The present ages of the father and his son are 50 and 30 years respectively.
What is an algebraic expression?An algebraic expression can be defined as an expression made up of constants, variables, terms, coefficients, and factors.
These expressions are also made up of mathematical or arithmetic operations, which includes;
BracketDivisionAdditionSubtractionMultiplicationParentheses, etcFrom the information given;
Let the son's age be x
Let the father's age be x + y
x + x + y = 80
2x + y = 80
Then, 2x - y = 40
From equation (1), make 'y' the subject
y = 80 - 2x
Substitute the value
2x - (80 - 2x) = 40
2x - 80 + 2x = 40
collect like terms
4x = 120
x = 30
y = 80- 2(30)
y = 20
Hence, their ages are 30 years and 50 years
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A printer takes seconds to print a lyer. It took 75 seconds to print a batch of lyers without stopping. How many lyers were in the batch?
If it takes a printer seconds to print a single lyer, and it took 75 seconds to print a batch of lyers without stopping, the number of lyers in the batch is 75 / . This is because if it takes seconds to print a lyer, and we have 75 seconds available to print lyers, we can divide the total time available by the time it takes to print each lyer to find out how many lyers we can print.
For example, if it takes 3 seconds to print a single lyer, the number of lyers in the batch is 75 / 3 = 25. If it takes 2 seconds to print a single lyer, the number of lyers in the batch is 75 / 2 = 37.5.
Therefore, the number of lyers in the batch depends on the time it takes to print a single lyer. To find the exact number of lyers in the batch, we need to know the time it takes to print a single lyer.
61 Développer et réduire l'expression suivante.
B(x)=(x-1)² + x² + (x + 1)²
b. Déterminer trois entiers naturels consécutifs dont
la somme des carrés est 4 802.
Pour les
à l'aide
68 a.
c. 422-
69
Answer:
Step-by-step explanation:
iven, the equation is (x - 1)² + 2(x + 1) = 0. We have to determine if the equation has a real root. By using algebraic identity, (a - b)² = a² - 2ab + b² (x - 1)² = x² - 2x + 1.
the multiple regression/correlation model is a model with: group of answer choices multiple dependent variables and multiple independent variables multiple dependent variables and a single independent variable. single dependent variable and multiple independent variables single dependent variable and single independent variable
The multiple regression model is a model with single dependent variables and multiple independent variables.
The term regression referred as a statistical method that helps us to analyze and understand the relationship between two or more variables of interest.
Here we have to find the missing term in the statement "the multiple regression/correlation model is a model with"
In order to find the solution, we must know the definition of multiple regression model.
Multiple Regression model in statistics is defined as the is a statistical technique that can be used to analyze the relationship between a single dependent variable and several independent variables.
Based on these definition, we have identified that it has single dependent variable and multiple independent variable.
Therefore, option (c) is correct.
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Describe the Vertex Form of a Quadratic
equation in words.
The vertex form of a quadratic equation is a standard form of a quadratic equation that is written in the form:
y = a(x-h)^2 + k
where a, h, and k are constants. This form is called the vertex form because it represents the graph of the quadratic equation as a parabola, with the vertex of the parabola located at the point (h,k).
The vertex form of a quadratic equation is useful because it allows us to easily identify the vertex of the parabola and the direction in which the parabola opens. If a is positive, the parabola opens upwards and the vertex is the minimum point of the parabola. If a is negative, the parabola opens downwards and the vertex is the maximum point of the parabola.
Overall, the vertex form of a quadratic equation is a standard form that represents the graph of a quadratic equation as a parabola with a specific vertex location. It is useful for identifying the characteristics of the graph and for solving problems involving quadratic equations.
find the area of this triangle
Answer: a is about 7.416, rounding to two significant digits, 7.4, to one significant digit, 7.
Step-by-step explanation:
We will use the Pythagorean Theorem.
a²+b²=c²
c² is the longest side, so 8cm.
lets make the bottom side b², so 3cm
We are trying to find h, so let's make that a².
Applying the Theorem:
a²+3²=8²
--- a² + 9 = 64
subtract 9 from both sides.
