are the answers highlighted in yellow

correct?

Answer:

Marcela used the Associative Property of Addition.

Step-by-step explanation:

The Associative Property of Addition states that when adding three or more numbers, the grouping of the addends does not change the sum. In other words, no matter how the addends are grouped, the sum remains the same. More specifically:

For any three numbers a, b, and c, (a + b) + c = a + (b + c)

For example: (2 + 3) + 4 = 2 + (3 + 4) = 9

So, if Marcela used the Associative Property of Addition to add her grocery bills, she grouped the addends in a different order, but still arrived at the same sum.

The measure of angle a is 35°

The chord of a circle is the line segment joining any two points on the circumference of the circle.

The diameter is the longest chord of a circle which passes through the center of the circle.

For chords that meet inside of a circle, the measure of the angle formed is one-half the sum of the measure of the arcs intercepted by the angle and its vertical angle.

Using the above concept (That is the given hint in the question), we can say:

∠a = (29 + 41)/2

∠a = 70/2

∠a = 35°

Therefore, the measure of angle a is 35°

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Complete Question

Check attached image

The minimum number of times Johnny needs to use to the wheelbarrow until the delivery truck is filled up to 70%, whereby the shape of the truck is a rectangular prism is about 41 times

A rectangular prism is a three dimensional geometric figure with three pairs of parallel facing sides, and perpendicular adjacent faces.

Whereby the wheelbarrow and the truck are rectangular prisms, we get;

The dimensions of the wheel barrow are;

2 feet by 3 feet by 1.5 feet

The dimensions of the truck are;

11 feet by 8 feet by 6 feet

The amount of soil John puts in the truck = 70% of the volume of the truck

Therefore;

The amount of soil John puts in the truck = 11 feet × 8 feet × 6 feet × 70%

11 feet × 8 feet × 6 feet × 70% = 528 ft³ × 70% = 369.6 ft³

The number of times to use the wheelbarrow, n, is therefore;

n = 369.6 ft³ ÷ (2 ft × 3 ft × 1.5 ft) ≈ 41.0

The minimum number of times Johnny needs to use the wheelbarrow until the delivery truck is 70% filled is therefore 41  = 41 times

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The total area of the figure formed by the congruent triangles and the square is 60 sq in

For square

A = s²

where s is the side

Given:

s = 6 in

Area = 6 * 6

= 36 sq in

Area of triangle = 0.5bh

where b is the base

h is the height

Given:

b = 6 in

h = 4 in

A = 0.5 * 6 * 4

= 12 sq in

Total area of the figure = 2 * Area of triangle + area of square

= 2 * 12 + 36

= 24 + 36

= 60 sq in

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[tex]\large \maltese \:{ \underline { \underline{ \pmb{ \sf{SolutioN }}}}} : -[/tex]

we have given ,

★ According to Angle sum property of triangle, the sum of interior angles of a triangle is 180°.

➝ ∠ A + ∠ B + ∠ C = 180°

➝ 60° + 60° + ∠ C = 180°

➝ 120° + ∠ C = 180°

➝ ∠ C = 180° - 120°

➝ ∠ C = 60°

Now,

★ Calculating for x :-

↝ ∠ C + x = 180°

↝ 60° + x = 180°

↝ x = 180° - 60°

↝ x = 120°

Hence, The value of x will be 120°.

Answer:

The major of the exterior angle is 120°

Step-by-step explanation:

In given triangle we have to find the value of exterior angle and in interior of the triangle there are two angles 60 degree and second one is also 60 degree and we have to find value of exterior angle which is x.

So, here we apply exterior angle property which is exterior angle is equal to the sum of the two interior opposite angles. Here, there are two opposite interior angles so we have to add these two and we get the value of exterior angle.

Exterior angle property :-

[tex] \implies \sf \angle60 \degree + \angle60 \degree[/tex]

[tex] \implies\angle120 \degree[/tex]

Some important properties :-

Exterior angle property :- An exterior angle of a triangle is equal to the sum of its interior opposite angles.

Angle sum property :- The total measure of the three angles of a triangle is 180°

Step-by-step explanation:

First thing to solve expression, use the Reverse-Inverse PEMDAS

PEMDAS is order of operations where

we

evaluate parethiss first

then exponents

then multiplication/division(which ever comes first while reading left to right )

then addition and subtraction(which ever comes first while reading left to right)

We will go in reverse to solve for x.

Are there any addition and subtraction.

Yes, there is addition when we add 4, therefore we do the Inverse and subtract 4 from both sides

[tex] - \frac{4}{9} x = \frac{2}{3} - 4[/tex]

[tex] - \frac{4}{9} x = \frac{2}{3} - \frac{4}{1} [/tex]

Use Butterfly Method to simplify

[tex] - \frac{4}{9} x = \frac{ - 10}{3} [/tex]

Is there any multiplication or division happening to our variable of interest

Yes, there is multiplication happening as our variable is being multiplied by -4/9.

To get rid of this, we do the Inverse and divide by -4/9 on both sides.

Divide by -4/9 is the sames as multiplying by -9/4

[tex]x = \frac{ - 10}{3} \times - \frac{9}{4} = \frac{15}{2} [/tex]

So our answer is 15/2

Answer:

The answer to this question is vertical angles

Step-by-step explanation:

angle 5 and 8

 Those are vertical angles formed by two crossing lines and they are equal

The cost of the fondue pot after the 45% discount and 6% sales tax is calculated using the following equations:

In this example, the original price of the fondue pot is $92 and the discount is 45%, which would make the discount amount $41.40. The sales tax is 6%, which would be $2.48

Therefore, the final price of the fondue pot would be $43.88

The salary $50,780 per year is lower than the yearly median.

The yearly median earnings for a male with a bachelor's degree are $40,404 higher than those for a male with a high school diploma.

a. As, the median weekly earnings for males with a bachelor's degree are $1,384.

To convert this to yearly earnings, we can multiply by the number of weeks in a year (52):

= $1,384 x 52

= $71,968

So, the salary $50,780 per year is lower than the yearly median earnings for a male with a bachelor's degree.

b. Now, The yearly median earnings for a male with a high school diploma (no college) are $607 per week. Converting this to yearly earnings:

Yearly median earnings for a male with a high school diploma

= $607 x 52 = $31,564

The difference between the yearly median earnings for a male with a bachelor's degree and a male with a high school diploma is:

= $71,968 - $31,564 = $40,404

So, the yearly median earnings for a male with a bachelor's degree are $40,404 higher than those for a male with a high school diploma.

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The value of c that makes z = 4 an extraneous solution is c = -1.

We need to find the value of c that makes z = 4 an extraneous solution, which means that 4 is not a valid solution of the original equation but appears to be one when substituted into the equation.

First, we substitute z = 4 into the equation:

√ (3/2 x + 10) = cz + 8

√ (3/2 x + 10) = c(4) + 8

√(16) = 4c + 8

4 = 4c + 8

4c = -4

c = -1

Therefore, the value of c that makes z = 4 an extraneous solution is c = -1.

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The properties of quadratic functions cause this "death ray" effect is discussed below.

The "death ray" effect refers to the phenomenon where a quadratic function appears to have a sharp point or vertex that shoots off to infinity in a graph. This effect is caused by the properties of quadratic functions, specifically:

The degree of the quadratic function: Quadratic functions have a degree of 2, which means they have a leading term that is a squared variable (x²). This leads to a graph that is a parabola.

The coefficient of the squared term: The coefficient of the squared term in the quadratic function determines the shape of the parabola. If the coefficient is positive, the parabola opens upward, and if the coefficient is negative, the parabola opens downward.

However, when the coefficient of the squared term is negative (a < 0), the graph of the quadratic function opens downward, and the vertex represents the maximum point of the parabola.

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The orbital increased by factor [tex]2^3^/^2[/tex] .Hence, correctander is option D by equation  T²=A³

The relationship between a planet’s orbital period(T) and the planet’s mean distance from the sun(A)  is given by equation T²=A³

Given equation is T²=A³

The distance between the planet X and sun is represented by d

Time-period of the planet X:

T²=d³

Distance between planet Y and the sun is represented by d'

d'= 2d

T'²=d'² = (2d)³ = 8d³

On dividing  (1)and (2).

T'/T = 8d³/d³

=8

=2√2

=[tex]2^3^/^2[/tex]

Hence, the orbital increased by factor [tex]2^3^/^2[/tex] .

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The equation T^2=A^3 shows the relationship between a planet’s orbital period, T, and the planet’s mean distance from the sun, A, in astronomical units, AU. If planet Y is twice the mean distance from the sun as planet X, by what factor is the orbital period increased? A. 2^1/3. B. 2^1/2. C. 2^2/3. D. 2^3/2

Answer:

7

Step-by-step explanation:

yw ;)

The amount of fencing you will get is 5 feet.

Math operations include division as one of its types. This technique involves splitting the phrases or numbers into the same amount of components.

If $18 is the cost for every 3 feet of fencing, then as per the division operation the cost per 1 foot of fencing is,

$18/3 = $6.

So, if it costs $30, then the amount of fencing you will get is $30/$6 = 5 feet.

Therefore, the required amount of fencing is 5 feet.

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The value of the principal is $10,000.

The equation A = P(1 + 0.043t) represents the amount of money earned on a savings account with 4.3% annual simple interest A is the account balance after t years P is the principal amount, and 0.043 is the interest rate per year.

The account balance is $15,160 after 12 years.

Substituting these values into the equation, we get:

15,160 = P(1 + 0.043(12))

Simplifying the right-hand side, we get:

15,160 = P(1 + 0.516)

15,160 = P(1.516)

Dividing both sides by 1.516, we get:

P = 10,000

This means that the account was initially opened with a principal of $10,000 and it earned simple interest of 4.3% per year for 12 years resulting in an account balance of $15,160.

The principal and it does not take into account the interest that is earned on the interest itself.

In contrast compound interest takes into account the interest that is earned on both the principal and the previously earned interest.

The account in question had been earning compound interest instead of simple interest the final account balance after 12 years would have been higher than $15,160.

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The domain of the exponential function is all real numbers.

The domain of a function refers to the set of all possible input values (also known as the independent variable) for which the function is defined.

For the exponential function y = 2ˣ + 6, the domain includes all real numbers.

This is because there are no restrictions on the input values that can be plugged into the function.

We can take any real number x, substitute it into the expression 2ˣ, and then add 6 to get a corresponding output value y.

Hence,  the domain of the exponential function is all real numbers.

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The value of the limit of the function f(x) = x² - 2 is 7.

The value of the limit of the function f(x) = -3x + 15 is -6.

We have,

To evaluate the limit as x approaches 3, we need to find the limit of function f(x) as x approaches 3 from both sides of 3.

First, let's evaluate the limit from the left side of 3:

lim x → 3⁻ f(x) = lim x → 3⁻ (x^2 - 2)

Substituting x = 3 - h (where h approaches zero) gives:

lim h → 0⁺ [(3 - h)^2 - 2]

= lim h → 0⁺ [9 - 6h + h^2 - 2]

= lim h → 0⁺ [h^2 - 6h + 7]

= 7

(since the limit of a quadratic function as h approaches zero is the constant term)

Next, let's evaluate the limit from the right side of 3:

lim x → 3⁺ f(x)

= lim x → 3⁺ (-3x + 15)

= -6

Since the limit from the left side is not equal to the limit from the right side, the limit of f(x) as x approaches 3 does not exist.

Thus,

The value of the limit of the function f(x) = x² - 2 is 7.

The value of the limit of the function f(x) = -3x + 15 is -6.

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Answer:

2 forms

Step-by-step explanation:

hope this helps <3

[tex] \sf \longrightarrow \: \frac{8}{5} \div 6 \\ [/tex]

[tex] \sf \longrightarrow \: \frac{5}{8} \times 6 \\ [/tex]

[tex] \sf \longrightarrow \: \frac{5 \times 6}{8} \\ [/tex]

[tex] \sf \longrightarrow \: \frac{30}{8} \\ [/tex]

[tex] \sf \longrightarrow \: \frac{8}{30} \\ [/tex]

[tex] \sf \longrightarrow \: 0.26 \\ [/tex]

_____________________________

An exponential function that best models the data include the following: A. [tex]r(x) = 223.06(1.09)^x[/tex]

In this scenario, the Company Time, x (months) would be plotted on the x-axis (x-coordinate) of the scatter plot while the Net Revenue, r(x (millions of dollars) would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.

On the Microsoft Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an exponential equation for the line of best fit (trend line) on the scatter plot.

From the scatter plot (see attachment) which models the relationship between the Company Time, x (months) and the Net Revenue, r(x (millions of dollars), an exponential equation for the line of best fit is given by:

[tex]r(x) = 223.06(1.09)^x[/tex]

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The answer is 23/24

there are 23 out of the 24 crayons that arent light blue and that gives you the odds against the light blue crayon

Answer:

Step-by-step explanation:

Set h=0 for ground height, then solve for t

-16t^2 -20t +240 = 0

divide by -4

4t^2 +5t - 60 = 0

use the quadratic formula

t= -5/8 + or - (1/8)square root of (25 +4(4)(60)).  Ignore the negative square root

 =-5/8 + (1/8)sqr(960+25)

= -5/8 + (1/8)sqr(985)

