Simplify brackets
10x - 4 = 8x + 14
Add 4 to both sides
10x = 8x + 14 + 4
Simplify 8x + 14 + 4 to 8x + 18
10x = 8x + 18
Subtract 8x from both sides
10x - 8x = 18
Simplify 10x - 8x to 2x
2x = 18
Divide both sides by 2
x = 18/2
Simplify 18/2 to 9
x = 9
10x - 4 = 8x + 14
Step 1: Combine like terms
x's go with x's (10x and 8x). To do this subtract 8x to both sides
(10x - 8x) - 4 = (8x-8x) + 14
2x - 4 = 14
Normal numbers go with normal numbers (-4 and 14). To do this add 4 to both sides
2x + (-4 + 4) = 14 + 4
2x = 18
Step 2: Isolate x by dividing 2 to both sides
2x/2 = 18/2
x = 9
Hope this helped!
write a point slope equation for the line that has slope 13 and passes through the point (15,12) do not use parenthesis on the y side
Answer:
[tex]y-12=13(x-15)[/tex]
Step-by-step explanation:
we know that
The equation of the line into point slope form is equal to
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=13[/tex]
[tex](x1,y1)=(15,12)[/tex]
substitute
[tex]y-12=13(x-15)[/tex] -----> equation of the line into point slope form
Answer:
Y-12=13(x-15)
Step-by-step explanation:
The prism below is made of cubes which measure 1/3 of an inch on one side. What is the volume?
a. 10/9 cubic in
b. 10 cubic in.
c. 30 cubic in.
d. 10/3 cubic in
Answer:
the answer is A. 10/8 cubic in.
Step-by-step explanation:
V = LWH
length is 2 (1/3 in)
width is 3 (1/3 in)
height is 5 (1/3 in)
V = 2/3 in * 3/3 in * 5/3 in.
V = 10/9 cubic in.
The volume of the prism is 10 cubic inches, making the correct answer option b.
To find the volume of the prism made up of cubes each measuring 1/3 of an inch on one side, we first need to understand the volume of one cube.
The volume of a cube is calculated using the formula:
Volume = side³Given that each side of the small cube is 1/3 inch, we calculate:
(1/3 inch)³ = 1/27 cubic inchesNext, we need to determine the total number of these small cubes that make up the prism. Let's assume the prism consists of 270 of these small cubes.
The total volume of the prism is calculated by multiplying the volume of one small cube by the total number of cubes:
Volume of prism = 270 × 1/27 cubic inches = 10 cubic inchesThus, the correct answer is:
Option b. 10 cubic in.At a local company, the ages of all new employees hired during the last 10 years are normally distributed. The mean age is 32 years old, with a standard deviation of 10 years. Find the percent of new employees that are at least 25 years old. Round to the nearest percent.
Answer:
P = 76%
Step-by-step explanation:
We look for the percentage of employees who are at least 25 years old.
We know that:
μ = 32 years
[tex]\sigma = 10[/tex] years
And we want to find
[tex]P(X\geq25) [/tex]
Then we find the z-score
[tex]Z =\frac{X - \mu}{\sigma}[/tex]
So
[tex]Z = -0.7[/tex]
Then
[tex]P (X\geq25) = P(\frac{X- \mu}{\sigma}\geq\frac{25-32}{10})\\\\\P (X\geq25) = P (Z\geq -0.7)[/tex]
By symmetry of the distribution
[tex]P(Z\geq -0.7)= 1-P(Z<-0.7)[/tex]
[tex]P(Z\geq -0.7)= 1-0.242[/tex]
Looking in the normal standard tables
[tex]P(Z\geq -0.7)= 0.758[/tex]
Finally P = 76%
Finding the perimeter of each rectangle 96ft width 124ft length
Answer:
440 ft
Step-by-step explanation:
Perimeter(p) of a rectangle is 2l + 2w
Where 'l' is the length and 'w' is the width.
p = 2(96ft) + 2(124ft) = 192 ft + 248 ft = 440 ft
solve using the substitution method -2x +y=4 y=3x+1
Answer: (3, 10)
Step-by-step explanation:
X=3 y=10
Answer:
x = 3
y = 10
Step-by-step explanation:
Equation (1) : -2x + y = 4
Equation (2) : y = 3x + 1
Substitute (2) into (1):
-2x + (3x + 1) = 4
-2x + 3x + 1 = 4
x + 1 = 4
x = 3
Sub x = 3 into (2):
y = 3(3) + 1
y = 10
Find the slope of the straight line that passes through (–2, –4) and (3, –5)
Answer:
YOur answer would be -1/5.
