Triangle a b c. side a c is 9 units, c b is 9 units, a b is 7 units. dilate triangle abc about point a by a scale factor of 1/3. what is the length of ac'? what is the length of ab'?

Answer:

[tex]\large\boxed{\mathtt{x = 10}}[/tex]

Step-by-step explanation:

[tex]\textsf{We are asked for the value of x.}[/tex]

[tex]\textsf{Because E is a Midpoint,} \ \overline{DE} \cong \ \overline{EF}.[/tex]

[tex]\textsf{Let's set them equal to each other.}[/tex]

[tex]\mathtt{45=3(x+5)}[/tex]

[tex]\large\underline{\textsf{Begin Solving:}}[/tex]

[tex]\mathtt{45= ( 3 \times x ) +(3 \times 5)}[/tex]

[tex]\mathtt{45= 3x+15}[/tex]

[tex]\large\underline{\textsf{Subtract 15 from Both Sides:}}[/tex]

[tex]\mathtt{3x=30}[/tex]

[tex]\large\underline{\textsf{Divide by 3:}}[/tex]

[tex]\large\boxed{\mathtt{x = 10}}[/tex]

Answer:

x = 10

Step-by-step explanation:

To find:-

Answer:-

We are here given that, E is the midpoint of DF. The value of DE is 45 and that of EF is 3(x+5) . We are interested in finding out the value of "x" .

According to Euclid's first axiom , Things which are half of the same thing are equal to one another. So here;

[tex]\sf:\implies DF = DF \\[/tex]

[tex]\sf:\implies \dfrac{DF}{2}=\dfrac{DF}{2} \\[/tex]

[tex]\sf:\implies DE = EF \\[/tex]

On substituting the respective values, we have;

[tex]\sf:\implies 45 = 3(x+5) \\[/tex]

[tex]\sf:\implies 45 = 3x + 15 \\[/tex]

[tex]\sf:\implies 3x = 45-15\\[/tex]

[tex]\sf:\implies 3x = 30 \\[/tex]

[tex]\sf:\implies x =\dfrac{30}{3}\\[/tex]

[tex]\sf:\implies \red{x = 10}\\[/tex]

Hence the value of x is 10 .

The simplified mοnοmial is [tex]-9x^9y^5[/tex].

In algebra, a mοnοmial is an expressiοn that has a single term, with variables and a cοefficient. Fοr example, 2xy is a mοnοmial since it is a single term, has twο variables, and οne cοefficient. Mοnοmials are the building blοcks οf pοlynοmials and are called 'terms' when they are a part οf larger pοlynοmials. In οther wοrds, each term in a pοlynοmial is a mοnοmial.

Mοnοmial is defined as an expressiοn that has a single nοn-zerο term. It cοnsists οf different parts like the variable, the cοefficient, and its degree. The variables in a mοnοmial are the letters present in it. The cοefficients are the numbers that are multiplied by the variables οf the mοnοmial. The degree οf a mοnοmial is the sum οf the expοnents οf all the variables.

When we multiply mοnοmials with the same base, we add their expοnents. Using this prοperty, we can simplify the expressiοn as fοllοws:

[tex](-8x^4y^3)(2x^5y^2)+7x^9y^5[/tex]

[tex]= (-8 * 2)(x^4 * x^5)(y^3 * y^2) + 7x^9y^5[/tex]

[tex]= -16x^9y^5 + 7x^9y^5[/tex]

[tex]= (7 - 16)x^9y^5[/tex]

[tex]= -9x^9y^5[/tex]

Therefοre, the simplified mοnοmial is [tex]-9x^9y^5[/tex].

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Answer:

8.9 g/cm^3

Step-by-step explanation:

Volume = 5 x 2 x 6 = 60 cm^2

density = m/V = 534/60 = 8.9 g/cm^3

The image of the point after the reflection is (-3, -6).

To reflect a point across the y-axis, we simply negate its x-coordinate while keeping the y-coordinate the same.

Thus, the image of point (3, -6) reflected across the y-axis would be (-3, -6).

We can visualize this by drawing a line passing through the point (3, -6) and the y-axis.

The reflection of the point will be at the same distance from the y-axis but on the opposite side.

So, the reflection of the point (3, -6) across the y-axis is (-3, -6).

