Please fill the blanks

Answer:

a = 15

Step-by-step explanation:

Given

3a + b = 54 ← substitute b = 9

3a + 9 = 54 ( subtract 9 from both sides )

3a = 45 ( divide both sides by 3 )

a = 15

The value of x in the equation 4x + 8y = 40 is 8.4. and the value of a in the equation 3a + b = 54 is 15.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

Given;

A) 4x + 8y = 40

Now substitute y = 0.8

4x + 8(0.8) = 40

4x = 40 - 6.4

x =  8.4

B) 3a + b = 54

Now substitute b = 9

3a + 9 = 54 ( subtract 9 from both sides )

3a = 45 ( divide both sides by 3 )

a = 15

Learn more about equations here;

https://brainly.com/question/10413253

#SPJ2

Start by adding the whole part of the numbers

then add the fractions

since the fraction also gave a mixed number it can be added to the whole part we already had

The correct answer option is the fourth one.

Answer:

f

(

x

)

=

5

x

2

+

2

x

−

5

,

g

(

x

)

=

7

x

+

8

,

h

(

x

)

=

4

x

2

−

10 i think is is right

Answer:where is the question

Step-by-step explanation:

Answer:

13 ft

Step-by-step explanation:

we need to find the square root of 169

√169 = 13

Answer:

m>3

Step-by-step explanation:

2m >6

Divide by 2

2m/2 > 6/2

m >3

Answer:

m>3

Step-by-step explanation:

The domain restrictions of the expression q²−7q−8/q²+3q−4 are q ≠ -4 and q ≠ 1. (option c)

The denominator of the expression is q²+3q−4. To determine the values that would make the denominator equal to zero, we can set it equal to zero and solve for q:

q² + 3q - 4 = 0

Now, we can factorize the quadratic equation:

(q + 4)(q - 1) = 0

To find the values of q, we set each factor equal to zero and solve for q:

q + 4 = 0 or q - 1 = 0

Solving these equations, we get:

q = -4 or q = 1

So, the values of q that would make the denominator equal to zero are q = -4 and q = 1. These are the values we need to exclude from the domain of the expression to avoid division by zero.

Therefore, the correct answer is option c) q ≠ 1 and q ≠ -4.

To know more about domain here

https://brainly.com/question/28599653

#SPJ4

Complete Question:

What are the domain restrictions of q²−7q−8/q²+3q−4?

a) q≠1 and q≠−8

b) q≠−1 and q≠4

c) q≠1 and q≠−4

d) q≠−1 and q≠8

It will take approximately 39.532 days for $9500 to earn $800 at an annual interest rate of 8.25%.

To find the number of days it will take for $9500 to earn $800 at an annual interest rate of 8.25%, we need to use the formula for simple interest:

Interest = Principal * Rate * Time

In this case, we are given the interest ($800), the principal ($9500), and the annual interest rate (8.25%). We need to solve for time.

Let's denote the time in years as "t". Since we're looking for the number of days, we'll convert the time to a fraction of a year by dividing by 365 (assuming a standard 365-day year).

$800 = $9500 * 0.0825 * (t / 365)

Simplifying the equation:

800 = 9500 * 0.0825 * (t / 365)

Divide both sides by (9500 * 0.0825):

800 / (9500 * 0.0825) = t / 365

Simplify the left side:

800 / (9500 * 0.0825) ≈ 0.1083

Now, solve for t by multiplying both sides by 365:

0.1083 * 365 ≈ t

t ≈ 39.532

Therefore, it will take approximately 39.532 days for $9500 to earn $800 at an annual interest rate of 8.25%.

for such more question on annual interest rate

https://brainly.com/question/29451175

#SPJ8

Answer:

 (-18, 10)

Step-by-step explanation:

If the other end point is Q, the midpoint is ...

  M = (P +Q)/2

  2M = P +Q

  Q = 2M -P = 2(-4, 8) -(10, 6) = (-8-10, 16-6)

  Q = (-18, 10)

The other end point is (-18, 10).

