PLEASEEEEEEEEEEEEEEEE HELP!! Esther purchased two rock tumblers and one spy pen for $74. Eli purchased two puzzles
and a spy pen for $50. Sabine purchased a rock tumbler and two puzzles for $57. Based
on this, how much does one puzzle cost?

Answer:

x=56

Step-by-step explanation:

There are 3 angles in the triangle

x, 60 and the unknown angle we will call y

y  and 2x+4 make a straight line, so that adds to 180

y + 2x+4 = 180

Solve for y

y = 180 - (2x+4)

y = 180 -2x-4

y = 176 -2x

The three angles in a triangle add to 180

x + 60 + y = 180

Substitute in for y

x + 60 + 176 -2x = 180

Combine like terms

-x +236 = 180

Subtract 236 from each side

-x+236-236 = 180-236

-x = -56

Multiply by -1

x = 56

The actual value of sin(π/3) is (√3)/2 ≈ 0.86602540.

If the sine function is approximated by y=x (no error at x = 0), then the error at x=π/3 is ...

... x -sin(x) @ x=π/3

... π/3 -(√3)/2 ≈ 0.18117215 ≈ 0.1812

You know right away this is a bad approximation, because the approximate value is π/3 ≈ 1.04719755, a value greater than 1. The range of the sine function is [-1, 1] so there will be no values greater than 1.

___

If the sine function is approximated by y=(x+1-π/4)/√2 (no error at x=π/4), then the error at x=π/3 is ...

... (x+1-π/4)/√2 -sin(x) @ x=π/3

... (π/12 +1)/√2 -(√3)/2 ≈ 0.026201500 ≈ 0.02620

Therefore, the error due to linear interpolation to estimate the value of [tex]\( \sin\left(\frac{\pi}{3}\right) \)[/tex] is approximately [tex]\( 29.59 \% \).[/tex]

To estimate the error due to linear interpolation for [tex]\( \sin(x) \)[/tex] at [tex]\( x = \frac{\pi}{3} \)[/tex], we need to compare the actual value of [tex]\( \sin\left(\frac{\pi}{3}\right) \)[/tex] with the value obtained through linear interpolation.

The actual value of [tex]\( \sin\left(\frac{\pi}{3}\right) \)[/tex] is [tex]\( \frac{\sqrt{3}}{2} \)[/tex], which is approximately [tex]\( 0.8660 \)[/tex] .

For linear interpolation, we typically use two nearby points to estimate the value of a function at an intermediate point. Let's consider the points [tex]\( (\frac{\pi}{4}, \sin(\frac{\pi}{4})) \) and \( (\frac{\pi}{2}, \sin(\frac{\pi}{2})) \)[/tex], which are [tex]\( \left(\frac{\pi}{4}, \frac{\sqrt{2}}{2}\right) \) and \( \left(\frac{\pi}{2}, 1\right) \)[/tex], respectively.

Now, we'll use linear interpolation to estimate [tex]\( \sin\left(\frac{\pi}{3}\right) \):[/tex]

[tex]\[ \sin\left(\frac{\pi}{3}\right) \approx \sin\left(\frac{\pi}{4}\right) + \left(\frac{\pi}{3} - \frac{\pi}{4}\right) \cdot \frac{\sin\left(\frac{\pi}{2}\right) - \sin\left(\frac{\pi}{4}\right)}{\frac{\pi}{2} - \frac{\pi}{4}} \][/tex]

[tex]\[ \sin\left(\frac{\pi}{3}\right) \approx \frac{\sqrt{2}}{2} + \left(\frac{\pi}{3} - \frac{\pi}{4}\right) \cdot \frac{1 - \frac{\sqrt{2}}{2}}{\frac{\pi}{2} - \frac{\pi}{4}} \][/tex]

[tex]\[ \sin\left(\frac{\pi}{3}\right) \approx \frac{\sqrt{2}}{2} + \left(\frac{\pi}{3} - \frac{\pi}{4}\right) \cdot \frac{1 - \frac{\sqrt{2}}{2}}{\frac{\pi}{4}} \][/tex]

[tex]\[ \sin\left(\frac{\pi}{3}\right) \approx \frac{\sqrt{2}}{2} + \left(\frac{\pi}{3} - \frac{\pi}{4}\right) \cdot \frac{1 - \frac{\sqrt{2}}{2}}{\frac{\pi}{4}} \][/tex]

[tex]\[ \sin\left(\frac{\pi}{3}\right) \approx \frac{\sqrt{2}}{2} + \left(\frac{\pi}{3} - \frac{\pi}{4}\right) \cdot \frac{1 - \frac{\sqrt{2}}{2}}{\frac{\pi}{4}} \][/tex]

