Step-by-step explanation:
15=3
35=x
15x=3×35
x= 3×35÷15
x=105÷15
x=7
what is the midpoint between (-7,-9) and (-0.5,-3)
The midpoint between (-7,-9) and (-0.5,-3) is (-3.75,-6)
The midpoint between two points in a Cartesian plane is the point that is equidistant from both points and is located exactly in the middle of the line segment connecting the two points. To find the midpoint, we need to average the x-coordinates and the y-coordinates of the two given points.
Given the points (-7,-9) and (-0.5,-3), the midpoint can be found by:
averaging the x-coordinates (-7 + -0.5) / 2 = -3.75
averaging the y-coordinates (-9 + -3) / 2 = -6
So, the midpoint between (-7,-9) and (-0.5,-3) is (-3.75,-6)
Alternatively, the midpoint formula is:
(x1+x2)/2 , (y1+y2)/2
So for the given points,
(x1,y1)= (-7,-9) and (x2,y2)= (-0.5,-3)
Midpoint (x,y) = (-7+(-0.5))/2 ,(-9+(-3))/2
= (-3.75,-6)
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Compute the lower Riemann sum for the given function f(x) = x^2 over the interval x E [-1,1] with respect to the partition P = [-1, -1/4, 1/2, 3/4, 1]
Answer:
[tex]\dfrac{1}{4}=0.25[/tex]
Step-by-step explanation:
The Riemann sum is a method by which we can approximate the area under a curve using a series of rectangles.
The Lower Riemann Sum uses the minimum height of the rectangle on each subinterval.
As the Lower Riemann Sum is entirely below the curve, it is an underestimation of the area under the curve.
The number of partitions is the number of rectangles used.
Partitions can be of equal length or not of equal length.
Given:
Function: f(x) = x²Interval: [-1, 1]Partition, P = [-1, -1/4, 1/2, 3/4, 1]The given partition divides the interval [-1, 1] into 4 subintervals:
[-1, -1/4], [-1/4, 1/2], [1/2, 3/4] and [3/4, 1]To calculate the areas of the rectangles, multiply the width of each rectangle by its height.
The width is the difference between the x-values of each subinterval.
The height is the minimum value of the function across the subinterval.
First rectangle [-1, -1/4]:
[tex]\begin{aligned}\implies \left(-\dfrac{1}{4}-(-1)\right) \cdot f\left(-\dfrac{1}{4}\right)&=\dfrac{3}{4} \cdot \left(-\dfrac{1}{4}\right)^2\\\\&=\dfrac{3}{4} \cdot \dfrac{1}{16}\\\\&=\dfrac{3}{64}\end{aligned}[/tex]
Second rectangle [-1/4, 1/2]:
[tex]\begin{aligned}\implies \left(\dfrac{1}{2}+\dfrac{1}{4}\right) \cdot f\left(0\right)&=\dfrac{3}{4} \cdot (0)^2\\\\&=\dfrac{3}{4} \cdot 0\\\\&=0\end{aligned}[/tex]
Third rectangle [1/2, 3/4]:
[tex]\begin{aligned}\implies \left(\dfrac{3}{4}-\dfrac{1}{2}\right) \cdot f\left(\dfrac{1}{2}\right)&=\dfrac{1}{4} \cdot \left(\dfrac{1}{2}\right)^2\\\\&=\dfrac{1}{4} \cdot \dfrac{1}{4}\\\\&=\dfrac{1}{16}\end{aligned}[/tex]
Fourth rectangle [3/4, 1]:
[tex]\begin{aligned}\implies \left(1-\dfrac{3}{4}\right) \cdot f\left(\dfrac{3}{4}\right)&=\dfrac{1}{4} \cdot \left(\dfrac{3}{4}\right)^2\\\\&=\dfrac{1}{4} \cdot \dfrac{9}{16}\\\\&=\dfrac{9}{64}\end{aligned}[/tex]
Therefore, the Lower Reimann Sum for the given function over the given interval and partitions is the sum of the area of the rectangles:
[tex]\implies \dfrac{3}{64}+0+\dfrac{1}{16}+\dfrac{9}{64}=\dfrac{1}{4}=0.25[/tex]
Line m : y=4x+10
What would be the slope of a parallel line?
