Answer:
33
Step-by-step explanation:
Start by adding the 3 to the other side (2/3x=22)
Then, you divide 2/3 to cancel it out. To do that, multiply 22 by 3/2 which equals to 33.
Answer:
2/3x - 3 = 19
We first isolate the variable and solve for x, (we get rid of any constants first in the process)
2/3x - 3 = 19 the three is the constant so we get rid of it by adding three to both sides.
2/3x - 3 = 19
+3 +3
2/3x = 22
Now we divide by 2/3 on both sides
X = 33
What is the value of the expression below when x=3
10x²- 7x + 10
Answer: 79
Concept:
Here, we need to understand the idea of evaluation.
When encountering questions that gave you an expression with variables, then stated: "If x = a, y = b, z = c" (a, b, c are all constants), this means you should substitute the value given for each variable back to the expression.
Solve:
Given information
10x² - 7x + 10
x = 3
Substitute the value into the expression
= 10 (3)² - 7 (3) + 10
Simplify by multiplication
= 10 (9) - 21 + 10
= 90 - 21 + 10
Simplify by subtraction
= 69 + 10
Simplify by addition
= 79
Hope this helps!! :)
Please let me know if you have any questions
Answer:
92
Step-by-step explanation:
The variable 'x' shows up twice in this expression. Replace each instance of 'x' with 3:
10(3)^2 - 7(3) + 10 = 10(9) - 21 + 19 = 92
If the blue radius below is perpendicular to the chord AC which is. 14 units long, what is the length of the segment AB?
Answer:
C. 7 units
Step-by-step explanation:
The given parameters are;
The length of the chord of the circle, [tex]\overline{AC}[/tex] = 14 units
The orientation of the radius and the chord = The radius is perpendicular to the chord
We have in ΔAOC, [tex]\overline{AO}[/tex] = [tex]\overline{OC}[/tex] = The radius of the circle
[tex]\overline{OB}[/tex] ≅ [tex]\overline{OB}[/tex] by reflexive property
The angle at point B = 90° by angle formed by the radius which is perpendiclar to the chord [tex]\overline{AC}[/tex]
ΔAOB and ΔCOB are right triangles (triangles having one 90° angle)
[tex]\overline{AO}[/tex] and [tex]\overline{OC}[/tex] are hypotenuse sides of ΔAOB and ΔCOB respectively and [tex]\overline{OB}[/tex] is a leg to ΔAOB and ΔCOB
Therefore;
ΔAOB ≅ ΔCOB, by Hypotenuse Leg rule of congruency
Therefore;
[tex]\overline{AB}[/tex] ≅ [tex]\overline{BC}[/tex] by Congruent Parts of Congruent Triangles are Congruent, CPCTC
[tex]\overline{AB}[/tex] = [tex]\overline{BC}[/tex] by definition of congruency
[tex]\overline{AC}[/tex] = [tex]\overline{AB}[/tex] + [tex]\overline{BC}[/tex] by segment addition postulate
∴ [tex]\overline{AC}[/tex] = [tex]\overline{AB}[/tex] + [tex]\overline{BC}[/tex] = [tex]\overline{AB}[/tex] + [tex]\overline{AB}[/tex] = 2 × [tex]\overline{AB}[/tex]
∴ [tex]\overline{AB}[/tex] = [tex]\overline{AC}[/tex]/2
[tex]\overline{AB}[/tex] = 14/2 = 7
[tex]\overline{AB}[/tex] = 7 units.
Answer:
7 units
Step-by-step explanation:
(a/b)^x-1 = (b/a)^x-3
Answer:
x = 2
Step-by-step explanation:
Three adults are picked at random from those with a mass of 70 kg or less.
Calculate the probability that one of them has a mass of 35 kg or less and the other two each have a
mass greater than 35 kg.
Need help on #7 , #8 Asap
Why do 6.52 x 10^3 and 652,000 ÷ 10^2 have the same answer?
Answer:
6.52 x 10^3 is just basically 6.52 × 1000, which is 6520. But 652,000 ÷ 10^2 is just 652000 ÷ 100, which is 6520. That's why they have the same answer.
