Answer:
To subtract the second polynomial from the first, we need to distribute the negative sign to all terms inside the second set of parentheses, and then combine like terms:
(8s^2 - 3s - 3) - (-4s^2 + s - 13)
= 8s^2 - 3s - 3 + 4s^2 - s + 13 (distributing the negative sign)
= 12s^2 - 4s + 10 (combining like terms)
The resulting polynomial is already in standard form because the terms are arranged in descending order of degree. Therefore, the final answer in standard form is:
12s^2 - 4s + 10
Roderick earns an interest of $30 per year for every $500 deposited in his savings account calculate the interest earned if he has $1,250 in his account
Answer:
1250/500
=2.5
Multiplied by interest rate (30)
2.5 times 30
= $75.00
Step-by-step explanation:
Hope I helped.
BRAINLIEST PLEASE!!!Roderick earns an interest of $30 per year for every $500 deposited in his savings account. This means that the interest rate per $500 deposit is:Interest rate per $500 = $30/$500 = 0.06 or 6%To calculate the interest earned on Roderick's savings account, we first need to determine how many $500 deposits he has. We can do this by dividing his total savings by $500:Number of $500 deposits = $1,250/$500 = 2.5
if 1 kg is equal to 1,000 G how many grams are in 7.28 kg explain how you found your answer
Answer:
here is your answer attached
Step-by-step explanation:
A water trough is 10 m long and has a cross-section in the shape of an isosceles trapezoid that is 40 cm wide at the bottom, 90 cm wide at the top, and has height 50 cm. If the trough is being filled with water at the rate of 0.1 m3/min, how fast (in m/min) is the water level rising when the water is 10 cm deep?
Answer:
Let's start by finding the volume of water in the trough as a function of its depth.
At a depth of h cm, the cross-sectional area of the water is an isosceles trapezoid with bases of length b1 = 40 + (h/5) cm and b2 = 90 + (h/2) cm, and height 50 cm. The average width of the trapezoid is (b1 + b2)/2 = 65 + (3h/10) cm. Therefore, the volume of water in the trough at this depth is:
V(h) = 10 m x [(65 + (3h/10)) / 100 cm] x h cm
Simplifying this expression, we get:
V(h) = (13/2000) h^2 m^3
Now, we can use the chain rule to find the rate of change of V with respect to time t, given that dV/dt = 0.1 m^3/min:
dV/dt = (dV/dh) x (dh/dt) = (26/2000) h (dh/dt)
At the moment when the water is 10 cm deep, we have:
h = 10 cm
dV/dt = 0.1 m^3/min
Plugging in these values, we get:
0.1 m^3/min = (26/2000) x 10 cm x (dh/dt)
Solving for dh/dt, we get:
dh/dt = 0.1 m^3/min / (26/2000) / 10 cm
dh/dt ≈ 0.192 m/min
Therefore, the water level is rising at a rate of approximately 0.192 m/min when the water is 10 cm deep.
what is the perimeter for a 141 by 234
Step-by-step explanation:
the width is 23.5ft and the length is 47ft
Yellow Sticker Company’s variable expenses are 40% of sales. The company has monthly fixed expenses of $15,000 and sells each unit for $0.50. The monthly target operating income is $8,250.
a. What is the monthly margin of safety in dollars if Yellow Sticker Company achieves its operating income goal?
If Yellow Sticker Business meets its operating income goal, the quarterly safety margin in dollars will be $4,583.33.
Which financial objectives are sound?Budgeting, debt reduction, and setting up an emergency fund are important short-term objectives. Key insurance policies should be included in medium-term goals, whilst retirement should be the primary emphasis of long-term objectives.
Next, we deduct our break-even sales from actual sales at the goal operating income level to determine the margin of safety:
Real sales are determined by dividing target operating income by total fixed costs and contribution margin ratio.
Real sales equal $8,250 plus $15,000 / 0.60.
Real sales were $29,583.33
Safety margin = Real sales Breakeven sales
Margin of safety is calculated as $29,583.33 - ($0.50 x 50,000 units).
$25,000 - 29,583.33 is the margin of safety.
$4,583.33 is the safety margin.
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Question What is the value of the expression? (9 1/2 − 3 7/8)+(4 4/5 − 1 1/2) Enter your answer as a mixed number in simplest form by filling in the boxes. $$
Answer:
To add mixed numbers, we need to add the whole numbers separately and fractions separately.
