Answer:
x=-13
Step-by-step explanation:
1. Divide both sides by -0.4
2. Subtract -3 on both sides.
3. -10-3=-13
If DC = 10 centimeters, SR = 15 centimeters, and the area of ABCD is 72 square centimeters, then the area of PQRS is square centimeters.
The area of the figure PQRS can be found by applying the rule of areas in proportional shapes. The area of PQRS equals 32 square centimeters after rounding the calculated value.
Explanation:The given problem involves the calculation of area and the application of ratios. It mentions two figures, ABCD and PQRS, along with certain dimensions and the area of the first figure. To find the area of the figure PQRS, we apply a rule of ratios used in geometry that states the areas of two similar figures is equal to the square of the ratio of their corresponding sides.
The corresponding sides here are DC and SR. So the ratio of their areas would be (DC/SR)². Plugging in the values we get = (10 centimeters/15 centimeters)² which simplifies to 0.444 (after rounding).
Then, to find the area of PQRS, we multiply the area of ABCD (which is 72 square centimeters) with the calculated square of the ratio. Therefore, the area of figure PQRS is 72 * 0.444 which equals 31.968 square centimeters (rounded to 32 square centimeters).
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What are the coordinates of the x-intercepts of the parabola y = x² - 8x + 15?
(3, 0) and (5, 0)
(3, 0) and (-5, 0)
(-3, 0) and (5, 0)
(-3, 0) and (-5, 0)
Answer:
(3, 0) and (5, 0)
Step-by-step explanation:
we have
[tex]y=x^{2}-8x+15[/tex]
we know that
The x-intercepts are the values of x when the value of y is equal to zero
so
For y=0
[tex]x^{2}-8x+15=0[/tex]
The formula to solve a quadratic equation of the form
[tex]ax^{2} +bx+c=0[/tex]
is equal to
[tex]x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}[/tex]
in this problem we have
[tex]x^{2}-8x+15=0[/tex]
so
[tex]a=1\\b=-8\\c=15[/tex]
substitute in the formula
[tex]x=\frac{-(-8)\pm\sqrt{-8^{2}-4(1)(15)}} {2(1)}[/tex]
[tex]x=\frac{8\pm\sqrt{4}} {2}[/tex]
[tex]x=\frac{8\pm2} {2}[/tex]
[tex]x=\frac{8+2} {2}=5[/tex]
[tex]x=\frac{8-2} {2}=3[/tex]
so
x=3, x=5
therefore
The x-intercepts are (3,0) and (5,0)
How many terms are in the algebraic expression Negative 7 + 12 x 4 minus 5 y 8 + x?
Answer:
Therefore,
There are Four i.e 4 terms in the expression,
[tex]-7+12x^{4}-5y^{8}+x[/tex]
Step-by-step explanation:
Algebraic Expression:
An algebraic expression is a mathematical expression that consists of variables, numbers and operations.
Variables with the coefficient is called as Term.Number is also a term.Here the Expression is
[tex]-7+12x^{4}-5y^{8}+x[/tex]
So,
[tex]-7 = One\ Term\\12x^{4}=Second\ Term\\-5y^{8}=Third\ Term\\x=Fourth\ Term[/tex]
In all there are Four i.e 4 terms in the given expressions.
Therefore,
There are Four i.e 4 terms in the expression,
[tex]-7+12x^{4}-5y^{8}+x[/tex]
4 is the answer and no explanation
hope this helps and on edgenuity it is D
a teaspoon of common table salt contains about 2,000 mg of sodium. how many grams of sodium is this?
Answer:
2 grams
Step-by-step explanation:
multiply by 1000
Paul bought 3 1/3 pounds of bananas and
apples. If he bought 1 4/5 pounds of apples,
how many pounds of bananas did he
buy?
Paul bought 23 / 15 pounds of bananas.
What are mathematical operations?Calculate the answer using a math operator is referred to as a mathematical operation.
Basic mathematical operations are addition, multiplication, subtraction and division.
