Calculate the following sum of mixed fractions:
[tex]517\frac{37}{50}+312\frac{3}{100}[/tex]Before adding the fractions, we should express them as improper fractions:
[tex]517+\frac{37}{50}+312+\frac{3}{100}[/tex]We can add the integers 517+312=829
And now the fractions:
[tex]\frac{37}{50}+\frac{3}{100}[/tex]Expand the first fraction to have a denominator 100:
[tex]\frac{2\cdot37}{2\cdot50}+\frac{3}{100}=\frac{74}{100}+\frac{3}{100}=\frac{77}{100}[/tex]Now we simply join the integer part with the proper fraction:
[tex]829\frac{77}{100}[/tex]It's the final answer
Let's elaborate on the sum:
[tex]\frac{37}{50}+\frac{3}{100}[/tex]We need to make both denominators equal and then add the numerators easily
For example:
[tex]\frac{3}{8}+\frac{4}{8}=\frac{7}{8}[/tex]Note the fraction 37/50 does not have the same denominator as 3/100
How can we make them equal?
Multiply by 2
both the 37 and 50
To express the result as decimal, we divide the fraction and add it to the integer:
[tex]829\frac{77}{100}=829+\frac{77}{100}=829+0.77=829.77[/tex]Directions - Graph the following slope intercept equation:y=-1/3x+4
Answer:
See below for graph
Explanation:
Given the slope-intercept equation:
[tex]y=-\frac{1}{3}x+4[/tex]To graph it, first, we find the x and y-intercepts.
When x=0
[tex]\begin{gathered} y=-\frac{1}{3}(0)+4 \\ y=4 \end{gathered}[/tex]We have the point (0,4).
When y=0
[tex]\begin{gathered} 0=-\frac{1}{3}x+4 \\ \frac{1}{3}x=4 \\ x=12 \end{gathered}[/tex]We have the point (12,0).
We then draw a line joining points (0,4) and (12,0).
find the height of a cone with a diameter of 12m whose volume is 264m ^3 . use 3.14 for π and round your answer to the nearest meter . A. 42m B. 6m C. 7mD. 2m
find the height of a cone with a diameter of 12m whose volume is 264m ^3 . use 3.14 for π and round your answer to the nearest meter .
A. 42m
B. 6m
C. 7m
D. 2m
we have that
The volume of a cone is equal to
[tex]V=\frac{1}{3}\cdot\pi\cdot r^2\cdot h[/tex]we have
V=264 m3
pi=3.14
r=12/2=6 m ------> the radius is half the diameter
substitute
[tex]264=\frac{1}{3}\cdot3.14\cdot6^2\cdot h[/tex]solve for h
[tex]\begin{gathered} h=\frac{264\cdot3}{3.14\cdot36} \\ \\ h=7\text{ m} \end{gathered}[/tex]answer is option C
write the slope intercept form:through: (-2, 3), perp. to x=0
write the slope intercept form:
through: (-2, 3), perp. to x=0
we know that
If the line is perpendicular to x=0 (y-axis), then we have a horizontal line
and the equation of a horizontal line (slope is equal to zero) is
y=3if the area of a rectangle is 6 m, then the dimension would be 2 meters by 3 meters?True or False
To be able to verify the statement, let's first recall the formula in getting the area of a rectangle:
Solve for x. 6 244 - 21.A. 0.53B. 0.45 C. 0.06 D. 0.24
ANSWER:
B. 0.45
STEP-BY-STEP EXPLANATION:
We have the following equation:
[tex]6\cdot2^{4x}^{}=21[/tex]We solve for x:
[tex]\begin{gathered} 2^{4x}=\frac{21}{6} \\ \ln \: \mleft(2^{4x}\mright)=\ln \: \mleft(\frac{7}{2}\mright) \\ 4x\cdot\ln (2)=\ln \: \mleft(\frac{7}{2}\mright) \\ x=\frac{\ln \: \mleft(\frac{7}{2}\mright)}{4\cdot\ln (2)} \\ x=0.45 \end{gathered}[/tex]The value of x is 0.45
Solve the compound inequality.2u+6<18
Given:
An inequality 2u+6<18
To find:
We have to solve the given inequality.
