Answer:
x = 9x5 / 4
x = 45/4
(either one)
Step-by-step explanation:
[tex]\frac{4}{5}[/tex] = [tex]\frac{9}{x}[/tex]
Multiple known diagonals and divide by number opposite to unknown number (x).
Hope that helped!!! k
Answer:
(b) 4 x = 4 5 is the needed expression to solve for the value of x.
Step-by-step explanation:
Here, the given proportion is simplified as:
4/5=9/x
Now, to simplify any proportion of the form the simplest way is cross multiplication.
So, cross multiplying a/b=c/d -> ad=bc
Similarly cross multiplying 4/5=9/x, we get:
4 (x) = (9) (5)
PLease answer !!! Find constants $A$ and $B$ such that \[\frac{x + 7}{x^2 - x - 2} = \frac{A}{x - 2} + \frac{B}{x + 1}\] for all $x$ such that $x\neq -1$ and $x\neq 2$. Give your answer as the ordered pair $(A,B)$. and Find all values of $t$ such that $\lfloor t\rfloor = 2t + 3$. If you find more than one value, then list the values you find in increasing order, separated by commas.
Answer:
1. [tex](A,B) = (3,-2)[/tex]
2. The values of t are: -3, -1
Step-by-step explanation:
Given
[tex]\frac{x + 7}{x^2 - x - 2} = \frac{A}{x - 2} + \frac{B}{x + 1}[/tex]
[tex]|t| = 2t + 3[/tex]
Required
Solve for the unknown
Solving [tex]\frac{x + 7}{x^2 - x - 2} = \frac{A}{x - 2} + \frac{B}{x + 1}[/tex]
Take LCM
[tex]\frac{x + 7}{x^2 - x - 2} = \frac{A(x+1) + B(x-2)}{(x - 2)(x-1)}[/tex]
Expand the denominator
[tex]\frac{x + 7}{x^2 - x - 2} = \frac{A(x+1) + B(x-2)}{x^2 - 2x + x -2}[/tex]
[tex]\frac{x + 7}{x^2 - x - 2} = \frac{A(x+1) + B(x-2)}{x^2 - x -2}[/tex]
Both denominators are equal; So, they can cancel out
[tex]x + 7 = A(x+1) + B(x-2)[/tex]
Expand the expression on the right hand side
[tex]x + 7 = Ax + A + Bx - 2B[/tex]
Collect and Group Like Terms
[tex]x + 7 = (Ax + Bx) + (A - 2B)[/tex]
[tex]x + 7 = (A + B)x + (A - 2B)[/tex]
By Direct comparison of the left hand side with the right hand side
[tex](A + B)x = x[/tex]
[tex]A - 2B = 7[/tex]
Divide both sides by x in [tex](A + B)x = x[/tex]
[tex]A + B = 1[/tex]
Make A the subject of formula
[tex]A = 1 - B[/tex]
Substitute 1 - B for A in [tex]A - 2B = 7[/tex]
[tex]1 - B - 2B = 7[/tex]
[tex]1 - 3B = 7[/tex]
Subtract 1 from both sides
[tex]1 - 1 - 3B = 7 - 1[/tex]
[tex]-3B = 6[/tex]
Divide both sides by -3
[tex]B = -2[/tex]
Substitute -2 for B in [tex]A = 1 - B[/tex]
[tex]A = 1 - (-2)[/tex]
[tex]A = 1 + 2[/tex]
[tex]A = 3[/tex]
Hence;
[tex](A,B) = (3,-2)[/tex]
Solving [tex]|t| = 2t + 3[/tex]
Because we're dealing with an absolute function; the possible expressions that can be derived from the above expression are;
[tex]t = 2t + 3[/tex] and [tex]-t = 2t + 3[/tex]
Solving [tex]t = 2t + 3[/tex]
Make t the subject of formula
[tex]t - 2t = 3[/tex]
[tex]-t = 3[/tex]
Multiply both sides by -1
[tex]t = -3[/tex]
Solving [tex]-t = 2t + 3[/tex]
Make t the subject of formula
[tex]-t - 2t = 3[/tex]
[tex]-3t = 3[/tex]
Divide both sides by -3
[tex]t = -1[/tex]
Hence, the values of t are: -3, -1
What's the perimeter of rectangle DEFG, shown? A) 17 B) 28 C) 40 D) 34
Answer:
[tex]\huge\boxed{Perimeter = 34\ units}[/tex]
Step-by-step explanation:
DE = 10 units
GF = 10 units
DG = 7 units
EF = 7 units
Perimeter of rectangle = Sum of all sides
P = DE + GF + DG + EF
P = 10 + 10 + 7 + 7
Perimeter = 34 units
Answer:
D) 34 units
Step-by-step explanation:
Coordinates:
D: (-5,4)
E: (5,4)
F: (5, -3)
G: (-5,-3)
Distance between points D and E = Distance between points F and G = 10
Distance between points E and F = Distance between points G and D = 7
Formula for perimeter of your rectangle:
2(x) + 2(y) =
2(10) + 2(7) =
20 + 14 = 34 units
That's your answer!
