Step-by-step explanation:
Part A:
4x² - 7x - 15
a, b, c = 4, -7, -15
ac = -60
factors that add up to -7 and multiply to -60 are (-12, 5)
rewrite equation
(4x² - 12x) + (5x - 15)
factor out GCF from both groups
4x(x - 3) + 5(x - 3)
(4x+5)(x-3)
Part B:
Using the factored form from the previous part we can set both factors equal to 0 to solve for x.
4x+5 = 0
4x = -5
x = -5/4
x-3 = 0
x = 3
the two x-intercepts are -5/4 and 3
Part C:
Since the leading coefficient is positive, the right side of the function will be going up or to positive infinity as x goes towards positive infinity. Since the degree is even both sides go in the same direction so on the left side it also goes towards positive infinity as x goes towards negative infinity.
Using the following image, solve for JI.
J
2x + 28
x + 22
5
H
In the given image, the length of JI is 6
Solving linear equationsFrom the question, we are to solve for JI
From the given image, we can write that
JI + IH = JH
Then,
2x + 28 + 5 = x + 22
Solving for x
2x + 28 + 5 = x + 22
First, collect like terms
2x - x = 22 - 28 - 5
Simplifying
x = -11
But,
JI = 2x + 28
∴ JI = 2(-11) + 28
JI = -22 + 28
JI = 6
Hence, the length of JI is 6
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The function f(x) = x² has been translated 9 units up and 4 units to the right to form the function g(x). Which represents
g(x)?
O g(x) = (x + 9)² + 4
O g(x) = (x + 9)²-4
Og(x)=(x-4)² +9
Og(x) = (x+4)² +9
Answer:
g(x) = (x-4)² +9
Step-by-step explanation:
If f(x) is moved up 9 units, it becomes x² + 9, as only the 'y' value is changed by 9. Then, if it is moved 4 units to the right, it becomes (x+4)² +9, as only the 'x' value is changed by -4.
The function g(x) that represents the translation of f(x) = x² with 9 units up and 4 units to the right is,
⇒ g(x) = (x-4)² + 9.
What is Translation?A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.
Now, To translate the function f(x) = x² with 9 units up and 4 units to the right, we need to use the following formula:
⇒ g(x) = f (x - 4) + 9
Substituting f(x) with its equivalent form:
⇒ g(x) = ( x - 4 )² + 9
Therefore, The function g(x) that represents the translation of f(x) = x² with 9 units up and 4 units to the right is,
⇒ g(x) = (x-4)² + 9.
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A stockbroker has money in three accounts. The interest rates on the three accounts are 10 % ,11 %, and 12 %. If
she has twice as much money invested at 11% as she does in 10 %, three times as much at 12% as she has at be
10%, and the total interest for the year is $340, how much is invested at each rate?
City worker drain a community pool that contains 403,920 gallons of water. The pump they use removes water at a rate of 40 cubic feet per minute. One cubic foot of water contains 7.48 gallons how long in hours will it take to remove all the water from the pool
Answer:
22.5 hours
Step-by-step explanation:
One cubic foot of water contains 7.48 gallons, so 40 cubic feet of water would equal 7.48 × 40, or 299.2 gallons. So the pumping rate is 299.2 gallons per minute. Multiplying 299.2 by 60, we have
299.2 × 60, or 17952 gallons per hour. Finally, divide 403,920 by 17,952 to find the number of hours to remove all the water: 403,920 ÷ 17,952 = 22.5 hours
i do not now these questions
Using proportions, it is found that:
a) 5 people are needed.
b) Yes.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
Item a:
Each person works for 32 hours, and 150 hours are needed, hence the number of people needed is given by:
150/32 = 4.6875.
However, an integer number is needed, hence 5 people are needed.
Item b:
With 30 hours, the number of people needed is given by:
150/30 = 5.
Which remains the same.
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Help please answer this point an brainlist
Jamaal is allowed to walk no farther than three blocks in either direction from his house. If his house is located on the 57th block of the town, which absolute value equation can be used to determine the farthest block to which Jamaal is allowed to walk?
|x – 57| = 0
|57 – 3| = x
|3 – 57| = x
|x – 57| = 3
Answer:
| x - 57 | = 3
Step-by-step explanation:
Since the house is on the 57th block, Jamaal must stop walking on the 54th block or the 60th block.
