Answer:
Values of x are ±4 and ±5
Step-by-step explanation:
Let y = [tex]x^{2}[/tex]
Which means: [tex]y^{2} = x^{4}[/tex]
Therefore:
A quadratic equation is formed:
[tex]y^{2} - 41y + 400 = 0[/tex]
The above quadratic equation can be simplified either by The Double Bubble Method or using the quadratic formula
Double Bubble Method:
[tex]y^{2} - 41y + 400 = 0[/tex]
The pair of factors of 400 that add together to give 41 are 25 and 16. Use these two factors to rewritre -41y:
[tex]y^{2} - 25y - 16y + 400 = 0[/tex]
Then do Factorization by grouping (i.e group the terms with common factors before factorizing):
[tex]y(y -25) - 16(y - 25) = 0[/tex]
[tex](y - 25)(y - 16) = 0[/tex]
The product of two expressions is zero, which means either of the two expressions is equal to Zero:
Either: [tex]y - 25 = 0[/tex]
Substituting [tex]y = x^{2}[/tex]:
= [tex]x^{2} - 25 = 0[/tex]
= [tex]x^{2} = 25[/tex]
= [tex]\sqrt{x^{2}} = \sqrt{25}[/tex]
∴ x = ±5
Or: [tex]y - 16 = 0[/tex]
Substituting [tex]y = x^{2}[/tex]
[tex]= x^{2} - 16 = 0[/tex]
[tex]= x^{2} = 16[/tex]
[tex]= \sqrt{x^{2}} = \sqrt{16}[/tex]
∴ x = ±4
∴Values of x are ±4 and ±5
A, B, C and D form the vertices of a parallelogram.
AD = 10.1cm, AB = 15.9cm and
∠
BAD = 61°.
Find the area of the parallelogram. Round to 1 DP
5) Imani and lea are selling wrapping paper for a school fundraiser. Customers can buy rolls of plain wrapping paper and rolls of holiday wrapping paper. Imani sold 2 rolls of plain wrapping paper and 11 rolls of holiday wrapping paper for a total of $208. Lea sold 11 rolls of plain wrapping paper and 9 rolls of holiday wrapping paper for a total of $320. What is the cost each of one roll of plain wrapping paper and one roll of holiday wrapping paper?
Answer: Let's represent the cost of one roll of plain wrapping paper as x, and the cost of one roll of holiday wrapping paper as y. We can write two equations based on the information given:
2x + 11y = 208
11x + 9y = 320
We can use these equations to find the values of x and y. Solving the first equation for y:
y = (208 - 2x) / 11
We can substitute this expression for y into the second equation to eliminate y:
11x + 9((208 - 2x) / 11) = 320
11x + 208 - 18x / 11 = 320
11x - 18x / 11 = 320 - 208
-7x / 11 = 112 / 11
-7x = 112
x = -16
So one roll of plain wrapping paper costs -16 dollars, which is not possible. This means there is no solution for this system of equations, and therefore the problem has no solution.
Step-by-step explanation:
Quadrilateral MNOP is similar to quadrilateral QRST. Find the measure of side RS.
Figures are not drawn to scale.
The measure of side RS is 7.6 units .
Similar quadrilaterals:
A quadrilateral's interior angles add up to 360 degrees. Two quadrilaterals are said to be identical when two adjacent sides have the same ratio and all three matching angles are equal (the fourth angle automatically becomes equal because the internal angle sum equals 360 degrees).
The corresponding angles of similar quadrilaterals should be equal in accordance with the similarity of quadrilaterals. Since we know that every angle in a square is 90 degrees, every matching angle in any two squares will be the same.
In the given question ,
Quadrilateral MNOP is similar to quadrilateral QRST .
[tex]\frac{ON}{NM} =\frac{RS}{RQ} \\\\\frac{2}{4} = \frac{RS}{15.2} \\\\\frac{1}{2} =\frac{RS}{15.2} \\\\RS=\frac{15.2}{2} \\\\RS=7.6units[/tex]
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5. A company produced 9,800 pairs of sunglasses
in one week, and 49 of the sunglasses failed
a quality inspection. If the company produces
1,400 pairs of sunglasses in one day, how many
would you expect to fail the quality inspection
The number of sunglasses that will fail the quality inspection are 7.
What is a ratio?
A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six.
We are given that, A company produced 9,800 pairs of sunglasses
in one week, and 49 of the sunglasses failed a quality inspection.
And based on this data we are asked to find the number of sunglasses which will fail the quality inspection If the company produces
1,400 pairs of sunglasses in one day
Let the number of sunglasses failing the quality inspection be x
hence the ratio becomes
9800/49 = 1400/x
x= 1400*49/9800
x= 7
The number of sunglasses that will fail the quality inspection are 7.