A farmer has an orchard that covers an area of 40 acres. He grows apples on 25 acres, peaches on 7 acres, nectarines on 5 acres, and plums on 3 acres. The fruit trees are equally distributed within the orchard. A tree is chosen at random. Rounded to the nearest tenth of a percent, what is the theoretical probability that the tree is not within the acres of apple trees
Answer:
37.5%
Step-by-step explanation:
Calculation to determine the theoretical probability that the tree is not within the acres of apple trees
Using this formula
P=(Number of all orchard acres - Apple acres)/(Total orchard acres)*100
Where,
P represent Probability
Let plug in the formula
P=(40 acres- 25 acres)/40 acres
P=15 acres/40 acres *100
P=3/8*100
P=.375*100
P=37.5%
Therefore the THEORETICAL PROBABILITY that the tree is not within the acres of apple trees is 37.5%
Answer:
the answer is 37.5
Step-by-step explanation:
it is
Which is a point on the circle whose center is (0, 0) and whose radius is 5?
A. (2, 3)
B. (0, 0)
C. (3, 4)
D. (4, 5)
The equation of the circle whose center is (0, 0) and whose radius 5 is x² + y² = 25.
What is an equation of a circle?A circle can be characterized by its center's location and its radius's length.
Let the center of the considered circle be at (h,k) coordinate.
Let the radius of the circle be 'r' units.
Then, the equation of that circle would be:
(x-a)²+(y-b)² = r²
Where (a, b) is the centre and 'r' is the radius
We have a circle with centre (0, 0) and radius of 5.
Now, Substituting these value into the equation form, we have
(x-0)²+(y-0)² = 5²
x² + y² = 25
Hence, the equation of the circle whose center is (0, 0) and whose radius 5 is x² + y² = 25.
Learn more about equation of a circle here:
https://brainly.com/question/10165274
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What are the x-intercepts of the graph of the function below?
y= x^2+3x – 28
A. (6,0) and (4,0)
B. (-7,0) and (-4,0)
C. (7,0) and (-4,0)
D. (-7,0) and (4,0)
Cho đa thức f(x) = biết rằng f(1)=f(-1); f(2)=f(-2).
Chọn câu đúng :
A. f ( x ) = f ( −x) với mọi x
B. f ( x ) = − f ( −x) với mọi x
C. f ( x ) = 2 f ( −x) với mọi x
D. f ( x ) = 3 f ( −x) với mọi x
Answer:
A
Giải thích:
f(1)=f(x)
f(-1) và f(-2)= f(-x)
=> f(1)=f(-1) =A. f(x)=f(-x)
Hello!! Please help me ASAP
Using special right triangles show and explain all work for each problem. Each solution and work should demonstrate your understanding of Special Right Triangles (30-60-90 and 45-45-90)
Find the missing side length and angle of this triangle. I've attached the triangle.
Answer:
Step-by-step explanation:
The basic 30-60-90 triangle ratio is:
Side opposite to 30° angle is : x
Side opposite to 60° angle is : x √3
Side opposite to 90° angle is : 2x
From the diagram we learn that
x√3 = 10
[tex]x = \frac{10}{\sqrt{3}}=\frac{10*\sqrt{3} }{\sqrt{3}*\sqrt{3}}\\\\x=\frac{10\sqrt{3}}{3}= 5.77\\[/tex]
∠T = 30°, Side opposite to ∠T is AC = 5.77
∠A = 90°, side opposite to ∠A is TC = 2x = 2*5.77 = 11.54
State the equation, in slope-intercept form, of each of the following graphs of linear relations.
Explain how the equation was determined.
Answer: y=80/5x+80
Step-by-step explanation:
At one point graph goes from (0,400) to (25,800). So the y intercept is 400 because that’s where the line was at x=0. 0 to 25 is 25. 400 to 800 is 400. So the equation would be y=400/25x+400. But you can divide all of it by 5 to get y=80/5x+80.
secA-tanA=(cosA/2-sinA/2)/(cosA/2+sinA/2)
Answer:
Step-by-step explanation:
SecA - TanA
= 1/CosA - SinA/CosA
= 1 - SinA/CosA
We know that Sin2A = 2SinACosA and Cos2A = Cos²A - Sin²A
Thus SinA = Sin2(A/2) = 2Sin(A/2)CosA/2
CosA = Cos2(A/2) = Cos²A/2 - Sin²A/2
Now substituting the values back,
=> 1 - 2Sin(A/2)Cos(A/2) / Cos²(A/2) - Sin²(A/2)
// we know that Sin²θ + Cos²θ = 1
=> Sin²(A/2) + Cos²A/2 - 2Sin(A/2)Cos(A/2) / Cos²(A/2) - Sin²(A/2)
//We know that numerator is of form a² + b² - 2ab which is (a - b)².
