Answer:
x = 19
Step-by-step explanation:
When a triangle is cut by a line parallel to its base, the resulting two triangles are similar. That means corresponding sides are proportional (their ratios are equal).
There are several ways the ratios can be written, but I like to choose one that has the variable in the numerator. Here's the proportion and its solution.
[tex]\dfrac{x+5}{16}=\dfrac{30}{20}\\\\x+5=24\qquad\text{multiply both sides by 16}\\\\x=19\qquad\text{subtract 5 from both sides}[/tex]
_____
Additional comment
Technically, the corresponding sides of the triangles would be ...
entire long side of larger triangle: ((x+5) +30) and long side of smaller triangle (30)entire short side of larger triangle (36) and short side of smaller triangle (20)Since the parts labeled (x+5) and 16 are each the same fraction of their entire side, those parts are corresponding also, and will have the same proportion as other corresponding sides.
Fill in the table using this function rule
Lia can rent a van for either $90 per day with unlimited mileage or $50 per day with 250 free miles and 25 cents for each mile over 250. for what number of miles traveled in one day would the unlimited mileage plan save Lia money?
Answer:
The unlimited mileage plan would save money for Lia from 410 miles onwards.
Step-by-step explanation:
Since Lia can rent a van for either $ 90 per day with unlimited mileage or $ 50 per day with 250 free miles and an extra 25 ¢ for each mile over 250, to determine for what number of miles traveled in one day would the unlimited mileage plan save Lia money, the following calculation must be performed:
90.25 - 50 = 40.25
40.25 / 0.25 = 161
161 + 250 = 411
Therefore, the unlimited mileage plan would save money for Lia from 410 miles onwards.
How do find the median and range..?
give examples!
Answer:
Count how many numbers you have. If you have an odd number, divide by 2 and round up to get the position of the median number. If you have an even number, divide by 2. Go to the number in that position and average it with the number in the next higher position to get the median.
The range is calculated by subtracting the lowest value from the highest value.
Step-by-step explanation:
hope this helped!
Answer:
It is the number in the middle of a set of numbers arranged in ascending order, it will be easier to find median if the set of given numbers are even if its an odd number, then divide the number by 2.
To find the range subtract the lowest value from the highest value
Step-by-step explanation:
on
ning
Solve for x and y.
x
128°
у
Answer:
y88 porty forty
YoungBoy
Answer:
x = 52°
y = 128°
Step-by-step explanation:
This is an isosceles trapezoid as the legs are the same length (denoted by the double dashes).
For an isosceles trapezoid, the sets of angles adjoined by parallel lines are equal. Therefore, for this trapezoid, y = 128 and the two remaining angles are both x.
The interior angles of a trapezoid = 360°
Therefore, x + x + 128 + y = 360
Since we know y = 128:
2x + 128 + 128 = 360
⇒ 2x = 104
⇒ x = 104 ÷ 2 = 52
What is the factorization of the trinomial below?
3x2 - 21x + 30
O A. 3(x-6)(x - 5)
O B. 3(x-2)(x - 5)
O C. 3x(x-2)(x-5)
O D. 3x(x-6)(x - 5)
B if not C, with the exponent of the coefficient
The factorization of the trinomial is A = 3 ( x - 2 ) ( x - 5 )
What is Factorizing?Brackets should be expanded in the following ways to factorize an expression
For an expression of the form A = a ( b + c ) , the expanded version is given by A = ab + ac, i.e., multiply the term outside the bracket by everything inside the bracket
For an expression of the form A = ( a + b ) ( c + d ) , the expanded version is given by A = ac + ad + bc + bd, in other words everything in the first bracket should be multiplied by everything in the second.
Given data ,
Let the expression be represented as A
Now , the value of A is
A = 3x² - 21x + 30 be equation (1)
On simplifying , we get
Taking 3 as the common factor of the expression , we get
A = 3 ( x² - 7x + 10 )
A = 3 ( x² - 2x - 5x + 10 )
On factorizing , we get
A = 3 ( x - 2 ) ( x - 5 )
Hence , the expression is A = 3 ( x - 2 ) ( x - 5 )
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4(x+6)≤−56 it says Solve the inequality.