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In response to the stated question, we can state that here  Hence, the linear equation (6 2 • 35) 2 equals 1/4096

A linear equation is one that satisfies the algebraic formula y=mx+b. m is the y-intercept, while B is the slope. The foregoing sentence is sometimes referred to as a "linear equation with two variables" because y and x are variables. Bivariate linear equations are two-variable linear equations. Examples of linear equations include 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. An equation is said to be linear if its formula is y=mx+b, where m denotes the slope and b the y-intercept. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.

We must do the following operations in the correct order to simplify the formula (62 • 35)2:

To start, we must multiply 2 by 35, which results in the number 70.

The result is -64 when we remove 70 from 6.

The final step is to raise the unfavorable integer -64 to the power of -2.

Hence, we can write:

[tex](6-2 * 35)-2 = (-64)^{-2}[/tex]

To make this statement easier to understand, keep in mind that taking the reciprocal of a number raised to a positive power is the same as raising it to a negative power. With those words:

[tex]a^-n = 1/a^n\\(-64)^-2 = 1/(-64)^2\\1/(-64)^2 = 1/4096[/tex]

Hence, the expression (6 2 • 35) 2 equals 1/4096.

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The answer of the given question based on finding the new coordinate of c is  (1, 5). and to determine if the image of Triangle ABC is similar or congruent to the original triangle is AB / A'B' = BC / B'C' = CA / C'A' = √(2).

Congruent triangles are triangles that have the same shape and size. More specifically, if two triangles have exactly the same size and shape, then they are congruent triangles. This means that all the corresponding sides and angles of two triangles are equal. Congruent triangles can be thought of as being identical to each other, but they may be positioned and oriented differently in space.

To rotate a point 180° degrees counterclockwise about the origin, we can simply multiply its coordinates by the matrix:

[ -1  0 ]

[  0 -1 ]

So, the coordinates of the rotated point C would be:

[ -1  0 ]   [ 3 ]

[  0 -1 ]*[ 8 ] =[ -3 ]

           [  1 ]

we translate this point 4 units to the right and 4 units up by adding 4 to the x-coordinate and 4 to the y-coordinate:

[ -3 + 4 ]

[  1 + 4 ] = [ 1, 5 ]

Therefore, the new coordinates of point C are (1, 5).

To determine if the image of triangle ABC is similar or congruent to the original triangle, we can check if the ratios of the corresponding sides are the same. Let's calculate the lengths of the sides of the original triangle:

AB = √((8-3)² + (3-3)²) = 5

BC = √((3-8)² + (8-3)²) = 5*√(2)

CA = √((3-3)² + (3-8)²) = 5

Now, let's calculate the lengths of the sides of the image triangle, using the new coordinates:

A'B' = √((8-1)² + (3-5)²) = 5*√(2)

B'C' = √((1-1)² + (5-8)²) = 3

C'A' = √((1-8)² + (5-3)²) = 5*√(2)

We can see that the ratios of the corresponding sides are the same:

AB / A'B' = BC / B'C' = CA / C'A' = √(2)

Therefore, the image of triangle ABC is similar to the original triangle.

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The thickness of a hollow cylinder which is also the thickness of the metal is 1cm

To calculate the thickness of a hollow cylinder, subtract the inner and outer cylinder radii, r and R:

the thickness of the solid is:t = R - r

And if we are working with the diameter, we subtract the diameters and divide by 2VH = π × h(D² - d²)/4

where

Vh = Volume of hollow cylinder = 748cm  

h = height of cylinder = 14cm

D = external diameter = 9 x 2 = 18cm

d = internal diameter = ??