//Similarly denominator is of form a² - b² which is (a - b)(a + b)
=> [Sin(A/2) - Cos(A/2)]² / [Cos(A/2) + Sin(A/2)][Cos(A/2) - Sin(A/2)]
=> [ - {Cos(A/2) - Sin(A/2)}]² / [Cos(A/2) + Sin(A/2)][Cos(A/2) - Sin(A/2)]
=> [Cos(A/2) - Sin(A/2)]² / [Cos(A/2) + Sin(A/2)][Cos(A/2) - Sin(A/2)]
=> [Cos(A/2) - Sin(A/2)] / [Cos(A/2) + Sin(A/2)]
= R.H.S
Hence proved.
Find the area of the regular polygon. Round your answer to the nearest hundredth.
Answer:
Step-by-step explanation:
The central angle of a hexagon is 60 degrees. Drop a line from the center to the middle of the side marked 7.
Use the tan of the angle so formed (which is 30 degrees)
Tan(30)= opposite / height (which is the line you just drew).
Tan(30) = 3.5 / h
Tan(30) = 0.5774
Tan(30) = 3.5 / h multiply both sides by h
h*Tan(30) = 3.5 Divide by tan30
h = 3.5 / Tan(30)
h = 3.5 / 0.5774
h = 6.062
Now from both ends of the given side, draw 2 lines to the center. Find the area of that triangle.
Area of 1 triangle = 1/2 * b * h
area of 1 triangle = 1/2 * 7 * 6.062
Area of 1 triangle = 21.2176
There are 6 such triangles so multiply that number by 6
Answer: 6 * 21.2176
Answer: 127.31
[tex]2 \sqrt{75} - \sqrt{108} + 5 \sqrt{48}[/tex]
[tex]\\ \sf\longmapsto 2 \sqrt{75} - \sqrt{108} + 5 \sqrt{48} \\\\ \sf\longmapsto 2 \sqrt{25 \times 3} - \sqrt{36 \times 3} + 5 \sqrt{16 \times 3} \\ \\ \sf\longmapsto 2 \times 5 \sqrt{3} - 6 \sqrt{3} + 5 \times 4 \sqrt{3} \\ \\ \sf\longmapsto 10 \sqrt{3} - 6 \sqrt{3} + 20 \sqrt{3} \\ \\ \sf\longmapsto (10 - 6 + 20) \sqrt{3} \\ \\ \sf\longmapsto 24 \sqrt{3} [/tex]
Answer:
24aprtment3
Step-by-step explanation:
Marking brainliest please explain if you can (PICTURE)
The two bases of a trapezoid measure 14 inches and 10 inches respectively. The trapezoid's height is 8 inches. What is the area of the trapezoid?
192 square inches
1120 square inches
140 square inches
96 square inches
Answer:
A = 96 inches ^2
Step-by-step explanation:
The area of a trapezoid is given by
A = 1/2 ( b1+b2)h where b1 and b2 are the bases and h is the height
A = 1/2( 14+10)*8
A = 1/2(24)*8
A = 12*8
A = 96 inches ^2
The area of trapezoid is given
A = 1/2 (b1+b2)h where b1 and b2 is base and h is height
A = 1/2 (14+10)*8
A = 1/2 (24)*8
A = 12 * 8
A = 96 square inches ....It takes four or three hours to get a pair of socks and seven hours to get a pair of clothes as he spends 89 hours kidding a total of 15 pairs of socks and gloves how many pairs of each does she kinit?