Answer:

Dear Karen, I am the manager. You are now banned from Starbucks.

Step-by-step explanation:

108 customers

The expected number of visitors to  buy more than one costume is 48.

64 visitors purchased no costume,

376 purchased exactly one costume.

The number of visitors who purchased more than one costume is 47 .visitors

Total visitors visited the website

= 64visitors + 376 visitors + 47

= 487

Out of the 487 visitors who purchased at least one costume, 376 purchased exactly one costume.

To estimate how many visitors would buy more than one costume out of the expected 500 visitors,

Use the concept of proportions,

47 visitors / 487 visitors = x visitors / 500 visitors

Cross-multiplying, we get,

⇒x visitors = 500 visitors ×  47 visitors / 487 visitors

Simplifying this expression, we get,

⇒ x visitors = 48.2546 visitors

⇒ x visitors ≈ 48 visitors (Rounding to the nearest whole number)

Therefore, the expected number of about 48 visitors to buy more than one costume out of the 500 expected visitors.

learn more about expected number here

brainly.com/question/29624248

#SPJ1

The given statement is 1. Always true

2. Always true

3. Always true

4. Sometimes true

5. Never true

Statement 1: A line and a point are always coplanar.

Answer: Always true.

Reason: This statement is always true because a line and a point can always be found on the same plane. In Euclidean geometry, a plane is a flat surface that extends infinitely in all directions, and any two points on the plane can be connected by a straight line. Therefore, a line and a point will always lie on the same plane.

Statement 2: Congruent angles form vertical angles.

Answer: Always true.

Reason: Vertical angles are formed by the intersection of two lines. When two angles are congruent, it means they have the same measure. If two angles have the same measure and are formed by the intersection of two lines, then they are vertical angles. Therefore, congruent angles always form vertical angles.

Statement 3: Linear pairs that are congruent are right angles.

Answer: Always true.

Reason: A linear pair consists of two adjacent angles that share a common side and form a straight line. If the two angles of a linear pair are congruent, it means they have the same measure. In Euclidean geometry, a straight angle measures 180 degrees. If two angles in a linear pair are congruent and their measures add up to 180 degrees, then each angle must measure 90 degrees, which is the measure of a right angle. Therefore, linear pairs that are congruent are always right angles.

Statement 4: The sum of angles that form a linear pair is less than 180 degrees.

Answer: Sometimes true.

Reason: The sum of angles that form a linear pair is always equal to 180 degrees, not less than 180 degrees. This is based on the definition of a linear pair, which states that the two angles in a linear pair are supplementary, meaning their measures add up to 180 degrees. However, if the statement said "less than or equal to 180 degrees," then it would be always true.

Statement 5: Vertical angles are complementary.

Answer: Never true.

Reason: Vertical angles are not complementary. Complementary angles are two angles that add up to 90 degrees. Vertical angles, on the other hand, are a pair of non-adjacent angles formed by the intersection of two lines. They do not necessarily have any specific relationship to each other in terms of their angle measures. Therefore, vertical angles are not complementary by definition.

Learn more about Vertical angles here

https://brainly.com/question/24566704

#SPJ4

The truth of each statement depends on the properties of angles and theorems that support them. A line and a point are always coplanar, congruent angles can sometimes form vertical angles, congruent linear pairs are not always right angles, the sum of angles that form a linear pair is always 180 degrees, and vertical angles are never complementary.

To determine the truth of each statement, we need to consider the properties of angles and theorems that support them.

About angles here:

https://brainly.com/question/13954458

#SPJ11

The area of the regular octogon is 196.15 square inches.

For a regular octogon with apothem A and side length L, the area is given by:

area =(2*A*L) * (1 + √2)

Here we know that:

A = 7in

L = 5.8 in

Replacing these values in the area for the formula, we will get the area:

area = (2*7in*5.8in) * (1 + √2)

area = 196.15 in²

Learn more about area at:

https://brainly.com/question/24487155

#SPJ1

The productivity of the painter is 0.66 up to two decimal places. It is attained by applying the knowledge of the division of two numbers and decimals to the provided problem.

What is decimal?

A decimal is a quantity that is distributed into two components, namely a whole and a fraction. A decimal number represents the numerical value lying in between the two integers. A decimal point (.) is used to segregate the fractional part from the whole part of a number.

E.g. 1.5, 0.06, 7.05, etc.

Calculation of the productivity of the painter

Productivity of the painter is obtained by dividing the number of houses painted by the number of days taken to paint them

The number of houses painted is 4

The number of days taken to paint 4 houses is 6 days

Productivity = 4 ÷ 6

                  = 0.666

Thus, the productivity of the painter is 0.66 up to two decimal places.

To learn more about the decimal of a given number, visit the link below:

https://brainly.com/question/20720302

#SPJ4

The response y(t) graphically, we can first plot the individual functions h(t) and x(t) on a graph, and then determine their convolution to obtain y(t). Let's go step by step:

Plotting h(t):

The function h(t) is defined as h(t) = [u(t-1) - u(t-4)].

The unit step function u(t-a) is 0 for t < a and 1 for t ≥ a. Based on this, we can plot h(t) as follows:

For t < 1, h(t) = [0 - 0] = 0

For 1 ≤ t < 4, h(t) = [1 - 0] = 1

For t ≥ 4, h(t) = [1 - 1] = 0

So, h(t) is 0 for t < 1 and t ≥ 4, and it jumps up to 1 between t = 1 and t = 4. Plotting h(t) on a graph will show a step function with a jump from 0 to 1 at t = 1.

Plotting x(t):

The function x(t) is defined as x(t) = t[u(t) - u(t-2)].

For t < 0, both u(t) and u(t-2) are 0, so x(t) = t(0 - 0) = 0.

For 0 ≤ t < 2, u(t) = 1 and u(t-2) = 0, so x(t) = t(1 - 0) = t.

For t ≥ 2, both u(t) and u(t-2) are 1, so x(t) = t(1 - 1) = 0.

So, x(t) is 0 for t < 0 and t ≥ 2, and it increases linearly from 0 to t for 0 ≤ t < 2. Plotting x(t) on a graph will show a line segment starting from the origin and increasing linearly with a slope of 1 until t = 2, after which it remains at 0.

Obtaining y(t):

To obtain y(t), we need to convolve h(t) and x(t). Convolution is an operation that involves integrating the product of two functions over their overlapping ranges.

In this case, the convolution integral can be simplified because h(t) is only non-zero between t = 1 and t = 4, and x(t) is only non-zero between t = 0 and t = 2.

The convolution y(t) = h(t) * x(t) can be written as:

y(t) = ∫[1,4] h(τ) x(t - τ) dτ

For t < 1 or t > 4, y(t) will be 0 because there is no overlap between h(t) and x(t).

For 1 ≤ t < 2, the convolution integral simplifies to:

y(t) = ∫[1,t+1] 1(0) dτ = 0

For 2 ≤ t < 4, the convolution integral simplifies to:

y(t) = ∫[t-2,2] 1(t - τ) dτ = ∫[t-2,2] (t - τ) dτ

Evaluating this integral, we get:

\(y(t) = 2t - t^2 - (t - 2)^2 / 2,\) for 2 ≤ t < 4

For t ≥ 4, y(t) will be 0 again.

Maximum value of y(t):

To find the value of t at which y(t) reaches its maximum value, we need to examine the expression for y(t) within the valid range 2 ≤ t < 4. We can graphically determine the maximum by plotting y(t) within this range and identifying the peak.

Plotting y(t) within the range 2 ≤ t < 4 will give you a curve that reaches a maximum at a certain value of t. By visually inspecting the graph, you can determine the specific value of t at which y(t) reaches its maximum.

Learn more about function here:

https://brainly.com/question/11624077

#SPJ11

Answer:

C= 27

G= 37

J=57

Z= 1

Step-by-step explanation:

These are the degrees because of the Triangle Sum Theorem which states that The sum of the measures of the angles in a triangle is 180°. So angle C for example is 27 because angle A is 53 and angle B is 100 add both of those and you get 153 so our equation would be 153+c=180, c being the angle, so then to solve this you do do 180-153 and that equals 27 so therefore, 153+27=180. This process applys to all the other angles as well ^w^

Answer:

The range of this quadratic function is

-infinity < y ≤ 2.

The two trapezoids in the figure are similar. Thus, the value of x would be equal to 33.

A trapezoid is a quadrilateral with at least one pair of sides parallel.

The two trapezoids in the figure are similar.

Since the figures are similar, the corresponding sides have the same ratio.

Here, the side must be proportional

So,

\(\sf \dfrac{40.5}{x}=\dfrac{54}{44}\)

\(\sf 1782=54x\)

Divide 54 on both sides

\(\sf x= \dfrac{1782}{54}\)

\(\sf x=33\)

Thus, the value of x is 33.

Learn more about trapezoids at:

https://brainly.com/question/31380175

y = log2 ( -x)

Since the log function must have a positive input, the domain must be x < 0

Domain ( - inf, 0)

The range is the values that y can take. The log goes from - infinity to infinity

Range (-inf, inf)

The asymptote is at x=0 since log must be greater than zero

The first four nonzero terms in the Maclaurin series for f(x) = e^(-5x)sin(x) are:x - 5x^2 + (23/2)x^3 - (5/3)x^4

To find the first four nonzero terms in the Maclaurin series for f(x) = e^(-5x)sin(x), we can use the Taylor series expansion for the functions e^(-5x) and sin(x), and then multiply the resulting series.

The Maclaurin series for e^(-5x) can be expressed as:

e^(-5x) = 1 - 5x + (25/2)x^2 - (125/6)x^3 + ...

Maclaurin series for f(x) = e^(-5x)sin(x) are:

x - 5x^2 + (23/2)x^3 - (5/3)x^4 series for sin(x) can be expressed as:

sin(x) = x - (1/6)x^3 + ...

Multiplying these two series term by term, we can find the first four nonzero terms:

f(x) = (1 - 5x + (25/2)x^2 - (125/6)x^3) * (x - (1/6)x^3 + ...)

Expanding and collecting the terms, we get:

f(x) = (x - 5x^2 + (23/2)x^3 - (5/3)x^4 + ...)

Therefore, the first four nonzero terms in the Maclaurin series for f(x) = e^(-5x)sin(x) are:

x - 5x^2 + (23/2)x^3 - (5/3)x^4

To learn more about non zero terms click here:

brainly.com/question/32625535

#SPJ11

Answer:

x = 1/64

Step-by-step explanation:

2x = 1/32

Divide both sides by 2.

Simplify, and you will get 1/64.

Answer:

Its -5

Step-by-step explanation:

To create the two groups, the researcher should take into account the fact that (B) each pair of students has a similar IQ or level of mathematical proficiency.

Pair testing is a software development technique in which two team members evaluate the software application while seated at the same keyboard.

One person conducts the testing while the other assesses or analyzes the testing.

One tester can work alongside a developer or business analyst, or two testers can collaborate on this, with each taking turns using the keyboard.

In agile software development, where two team members sit side by side to test the software application, this may be more relevant to pair programming and exploratory testing.

This will enable both participants to gain additional knowledge about the application.

This will enable ongoing testing while also focusing on the issue's primary source.

So, in the given situation the researcher should consider the fact that each pair of students has a similar IQ or level of mathematical skill when forming the two groups.

Therefore, to create the two groups, the researcher should take into account the fact that (B) each pair of students has a similar IQ or level of mathematical proficiency.

Know more about Pair testing here:

https://brainly.com/question/16448112

#SPJ1

Complete question:

A researcher wants to determine if eating more vegetables helps high school juniors learn algebra. One junior class has extra vegetables and another junior class does not. After 2 weeks, the entire both classes take an algebra test and the results of the two groups are compared. To be a valid matched pair test, what should the researcher consider in creating the two groups?

