The sum of two numbers is 88. If one number is 4 more than half the other number, determine the two numbers by setting up a linear equation.

a.44
b.56
c.61.3
d.126
e.138
f.176
Need answer ASAP. Please no answer links. Will mark brainliest if you want.

Using similar triangles, it is found that the measure of angle B is of 74º.

Similar triangles are triangles that have the same angle measures, and whose side lengths are proportional.

In this problem, the triangle ABC was translated, resulting in triangle A'B'C'. A translation does not change the measures of the angles, hence their angles are given as follows:

80º, 26º and B.

The sum of the internal angles of a triangle is of 180º, hence:

80 + 26 + B = 180

B = 74º.

The measure of angle B is of 74º.

More can be learned about similar triangles at https://brainly.com/question/305520

#SPJ1

Using a linear function, it will take 8 years for the Springfield zoo to have 35 gorillas.

A linear function is modeled by:

y = mx + b

In which:

For this problem, the parameters are given as follows:

m = 4, b = 3.

Hence the number of gorillas after x years is given by:

G(x) = 3 + 4x.

It will have 35 gorillas when:

G(x) = 35.

Hence:

3 + 4x = 35.

4x = 32.

x = 32/4

x = 8.

It will take 8 years for the Springfield zoo to have 35 gorillas.

More can be learned about linear functions at https://brainly.com/question/24808124

#SPJ1

[tex]\textit{Amount for Exponential Decay using Half-Life} \\\\ A=P\left( \frac{1}{2} \right)^{\frac{t}{h}}\qquad \begin{cases} A=\textit{current amount}\dotfill &11\\ P=\textit{initial amount}\dotfill &160\\ t=\textit{elapsed time}\\ h=\textit{half-life}\dotfill &14 \end{cases} \\\\\\ 11=160\left( \frac{1}{2} \right)^{\frac{t}{14}}\implies \cfrac{11}{160}=\left( \cfrac{1}{2} \right)^{\frac{t}{14}}\implies \log\left( \cfrac{11}{160} \right)=\log\left[ \left( \cfrac{1}{2} \right)^{\frac{t}{14}} \right][/tex]

[tex]\log\left( \cfrac{11}{160} \right)=\cfrac{t}{14}\log\left[ \left( \cfrac{1}{2} \right)\right]\implies \cfrac{\log\left( \frac{11}{160} \right)}{\log \left( \frac{1}{2} \right)}=\cfrac{t}{14} \\\\\\ 14\left( \cfrac{\log\left( \frac{11}{160} \right)}{\log \left( \frac{1}{2} \right)} \right)=t\implies {\LARGE \begin{array}{llll} \stackrel{mins}{54.1}\approx t \end{array}}[/tex]

Square root of Two is an irrational number. because we are unable to express it in the form a/b, where a and b are whole numbers and b is not zero.

Any real number that cannot be written as the quotient of two integers—that is, as p/q, where p and q are both integers—is an irrational number. For instance, the square root of 2 cannot be represented by an integer or a fraction.

Because these numbers may be represented on a number line, they are real numbers rather than complex numbers.

To know more about  irrational number visit :

https://brainly.com/question/4031928

#SPJ9

Answer:

Step-by-step explanation:

To find y = f(g(x)) replace the x in f(x) by g(x):-

y = 4^(x - 3)

---> y = 4^x  * 4^-3

---> y = (4)^x / 64

Answer: 5859375

Step-by-step explanation:

3, 15, 75...

75/15=5

15/3=5

Every term multiplied by 5 is the next term. Hence, the equation for this sequence can be expressed as:

y=3*[tex]5^{x-1}[/tex]    ==> y is the term when x is the term number and 3 is the first number in the sequence

Now let's solve for the 10th term:

y=3*[tex]5^{10-1}[/tex]

y=3*[tex]5^{9}[/tex]

y=3*1953125

y=5859375

Answer:

Step-by-step explanation:

According to the given data The value of p is[tex]0.0351<0.1[/tex](alpha) so reject H₀

A left-tailed test is used when the alternative hypothesis claims that the true value of the parameter suggested by the null hypothesis is lower than the null hypothesis implies. If the sample being tested is within the one-sided critical zone, the alternative hypothesis will be accepted rather than the null hypothesis.

