If the ratio of the dimensions is 4:7 and the shorter dimension is 10ft, we know that the 10ft corresponds to the 4 in this scenario. We can set up the equation as follows:
[tex]\frac{4}{7} =\frac{10}{x}[/tex]
You have to multiply by 2.5 to get from 4 to 10. And since we want to make sure we are maintaining the ratio, we have to multiply the denominator, 7, by 2.5 as well.
[tex]\frac{4}{7}*\frac{2.5}{2.5}=\frac{10}{17.5}[/tex]
This means your shorter side has a length of 10ft and your longer side has a length of 17.5ft.
AREA
The formula for the area of a rectangle is: [tex]w*l[/tex]
So we can plug our dimensions into the formula: [tex]10*17.5=175[/tex]
So 175 is our area. But we can't forget about units! Since this is area and we multiplied our units together, our units would be squared. That means our answer is 175 square feet.
PERIMETER
The formula for the perimeter of a rectangle is: [tex]2(w+l)[/tex]
We can plug our dimensions into the formula: [tex]2(10+17.5)=55[/tex]
So 55 is our perimeter. Of course, we can't forget about our units. Because this is perimeter, we only added our units together, so they don't change. That means our answer is 55 feet.
Find the mean of the following data set: 20, 22, 24, 25, 29, 30, 32, 36
Answer:
27.25
Step-by-step explanation:
we find the mean by adding all the values and dividing by the number of values.
find the value of x round to the nearest 10th
I will give brainliest
10.9
Step-by-step explanation:[tex]According\ to\ the\ question,\ we\ con\ spe\ that[/tex]
[tex]\sin{40}[/tex]° [tex]=\frac{7}{x}[/tex]
[tex]x=\frac{7}{\sin{40degrees}}\\ x\approx 10.9[/tex]
I hope this helps you
:)
the height of a triangle is 4 meters less than the base. if the area of the triangle is 6 m^2 what is the height of the triangle. pls help. solve using applications of quadratics
Answer:
[tex]2m[/tex]
Step-by-step explanation:
Alrighty let's do this.
We know that formula for the Area of a triangle is:
[tex]A = \frac{1}{2}bh[/tex]
They give us the area as [tex]6m^2[/tex], so let's include it in the equation.
[tex]6 = \frac{1}{2}bh[/tex]
Now we reach a stage where we have 2 unknown variables! That means we can't solve it in its current state. So the idea you should have in cases like these where you have 2 or more unknown variables is, "Can I represent this one variable in terms of another variable?" In this case you can do exactly that. You can represent height in terms of length of the base. We are told the height of the triangle is 4 meters less than the base. That is telling us that [tex]h = b-4[/tex]
So replace [tex]h[/tex] in the equation with [tex]b-4[/tex].
You will now get:
[tex]6 = \frac{1}{2}b(b-4)[/tex]
Now we can work towards solving. Let's get simplifying.
[tex]12 = b(b-4)\\12 = b^2 - 4b\\[/tex]
bring everything to one side so we can make a quadratic and factor:
[tex]0 = b^2 - 4b - 12\\0 = (b-6)(b+2)\\\\b = 6\\b\neq -2[/tex]
We get that [tex]b=6[/tex].
Since we need the height of the triangle we'll need to call back on what h is. We found earlier that [tex]h = b - 4[/tex], so to find h, we just sub in our b value into that.
[tex]h = (6) - 4 = 2[/tex]
We find that [tex]h=2[/tex]
Find the value of X
4.5
8.9
6.5
X
13
b
11
can someone answer
Solve the equation 4 ( c - 3 ) = 8
Answer:
c=5
Step-by-step explanation:
4(c-3)=8 Distribute
4c-12=8 Add 12 to both sides
4c=20 Divide by 4 on both sides
c=5
Answer:
c = 5Step-by-step explanation:
METHOD 1:
4(c - 3) = 8 |divide both sides by 4
4(c - 3)/4 = 8/4
c - 3 = 2 |add 3 to both sides
c - 3 + 3 = 2 + 3
c = 5
METHOD 2:
4(c - 3) = 8 |use the distributive property: a(b - c) = ab - ac
4 · c - 4 · 3 = 8
4c - 12 = 8 |add 12 to both sides
4c - 12 + 12 = 8 + 12
4c = 20 |divide both sides by 4
4c/4 = 20/4
c = 5
Angel had $21 to spend on two notebooks. After buying them he had $13 left. How much did each note book cost?
Answer:
each notebook would cost $4
Step-by-step explanation:
21-13=8. 8/2=4
Please someone help I will give brainliest
Answer: 42.0
Step-by-step explanation:
Create a tree diagram to show the different options for the lunch options: Salad Sandwich Soup Tortellini Roast Beef Caesar Macaroni Ham Lentil Turkey
Answer:
is there a picture of the answers?