Step-by-step explanation
rise/run
-4--5/-2-3
=-1/5
For this case we have by definition, that the slope of a line is given by:
the following formula:
[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}}[/tex]
Having two points through which the line passes:
[tex](x_ {1}, y_ {1}): (- 2, -4)\\(x_ {2}, y_ {2}) :( 3, -5)[/tex]
Substituting:
[tex]m = \frac {-5 - (- 4)} {3 - (- 2)}\\m = \frac {-5 4} {3 2}\\m = \frac {-1} {5}[/tex]
Finally, the slope of the line is:
[tex]m = - \frac {1} {5}[/tex]
Answer:
[tex]m = - \frac {1} {5}[/tex]
Angles R and S are vertical angles. Angle R has a measure of (4x + 20). Angle S has a measure of 84. What is the value of x?
Answer:
x = 16
Step-by-step explanation:
Note that vertical angles are congruent, hence
4x + 20 = 84 ( subtract 20 from both sides )
4x = 64 ( divide both sides by 4 )
x = 16
o
Simplifying Exponential Expressions
Warm-Up
Match the expression to its simplified form.
1/16
125
24
125
Answer: 1/16=1/4*1/4
125=5*5*5
24= (2*6)*2
125= 5*5*5
Step-by-step explanation:
Please Help! 35 points! Brainliest awarded!
What value of x would make the expression below equal to 8?
Answer:
x = 5/3
Step-by-step explanation:
We have the fifth root of 8^3 and we want it equal to 8
(8^3) ^ (1/5) ^x = 8
We know that a^b^c = a^ (b*c)
8 ^ (3*1/5x) = 8
8 ^ (3/5x) = 8
We can rewrite 8 as 8^1
8 ^ (3/5x) = 8^1
The exponents must be the same
3/5 x = 1
Multiply each side by 5/3 to isolate x
5/3 * 3/5x = 1 * 5/3
x = 5/3
Jane will roll a number cube 30 times.How may times would Jane expect to roll a number larger that 4?
Answer: 5
Step-by-step explanation:
= P(roll 4) = 1/6
= Expected # of 4 in 30 rolls = (1/6)*30 = 5
Therefor, the answer is 5
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Pam has monthly mortgage payment of $750. Her annual property taxes are $1200,her PMI is $55/month, and her homeowners insurance is $800 per year. How much is deposited into Pam’s escrow account each month?
Answer:
$100 + $66.67 + $55 = $221.67/month, which is the amount that must be deposited into Pam's escrow account each month....
Step-by-step explanation:
Pam's annual taxes are $1200 per year. It means her escrow each month needs to have 1/12 of that amount. 1200/12 = $100 per month
Her homeowner's insurance is $800 per year, that's 1/12 of that needs to be in her escrow account each month:
$800 / 12, or $66.67/month.
And PMI is $55/month
Add these three together:
$100 + $66.67 + $55 = $221.67/month, which is the amount that must be deposited into Pam's escrow account each month....
Identify the radius of the circle whose equation is (x-2)^2 + (y-8)^2 = 16
Answer:
radius = 4
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
(x - 2)² + (y - 8)² = 16 ← is in standard form
with r = [tex]\sqrt{16}[/tex] = 4
Solve for x: 15x – 30 = 45
Answer:
x = 5
Step-by-step explanation:
Answer:
x=5
Step-by-step explanation:
15x-30=45
+30 +30
15x=75
15/15=1
75/15=5
x=5
Two vertices of a right triangle have coordinates (4, 2) and (5, -3). Select each ordered pair that could be the coordinates of the third vertex.
The answer is A.) ( 4, -3 )
if sally had 3 apples and gave 2 away how many does sally have now
Answer:
Step-by-step explanation:
3 - 2 = 1 apple
Sally has 1 apple.
Hope this helps.
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Jethro walked at an average speed of 3 miles per hour for 2 hours. Randy walked at an average of 4 miles per hour for 3 hours.
Which explanation correctly tells how to calculate the total number of miles the two boys walked?
A.Step 1: Multiply 3 × 2.
Step 2: Multiply 4 × 3.
Step 3: Add the two products.