The slope of parallel lines is the same. The slope of both lines is 4 if somehow the path y = 4x - 10 is perpendicular to it.
In arithmetic, what is a slope?A line's angle of incidence might well be determined by looking at its slope. Slope is computed mathematically as "rise under flow" (change in y divided by change in x). A bridge's slope usually indicates the slopes and direction of the line. By calculating the change between both the measurements of the two locations, (x1,y1) and (x2,y2), it is simple to estimate the slopes of a horizontal path between them. The letters "m" is sometimes used this to represent slope.
In the point slope form, replace m = 1 with to create the equation (1,13).
y - y₁ = m(x - x₁)
y - 13 = 4 (x-1)
y - 13 = 4x - 4
y = 4x + 9
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The complete question is-
What is an equation of the line that is parallel to y=4x-10 and passes through (1,13)?
(9.42x10^4)(6.45x10^2)
Simplify using a scientific calculator.
Write each answer in scientific notation.
Sone help me understand how to do this
60.759×10⁶ is the value of the expression (9.42×10⁴)(6.45×10²).
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is (9.42×10⁴)(6.45×10²)
We have to find the value of the expression.
9.42×6.45×10²×10⁴
60.759×10²×10⁴
Bases are same then the powers will be added.
60.759×10⁶
Hence, 60.759×10⁶ is the value of the expression (9.42×10⁴)(6.45×10²).
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X^5 = -5 complex numbers using square roots
Poopy man is my husband uwu
anyways ur answer is 3^x
Mari suspects that there is a relationship between the number of text messages high school students send and their academic achievement. To explore this, she asks a random sample of 52 students at her school how many text messages they sent yesterday and what their grade point average (GPA) was during the most recent marking period. Her data are summarized in the scatter plot below. The line of best fit is also shown as y=3.8-0.005x.
what is the GPA of someone who texted 200 and 90 times?
Answer:
Interpretation of the slope: For students at this school, the predicted GPA decreases by 0.005 for each additional text message sent OR the GPA decreases by 0.005, on average, for each additional text message sent.
Interpretation of intercept: The model predicts that students at this school who send no text messages have, on average, a GPA of 3.8.
Step-by-step explanation:
The purpose of this task is to assess the ability to interpret the slope and intercept of the line of best fit in context. There are two common errors that students make when interpreting the slope. Students may not make it clear that the slope is the predicted change (not necessarily an actual change) in GPA associated with an increase of 1 in the number of text messages sent. They also often do not communicate that the slope describes the change
You might want to point out that it is not always reasonable to interpret the intercept as the predicted y value when x = 0, as this often involves extrapolation far beyond the range of the x values in the data set. In this example, however, it is appropriate because there are observations with x = 0 in the data set.
You can also point out that the interpretation of the slope and intercept represents a generalization from the sample of 52 students to the population of all students at the school. This is appropriate because the sample was a random sample of students from the school.
Although this task is short and looks simple, some of the points brought out in this task are subtle. It might be a good strategy to engage in a whole class discussion of the correct interpretations.
For each value below, enter the number correct to four decimal places.
Suppose an arrow is shot upward on the moon with a velocity of 28 m/s, then its height in meters after t seconds is given by h(t) = 28t − 0.83t^2. Find the average velocity over the given time intervals.
A. [10, 11]:
B. [10, 10.5]:
C. [10, 10.1]:
D. [10, 10.01]:
E. [10, 10.001]:
The average velocity over the given time intervals [10, 11], [10, 10.5], [10, 10.1], [10, 10.01], and [10, 10.001] are -2.1425 m/s, -4.7475 m/s, -9.1260 m/s, -98.4300 m/s, and -984.3000 m/s, respectively.
A. [10, 11]: -2.1425 m/s
The average velocity over the given time interval is given by:
v_avg = (h(b)-h(a))/(b-a)
where a is the initial time and b is the final time.
In this case, a = 10 and b = 11.
Therefore,
v_avg = (h(11)-h(10))/(11-10)
= (28×11 - 0.83×11² - (28×10 - 0.83×10²))/(11-10)
= (-2.83)/1
= -2.83 m/s
Rounding to four decimal places, we get the answer as -2.1425 m/s.
B. [10, 10.5]: -4.7475 m/s
The average velocity over the given time interval is given by:
v_avg = (h(b)-h(a))/(b-a)
where a is the initial time and b is the final time.
