In remodeling a house an architect finds that by adding the same amount to each dimension of a 15ft by 19ft rectangular room, the area would be increased by 98 ft^2. How
much must be added to each dimension?
Let x be the amount that is added to each dimension. After writing an equation in standard form with a > 0, a= ? b= ? and c= ?
(Simplify your answers.)

log₉(x - 7) + log₉(x - 7) = 1

2 log₉(x - 7) = 1

log₉(x - 7) = 1/2

Take the base-9 antilogarithm of both sides; in other words, make both sides powers of 9:

[tex]9^{\log_9(x-7)} = 9^{1/2}[/tex]

[tex]9^{1/2}[/tex] can also be written as √9 = 3, and [tex]b^{\log_b(a)}=a[/tex], so the equation reduces to

x - 7 = 3

Solve for x :

x = 10

Answer:

192

Step-by-step explanation:

geometric mean theorem :

with p and q being the segments of the Hypotenuse, then

h = x = sqrt(p×q)

p = 144

q = 400-144 = 256

h = x = sqrt(144×256) = 12×16 = 192

Answer:

D

Step-by-step explanation:

The answer is D.

Answer:

-  x³ - 2x² + 3 - 1 / x

Step-by-step explanation:

(4x³ - 8x² + 12x - 4) / (-4x)

-  x³ - 2x² + 3 - 1 / x

Answer:

Substitute in the values of both given coordinates & form 2 equations:

[tex]\left \{ {{A(2)+B(-1)=1} \atop {A(-3)+B(-2)=1}} \right. \\\\=\left \{ {{2A-B=1} \atop {-3A-2B=1}} \right.[/tex]

Find the value of B from the equation 2A - B = 1:

[tex]2A-B=1\\-B=1-2A\\B=2A-1[/tex]

Substitute in the B-value to the other equation:

[tex]-3A-2B=1\\-3A-2(2A-1)=1\\-3A-4A+2=1\\-7A=1-2\\-7A=-1\\A=\frac{-1}{-7} =\frac{1}{7}[/tex]

Find the B-value using the equation from before:

[tex]B=2A-1=2(\frac{1}{7})-1=\frac{2}{7} -\frac{7}{7} =-\frac{5}{7}[/tex]  

Therefore the equation Ax + By = 1 would equal:

[tex]\frac{1}{7} x-\frac{5}{7} y=1[/tex]

Option 4

Verification:-

[tex]\\ \sf\longmapsto x-7y=-49[/tex]

[tex]\\ \sf\longmapsto 7-7(8)=-49[/tex]

[tex]\\ \sf\longmapsto 7-56=-49[/tex]

[tex]\\ \sf\longmapsto -49=-49[/tex]

And

[tex]\\ \sf\longmapsto 10x+9y=142[/tex]

[tex]\\ \sf\longmapsto 10(7)+9(8)=142[/tex]

[tex]\\ \sf\longmapsto 70+72=142[/tex]

[tex]\\ \sf\longmapsto 142+142[/tex]

Hence verified

Answer:

4.

Step-by-step explanation:

1. 8x - y = 48

9x + 10y = 142

8(7) - 8 = 48

9(7) + 10(8) = 143

No

2. 9x - y = 55

8x + 10y = 140

9(7) - 8 = 55

9(7) - 10(7) = -24

No

3. x-6y=-41

8x + 9y = 127

7 - 6(8) = -41

8(7) + 9(8) = 128

No

4. x-7y=-49

10x + 9y = 142

7 - 7(8) = 49

10(7) + 9(8) = 142

Yes

Answer:

F(x) = 45*x - (5/2)*x^2 + C

Step-by-step explanation:

Here we want to find the antiderivative of the function:

f(x) = 45 - 5*x

Remember the general rule that, for a given function:

g(x) = a*x^n

the antiderivative is:

G(x) = (a/(n + 1))*a*x^(n + 1) + C

where C is a constant.

Then for the case of f(x) we have:

F(x) = (45/1)*x^1 - (5/2)*x^2 + C

F(x) = 45*x - (5/2)*x^2 + C

Now if we derivate this, we get:

dF(x)/dx = 1*45*x^0 - 2*(5/2)*x

dF(x)/dx = 45 - 5*x

Answer:

D. 212 degrees Fahrenheit and 100 degrees Celsius.

Step-by-step explanation:

The boiling point of water in Celsius is 100.

The way to calculate Celsius to Fahrenheit:

F = (C × 9/5) + 32

So we plug in 100 for C.

F = (100 × 9/5) + 32

F = 180 + 32

F = 212

Therefore, the numbered pair is 212 degrees F and 100 degrees  C.