B.Step 1: Divide 3 ÷ 2.
Step 2: Divide 4 ÷ 3.
Step 3: Add the two quotients.
C.Step 1: Divide 3 ÷ 2.
Step 2: Divide 4 ÷ 3.
Step 3: Subtract the two quotients.
D.Step 1: Multiply 3 × 2.
Step 2: Multiply 4 × 3.
Step 3: Subtract the two products.
the answer is A multiply 3x2 and multiply 4x3 then add hope that helps
Answer:
A
Step-by-step explanation:
It is asking for the total amount of miles the boys walked therefore addition for step 3.
What percent is the shaded portion of the entire diagram?
9%
40%
45%
90%
45% :) Step-by-step explanation:
In this diagram, there are a total of 20 squares, and 9 of them are shaded. This means that 9/20 of them are shaded, and to find what percent this is, divide 9 by 20 and multiply what you get by 100.
9 divided by 20 =0.45
0.45 x 100 = 45%.
45% is your final answer!
I hope this helps and have a great rest of your day!
solve the inequality
Answer:
[tex]\large\boxed{-1<x<4}[/tex]
Step-by-step explanation:
[tex]-6<2x-4<4\qquad\text{add 4 to all sides}\\\\-6+4<2x-4+4<4+4\\\\-2<2x<8\qquad\text{divide all sides by 2}\\\\\dfrac{-2}{2}<\dfrac{2x}{2}<\dfrac{8}{2}\\\\-1<x<4[/tex]
If 62% of the people at a certain conference are doctors, 48% are women, and 36% are female doctors, what is the probability that a person selected at random at this conference is a doctor or woman (or both)?
62 plus 48 is 110
Then add everyone together to find the total 62+48+36 which is 152
110 over 152 is the probability that a person selected at random will be a doctor or woman
Hope this helps;)
The probability that a person at random from the conference is either a doctor or a woman (or both) is 74%, computed from the principle of inclusion and exclusion.
Explanation:The probability of a person at the conference being a Doctor or a Woman (or both) can be found by adding the individual probabilities - that of being a woman and that of being a doctor - and subtracting the probability of being both a doctor and a woman because this is counted twice in the addition. This is called the principle of inclusion and exclusion in probability theory. So by substituting the given percentages, P(Doctor or Woman) = P(Doctor) + P(Woman) - P(Doctor and Woman) = 62% + 48% - 36% = 74%. So, the probability that a person chosen at random from the conference is either a doctor or a woman (or both) is 74%.
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Solve the equation for x 1/3 (6x-15) = 1/2(10x-4)
For this case we must solve the following equation for x:
[tex]\frac {1} {3} (6x-15) = \frac {1} {2} (10x-4)[/tex]
We apply distributive property to the terms of parentheses:
[tex]2x-5 = 5x-2[/tex]
We subtract 5x on both sides of the equation:
[tex]2x-5x-5 = -2\\-3x-5 = -2[/tex]
Suamos 5 on both sides of the equation:
[tex]-3x = -2 + 5\\-3x = 3\\x = - \frac {3} {3}\\x = -1[/tex]
Answer:
[tex]x = -1[/tex]
Dernea Gardening sells wheelbarrows. A wheelbarrow costs $6.94 to produce and it sells for $42.50. The company employs two salespeople, each of whom earns a different commission per wheelbarrow sold, as shown in the table below.
Answer:
The answer is C! I just took the quiz and got 100% shout out to all the cheaters out there, let's get this E2020 bread!
The percentage profit on a wheelbarrow is 512%
What is percentage profit?The percentage profit of an item is the amount of profit when the item is sold, expressed in terms of percentage
The selling price is given as:
SP = $42.50
The cost price is given as:
CP = $6.94
The percentage profit is then calculated as:
[tex]Profit = \frac{SP - CP}{CP} * 100\%[/tex]
This gives
P = (42.50 - 6.94)/6.94 * 100%
Evaluate the difference
P = 35.56/6.94 * 100%
Evaluate the quotient
P = 5.12 * 100%
Evaluate the product
P = 512%
Hence, the percentage profit on a wheelbarrow is 512%
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What can you say about the yvalues of the two functions f(x)=3^x-3 and g(x)=7x^2-3 please answer
Answer:
Step-by-step explanation:
This question is too general. We can take a look at the behaviors of the two different graphs:
f(x)=3^x-3 is an exponential function whose y-intercept is (0, -2). Note that 3^0 = 1. To draw this function, we'd drawn f(x)=3^x first and then translate the whole graph down by 3 units. The graph appears in Quadrants III, IV and I, in that order.
g(x)=7x^2-3 is not an exponential function, but rather a quadratic whose graph is a parabola. Here the parabolic graph opens up. Its y-intercept is (0, -3). This graph will intersect that of f(x)=3^x-3 in two places.