[tex]\[ \sin\left(\frac{\pi}{3}\right) \approx 0.7071 + \left(\frac{\pi}{3} - 0.7854\right) \cdot \frac{1 - 0.7071}{0.7854} \][/tex]

[tex]\[ \sin\left(\frac{\pi}{3}\right) \approx 0.7071 + (0.5236 - 0.7854) \cdot \frac{0.2929}{0.7854} \][/tex]

[tex]\[ \sin\left(\frac{\pi}{3}\right) \approx 0.7071 + (-0.2618) \cdot 0.3732 \][/tex]

[tex]\[ \sin\left(\frac{\pi}{3}\right) \approx 0.7071 - 0.0977 \][/tex]

[tex]\[ \sin\left(\frac{\pi}{3}\right) \approx 0.6094 \][/tex]

Now, we can find the error:

[tex]\[ \text{Error} = \left| \frac{\text{Actual value} - \text{Interpolated value}}{\text{Actual value}} \right| \times 100 \% \][/tex]

[tex]\[ \text{Error} = \left| \frac{0.8660 - 0.6094}{0.8660} \right| \times 100 \% \][/tex]

[tex]\[ \text{Error} = \left| \frac{0.2566}{0.8660} \right| \times 100 \% \][/tex]

[tex]\[ \text{Error} = 0.2959 \times 100 \% \][/tex]

[tex]\[ \text{Error} = 29.59 \% \][/tex]

Answer:

see attached plot for  y ≥ |x - 1|

Step-by-step explanation:

Answer:

Graph below. x=1.

Step-by-step explanation:

1) Check the graph below. Take a closer look at the green area. This great Triangle intercepts the y-axis at the point (0,1) since it's an absolute value.

2) Algebraically, turning this function into an equation, since modulus

|x|=0, x=0.

[tex]y\geq |x-1|\\ |x-1|\geq 0\\ x-1\geq 0\\ x-1+1\geq 0+1\\ x\geq 1[/tex]

Answer:

1. x =8

2.  x=9

Step-by-step explanation:

Since these figures are parallelograms, the opposite sides are equal.

1.     6 = 2x-10

Add 10 to each side

   6+10 = 2x-10+10

   16 = 2x

Divide  each side by 2

16/2 = 2x/2

 8 =x

2.  x+14 =23

    Subtract 14 from each side

x+14-14 = 23-14

x = 9

3 11/15 cm

AE is the angle bisector of ∠A, so divides the sides of the triangle into a proportion:

... BE:CE = BA:CA = 7:8

Then ...

... BE:BC = 7 : (7+8) = 7:15

ΔDBE ~ ΔABC, so DE = 7/15 × AC

... DE = 7/15 × 8 cm = (56/15) cm

... DE = 3 11/15 cm

To find the side of the inscribed rhombus, we can use the Pythagorean theorem and the properties of inscribed rhombuses.

To find the side of the rhombus, we need to understand the properties of inscribed rhombuses. In an inscribed rhombus, the diagonals are perpendicular bisectors of each other.

Let's label the side of the rhombus as 's'.

Using the given information, we can see that AB and AC are the diagonals of the rhombus.

Since AB = 7 cm and AC = 8 cm, we know that the diagonals bisect each other and form right angles.

Therefore, we can use the Pythagorean theorem to find the side of the rhombus:
s^2 = (AB/2)^2 + (AC/2)^2
s^2 = (7/2)^2 + (8/2)^2
s^2 = (49/4) + (64/4)
s^2 = (113/4)
s = sqrt(113/4)

Answer:

∠MSR is right angle

Step-by-step explanation:

It is given that RHOM is a Rhombus

Also ΔHOM, ΔMHR, ΔRHO and ΔOMR are isosceles triangles

Let us take ΔMSR and ΔRSH

∠MRS =∠HRS            ( since it is given that the diagonal RO bisects ∠R)

∠RMS =∠RHS     ( since Δ MRH is isosceles triangle )

RS = RS        ( common side )

By AAS congruency rule ΔMSR ≅ ΔHSR

so we have

∠MSR=∠RSH  ( corresponding parts of congruent triangles are congruent)

also we have

∠MSR +∠RSH =180°   ( supplementary angles)

∠MSR +∠MSR=180°          ( since ∠MSR=∠RSH)

2∠MSR= 180°

∠MSR =90°

Hence ∠MSR is right angle

Answer:

It must be a right angle.

Step-by-step explanation:

The figure attached shows the rhombus RHOM with RO and HM as diagonals and are the angle bisectors of the vertex angles.