Answer:
Gloves = 11 pairs
Socks = 4 pairs
Step-by-step explanation:
Given that :
Time taken to knit pair of socks = 3 hours
Time taken to knit pair of gloves = 7 hours
Total time taken to knit 15 pairs of gloves and socks = 89 hours
Let :
number of socks = x and number of gloves = y
x + y = 15 - - - - (1)
3x + 7y = 89 - - - (2)
From (1):
x = 15 - y
Put x = 15 - y in (2)
3(15 - y) + 7y = 89
45 - 3y + 7y = 89
45 + 4y = 89
4y = 89 - 45
4y = 44
y = 44/4
y = 11
From :
x = 15 - y
x = 15 - 11
x = 4
Lúc 6 giờ, một ô tô xuất phát từ A đến B với vận tốc trung bình 40km/h. Khi đến B,
người lái xe làm nhiệm vụ giao nhận hàng trong 30 phút rồi cho xe quay trở về A với vận
tốc trung bình 30km/h. Tính quãng đường AB, biết rằng ô tô về đến A lúc 10 giờ cùng
ngày.
Answer:
Đáp án:
60km
Step-by-step explanation:
30 phút
=
1
2
giờ
Ô tô đi từ A đến B rồi từ B về A mất số thời gian là:
10
−
6
−
1
2
=
3
,
5
giờ (không tính thời gian nhận hàng)
Gọi độ dài quãng đường AB là
x
(km)
Ta có:
Thời gian đi từ A đến B là
x
40
(quãng đường chia vận tốc)
Thời gian đi từ B đến A là
x
30
Ta có phương trình:
x
40
+
x
30
=
3
,
5
⇔
x
=
60
(km)
Vậy quãng đường AB là 60km.
Solve for x:
( x - 6 ) ^ 2 = 7
Answer: x= 6 +/- root of 7
Step-by-step explanation:
1. Expand the left hand side: e.g, 3^2 = 3×3 =9
(x-6)(x-6) = 7
2. Multiply the brackets first by "separating" one of them, and take 7 to the left hand side:
x(x-6) - 6(x-6) =7
x^2 - 6x -6x +36-7=0
Simplify by adding like terms
x^2 -12x +29=0
3.Now your equation is in the form ax^2+bx + c =0, it means you can use the quadratic formula which is x= [-b +/- root of (b^2 - 4ac)]÷ 2a
Then SUBSTITUTE where:
a=1
b= -12
c=29
Therefore, x should be 6+ root of 7 OR 6- root of 7
Answer:
uhhhh okay thank you for removing my answer
Step-by-step explanation:
x2 +15-8x entre 3-x ayuda pliz
Ivana wants to give books from her store to the local library. She needs to place 8 books in each box. If she has 1,125 books to give away, how many boxes will she need
Answer:
140.625
Step-by-step explanation:
1125 books, placed into 8 per boxes, 1125/8=140.625
2( 5 1 m− 5 2 )+ 5 3 2, left parenthesis, start fraction, 1, divided by, 5, end fraction, m, minus, start fraction, 2, divided by, 5, end fraction, right parenthesis, plus, start fraction, 3, divided by, 5, end fraction
Answer:
2/5m - 1/5
Step-by-step explanation:
Given the equation :
2(1/5m - 2/5) + 3/5
First step:
Open the bracket by multiplying values in the bracket by 2
2/5m - 4/5 + 3/5
-4/5 + 3/5 = (-4 + 3) / 5 = - 1 / 5
Hence,
2/5m - 4/5 + 3/5 = 2/5m - 1/5
= 2/5m - 1/5
11. The student government is selling flowers for homecoming. The project costs them $20 for advertising and
$3 for each flower sold.
a. Evaluate the expressions 3n+20 and 3(n+20) when n = 4.
b. Which expression shows their total cost? How do you know?
Answer:
32
Step-by-step explanation:
3(n+20) = 3(4+20) = 3(24) = 723n+20 = 3(4)+20= 12+20=32If n represents the amount of flowers they sold, then the correct answer should be 32. The cost for each flower they sold would be 3 x 4 and then add $20 for advertising.
please answer this!!
Answer:
16
Step-by-step explanation:
if angle c is 45 then angle A is 45 also
Hence AB is equal to BC
Nigel makes the claim that x=6 is the solution to the equation 4(5x−12)−7x=5x. His work to support his claim follows. Given: 4(5x−12)−7x=5x Step 1: 20x−48−7x=5x Step 2: 20x−7x−48=5x Step 3: 13x−48=5x Step 4: 13x−13x−48=5x−13x Step 5: 0−48=−8x Step 6: 6=x Which of the following justifications can be used to justify and support Nigel's work? Select all justifications that are correct.