In this case, a = 10 and b = 10.5.
Therefore,
v_avg = (h(10.5)-h(10))/(10.5-10)
= (28×10.5 - 0.83×10.5² - (28×10 - 0.83×10²))/(10.5-10)
= (-4.83)/0.5
= -9.66 m/s
Rounding to four decimal places, we get the answer as -4.7475 m/s.
C. [10, 10.1]: -9.1260 m/s
The average velocity over the given time interval is given by:
v_avg = (h(b)-h(a))/(b-a)
where a is the initial time and b is the final time.
In this case, a = 10 and b = 10.1.
Therefore,
v_avg = (h(10.1)-h(10))/(10.1-10)
= (28×10.1 - 0.83×10.1² - (28×10 - 0.83×10²))/(10.1-10)
= (-9.843)/0.1
= -98.43 m/s
Rounding to four decimal places, we get the answer as -9.1260 m/s.
D. [10, 10.01]: -98.4300 m/s
The average velocity over the given time interval is given by:
v_avg = (h(b)-h(a))/(b-a)
where a is the initial time and b is the final time.
In this case, a = 10 and b = 10.01.
Therefore,
v_avg = (h(10.01)-h(10))/(10.01-10)
= (28×10.01 - 0.83×10.01² - (28×10 - 0.83×10²))/(10.01-10)
= (-9.843)/0.01
= -984.3 m/s
Rounding to four decimal places, we get the answer as -98.4300 m/s.
E. [10, 10.001]: -984.3000 m/s
The average velocity over the given time interval is given by:
v_avg = (h(b)-h(a))/(b-a)
where a is the initial time and b is the final time.
In this case, a = 10 and b = 10.001.
Therefore,
v_avg = (h(10.001)-h(10))/(10.001-10)
= (28×10.001 - 0.83×10.001² - (28×10 - 0.83×10²))/(10.001-10)
= (-9.843)/0.001
= -9843 m/s
Rounding to four decimal places, we get the answer as -984.3000 m/s.
Hence,
A. -2.1425 m/s
B. -4.7475 m/s
C. -9.1260 m/s
D. -98.4300 m/s
E. -984.3000 m/s
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The average velocity over the given time intervals [10, 11] will be -2.83 m/s, [10, 10.5] will be -9.66 m/s, [10, 10.1] will be -98.43 m/s, [10, 10.01] will be -984.3 m/s, and [10, 10.001] will be -9843 m/s
A. The given time interval is: [10, 11]
The average velocity throughout the specified time span may be calculated as follows:
[tex]v_avg = (h(b)-h(a))/(b-a)[/tex]
where a is the initial time and b is the final time.
In this case, a = 10 and b = 11.
Therefore, the value of the average velocity will be
v_avg = (h(11)-h(10))/(11-10)
= (28×11 - 0.83×11² - (28×10 - 0.83×10²))/(11-10)
= (-2.83)/1= -2.83 m/s
B. The given time interval is: [10, 10.5]
The average velocity throughout the specified time span may be calculated as follows:
v_avg = (h(b)-h(a))/(b-a)
where a is the initial time and b is the final time.
In this case, a = 10 and b = 10.5.
Therefore,
v_avg = (h(10.5)-h(10))/(10.5-10)
= (28×10.5 - 0.83×10.5² - (28×10 - 0.83×10²))/(10.5-10)
= (-4.83)/0.5
= -9.66 m/s
C. The given time interval is: [10, 10.1]
The average velocity throughout the specified time span may be calculated as follows:
v_avg = (h(b)-h(a))/(b-a)
where a is the initial time and b is the final time.
In this case, a = 10 and b = 10.1.
Therefore,
v_avg = (h(10.1)-h(10))/(10.1-10)
= (28×10.1 - 0.83×10.1² - (28×10 - 0.83×10²))/(10.1-10)
= (-9.843)/0.1= -98.43 m/s
D. The given time interval is: [10, 10.01]
The average velocity throughout the specified time span may be calculated as follows:
where a is the initial time and b is the final time.
In this case, a = 10 and b = 10.01.
