Which equation accurately represents this statement? Select three options. Negative 3 less than 4.9 times a number, x, is the same as 12.8. Negative 3 minus 4.9 x = 12.8 4.9 x minus (negative 3) = 12.8 3 + 4.9 x = 12.8 (4.9 minus 3) x = 12.8 12.8 = 4.9 x + 3

The angle of CAE is 22

A line known as a perpendicular bisector cuts a specified line segment precisely in half, creating a 90° angle at the junction. The intersection of a line segment's midpoint with a perpendicular bisector. It can be built with a compass and a ruler. On both sides of the line segment being divided, it forms a 90° angle.

Perpendicular bisector of ABC's side AB crosses BC at point E and side AB at point D. Additionally, m CAB = 82 and m C = 68.

Adopt A E.

In ABC, the triangle's angle sum property is A+B+C=180°.

82°+∠B+68°=180°

∠B= 180°-150°

∠B=30°

AD=B DDE is a perpendicular bisector in A DE and B DE.

If ADE=BDE=90°

DE is common.

Δ A DE ≅ Δ E DB→→[S AS]

∠DEB=∠D A E→→[CPCT]----(1)

In Δ DBE

∠EDB + ∠DBE+∠BED=180°→→Angle sum property of Triangle.

90° +30°+∠BED=180°

∠BED=180°-120°

∠BED=60°

So, ∠BAE=∠BED=60°------[using (1)]

∠CAE=∠CAB - ∠BAE

= 82°-60°

= 22°

Therefore the angle CAE is 22

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Answer:

Below

Step-by-step explanation:

Sum of interior angles for the uppr right triangle = 180

52 + 90 + '2' = 180

'2' =38°

The amount of medicine required for a patient whose weight is 173.75 pounds will be equal to 217.18 milligrams.

The ratio notion is used in mathematics when evaluating two or more numbers. It works as a comparison tool to demonstrate how big or small a particular number is. A ratio divides two quantities to compare them.

As per the data given in the question,

Weight of patient = 164 pounds

Medicine for 164 pounds weight = 205 milligrams

Weight of another patient = 173.75 pounds

Let the amount of medicine required is x.

So,

164 pounds = 205 milligrams and,

173.75 pounds = x milligrams

Perform Cross-multiplication,

164x = 205 × 173.75

x = 35618.75/164

x = 217.18 milligrams.

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Answer:

60%

Step-by-step explanation:

Shaun won 60% percent of the games.

Answer:

Shaun won 60% out of the 10 video games he played.

Step-by-step explanation:

If Shaun played 10 video games and only won six out of all of them, he won 60% since we can count 10 as 100% and 6 as 60%.

Answer:

[tex](4 , -5)[/tex]

Step-by-step explanation:

Note that when you move left or right any amount of units, you will be making the changes to the x-variable. If you move up or down any amount of units, you will be making the changes to the y-variable.

In this case, it is given that:

(x , y) = (-3 , -5)

You will want to move right 7 units, as you are trying to find your starting position. Add 7 from the x variable:

[tex](x , y) = (-3 , -5) = (-3 (+7) , -5)\\\\= (-3 (+7) , -5)\\= ((-3 +7) , -5)\\= (4 , -5)[/tex]

[tex](4 , -5)[/tex] is your starting position.

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Answer:

Your answer is [tex]x=2[/tex] and [tex]y = 0[/tex]

Step-by-step explanation:

(attached)

Answer:

(2,0)

x=2, y=0

Step-by-step explanation:

(-2)3x-7y=6(-2)

(3)2x+7y=4(3)

-6x+14y=-12

6x+21y=12

-6x+14y=-12+6x+21y=12

35y=0

y=0

sub into one of the original equations

2x+7(0)=4

2x=4

x=2

Answer:

a and f are 14°

Angles b, c, d, and e are all 166°

Step-by-step explanation:

Alternate interior angles are congruent

x + 9 = 4x - 6  Subtract x from both sides

9 = 3x - 6    Add 6 to both sides

15 = 3x  Divide both sides by 3

5 = x

Plug this back into the equation for find the angles measurements

x + 9

5 + 9

14

or

4x _ 6

4(5) -6

20 - 6

14

angles a and f are vertical angles so they are congruent and equal to 14

B ,c , d and e are all supplements to the found angles

180-14 = 166

Cutting perfect slices of pie can be tricky. Crusts can crumble, bottoms can buckle and fillings can spill over, but there are a lot of tricks for a good slice.

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The number of years for the value of $900 to reach $1,800 if the rate of interest is 4%, is 25 years.

When the loan is given to you, then some amount is charged to you for the principal amount and that is called interest.

