Answer:
q = ± 5[tex]\sqrt{5}[/tex]
Step-by-step explanation:
f(q) = q² - 125
to find the roots , let f(q) = 0 , that is
q² - 125 = 0 ( add 125 to both sides )
q² = 125 ( take square root of both sides )
q = ± [tex]\sqrt{125}[/tex] = ± [tex]\sqrt{25(5)}[/tex] = ± ([tex]\sqrt{25}[/tex] × [tex]\sqrt{5}[/tex] ) = ± 5[tex]\sqrt{5}[/tex]
1 in 3 ft
1 in 8.25 ft
Above are two different models of the same rectangle. If the width of the model on the left is 11 in, what is the width of the model on
the right?
The width of the model on the right if the width of the left model is 11 in is 4 inches.
What is multiplication?One of the four fundamental mathematical operations, along with addition, subtraction, and division, is multiplication. Multiply in mathematics refers to the continual addition of sets of identical sizes.
Given:
1 in = 3 ft and 1 in = 8.25 ft
If the width of the left model is 11 in, calculate the actual width as shown below,
Actual width = 11 × 3
Actual width = 33 ft
Calculate the width of the model on the right as shown below,
33 = x × 8.25 (x is the width of the right model)
x = 33 / 8.25
x = 4 in
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what is the answers for these questions
Answer:
1) 6 kids have hamsters
13 kids have dogs
2) Tia scored more in English
She scored around 15 points more
Her range is around 15
Step-by-step explanation:
Answer:
for the first three questions:
1. fill out two boxes in the cat section
2. 6 students
3. 13 students
for the last questions:
1. just fill the lines up to the numbers in the question
2. english
3. about 18%? (not sure)
Step-by-step explanation:
solve for x. log49^x=1/2
Answer:
x = 0.295
Step-by-step explanation:
1/5/2023
7:24PM
Fabian says that 25% of a number will always be greater than 10% of any other number.
Complete one inequality to support Fabian's claim and one to show that he is incorrect.
The claim that is being made by Fabian is wrong and this can be proven by the steps below.
What is percentage of a number?The percentage of a number is the part of the number that is being represented by per hundred when it is divided by the whole and multiply by 100.
The 25% of a number can not always be greater than the 10% of any other number and this can be proven by using two different numbers.
For example, the 25% of 150 = 25/100 ×150 = 3750/100
= 37.5
Using another number such as 1500, the 10% of the given number is calculated as follows:
10/100 × 1500 = 15000/100 = 150
From the given examples, the 25% of 150 is not greater than the 10 percent of 1500, therefore, 25% of a number can not always be greater than the 10% of any other number and this can be proven by using two different numbers.
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etermine T10 of the following geometric sequences
a)T2=-10 and T6=-160
The T10 of the sequence is
T10 =-10.00
What is a geometric sequence?Generally, To determine the T10 of a geometric sequence, you will need to know the common ratio of the sequence.
If T2=-10 and
T6=-160, we can use these terms to find the common ratio.
The formula for any term in a geometric sequence is:
Tn = a * r^(n-1)
Where
Tn is the nth term, a is the first term, and r is the common ratio.We can use the terms you provided to find the common ratio:
-160 = -10 * r^(6-1)
-160 = -10 * r^5
r = (-160/-10)^(1/5)
Now that we know the common ratio, we can find T10:
T10 = a * r^(10-1)
T10 = -10 * r^9
So the T10 of the geometric sequence is
T10= -10 * (-160/-10)^(1/5)^9
T10 =-10.00
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After completing your analysis of the rating system, you determine that any rating greater than or equal to 3.5 points can be considered a high rating. You also know that Chocolate and Tea considers a bar to be super dark chocolate if the bar's cocoa percent is greater than or equal to 70%. You decide to create a new data frame to find out which chocolate bars meet these two conditions.
Assume the first part of your code is:
best_trimmed_flavors_df <- trimmed_flavors_df %>%
You want to apply the filter() function to the variables Cocoa.Percent and Rating. Add the code chunk that lets you filter the data frame for chocolate bars that contain at least 70% cocoa and have a rating of at least 3.5 points.
