question 54 of 99 a teacher wanted to buy a chair, a bookshelf, two tables and a desk. she spent $900 for all five items and the chair and the desk combined cost 70% of her total. if the bookshelf cost $50, how much did each of the tables cost

The non zero vector orthogonal to the plane through P,Q and R is ⟨0,18,−9⟩

A non-zero vector orthogonal to the plane through the points P, Q, and R can be found by taking the cross product of two vectors that lie in the plane. One way to do this is to take the difference vector of two of the points, and then take the cross product of that difference vector with the difference vector of the third point.

For example, we can use the difference vector QP = (-2,1,3) - (1,0,1) = (-3,1,2) and the difference vector RP = (4,2,5) - (1,0,1) = (3,2,4)  

The cross product of these two vectors is:

(-3,1,2) x (3,2,4) =⟨0,18,−9⟩

so the non-zero vector orthogonal to the plane through the points P, Q, and R is ⟨0,18,−9⟩

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Answer:

.

Step-by-step explanation:

If a=-2 and b=1 the value of a+2b=0

A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is utilized.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

According to the given question;

If a=-2 and b=1 the value of a+2b=0

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Answer:

D

Step-by-step explanation:

If you folded the figure on the line of symmetry.  The right side would fit perfectly over the left side.

Answer:

4 I think

Step-by-step explanation:

A vertex is a point where two or more edges meet (i.e the sharp points of the figure).

A vertex (plural: vertices) is a point where two or more line segments meet. It is a Corner.

Answer:

$60 / 6 barbecue sticks = $x / 1 barbecue stick

Where x is the value of 1 barbecue stick.

To find the value of x, we can cross-multiply and divide by 6:

$60 = 6 barbecue sticks * $x/1

$60 = $6x

$x = $10

So, $10 will equal 1 barbecue stick, if $60 = 6 barbecue sticks.

We know that you earned $300, so we can substitute that into the proportion:

$60 / 6 barbecue sticks = $300 / n barbecue sticks

We can cross-multiply and divide by 60:

6 barbecue sticks * $300 = $60 * n barbecue sticks

n barbecue sticks = $300 * 6 / $60

n barbecue sticks = 30

Therefore, you sold 30 barbecue sticks.

The expressions that are equivalent to 9/7x−3/4 are:

(9/7)x - (3/4)

(9/7)x - 3/(4*7/9)

(9/7)x - 3/28

(9/7)*x - (3/4)

(9x)/(7x) - (3/4)

(9x)/(7x) - (3/(4*x))

(9x - 3x)/(4*x)

(6x)/(4x)

(3x)/(2x)

What is the linear equation?

The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line. An example of a linear equation is y=mx + b.

All of the following expressions are equivalent to 9/7x−3/4:

(9/7)x - (3/4)

(9/7)x - 3/(4*7/9)

(9/7)x - 3/28

(9/7)*x - (3/4)

(9x)/(7x) - (3/4)

(9x)/(7x) - (3/(4*x))

(9x - 3x)/(4*x)

(6x)/(4x)

(3x)/(2x)

When you multiply or divide both the numerator and denominator of a fraction by the same non-zero number, the fraction remains equivalent.

Hence, the expressions that equivalent to 9/7x−3/4 are:

(9/7)x - (3/4)

(9/7)x - 3/(4*7/9)

(9/7)x - 3/28

(9/7)*x - (3/4)

(9x)/(7x) - (3/4)

(9x)/(7x) - (3/(4*x))

(9x - 3x)/(4*x)

(6x)/(4x)

(3x)/(2x)

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Answer:

Inconsistent as there are two same equations with different values.

So this doesn't make sense.

Answer: C - The statement is false.

Step-by-step explanation: Rhombuses also have perpendicular diagonals.

If the graph only touches the x-axis at the x-intercept, then it is said to "touch" the x-axis. This indicates that the graph does not pass through the x-axis at the x-intercept, but rather just touches it.

The x-intercept of a graph is the point at which the graph crosses the x-axis. It is also known as the abscissa. The x-coordinate of the x-intercept is the value where the graph intersects the x-axis.

The x-intercept of a graph is the point at which the graph crosses (or, in some cases, touches) the x-axis. A graph can have one or more x-intercepts. If the graph only crosses the x-axis once, then it has only one x-intercept. If the graph crosses the x-axis twice or more, then it has multiple x-intercepts. In either case, the x-intercepts can be described as either "crosses" or "touches" the x-axis.