Given:

The amount after some years, A = $1800,

The rate of interest, r = 4% per annum,

The principal amount, p = $900,

Calculate the number of years as shown below,

A = P + SI

1800 = 900 + p × r × t / 100

Here, t is the time in years,

1800 - 900 = 900 × 4 × t / 100

900 = 3600t / 100

900 = 36t

t = 900 / 36

t = 25

Thus, the number of years will be 25.

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Answer:56.6%

Step-by-step explanation:

30 - 13 = 17

17 /30 x 100 = 56.6 %

Answer:

10,5 should be changed

Step-by-step explanation:

hope this helps

The value of x is 135°

What is Exterior Angle Theorem?

The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two opposite(remote) interior angles of the triangle.

An exterior angle is supplementary to its adjacent interior angle as they form a linear pair of angles.

Linear pair of angles are,

∠1 + ∠2 = 180°

where, ∠1 is exterior angle

and, ∠2 is interior angle

Given ,

One angle is = 90°

Then other two angle will be = 45° and 45°

Now, According to Exterior angle property,

x + 45 = 180

x = 180 - 45

x = 135°

Hence, the value of x is 135°

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An equation of line having slope 1/6 and passes through the point (0,-3) is y = 1/6x - 3

We know that the slope-point form of line is:

(y - y1) = m(x - x1)

Here, we need to find an equation of line having slope 1/6 and passes pae through the point (0,-3)

let (x1, y1) = (0, -3)

and m = 1/6

substitute values in above formula,

(y - (-3)) = 1/6 (x - 0)

y + 3 = 1/6 (x)

y = 1/6x - 3

which is slope-intercept form of line (y = mx + b)

Therefore, equation of line is y = 1/6x - 3

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Applying the properties of a rhombus, the measures of the numbered angles are:

m<1 = 58°

m<2 = 90°

m<3 = 32°

m<4 = 58°

Some properties of a rhombus include:

Given the rhombus in the image above, the numbered angles are:

m<3 = 32° [opposite angles are equal]

m<2 = right angle = 90°

m<1 = 180 - 90 - 32 = 58°

m<1 = m<4

m<4 = 58°

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Answer:

Step-by-step explanation:

regergergr

The equation of line s is y + 7 = -7/6(x - 7).

What is slope of a line?

A line's steepness and direction are measured by the line's slope. A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates,  Δy, Δx respectively. Consequently, it is possible to write the change in y coordinate with respect to the change in x coordinate as m = Δy/Δx

Given equation of line r is y = 6/7x+1.

The slope of line r is m = 6/7

The slope of the line that is perpendicular to line r is -1/m = - 7/6.

The equation of line that passes through the point (x₁, y₁) with slope m is y - y₁ = m(x - x₁).

Putting m = - 7/6, x₁ = 7 and y₁ = -7 in y - y₁ = m(x - x₁):

y - (-7) = - 7/6(x - 7)

y + 7 = - 7/6(x - 7)

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The inverse of the function f(x) = 4(x - 3) is f⁻¹(x)=(x+12)/4.

A function that "undoes" another function is known as an inverse in mathematics. In other words, if f(x) generates y, then y entered into f's inverse creates x. x . Invertible refers to a function that has an inverse, which is represented by the symbol f1.

Inverse functions are functions that "reverse" one another in the broadest sense. If f, for instance, goes from a to b, then its inverse, f 1 f -1 f 1f, start superscript, minus 1, end superscript, must go from b to a.

Make f a function. Any horizontal line that crosses the f graph more than once indicates that f lacks an inverse. F has an inverse if there are no horizontal lines that cross the graph of f more than once.

Let f(x)=y

f(x)=4(x-3)

f(x)=y

y=4(x-3)

x=4(y-3)

x=4y-12

4y=x+12

y=(x+12)/4

Therefore, f⁻¹(x)=(x+12)/4

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Answer:

Step-by-step explanation:

TQ = 44 + 25 = 69°

QR = 180 - 25 = 155°

TS = 180 -(44 + 25) = 180 - 69 = 111°

SQR = 180 + 155 = 335°


RQT = 180 + 44 = 224°

The unknowns in the given matrix total must have the values w = -5, z = 15, and y = 1.

Given,

To determine the value of the unknowns in the matrix,

A matrix is a rectangular array made up of numbers that are arranged in rows and columns. The figures are known as matrix elements or entries. Matrices are widely utilized in engineering, physics, economics, and statistics, as well as many other.

Here,

From the above matrix,

Equation formed,

2z -18 = 12
z = 15

2w + 6 = 16,
w = 5,

10 - 6 = 4y
y = 1

Thus, The unknowns in the given matrix total must have the values w = -5, z = 15, and y = 1.

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Given that x is in quadrant 3, its value for tan x=1/2 will be 206.565°, and its value for cos(206.565°) will be -0.894.

