evaluate the expression when a= -7 and b=4 for 3b-a

The number which represent tens digit of a number is twice the ones digit is;

Complete question:

The tens digit of a number is twice the ones digit. The sum of the digits in the number is

12. What is the number?

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In this problem we are given an angle and two sides. Therefore, we should use a trigonometric function to solve for x.

Trigonometric Functions: SOH-CAH-TOA

Looking from the 23 degree angle, we have the adjacent side and the opposite side. Therefore, we should use the tangent function.

tan(23) = x / 2

x = tan(23) * 2

x = 0.8489

x = 0.8

Hope this helps!

Step-by-step explanation:

Answer:

Step-by-step explanation:

Solution

The factored form is going to be the HCF (highest common factor)

The fest way to do this is to turn this into primes.

8x^2 + 12x

8x^2 = 2*2*2*x*x

12x = 2 * 2 * x

Now bold the HCF.

8x^2 = 2*2*2*x*x

12x = 2 * 2 * x

The HCF = 2*2*x

Divide that into the original question to determine the second factor.

8x^2 / 4x = 2x

12x / 4x = 3         Notice how the x-s cancel

Answer

4x (2x + 3)

Answer:(4,7/2)

Step-by-step explanation:

Answer:

Option (2)

Step-by-step explanation:

cos 50° = y/z

z = y/cos 50°

Answer:

  f(x) = -5x +48

Step-by-step explanation:

A fairly easy way to write the equation of the perpendicular line is to swap the x- and y-coefficients, negating one of them. Then choose the constant in the equation to make it true at the given point.

In this instance, we find it convenient to leave the coefficient of y as positive.

  5y = x -10 . . . . . . original equation

  y = -5x +c . . . . . . with coefficients swapped, x-coefficient negated

At the given point, the equation becomes ...

  8 = -5(8) +c

  48 = c . . . . . . . add 40

The equation of the line is then ...

  y = -5x +48

  f(x) = -5x +48 . . . . . . in functional notation

Answer: according to my work i got

LCM - Lowest Common Factor

HCF - Highest common factor

Step-by-step explanation:

please mark brainlest!!

yw! =^.^=

Answer:

[tex]-5x-5[/tex]

Step-by-step explanation:

original functions:

[tex]f(x)=3x-8\\g(x)=8x-3[/tex]

Subtract the polynomials:

[tex]f(x)-g(x) = (3x-8) - (8x-3)[/tex]

Distribute the negative sign:

[tex]3x-8-8x+3[/tex]

Combine like terms:

[tex](3x-8x)+(-8+3)[/tex]

Add like terms:

[tex]-5x-5[/tex]

The number of months that it will take the latest model's battery life to reach 1,008.9 minutes is; 8 months

Each month, there is an increase by a factor of 0.06 of the previous months model.

From geometric sequence formula of aₙ = ar^(n - 1),

where;

a is first term

r is common ratio

aₙ is nth term

we have;

1,008.9 = 671 * 1.06^(n - 1)

1008.9/671 = 1.06^(n - 1)

In 1.504 = (n - 1) In 1.06

0.408 = (n - 1) * 0.058

n - 1 = 0.408/0.058

n = 7.03 + 1

n ≈ 8 months

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Answer:

Every natural number is also a rational number but not every rational number is a natural number because the set of natural numbers is a subset of the set of rational numbers.

Explanation:

Since all natural numbers, n can be written as n/1. Thus all natural numbers are rational. Since 3/4 is a rational number but not natural thus all rational numbers are not natural.

Hint:

Natural numbers : All positive numbers except zero.

Rational numbers: All numbers in the form of p/q, where q ≠ 0 (p,q are integers)

The total amount of interest Dominick will pay throughout the life of the loan is $1350

Simple Interest is the interest applied only on the Principal amount invested or borrowed .

It is calculated by the formula

I = ( P * R * T ) /100

P is the Principal

R is the Rate of Interest

T is the Time Period

Here

P = $ 6000

R= 9 %

T = 30 months = 30/12 year = 2.5 years

I = ( 6000 * 9 * 2.5 ) / 100

Interest = $1350

Therefore , the total amount of interest Dominick will pay throughout the life of the loan is $1350

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Answer: Line 3 to line 4

Step-by-step explanation:

When dividing by a negative, you need to flip the inequality sign.