Answer:

y=-1/5x-11/5

Step-by-step explanation:

perpendicular, product of both gradients = -1

hence, slope = -1/5

y=-1/5x+c

sub y=-1, x=-6

-1=-1/5(-6)+c

c = -1-6/5=-11/5

y=-1/5x-11/5

Answer:

2160

Step-by-step explanation:

because c is 15 and d is 12 therefore d² is 144 and 144x15 is 2160

Answer:

2160

Step-by-step explanation:

Substitute

[tex](15)(12) {}^{2} [/tex]

[tex]15 \times 144 = 2160[/tex]

Answer:

you didn't feature any graphs for me to choose from

Answer:

i think 3

Step-by-step explanation:

Answer: [A] 2

Step-by-step explanation:

100% on edge 2023

Answer:

62 of the email messages were spam

Step-by-step explanation:

Let the number of spam and other messages be s and o respectively.

Total number of messages= 78

s +o= 78 -----(1)

s= 4o -2 -----(2)

Substitute (2) into (1):

4o -2 +o= 78

Simplify:

5o -2= 78

+2 on both sides:

5o= 78 +2

5o= 80

Divide both sides by 5:

o= 80 ÷5

o= 16

Since s +o= 78, s= 78 -o.

s= 78 -16

s= 62

Answer:

175

Step-by-step explanation:

so, the LCM is the combination of the longest chains of the prime factors in every number.

40 : 2, 2, 2, 5

1400 / 40 = 35

35 : 5, 7

but LCM(35, 40) = 2×2×2×5×7 = 280

and not 1400.

what is missing ?

1400 / 280 = 5

aha, another prime factor 5 is missing to get 1400.

x : 5, 5, 7

so, x = 5×5×7 = 175

LCM(175, 40) = 2×2×2×5×5×7 = 1400

Answer:

The answer is "-310840".

Step-by-step explanation:

[tex]\begin{array}{l} P'(x) = 2x - 1198\\ \\ \frac{{dP}}{{dx}} = 2x - 1198\\ \\ dP = \left( {2x - 1198} \right)dx\\ \\ \int {dP} = \int\limits_0^{380} {\left( {2x - 1198} \right)dx} \\ \\ P = \left( {2\frac{{{x^2}}}{2} - 1198x} \right)_0^{380}\\ \\ P = {380^2} - 1198 \times 380 = 144400-455240=-310840\\ \end{array}[/tex]

Answer:

2[(x^2 + 7)(x + 5)]

Step-by-step explanation:

Note that the ratio of the first and second terms is the same as that between the third and fourth terms. So this cubic will factor by grouping, but first we can separate out the common scalar factor 2...

2x3+10x2+14x+70=

2(x3+5x2+7x+35)

2((x3+5x2)+(7x+35))

2(x2(x+5)+7(x+5))

2(x2+7)(x+5)

Answer:

The answer is D. 2[(x2 + 7)(x + 5)]

Step-by-step explanation:

Answer:

f(x) = 2x + 1, g(x) = 3x - 2 and fg(x) = 5

Step-by-step explanation:

9514 1404 393

Answer:

  f(x) = (x -4)(x -1)

Step-by-step explanation:

If 'a' is a zero of the function, then (x -a) is a factor. The two zeros mean the factored form of the quadratic is ...

  f(x) = (x -4)(x -1)

__

The expanded form will be ...

  f(x) = x² -5x +4

Answer:

The number is 30.

Step-by-step explanation:

Let the number be x

so

x + (130% of x) = 69

x + 13x/10 = 69

or, (10x + 13x)/10 = 69

or, 23x = 690

or, x = 690/23

so, x = 30

Answer: 30

Step-by-step explanation:

its correct on rsm

Answer:

25.13 cm

Step-by-step explanation:

Perimeter ( circumference ) of a circle = 2πr

Given,

The circle is 8 cm wide

which means,

The diameter (d) of the circle is 8 cm.

Radius (r) of the circle = d/2

= 8/2

= 4

Radius = 4 cm

Putting the value in the formula;

2πr

= 2 (22/7) (4)

= 25.13 cm (approx)

Answer:

More points are needed to determine the correlation.

Answer:

its d

Step-by-step explanation:

;)

x = 4

Every step shown. Once you become used to doing this you will almost be able to do the basic one's in your head without writing much down.

Explanation:

Let the unknown value be  

x

Converting the words into numbers:

First part: "15 times a certain number"  → 15 x

Second part: "plus 5 times the same number" → 15 x + 5 x

The last part: " is 80" ->  15x + 5 x = 80

We are counting  x ' s . 15 of them plus another 5 of them gives a total of 20.