Solution:
Subtract 6 from both sides to get:
[tex]\begin{gathered} 2u+6-6<18-6 \\ 2u<12 \end{gathered}[/tex]Divide by 2 both sides:
[tex]\begin{gathered} \frac{2u}{2}<\frac{12}{2} \\ u<6 \end{gathered}[/tex]Thus, the solution to the inequality is u < 6.
Here’s math questions see below:Find and simplify the difference quotient f(x+h)-f(x) ___ hfor the given function: f(x)=2x-5
The given function is:
[tex]\begin{gathered} f(x)=2x-5 \\ f(x+h)=2(x+h)-5=2x+2h-5 \end{gathered}[/tex]So the expression is evaluated as follows:
[tex]\begin{gathered} \frac{f(x+h)-f(x)}{h}=\frac{2x+2h-5-(2x-5)}{h} \\ =\frac{2x+2h-5-2x+5}{h} \\ =\frac{2h}{h} \\ =2 \end{gathered}[/tex]So the value of the expression is 2.
A kid is selling cupcakes, each cupcake sold for $1.25 and cookies for $1.75, Jason sold 92.50 worth of cake and cookies if he sold both combined how many cakes were sold and how many cookies
Set x and y to be the number of cupcakes and cookies, respectively.
Therefore, according to the question,
[tex]Cost=1.25x+1.75y[/tex][tex]\Rightarrow1.25x+1.75y=92.50[/tex]There is only one provided equation; therefore, we cannot determine x and y but just x in terms of y or vice versa. To determine x and y, more information is needed.Solving for x,
[tex]x=\frac{92.50-1.75y}{1.25}[/tex]Find the y-intercept of a line that passes through (-2,6) and has a slope of -5
First find the equation of the line whose slope is -5 and passes through (-2, 6).
[tex]\begin{gathered} y-6=-5(x-(-2)) \\ y-6=-5(x+2) \\ y-6=-5x-10 \\ y=-5x-4 \end{gathered}[/tex]For y-intercept, substitute x = 0.
[tex]\begin{gathered} y=-5(0)-4 \\ y=-4 \end{gathered}[/tex]Thus, the y-intercept is -4.
It takes Anastasia 50 minutes to walk 3 1/2 miles to the park. At this rate, about how many minutes should it take her to walk 5 miles?
Answer:
about 71minutes
Explanation:
If it takes Anastasia 50 minutes to walk 3 1/2 miles to the park, then;
50 minutes = 3.5 miles
To get the time taken for her to walk 5miles;
x = 5miles
Divide both expressions
50/x = 3.5/5
Cross multiply
3.5x = 50*5
3.5x = 250
x = 250/3.5
x = 71.42miles
Hence it will take her about 71minutes to walk 5miles
A company produces standard size American flags with a measurement of 3’ x 5’. Another company produces mega American flags that are similar to this size. If the shorter side of the mega flag is 48',. What is the length of the longer side?
Solution:
Given:
[tex]\text{Standard size American flag of 3' x 5'}[/tex]Let L be the longer side of the mega flag.
Another company produces a similar flag of 48' x L
Since both flags are similar, then the ratio of the corresponding sides is equal.
Hence,
[tex]\begin{gathered} \frac{3}{5}=\frac{48}{L} \\ \\ \text{Cross multiplying the equation,} \\ 3\times L=5\times48 \\ 3L=240 \\ \\ \text{Dividing both sides by 3,} \\ L=\frac{240}{3} \\ L=80^{\prime} \end{gathered}[/tex]Therefore, the length of the longer side of the mega flag is 80'
x^2 - 9x - 36 = 0Use zero product property. Solve for x
Given the Quadratic Equation:
[tex]x^2-9x-36=0[/tex]You need to remember that the Zero Product Property states that if:
[tex]ab=0[/tex]Then:
[tex]a=0\text{ }or\text{ }b=0[/tex]In this case, you can factor the given equation by finding two numbers whose sum is -9 and whose product is -36. These numbers are 3 and -12. Then:
[tex](x+3)(x-12)=0[/tex]Based on the Zero Product Property, you know that:
[tex](x+3)=0\text{ }or\text{ }(x-12)=0[/tex]Then, by solving each part by "x", you get:
[tex]x=-3\text{ }or\text{ }x=12[/tex]Hence, the answer is:
[tex]x=-3\text{ }or\text{ }x=12[/tex]What is the x-intercept of the following graph?a. (0,2)b. (2,0)C. (0, -4)d. (-4,0)
The x-intercept is the point where the curve (line) cuts the x-axis.