Let S be the point where the diagonals RO and HM intersects each other.

ΔHOM, ΔMHR, ΔRHO, ΔOMR are four isosceles triangles in the given rhombus.

Since, Diagonals of a rhombus bisect each other at right angle.

Therefore, we have ∠MSR= 90°

That is, ∠MSR is a right angle.

Answer:

0.009

Step-by-step explanation:

So 9/1000 can be written as 0.009

Answer:

The answer is 0.009.

Step-by-step explanation:

The total number of people from which only 9 earned a perfect score = 1,000.

The number of people who earned a perfect score = 9

The decimal that represents the number of people who earned a perfect score = The number of people who earned a perfect score ÷ The total number of people concerned = 9 ÷ 1,000 = 0.009.

Answer: They are fed 4/9 of what the polar bears are fed.

Step-by-step explanation:

7/9*4/7=

1/9*4/1=4/9

The 7's get cancelled out.

The penguins at the zoo are fed 4/9 bucket of fish a day. This fraction has been calculated by multiplying the amount of food the polar bears get (7/9 bucket) by 4/7 as specified in the problem.

To find out how much the penguins are fed, we first understand the given units involving the polar bears and penguins. The polar bears are fed 7/9 bucket of fish a day, and the penguins are fed 4/7 that amount. Therefore, to calculate the amount the penguins are fed, we multiply the amount the polar bears are fed by 4/7.

We get this by performing the calculation (7/9) * (4/7). The sevens cancel out, leaving us 4/9, which is the fraction of the bucket of fish that the penguins are fed each day.

https://brainly.com/question/29633725

#SPJ2

The first step is correct, because you changed the order of two terms in an addition, and the property [tex] a+b=b+a [/tex] is indeed called commutative property of addition.

In the second step, you do the same, but with multiplication: you use [tex] (6x)\cdot y = y \cdot (6x) [/tex]. This means that you're using the commutative property again, except for multiplication. So, the answer should be "commutative property of multiplication.

Finally, the third step is correct, because you're distributing the multiplication by 3 to both terms in the parenthesis, and this is called distributive property: it states that

[tex] a(b+c)=ab+ac [/tex]

c. Both A and B

A function is a mapping that maps each element of its domain (student's name) to exactly one element of its co-domain (favorite ...). Assuming student names are unique and the notion of "favorite" is exclusive (can't have two or more "favorites" of the same type), then both A and B describe mappings that are functions.

Answer:

c. Both A and B

Step-by-step explanation:

A function means each input  goes to only one output.  As long as each student is only entered once,  and they only have one favorite color and one favorite math teacher, then A and B are functions.

tan(Q) = RS/RQ

The mnemonic SOH CAH TOA reminds you that ...

... Tan = Opposite/Adjacent

The side opposite angle Q is RS. The side adjacent is RQ. (QS is the hypotenuse, which does not come into play in the tangent function.)

Then ...

... tan(Q) = Opposite/Adjacent = RS/RQ

In right triangle QRS, with angle R being 90 degrees, tan Q is represented by the length of the side opposite to angle Q divided by the length of the side adjacent to Q which tan Q = SR/ QR.

In right triangle QRS, with angle R being 90 degrees, the ratio that represents tan Q is the length of the opposite side to angle Q divided by the length of the adjacent side.

In trigonometry, the tangent (tan) of an angle in a right triangle is a ratio of the length of the side opposite to the angle to the length of the side adjacent to the angle.

Therefore, if we label the sides opposite and adjacent to angle Q as opposite and adjacent respectively, the formula for tan Q would be:

tan Q = opposite/adjacent

         = SR/QR

For example, if a right triangle has sides of lengths 3, 4, and 5, with the side lengths of 3 and 4 being adjacent to and opposite angle Q respectively, the tan Q would be calculated as 4/3.

Answer:

D U E = { 6,8,9,10,11}

Step-by-step explanation:

U stands for union, which is join the sets together

D U E = { 6,8,9,10,11}

Answer:

The answer is 96 when X= 8

Step-by-step explanation:

We have given that :

AE= [tex]x^2-16[/tex]  and CE=[tex]6x[/tex]

where AE and CE are the diagonals of the paralleogram

The diagonals of parallelogram bisect each other therefore,

 [tex]x^2-16 = 6x[/tex]

⇒ [tex]x^2-6x-16=0[/tex]

factors are (x+2)(x-8)=0

setting to each factor 0 the value of x= -2 or x= 8

therefore, two values of AC is

X= -2  ,AC= 2([tex]x^2-16[/tex])=2(-12)=-24

X= 8 ,AC= 2([tex]x^2-16[/tex])=2(48)=96

The answer is 96 when X= 8

Answer:

A is the answer or (6 1/2, 8 1/2)  or (13/2, 17/2) or (6.5,8.5)

Step-by-step explanation:

Given : A line segment AB with

[tex]A= (x_1,y_1)=(4,8)[/tex] and [tex]B= (x_2,y_2)=(14,10)[/tex]

let C partitioned the line AB by 1:3  let m:n = 1:3

shown in the figure attached

Formula used:

[tex]C= (\frac{n x_1 + m x_2 }{m+n},\frac{n y_1+ m y_2 }{m+n})[/tex]

putting value in formula we get,

[tex]C= (\frac{(4) (3)+ (14)(1) }{1+3},\frac{(8)(3)+ (10)(1)}{1+3})[/tex]

[tex]C= (\frac{(13 }{2},\frac{17}{2})[/tex]

[tex]C= (6.5 ,8.5)[/tex]

[tex]C= ( 6 1/2,8 1/2)[/tex]

therefore, A is the answer

[tex]9.36\cdot10^4=9.36\cdot10,000=93,600[/tex]

Answer:

The Answer is 48 miles.

Step-by-step explanation:

Linda has driven 36 miles home and that is 3/4 of the way home.  If you divide 36 by 3 equals 12 miles per 1/4 drive.  Multiply 12x4 and the answer is 48.

Hope that helps!

To determine the number of ways to choose two students to go first and second in a group of 17 students, we use permutations, resulting in a total of 17 * 16 = 272 ways.

The question inquires about the number of ways two students can be chosen from a group of 17 to go first and second in a spelling bee, which can be solved using combinatorics.

To choose the first student, we have 17 options. After choosing the first student, we have 16 remaining students to choose from for the second student. Therefore, the total number of ways to choose students for these two positions is the product of these two numbers. This scenario calls for a permutation calculation since the order in which we select the students matters.

The formula is n!/(n-r)!, where n is the total number of items to pick from, and r is the number we are picking. For our case, n = 17 and r = 2.

Total number of ways (permutations) = 17 * 16 = 272 ways.

102°

Opposite angles of an inscribed quadrilateral are supplementary.

∠Q = 180° -∠A = 180° -78°

∠Q = 102°

Answer:

g + h =  -4

g - h =  -10

h -g = 10

gh =  -21

g+ h^2 =  2

g^2 -h =  46

Step-by-step explanation:

We know g = -7 and h = 3

g + h = -7 +3 = -4

g - h = -7 - 3 = -10

h -g = 3 --7 = 3+7 = 10

gh = (-7) * 3 = -21

g+ h^2 = -7 + (3)^2 = -7+9 = 2

g^2 -h = (-7)^2 -3 = 49 -3 = 46

Find the x and y for each dot:

5,35

10,70

15,105

etc.

Divide the Y by the X:

35 / 5 = 7

70 / 10 = 7

etc.

The answer would be C) y = 7x

Answer:

Option C is correct

[tex]y = 7x[/tex]

Step-by-step explanation:

Direct variation states that:

[tex]y \propto x[/tex]          ......[1]

then, the equation is in the form of:

[tex]y=kx[/tex], where k is the constant of variation

From the given graph we have points in the form of (x, y) i.e,

(0, 0), (5, 35), (10, 70), (15, 105), (20, 140), (25, 175) and (30, 210)

Substitute any points i.e (5, 35) in [1] we have;

[tex]35 = 5k[/tex]

Divide both sides by 5 we have;

7 = k

or

k = 7

then;

[tex]y = 7x[/tex]

Therefore, the constant of  proportionality for the graph is, 7 and its form is, [tex]y = 7x[/tex]

Answer:

8763

Step-by-step explanation:

Let x represent the number of students the college had last year. Then this year's enrollment is ...

... x - 3%·x = 8500

... x(1 - 0.03) = 8500 . . . . . collect terms

... x = 8500/0.97 ≈ 8762.89 . . . . divide by the coefficient of x

Enrollment last year was about 8763.

_____

Of course, you know 3% = 3/100 = 0.03.

Answer:

Null Hypothesis : The true mean height of children is more than 60 inches.

Step-by-step explanation: Null Hypothesis is defined as a hypothesis that there is no significant difference between the observed and sampled mean.