The bisection method will converge to the solution after three iterations.

It should be noted that after one iteration, x1 will be:

= (1 + 9)/2

= 10/2

= 5

Since f(x¹) > 0, x² will then replace x1. Now x0 = 1 and x1 = 5.

After the second iteration, x2 will be:

= (1 + 5)/2

= 3

Also, this is greater than 0. The third iteration will be:

m= (1 + 3)/2

= 2.

Now, f(2) = 2⁴ -2³ - 2² - 4

= 0

Therefore, the method converges exactly to the root in 3 iterations.

Complete question:

The bisection method is applied to compute the zero to a function f(x) = x⁴ - x³ - x² - 4 in the interval (1, 9). The method converges y a solution after .............. iterations.

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Answer: The base graph has been shifted down 90 units.

Step-by-step explanation:

See attached image.

Answer: 196m squared

Step-by-step explanation: A square has equal sides, so if one side were to be equal to 14m, the other would too. 14 x 14 = 196.

Final answer:

Area of tile is 14 cm².

Step-by-step explanation:

Area of triangle is:

[tex]\frac{1}{2} base.height[/tex]

Putting [tex]b=3.5[/tex] and [tex]h=8[/tex] in [tex]\frac{1}{2} base.height[/tex]

[tex]\frac{1}{2}bxh=\frac{1}{2}3.5x8[/tex]

[tex]=3.5x4[/tex]

[tex]=14[/tex]

Answer:

•3✓7

✓3.✓21

=✓3×✓3✓7

=3✓7

Answer:

3rd answer is correct

Step-by-step explanation:

√3 × √21

√3 × √(7 × 3)

√( 3 × 3 × 7 )

√ ( 3 × 3 ) × √7

3√7

The measure of angle x from the diagram is 100 degrees

The formula for calculating the sum of interior angle of a polygon is given as:

s = (n-2)180

Since hexagon has 6 interior angles, the sum of the interior will be 720 degrees. Hence

x  + 620 = 720

x = 720 - 620

x= 100

Hence the measure of angle x from the diagram is 100 degrees

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After 20 years of depositing and investing there will be 168474.01 dollars in your account.

It is defined as the interest on the principal value or deposit and the interest which is gained on the principal value in the previous year.

We can calculate the compound interest using the below formula:

[tex]\rm A = P(1+\dfrac{r}{n})^{nt}[/tex]

Where A = Final amount

          P = Principal amount

          r  = annual rate of interest

          n = how many times interest is compounded per year

          t = How long the money is deposited or borrowed (in years)

The formula for calculating how much money will your account be worth after 20 years of depositing and investing is:

P = $250, r = 9% = 0.09, t = 20 years, n = 12 and PMD = $250(per month deposit)

[tex]\rm A = P(1+\dfrac{r}{n})^{nt}+\dfrac{PMD((1+\dfrac{r}{n})^{nt}-1)}{\dfrac{r}{n}}[/tex]

[tex]\rm A = 250(1+\dfrac{0.09}{12})^{12\times20}+\dfrac{250((1+\dfrac{0.09}{12})^{12\times12}-1)}{\dfrac{0.09}{12}}[/tex]

A = 1502.287 + 166971.717

A = $168474.01

Thus, after 20 years of depositing and investing there will be 168474.01 dollars in your account.

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Answer:

Step-by-step explanation:

the objects which have less density than water will float

and the objects which have more density than the density of liquid will sink in liquid or will not float.

Given: f(x) = 3x² -5x + 4

To find f(-2), simply substitute x = -2 in function f(x).

f(-2) = 3(-2)² -5(-2) + 4

f(-2) = 12 + 10 + 4

f(-2) = 26

Answer: 26

For an ordered pair (x, y) in a relation, the y element represents the range.

Answer: range

The conclusion will be; Since the P-value is less than α = 0.05, reject the null hypothesis. There is enough evidence to support the claim that there is a difference in the weights of running shoes. Option B.