Looking at the graph, the x-intercept is at x = 2.
In coordinates, it is
(2,0)
Correct Answer is B
For the function f(x)= 8/9+4xfind f-1(x)
The inverse of the function is f⁻¹(x) = x/4 - 2/9
The given function is :
f(x)= 8/9+4x
This can be written in the form of an equation such as
y = 8/9+4x
Now we have to find the value of x in terms of y
4x = y - 8 / 9
or, x = y/4 - 2/9
When a code is formed, the domain and its codomain are sometimes not clearly given, and without doing a calculation, one may just be aware that such a domain is a part of a bigger set.
A function from X to Y" often refers to an action that may accept a sufficient subset of X as its domain in mathematical analysis. A "function as from reals here to reals" might be used to explain the function of a valid real variable, for example.
Instead of the entire set of real numbers, a "function out from reals to the reals" refers to a group of real numbers with a non-empty open interval. This kind of job is
Hence the inverse of the function is given by f⁻¹(x) = x/4 - 2/9
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I need some help please out
Question:
Solution:
Let the following equation:
[tex]\sqrt[]{12-x}=\text{ x}[/tex]this is equivalent to:
[tex](\sqrt[]{12-x})^2=x^2[/tex]this is equivalent to:
[tex]12-x=x^2[/tex]this is equivalent to:
[tex]x^2+x-12=\text{ 0}[/tex]thus, we can conclude that
x= 3.
Use trigonometric ratios to determine the length of x in the right triangle below.71°5 cmRound your answer to the nearest tenth, and do not include "x ="or the units in your answer. Just enter the numericalvalue
For the given right triangle, one angle is 71 degree, and perpendicular side for angle 71 degree is x and base side is 5 cm.
Determine the measure of side x by using trigonometric ratio.
[tex]\begin{gathered} \tan 71=\frac{x}{5} \\ x=5\cdot\tan 71 \\ =14.5210 \\ \approx14.5 \end{gathered}[/tex]So value of x is 14.5 cm
Answer: 14.5
Evaluate the first operation 6^2?options: 12, 36, 6-1, 62
The operation
[tex]6^2[/tex]means that
[tex]6^2=6\times6[/tex]since 6 times 6 is equal to 36, the answer is option 2.
8 increased by 3 times a number t in expression
Question 21 and 22 list all 6 zeros, write in factored form
the zeros are
x=-1.5 -----> multiplicity 1
x=0
x=2 ----> multiplicity 2
possible function
y=-x(x+1.5)(x+2)^2 -----> leading coefficient must be negative
represents holly records
The holly records a temperature at 15 below zero
This implies that the temperature i
(1,-4) (-2,5) in slope intercept form
We want the equation of the line through the points (1, -4) and (-2, 5)
So we start by finding the slope of the segment that joins those two points using the formula for slope:
slope = (y2 - y1) / (x2 - x1)
slope = (5 - -4) / (-2 - 1) = 9 / (-3) = -3
Then the slope is -3
Now we use the general slope-intercept form of a line:
y = m x + b
with m = -3
y = -3 x + b
and request one of the points to be on the line in order to determine "b"
-4 = -3 (1) + b
- 4 = -3 + b
add 3 to both sides to isolate b on the right
- 4 + 3 = b
then b = -1
Then the equation of the line is:
y = -3 x - 1
B. When are the y-values the same? When are theydifferent?
B. When are the y-values the same? When are they
different?
Since there are absolute values, and the y =|x| and y =x will be the same when the values of x are positive and they're going to be different when the values for x are negative ones.
Like this:
y =x | y = |x|
3 y =3
-3 3
It rained 3.5 inches in the month of April. It rained 45 less in the month of May. How much did it rain in May?
It rained 1.925 inch in the month of may as the question said "It rained 3.5 inches in the month of April. It rained 45% less in the month of May".
