Answer:
The product is the difference of squares is [tex]$$(9c-2d)(9c+2d)=81{{c}^2}-4{{d}^2}$$[/tex]
Step-by-step explanation:
Explanation
The given expression is (9c-2d)(9c+2d).We have to multiply the given expression.Square the first term 9c. Square the last term 2d.[tex]$$\begin{aligned}&(9 c-2 d)(9 c+2 d)=(9 c)^{2}-(2 d)^{2} \\&(9 c-2 d)(9 c+2 d)=81 c^{2}-4 d^{2}\end{aligned}$$[/tex]
A rocket is launched at the top of a building. The height of the rocket (in meters) written
in terms of time (seconds) can be modeled by h (t) = -4.9t2 +9.8t + 73.5. What is
the maximum height?
The maximum height of the rocket is 78.4m
Maximum height of a functionGiven the function that represents the height of a function expressed as:
h(t) = -4.9t² +9.8t + 73.5.
The rocket will reach its maximum height at the point where h'(t) = 0
h'(t) = -9.8t +9.8
Equate to zero
0 = -9.8t + 9.8
9.8t = 9.8
t = 1
Substitute
h(1) = -4.9(1)²+9.8(1) + 73.5
h(1) = 4.9 + 73.5
h(1) = 78.4m
Hence the maximum height of the rocket is 78.4m
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Place the following equation into quadratic form.
-7 = (x + 8)^
The representation of the equation as a standard quadratic equation is given by:
x² + 16x + 71 = 0.
What is the standard representation of a quadratic equation?The standard representation of a quadratic equation is given by:
ax² + bx + c = 0.
In this problem, the equation is:
-7 = (x + 8)²
Then:
x² + 16x + 64 = -7.
x² + 16x + 71 = 0.
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which of the following has the same unit rate as $5 for 2 pounds
a. $20 for 8lb
b. $16 for 6lb
c. $24 for 8lb
d. $12 for 4lb
make sure to show your work
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
[ a ] $ 20 for 8 lb
[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]
[tex]❖ \: \sf \:unit \: \: rate = simplest \: \: ratio \: in \: which \: it\: exists[/tex]
[tex] \qquad◈ \: \: \sf \: \cfrac{5}{2} \: \: \$ \:per \: \: lb[/tex]
Now, check out the options -
[ a ]
[tex] \qquad◈ \: \: \sf \: \cfrac{20}{8} [/tex]
( on simplifying )
[tex] \qquad◈ \: \: \sf \: \cfrac{5}{2} \: \: \$ \:per \: \: lb[/tex]
Same as the given one.
[ b ]
[tex] \qquad◈ \: \: \sf \: \cfrac{16}{6} [/tex]
( on simplifying )
[tex] \qquad◈ \: \: \sf \: \cfrac{8}{3} \: \: \$ \:per \: \: lb[/tex]
Not the same.
[ c ]
[tex] \qquad◈ \: \: \sf \: \cfrac{24}{8} [/tex]
( on simplifying )
[tex] \qquad◈ \: \: \sf \: 3 \: \: \$ \:per \: \: lb[/tex]
Not the same.
[ d ]
[tex] \qquad◈ \: \: \sf \: \dfrac{12}{4} \: \: [/tex]
( on simplifying )
[tex] \qquad◈ \: \: \sf \: 3 \: \: \$ \:per \: \: lb[/tex]
Not the same.
[tex] \qquad \large \sf {Conclusion} : [/tex]
The Correct answer is [ a ] $ 20 for 8 lb
Graph the inequality. -3 < y - 7x < 15
The graph of the inequality can be seen in the image below.
How to graph the inequality?
Here we have:
-3 < y - 7x < 15
Isolating y, we get:
-3 + 7x < y < 15 + 7x
So we need to graph two linear inequalities:
y > -3 + 7x
y < 15 + 7x
So we need to graph two parallel lines (with dashed lines, the lines aren't solutions) and shade the region above the first line and below the second line.
