Answer:
545
Step-by-step explanation:
find three consecutive integers such that the first plus 4 times the second total 210 more than the third
Three consecutive integers such that the first plus 4 times the second total 210 more than the third are 52, 53, 54
Consecutive integers are what?Integers that are listed in a consistent counting pattern are referred to as consecutive integers. There are no numbers missed while listing consecutive integers in a sequence, so the difference between them is always fixed. The difference between each successive integer, for instance, can be written as -4, -3, -2, -1, 0, 1, 2, 3, and so on.
Let the three numbers be x, x+1, x+2
As per given question,
⇒ x + 4(x + 1) + = 210 + x + 2
⇒ x + 4x + 4 = 210 + x + 2
⇒ 4x + 4 = 212
⇒ 4x = 208
⇒ x = 52
∴ The three consecutive integers will be 52, 53, 54
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Nisha did the work below to solve an equation.
Step 1 7 b + 3.2 b minus 5 = 18.92
Step 2 10.2 b minus 5 = 18.92
Step 3 5.2 b = 18.92
Step 4 b = 3.64
In which step did Nisha make her first error?
a. Step 1
b. Step 2
c. Step 3
d. Step 4
Nisha solved an equation given, and she made a mistake in the third step. The correct option is c. step 3.
What is an error?An error in math is a mistake in solving any arithmetic equation or calculation. It can be calculating wrong or left a step.
Given;
Step 1: 7 b + 3.2 b - 5 = 18.92
Step 2: 10.2 b - 5 = 18.92 (Combining like terms in left side)
Step 3: 10.2b = 23.92 (Adding 5 on both sides)
Step 4: b = 3.64 (Dividing both sides by 10.2)
But in step 3, she did not add 5 on both sides.
5.2 b = 18.92 incorrect. The correct equation is 10.2b = 23.92
Therefore, the correct option is c. Step 3.
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If r = -6, s = -2, v = 10, and w = 3; then
vs(r - s) ÷ 2 + rw =
Responses
A -98
B 58
C -22
D 22
E -62
If r = -6, s= -2, v=10 and w = 3 then the response of the expression vs(r-s)÷2+rw is option (d) 22
The expression is
vs (r-s) ÷ 2 + rw
To find the response, we have to substitute the values in the expression
The values of the term
r = -6
s = -2
v = 10
w = 3
Substitute the values in the given expression
= 10×-2(-6-(-2)) ÷ 2 + (-6)×3
Do the arithmetic operations in bracket
= 10×-2(-4) ÷ 2 + (-6)×3
Do the multiplication
= 80 ÷2 - 18
Do the division
= 40 - 18
= 22
Hence, if r = -6, s= -2, v=10 and w = 3 then the result of the expression vs(r-s)÷2+rw is option (d) 22
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(y=
{ y =
4
²/x - 3
x + 1
5
4
5
How many solutions does this system of equations have? Show how you know
The system of equations containing equations y = 5/2 x + 2 and 2y = 5 x + 4 will have infinitely many solutions.
What is system of equations?
A finite collection of equations for which we searched for the common solutions is referred to in mathematics as a system of equations, sometimes known as a set of simultaneous equations or an equation system. Similar to single equations, a system of equations can be categorized. In everyday life, systems of equations are used to model problems when the unknown values can be represented by variables.
Given equations:
y = 5/2 x + 2
2y = 5 x + 4
We will use the substitution method, to get the values of x and y:
2 ( 5/2 x + 2 ) = 5 x + 4
5 x + 4 = 5 x + 4
0 · x = 0
x , y ∈ R
Therefore, this system of equations will have infinitely many solutions.
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Complete question
How many solutions does the following system of equations have?
y = 5/2x + 2,
2y = 5x + 4.
1 An amount of Php 2,000,000 is invested for 5 years at a 5% interest rate. 2. An amount of Php 500,000 is invested in a financial institution. At what interest rate will it earn Php 4,000 in 18 months?
Answer:
it may be in round about 3600000000..