Financial analysts employ the one-tailed test to confirm an investment or portfolio hypothesis.

If our statistical analysis finds that the significance level is smaller than the set cut-off value, we reject the null hypothesis and accept the alternative hypothesis (for example, either 0.05 or 0.01).

z = -1.81alpha

= 0.1p [tex]( z < -1.81 )p ( z < -1.81 )[/tex]

= 0.0351 ( from z table )P &lt;

alpha, reject H₀

When the p-value is less than or equal to alpha, hypothesis H0 is rejected;

however,

if the p-value is greater than alpha, hypothesis H0 is not rejected.

To know more about left-tailed test visit:

https://brainly.com/question/17111749

#SPJ4

The number of groups of three that the college can select is 56.

Total number of students = 8

Number of assistantships available = 3

Groups of three can be selected by the college means that out of the eight students three need to be selected at random and this can be done in ⁸[tex]C_{3}[/tex] ways.

In this case, we use combination and not permutation because the order of selection of the students does not matter.

Now, we know

ⁿ[tex]C_{r}[/tex] = ( n! )/( r! (n-r )!)

Here, n = 8 and r = 3

⁸[tex]C_{3}[/tex]  = ( 8! )/( 3! (8-3)! )

⁸[tex]C_{3}[/tex]  =  ( 8 × 7 × 6 × 5! )/ ( 3 × 2 × 1 × ( 5! ) )

⁸[tex]C_{3}[/tex]  = ( 8 × 7 × 6 )/ ( 3 × 2 )

⁸[tex]C_{3}[/tex]  = 56

The number of groups of three that the college can select is 56.

To know more about Combination and Permutation Refer to the link:

https://brainly.com/question/11732255

#SPJ4

The total amount that Mikaela spent on the paddleboard is $514.16

The given parameters are:

Original cost = $799

Discount = 40%

State tax = 7.25%

The total amount that Mikaela spent on the paddleboard is calculated as

Amount = Original cost * (1 - Discount) * (1 + State tax)

This gives

Amount = 799 * (1 - 40%) * (1 + 7.25%)

Evaluate

Amount = 514.16

Hence, the total amount that Mikaela spent on the paddleboard is $514.16

Read more about discount at:

https://brainly.com/question/7459025

#SPJ1

Answer:

(B)  $514.16

Step-by-step explanation:

Correct on my quiz.

We get that the number of pots that can be filled are 20 pots.

We are given that:

The total amount of yoghurt with Geela = 20 liters.

The amount of yoghurt in 1 pot = 1 liter

Now, we need to find the number of pots that can be filled.

So, we will do this by using division.

We get that:

Number of pots that can be filled. = 20 / 1

Number of pots that can be filled. = 20 pots

Therefore, we get that the number of pots that can be filled are 20 pots.

Learn more about division here:

https://brainly.com/question/25289437

#SPJ9

Answer:

1. 13 As there are 13 points indicating there are 13 students 2. 39.

Step-by-step explanation:

Answer:

x=5

Step-by-step explanation:

3(5+5) = 30

3(10) = 30

<3

The total number of bags Sharon have is 7 and the total number of apples Sharon have is 45.

Let total number of bags = x

Let total number of apples Sharon has = y

If she packs 6 apples in each bag, she will have 3 apples left. So, mathematically we can write

6x + 3 = y                                                       equation 1

If she packs 7 apples in a bag, she will be four apples short. So, mathematically we can write

7x - 4 = y                                                         equation 2                

On subtracting equation 1 from equation 2 , we get

x - 7 = 0

⇒ x = 7

Substitute x = 7 in equation 1 , we get

6 ( 7 ) + 3 = y

⇒ y = 45

The total number of bags Sharon have is 7 and the total number of apples Sharon have is 45.