Starting with the whole numbers, we have:
9 1/2 − 3 7/8 + 4 4/5 − 1 1/2
= (9 + 4) − (3 + 1) + (4/5 − 1/2) + (1/8 − 7/8) (grouping the terms)
= 10 − 4 + (8/10 − 5/10) + (−6/8) (converting fractions to have a common denominator)
= 6 + 3/10 − 3/4 (simplifying fractions and adding whole numbers)
= 5 7/20 (expressing the result as a mixed number in simplest form)
Therefore, the value of the expression is 5 7/20.
Which measurements could create more than one triangle?
A.
A triangle with sides measuring 50 mm and 35 mm and a nonincluded angle measuring 25°
B.
A triangle with sides measuring 5 cm, 10 cm, and 15 cm
C.
A triangle with sides measuring 8 cm and 12 cm and an included angle measuring 85°
D.
A triangle with sides measuring 5 inches, 7 inches, and 9 inches
Answer:
D. A triangle with sides measuring 5 inches, 7 inches, and 9 inches. This is because the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In option A, the side lengths satisfy this condition since 50 + 35 > 25. In option B, the side lengths do not satisfy this condition since 5 + 10 < 15. In option C, the side lengths satisfy this condition since 8 + 12 > 85. In option D, the side lengths do not satisfy this condition since 5 + 7 < 9, 7 + 9 > 5, and 5 + 9 > 7.
A father and son are buying hot dogs and lemonade for a family picnic. They have only a $20 bill to spend. Lemonade costs $3.50 per bottle and they must buy one bottle. Hot dogs cost $2.50 per package. What is the maximum number of packages of hot dogs they can buy?
Answer:
Step-by-step explanation:
subtract 20-3.50 you will get 16.50
Multiply 2.50x6 you will get 15
Subtract 16.50-15.00 you will get 1.50
A researcher asked 520 randomly selected people of three different age groups (teen, young adult, and adult) about their favorite music genre. The two-way table displays the distribution of the responses.
A 4-column table with 3 rows. Column 1 has entries country, rock, oldies. Column 2 is labeled Teen with entries 61, 94, 15. Column 3 is labeled young adult with entries 65, 84, 36. Column 4 is labeled Adult with entries 49, 54, 62. The columns are labeled age and the rows are labeled music.
A participant is randomly selected. Let C be the event that the participant prefers country music and let T be the event that the participant is a teen. What is the value of P(C or T)?
0.12
0.33
0.55
0.66
The probability that the participant either is a teen or prefers country music is given as follows:
P(C or T) = 0.55.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
The desired outcomes for this problem are given as follows:
61 + 94 + 15 = 170 teens.65 + 49 = 114 people that are not teens but prefer country music.There were 520 people in the research, hence the probability that the participant either is a teen or prefers country music is given as follows:
P(C or T) = (170 + 114)/520
P(C or T) = 0.55.
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The scatter plot shows the resale value of the same make
and model car and the age of the car in years. Predict the
price you would pay if you purchase one of these cars that
is 9.5 years old.
What ordered pair contains the y-intercept of y= -2x^ -4x -5
(-1,3)
(0,-5)
(-5,0)
(0,-2)
Answer:
To find the y-intercept, we can set x = 0 in the equation y= -2x^2 -4x -5, which gives us:
y = -2(0)^2 - 4(0) - 5 = -5
So the y-intercept is (0, -5). Therefore, the correct answer is (0,-5).
Find the length of side x to the nearest tenth.
Given:-
A right angled triangle is given to us .Two angles are 60° and 30° , longest side is x and another side is "2" .To find:-
The value of x .Answer:-
In the given right angled triangle, we may use the trigonometric ratios. We can see that the measure of the longest side is "x" which is hypotenuse and it needs to be find out. The perpendicular in this case is "2" .
We may use the ratio of sine here as , we know that in any right angled triangle,
[tex]\implies\sin\theta =\dfrac{p}{h} \\[/tex]
And here , p = 2 and h = x , so on substituting the respective values, we have;
[tex]\implies \sin\theta = \dfrac{2}{x} \\[/tex]
Again here angle is 60° . So , we have;
[tex]\implies \sin60^o =\dfrac{2}{x} \\[/tex]
The measure of sin45° is √3/2 , so on substituting this we have;
[tex]\implies \dfrac{\sqrt3}{2}=\dfrac{2}{x} \\[/tex]
[tex]\implies x =\dfrac{2\cdot 2}{\sqrt3}\\[/tex]
Value of √3 is approximately 1.732 . So we have;
[tex]\implies x =\dfrac{4}{1.732} \\[/tex]
[tex]\implies \underline{\underline{\red{\quad x = 2.31\quad }}}\\[/tex]
Hence the value of x is 2.31 .