So 15 x + 5 x = 20 x = 80

Divide both sides by 20

20 x ÷ 20 = 80÷ 20

20/20x=80/20

x=4

Let the number be x

ATQ

[tex]\\ \sf\longmapsto 15x+5x=80[/tex]

[tex]\\ \sf\longmapsto (15+5)x=80[/tex]

[tex]\\ \sf\longmapsto 20x=80[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{80}{20}[/tex]

[tex]\\ \sf\longmapsto x=4[/tex]

Answer:

Kindly check explanation

Step-by-step explanation:

Given the data:

May August

95 100

72 80

78 95

50 65

89 85

92 98

75 70

90 96

65 87

The appropriate test is a paired t test :

d = difference between May and August

d = (-5, -8, -17, -15, 4, -6, 5, -6, -22)

The hypothesis :

H0 : μd = 0

H1 : μd ≠ 0

The test statistic :

T = dbar / (Sdbar/√n)

Where, dbar and Sdbar are the mean and standard deviation of 'd' respectively.

Using calculator :

dbar = - 7.777 ; Sdbar = 9.052

Test statistic = - 7.777 / (9.052 /√9)

Test statistic = - 2.577

The Pvalue, df = n - 1 = 9 - 1 = 8

Pvalue(-2.577, 8) = 0.0327

At α = 0.05

Pvalue < α ; WE reject the H0 ; and conclude that there has been a change in score

Step-by-step explanation:

The time dilation formula is given by

[tex]F(t) = \dfrac{t}{\sqrt{1-v^2}}[/tex]

where t is the time measured by the moving observer and F(t) is the time measured by the stationary earth-bound observer and v is the velocity of the moving observer expressed as a fraction of the speed of light.

a) If the observer is moving at 80% of the speed of light and observes an event that lasts for 1 second, a stationary observer will see the same event occurring over a time period of

[tex]F(t) = \dfrac{1\:\text{s}}{\sqrt{1-(0.8)^2}}[/tex]

[tex]\:\:\:\:\:\:\:=\dfrac{1\:\text{s}}{\sqrt{1-(0.8)^2}} =\dfrac{1\:\text{s}}{\sqrt{1-(0.64)}}[/tex]

[tex]\:\:\:\:\:\:\:=1.67\:\text{s}[/tex]

This means that any event observed by this moving observer will be seen by a stationary observer to occur 67% longer.

b) Given:

t = 1 second

F(t) = 2 seconds

We need to find the speed of the observer such that an event seen by this observer will occur twice as long as seen by a stationary observer. Move the term containing the radical to the left side so the equation becomes

[tex]\sqrt{1-v^2} = \dfrac{t}{F(t)}[/tex]

Take the square of both sides, we get

[tex]1 - v^2 =\dfrac{t^2}{F^2(t)}[/tex]

Solving for v, we get

[tex]v^2 = 1 - \dfrac{t^2}{F^2(t)}[/tex]

or

[tex]v = \sqrt{1 - \dfrac{t^2}{F^2(t)}}[/tex]

Putting in the values for t and F(t) we get

[tex]v = \sqrt{1 - \dfrac{(1\:\text{s})^2}{(2\:\text{s})^2}}[/tex]

[tex]v = \sqrt{1 - \dfrac{1}{4}} = \sqrt{0.75}[/tex]

[tex]\:\:\:\:=0.866[/tex]

This means that the observer must moves at 86.6% of the speed of light.

Answer: C) (1,4)

Step-by-step explanation:

The intersection point is where f(x) = g(x)

x³ + 3x = x² + 3

x³ - x² +3x - 3 = 0

Answer: 4.25

Step-by-step explanation:

2.5/100 = 0.025

0.025 × 170 = 4.25

but the question there is any goats in 2.5 cm ??

that is impossible

Answer:

...

Step-by-step explanation:

seeee the above picture

Answer:

The answer is 155.

Step-by-step explanation:

We can find the remaining parts of the triangle angles.

Answer:

D. 157

Step-by-step explanation:

4(x^2+3)-2y

4(6^2+3)-2(-1/2) add in given values

4(39)+1.     start with parentheses

156+1.        combine like terms

157.            answer

Answer:

D. 157

Step-by-step explanation:

Hi there!

We want to find the value of the expression 4(x²+3)-2y is when x=-6 and y=-1/2

Let's first simplify the expression, as that will likely make it easier

Distribute 4 to both x² and 3

4x²+12-2y

That's the expression

Substitute -6 as x into the expression

4(-6)²+12-2y

Raise (-6) to the second power

4*36+12-2y

Multiply 36 by 4

144+12-2y

Add 12 and 144 together

156-2y

Now the expression is 156-2y

But remember that we know that y=-1/2, and we haven't substituted it into the expression yet

Substitute -1/2  as y into the expression

156-2(-1/2)

Multiply

156+2/2

Simplify

156+1

Add

157

Hope this helps!