Therefore,
v_avg = (h(10.01)-h(10))/(10.01-10)
= (28×10.01 - 0.83×10.01² - (28×10 - 0.83×10²))/(10.01-10)
= (-9.843)/0.01 = -984.3 m/s
E. The given time interval is: [10, 10.001]
The average velocity throughout the specified time span may be calculated as follows:
v_avg = (h(b)-h(a))/(b-a)
where a is the initial time and b is the final time.
In this case, a = 10 and b = 10.001.
Therefore,
v_avg = (h(10.001)-h(10))/(10.001-10)
= (28×10.001 - 0.83×10.001² - (28×10 - 0.83×10²))/(10.001-10)
= (-9.843)/0.001= -9843 m/s
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Which number from the set {1, 2, 3,4} makes the inequality 5x² > 12x + 9 true for x?
Is it 1 or 2 or 3 or 4?
Answer:
4
Step-by-step explanation:
substitute the values from the set into the inequality and check validity.
x = 1
5(1)² > 12(1) + 9
5(1) > 12 + 9
5 > 21 ← False
x = 2
5(2)² > 12(2) + 9
5(4) > 24 + 9
20 > 33 ← False
x = 3
5(3)² > 12(3) + 9
5(9) > 36 + 9
45 > 45 ← False
x = 4
5(4)² > 12(4) + 9
5(16) > 48 + 9
80 > 57 ← True
thus the value 4 from the set makes the inequality true
You plant a rectangular garden that is 7 1⁄2' wide and has an area of 78.75 square ' you have 10 yd of wire fencing do you have enough wire fencing to enclosed the garden?
Someone has no enough wire fencing to enclose the rectangular garden.
Does someone have enough wire fencing to enclose the garden?
Herein we find the case of a rectangular garden, of which someone wants to enclose with wire fencing and we need to determine whether such fencing is enough to enclose that place with given dimensions (Width: 7.5 feet, area: 78.75 square feet).
The area of the rectangular garden is described by following formula:
A = w · l
Where:
w - Width, in feet.l - Length, in feet.First, determine the length of the rectangular garden:
l = A / w
l = 78.75 / 7.5
l = 10.5 ft
Second, calculate the perimeter of the rectangular garden:
p = 2 · (w + l)
p = 2 · (7.5 ft + 10.5 ft)
p = 36 ft
Thrid, determine if the fencing wire is enough to enclose the garden: (1 yard - 3 feet)
l = 36 ft × 1 yd / 3 ft
l = 12 ft
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The Cheese Spread restaurant makes a grilled cheese sandwich with 2 oz of Swiss cheese and 4 oz of cheddar cheese. Which table represents the description of the proportional relationship?
Swiss Cheese (oz) 2 4 6
Cheddar Cheese (oz) 4 8 12
Swiss Cheese (oz) 4 8 12
Cheddar Cheese (oz) 2 4 6
Cheddar Cheese (oz) 2 1 0
Swiss Cheese (oz) 4 3 2
Cheddar Cheese (oz) 4 3 2
Swiss Cheese (oz) 2 1 0
PLS HELP WILL MARK BRAINLYIST HURRY PLSSS
A table between both the cheeses is given as,
Swiss Cheese (oz) 2 4 6
Cheddar Cheese (oz) 4 8 12, Option A is correct.
proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.
Here,
Let x be the amount of Swiss cheese and y be the amount of cheddar cheese.
According to the question,
y = kx
put y = 4 and x = 2
k = 2
Now,
y = 2x
From the above relation, a table between both the cheeses is given as,
Swiss Cheese (oz) 2 4 6
Cheddar Cheese (oz) 4 8 12
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W^2-7w+10 divided by w-5
Answer:
[tex] {w}^{2} - 7w + 10 = (w - 2) ( w- 5) \\ ( {w}^{2} - 7w + 10) \div (w - 5) = (w - 2)[/tex]
You deposit $2,000 in an account earning 3% interest compounded monthly.
a. How much will you have in the account in 20 years?
b. How much interest will you earn?
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$2000\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &20 \end{cases}[/tex]
[tex]A = 2000\left(1+\frac{0.03}{12}\right)^{12\cdot 20}\implies A=2000(1.0025)^{240} \implies \boxed{A \approx 3641.51} \\\\\\ 3641.51~~ - ~~2000~~ \approx~~ \stackrel{earned~interest}{\boxed{1641.51}}[/tex]
On a recent test, students had to determine whether the relation represented by the ordered pairs (1,2) (6,12) (12,24) (18,36) is a function. Bobby drew the arrow diagram on the right and said the relation was not a function. What error did Bobby most likely make?
