x-4[x-2(x+6)]=5x+3
[tex]x - 4 [ x - 2(x + 6)] = 5x + 3[/tex]


​

Answer:

Step-by-step explanation:

Step 1: Calculate the slant height of the pyramid.

Slant Height = √(6.9^2 + 8^2) = 10.1 cm

Step 2: Calculate the lateral surface area of the pyramid.

Lateral Surface Area = 4 * (1/2 * 6.9 * 10.1) = 176.5 cm^2

Step 3: Calculate the total surface area of the pyramid.

Total Surface Area = Lateral Surface Area + Base Area

Total Surface Area = 176.5 cm^2 + (1/2 * 6.9 * 8) = 227.7 cm^2

Answer: y = -1/6x + 1 1/3

Step-by-step explanation:

Answer:

A. Circle Graph, also known as a pie chart, is the most appropriate to illustrate the results of Justina's survey.

Step-by-step explanation:

A circle graph, also known as a pie chart, is the most appropriate to illustrate the results of Justina's survey.

A circle graph is used to display the proportion of different categories of data. In the case of Justina's survey, the categories would be the different sports that the students play, and the proportion of students who play each sport would be represented by the size of the corresponding wedge in the circle graph. The circle graph allows for a clear and easy-to-understand comparison of the relative popularity of different sports among the surveyed students.

A Venn diagram is used to show the relationships between different sets of data. It's not appropriate in this case as the students are not being asked to pick two or more sports they play, but the number of sports they play.

A stem-and-leaf plot is used to display the distribution of numerical data, it's not appropriate for this case because it does not show the proportion of students playing each sport.

A double line graph is used to compare two sets of data over time. It's not appropriate for this case because it doesn't show the proportion of students playing each sport.

Answer:

Horizontal translation 3 units left

Vertical translation 2 units down

Step-by-step explanation:

Inside the parent function is horizontal.

Outside the parent function is vertical.

The correct option regarding the solution to the system of equations is given as follows:

It is a solution to f(x) = g(x) because it is the x-coordinate where the two graphs intersect.

We want to obtain the graphic solution for the system of equations, hence we obtain the point of intersection of the two equations.

The point of intersection in this problem has a x-coordinate of 3, hence the third option is the correct option.

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Answer:

choice B ( 7/20) is the right answer.

Step-by-step explanation:

If Gavin's mother poured 1 cup of milk in the glass and Gavin drinks 1/5 of the milk, the fraction of the milk that will remain in the glass is (4/5) of 1 cup.

So, B ( 7/20) is the right answer.

a) The sum will be around 100, give or take 10 or so. - True

b) There is about a 68% chance that the sum will be in the range of 90 to 110. - True

a) True. The expected value of a single draw is (0.990)+(0.011)=0.01, and the expected value of 10,000 draws is 0.0110,000=100. The standard deviation of a single draw is the square root of (0.990^2)+(0.011^2)=0.01. So, the standard deviation of 10,000 draws is sqrt(10,0000.01)=10. This means that the sum of 10,000 draws will be around 100, give or take 10 or so.

b) True. The sum of 10,000 draws follows a normal distribution with a mean of 100 and a standard deviation of 10. Using the 68-95-99.7 rule, 68% of the data falls within one standard deviation of the mean. So, the chance that the sum will be in the range of 90 to 110 is 68%.

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Answer: 1/16

Step-by-step explanation:

4^4*4^(-7)*4

= 4^(-3)*4

=4^(-2)

= 1/16

The required required value of angles are  31, 118, 31.

An Isosceles triangle is a triangle that has two equal sides. Also, the two angles opposite the two equal sides are equal. In other words, we can say that “An isosceles triangle is a triangle which has two congruent sides“.

We have,

∠Q = 8x-17, ∠R = 19x+4, ∠S = 5x+1

So,

∠Q + ∠R + ∠S = 180

= 8x-17 + 19x+4 + 5x+1

= 32x - 12 = 180

= 32x = 192

x = 6

Angles are;

∠Q = 8x-17 = 8(6)-17 = 31

∠R = 19x+4 = 19(6)+4 = 118

∠S = 5x+1 = 5(6)+1 = 31

Thus, required value of angles are  31, 118, 31.

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The system of linear equations y = x - 6.7 and y = - x + 1.7 have solution at point (x, y) = (4.2, - 2.5).

In this problem we need to construct a system of two linear equations whose solution is point (x, y) = (4.2, - 2.5). Linear equations are algebraic equations of the form:

y = m · x + b

Where:

The procedure is shown below. First, obtain the intercept of the first equation:

b = y - m · x

(x = 4.2, y = - 2.5, m = 1)

b = - 2.5 - 4.2

b = - 6.7

Second, write the first linear equation:

y = x - 6.7

Third, find the intercept of the second equation:

b = y - m · x

(x = 4.2, y = - 2.5, m = - 1)

b = - 2.5 - (- 1) · (4.2)

b = - 2.5 + 4.2

b = 1.7

Fourth, write the second linear equation:

y = - x + 1.7

Please see the image attached below for a representation of the system of linear equations.