The graph is below:
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A six-sided die is rolled. What are the odds that a number greater than 4 is rolled?
Answer: [tex]\frac{1}{3}[/tex] or about 33%
Step-by-step explanation:
We will divide the wanted outcomes by the possible outcomes.
[tex]\displaystyle \frac{\text{wanted outcomes}}{\text{possible outcomes}} =\frac{\text{Number of numbers greater than 4}}{\text{number of numbers 1 through 6}} =\frac{2}{6}=\frac{1}{3}\;\; \text{or about 33\%}[/tex]
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Answer: 1/3
Step-by-step explanation:
There are only 2 numbers greater than 4. 5 and 6.
2/6= 1/3 chance
Robyn, Rachel and Rocky bought a set of LEGO blocks, Robyn paid $45, Rachel paid $65 and Rocky paid $60. What
fraction of the total amount Rocky paid?
Answer:
6/17
Step-by-step explanation:
Robyn paid $45,
Rachel paid $65
Rocky paid $60.
Total amount paid = $45 + $65 + $60 = $170
Fraction paid by Rocky will be:
= 60/170
= 6/17
the sewing and fabric shop sells different colored ribbons in meter lengths. laura pays £64.32 for 12 meters of blue ribbon. how much does the ribbon cost per meter?
Answer: £5.36
Step-by-step explanation: You can find this by dividing £64.32 by 12
can someone solve this for me pls¿
Jaime spent $7.61 at the concession stand. This is $3.50 more than 3 times the amount of
money that Erin spent. How much money did Erin spend?
Answer:
jsjsjd b ebejisnskskhdbd zkzkz z.
A 20 inch tall plant grows 4 inches per month. What would be the height of the plant after 10
months?
60 inches
40 inches
80 inches
100 inches
Answer:
60inches
Step-by-step explanation:
this because If you multiply 4 by 10 equals 40 add 40 to 20 equals 60
Fatima evaluated the expression StartFraction 4 m Superscript negative 3 Baseline n Superscript negative 2 Baseline Over m Superscript negative 1 Baseline n EndFraction, when m = negative 2 and n = 4. Her work is shown below.
StartFraction 4 m Superscript negative 3 Baseline n Superscript negative 2 Baseline Over m Superscript negative 1 Baseline n EndFraction = 4 m Superscript negative 2 Baseline n Superscript negative 3 Baseline = 4 (negative 2) Superscript negative 2 Baseline (4) Superscript negative 3 Baseline = StartFraction 1 Over 64 EndFraction times StartFraction 1 Over 64 EndFraction = StartFraction 1 Over 4,096 EndFraction
What was Fatima’s error?
She subtracted the exponents incorrectly when simplifying the expression.
She substituted the wrong values for the variables.
She applied the exponent Negative 2 to 4 (negative 2) instead of applying the exponent to just Negative 2.
She found an incorrect value for (Negative 8) Superscript negative 2 since the value should be negative.
The error of Fatima is: C. She applied the exponent -2 to "4(-2) instead of only to "(-2).
What is an Exponent?An exponent in any expression is the letter or number on the right of a base in an expression.
In the evaluated expression shown, the base that the exponent "-2" applies to is "m", and does not include 4. If we substitute the value of m = -2, into the evaluated expression, the base that the exponent "-2" applies to is "-2" and does not include "4".
Therefore, Fatima's mistake is: C. She applied the exponent -2 to "4(-2) instead of only to "(-2).
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someone please tell formula
Answer:
(i) Total cost of the flat is Rs. 540000.
(ii) Expenditure incurred on labour is Rs. 150000
Step-by-step explanation:
According to the question, cement cost is Rs. 112500, which represents 75° in the pie chart.
(i) The total cost of the flat is represented by the total 360° in the pie chart.