12. Last month, a store sold a total of 182 pairs of jeans and shorts. The
number of shorts sold was 28 fewer than twice the number of jeans sold.
How many pairs of jeans were sold?
C. 105
A 51
D. 112
B. 70
Answer:
B. 70
Explanation:
A total of 182 pairs of jeans and shorts were sold and the number of shorts sold was 28 fewer than twice the number of jeans. This can be expressed with j being the number of jeans as:
j2 - 28 = number of shorts
As the number of shorts is 28 lower than twice the number of jeans, this means it can not be C or D, as these numbers are larger than 182 when doubled. The process of elimination can be done with the remaining using our equation.
51(2) - 28 = 102 - 28 = 74
70(2) - 28 = 140 - 28 = 112
Now that we have the number of shorts sold by using the equation, we can add them with what number was used as their number of jeans.
74 + 51 = 125
112 + 70 = 182
So the number of jeans sold is B. 70.
18 A student has 273 matchsticks with which to make a pattern of nested triangles. Fig. 18.9 shows the first three triangles. Fig. 18.9 If all the matchsticks are used, how many matchsticks will each side of the biggest triangle contain? 18 A student has 273 matchsticks with which to make a pattern of nested triangles . Fig . 18.9 shows the first three triangles . Fig . 18.9 If all the matchsticks are used , how many matchsticks will each side of the biggest triangle contain ?
The number of matchsticks that each side of the biggest triangle contains is; 137 matchsticks
How to find the biggest side of a triangle?We know that for a diagram to be a triangle, then two smallest sides must not be greater than the third side.
Now, if there are 273 matchsticks, then the greatest side of the triangle must not be less than 273/2 = 136.5 ≈ 137
Thus, the largest side will have at least 137 matchsticks
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3,-1, √5, 13, -11 arrange in ascending order
Answer:
The answer will be
= -11, -1, √5, 3, 13
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Unit 8:Right triangles & Trigonometry
Answer:
[tex]24\sqrt{5}[/tex]
Step-by-step explanation:
So for this problem you can use the law of sines which states
[tex]\frac{a}{sin A} = \frac{b}{sin B}\\[/tex]
Since the angle is a right triangle we can find the hypotenuse by plugging in the values.
[tex]\frac{4\sqrt{15}}{sin 60} = \frac{hypotenuse}{sin 90}\\\\\frac{4\sqrt{15}}{sin 60} = hypotenuse\\hypotenuse = \frac{4\sqrt{15}}{\frac{\sqrt{3}}{2}} = \frac{8\sqrt{15}}{\sqrt{3}}\\hypotenuse = \frac{8\sqrt{45}}{3} = \frac{24\sqrt{5}}{3}\\[/tex]
we now just multiply that side by 3since all the sides should be equal since all the angles are equal and we get the length of 24sqrt(5)
Ethan works in a department store selling clothing. He makes a guaranteed salary of $500 per week, but is paid a commision on top of his base salary equal to 25% of his total sales for the week. How much would Ethan make in a week in which he made $1250 in sales? How much would Ethan make in a week if he made xx dollars in sales?
Total earnings when selling $1250:
Total earnings when selling $x:
need answer fast
The total amount of money Ethan made in a week including commission is $812.5
Total incomeTotal sales for the week = $1250Base salary = $500Percentage commission = 25%Amount of commission earned = 25% of $1250
= 25/100 × $1,250
= 0.25 × 1250
= $312.5
Total earnings = Base salary + Amount of commission earned
= $500 + $312.5
= $812.5
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write an equation in slope intercept form of the line with the given characteristics: a) passes through (-3,0) and (-5,-3)
The equation of the line in slope-intercept form is [tex]\bf{y= \frac{3}{2} x + \frac{9}{4}} [/tex].
What is slope-intercept form?y=mx +c, where m is the slope and c is the y-interceptStepsFind the slopeSubstitute value of the slope into the equationSubstitute a pair of coordinatesSolve for cRewrite equation with value of m and cWorkingThe first step is to calculate the slope of the line.