If the graph crosses the x-axis at the x-intercept, then it is said to "cross" the x-axis. This indicates that the graph passes through the x-axis at the x-intercept.

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Answer:

[tex]26u + 14v[/tex]

Step-by-step explanation:

[tex]2(8u - 2v) + 2(5u + 9v) \\ 16u - 4v + 10u + 18v \: \: \\ 26u + 14v \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

Answer:

|x+3|=2

Step-by-step explanation:

We need to make the equation so that -5 and -1 both work, so this equation is one of many that we can construct.

Answer: i cant see

Step-by-step explanation:

The probability of getting 1st even and second odd is 9/36 = 1/4

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has included probability to forecast the likelihood of certain events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a certain event will occur.

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can vary from 0 to 1, with 0 being an impossibility and 1 denoting a certainty. For pupils in Class 10, probability is a crucial subject since it teaches all the fundamental ideas of the subject. One is the sum of the probabilities of all the events in a sample space.

Number of outcomes with 1st even and second odd is 9

Total number of outcomes = 36

So, the probability of getting 1st even and second odd is 9/36 = 1/4

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Think of a bracelet made of five different coloured beads. Be sure to account for flipping and rotating. Check to see whether your solution is right by applying the same logic to a bracelet with four beads of four different colours.

Properties. The form with the biggest area for a given perimeter is a circle (see Isoperimetric inequality). The circle has excellent spherical shape around the centre for all angles and every line thru the centre generates a path of reflection symmetry.

My response is: There are (n-1)!/2 potential bracelets for n different colours, as in our example. Therefore, there are 4!/2=12 various bracelets that might be made for n=5.

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The smallest number of coins Freddie would need is 4 (one penny, one nickel, one dime, and one quarter).

What is algebra ?

Algebra is a branch of mathematics that deals with mathematical symbols and the rules for manipulating these symbols. It includes the study of operations such as addition, subtraction, multiplication, division, and the extraction of roots, as well as the properties of operations such as commutativity, associativity, and distributivity.

In order to be able to pay any amount of money less than a dollar, Freddie would need to have at least one coin of each denomination: pennies, nickels, dimes, and quarters. The smallest number of coins he would need to achieve this is 4. With one penny, one nickel, one dime, and one quarter, he would be able to pay any amount of money less than a dollar by using combinations of these coins.

Therefore , The smallest number of coins Freddie would need is 4 (one penny, one nickel, one dime, and one quarter).

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I) we can substitute x + d = 2x + 1 and x + 2d = 11 into the equation for d:

x - 1 = 2x + 1 - x = 2x - x + 1 = x + 1

x = 0

II) The 30th term of this arithmetic sequence is 29.

To solve this problem, we can use the fact that in an arithmetic sequence, the difference between consecutive terms is constant.

(i) Let's call the common difference d. Then we can set up the equation:

x + d = 2x + 1

d = x - 1

Since we know that x; 2x + 1; 11 are three consecutive terms of an arithmetic sequence, we can substitute x + d = 2x + 1 and x + 2d = 11 into the equation for d:

x - 1 = 2x + 1 - x = 2x - x + 1 = x + 1

x = 0

(ii) To find the 30th term, we can use the formula for the nth term of an arithmetic sequence:

an = a1 + (n - 1)d

where a1 is the first term, d is the common difference, and n is the number of the term we want to find.

Substituting the known values into this formula:

a30 = x + (30 - 1)d

a30 = 0 + (29)(1)

a30 = 29

So the 30th term of this arithmetic sequence is 29.

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[tex]\sqrt[3]{6x}[/tex] has no real end behavior as x can be both positive and negative.

[tex]\sqrt[3]{x-5}-6[/tex] will approach negative infinity as x approaches negative infinity and positive infinity as x approaches positive infinity.

[tex][-3 \sqrt[3]{x+3}+7][/tex]will approach positive infinity as x approaches positive infinity and negative infinity as x approaches negative infinity.

Generally, The behavior of a function's graph at the "ends" of the x-axis is referred to as the function's "end behavior," and it is described by the symbol f. To put it another way, the trend of the graph may be described by the end behavior of a function if we look to the right end of the x-axis (as x approaches +) and to the left end of the x-axis (as x approaches ).