-- a² = 55
Take the square root of both sides
a is about 7.416, rounding to two significant digits, 7.4, to one significant digit, 7.
Answer:
22.249 cm^2 (THIS IS ROUNDED)
Step-by-step explanation:
to find the area we first need to find h using Pythagorean theorem
a^2+b^2=c^2
We need to isolate a^2 on one side
a^2+b^2=c^2
-b^2. -b^2
a^2=c^2-b^2
a^2=8^2-3^2
a^2=64-9
a^2=55
√. √
a=7.416
Now we multiply by 3 to find the area
7.416x3
About 22.249 cm^2
Hopes this helps
A bank offers a saving account with an introductory interest rate of 7% for the first year,
and a follow-on rate of 5%, compounded annually.
If £500 is invested in the account for 3 years, how much interest will be earned?
Answer:
=£5898.38
Step-by-step explanation:
5000×1.07×1.05^(2)
=£5898.38
Bonsoir j'ai cette exercice a faire pour demain on peut m'aider ?
Explain how to find the volume and surface area
The volume and the surface area of the regular octogonal prism are given as follows:
Volume: [tex]56(1 + \sqrt{2})[/tex] cubic inches.Surface area: [tex]S = 128 + 8\sqrt{2}[/tex] square inches.How to obtain the volume of the prism?
The volume of the prism is given by the multiplication of the base area of the prism by the height of the prism.
The base is a regular octagon of side length 2 inches, hence it's area is given as follows:
[tex]A = 2a^2(1 + \sqrt{2})[/tex]
Hence, considering that a = 2, the base area is given as follows:
[tex]A = 8(1 + \sqrt{2})[/tex]
The height is of 7 inches, hence the volume, in cubic inches, is given as follows:
[tex]V = 7 \times 8(1 + \sqrt{2}) = 56(1 + \sqrt{2})[/tex]
How to calculate the surface area?The prism is composed by:
Eight rectangles of dimensions 2 inches and 7 inches.Two regular octagons of side length 2 inches.Hence the surface area of the prism, in square inches, is calculated as follows:
[tex]S = 2 \times 8(1 + \sqrt{2}) + 8 \times 2 \times 7[/tex]
[tex]S = 128 + 8\sqrt{2}[/tex]
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The normal cost of a pair of boots is £120.
In a sale the cost of the boots is reduced by 45%.
Work out the sale price of the boots.
Answer:
£54
Step-by-step explanation:
Write 45% as
45
100
Since finding the fraction of a number is the same as multiplying the fraction with the number, we have
45
100
of 120 =
45
100
× 120
Therefore, the answer is 54
If you are using a calculator, simply enter 45÷100×120 which will give you 54 as the answer.
the famous kate lynn horsefeed is building a box as part of her science project. it is to be built from a rectangular piece of cardboard measuring 25 cm by 40 cm bycutting out a square from each corner and then bending up the sides. find the size of the corner square which will produce a container that will hold the most.
The original cardboard measures 25 cm by 40 cm. By cutting out a 10 cm by 10 cm corner square, the new measurement of the cardboard will be 15 cm by 30 cm. The volume of the container will be 4500 cm^3.
The goal of this project is to build a container out of a rectangular piece of cardboard measuring 25 cm by 40 cm. To do this, a square must be cut out of each corner of the cardboard and the sides must then be bent up. In order to produce a container with the most internal volume, the corner square should be 10 cm by 10 cm. This will result in four equal sides and a larger internal volume. The larger internal volume will allow the container to hold more material, thus making it more efficient for the project.
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Pleaseeee helppppp meee
Answer:
A
Step-by-step explanation:
w = 12500p + 250
250 is a fixed number of words.
12500 is the slope
For each dollar the price increases, the number of words increases by 12,500.
Answer: A
if the residuals from a fitted regression violate the assumption of homoscedasticity, we know that a. they are normally distributed. b. they are independent of one another. c. there are extreme outliers. d. their variance is not constant.
Option D is the correct answer. if the residuals from a fitted regression violate the assumption of homoscedasticity their variance is not constant.