Answer:
The length of side x to the nearest tenth is 2.3.
Step-by-step explanation:
From inspection of the given right triangle, we can see that the interior angles are 30°, 60° and 90°. Therefore, this triangle is a 30-60-90 triangle.
A 30-60-90 triangle is a special right triangle where the measures of its sides are in the ratio 1 : √3 : 2. Therefore, the formula for the ratio of the sides is b: b√3 : 2b where:
b is the shortest side opposite the 30° angle.b√3 is the side opposite the 60° angle.2b is the longest side (hypotenuse) opposite the right angle.We have been given the side opposite the 60° angle, so:
[tex]\implies b\sqrt{3}=2[/tex]
Solve for b by dividing both sides of the equation by √3:
[tex]\implies b=\dfrac{2}{\sqrt{3}}[/tex]
The side labelled "x" is the hypotenuse, so:
[tex]\implies x=2b[/tex]
Substitute the found value of b into the equation for x:
[tex]\implies x=2 \cdot \dfrac{2}{\sqrt{3}}[/tex]
[tex]\implies x=\dfrac{4}{\sqrt{3}}[/tex]
[tex]\implies x=2.30940107...[/tex]
[tex]\implies x=2.3\; \sf (nearest\;tenth)[/tex]
Therefore, the length of side x to the nearest tenth is 2.3.
The graph shows g(x) = x2 − 9x + 20. graph of parabola falling from the left, passing through 3 comma 2 to about 4 and one half comma negative one fourth, and rising to the right, passing through 6 comma 2 What are the x-intercepts of g(x)? (4.5, 0) and (5, 0) (0, 4.5) and (0, 5) (0, 5) and (0, 4) (5, 0) and (4, 0)
Parabola intersects x-axis at two points: (-5,0) and (-4,0)
What does a parabola actually mean?
Each point on a parabola with a U-shape is equally spaced from both the focus, a fixed point, and the directrix, a fixed line. As the topic of conic sections depends heavily on the parabola, all of the parabola-related concepts are covered here.
The x-intercepts of a parabola are where the parabola intersects the x-axis on its graph. There are a number of ways to find the x-intercepts of a parabola, and each one is usually specific to each situation.
In the case, when you are given the graph, the easiest way to find x-intercepts is to identify points at which parabola intersects the x-axis.
From your graph, parabola intersects x-axis at two points: (-5,0) and (-4,0)
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Which set of ordered pairs is made up of points on the graph of the function below?
y=-2x+8
A. (10,-1), (8,0), (1,6), (2,4)
B. (-1,10), (0,8), (1,6), (2,4)
C. (10,-1), (8,0), (6,1), (4,2)
D. (-1,10), (8,0), (1,6), (4,2)
Answer:0
Step-by-step explanation: just like you did on my question and stole the points :) xx
b. Rewrite 4 x 63 as the product of a unit fraction and a whole number.
Solve.
Rewriting 4 x 3/6 as the product of a unit fraction and a whole number is: 12 * 1/6
How to multiply fractions?The parameters are given as:
Number - 4
Fraction - 3/6
The following steps can be used to determine the product as the product of a whole number and a unit fraction:
Step 1 - Remember the whole number are those numbers that involve all positive integers and zero.
Step 2 - Also remember that the unit fraction is nothing but a fraction whose numerator is 1.
Step 3 - Write the given expression.
4 * 3/6
Step 4 - Convert the given fraction into a unit fraction by multiplying 4 by 3 in the above expression.
4 * 3 * 1/6
Step 5 - Simplify the above expression.
12 * 1/6
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I need to know how to solve this problem and the answer of it.
Answer:
P = 8g⁵ - 15g + 14
Step-by-step explanation:
This question has expressions to represent the side lengths of a triangle.
The side lengths are:
-8g⁵ - 7g
10g⁵ - 8g
6g⁵ + 14
They ask for a simplified expression for the perimeter. The purpose of this question is to combine like terms.
P = s₁ + s₂ + s₃ where s is a side length of the triangle.
P = (-8g⁵ - 7g) + (10g⁵ - 8g) + (6g⁵ + 14)
P = 8g⁵ - 15g + 14
Elena drinks 9 glasses of water during the day. Each glass is 250 milliliters. How many
liters of water does Elena drink during the day? Explain or show your reasoning.
Spar
Answer:
2.25
Step-by-step explanation:
9 × 250 m = 2250 mL
1 L = 1000 m
2250 mL × (1 L)/(1000 mL) = 2.25 L
The design dept is planning a new model of tent in the shape of a triangular pyramid. They intend to make two sizes of the new model
By taking these factors into account, they can create a product that meets the needs of potential customers and is a success in the market. the tent design, size options, materials, features, and pricing when planning the new model of triangular pyramid tents.
What is the design dept is planning a new model ?Triangular Pyramid Tent Design:
The triangular pyramid tent design is a unique shape that could potentially offer better stability against wind and other weather conditions. However, it may also require more complex construction and assembly than a traditional rectangular tent.
The design department should consult with engineers and experienced tentmakers to ensure that the triangular pyramid tent can be manufactured in a cost-effective and user-friendly manner.
Size options:
The design department has decided to make two sizes of the triangular pyramid tent. They should consider the intended use of the tents and the needs of potential customers when determining the size options.
For example, a smaller size might be suitable for backpackers or solo campers, while a larger size could accommodate families or groups.
Therefore, the tent design, size options, materials, features, and pricing when planning the new model of triangular pyramid tents.
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Solve for x. Round to the nearest tenth.
x =
Use the distributive property to multiply the expression 9(7m+2)
Answer:
63m+18
Step-by-step explanation:
9*7m is 63m and 9*2 is 18
Combine them and you get 63m+18!
Use the simple interest formula to determine the missing value.
P= $1275, R= ?, T= four years, I= $112.20.
R= —-%
Do not round into the final answer, then round to one decimal place as needed
Step-by-step explanation:
2.2 percentage answer you silly
The ratio of new car sales to used car sales at the car lot is 3:5. If the total car sales were $287,400 last month, what was the total of the used car sales?
Answer:
Therefore, the total used car sales were $179,625.
Step-by-step explanation:
Let's assume that the ratio of new car sales to used car sales is 3x:5x, where x is a constant.
The total car sales were $287,400, which means the sum of the new car sales and used car sales is $287,400:
3x + 5x = 8x
So, the total sales can be expressed as:
8x = $287,400
To find the value of x, we need to divide both sides by 8:
x = $35,925
Now, we can calculate the used car sales by multiplying 5x by the value of x:
Used car sales = 5x * x = 5 * $35,925 = $179,625
Therefore, the total used car sales were $179,625.
A rubber bouncy ball is dropped from a
height of 187.00 cm onto a hard flat floor.
After each bounce, the ball returns to a
height that is 3/4 of the previous
maximum height. What is the maximum
height reached after the 13th bounce?
The maximum height reached after the 13th bοunce is 6.14 cm.
What is height οf bοunce?The height οf bοunce is the height tο which an οbject rebοunds after cοIIiding with a surface, such as a baII bοuncing οn the grοund οr a diver bοuncing οff a diving bοard. The height οf the bοunce depends οn severaI factοrs, incIuding the initiaI height οf the οbject, the surface it cοIIides with, the eIasticity οf the οbject and the surface, and the angIe οf incidence.
Tο sοIve this prοbIem, we need tο use the fοrmuIa fοr the height οf each bοunce:
[tex]h = (3/4)^{{n}} \times H[/tex]
where h is the height οf the nth bοunce, H is the initiaI height (in this case, 187.00 cm), and n is the number οf bοunces.
We want tο find the maximum height reached after the 13th bοunce, which means we need tο find the height οf the 13th bοunce and then muItipIy it by 3/4 tο get the maximum height.
Using the fοrmuIa abοve, we can find the height οf the 13th bοunce:
[tex]h = (3/4)^{{13}} \times 187.00[/tex]
h ≈ 8.18 cm
Nοw we can find the maximum height:
maximum height = (3/4) × h
maximum height = (3/4) ×8.18
maximum height ≈ 6.14 cm
Therefοre, the maximum height reached after the 13th bοunce is apprοximateIy 6.14 cm.
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Ava is going on holiday with Fly Away airlines. The maximum weight her suitcase can be is 2020 kg.
When empty her suitcase weighs 33 kg.
The clothes she plans on taking have a combined weight of 55 kg.
Her electrical accessories have a combined weight of 44 kg.
She is also taking 55 hardback books, which each weigh 720720 g.
Finally, the toiletries she is taking have a combined weight of 46004600 g.
How much over the maximum weight will Ava's suitcase be? Give your answer in grams.
As a result, Ava's luggage will weigh 123622200 grams more than the permitted maximum.
What exactly is weight?Weight is the force of gravity that pulls objects toward the core of the Earth. The resulting force that pulls a substance toward Earth is known as gravity. In contrast to gravity force, which occurs among any two masses, this only occurs between Earth as well as a mass.
