Answer:
(a) 6ab² - 8a²b + 3ab
Step-by-step explanation:
Given: 5ab² - 12a²b + 3ab + ab² + 4a²b
In this question, we will be combining like terms.
What are like terms?
Like terms are terms with the same variables and power. For example, 2x and 4x, as well as 2a² and 4a².
Combine like terms:
5ab² - 12a²b + 3ab + ab² + 4a²b
(5ab² + ab²) + (-12a²b + 4a²b) + 3ab
6ab² - 8a²b + 3ab
If [2a -1] [-3-a]= (10), find the value of a.
Step-by-step explanation:
Step-by-step explanation:-6a-2a^2+3+a=10-7a-2a^2=10-32a^2+7a+7=0On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 3, negative 7) and (0, 2). Everything to the left of the line is shaded.
Which linear inequality is represented by the graph?
y < 3x + 2
y > 3x + 2
y < One-thirdx + 2
y > One-thirdx + 2
The inequality described can be written as:
y < 3x + 2.
How to get the inequality?First, we know that we have a dashed line, and the region to the left of that line is shaded, then we will have:
y < line.
The linear equation is of the form:
y = a*x + b
Where a is the slope and b is the y-intercept.
Remember that if a line passes through the points (x₁, y₁) and (x₂, y₂), then the slope is:
[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Here we know that the line passes through (-3, -7) and (0, 2), so the slope is:
[tex]a = \frac{2 - (-7)}{0 - (-3)} = 9/3 = 3[/tex]
And because the line passes through (0, 2), the y-intercept is 2, then the inequality is:
y < 3x + 2.
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Fill in the missing number in this sequence:
324, 108, 36, 12, { }
Answer:
4
Step-by-step explanation:
Every number is divided by 3
Hi student, let me help you out! :)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
We are asked to find the missing number in the sequence
[tex]\star~\mathrm{324,108,36,12,(~~)}[/tex]
[tex]\triangle~\fbox{\bf{KEY:}}[/tex]
Take a look at the common ratio.Since every number here is divided by 3, we divide 12 by the common ratio, 3:
[tex]\mathrm{12\div3}[/tex]
[tex]\star~\star~\mathrm{4}\star~\star[/tex]
Hope it helps you out! :)
Ask in comments if any queries arise.
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~Just a smiley person helping fellow students :)
what is the value of 50 US dollar in philippine money?
Answer:
Answer is $2,637.38
Step-by-step explanation:
32, 28, 36, 38, 40, 26, 29, 37 in least to greatest order
Answer:
26, 28, 29, 32, 36, 37, 38, 40
Step-by-step explanation:
How to solve for the x??? Pls hep
Answer:
x = 97.5 degrees
Step-by-step explanation:
First, we need to know what the total sum of interior angles. We use the formula (n-2) * 180, n being the number of sides.
Since this is a 6-sided polygon, the sum is (6-2) * 180, or 720 degrees.
We have the total sum of interior angles, so now we have all the information we need.
720 degrees = (2x-50) + (x+40) + 80 + (x+20) + 90(right angle symbol) + 150
720 = 4x + 330 (subtract 330 from both sides)
390 = 4x (divide by 4)
x = 97.5 degrees
In a class of 75 students, 50 like visiting and 50 like Picnic. If each student like at least one activity, using Venn diagram, find the number of students who like both.
please help me with this question.
If each student like at least one activity, the number of student that like both is 25
How to solve Venn diagram?The class have 75 students.
50 like visiting and 50 like picnic.
Therefore, if each student like at least one activity, the number of student that like both can be calculated as follows;
let
x = student that like both
75 = 50 + 50 - x
Therefore,
75 = 100 - x
75 - 100 = -x
-25 = -x
x = 25
Therefore, the number of students who like both are 25.
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please simplify the answer
Answer:
[tex] 56\: in^2[/tex]
Step-by-step explanation:
Surface area of the net = 4* Area of one triangle + Area of square[tex] = 4*\frac{1}{2}*4*5 + (4)^2[/tex][tex] = 40 + 16[/tex][tex] = 56\: in^2[/tex]Bentley leans a 22-foot ladder against a wall so that it forms an angle of 74 degrees with the ground. How high up the wall does the ladder reach? Round your answer to the nearest hundredth of a foot if necessary
The Sine or Sin(θ) in a right angle triangle is the ratio of its perpendicular to its Hypotenuse. The Height on the wall till which the ladder reaches is 21.148 ft.