[tex]\boxed{ slope = \frac{y _{1} - y_2 }{x_1 - x_2} }[/tex]
Slope
[tex] = \frac{ - 3 - 0}{ - 5 -( - 3)} [/tex]
[tex] = \frac{ - 3}{ - 5 + 3} [/tex]
[tex] = \frac{ - 3}{ - 2} [/tex]
[tex] = \frac{3}{2} [/tex]
Substitute the value of m into y= mx +c:
[tex]y = \frac{3}{2} x + c[/tex]
Next, substitute a pair of coordinates that the line passes through. Here, I will substitute (-3, 0) into the equation.
When x= -3, y= 0,
[tex]0 = \frac{3}{2} ( - 3) + c[/tex]
Find the value of c:
[tex]0 = - \frac{9}{2} + c[/tex]
[tex]c = \frac{9}{2} [/tex]
Substitute the value of c into the equation:
Thus, the equation of the line is [tex]y = \frac{3}{2} x + \frac{9}{2} [/tex].
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2^x - 3^x = √(6^x - 9^x)
[tex]2^x-3^x=\sqrt{6^x-9^x}\\\\D:6^x-9^x\geq0 \wedge 2^x-3^x\geq0\\D: 6^x\geq 9^x \wedge 2^x\geq3^x\\D:x\leq0 \wedge x\leq 0\qquad(\text{if }a < b \text{ then } a^x < b^x\text{ for } x > 0 \text{ and } a^x > b^x \text{ for } x < 0 )\\D:x\leq 0\\\\(2^x-3^x)^2=6^x-9^x\\(2^x-3^x)^2=3^x(2^x-3^x)\\\\\text{We divide both sides by } 2^x-3^x \text{ assuming }2^x-3^x\not=0\Leftrightarrow x\not=0.\\\\2^x-3^x=3^x\\2^x=2\cdot3^x\\\ln 2^x=\ln (2\cdot3^x )\\x\ln 2=\ln 2+\ln 3^x\\x\ln 2=\ln 2+x\ln 3[/tex]
[tex]x\ln 2-x\ln 3=\ln 2\\x(\ln 2-\ln 3)=\ln 2\\x=\dfrac{\ln 2}{\ln 2-\ln 3}=-\dfrac{\ln 2}{\ln 3-\ln 2}=-\dfrac{\ln 2}{\ln \frac{3}{2}}\approx-1.7[/tex]
For [tex]x=0[/tex], our initial equation is obviously true.
Therefore [tex]x\in\left\{-\dfrac{\ln 2}{\ln \frac{3}{2}},0\right\}[/tex].
Answer to the miscellaneous equation, is x=0 and x=-1.71
Miscellaneous equation are the equations which are not polynomial
The question can be solved by:
Factorising Splitting the terms to find the required solution
Completing the squares, etc
2ˣ - 3ˣ = √(6ˣ - 9ˣ)
Squaring both sides,
2²ˣ+3²ˣ -2.2ˣ.3ˣ=2ˣ.3ˣ - 3²ˣ
2²ˣ+2.3²ˣ -3.2ˣ.3ˣ=0
Factorising the terms,
2ˣ(2ˣ-3ˣ) -2.3ˣ(2ˣ-3ˣ)=0
(2ˣ-3ˣ)(2ˣ-2.3ˣ)=0
Equating the braces to zero,
Either,
2ˣ=3ˣ
x=0
or
2ˣ=2.3ˣ
Taking log on both sides
xln2=ln2+xln3
x=ln2/(ln2-ln3)
=-1.71
Therefore, x=0 and x=-1.71 is the only solution
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(Giving 45 points, and brainly if correct! Please hurry!)
Point A is on point −6 and Point B is on point 0. Let's use the Ruler Postulate to find the length of AB¯.
AB=|a−b|
AB=|−6−0|
AB=|−6|
AB=6
The length of AB¯¯ is 6. We can also write this as AB=6 or mAB¯¯=6.
Find the Length of CD¯¯
Now, let's find the length of CD¯¯. Point C is on point 4 and Point D is on point 8.