The interest rate earned in 18 months will be $300
What is interest rate?The amount that a lender charges a borrower for the use of assets on top of the principal is known as the interest rate.The money generated from a deposit account at a bank or credit union is likewise subject to an interest rate.Simple interest is used in most mortgages. Compound interest, which is applied to both the principle and the accrued interest from earlier periods, is used in some loans, nevertheless.The interest rate will be lower for a borrower who the lender deems to be low risk. The interest rate on a loan will be greater if it is thought to be high risk.The interest rate on savings accounts and certificates of deposit that is earned at a bank or credit union is known as the annual percentage yield (APY). Compound interest is used in savings accounts and CDs.First, converting R percent to r a decimal
r = R/100 = 5%/100 = 0.05 per year,
putting time into years for simplicity,
18 months ÷ 12 months/year = 1.5 years,
then, solving our equation
I = 4000 × 0.05 × 1.5 = 300
I = $300.00
The simple interest accumulated
on a principal of $4,000.00
at a rate of 5% per year
for 1.5 years (18 months) is $300.00.
Therefore, the interest rate earned in 18 months will be $300
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For f(x) = -x-4 find the value of x for which f (x) = 1
Answer:
x = -5
Step-by-step explanation:
f(x) = -x-4
Let f(x) = 1
Find x
1 = -x-4
Add 4 to each side
1+4 = -x-4+4
5 = -x
Multiply each side by -1
-5 =x
x = -5
Answer:
x = -5
Step-by-step explanation:
Given that,
f ( x ) = - x - 4
If, f ( x ) = 1,
Let us find the value of x.
For that, replace f ( x ) with 1.
f ( x ) = - x - 4
1 = - x - 4
First, add x to both sides.
x + 1 = -4
Now, subtract 1 from both sides.
x = -4 - 1
x = -5
What is the slope of the line that passes through the points (10,3) and (7,0)? Write your answer in simplest form.
Given two points on a line, we can find its slope using the formula below
[tex]\begin{gathered} (x_1,y_1),(x_2,y_2) \\ \Rightarrow slope=\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex]Therefore, in our case,
[tex]\begin{gathered} (10,3),(7,0) \\ \Rightarrow slope=\frac{10-7}{3-0}=\frac{3}{3}=1 \end{gathered}[/tex]Thus, the slope is equal to 1.
Jabari's art club raises $300 to pay for a trip to a local museum.
The bus costs $90, and admission is $6 per student. Jabari writes
an expression for the amount the club has left based on the number
of students who go to the museum. If x is the number of students
who to the museum, the amount remaining is 300-90-6x.
a. What is the amount remaining after paying field trip expenses
for 28 students For 29 students? For 30 students?
b. What is the greatest number of students who can go on
the field trip for $300
Answer:
Answers below
Step-by-step explanation:
For 28 Students 300-90-(6*28) the answer is 42.
For 29 Students 300-90-(6*29) the answer is 36.
For 30 Students 300-90-(6*30) the answer is 30.
The greatest number of students that can go on the field trip for $300 is 35.
I've gotten this answer by doing 300-90-(6*35) which equals to 0.
All of the following names of the polygon above are correct EXCEPT for:
Answer: Uhhhh there are no names for me to choose from- but it's basically any shape with straight lines and is closed. hope this helps
Step-by-step explanation:
So if 3x=21, how would i find the value of 22-4x?
Answer:
-6
Step-by-step explanation:
x= 21/3
x=7
using this value,
22-4x= 22-4*7
=22-28
=-6
Please solve the following question
Answer: Therefore, the value of k is -20
Step-by-step explanation:A=-26-3= -29
B=-3x+2
C = -2x + 7
A+B+C= -29 -3x +2 -2x +7
A+B+C= -29 +2+7 -3x -2Xx
A+B+C= -20-5x
The ratio of pennies to dimes I have is 3:5. I have a 2:3 ratio of dimes to quarters. If I have 75 quarters, how many pennies do I have? A. 30 pennies B. 48 pennies C. 50 pennies D. 72 pennies
They have [tex]30[/tex] pennies. So the option A is correct.
The ratio of pennies to dimes they have is [tex]3:5[/tex].
They have a [tex]2:3[/tex] ratio of dimes to quarters.
They have [tex]75[/tex] quarters.
We have to find the how many pennies they have.