Therefore , the solution to the given problem of ordered pair comes out to be Bobby might have made a mistake by using the two 12s that are present on each side of a mapping as the x-values.
What exactly are ordered pairs?A pairing of two variables that is presented in such a way as to imply a particular order is referred to as a "ordered pair."The x- and y-coordinates are indicated by the first and second terms, respectively, in an order pair. Close brackets are used to write the ordered pair, as seen in the example below.
Here,
The following are the ordered pairs:
(x,y) = (1, 2), (6, 12), (12, 24), (18, 36) (18, 36)
The following is what arrows show us:
1 -> 2
6-> 12
12->24
18 -> 36
The relational mapping shown above is a function.
This is the case since every x-value points to the same y-value.
Therefore , the solution to the given problem of ordered pair comes out to be Bobby might have made a mistake by using the two 12s that are present on each side of a mapping as the x-values.
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For the following two numbers, find two factors of the first number such that their product is the first number and their sum is the second number.
36,13
The two factors of the first number 36 which their sum is equal to 13 are 4 and 9.
What is factor of a numberFactor is a number that divides another number without a remainder. That is if multiplying two whole numbers gives us a product, then the numbers we are multiplying are factors of the product.
The first number 36 have the following factors:
1, 2, 3, 4, 6, 9, 12, 18, and 36.
the factors 4 and 9 will be the factors in question because;
4 × 9 = 36
4 + 9 = 13
Therefore, 4 and 9 are the two factors of 36 that their product is the first number 36 and their sum is the second number 13.
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What is 3,879 rounded to nearest 100
PLEASE HELP IM AWARDING HIGH POINTS
The polynomial [tex]-15\:y^4+12\:y^2-9\:y[/tex] as the sum of other polynomials. Each of the product's polynomials is written as = 3y (-5y³ + 4y - 3)
What is meant by polynomials?Using mathematical operations like addition, subtraction, multiplication, and division, a polynomial is an equation made up of variables, constants, and exponents (No division operation by a variable) Sums of terms with the pattern kxn where k is any positive integer and n is an arbitrary number are known as polynomials. A polynomial is something like 3x+2x-5. Polynomials: An introduction In this video, basic terms such terms, degrees, standard form, monomial, binomial, and trinomial are covered. The formulas that only contain addition, subtraction, multiplication, and non-negative integer exponents are those that can be used to identify the polynomials. The expressions with other operations will be non-polynomial expressions.Given,
[tex]-15 y^4+12 y^2-9 y[/tex]
[tex]& y^2=y y \\[/tex]
[tex]& y^4=y^3 y \\[/tex]
[tex]& =-15 y^3 y+12 y y-9 y[/tex]
[tex]=-3 \cdot 5 y^3 y+3 \cdot 4 y y-3 \cdot 3 y[/tex]
Factor out common term 3y
= 3y (-5y³ + 4y - 3)
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Can you please help me i want to know the steps to solve this problem i dont want the answer so i can learn to do this on my own
Answer:
Hint: everything in that big [] is to the power of zero. anything to the power of zero is one. so
1+(6-8)=?
In 1927, Charles Lindbergh had his first
solo flight across the Atlantic Ocean. He
flew 3,610 miles in 33.5 hours. If he flew
about the same number of miles each
hour, how many miles did he fly each
hour?
To find out how many miles Charles Lindbergh flew per hour, we can use the formula:
miles per hour = total miles / total hours
In this case, the total miles is 3,610 and the total hours is 33.5. Plugging in these values, we get:
miles per hour = 3,610 / 33.5
miles per hour = 107.7 (approximately)
So Charles Lindbergh flew about 107.7 miles per hour during his first solo flight across the Atlantic Ocean.
Find the length of the indicated side.
3/2X+6 =2/5x+9
The length of side AB is
If the equation be 3/2X+6 =2/5x+9 then the length of side AB is -15/11.
What is meant by equation?The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal. Two expressions joined by an equal sign form a mathematical statement known as an equation.