What rating appears in row 1 of your tibble?
0 / 1 point
3.75
3.50
4.25
4.00
As a result, option two (3.50) is correct.
Step-by-step explanation:
The code chunk that allows you to filter the data frame for chocolate bars with at least 70% cocoa and a rating of at least 3.5 pounds is as follows
∴ filter(Cocoa, percent>='70%'&Rating>=3.5)
Therefore, the code you write is facet wrap(Cocoa. Percent). Facet wrap() is a function in this code chunk that allows you to wrap a variable's facets. All of the ingredients are derived from cocoa beans. Cacao solids (the "brown" part, which contains health benefits and the unmistakable chocolatey flavor) and cacao butter (the "white" part, which contains the chocolate's fatty component) are split in proportion.
As a result, 3.5 appears in row 1 of your Tibble.
Other options I (iii), and (iv) are incorrect because the question states that any rating greater than or equal to 3.5 points can be considered a
high rating, and the rating here should be 3.5, not 3.75, 4.25, or 4
So, option (ii) is correct.
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20. DEPRECIATION Depreciation is the decrease in the value of an item resulting from its age or weac. When an item loses about the same percent of its value each year, an exponential function can be used to model its decreasing value over time. The function g(x)=12,000(0.85)'' can be used to model the value of a $12,000 car as it depreciates at an annual rate of 15% over x years. g(x) is a dilation of the parent function f(x)=0.85*. The graph shows the function g(x).
a. Write the equation of a function h(x) that represents the depreciation of a $20,000 car depreciating at the same rate over x years.
b. Describe h(x) as it relates to the parent function.
c. What is the difference between the values of the $12,000 car and the $ 20,000 car after 5 years?
a). The equation of a function h(x) as required to be determined is; h (x) = 20,000 (0.85)^x.
b). The function h (x) as required to be described in terms of the parent function f(x) is a dilation of the parent function using a scale factor of 20,000.
c). The difference between the values of the $12,000 and the $20,000 car is; $3549.6.
What is the equation of the function h(x) as required?It follows from the task content that the equation of the function g (x) is given as;
g (x) = 12,000 (0.85)^x.
a). On this note, since the rate of depreciation is same for the $20,000 car too; it follows that the exponential function which represents the situation is;
h (x) = 20,000 (0.85)^x.
b). Also, since the parent function f (x) = 0.85^x, the function g(x) can be described relative to the parent function as a dilation of the parent function using a scale factor of; 20,000.
c). The value of the $12,000 item after 5 years is;
g (5) = 12,000 (0.85)⁵ = $5324.5.
Also, the value of the $20,000 car after 5 years is;
h ( 5 ) = 20,000 (0.85)⁵ = $8874.1.
On this note, the difference between the values of the two items is; 8874.1 - 5324.5 = $3549.6.
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Name atleast two independent variables that could result in a change in a monthly cell phone bill
Answer:
physical size of products
skill level of operators of machines
Step-by-step explanation:
the independent variable are the determining factors that influence how a dependent variable change
monthly electricity bill is a dependent variable which is dependent on the following: -physical size of products
-skill levels of operators of machines
-non production machines utilising electricity among others
An airplane is flying 2000 miles at a planned speed of 600 mph. The flight will have an average headwind (flying directly into the wind) of w mph. The time (T) , in hours, of the flight is a function of the speed of the headwind w, in mph, can be modeled by the function T(w)=2000/600−w. The graph is shown below.
At what value of w does the graph have a vertical asymptote. Explain how you know and what this asymptote means in the context of this situation.
Answer:
Below
Step-by-step explanation:
The equation should read t = 2000/ (600-w)
the asymptote will be at w = 600 as this would create a value of zero in the denoiminator.... when the windspeed approaches 600 the time to complete the flight approaches infinity as the windspeed subtracts from the 600 mph plane speed.....then the forward ground speed gets smaler and smaller approaching zero mph.
46. A microscope shows an image of an object that is 70 times the object's actual size. So, the
scale factor of the enlargement is 70. An insect has a body length of 6 millimeters. What is the
body length of the insect under the microscope?
