Answers
1) The roots of the equation are x = -7/3 and 5/2
And the correct options are option (A) and option (B)
2) Amber needs to draw the straight line y = 4x. And the point of intersection of both the graphs (y = 3x² and y = 4x)would give the solutions to given equation i.e., x = 1.33 and x = 0
Consider the first question,
We need to find the roots of given equation (3x + 7)(2x - 5) = 0
From above equation we can say that either 3x + 7 = 0 or 2x - 5 = 0
If 3x + 7 = 0
3x = -7
x = -7/3
And is 2x - 5 =0
2x = 5
x = 5/2
So, the roots of the equation are x = -7/3 and 5/2
Hence, the correct options are option (A) -7/3 and option (B) 5/2
Consider 2nd question,
Amber is trying to solve 3x² - 4x = 0 using graphical method.
She drew the graph of y = 3x² which is parabolic in nature.
we need to draw the straight line to solve the given equation.
If we draw the line y = 4x and then subtract it from y = 3x², then we get the original equation 3x² - 4x = 0
So, we need to draw the straight line y = 4x
Therefore, Amber needs to draw the line y = 4x the point of intersection of both the graphs would be the solutions to given equation.
i.e., x = 1.33 and x = 0
The graph is as shown below.
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Related Questions
the formula t=((sqrt(h))/(4)) represents the time t in seconds that is takes an object to fall from a height of h feet , if a rock falls from 125 feet , estimate how long it will take the rock to hit the ground , estimate the square root to the nearest integer .
Answers
The time taken by the rock to hit the ground is 3 seconds.
It is given in the question that:-
[tex]t=\frac{\sqrt{h} }{4}[/tex]
Where,
t represents the time (in seconds) taken by the object to reach the ground, and
h represents the height from which the object is falling
We have to find the time taken by a rock to hit the ground after falling from a height of 125 feet.
Using the formula given in the question, we can write,
[tex]t=\frac{\sqrt{125} }{4}=\frac{5\sqrt{5} }{4}[/tex]
We know that,
[tex]\sqrt{5}[/tex] ≈ 2.23
Hence, we can write,
t ≈ (5*2.23)/4 ≈ 2.7875 ≈ 3 seconds (estimated to nearest integer)
Hence, it takes around 3 seconds for the rock to hit the ground after falling from a height of 125 feet.
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8 + 3x = 1 + 7.9x can someone help me out?
Answers
GROUP LIKE TERMS TOGETHER.
[tex]3x - 1.79x = 1 - 8 \\ 1.21x = - 7 \\ \frac{1.21x}{1.21} = \frac{ - 7}{1.21 \\ } \\ x = 5.7851239669[/tex]
Answer:
x=[tex]\frac{10}{7}[/tex]
Step-by-step explanation:
8 + 3x = 1 + 7.9x
1. multiply everything by 10 so there is no longer a decimal in the equation
80+30x=10+79x
2. get the x on one side so we -10 and 30x from both side
70=49x
3. divide by 49 on each side as we want to find the value of x
[tex]\frac{70}{49}[/tex]=x
4. the fraction can be simplified to
[tex]\frac{10}{7}[/tex]=x
4. the final answer is
[tex]\frac{10}{7}[/tex]=x
HELP PELASE
Jerry is planning a 500-mile trip and estimates it will take 10 hours. Approximately how fast will he be traveling?
If it helps i have the image here :]
Answers
Answer:
50miles an hour
Step-by-step explanation:
50miles an hour because R = d/t so 500 / 10 is 50
so rate is 50/hour
Which of the following is an equivalent expression of 18x2 +14x + 7?
7(18x2 + 14x)
14x + 18x2 + 7
32x3 + 7
18x2(14x + 7)
Answers
An expression which is equivalent to the given expression 18x² +14x + 7 is given by 14x + 18x² + 7.
As given in the question,
Given expression is :
18x² +14x + 7
Simplify all the optional expression to check which one is equivalent to given expression:
a. 7(18x² + 14x)
= 126x² + 98x
Not equivalent.
b. 14x + 18x²+ 7
Rearrange it
18x²+14x + 7 .
Equivalent.
c. 32x³ + 7
Degree is 3.