First, we need to convert all the weights to grams, since the weight limit is given in kilograms and the weights of clothes, electrical accessories, and toiletries are given in grams.
Maximum weight limit = 2020 kg = 2020000 g
Weight of empty suitcase = 33 kg = 33000 g
Weight of clothes = 55 kg = 55000 g
Weight of electrical accessories = 44 kg = 44000 g
Weight of 55 hardback books = 55 x 720720 g = 39639600 g
Weight of toiletries = 46004600 g
Total weight of suitcase and contents = 33000 + 55000 + 44000 + 39639600 + 46004600 = 125642200 g
Amount over maximum weight limit = total weight - maximum weight limit = 125642200 - 2020000 = 123622200 g
Therefore, Ava's suitcase will be over the maximum weight limit by 123622200 grams.
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solve equation
log 4x=2
Answer: x=25
Step-by-step explanation:
log 10 4x = 2
10^2 = 4x
100 = 4x
25 = x
I need some help please
Answer:
question where is the question?
A dilation centered at the origin maps the point (4,6) to the point (5/2,15/4). What is the scale factor of the dilation
We may be confident that this is the correct scale factor because both equation equations yield the same value of k. As a result, the dilatation has a scale factor of 5/8 and is centered at the origin.
What is equation?An equation is a statement in mathematics that states the equality of two expressions. An equation has two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the value "9". The purpose of equation solving is to determine which variable(s) must be changed in order for the equation to be true. Simple or complex equations, regular or nonlinear equations, and equations with one or more elements are all possible. In the equation "x2 + 2x - 3 = 0," for example, the variable x is raised to the second power. Lines are employed in a variety of mathematical disciplines, including algebra, calculus, and geometry.
Let (x,y) be a point on the plane and k be the dilation scale factor centred at the origin. The image of (x,y) under dilation is thus given by (kx, ky).
The dilation is given as (4,6) to (5/2,15/4). That is to say:
[tex]k(4) = 5/2 \sk(6) = 15/4\\k = 5/8 \sk = 5/8[/tex]
We may be confident that this is the correct scale factor because both equations yield the same value of k. As a result, the dilatation has a scale factor of 5/8 and is centered at the origin.
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Patrick biked 27 miles last week. He biked 9 miles more than Ibrain. The equation m + 9 = 27 gives the number of miles m that Ibrain biked last week. Which is the solution of the equation?
Answer:
Step-by-step explanation:
We can solve the equation m + 9 = 27 by subtracting 9 from both sides to isolate m:
m + 9 - 9 = 27 - 9
m = 18
Therefore, Ibrain biked 18 miles last week.
What is the least amount of wrapping paper needed to wrap a gift box that measures 8 inches by 8 inches by 10 inches.
The first thing we must do for this case is to find the surface area of the rectangular prism.
We have then:
[tex]A = 2 \times (l \times h) + 2 \times (h \times w) + 2 \times (w \times l)[/tex]
Where,
w: width
l: long
h: height
Substituting values we have:
[tex]A = 2 \times (10 \times 8) + 2 \times (8 \times 8) + 2 \times (8 \times 10)[/tex]
[tex]A = 448 \ in ^ 2[/tex]
Answer:
the least amount of wrapping paper needed to wrap the gift box answer is:
A = 448 in²
Given sin(a) = 7/9 and a is in quadrant I, find the exact value of sin(a/2).
Note: You are not allowed to use decimals in your answer.
Answer:
We can use the half-angle formula for sine to find the exact value of sin(a/2) in terms of sin(a):
sin(a/2) = ±√[(1 - cos(a))/2]
where the ± sign depends on the quadrant of a/2.
To use this formula, we first need to find cos(a). We can do this using the identity:
sin^2(a) + cos^2(a) = 1
Substituting sin(a) = 7/9, we get:
(7/9)^2 + cos^2(a) = 1
Simplifying and solving for cos(a), we get:
cos(a) = ±4/9
Since a is in quadrant I, we take the positive value of cos(a):
cos(a) = 4/9
Now we can use the half-angle formula for sine to find sin(a/2):
sin(a/2) = ±√[(1 - cos(a))/2]
Substituting cos(a) = 4/9, we get:
sin(a/2) = ±√[(1 - 4/9)/2]
Simplifying, we get:
sin(a/2) = ±√(5/18)
Since a is in quadrant I, a/2 is also in quadrant I, so we take the positive value of sin(a/2):
sin(a/2) = √(5/18)
Therefore, the exact value of sin(a/2) is √(5/18)