The above statements can then be represented as:

4 x 748 = 22/7 x 14 (18² - d²)

Evaluate the products, quotients and exponents

68 = 324 - d²

So, we have

d² = 256

Take the square roots

d = 16 cm

From here we can get the thickness by subtracting the external and internal diameter and dividing by 2

thickness = (18 - 16)/2

thickness = 2/2

thickness = 1cm

So, the thickness is 1 cm

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Answer:

Step-by-step explanation:

Using little bottom triangle:

[tex]y^2=10^2+20^2[/tex]   (Pythagoras Theorem)

[tex]y^2=500[/tex]

Using big triangle:

[tex]y^2+z^2=(10+x)^2[/tex]   (Pythagoras Theorem)

[tex]500+z^2=(10+x)^2[/tex]   (Since we know [tex]y^2=500[/tex])

[tex]500+z^2=x^2+20x+100[/tex]      

[tex]z^2=x^2+20x-400[/tex]   [tex](a)[/tex]          

Using little top triangle:

[tex]z^2=x^2+20^2[/tex]      (Pythagoras Theorem)

[tex]z^2=x^2+400[/tex]   [tex](b)[/tex]

Substitute [tex](a)[/tex]  into  [tex](b)[/tex]:

[tex]x^2+20x-400=x^2+400[/tex]      (since we know both sides[tex]=z^2[/tex])

[tex]20x=800[/tex]

[tex]x=40[/tex]

The total tax on the items is $6.12.

Tax is a financial charge or other levy imposed upon a taxpayer (an individual or other legal entity) by a state or the functional equivalent of a state such that failure to pay is punishable by law.

The total amount of the items purchased is $102+$60+$35 = $197.

Raincoat is priced at $102 which is higher than $75 and is subject to 6% sales tax.

Therefore, the tax on raincoat is $102 x 6% = $6.12.

Slacks and shirt is priced below $75 and are not subject to sales tax. Therefore, the tax on slacks and shirt is $0.

The total tax on the items purchased is $6.12 + $0 = $6.12.

Hence, the correct answer is $6.12.

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The length and width of the rectangle are 10 yards and 5 yards

From the question, we have the following parameters that can be used in our computation:

The length of a rectangle is 5 yd less than three times the width

This means that

Length = 3x - 5

Width = x

So, we have

Area = (3x - 5)* x

Substitute the known values in the above equation, so, we have the following representation

(3x - 5)* x = 50

Using a graphing tool, we have

x = 5

So, we have

Length = 3 * 5 - 5

Width = 5

Evaluate

Length = 10

Width = 5

Hence, the length is 10 yards

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The circumference and area of the circle with the arc of length 21 meters and a central angle of 287° are 4.35 meters and 1.16 square meters.

An arc of length 21 meters subtends a central angle of 287° in a circle. The circumference of the circle and area are required to be determined.

Here is the solution:

Let us suppose that the radius of the circle is r. Thus, we can write:

r = (L/θ) r = (21/287)

Let us substitute the values of r in the formulae of the circumference of the circle and area of the circle.

Circumference of the circle:

C = 2πr

C = 2π (21/287)

C ≈ 4.35 meters

Area of the circle:

A = πr²

A = π (21/287)²

A ≈ 1.16 square meters

Therefore, the circumference of the circle is 4.35 meters and the area of the circle is 1.16 square meters.

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This is a single displacement reaction. Specifically, this is a metal displacement reaction. We can use a calorimeter to measure the amount of energy released.

A reaction, in chemistry, is a process in which two or more substances (reactants) interact with each other to form new substances (products). Reactions involve the breaking and forming of chemical bonds between atoms or molecules, which results in the rearrangement of atoms into new chemical compounds.

Reactions can be classified into several different types, depending on the nature of the reactants and products, the conditions under which the reaction occurs, and the rate of the reaction. Some common types of reactions include:

Combination (or synthesis) reactions, in which two or more substances combine to form a single product.

Decomposition reactions, in which a single substance breaks down into two or more simpler substances.

Single replacement (or displacement) reactions, in which one element replaces another element in a compound.

Double replacement (or metathesis) reactions, in which two compounds exchange ions to form two new compounds.

Acid-base reactions, in which an acid reacts with a base to form a salt and water.

Redox (or oxidation-reduction) reactions, in which electrons are transferred between reactants.

This is a single displacement reaction.

Specifically, this is a metal displacement reaction.

We can use a calorimeter to measure the amount of energy released.

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The given chemical equation represents a single displacement reaction and a calorimeter can be used to measure the amount of energy released during the reaction.

The given chemical equation represents a single displacement reaction. This is because one element (Li) displaces another element (H) in a compound (Hd₂O5) to form a new compound (Li₂O) and free element (Hd) along with the release of energy.