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What type of graph is shown, and what is the growth factor?
linear function; growth factor of 2
linear function; growth factor of 4
exponential function; growth factor of 2
exponential function; growth factor of 4
The graph is a linear function with a growth factor of 4
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
The graph has the shape of a straight line, so it is linear.
The graph starts at point (0, 0). It passes through point (1, 4).
slope = 4/1 = 4
The slope is 4. Growth factor is the same as slope for a linear function.
Hence, the graph is a linear function with a growth factor of 4
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The circumfrence is 26cm what is the diameter to 1dp
Answer:
The diameter is 8.3cm.
Step-by-step explanation:
The circumference is the distance all the way around a circle. To find circumference, multiply pi times diameter:
C = pi • d
Fill in given circumference.
26 = pi • d
Divide both sides by pi (you should use a calculator) in this question it doesn't happen to matter if you use a pi button or 3.14 for pi.
26/3.14 = d
8.276057 = d if you use the pi button.
or,
8.28025 = d if you use 3.14
Both of these round to 8.3, since the question asked for one decimal place (1dp)
The diameter is 8.3cm.
I can’t figure it out
Answer:
Step-by-step explanation:
x/y=(5/6)/(3/4) = 5/6*4/3 = 10/9
x/y=10/9
y/x=9/10
y=9/10 * x
Second option
Answer:
y=5/8x
Step-by-step explanation:
What is the ratio of dL to L?
Answer:
Step-by-step explanation:
The ratio of a change in a quantity (dL) to the original quantity (L) is given by:
dL/L
This ratio can also be expressed as a percentage change, which is calculated by multiplying the ratio by 100:
(dL/L) * 100 = percent change
In general, the ratio of dL/L represents the fractional change in the quantity L and is used to quantify the effect of small changes in a system or process. For example, if L is the length of an object and dL is a small change in length, then dL/L represents the fractional change in length due to this change.
Help w/ this question its due today!
The 40th customer who gets the t-shirt and water bottle.
If the sporting goods store has 100 gifts each in stock, then the number of customers who get t-shirts and drinking bottles are 2 customers, namely the 40th customer and the 80th customer.
Determine the LCM(Least Common Multiples)In finding the LCM, we also use prime factorization, namely multiplying all the factor numbers and if there are the same, take the largest value, if both are the same, then take one of them.
For example, determine the LCM of 30 and 48
30 = 2 x 3 x 5
48 = 2 x 2 x 2 x 2 x 3 = 2⁴ x 3
The LCM of 30 and 48 is 2⁴ x 3 x 5 = 240
The above Question can be solved with the concept of LCM
where the 8th customer gets a T-shirt and the 10th customer gets a water bottle. To find out which customer gets the two gifts, then look for LCM from 8 and 10
LCM(8, 10) =2×2×2×5=40
LCM of 8 and 10 is 40.
So the 40th customer who gets the t-shirt and water bottle.
If the store has 100 gifts each in stock, then the number of customers who get t-shirts and drinking bottles are 2 customers, namely the 40th customer and the 80th customer.
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which expression is equivalent to 3.5b + 4.5 + 0.5b - 0.5 - 1.5b
[tex]3.5b + 4.5 + 0.5b - 0.5 - 1.5b[/tex]
Combine Like Terms:
[tex](3.5b+0.5b-1.5b)+(4.5-0.5)[/tex]
[tex]\boxed{2.5b+4}[/tex]
Abbie has put $40 into her savings account. She has made 5 deposits of the same amount. How much was the amount of each deposit?
The amount of each deposit that Abbie made was $8
Calculate amount of depositThe amount of each deposit that Abbie made can be found by dividing the total amount she put into her savings account by the number of deposits she made.
In this case, we can use the formula: Amount of each deposit =
Total amount / Number of deposits
Substituting the given values into the formula, we get:
Amount of each deposit = $40 / 5
Amount of each deposit = $8
Therefore, the amount of each deposit that Abbie made was $8. In conclusion, if Abbie has put $40 into her savings account and has made 5 deposits of the same amount, then the amount of each deposit is $8.
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(Answer for 30 points) Penelope is collecting coins to raise money for a charity so far she collected
• twice as many dimes as quarters
• 4 times nickels than dimes, and
• three times as many pennies as quarters
If Penelope has collected 780 coins, how many of each type of coin she collected.
Penelope has, 52quarters, 104 dimes, 416 nickels, and 162 pennies.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
From the given information let, 'x' be the number of quarters,
Therefore, Dimes is 2x, Nickels is 8x and Pennies is 3x.
So, x + 2x + 8x + 4x = 780.
15x = 780.
x = 52, The number of quarters.
2×52 = 104, The number of Dimes.
8×52 = 416 Nickels.
3×52 = 162 Pennies.