Given that,
The total quantity of bananas and apples bought by Paul = 3 ¹/₃
Also, Paul bought 1 ⁴/₅ pounds of apples.
To find the quantity of bananas that Paul bought.
Use subtraction property,
Quantity of bananas = total quantity - quantity of apples
= 3 ¹/₃ - 1 ⁴/₅
= 10 / 3 - 9 / 5
= 50 - 27 / 15
= 23 / 15
The required quantity of bananas is 23 / 15.
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What is the value of x in the equation 2(x+3)=4(x-1) a.1 b.2 c.3 d.5
Answer:
5
Step-by-step explanation:
2(x+3)=4(x-1)
2x+6=4x-4
6=4x-2x-4
6=2x-4
2x=6+4
2x=10
x=10/2
x=5
f the measure of ∠BAD = 80°, what is the measure of ∠BCD?
A) 10°
B) 40°
C) 80°
D) 100°
Answer:
Option D.) [tex]100 \textdegree[/tex] is correct.
Step-by-step explanation:
In a quadrilateral, ABCD, opposite angles are supplementary.
[tex]\angle BCD + \angle BAD = 180\textdegree[/tex]
therefore [tex]\angle BCD = 180\textdegree - \angle BAD = 180\textdegree - 80\textdegree = 100 \textdegree[/tex]
therefore option D.) [tex]100 \textdegree[/tex] is correct.
Answer:
Answe is 100
Step-by-step explanation:
Foster Publishers' printing can print 5 dictionaries in 8 minutes. How many dictionaries can it print in 10 minutes?
Based on the proportion of 5 dictionaries in 8 minutes, Foster Publishers would be able to print approximately 6.25 dictionaries in 10 minutes.
Explanation:This question involves proportions, which often show up in mathematical problems like this one. A proportion is a statement that two ratios are equivalent. In this question, we know that Foster Publishers can print 5 dictionaries in 8 minutes, which establishes our first ratio (5/8).
We want to find out the number of dictionaries it can print in 10 minutes. This establishes a second ratio, but we don't know the numerator yet. We can set it up as follows: x/10 = 5/8, where x is the number of dictionaries that can be printed in 10 minutes.
6.25 dictionaries in 10 minutes if it continues at the same rate of production.
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The graph shows the amount of money paid when purchasing bags of peanuts at the zoo: What is the constant of proportionality? (4 points) Select one: a. 1 b. 4 c. d.
Answer:
The constant of proportionality is equal to 4
Step-by-step explanation:
The picture of the question in the attached figure
Let
y ----> the total cost in dollars
x ----> the number of bags of peanuts
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]k=\frac{y}{x}[/tex] or [tex]y=kx[/tex]
To find out the constant of proportionality, we need to take one point from the graph
take the point (1,4)
Find the value of k
[tex]k=\frac{y}{x}[/tex]
substitute the value of x and the value of y
[tex]k=\frac{4}{1}=\$4\ per bag[/tex]
Answer:
4
Step-by-step explanation:
Echo is creating a garden that is 36 feet wide and can fit one row of shrubs. Each shrub is 4.5 feet wide. Each shrub costs $15.32. She plants the maximum number of shrubs for the garden.
What is the total cost for Echo’s shrubs?
Answer:
Echo can plant a maximum of 8 shrubs.
The total cost for Echo's shrubs is = 8 [tex]\times[/tex] $15.32 = $122.56
Step-by-step explanation:
i) Garden is 36 feet wide
ii) Each shrub is 4.5 feet wide.
iii) therefore the maximum number of shrubs that can be planted are
[tex]= \frac{36}{4.5} = 8[/tex]
Therefore Echo can plant a maximum of 8 shrubs.