The ratio of pennies to dimes [tex]=3:5[/tex]
We can write it as
Pennies : Dimes[tex]=3:5[/tex]
The ratio of dimes to quarters [tex]=2:3[/tex]
We can write it as
Dimes : Quarter [tex]=2:3[/tex]
When we see both ratio then we can notice that the ratio of dimes is different in both ratio.
So firstly we equal the ratio of dimes.
We can equal the ratio of dime in the ratio of pennies to dimes by multiplying with [tex]2[/tex] in both ratio and in the ratio of dimes to quarters by multiplying [tex]5[/tex] on both side.
Now we get after multiplying in the ratio.
Pennies : Dimes[tex]=3\times2:5\times2[/tex]
Pennies : Dimes[tex]=6:10[/tex]
Dimes : Quarter [tex]=2\times5:3\times5[/tex]
Dimes : Quarter [tex]=10:15[/tex]
The number of quarter is [tex]75[/tex].
They given in the ratio which means there have any number in the multiple of ratio. That which we can get real value from the ratio.
So we used [tex]x[/tex] as a multiple of ratio.
If we see in the ration of Dimes and Quarter the ratio of quarter is [tex]15x[/tex].
Now the value of quarter
[tex]15x=75[/tex]
Now the value of [tex]1[/tex] quarter
Divide by [tex]15[/tex] on both side.
[tex]\frac{15}{15}x=\frac{75}{15}[/tex]
[tex]x=5[/tex]
Hence, the value of [tex]x[/tex] is [tex]5[/tex].
Now we have to find the value of pennies.
In the ratio we can see that the ratio of pennies is [tex]6[/tex].
We can find the value of pennies by multiplying with [tex]5[/tex].
After multiplying we get [tex]30[/tex].
Hence, they have [tex]30[/tex] pennies. So the option A is correct.
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Answer: A
Step-by-step explanation:
10 t Which angle supplements angle 3? * (5 Points) a 2/1 3 4 b 6/5 7 00
Suplementsry angles are
Form a sum of 180°
Then in figure
Suplements for angle 3 are, Angles 2 and 4
Because <3 + <4 = 180°
and also
<3 + <2 = 180 °
Then answer is
Option B) Angle 4
jackie used to be on the phone 3 1/2 times as much as her brother. Her parents threatened to take away the phone, so she cut down to 2/5 of the time she used to be on the phone. How many times as much as her brother is jackie now on the phone?
The number of times as much as her brother is Jackie now on the phone is 1 2/5 times.
How to calculate the fraction?From the information, Jackie used to be on the phone 3 1/2 times as much as her brother and her parents threatened to take away the phone, so she cut down to 2/5 of the time she used to be on the phone.
Therefore, the times that she's using as much as her brother will be:
= Original times × Fraction cut
= 3 1/2 × 2/5
= 7/2 × 2/5
= 7/5
= 1 2/5 times.
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Solve (x - 5)² = 3.
A. x=-51-√3
B. x=8 and x= -2
C. x=3+√5
D. x=5+√3
The number of cases of a new disease can be modeled by the quadratic regression equation y = -2x^2 + 36x + 6, where x represents the year.
Which is the best prediction for the number of new cases in year 15?
Answer:
A hope it helps follow please
Step-by-step explanation:
hope you have a great day today
Which of the number below are whole numbers?
Answer:
D and F
Step-by-step explanation:
8060 and 609 are whole numbers.
whole numbers: Whole numbers include 0 and natural numbers (1,2,3,4......). They don't include fractions, decimal and negative integers.
Please help me!!
A model is built having a scale of 1:15,000. How high would a 48,800-ft mountain be in the model? Give your answer to the nearest tenth of an inch.
(A.) 585600 in.
(B.) 19.5 in.
(C.) 3.3 in.
(D.) 39.0 in.
According to the scale the model mountain would be 39.04 inches.
Scale factor is the ratio of an object's original scale to that of a new object that is a representation of it but in a variety of sizes (bigger or smaller).
For instance, by increasing each side by, say, 2, we can expand the size of a rectangle with sides of 2 cm and 4 cm. The second figure will mimic the first figure, but every dimension of the second rectangle will be double that of the first figure. In this instance, the scale factor will be indicated by the number 2.