[tex] \huge\tt\boxed{\tt x \leqslant −20}[/tex]
Step-by-step explanation:
[tex] \looparrowright \sf4x+24 \leqslant −56[/tex]
[tex] \\ \\ [/tex]
[tex] \looparrowright \sf4x \leqslant −56 - 24[/tex]
[tex] \\ \\ [/tex]
[tex] \looparrowright \sf4x \leqslant −80[/tex]
[tex] \\ \\ [/tex]
[tex] \looparrowright \sf x \leqslant −80 \div 4[/tex]
[tex] \\ \\ [/tex]
[tex] \looparrowright \sf x \leqslant −20[/tex]
The probability that an event will happen is
37/41. Find the probability that the event will not happen.
Answer: 4/41?
Step-by-step explanation:
Is that what you wanted?
Or do you need it as a percentage?
please help me i am stuck, i need better instructions. i dont want an answer. tysm for ur time.
Answer:
38 in²
Step-by-step explanation:
5 faces:
front: area = 2*6/2 = 6
back = front = 6
left = 3 * 2 = 6
right = 4*2 = 8
bottom = 6*2 = 12
total = 6 + 6 + 6 + 8 + 12 = 38 in²
A spinner contains four sections red, blue, green, and yellow. Joaquin spins the spinner twice. The set of outcomes is
given as S = (RB, RG, RY, RR, BR, BG, BY, BB, GR, GB, GY, GG, YR, YB, YG, YY). If the random variable is "yellow
(Y)," which of the
following is the correct probability distribution?
Answer:
its A
Step-by-step explanation:
The solution is, the correct probability distribution is 1/16.
What is probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
here, we have,
Given that,
spinner contains four sections: red, blue, green, and yellow. Joaquin spins the spinner twice. The set of outcomes is given as
S = {RB, RG, RY, RR, BR, BG, BY, BB, GR, GB, GY, GG, YR, YB, YG, YY}.
If the random variable is “yellow (Y),” let us first find the values that Y can take.
From the sample space given above, we find that Y can take only 3 values 0,1,2
In the sample space of 16 entries, Y occurs 0 times in 9 times
1 time in 6 times and 2 times 1 time
Hence probability = no of favouable outcomes/number in sample space
So
P(Y=0) = 9/16
P(Y=1) = 6/16 = 3/8
P(Y=2) = 1/16
Hence, The solution is, the correct probability distribution is 1/16.
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Find the volume and surface area of this triangular prism. 12 cm 13 cm 18 cm and 5 cm
Answer:
V=180
Step-by-step explanation:
volume of the triangle =b×h
B means that the base of the prism.
to find the base use heron's formula.
and multiple with hight.
s=A+B+C/2
s=5+12+13/2=15
A=root over 15 (15-5)(15-12)(15-13) = 30
V=b×h
V=30×6
V=180
help please whats the distance
someone please help me please please please help me please please please please please please please please please with these quadratic equations
Answer:
5, 22, 16
Step-by-step explanation:
10. t = 5
11. k = 22
12. z = 16
Find the volume of the irregular figure 1cm 2cm 8cm 1cm 3x 3pm 5cm
Solve for x.
−4/5x+3/10<8/10
Answer:
for (−4/5)x + 3/10 < 8/10: solution is x > -5/8
for −4/(5x) + 3/10 < 8/10: solution is x > -8/5
Step-by-step explanation:
I'm not exactly sure if you mean -4 divided by 5x or (-4/5)x, so I've done both! :)
[tex]-\frac{4}{5}x+ \frac{3}{10} < \frac{8}{10}[/tex]
subtract 3/10 from both sides: [tex]-\frac{4}{5}x < \frac{5}{10}[/tex]
Divide both sides by 4/5: [tex]-x < \frac{5}{8}[/tex]
Divide both sides by -1 (reverse sign): [tex]x > -\frac{5}{8}[/tex]
[tex]-\frac{4}{5x}+ \frac{3}{10} < \frac{8}{10}[/tex]
subtract 3/10 from both sides: [tex]-\frac{4}{5x} < \frac{5}{10}[/tex]
Multiply both sides by 5x: [tex]-4 < \frac{5}{2}x[/tex]
Divide both sides by 5/2: [tex]x>- \frac{8}{5}[/tex]
[tex]\\ \tt\longmapsto \dfrac{-4}{5}x+\dfrac{3}{10}<\dfrac{8}{10}[/tex]
[tex]\\ \tt\longmapsto \dfrac{-4}{5}x<\dfrac{5}{10}[/tex]
[tex]\\ \tt\longmapsto -4/5x<1/2[/tex]
[tex]\\ \tt\longmapsto x>-5/8[/tex]
Ling Ling collected(587) stickers and Jia Jia collected 245 stickers. After giving 40 stickers to their cousin, they put the remainder equally into(36 boxes. How many stickers were there in each box?