∴ Using unitary method
75° represents Rs. 112500
⇒ 360° represents = [tex]\frac{112500}{75}[/tex] × 360
= Rs. 540000
∴ Total cost of flat = Rs. 540000
(ii) Similarly, to calculate the cost of labour, represented by 100° in the pie chart, we can use the unitary method:
75° represents Rs. 112500
⇒ 100° represents = [tex]\frac{112500}{75}[/tex] × 100
= Rs. 150000
∴ Cost of labour = Rs. 150000
In the diagram below, if AB = 25, AC = 15, and BD = 5, then find the length of DC.
B
Select one:
a. 15
b. 5
c. 25
d. 3
D
PC
The length of DC based on the information given about the triangle is 19.37.
How to calculate the length?Based on the given information, it should be noted that:
AB² = AD² + BD²
25² = AD² + 5²
625 = AD² + 25
AD² = 625 - 25
AD² = 600
AD = √600
AD = 24.5
DC² = AD² + - AB² (Pythagoras theorem)
DC² = 24.5² + 15²
DC² = 375.25
DC = 19.37
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To factor the expression 3x2 – 9x, Caleb found the GCF as shown.
List the factors:
3x2 = 3 • x • x
9x = 3 • 3 • x
GCF = 3 • 3 • x • x = 9x2
What is Caleb’s error?
Answer:
Caleb’s error was :
instead of selecting the least exponent ,Caleb took the highest exponent.
Step-by-step explanation:
3x² = 3 • x • x
(in this factorization the exponent of 3 is 1 and the exponent of x is 2)
9x = 3 • 3 • x
(in this factorization the exponent of 3 is 2 and the exponent of x is 1)
• The common factors of 3x² and 9x are 3 and x
In order to determine the GCF ,we have to Compare the exponents of the common factors then take the numbers which have the least exponent value.
• in the factorization of 3x² the exponent of 3 is 1
and in the factorization of 9x the exponent of 3 is 2
The least exponent is 1 Then we take it.
• in the factorization of 3x² the exponent of x is 2
and in the factorization of 9x the exponent of x is 1
The least exponent is 1 Then we take it.
Conclusion:
GCF(3x² , 9x) = 3¹ × x¹ = 3x
Franklin had 20 minutes to do a three-problem quiz. He spent 10 9/10 minutes on question A and 5 3/5 minutes on question B. How much time did he have left for question C?
Answer:
5
Step-by-step explanation:
10+5=15
20-15=5 . that is the solution
You purchase a dishwasher for $1249.99 plus 4% sales tax.
The appliance store offers an installment loan that allows you to pay for
the dishwasher by making 12 equal monthly payments of $124.58. What
is the cost of credit, in dollars, for this loan? Round your answer to the
nearest cent.
$194.97 is the cost of the credit loan.
What is percentage?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.
The total cost of the dishwasher with sales tax can be found by multiplying the price by 1.04:
$1249.99 × 1.04 = $1299.99
The cost of credit is the total amount paid through the installment loan minus the cost of the dishwasher:
12 × $124.58 = $1494.96
$1494.96 - $1299.99 = $194.97
Therefore, the cost of credit for this loan is $194.97.
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Select the correct answer from each drop-down menu.
Consider triangles ABC and QPRshown.
Triangle ABC is
triangles are
B
triangle QPR. Since the transformations
Reset
Next
, the
Triangle ABC and triangle QPR are similar triangle based on the side-angle-side similarity theorem.
What are similar triangles?Two triangles are said to be similar if they have the same shape and the ratio of their corresponding sides are in the same proportion. Also, corresponding angles are congruent.
Triangle ABC and triangle QPR are similar triangle based on the side-angle-side similarity theorem.
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Answer:
down below
Step-by-step explanation:
Hope this helps =)
The height of AXYZ is the
distance from point Y to XZ
Find the area of the
triangle. Round your answer
to the nearest tenth, if
necessary. y(4,5) a(2,1) x(0,2) z(4,0)
pls help quick:(
Answer:
areas of AXYZ=10 square units1
Answer:
10 units squared
Step-by-step explanation:
Area of a triangle = 1/2 × base × height
Use the distance between two points formula to find the measure of the height and base of ΔXYZ.
