms,
[tex][2-4]+[8-4]+[18-4]+[32-4][/tex]
Subtracting the values within the bracket term, we get,
[tex]-2+4+14+28[/tex]
Now, adding all the terms, we get the sum of the series,
[tex]\sum_{k=1}^{4}\left(2 k^{2}-4\right)=44[/tex]
Thus, the sum of the series is [tex]\sum_{k=1}^{4}\left(2 k^{2}-4\right)=44[/tex]
Hes right its 44
444444444444444444444
16. y = -5, x = 5
Determine whether the lines are perpendicular.
Answer:
yes, they are
Step-by-step explanation:
y = -5 is a horizontal line.
x = 5 is a vertical line.
Horizontal and vertical lines are perpendicular to each other. These lines are perpendicular.
WILL GIVE BRAINLIEST
What is X?
Answer:
x = 20
Step-by-step explanation:
2x + 7x = 180
⇔ 9x = 180
⇔ x = 180/9 = 20
An employee working 40 hours per week earns a salary of $600 per week but gets a
second job offer to work 40 hours per week, hourly at $20 an hour. Which position
generates the most income and how much more does that position make? Show
your work or explain how you got your answer.
Answer:
Step-by-step explanation:
40 hours per week*20 dollars per hour=800 dollars per week. This job makes 200 more dollars than the other job.
The amount of generation of the most income in the second job offer will be more which is $800 per week.
What is the rate?The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.
An employee working 40 hours per week earns a salary of $600 per week. Then the rate is given as,
Rate = $600 per week
But gets a second job offer to work 40 hours per week, hourly at $20 an hour. Then the rate is given as,
Rate = $20 x 40
Rate = $800 per week
The amount of generation of the most income in the second job offer will be more which is $800 per week.
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The smith family went out to dinner. Their bill came to $67.80. If they left a 15% tip and used a $100 gift card to pay for the bill, including the tip, what is the remaining balance on the card?
Answer: $22.03
Step-by-step explanation: 15% 67.8= 10.17. 67.8+10.17=77.97. x=remain balance. x=100.00-77.97=22.03.
for elimination what is the 2 ordered pairs
-4x + 3y = -19
-4x - y = -15
Answer:
I would eliminate both of the -4x because they are identical.
Step-by-step explanation:
Cancel out the both of the -4x by eliminating them. Then subtract the 3y - y. Subtract the -19 - 15. You then will be left with 2y = -34. Solve for y. Then plug y back into the equation to solve for the x.
Hope this helped. :^)
Paolo wrote the following equation for the perimeter of a rectangle.
P=2(t+W)
Which equation is equivalent to the equation Paolo wrote?
Paolo wrote the following equation for the perimeter of a rectangle.
P=2(l+w)
Which equation is equivalent to the equation Paolo wrote?
Answer:The equivalent equations are:
[tex]w = \frac{p-2l}{2}\\\\l = \frac{p-2w}{2}\\\\p = 2l+2w[/tex]
Solution:Given that:
The equation for perimeter of rectangle written by Paolo is:
P = 2(l + w)
where
l = length side of rectangle
w = width side of the rectangle
We have to find the equivalent equation
Let us solve the equation for "w"
[tex]P = 2(l + w)[/tex]
Divide by 2 both sides
[tex]\frac{P}{2} = \frac{2(l+w)}{2}\\\\\frac{P}{2} = l + w[/tex]
[tex]\text{Subtract L on both sides of equation }[/tex]
[tex]\frac{P}{2} - l = l + w - l\\\\\frac{P}{2} - l =w[/tex]
[tex]w = \frac{p-2l}{2}[/tex]
Similarly solving for "l" we get,
[tex]l = \frac{P-2w}{2}[/tex]
Also, given equation can be written as,
[tex]P = 2(l+w)\\\\P = 2l + 2w[/tex]
Thus the equivalent equations are found
Final answer:
The equivalent equation to Paolo's originally written P=2(t+W) for a rectangle's perimeter should be P=2t+2u, assuming 't' stands for width and 'u' for length. The area function a(t) for the rectangle based on width and fixed perimeter is valid within the domain 0 <= t <= L/2.
Explanation:
The question pertains to the formation of equivalent equations to express the perimeter of a rectangle. Paolo wrote the equation P=2(t+W). However, it seems there may have been a typographical error as the correct variables should have been 't' for width and 'u' for length. Given this, the equivalent equation to Paolo's should be P = 2t + 2u, also stated as P = 2(t + u) which confirms the relationship between perimeter, length, and width for a rectangle.
From the provided context, it's also understood that the function representing the area of the rectangle, when written in terms of width (t), is a(t) = t(L/2 - t), which is valid within the domain 0 <= t <= L/2. This function helps in determining the maximum area of the rectangle for a given perimeter (L).