Not equivalent.
d. 18x²(14x + 7)
= 252x³ +126x²
Not equivalent.
Therefore, an equivalent expression of 18x²+14x + 7 is 14x + 18x²+ 7.
The complete question is:
Which of the following is an equivalent expression of 18x²+14x + 7?
7(18x² + 14x)
14x + 18x²+ 7
32x³ + 7
18x²(14x + 7)
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Geometry
In the diagram, ZJKM is a straight angle
Intro
K
M
Which statements about the diagram are true? Check
all that apply.
Dk is an angle bisector.
OLKQ is bisected.
Dm/JKL=45"
Om MKQ+m/PKQ = m/PKM
OPK is an angle bisector.
OZJKL
Answers
The statements that are true are:
3) m∠JKL = 45°
4) m∠MKQ + m∠PKQ = m∠PKM
5) line PK is an angle bisector
1) This statement says that KQ is an angle bisector. This is false because the line KQ does not pass through the diagonal vertex of the right angled symbol at point K.
2) Second statement says that ∠LKQ is bisected. This statement is false because PK is just a perpendicular line to JKM that divides it into 2 equal parts and not a bisector of ∠LKQ
3) The third statement states that m∠JKL = 45°. This statement is true because from the image it is clear that the line KL divides m∠PKJ into two equal parts.
4) Fourth statement says that m∠MKQ + m∠PKQ = m∠PKM. This statement is true. Now, although KQ doesn't bisect m∠PKM into 2 equal parts, nevertheless it divides it into 2 angles namely m∠MKQ and m∠PKQ. This means the sum of m∠MKQ + m∠PKQ must yield m∠PKM.
5) The fifth statement says that the line PK is an angle bisector. This statement is true because JKM is a straight angle. Thus as PK is perpendicular to it, it has bisected it into two equal parts.
6) The fifth statement says that ∠JKL ≅ ∠QKM. This statement is false because ∠JKL is a bisected angle which is 45° whereas, ∠QKM is not a bisected angle and thus not equal to 45°.
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Help pls!! Will give brainlyist
Answers
Answer: The correct answer is B.
Step-by-step explanation:
To evaluate this expression you must divide x-1 though the expression or factor out the upper half of the equation and cancel out what is necessary.
The division method: attached below :)
Since 2 is further left on a number line than 5, 2 < 5. Let’s consider the opposites of these numbers.
Identify the opposite of 2 on the number line.
Identify the opposite of 5 on the number line.
Using your results, which statement is true?
Since –2 is further
.
Answers
what is the square of 77.5?
Answers
A cuboid is of dimensions 60 cm × 54 cm × 30 cm. How many small cubes with side 12 cm can be placed in the given cuboid?
Answers
Answer:
56.25
Step-by-step explanation:
We know that, Volume of the cuboid = l × b × h
= 60 cm × 54 cm × 30 cm
= 97200 cm³
Side of the cube = 12 cm
The volume of the cube = side³
= 12³
= 1728 cm³
Required number of cubes = volume of cuboid/volume of the cube
= 97200 / 1728
= 56.25
Thus, 56.25 cubes can be placed in the given cuboid.
Which ones are paralel? Justify your answer please!!!!!!!!
Answers
Answer: I think that FG and MB are parellel, but I think the way to confirm is to measure with a ruler
Step-by-step explanation:
What is the volume of a cube with edge length 13 cm in cubes
Answers
Which set of ordered pairs does not represent a function?
{(5,7), (4,-2), (-8,8), (4,-9)}
{(6,-2), (-2, -7), (-9,-4), (8,-7)}
{(-6,-7), (0,9), (6,-7), (3, -4)}
{(4,6), (9,-8), (3,2), (-9,-8)}
Answers
the scale of a map is 1:10000000. what is the real distance between two cities if the distance between them is 1.7dm
Answers
Answer:
See below:
Explanation:
1.7 dm = .17 m assuming dm is decimeter
.17m * 10^7 scale = 1.7 x 10^6 m = 1.7 x 10^3 km = 1700 km
Luana states that -x+2--10 is true when
x=12. Is she correct? Jutify your response.
Answers
Answer:
Luana is correct
Step-by-step explanation:
Hello!