Answer:
22 stickers in each box
Step-by-step explanation:
Ling Ling = 587 stickers
Jia = 245 stickers
Therefore, total number of stickers = 587 + 245 = 832
if they gave 40 stickers to their cousin, then
remaining stickers = 832 - 40 = 792
If they put the remaining 792 stickers equally into 36 boxes, then
number of stickers in each box = 792 ÷ 36 = 22
Susan Marciano invested part of her 28,000 bonus in a fund that paid an 11% profit and invested the rest in stock that suffered a 5% loss. Find the amount of each investment if her overall profit was 2,920
a = amount that paid 11% profits
b = amount that lost 5% profits
we know that whatever those values are, a + b = 28000.
how much is 11% of "a"? well, (11/100) * a = 0.11a.
how much is 5% of "b"? well (5/100) * b = 0.05b.
[tex]a+b=28000\implies b=28000 - a \\\\[-0.35em] ~\dotfill\\\\ \stackrel{paid~11\%}{0.11a}~~ \stackrel{\stackrel{loss}{\downarrow }}{-} ~~\stackrel{lost~5\%}{0.05b}~~ = ~~\stackrel{overall~paid}{2920} \\\\\\ \stackrel{\textit{substituting on the 2nd equation}}{0.11a~~ - ~~0.05(28000-a)}=2920\implies 0.11a+0.05a-1400=2920 \\\\\\ 0.16a-1400=2920\implies 0.16a=4320\implies a=\cfrac{4320}{0.16} \\\\\\ \boxed{a=27000}~\hspace{10em}\boxed{\stackrel{28000-a}{b=1000}}[/tex]
Rotate Polygon HJKL 180° about
the origin, reflect it across the
y-axis, and then reflect it across
the x-axis. Write the coordinates
of the vertices of the image
Polygon H'U'K'L'. How do the
vertices of Polygon H'U'K'L'
compare to the corresponding
vertices of Polygon HJKL?
Please help, I will
mark as brainliest ;)
Which statement is true about liabilities but not expenses
A. They have a normal debit balance.
B. They are due in the period they are incurred.
C. They are on the company’s income statement
D. They are recorded when owed
Answer:
B. They are recorded when owed
Step-by-step explanation:
Hope this helps
A line passes through the point (3,6) and has a slope of 7. Write an equation in point-slope form for this line.
[tex](\stackrel{x_1}{3}~,~\stackrel{y_1}{6})\qquad \qquad \stackrel{slope}{m}\implies 7 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{7}(x-\stackrel{x_1}{3})[/tex]
Answer:
[tex]y=7x-15[/tex]
Step-by-step explanation:
Given the following question:
Point A = (3, 6) = (x1, y1)
m (slope) = 7
We will find the equation of this line by finding the slope intercept.
[tex]y=mx+b[/tex]
[tex]y=6[/tex]
[tex]m=7[/tex]
[tex]x=3[/tex]
[tex]6=7(3)+b[/tex]
[tex]7\times3=21[/tex]
[tex]21-21=0[/tex]
[tex]6-21=-15[/tex]
[tex]b=-15[/tex]
[tex]y=7x-15[/tex]
Hope this helps.
Select each value of a for which you can solve the system by elimination without multiplying first.
2x+5y=16
ax+3y=6
Answer: dddss Ggg. Nj
Step-by-step explanation:
can you please solve this question please
Answer:
B. False.
Step-by-step explanation:
4 (x + 6) = 24
4x + 24 = 24
4x = 0
x = 0
Therefore, answer choice B is the correct answer.
........................................................................................................................................................................................................................................................................................................
Answer:
what in the world is this?