Trigonometry is the study of angles and the angular relationships between planar and three-dimensional shapes. The cosecant, cosine, cotangent, secant, sine, and tangent are among the trigonometric functions (also known as the circle functions) that make up trigonometry. The sine, cosine, and tangent are the three fundamental trigonometric operations. The cotangent, secant, and cosecant functions are derived from these three basic functions. On these functions, all trigonometrical concepts are built.

Here,

Tan x=1/2

π<x<3π/2

x=tan⁻¹/²(1/2)

x=26.565°

As the x is in quadrant 3,

=180+26.565°

=206.565°

cos(206.565°)=-0.894

The value of x for tan x=1/2 will be 206.565° as x is in quadrant 3 and for the same value of x, cos(206.565°) will be -0.894.

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Answer:

-sqrt 5 - 2 sqrt 5/10

Step-by-step explanation:

Edge 2023

Answer:

Step-by-step explanation:

$38, 20% off = $30.40

$30.40, 10% off = $27.36

$27.36 is the final price of the shirt

The cost of each DVD as per the given data will be 20.08  without tax.  and 21.35 with sales tax.

Cost of DVD,

with sales tax

(40.15 + 2.55) / 2

= 42.70/2

= 21.35 per DVD

without sales tax

40.15 / 2

= 20.08 per DVD

Sales taxes are a type of tax that is paid to a governing body when goods and services are sold. Sales tax is an indirect tax that is often assessed at the time that certain taxable products are purchased or exchanged. It is assessed as a percentage of the item's retail price.

The government in power and the specific rules it enforces determine the sales tax, which is typically easy to calculate and collect. The sales tax can be thought of simply as an additional sum of money paid while buying products or services.

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Answer:

53 degrees

Step-by-step explanation:

This is a transversal question (look at attached). Because the lines are parallel, g will equal to 180(a straight line is 180 degrees) - a. Then, because g + f + e = 180 (since it is a straight line), substitute the values that we know and solve. (61) + f +(66) = 180. f = 53

The factorization given is not a prime factorization.

Given that,
A factorization of a number is given we have to discuss whether the factors are prime factors or not.

A number or algebraic expression that evenly divides another number or expression—i.e., leaves no remainder—is referred to as a factor.

here,
Given factorization = 2² + 3 + 5⁴ + 8 + 11².
Since the above 8 cannot be taken in prime factor,
So the given factorization is not the prime factorization of the number.

Thus, the factorization given is not a prime factorization.

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The fraction is 7/9 according to given information.

What is fraction?

A fraction, which derives from the Latin word fractus, which means "broken," is a portion of a whole or, more broadly, any number of equal parts. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many parts of a particular size there are when spoken of in everyday English. A common, vulgar, as well as simple fraction is one that has a non-zero denominator displayed below (or after) the line that separates the numerator from the denominator. Compound fractions, complex fractions, as well as mixed numeral fractions are examples of uncommon fractions that use numerators and denominators.

Main Body:
Let the fraction be a/b
In First condition
b = a + 2(1)
In Second condition
a + 1/b + 1 = 4/5
5(a + 1) = 4(b + 1)
5a + 5 = 4b + 4
5a - 4b = 4 - 5
5a - 4b = -1
Using 1
5a - 4(a + 2) = -1
5a - 4a - 8 = -1
a = 8 - 1
a = 7
Now,
Using 1
b = a + 2
b = 7 + 2
b = 9
Fraction = a/b = 7/9
hence , the fraction is 7/9.

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The value of k will be equal to 4/3 and there will be two real and different roots.

It is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.

Given that the equation is k + 4/x +3/x² =0. The value of k will be calculated as,

k + 4/x +3/x² =0.

kx² + 4x + 3 = 0

b² - 4ac =0

4² = 4 x k x 3

16 = 12k

k = 4/3

Therefore, the value of k will be equal to 4/3 and there will be two real and different roots.

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The half-life of radon-222 is 3 days, it will take an additional 3 days for the remaining 42% of the sample to decay, for a total of 6 days for the sample to decay completely.

The half-life of a radioactive is time for 50% of its particles to decay or disintegrate into a new element. The pace at which a radioactive material will decay is predicted using this indicator of an isotope's stability. An element's half-life, which differs substantially across various elements, is based on the unique characteristics of its nucleus.

For instance, the half-life of uranium-238 is 4.5 billion years whereas that of carbon-14 is 5,730 years. This indicates that half of the carbon-14 atoms in a sample will have decayed after 5,730 years, and half of the uranium-238 atoms will have decayed after 4.5 billion years.

How to solve?

(a) After 3 days, the sample has decayed to 58% of its original amount, which means that half of the original amount has already decayed. Therefore, the half-life of radon-222 is 3 days.

(b) Since the half-life of radon-222 is 3 days, it will take an additional 3 days for the remaining 42% of the sample to decay, for a total of 6 days for the sample to decay completely.

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