According to the question, we are supposed to check whether Luana is right
Oops you made a typo
It's supposed to be -x+2 = --10 not -x+2--10
-x+2 = --10
Add values
When, x = 12
-(+12) + 2 = -10
-12 + 2 = -10
Calculate
-10 = -10
She is correct
When solving
−x+2=−10
Step 1: Subtract 2 from both sides.
−x+2−2=−10−2
−x=−12
Step 2: Divide both sides by -1.
−x/−1 = −12/−1
x=12
So, she's correct
help pls, thank you
Answers
-17 -17
4x = 84
/4 /4
X=21
Both angels are the same
Is the function represented by the table non-linear?
X
6
7
8
9
y
4
2
0
-2
OYes, because it has a constant rate of change.
O Yes, because it does not have a constant rate of change.
O No, because it has a constant rate of change.
O No, because it does not have a constant rate of change.
Answers
if a baseball player has a batting average of 0.330, what is the probability that the player will get the following number of hits in the next four times at bat?
Answers
The player has a 0.293 percent probability of getting the subsequent number of hits in the subsequent four at-bats.
What does probability mean in math?Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or of a proposition being true. The probability of an event is a number between 0 and 1, with 0 approximately denoting impossibility and 1 denoting certainty.
In light of the information provided,
designate X as the random variable indicating the player's hit total during his subsequent four at-bats.
Assume that the player hits or misses on each of the following four at-bats in a random order. Consider it a success if the player gets a hit as well.
The probability of "success" is because of the batting average, which is 0.330.
In this case, x can be thought of as the overall success rate across the four at-bats. Inferring that X has a binomial distribution with p=0.330 as its parameters
n=4 p=0.330
Since p denotes the probability of success, the probability of failure is
q=1-0.330
=670
The probability mass function of x here is
f(x)={(4 0)*(0.330)ˣ (0.670)⁽⁴⁻ˣ⁾
The probability that the player will get exactly 2 hits, that is, is calculated below:
P(2)=F(2)={(4+2)*(0.330)² (0.670)²
=6[0.04888]
=0.29328
Thus, the probability that the player will get exactly 2 hits is 0.239.
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Help please it's true or false
Answers
Answer:true
Step-by-step explanation:
because the first one
Write a two column proof for this:
Answers
Using angle addition postulate when ∠1 ≅ ∠4 it is proved that ∠2 ≅ ∠3.
As given in the question,
Given: ∠1 ≅ ∠4. Prove ∠2 ≅ ∠3.
(Using angle addition postulate)
Statements Reasons
1. ∠1 ≅ ∠4 Given
2. ∠1 = 180 - ∠2 Being supplementary angles (angle addition postulate)
3. ∠4 = 180 - ∠3 Being supplementary angles (angle addition postulate)
4. 180 - ∠2 = 180 - ∠3 Substituting Statements 2 & 3 into Statement 1.
5. ∠2 = ∠3 Simplifying Statement 4 algebraically.
In statement 4, the constants 180 cancel out from either of left hand side (LHS) and right hand side (RHS). Thus the equation gets simplified to Statement 5. It is worthwhile to mention that Supplementary angles or linear pair always sum up to 180° in measure. Additionally linear pair form a straight line together.
Therefore, using angle addition postulate when ∠1 ≅ ∠4 it is proved that ∠2 ≅ ∠3.
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A production process is checked periodically by a quality control inspector. The inspector selects simple random samples of finished products and computes the sample mean product weight. If test results over a long period of time show that of the values are over pounds and are under pounds, what are the mean and the standard deviation for the population of products produced with this process?.
Answers
The mean and the standard deviation for the population of products are 2.0 and 0.3329, respectively.
What is defined as the standard deviation?A standard deviation (or) is a measure of how widely distributed the data is in regards to the mean. A low standard deviation indicates that data is clustered around the mean, whereas a high standard deviation implies that data is more spread out.The mean and standard deviation of the population of products produced by the process are 2.0 and 0.3329, respectively.
Start by determining the population mean which use:
μ = (L + U)/2
Where:
L = 1.9 and U = 2.1
Put the values;
μ = (1.9 + 2.1)/2
μ = 2.0
When p = 5%, the z value from the probability z table is:
z = -1.645
In addition, the z-score is:
z = (x - μ)/(σ/√n)
Put the values;
-1.645 = (1.9 - 2.0)/(σ/√30)
Simplify the equation.