7 times as much as the sun of 1/3and 4/5
Answer:
Step-by-step explanation:
First of all, you add 1/3 and 4/5, so you get:
To add 2 fractions, they need to have the same denominator. Since 3 and 5 don't have a common factor, so you multiply 1/3 by 5, and 4/5 by 3, so you get:
Now, the two fractions got the same denominator, and you can add them by adding the numerators over the same denominator. (You don't add denominators in addition) so you get:
That's the sum of 1/3 + 4/5.
Now, they want the sum of the 2 fractions 7 times. So you multiply 17/15 by 7. And as you know, 7 = 7/1. So you get:
In multiplication no need to have the same denominator. You multiply nominators by nominators and denominators by denominators. So you get:
Since 119 and 15 don't have a common factor, so they can't be simplified.
So, the answer is 119/15.
Hope this Helps! :D
Hunter is filling his swimming pool with water. Write a description of what is happening in the graph below.
Answer:The more gallons, the more time Hunter spent to fill it.
Step-by-step explanation:
Both increase as they grow.
Brainliest if correct
Answer:
x=29
Step-by-step explanation:
We know y is 16. We can write 16 instead of y in the equation.
y=x-13
16=x-13
Now we can add 13 to both sides of the equation.
16+13=x-13+13
29=x
x is equal to 29.
Answer:
x = 29
Step-by-step explanation:
since y = 16
16 = x -13
Add 13 to both sides of the equation
16 + 13=x-13+13
Simplify
x = 29
[RevyBreeze]
Choose Yes or No to tell if the fraction will make each equation true.
Answer:
#1 Is Yes
#2 is no
#3 is no
#4 is yes
Divide each number line into the given fraction unit. Then, place the fractions. Write each whole as a fraction 10/6 18/6 15/6
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\boxed{\mathsf{\dfrac{10}{6}\rightarrow \dfrac{10\div2}{6\div2}\rightarrow \bf \dfrac{5}{3} \rightarrow 1\dfrac{2}{3}}}[/tex]
[tex]\large\boxed{\mathsf{\dfrac{18}{6}\rightarrow\dfrac{18\div3}{6\div3}\rightarrow \bf \dfrac{6}{2}\rightarrow \dfrac{3}{1}\rightarrow 3}}[/tex]
[tex]\large\boxed{\mathsf{\dfrac{15}{6}\rightarrow \dfrac{15\div3}{6\div3}\rightarrow\bf \dfrac{5}{2}\rightarrow 2 \dfrac{1}{2}}}}[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]A force of 128 lb is required to hold a spring stretched 2 ft beyond its natural length. How much work W is done in stretching it from its natural length to 9 inches beyond its natural length
We have that the workdone in stretching natural length to is mathematically given as
W=9/2lbft
Workdone in stretching natural lengthQuestion Parameters:
A force of 128 lb is required to hold a spring stretched 2 ft beyond its natural length.Stretching it from its natural length to 9 inches beyond its natural lengthGenerally the Hookes equation for the Force is mathematically given as
F=Kx
Where
3.2lb=2ft*k
Thereofore
k=16
Force becomes
f=kx
f=16x
Hence
[tex]W=8[x^2]^{3/4}_{0}[/tex]
W=9/2lbft
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The values shown represent the y-values that correspond to x-values from x = 1 through x = 5.
What is the rate of change for the associated linear function?
A 2
B 5
C 9
D 10
This is Linear Equation. The Sum of three numbers is 27. The second number is three times the first, while the third is twice the first, Find the average.
Answer:
average = 9
(the third number is the average)
Step-by-step explanation:
If the sum of three numbers is 27, then the average (mean) is the total (27) divided by the number of values (3):
⇒ 27 ÷ 3 = 9
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
However, if you want to find the actual numbers:
Let x = first number
Let y = second number
Let z = third number
Given:
The sum of three numbers is 27 ⇒ x + y + z = 27The second number is three times the first ⇒ y = 3xThe third number is twice the first ⇒ z = 2xSubstitute y = 3x and z = 2x into x + y + z = 27 and solve for x:
⇒ x + 3x + 2x = 27
⇒ 6x = 27
⇒ x = 4.5
y = 3x
⇒ y = 3 x 4.5
⇒ y =13.5
z = 2x
⇒ z = 2 x 4.5
⇒ z = 9
Therefore, x = 4.5 y = 13.5 and z = 9
which means z (the third number) is same value as the average