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Answer:

95

Step-by-step explanation:

The equation that can be used to answer this question concerning speed would be = d=(0.6)(30). That is option C.

Constant speed is defined as the quantity that expresses the an object which travels the same distance in the same period of time.

The constant speed of the zebra = 0.6 miles per minute

Therefore, if 0.6 miles = 1 minute

d miles = 30 minutes

d miles = 30 × 0.6/1

d miles = 18 miles

Therefore the expression that can be used to answer this question would be = d=(0.6)(30).

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The other information required while using the intermediate value theorem to show the existence of zero for the polynomial function plotted is

f(x₁) < 0 and f(x₂) > 0

The intermediate value theorem says that if "f" is a continuous function across a closed interval [a, b] with values f(a) and f(b) at its endpoints, then the function takes any value at a point inside the interval that is between the values of f(a) and f(b).

The root of a polynomial is the value of y when x is zero. hence to show that there is a zero between the points x₁ and x₂ there is a need to show there was a change of sign in the output value

Using the graph

At the point of change of sign is the required zero

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Answer: An isosceles trapezoid is a trapezoid with two sides of equal length, and those are called legs.

Using the given information that the shorter base is 21, the longer base is 47 and the legs are 50, we can use the Law of Cosines to find the angle between the legs and the longer base.

The Law of Cosines states that for any triangle with sides of length a, b, and c and the angle opposite side c is denoted as C:

c^2 = a^2 + b^2 - 2ab * cos(C)

We will use the legs (a = b = 50) and the longer base (c = 47) as our sides and call the angle we are looking for angle x:

50^2 = 50^2 + 47^2 - 2(50)(47) * cos(x)

Solving for cos(x) will give us the angle x in terms of a cosine. To get the angle x in degrees, we will use the inverse cosine function, which gives the angle in degrees whose cosine is the input value.

cos(x) = (50^2 + 47^2 - 50^2) / (2(50)(47)) = 47/100

x = acos(47/100)

x = approx 126.6

So, the lower base angle in this isosceles trapezoid is approximately 126.6 degrees.

Step-by-step explanation:

The interest rate on 7,000 for 10 years with a simple interest of 3500 is 5.

Simple interest is the amount paid on a principal amount of money that is borrowed or loaned to someone. It is calculated using the formula: SI = (P × R × T) / 100. Interest Rate (R) is a percent of the principal earned or paid.

From the question;

P = 7,000

T = 10

SI = 3500

we shall evaluate for the rate R as follows:

3500 = (7,000 × R × 10)/ 100

3500 = 70R

divide through by 70

3500/70 = 70R/70

R = 35/7

R = 5

Therefore, the rate for the amount 7,000 that will give a simple interest of 3500 for 10 years is 5

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The y-intercept of the expression y=x^2-6x+8 is y(0,8).

What are intercepts?

The term "intercept" refers to the location where a line or curve crosses a graph's axis. The x-intercept is the point at which the x-axis is crossed. The y-intercept is the point at which the y-axis is crossed.

The given expression is -

y = x²-6x+8

To find the y-intercept, substitute the value of x with 0.

y = x²-6x+8

y = (0)²-6(0)+8

y = 8

Therefore, the y-intercept is (0,8).

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A given information is inversely proportional when one value decreases at the same rate that the other increases. It should be noted that an example is speed and travel time

Only when two variables are directly proportional to one another's reciprocal can two variables be said to be inversely proportional. Alternately, we can state that when two variables or quantities are in inverse proportion, their product has a constant value.

One kind of proportionality relationship is inverse proportion. If two quantities are inversely related, one will increase while the other will decrease.

Note that your information is incomplete and a overview was given.

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Answer:

Step-by-step explanation:

So, to compare fractions, we need them to have the same denominators because for example, 4/1 = 4 and 4/2 = 2 is totally different.

(in that case, we could have looked at the denominators, and the fraction with the smallest denominator would be the greater one since the numerators are the same, but it was just an example)

To do that, we look at them : we see -3/5 and -2/3

3 is not a multiple of 5, neither 5 is a multiple of 3, so we use 3*5 =15

(if it was 3 and 6, we could have used 6/2 = 3 or 3*2 = 6)

Next move, we put the fractions on 15 : [tex]\frac{-2}{3} =\frac{-2*5}{3*5} =\frac{-10}{15}[/tex] and [tex]\frac{-3}{5} =\frac{-3*3}{5*3} =\frac{-9}{15}[/tex]

Now, we look at the numerators : -10 < -9

(don't forget they're negative numbers )

And to conclude :

[tex]\frac{-10}{15} < \frac{-9}{15\\}\\\frac{-2}{3} < \frac{-3}{5}[/tex]  hope it helps :)

Using the scale, 1 inch is equal to 35 miles, the distance between Danton and Crowley is  19.2 inches.