σ = 0.3329
As a result, the mean and standard deviation again for population of products manufactured by the process are 2.0 and 0.3329, respectively.
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The complete question is-
A production process is checked periodically by a quality control inspector. The inspector selects simple random samples of 30 finished products and computes the sample mean product weights x¯. If test results over a long period of time show that 5% of x¯ the values are over 2.1 pounds and 5% are under 1.9 pounds, what are the mean and the standard deviation for the population of products produced with this process?
After 5 years, $8,000 deposited in a savings account with simple interest had earned $3,600 in interest. What was the interest rate?
Answers
Answer:
9%
Step-by-step explanation:
So first we need to find how much interest he got in a single year.
3600 ÷ 5 = 720
Now we find out how much 720 is compared to 8000.
720 ÷ 8000 = 0.09
Then we make that a percentage:
9%
Find X? x+14+x3=78 How can I find X? Please answer. Thanks so much! (This is my older sister's account btw)
Answers
The value of variable x in the equation is 16.
How to find the variable x in the equation?The equation represented as follows:
x + 14 + x³ = 78
The value x is the variable.
A variable is number represented with a letter in an equation.
Therefore,
x + 14 + 3x = 78
subtract 14 from both sides of the equation
x + 3x + 14 - 14 = 78 - 14
x + 3x = 64
Therefore,
4x = 64
divide both sides by 4
4x / 4 = 64 / 4
x = 16
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Find the measures of two supplementary angles if the difference between the
measures of the two angles is 35
Answers
Answer:
107.5 and 72.5
Step-by-step explanation:
find both the number combinations in the number of permutations for 9 objects taken 7 at a time
Answers
Answer
There are 36 combinations and 181440 permutations
Explanation
The number of combinations of n object taking r at a time is given by the formula;
[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]From the question, n = 9 and r = 7, then substitute these values into the formula
[tex]^9C_7=\frac{9!}{7!(9-7)!}=\frac{9!}{7!\text{ }2!}=\frac{9\cdot8\cdot7!}{7!\times2}=\frac{72}{2}=36[/tex]The number of permutations of n object taking r at a time is given by the formula;
[tex]^nP_r=\frac{n!}{(n-r)!}[/tex]Also, n = 9 and r = 7, then substitute these values into the formula to get the number of permutations
[tex]^9P_7=\frac{9!}{(9-7)!}=\frac{9!}{2!}=\frac{9\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2!}{2!}=181440[/tex]Therefore, there are 36 combinations and 181440 permutations
Your answer is
Dante will run at least 33 miles this week. So far, he has run 15 miles. What are the possible numbers of additional miles he will run?
Use t for the number of additional miles he will run.
Write your answer as an inequality solved for t.
Answers
The number of possible additional miles that he needs to run will be 18.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
Dante will run at least 33 miles this week. So far, he has run 15 miles.
Then the number of possible additional miles that he needs to run.
Let t be the number of additional miles he will run. Then the inequality is given as,
15 + y ≤ 33
y ≤ 33 - 15
y ≤ 18
The number of possible additional miles that he needs to run will be 18.
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To construct the angle bisector of ∠ABC, first set the point of the compass on and draw an arc through and
Answers
The construction of the angle bisector of [tex] \angle ABC[/tex], gives the completed statement as follows;
Set the point of the compass on B and draw an arc through arms AB and BCWhat is an angle bisector?An angle bisector is the ray or line, dividing an angle into two congruent angles.
The steps required to construct the angle bisector of [tex] \angle ABC[/tex] is presented as follows;
Place the compass at point B which is the vertex of [tex] \angle ABC[/tex] and draw arcs to intersect the arms or segments BA and BCLabel the point of intersection of the arcs and the arms of the angle [tex] \angle ABC[/tex] as points D and EPlace the compass at point D and draw an arc on the inside of [tex] \angle ABC[/tex] and on the side further from point B than D Repeat the above process by placing the compass at point E and drawing an arc to intersect the arc drawn from point D at point FJoin the points B and F with the straightedge to complete the construction of the angle bisector of [tex] \angle ABC[/tex], which is segment BFThe complete statement is therefore;
To construct the angle bisector of.[tex] \angle ABC [/tex], first set the point of the compass on B and draw an arc through BA and BC
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The fuel tank of a certain airplane can hold up to 200 gallons of fuel. Let W be the total weight of the airplane (in pounds). Let F be the total amount of fuel in
Its tank (in gallons). Suppose that W=5F+4000 gives W as a function of F.