A condition on a variable (or variables) is a pair of expressions in the variable (or variables) that have the same value. The solution, also known as the root of the equation, is the quantity for which the equation holds true. Even if the LHS and RHS are switched, an equation still holds true.
Let the equation be 3/2X + 6 = 2/5x + 9
simplifying the equation, we get
15x + 27 = 4x + 12
15x = 4x - 15
11x = -15
Divide both sides by 11, we get
[tex]$\frac{11 x}{11}=\frac{-15}{11}$$[/tex]
[tex]$x=-\frac{15}{11}$$[/tex]
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What is the measure of each angle inside the figure (the value of x)?
(Hint-This equals 360° divided by the number of sides of the figure.)
Answer:
60
Step-by-step explanation:
360 degrees divided by 6 sides equal 60 degrees
Represent Multiplication of
Whole Numbers by Fractions
raw a visual model to find the product.
2x
ME Critique Reasoning Barbara picked 36 apples. She
needs to put of the apples in a basket. Barbara says she
will put 12 apples in the basket. Is Barbara correct? HELP MEE
Barbara would choose the apples three times, so a visual model using Whole Numbers by Fractions would be created to determine the outcome. 2x
what is fraction ?A whole can be represented by any number of equal parts, or fractions. The number of units of a particular size is expressed as a fraction in standard English. 8, 3/4. Fractions are included in wholes. Numbers are expressed in mathematics as the ratio of the numerator to the denominator. In simple fractions, each of these is an integer. A complicated fraction contains a fraction in either the numerator or denominator. There is a difference between the numerators and denominators of true fractions. A sum that is a fraction of a whole is referred to as a fraction. You can evaluate it by dissecting the whole into smaller pieces. For example, 12 is used to represent one-half of a full number or item.
given
she is correct as Barbara picked 36 apples
in one time she put 12 apples in the basket
Barbara would choose the apples three times, so a visual model using Whole Numbers by Fractions would be created to determine the outcome. 2x
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A local bar and grill is having a quarter wing night during which chicken wings cost a quarter each.
As you leave home to join your friends there, all you grab is a $20 bill. Determine how many wings
you can purchase if you also want to buy a pitcher of your favorite beverage for $5 and ranch dip
for $1.50. There is also sales tax of 8.5%. You will leave a 20% tip on your bill after tax.
(enter number only)
Answer: Here is the calculation:
The cost of the wings is $0.25 per wing
The cost of the pitcher of beverage is $5
The cost of the ranch dip is $1.50
Sales tax is 8.5%, so you need to add 8.5/100 * (5+1.5) = 0.0825 to the cost of the beverage and dip.
The cost of the beverage and dip after tax is 5+1.5+0.0825 = 6.5825
The total cost of the wings, beverage, and dip before tip is 6.5825 + 20 = 26.5825
You need to leave a 20% tip, so you need to add 0.2*26.5825 =5.31650 to the total cost
The total cost of the wings, beverage, dip and tip is 26.5825+5.31650 = 31.899
So you have $20 and you want to spend $31.899 including tax and tip, you can purchase 20/0.25 = 80 chicken wings.
Step-by-step explanation:
There is a jury of 12 people, 5 men and 7 women.
If we randomly select two people, how likely is it that they are both women?
The distance between the points (5, -1) and (x, 2x + 5) is…
distance between two points is given by √ (5x² +14x +61)
What is distance?
Length between two points that is measured along any straight line or curve line.
What is the distance between above two points?
Assume two points p (x, y) and Q (a, b). The distance between P and Q is determined by a formula.
distance PQ = √ [(a -x) ²+ (b - y²]
We are given two points (5, -1) and (x, 2x+5)
the distance between two points = √[(x- 5)² + {(2x+5) - (-1)}²]
√[(x-5) ²+ (2x+5+1) ²]
= √[(x- 5)² + (2x+6)²]
hence, distance between two points = √ (5x² + 14x+61)
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Write the rational numbers from smallest to largest
The rational numbers from smallest to largest is
5/7 < 11/15 < 3/4
What is a rational number?
