What is the true solution to the logarithmic equation below?

log Subscript 4 Baseline left-bracket log Subscript 4 Baseline (2 x) right-bracket = 1

Answer:

[tex]- ab - 8a + 9[/tex]

Step-by-step explanation:

[tex](6ab - 8a + 8) - (7ab - 1) \\ 6ab - 8a + 8 - 7ab + 1 \\ - ab - 8a + 9[/tex]

hope this helps you.

Answer:

-ab - 8a + 9

Step-by-step explanation:

(6ab - 8a + 8) - (7ab - 1) =

= 6ab - 8a + 8 - 7ab + 1

= -ab - 8a + 9

Answer:

y = (1/4)x² - (5/4)x + 1

Step-by-step explanation:

The x-intercepts of the quadratic equation are simply it's roots.

Thus, we have;

(x + 1) = 0 and (x - 4) = 0

Now, formula for quadratic equation is;

y = ax² + bx + c

Where c is the y intercept.

At y-intercept: (0,1), we have;

At (-1,0), thus;

0 = a(1²) + b(1) + 1

a + b = -1 - - - (1)

At (4,0), thus;

0 = a(4²) + b(4) + 1

16a + 4b = -1

Divide both sides by 4 to get;

4a + b = -1/4 - - - (2)

From eq 1, b = -1 - a

Thus;

4a + (-1 - a) = -1/4

4a - 1 - a = -1/4

3a - 1 = -1/4

3a = 1 - 1/4

3a = 3/4

a = 1/4

b = -1 - 1/4

b = -5/4

Thus;

y = (1/4)x² - (5/4)x + 1

Answer:

since y is across from 60 so

y=60

and on the bottom it is 15 so

x+3=15

x=12

Hope This Helps!!!

Answer:

12* 8 * 4 = 384

Step-by-step explanation:

Answer:

3264:221

Step-by-step explanation:

If by last year there were 221 students and 12 teachers at Hilliard School, then;

221students = 12teachers

To find the equivalent ratio for 272students, we can say;

272students = x teachers

Divide both expressions

221/272 = 12/x

Cross multiply

221 * x = 272 * 12

221x = 3264

x = 3264/221

x = 3264:221

This gives the required proportion

Answer:

ok so we have to find the perimiter so

60+60=120

30+30=60

120+60=180

Hope This Helps!!!

Answer: D

Step-by-step explanation:

5²-11=14

6^2-11= 25

14>25

as the question asks for something lower than 25 not lower/equal to the answer is D.

The range of values for which f(x) < 25 are -6 < x < 6. The correct answer choice is e).

To find the values of x for which f(x) < 25, we substitute the expression for f(x) into the inequality and solve for x.

Given f(x) = x² - 11, we need to find the values of x that make f(x) less than 25.

x² - 11 < 25

Adding 11 to both sides, we have:

x² < 36

To determine the values of x that satisfy this inequality, we take the square root of both sides. Since the square root of a number can be positive or negative, we consider both positive and negative solutions.

x < √36

x > -√36

Simplifying, we get:

x < 6

x > -6

Therefore, the correct answer choice is e) -6 < x < 6, as it represents the range of values for which f(x) < 25. This means that x can take any value between -6 and 6 (excluding -6 and 6) for the inequality to hold true.

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Answer:

Saleh is x years old. And 10 years ago he was 100 years old.

Suha is x years old. Saleh is 10 years younger than Suha. Saleh is 100 years old.

Answer:

SAS

Step-by-step explanation: every triangle contains a total of 180 degrees if you substract 180 by 60+70(which is 130) you would get 50 degrees which is the exact degree missing in the first triangle, so after confirming that both triangles have an equal degrees on each side the answer would be SAS (which stands for Side-Angle-Side), SAS is the answer you would give to triangles that are congruent(equal)

Answer:

y = 25

Step-by-step explanation:

Given y = kx and k = 5 then

y = 5x ← equation of variation

When x = 5 , then

y = 5 × 5 = 25

Answer:

(D) 2

Step-by-step explanation:

The scale factor of the enlargement of ΔABC to ΔA'B'C' is given by the ratio of the length of the corresponding sides of ΔA'B'C' and ΔABC

Therefore, we have;

[tex]The \ scale \ factor = \dfrac{Length \ of \overline {B'C'}}{Length \ of \overline {BC}} = \dfrac{Length \ of \overline {A'C'}}{Length \ of \overline {AC}} = \dfrac{Length \ of \overline {A'B'}}{Length \ of \overline {AB}}[/tex]

[tex]\dfrac{Length \ of \overline {B'C'}}{Length \ of \overline {BC}} = \dfrac{2 \ units}{1 \ unit} = 2[/tex]

[tex]\dfrac{Length \ of \overline {A'C'}}{Length \ of \overline {AC}} = \dfrac{4 \ units}{2 \ units} = 2[/tex]

[tex]\dfrac{Length \ of \overline {A'B'}}{Length \ of \overline {AB}} = \dfrac{2 \cdot \sqrt{5} \ units}{\sqrt{5} \ units} = 2[/tex]

Therefore, the scale factor = 2

Answer:

Step-by-step explanation:

Step-by-step explanation:

.hhx cvs Gunther b but kcm

Answer:

-1

Step-by-step explanation:

1. Sets the exponents equal

3b-1 = b-3

2. collect like terms and calculate it

3b-b=1-3

2b= -2

(divide both side by 2)

b=-1

Answer:

I believe it would be A 3^2(2-sqr2)

Answer:

10

Step-by-step explanation:

last year he planted 12.