Homoscedasticity: It is an assumption of equal or similar variances in different groups are being compared. It is a condition in which the variance of the residual, or error term, in a regression model, is constant.
This is one of the most important assumptions of parametric statistical tests because they are sensitive to any dissimilarities. It is valid when X and Y are independent.
To deal with this First, we have attempted to transform your target using square root, log, reciprocal square root, or reciprocal transformations.
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I need help in this please help me at it
Step-by-step explanation:
come on, use some common sense.
length to breadth = 3/2.
so, when the breadth is 24, what is the factor compared to the original 2 of 3/2 ? 12.
2 × 12 = 24 cm
and then, we need to multiply the other ratio part by the sand factor
3 × 12 = 36 cm
when the length = 60 cm, then the factor compared to the original 3 of 3/2 is 20.
3 × 20 = 60 cm
and multiplying the other ratio part by the same factor
2 × 20 = 40 cm
when the breadth is 52, the factor compared to the original 2 of 3/2 is 26.
2 × 26 = 52 cm
and multiplying the other ratio part by the same factor
3 × 26 = 78 cm
include working out please
Answer:
y = 3x + 4
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 4) and (x₂, y₂ ) = (- 2, - 2) ← 2 points on the line
m = [tex]\frac{-2-4}{-2-0}[/tex] = [tex]\frac{-6}{-2}[/tex] = 3
the line crosses the y- axis at (0, 4 ) ⇒ c = 4
y = 3x + 4 ← equation of line
Answer:
y=3x+4
Step-by-step explanation:
The formula used is point slope, or y=mx+b
here, the m is the slope, and the b is the y-intercept
The y-intercept is where the graph crosses the y-axis, also known as when x=0
In this case, the y intercept is at the point (0,4) so you'd plug in 4 for the 'b' in the equation
To find the slope, use the rise over the run of the graph.
To do this, pick two points along the graph, and count how many units up/down, and to the left/right between the two points
The units up/down goes on top, being positive if they're up, and negative if they're down
The units left/right go on bottom, being positive if they're right, and negative if they're left
In this case you go 3 units up, and 1 unit right, so the slope would be 3/1 or 3
A group of 3 friends went to a sporting event. It cost 30 for each of them to get in. What was the total cost for all of them to get in?
Answer:
£90
Step-by-step explanation:
1 friend = £30
all together there are 3 friends
30 x 3 = 90
or you can simplify and do 3x3 which is 9
and add the 0 at end (90)
each person = 30($)
people = 3
cost($) * number of people
[tex]30\times3[/tex]
[tex]=\fbox{90}[/tex]
Anwered
Nakeiha' family took a road trip to Mount Ruhmore. Nakeiha fell aleep 18% of the way through the trip. If the total length of the trip wa 400 mile, how many mile had they travelled when Nakeiha fell aleep?
After solving the percentage the distance through which Nakeiha fell asleep along the trip is 72miles.
What is percentage?Percentage is a number expressed as a fraction of 100. The % sign means to divide the number by 100.
How to solve percentages?To solve this question, we will do 18% x 400.
= (18/100) x 400
= 72 miles
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Question 6 of 7
Submit Test
22-23 Geometry Unit 3 EUA
Tyler was trying to prove that all rhombuses are similar. He thought, "If I draw 2 rhombuses. I can find dilations that will take one rhombus exactly onto the other." Then he wrote a proof.
All rhombuses are not similar. Which steps in Tyler's proof have flaws? Explain what is wrong with each step that is wrong.
Step 1: Let A BCD and W XYZ be rhombuses. By the definition of a rhombus, AB = BOECDE DA and WXEXY AYZEZW.
Step 2: Dilate rhombus ABC D by the scale factor given by
WX
4B Side A'B' will be the same length as W X because of how I chose the scale factor. Because all sides ofa
thombus are congruent, B'C' will be the same length as W X and therefore the same length as XY, C'D' will be the same length as Y Z, and A'D' will be the same length as W Z. That means all the corresponding sides of A' B'C'D and W XY Z will be the same length.