Therefore the total cost for Echo's shrubs is = 8 [tex]\times[/tex] $15.32 = $122.56
What is the answer and step by step equations of 6=a/4 +2
Answer:
Step-by-step explanation:
Try photomath
Answer:
a= 16
Step-by-step explanation:
6 = a/4 + 2
6 - 2 = a/4
4 = a/4
a= 16
the sum of two numbers is 15. if one number is subtracted from the other, the result is -3. find the numbers
Answer:
The numbers are 6 and 9
Step-by-step explanation:
Let the two numbers be x and y.
Given :
The sum of two numbers [tex]x+y=15[/tex] equation:1
Also the difference of x and y [tex]x-y= -3[/tex] equation:2
On solving equation:2
[tex]x=y-3[/tex] equation:3
Putting this value of x in equation 1.
[tex]x+y=15\\\\(y-3)+y=15\\2y-3=15\\2y=15+3\\2y=18\\y=18/2\\y=9[/tex]
Putting value of y in equation:3 to find x
[tex]x=y-3\\x=9-3\\x=6[/tex]
How to solve fractions with different denominators
Step-by-step explanation:
To solve such fractions you need to make their denominators equal. For example:
[tex] \frac{5}{6} + \frac{4}{7} = \frac{5 \times 7 + 4 \times 6}{6 \times 7} = \frac{35 + 24}{42} \\ = \frac{59}{42} \\ [/tex]
7/8 x+ 3/4 x+ 7/16 x− 1/16 = 5/8
Answer:
Therefore [tex]x =\frac{1}{3}[/tex]
Step-by-step explanation:
[tex]\frac{7}{8} x+\frac{3}{4} x+\frac{7}{16} x-\frac{1}{16} =\frac{5}{8}[/tex]
[tex]\Leftrightarrow \frac{7}{8} x+\frac{3}{4} x+\frac{7}{16} x =\frac{5}{8}+\frac{1}{16}[/tex]
[tex]\Leftrightarrow \frac{14x+12x+7x}{16} =\frac{10+1}{16}[/tex] [ L.C.M of 8,4,16 =16 and L.C.M of 8,16 =16]
[tex]\Leftrightarrow \frac{33x}{16} =\frac{11}{16}[/tex]
[tex]\Leftrightarrow x =\frac{11\times 16}{16\times 33}[/tex]
[tex]\Leftrightarrow x =\frac{1}{3}[/tex]
Therefore [tex]x =\frac{1}{3}[/tex]
A telephone pole casts a shadow 30 feet
long while a nearby fence post 4 feet
high casts a shadow 3 feet long. How
high is the pole?
Answer:
The height of the pole is 40 feet.
Step-by-step explanation:
Answer:
Step-by-step explanation:
37.5 feet
There are white, blue, and red boats in a marina. Five-sixths of the boats in the marina are white,
2
5
of the remaining boats are blue, and the rest are red. If there are 12 red boats, how many boats are in the marina?
Final answer:
To find the number of boats in the marina, we use the information given about the proportion of white, blue, and red boats. By setting up an equation and solving for the total, we find that there are 222 boats in the marina.
Explanation:
To find the number of boats in the marina, we need to start with the information given. The problem tells us that five-sixths of the boats in the marina are white, and then 25 of the remaining boats are blue. The rest of the boats are red, with a total of 12 red boats.
We can start by finding the fraction of boats that are red. Since five-sixths are white, the remaining fraction of boats that are not white is one-sixth. We know that 25 boats are blue, so if we subtract this from the one-sixth, we are left with the fraction that represents the red boats.
Let's set up an equation to solve for the total number of boats:
1/6 - 25 = 12
Simplifying the equation, we have:
1/6 = 12 + 25
1/6 = 37
Multiplying both sides of the equation by 6, we get:
1 = 37*6
1 = 222
Therefore, there are a total of 222 boats in the marina.
