Which algebraic expression represents the phrase "seven more than half of a number"?

Please help me solve this :)

Effectus [21]

Answer:

105 cm

Step-by-step explanation:

Table + cat - mouse = 120 ...(1)

table + mouse - cat = 90 ...(2)

(1)+(2): 2*Table = 210

Table = 105

8 0

3 years ago

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Can some one plz help me?

spin [16.1K]

Volume = base area x height

Base area = 6 (1/2 x 3 x 2.6) = 23.4 cm²

Volume = 23.4 x 7 = 164 cm³ (nearest wole number)

Answer: Volume = 164 cm³

4 0

3 years ago

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Jack bought a new car in 2014 for 28,000. If the value of the car decreases by 14% each year, write an exponential model for the

elena55 [62]

Answer:

In 2026 car will have a value of $5,000.

Step-by-step explanation:

We have been given that Jack bought a new car in 2014 for 28,000. If the value of the car decreases by 14% each year.

Since we know that an exponential function is in form: $y=a*b^x$ , where,

a = Initial value,

b = For decay or decrease b is in form (1-r), where r represents decay rate in decimal form.

Let us convert our given decay rate in decimal form.

$14\%=\frac{14}{100}=0.14$

Upon substituting a =28,000 and r=0.14 in exponential decay function we will get,

$y=28,000(1-0.14)^x$ , where x represents number of years after 2014.

Therefore, the function $y=28,000(0.86)^x$ represents the value of car x years after 2014.

To find the number of years it will take to car have the value of $5,000, we will substitute y=5,000 in our function.

$5,000=28,000(0.86)^x$

Let us divide both sides of our equation by 28,000.

$\frac{5,000}{28,000}=\frac{28,000(0.86)^x}{28,000}$

$0.1785714285714286=(0.86)^x$

Let us take natural log of both sides of our equation.

$ln(0.1785714285714286)=ln((0.86)^x)$

Using natural log property $ln(a^b)=b*ln(a)$ we will get,

$ln(0.1785714285714286)=x*ln(0.86)$

$\frac{ln(0.1785714285714286)}{ln(0.86)}=\frac{x*ln(0.86)}{ln(0.86)}$

$\frac{-1.7227665977411033893}{-0.1508228897345836}=x$

$x=11.422447\approx 12$

As in the 12th year after 2014 car will have a value of $5,000, so we will add 12 to 2014 to find the year.

$2014+12=2026$

Therefore, in 2026 car will have a value of $5,000.

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3 years ago

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A rectangle has a width that is 5 feet less than the length. The area of the rectangle is 126 square feet. Find the dimensions o

mr_godi [17]

Given:

A rectangle has a width that is 5 feet less than the length. The area of the rectangle is 126 square feet

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❍Let's assume, Length of rectangle x feet and width of the rectangle x - 5 feet respectively.

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To calculate the dimensions of the rectangle we will use the formula of Area of rectangle:

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$\: \: \: \: \: \: \: { \underline{ \boxed{ \pmb{ \frak{ Area_{(rectangle)} = Length \times width }}}}} \\ \\$

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$\underline {\sf{Substituting \: the \: values~ in~ above~formula: }} \\$

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$: \implies \sf \:x \times (x - 5) = 126 \\ \\ \\ : \implies \sf \:x^2 - 5x = 126 \\ \\ \\ : \implies \sf \:x^2 - 5x - 126 = 0 \\ \\ \\ : \implies \sf \:x^2 - 14x - 9x - 126 = 0 \\ \\ \\ : \implies \sf \:x (x - 14) - 9 (x + 14) = 0 \\ \\ \\ : \implies \sf \:(x - 14)(x - 9) = 0 \\ \\ \\ : \implies { \boxed { \purple{\pmb { \: x = 14 \: \: or \: \: x = -9}}} } \\ \\ \\$