The angle marked a=92 degrees.
work out the angle marked x.

In general, they're not similar.

In any triangle with side lengths a, b, and c, we have the aptly-named triangle inequality that says the largest side is no larger than the sum of the smaller sides. In other words, if a and b are both smaller than c, then

a + b ≥ c

Suppose x < 12. Then BC corresponds to either YZ or XY.

• If BC corresponds to YZ, then the triangles are similar if and only if

BC/YZ = AB/XY = AC/XZ

x/2 = 9/3 = 12/4 = 3   ⇒   x = 6

• If BC corresponds to XY, then triangle similarity means

BC/XY = AB/YZ = AC/XZ

x/3 = 9/2 = 12/4

but this fails because 9/2 ≠ 12/4 = 3.

Suppose x > 12. Then BC corresponds to XZ, and

x/4 = 12/3 = 9/2

but this also fails because 12/3 = 4 ≠ 9/2.

(We ignore the case of x = 12 because that would make ∆ABC isosceles, and ∆XYZ certainly is not.)

So ∆ABC and ∆XYZ are similar only if x = 6. Under this condition, similarity would follow from the SSS similarity theorem.

Answer:

x<-4 or x≤4

Step-by-step explanation:

The solution of the inequality is x > -4 and x ≤ 4.

So, the graph B is correct.

Given is an inequality, x+7 > 3 and x-5 ≤ -1, we need to solve and identify the graph,

To solve the compound inequality, let's solve each inequality separately and then find the intersection of the solutions.

Inequality 1: x + 7 > 3

Subtract 7 from both sides:

x > 3 - 7

x > -4

Inequality 2: x - 5 ≤ -1

Add 5 to both sides:

x ≤ -1 + 5

x ≤ 4

Now, we need to find the intersection of the solutions for both inequalities.

Since the conjunction between the two inequalities is "and," we need to find the common solution.

The common solution is the values of x that satisfy both x > -4 and x ≤ 4. From the two inequalities, we can see that the common solution range is from -4 to 4, including -4 but not including 4.

Therefore, the solution to the compound inequality is: -4 < x ≤ 4

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Answer:

y = 3x - 4

Step-by-step explanation:

The general structure of a line in slope-intercept form is:

y = mx + b

In this form, "m" is the slope and "b" is the y-intercept.

(Step 1)

Before you can determine this equation, you need to find the value of "m". Since you were given the value of two points, you can find this by using the point-slope form. The general structure of the point-slope equation is:

y₁ - y₂ = m(x₁ - x₂)

y₁ - y₂ = m(x₁ - x₂)                              <---- Point-slope equation

-1 - 8 = m(1 - 4)                                  <---- Insert "x" and "y" values from table

-9 = m(1-4)                                         <---- Simplify left side

-9 = -3m                                            <---- Simplify inside parentheses

3 = m                                                 <---- Divide both sides by -3

(Step 2)

Now that you know "m", you can plug it and the "x" and "y" values of one point into the slope-intercept equation to find the value of "b".

y = mx + b                                         <---- Slope-intercept equation

y = 3x + b                                          <---- Plug 3 into "m"

-1 = 3(1) + b                                        <---- Plug "x" and "y" values in

-1 = 3 + b                                           <---- Multiply 3 and 1

-4 = b                                                 <---- Subtract 3 from both sides

(Step 3)

Now that you know that m = 3 and b = -4, you can substitute these values into the slope-intercept form to find your final answer. You can check your answer by plugging the "x" values from the table into the equation to verify that you get the correct "y" values.

y = 3x - 4

The graph described is the graph of a quadratic function.

The x-intercept of the function is at; (8, 0).

It follows from the description box of the graph that it begins in the third quadrant, and rises through a series of points in the first quadrant before it exits the first quadrant.

Hence, it follows that the graph is a quadratic function and its x-intercept is at point; (8,0).

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Answer: 1. Square root

2.(8,0)

Step-by-step explanation:

Answer:

CE = 3.2 cm

DH = 4.5 cm

Explanation:

Given:

MNPR ≅ CEDH

≅ - means approximately equal

Lengths of the shape:

MN = CE = 3.2 cm

NP = ED = 6.5 cm

PR = DH = 4.5 cm

RM = HC = 9 cm

Answer:

35 ways

Step-by-step explanation:

Seven juniors to choose three from

  7 C 3 = 7! / ( 4! 3!) = 35

[tex] \huge \tt \color{pink}{A}\color{blue}{n}\color{red}{s}\color{green}{w}\color{grey}{e}\color{purple}{r }[/tex]

▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂

▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂

that is :-

[tex]{ \boxed{✠\underline{ \boxed{ \sf{ \red✰Cost \: price =100 \times \frac{selling \: price}{100 + profit\%} }}}✠}}[/tex]

▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂

▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂

[tex]\rm{➾x = 100 \times \frac{690}{100 + 15}} \\\rm{➾x \frac{100 \times 690}{100 + 15}~~~~~~~~~~~~~~~ } \\ \rm{➾x = \frac {100 \times \cancel{ 690}}{ \cancel{115}}}~~~~~~~ \\ \rm{➾x = 100 \times 6}~~~~~~~~~~~~~~~ \\ \rm{➾x =106}~~~~~~~~~~~~~~~[/tex]

▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂

➣ Hence "x" (Cost price) of the item

[tex] \large{ \boxed{✠\underline{ \boxed{ \sf{ Rs.106\green✓}}}✠}}[/tex]

▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂☘

Hope it helps !

Answer:

x = 3

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]26=-1+\left( 27x\right)^{\frac{3}{4} }[/tex]

[tex]\Longleftrightarrow 27=\left( 27x\right)^{\frac{3}{4} }[/tex]

[tex]\Longleftrightarrow \left( 27\right)^{\frac{4}{3} } =\left[ \left( 27x\right)^{\frac{3}{4} } \right]^{\frac{4}{3} }[/tex]

[tex]\Longleftrightarrow \left( 27\right)^{\frac{4}{3} } =\left( 27x\right)^{\frac{3}{4} \times \frac{4}{3} }[/tex]

[tex]\Longleftrightarrow \left( 27\right)^{\frac{4}{3} } =27x[/tex]

[tex]\Longleftrightarrow x=\frac{27^{\frac{4}{3} } }{27}[/tex]

[tex]\Longleftrightarrow x=27^{\frac{4}{3} -1}[/tex]

[tex]\Longleftrightarrow x=27^{\frac{1}{3} }[/tex]

[tex]\Longleftrightarrow x=\sqrt[3]{27}[/tex]

[tex]\Longleftrightarrow x=3[/tex]

Answer:

4

Step-by-step explanation:

(3 × 14) × 3 = 126

7 × 18 = 126

Boubacar will have to increase each dimension by 4 ft so that its area is triple.

The area of a rectangle is given by -

A[R] = L x B

where -

L is Length of rectangle

B is Breadth or width of rectangle.

Given is a deck that measures 3 feet by 14 feet. Boubacar wants to increase each dimension by equal lengths so that its area is tripled.

Assume that he increases the dimensions by x ft.

Initial Area = [A] = 3 x 14 = 42 ft².

Final Area = [A'] = 3[A] = 3 x 42 = 126 ft²

Initial dimensions = (L x B) = 3 feet x 14 feet

Final dimensions = (L' x B') = (3 + x) × (14 + x)

Now -

(L' x B') = 126

(3 + x)(14 + x) = 126

3(14 + x) + x(14 + x) = 126

42 + 3x + 14x + x² = 126

x² + 17x - 84 = 0

Solving the equation, we get -

x = 4  [ non negative number ]

Therefore, Boubacar will have to increase each dimension by 4 ft so that its area is tripled.

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Answer:

Option 1 ========>  p = ∛8

Step-by-step explanation:

In order to make p the subject we would need to cube root both sides and would therefore get :

∛(p³) = ∛8

p = ∛8

Just a side not but you wrote the first option wrong but it's fine as you attached an image.

Hope this helped and have a good day

The calculation p=∛8  can be used to find the value of p in the equation p³= 8

An expression is combination of variables, numbers and operators.

The given equation is  p³= 8

p to the power of three equal to eight

p is the variable in the given equation

We have to find the value of p from the equation

Take cube root on both the side

∛ p³= ∛8

On left hand side the cube will be cancelled and left with p

p=∛8

Hence, p=∛8 calculation can be used to find the value of p in the equation p³= 8

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Answer:

[tex](x+1-i)(x+1+i)[/tex]

Step-by-step explanation:

[tex](x+1-i)(x+1+i)\\\\=(x+1)^2 -i^2~~~~~~~~~~~~~;[a^2 -b^2 = (a+b)(a-b)]\\\\=x^2 +2x +1 -(-1)\\\\=x^2 +2x +1+1\\\\=x^2 +2x +2[/tex]

If an angle is a central angle, meaning that it goes through the center, then its corresponding arc has the same measure.

AOT is a central angle, which means that AT will have the same measure.

AOT = 97, AT = 97

Answer: A, 97

Hope this helps!