The ratio of fish to hamsters is 5:3 there are 48 pets total how many of each type of pet are there
Daniella is drawing plans for a garden, measured in feet, which is shown below on the coordinate plane. Daniella has two vertices of the garden at points (Negative3, Negative 1) and (4, Negative 1). On a coordinate plane, points (negative 3, negative 1) and (4, negative 1) are plotted. At which points should Daniella have the other two vertices in order to make the area of her garden 35 square feet? (Negative 3, 1) and (4, 1) (Negative 3, 2) and (4, 2) (Negative 3, 3) and (4, 3) (Negative 3, 4) and (4, 4)
Answer:
d
Step-by-step explanation:
We know that the length of the garden is 4 - (-3) = 7 feet, the answer is (Negative 3, 5) and (4, 5).
What are vertices?A vertex is a point in geometry where two or more curves, lines, or edges intersect.
As a result of this definition, vertices are the points where two lines intersect to form an angle, as well as the corners of polygons and polyhedra.
Let's assume that the other two vertices are at points (a, b) and (c, d). The area of the garden can be calculated as follows:
Area = Length × Width
35 = 7 × (b - (-1)) [since the width is the distance between the y-coordinates of the vertices]
Simplifying the above equation, we get:
b - (-1) = 5
b = 4
So, one of the vertices should be at (a, 4) and the other at (c, 4). Since the garden is symmetrical about the x-axis, the y-coordinate of the missing vertices is 1 more than the y-coordinate of the given vertices. Hence, the other two vertices should be at (−3, 5) and (4, 5).
Therefore, the answer is (Negative 3, 5) and (4, 5).
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through (-2,0) and (3, 10) write a equation
Answer:(-2+0)(3+10)
Step-by-step explanation:
Answer:
y = 2x + 4
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 2, 0) and (x₂, y₂ ) = (3, 10)
m = [tex]\frac{10-0}{3+2}[/tex] = [tex]\frac{10}{5}[/tex] = 2, thus
y = 2x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (- 2, 0), then
0 = - 4 + c ⇒ c = 0 + 4 = 4
y = 2x + 4 ← equation of line
The Tennis Teams of Atlanta need to older tennis balla for the upcoming tournament.They will need 2,367 tennis balls. If each can hold 5 tennis balls,how Many will they purchase
Answer:473
Step-by-step explanation:
Final answer:
To determine how many cans are needed to hold 2,367 tennis balls, with each can holding 5 balls, you divide the total number of tennis balls by 5 and round up to the nearest whole number, resulting in 474 cans.
Explanation:
The subject of the question is Mathematics, as it involves a division problem. The question entails calculating the number of cans needed to hold 2,367 tennis balls, given that each can hold 5 tennis balls. To determine the number of cans required, we divide the total number of tennis balls by the number of balls that can fit in each can.
To find the solution:
Divide 2,367 by 5, which equals 473.4.
Since you can't have a fraction of a can, you would need to round up because you will need part of another can to hold the remaining balls. So, rounding 473.4 up, you get 474 cans.
Therefore, the Tennis Teams of Atlanta need to purchase 474 cans to hold 2,367 tennis balls.
Tickets for a cinema cost £a for adults and £c for children. 2 adults and 3 children cost £42.70. 3 adults and 5 children cost £67.30.
How much does it cost for 1 adult and 1 child?
Answer:
c = 6.5, a = 11.6
Step-by-step explanation:
2a + 3c = 42.7
3a + 5c = 67.3
Elimination
(2a+3c = 42.7)*3
(3a+5c = 67.3)*2
(1) 6a+9c = 128.1
(2) 6a+10c = 134.6
(2) - (1)
c = 6.5
Substitue 'c' in any of the equation
2a + 3(6.5) = 42.7 or 3a + 5(6.5) = 67.3
2a + 19.5 = 42.7 3a + 32.5 = 67.3
2a = 42.7 - 19.5 3a = 67.3 - 32.5
2a = 23.2 3a = 34.8
a = 11.6 a = 11.6
You and your friend are selling your old CDs. Your friend sells 14 the first day, and x the next day. You sell y the first day and 6 the next day. Write an expression that shows the total number of CDs sold both days. Rewrite your answer using the Commutative Property of Addition.