A. that the group without extra vegetables receives different instruction

B. That each pair of students has similar IQs or abilities in mathematics

C. that each class of students has similar ages at the time of the testing

D. that each class has similar average IQs or abilities in mathematics

4x + 8y ≤ -24 is the example of linear inequality in two variables.

Linear equations are one-degree equations. It is a straight-line equation. A linear equation with parameters a and b equal to zero has the conventional form ax + by + c = 0.

The graph of a two-variable inequality is the set of points that describe all solutions to the inequality. The coordinate plane is split in half by a boundary line created by a linear inequality, with one-half representing the solutions to the inequality.

It's a line with a shaded side on one side to show which xy pairings are the inequality's solutions.

For example -

Let us take a equation, 4x + 8y ≤ -24

Now, solve the above equation in the form of slope-intercept.

4x + 8y ≤ -24

or, 8y ≤ - 4x - 24

or, y ≤ -(1/2)x - 3

To know more about linear inequality refer to:

brainly.com/question/11234618

#SPJ4

Answer: 24 cubic meters

Step-by-step explanation:

Answer:

24 cubic meters

Step-by-step explanation:

Khan Academy

Answer:

........12......... ...............

If the Wilson family drove 472 miles in 8 hours. The family that traveled at the higher rate of speed  and  rate is: D: Wilson; 59 mi/h

Using this formula to find the speed

Speed = Distance /Time

Let plug in the formula

Rate of speed for Gonzalez family

Rate of speed  = 342 ÷ 6

Rate of speed = 57 mph

Rate of speed  for Wilson family

Rate of speed = 472 ÷ 8

Rate of speed = 59 mph

Therefore the correct option is D.

Learn more about rate of speed here:https://brainly.com/question/26046491

#SPJ1

The probability will be b) 4/(52 13)

In a standard deck, there are four suits (hearts, diamonds, clubs, and spades), each containing 13 cards. To find the probability of obtaining a bridge hand with all 13 cards of the same suit, we need to determine the number of favorable outcomes (hands with all 13 cards of the same suit) and divide it by the total number of possible outcomes (all possible bridge hands).

Calculate the number of favorable outcomes

There are four suits, so for each suit, we can choose 13 cards out of 13 in that suit. Therefore, there is only one favorable outcome for each suit.

Calculate the total number of possible outcomes

To determine the total number of possible bridge hands, we need to calculate the number of ways to choose 13 cards out of 52. This can be represented as "52 choose 13" or (52 13) using the combination formula.

Calculate the probability

The probability is given by the ratio of the number of favorable outcomes to the total number of possible outcomes. Since there is one favorable outcome for each suit and a total of 4 suits, the probability is 4 divided by the total number of possible outcomes.

Therefore, the probability that a bridge hand will contain all 13 cards of the same suit is 4/(52 13).

Learn more about probability

brainly.com/question/31828911

#SPJ11

The “yearly tuition costs” as an independent variable which should be plotted on X-axis and “mid-career salary” as a dependent variable on Y-axis. The scatterplot is made of them.

Based on the table provided, it is possible to observe that there is not necessarily a clear relationship between the cost of tuition and mid-career salary.

While some of the colleges with higher tuition costs (such as MIT and Stanford) have high mid-career salaries, others (such as Harvey Mudd and Caltech) also have high mid-career salaries despite lower tuition costs. Additionally, some colleges with low or zero tuition costs (such as the US Naval Academy and West Point) also have high mid-career salaries.

Therefore, it is not safe to assume that a higher cost of tuition will necessarily translate into higher-paying jobs. The scatter plot of yearly tuition costs and mid-career salary is made.

To know more about Scatter plot:

https://brainly.com/question/29231735

#SPJ4

Answer:

-3/2 = -1.5

Step-by-step explanation:

u can use wolfram alpha for stuff like that