The Davidson family wants to expand its rectangular patio, which currently measures 15 feet by 12 feet They want to extend the length and width the same amount to increase the total area of the patio by 160 ft squared Which quadratic equation best models the situation? cap A is equal to l w
The solutions to a quadratic equation are x is equal to 2 and x is equal to 7 If k is a nonzero constant, which of the following must be equal to the quadratic equation?
A company is producing picture frames as well as the glass for the front of the frames. The amount of wood required for the frame is represented by the function cap w times x , and the amount of glass is represented by the function cap g of x The frames have lengths represented by the function f of x and widths represented by g of x x cap w times x is equal to 2 times open paren f plus g close paren of x cap g of x is equal to open paren f times g close paren of x 2 14 6 3 24 27 4 34 60 5 44 105 Which statement describes the combined functions cap w times x and cap g of x ?
The main cable of a suspension bridge forms a parabola modeled by the equation y is equal to A times open paren x minus h close paren squared plus k where y is the height in feet of the cable above the road, x is the horizontal distance in feet from the right bridge support, A is a constant, and open paren h comma k close paren is the parabola’s vertex. What is the maximum and minimum height of the bridge modeled by the equation y is equal to 0 point 0 0 5 times open paren x minus 60 close paren squared plus 8 ?
The total area of two square windows is 1 comma 025 in. squared Each side of the larger window is 5 in. longer than the sides of the smaller window. How long are the sides of the smaller window? cap A is equal to s squared
The owner of an office building is expanding the length and width of a parking lot by the same amount. The lot currently measures 120 feet by 80 feet , and the expansion will increase its area by 4 comma 400 ft squared By how many feet should the length of the parking lot be increased? cap A is equal to l w
Adding two functions results in h of x is equal to 4 x , while multiplying the same functions results in j times x is equal to negative 5 x squared minus 12 x minus 4 Which statements describe f of x and g of x , the original functions? Choose two correct answers.
A shipping company charges based on calculations of the volume of a rectangular box and the sum of the dimensions of the box. A square rectangular prism has a side length represented by the linear function f of x , and a height represented by the linear function g of x x cap v times x is equal to open paren f times f times g close paren times x cap s times x is equal to open paren f plus f plus g close paren times x 3 15 8 4 24 10 5 35 12 6 48 14 Which statement describes the combined functions cap v times x and cap s times x ?
Justin and Elena each launched a toy rocket into the air. The height of Justin’s rocket is modeled by the equation h is equal to negative 16 t squared plus 60 t plus 2 Elena launched his rocket from the same position, but with an initial velocity double that of Justin’s. Which equation best models the height of Elena’s rocket? h of t is equal to A t squared plus v t plus h sub 0
A projectile is launched straight up from the ground with an initial velocity of 120 feet per second If acceleration due to gravity is negative 16 the fraction with numerator ft and denominator s squared , after about how many seconds will the object reach a height of 200 feet ? h of t is equal to A t squared plus v t plus h sub 0
A rectangular patio is 9 ft by 6 ft. When the length and width are increased by the same amount, the area becomes 88 sq ft. Ginger is using the zero product property to solve the equation open paren 6 plus x close paren times open paren 9 plus x close paren is equal to 88 What does the value of x in her solutions represent?
The square of 9 less than a number is 3 less than the number. What is the number?
A rectangular deck is 12 ft by 14 ft. When the length and width are increased by the same amount, the area becomes 288 sq. ft. By how much were the dimensions increased?
Use the zero product property to find the solutions to the equation open paren x plus 2 close paren times open paren x plus 3 close paren is equal to 12
Two functions are combined resulting in the function j times x is equal to 1 point 5 x squared plus 4 x minus 3 Which operations applied to the specified functions could result in j times x ? Choose three correct answers.
Two functions are combined resulting in the function j times x is equal to negative 3 x squared plus 5 Which operations applied to the specified functions could result in j times x ? Choose three correct answers.
A contractor is calculating the number of decorative stones for a new rectangular patio. The bids always include a count for the number of stones for the edging, cap e times x , and the number of stones for the center of the patio, cap c times x The various patio sizes have lengths represented by the function f of x and widths represented by g of x x cap e times x is equal to 2 times open paren f plus g close paren of x cap c times x is equal to open paren f times g close paren of x 2 34 62 3 52 133 4 70 260 5 88 435 Which statement describes the combined functions cap e times x and cap c times x ?
Adam is using the equation x times open paren x plus 2 close paren is equal to 255 to find two consecutive odd integers with a product of 255 When Adam solves the problem using the zero product property, what do those solutions represent?
A firework is launched into the air from ground level with an initial velocity of 128 ft/s If acceleration due to gravity is negative 16 the fraction with numerator ft and denominator s squared , what is the maximum height reached by the firework? h of t is equal to A t squared plus v t plus h sub 0
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