To know more about Mathematical Problems involving equations refer to the link :

brainly.com/question/14564489

#SPJ4

Answer:

  x = 4

Step-by-step explanation:

You want the equation of the vertical line through (4, 6).

Slope is the ratio of rise to run for a line. When the "run" is zero, that ratio becomes undefined. The "run" will be zero for any rise when the line is vertical.

The equation of such a line has the form ...

  x = c . . . . . for some constant c

In order for this equation to be satisfied when (x, y) = (4, 6), the value of the constant must match the x-coordinate of the point.

The equation is x = 4.

Answer:

A

Step-by-step explanation:

x² + 7x + 12 = 0

consider the factors of the constant term (+ 12) which sum to give the coefficient of the x- term (+ 7)

the factors are + 3 and + 4 , since

3 × 4 = + 12 and 3 + 4 = + 7 , then

(x + 3)(x + 4) = 0

equate each factor to zero and solve for x

x + 3 = 0 ⇒ x = - 3

x + 4 = 0 ⇒ x = - 4

Answer:

P=6

Because 6/3=2

And 2+9=11

Step-by-step explanation:

Missy rode her bicycle 16 miles in 1 1 4 hours. Her average speed in miles per hour is 12.8 mph

Calculating average speed involves dividing the whole distance traveled by the total time it takes to cover that distance.

Speed is the rate of movement of anything at a specific time. Average speed refers to the average speed during the course of a journey. Typically, average speed refers to the speed of moving objects like cars, trains, and aircraft. It is frequently expressed in kilometers per hour (kph) or miles per hour (mph) (kph).

In many different disciplines, such as physics, astronomy, and transportation, average speed is employed.

As we know,

average speed is distance traveled divided by time taken

⇒ average speed = 16 miles × 5/4

⇒ average speed = 12.8 miles/hour

To learn more about average speed from given link

https://brainly.com/question/24739297

#SPJ4

three digits hope this helped

Answer:

1080

Step-by-step explanation:

Answer:

97th term of arthmetic progression is

-16+ 96* 18

Step-by-step explanation:

Based on the calculations, the length, in cm, of an adjacent side of this rectangle is equal to 6.0 centimeters.

Given the following data:

Perimeter of rectangle = 40.0 centimeters.

Length of rectangle = 14.0 centimeters.

Mathematically, the perimeter of a rectangle can be calculated by using this formula;

P = 2(L + W)

Where:

Note: The length of an adjacent side refers to the the width of this rectangle.

Substituting the parameters into the formula, we have;

40.0 = 2(14.0 + W)

40.0 = 28.0 + 2W

2W = 40.0 - 28.0

2W = 12.0

W = 12.0/2

Width, W = 6.0 centimeters.

Read more on perimeter of a rectangle here: brainly.com/question/17297081

#SPJ4

Answer: 2,8865 million acres of cropland in florida

Step-by-step explanation: To solve this problem we can multiply Alabama's cropland of 2.51 million acres by 1.15 giving: 2.51 million ×1.15=2.8865 million acres of cropland in Florida.

I Hope this helps :)

Answer: Florida has 2.8865 million acres of cropland.

Step-by-step explanation:

We can first do the multiplication, 2.51 x 1.15, and then add 1,255 + 2,510 + 25,100 then we get the answer: 2.8865

Answer:

A

Step-by-step explanation:

assuming you meant y = x² + 12x - 7 , then

given a quadratic in standard form

y = ax² + bx + c (a ≠ 0 )

the x- coordinate of the vertex is

x = - [tex]\frac{b}{2a}[/tex]

y = x² + 12x - 7 ← is in standard form

with a = 1 , b = 12 , then x- coordinate of vertex is

x = - [tex]\frac{12}{2}[/tex] = - 6

substitute x = - 6 into the equation for corresponding y- coordinate

y = (- 6)² + 12(- 6) - 7

  = 36 - 72 - 7

 = - 43

vertex = (- 6, - 43 )

The number of overtime hours done by electrician, as found by unitary method, is 4.

A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary method.

Now,

Given:

To find: Number of Overtime hours

FInding:

Let the number of overtime hours be 'x'.

By unitary method, Charge of 1 regular hour = $24

Charge of 8 regular hours = $24(8) = $192

Again, by unitary method, Charge of 1 overtime hour = $36

Charge of x overtime hours = $36(x)

Cost of Materials = $202

Now, total bill = sum of all the expenses

=> 538 = 192 + 36x + 202

=> 538 - 294 = 36x

=> 144 = 36x

=> 4 = x

Hence, the number of overtime hours as found by unitary method is 4.

To learn more about unitary method, refer to the link: https://brainly.com/question/24587372

#SPJ4

Answer:

-21 degrees

Step-by-step explanation:

-14 - 7 = 21

16 times larger is the new area when compared to the original.

Given that, the length of each side of the square is quadrupled.

We need to find how many times larger is the new area when compared to the original.

A square is a closed two-dimensional shape with four equal sides and four equal angles. The four sides of the square form the four angles at the vertices. The sum of the total length of the sides of a square is its perimeter, and the total space occupied by the shape is the area of the square. The formula to calculate the area of a square is a².

Let the length of each side of the square be x.

Then the length of each side of the new square will be 4x.

Now, the area of the original square = x²

The area of the new square = (4x)² = 16x²

So, the new square = 16 × the original square

Therefore, 16 times larger is the new area when compared to the original.

To learn more about the area of a square visit:

https://brainly.com/question/1561162.

#SPJ1

Answer: The m<A = 55

Step-by-step explanation:

1. We know that m<A is likely congruent to m<B (know that m< means measure of angle) {Also noting congruent means same}

2. With that, we can tell that the given info is telling us that 124 is the total degree for m<D.

3. So, this tells us that 2x + x + 41.5 = 124 is the formula we will use.
       3a. 3x + 41.5 = 124 (Simplify)
               3b. 3x = 82.5 (Combine like Terms)
                         3c. x = 27.5 (Divide)

4. Now we know what x is, so finding m<A is easy, 2(27.5) equals to 55, meaning m<A is 55. For m<B, 27.5 + 41.5 equals to 69. To make sure 55 + 69 equals to 124

5. So:
m<A = 55
m<B = 69
m<D = 124

Answer:

Hope this helps :)

21) 31 + 14

22) 16 - 9

23) 7 + 4 + 18

24) 3 × 40

25)

26) 81 ÷ 3 OR 81/3 (the fraction bar also means divide)

27) 3 × 2 = 6

28) 7 x 6 = 42 (7 days in a week times by 6 weeks equal 42 days)

Answer:

thsnk

Step-by-step explanation:

The expressions of all the functions are;

1) f(x) = 0.75x

2)g(x) = 0.8x

3) (f o g)(x) = 0.6x

4) (g o f)(x) = 0.6x

We are told that f(x) is the price with the $20 coupon applied, and

g(x) is the price with the 15% discount applied. Thus;

1) An expression for f(x) is;

f(x) = (1 - 0.25)x = 0.75x

f(x) = 0.75x

2) An expression for g(x) is;

g(x) = (1 - 0.2)x = 0.8x

g(x) = 0.8x

3) An expression for (f o g)(x) is;

(f o g)(x)  = f(g(x)) = 0.75(0.8x) = 0.6x

(f o g)(x) = 0.6x

4) An expression for (g o f)(x) is;

(g o f)(x) = 0.8(0.75x) = 0.6x

(g o f)(x) = 0.6x

Read more about Algebraic Expression at; https://brainly.com/question/4344214

#SPJ1