Distance between two points
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]\textsf{where }(x_1,y_1) \textsf{ and }(x_2,y_2)\:\textsf{are the two points}[/tex]
Height of Triangle
Define the points:
[tex]\textsf{Let }(x_1,y_1)=(2,1)[/tex][tex]\textsf{Let }(x_2,y_2)=(4,5)[/tex]Substitute the points into the distance formula to find the height of the triangle:
[tex]\begin{aligned}\implies \sf height & =\sqrt{(4-2)^2+(5-1)^2}\\& = \sqrt{2^2+4^2}\\& = \sqrt{20}\end{aligned}[/tex]
Base of Triangle
Define the points:
[tex]\textsf{Let }(x_1,y_1)=(0,2)[/tex][tex]\textsf{Let }(x_2,y_2)=(4,0)[/tex]Substitute the points into the distance formula to find the height of the triangle:
[tex]\begin{aligned}\implies \sf base & =\sqrt{(4-0)^2+(0-2)^2}\\& = \sqrt{4^2+(-2)^2}\\& = \sqrt{20}\end{aligned}[/tex]
Area of Triangle
[tex]\begin{aligned}\implies \sf Area & = \dfrac{1}{2} \times \sf base \times height\\& = \dfrac{1}{2}\sqrt{20}\sqrt{20}\\& = \dfrac{1}{2}(20)\\& = 10 \sf \:\:units^2 \end{aligned}[/tex]
There are some frogs and some lily pads at a pond. If lily pads with frogs on them have two frogs each, then there are 3 lily pads with no frogs on it. If each lily pad has exactly one frog on it, then there are 3 frogs with no lily pad. How many frogs are at the pond
Frogs are at the pond = 12.
Given,
There are some frogs and some lily pads at a pond. If lily pads with frogs on them have two frogs each, then there are 3 lily pads with no frogs on them. If each lily pad has exactly one frog on it, then there are 3 frogs with no lily pad.
= 2( n-3) = n+3
= 2n -6 = n+3
=> n = 9
9 pads, 12 frogs.
Hence, Frogs are at the pond = 12.
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If,0 < 3x - 2 < 1, what is one possible value for x?
Answer:
one possible solution is 5/6
Step-by-step explanation:
Solving for x
0 < 3x - 2 < 1
Add 2 to each side
0+2 < 3x - 2+2 < 1+2
2 < 3x<3
Divide each side by 3
2/3 < 3x/3 < 3/3
2/3 < x < 1
X must be between 2/3 and 1
Getting a common denominator
4/6 < x < 6/6
So x can be 5/6
3 The ratio of hotdogs to hamburgers at the cookout 3:6. What is the difference between the number of hotdogs and hamburgers if there are 120 hamburgers?
The difference between the number of hotdogs and hamburgers is 60
How to determine the difference?The ratio is given as:
Hotdog : Hamburger = 3 : 6
When the total hamburger is 120.
We have:
Hotdog : 120 =3 : 6
Multiply 3 : 6 by 20
Hotdog : 120 =3 * 20 : 6 * 20
Evaluate
Hotdog : 120 = 60 : 120
By comparison, we have
Hotdog = 60
So, the difference is
Difference = 120 - 60
Evaluate
Difference = 60
Hence, the difference is 60
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I'm renting to own a house for $80,000. I paid down $6,000.00, leaving a balance of $74,000. For the past eight years I’ve paid 768.57 a month. How much have I paid from May 2014 to July 2022?
The total amount of money I have paid from May 2014 to July 2022 is $75,319.86.
How much I have paid?The first step is to determine the total number of months from May 2014 to July 2022.
