10. Find a third number so that the three numbers form a right triangle:
i) 9,41, _
ii) 13,85, _

Check each number's prime factorization, then add any factors necessary to make each one a cube.

(a) 3

[tex]3087 = 3^2 \times 7^3 \implies \boxed{3}\times3087 = (3\times7)^3 \implies 9261=21^3[/tex]

(b) 25

[tex]2560 = 2^9\times5^1 \implies \boxed{5^2}\times2560 = \left(2^3\times5\right)^3 \implies 64000 = 40^3[/tex]

Answer:

Step-by-step explanation:

hello

calculate x : 3x+2 =5

means : 3x+2-2 =5-2

3x = 3

so : x = 3/3 =1

1 is the  element in domain has the image 5 under function f(x)= 3x+ 2

Answer:

Creditable

Step-by-step explanation:

Could also be:
up-to-date

Answer:

x = -8, 1.

Step-by-step explanation:

x^2 + 7x - 8 = 0

(x + 8)(x - 1) = 0

x = -8, 1.

Answer:

-8 and 1

Step-by-step explanation:

Quadratic expression.

A quadratic expression is an expression with 2 as the highest power of the unknown.

Solving the question:

[tex]x {}^{2} + 7x - 8 \\ x {}^{2} + 8x - x - 8 \\ x(x + 8) - 1(x + 8) \\ (x - 1)(x + 8) \\ x = 1 \: or \: x = - 8[/tex]

Answer:

Exact Form: x = -5/2

Decimal Form: x = -2.5

Mixed Form: x = 2 1/2

Answer:

Step-by-step explanation:

5(x+2)=3x+5

5x+10=3x+5

5x=3x-5

2x=-5

x=-0.4

Answer:

see explanation

Step-by-step explanation:

[tex]\frac{3\pi }{4}[/tex] is an angle in the second quadrant where sin > 0 and cos < 0

cos([tex]\frac{3\pi }{4}[/tex] )

= cos (π - [tex]\frac{3\pi }{4}[/tex] )

= - cos ([tex]\frac{\pi }{4}[/tex] )

= - [tex]\frac{\sqrt{2} }{2}[/tex]

and similarly

sin ([tex]\frac{3\pi }{4}[/tex] )

= sin ([tex]\frac{\pi }{4}[/tex] )

= [tex]\frac{\sqrt{2} }{2}[/tex]

Answer: 21 units²

Step-by-step explanation:

Since there is a pair of parallel sides, this figures is a trapezoid. The formula for the area of a trapezoid is [tex]\frac{1}{2}(a+b)h[/tex], where a and b are the parallel sides and h is the height.

Here, a and b are 5 and 9, while 3 is the height. Let's put all 3 values into the formula.

[tex]A=\frac{1}{2}(5+9)*3[/tex]

[tex]A=\frac{1}{2}(14)*3[/tex] [Adding in the parentheses]

[tex]A=7*3[/tex] [Multiplying one-half by 14]

[tex]A=21[/tex] [Multiplying 7 and 3]

The area is 21 units².

Check the picture below.

Answer:

C.  (x,y) ⇒ (x + 8, y − 3)

Step-by-step explanation:

See attached image.

Answer:

Step-by-step explanation:

cos A = √( 1 - (5/13)²) = √( 1 - 25/169) = √(144/169) = - 12 /13

in 2 A = 2 sin A cos A

sin 2 A = 2 *5/13 ( - 12/13 ) = - 120 / 169

the answer is -120/169

Theo's base salary  using a simultaneous equation approach is $2,996.22 .

In order to determine the base salary of Theo, we can express the two earnings and sales amounts using simultaneous equation, that we would solve to arrive at the base salary

Bear in mind that total earnings are determined as base salary plus commission

Let X be the base salary

Let R be the rate of commission

commission =sales*rate of commission

When earnings were $3,835.25 and sales is $12,850, we have the below equation:

X+(12,850*R)=3,835.25

X+12850R=3,835.25  .................... equation (1)

When earnings were $3,641 and sales is $9,875, we have the below equation:

X+(9,875*R)=3641

X+9875R=3641 .........................  equation (2)

subtract equation 2 from 1

2975R=194.25

R=194.25/2975

R=commission rate=6.52941176470588%

substitute for R in equation 1 to arrive at X(base salary)

X+(12850*6.52941176470588%)=3,835.25

X=3,835.25-(12850*6.52941176470588%)

X=base salary=$2,996.22

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Y=4x+5 and y=4x-5 has no solution

What are Linear Equations in two Variables?

The formula for a two-variable linear equation is Ax + By + C = 0, where A and B are the coefficients, C is a constant term, and x and y are the two variables, each with a degree of 1. A linear equation with two variables, for instance, is 7x + 9y + 4 = 0. These two linear equations are referred to be simultaneous linear equations if we take them into consideration.

Steps

[tex]Y=4x+5\\ Y=4x-5[/tex]

Substitute y=4x+5

[tex][4x+5=4x-5][/tex]

Refine [tex][4x+5=4x-5][/tex]

-10=0

-10=0 is a false ,therefore the system of a equation have no solution

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A, C, D are correct. In this question the options that are correct are

We have first with legs height to be =529 m and 229 m;

second with legs height =529 m and 347 m.