Identify the correct description of the values in both the domain and range of the function. Then, for each, choose the most appropriate set of values.
Set of Values
(Choose one)
Domain:
Range:
Description of Values
Oweight of airplane (in pounds)
Oamount of fuel in airplane's tank (in gallons)
Oweight of airplane (in pounds)
amount of fuel in airplane's tank (in gallons)
(Choose one)
X
28
180
Answers
The correct description of domain and range for the weight of aeroplane are-
Domain - [0 , 200]Range - [4,000 , 5,200]What is meant by the term domain and range?The domain of the a function is the value set that can be plugged into it. This set contains the x values together in function like f. (x). A function's range is the number of values that even the function can take. This is the set of values which the function returns after we enter an x value.For the given question, the values are-
Function W = 5F + 4000
Full amount of fuel = 200 gallons
No amount of fuel = 0 gallons
Domain : amount of fuel = [0 , 200]
Now, calculate for the range.
If F = 0
W = 5F + 4,000
W = 5(0) + 4,000
W = 4,000
If F = 200
W = 6F + 4,000
W = 6(200) + 4,000
W = 5,200
Range of weight = [4,000 , 5,200]
Thus, the value of range for the total weight of the aeroplane is [4,000 , 5,200].
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What are the terms in the expression 5y -x + 7? A. Sy, -X B. 3,-1,7 C. 5y, -x, 7 D. Sy, x, 7
Answers
The two factors means that the two value will equate with zero
A) 2x-6
They can be aslo simplified as :
2x-6=0
2x=6
x=3
Thus they gave only one values and cannot be expressed as the factors of two product
B) 2x+6
In this expression
we can simplify as :
2x+6
2x+6=0
2x=-6
x=-3
Thus , they are also not expressed as the factors of the two product
C) 2(x+6)
In this expression
we can simplify as :
2x+12
2x+12=0
2x=-12
x=-6
Thus , they are also not expressed as the factors of the two product
D) (2+x)÷(6+x)
They can express as fraction
[tex]\begin{gathered} (2+x)\div(6+x)=\frac{(2+x)}{(6+x)} \\ (2+x)\div(6+x)=(2+x)(6+x)^{-1} \end{gathered}[/tex]Thus, They express as the product of the tewo factors
Answer : D) (2+x)÷(6+x)
Linear equation where m=-4 and passes through (5,9)
Answers
The linear equation where m = -4 and passes through (5,9) is y = - 4x + 29
What is Linear Equation ?Linear Equation = an equation between two variables that gives a straight line when plotted on a graph is known as linear equation.
For this statement we need to use the point slope form of linear equation.
What is Point Slope Form ?The equation of a straight line in the form y − y1 = m(x − x1) where m is the slope of the line and (x1, y1) are the coordinates of a given point on the line — compare slope-intercept form is known as point slope form.
Using point slope form,
y - y1 = m (x - x1)
y - 9 = -4 (x - 5)
y - 9 = -4x + 20
y = -4x + 20 + 9
y = -4x + 29
Therefore, where m = -4 and passes through (5,9) the linear equation will be y = -4x + 29
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The Highest Common Factor of a
and b is 48 and the Lowest
Common Multiple is 1680.
Given that a < b and that both
numbers are greater than 48,
work out the values of a and b.
Answers
Answer:
a = 240
b = 336
Step-by-step explanation:
To find LCM of 2 number:
list all prime factors that appear in either numbers. If a factor appears more than once in one of the numbers list it that many times. Multiply these together to get LCMTo find HCF of 2 numbers:
List all prime factors both numbers. Multiply these together to find HCFIn this question LCM and HCF is already given but the numbers a and B are unknown.
To find a and B we do the opposite.
Further explanation is in the attached file please open as you will get a clear understanding of the answer.