Step 3: If all the sides in 2 figures are proportional, then those 2 figures are similar, so there must be a sequence of transformations that take ABC D onto W XYZ using dilations and rigid motions.
Step 4: Translate A' B'C'D' by the directed line segment A'W so that A" and W coincide.
Step 5: Rotate A" B"C" D" by angle B"W X so that B/' and X coincide. Now segments A' B'' and WX coincide.
Step 6: If needed, reflect A" B''O' D'' over segment W X so that D'' and Z are on the same side of WIX. Now segments A"' D' and WZ coincide.
Answer:
Step-by-step explanation: Step 1: Tyler correctly states that rhombuses have all sides congruent.
Step 2: Tyler correctly states that dilating a rhombus by a scale factor will result in sides of the same length, but he does not provide a justification for why he chose the scale factor of WX/AB.
Step 3: Tyler correctly states that if all sides in two figures are proportional, then the figures are similar, but he does not provide a justification for why this is true.
Step 4: Tyler correctly states that he will translate A'B'C'D' by the directed line segment A'W, but he does not provide a justification for why this will result in A'' and W coinciding.
Step 5: Tyler correctly states that he will rotate A"B"C"D" by the angle B"WX, but he does not provide a justification for why this will result in B'' and X coinciding.
Step 6: Tyler correctly states that he will reflect A"B''C''D'' over segment WX if needed, but he does not provide a justification for why this will result in D'' and Z coinciding.
Helen draws a random circle.
She then measures its diameter and circumference.
She gets a circumference, C, of 405 mm correct to 3 significant figures.
She gets a diameter, d, of 130 mm correct to 2 significant figures.
Helen wants to find the value of T using the formula TC
C
Calculate the lower bound and
upper bound for Helen's value of T.
Give your answers correct to 3 decimal places.
The value that Helen wants to use is Pi = C/D. The lower bound value is 3.065, and the upper bound for Helen's value is 3.165.
What is circumference?
The circumference is the perimeter of the circle.
Given, the circumference, C, at 405 mm to three significant numbers.
She correctly estimates the diameter, d, to be 130 mm to two significant numbers.
Helen wants to find the value of Pi using the formula pi=C/D
We have, the circumference of the circle = C = 405 mm
The diameter of the circle = d = 130 mm
Pi = C/D
= 405 mm / 130 mm
= 405 / 130
= 3.115
3.115, measured to the nearest 0.1.
The degree of accuracy is nearest 0.1.
0.1/2 = 0.05
Upper bound = 3.115 + 0.05 = 3.165
Lower bound = 3.115 - 0.05 = 3.065
Therefore, the lower bound and upper bound for Helen's value are 3.165, and 3.065.
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is (x+1) a factor of polynomial x^3+2x^2-19x-20
Answer:
Step-by-step explanation:
3
Suppose that 6 < x < 7 and 10 < y < 12. Find all possible values of each expression.
y - x
The set of all possible y-x values is between 3 and 6, excluding both endpoints.
===================================================
Explanation:
The y-x value is smallest when:
The y value is as small as possibleThe x value is as large as possibleI recommend to draw out a number line. The idea is to place x and y as close as possible to each other.
Based on those two conditions, we use y = 10 and x = 7 respectively. That gives y-x = 10-7 = 3 as the smallest possible difference. Keep in mind we can't actually reach this value so we would write y-x > 3 which is the same as 3 < y-x.
--------------------
Similarly, y-x is largest when:
The y value is largestThe x value is smallestLike earlier, use a number line to see why this would be the case. We're trying to space x and y out as far as possible.
The largest y value and smallest x value are y = 12 and x = 6 in that order. So the upper bound is y-x = 12-6 = 6. Like before, we can't actually reach this number which means we write y-x < 6.
--------------------
Recap:
In the 1st section, we found that 3 < y-xIn the 2nd section, we found that y-x < 6Put those two results together in a tidy compound inequality to get the final answer 3 < y-x < 6
It says: The expression y-x is between 3 and 6, excluding both endpoints.