What is inch?In both the British imperial and American customary systems of measurement, the inch serves as a unit of length. It is equivalent to 1/12 of a foot or 1/36 of a yard. The definition of an inch during King Edward II's reign was "three dry, round grains of barley placed end to end lengthwise." The lengths of 12 poppyseeds combined have also been used at various times to define an inch. Since 1959, 2.54 cm has been the official definition of an inch. One inch is exactly equal to 2.54 cm in the metric system, according to the relationship between the two units. The prefix "in" can be used to denote inches. For instance, five feet ten inches could be written as five ft ten in or five feet ten inches.
Here,
45% of 3.5 inch=1.575 inch
Since it rained 45% less than 3.5 inch so,
3.5-1.575=1.975 inch
it rained 1.925 inch in the month of may.
According to the question, it rained 1.925 inches in the month of May "In April, there was 3.5 inches of rain. May saw a 45% decrease in rainfall ".
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1. m = -2; b=5
Write an equation in slope-intercept form
Answer:
y=-2x+5
Step-by-step explanation:
Slope-intercept form is y=mx+b
BD bisects ZABC such that mZABD =(4x – 5) and mZDBC =(3x + 2)Find the value of ..17
Solution
For this case we know that
m m < DBC = 3x+2
So then we can do the following:
4x -5 = 3x+2
4x-3x = 5+2= 7
x = 7
solve using the an=a1+(n-1)d formulaa1= -20, d=-4
Answer:
[tex]a_n=-20-4(n-1)[/tex]
Explanation:
We have the formula:
[tex]a_n=a_1+(n-1)d[/tex]And we are given:
a_1 = -20
d = -4
Thus:
[tex]a_n=-20+(n-1)(-4)=-20-4(n-1)[/tex]Which type of association does the scatter plot show? ту 00:00 Weak positive 00:00 Strong negative Strong positive Nonlinear
SOLUTION
From the diagram, we can see that Scatter Plot is NON- LINEAR.
A spinner with 5 equally sized slices has 2 red slices, 2 yellow slices, and 1 blue slice. Keiko spun the dial 1000 times and got the following results. From Keiko's results, compute the experimental probability of landing on yellow
Probability is expressed as
number of favorable outcomes/number of total outcomes
But probability can also be classified as theoretical probability and experimental probability. The theoretical probability is the normal probability of each outcome while the expreimental probability is the probability of an outcome given that trials have been made.
In this scenario,
total number of trials = 400 + 195 + 405 = 1000
favorable outcomes = number of times that we landed on yellow = 405
the experimental probability of landing on yellow is
405/1000 = 0.405
caluculate the length of AC to 1 decimal place in the trapezium below.
Check the picture below.
usign the pythagorean theorem let's find the side CD, then let's get the side AC using the same pythagorean threorem.
[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2 - b^2}=a \qquad \begin{cases} c=\stackrel{hypotenuse}{16}\\ a=\stackrel{adjacent}{CD}\\ b=\stackrel{opposite}{7}\\ \end{cases} \\\\\\ \sqrt{16^2 - 7^2}=CD\implies \sqrt{207}=CD \\\\[-0.35em] ~\dotfill[/tex]
[tex]c^2=a^2+b^2\implies c=\sqrt{a^2 + b^2} \qquad \begin{cases} c=\stackrel{hypotenuse}{AC}\\ a=\stackrel{adjacent}{CD}\\ b=\stackrel{opposite}{11}\\ \end{cases} \\\\\\ AC=\sqrt{(\sqrt{207})^2~~ + ~~11^2}\implies AC=\sqrt{207 + 121}\implies \boxed{AC\approx 18.1}[/tex]
Use the information in the table to complete the remaining information. Note: The section to the right of the table states "Rewrite the information from the table as a list of ordered pairs in the form of (height, shoe size).
Given:
A table represents the height and the shoe size of seven students
We will rewrite the information from the table as a list of ordered pairs in the form of (height, shoes size).
So, the order pairs will be as follows:
[tex]\lbrace(5^{\prime}6^{\prime}^{\prime},8),(5^{\prime}7^{\prime}^{\prime},9),(5^{\prime}8^{\prime}^{\prime},9),(5^{\prime}10^{\prime}^{\prime},10),(6^{\prime}6^{\prime}^{\prime},13),(5^{\prime}10^{\prime}^{\prime},12),(5^{\prime}8^{\prime}^{\prime},11)\rbrace[/tex]A mapping diagram:
The table could be represented by the relationship as shown in the following figure: