Answers
x/8 = 3/4
cross multiply...multiply denominator of one, by numerator of the other and vice-versa
(4)(x) = (3)(8)
4x = 24
x = 24/4
x = 6
sub it back into the proportion
6/8 = 3/4.....notice that if u reduce 6/8, it equals 3/4. Proportions are nothing but equivalent fractions.
====================
2/5 = x/40
cross multiply
(5)(x) = (40)(2)
5x = 80
x = 80/5
x = 16
check..
2/5 = 16/40... u can aslo cross multiply to check
(2)(40) = (5)(16)
80 = 80...correct
===================
1/8 = x/12
cross multiply
(8)(x) = (1)(12)
8x = 12
x = 12/8
x = 3/2
check...
1/8 = (3/2) / 12
cross multiply
(8)(3/2) = (12)(1)
24/2 = 12
12 = 12 (correct)
=================
I am gonna leave u with the last one....u can do this :)
Related Questions
How do you simplify the square root of 27?
Answers
[tex] \sqrt{27} = \sqrt{9*3} [/tex]
Now break up the 9 into its perfect square:
[tex] \sqrt{(3*3)*3} [/tex]
Because there are 3 3's you can pull out the root of 9, which is one of those 3's. It will then simplify to
[tex]3 \sqrt{3} [/tex]
If you had the square root of 8, that would simplify to
[tex] \sqrt{8} = \sqrt{4*2} [/tex]
4 is a prfect square (2 times 2), so you can pull out a 2, leaving the other 2 under the radical
[tex] \sqrt{4*2} = \sqrt{(2*2)*2} =2 \sqrt{2} [/tex]
Hope that makes sense. If you'd like some more examples to help clarify, just ask!
What is the number of degrees in the measure of each exterior angle of a regular polygon of 18 sides?
Answers
If 4 less than a number is less than 4 and greater than -3, find the number.
Answers
many (if integers: 2, 3, 4, 5, 6, and 7) Are you sure it is greater than -3?
In ΔABC shown below, point A is at (0, 0), point B is at (x2, 0), point C is at (x1, y1), point D is at x sub 1 over 2, y sub 1 over 2, and point E is at the quantity of x sub 1 plus x sub 2 over 2, y sub 1 over 2: Triangle ABC is shown. Point D lies on segment AC and point E lies on segment BC. A segment is drawn between points D and E. Point A is at the origin. Prove that segment DE is parallel to segment AB.
Answers
Segment AB has slope 0. Segment DE, with midpoints of AC and BC, also has slope 0. Thus, DE is parallel to AB.
To prove that segment DE is parallel to segment AB, we need to show that the slopes of both segments are equal.
The slope of segment AB, denoted as [tex]\( m_{AB} \)[/tex], can be calculated using the coordinates of points A and B:
[tex]\[ m_{AB} = \frac{{y_B - y_A}}{{x_B - x_A}} \][/tex]
Given that point A is at (0, 0) and point B is at [tex]\((x_2, 0)\)[/tex], the slope [tex]\( m_{AB} \)[/tex] is:
[tex]\[ m_{AB} = \frac{{0 - 0}}{{x_2 - 0}} = 0 \][/tex]
Now, let's find the coordinates of points D and E.
Point D lies on segment AC, so it is at the midpoint of segment AC. Therefore, the coordinates of point D, denoted as [tex]\((x_{D}, y_{D})\)[/tex], are the average of the coordinates of points A and C:
[tex]\[ x_{D} = \frac{{x_1 + 0}}{2} = \frac{{x_1}}{2} \][/tex]
[tex]\[ y_{D} = \frac{{y_1 + 0}}{2} = \frac{{y_1}}{2} \][/tex]
Similarly, point E lies on segment BC, so it is at the midpoint of segment BC. Therefore, the coordinates of point E, denoted as [tex]\((x_{E}, y_{E})\)[/tex], are the average of the coordinates of points B and C:
[tex]\[ x_{E} = \frac{{x_1 + x_2}}{2} \][/tex]
[tex]\[ y_{E} = \frac{{y_1 + 0}}{2} = \frac{{y_1}}{2} \][/tex]
Now, let's calculate the slope of segment DE, denoted as [tex]\( m_{DE} \)[/tex]:
[tex]\[ m_{DE} = \frac{{y_{E} - y_{D}}}{{x_{E} - x_{D}}} \][/tex]
Substituting the coordinates of points D and E:
[tex]\[ m_{DE} = \frac{{\frac{{y_1}}{2} - \frac{{y_1}}{2}}}{{\frac{{x_1 + x_2}}{2} - \frac{{x_1}}{2}}} \][/tex]
[tex]\[ m_{DE} = \frac{0}{{\frac{{x_1 + x_2 - x_1}}{2}}} \][/tex]
[tex]\[ m_{DE} = 0 \][/tex]
Since the slopes of segments AB and DE are both equal to 0, we can conclude that segment DE is parallel to segment AB.
Name the binomial you can multiply by (x + 9) to get the product x 2 + 5x – 36. A. 4 – x B. x + 6 C. x – 4 D. x – 6
Answers
To factor the quadratic equation, find two numbers that add to 5 and multiply to -36.
I got 9 and -4.
So, the factors are (x + 9) and (x - 4).
So, C x - 4 is the answer.
7x7-9exponent x 7 7exponent
Answers
[tex]7 * 7 ^{-9}* 7 ^{7}= \\ =7 ^{1-9+7}= \\ = 7 ^{-1} [/tex] = 1/7
Answer: 1/7
Answer:
1/7
Step-by-step explanation:
Grace is half her father joseph's age. in 10 years grace will be three-fifths joseph's age. ten years ago, grace was one third joseph's age. how old are grace and joseph now
Answers
After setting up a system of equations based on the given age relationships and solving for both Grace and Joseph, we deduce that Grace is 20 years old and Joseph is 40 years old currently.
Let's denote Grace's current age as G and Joseph's current age as J. According to the problem, Grace is half of Joseph's age, so we have the first equation:
G = 0.5 * J
In 10 years, Grace will be three-fifths of Joseph's age, giving us the second equation:
G + 10 = (3/5) * (J + 10)
Ten years ago, Grace was one-third of Joseph's age, which gives us the third equation:
G - 10 = (1/3) * (J - 10)
We now have a system of three equations with two variables. We can solve this system to find the current ages of Grace and Joseph. After solving for G and J, we find that Grace is 20 years old and Joseph is 40 years old.
Use allfour operations only once without parentheses to write an expression that has a value of 100 only using 3's
Answers
There are a lot of ways to write an expression using only 3 to get an answer of 100. Some examples are:
1st example:
3 / 3 + 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3
= 1 + 99
= 100
2nd example:
3 / 3 + 3 * 3 * 3 * 3 + 3 * 3 * 3 – 3 * 3
1 + 81 + 27 – 9 = 100
The estimated measurements of the objects are shown below.
-length of a grain of salt: 0.0002 centimeters
-width of a key ring: 0.02 centimeters
Find the measurements written in standard notation to the estimated measurements in scientific notation.
Answers
The standard notation 0.0002 cm becomes 2 × 10^-4 and 0.02 cm becomes 2 × 10^-2, both in scientific notation.
Explanation:The standard notation for 0.0002 centimeters is 2 × 10^-4 in scientific notation. Meanwhile, the standard notation for 0.02 centimeters is 2 × 10^-2 in scientific notation.
You arrive at these translations by recognizing that the number 0.0002 means you've moved the decimal point four units to the right from 2 (thus raising 10, the base, to -4), and 0.02 represents moving the decimal point two units to the right from 2 (thus raising 10 to the -2).
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In which one of the above figures is AB = AC?
A. Figure B
B. Figure C
C. Figure A
D. Figure D
Answers
Answer: The answer is (D). the image is attached.
Step-by-step explanation: We are given four figures from which we are to select the one with AB = AC.
In figure (A), AB and AC are two chords of the circle with common point A. Since the lengths of two chords of a circle may not be equal, so AB may not be equal to AC. This option is not correct.
In figure (B), AB is a tangent at point B and AC is the extension of a chord which meets the tangent AB at point A. Since the lengths of AB and AC may not be equal, so this option is also incorrect.
In figure (C), AB and AC are extensions of two chords which meets at point A outside the circle, so they may not be congruent. So, this option will also not work.
In figure (D), AB and AC are two tangents from a common point A to the circle at B and C respectively.
We have the Two-Tangent Theorem which states that if two tangent segments are drawn to one circle from the same external point, then they are congruent.
So, we have AB ≅ AC.
Thus, (D) is the correct option.
In which section of the number line is √32?
Answers
sqrt(32) = 5.66
so it is in section B
Answer:
section B.
YOUR WELCOME
The scatter plot shows the test scores of a group of students who surfed the Internet for different amounts of time in a day.
What will most likely happen to the test scores of students if the number of hours they surf the Internet increases?
Test scores will decrease because the graph shows a negative association.
Test scores will increase because the graph shows a positive association.
Test scores will increase because the graph shows a negative association.
Test scores will decrease because the graph shows a positive association.
Answers
Answer: The correct answer is "Test scores will increase because the graph shows a negative association."
Step-by-step explanation: Negative association is decreasing and positive is increasing but in this case we flip it to get our answer.
The impact of time spent surfing the internet on students' test scores depends on whether the association represented on the scatter plot is positive or negative. In a positive association, scores increase with increased internet time, while in a negative association, scores decrease.
Explanation:Based on the question, it seems there is a relationship between the time spent surfing the Internet and students' test scores which is represented by a scatter plot. The association between these variables can be either positive, negative, or no association. A positive association means as the hours of surfing the internet increase, the test scores also increase. A negative association implies that as the hours of surfing the internet increase, the test scores decrease.
However, the question didn't provide the information about whether the scatter plot shows a positive or a negative association between these two variables, which is crucial to determine what happens to the test scores as internet surfing time increases.
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A game spinner is divided into 5 equal sections numbered 1 to 5. How many outcomes are in the sample space for 4 spins of this spinner? a. 625 b. 125 c. 20 d. 500
Answers
spin 2 ~ 5
spin 3 ~ 5
spin 4 ~ 5
5 * 5* 5 * 5 = 5^ 4 = 625
Letter A
The correct option is a. 625.
The total number of outcomes in 4 spins of the spinner can be found by multiplying the number of outcomes in one spin by itself 4 times, resulting in 625 outcomes.
The sample space for 4 spins of the spinner can be calculated by raising the number of outcomes in one spin to the power of the number of spins.
In this case, as there are 5 outcomes on the spinner, the total number of outcomes in 4 spins would be 5^4 = 625.
Therefore, the correct option is a. 625.
If the area of a rectangle is 16 then the length is 4 and the width is 4 what is the counterexample
Answers
A file that is 256 megabytes is being downloaded. If the download is 18.6% complete, how many megabytes have been downloaded? Round your answer to the nearest tenth.
Answers
The calculation would be: 256 megabytes x 0,186= 47.616 megabytes.
If you round up the answer to nearest tenth it will be 47.6 megabytes
the line of best fit drawn on a scatter plot ____
A. is a line that goes through each data plot.
B. always has a positive slope.
C. is a line drawn through the first and last points.
D. approximates the linear relationship of the data.
Answers
A city's current population is 1,000,000 people. It is growing at a rate of 3.5% per year. The equation P=1,000,000(1.035)^x models the city's population growth where x is the number of years from the current year. In approximately how many years will the pooulation be 1,400,000? Round to nearest tenth
Answers
P=1,000,000(1.035)^x
We substitute the population desired to be reached to the equation and evaluate the value of x.
P=1,000,000(1.035)^x
1400000=1,000,000(1.035)^x
7/5 = 1.035^x
ln 7/5 = ln 1.035^x
x = ln 7/5 / ln 1.035
x = 9.78
Therefore, the number of years needed to reach a population of 1400000 with a starting population of 1000000 would be approximately 10 years.
2[18-(5+9)÷7]
show how you did it
Answers
PEMDAS
do parntheases
then exponents
then mutiply or divide, whichever coms first
then addd or subtract, whichever comes first
so
when doing parenthases, simplify innermost parenthsees first
so
2(18-(5+9)/7)
innermost is (5+9)=14
now we gots
2(18-(14)/7)
we can distribute or multiply the invisible -1 in front of the 14
2(18-14/7)
now divide because division comes before adition
remember that it is -14/7, not just 14/7 because the negative is part of the 14
2(18-2)
now simplify parenthasees
18-2=16
so
2(16)
multiply
32
the result is 32
Help thank you :((((((((((((((((((
Answers
The line is not dashed, so it is more than or equal to since the shading is above the line.
The slope of the line going up is 1 (rise over run). The line is dashed and it is shaded below the line so the sign must be <.
Final answer: D
Use a translation rule to describe the translation of X that is 1 units to the left and 6 units up.
A.
T < -1, 6> (x)
B.
T < -1, -6> (x)
C.
T < 1, 6> (x)
D.
T < 1, -6> (x)
Answers
Answer:
C. < 1,6 > (x)
Step-by-step explanation:
We know that,
Translation is the transformation that shifts the image in any direction.
The general form of horizontal translation of f(x) to f(x±k) and vertical translation of f(x) to f(x)±k where k is any constant.
Now, as the given function 'X' is translated 1 unit to the left i.e. translated horizontally by 1 unit i.e. X+1.
Also, the function is translated 6 units up i.e. translated vertically by 6 units i.e. X+6.
Hence, the solution is < 1,6 >(x).
Using the Degree minute second method to describe an angle, one degree of angle measurement can be divided into how many minutes?
Answers
Indicate a general rule for the nth term of this sequence. 12m, 15m, 18m, 21m, 24m,...
a. = 3mn + 9m
b. = -3mn - 9m
c. = -3mn + 9m
d. = 3mn - 9m
Answers
12m, 15m, 18m, 21m, 24m, ...,
The 1st term is a₁ = 12m
The 2nd term is a₂ = 15m = a₁ + 3m = a₁ + (2-1)*3m
The 3rd term is a₃ = 18m = a₂ + 3m = a₁ + (3-1)*3m
Because each successive term is 3m more than the previous term, we have an arithmetic sequence with a common difference of 3.
Answer:
The n-th term is
[tex]a_{n} = a_{1} + (n-1)*(3m),\\for\, n=1,2,3,\,...,[/tex]
In recursive form,
[tex]a_{n+1}=a_{n}+3m[/tex]
I just need the answers for this.im really confused
Answers
We have weekly saving of $2.50, the target amount of $85.98 and the amount carried forward from birthday present of $35, We want to work out the number of weeks we need to save to buy season pass
By working backwards, the steps are
[tex]85.98-35=50.98[/tex] ⇒ We subtract the birthday money from the season-pass fee
[tex]50.98/2.50 = 20.392[/tex] ≈ 21 Weeks ⇒ We divide by the amount we save every week
The answer is rounded up to 21 weeks
Question b)
Let the number of weeks be '[tex]x[/tex]' and the season-pass fee be '[tex]y[/tex]'
The equation that represents the context is
[tex]y=35+25x[/tex]
In words: To achieve the value [tex]y[/tex] we need to multiply [tex]x[/tex] by $2.50 (saving) and add $35 (birthday money)
We know that [tex]y=85.98[/tex] as this is the amount we aim to achieve by saving $2.50 per week. Substituting this into the equation we formed earlier we have
[tex]85.98=35+2.5x[/tex] ⇒ Subtract 35 from both sides
[tex]85.98-35=35-35+2.5x[/tex]
[tex]50.98=2.5x[/tex] ⇒ Divide both sides by 2.5
[tex] \frac{50.98}{2.5}= \frac{2.5x}{2.5} [/tex]
[tex]x=20.392[/tex] ≈ 21
We round the answer to 21 weeks. We achieve the same answer with part a)
Question c)
This time, we aim to save $85.98 by the end of 11th week. We might need to adjust the amount we save per week. We will use the same equation we form in part b) but this time we will use the variable [tex]'s'[/tex] to represent the amount of weekly saving.
[tex]y=35+11s[/tex] ⇒ where [tex]y[/tex] is the season pass fee, '35' is the birthday money, '11' is the number of weeks, and [tex]'s'[/tex] is the amount of saving
We have [tex]y=85.98[/tex]
[tex]85.98=35+11s[/tex]
[tex]85.98-35=11s[/tex]
[tex]50.98=11s[/tex]
[tex]s= \frac{50.98}{11}=4.6345 [/tex] ≈ 5
The answer is $5 to be saved for 11 weeks to achieve $85.98
----------------------------------------------------------------------------------------------------------------
Use the same equation to work out the number of weeks we need to save $2.50 per week if we have to pay the higher price of season pass fee of $120.98
[tex]y=35+2.50x[/tex]
[tex]120.98=35+2.5x[/tex]
[tex]120.98-35=2.5x[/tex]
[tex]85.98=2.5x[/tex]
[tex]x= \frac{85.98}{2.5}=34.392 [/tex]≈ 35 weeks
-----------------------------------------------------------------------------------------------------------
If we can start saving as early as possible, then 21 weeks of $2.50/week would work for the cheaper price of season-fee and we don't need to adjust the budget. However, if we still want to aim for $85.98 season pass fee, but only have fewer weeks to save, then adjusting budget is necessary. We can perhaps decide not to go bowling every week so we can use the budget for saving instead, or we can alternate between bowling and movie every week.
Question d)
Using the original budget, we work out a third of $2.50 which is 2.5÷3 = 0.83
It means we have 2.5-0.83 = 1.6 left to save weekly.
Using the same equation with part b)
[tex]y=35+1.6x[/tex] ⇒ Notice that we adjust the constant 2.5 to 1.6
[tex]85.98 = 35+1.6x[/tex] ⇒ We still aim to save for the cheapest season-pass
[tex]85.98-35=1.6x[/tex]
[tex]50.98=1.6x[/tex]
[tex]x= \frac{50.98}{1.6}=31.8625 [/tex] ≈ 32 weeks
We will have 32 weeks × $0.83 = $26.56 to buy gift for Mother.
Question e)
From information from part a) to part d), there are many different ways to adjust the budget.
Evaluate the function rule for the given value. Y=12×3^x for x=-2
Answers
3^-2= 1/(3^2)
3^-2=1/9
Now plus this value in to the rest of the equation.
y=12*1/9
12/9 simplifies to 4/3
y=4/3
Answer:
The value of function at x = -2 is [tex]\frac{4}{3}[/tex].
Step-by-step explanation:
Given : Function [tex]Y=12\times 3^x[/tex]
We have to evaluate the given function at x = - 2
Consider the given function [tex]Y=12\times 3^x[/tex]
Since, y is a function in terms of x.
So, put x = - 2 in given function.
We get,
[tex]Y=12\times 3^{-2}[/tex]
Since, [tex]3^{-2}=\frac{1}{3^2}=\frac{1}{9}[/tex]
[tex]Y=12\times \frac{1}{9}[/tex]
Simplify, we have,
[tex]Y=\frac{4}{3}[/tex]
Thus, The value of function at x = 2 is [tex]\frac{4}{3}[/tex].
The point-slope form of the equation of the line that passes through (–9, –2) and (1, 3) is y – 3 = 1/2 (x – 1). What is the slope-intercept form of the equation for this line?
Answers
[tex]y-3= \frac{1}{2} (x-1)[/tex]
[tex]y-3= \frac{1}{2}x- \frac{1}{2} [/tex]
[tex]y= \frac{1}{2} x- \frac{1}{2} +3[/tex]
[tex]y= \frac{1}{2} x- \frac{1}{2} + \frac{6}{2} [/tex]
[tex]y= \frac{1}{2} x+ \frac{5}{2} [/tex]
Answer:
[tex]y=\frac{x}{2}+\frac{5}{2}[/tex]
Step-by-step explanation:
Hello
thanks for asking this question, I think I can help you with this
if you have the point-slope form of the equation of a line, just isolate "y" to find the slope-intercept form
Step 1
[tex]y-3=\frac{1}{2} (x-1)\\\\y-3=\frac{x}{2}-\frac{1}{2} \\Add\ 3\ in\ both sides\\\\y-3+3=\frac{x}{2}-\frac{1}{2} +3\\y=\frac{x}{2}-\frac{1}{2}+3\\y=\frac{x}{2}+\frac{5}{2}[/tex]
so the answer is
[tex]y=\frac{x}{2}+\frac{5}{2}[/tex]
where 1/2 is the slope, and 5/2 is the intercept with y-axis
I really hope it helps , Have a great day.
The tile pattern shown was used in Pompeii for paving. If the diagonals of each rhombus are 2 inches & 3 inches, what area makes up each cube in the pattern?
Answers
A ( rhombus ) = d1 * d2 / 2
d1 = 2 in, d2 = 3 in.
A ( rhombus ) = 2 * 3 / 2 = 3 in²
Finally: 3 * 3 = 9 in²
Answer: Area of each cube in the pattern is 9 in².
Someone pls help me!! and thank you if you do !
Answers
Q and R are independent events. If P(Q)= 1/8 and P(R)=2/5 find P(Q and R).
Answers
To find P(Q and R), you have to multiply P(Q) by P(R) to get the probability that both events will occur. P(Q) = 1/8, and P(R) = 2/5, so when multiplied together, you get 2/40. This simplifies to 1/20, meaning P(Q and R) = 1/20.
The probability of independent events Q and R both occurring is calculated by multiplying the individual probabilities of each event. Thus in this case, P(Q and R) = (1/8) * (2/5) = 1/20.
Explanation:The question posed asks for the probability of events Q and R both occurring. Given that Q and R are independent events, the likelihood of both happening is calculated by multiplying the probabilities of each event.
That is, P(Q and R) = P(Q)P(R). From the question, we know that P(Q) is 1/8 and P(R) is 2/5.
Therefore, the probability of both Q and R occurring would be (1/8) * (2/5) = 1/20.
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How were the numbers 1 10 100 and 1000 written by romans?
Answers
10 -- X
100 -- C
1000 -- M
Which of the following is a solution to the inequality y < –2x + 3?
A. (1,1)
B. (3,0)
C. (-3,10)
D. (0,0)
Please select the best answer from the choices provided
Answers
y < -2x +3
A. (1, 1) → x = 1, y = 1
substitute:
1 < -2(1) + 3
1 < 1 FALSE
B. (3, 0) → x = 3, y = 0
substitute
0 < -2(3) +3
0 < -3 FALSE
C. (-3, 10) → x = -3, y = 10
substitute
10 < -2(-3) +3
10 < 9 FALSE
D. (0, 0) → x = 0, y = 0
substitute
0 < -2(0) + 3
0 < 3 CORRECT
Answer: D. (0, 0)