Hope that helps and maybe earns a brainliest!
Have a terrific day! > <
U
wat is (12+6-5*3)*(2*2+1-7+2)=
Answer:
[tex]\huge\boxed{0}[/tex]
Step-by-step explanation:
First we have to do the operation of multiplication
=> (12+6-15)*(4+1-7+2)
Now, Solving the terms inside the brackets
=> (18-15)*(5-7+2)
=> (3)*(-2+2)
=> (3)*(0)
=> 0
Answer:
[tex]\Huge \boxed{{0}}[/tex]
Step-by-step explanation:
[tex](12+6-5*3)*(2*2+1-7+2)[/tex]
Solve brackets.
[tex](12+6-15)*(4+1-7+2)[/tex]
[tex](3)*(0)[/tex]
Multiply both numbers.
[tex]3 \times 0 = 0[/tex]
4x = 2x + 2x + 5(x-x) does this have one solution, no solution or infinite solutions
Answer:
infinite solutions
Step-by-step explanation:
4x = 2x + 2x + 5(x-x)
Simplify
4x = 2x + 2x + 5*0
4x = 2x + 2x
4x = 4x
Divide by x
4 =4
This is always true so this has infinite solutions
What is the expression in SIMPLEST radical form? (20)∧5/2
Answer:
The expression in the question can, and should, be written clearly as either 205(2)=8 or as 205(2)=2 . Relying on a left-to-right or right-to-left interpretation is not a good idea.
In cases of associative operators, like a⋅b⋅c , the parenthesis or other grouping can be omitted because any reasonable interpretation will yield the same result. But this isn’t true of division, which is not associative, nor is it true of mixed operators at the “same level” of precedence, like multiplication/division.
The other answers which say the result is 8 may not be wrong, but they are missing the main issue in that this expression should not be used because of the ambiguity
Step-by-step explanation:
Find an equation of the line with the slope m= 3 that passes through the point (2,2). Write the equation in the form Ax+By = C.
Answer:
[tex]y = 3x-4[/tex]
Step-by-step explanation:
We know that if we were to write an equation with the slope of 3, it would be [tex]y=kx[/tex], where k is the constant (in this case 3.)
So right now, we have [tex]y=3x[/tex].
However, this will not pass through the point (2,2). To do this, we need to add a y-intercept in which (2,2) will be crossed through.
If we have a y-intercept of -4, the points will be:
(0, -4)
(1, -1)
(2, 2)
So our final equation is [tex]y = 3x-4[/tex].
Hope this helped!
Answer: 3x-1y=4 in Ax+By=C form
Step-by-step explanation:
the intercept form is y=3x-4
subracting 3x from both sides would get -3x+y=-4
distributing -(-3x+y=-4) would get 3x-y=4.
Express the product of 3x^2 - 4x +6 and x-2 in standard form.
Answer:
3x³ - 10x² + 14x - 12
Step-by-step explanation:
(3x² - 4x + 6) × (x - 2)
3x³ - 4x² + 6x - 6x² + 8x - 12
3x³ - 10x² + 14x - 12
Thus, the product of 3x² - 4x + 6 and x - 2 in standard form is 3x³ - 10x² + 14x - 12
Help plz, show work
Answer:
63°50° , 40°Step-by-step explanation:
1.
[tex]3 :7 \\Acute \: angle = 90\°\\7+3 = 10\\\frac{7}{10} \times 90\\\\= \frac{630}{10}\\ = 63 \°\\[/tex]
2.
[tex]Let \:the\: other\:acute \:angle\: be \:x\\According\:to \:the \:question ; \\ \:\\(2x-30)+x =90\\2x - 30 +x =90\\2x +x = 90+30\\3x = 120\\\frac{3x}{3} =\frac{120}{3} \\x = 40 \\\\(2x -30)\\2(40) -30\\80 - 30 = 50\\\\\\Angle \:1 = 50\°\\Angle \: 2 = 40\°\\[/tex]
The large rectangle below represents one whole. What percent is represented by the shaded area? (URGENT)
Answer:
40%
Step-by-step explanation:
The whole rectangle is split into 5 parts. Two out of 5 parts are shaded.