42 millimeters
420 centimeters
420 millimeters
4,200 millimeters
Answer:
420 millimeters
Step-by-step explanation:
If the scale factor of the enlargement is 70, and the body length of the insect is 6 millimeters, then the body length of the insect under the microscope is 6 millimeters * 70, which is 420 millimeters. So the correct answer is 420 millimeters.
What is the measure of F∠ ?
Answer:
Below
Step-by-step explanation:
All of the internal angles of any triangle sum to 180
find 'x' then F = 5x - 7
8x -18 + 6x-4 + 5x-7 = 180 °
19x -29 = 180
x = 11°
F = 5x -7 = 5(11) - 7 = 48°
Hi, I am wondering how to do this math problem step-by-step.
[ -4 - ( -26)] + 19 ÷ 24 + (7^2 – 35)
Thank you! :)
Answer: Step 1: Start by evaluating the expressions inside the parentheses first.
For the first set of parentheses: -4 - (-26) = -4 + 26 = 22
For the second set of parentheses: 7^2 - 35 = 49 - 35 = 14
Step 2: Next, substitute the values from step 1 into the original expression and perform the arithmetic in the order of operations:
BODMAS rule
Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)
[22] + 19 ÷ 24 + 14
Step 3: Perform the division: 19 ÷ 24 = 0.7916666666666667
Step 4: Perform the addition: 22 + 0.7916666666666667 + 14 = 36.791666666666664
So the final answer is 36.791666666666664
Step-by-step explanation:
I’ll give BRAINLIEST if correct
Answer:
Step-by-step explanation:
3rd
Answer:
It is the fourth option
Step-by-step explanation:
II,I,III,IV
II HAS 1 DEGREE
I HAS 2 DEGREE
III HAS 4 DEGREE
IV HAS 5 DEGREE
(a) An angle measures 55 degrees . What is the measure of its complement?
(b) An angle measures 82 degrees. What is the measure of its supplement?
Answer:
a) 35 degrees
b) 98 degrees
Step-by-step explanation:
Complementary angles measure up to 90 degrees. So if one angle measures 55 degrees, the other would have to be 35 degrees as
55 + 35 = 90
Supplementary angles measure up to 180 degrees. So if one angle measures 82 degrees, the other would have to be 98 degrees as
82 + 98 = 180
Determine whether the orthocenter is inside, on, or outside the triangle. Then find the coordinates of the orthocenter.L (-3, 2) ,M (5, 2) , N (-3, 6)
The coordinates of the orthocenter is (1,4)
What is the orthocenter of a triangle?The orthocenter of a triangle is the intersection of the perpendicular bisectors of the sides of the triangle. To determine if the orthocenter is inside, on, or outside the triangle, we first need to find the coordinates of the orthocenter.
We can find the equation of the perpendicular bisector of a line segment with the coordinates of its endpoints using the midpoint formula and the slope-intercept form of a line. The midpoint of a line segment with endpoints (x1, y1) and (x2, y2) is ((x1+x2)/2, (y1+y2)/2). The slope of the line perpendicular to a line with slope m is -1/m.
For example, the equation of the perpendicular bisector of side LM of the triangle is:
Midpoint of side LM: ((-3+5)/2, (2+2)/2) = (1,2)
Slope of side LM: (2-2)/(5-(-3)) = 0. Therefore the slope of the line perpendicular to it is undefined.
Equation of the perpendicular bisector: x = 1
Similarly, we can find the equations of the perpendicular bisectors of the other sides. The intersection of these lines gives us the coordinates of the orthocenter, which is (1,4)
Since the orthocenter is inside the triangle, it's inside the triangle.
The coordinates of the orthocenter is (1,4)
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The base of the flange shown in the drawing is actually 24
in. Its drawing width is 5 in.
(a) What will be the actual dimension A if A is 1.25 in. on the
drawing?
(b) Find the scale factor of the drawing.
The scale factor is 5 / 24. And the actual dimension A if A is 1.25 in will be 6 inches.
What is dilation?Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered. There is no effect of dilation on the angle.
The base of the flange shown in the drawing is actually 24 in. Its drawing width is 5 in.
The scale factor is given as,
Scale factor = 5 / 24
Then the actual dimension A if A is 1.25 in will be given as.
⇒ 1.25 / (5/24)
⇒ 1.25 x (24 / 5)
⇒ 6 inches
The scale factor is 5 / 24. And the actual dimension A if A is 1.25 in will be 6 inches.
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1 1 _x² - 7x+10
Solve +
2 2x
4x
-
Which proportion is equivalent to the original
equation?
O
x+2_x²-7x+10
4x
2x
x-1_x²-7x+10
4x
2x
x+1_x²²-7x+10
4x
2x
by rewriting the equation as a proportion.
DONE
The value of x from the system of equation will be 1 and 8 and the proportion equivalent is x² - 9x + 8 =0.
What is Polynomial?Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables
Given the expression 1/2+1/2x=x² - 7x+10/4x
Multiply the first term by 2x/2x and second term by 2/2 to have:
2x/4x + 2/4x = (x² - 7x+10)/4x
Multiply through by 4x to have:
2x+2=x² - 7x+10
Collect the like terms and factorize
x² - 7x+10-2x-2=0
x²-9x+8=0
Now factorize the given equation
x²-8x-x+8=0
x(x-8)-1(x-8)
(x-1)(x-8)=0
x=1 and x=8
Hence, the value of x from the system of equation will be 1 and 8 and the proportion equivalent is x² - 9x + 8 =0.
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round 7.18 + 5.89 to the nearset whole.number
Answer:
13
Step-by-step explanation:
Solution Given:
7.18+5.89=13.07
since the number after decimal is less than 5 so
we keep the real number same
so
nearest whole number is 13.
Answer:
13
Step-by-step explanation:
7.18+5.89
,= 13.07
so overall whole number is
Find the sum and express it in simplest form.
(8a²+ 6a+ 5) + (-3a² - 2a)
108
Clear all
Enter the correct answer.
DOO
?
DONE
The given expression can be simplified to obtain as 5a² + 4a + 5.
What is an Algebraic expression?An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.
The variable part of an algebraic expression can never be added or subtracted from the constant part.
The given expression is (8a²+ 6a+ 5) + (-3a² - 2a).
It can be simplified as,
(8a²+ 6a+ 5) + (-3a² - 2a)
Arrange the like terms as,
⇒ 8a² - 3a² + 6a - 2a + 5
⇒ 5a² + 4a + 5
Hence, the simplification is obtained as 5a² + 4a + 5.
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which values of x would make a polynomial equal to zero if the factors of the polynomial were (x+6) and (x+9)
Answer:
-6 and -9
Step-by-step explanation:
The values of x that would make a polynomial equal to zero if the factors of the polynomial were (x+6) and (x+9) are -6 and -9.
x+6=0 x+9=0
x=-6 x=-9
Answer:
The value of x that would make the polynomial equal to zero is -6.
Step-by-step explanation:
Which expression is equivalent to
5
NIF
NIN
X
no
5/5
PA
2
y
? Assume y* 0.
Expression [tex]\frac{\sqrt[7]{x} ^{2} }{\sqrt[5]{ y^{3}} }[/tex] is equal to [tex]x^{2/7} /y^{-3/7}[/tex]
The correct option is 1.
What is algebraic expression?An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.). Expressions are made up of terms.
Examples:
3x + 4y – 7, 4x – 10, etc.
Given expression is
[tex]\frac{\sqrt[7]{x} ^{2} }{\sqrt[5]{ y^{3}} }[/tex]
⇒[tex]x^{2.1/7} /y^{3.1/5}[/tex]
⇒[tex]x^{2/7} /y^{3/5}[/tex]
⇒[tex]x^{2/7} . y^{-3/5}[/tex]
Hence [tex]\frac{\sqrt[7]{x} ^{2} }{\sqrt[5]{ y^{3}} }[/tex] is equivalent to [tex]x^{2/7} /y^{-3/7}[/tex].