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Write a ratio for each scenario using a colon(:).
1. Two cookies per student. __:__
2. The odds of the horse winning the race are 2 to 5. __:__
3. Colorado State University, there are 4 female students for every 3 male students. __:__
PLEASE BE ACCURATE!!! THANK YOU!!!
Answer:
2:1
2:5
4:3
Step-by-step explanation:
In these examples the comparison words "per", "to", "for every" is the colon.
Then just put the numbers in the same order they are in in the problem
1. Two cookies per student. __:__
Means 2 cookies per 1 student
We're writing the ratio
cookies:students
2:1
2. The odds of the horse winning the race are 2 to 5. __:__
The "to" is the colon
2:5
3. Colorado State University, there are 4 female students for every 3 male students. __:__
We are comparing
female:male
4:3
A. Find the probability of getting a five card hand that has three Jacks and two Queens. Round your answer to six decimal places.
b. A five card hand, where four of the cards are the same, i. E. Four Aces, or four Kings, etc. , is called getting a "four of a kind". What is the probability of getting a "four of a kind"? Round your answer to five decimal places
The probability of getting: A. a five-card hand that has three Jacks and two Queens is 0.000009, or 0.000923% and B. a "four of a kind" is 0.00024, or 0.02401%.
A. The probability of getting a five-card hand that has three Jacks and two Queens can be calculated by using the formula:
P(3 Jacks and 2 Queens) = C(4,3) x C(4,2) / C(52,5)
Where C(n,k) is the combination of n items taken k at a time.
= (4 x 6) / 2598960
= 24 / 2598960
= 0.00000923
Therefore, the probability of getting a five-card hand that has three Jacks and two Queens is 0.000009, or 0.000923% when rounded to six decimal places.
B. The probability of getting a "four of a kind" can be calculated by using the formula:
P(four of a kind) = (C(13,1) x C(4,4) x C(12,1) x C(4,1)) / C(52,5)
= (13 x 1 x 12 x 4) / 2598960
= 624 / 2598960
= 0.00024010
Therefore, the probability of getting a "four of a kind" is 0.00024, or 0.02401% when rounded to five decimal places.
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How to solve your problem: 8d+d+3d+2+4d
Answer:
d= -1/8
Step-by-step explanation:
8d+d+3d+2+4d= 16d+2
16d= -2
d= -1/8
What angle in degrees does the guy wire make with the ground?
Answer:
45? I'm not 1000% sure tog
Step-by-step explanation:
What is the symbol 1 to 10?
A brownie recipe calls for 1 cup of butter for every 2 cups of flour. Erika is using 8 cups of flour. How much butter should she use?
find the value for x that makes the equation true.
4x +2x + 12 =3(3x + 6)
Answer :
x = -2
-8 + -4 + 12 = 3(-6 + 6)
Im not sure
Triangle rst is congruent to triangle wxy. If the area of triangle wxy is 20 square inches, then the area of triangle rst is _____. 10 in 2 40 in 2 80 in 2 20 in 2.
Triangle rst is congruent to triangle wxy. If the area of triangle wxy is 20 square inches, then the area of triangle rst is 20 square inches.
When two triangles are congruent, it means that they are exactly the same in every aspect, including their size and shape. This means that their corresponding sides and angles are equal in length and measure, respectively.
In terms of area, if two triangles have the same shape and size, then they will have the same area. This is because the area of a triangle is determined by the length of its sides and the angles between them, and if two triangles are congruent, then their sides and angles are equal.
Therefore, if the area of triangle WXY is 20 square inches, then the area of triangle RST must also be 20 square inches. This is because triangle RST has the same size and shape as triangle WXY, and therefore must have the same area.
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Determine the number of 4g cremora sachets that will make 1kg cremora box.
A total of 250 packets of 4g cremora will make 1kg cremora box.
What is function?A function is a elation between a dependent and independent variable.
Given are 4g cremora sachets.
We can write the total number of cremora sachets that will make 1kg cremora box as -
{n} = 1000/4
{n} = 250
Therefore, a total of 250 packets of 4g cremora will make 1kg cremora box.
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Choose ALL answers that describe the polygon QRST if QR = 12, RS = 12, ST = 12, TQ = 12, m
Answer:
quadrilaterals
ok I only guss it
Help pls due tomorrow
The angle measure of the missing angle is 630 - 11x.
What is the interior angle?Angles inside a polygon are referred to as interior angles. A triangle, for instance, has three internal angles. Interior angles are sometimes defined as "angles confined in the interior area of two parallel lines when they are crossed by a transversal."
Given:
A non-regular hexagon.
The sum of all the interior angles of the hexagon is,
= (6 - 2) 180
= 4(180)
= 720
Now, the angle measure of the missing angle,
= 720 - 2x - 3x - 2x - 4x - 90
= 630 - 11x
Therefore, 630 - 11x is the required expression.
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SMENT UNIT 22 SY23 / SECTION 1/1 OFS /
Kane Laboratories is studying the impact of various enriched growth mediums on different bacteria. They
are currently studying the impact of placing Bacillus Megaterium into a culture of sucrose salts. The table
below shows the growth rate of the bacteria during the growth phase. The generation time for Bacillus
Megaterium is 25 minutes in this culture.
Generation
Number, n
Bacteria
Population, P
B. P (n) = 12+2n
OC. P (n) = 12 (n+1)
OD. P (n) = 12-4-1
0
12
1
24
2
3
48 96
4
20%
192
Which function models the growth of the Bacillus Megaterium over each generation?
O A P (n) = 12-2
The function that models the growth of the Bacillus Megaterium over each generation is B. P (n) = 12 + 2n.
Please help asap thank you so much if you do
the relation has the domain of -4> x> 4 and the given relation is continuous for the given range.
What is the range or domain of a function?The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.
Given a graph,
The relation that defines the set of inputs to the set of outputs is called the functions. In function, each input in set X has exactly one output in set Y. Note: All functions are relations but all relations are not functions.
thus the given graph is a relation but not a function.
Given relation is continuous in the domain.
since the domain of the relation is The set which contains all the first elements of all the ordered pairs of relation R.
the given relation and has x values from -4 to 4 thus, the domain of the relations -4> x> 4.
Therefore, the relation has the domain of -4> x> 4 and the given relation is continuous for the given range.
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Which of the following is the product of the rational expressions shown
below?
x+6 2-6
x+3 x-3
A. 22-12
B. 2-12
C. 2-366
9
OA.
OD. 12
The product of the rational expression shown above include the following: B. x² - 36/(x² - 9).
What is a rational expression?In Mathematics, a rational expression simply refers to a type of expression which is expressed as a fraction. This ultimately implies that, a rational expression is composed of two (2) main parts and these include the following:
NumeratorDenominatorIn this exercise, we would determine the product of the numerator for this rational expression and the product of the denominator for this rational expression as follows;
Product of numerator = (x + 6)(x - 6)
Product of numerator = x² + 6x - 6x - 36
Product of numerator = x² - 36
For the denominator, we have the following:
Product of denominator = (x + 3) × (x - 3)
Product of denominator = x² - 3x + 3x - 9
Product of denominator = x² - 9
Therefor, the product of the rational expression is given by x² - 36/(x² - 9).
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Use the formula d = rt. Find r for t = 5h and d = 240 m.
The value of the variable r when t = 5h and d = 240m is 48m/h
What are algebraic expressions?Algebraic expressions are described as expressions that are composed of terms, variables, factors, coefficients and constants.
They are also made up of mathematical operations like subtraction. division, addition, multiplication, floor division, etc
From the information given, we have the equation;
d = rt
Make 'r' the subject of formula
r = d/t
Now, substitute the values into the equation, we get
r = 240/5
Divide the values
r = 48m/h
Hence, the value is 48m/h
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Given f(x)=-5x-3, find f-^1(x).
The inverse of the given function f(x) = -5x-3, is f⁻¹(x) = -x/5-3/5
What is an inverse function?An inverse function is a function that undoes the action of the another function. A function g is the inverse of a function f if whenever y=f(x) then x=g(y).
Given that a finction f(x) = -5x-3, we need to find the inverse of the function,
We can write,
y = -5x-3,
Interplace, x and y,
x = -5y-3
-5y = x+3
y = -(x+3)/5
y = -x/5-3/5
f⁻¹(x) = -x/5-3/5
Hence, the inverse of the given function f(x) = -5x-3, is f⁻¹(x) = -x/5-3/5
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What is the surface area of a rectangular prism if the digits are 10ft, 1ft, and 5ft
The surface area of the rectangular prism is 130ft^2.
Determine surface areaThe surface area of a rectangular prism can be calculated by finding the area of each of the six faces and then adding them together.
The formula for the surface area of a rectangular prism is 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height.
In this case, the length is 10ft, the width is 1ft, and the height is 5ft. Plugging these values into the formula, we get:
Surface area = 2(10ft)(1ft) + 2(10ft)(5ft) + 2(1ft)(5ft)
Surface area = 20ft^2 + 100ft^2 + 10ft^2
Surface area = 130ft^2
Therefore, the surface area of the rectangular prism is 130ft^2.
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Cory and Veronica each multiplied one/2×5/2 Cory got six/ four and Veronica Cook got five over four which student found the correct answer explain
Answer:
Veronica is correct
Step-by-step explanation:
1/2 x 5/2 = 5/4
1/2 + 5/2 = 6/4