We now that 48800 feet = 48800 × 12 inches = 585600 inches
Scale = 1:15,000
height of model = 585600 ÷ 15000 = 39.04 inches
Hence the length of the model is 39.04 inches.
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Constant of Proportionality PROPORTIONALITY OF EACH GRAPH. NOT ALL CHOICES WU BE USED. 1/2 3 4 1 I 2 2. 1/4
Choose any point on each line different from (0,0) to find the constant of proportionality.
Notice that, for example, in the first graph, the point (4,4) lies in the line.
Divide the y-coordinate over the x-coordinate to find the constant of proportionality. This method is only valid when the point (0,0) is in the line.
For the first graph, the constant of proportionality is:
[tex]\frac{4}{4}[/tex]Which is equal to 1.
For the second graph, notice that the point (8,4) is in the line. Again, divide the y-coordinate over the x-coordinate to find the constant of proportionality:
[tex]\frac{4}{8}[/tex]Which is equal to 1/2.
For the third graph:
Notice that the point (4,8) is in the line of the third graph.
By dividing 8/4, we notice that the constant of proportionality is equal to 2.
Choose the correct answers for (a) the total installment price, (b) the carrying charges, and (c) the number of months needed to save the money at the monthly rate to buy the item for its cash price.
A computer with a cash price of $1,900 at $150.00 down and $87.50 per month for 24 months.
If a computer with a cash price of $1,900 at $150.00 down and $87.50 per month for 24 months. a. The total installment price is $2250, b. The carrying charges, and (c) the number of months needed to save the money at the monthly rate to buy the item for its cash price is 22 months.
Total installment pricea. Total installment price:
Total installment price = 150 + 87.50 (24)
Total installment price =150 + 2100
Total installment price =2250
b. Carrying charges :
Carrying charges = Total installment price - Cash price
Carrying charges = 2250 -1900
Carrying charges = 350
c. Number of months needed:
Number of months needed = Cash price / 87.50 per month
Number of months needed = 1900 / 87.50 per month
Number of months needed = 21.7 months
Number of months needed = 22 months (Approximately)
Therefore installment price is 2250, charges is 350 and the number of months is 22.
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help me please!!( 30 POINTS IF ANSWERED!!)
Answer:
Step-by-step explanation:
b
write the equation of a line that passes through the point (9,-2) and is parallel to the line y+1=2(x-3)
Answer:
y = 2x - 20
Step-by-step explanation:
Equation of line: y =mx +bwhere m is slope and b is y-intercept.
y + 1 = 2(x - 3)
Write this equation in y = mx + b form.
y + 1 = 2x - 2*3
y + 1 =2x - 6
y = 2x - 6 - 1
y = 2x - 7
m =2
Parallel lines have same slope.
Slope of the required line = 2
y = 2x + b
The point (9,-2) passes through the line. Substitute in the above equation and find the value of 'b'.
-2 = 9*2 + b
-2 = 18 + b
-2 - 18 = b
[tex]\sf \boxed{b = -20}[/tex]
Equation of the required line:
y = 2x - 20
hi! last question for me so i would appreciate the help :))
The equation of the line passing through the point (-6, 4) and (-2, 2) is y = -(1/2)x + 1
How to solve an equationAn equation is an expression that shows the relationship between two or more numbers and variables.
The standard form of a linear equation is:
y = mx + b
Where m is the slope and b is the y intercept.
The equation of a line passing through the point (-6, 4) and (-2, 2) is:
y - 4 = [(2 - 4)/(-2 - (-6))](x - (-6))
y - 4 = -(1/2)(x + 6)
y - 4 = -(1/2)x - 3
y = -(1/2)x + 1
The equation of the line is y = -(1/2)x + 1
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10. Peter launched a water balloon from the
top of a building that is 15 yards tall.
The graph shows the height of the water
balloon as a function of x, the distance
from the building in yards. Which best
represents the domain of the situation?
a. 15 ≤x≤ 30
b. 0≤x≤8
C. 0≤ y ≤30
All real numbers
Peter threw a water balloon out of the top of a 15-yard-tall structure. The Option b is correct because it asks the domain so the option a and c are wrong from the graph can we know 0≤x≤8.