CD=|c−d|
CD=|4−8|
CD=|−4|
CD=4
The length of CD¯¯ is 4. We can also write this as CD=4 or mCD¯¯=4
Your Turn
1. What is the length of BC¯¯?
2. What is the length of AC¯¯?
3. What is the length of AD¯¯?
The length of BC , AC and AD is 4 , 10 , 14.
What is Length ?Length is the distance between two points , It is measured in cm , m , km etc.
It is asked to calculate the length of BC , AC , AD
For BC
Point B is on point 0 and Point C is on point 4.
BC=|b−c|
BC=|0−4|
BC=4
For AC
Point A is on point -6 and Point C is on point 4.
AC=|a−c|
AC=|-6−4|
AC= 10
For AD
For AC
Point A is on point -6 and Point D is on point 8.
AD=|a−c|
AD=|-6−8|
AD= 14
Therefore the length of BC , AC and AD is 4 , 10 , 14.
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Area of a triangular prism
Answer:
if you mean the formula it is (1/2) · b · (6 · h + sqrt(3) · b)
Step-by-step explanation:
copy machine can make 250 copies in 4 minutes. Represent
rate of change in copies per minute.
Answer:
62.5 copies per minute
Step-by-step explanation:
Note that the word "per" means divide. So, a rate of change in "copies per minute", means a number of copies divided by a number of minutes
If the copy machine can make 250 copies in 4 minutes, then the number of copies is 250 copies, and the number of minutes is 4 minutes:
[tex]\text{rate of change in copies per minute}=\dfrac{\text{number of copies}}{\text{number of minutes}}[/tex]
[tex]\text{rate of change in copies per minute}=\dfrac{\text{250 copies}}{\text{4 minutes}}[/tex]
[tex]\text{rate of change in copies per minute}=62.5\dfrac{\text{copies}}{\text{minute}}[/tex]
If 24 marbles have a mass of 60g, what would the mass of 60 marbles be?
If 24 marbles have a mass of 60 g, then each marble has a mass of [tex]60/24=2.5 \text{ g}[/tex].
So, 60 marbles have a mass of 60(2.5)=150 g
Answer:
150 g
Step-by-step explanation:
24 marbles = 60 g
1 marble = 60÷24 = 2.5 g
60 marbles = 2.5 × 60 = 150 g
Hope this helped and have a good day
how many eggs are in 2 3/4 dozen?
please answer this one...i need it today
Step-by-step explanation:
please mark me as brainlest
Answer:
33 eggs
Step-by-step explanation:
1 Dozen = 12 units
2 dozen = 2*12 = 24 units
3/4 dozen = 12*3/4 = 36/4 = 9 units
2 3/4 = 2 + 3/4 = 24 + 9 = 33 units
The tables represent the functions f(x) and g(x). f(x) -5 -2 -1 0 1 2 -3 -1 1 3 w 5 X -3 -2 -1 0 1 2 g(x) -13 -9 -5 -1 3 7 Which input value produces the same output value for the two functions? x = -3 O x = -1 x = 0 Ox=1 The tables represent the functions f ( x ) and g ( x ) . f ( x ) -5 -2 -1 0 1 2 -3 -1 1 3 w 5 X -3 -2 -1 0 1 2 g ( x ) -13 -9 -5 -1 3 7 Which input value produces the same output value for the two functions ? x = -3 O x = -1 x = 0 Ox = 1
Answer:
x=1
Step-by-step explanation:
There are two functions (f & g), each of which have a table of inputs and outputs. The same list of inputs is given to both functions, but the outputs are different.
Imagine that you asked your Father 6 questions, (weirdly instead of numbered 1 through 6, numbered -3 through 2), and that he gave you a list of answers.
Imagine that you asked your Grandfather the same 6 questions, and you got a list of answers from him.
On which question did they give the same answer?
It was on question number "1", (really the 5th question, but as we've numbered things from -3 to 2, it's question "1").