Maria and Franco are mixing port drink for a track meet. Maria ue 3/4cup of powdered mix for every 3 gallon of water. Franco ue 1 2/3 cup of powdered mix for every 5 gallon of water. Quetion 1 Part A What i the unit rate of cup of powered mix per gallon for each peron? Enter the correct anwer in the boxe. Maria: $$ cup of powdered mix per gallon Franco: $$ cup of powered mix per gallon
The unit rate of cup of powered mix per gallon for each person by
Maria: 3 cups
Franco: 1/3 cups
Rate of powdered mix = number of cups ÷ number of gallons of water
Keep the values in formula to find the unit rate of cup of powdered mix
Rate of powdered mix by Maria = (3/4)÷3
Rate of powdered mix by Maria = 3/(4×3)
Cancelling 3 as it is common
Rate of powdered mix by Maria = 3 cups per gallon
Firstly converting the amount of cups from mixed fraction to fraction
Amount of cups = 1 [tex] \frac{2}{3} [/tex]
Amount of cups = 5/3 cups
Rate of powdered mix by Franco = (5/3)÷5
Rate of powdered mix by Franco = 5/(5×3)
Cancelling 5 as it is common
Rate of powdered mix by Franco = 1/3 cups per gallon
Thus, Maria's powdered mix is 3 cups per gallon while Franco's powdered mix is 1/3 cups per gallon.
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You pay $54 of interet on a loan of $1600 that had a 4. 5% interet rate. How long did it take you to pay off the loan?
The time required to pay off the loan at 4.5% interest rate 0.75 years.
The equation of simple interest will be used for calculation of time. The formula will be -
S. I. = Principal × Rate × Time/100
Keep the values in formula to find the value of time -
54 = 1600 × 4.5 × time/100
Rewriting the equation -
Time = (54 × 100)/(1600 × 4.5)
Performing multiplication on Right Hand Side of the equation
Time = 5400/7200
Performing division on Right Hand Side of the equation
Time = 0.75 years
I will need to take 0.75 years time to pay off the loan.
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The combined volume of all the tanks at an aquarium is 1.25x10^6
gallons. The aquarium plans to install a new dolphin tank with a volume of 250,000gallons. What will be the total volume of all of the tanks at the aquarium after the new dolphin tank is installed?
Answer: The total volume of all the tanks at the aquarium after the new dolphin tank is installed will be 1.25x10^6 gallons + 250,000 gallons = 1.5x10^6 gallons.
This is the equivalent of 1,500,000 gallons.
Step-by-step explanation:
Katelyn want to build a dek for her doll. Her actual dek i 3 feet tall. The clae i 10 in = 1ft. How tall will the doll dek be?
The height of the desk for the doll according to conversion scale given is 1.5in.
Based on the information provided, the height of Katelyn’s actual desk is 3 feet. She wants to build a desk for her doll and she wants to use a scale of 0.5 in: 1feet to convert the measurements. A conversion scale refers to a scale which indicates the relationship between two different units of measurement.
According to the given conversion scale,
1 feet = 0.5in
If the height is 3 feet, the measurement in inches would be:
3 feet = 3 feet * 0.5 in/ 1 feet = 1.5 in
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What are the values of x and y? Question options:
A) x = 18√3 y = 9√3
B) x = 9; y = 9√3
C) x = 9√2 ; y = 9
D) x = 9√3 ; y = 9
Answer:
Given:
A figure of a triangle.
To find:
The values of x and y.
Solution:
From the given triangle it is clear that the base angles of the triangle are equal, so the triangle is an isosceles triangle.
Altitude on the base of the isosceles triangle from from the opposite angle is a median. It means, it divides the base in two equal parts.
In the given triangle, the altitude divides the base in two equal parts and the measure of each part is 9 units.
Step-by-step explanation:
Answer:
B) x = 9; y = 9√3
Step-by-step explanation:
x = 9 = ( 9 )
y = 9√3 = ( 15.588 )
Hope this helps!
The table shows the number of miles people in the U.S. traveled by car annually from 1975 to 2015.