Given that,
Peter threw a water balloon out of the top of a 15-yard-tall structure.
The water balloon's height is plotted as a function of x, or the building's distance from the location in yards.
We have to find which one most domain reflects the situation's context.
The Option b is correct because it asks the domain so the option a and c are wrong from the graph can we know 0≤x≤8.
Therefore, Option b is correct.
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Order from greatest to least
1.62 , 16.2% ,15/20
Answer:
1.62, 15/20, 16.2%
Step-by-step explanation:
Let us consider all the answers out of one. In percentages, 100% always equals 1. (If you ate 100% of a cookie, you would have eaten 1 cookie), 16.2% is much less than 100% and not even half of 100%.
16.2%<0.5
Following the same logic, imagine there are 20 cookies this time. 15/20 would be 15 out of the 20 cookies which is more than half.
15/20>0.5
Finally, 1.62 is greater than 1
1.62>1
You can tell I'm hungry rn lol, also I would appreciate if you could give Brainliest, I'm kind of on a streak
Find the value of x.
Answer:
10
Step-by-step explanation:
They (50 & 5x) are parallel angles, therefore 5x equals 50.
This means that to find x, you will need to find a common factor between 5 and 50, which is 5. 50/5=10
x=10
Becca exercises for 1 1/2 hours. She dances for 5/6 of the time she spends exercising.
How much time does Becca spend dancing?
Answer:
1 1/4 hours
Step-by-step explanation:
3/2 x5/6
15/12
1 3/12
1 1/4
Hopes this help please mark brainliest
7. The floor area of a passage is 2,4 m². The floor has to be tiled with square tiles of which the length of the sides is 200 mm. How many tiles do you need to cover the floor?
The number of tiles needed to cover the floor is 60 tiles.
Given Information,
The floor area of the passage = 2.4 m²
Length of a side of square tile = 200mm
Length of the side is in mm which needs to be converted in its standard form which is meters.
Therefore, the length of side = 200/1000 m
= 0.2 m
Area of the square tile = 0.2 x 0.2
= 0.04 m²
Let the number of tiles be x.
∴ Number of tiles = [tex]\frac{Area of passage}{Area of each tile}[/tex]
x = 2.4/0.04
x = 60
∴ The number of tiles needed to cover the floor is 60 tiles.
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Which equation is most likely represented by the circle graphed above? (PC G.12)(1 point) 1 -5 10 O A. (x + 1)² + (y + 6)? = 16 O B. (x - 1)2 – (7-6)= 16 O c. (x - 1)2 + (5-6)2 = 16 O D. (x + 1)2 – (y + 6) = 16
We want to know which equation is most likely represented by the circle graphed.
For doing so, we remember the general equation of a circle:
[tex](x-h)^2+(y-k)^2=r^2[/tex]In the equation, (h,k) is the center of the circle, and r is the radius. Thus, if we obtain the center and the radius of the circle, we will be able to obtain its equation. The center is on the point (-1, -6), as we see on the figure:
And the radius (the distance from the center to a point of the circle) is 4:
Replacing on the formula, we obtain that the equation that represents the circle graphed is:
[tex]\begin{gathered} (x-(-1))^2+(y-(-6))^2=4^2 \\ (x+1)^2+(y+6)^2=16 \end{gathered}[/tex]There are 400 counters in a box.
The counters are red or yellow or green.
3
of the counters are red.
82 of the counters are yellow.
What percentage of the counters are green?
the green would be 15% of the counters
The number of counters that are green is 162 and the percentage of counters that are green is 42 %
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
The total number of counters = 400
The number of counters that are red = 3/8 of total number of counters
= ( 3/8 ) x 400
= 3 x 50
= 150 counters
The number of counters that are yellow = 82 counters
So , the number of counters that are green =
Total number of counters - number of counters that are red - number of counters that are yellow
The number of counters that are green = 400 - 150 - 82
= 168 counters
Now , the percentage of counters that are green =
( number of counters that are green / total number of counters ) x 100
The percentage of counters that are green = ( 168 / 400 ) x 100
= 168 / 4
= 42 %
Hence , the number of counters that are green is 168 and the percentage of counters that are green is 42 %
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