Parameters

Group 1

n1=10

x=18.47

[tex]s^2_1[/tex]=2.12

Group 1

n2=15

x2=10.01

[tex]s^2_2[/tex]=0.62

Generally, the equation for the hypothesis is mathematically given as

[tex]H_0=\mu_1 =\mu=2 \\\\H_a= \mu_1 \neq \mu=2[/tex]

Therefore

[tex]t=\frac{12.47-10.01}{\sqrt{\frac{2.12}{10}+\frac{0.61}{15}}}[/tex]

t=4.8966

In conclusion, The pvalue from table is

p-value (4.8966, [tex]\alpha[/tex] =0.06)

[tex]p-value < \alpha=0.05[/tex]

since [tex]p-value < \alpha=0.05[/tex] we reject the null hypothesis and state that there is no difference b/w the two means.

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The slope is m=6 and length of line is 3.5√37.

The slope of a line is a measure of its steepness.

Given:

endpoints of are A(2, 2) and B(3, 8). is dilated by a scale factor of 3.5

slope= 8-2/3-2= 6

Now, using distance formula,

d= √(3-2)² + (8-2)²

d= √1+ 36

d= √37

As, Line AB is dilated by a scale factor of 3.5.    

So, new d= √37*3.5

new d= 3.5√37

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Note that the difference keeps increasing by a value of 10. Hence the next term of the sequence is 110

Geometric sequence are sequence that increase in an exponential manner.

Given the recursive sequence 0, 2, 14, 36, 68

From the sequence

0 + 2 = 2

2 + 12 = 14

14 + 22 = 36

36 + 32 = 68

68 + 42 = 110

Note that the difference keeps increasing by a value of 10. Hence the next term of the sequence is 110

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The figure that will depict a line of reflectional symmetry of letter T is: Option C: A letter T folded vertically through the middle.

A line of reflectional symmetry is defined as an imaginary line that divides a figure into two halves in such a way that each of the halves are a mirror image of the other.

When a line divides letter T vertically, it means that two mirror images will be created.

Therefore, the figure that will depict a line of reflectional symmetry of letter T would be: A letter T folded vertically through the middle.

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Step-by-step explanation:

this is an arithmetic sequence :

a1 = 1

an = an-1 + 2 = a1 + (n-1)×2

the sum of n terms of an arithmetic sequence is

S = n×(a1 + an)/2

n = 5000

an = a1 + 4999×2 = 9999

S = 5000×(1 + 9999)/2 = 5000×5000 = 25,000,000

The ordered pairs that represent functions are:

For a set of ordered pairs to represent a function, the following must be true:

The x value must point to only one y value

In {(-3, 10), (-2, 13), (3, 13), (8, 12)}  and {(-4,11), (5, 10), (-3, 3), (-1, 10)}, the x value point to only one y value

Hence, {(-3, 10), (-2, 13), (3, 13), (8, 12)}  and {(-4,11), (5, 10), (-3, 3), (-1, 10)} are functions

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Answer:

-8

Step-by-step explanation:

Slope = (y1-y2) / ( x1-x2)

            = ( f-4) / (-8 - -6)      =  6

                  (f-4) / -2    = 6

                    f-4 = -12

                     f = - 8

Answer:

f = -8

Explanation:

Find slope:

[tex]\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} = \dfrac{\triangle y}{\triangle x} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]

Here given:

Inserting into slope formula:

[tex]\sf \rightarrow \dfrac{4-f}{-6-(-8) } = 6[/tex]

[tex]\sf \rightarrow \dfrac{4-f}{2 } = 6[/tex]

[tex]\sf \rightarrow 4-f = 12[/tex]

[tex]\sf \rightarrow -f = 12-4[/tex]

[tex]\sf \rightarrow -f =8[/tex]

[tex]\sf \rightarrow f =-8[/tex]

The vertical stretch of f(x) to g(x) is a factor of 5

The functions are given as:

f(x) = x

g(x) = 5x

Substitute f(x) = x in g(x) = 5x

g(x) = 5f(x)

In th above equation, the factor is 5.

5 is greater than 1 (this means vertical stretch)

Hence, the vertical stretch of f(x) to g(x) is a factor of 5

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