A: False. It is g that has minimum y value of -3. The minimum y value of f is -2.
B: The smallest y value f can have is just above y = -2. y = -2 is the horizontal asymptote for this function. The smallest y value g can have is -3. So B is False.
C: True. g has the smallest possible y-value; it is -3.
D: True. The min. y-value of g is -3.
Answer: C and D are true
Step-by-step explanation:
A P E X
Can anyone help me with these two plz
Answer:
Part 1) The scale factor is [tex]1.5[/tex]
Part 2) The altitude QS is [tex]4\ units[/tex]
Part 3) The scale factor is [tex]\frac{2}{3}[/tex]
Part 4) The value of x is [tex]12\ units[/tex]
Part 5) The perimeter of ABCDE is [tex]46\ units[/tex]
Step-by-step explanation:
Part 1) Find the scale factor of triangle TQR to triangle NQP
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor
Let
z-----> the scale factor
[tex]z=\frac{NP}{RT}[/tex]
substitute the values
[tex]z=\frac{24}{16}=1.5[/tex]
Part 2) Find the length of the altitude QS
we know that
To find the altitude QS, divide the altitude of triangle NQP by the scale factor
so
[tex]QS=\frac{6}{1.5}=4\ units[/tex]
Part 3) Find the scale factor of FGHJK to ABCDE
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor
Let
z-----> the scale factor
[tex]z=\frac{AB}{FG}[/tex]
substitute the values
[tex]z=\frac{10}{15}=\frac{2}{3}[/tex]
Part 4) Find the value of x
we know that
The value of x is equal to multiply the length side FK by the scale factor
so
[tex]AE=FK(z)[/tex]
substitute the values
[tex]AE=18(2/3)=12\ units[/tex]
Part 5) Find the perimeter of ABCDE
we know that
If two figures are similar, then the ratio of its perimeters is equal to the scale factor
Let
z-----> the scale factor
x-----> the perimeter of ABCDE
y-----> the perimeter of FGHJK
[tex]z=\frac{x}{y}[/tex]
we have
[tex]z=\frac{2}{3}[/tex]
[tex]y=15+9+12+15+18=69\ units[/tex]
substitute the values
[tex]z=\frac{x}{y}[/tex]
[tex]x=(z)(y)=\frac{2}{3}(69)=46\ units[/tex]
a father is 10 times as old as his son. in 5 years he will be 5 times as old as his son. how old is the father and the son now
Answer:
The father is 40 and the son is 4.
Step-by-step explanation:
40 + 5 = 45.
4 +5=9.
45 divided by 5 = 9
Answer:
The father is 40 and the son is 4.
Step-by-step explanation:
find the recursive formula of the arithmetic sequence
14,30,46,62
Answer:
[tex]a_n=a_{n-1}+16[/tex]
Step-by-step explanation:
The given arithmetic sequence is
14,30,46,62
The first term of this sequence is
[tex]a_1=14[/tex]
The common distance is obtained by subtracting a subsequent term from a previous term;
d=30-14
The common difference is
d=16
The recursive formula is given by:
[tex]a_n=a_{n-1}+d[/tex]
We now plug in the known value for the common difference to get;
[tex]a_n=a_{n-1}+16[/tex]
The recursive formula for the arithmetic sequence 14, 30, 46, 62 is an = aₙ₋₁ + 16 with the initial term a₁ = 14.
An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. In this case, we have the sequence: 14, 30, 46, 62.
Step-by-Step Process
1. Determine the common difference (d) by subtracting the first term from the second term:
d = 30 - 14 = 162. Using the first term (a1) and the common difference (d), we can now write the recursive formula.
The recursive formula of an arithmetic sequence is given by: aₙ = aₙ₋₁ + dFor this sequence, the recursive formula can be written as: aₙ = aₙ₋₁ + 16, with the initial term a₁ = 14Therefore, each subsequent term is obtained by adding 16 to the previous term.
At a local company, the ages of all new employees hired during the last 10 years are normally distributed. The mean age is 34 years old, with a standard deviation of 10 years. Find the percent of new employees that are no more than 40 years old. Round to the nearest percent.
Answer:
P = 73%
Step-by-step explanation:
We look for the percentage of employees who are not more than 40 years old.
This is:
[tex]P = \frac{x}{n} *100\%[/tex]
Where x is the number of new employees who are not over 40 years old and n is the total number of new employees.
We do not know the value of x or n. However, the probability of randomly selecting an employee that is not more than 40 years old is equal to [tex]P = \frac{x}{n}[/tex]
Then we can solve this problem by looking for the probability that a new employee selected at random is not more than 40 years old.
This is:
[tex]P(X< 40)[/tex]
Then we find the z-score
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
We know that:
μ = 34 years
[tex]\sigma = 10[/tex] years
So
[tex]Z = 0.6[/tex]
Then
[tex]P (X<40) = P (\frac{X- \mu}{\sigma} < \frac{40-34}{10})\\\\P(X<40) = P(Z<0.6)[/tex]
So we have
[tex]P(Z<0.6)[/tex]
Looking in the normal standard tables:
[tex]P(Z<0.6)=0.726[/tex]
Finally P = 73%
Amy has a bowl of cereal for breakfast. the amount of cereal in the box (y) is determined by the number of days (x) that have passed since she purchased the cereal. The graph below shows that this relationship is a linear function. Consider an appropriate domain for this situation. What would be the greatest value for this domain?
I can't upload the graph. It's not working but here are the plotted coordinates:
0,48
1,44
2,40
3,36
4,32
There's no line connecting them.
Answer:
d=[0,12]
Step-by-step explanation:
Answer:
The function is f(4)=32, so the domain is (-infinity,infinty)
The domain is infinty :)
t B'(4, -8) was transformed using the translation (x - 2, y + 3). What were the coordinates of B?
Answer:
(6, -11)
Step-by-step explanation:
The translation (x-2,y+3) means "subtract 2 from x coordinate" and "add 3 to the y coordinate".
After the transformation, we have the point B'(4,-8). Which point, let it be (x,y), after being transformed is B'(4,-8)??
According to the transformation rule, we have to "subtract 2 from x coordinate" and "add 3 to the y coordinate", thus
x-2=4
x=4+2
x=6
and
y+3=-8
y=-8-3
y=-11
THe coordinate of B are (6,-11)
What are three types of life cycle
Answer: three type of life cycles are Haploid life cycle,Diploid life cycle, and alternation of generations.
The three main life cycles in multicellular organisms are the haploid life cycle, found in some fungi and algae, the diploid life cycle, common in animals like humans, and the alternation of generations, seen in plants and some algae. Insects may undergo complete metamorphosis, with distinct life stages.
Explanation:Types of Life Cycles in Multicellular Organisms
There are three main types of life cycles in multicellular organisms, which are characterized by the prominence of either the haploid or diploid stages and the process of alternation between these stages. In the haploid life cycle, organisms spend most of their life in the haploid state, such as many single-celled eukaryotes. Fertilization briefly produces a diploid zygote, which immediately undergoes meiosis to form new haploid gametes. An example of this life cycle can be found in certain fungi and algae.
The diploid life cycle is where organisms spend the majority of their lives as diploid individuals. Here, only the gametes are haploid. Most animals, including humans, follow this type of life cycle.
The alternation of generations life cycle is characterized by alternating haploid and diploid stages. This is common in plants and some types of algae. The diploid stage, called the sporophyte, produces haploid spores by meiosis that develop into the haploid stage, known as the gametophyte, which in turn creates haploid gametes. Fertilization of these gametes will result in a new sporophyte, continuing the cycle.
In summary, sexual reproduction leads to varying life cycle types based on the dominancy and alternation of haploid and diploid stages, each vital for the propagation and genetic diversity of species.
Additionally, in the context of insects, which undergo distinct transformations, there are three types of metamorphosis: no metamorphosis, gradual metamorphosis (or incomplete), and complete metamorphosis. Most insects, such as butterflies, undergo complete metamorphosis, exhibiting different forms at each stage of their life cycle: egg, larva, pupa, and adult.
Subtract (5x + 3) from (9x – 7).
Answer:
4i - 10
Step-by-step explanation:
9x - 7 - 5x - 3 = 4i -10