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The radius of a cylinder is doubled and its height is tripled. If its original volume was 10 cubic feet, what is its volume now, in cubic feet?
The new volume of the cylinder is now 120 cubic feet.
Original volume = 10 cubic feet
Original radius = r
Original height = h
New radius = 2r
New height = 3h
New volume = V
V = π * (2r)^2 * 3h
= π * 4r^2 * 3h
= 120π cubic feet
= 120 cubic feet
The original volume of the cylinder was 10 cubic feet. The radius of the cylinder was doubled and its height was tripled. Therefore, the new radius is twice the original radius and the new height is three times the original height. The new volume of the cylinder can be calculated using the formula V = π * (2r)^2 * 3h. This gives us a new volume of 120 cubic feet.
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If the radius of the cylinder is doubled and its height is tripled , then the new volume of the cylinder will be 120 cubic feet .
The Volume of the cylinder is calculated by the formula , V = πr²h ,
where r is the radius and h is height ,
the volume (V) of the cylinder is = 10 cubic feet ,
given that the radius is doubled , and height is tripled ,
So , we substitute r = 2r and h = 3h ,
Let V' be the volume of the new cylinder ,
We get , V' = π(2r)²(3h)
= π × 4r² × 3h
= 12πr²h
= 12 × V ,
substituting V = 10 ,
we get ,
V' = 120 cubic feet .
Therefore , the volume of the new cylinder is 120 cubic feet .
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Two numbers less than 100 are composed of the same digits, but are in reverse order. If their sum is 110 and difference is 18, find the numbers. The sum of four consecutive even numbers is 92, find the numbers.
Answer:
First part: 64 and 46
Second part, 10, 12, 14, 16.
Step-by-step explanation:
First number has his first digit A, and second digit B, ie it can be written as 10A+B. Second number becomes then 10B+A.
Add them together, the sum becomes 11A + 11B = 110. (or A+B = 10 by dividing by 11).
Subtract them from each other, and you get 9A-9B = 18 (or dividing by 9 A-B=2)
At this point it's easy to find the solution A=6, B=4 which makes the two numbers 64 and 46.
Callthe first number of the chain 2x, the second 2x+2, third is 2x+4, fourth is 2x+6. Add them together, you get 8x +2+4+6= 8x+ 12=92 which easily solves for x = 10 and the four numbers are 10, 12, 14, 16.
3.566 rounded to nearest tenth
Answer: 3.5
Step-by-step explanation: The 5 is in the tenth place.
You now have a lot of experience working with equations that compare two quantities. For example, while working on the Big Race, you found relationships of the form y = mx + by=mx+b, which compared x (time in seconds) with y (distance in meters). If a participant's race can be modeled with the equation y= 3x+4y=3x+4: a. How much of a head start did the participant get? How can you tell from the equation? b. What was participant's rate of speed? That is, how fast did they go? Justify your answer.
The participant received a head start of 4 meters. The 4 in the equation represents the initial position of the participant.
The participant's rate of speed of the participant is 3 meters per second.
How to determine how much of a head start the participant gets?a. The participant received a head start of 4 meters.
The 4 in the equation represents the initial position (y-intercept, c) of the participant, so this is the head start that the participant received.
b. The participant's rate of speed of the participant is 3 meters per second.
This means that for every 1 second (represented by x in the equation), the participant covers a distance of 3 meters. So the participant's rate of speed is 3 meters per x second
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Which of the following best describes the graph below?
The correct option is A one to one function.
What is a One to One Function?A normal function can actually have two different input values that can produce the same answer, whereas a one to one function does not. Let’s go ahead and start with the definition and properties of one to one functions.
Given here, the function has unique image for every point x in the domain as we can observe and is one-one as it passed the horizontal line test (as the horizontal line passes through only one point of the graph every time)
Hence, The correct option is A one to one function
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If x + 3y = 7 and y = 2, then x equals
A
1
B
C
D
2
3-1/2
13
Click the button or type the let
The value of the variable x at the value y = 2 is 1. The correct option is A.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the expression is x + 3y = 7 and the value of y is 2. The value of x will be calculated as,
x + 3y = 7
x + ( 2 x 3 ) = 7
x = 7 - 6
x = 1
Hence, the value of x will be 1.