Then tan x = 529/229

tan y = 529/347

We can see that tanx > tany

Hence x> y

We have alternate angles in the question. This makes x=v, y=w

For D

x > y while x = v

This tells us that v>y

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Answer:

acd

Step-by-step explanation:

Answer: 156 degrees

Step-by-step explanation:

Answer:

x=17

Step-by-step explanation:

Since they are intersecting lines, 3x=51

x=17

Answer:

x = 17

Step-by-step explanation:

When two lines intersect each other, the opposite angles are identical. Therefore, you can set both angles equal to each other to find the value of "x".

3x = 51

x = 17

From statement equation, the number of correct answers will result in a passing grade is 9.3

Given that each question on the quiz is worth 8 points.

Also given a score of 75 is a passing grade.

Let the number of correct answered questions be x

Thus the total score of the correct answers is 8x

The statement equation is -

⇒ 8x = 75

⇒ x = 75/8 = 9.3

∴  x ≈ 9

Therefore, from statement equation, the number of correct answers will result in a passing grade is 9.3

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Answer:

Step-by-step explanation:

First prime factorize 135,

135 = 5×3×3×3

Now prime factorize 128,

128=2×2×2×2×2×2×2 = 2^7

the highest prime factor of 135 is 5,

Let 5 be x

the highest power of the lowest prime factor of 128 which is the power 2 is 7

Let 7 be y

According to the question x^y = 5^7

Answer:

Answer

Step-by-step explanation:

(a) B ⊄ A (b) C ⊂ A (c) B ⊄ C (d) ∅ ⊂ B (empty set is an element of any set)

(e) C ⊂ C (reflexitivity).

The total surface area of the composite figure is calculated as 444 m².

Total surface area = surface area of the bottom rectangular prism + surface area of the top triangular prism - area of the shared surface.

Surface area of the triangular prism = (S1 + S2+ S3)L + bh = (16 + 10 + 10)5 + (6)(16) = 276 m²

Rectangular prism surface area = 2(wl + hl + hw) = 2(5×16 + 4×16 + 4×5) = 328 m²

Area of shared surface = 2(16)(5) = 160 m²

Total surface area = 328 + 276 - 160 = 444 m².

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The x-intercepts from the graph are -3.646 and 1.646 with the parabolic curve facing upwards

Quadratic functions are functions that has a leading coefficient of 2.

According to the question, we are to graph the quadratic function f(x) = x^2 + 2x - 6. The curve will be parabolic in nature and facing upwards since it is a quadratic function.

The x-intercepts from the graph are -3.646 and 1.646 as shown in the attached graph.

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Since the height (feet) of the spray of water is given by this equation h(x) = -x² + 10x + 9.5, we can logically deduce that the irrigation system is positioned 9.5 feet above the ground to start.

For any quadratic equation with a parabolic curve, the axis of symmetry is given by:

Xmax = -b/2a

Xmax = -10/2(-1)

Xmax = 5.

Thus, the maximum height on the vertical axis is given by:

h(x) = -x² + 10x + 9.5

h(5) = -(5)² + 10(5) + 9.5

h(5) = -25 + 50 + 9.5

h(5) = 34.5 feet.

Therefore, the spray reaches a maximum height of 84.5 feet at a horizontal distance of 5 feet away from the sprinkler head.

Also, the spray reaches all the way to the ground at about:

Maximum distance = √34.5 + 5

Maximum distance = 10.87 feet.

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Complete Question:

An irrigation system (sprinkler) has a parabolic pattern. The height, in feet, of the spray of water is given by the equation h(x) = -x² + 10x + 9.5, where x is the number of feet away from the sprinkler head (along the ground) the spray is.

1. The irrigation system is positioned____ feet above the ground to start.

2. The spray reaches a maximum height of ____feet at a horizontal distance of feet away from the sprinkler head.

3. The spray reaches all the way to the ground at about_____ feet away​

Answer:

Length is equal to 18

Step-by-step explanation:

The formula for finding the area(A) of a rectangle in Length(L) times width(W): A=(W)(L). If we plug in the given information into the equation, you will get 144=(8)(L). From there we solve for L.

144 = (8)(L)

144/8 = (8)/8 (L)

18 = L

Answer:

A

Step-by-step explanation:

His commision was 0.06(160000-20000) = $8400.

His salary was $10,000.

His bonus was $500.

Adding these together, we get $18,900.

Answer:

-1

Step-by-step explanation:

Expanding (x² − x + 2)(x − 1) we get [tex]x^{3} -x^{2} -x^{2} +x+2x-2[/tex]. When we simplify that, we get [tex]x^{3} -2x^{2} +3x-2[/tex] which fits the form Ax³ + Bx² + Cx + D.

We can see that A = 1, B = -2, C = 3, D = -2. Thus A + D = 1 - 2 = -1.

Therefore your answer is -1

Answer:

A + D = -1

Step-by-step explanation:

Given: (x² − x + 2)(x − 1) = Ax³ + Bx² + Cx + D

Step 1: Simplify using the Distributive Property.