To measure the amount of energy released during the reaction, we can use a calorimeter. A calorimeter is a device that measures the heat change in a chemical reaction.

It consists of an insulated container that holds the reactants and a thermometer to measure the temperature change.

The heat released or absorbed during the reaction causes a change in temperature, which can be measured and used to calculate the energy released or absorbed by the reaction.
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Answer:

1582÷

Step-by-step explanation:

because u haven't told to divide wth any number

Answer:

Your question isn't complete. Kindly correct it.

if the vertex is at the origin, and the focus point horizontally to the right-side 1/8 units away from the vertex, well, that means is a horizontal parabola with a "p" value of +1/8, so

[tex]\textit{horizontal parabola vertex form with focus point distance} \\\\ 4p(x- h)=(y- k)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h+p,k)}\qquad \stackrel{directrix}{x=h-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{p~is~negative}{op ens~\supset}\qquad \stackrel{p~is~positive}{op ens~\subset} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{cases} h=0\\ k=0\\ p=\frac{1}{8} \end{cases}\implies 4(\frac{1}{8})(~~x-0~~) = (~~y-0~~)^2\implies \cfrac{1}{2}x=y^2\implies \boxed{x=2y^2}[/tex]

Answer:

7

Step-by-step explanation:

Answer:

To calculate the range of inferences, we need to find the minimum and maximum percentages based on the results of the three surveys.

Desiree's survey found that 48 out of 60 students prefer to listen to music while completing homework, which is 80%.

Marina's survey found that 39 out of 60 students prefer to listen to music while completing homework, which is 65%.

Raúl's survey found that 42 out of 60 students prefer to listen to music while completing homework, which is 70%.

To find the minimum percentage, we can take the lowest value of the three surveys, which is 65%. To find the maximum percentage, we can take the highest value of the three surveys, which is 80%. Therefore, a reasonable range of inferences is:

From 65% to 80% of the school population prefers to listen to music while completing homework.

Thus, cos x/2 = (sqrt(2))/2 has the solution for x =  4kx ± π/2 in the intervals  [0, 2pi).

The ratio of the hypotenuse to the side adjacent to the acute angle together in right triangle is the cosine function, which is a trigonometric function.

This cosine function for only a specified range of angles is represented graphically by the cos graph. A trigonometric graph's horizontal axis is the angle, which is typically denoted by the symbol, and the y-axis is really the sine function of just that angle. The maximum and minimum values are 1 and 1.

There are amplitudes for both the sine and cosine functions. This is due to the scope limitations of each function. Both functions typically have an amplitude of 1, though this can vary depending on the way the function is constructed.

Given function:

cos x/2 = (sqrt(2))/2

OR,

cos x/2 = √2/2

cos x/2 = cos (2kx ± π/4) , k ∈ R (real number)

x/2 = 2kx ± π/4

x =  4kx ± π/2

Thus, cos x/2 = (sqrt(2))/2 has the solution for x =  4kx ± π/2 in the intervals  [0, 2pi).

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Answer:

W = -X + 5y

Step-by-step explanation:

Now we have to,

→ Find the required value of W.

The equation is,

→ X = 5y - W

Then the value of W will be,

→ X = 5y - W

→ 5y - W = X

→ -W = X - 5y

→ [ W = -X + 5y ]

Hence, value of W is -X + 5y.

Answer: Let's call the height of the steeple "h". We can use the tangent function to set up an equation involving the angles of elevation:

tan(40°) = h / x

tan(49° 40') = (h + y) / x

where "x" is the distance from the point to the base of the steeple, and "y" is the height of the point above the ground.

We are given that the distance from the point to the church is 48 feet, so we can use the Pythagorean theorem to find the value of "y":

y^2 = x^2 - 48^2

We can substitute this expression for "y" into the second equation above:

tan(49° 40') = (h + √(x^2 - 48^2)) / x

We can now solve this equation for "h":

h = x tan(49° 40') - x √(1 + tan^2(49° 40')) + 48 tan(40°)

Plugging in the values for the angles and solving for "h", we get:

h ≈ 83.9 feet

Therefore, the height of the steeple is approximately 83.9 feet.

Step-by-step explanation:

The company would use 19.5 yards of blue fabric when 63 yards of red fabric are used, according to the given ratio and diagram.