According to the map given , considering that the distance in miles between Danton and Crowley is 672 miles, to find the distance in inches we use the scale given by the map where 1 in.:35 mi.

To solve for distance in inches;

35 miles = 1 inch

672 miles = 672 / 35 x 1 = 19 .2 inches.

The distance between Danton and Crowley at 1 in = 35 mi is 19. 2 inches meaning it will take Danton 19. 2 inches of a ride or walk to get to Crowley.

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Answer:  D

Step-by-step explanation:

Aaliyah need to read for 8.75 hours with reading speed of 40 pages/hour in order to fulfill her promise of reading 50 more pages than Yohance.

What is reading speed?

Reading speed is the rate at which a person reads written text (printed or electronic) in a specific unit of time. Reading speed is generally calculated by the number of words read per minute.

Reading speed is determined by a number of factors, including a reader's purpose and level of expertise as well as the relative difficulty of the text.

Now,

Reading speed of both=40 pages/hour

yohance reads for 7.5 hours and reads total pages=40*7.5=300

Now, to read 350 pages Aaliyah will read for time=350/40=8.75 hours

Aaliyah need to read for =8.75 hours in order to fulfill her promise of reading 50 more pages than Yohance.

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The closing balance of the accumulated depreciation account, obtained from the values in the table is; $3,000

Depreciation is the cost of an asset during the indicated useful life of the asset

The closing balance of the accumulated depreciation account can be found as follows;

The accumulated depreciation is the sum of the depreciation charged on an asset up to the current date.

The formula for calculating the accumulated depreciation can be presented as follows;

Accumulated depreciation = [tex]\frac{(Cost \ of\ asset - Salvage\ Value)}{Life\ of\ Asset}[/tex] × Indicated Period

The indicated period is the number of years of use for the asset

The specified table is the accumulated depreciation account which is a contra asset (that reduces the value of the asset) account, therefore, the amounts stated indicates the depreciation during a specified period

The balance b/f on January 1, 2012, (beginning of the year) is the depreciation balance brought forward, which in the table is $1,000

The depreciation on Dec 31, 2012, (the end of the year) which is the depreciation during the year is; $2000

The accumulated depreciation is therefore; $1,000 + $2,000 = $3,000

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The value of expression after subtraction is, 2,226.

Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.

We have to given that;

The expression is,

⇒ three hundred fifty - two thousand five hundred seventy-six

Now, We can write the expression as;

⇒ three hundred fifty - two thousand five hundred seventy-six

⇒ 350 - 2,576

After subtraction we get;

⇒ - 2,226

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Answer:

Graph a right triangle with the two points forming the hypotenuse. Using the sides, find the distance between the two points in simplest radical form. (-4,3) and (-8, -1) *Click twice to draw a line. Click a segment to erase it." 30 4 -10 - -6-5-43 -8 This problem has been solved!

Step-by-step explanation:

Treat the,, >, or sign as a = sign when graphing an inequality.

Draw a circle over the number to begin plotting an inequality on a number line, such as x>3 (e.g., 3). The circle should be filled in if the sign also includes equal to (or). Leave the circle blank if the sign doesn't contain the equal to symbol (> or ).

By treating the,, >, or sign as a = sign, the inequality can be shown graphically. Make a dotted line graph of the equation if the inequality is either or. Make a solid line out of the equation if the inequality is either or.

Using a straight line and either an open circle or a closed circle to indicate the end points, we can depict inequalities on a number line by displaying the range of integers. The value is not included, as indicated by the open circle. The value is included, as indicated by the closed circle.

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Answer:

b = a - 7

Step-by-step explanation:

subtract 7 from both sides of the equation

The solution set of the system of linear equations represented by the augmented matrix is (x1, x2, x3, x4) = (2, 4, 2, -1)

To determine the values, first express the system of linear equation as represented by the augmented matrix.

The system of linear equations represented by the augmented matrix is:

1x1 + 2x2 + 0x3 + x4 = 3

0x1 + 1x2 + 2x3 + x4 = 3

0x1 + 0x2 + 1x3 + 2x4 = 1

0x1 + 0x2 + 0x3 + 1x4 = 4

By applying row operations to the matrix we can find the solution set

R2 - R1

0 -1 2 0 0

0 0 1 2 1

0 0 0 1 4

R3 - 2R1

0 -1 2 0 0

0 0 1 2 1

0 0 0 -3 2

R4 - 4R1

0 -1 2 0 0

0 0 1 2 1

0 0 0 -7 8

R3 - R2

0 -1 2 0 0

0 0 0 -1 3

0 0 0 -7 8

R4 - 7R2

0 -1 2 0 0

0 0 0 -1 3

0 0 0 0 -1

R4/ -1

0 -1 2 0 0

0 0 0 -1 3

0 0 0 1 -1

x4 = -1

x3 = 3x4 + 1 = 2

x2 = 2x3 = 4

x1 = 3 - 2x2 - x4 = 2

Therefore, the solution set is (x1, x2, x3, x4) = (2, 4, 2, -1)

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