What is Sine (Sinθ)?The Sine or Sin(θ) in a right angle triangle is the ratio of its perpendicular to its Hypotenuse. it is given as,
Sin(θ) = Perpendicular/Hypotenuse
where,
θ is the angle,
Perpendicular is the side of the triangle opposite to the angle θ,
The hypotenuse is the longest side of the triangle.
The height of the wall can be found by using the trigonometry ratios, therefore, the height of the wall can be determined as,
Sin(74°) = (Height on the wall)/(Length of the wall)
Sin(74°) = (Height on the wall)/22 ft
(Height on the wall) = 21.148 ft
Hence, the Height on the wall till which the ladder reaches is 21.148 ft.
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Answer:
21.15
Step-by-step explanation:
Which of the following best describes the graph below A.it is a one to one function B. It is not a function C.it is a many to one function D.It is a function,but it is not one to one
The graph is a one to one function , Option A is the correct answer.
What is a function ?A function is defined as the algebraic expression that identifies relation between a dependent and an independent variable.
All the function have a defined domain and Range.
To test that the given graph is a function ,
A vertical line test will be done , A vertical is passes through different points of the graph and for every unique value of x , we get a single solution of y , therefore it is a function
Then horizontal Line test is done to determine if it is a one to one function, for every y value there is only one x value.
The graph passes the horizontal line test.
Therefore The graph is a one to one function , Option A is the correct answer.
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Shawnee richards and her husband have decided to purchase a cabin in the county. they have applied for a mortgage loan of 80,000 at 6% for a period of 25 years. they will pay it off in equal monthly payments that include interest.
Using it's formula, it is found that their monthly payments for the mortgage loan will be of $515.45.
What is the monthly payment formula?It is given by:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
In which:
P is the initial amount.r is the interest rate.n is the number of payments.In this problem, we have that the parameters are given as follows:
P = 80000, r = 0.06, n = 25 x 12 = 300.
Hence:
r/12 = 0.06/12 = 0.005.
Then, the monthly payment will be of:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
[tex]A = 80000\frac{0.005(1.005)^{300}}{(1.005)^{300} - 1} = 515.45[/tex]
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[tex]\sf\large\green{\underbrace{\red{Question*}}}:[/tex]
[tex] \mathbb\blue{SOLVE} [/tex]
[tex] \pink{1. \: \: \: \: \: \: (3 - x)(x + 2) = 0}[/tex]
[tex] \pink{2. \: \: \: \: \: {(q + 2)}^{2} - 40}[/tex]
[tex]\large{\underline{\underline{\pmb{\sf{\color {red}{Solve:}}}}}}[/tex]
[tex] \sf \red{1. \: (3x - x) (x + 2) = 0}[/tex]
[tex] \sf \red{2. \: (q + 2)^{2} - 40}[/tex]
[tex]\large{\underline{\underline{\pmb{\frak {\color {blue}{Answer:}}}}}}[/tex]
2.soln:
(q + 2)² - 40
=> (q)² + 2.q.2 + (2)² - 40
=> q² + 4q + 4 - 40
=>q² + 4q - 36
Here, a = 1, b = 4 and c = - 36
By, using Quadratic formula
See the attachment
What is the solution of 4 + StartRoot 5 x + 66 EndRoot = x + 10? x = –10 x = 3 x = –10 or x = 3 no solution
The solution to the equation 4 + √(5x + 66) = x + 10 is x = -10 and x = 3
How to determine the solution to the equationFrom the question, we have the following parameters that can be used in our computation:
4 + √(5x + 66) = x + 10
Subtract 4 from both sides
So, we have
√(5x + 66) = x + 6
Take the square of both sides
5x + 66 = x² + 12x + 36
So, we have
x² + 7x - 30 = 0
When expanded, we have
x² + 10x - 3x - 30 = 0
So, we have
(x + 10)(x - 3) = 0
Solve for x
x = -10 and x = 3
Hence, the solution to the equation 4 + √(5x + 66) = x + 10 is x = -10 and x = 3
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What is the scale factor for XYZ TO UVW?
Answer:
D. 2
Step-by-step explanation:
If you multiply any side from XYZ by 2 it will equal the same length of one of the sides of UVW.
MODELING WITH MATHEMATICS Three tennis balls are stored in a cylindrical container with a height of 8 inches and a radius of 1.43 inches. The circumference of a tennis ball is 8 inches. Round your answers to the nearest hundredth.