Set up a fraction:
[tex]\frac{\text{Shaded}}{\text{Whole}}=\frac{2}{5}[/tex]
Convert into a decimal:
[tex]\frac{2}{5}= 0.4[/tex]
Multiply the decimal by 100 to get the percent:
[tex]0.4*100=40[/tex]
So, forty percent of the rectangle is shaded.
Hope this helps.
The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Required percentage value = a
total value = b
Percentage = a/b x 100
The percentage of the shaded rectangular boxes in the large rectangle is 40%.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Number of rectangular boxes in the large rectangle = 5
Number of shaded rectangular boxes in the large rectangle = 2
The percentage of shaded rectangular boxes.
= 2/5 x 100
= 2 x 20
= 40%
Thus,
The percentage of the shaded rectangular boxes in the large rectangle is 40%.
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(08.01) Two lines, A and B, are represented by the following equations: Line A: y = x − 1 Line B: y = −3x + 11 Which of the following options shows the solution to the system of equations and explains why? (3, 2), because the point does not lie on any axis (3, 2), because one of the lines passes through this point (3, 2), because the point lies between the two axes (3, 2), because both lines pass through this point
Answer:
the answer is D
Step-by-step explanation:
y=x-1
2=3-1
2=2
y=-3x+11
2=-3(3)+11
2=-9+11
2=2
Answer:
Step-by-step explanation:
If both lines pass through the point (3, 2), we automatically know that (3, 2) is the soution of the system of linear equations given here, AND that (3, 2) is a solution of equation A and equation B both.
Find the measure of the remote exterior angle. m∠x=(4n−18)°m∠y=(n+9)°m∠z=(151−5n)° A. 71 B. 16 C. 100 D. 46
Answer: A.71
Step-by-step explanation: 1.set up the equation
2. 4n-18+n+9=151-5n
3.combine like terms -> 5n-9=151-5n
4.solve for n
5.10n=160
n=16
now you have to plug 16 in for n in order to get the remote exterior angle.
151-5(16)
151-80
71°
The sum of any two interior angle is equal to the third exterior angle. The value of n will be 16°. Then the correct option is B.
What is the triangle?A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
The triangle having the interior angle x and y, and z is the exterior angle of triangle.
m∠x = (4n − 18)°, m∠y = (n + 9)°, and m∠z = (151 − 5n)°
Then the value of n will be
We know that the sum of any two interior angle is equal to the third exterior angle. Then we have
∠x + ∠y = ∠z
4n - 18 + n + 9 = 151 - 5n
10n = 160
n = 16°
Then the correct option is B.
More about the triangle link is given below.
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In which situation can a constant of proportionality be identified A. Allison earns $8 per hour for h hours and an $8 bonus for each cell phone plans she sells. B. Ben buys x cans of dog food for $1.25 each and uses a coupon $7 off his entire purchase. C. Claire orders b books online for $4.50 each plus shipping charges $0.30 for each book. D. John runs 3 miles per day for m days in a week and bicyles 20 miles/day the remaining days in the week.
Answer:
C
Step-by-step explanation:
C is the only situation in which there is a clear constant of proportionality and no offset (no initial value). Claires rate is ($4.50 + $0.30)/book, or $4.80/book.
Determine whether the lines given by the vector equations r1=2i+3j+k+s(4i−k) and r2=2i+3j+k+t(2i+2j+k) intersect. If they intersect, give the coordinates of their point of intersection.
They do. the initial point is same in both lines.
formally,
[tex] \vec{r_1}=(2\hat i+3 \hat j+\hat k)+s(4\hat i-\hat k)[/tex]
$\vec{r_2}=(2\hat i +3 \hat j +\hat k)+t(2\hat i+2\hat j +\hat k)$
if they intersect then $\begin{vmatrix} 4 & 0 & -1 \\ 2 & 2 & 1 \\ (2-2) & (3-3) & (1-1) \end{vmatrix}=0$
(which obviously is zero)
Michael just drank a cup of coffee to help him stay awake. The coffee had 110 milligrams of caffeine in it. If his body processes 5% of the caffeine every hour, how much will be left in 8 hours? A.74 B.72 C.56 D.73
Answer:C
Step-by-step explanation:
Someone pls help me in this plss
Im really confused in this
Answer:
Step-by-step explanation:
find LCM of the denominators= 77
so 66/77 - 63/77
3/77
hope this help you pls mark me as brainliest
working for division is on this question is
6/7 divide 9/11
so 6/7 *11/9
66/63 and then you can find its standard form and it cannot be do not
The projected worth (in millions of dollars) of a large company is modeled by the equation w = 221(1.09) t. The variable t represents the number of years since 2000. What is the projected annual percent of growth, and what should the company be worth in 2008? A. 9%; $440.36 million B. 19%; $479.99 million C. 9%; $404.00 million D. 19%; $240.89 million
Answer:
A. 9%; $440.36 million
Step-by-step explanation:
Using A(1+r)t, we can subtract 1-1.09=.09*100=9%.
That means the projected annual growth is 9%
Now we can calculate the worth of the company by replacing t=8, 2008-2000=8
[tex]w=221(1.09)^8\\=440.356=440.36 million[/tex]
John and Maria also want to put new tile in their living room. The floor measures 20 feet long by
20 feet wide. The tiles they want to purchase cost $2.25 each, and each tile covers exactly 1 square
foot of floor space. How much will they need to spend on tile? (Section 10.8) (1 point)
Answer:
$900
Step-by-step explanation:
First, find the area of the floor with the equation A = lw
A = lw
A = (20)(20)
A = 400 ft²
Since each tile covers 1 sq ft and the floor's area is 400 sq ft, they will need 400 tiles.
To calculate the total cost, multiply 400 by 2.25
400(2.25) = 900
= $900
Please Help Will Mark as Brainlist
Answer:
Hey there!
We can write this equation: 2x+4x=180
6x=180
x=30
Hope this helps :)
The two angles are supplementary angles. When added together they equal 180 degrees.
2x + 4x = 180
Combine like terms:
6x = 180
Divide both sides by 6:
X = 180/6
X = 30
What is 2,871 divided by 33? A) 77 B) 83 C) 87 D) 93
Answer:
(C) 87
Step-by-step explanation:
We can use long division to solve this.
[tex]33\overline{\smash{)}#2871}[/tex]
33 goes into 287 8 times and 33 goes into 231 7 times.
So, 87.
Hope this helped!
Answer: C) 87
Step-by-step explanation:
2,871 ÷ 33 = 87
Jill has two dimes she is going to use to perform a probability experiment. What is the theoretical probability that at least one of the two coins will turn up
heads?
75%
50%
Answer:
50%
Step-by-step explanation:
its a 50/50 chance on it landing either heads or tails
Solve the equation. 4(4x - 2) = x + 4
Answer:
x = 0.8
Step-by-step explanation:
4(4x - 2) = x + 4
4*4x + 4*-2 = x + 4
16x - 8 = x + 4
16x - x = 4 + 8
15x = 12
x = 12/15
x = 0.8
Check:
4(4*0.8 - 2) = 0.8 + 4
4(3.2 - 2) = 4.8
4(1.2) = 4.8
Answer:
0.8 in decimal form
Step-by-step explanation:
what is the largest amount of postage in cents that cannot be made by using only 3 cent and 5 cent stamps?
Answer:
29
Step-by-step explanation:
The amounts greater than 40 cents can be formed.
What is Modulo ?After dividing one number by another, the modulo operation yields the remainder or signed remainder of the division.
Given:
According to the situation the equation can be
C = 5x + 11y, where x and y are non negative integers.
Now, We will fix y-values first, because there are fewer indices modulo 5:
y = 0 --> 0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55,... 5y
y = 1 --> 11, 16, 21, 26, 31, 36, 41, 46, 51, 56,... 5y + 11
y = 2 --> 22, 27, 32, 37, 42, 47, 52, 57, ...5y + 22
y = 3 --> 33, 38, 43, 48, 53, 58, ...5y + 33
y = 4 --> 44, 49, 54, 59, ...5y + 44
Then, 39 may be verified to be the smallest number that is impossible to obtain.
By examining each index (0, 1,..., 4), we may demonstrate this by observing that for y = 1, 6 is the largest positive integer congruent to 1 mod 5 that cannot be made, 17 is the largest positive number congruent to 2 mod 5, etc.
The largest of these improbable numbers is 39.
We could say that since 40, 41, ..., 44 are all obtainable, then we can induct by adding a multiple of 5 (i.e. if k is possible, so is k+5),
Hence, all amounts greater than 40 cents can be formed.
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-1.68j+1.24=13 need help thanks
Answer:
-7
Step-by-step explanation:
-1.68j+1.24=13
-1.68j=13-1.24
-1.68j=11.76
j=11.76/-1.68
j=-7
Hi there! Hopefully this helps!
-----------------------------------------------------------------------------------------------------------
Answer: j = -7
You can also rewrite the equation(replace "j" with the answer):
-1.68(-7) + 1.24 = 13.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
How I solved it:
-1.68j + 1.24 = 13.
We subtract 1.24 from both sides.
-1.68j = 13 - 1.24
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-1.68j = 13 - 1.24
We subtract 1.24 from 13 to get 11.76.
-1.68j = 11.76
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-1.68j = 11.76
We then divide both sides by -1.68.
j = [tex]\frac{11.76}{-1.68}[/tex]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Expand [tex]\frac{11.76}{-1.68}[/tex] ≈ -7 by multiplying both the numerator and the denominator by 100.
j = [tex]\frac{1176}{-168}[/tex]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Divide 1176 by -168 to get -7.
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the
correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag
the item to the trashcan. Click the trashcan to clear all your answers.
Type the expressions as radicals
y3/5
Answer:
[tex]\sqrt[5]{y^3}[/tex]
Step-by-step explanation:
[tex]y^{3/5}[/tex] is simply [tex]\sqrt[5]{y^3}[/tex]
If the degree measures of the angles of a triangle are in the ratio 3 : 3 : 4, what is the degree measure of the largest angle of the triangle? (Sum of all three angles is 180)
x=3k
y=3k
z=4k
x+y+z=180
3k+3k+4k=180
10k=180
k=180/10
k= 18
z=4*18
z=72
answer: 72
Answer:72 degrees
Step-by-step explanation:
3:3:4 is the ratio of the angles of a triangle and we have been asked the degree measure of the largest angle.
First of all...add the three ratios
3+3+4=10
;Ratio 10=180 degrees(the sum of all the angles;ratios add up to the sum of all three angles)
10=180 how about ratio 3?
Cross multiply...3 times 180 over 10= 54 degrees
Both angles with ratio 3 are 54 degrees
180-108=72
The angle with ratio 4 has 72 degrees which makes it the largest angle
If you're good at angles of depression please help meeeeee and show full working out tyyyyyyyyyy
Answer:
236.9 m
Step-by-step explanation:
Let x and y represent the distances to the near and far cars, respectively. You know from the definition of the tangent of an angle that ...
tan(angle of depression) = building height/distance to car
tan(10°39') = 150/x
x = 150/tan(10°39')
and
tan(8°15') = 150/y
y = 150/tan(8°15')
The difference of these two distances is the distance between the cars:
y - x = 150/tan(8°15') -150/tan(10°39')
__
The minutes of arc can be converted to fractional degrees:
15' = 15'/(60'/1°) = (15/60)° = 0.25°
39' = 39'/(60'/1°) = (39/60)° = (13/20)° = 0.65°
So, the distance of interest is ...
distance between cars = (150 m)(1/tan(8.25°) -1/tan(10.65°)) ≈ 236.86 m
The cars are about 236.9 meters apart.
What is the area of the figure? The figure is not drawn to scale.\ A. 27.36 cm2 B. 13.7 cm2 C. 9.1 cm2 D. 5.3 cm2
Answer:
B. 13.7 cm^2
Step-by-step explanation:
To find the height of any parallelogram, you must multiply the base x height.
The base is 1.9 cm. The height is 7.2 cm.
A = bh
A = (1.9)(7.2)
A = 13.68
13.7 is the closest answer we can get if we can round, but it really should be 13.68 cm^2.
Answer:
B. 13.7
Step-by-step explanation:
A = bh
A = 1.9*7.2
A = 13.68
(13.68 rounds up to 13.7)
-15 POINTS PLS HURRY- Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator. 4.5 cm to 4 cm
Hi there! :)
Answer:
[tex]\huge\boxed{\frac{9cm}{8cm}}[/tex]
We can disregard the units temporarily to create a ratio for 4.5 to 4:
4.5 is not a whole number- we can convert this number in the ratio to a whole number by multiplying both numbers by 2:
2 · (4.5 : 4) = 9 : 8
Express as a fraction:
[tex]9cm : 8cm = \frac{9cm}{8cm}[/tex]
Please help me with this geometry question:((
Answer:
x = 13
RQ = 160°
Step-by-step explanation:
Inscribed angles are half the intercepted arc angle.
5x + 15 = ½ (RQ)
RQ = 10x + 30
Arc angles add up to 360°.
10x + 30 + 9x + 17 + 6x − 12 = 360
25x + 35 = 360
25x = 325
x = 13
Therefore, RQ = 160°.
Write the equation for the following table:
Answer:
y = 10x + 20
Step-by-step explanation:
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Slope-Intercept Form: y = mx + b
Step 1: Find slope m
m = (20 - 10)/(0 - -1)
m = 10/(0 + 1)
m = 10/1
m = 10
y = 10x + b
Step 2: Find y-intercept
(0, 20) is y-int from graph
Step 3: Plug into form
y = 10x + 20