Word problems are mathematical problems expressed in words, often used to apply mathematical concepts to real-life situations.

To find the number of yards of blue fabric used when 63 yards of red fabric are used, we can use the given ratio of 9 yards of red fabric to 17 yards of blue fabric.

To determine the number of units of red fabric needed for 63 yards divide the number of yards of red fabric by the scale factor for red fabric, which is 3. So, 63 yards ÷ 3 units per yard = 21 units of red fabric.

Use the ratio to determine the number of units of blue fabric needed. Since the ratio of red to blue fabric is 9:17.So, to find the number of units of blue fabric needed for 21 units of red fabric, we can multiply 21 by 17/9, which gives us 39 units of blue fabric.

So, 39 units of blue fabric ÷ 2 units per yard = 19.5 yards of blue fabric.

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The probability of 3 successes in 64 trials with a probability of 0.04 of success on a single trial is 0.375.

The probability of x successes in n trials with a probability p of success on a single trial can be calculated using the binomial probability formula. This formula is P(x successes) =[tex]nCx * (p^x) * (1-p)^(n-x)[/tex]. In this case, n = 64, x = 3, p = 0.04. Therefore, P(x successes) =[tex]64C3 * (0.04^3) * (1-0.04)^(64-3)[/tex]. Calculating this gives us P(x successes) = 0.375. Therefore, the probability of x successes in n trials with a probability p of success on a single trial is 0.375.

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The height of the cylinder is 27 yards.

To find the height of a cylinder, we need to use the formula V = πr^2h, where V is the volume, π is the constant pi (3.14), r is the radius, and h is the height.

In this problem, we know the radius is 5 yards, and the volume is 1,177.5 cubic yards. We can rearrange the formula to calculate the height as h = V / (πr^2). Substituting the given values into the equation, we get: h = 1177.5 / (3.14 * 25) = 27 yards. Therefore, the height of the cylinder is 27 yards.

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Answer: y=mx+b

Step-by-step explanation:

To change the equation into slope-intercept form, we write it in the form y=mx+b .

Answer:

X=60

Step-by-step explanation:

Firstly you must know that a triangle has 180° angle in it's all side.. so in this case you can say x+½x+(1,5)x= 180°

here x equal to 60°

this is a simple way to expres how can find the x angle

And to second way about how to find the x we have to know the lineer algebra. so lineer algebra is a strong way and useful to not only geometric shapes and for all mathematic calculate..

Answer:

b) Negative one-half

Step-by-step explanation:

according to the equation:

[tex]\tan(b)=-2\\\therefore b=\tan^1(-2})\\b=-63.44^\circ[/tex]

This value is located in the IV quadrant, however we can add 180 degrees and still remain the same value

[tex]b \equiv -63.44+180\\b \equiv 116.56^\circ[/tex]

Now, "b" is located in the II quadrant, so:

[tex]cot(116.56)= ?[/tex]

I guess you want to get the result with calculator, so we will use an identity to be able to enter this value into the calculator.

[tex]cot(116.56)= \frac{1}{tan(116.56)} \approx -0.5[/tex]

Therefore, we have found the solution to the exercise.

[tex]\text{-B$\mathfrak{randon}$VN}[/tex]

Answer:

In the equation X + y = 9, X and y are variables. Variables are used to represent unknown quantities or quantities that can vary. In this case, X and y represent two unknown numbers whose sum is equal to 9. We can use algebraic techniques to solve for either X or y, or both, depending on the situation. The values of X and y could represent anything, such as the number of apples and oranges in a basket, the length and width of a rectangle, or the ages of two people.

Answer:

Since the pole is in the shape of a cylinder, its volume can be calculated using the formula V = πr²h, where r is the radius and h is the height (or length in this case). We are not given the radius, so we cannot calculate the exact volume. However, we can use an approximation assuming a reasonable radius.

Let's assume a radius of 1 foot. Then, the volume would be V ≈ π(1)²(15) = 15π ≈ 47.1 cubic feet.

The closest answer choice to this approximation is D) 141 ft². However, note that volume is measured in cubic units (feet cubed or ft³), not square units (feet squared or ft²). Therefore, none of the answer choices are in the correct units for the volume of a cylinder.