There will be 36 squares in the 8th step of the pattern

The pattern and the squares are represented as:

Pattern   Squares

1                 1

2                3

3               6

4             10

This can be rewritten as:

Pattern   Squares

1                 1

2                1 + 2

3                1 + 2 +3

4                1 + 2 + 3 +4

So, the number of squares on the 8th pattern is:

8th pattern = 1 + 2 + 3 +4 + 5 + 6 + 7 + 8

Evaluate

8th pattern = 36

Hence, there will be 36 squares in the 8th step

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The equation that has infinitely many solutions is A. 4x + 5(2x + 6) = 14x + 30

An equation with infinitely many solutions is represented as:

ax + b = ax + b

This means that both sides of the equation must be the same.

Next, we test the options:

4x + 5(2x + 6) = 14x + 30

Open the bracket

4x + 10x + 30 = 14x + 30

Evaluate the like terms

14x + 30 = 14x + 30

Both sides of the equation must be the same.

Hence, the equation that has infinitely many solutions is A. 4x + 5(2x + 6) = 14x + 30

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Answer:

3 * (x + 3) = x * 5 - 3

By applying concepts from vectorial calculus, we conclude that the gradient of the one variable function y = 2 · x³ - 7 · x + 4 when x = -2 is equal to 17.

A gradient is a generalization of the tangent curve used for multivariate function, that is, a function with more than one variable. In this case we have a function with one variable, which means that the gradient is equal to the slope:

[tex]\nabla f = \frac{df}{dx}[/tex]     (1)

Now we proceed to calculate the gradient of the curve:

[tex]\nabla f = 6\cdot x^{2}-7[/tex]

[tex]\nabla f = 6\cdot (-2)^{2}-7[/tex]

[tex]\nabla f = 17[/tex]

By applying concepts from vectorial calculus, we conclude that the gradient of the one variable function y = 2 · x³ - 7 · x + 4 when x = -2 is equal to 17.

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Answer:

  dilation by a factor of 1/3 about the origin

Step-by-step explanation:

Each side of triangle B is 1/3 the length of the corresponding side of triangle A. This tells you dilation using a scale factor of 1/3 is involved.

Lines joining corresponding points of triangles A and B converge on the origin. This tells you the center of dilation is the origin.

The one transformation that maps A to B is ...

  dilation by a factor of 1/3 about the origin

_____

Additional comment

No rotation, reflection, or translation are needed, since the triangles have the same orientation, and dilation fully accounts for their relative position.

Answer:

Let b the cost of the manicure

15% of b= 5.10$

15% × b= 5.10$

b= 5.10×100/15

b= 34$

Answer: 1. Dilation.

Step-by-step explanation: All of these transformations do not change the shape's form except for a dilation. It is nessacary to change the shape, so it is a dilation.

The least number of computers that must be shipped is 10.

In order to determine the least number of computers that must be shipped, the equation that represents the cost of shipping should be equal to the selling price of the computers.

3000 + 100x = 400x

In order to determine the value of x, take the following steps:

3000 = 400x - 100x

3000 = 300x

x = 3000 / 300

x = 10

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The probability that the next spin lands on red is

The table of values is given as:

Red = 4

Blue = 3

Green = 20

Yellow = 14

Purple = 16

The probability that the next spin lands on red is:

P(Red) = Red/Total

This gives

P(Red) = 4/(4+3+20+14+16)

Evaluate

P(Red) = 7%

Hence, the probability that the next spin lands on red is

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Answer:8%

Step-by-step explanation:

[tex]\dfrac{5-i}{4+3i}=\dfrac{(5-i)(4-3i)}{(4+3i)(4-3i)}=\dfrac{20-15i-4i-3}{16+9}=\dfrac{17-19i}{25}=\dfrac{17}{25}-\dfrac{19}{25}i[/tex]

Answer:

30

Step-by-step explanation:

Answer:

are you from Philippines?

Step-by-step explanation:

because I want to know gehe

Answer:

[tex]8^{14}[/tex]

Step-by-step explanation:

When we multiply exponents with the same base, the product it the base to the power of the exponents added together. In this case, the base will remain as 8 and the exponent will be 10 + 4 = 14. Therefore, the answer is [tex]8^{14}[/tex].

Answer:

[tex]\large\boxed{\sf \sf 8^{14}}[/tex]

Explanation:

[tex]\rightarrow \sf 8^{10} \ \ x \ \ 8^4[/tex]

apply exponent rule: [tex]\sf \bf a^b\cdot \:a^c=a^{b+c}[/tex]

[tex]\rightarrow \sf 8^{10+4}[/tex]

[tex]\rightarrow \sf 8^{14}[/tex]