I just need help with part b
A picture shows three tennis balls placed one above another in a cylindrical container.
a. Find the volume of a tennis ball. Round your answer to the nearest hundredth.
The volume of a tennis ball is about
cubic inches.
Answer is about 8.65
b. Find the amount of space within the cylinder not taken up by the tennis balls. Round your answer to the nearest hundredth.
The volume of the space within the cylinder not taken up by the tennis balls is about
cubic inches.
The volume of a tennis ball is about 8.65 cubic inches
The volume of the space within the cylinder not taken up by the tennis balls is about 25.44 cubic inches
Calculating volumeFrom the question, we are to determine the volume of a tennis ball
From the given information,
The circumference of a tennis ball is 8 inches
That is,
C = 2πr (C is circumference)
8 = 2πr
∴ r = 8/2π
r = 4/π inches
This the radius of a tennis ball
Now, for the volume of a tennis ball
Using the formula for calculating the volume of a sphere
[tex]V = \frac{4}{3}\pi r^{3}[/tex]
Then, the volume of a tennis is
[tex]V = \frac{4}{3}\pi \times (\frac{4}{\pi})^{3}[/tex]
[tex]V = \frac{4}{3}\pi \times \frac{64}{\pi^{3}}[/tex]
[tex]V = \frac{256}{3\pi^{2}}[/tex]
V = 8.64607 cubic inches
V ≅ 8.65 cubic inches
Hence, the volume of a tennis ball is about 8.65 cubic inches
b. To find the amount of space within the cylinder not taken up by the tennis balls
First, we will calculate the volume of the cylinder
Using the formula for calculating the volume of a cylinder
V = πr²h
Where V is the volume
r is the radius
and h is the height
From the given information,
r = 1.43 inches
h = 8 inches
Putting the parameters into the formula, we get
V = π × 1.43² × 8
V = 16.3592π
V = 51.39 cubic inches
This is the volume of the cylinder
Now, for the amount of space within the cylinder not taken up by the tennis balls
Since there are three tennis balls,
The amount of space not taken up will be
51.39 cubic inches - 3(8.65 cubic inches)
51.39 cubic inches - 25.95 cubic inches
= 25.44 cubic inches
Hence, the volume of the space within the cylinder not taken up by the tennis balls is about 25.44 cubic inches
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PLEASE HELP I’LL MAKE YOU THE BRAINIEST Find the area of the parallelogram
Answer:
A=5.4×4.4=23.76 in
because the are of the paralelogram is base ×high
Circle O has secant lines AB and BD intersects circle O at points C and D. if AD=40 degrees and BC=120 degrees, find
Answer:
Angle AED: 40
Angle BEC: 105
Explanation:
1) To find Angle AED, you have to do arc BC minus arc AD then divide by 2.
120 - 40 = 80.
80 / 2 = 40
2) To find Angle BEC, you have to do arc BA + CD then divide by 2. But that's only angle CED. You'll have to double the number because BEA is vertical; then minus 360.
62 + 88 = 150
150 / 2 = 75
75 times 2 = 150
360 - 150 = 210
210 / 2 = 105
- You'll divide 210 by 2 because of the vertical angles of AED and BEC.
In circle O, ST is a diameter.
Circle O is shown. Line segment S T is a diameter. Line segments R O and U O are radii. Angles R O U and U O T are congruent. The measure of arc R S is (2 x + 8) degrees, the measure of arc R U is (3 x minus 14) degrees, and the measure of arc U T is (3 x minus 14) degrees.
What must be the value of x?
22.0
25.0
25.4
37.2
A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant. The correct option is B.
What is a circle?A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.
Given the measure of arc, RS is (2 x + 8) degrees, the measure of arc R U is (3 x minus 14) degrees, and the measure of arc U T is (3 x minus 14) degrees.
(3x-14)° + (3x-14)° + (2x+8)° = 180°
8x -20 = 180
8x = 200
x = 25
Hence, the correct option is B.
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A parade route is 3 4 mile long. there will be a refreshment stand at the beginning and end of the route. there will also be 8 refreshment stands along the route. all the refreshment stands are equally-spaced apart. how far apart are the refreshment stands in feet?
396
440
495
520
The distance between the refreshment stands is 440 feet
Calculating distanceFrom the question, we are to determine how far apart are the refreshment stands in feet
From the given information,
The parade route is 3/4 mile long
and
There are refreshment stands at the beginning and end of the route. And there will also be 8 refreshment stands along the route.
This means there will be 10 refreshment stands in all.