The equation for the line of best fit is y=0.048x + 1.345, where x is the number of years since 1975
and y is the number of vehicle-miles traveled in trillions. What do the slope and y-intercept
represent? Estimate the number of miles people in the U.S. traveled in 2007. What is a reasonable
prediction for the number of miles people in the U.S. will travel in 2022?
What the slope and the y-intercepts represent are;
Slope means that the rate at which the number of miles people in the U.S. traveled per year increased was 0.048
y-intercept means that the number of vehicle-miles traveled in 1975 is; 1.345 (in trillions)
A reasonable prediction for the number of miles people in the U.S. will travel in 2022 is; 3.601 (in trillions)
How to interpret the equation of line of best fit?
The equation for the line of best fit is given as;
y = 0.048x + 1.345
where;
x is the number of years since 1975
y is the number of vehicle-miles traveled in trillions
The equation of a line in slope intercept form has the general form as;
y = mx + c
where;
m is slope
c is y-intercept
Thus;
Slope = 0.048 which is the rate at which the number of miles people in the U.S. traveled per year increases.
y-intercept = 1.345 (in trillions) which is the number of vehicle-miles traveled in 1975
The year 2022 will be 47 years since 1975 and so the prediction is;
y = 0.048(47) + 1.345
y = 3.601 (in trillions)
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If the term of a sequence increases in value what is true about the common difference
Answer:
Common Difference is positive
Step-by-step explanation:
If the common difference is negative, the value is decreasing every time the term increases.
If the common difference is positive, the value is increasing every time the term increases.
Because, in this case, when the term increases, the value increases, the common difference is positive.
what is an equation of the line that passes through the points (8,-3) and (4,2)
Answer:
y = –5x/4 + 7
Step-by-step explanation:
x1 = 8 ,x2 = 4, y1 = –3 , y2 = 2
lets find the slope(m)
m = y2–y1/x2–x1
m = 2 – (–3)/ 4 – 8
m = 5/ –4
m= –5/4
to find the equation of a line using this as our guider y = mx + b
we will make use of one coordinate
(8,–3)
using the formula for one point
y – y1 = m(x – x1)
y – (–3) = –5/4(x – 8)
y + 3 = –5x/4 + 10
y = –5x/4 + 10 –3
y = –5x/4 + 7
i hope i helped pls rate the answer as brainliest if i deserve it
thanks
The time spent (in days) waiting for a heart transplant for people ages 35-49 in a recent year follows a normal distribution with a mean wait time of 204 days and standard deviation 25. 7 days. The 12% of people who wait the shortest for a heart transplant wait no more than how many days?.
Using the table of Z-normal distribution and with the value of mean, standard deviation and the 12% who wait the shortest, The answer is
173.80 days.
What do you mean by probability distributions?A mathematical function called a probability distribution explains the likelihood of many alternative values for a variable. Graphs or probability tables are frequently used to represent probability distributions. The probability distribution of X is defined as the function f(x) p(x)= P(X=x) for any x falling within the range of X. The probability mass function for the discrete random variable X is another name for it.
What is a Z-normal distribution?A unique type of normal distribution with a mean of 0 and a standard deviation of 1 is known as the standard normal distribution, or z-distribution. By transforming the values of any normal distribution into z scores, it is possible to standardize it. Z scores provide the number of standard deviations from the mean that each value falls within.
[tex]P(x < Z) = 0.12\\Z = -1.175[/tex](From Z-normal table)
[tex]\frac{x-204}{25.7} = -1.175\\x= -1.175*25.7 +204\\x=173.80\\[/tex]
Days = 173.80 days .
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What is the relationship between the circumference C of the circle in which the degree measure A of a central angle of a circle intercepts an arc length s of the arc?
Answer: The circumference itself can be considered a full circle arc length. Arc Measure: In a circle, the degree measure of an arc is equal to the measure of the central angle that intercepts the arc. Arc Length: In a circle, the length of an arc is a portion of the circumference.
An arc length is a portion of the circumference of a circle. You can use the measure of the arc (in degrees) to find its length (in linear units). In a circle, the ratio of the length of a given arc of the circumference is equal to the ratio of the measure of the arc to 360°.
It will help you.
Step-by-step explanation: