Step-by-step explanation:
Given,
The length of a rectangle(l) = 2(x + 1) meters and
The perimeter of a rectangle = 60 meters
To find, the width of a rectangle(b) = ?
We know that,
The perimeter of a rectangle = 2(l + b)
⇒ 2(2(x + 1) + b) = 60
⇒ 2(x + 1) + b =[tex]\dfrac{60}{2} =30[/tex]
⇒ b = 30 - 2(x + 1)
⇒ b = 30 - 2x - 2
⇒ b = 28 - 2x
⇒ b = 2(14 - x)
∴ The width of a rectangle(b) = 2(14 - x)
Hence, the width of a rectangle(b) = 2(14 - x)
what is the answer to -2 1/2 +4
if 4cos° + 3sin° =5 ..find sin° and cos°
please anyone
Answer:
x = 36.87 degrees.
Step-by-step explanation:
4 cos x + 3 sin x = 5
Use the Auxiliary angle method:
R sin (α + x) = R sin α cos x + R cos α sin x
Comparing coefficients:
R sin α = 4 and R cos α = 3
R sin α / R cos α = 4/3
So tan α = 4/3
α = 53,13 degrees.
Now R^2(sin^2 α + cos^2 α ) = 3^2 + 4^2 = 25
R^2 = 25
R = 5.
R sin (x + 53.13) = 5
5 sin ( x + 53.13) = 5
sin (x + 53.13) = 1
x + 53.13 = 90
x = 36.87 degrees.
11 - 3x is greater than or equal to 32
Answer:
x ≤ -7
Step-by-step explanation:
Symbolically, we have 11 - 3x ≥ 32
and we can solve this for x as follows:
Add 3x to both sides. We get:
11 - 3x + 3x ≥ 32 + 3x
Then 11 ≥ 32 + 3x
Reversing the order, we get 3x + 32 ≤ 11
Subtracting 32 from both sides, we get:
3x ≤ -21
Finally, dividing both sides by 3 yields:
x ≤ -7
Allie measured a house and its lot and made a scale drawing. She used the scale 9 inches = 5 feet. What scale factor does the drawing use
Answer:
Therefore the scale used is 1 inch : 6.667 inches
Step-by-step explanation:
i) Scale used is 9 inches = 5 feet
ii) Scale used 9 inches = 5 [tex]\times[/tex] 12 inches = 60 inches
iii) Scale used is 1 inch [tex]= \dfrac{60}{9}\hspace{0.2cm} = \hspace{0.2cm}\dfrac{20}{3} \hspace{0.2cm} = 6.667\hspace{0.2cm} inches[/tex]
iv) Therefore the scale used is 1 inch : 6.667 inches
What are the coordinates of point A?
Answer:
by definition
The coordinates of point A are:
(cosθ , sinθ)
is the expression 3(x + 1 1/2) equivalent to 3x + 1 1/2
Answer:
No
Step-by-step explanation:
You only distribute the 3 to the x but not to 1 1/2. In order for the two equations to be the same, you have to distribute 3 to both the x and 1 1/2. Then the answer will look like this : 3x + 4 1/2 or 3x + 9/2
The original expression 3(x + 1 1/2) is not equivalent to 3x + 1 1/2; rather,it simplifies to 3x + 4.5 after distribution and simplification.
Step 1: Distribute the Number Outside the Parentheses:
To determine equivalence, distribute the 3 to both terms inside the parentheses: 3(x) + 3(1 1/2).
Step 2: Simplify Inside the Parentheses:
Multiply 3 by x: 3x.
Multiply 3 by 1 1/2: 3 × 1 + 3 × 1/2
= 3 + 1.5
= 4.5.
Step 3: Combine the Terms:
The distributed expression simplifies to 3x + 4.5.
Step 4: Evaluate the Expression in Question:
The expression provided is 3(x + 1 1/2).
The equivalent expression, as derived, is 3x + 4.5.
Step 5: Compare the Expressions:
The expression 3(x + 1 1/2) simplifies to 3x + 4.5, not 3x + 1 1/2.
Therefore, the original expression 3(x + 1 1/2) is not equivalent to 3x + 1 1/2; rather,it simplifies to 3x + 4.5 after distribution and simplification.
An investment advisor invested &14,000 in tow accounts. One investment earned 8% annual simple interest. And the other 6.5% annual simple interest. The amount of interest earned for 1 year was $1,027 how much was invested
Answer:
Investor invested $7,800 at 8% and $6,200 at 6.5%
Step-by-step explanation:
Use formula
[tex]I=P\cdot r\cdot t,[/tex]
where
I = interest
P = principal
r = rate (as decimal)
t = time
First investment:
[tex]P_1=x\\ \\r_1=0.08\\ \\t_1=1[/tex]
then
[tex]I_1=x\cdot 0.08\cdot 1\\ \\I_1=0.08x[/tex]
Second investment:
[tex]P_2=14,000-x\\ \\r_2=0.065\\ \\t_2=1[/tex]
then
[tex]I_2=(14,000-x)\cdot 0.065\cdot 1\\ \\I_2=0.065(14,000-x)[/tex]
The amount of interest earned for 1 year was $1,027, then
[tex]I_1+I_2=1,027\\ \\0.08x+0.065(14,000-x)=1,027\\ \\0.08x+910-0.065x=1,027\\ \\0.08x-0.065x=1,027-910\\ \\0.015x=117\\ \\x=7,800\\ \\14,000-x=6,200[/tex]
Investor invested $7,800 at 8% and $6,200 at 6.5%
5. If APQR = ASTU.
Find the measure of angle U.
Answer:
∠ U = 117°
Step-by-step explanation:
Since the triangles are congruent then corresponding angles are congruent.
∠ T = ∠ Q = 27°
The sum of the 3 angles in a triangle = 180°, thus
∠ U = 180° - (∠ s + ∠ T) = 180° - (36 + 27)° = 180° - 63° = 117°
What kind of angle is shown in the image below
Answer:
Your answer is C Straight angle
Step-by-step explanation:
There are 6 red marbles, 8 blue marbles, and 11 green marbles in a bag. What is the probability that you
will randomly draw either a red or a blue marble?
24%
56%
O 32%
o
10%
NEXT QUESTION
ASK FOR HELP
TURN IT IN
TERMS OF USE
Answer:
14/25
Step-by-step explanation:
p(red or blue)=6/(6+8+11) +8/(6+8+11)=6/25+8/25=14/25
Answer:
56% yall
Step-by-step explanation:
An account was overdrawn. The status of his account was -$248. He did not realize the problem and wrote another check for $73. The bank charged him $15. What was the new status of the account?
Answer:
-$336.00
Step-by-step explanation:
-$248.00+-$73.00+-$15.00=-$336.00
Find the coordinates of the midpoint MM of ST. Then find the distance between points SS and TT. Round the distance to the nearest tenth. S(−2, 4) and T(3, 9)
The midpoint is [tex](\frac{1}{2}, \frac{13}{2})[/tex]
The distance between points S and T is 7.1 units
Solution:
Given points are S(−2, 4) and T(3, 9)
Find the coordinates of the midpoint of ST
The midpoint is given as:
[tex]m(x, y)=\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)[/tex]
Here in this sum,
[tex](x_1, y_1) = (-2, 4)\\\\(x_2, y_2) = (3, 9)[/tex]
Substituting the values, we get
[tex]m(x, y)=\left(\frac{-2+3}{2}, \frac{4+9}{2}\right)\\\\m(x, y)=\left(\frac{1}{2}, \frac{13}{2})[/tex]
Thus the midpoint is [tex](\frac{1}{2}, \frac{13}{2})[/tex]
Find the distance between points
The distance is given by formula:
[tex]d=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}[/tex]
Here in this sum,
[tex](x_1, y_1) = (-2, 4)\\\\(x_2, y_2) = (3, 9)[/tex]
Substituting the values, we get
[tex]\begin{aligned}&d=\sqrt{(3-(-2))^{2}+(9-4)^{2}}\\\\&d=\sqrt{5^{2}+5^{2}}\\\\&d=\sqrt{25+25}\\\\&d=\sqrt{50}=7.071 \approx 7.1\end{aligned}[/tex]
Thus the distance between points S and T is 7.1 units
The coordinates of the midpoint [tex]\( M \) are \( (0.5, 6.5) \),[/tex] and the distance between points S and T approximately 7.0 units.
To find the coordinates of the midpoint M of the line segment ST, we use the midpoint formula:
[tex]\[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \][/tex]
Given the coordinates of [tex]\( S \) and \( T \) are \( S(-2, 4) \) and \( T(3, 9) \)[/tex] respectively, we substitute these values into the formula:
[tex]\[ M = \left( \frac{-2 + 3}{2}, \frac{4 + 9}{2} \right) \][/tex]
[tex]\[ M = \left( \frac{1}{2}, \frac{13}{2} \right) \][/tex]
[tex]\[ M = (0.5, 6.5) \][/tex]
Now, to find the distance between points S and T, we use the distance formula:
[tex]\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]
Substituting the coordinates of S and T into the formula:
[tex]\[ d = \sqrt{(3 - (-2))^2 + (9 - 4)^2} \][/tex]
[tex]\[ d \approx 5 \times 1.4 \][/tex]
[tex]\[ d \approx 7 \][/tex]
The coordinates of the midpoint [tex]\( M \) are \( (0.5, 6.5) \),[/tex] and the distance between points S and T is approximately 7.0 units.
If LO = 15x+19 and QN = 10x+2 find PN
Answer:
[tex]PN=64\ units[/tex]
Step-by-step explanation:
The complete question is
Given the quadrilateral is a rectangle, if LO = 15x+19 and QN = 10x+2 find PN
see the attached figure to better understand the problem
we know that
The diagonals of a rectangle are congruent and bisect each other
so
[tex]QN=\frac{1}{2}LO[/tex]
substitute the given values
[tex]10x+2=\frac{1}{2}(15x+19)[/tex]
solve for x
[tex]20x+4=15x+19\\20x-15x=19-4\\5x=15\\x=3[/tex]
Find the length of PN
Remember that
[tex]PN=LO[/tex] ----> diagonals of rectangle are congruent
[tex]LO=15x+19[/tex]
substitute the value of x
[tex]LO=15(3)+19=64\ units[/tex]
therefore
[tex]PN=64\ units[/tex]
Simplify -5/1 the slope
Answer:
Step-by-step explanation:
The only possible simplification of the slope -5/1 is -5.
apply the distributive property to Factor out the greatest common factor of 75+20
Final answer:
The greatest common factor of 75 and 20 is 5, and by applying the distributive property, the expression 75+20 can be factored as 5(19).
Explanation:
The greatest common factor (GCD) of 75 and 20 is 5. Applying the distributive property to factor out 5, we get:
75 + 20 = 5 × (15 + 4)
Here's the breakdown:
Find the GCD: The largest factor that divides both 75 and 20 is 5.
Divide each term by the GCD: Divide 75 by 5 to get 15 and divide 20 by 5 to get 4.
Rewrite with the GCD factored out: Combine the results from step 2 and multiply by the GCD: 5 × (15 + 4).
Therefore, the factored expression using the distributive property is 5 × (15 + 4).
Thus, the factored form of the expression 75+20 is 5(19).
Please help for 60 points and brainliest for best answers!
Answer:
6. ○ [tex]\displaystyle 33,1°; 123,1°[/tex]
5. [tex]\displaystyle See\:above\:image[/tex]
4. [tex]\displaystyle See\:above\:image[/tex]
Explanation:
6. Supplementary Angles sum up to 180°, whereas complementary angles sum up 90°. So, use subtraction for both types of angles:
[tex]\displaystyle 123,1° = -56,9° + 180° \\ 33,1° = -56,9° + 90°[/tex]
* Make sure that they are in the exact same order that exercise gives you.
5. Acute Angles measure greater than 0° and less than 90°.
4. Every segment must have C in it, and you must be EXTREMELY CAREFUL of their markings [ray, segment, and line].
I am joyous to assist you anytime.
A theater group made appearances into cities the hotel charge before tax and the second city was 1500 higher than the first the tax and the first city was 6% and the tax and the second city was 10% total hotel tax paid for two cities with $670 how much was the hotel charge in each city before tax
Answer:
The hotel charge in each city before tax was $5125 of the first city and $3625 of the second city.
Step-by-step explanation:
Given:
A theater group made appearances into cities the hotel charge before tax and the second city was 1500 higher than the first.
The tax of the first city was 6% and the tax of the second city was 10%.
Total hotel tax paid for two cities with $670.
Now, to find the hotel charge in each city before tax.
Let the hotel charge in first city before tax be [tex]x.[/tex]
And the hotel charge in second city before tax be [tex]y.[/tex]
So, as the hotel charge of the second city was 1500 higher than the first.
Thus,
[tex]y=x-1500[/tex] ........(1)
And as given, the tax of the first city was 6% and the tax of the second city was 10%, total hotel tax paid for two cities with $670.
6% of [tex]x[/tex] + 10% of [tex]y[/tex] = $670.
[tex]\frac{6x}{100} +\frac{10y}{100} =670[/tex]
[tex]0.06x+0.10y=670[/tex]
Substituting the value of [tex]y[/tex] from equation (1) we get:
[tex]0.06x+0.10(x-1500)=670[/tex]
[tex]0.06x+0.10x-150=670[/tex]
[tex]0.16x-150=670[/tex]
Adding both sides by 150 we get:
[tex]0.16x=820[/tex]
Dividing both sides by 0.16 we get:
[tex]x=5125.[/tex]
The hotel charge in first city before tax = $5125.
Now, substituting the value of [tex]x[/tex] in equation (1) we get:
[tex]y=x-1500[/tex]
[tex]y=5125-1500[/tex]
[tex]y=3625.[/tex]
The hotel charge in second city before tax = $3625.
Therefore, the hotel charge in each city before tax was $5125 of the first city and $3625 of the second city.
If
f
(
x
)
=
x
6
+
3
x
−
1
f(x)=x
6
+3x−1, then what is the remainder when
f
(
x
)
f(x) is divided by
x
+
1
x+1?
y= -7x proportional or non proportional
Answer:
it is proportional
Step-by-step explanation:
Proportional functions will be in the form y = kx and non-proportional functions will be in the form y = mx + b
What is -2 1/2 + 1 1/3 in fraction form?
[tex]-2\frac{1}{2} +1\frac{1}{3}=\frac{-1}{6}[/tex]
Solution:
Given expression is [tex]-2\frac{1}{2} +1\frac{1}{3}[/tex].
Let us first convert mixed fraction into improper fraction.
[tex]-2\frac{1}{2} +1\frac{1}{3}=\frac{(-2\times 2) +1}{2} +\frac{(1\times 3) + 1}{3}[/tex]
[tex]=\frac{-4 +1}{2} +\frac{3 + 1}{3}[/tex]
[tex]=\frac{-3}{2} +\frac{4}{3}[/tex]
Take LCM for the denominators (LCM of 2, 3 = 6) and make the same.
[tex]=\frac{-3\times3}{2\times3} +\frac{4\times2}{3\times2}[/tex]
[tex]=\frac{-9}{6} +\frac{8}{6}[/tex]
[tex]=\frac{-1}{6}[/tex]
[tex]-2\frac{1}{2} +1\frac{1}{3}=\frac{-1}{6}[/tex]
Hence the fraction form of [tex]-2\frac{1}{2} +1\frac{1}{3}[/tex] is [tex]\frac{-1}{6}[/tex].
help quick pls 20 points
Answer:
your answer is 70
Step-by-step explanation:
Help with matrices please? Any wrong/not applicable answers will be reported and BLOCKED
m x H = [tex]\left[\begin{array}{ccc}-25&37.5&-12.5\\\9\end{array}\right][/tex]
Step-by-step explanation:
Step 1; Multiply 5 with this matrix [tex]\left[\begin{array}{ccc}-1&2\\4&8\\\end{array}\right][/tex] and we get a matrix [tex]\left[\begin{array}{ccc}-5&10\\20&40\\\end{array}\right][/tex]
Multiply the fraction [tex]\frac{2}{5}[/tex] with the matrix [tex]\left[\begin{array}{ccc}-1&2\\4&8\\\end{array}\right][/tex] and we get [tex]\left[\begin{array}{ccc}-\frac{2m}{5} &\frac{4m}{5} \\\frac{8m}{5} &\frac{16m}{5} \\\end{array}\right][/tex]
Step2; Now equate corresponding values of the matrices with each other.