If there are 10 refreshment stands in all, then there will be 9 spaces between the refreshment stands.
∴ The distance between any two refreshment stands will be
3/4 mile ÷ 9 = 3/36 mile = 1/12 mile
Now, we will convert this to feet
NOTE: 1 mile = 5280 feet
∴ 1/12 mile = 1/12 × 5280 feet
= 440 feet
Hence, the distance between the refreshment stands is 440 feet.
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Consider a triangle ABC like the one below. Suppose that a = 42, b=44, and c= 52. (The figure is not drawn to scale.) Solve the triangle
Carry your intermediate computations to at least four decimal places, and round your answers to the nearest tenth.
there is more than one solution, use the button labeled "or".
In the triangle , Angle A is 51.1 degrees, B is 54.5 degrees , C is 74.4 degrees.
What is a Triangle ?A triangle is defined as a polygon with three sides , three angles and three vertices.
Using the Law of Cosine to solve the Triangle and to determine the value of all the angles
c² = a²+ b² -2abCosC
a = 42 , b=44 , c = 52
52² = 42² + 44² -2 * 42 * 44 cos C
2704 = 1764 + 1936 -3696 cos C
cos C = 0.269
C =74.4 ° (degrees)
Similarly calculating for A and B will give
Angle A is 51.1 degrees
Angle B is 54.5 degrees
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what is the function
Answer: Exponential
After plotting the points as shown in the image, it is obvious they follow an exponential trend.
An adult African elephant weighs approximately 8 tons. Which comparison is true
find the slope of the line
x-intercept is twice as y-intercept
Answer:
-1/2
Step-by-step explanation:
It mentions that the x-intercept is equal to twice the y-intercept.
=============================================================
Let :
⇒ x-intercept = (2a, 0)
⇒ y-intercept = (0, a)
==============================================================
Slope formula :
m = y₂ - y₁ / x₂ - x₁
=============================================================
Solving :
⇒ m = a - 0 / 0 - 2a
⇒ m = a / -2a
⇒ m = -1/2
Find the slant height x of the pyramid shown, to the nearest tenth.
5 mm
9 mm
9 mm
The slant height of the pyramid can be calculated using Pythagoras theorem. Therefore, the slant height is 6.7 mm
How to find slant height of a pyramid?
The slant height x, can be found using Pythagoras theorem,
Therefore,
c² = a² + b²
where
c = hypotenusea and b are other two legs.Therefore,
x² = 4.5² + 5²
x² = 20.25 + 25
x² = 45.25
x = √45.25
x = 6.72681202354
x = 6.7 mm
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In August, Sara and Mel decided to spend a week fishing. On the first day, Sara caught 2 fish, and Mel caught 4 fish. The next day, Sara had 4 fish altogether, and Mel had 8 fish. On the third day Sara had 6 fish altogether while Mel had 12 fish altogether.
1. If the pattern continues, how many fish will each of them have caught by the end of the week? Fill in the rest of the chart.
Fish caught altogether:
Days
1
2
3
4
5
6
7
Sara
2
4
6
Mel
4
8
12
1. If the pattern continues, how many fish will each of them have caught by the end of the week? Fill in the rest of the chart.
Fish caught altogether:
Days
1
2
3
4
5
6
7
Sara
2
4
6
Mel
4
8
12
2. What is the pattern that describes how many fish Sara caught each day? What is the pattern that describes how many fish Sara caught altogether?
3. What is the pattern that describes how many fish Mel caught each day? What is the pattern that describes how many fish Mel caught altogether?
4. What do you notice when you compare Sara’s pattern and Mel’s Pattern?
5. If Sara and Mel continued fishing, how many fish would they have caught by day 10?
this is worth 100 points
Turn into coordinates pair
(2,4)(4,8)(6,12)Slope
m=8-4/4-2=2Equation
y=2x#1
A week is of 7 days
total fishes Sara has=2(7)=14
Total mel will have
y=14(2)=28fishes#2
The each day Sara caught 2fishes
pattern for Sara 's total
2dd is days
#3
Mel also caught 2(2)=4 fishes a day
Mel caught all together is 2(Sara)
#4
They are in proportion to each other
#5
Sara would have 10(2)=20fishes
Mel would have.
20(2)=40fishesAnswer:
Q1)
The number of fish Sara caught increases by 2 each day.
The number of fish Sara caught increases by 4 each day.