12 months = 1 year
May 2022 - May 2014 = 8 years x 12 = 96 months
Number of months from may 2022 to july 2022 = 2 months
Total number of months = 96 + 2 = 98 months
Total amount paid = 98 x 768.57 = $75,319.86
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A table representing the function f(x) = 2(three-halves) Superscript x is shown below.
The truth of the given function that we have here is The function increases at a constant multiplicative rate.
How to solve for the multiplicative rate of the constantThe table is given as
x 0 1 2 3
f(x) 2 3 4.5 6.75
We have x ranging from 0 to 3 while y ranges from 2 to 6.75.
The observations that we can make about the y values is that they produce the next value at the same rate of multiplication.
This is shown here
2 x 1.5 = 3
3 x 1.5 = 4.5
4.5 x 1.5 = 6.75
Hence we can conclude that it increases at a constant multiplicative rate of 1.5.
Complete questionA table representing the function f(x) = 2(three-halves) Superscript x is shown below. A 2-column table has 4 rows. The first column is labeled x with entries (0, 1, 2, 3). The second column is labeled f (x) with entries 2, 3, 4.5, 6.75. What is true of the given function? The function increases at a constant additive rate. The function increases at a constant multiplicative rate. The function has an initial value of 0. As each x value increases by 1, the y values increase by 1.
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A rectangle has a height of 7x^27x 2 7, x, squared and a width of 3x^2+8x+73x 2 +8x+73, x, squared, plus, 8, x, plus, 7. Express the area of the entire rectangle.
The expression 21x⁴ + 56x³ + 49x² represents the area of the entire rectangle.
What is the area of the rectangle?It is defined as the area occupied by the rectangle in two-dimensional planner geometry.
The area of a rectangle can be calculated using the following formula:
Rectangle area = length x width
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
The area of the rectangle = length x width
= (3x² + 8x + 7)(7x²)
[tex]\rm =7x^2\cdot \:3x^2+7x^2\cdot \:8x+7x^2\cdot \:7[/tex]
= 21x⁴ + 56x³ + 49x²
Thus, the expression 21x⁴ + 56x³ + 49x² represents the area of the entire rectangle.
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find the value of x
Answer:
70
Step-by-step explanation:
In physics, a deceleration (the slowing down of an object in motion) is considered a negative acceleration (in other words, the opposite of speeding up). If you crash a small toy car into a wall, and the acceleration of the car is -3 m/s2, what would be the total acceleration you would have applied to the car, if you repeated the crash eleven times?
Using proportions, the total acceleration you would have applied to the car would be of -33 m/s².
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
For one crash, the acceleration is of -3 m/s². Hence, for 11 crashes, the total acceleration would be of:
a = -3 x 11 = -33 m/s².
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What standard form polynomial expression represents the area of the triangle area = 1/2 bh
helpp quick pleaseee
What is the probability of choosing a triangle?
Answer:
52.9%
Step-by-step explanation:
There are 17 shapes total. Nine of those shapes are triangles. Therefore the probability of choosing a triangle is 9/17.
To find that as a percentage type 9 divided by 17 into the calculator. The answer to that is 0.5294117647058824. To turn a decimal into a percentage move the decimal point two places over making the percentage: 52.94117647058824%.
Since the yellow text states to round the answer to the nearest hundredth of the percent the answer is 52.9%.
52.94%
Step-by-step explanation:
there are 17 objects and you divide the 9 triangles by 17 and get .529411765. Which is 52.94 percent.
The equivalent expression of 2a + 8 is ________.
Answer:
8+2aStep-by-step explanation:
Switching the order of the terms comes out as an equivalent expression.
Whatever A is, if we multiply it by 8 and add 2, it will be equivalent to the sum of the same number times multiplied by 8 and 2.
I hope that helps!
Answer:
2(a +4)
Step-by-step explanation:
Distributive property: a*b + a * c = a*(b+c)
Factorize 2 & 8 and find GCF of 2 & 8
2 = 2
8 = 2* 2*2
GCF = 2
2a + 8 = 2a + 2*4
= 2(a + 4)