1/3 of that is 12/3 = 4.

6 more than that is 4 + 6 = 10.

Answer: C.)  10

Step-by-step explanation:

Answer:

Please find attached the graph of the function created with MS Excel showing the relevant points required to draw an approximate graph of the function on a graph paper

Step-by-step explanation:

The given quadratic function is f(x) = -2·x² + 7·x + 4

The range of the input (x) values = -1 ≤ x ≤ 5

The coefficient of the quadratic is negative -2, the graph is n shape

The intercept form of the function is given as follows;

-2·x² + 7·x + 4 = -1 × (2·x² - 7·x - 4)

-1 × (2·x² - 7·x - 4) = -1 × (2·x² + x - 8·x - 4)

-1 × (2·x² + x - 8·x - 4) = -1 × (x · (2·x + 1) - 4·(2·x + 1))

∴ -1 × (x · (2·x + 1) - 4·(2·x + 1)) = -1 × (2·x + 1)·(x - 4)

∴ f(x) = -2·x² + 7·x + 4 = -1 × (2·x + 1)·(x - 4)

At the x-intercepts, (2·x + 1) = 0 or (x - 4) = 0, which gives;

x = -1/2 or x = 4

Therefore, the x-intercepts are (-1/2, 0), (4, 0)

The equation in vertex form is given as follows;

f(x) = -2·x² + 7·x + 4 = -2·(x² - 7·x/2 + 2)

By applying completing the squares method, to x² - 7·x/2 - 2, we get;

Where x² - 7·x/2 - 2

x² - 7·x/2 = 2

x² - 7·x/2 + (-7/4)² = 2 + (-7/4)² = 81/15

(x - 7/4)² = 81/16

∴ (x - 7/4)² - 81/16 = 0 = x² - 7·x/2 - 2

∴ x² - 7·x/2 - 2 = (x - 7/4)² - 81/16

-2·(x² - 7·x/2 + 2) = -2·((x - 7/4)² - 81/16) = -2·(x - 7/4)² + 81/8

The vertex = (7/4, 81/8)

When x = 0, we get;

f(0) = -2 × 0² + 7 × 0 + 4 = 4

The y-intercept = (0, 4)

The sketch of the function should pass through the x-intercepts (-1/2, 0), (4, 0), the y-intercept (0, 4), and the y-intercept (0, 4), and the vertex, (7/4, 81/8) on a graph sheet

Please find attached a drawing of the function of the function created with MS Excel

Answer:

[tex]f^{-1}[/tex] (x) = [tex]\frac{5x}{x-2}[/tex]

Step-by-step explanation:

let y = f(x) and rearrange making x the subject

y = [tex]\frac{2x}{x-5}[/tex] ( multiply both sides by x - 5 )

y(x - 5) = 2x ← distribute left side

xy - 5y = 2x ( subtract 2x from both sides )

xy - 2x - 5y = 0 ( add 5y to both sides )

xy - 2x = 5y ← factor out x from each term on the left side )

x(y - 2) - 5y ← divide both sides by y - 2

x = [tex]\frac{5y}{y-2}[/tex]

Change y back into terms of x with x = [tex]f^{-1}[/tex] (x) , then

[tex]f^{-1}[/tex] (x) = [tex]\frac{5x}{x-2}[/tex]

Look into the image. I hope it helps❤

Answer:

125 cm³

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Geometry

Volume of a Cube Formula: V = a³

Step-by-step explanation:

Step 1: Define

Identify variables

a = 5 cm

Step 2: Find Volume

Answer:

[tex]\huge\boxed{V=125cm^3}[/tex]

Step-by-step explanation:

The formula of a volume of a cube with edge [tex]a[/tex]:

[tex]V=a^3[/tex]

We have [tex]a=5cm[/tex].

Therefore the volume is:

[tex]V=(5cm)^3=5cm\cdot5cm\cdot5cm=125cm^3[/tex]

Answer:

Solution given:

Let there be a point P(x, y) equidistant from

A(-3, 2) and B(0,4),

so PA = PB,

[tex]\sqrt{(x+3)²+(y-2)²}=\sqrt{(x-0)²+(y-4)²}[/tex]

squaring both side

[tex](\sqrt{(x+3)²+(y-2)²})^{2}=(\sqrt{(x-0)²+(y-4)²})²[/tex]

x²+6x+9+y²-4y+4=x²+y²-8y+16

x²+6x+y²-4y-x²-y²+8y=16-4-9

6x-4y+8y=3

6x-4y=3 is a required locus

Actually:

A locus is a curve or other figure formed by all the points satisfying a particular equation of the relation between coordinates, or by a point, line, or surface moving according to mathematically defined conditions.