[tex]\large \begin{array}{| c | c | c |}\cline{1-3} & \sf SARA& \sf MEL\\\sf Days & \sf fish\:caught & \sf fish\:caught \\& \sf altogether & \sf altogether\\\cline{1-3} 1 & 2 & 4 \\\cline{1-3} 2 & 4 & 8 \\\cline{1-3} 3 & 6 & 12 \\\cline{1-3} 4 & 8 & 16 \\\cline{1-3} 5 & 10 & 20 \\\cline{1-3} 6 & 12 & 24 \\\cline{1-3} 7 & 14 & 28 \\ \cline{1-3}\end{aligned}[/tex]
Q2)
Sara caught 2 fish each day.
The pattern that describes how many fish Sara caught altogether is:
2 times the number of days
Q3)
Mel caught 4 fish each day.
The pattern that describes how many fish Mel caught altogether is:
4 times the number of days
Q4)
The number of fish Mel caught altogether is twice the number of fish Sara caught altogether.
Q5)
The number of fish Sara and Mel would have caught by day 10:
Sara = 10 × 2 = 20 fishMel = 10 × 4 = 40 fishThe height of a baseball hit from a bat is modeled by a quadratic function of time, h(t). What does the second coordinate of the vertex of the quadratic function represent?
the minimum height of the baseball
the time at which the baseball hits the ground
the time at which the baseball hits the maximum height
the maximum height of the baseball
The correct answer is option D which is the second coordinate of the vertex of the quadratic function that represents the maximum height of the baseball.
What is a quadratic equation?The polynomial having a degree of two or the maximum power of the variable in a polynomial will be 2 is defined as the quadratic equation and it will cut two intercepts on the graph at the x-axis.
The second coordinate of the vertex of the quadratic function represents the maximum height of the ball.
The height of a baseball hit from a bat is modeled by a quadratic function of time, h(t)
General form of h(t) will be -16x² + v(t) + h
Where v represents initial velocity and h represents the initial height
h(t) represents the height of the baseball
h(t) is negative so the height reaches the maximum
vertex (h,k) represents maximum height (k) when time t=h
So the second coordinate of the vertex of the quadratic function represents the maximum height of the ball.
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Answer: D
Step-by-step explanation
Persevere with Problems The table shows the highway fuel economy of various popular vehicles.
The mean absolute deviation of highway fuel economy of various popular vehicles is 4.9
How to find mean absolute deviation?Find the mean of the data set
= (38 + 48 + 25 + 35 + 33 + 37 + 32 + 34 + 23 + 30) / 10
= 335 / 10
= 33.5
Mean deviation of each set;
38 - 33.5 = 4.5
48 - 33.5 =14.5
25 - 33.5 = -8.5
35 - 33.5 = 1.5
33 - 33 .5 = -0.5
37 - 33.5 = 3.5
32 - 33.5 = -1.5
34 - 33.5 = 0.5
23 - 33.5 = -10.5
30 - 33.5 = -3.5
Absolute deviation of each value
|4.5| = 4.5
|14.5| = 14.5
|8.5| = 8.5
|1.5| = 1.5
|-0.5| = 0.5
|3.5| = 3.5
|-1.5| = 1.5
|0.5| = 0.5
|-10.5| = 10.5
|-3.5| = 3.5
Total absolute deviation = 4.5 + 14.5 + 8.5 + 1.5 + 0.5 + 3.5 + 1.5 + 0.5 + 10.5 + 3.5
= 49
Mean absolute deviation = Total absolute deviation / mean
= 49/10
= 4.9
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Click on the correct symbol to compare the measurements.
19 in. 2 yd 4 in.
Answer:
I don't see any symbols, so I'll simply compare the two measurements.
Step-by-step explanation:
2 yards and 4 inches
Each yard has 3 feet. Each foot has 12 inches. The total inches in 3 yards is therefore:
(2 yards)*(3 feet/yard)*(12 inches/Foot) = 72 inches [Note how the units cancel to leave only inches]
This means we have a total of 72 + 4 inches = 76 inches total
19 Inches
Compared to 19 inches, 72 inches is almost 3.79 times longer.
What is the distance between the following points?
Answer:
if im not mistaken the andswer is D
How do I find the vertex function
Answer:
oh ok. So, first, you get the equation in the form y=ax2+bx+c. Next, you calculate -b / 2a. This is the x-coordinate of the vertex. Then finally, you plug in the value of -b / 2a into the equation into the x variable and solve for the y variable. This is the coordinate of the vertex.
Step-by-step explanation:
Hope this helps!