Answer: 30+x+y
Step-by-step explanation:
Commutative Property of Addition : a+b= b+a , where a and b are any arbitrary numbers.Given : Number of CDs sold by friend on first day = 14
Number of CDs sold by friend on next day = x
Total CDs sold by friend = 14 +x
Number of CDs sold by you on first day = 16
Number of CDs sold by you on next day = y
Total CDs sold by you = 16+y
The expression that shows the total number of CDs sold both days =
Total CDs sold by friend + Total CDs sold by you
= 14 +x+ 16+y
= 14 +(x+ 16)+y
= 14 +(16+x)+y [By Commutative Property of Addition.]
= 14+16+x+y
= 30+x+y
Hence, the expression that shows the total number of CDs sold both days :
30+x+y
What is the missing constant term in the perfect square thar starts with x2 + 6x
Answer:
(-9)/54*9
Step-by-step explanation:
Answer:
9
Step-by-step explanation:
What is 3822 devided by 39
Answer:
98
Step-by-step explanation:
0 0 9 8. 0 0 0
3 9 3 8 2 2. 0 0 0
− 0
3 8
− 0
3 8 2
− 3 5 1
3 1 2
− 3 1 2
0 0
− 0
0 0
− 0
0 0
− 0
0
Answer: 98
Step-by-step explanation:
plz help meeeeeeeeeeeeeee
Answer:
its 9.4 im pretty sure
what is the volume of the cylinder if the height is 2x+7 and the radius is x-3
Answer:
Therefore the volume of the cylinder[tex]=\pi(2x^3-5x^2-24x+63)[/tex] cubic units
Step-by-step explanation:
Given height of a cylinder is (h) =2x+7
and radius (r)= x-3
Volume of the cylinder = [tex]\pi r^2 h[/tex]
[tex]=\pi (x-3)^2(2x+7)[/tex]
[tex]=\pi (x^2-6x+9)(2x+7)[/tex]
[tex]=\pi (2x^3-12x^2+18x+7x^2-42x+63)[/tex]
[tex]=\pi(2x^3-5x^2-24x+63)[/tex] cubic units
Therefore the volume of the cylinder[tex]=\pi(2x^3-5x^2-24x+63)[/tex] cubic units
The relationship between the amount of time a zebra run at maximum speed in the distance it covers is shown.
Write an equation to describe this relationship.
Use the equation to find the distance the zebra would travel in 48 minutes.
Answer:
72 minutes in 48 hours.
Step-by-step explanation:
You have to do 8 times six.
Puppy A weighs 8 pounds which is about 25% of its adult weight what will be the adult weight of a puppy A
Answer:
Step-by-step explanation:
Let x be the adult weight of a puppy A
25% of x = 8 pounds
[tex]\frac{25}{100}*x=8\\\\ x=\frac{8*100}{25}\\\\ =8*4=32pounds\\[/tex]
Final answer:
To calculate the adult weight of Puppy A, divide the current weight of 8 pounds by 0.25 since 8 pounds is 25% of the adult weight. The adult weight of Puppy A is 32 pounds.
Explanation:
The student is asking how to find the adult weight of Puppy A, given that its current weight is 25% of its adult weight. To solve this, we need to use the concept of percentages. If Puppy A currently weighs 8 pounds and this represents 25% of the adult weight, we can set up a proportion:
25% (current weight) / 100% (adult weight) = 8 pounds / adult weight
To find the adult weight, we divide 8 pounds by 25% (0.25 in decimal form):
Adult weight = 8 pounds / 0.25
Adult weight = 32 pounds
Therefore, the adult weight of Puppy A is expected to be 32 pounds.
How do you compare and order fractions?
Answer:
Give each a common denominator
Step-by-step explanation:
So let’s say you have 1/2 and 2/4 how would you know which is bigger well we know both 2 and 4 go into 4 so 1/2 x2 = 2/4 so these 2 are equal
a) Write down your full calculator display.
b) Write your answer to part (a) correct to 2 decimal places.