So, if alternative hypothesis is " the true mean height of children is less than 60 inches" which denotes there is significant difference between sampled and observed mean heights so null hypothesis is taken as " true mean height of children is more than 60 inches"

C. AB ║ DC

The congruence of the two triangles means ∠ABD≅∠CDB. These, then, are alternate interior angles on either side of transversal BD between lines AB and DC. If alternate interior angles are congruent, the lines are parallel:

... AB ║ DC

_____

Congruence of the triangles does not require ∠B to be bisected or that it be 90°.

All the three sides of the given triangles are equal to the sides of another triangle then, [tex]\rm \overline{AB}=\overline{DC}[/tex]. Therefore the correct option is C).

Given :

Triangle ABD is congruent to the triangle CBD.

A triangle has three sides and the sum of all the interior angles are equal to [tex]180^\circ[/tex].

If the triangle ABD is congruent to the triangle CBD then:

AB = DC

AD = BC

BD = BD

If all the three sides of the given triangles are equal to the sides of another triangle then, [tex]\rm \overline{AB}=\overline{DC}[/tex]. Therefore the correct option is C).

For more information, refer to the link given below:

https://brainly.com/question/19325053

5/2

The ratio of perimeters is the same as the ratio of corresponding sides:

... (140 cm)/(56 cm) = 5/2

Answer:

5:2

Step-by-step explanation:

We have been given that triangles △ABC and △DFG are similar. The lengths of the two corresponding sides are 1.4 m and 56 cm.

Since both triangles are similar, therefore all corresponding sides will have same proportion.

Let us find proportion of corresponding sides of both triangles.

1 meter = 100 centimeter

1.4 meter = 1.4* 100 centimeters = 140 centimeters.

[tex]\frac{\text{Side of triangle ABC}}{\text{Side of triangle DFG}}=\frac{140}{56}[/tex]

[tex]\frac{\text{Side of triangle ABC}}{\text{Side of triangle DFG}}=\frac{5}{2}[/tex]

The ratio of sides of △ABC to sides of△DFG is 5:2.

Since perimeter of a triangle is sum of lengths of three sides of the triangle and all sides of both triangle have the ratio 5:2, therefore, their perimeters will be in same ratio, that is 5:2.

Answer: 45

Step-by-step explanation:

Divide 90 by 2 and you will the the answer of 45.

Answer:

The coefficient is 9

Step-by-step explanation:

(a)(b)(c)+(a)(2c)(2a)+(2b)(b)(c)+(2b)(2c)(2a)

abc+4ca^2+2cb^2+8abc

9abc+4ca^2+2cb^2

For each birdhouse built, the total cost increases by $3.50.

The number 3.5 multiplies b, so when b increases by 1, f(b) increases by 3.5. Making 1 more birdhouse increases the total cost by $3.50.

Answer: For each birdhouse built, the total cost increases by $3.50.

Step-by-step explanation:

Given: The total cost for Sophia to build b birdhouses is represented by the function [tex]f(b)=3.5b+24[/tex]

We can see in the function 3.5 is multiplied to b, so when b increases , f(b) increases by 3.5.

[tex]f(1)=3.5(1)+24=3.5+24=27.5[/tex]

[tex]f(2)=3.5(2)+24=7+24=31[/tex]

[tex]f(3)=3.5(3)+24=10.5+24=34.5[/tex]

and [tex]f(2)-f(1)=f(3)-f(2)=3.5[/tex]

Therefore, the value of 3.5 represents that for each birdhouse built, the total cost increases by $3.50.

C. 4(x-3)-x

All of the given expressions are equivalent to 3x+12 except selection C. Using that in your equation makes it be ...

... 3(x +1) +9 = 4(x -3) -x

... 3x +12 = 3x -12

... 12 = -12 . . . . . false

There is no value of x that will make this true, hence NO SOLUTION.

_____

Comment on the other choices

3x+12 = 3x+12 has an infinite number of solutions, as any value of x will make this true.

c

BECAUSE I SAID SO HUH YOU GOTTA PROBLEMO??

y = 21·0.7^x

The pair (0, 21) tells you the multiplier is 21. (The exponential factor is 1 for x=0.)

Any adjacent pair of y-values can tell you the common ratio, hence the base of the exponential term. For example, using the y-values associated with x=0 and x=1, we find the base to be ...

... 14.7/21 = 0.7

Then the equation is ...

... y = multiplier · base^x

... y = 21·0.7^x

Answer:

B

Step-by-step explanation:

Answer:

Step-by-step explanation:

If a polynomial function P(x) with rational coefficients has a root z. the so is the complex conjugate of z is a root. (In order to see that, take the complex conjugates of the equation P(x)=0, and note that complex conjugates of rational numbers equal to itself.)

Therefore the complex conjugates of the given roots i and 7+8i , are -i and 7-8i is the required answer.