Take a look at the leading term of the polynomial function to get an idea of how it will behave in the end.

Because the power of the leading term is more than that of the other terms, whether x is made extremely big or very tiny, the leading term's behavior will predominate the graph because it will increase substantially quicker than the growth of the other terms.

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We would need more information to answer this question. For example, Sally’s speed.

Step-by-step explanation:

A function can be obtained from the table provided with the values of x and y in the form of a y=mx+b equation.

The above equation can be solved by plotting the graph or from table itself and after calculating its y-intercept, the value of y in the form of y= mx+ b can be obtained. Suppose the table has values of x and y as follows:

x: 0   1   2  3

y: 2  4   6  8

However, it can be seen that when x=0, y= 2, so the y-intercept i.e. the value of y obtained at x=0 is 2. And the slope can be calculated as:

m=[tex]\frac{change in y}{ change in x}[/tex]

m= [tex]\frac{4-2}{1-0}[/tex]

m=2

So the function can be written as y=2x+2

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On solving the provided question, we can say that Area of square = SxS=846 and perimeter of square = 4xS= 846/4=S= 211.5=Side.

A square is an equilateral quadrilateral with four equal sides and four equal angles according to Euclidean geometry. It is also known as a rectangle with two neighboring sides that have the same length. Having all four equal sides and all four equal angles, a square is an equilateral quadrilateral. 90 degree or straight angles are square angles. In addition, the square's diagonals are equally spaced and split at a 90-degree angle. a neighboring rectangle with two equal sides. a quadrilateral with four right angles and four sides of equal length. a parallelogram having two adjacent, equal sides that form a right angle. straight-sided rhombus.

Area of square = SxS=846

Perimeter of square = 4xS= 846/4=S= 211.5=Side.

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The correct question is -

A parking lot is shaped like a trapezoid as shown. If the area of the parking lot is 846 square meters, what is the perimeter? (Hint: The formula for the area of a trapezoid is (A=h2(b1+b2)

The dividing by 0.5 is not the same as dividing by 2 , because 0.5 and 2 are different numbers  .

Let us understand the Division with the help of example ;

let the number be 10 ;

first we divide the number 10 by 0.5 ;

this can be written mathematically as ⇒ [tex]\frac{10}{0.5}[/tex]  ;

⇒ [tex]\frac{10}{\frac{1}{2} }[/tex] = [tex]10\times2[/tex] = 20 ;

So , on dividing 10 by 0.5 , we get the answer as 20 .

Second , the number 10 is divided by 2 ;

this can be written mathematically as ⇒ [tex]\frac{10}{2}[/tex] ;

⇒ [tex]\frac{10}{2 }[/tex]  = 5  ;

So , on dividing 10 by 2 , we get the answer as 5  .

Therefore , dividing by 0.5 is not same as dividing by 2 .

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By using the piecewise function that shows the amount of money that will be charged for people in the amusement park , then the value of C(25) is $1425  .

The Piecewise function is given as ⇒ [tex]\{ \begin{array}{lr} 65p \; , & 0\leq P\leq 10\\ 55+100 \; , & 10 < P\leq 20\\ 45p+300 , & 20 < p\leq 30\\ 35p+600& 30 < p \end[/tex]   ;

we need to find the value of C(25) , that  means we have to find the amount of money that will be charged for 25 people in the amusement park ,

From the given piecewise function , we can see that [tex]p =25[/tex] lies  in the range [tex]20 < p\leq 30[/tex] ,

So , we substitute [tex]p =25[/tex] in [tex]C(p)= 45p+300[/tex] ;

we get ;

C(25) = [tex]45 \times 25 + 300[/tex]

= [tex]1125+300[/tex]

= 1425 .

Therefore , the amount that will be charged for 25 persons will be $1425 .

The given question is incomplete , the complete question is

Use the piecewise function showing the amount of money that will be charged, C(p) , for a group to go to an amusement park based on the number of people, p , n the group .

[tex]C(p)= \{ \begin{array}{lr} 65p \; , & 0\leq P\leq 10\\ 55+100 \; , & 10 < P\leq 20\\ 45p+300 , & 20 < p\leq 30\\ 35p+600& 30 < p \end[/tex]

Find C(25) ?