Step-by-step explanation:
also can u help me with my question pls
I need help on this question
0.007 kg
Step-by-step explanation:[tex]1000\ grams=1\ kg\\ 7\ grams=0.007\ kg\\ Check\ conversion[/tex]
I hope this helps you
:)
4 2/4 + 1/9 =
what is the answer i need to know now
Answer:
4.61
Step-by-step explanation:
Step-by-step explanation:
[tex] = 4 \frac{2}{4} + \frac{1}{9} \\ = \frac{4 \times 4 + 2}{4} + \frac{1}{9} \\ = \frac{18}{4} + \frac{1}{9} [/tex]
Find the LCM
[tex] = \frac{18}{4} \times \frac{9}{9} + \frac{1}{9} \times \frac{4}{4} \\ = \frac{162}{36} + \frac{4}{36} \\ = \frac{166}{36} [/tex]
Convert into lowest term
[tex] \frac{83}{16} \\ [/tex]
In a basketball game, you made 4 baskets out of 12 attempts. Your teammate made 3 baskets out of 8 attemps
Answer:
4/12 and 3/8
Step-by-step explanation:
A dilation with a scale factor of 2 is applied to the three line segments shown. The resulting images are P'Q' A'B' and M'N' 2 cm 1.5 cm M 3 cm N B What are the lengths of the images? Drag the answer into the box to match each segment. Ρ'Ο AB 1 M'N' ໃ & 0.75 cm 1 cm 1.5 cm 3 cm 4 cm 6 cm
need to do this QUICK!
The value of the dilated line segments P'Q', A'B' and M'N' are 4 cm. 3 cm and 6 cm
What is dilation?
Dilation is the increase or decrease in the size of an figure or object.
A dilation with a scale factor of 2 is applied to the three line segments shown to form P'Q', A'B', and M'N'.
Hence:
P'Q' = scale factor * PQ = 2 * 2 = 4 cm
A'B' = 2 * 1.5 = 3 cm
M'N' = 2 * MN = 2 * 3 = 6 cm
The value of the dilated line segments P'Q', A'B' and M'N' are 4 cm. 3 cm and 6 cm
Find out more on dilation at: https://brainly.com/question/10253650
Nezzie invests in 300 shares of stock in the fund shown below. name of fund nav offer price lkit mid-cap $16.58 $16.99 nezzie plans to sell all of her shares when she can profit $5,000. what must the net asset value be in order for nezzie to sell? a. $16.67 b. $33.25 c. $33.57 d. $33.66
The value of net asset to be in order for Nezzie to sell all of her shares when she can profit $5,000 is $33.66.
How to find the net asset value?The net asset value is the difference of total asset value of the company to the total liabilities value of that company.
Nezzie invests in 300 shares of stock in the fund shown below. Name of fund nav offer price lkit mid-cap $16.58 $16.99.
Nezzie plans to sell all of her 300 shares of stock when she can profit $5,000.
To find the net asset for this case, divide the profit with the number of shares and the higher price in that.
[tex]\rm Net Asset=\dfrac{5000}{300}+16.99\\\rm Net Asset=33.66\\[/tex]
Thus, the value of net asset to be in order for Nezzie to sell all of her shares when she can profit $5,000 is $33.66.
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40 students go to a sport centre in buses. a bus can hold 14 students. find the number of buses needed
Answer:
The answer is 3 buses
Step-by-step explanation:
40 divided by 14 is 2.85714285714 buses well you cant have 3/4 of a bus so you round it up to 3 buses
Which point is not on the graph of the function y = x + 2?
(3, 5)
(6, 8)
(7, 9)
(2, 0)
Answer:
(2,0) is not a point on the graph of the function y=x+2
Step-by-step explanation:
Go to the TI-84 plus calculator and go to the y= button and then type in x+2 and then press the 2nd button and then the graph button and then you should get your answer.
Select the two values of x that are roots of this equation.
Answer:
C and D :)
Step-by-step explanation:
Answer:
c and d
Step-by-step explanation:
solve systems by substitutions
y=x + 10
y= -6x-18
x + 10 = - 6x - 18
7x = - 28
x = - 4
and y = - 4 + 10 = - 6
Hi ..
I really need help on this one
Answer:
LCM of 3 and 2 is 6
so, firstly we had to make the denominator same:-
[tex] \frac{2(2a + 1) + 3(3a - 1)} {6} [/tex]
[tex] \frac{4a + 2 + 9a - 3}{6} [/tex]
[tex] \frac{13a - 1}{6} [/tex]
Step-by-step explanation:
hope this helps you!!!