-5 = [tex]\frac{-2m}{5}[/tex] and so on. By equating we get the value of m as [tex]\frac{25}{2}[/tex]
Step 3; Add the matrices to get the value of matrix m.
Adding the three matrices on the RHS we get [tex]\left[\begin{array}{ccc}2&9&-9\\\end{array}\right][/tex].
Step 4; Adding the matrices on the LHS we get the resulting matrix as H +
[tex]\left[\begin{array}{ccc}4&6&-8\\\9\end{array}\right][/tex]. Equating the matrices from step 3 and 4 we get the value of H as [tex]\left[\begin{array}{ccc}-2&3&-1\\\9\end{array}\right][/tex]
Step 5; Now to find the value of m x H we need to multiply the value of [tex]\frac{25}{2}[/tex] with the matrix [tex]\left[\begin{array}{ccc}-2&3&-1\\\9\end{array}\right][/tex]
Step 6; Multiplying we get the matrix m x H = [ -25 [tex]\frac{75}{2}[/tex] [tex]\frac{-25}{2}[/tex] ]
8. (5 + 4 - 2) * (-2) = ?
A. -14
B.-22
O c. 14
D. 22
Answer: A. -14
Step-by-step explanation:
Answer: A. -14
Step-by-step explanation: Use PEMDAS
(5+4-2) x (-2)
= (9-2) x (-2)
= 7 x (-2)
= -14
Show me how you got Christmas paper that was 8 feet long and 8 ft wide and the perimeter is 32 how
Answer:
The Proof is below.
Therefore the Perimeter of Christmas paper is 32 feet ..Proved
Step-by-step explanation:
Let the Christmas Paper have Dimensions as
Length = 8 feet
Width = 8 feet
To Show:
Perimeter of Christmas Paper = 32
Solution:
Christmas Paper is in Rectangle Shape,
Therefore Perimeter of a Rectangle is given as
[tex]Perimeter\ of\ Rectangle=2(Length+Width)[/tex]
Substituting the values we get
[tex]Perimeter=2(8+8)=2\times 16=32\ feet[/tex]
Therefore the Perimeter of Christmas paper is 32 feet ..Proved
The perimeter of a square is calculated by adding the lengths of all four sides. An 8 ft by 8 ft square has a perimeter of 32 ft, because 8 ft multiplied by 4 (the number of sides in a square) equals 32 ft.
Explanation:This question involves understanding the concept of perimeter in the context of a square. If you have a piece of Christmas paper that is 8 feet long and 8 feet wide, you actually have a square because all sides are of equal length. To calculate the perimeter of a square, you simply add up the lengths of all four sides.
Since each side is 8 feet, the perimeter P is given by:
P = side + side + side + side
P = 8 ft + 8 ft + 8 ft + 8 ft
P = 32 ft
So, the perimeter of the Christmas paper, if shaped like a square, is 32 feet, which is simply four times the length of one side.
Solve the system of equations by the addition method.
x- y=-9
x+y=-5
Answer:
x=-7, y=2. (-7, 2).
Step-by-step explanation:
x-y=-9
x+y=-5
-----------
2x=-14
x=-14/2
x=-7
-7-y=-9
y=-7-(-9)
y=-7+9
y=2
What is the value of this expression
when b = 5?
6(26-4)
Answer:
6(26-4)= 132
Step-by-step explanation:
There isn't any variable in the equation
David cooks 6 cups of rice for his family. They eat 4 cups. What fraction of the rice is uneaten
Answer:
1/3
Step-by-step explanation:
David cooks 6 cups of rice and his family eats 4 cups. To find the fraction, we must first do 6-4 to get 2. We place 2 in the numerator and 6 in the denominator. We have 2/6. We can simplify 2/6 by dividing both the numerator and the denominator by 2 to get 1/3.
what is the answer to -x times x
Answer:
-x^2
Step-by-step explanation:
Answer:
-x^2
Step-by-step explanation:
solve this problem
-5(1+6n)=5n-5
bless me with the answers
Answer:
5) The correct answer is D.
6) The correct answer is A.
7) m = (10 - 6)/(1 - 0) = 4/1 = 4
The correct answer is C.
8) The correct answer is B.