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The angle is acute and the answer rounded to the nearest degree is 13.2 degrees for (a) and 71.8 degrees for (b)

(a) To find the acute angle between the lines, we need to find the slope of each line and use the inverse tangent function to find the angle between them. The slope-intercept form of the first line is y = -9x + 5 and the slope-intercept form of the second line is y = 3x - 6.

The slope of the first line is -9 and the slope of the second line is 3. To find the acute angle between the lines, we can use the formula:

angle = atan2(|m1-m2|,1+m1*m2)

where m1 and m2 are the slopes of the lines.

angle = atan2(|-9-3|,1-9*3)

= atan2(6, -24)

= atan2(6/sqrt(24^2+6^2),-24/sqrt(24^2+6^2))

= atan2(6/sqrt(600),-24/sqrt(600))

= atan2(6/24.4987, -24/24.4987)

= atan2(0.244, -0.976)

= atan2(0.244/sqrt(0.244^2+0.976^2),-0.976/sqrt(0.244^2+0.976^2))

= atan2(0.244/1, -0.976/1)

= atan2(0.244, -0.976) = 13.2 degree.

(b) The slope-intercept form of the first line is y = (7-x)/2 and the slope-intercept form of the second line is y = (2-5x)/(-1).

The slope of the first line is -1/2 and the slope of the second line is 5. To find the acute angle between the lines, we can use the formula:

angle = atan2(|m1-m2|,1+m1*m2)

where m1 and m2 are the slopes of the lines.

angle = atan2(|-1/2-5|,1-(-1/2)*5)

= atan2(5.5, -2.5)

= atan2(5.5/sqrt(5.5^2+2.5^2),-2.5/sqrt(5.5^2+2.5^2))

= atan2(5.5/6.1213, -2.5/6.1213)

= atan2(0.901, -0.408)

= atan2(0.901/sqrt(0.901^2+0.408^2),-0.408/sqrt(0.901^2+0.408^2))

= atan2(0.901/1,-0.408/1)

= atan2(0.901,-0.408) = 71.8 degrees.

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The measure of the angle ∠CFE is 330°.

Arc length is more accurately described as the length along the perimeter of any circle or curve (arc). The arc length is the measurement of any distance along the curved path that forms the arc.

Arc refers to a segment of a curve or the circumference of a circle. Each of them is shaped like a curve. An arc's length is more than the distance in a straight line between its endpoints (a chord).

The angle ∠CFE is calculated as:-

∠CFE = 360 - ∠CEF

∠CFE = 360 - 30

∠CFE = 330

Hence, the angle ∠CFE is 330°.

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William should use 0.625 pounds of peanuts, and 0.375 pounds of cashews in the mixture.

Given that,

The selling price of peanuts= $2.40

The selling price of cashews= $3.20

Let x be the amount of that pound composed of peanuts. (1-x) of that pound is composed of cashews.

The total price of such a pound mix is 2.4x + 3.2(1-x) = 2.7

2.4x + 3.2(1-x) = 2.7

2.4x + 3.2 - 3.2x = 2.7

-0.8x + 3.2 = 2.7

-0.8x = -0.5

x = 5/8 = 0.625 pounds of peanuts, and 1-5/8=3/8= 0.375 pounds of cashews.

Thus, William should use 0.625 pounds of peanuts, and 0.375 pounds of cashews in the mixture.

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Answer: [tex]110^{\circ}[/tex]

Step-by-step explanation:

[tex]\angle ACB \cong \angle HFB[/tex] by the corresponding angles theorem.

The number that comes immediately before 4099 in the sequence is 2051.

You can get this by using the rule given: "double the last number and then subtract 3"

4099/2-3 = 2049

Consequently, the yield to maturity of a P7000 bond purchased at 90 with 15 years left to maturity is approximately 6.769%.

The rate of return an investor will receive if they hold the bond until maturity is known as the yield to maturity (YTM) of the bond. We need to know a bond's face value, coupon rate, market price, and time until maturity in order to determine its YTM.

Here,

Given :

Face value (FV) equals P7,000

Discount rate is 6%.

Market price as of today (CP) is $90.

15 years is the time to maturity (T).

To determine the YTM, we can use the bond pricing formula:

CP is equal to (FV * C) / (1 + r)T plus (FV / (1 + r)T)

Where:

(FV * Coupon Rate) / 2r = YTMT = time to maturity in years, where C is the annual coupon payment.

The result of solving the equation is 6.769% for the YTM.

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