XxITSCHOCOLOVERxX
The simplified equation of [tex]\frac{2a+1}{3}+\frac{3a-1}{2}[/tex] is [tex]\frac{13a-1}{6}[/tex]
How to simplify an equation?[tex]\frac{2a+1}{3}+\frac{3a-1}{2}[/tex]
[tex]\frac{2a+1}{3}+\frac{3a-1}{2} = \frac{2(2a+1)+3(3a-1)}{6}[/tex]
open the bracket in the numerator
Therefore,
[tex]\frac{2(2a+1)+3(3a-1)}{6}=\frac{4a+2 + 9a-3}{6}[/tex]
combine like terms in the numerator
[tex]\frac{4a+2 + 9a-3}{6}=\frac{4a+9a+2-3}{6}[/tex]
Hence,
[tex]\frac{4a+9a+2-3}{6}=\frac{13a-1}{6}[/tex]
Therefore, the final equation is as follows
[tex]\frac{2a+1}{3}+\frac{3a-1}{2}=\frac{13a-1}{6}[/tex]
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Write two different expressions that
represent the quantity x decreased
by 30%.
Answer:
Step-by-step explanation:
x - 30 = 14 - 3x
4x = 44
x = 11
Let's call the unknown number x
Now let's decrease it by 30, that is x-30
Now let's write out "14 decreased by three times the number", that is 14 - 3x
The problem says these are the same, that is x - 30 = 14 - 3x
We now want to isolate, or solve for, x
Move the x to one side of the equation by adding 3x to both sides
3x + x -30 = 14 - 3x + 3x
4x -30 = 14
Now move the 30 to the right hand side by adding 30 to both sides
4x - 30 + 30 = 14 + 30
4x = 44
Now all we have to do to get x is divide both sides by 4
4x/4 = 44/4
x = 11
Change 7 kilometres to metres ?
What is the measure of arc c e d? 106° 108° 148° 212°.
Answer:
Can you please give us figure of following ?
Answer:
its the last one 212°
212°
212°
212°
212°
212°
Step-by-step explanation:
212°
Jamal would like to purchase a pair of shoes for $80.00. At the store he can spin the spinner below to receive a discount
John paid $75 for a pair of shoe that cost $100 at a discount of 25 percent.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let us assume that the shoe cost $100, he spins the spinner and gets a discount of 25%, hence:
Money paid = 100 - 25% of 100
Money paid = 100 - 25 = $75
John paid $75 for a pair of shoe that cost $100 at a discount of 25 percent.
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If two coins are flipped, what is the probability both of the coins will land on tails?
help please this assignment is due in a few minutes
Answer:
C. 200 hours
Step-by-step explanation:
According to the given Question ,
Speed of Aeroplane is 400miles/hourIt means that the aeroplane covers 400 miles in 60 minutes.
and it is asked for 30 minutes , so
We know that 30 minutes is equal to 0.5 hours
By the formula ,
Distance = Speed × Time
putting the values given , we get
= 400×0.5
Distance = 200 miles
A small bag of chips contains 0.3 of a cup of sugar. if a large bag of chips is the same as 6.4 small bags, how much sugar does a large bag contain?
In each diagram shown below, solve for the length of side CD using the information given. Show the trig ratio you use and your algebra to find your final answer. Round all answers to the nearest tenth
Applying the trigonometry ratios, we have:
a. CD = 63.6
b. CD = 33.8
c. CD = 16.1
d. CD = 15.9
What are the Trigonometry Ratios?The trigonometry ratios are used to find a length or angle in any right triangle. They are:
SOH, which is sin ∅ = opp/hypCAH, which is cos ∅ = adj/hypTOA, which is tan ∅ = opp/adja. ∅ = 32°
hyp = 75
adj = CD
Apply CAH:
cos 32 = CD/75
CD = cos 32 × 75
CD = 63.6
b. ∅ = 56°
opp = 28
hyp = CD
Apply SOH:
sin 56 = 28/CD
CD = 28/sin 56
CD = 33.8
c. ∅ = 43°
opp = 15
adj = CD
Apply TOA:
tan 43 = 15/CD
CD = 15/tan 43
CD = 16.1
d. ∅ = 27°
hyp = 35
opp = CD
Apply SOH:
sin 27 = CD/35
CD = sin 27 × 35
CD = 15.9
Learn more about the trigonometry ratios on:
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Will choose Brainliest.
Jessica and Martha each have a bag of cookies with unequal quantities. They have 30 cookies total between the two of them. Each of them ate 6 cookies from their bag. The product of the number of cookies left in each bag is not more than 80.
How many more cookies will Jessica have than Martha?
If x represents the number of cookies Jessica started with, complete the statements below.