[tex]\\\implies (x^2 - x + 2)(x - 1) \\\\\implies x(x^2 - x + 2) + -1(x^2 - x + 2)\\\\\implies x^3 - x^2 + 2x - x^2 + x - 2\\\\\implies \bold{1}x^3 -\bold{2}x^2 + \bold{3}x - \bold{2}[/tex]

Step 2: Determine the value of the coefficients.

[tex]\implies {\sf A} = 1, {\sf B} = -2, {\sf C} = 3, {\sf D} = -2[/tex]

Step 3: Find the value of A + D.

[tex]\implies {\sf A} + {\sf D} \Rightarrow 1 - 2 = \boxed{-1}[/tex]

The solution of the system is:

x = 62/7

y = 30/7

Here we have the system:

4x + 5y = -14

-5x - 8y = 10

To solve it by combining the equations, we need to try to remove one of the variables.

If we take the sum of 5 times the first equation and 4 times the second equation we get:

5*(4x + 5y) + 4*(-5x - 8y) = 5*(-14) + 4*10

If we simplify that we get:

20x  + 25y - 20x - 32y = -30

-7y = -30

Now we can solve that for y:

y = -30/-7 = 30/7

Now to get the value of x, we can replace the value of y in any of the given equations:

Using the first one:

4x + 5y = -14

x = (-14 - 5y)/4

x = (-14 - 5*30/7)/4 = (-98/7 - 150/7)/4 = 248/28 = 124/14 = 62/7

The solution of the system is:

x = 62/7

y = 30/7

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Here, Given

Area of Equilateral triangle = 3cm2

therefore, we know;

Area of Equilateral triangle =( [tex]\sqrt{3}[/tex]÷4)×[tex]a^{2}[/tex]

so,

3 =( [tex]\sqrt{3}[/tex]÷4)×[tex]a^{2}[/tex]

3÷( [tex]\sqrt{3}[/tex]÷4) = [tex]a^{2}[/tex]

2.63 cm = a .

The area of ​​an equilateral triangle is the area covered by an equilateral triangle on a two-dimensional plane. An equilateral triangle is a triangle with all sides equal and all angles at 60 degrees. The area of ​​the shape is the number of unit squares that fit inside.

Here, "unit" refers to 1, and a unit square is a square with one side. Alternatively, the area of ​​an equilateral triangle is the total amount of space it surrounds in a two-dimensional plane.

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The student with the correct list of steps is student B

The list of steps is to create a line parallel to line AB

Both students are correct in step (1).

However, the step (2) of student A is incorrect.

This is so because, the student did not provide how points C and G are created

Hence, the student with the correct list of steps is student B

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Using proportions to find the radius of figure 2, we have that:

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

The rule of three to find the radius of figure 2 is given as follows:

[tex]\frac{5}{9} = \frac{r}{4.5}[/tex]

Applying cross multiplication:

9r = 4 x 4.5

r = 4 x 4.5/9

r = 2 in

The circumference of a circle of radius r is given by:

[tex]C = 2\pi r[/tex]

In this problem, we have that r = 2 inches, hence:

[tex]C = 2\pi \times 2 = 4\pi[/tex]

The area of a circle of radius r is given by pi multiplied by the radius squared, as follows:

[tex]A = \pi r^2[/tex]

Hence:

[tex]A = 4\pi[/tex]

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Answer: First one is 5, Second is 6.25

Step-by-step explanation: Correct on Edmentum/Plato

Snow reaches at a 15 inches after 16 hours. and 8 inches melt in next 6 hours.

According to the statement

we have a given that there was 1 inch snow on the ground before the snowstorm starts.

then snow fell at constant rate of 3 inches every 2 hours until the snow level reaches at 12 inch had fallen

It means after that there was 13 inch snow on the ground.

and in 1 hour only 1.5 inches snow increases

and if snow takes 2 hours to increase at 3 inches then

it takes 10 hours to reach at 12 inches.

So, snow falls for 10 hours to increase at 12 inches.

And then the snow falls at constant rate of 1 inch per hour for 2 hours.

It means now snow reaches at a 15 inches after 16 hours.

Then sun melt the snow at a 4 inches per 3 hours and sun came for 6 hours then

it means now the level of snow reduced and came at the 7 inches.

because sun reduced 8 inches snow in 6 hours.

So, this is the data collected by a person.

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Answer:

A and B

Step-by-step explanation:

A : (a²+b²=c²) 11²+13²=290 (c²); c=√290

B : 7²+24²=625; c=√625=25

C : 2²+5²=29≠7²

According to the Pythagorean triple, the side lengths that will form a right triangle are:

A. 11, 13, √290

B. 7, 24, 25

The Pythagorean triple are three set of sides that can form a right triangle if the square of the longest side equals the sum of the squares of the other two smaller sides.

11² + 13² = (√290)²

290 = 290 [correct]

7² + 24² = 25²

625 = 625 [correct]

2² + 5² = 7²

29 ≠ 49 [correct]

Therefore, the side lengths that will form a right triangle are:

A. 11, 13, √290

B. 7, 24, 25

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