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The Columbus Junior Soccer League is
selling raffle tickets to raise money for new
uniforms and equipment. So far, league
members have earned $1,218 from selling
84 tickets. Use the equation 1,218 +84 = r
to find the cost of each raffle ticket. Then
use the answer to find what the total
earnings will be after 90 raffle tickets have
been sold.
A cow is tied with a rope in the centre of a circular lawn of diameter 28cm.If the length of the rope is 7cm, find the area of the lawn which the cow graze.Also find the remaining area of thelawn.
Diameter of Lawn = 28 cm
Length of rope tied at the centre of lawn = 7cm.
As the cow, tied to the rope grazes the lawn it forms a circle with radius 7cm.
Area of lawn grazed by cow
= pi*7^2. ( pi = 3.14)
= 3.14 * 49
= 153.86 sq. cm
Area of the lawn with radius 14 cm
= pi * 14^2. (pi = 3.14)
= 3.14 * 14^2
= 615.44 sq cm
Remaining area = Area of the Lawn - Area of the lawn grazed by cow
= 615.44 - 153.86
= 461.58 sq cm
i need help with these.
The solution is
a) The measure of diagonal of rectangle BD = 24
b) The measure of ∠EBC of rhombus = 51°
c) The measure of EF of parallelogram = 17
What is a Parallelogram?A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure
The four types are parallelograms, squares, rectangles, and rhombuses
Properties of Parallelogram
Opposite sides are parallel
Opposite sides are congruent
Opposite angles are congruent.
Same-Side interior angles (consecutive angles) are supplementary
Each diagonal of a parallelogram separates it into two congruent triangles
The diagonals of a parallelogram bisect each other
Given data ,
Let the equation be represented as A
Now , the value of A is
a)
Let the diagonals of the rectangle ABCD intersect at E
The measure of AE = x + 4
The measure of CE = 3x - 12
Now , the measure of BD = 2AE
For a rectangle , the diagonals are equals
So , x + 4 = 3x - 12
On simplifying the equation , we get
Subtracting x on both sides of the equation , we get
2x - 12 = 4
Adding 12 on both sides of the equation , we get
2x = 16
Divide by 2 on both sides of the equation , we get
x = 8
Now , the measure of AE = x + 4 = 12
The measure of BD = 2AE = 2 x 12
The measure of BD = 24
b)
For a rhombus , the adjacent angles of a rhombus add up to 180° and the diagonals of a rhombus are perpendicular to each other
The measure of ∠EBC = 8a - 5
The measure of ∠ECB = 5a + 4
And , 2 ( measure of ∠EBC + measure of ∠ECB ) = 180°
2 ( 8a - 5 + 5a + 4 ) = 180°
On simplifying the equation , we get
Divide by 2 on both sides of the equation , we get
8a - 5 + 5a + 4 = 90
13a - 1 = 90
Adding 1 on both sides of the equation , we get
13a = 91
Divide by 13 on both sides of the equation , we get
a = 7
Now , substitute the value of a in m∠EBC , we get
The measure of ∠EBC = 8a - 5
The measure of ∠EBC = 8 ( 7 ) - 5
The measure of ∠EBC = 56 - 5 = 51°
Therefore , the measure of ∠EBC is 51°
c)
The median of a trapezoid is parallel to the bases and is one-half of the sum of measures of the bases
So ,
The measure of EF = ( 1/2 ) ( measure of DC + measure of AB )
Substituting the values in the equation , we get
2x + 1 = ( 1/2 ) ( 2x - 2 + 3x - 4 )
Multiply by 2 on both sides of the equation , we get
4x + 2 = 5x - 6
Subtracting 4x on both sides of the equation , we get
x - 6 = 2
Adding 6 on both sides of the equation , we get
x = 8
So , the measure of EF = 2x + 1
The measure of EF = 2 ( 8 ) + 1
The measure of EF = 17
Hence , the equations are solved
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