 =-5/8 + (1/8)sqr(5(197))= slightly less than -5/8 +(10/8)(sqr10) = about -5/8 +32/8 = 27/8 = 3.3 seconds

the ball's initial velocity is negative, meaning the ball was thrown downward. Then add the effect of gravity, and it should hit the ground in a short time, even when thrown from an initial height of 240 feet.

plug t=2 into the original equation for height.  You should get slightly above ground, near zero

-16(2)^2 -20(2) +240 = -64 -40+240 = 136

try t=3

-16(9) -20(3) +240 = -144 -60 +240 = 36

try t=4

-16(16) -20(4) +240 =-256 -80 +240 =-96

the time to hit ground should be between t=3 and 4, but closer to t=3, maybe about 3 1/3 seconds

Answer:

The Answer to This question Is x + 5 So Basically 5

The linear equation that shows a proportional relationship is y = 1/4x.

A proportional relationship is one in which there is a constant ratio between the values of two variables.

In the given options, the linear equation that shows a proportional relationship is:

y= 1/4 (x- 5) and y = -1/4x

In this equation, the coefficient of x is 1/4, indicating that for every increase or decrease in x, y will change in proportion to that change.

Now, y= 1/4x

In a proportional relationship, the ratio of y to x remains constant. In this equation, y is directly proportional to x with a constant of proportionality of 1/4. This means that as x increases or decreases, y will also increase or decrease by a quarter of the amount.

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The calculated volumes of the figures are 11264 cubic units, 14482.28 cubic units, 3744 cubic units, 475.2 cubic units, 18824.14 cubic units and 91.99 cubic units

The cylinder

The volume is calculated as

V = πr²h

Where

r = Radius

h = Height

So, we have

V = 22/7 * (32/2)² * 14

Evaluate

Volume = 11264

The cylinder

The volume is calculated as

V = πr²h

Where

r = Radius

h = Height

So, we have

(2r)² = 40² - 32²

(2r)² = 576

So, we have

r = 12

So, we have

V = 22/7 * (12)² * 32

Evaluate

Volume = 14482.28

The rectangular prism

The volume is calculated as

V = lwh

Where

l = Length

w = Width

h = Height

So, we have

V = 8 * 12 * 39

Evaluate

Volume = 3744

The triangular prism

The volume is calculated as

V = 1/2lwh

Where

l = Length

w = Width

h = Height

So, we have

V = 1/2 * 11 * 5.4 * 16

Evaluate

Volume = 475.2

The sphere

The volume is calculated as

V = 4/3πr³

Where

r = Radius

So, we have

V = 4/3 * 22/7 * (33/2)³

Evaluate

Volume = 18824.14

The sphere

The volume is calculated as

V = 4/3πr³

Where

r = Radius

So, we have

V = 4/3 * 22/7 * 2.8³

Evaluate

Volume = 91.99

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Stem-leaf plot for the given data:

1 | 2 3 4 5

2 | 1 2 2

3 | 3 3

4 | 1

The stem represents the tens digit and the leaf represents the ones digit of the data points. For example, the number 18 is represented as 1|8 in the plot.

A stem-and-leaf plot for the given data:

1 | 2 3 4

---+-------

1 | 2 2

2 | 2 2 3 8

3 | 3 3

4 | 1

5 |

6 | 6

7 | 7

8 |

In this plot, the tens digit is used as the stem, and the ones digit is used as the leaf. For example, the first two numbers in the data set are 18 and 17, which have stems of 1 and leaves of 8 and 7, respectively. These are shown in the first row of the plot as "1 | 8 7". Similarly, the number 23 has a stem of 2 and a leaf of 3, so it is shown in the second row as "2 | 3". The remaining numbers are arranged in the same way.

The numbers are arranged in ascending order within each row, and there are blank spaces for stems that do not appear in the data.

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Answer:

[tex] \frac{41}{3} \times 3 \times \frac{62}{3} = \frac{806}{3} = 268 [/tex]

From the given table, the following statements can be determined:

C. There is a y-intercept at (-12, 0).

B. In the interval from x = -4 to x = 0, F(x) is decreasing.

A y-intercept is the point where the graph of a function intersects the y-axis. In this case, the y-intercept is at (-12, 0), which means that when x = 0, the value of f(x) is 0.

A function is decreasing in an interval if the values of the function decrease as the input values increase. In this case, we can see that the values of f(x) decrease as x increases from -4 to 0.

The statement A is incorrect because there is only one x-intercept at (0, 4). The statement D is incorrect because there is no line of symmetry at x=0.5.

Therefore, the statements C and B can be determined from the given table.

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