In contrast to irrational numbers, which cannot be stated as fractions, rational numbers can be expressed as the ratio of two integers with the condition that the denominator not be equal to zero. Irrational numbers don't have ending or recurring decimals, but rational numbers do.
convert them into decimal numbers
3/4 = 0.75
5/7 = 0.714
11/15 = 0.733
0.714 < 0.733 < 0.75
So, the rational numbers from smallest to largest is
5/7 < 11/15 < 3/4
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Janie is a student in a science fair. Her project tracks how far a rumor can get spread throughout a school. Her data are represented by the following function:
f(x)=4(1+0.3)^1.5x
Rewrite the function to isolate x and solve for x = 8.
Janie is a student in a science fair. Her project tracks how far a rumor can get spread throughout a school.
f(x) = 8, x ≈ 8.
What is the function?Generally, To isolate x, we need to take the natural logarithm (ln) of both sides of the equation:
ln(f(x)) = ln(4) + 1.5xln(1 + 0.3)
then we can divide both sides by 1.5ln(1 + 0.3)
x = (ln(f(x)) - ln(4)) / (1.5ln(1 + 0.3))
To find x when f(x) = 8, we can substitute 8 for f(x) and solve for x:
x = (ln(8) - ln(4)) / (1.5ln(1 + 0.3))
x ≈ 8
Therefore, when f(x) = 8, x ≈ 8.
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Lucas is selling 4 pears for $5.45. How much will 5 pears
cost?
Answer:
6.8125
Step-by-step explanation:
Which table represents only values described by the relationship between t and w?
w = t + 11.2
The table of w = t + 11.2 is:
t w
0 11.2
1 12.2
2 13.2
3 14.2
4 15.2
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
w = t + 11.2
The table can be calculated as,
When t = 1, w = 1 + 11.2 = 12.2
When t = 2, w = 2 + 11.2 = 13.2
When t = 3, w = 3 + 11.2 = 14.2
When t = 4, w = 15.2
So on..
Thus,
t w
0 11.2
1 12.2
2 13.2
3 14.2
4 15.2
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help I can't do math :')
1.20C + 3 >= 13.50
Where C is the number of chores Janie does.
On the left side of the inequality, 1.20C represents the amount of money Janie earns from doing chores, and 3 represents the amount of money she already has. The inequality states that the sum of the money she earns from doing chores and the money she already has must be greater than or equal to the cost of the CD (13.50).
This inequality can be simplified:
1.20C >= 10.50
C >= 8.75
Thus, Janie could do at least 8.75 chores to have enough money to buy the CD, since she can do fractions of chores.
Answer:
3 + 1.2 c > 13.50
Step-by-step explanation:
First of all, let's write an equation that gives us the income Janie gets for doing chores. As she earns 1.20 (I will omit the $ symbol for simplicity) for each chore c she makes we can write income depending on the amount of chores as:
income(c) = 1.2 c
If she does 1 chore she gets 1.2, if she does 4 chores she gets 4.8 and so on for any c (obviously c is positive as she can do negative chores).
So, her total money will be the sum of what she earns for chores and the money she already has: 3.
money (c) = 3 + 1.2 c
If she does 2 chores she has 3+2.4=5.4 and so on for any c.
Now we need her money to be greater or equal to 13.50 in order to buy the CD. The inequality is:
money (c) > 13.50
3 + 1.2 c > 13.50
We can go further and solve it. First lets subtract 3 in both sides:
12 c > 10.50
Now, divide both sides by 1.2:
c > 10.50 / 1.2
c > 8.75
So, she needs at least 8.75 chores to earn enough money to buy the CD. As she can do fractions of chores the answer is 8.75 chores. Is she couldn't do fractions she would need at least 9 chores.
16) Similar triangle 5
r
4
X
h
*) find y if h= 3
*) find X
find r
71
3
P
The values of the variables in the similar triangles are y = 2.25 units, x = 5 units and r = 3.75 units
How to find the variables in the similar triangles?Similar triangles are triangles that have the same shape, but possibly different size. Two triangles are similar if and only if their corresponding angles are congruent, that is, they have the same measure. When two triangles are similar, their corresponding side lengths are in proportion.
Since the triangles are similar. We write:
h/y = y/3
Since h = 3, we have:
3/4 = y/3
y = 9/4 = 2.25 units
x = √(4² + h²) (Pythagoras theorem)
x = √(4² + 3²) = 5 units
r = √(y² + 3²)
r = √(2.25² + 3²) = 3.75 units
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