The inequality that describes the relationship between the number of cookies each one of them has is x^2- _ x + 224 ≥ 0
Jessica has at least
_ cookies more than Martha.
Answer:
Part A: [tex]x^2-30x+224\geq 0[/tex]
Part B: Jessica has at least 2 cookies more than Martha
Step-by-step explanation:
Since there are 2 question-
Let,
How many more cookies will Jessica have than Martha?If x represents the number of cookies Jessica started with, complete the statements below. Be Part A:
Let,
The inequality that describes the relationship between the number of cookies each one of them has is x^2- _ x + 224 ≥ 0 Jessica has at least _ cookies more than Martha.
Be Part B:
Hint:
J=Jessica
30-J=Martha
(J-6)*((30-J)-6)<=80
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Solve:
Starting with Part A: Find the inequality that describes the relationship between the number of cookies each one of them has
Let,
"x" be the number of cookies when Jessica started
"30-x" be the number of cookies when Martha started
Given us that:
Each of them ate 6 cookies from their bag
Therefore,
Cookie left in each bag are:
(x-6) which is - Jessica
30 - x - 6 = (24 - x) - Martha
Solution - (x-6)(24-x)
The product of the number of cookies left in each bag is not more than 80.
Thus,
[tex](x-6)(24-x\leq 80[/tex]
[tex]24x-x^2-144+6x\leq 80[/tex]
[tex]-x^2+30x-144-80\leq 0[/tex]
[tex]-x^2+30x-244\leq 0[/tex]
[tex]\mathrm{Multiply\;by\;-1\;both\;sides}[/tex]
[tex]x^2-30x+224\leq 0[/tex]
Hence, Answer = [tex]x^2-30x+224\leq 0[/tex]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Solve:
Part B: Solve the quadratic equation:
[tex]\begin{bmatrix}\mathrm{Solution:}\:&\:14\le \:x\le \:16\:\\ \:\mathrm{Interval\:Notation:}&\:\left[14,\:16\right]\end{bmatrix}[/tex]
[tex]\left(x-14\right)\left(x-16\right)\le \:0[/tex]
[tex]14\le \:x\le \:16[/tex]
The solution is x=16 cookies
Thus, (30-x)=30-16=14 cookies
Now we know that;
The number of cookies when Jessica started was 16 cookies
The number of cookies when Martha started was 14 cookies
So,
The number of cookies left in each bag is equal to
Jessica:
16-6=10 cookies
Martha:
14-6=8 cookies
10 > 8
As a result, Jessica has at least 2 cookies more than Martha.
Fill in blank for:
The inequality that describes the relationship between the number of cookies each one of them has is x^2 - __30__ x +224 >= 0.
Jessica has at least __2__ cookies more than Martha.
~Lenvy~
An isosceles triangle has an angle that measures 38degrees. What measures are possible for the other two angles? Choose all that apply.
Answer:
71° and 71°.⠀
Step-by-step explanation:
The triangle having two sides equal along with one different side is called an isosceles triangle.
⠀
So, Let us assume the other sides (two equal sides) of the isosceles triangle as x. As the different side is already given in the question.⠀
We know that,
The sum of all angles of a triangle is 180°⠀
So, According to the question :
⠀
[tex]{\longrightarrow \it\qquad { \ { { 38 \: }^{ \circ} + x + x = 180{}^{ \circ} }}}[/tex]
⠀
[tex]{\longrightarrow \it\qquad { \ { { 38 \: }^{ \circ} + 2x = 180{}^{ \circ} }}}[/tex]
⠀
[tex]{\longrightarrow \it\qquad { \ { 2x = 180{}^{ \circ} - { 38 \: }^{ \circ}}}}[/tex]
⠀
[tex]{\longrightarrow \it\qquad { \ { 2x = 142{}^{ \circ} }}}[/tex]
⠀
[tex]{\longrightarrow \it\qquad { \ { x = \dfrac{142{}^{ \circ}}{2} }}}[/tex]
⠀
[tex]{\longrightarrow \it\qquad { \pmb { x = 71^{ \circ} }}}[/tex]
⠀
Therefore,
The measure of the two other angles of the isosceles triangle are 71° and 71°.The middle school will lose some of its funding if 50 or more students move away in any year. The principal claims he only loses about 30 students a year. Do the values in the table support his claim? Explain.
1) Find the slope of the line
2) Find the slope between the two points.
help please, thank you
Answer:
Slope formula;
y2(second y coordinate) - y1(first y coordinate)
____________________________________
x2(second x coordinate) - x1(first x coordinate)
Plug in values:
2 - 1 1
_______ = ________, your slope is -1/14.
-17 - (-3) -14