[tex] \sf Q) \: 19^{2} + 21^{2} = {?}[/tex]

[tex] \sf \to 19^{2} + 21^{2} [/tex]

[tex] \sf \to 361 + 441[/tex]

[tex] \sf \to 802[/tex] is the solution.

Answer:

0.7744 = 77.44% probability of getting two good coils when two coils are randomly selected

Step-by-step explanation:

For each coil, there are only two possible outcomes. Either it is good, or it is not. Since the coil taken is replaced, the probability of choosing a good coil on a trial is independent of any other trial, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

88 out of 100 are good:

This means that [tex]\pi = \frac{88}{100} = 0.88[/tex]

Find the probability of getting two good coils when two coils are randomly selected.

This is P(X = 2) when n = 2. So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 2) = C_{2,2}.(0.88)^{2}.(0.12)^{0} = 0.7744[/tex]

0.7744 = 77.44% probability of getting two good coils when two coils are randomly selected

Answer:

x=2

Step-by-step explanation:

We have

y = 2x-1

y= 4x-5

Therefore, as 2x-1=y=4x-5, we can say that

2x-1=4x-5

add 1 to both sides to make one side have only x components

2x = 4x-4

subtract 4x from both sides to separate the x components

-2x = -4

divide both sides by -2 to separate the x

x = 2

solution :-

here,

We know that interior opposite angles are equal.

So,

110° = 50° + x (being interior opposite angles)

110° - 50° = x

60° = x

the value of x =60°

hope it is helpful to you ☺️

Answer:

Step-by-step explanation:

Inches per hour is the rate we are looking for here, which will then be the slope of the linear equation. Slope is the same thing as the rate of change. While this may not seem all that important right now, it's actually a HUGE concept in higher math, especially calculus!

If the pool is filling at a rate of 2 inches per every 4 hours, then by dividing, we get that the rate is 1 inch every 2 hours, which translates to a slope of 1/2. Creating an equation with this slope:

[tex]w=\frac{1}{2}t[/tex]  Let's check it. We are told that after 4 hours there are 2 inches of water in the pool. That means if we plug in 4 for t and solve for w, we should get w = 2:

[tex]w=\frac{1}{2}(4)[/tex] and

w = 2. So we're good!

Answer:

none

Step-by-step explanation:

accellus

The inverse matrix or type none of the given matrix is given as [tex]\rm A^{-1} = \dfrac{1}{-5}\begin{bmatrix}3& 4\\2 & 1 \\\end{bmatrix}\\[/tex].

A matrix is a specific arrangement of items, particularly numbers. A matrix is a row-and-column mathematical structure. The a_{ij} element in a matrix, such as M, refers to the i-th row and j-th column element.

The matrix is given below.

[tex]A = \begin{bmatrix}3& 2\\4 & 1 \\\end{bmatrix}[/tex]

Then the transpose of a will be

[tex]\rm adj \ A = \begin{bmatrix}a_{11} & a_{21} \\a_{12} & a_{22} \\\end{bmatrix}\\\\\rm adj \ A = \begin{bmatrix}3& 4\\2 & 1 \\\end{bmatrix}[/tex]

Then the value of matrix A will be

[tex]\rm \left| A \right|= \begin{vmatrix}3& 2\\4 & 1\end{vmatrix}\\\\\left| A \right|= 3*1 - 4*2\\\\|A| = -5[/tex]

Then the inverse matrix is defined as

A⁻¹ = Adj A / |A|

Then we have

[tex]\rm A^{-1} = \dfrac{\begin{bmatrix}3& 4\\2 & 1 \\\end{bmatrix}}{-5}\\\\\\A^{-1} = \dfrac{1}{-5}\begin{bmatrix}3& 4\\2 & 1 \\\end{bmatrix}\\[/tex]

More about the matrix link is given below.

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Answer:

(1, -3)

Step-by-step explanation:

You can see where the two lines intersect - that's the solution.

Answer: 15 m

Step-by-step explanation:

Given

Total volume of the combined pyramid is [tex]V=2700\ mm^3[/tex]

Height of top and bottom pyramid is

[tex]h_t=16\ mm[/tex]

[tex]h_b=20\ mm[/tex]

If the base has a side length of x, its area must be [tex]x^2[/tex]

Volume of square prism is given by

[tex]\Rightarrow V=\dfrac{1}{3}Bh\quad [\text{B=base area}]\\\\\text{Total volume will be the sum of the two pyramids}\\\\\Rightarrow 2700=\dfrac{1}{3}\times x^2\times 16+\dfrac{1}{3}\times x^2\times 20\\\\\Rightarrow 2700=\dfrac{1}{3}\times x^2\times (16+20)\\\\\Rightarrow x^2=225\\\Rightarrow x=15\ mm[/tex]

Thus, the value of [tex]x[/tex] is 15 m.