Since the "questions" were the input, "x", x=1.
he height of a rocket a given number of seconds after it is released is modeled by h (t) = negative 16 t squared + 32 t + 10. What does t represent?
the number of seconds after the rocket is released
the initial height of the rocket
the initial velocity of the rocket
the height of the rocket after t seconds
Answer: the number of seconds after the rocket is released
MATHHH. Probability section!!! HELP!
please give the right answer.
Answer:
answer = 1/4 < 7/25
Step-by-step explanation:
the theoretical probability is that because the spinner has 4 equal sized sections, it should land on each 25 times, 25/100 is 1/4
28/100 is the experimental probability of landing on H, so that can be simplified to 7/25 as both numbers can be divisible by 4.
Hope this helps:)
A building 190 feet tall casts a 90 foot long shadow. if a person stands at the end of the shadow and looks up to the top of the building, what is the angle of the person's eyes to the top of the building
Answer:
About 64.65 degrees
Step-by-step explanation:
[tex] \tan(x) = \frac{190}{90} [/tex]
[tex]x = { \tan}^{ - 1} \frac{190}{90} = 64.65[/tex]
Make sure your calculator is in degree mode.
For the graph below, what should the domain be so that the function is at least 300? (1 point) graph of y equals minus 2 times the square of x plus 50 times x plus 300 a x ≥ 0 b −5 ≤ x ≤ 30 c 0 ≤ x ≤ 25 d all real numbers
The function is a quadratic function, then the domain will be all real numbers. Then the correct option is D.
What are domain and range?The domain means all the possible values of x and the range means all the possible values of y.
The function is given below.
y = -2x² + 50x + 300
Then the function is a quadratic function, then the domain will be all real numbers.
Then the correct option is D.
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SA = 2πr² + 2πrh Use 3.14 for.- Find the surface area of a cylinder with a height of 6 feet and base radius of 3 feet. SA = 2πr² + 2πrh Use 3.14 for. Find the surface area of a cylinder with a height of 6 feet and base radius of 3 feet .
Answer:
SA = 169.56 ft²
Step-by-step explanation:
Just replace the variables r and h
by their values in the expression :
SA = 2πr² + 2πrh
= 2×(3.14)×3² + 2×(3.14)×3×6
= 169.56
While traveling to Europe, Phelan exchanged 250 US dollars for euros. He spent 150 euros on his trip. After returning to the United States he converts his money back to US dollars. How much of the original 250 US dollars does Phelan now have? Round to the nearest cent.
1 European euro = 1.3687 US dollars
Answer:
44.70 US dollars
Step-by-step explanation:
Begin by converting the Euros to US dollars by dividing 250 by 1.3687
250/1.3687=182.655
Then subtract 150
182.655-150=32.655
Multiply by 1.3687 to convert back to US dollars
32.655x1.3687=44.70
Practice A
Get a coin and toss it five times. Record the outcomes on the table below. Then, answer the questions that follow.
Head
Tail
1st toss
2nd toss
3rd toss
4th toss
5th toss
Total
Answer:
You can just flip a coin five times either with a real one (heads being a face or a picture and tails being the other side) or online, then put a tick on either heads or tails depending on what you got on that toss. Then just put how many times you got heads in the first question.
Hope this helps I guess.
Please help! I'm not quite understanding this.
Answer:
d.) 21
Explanation:
Rules:
-|a| = -a|-a| = ax = |a| then x = ±aSolve:
[tex]\rightarrow \sf \dfrac{4|a|}{2} + |a-3|[/tex]
[insert a = -6]
[tex]\sf\rightarrow \dfrac{4|-6|}{2} + |-6-3|[/tex]
[simplify the following]
[tex]\sf\rightarrow \dfrac{4(6)}{2} + 9[/tex]
[tex]\sf\rightarrow 12 + 9[/tex]
[tex]\sf\rightarrow 21[/tex]
7 is what percent of 154?
Answer: 10.78
Step-by-step explanation:
Determine whether each set of ordered pairs shown below is from a geometric sequence or from an arithmetic sequence.
{(-3, 7.5) , (-2, 10) , (-1, 12.5)}
Write the equation of the graph for the set of ordered pairs.
{(1, 150) , (2, 112.5) , (3, 84.375)}
Write the equation of the graph for the set of ordered pairs.