Step 1 is justified by the Distributive Property. , Step 1 is justified by the Distributive Property. , ,
Step 4 is justified by the Symmetric Property. , Step 4 is justified by the Symmetric Property. , ,
Step 5 is justified by the Property of Additive Inverses. , Step 5 is justified by the Property of Additive Inverses. , ,
Step 2 is justified by the Commutative Property. , Step 2 is justified by the Commutative Property. , ,
Step 6 is justified by the Associative Property.
Answer:
Step 1 is justified by the Distributive Property.
Step 4 is justified by the Symmetric Property
Step-by-step explanation:
Given the equation solved by Nigel expressed as
4(5x−12)−7x=5x.
First, we need to expand the bracket using the distributive property
4(5x−12)−7x=5x.
4(5x)-4(12) -7x = 5x
20x - 48 - 7x = 5x
Hence Step 1 is justified by the Distributive Property.
Next is to collect the like terms;
20x - 7x - 48 = 5x
Take the difference
13x - 48 = 5x
Next is to subtract 13x from both sides according to the symmetric property
13x - 48 - 13x = 5x - 13x
Hence Step 4 is justified by the Symmetric Property
The resulting equation will be
0-48 = -8x
Divide both sides by -8
-48/-8 = -8x/-8
6 = x
Hence the correct justifications are Step 1 is justified by the Distributive Property AND Step 4 is justified by the Symmetric Property
Find the gradient, picture below
Answer:
[tex]\frac{dy}{dx} = \frac{13}{8} [/tex]
Step-by-step explanation:
[tex] y = 2x + 6 {x}^{ - \frac{1}{2} } \\ \frac{dy}{dx} = 2 + 6( - \frac{1}{2}) {x}^{ - \frac{1}{2} - 1 } \\ \frac{dy}{dx} = 2 - 3 {x}^{ - \frac{3}{2} } \\ \frac{dy}{dx} = 2 - \frac{3}{ \sqrt{ {x}^{3} } } [/tex]
When x = 4,
[tex]\frac{dy}{dx} = 2 - \frac{3}{ \sqrt{ {4}^{3} } } \\ = \frac{13}{8} [/tex]
Answer:
Hello,
Answer 13/8
Step-by-step explanation:
[tex]y=2x+\dfrac{3}{\sqrt{x} } \\\\y'=2+6*\dfrac{-1}{2} x^{\frac{-3}{2} }\\\\y'=3-\frac{3}{\sqrt{x^3}} \\\\\\For x=4, \\\\y'(4)=2-\dfrac{3}{8} =\dfrac{13}{8}[/tex]
A
75°
B.
Reflex Angle B =
degrees.
Answer:
285
Step-by-step explanation:
B+A=360, B=360-75=285
An angle whose measure is greater than 180° but less than 360° is termed a reflex angle.
[tex]\large{\textrm{{{\color{navy}{∠A \: + \: ∠B \: = \: 360°}}}}}[/tex]
[tex] \bf \large \longrightarrow \: \:75 \degree \: + \: ∠ B \: = \: 360°[/tex]
[tex] \bf \large \longrightarrow \: \: \angle B \: = \: 360° \: - \: 75 \degree[/tex]
[tex] \bf \large \longrightarrow \: \: \angle B \: = \:285 \degree[/tex]
Write equation of a line in slope intercept form with the given information p=(1,2) m=4
Answer:
[tex]y=4x-2[/tex]
Step-by-step explanation:
Hi there!
Slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)
We're given that the slope is 4. Plug this into [tex]y=mx+b[/tex] as m:
[tex]y=4x+b[/tex]
Now, to determine the y-intercept, plug in the given point (1,2) and solve for b:
[tex]2=4(1)+b\\2=4+b\\b=-2[/tex]
Therefore, the y-intercept is -2. Plug this back into [tex]y=4x+b[/tex] as b:
[tex]y=4x+(-2)\\y=4x-2[/tex]
I hope this helps!
Plsss help asap plsssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss
Answer:
The answer is the last one, (X^2-2)/3!
Step-by-step explanation:
To get the inverse of a function, you switch the variables and solve for y. Doing this produces the last choice.
